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 is 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 * Objects of type C<isl_union_pw_multi_aff> can no longer contain
216 two or more C<isl_pw_multi_aff> objects with the same domain space.
218 =item * The function C<isl_union_pw_multi_aff_add> now consistently
219 computes the sum on the shared definition domain.
220 The function C<isl_union_pw_multi_aff_union_add> has been added
221 to compute the sum on the union of definition domains.
222 The original behavior of C<isl_union_pw_multi_aff_add> was
223 confused and is no longer available.
225 =item * Band forests have been replaced by schedule trees.
227 =item * The function C<isl_union_map_compute_flow> has been
228 replaced by the function C<isl_union_access_info_compute_flow>.
229 Note that the may dependence relation returned by
230 C<isl_union_flow_get_may_dependence> is the union of
231 the two dependence relations returned by
232 C<isl_union_map_compute_flow>. Similarly for the no source relations.
233 The function C<isl_union_map_compute_flow> is still available
234 for backward compatibility, but it will be removed in the future.
236 =item * The function C<isl_basic_set_drop_constraint> has been
239 =item * The function C<isl_ast_build_ast_from_schedule> has been
240 renamed to C<isl_ast_build_node_from_schedule_map>.
241 The original name is still available
242 for backward compatibility, but it will be removed in the future.
244 =item * The C<separation_class> AST generation option has been
251 C<isl> is released under the MIT license.
255 Permission is hereby granted, free of charge, to any person obtaining a copy of
256 this software and associated documentation files (the "Software"), to deal in
257 the Software without restriction, including without limitation the rights to
258 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
259 of the Software, and to permit persons to whom the Software is furnished to do
260 so, subject to the following conditions:
262 The above copyright notice and this permission notice shall be included in all
263 copies or substantial portions of the Software.
265 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
266 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
267 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
268 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
269 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
270 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
275 Note that by default C<isl> requires C<GMP>, which is released
276 under the GNU Lesser General Public License (LGPL). This means
277 that code linked against C<isl> is also linked against LGPL code.
279 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
280 library for exact integer arithmetic released under the MIT license.
284 The source of C<isl> can be obtained either as a tarball
285 or from the git repository. Both are available from
286 L<http://freshmeat.net/projects/isl/>.
287 The installation process depends on how you obtained
290 =head2 Installation from the git repository
294 =item 1 Clone or update the repository
296 The first time the source is obtained, you need to clone
299 git clone git://repo.or.cz/isl.git
301 To obtain updates, you need to pull in the latest changes
305 =item 2 Optionally get C<imath> submodule
307 To build C<isl> with C<imath>, you need to obtain the C<imath>
308 submodule by running in the git source tree of C<isl>
313 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
315 =item 2 Generate C<configure>
321 After performing the above steps, continue
322 with the L<Common installation instructions>.
324 =head2 Common installation instructions
328 =item 1 Obtain C<GMP>
330 By default, building C<isl> requires C<GMP>, including its headers files.
331 Your distribution may not provide these header files by default
332 and you may need to install a package called C<gmp-devel> or something
333 similar. Alternatively, C<GMP> can be built from
334 source, available from L<http://gmplib.org/>.
335 C<GMP> is not needed if you build C<isl> with C<imath>.
339 C<isl> uses the standard C<autoconf> C<configure> script.
344 optionally followed by some configure options.
345 A complete list of options can be obtained by running
349 Below we discuss some of the more common options.
355 Installation prefix for C<isl>
357 =item C<--with-int=[gmp|imath]>
359 Select the integer library to be used by C<isl>, the default is C<gmp>.
360 Note that C<isl> may run significantly slower if you use C<imath>.
362 =item C<--with-gmp-prefix>
364 Installation prefix for C<GMP> (architecture-independent files).
366 =item C<--with-gmp-exec-prefix>
368 Installation prefix for C<GMP> (architecture-dependent files).
376 =item 4 Install (optional)
382 =head1 Integer Set Library
384 =head2 Memory Management
386 Since a high-level operation on isl objects usually involves
387 several substeps and since the user is usually not interested in
388 the intermediate results, most functions that return a new object
389 will also release all the objects passed as arguments.
390 If the user still wants to use one or more of these arguments
391 after the function call, she should pass along a copy of the
392 object rather than the object itself.
393 The user is then responsible for making sure that the original
394 object gets used somewhere else or is explicitly freed.
396 The arguments and return values of all documented functions are
397 annotated to make clear which arguments are released and which
398 arguments are preserved. In particular, the following annotations
405 C<__isl_give> means that a new object is returned.
406 The user should make sure that the returned pointer is
407 used exactly once as a value for an C<__isl_take> argument.
408 In between, it can be used as a value for as many
409 C<__isl_keep> arguments as the user likes.
410 There is one exception, and that is the case where the
411 pointer returned is C<NULL>. Is this case, the user
412 is free to use it as an C<__isl_take> argument or not.
413 When applied to a C<char *>, the returned pointer needs to be
418 C<__isl_null> means that a C<NULL> value is returned.
422 C<__isl_take> means that the object the argument points to
423 is taken over by the function and may no longer be used
424 by the user as an argument to any other function.
425 The pointer value must be one returned by a function
426 returning an C<__isl_give> pointer.
427 If the user passes in a C<NULL> value, then this will
428 be treated as an error in the sense that the function will
429 not perform its usual operation. However, it will still
430 make sure that all the other C<__isl_take> arguments
435 C<__isl_keep> means that the function will only use the object
436 temporarily. After the function has finished, the user
437 can still use it as an argument to other functions.
438 A C<NULL> value will be treated in the same way as
439 a C<NULL> value for an C<__isl_take> argument.
440 This annotation may also be used on return values of
441 type C<const char *>, in which case the returned pointer should
442 not be freed by the user and is only valid until the object
443 from which it was derived is updated or freed.
447 =head2 Initialization
449 All manipulations of integer sets and relations occur within
450 the context of an C<isl_ctx>.
451 A given C<isl_ctx> can only be used within a single thread.
452 All arguments of a function are required to have been allocated
453 within the same context.
454 There are currently no functions available for moving an object
455 from one C<isl_ctx> to another C<isl_ctx>. This means that
456 there is currently no way of safely moving an object from one
457 thread to another, unless the whole C<isl_ctx> is moved.
459 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
460 freed using C<isl_ctx_free>.
461 All objects allocated within an C<isl_ctx> should be freed
462 before the C<isl_ctx> itself is freed.
464 isl_ctx *isl_ctx_alloc();
465 void isl_ctx_free(isl_ctx *ctx);
467 The user can impose a bound on the number of low-level I<operations>
468 that can be performed by an C<isl_ctx>. This bound can be set and
469 retrieved using the following functions. A bound of zero means that
470 no bound is imposed. The number of operations performed can be
471 reset using C<isl_ctx_reset_operations>. Note that the number
472 of low-level operations needed to perform a high-level computation
473 may differ significantly across different versions
474 of C<isl>, but it should be the same across different platforms
475 for the same version of C<isl>.
477 Warning: This feature is experimental. C<isl> has good support to abort and
478 bail out during the computation, but this feature may exercise error code paths
479 that are normally not used that much. Consequently, it is not unlikely that
480 hidden bugs will be exposed.
482 void isl_ctx_set_max_operations(isl_ctx *ctx,
483 unsigned long max_operations);
484 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
485 void isl_ctx_reset_operations(isl_ctx *ctx);
487 In order to be able to create an object in the same context
488 as another object, most object types (described later in
489 this document) provide a function to obtain the context
490 in which the object was created.
493 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
494 isl_ctx *isl_multi_val_get_ctx(
495 __isl_keep isl_multi_val *mv);
498 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
500 #include <isl/local_space.h>
501 isl_ctx *isl_local_space_get_ctx(
502 __isl_keep isl_local_space *ls);
505 isl_ctx *isl_set_list_get_ctx(
506 __isl_keep isl_set_list *list);
509 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
510 isl_ctx *isl_multi_aff_get_ctx(
511 __isl_keep isl_multi_aff *maff);
512 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
513 isl_ctx *isl_pw_multi_aff_get_ctx(
514 __isl_keep isl_pw_multi_aff *pma);
515 isl_ctx *isl_multi_pw_aff_get_ctx(
516 __isl_keep isl_multi_pw_aff *mpa);
517 isl_ctx *isl_union_pw_aff_get_ctx(
518 __isl_keep isl_union_pw_aff *upa);
519 isl_ctx *isl_union_pw_multi_aff_get_ctx(
520 __isl_keep isl_union_pw_multi_aff *upma);
521 isl_ctx *isl_multi_union_pw_aff_get_ctx(
522 __isl_keep isl_multi_union_pw_aff *mupa);
524 #include <isl/id_to_ast_expr.h>
525 isl_ctx *isl_id_to_ast_expr_get_ctx(
526 __isl_keep isl_id_to_ast_expr *id2expr);
528 #include <isl/point.h>
529 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
532 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
535 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
537 #include <isl/vertices.h>
538 isl_ctx *isl_vertices_get_ctx(
539 __isl_keep isl_vertices *vertices);
540 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
541 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
543 #include <isl/flow.h>
544 isl_ctx *isl_restriction_get_ctx(
545 __isl_keep isl_restriction *restr);
547 #include <isl/schedule.h>
548 isl_ctx *isl_schedule_get_ctx(
549 __isl_keep isl_schedule *sched);
550 isl_ctx *isl_schedule_constraints_get_ctx(
551 __isl_keep isl_schedule_constraints *sc);
553 #include <isl/schedule_node.h>
554 isl_ctx *isl_schedule_node_get_ctx(
555 __isl_keep isl_schedule_node *node);
557 #include <isl/band.h>
558 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
560 #include <isl/ast_build.h>
561 isl_ctx *isl_ast_build_get_ctx(
562 __isl_keep isl_ast_build *build);
565 isl_ctx *isl_ast_expr_get_ctx(
566 __isl_keep isl_ast_expr *expr);
567 isl_ctx *isl_ast_node_get_ctx(
568 __isl_keep isl_ast_node *node);
572 An C<isl_val> represents an integer value, a rational value
573 or one of three special values, infinity, negative infinity and NaN.
574 Some predefined values can be created using the following functions.
577 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
578 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
579 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
580 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
581 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
582 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
584 Specific integer values can be created using the following functions.
587 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
589 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
591 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
592 size_t n, size_t size, const void *chunks);
594 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
595 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
596 The least significant digit is assumed to be stored first.
598 Value objects can be copied and freed using the following functions.
601 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
602 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
604 They can be inspected using the following functions.
607 long isl_val_get_num_si(__isl_keep isl_val *v);
608 long isl_val_get_den_si(__isl_keep isl_val *v);
609 double isl_val_get_d(__isl_keep isl_val *v);
610 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
612 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
613 size_t size, void *chunks);
615 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
616 of C<size> bytes needed to store the absolute value of the
618 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
619 which is assumed to have been preallocated by the caller.
620 The least significant digit is stored first.
621 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
622 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
623 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
625 An C<isl_val> can be modified using the following function.
628 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
631 The following unary properties are defined on C<isl_val>s.
634 int isl_val_sgn(__isl_keep isl_val *v);
635 int isl_val_is_zero(__isl_keep isl_val *v);
636 int isl_val_is_one(__isl_keep isl_val *v);
637 int isl_val_is_negone(__isl_keep isl_val *v);
638 int isl_val_is_nonneg(__isl_keep isl_val *v);
639 int isl_val_is_nonpos(__isl_keep isl_val *v);
640 int isl_val_is_pos(__isl_keep isl_val *v);
641 int isl_val_is_neg(__isl_keep isl_val *v);
642 int isl_val_is_int(__isl_keep isl_val *v);
643 int isl_val_is_rat(__isl_keep isl_val *v);
644 int isl_val_is_nan(__isl_keep isl_val *v);
645 int isl_val_is_infty(__isl_keep isl_val *v);
646 int isl_val_is_neginfty(__isl_keep isl_val *v);
648 Note that the sign of NaN is undefined.
650 The following binary properties are defined on pairs of C<isl_val>s.
653 int isl_val_lt(__isl_keep isl_val *v1,
654 __isl_keep isl_val *v2);
655 int isl_val_le(__isl_keep isl_val *v1,
656 __isl_keep isl_val *v2);
657 int isl_val_gt(__isl_keep isl_val *v1,
658 __isl_keep isl_val *v2);
659 int isl_val_ge(__isl_keep isl_val *v1,
660 __isl_keep isl_val *v2);
661 int isl_val_eq(__isl_keep isl_val *v1,
662 __isl_keep isl_val *v2);
663 int isl_val_ne(__isl_keep isl_val *v1,
664 __isl_keep isl_val *v2);
665 int isl_val_abs_eq(__isl_keep isl_val *v1,
666 __isl_keep isl_val *v2);
668 The function C<isl_val_abs_eq> checks whether its two arguments
669 are equal in absolute value.
671 For integer C<isl_val>s we additionally have the following binary property.
674 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
675 __isl_keep isl_val *v2);
677 An C<isl_val> can also be compared to an integer using the following
678 function. The result is undefined for NaN.
681 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
683 The following unary operations are available on C<isl_val>s.
686 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
687 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
688 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
689 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
690 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
691 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
692 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
694 The following binary operations are available on C<isl_val>s.
697 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
698 __isl_take isl_val *v2);
699 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
700 __isl_take isl_val *v2);
701 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
702 __isl_take isl_val *v2);
703 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
705 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
706 __isl_take isl_val *v2);
707 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
709 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
710 __isl_take isl_val *v2);
711 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
713 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
714 __isl_take isl_val *v2);
716 On integer values, we additionally have the following operations.
719 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
720 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
721 __isl_take isl_val *v2);
722 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
723 __isl_take isl_val *v2);
724 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
725 __isl_take isl_val *v2, __isl_give isl_val **x,
726 __isl_give isl_val **y);
728 The function C<isl_val_gcdext> returns the greatest common divisor g
729 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
730 that C<*x> * C<v1> + C<*y> * C<v2> = g.
732 =head3 GMP specific functions
734 These functions are only available if C<isl> has been compiled with C<GMP>
737 Specific integer and rational values can be created from C<GMP> values using
738 the following functions.
740 #include <isl/val_gmp.h>
741 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
743 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
744 const mpz_t n, const mpz_t d);
746 The numerator and denominator of a rational value can be extracted as
747 C<GMP> values using the following functions.
749 #include <isl/val_gmp.h>
750 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
751 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
753 =head2 Sets and Relations
755 C<isl> uses six types of objects for representing sets and relations,
756 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
757 C<isl_union_set> and C<isl_union_map>.
758 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
759 can be described as a conjunction of affine constraints, while
760 C<isl_set> and C<isl_map> represent unions of
761 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
762 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
763 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
764 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
765 where spaces are considered different if they have a different number
766 of dimensions and/or different names (see L<"Spaces">).
767 The difference between sets and relations (maps) is that sets have
768 one set of variables, while relations have two sets of variables,
769 input variables and output variables.
771 =head2 Error Handling
773 C<isl> supports different ways to react in case a runtime error is triggered.
774 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
775 with two maps that have incompatible spaces. There are three possible ways
776 to react on error: to warn, to continue or to abort.
778 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
779 the last error in the corresponding C<isl_ctx> and the function in which the
780 error was triggered returns C<NULL>. An error does not corrupt internal state,
781 such that isl can continue to be used. C<isl> also provides functions to
782 read the last error and to reset the memory that stores the last error. The
783 last error is only stored for information purposes. Its presence does not
784 change the behavior of C<isl>. Hence, resetting an error is not required to
785 continue to use isl, but only to observe new errors.
788 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
789 void isl_ctx_reset_error(isl_ctx *ctx);
791 Another option is to continue on error. This is similar to warn on error mode,
792 except that C<isl> does not print any warning. This allows a program to
793 implement its own error reporting.
795 The last option is to directly abort the execution of the program from within
796 the isl library. This makes it obviously impossible to recover from an error,
797 but it allows to directly spot the error location. By aborting on error,
798 debuggers break at the location the error occurred and can provide a stack
799 trace. Other tools that automatically provide stack traces on abort or that do
800 not want to continue execution after an error was triggered may also prefer to
803 The on error behavior of isl can be specified by calling
804 C<isl_options_set_on_error> or by setting the command line option
805 C<--isl-on-error>. Valid arguments for the function call are
806 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
807 choices for the command line option are C<warn>, C<continue> and C<abort>.
808 It is also possible to query the current error mode.
810 #include <isl/options.h>
811 int isl_options_set_on_error(isl_ctx *ctx, int val);
812 int isl_options_get_on_error(isl_ctx *ctx);
816 Identifiers are used to identify both individual dimensions
817 and tuples of dimensions. They consist of an optional name and an optional
818 user pointer. The name and the user pointer cannot both be C<NULL>, however.
819 Identifiers with the same name but different pointer values
820 are considered to be distinct.
821 Similarly, identifiers with different names but the same pointer value
822 are also considered to be distinct.
823 Equal identifiers are represented using the same object.
824 Pairs of identifiers can therefore be tested for equality using the
826 Identifiers can be constructed, copied, freed, inspected and printed
827 using the following functions.
830 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
831 __isl_keep const char *name, void *user);
832 __isl_give isl_id *isl_id_set_free_user(
833 __isl_take isl_id *id,
834 __isl_give void (*free_user)(void *user));
835 __isl_give isl_id *isl_id_copy(isl_id *id);
836 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
838 void *isl_id_get_user(__isl_keep isl_id *id);
839 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
841 __isl_give isl_printer *isl_printer_print_id(
842 __isl_take isl_printer *p, __isl_keep isl_id *id);
844 The callback set by C<isl_id_set_free_user> is called on the user
845 pointer when the last reference to the C<isl_id> is freed.
846 Note that C<isl_id_get_name> returns a pointer to some internal
847 data structure, so the result can only be used while the
848 corresponding C<isl_id> is alive.
852 Whenever a new set, relation or similar object is created from scratch,
853 the space in which it lives needs to be specified using an C<isl_space>.
854 Each space involves zero or more parameters and zero, one or two
855 tuples of set or input/output dimensions. The parameters and dimensions
856 are identified by an C<isl_dim_type> and a position.
857 The type C<isl_dim_param> refers to parameters,
858 the type C<isl_dim_set> refers to set dimensions (for spaces
859 with a single tuple of dimensions) and the types C<isl_dim_in>
860 and C<isl_dim_out> refer to input and output dimensions
861 (for spaces with two tuples of dimensions).
862 Local spaces (see L</"Local Spaces">) also contain dimensions
863 of type C<isl_dim_div>.
864 Note that parameters are only identified by their position within
865 a given object. Across different objects, parameters are (usually)
866 identified by their names or identifiers. Only unnamed parameters
867 are identified by their positions across objects. The use of unnamed
868 parameters is discouraged.
870 #include <isl/space.h>
871 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
872 unsigned nparam, unsigned n_in, unsigned n_out);
873 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
875 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
876 unsigned nparam, unsigned dim);
877 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
878 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
880 The space used for creating a parameter domain
881 needs to be created using C<isl_space_params_alloc>.
882 For other sets, the space
883 needs to be created using C<isl_space_set_alloc>, while
884 for a relation, the space
885 needs to be created using C<isl_space_alloc>.
887 To check whether a given space is that of a set or a map
888 or whether it is a parameter space, use these functions:
890 #include <isl/space.h>
891 int isl_space_is_params(__isl_keep isl_space *space);
892 int isl_space_is_set(__isl_keep isl_space *space);
893 int isl_space_is_map(__isl_keep isl_space *space);
895 Spaces can be compared using the following functions:
897 #include <isl/space.h>
898 int isl_space_is_equal(__isl_keep isl_space *space1,
899 __isl_keep isl_space *space2);
900 int isl_space_is_domain(__isl_keep isl_space *space1,
901 __isl_keep isl_space *space2);
902 int isl_space_is_range(__isl_keep isl_space *space1,
903 __isl_keep isl_space *space2);
904 int isl_space_tuple_is_equal(
905 __isl_keep isl_space *space1,
906 enum isl_dim_type type1,
907 __isl_keep isl_space *space2,
908 enum isl_dim_type type2);
910 C<isl_space_is_domain> checks whether the first argument is equal
911 to the domain of the second argument. This requires in particular that
912 the first argument is a set space and that the second argument
913 is a map space. C<isl_space_tuple_is_equal> checks whether the given
914 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
915 spaces are the same. That is, it checks if they have the same
916 identifier (if any), the same dimension and the same internal structure
919 It is often useful to create objects that live in the
920 same space as some other object. This can be accomplished
921 by creating the new objects
922 (see L</"Creating New Sets and Relations"> or
923 L</"Functions">) based on the space
924 of the original object.
927 __isl_give isl_space *isl_basic_set_get_space(
928 __isl_keep isl_basic_set *bset);
929 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
931 #include <isl/union_set.h>
932 __isl_give isl_space *isl_union_set_get_space(
933 __isl_keep isl_union_set *uset);
936 __isl_give isl_space *isl_basic_map_get_space(
937 __isl_keep isl_basic_map *bmap);
938 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
940 #include <isl/union_map.h>
941 __isl_give isl_space *isl_union_map_get_space(
942 __isl_keep isl_union_map *umap);
944 #include <isl/constraint.h>
945 __isl_give isl_space *isl_constraint_get_space(
946 __isl_keep isl_constraint *constraint);
948 #include <isl/polynomial.h>
949 __isl_give isl_space *isl_qpolynomial_get_domain_space(
950 __isl_keep isl_qpolynomial *qp);
951 __isl_give isl_space *isl_qpolynomial_get_space(
952 __isl_keep isl_qpolynomial *qp);
953 __isl_give isl_space *isl_qpolynomial_fold_get_space(
954 __isl_keep isl_qpolynomial_fold *fold);
955 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
956 __isl_keep isl_pw_qpolynomial *pwqp);
957 __isl_give isl_space *isl_pw_qpolynomial_get_space(
958 __isl_keep isl_pw_qpolynomial *pwqp);
959 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
960 __isl_keep isl_pw_qpolynomial_fold *pwf);
961 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
962 __isl_keep isl_pw_qpolynomial_fold *pwf);
963 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
964 __isl_keep isl_union_pw_qpolynomial *upwqp);
965 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
966 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
969 __isl_give isl_space *isl_multi_val_get_space(
970 __isl_keep isl_multi_val *mv);
973 __isl_give isl_space *isl_aff_get_domain_space(
974 __isl_keep isl_aff *aff);
975 __isl_give isl_space *isl_aff_get_space(
976 __isl_keep isl_aff *aff);
977 __isl_give isl_space *isl_pw_aff_get_domain_space(
978 __isl_keep isl_pw_aff *pwaff);
979 __isl_give isl_space *isl_pw_aff_get_space(
980 __isl_keep isl_pw_aff *pwaff);
981 __isl_give isl_space *isl_multi_aff_get_domain_space(
982 __isl_keep isl_multi_aff *maff);
983 __isl_give isl_space *isl_multi_aff_get_space(
984 __isl_keep isl_multi_aff *maff);
985 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
986 __isl_keep isl_pw_multi_aff *pma);
987 __isl_give isl_space *isl_pw_multi_aff_get_space(
988 __isl_keep isl_pw_multi_aff *pma);
989 __isl_give isl_space *isl_union_pw_aff_get_space(
990 __isl_keep isl_union_pw_aff *upa);
991 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
992 __isl_keep isl_union_pw_multi_aff *upma);
993 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
994 __isl_keep isl_multi_pw_aff *mpa);
995 __isl_give isl_space *isl_multi_pw_aff_get_space(
996 __isl_keep isl_multi_pw_aff *mpa);
997 __isl_give isl_space *
998 isl_multi_union_pw_aff_get_domain_space(
999 __isl_keep isl_multi_union_pw_aff *mupa);
1000 __isl_give isl_space *
1001 isl_multi_union_pw_aff_get_space(
1002 __isl_keep isl_multi_union_pw_aff *mupa);
1004 #include <isl/point.h>
1005 __isl_give isl_space *isl_point_get_space(
1006 __isl_keep isl_point *pnt);
1008 The number of dimensions of a given type of space
1009 may be read off from a space or an object that lives
1010 in a space using the following functions.
1011 In case of C<isl_space_dim>, type may be
1012 C<isl_dim_param>, C<isl_dim_in> (only for relations),
1013 C<isl_dim_out> (only for relations), C<isl_dim_set>
1014 (only for sets) or C<isl_dim_all>.
1016 #include <isl/space.h>
1017 unsigned isl_space_dim(__isl_keep isl_space *space,
1018 enum isl_dim_type type);
1020 #include <isl/local_space.h>
1021 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1022 enum isl_dim_type type);
1024 #include <isl/set.h>
1025 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1026 enum isl_dim_type type);
1027 unsigned isl_set_dim(__isl_keep isl_set *set,
1028 enum isl_dim_type type);
1030 #include <isl/union_set.h>
1031 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1032 enum isl_dim_type type);
1034 #include <isl/map.h>
1035 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1036 enum isl_dim_type type);
1037 unsigned isl_map_dim(__isl_keep isl_map *map,
1038 enum isl_dim_type type);
1040 #include <isl/union_map.h>
1041 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1042 enum isl_dim_type type);
1044 #include <isl/val.h>
1045 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1046 enum isl_dim_type type);
1048 #include <isl/aff.h>
1049 int isl_aff_dim(__isl_keep isl_aff *aff,
1050 enum isl_dim_type type);
1051 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1052 enum isl_dim_type type);
1053 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1054 enum isl_dim_type type);
1055 unsigned isl_pw_multi_aff_dim(
1056 __isl_keep isl_pw_multi_aff *pma,
1057 enum isl_dim_type type);
1058 unsigned isl_multi_pw_aff_dim(
1059 __isl_keep isl_multi_pw_aff *mpa,
1060 enum isl_dim_type type);
1061 unsigned isl_union_pw_aff_dim(
1062 __isl_keep isl_union_pw_aff *upa,
1063 enum isl_dim_type type);
1064 unsigned isl_union_pw_multi_aff_dim(
1065 __isl_keep isl_union_pw_multi_aff *upma,
1066 enum isl_dim_type type);
1067 unsigned isl_multi_union_pw_aff_dim(
1068 __isl_keep isl_multi_union_pw_aff *mupa,
1069 enum isl_dim_type type);
1071 #include <isl/polynomial.h>
1072 unsigned isl_union_pw_qpolynomial_dim(
1073 __isl_keep isl_union_pw_qpolynomial *upwqp,
1074 enum isl_dim_type type);
1075 unsigned isl_union_pw_qpolynomial_fold_dim(
1076 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1077 enum isl_dim_type type);
1079 Note that an C<isl_union_set>, an C<isl_union_map>,
1080 an C<isl_union_pw_multi_aff>,
1081 an C<isl_union_pw_qpolynomial> and
1082 an C<isl_union_pw_qpolynomial_fold>
1083 only have parameters.
1085 The identifiers or names of the individual dimensions of spaces
1086 may be set or read off using the following functions on spaces
1087 or objects that live in spaces.
1088 These functions are mostly useful to obtain the identifiers, positions
1089 or names of the parameters. Identifiers of individual dimensions are
1090 essentially only useful for printing. They are ignored by all other
1091 operations and may not be preserved across those operations.
1093 #include <isl/space.h>
1094 __isl_give isl_space *isl_space_set_dim_id(
1095 __isl_take isl_space *space,
1096 enum isl_dim_type type, unsigned pos,
1097 __isl_take isl_id *id);
1098 int isl_space_has_dim_id(__isl_keep isl_space *space,
1099 enum isl_dim_type type, unsigned pos);
1100 __isl_give isl_id *isl_space_get_dim_id(
1101 __isl_keep isl_space *space,
1102 enum isl_dim_type type, unsigned pos);
1103 __isl_give isl_space *isl_space_set_dim_name(
1104 __isl_take isl_space *space,
1105 enum isl_dim_type type, unsigned pos,
1106 __isl_keep const char *name);
1107 int isl_space_has_dim_name(__isl_keep isl_space *space,
1108 enum isl_dim_type type, unsigned pos);
1109 __isl_keep const char *isl_space_get_dim_name(
1110 __isl_keep isl_space *space,
1111 enum isl_dim_type type, unsigned pos);
1113 #include <isl/local_space.h>
1114 __isl_give isl_local_space *isl_local_space_set_dim_id(
1115 __isl_take isl_local_space *ls,
1116 enum isl_dim_type type, unsigned pos,
1117 __isl_take isl_id *id);
1118 int isl_local_space_has_dim_id(
1119 __isl_keep isl_local_space *ls,
1120 enum isl_dim_type type, unsigned pos);
1121 __isl_give isl_id *isl_local_space_get_dim_id(
1122 __isl_keep isl_local_space *ls,
1123 enum isl_dim_type type, unsigned pos);
1124 __isl_give isl_local_space *isl_local_space_set_dim_name(
1125 __isl_take isl_local_space *ls,
1126 enum isl_dim_type type, unsigned pos, const char *s);
1127 int isl_local_space_has_dim_name(
1128 __isl_keep isl_local_space *ls,
1129 enum isl_dim_type type, unsigned pos)
1130 const char *isl_local_space_get_dim_name(
1131 __isl_keep isl_local_space *ls,
1132 enum isl_dim_type type, unsigned pos);
1134 #include <isl/constraint.h>
1135 const char *isl_constraint_get_dim_name(
1136 __isl_keep isl_constraint *constraint,
1137 enum isl_dim_type type, unsigned pos);
1139 #include <isl/set.h>
1140 __isl_give isl_id *isl_basic_set_get_dim_id(
1141 __isl_keep isl_basic_set *bset,
1142 enum isl_dim_type type, unsigned pos);
1143 __isl_give isl_set *isl_set_set_dim_id(
1144 __isl_take isl_set *set, enum isl_dim_type type,
1145 unsigned pos, __isl_take isl_id *id);
1146 int isl_set_has_dim_id(__isl_keep isl_set *set,
1147 enum isl_dim_type type, unsigned pos);
1148 __isl_give isl_id *isl_set_get_dim_id(
1149 __isl_keep isl_set *set, enum isl_dim_type type,
1151 const char *isl_basic_set_get_dim_name(
1152 __isl_keep isl_basic_set *bset,
1153 enum isl_dim_type type, unsigned pos);
1154 int isl_set_has_dim_name(__isl_keep isl_set *set,
1155 enum isl_dim_type type, unsigned pos);
1156 const char *isl_set_get_dim_name(
1157 __isl_keep isl_set *set,
1158 enum isl_dim_type type, unsigned pos);
1160 #include <isl/map.h>
1161 __isl_give isl_map *isl_map_set_dim_id(
1162 __isl_take isl_map *map, enum isl_dim_type type,
1163 unsigned pos, __isl_take isl_id *id);
1164 int isl_basic_map_has_dim_id(
1165 __isl_keep isl_basic_map *bmap,
1166 enum isl_dim_type type, unsigned pos);
1167 int isl_map_has_dim_id(__isl_keep isl_map *map,
1168 enum isl_dim_type type, unsigned pos);
1169 __isl_give isl_id *isl_map_get_dim_id(
1170 __isl_keep isl_map *map, enum isl_dim_type type,
1172 __isl_give isl_id *isl_union_map_get_dim_id(
1173 __isl_keep isl_union_map *umap,
1174 enum isl_dim_type type, unsigned pos);
1175 const char *isl_basic_map_get_dim_name(
1176 __isl_keep isl_basic_map *bmap,
1177 enum isl_dim_type type, unsigned pos);
1178 int isl_map_has_dim_name(__isl_keep isl_map *map,
1179 enum isl_dim_type type, unsigned pos);
1180 const char *isl_map_get_dim_name(
1181 __isl_keep isl_map *map,
1182 enum isl_dim_type type, unsigned pos);
1184 #include <isl/val.h>
1185 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1186 __isl_take isl_multi_val *mv,
1187 enum isl_dim_type type, unsigned pos,
1188 __isl_take isl_id *id);
1189 __isl_give isl_id *isl_multi_val_get_dim_id(
1190 __isl_keep isl_multi_val *mv,
1191 enum isl_dim_type type, unsigned pos);
1192 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1193 __isl_take isl_multi_val *mv,
1194 enum isl_dim_type type, unsigned pos, const char *s);
1196 #include <isl/aff.h>
1197 __isl_give isl_aff *isl_aff_set_dim_id(
1198 __isl_take isl_aff *aff, enum isl_dim_type type,
1199 unsigned pos, __isl_take isl_id *id);
1200 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1201 __isl_take isl_multi_aff *maff,
1202 enum isl_dim_type type, unsigned pos,
1203 __isl_take isl_id *id);
1204 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1205 __isl_take isl_pw_aff *pma,
1206 enum isl_dim_type type, unsigned pos,
1207 __isl_take isl_id *id);
1208 __isl_give isl_multi_pw_aff *
1209 isl_multi_pw_aff_set_dim_id(
1210 __isl_take isl_multi_pw_aff *mpa,
1211 enum isl_dim_type type, unsigned pos,
1212 __isl_take isl_id *id);
1213 __isl_give isl_multi_union_pw_aff *
1214 isl_multi_union_pw_aff_set_dim_id(
1215 __isl_take isl_multi_union_pw_aff *mupa,
1216 enum isl_dim_type type, unsigned pos,
1217 __isl_take isl_id *id);
1218 __isl_give isl_id *isl_multi_aff_get_dim_id(
1219 __isl_keep isl_multi_aff *ma,
1220 enum isl_dim_type type, unsigned pos);
1221 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1222 enum isl_dim_type type, unsigned pos);
1223 __isl_give isl_id *isl_pw_aff_get_dim_id(
1224 __isl_keep isl_pw_aff *pa,
1225 enum isl_dim_type type, unsigned pos);
1226 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1227 __isl_keep isl_pw_multi_aff *pma,
1228 enum isl_dim_type type, unsigned pos);
1229 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1230 __isl_keep isl_multi_pw_aff *mpa,
1231 enum isl_dim_type type, unsigned pos);
1232 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1233 __isl_keep isl_multi_union_pw_aff *mupa,
1234 enum isl_dim_type type, unsigned pos);
1235 __isl_give isl_aff *isl_aff_set_dim_name(
1236 __isl_take isl_aff *aff, enum isl_dim_type type,
1237 unsigned pos, const char *s);
1238 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1239 __isl_take isl_multi_aff *maff,
1240 enum isl_dim_type type, unsigned pos, const char *s);
1241 __isl_give isl_multi_pw_aff *
1242 isl_multi_pw_aff_set_dim_name(
1243 __isl_take isl_multi_pw_aff *mpa,
1244 enum isl_dim_type type, unsigned pos, const char *s);
1245 __isl_give isl_union_pw_aff *
1246 isl_union_pw_aff_set_dim_name(
1247 __isl_take isl_union_pw_aff *upa,
1248 enum isl_dim_type type, unsigned pos,
1250 __isl_give isl_union_pw_multi_aff *
1251 isl_union_pw_multi_aff_set_dim_name(
1252 __isl_take isl_union_pw_multi_aff *upma,
1253 enum isl_dim_type type, unsigned pos,
1255 __isl_give isl_multi_union_pw_aff *
1256 isl_multi_union_pw_aff_set_dim_name(
1257 __isl_take isl_multi_union_pw_aff *mupa,
1258 enum isl_dim_type type, unsigned pos,
1259 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1260 enum isl_dim_type type, unsigned pos);
1261 const char *isl_pw_aff_get_dim_name(
1262 __isl_keep isl_pw_aff *pa,
1263 enum isl_dim_type type, unsigned pos);
1264 const char *isl_pw_multi_aff_get_dim_name(
1265 __isl_keep isl_pw_multi_aff *pma,
1266 enum isl_dim_type type, unsigned pos);
1268 #include <isl/polynomial.h>
1269 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1270 __isl_take isl_qpolynomial *qp,
1271 enum isl_dim_type type, unsigned pos,
1273 __isl_give isl_pw_qpolynomial *
1274 isl_pw_qpolynomial_set_dim_name(
1275 __isl_take isl_pw_qpolynomial *pwqp,
1276 enum isl_dim_type type, unsigned pos,
1278 __isl_give isl_pw_qpolynomial_fold *
1279 isl_pw_qpolynomial_fold_set_dim_name(
1280 __isl_take isl_pw_qpolynomial_fold *pwf,
1281 enum isl_dim_type type, unsigned pos,
1283 __isl_give isl_union_pw_qpolynomial *
1284 isl_union_pw_qpolynomial_set_dim_name(
1285 __isl_take isl_union_pw_qpolynomial *upwqp,
1286 enum isl_dim_type type, unsigned pos,
1288 __isl_give isl_union_pw_qpolynomial_fold *
1289 isl_union_pw_qpolynomial_fold_set_dim_name(
1290 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1291 enum isl_dim_type type, unsigned pos,
1294 Note that C<isl_space_get_name> returns a pointer to some internal
1295 data structure, so the result can only be used while the
1296 corresponding C<isl_space> is alive.
1297 Also note that every function that operates on two sets or relations
1298 requires that both arguments have the same parameters. This also
1299 means that if one of the arguments has named parameters, then the
1300 other needs to have named parameters too and the names need to match.
1301 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1302 arguments may have different parameters (as long as they are named),
1303 in which case the result will have as parameters the union of the parameters of
1306 Given the identifier or name of a dimension (typically a parameter),
1307 its position can be obtained from the following functions.
1309 #include <isl/space.h>
1310 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1311 enum isl_dim_type type, __isl_keep isl_id *id);
1312 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1313 enum isl_dim_type type, const char *name);
1315 #include <isl/local_space.h>
1316 int isl_local_space_find_dim_by_name(
1317 __isl_keep isl_local_space *ls,
1318 enum isl_dim_type type, const char *name);
1320 #include <isl/val.h>
1321 int isl_multi_val_find_dim_by_id(
1322 __isl_keep isl_multi_val *mv,
1323 enum isl_dim_type type, __isl_keep isl_id *id);
1324 int isl_multi_val_find_dim_by_name(
1325 __isl_keep isl_multi_val *mv,
1326 enum isl_dim_type type, const char *name);
1328 #include <isl/set.h>
1329 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1330 enum isl_dim_type type, __isl_keep isl_id *id);
1331 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1332 enum isl_dim_type type, const char *name);
1334 #include <isl/map.h>
1335 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1336 enum isl_dim_type type, __isl_keep isl_id *id);
1337 int isl_basic_map_find_dim_by_name(
1338 __isl_keep isl_basic_map *bmap,
1339 enum isl_dim_type type, const char *name);
1340 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1341 enum isl_dim_type type, const char *name);
1342 int isl_union_map_find_dim_by_name(
1343 __isl_keep isl_union_map *umap,
1344 enum isl_dim_type type, const char *name);
1346 #include <isl/aff.h>
1347 int isl_multi_aff_find_dim_by_id(
1348 __isl_keep isl_multi_aff *ma,
1349 enum isl_dim_type type, __isl_keep isl_id *id);
1350 int isl_multi_pw_aff_find_dim_by_id(
1351 __isl_keep isl_multi_pw_aff *mpa,
1352 enum isl_dim_type type, __isl_keep isl_id *id);
1353 int isl_multi_union_pw_aff_find_dim_by_id(
1354 __isl_keep isl_union_multi_pw_aff *mupa,
1355 enum isl_dim_type type, __isl_keep isl_id *id);
1356 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1357 enum isl_dim_type type, const char *name);
1358 int isl_multi_aff_find_dim_by_name(
1359 __isl_keep isl_multi_aff *ma,
1360 enum isl_dim_type type, const char *name);
1361 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1362 enum isl_dim_type type, const char *name);
1363 int isl_multi_pw_aff_find_dim_by_name(
1364 __isl_keep isl_multi_pw_aff *mpa,
1365 enum isl_dim_type type, const char *name);
1366 int isl_pw_multi_aff_find_dim_by_name(
1367 __isl_keep isl_pw_multi_aff *pma,
1368 enum isl_dim_type type, const char *name);
1369 int isl_union_pw_aff_find_dim_by_name(
1370 __isl_keep isl_union_pw_aff *upa,
1371 enum isl_dim_type type, const char *name);
1372 int isl_union_pw_multi_aff_find_dim_by_name(
1373 __isl_keep isl_union_pw_multi_aff *upma,
1374 enum isl_dim_type type, const char *name);
1375 int isl_multi_union_pw_aff_find_dim_by_name(
1376 __isl_keep isl_multi_union_pw_aff *mupa,
1377 enum isl_dim_type type, const char *name);
1379 #include <isl/polynomial.h>
1380 int isl_pw_qpolynomial_find_dim_by_name(
1381 __isl_keep isl_pw_qpolynomial *pwqp,
1382 enum isl_dim_type type, const char *name);
1383 int isl_pw_qpolynomial_fold_find_dim_by_name(
1384 __isl_keep isl_pw_qpolynomial_fold *pwf,
1385 enum isl_dim_type type, const char *name);
1386 int isl_union_pw_qpolynomial_find_dim_by_name(
1387 __isl_keep isl_union_pw_qpolynomial *upwqp,
1388 enum isl_dim_type type, const char *name);
1389 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1390 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1391 enum isl_dim_type type, const char *name);
1393 The identifiers or names of entire spaces may be set or read off
1394 using the following functions.
1396 #include <isl/space.h>
1397 __isl_give isl_space *isl_space_set_tuple_id(
1398 __isl_take isl_space *space,
1399 enum isl_dim_type type, __isl_take isl_id *id);
1400 __isl_give isl_space *isl_space_reset_tuple_id(
1401 __isl_take isl_space *space, enum isl_dim_type type);
1402 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1403 enum isl_dim_type type);
1404 __isl_give isl_id *isl_space_get_tuple_id(
1405 __isl_keep isl_space *space, enum isl_dim_type type);
1406 __isl_give isl_space *isl_space_set_tuple_name(
1407 __isl_take isl_space *space,
1408 enum isl_dim_type type, const char *s);
1409 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1410 enum isl_dim_type type);
1411 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1412 enum isl_dim_type type);
1414 #include <isl/local_space.h>
1415 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1416 __isl_take isl_local_space *ls,
1417 enum isl_dim_type type, __isl_take isl_id *id);
1419 #include <isl/set.h>
1420 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1421 __isl_take isl_basic_set *bset,
1422 __isl_take isl_id *id);
1423 __isl_give isl_set *isl_set_set_tuple_id(
1424 __isl_take isl_set *set, __isl_take isl_id *id);
1425 __isl_give isl_set *isl_set_reset_tuple_id(
1426 __isl_take isl_set *set);
1427 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1428 __isl_give isl_id *isl_set_get_tuple_id(
1429 __isl_keep isl_set *set);
1430 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1431 __isl_take isl_basic_set *set, const char *s);
1432 __isl_give isl_set *isl_set_set_tuple_name(
1433 __isl_take isl_set *set, const char *s);
1434 const char *isl_basic_set_get_tuple_name(
1435 __isl_keep isl_basic_set *bset);
1436 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1437 const char *isl_set_get_tuple_name(
1438 __isl_keep isl_set *set);
1440 #include <isl/map.h>
1441 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1442 __isl_take isl_basic_map *bmap,
1443 enum isl_dim_type type, __isl_take isl_id *id);
1444 __isl_give isl_map *isl_map_set_tuple_id(
1445 __isl_take isl_map *map, enum isl_dim_type type,
1446 __isl_take isl_id *id);
1447 __isl_give isl_map *isl_map_reset_tuple_id(
1448 __isl_take isl_map *map, enum isl_dim_type type);
1449 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1450 enum isl_dim_type type);
1451 __isl_give isl_id *isl_map_get_tuple_id(
1452 __isl_keep isl_map *map, enum isl_dim_type type);
1453 __isl_give isl_map *isl_map_set_tuple_name(
1454 __isl_take isl_map *map,
1455 enum isl_dim_type type, const char *s);
1456 const char *isl_basic_map_get_tuple_name(
1457 __isl_keep isl_basic_map *bmap,
1458 enum isl_dim_type type);
1459 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1460 __isl_take isl_basic_map *bmap,
1461 enum isl_dim_type type, const char *s);
1462 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1463 enum isl_dim_type type);
1464 const char *isl_map_get_tuple_name(
1465 __isl_keep isl_map *map,
1466 enum isl_dim_type type);
1468 #include <isl/val.h>
1469 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1470 __isl_take isl_multi_val *mv,
1471 enum isl_dim_type type, __isl_take isl_id *id);
1472 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1473 __isl_take isl_multi_val *mv,
1474 enum isl_dim_type type);
1475 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1476 enum isl_dim_type type);
1477 __isl_give isl_id *isl_multi_val_get_tuple_id(
1478 __isl_keep isl_multi_val *mv,
1479 enum isl_dim_type type);
1480 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1481 __isl_take isl_multi_val *mv,
1482 enum isl_dim_type type, const char *s);
1483 const char *isl_multi_val_get_tuple_name(
1484 __isl_keep isl_multi_val *mv,
1485 enum isl_dim_type type);
1487 #include <isl/aff.h>
1488 __isl_give isl_aff *isl_aff_set_tuple_id(
1489 __isl_take isl_aff *aff,
1490 enum isl_dim_type type, __isl_take isl_id *id);
1491 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1492 __isl_take isl_multi_aff *maff,
1493 enum isl_dim_type type, __isl_take isl_id *id);
1494 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1495 __isl_take isl_pw_aff *pwaff,
1496 enum isl_dim_type type, __isl_take isl_id *id);
1497 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1498 __isl_take isl_pw_multi_aff *pma,
1499 enum isl_dim_type type, __isl_take isl_id *id);
1500 __isl_give isl_multi_union_pw_aff *
1501 isl_multi_union_pw_aff_set_tuple_id(
1502 __isl_take isl_multi_union_pw_aff *mupa,
1503 enum isl_dim_type type, __isl_take isl_id *id);
1504 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1505 __isl_take isl_multi_aff *ma,
1506 enum isl_dim_type type);
1507 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1508 __isl_take isl_pw_aff *pa,
1509 enum isl_dim_type type);
1510 __isl_give isl_multi_pw_aff *
1511 isl_multi_pw_aff_reset_tuple_id(
1512 __isl_take isl_multi_pw_aff *mpa,
1513 enum isl_dim_type type);
1514 __isl_give isl_pw_multi_aff *
1515 isl_pw_multi_aff_reset_tuple_id(
1516 __isl_take isl_pw_multi_aff *pma,
1517 enum isl_dim_type type);
1518 __isl_give isl_multi_union_pw_aff *
1519 isl_multi_union_pw_aff_reset_tuple_id(
1520 __isl_take isl_multi_union_pw_aff *mupa,
1521 enum isl_dim_type type);
1522 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1523 enum isl_dim_type type);
1524 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1525 __isl_keep isl_multi_aff *ma,
1526 enum isl_dim_type type);
1527 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1528 enum isl_dim_type type);
1529 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1530 __isl_keep isl_pw_aff *pa,
1531 enum isl_dim_type type);
1532 int isl_pw_multi_aff_has_tuple_id(
1533 __isl_keep isl_pw_multi_aff *pma,
1534 enum isl_dim_type type);
1535 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1536 __isl_keep isl_pw_multi_aff *pma,
1537 enum isl_dim_type type);
1538 int isl_multi_pw_aff_has_tuple_id(
1539 __isl_keep isl_multi_pw_aff *mpa,
1540 enum isl_dim_type type);
1541 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1542 __isl_keep isl_multi_pw_aff *mpa,
1543 enum isl_dim_type type);
1544 int isl_multi_union_pw_aff_has_tuple_id(
1545 __isl_keep isl_multi_union_pw_aff *mupa,
1546 enum isl_dim_type type);
1547 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1548 __isl_keep isl_multi_union_pw_aff *mupa,
1549 enum isl_dim_type type);
1550 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1551 __isl_take isl_multi_aff *maff,
1552 enum isl_dim_type type, const char *s);
1553 __isl_give isl_multi_pw_aff *
1554 isl_multi_pw_aff_set_tuple_name(
1555 __isl_take isl_multi_pw_aff *mpa,
1556 enum isl_dim_type type, const char *s);
1557 __isl_give isl_multi_union_pw_aff *
1558 isl_multi_union_pw_aff_set_tuple_name(
1559 __isl_take isl_multi_union_pw_aff *mupa,
1560 enum isl_dim_type type, const char *s);
1561 const char *isl_multi_aff_get_tuple_name(
1562 __isl_keep isl_multi_aff *multi,
1563 enum isl_dim_type type);
1564 int isl_pw_multi_aff_has_tuple_name(
1565 __isl_keep isl_pw_multi_aff *pma,
1566 enum isl_dim_type type);
1567 const char *isl_pw_multi_aff_get_tuple_name(
1568 __isl_keep isl_pw_multi_aff *pma,
1569 enum isl_dim_type type);
1570 const char *isl_multi_union_pw_aff_get_tuple_name(
1571 __isl_keep isl_multi_union_pw_aff *mupa,
1572 enum isl_dim_type type);
1574 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1575 or C<isl_dim_set>. As with C<isl_space_get_name>,
1576 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1578 Binary operations require the corresponding spaces of their arguments
1579 to have the same name.
1581 To keep the names of all parameters and tuples, but reset the user pointers
1582 of all the corresponding identifiers, use the following function.
1584 #include <isl/space.h>
1585 __isl_give isl_space *isl_space_reset_user(
1586 __isl_take isl_space *space);
1588 #include <isl/set.h>
1589 __isl_give isl_set *isl_set_reset_user(
1590 __isl_take isl_set *set);
1592 #include <isl/map.h>
1593 __isl_give isl_map *isl_map_reset_user(
1594 __isl_take isl_map *map);
1596 #include <isl/union_set.h>
1597 __isl_give isl_union_set *isl_union_set_reset_user(
1598 __isl_take isl_union_set *uset);
1600 #include <isl/union_map.h>
1601 __isl_give isl_union_map *isl_union_map_reset_user(
1602 __isl_take isl_union_map *umap);
1604 #include <isl/val.h>
1605 __isl_give isl_multi_val *isl_multi_val_reset_user(
1606 __isl_take isl_multi_val *mv);
1608 #include <isl/aff.h>
1609 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1610 __isl_take isl_multi_aff *ma);
1611 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1612 __isl_take isl_pw_aff *pa);
1613 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1614 __isl_take isl_multi_pw_aff *mpa);
1615 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1616 __isl_take isl_pw_multi_aff *pma);
1617 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1618 __isl_take isl_union_pw_aff *upa);
1619 __isl_give isl_multi_union_pw_aff *
1620 isl_multi_union_pw_aff_reset_user(
1621 __isl_take isl_multi_union_pw_aff *mupa);
1622 __isl_give isl_union_pw_multi_aff *
1623 isl_union_pw_multi_aff_reset_user(
1624 __isl_take isl_union_pw_multi_aff *upma);
1626 #include <isl/polynomial.h>
1627 __isl_give isl_pw_qpolynomial *
1628 isl_pw_qpolynomial_reset_user(
1629 __isl_take isl_pw_qpolynomial *pwqp);
1630 __isl_give isl_union_pw_qpolynomial *
1631 isl_union_pw_qpolynomial_reset_user(
1632 __isl_take isl_union_pw_qpolynomial *upwqp);
1633 __isl_give isl_pw_qpolynomial_fold *
1634 isl_pw_qpolynomial_fold_reset_user(
1635 __isl_take isl_pw_qpolynomial_fold *pwf);
1636 __isl_give isl_union_pw_qpolynomial_fold *
1637 isl_union_pw_qpolynomial_fold_reset_user(
1638 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1640 Spaces can be nested. In particular, the domain of a set or
1641 the domain or range of a relation can be a nested relation.
1642 This process is also called I<wrapping>.
1643 The functions for detecting, constructing and deconstructing
1644 such nested spaces can be found in the wrapping properties
1645 of L</"Unary Properties">, the wrapping operations
1646 of L</"Unary Operations"> and the Cartesian product operations
1647 of L</"Basic Operations">.
1649 Spaces can be created from other spaces
1650 using the functions described in L</"Unary Operations">
1651 and L</"Binary Operations">.
1655 A local space is essentially a space with
1656 zero or more existentially quantified variables.
1657 The local space of various objects can be obtained
1658 using the following functions.
1660 #include <isl/constraint.h>
1661 __isl_give isl_local_space *isl_constraint_get_local_space(
1662 __isl_keep isl_constraint *constraint);
1664 #include <isl/set.h>
1665 __isl_give isl_local_space *isl_basic_set_get_local_space(
1666 __isl_keep isl_basic_set *bset);
1668 #include <isl/map.h>
1669 __isl_give isl_local_space *isl_basic_map_get_local_space(
1670 __isl_keep isl_basic_map *bmap);
1672 #include <isl/aff.h>
1673 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1674 __isl_keep isl_aff *aff);
1675 __isl_give isl_local_space *isl_aff_get_local_space(
1676 __isl_keep isl_aff *aff);
1678 A new local space can be created from a space using
1680 #include <isl/local_space.h>
1681 __isl_give isl_local_space *isl_local_space_from_space(
1682 __isl_take isl_space *space);
1684 They can be inspected, modified, copied and freed using the following functions.
1686 #include <isl/local_space.h>
1687 int isl_local_space_is_params(
1688 __isl_keep isl_local_space *ls);
1689 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1690 __isl_give isl_space *isl_local_space_get_space(
1691 __isl_keep isl_local_space *ls);
1692 __isl_give isl_aff *isl_local_space_get_div(
1693 __isl_keep isl_local_space *ls, int pos);
1694 __isl_give isl_local_space *isl_local_space_copy(
1695 __isl_keep isl_local_space *ls);
1696 __isl_null isl_local_space *isl_local_space_free(
1697 __isl_take isl_local_space *ls);
1699 Note that C<isl_local_space_get_div> can only be used on local spaces
1702 Two local spaces can be compared using
1704 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1705 __isl_keep isl_local_space *ls2);
1707 Local spaces can be created from other local spaces
1708 using the functions described in L</"Unary Operations">
1709 and L</"Binary Operations">.
1711 =head2 Creating New Sets and Relations
1713 C<isl> has functions for creating some standard sets and relations.
1717 =item * Empty sets and relations
1719 __isl_give isl_basic_set *isl_basic_set_empty(
1720 __isl_take isl_space *space);
1721 __isl_give isl_basic_map *isl_basic_map_empty(
1722 __isl_take isl_space *space);
1723 __isl_give isl_set *isl_set_empty(
1724 __isl_take isl_space *space);
1725 __isl_give isl_map *isl_map_empty(
1726 __isl_take isl_space *space);
1727 __isl_give isl_union_set *isl_union_set_empty(
1728 __isl_take isl_space *space);
1729 __isl_give isl_union_map *isl_union_map_empty(
1730 __isl_take isl_space *space);
1732 For C<isl_union_set>s and C<isl_union_map>s, the space
1733 is only used to specify the parameters.
1735 =item * Universe sets and relations
1737 __isl_give isl_basic_set *isl_basic_set_universe(
1738 __isl_take isl_space *space);
1739 __isl_give isl_basic_map *isl_basic_map_universe(
1740 __isl_take isl_space *space);
1741 __isl_give isl_set *isl_set_universe(
1742 __isl_take isl_space *space);
1743 __isl_give isl_map *isl_map_universe(
1744 __isl_take isl_space *space);
1745 __isl_give isl_union_set *isl_union_set_universe(
1746 __isl_take isl_union_set *uset);
1747 __isl_give isl_union_map *isl_union_map_universe(
1748 __isl_take isl_union_map *umap);
1750 The sets and relations constructed by the functions above
1751 contain all integer values, while those constructed by the
1752 functions below only contain non-negative values.
1754 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1755 __isl_take isl_space *space);
1756 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1757 __isl_take isl_space *space);
1758 __isl_give isl_set *isl_set_nat_universe(
1759 __isl_take isl_space *space);
1760 __isl_give isl_map *isl_map_nat_universe(
1761 __isl_take isl_space *space);
1763 =item * Identity relations
1765 __isl_give isl_basic_map *isl_basic_map_identity(
1766 __isl_take isl_space *space);
1767 __isl_give isl_map *isl_map_identity(
1768 __isl_take isl_space *space);
1770 The number of input and output dimensions in C<space> needs
1773 =item * Lexicographic order
1775 __isl_give isl_map *isl_map_lex_lt(
1776 __isl_take isl_space *set_space);
1777 __isl_give isl_map *isl_map_lex_le(
1778 __isl_take isl_space *set_space);
1779 __isl_give isl_map *isl_map_lex_gt(
1780 __isl_take isl_space *set_space);
1781 __isl_give isl_map *isl_map_lex_ge(
1782 __isl_take isl_space *set_space);
1783 __isl_give isl_map *isl_map_lex_lt_first(
1784 __isl_take isl_space *space, unsigned n);
1785 __isl_give isl_map *isl_map_lex_le_first(
1786 __isl_take isl_space *space, unsigned n);
1787 __isl_give isl_map *isl_map_lex_gt_first(
1788 __isl_take isl_space *space, unsigned n);
1789 __isl_give isl_map *isl_map_lex_ge_first(
1790 __isl_take isl_space *space, unsigned n);
1792 The first four functions take a space for a B<set>
1793 and return relations that express that the elements in the domain
1794 are lexicographically less
1795 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1796 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1797 than the elements in the range.
1798 The last four functions take a space for a map
1799 and return relations that express that the first C<n> dimensions
1800 in the domain are lexicographically less
1801 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1802 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1803 than the first C<n> dimensions in the range.
1807 A basic set or relation can be converted to a set or relation
1808 using the following functions.
1810 __isl_give isl_set *isl_set_from_basic_set(
1811 __isl_take isl_basic_set *bset);
1812 __isl_give isl_map *isl_map_from_basic_map(
1813 __isl_take isl_basic_map *bmap);
1815 Sets and relations can be converted to union sets and relations
1816 using the following functions.
1818 __isl_give isl_union_set *isl_union_set_from_basic_set(
1819 __isl_take isl_basic_set *bset);
1820 __isl_give isl_union_map *isl_union_map_from_basic_map(
1821 __isl_take isl_basic_map *bmap);
1822 __isl_give isl_union_set *isl_union_set_from_set(
1823 __isl_take isl_set *set);
1824 __isl_give isl_union_map *isl_union_map_from_map(
1825 __isl_take isl_map *map);
1827 The inverse conversions below can only be used if the input
1828 union set or relation is known to contain elements in exactly one
1831 __isl_give isl_set *isl_set_from_union_set(
1832 __isl_take isl_union_set *uset);
1833 __isl_give isl_map *isl_map_from_union_map(
1834 __isl_take isl_union_map *umap);
1836 Sets and relations can be copied and freed again using the following
1839 __isl_give isl_basic_set *isl_basic_set_copy(
1840 __isl_keep isl_basic_set *bset);
1841 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1842 __isl_give isl_union_set *isl_union_set_copy(
1843 __isl_keep isl_union_set *uset);
1844 __isl_give isl_basic_map *isl_basic_map_copy(
1845 __isl_keep isl_basic_map *bmap);
1846 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1847 __isl_give isl_union_map *isl_union_map_copy(
1848 __isl_keep isl_union_map *umap);
1849 __isl_null isl_basic_set *isl_basic_set_free(
1850 __isl_take isl_basic_set *bset);
1851 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1852 __isl_null isl_union_set *isl_union_set_free(
1853 __isl_take isl_union_set *uset);
1854 __isl_null isl_basic_map *isl_basic_map_free(
1855 __isl_take isl_basic_map *bmap);
1856 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1857 __isl_null isl_union_map *isl_union_map_free(
1858 __isl_take isl_union_map *umap);
1860 Other sets and relations can be constructed by starting
1861 from a universe set or relation, adding equality and/or
1862 inequality constraints and then projecting out the
1863 existentially quantified variables, if any.
1864 Constraints can be constructed, manipulated and
1865 added to (or removed from) (basic) sets and relations
1866 using the following functions.
1868 #include <isl/constraint.h>
1869 __isl_give isl_constraint *isl_equality_alloc(
1870 __isl_take isl_local_space *ls);
1871 __isl_give isl_constraint *isl_inequality_alloc(
1872 __isl_take isl_local_space *ls);
1873 __isl_give isl_constraint *isl_constraint_set_constant_si(
1874 __isl_take isl_constraint *constraint, int v);
1875 __isl_give isl_constraint *isl_constraint_set_constant_val(
1876 __isl_take isl_constraint *constraint,
1877 __isl_take isl_val *v);
1878 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1879 __isl_take isl_constraint *constraint,
1880 enum isl_dim_type type, int pos, int v);
1881 __isl_give isl_constraint *
1882 isl_constraint_set_coefficient_val(
1883 __isl_take isl_constraint *constraint,
1884 enum isl_dim_type type, int pos,
1885 __isl_take isl_val *v);
1886 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1887 __isl_take isl_basic_map *bmap,
1888 __isl_take isl_constraint *constraint);
1889 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1890 __isl_take isl_basic_set *bset,
1891 __isl_take isl_constraint *constraint);
1892 __isl_give isl_map *isl_map_add_constraint(
1893 __isl_take isl_map *map,
1894 __isl_take isl_constraint *constraint);
1895 __isl_give isl_set *isl_set_add_constraint(
1896 __isl_take isl_set *set,
1897 __isl_take isl_constraint *constraint);
1899 For example, to create a set containing the even integers
1900 between 10 and 42, you would use the following code.
1903 isl_local_space *ls;
1905 isl_basic_set *bset;
1907 space = isl_space_set_alloc(ctx, 0, 2);
1908 bset = isl_basic_set_universe(isl_space_copy(space));
1909 ls = isl_local_space_from_space(space);
1911 c = isl_equality_alloc(isl_local_space_copy(ls));
1912 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1913 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1914 bset = isl_basic_set_add_constraint(bset, c);
1916 c = isl_inequality_alloc(isl_local_space_copy(ls));
1917 c = isl_constraint_set_constant_si(c, -10);
1918 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1919 bset = isl_basic_set_add_constraint(bset, c);
1921 c = isl_inequality_alloc(ls);
1922 c = isl_constraint_set_constant_si(c, 42);
1923 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1924 bset = isl_basic_set_add_constraint(bset, c);
1926 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1930 isl_basic_set *bset;
1931 bset = isl_basic_set_read_from_str(ctx,
1932 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1934 A basic set or relation can also be constructed from two matrices
1935 describing the equalities and the inequalities.
1937 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1938 __isl_take isl_space *space,
1939 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1940 enum isl_dim_type c1,
1941 enum isl_dim_type c2, enum isl_dim_type c3,
1942 enum isl_dim_type c4);
1943 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1944 __isl_take isl_space *space,
1945 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1946 enum isl_dim_type c1,
1947 enum isl_dim_type c2, enum isl_dim_type c3,
1948 enum isl_dim_type c4, enum isl_dim_type c5);
1950 The C<isl_dim_type> arguments indicate the order in which
1951 different kinds of variables appear in the input matrices
1952 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1953 C<isl_dim_set> and C<isl_dim_div> for sets and
1954 of C<isl_dim_cst>, C<isl_dim_param>,
1955 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1957 A (basic or union) set or relation can also be constructed from a
1958 (union) (piecewise) (multiple) affine expression
1959 or a list of affine expressions
1960 (See L</"Functions">).
1962 __isl_give isl_basic_map *isl_basic_map_from_aff(
1963 __isl_take isl_aff *aff);
1964 __isl_give isl_map *isl_map_from_aff(
1965 __isl_take isl_aff *aff);
1966 __isl_give isl_set *isl_set_from_pw_aff(
1967 __isl_take isl_pw_aff *pwaff);
1968 __isl_give isl_map *isl_map_from_pw_aff(
1969 __isl_take isl_pw_aff *pwaff);
1970 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1971 __isl_take isl_space *domain_space,
1972 __isl_take isl_aff_list *list);
1973 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1974 __isl_take isl_multi_aff *maff)
1975 __isl_give isl_map *isl_map_from_multi_aff(
1976 __isl_take isl_multi_aff *maff)
1977 __isl_give isl_set *isl_set_from_pw_multi_aff(
1978 __isl_take isl_pw_multi_aff *pma);
1979 __isl_give isl_map *isl_map_from_pw_multi_aff(
1980 __isl_take isl_pw_multi_aff *pma);
1981 __isl_give isl_set *isl_set_from_multi_pw_aff(
1982 __isl_take isl_multi_pw_aff *mpa);
1983 __isl_give isl_map *isl_map_from_multi_pw_aff(
1984 __isl_take isl_multi_pw_aff *mpa);
1985 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
1986 __isl_take isl_union_pw_aff *upa);
1987 __isl_give isl_union_map *
1988 isl_union_map_from_union_pw_multi_aff(
1989 __isl_take isl_union_pw_multi_aff *upma);
1990 __isl_give isl_union_map *
1991 isl_union_map_from_multi_union_pw_aff(
1992 __isl_take isl_multi_union_pw_aff *mupa);
1994 The C<domain_space> argument describes the domain of the resulting
1995 basic relation. It is required because the C<list> may consist
1996 of zero affine expressions.
1997 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
1998 is not allowed to be zero-dimensional. The domain of the result
1999 is the shared domain of the union piecewise affine elements.
2001 =head2 Inspecting Sets and Relations
2003 Usually, the user should not have to care about the actual constraints
2004 of the sets and maps, but should instead apply the abstract operations
2005 explained in the following sections.
2006 Occasionally, however, it may be required to inspect the individual
2007 coefficients of the constraints. This section explains how to do so.
2008 In these cases, it may also be useful to have C<isl> compute
2009 an explicit representation of the existentially quantified variables.
2011 __isl_give isl_set *isl_set_compute_divs(
2012 __isl_take isl_set *set);
2013 __isl_give isl_map *isl_map_compute_divs(
2014 __isl_take isl_map *map);
2015 __isl_give isl_union_set *isl_union_set_compute_divs(
2016 __isl_take isl_union_set *uset);
2017 __isl_give isl_union_map *isl_union_map_compute_divs(
2018 __isl_take isl_union_map *umap);
2020 This explicit representation defines the existentially quantified
2021 variables as integer divisions of the other variables, possibly
2022 including earlier existentially quantified variables.
2023 An explicitly represented existentially quantified variable therefore
2024 has a unique value when the values of the other variables are known.
2025 If, furthermore, the same existentials, i.e., existentials
2026 with the same explicit representations, should appear in the
2027 same order in each of the disjuncts of a set or map, then the user should call
2028 either of the following functions.
2030 __isl_give isl_set *isl_set_align_divs(
2031 __isl_take isl_set *set);
2032 __isl_give isl_map *isl_map_align_divs(
2033 __isl_take isl_map *map);
2035 Alternatively, the existentially quantified variables can be removed
2036 using the following functions, which compute an overapproximation.
2038 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2039 __isl_take isl_basic_set *bset);
2040 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2041 __isl_take isl_basic_map *bmap);
2042 __isl_give isl_set *isl_set_remove_divs(
2043 __isl_take isl_set *set);
2044 __isl_give isl_map *isl_map_remove_divs(
2045 __isl_take isl_map *map);
2047 It is also possible to only remove those divs that are defined
2048 in terms of a given range of dimensions or only those for which
2049 no explicit representation is known.
2051 __isl_give isl_basic_set *
2052 isl_basic_set_remove_divs_involving_dims(
2053 __isl_take isl_basic_set *bset,
2054 enum isl_dim_type type,
2055 unsigned first, unsigned n);
2056 __isl_give isl_basic_map *
2057 isl_basic_map_remove_divs_involving_dims(
2058 __isl_take isl_basic_map *bmap,
2059 enum isl_dim_type type,
2060 unsigned first, unsigned n);
2061 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2062 __isl_take isl_set *set, enum isl_dim_type type,
2063 unsigned first, unsigned n);
2064 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2065 __isl_take isl_map *map, enum isl_dim_type type,
2066 unsigned first, unsigned n);
2068 __isl_give isl_basic_set *
2069 isl_basic_set_remove_unknown_divs(
2070 __isl_take isl_basic_set *bset);
2071 __isl_give isl_set *isl_set_remove_unknown_divs(
2072 __isl_take isl_set *set);
2073 __isl_give isl_map *isl_map_remove_unknown_divs(
2074 __isl_take isl_map *map);
2076 To iterate over all the sets or maps in a union set or map, use
2078 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
2079 int (*fn)(__isl_take isl_set *set, void *user),
2081 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
2082 int (*fn)(__isl_take isl_map *map, void *user),
2085 The number of sets or maps in a union set or map can be obtained
2088 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2089 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2091 To extract the set or map in a given space from a union, use
2093 __isl_give isl_set *isl_union_set_extract_set(
2094 __isl_keep isl_union_set *uset,
2095 __isl_take isl_space *space);
2096 __isl_give isl_map *isl_union_map_extract_map(
2097 __isl_keep isl_union_map *umap,
2098 __isl_take isl_space *space);
2100 To iterate over all the basic sets or maps in a set or map, use
2102 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
2103 int (*fn)(__isl_take isl_basic_set *bset, void *user),
2105 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
2106 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
2109 The callback function C<fn> should return 0 if successful and
2110 -1 if an error occurs. In the latter case, or if any other error
2111 occurs, the above functions will return -1.
2113 It should be noted that C<isl> does not guarantee that
2114 the basic sets or maps passed to C<fn> are disjoint.
2115 If this is required, then the user should call one of
2116 the following functions first.
2118 __isl_give isl_set *isl_set_make_disjoint(
2119 __isl_take isl_set *set);
2120 __isl_give isl_map *isl_map_make_disjoint(
2121 __isl_take isl_map *map);
2123 The number of basic sets in a set can be obtained
2124 or the number of basic maps in a map can be obtained
2127 #include <isl/set.h>
2128 int isl_set_n_basic_set(__isl_keep isl_set *set);
2130 #include <isl/map.h>
2131 int isl_map_n_basic_map(__isl_keep isl_map *map);
2133 To iterate over the constraints of a basic set or map, use
2135 #include <isl/constraint.h>
2137 int isl_basic_set_n_constraint(
2138 __isl_keep isl_basic_set *bset);
2139 int isl_basic_set_foreach_constraint(
2140 __isl_keep isl_basic_set *bset,
2141 int (*fn)(__isl_take isl_constraint *c, void *user),
2143 int isl_basic_map_n_constraint(
2144 __isl_keep isl_basic_map *bmap);
2145 int isl_basic_map_foreach_constraint(
2146 __isl_keep isl_basic_map *bmap,
2147 int (*fn)(__isl_take isl_constraint *c, void *user),
2149 __isl_null isl_constraint *isl_constraint_free(
2150 __isl_take isl_constraint *c);
2152 Again, the callback function C<fn> should return 0 if successful and
2153 -1 if an error occurs. In the latter case, or if any other error
2154 occurs, the above functions will return -1.
2155 The constraint C<c> represents either an equality or an inequality.
2156 Use the following function to find out whether a constraint
2157 represents an equality. If not, it represents an inequality.
2159 int isl_constraint_is_equality(
2160 __isl_keep isl_constraint *constraint);
2162 It is also possible to obtain a list of constraints from a basic
2165 #include <isl/constraint.h>
2166 __isl_give isl_constraint_list *
2167 isl_basic_map_get_constraint_list(
2168 __isl_keep isl_basic_map *bmap);
2169 __isl_give isl_constraint_list *
2170 isl_basic_set_get_constraint_list(
2171 __isl_keep isl_basic_set *bset);
2173 These functions require that all existentially quantified variables
2174 have an explicit representation.
2175 The returned list can be manipulated using the functions in L<"Lists">.
2177 The coefficients of the constraints can be inspected using
2178 the following functions.
2180 int isl_constraint_is_lower_bound(
2181 __isl_keep isl_constraint *constraint,
2182 enum isl_dim_type type, unsigned pos);
2183 int isl_constraint_is_upper_bound(
2184 __isl_keep isl_constraint *constraint,
2185 enum isl_dim_type type, unsigned pos);
2186 __isl_give isl_val *isl_constraint_get_constant_val(
2187 __isl_keep isl_constraint *constraint);
2188 __isl_give isl_val *isl_constraint_get_coefficient_val(
2189 __isl_keep isl_constraint *constraint,
2190 enum isl_dim_type type, int pos);
2192 The explicit representations of the existentially quantified
2193 variables can be inspected using the following function.
2194 Note that the user is only allowed to use this function
2195 if the inspected set or map is the result of a call
2196 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2197 The existentially quantified variable is equal to the floor
2198 of the returned affine expression. The affine expression
2199 itself can be inspected using the functions in
2202 __isl_give isl_aff *isl_constraint_get_div(
2203 __isl_keep isl_constraint *constraint, int pos);
2205 To obtain the constraints of a basic set or map in matrix
2206 form, use the following functions.
2208 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2209 __isl_keep isl_basic_set *bset,
2210 enum isl_dim_type c1, enum isl_dim_type c2,
2211 enum isl_dim_type c3, enum isl_dim_type c4);
2212 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2213 __isl_keep isl_basic_set *bset,
2214 enum isl_dim_type c1, enum isl_dim_type c2,
2215 enum isl_dim_type c3, enum isl_dim_type c4);
2216 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2217 __isl_keep isl_basic_map *bmap,
2218 enum isl_dim_type c1,
2219 enum isl_dim_type c2, enum isl_dim_type c3,
2220 enum isl_dim_type c4, enum isl_dim_type c5);
2221 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2222 __isl_keep isl_basic_map *bmap,
2223 enum isl_dim_type c1,
2224 enum isl_dim_type c2, enum isl_dim_type c3,
2225 enum isl_dim_type c4, enum isl_dim_type c5);
2227 The C<isl_dim_type> arguments dictate the order in which
2228 different kinds of variables appear in the resulting matrix.
2229 For set inputs, they should be a permutation of
2230 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2231 For map inputs, they should be a permutation of
2232 C<isl_dim_cst>, C<isl_dim_param>,
2233 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2237 Points are elements of a set. They can be used to construct
2238 simple sets (boxes) or they can be used to represent the
2239 individual elements of a set.
2240 The zero point (the origin) can be created using
2242 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2244 The coordinates of a point can be inspected, set and changed
2247 __isl_give isl_val *isl_point_get_coordinate_val(
2248 __isl_keep isl_point *pnt,
2249 enum isl_dim_type type, int pos);
2250 __isl_give isl_point *isl_point_set_coordinate_val(
2251 __isl_take isl_point *pnt,
2252 enum isl_dim_type type, int pos,
2253 __isl_take isl_val *v);
2255 __isl_give isl_point *isl_point_add_ui(
2256 __isl_take isl_point *pnt,
2257 enum isl_dim_type type, int pos, unsigned val);
2258 __isl_give isl_point *isl_point_sub_ui(
2259 __isl_take isl_point *pnt,
2260 enum isl_dim_type type, int pos, unsigned val);
2262 Points can be copied or freed using
2264 __isl_give isl_point *isl_point_copy(
2265 __isl_keep isl_point *pnt);
2266 void isl_point_free(__isl_take isl_point *pnt);
2268 A singleton set can be created from a point using
2270 __isl_give isl_basic_set *isl_basic_set_from_point(
2271 __isl_take isl_point *pnt);
2272 __isl_give isl_set *isl_set_from_point(
2273 __isl_take isl_point *pnt);
2275 and a box can be created from two opposite extremal points using
2277 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2278 __isl_take isl_point *pnt1,
2279 __isl_take isl_point *pnt2);
2280 __isl_give isl_set *isl_set_box_from_points(
2281 __isl_take isl_point *pnt1,
2282 __isl_take isl_point *pnt2);
2284 All elements of a B<bounded> (union) set can be enumerated using
2285 the following functions.
2287 int isl_set_foreach_point(__isl_keep isl_set *set,
2288 int (*fn)(__isl_take isl_point *pnt, void *user),
2290 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2291 int (*fn)(__isl_take isl_point *pnt, void *user),
2294 The function C<fn> is called for each integer point in
2295 C<set> with as second argument the last argument of
2296 the C<isl_set_foreach_point> call. The function C<fn>
2297 should return C<0> on success and C<-1> on failure.
2298 In the latter case, C<isl_set_foreach_point> will stop
2299 enumerating and return C<-1> as well.
2300 If the enumeration is performed successfully and to completion,
2301 then C<isl_set_foreach_point> returns C<0>.
2303 To obtain a single point of a (basic) set, use
2305 __isl_give isl_point *isl_basic_set_sample_point(
2306 __isl_take isl_basic_set *bset);
2307 __isl_give isl_point *isl_set_sample_point(
2308 __isl_take isl_set *set);
2310 If C<set> does not contain any (integer) points, then the
2311 resulting point will be ``void'', a property that can be
2314 int isl_point_is_void(__isl_keep isl_point *pnt);
2318 Besides sets and relation, C<isl> also supports various types of functions.
2319 Each of these types is derived from the value type (see L</"Values">)
2320 or from one of two primitive function types
2321 through the application of zero or more type constructors.
2322 We first describe the primitive type and then we describe
2323 the types derived from these primitive types.
2325 =head3 Primitive Functions
2327 C<isl> support two primitive function types, quasi-affine
2328 expressions and quasipolynomials.
2329 A quasi-affine expression is defined either over a parameter
2330 space or over a set and is composed of integer constants,
2331 parameters and set variables, addition, subtraction and
2332 integer division by an integer constant.
2333 For example, the quasi-affine expression
2335 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2337 maps C<x> to C<2*floor((4 n + x)/9>.
2338 A quasipolynomial is a polynomial expression in quasi-affine
2339 expression. That is, it additionally allows for multiplication.
2340 Note, though, that it is not allowed to construct an integer
2341 division of an expression involving multiplications.
2342 Here is an example of a quasipolynomial that is not
2343 quasi-affine expression
2345 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2347 Note that the external representations of quasi-affine expressions
2348 and quasipolynomials are different. Quasi-affine expressions
2349 use a notation with square brackets just like binary relations,
2350 while quasipolynomials do not. This might change at some point.
2352 If a primitive function is defined over a parameter space,
2353 then the space of the function itself is that of a set.
2354 If it is defined over a set, then the space of the function
2355 is that of a relation. In both cases, the set space (or
2356 the output space) is single-dimensional, anonymous and unstructured.
2357 To create functions with multiple dimensions or with other kinds
2358 of set or output spaces, use multiple expressions
2359 (see L</"Multiple Expressions">).
2363 =item * Quasi-affine Expressions
2365 Besides the expressions described above, a quasi-affine
2366 expression can also be set to NaN. Such expressions
2367 typically represent a failure to represent a result
2368 as a quasi-affine expression.
2370 The zero quasi affine expression or the quasi affine expression
2371 that is equal to a given value or
2372 a specified dimension on a given domain can be created using
2374 #include <isl/aff.h>
2375 __isl_give isl_aff *isl_aff_zero_on_domain(
2376 __isl_take isl_local_space *ls);
2377 __isl_give isl_aff *isl_aff_val_on_domain(
2378 __isl_take isl_local_space *ls,
2379 __isl_take isl_val *val);
2380 __isl_give isl_aff *isl_aff_var_on_domain(
2381 __isl_take isl_local_space *ls,
2382 enum isl_dim_type type, unsigned pos);
2383 __isl_give isl_aff *isl_aff_nan_on_domain(
2384 __isl_take isl_local_space *ls);
2386 Quasi affine expressions can be copied and freed using
2388 #include <isl/aff.h>
2389 __isl_give isl_aff *isl_aff_copy(
2390 __isl_keep isl_aff *aff);
2391 __isl_null isl_aff *isl_aff_free(
2392 __isl_take isl_aff *aff);
2394 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2395 using the following function. The constraint is required to have
2396 a non-zero coefficient for the specified dimension.
2398 #include <isl/constraint.h>
2399 __isl_give isl_aff *isl_constraint_get_bound(
2400 __isl_keep isl_constraint *constraint,
2401 enum isl_dim_type type, int pos);
2403 The entire affine expression of the constraint can also be extracted
2404 using the following function.
2406 #include <isl/constraint.h>
2407 __isl_give isl_aff *isl_constraint_get_aff(
2408 __isl_keep isl_constraint *constraint);
2410 Conversely, an equality constraint equating
2411 the affine expression to zero or an inequality constraint enforcing
2412 the affine expression to be non-negative, can be constructed using
2414 __isl_give isl_constraint *isl_equality_from_aff(
2415 __isl_take isl_aff *aff);
2416 __isl_give isl_constraint *isl_inequality_from_aff(
2417 __isl_take isl_aff *aff);
2419 The coefficients and the integer divisions of an affine expression
2420 can be inspected using the following functions.
2422 #include <isl/aff.h>
2423 __isl_give isl_val *isl_aff_get_constant_val(
2424 __isl_keep isl_aff *aff);
2425 __isl_give isl_val *isl_aff_get_coefficient_val(
2426 __isl_keep isl_aff *aff,
2427 enum isl_dim_type type, int pos);
2428 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2429 enum isl_dim_type type, int pos);
2430 __isl_give isl_val *isl_aff_get_denominator_val(
2431 __isl_keep isl_aff *aff);
2432 __isl_give isl_aff *isl_aff_get_div(
2433 __isl_keep isl_aff *aff, int pos);
2435 They can be modified using the following functions.
2437 #include <isl/aff.h>
2438 __isl_give isl_aff *isl_aff_set_constant_si(
2439 __isl_take isl_aff *aff, int v);
2440 __isl_give isl_aff *isl_aff_set_constant_val(
2441 __isl_take isl_aff *aff, __isl_take isl_val *v);
2442 __isl_give isl_aff *isl_aff_set_coefficient_si(
2443 __isl_take isl_aff *aff,
2444 enum isl_dim_type type, int pos, int v);
2445 __isl_give isl_aff *isl_aff_set_coefficient_val(
2446 __isl_take isl_aff *aff,
2447 enum isl_dim_type type, int pos,
2448 __isl_take isl_val *v);
2450 __isl_give isl_aff *isl_aff_add_constant_si(
2451 __isl_take isl_aff *aff, int v);
2452 __isl_give isl_aff *isl_aff_add_constant_val(
2453 __isl_take isl_aff *aff, __isl_take isl_val *v);
2454 __isl_give isl_aff *isl_aff_add_constant_num_si(
2455 __isl_take isl_aff *aff, int v);
2456 __isl_give isl_aff *isl_aff_add_coefficient_si(
2457 __isl_take isl_aff *aff,
2458 enum isl_dim_type type, int pos, int v);
2459 __isl_give isl_aff *isl_aff_add_coefficient_val(
2460 __isl_take isl_aff *aff,
2461 enum isl_dim_type type, int pos,
2462 __isl_take isl_val *v);
2464 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2465 set the I<numerator> of the constant or coefficient, while
2466 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2467 the constant or coefficient as a whole.
2468 The C<add_constant> and C<add_coefficient> functions add an integer
2469 or rational value to
2470 the possibly rational constant or coefficient.
2471 The C<add_constant_num> functions add an integer value to
2474 =item * Quasipolynomials
2476 Some simple quasipolynomials can be created using the following functions.
2478 #include <isl/polynomial.h>
2479 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2480 __isl_take isl_space *domain);
2481 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2482 __isl_take isl_space *domain);
2483 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2484 __isl_take isl_space *domain);
2485 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2486 __isl_take isl_space *domain);
2487 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2488 __isl_take isl_space *domain);
2489 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2490 __isl_take isl_space *domain,
2491 __isl_take isl_val *val);
2492 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2493 __isl_take isl_space *domain,
2494 enum isl_dim_type type, unsigned pos);
2495 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2496 __isl_take isl_aff *aff);
2498 Recall that the space in which a quasipolynomial lives is a map space
2499 with a one-dimensional range. The C<domain> argument in some of
2500 the functions above corresponds to the domain of this map space.
2502 Quasipolynomials can be copied and freed again using the following
2505 #include <isl/polynomial.h>
2506 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2507 __isl_keep isl_qpolynomial *qp);
2508 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2509 __isl_take isl_qpolynomial *qp);
2511 The constant term of a quasipolynomial can be extracted using
2513 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2514 __isl_keep isl_qpolynomial *qp);
2516 To iterate over all terms in a quasipolynomial,
2519 int isl_qpolynomial_foreach_term(
2520 __isl_keep isl_qpolynomial *qp,
2521 int (*fn)(__isl_take isl_term *term,
2522 void *user), void *user);
2524 The terms themselves can be inspected and freed using
2527 unsigned isl_term_dim(__isl_keep isl_term *term,
2528 enum isl_dim_type type);
2529 __isl_give isl_val *isl_term_get_coefficient_val(
2530 __isl_keep isl_term *term);
2531 int isl_term_get_exp(__isl_keep isl_term *term,
2532 enum isl_dim_type type, unsigned pos);
2533 __isl_give isl_aff *isl_term_get_div(
2534 __isl_keep isl_term *term, unsigned pos);
2535 void isl_term_free(__isl_take isl_term *term);
2537 Each term is a product of parameters, set variables and
2538 integer divisions. The function C<isl_term_get_exp>
2539 returns the exponent of a given dimensions in the given term.
2545 A reduction represents a maximum or a minimum of its
2547 The only reduction type defined by C<isl> is
2548 C<isl_qpolynomial_fold>.
2550 There are currently no functions to directly create such
2551 objects, but they do appear in the piecewise quasipolynomial
2552 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2554 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2556 Reductions can be copied and freed using
2557 the following functions.
2559 #include <isl/polynomial.h>
2560 __isl_give isl_qpolynomial_fold *
2561 isl_qpolynomial_fold_copy(
2562 __isl_keep isl_qpolynomial_fold *fold);
2563 void isl_qpolynomial_fold_free(
2564 __isl_take isl_qpolynomial_fold *fold);
2566 To iterate over all quasipolynomials in a reduction, use
2568 int isl_qpolynomial_fold_foreach_qpolynomial(
2569 __isl_keep isl_qpolynomial_fold *fold,
2570 int (*fn)(__isl_take isl_qpolynomial *qp,
2571 void *user), void *user);
2573 =head3 Multiple Expressions
2575 A multiple expression represents a sequence of zero or
2576 more base expressions, all defined on the same domain space.
2577 The domain space of the multiple expression is the same
2578 as that of the base expressions, but the range space
2579 can be any space. In case the base expressions have
2580 a set space, the corresponding multiple expression
2581 also has a set space.
2582 Objects of the value type do not have an associated space.
2583 The space of a multiple value is therefore always a set space.
2584 Similarly, the space of a multiple union piecewise
2585 affine expression is always a set space.
2587 The multiple expression types defined by C<isl>
2588 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2589 C<isl_multi_union_pw_aff>.
2591 A multiple expression with the value zero for
2592 each output (or set) dimension can be created
2593 using the following functions.
2595 #include <isl/val.h>
2596 __isl_give isl_multi_val *isl_multi_val_zero(
2597 __isl_take isl_space *space);
2599 #include <isl/aff.h>
2600 __isl_give isl_multi_aff *isl_multi_aff_zero(
2601 __isl_take isl_space *space);
2602 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2603 __isl_take isl_space *space);
2604 __isl_give isl_multi_union_pw_aff *
2605 isl_multi_union_pw_aff_zero(
2606 __isl_take isl_space *space);
2608 Since there is no canonical way of representing a zero
2609 value of type C<isl_union_pw_aff>, the space passed
2610 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2612 An identity function can be created using the following
2613 functions. The space needs to be that of a relation
2614 with the same number of input and output dimensions.
2616 #include <isl/aff.h>
2617 __isl_give isl_multi_aff *isl_multi_aff_identity(
2618 __isl_take isl_space *space);
2619 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2620 __isl_take isl_space *space);
2622 A function that performs a projection on a universe
2623 relation or set can be created using the following functions.
2624 See also the corresponding
2625 projection operations in L</"Unary Operations">.
2627 #include <isl/aff.h>
2628 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2629 __isl_take isl_space *space);
2630 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2631 __isl_take isl_space *space);
2632 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2633 __isl_take isl_space *space,
2634 enum isl_dim_type type,
2635 unsigned first, unsigned n);
2637 A multiple expression can be created from a single
2638 base expression using the following functions.
2639 The space of the created multiple expression is the same
2640 as that of the base expression, except for
2641 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2642 lives in a parameter space and the output lives
2643 in a single-dimensional set space.
2645 #include <isl/aff.h>
2646 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2647 __isl_take isl_aff *aff);
2648 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2649 __isl_take isl_pw_aff *pa);
2650 __isl_give isl_multi_union_pw_aff *
2651 isl_multi_union_pw_aff_from_union_pw_aff(
2652 __isl_take isl_union_pw_aff *upa);
2654 A multiple expression can be created from a list
2655 of base expression in a specified space.
2656 The domain of this space needs to be the same
2657 as the domains of the base expressions in the list.
2658 If the base expressions have a set space (or no associated space),
2659 then this space also needs to be a set space.
2661 #include <isl/val.h>
2662 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2663 __isl_take isl_space *space,
2664 __isl_take isl_val_list *list);
2666 #include <isl/aff.h>
2667 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2668 __isl_take isl_space *space,
2669 __isl_take isl_aff_list *list);
2670 __isl_give isl_multi_union_pw_aff *
2671 isl_multi_union_pw_aff_from_union_pw_aff_list(
2672 __isl_take isl_space *space,
2673 __isl_take isl_union_pw_aff_list *list);
2675 As a convenience, a multiple piecewise expression can
2676 also be created from a multiple expression.
2677 Each piecewise expression in the result has a single
2680 #include <isl/aff.h>
2681 __isl_give isl_multi_pw_aff *
2682 isl_multi_pw_aff_from_multi_aff(
2683 __isl_take isl_multi_aff *ma);
2685 Similarly, a multiple union expression can be
2686 created from a multiple expression.
2688 #include <isl/aff.h>
2689 __isl_give isl_multi_union_pw_aff *
2690 isl_multi_union_pw_aff_from_multi_aff(
2691 __isl_take isl_multi_aff *ma);
2692 __isl_give isl_multi_union_pw_aff *
2693 isl_multi_union_pw_aff_from_multi_pw_aff(
2694 __isl_take isl_multi_pw_aff *mpa);
2696 A multiple quasi-affine expression can be created from
2697 a multiple value with a given domain space using the following
2700 #include <isl/aff.h>
2701 __isl_give isl_multi_aff *
2702 isl_multi_aff_multi_val_on_space(
2703 __isl_take isl_space *space,
2704 __isl_take isl_multi_val *mv);
2707 a multiple union piecewise affine expression can be created from
2708 a multiple value with a given domain or
2709 a multiple affine expression with a given domain
2710 using the following functions.
2712 #include <isl/aff.h>
2713 __isl_give isl_multi_union_pw_aff *
2714 isl_multi_union_pw_aff_multi_val_on_domain(
2715 __isl_take isl_union_set *domain,
2716 __isl_take isl_multi_val *mv);
2717 __isl_give isl_multi_union_pw_aff *
2718 isl_multi_union_pw_aff_multi_aff_on_domain(
2719 __isl_take isl_union_set *domain,
2720 __isl_take isl_multi_aff *ma);
2722 Multiple expressions can be copied and freed using
2723 the following functions.
2725 #include <isl/val.h>
2726 __isl_give isl_multi_val *isl_multi_val_copy(
2727 __isl_keep isl_multi_val *mv);
2728 __isl_null isl_multi_val *isl_multi_val_free(
2729 __isl_take isl_multi_val *mv);
2731 #include <isl/aff.h>
2732 __isl_give isl_multi_aff *isl_multi_aff_copy(
2733 __isl_keep isl_multi_aff *maff);
2734 __isl_null isl_multi_aff *isl_multi_aff_free(
2735 __isl_take isl_multi_aff *maff);
2736 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2737 __isl_keep isl_multi_pw_aff *mpa);
2738 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2739 __isl_take isl_multi_pw_aff *mpa);
2740 __isl_give isl_multi_union_pw_aff *
2741 isl_multi_union_pw_aff_copy(
2742 __isl_keep isl_multi_union_pw_aff *mupa);
2743 __isl_null isl_multi_union_pw_aff *
2744 isl_multi_union_pw_aff_free(
2745 __isl_take isl_multi_union_pw_aff *mupa);
2747 The base expression at a given position of a multiple
2748 expression can be extracted using the following functions.
2750 #include <isl/val.h>
2751 __isl_give isl_val *isl_multi_val_get_val(
2752 __isl_keep isl_multi_val *mv, int pos);
2754 #include <isl/aff.h>
2755 __isl_give isl_aff *isl_multi_aff_get_aff(
2756 __isl_keep isl_multi_aff *multi, int pos);
2757 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2758 __isl_keep isl_multi_pw_aff *mpa, int pos);
2759 __isl_give isl_union_pw_aff *
2760 isl_multi_union_pw_aff_get_union_pw_aff(
2761 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2763 It can be replaced using the following functions.
2765 #include <isl/val.h>
2766 __isl_give isl_multi_val *isl_multi_val_set_val(
2767 __isl_take isl_multi_val *mv, int pos,
2768 __isl_take isl_val *val);
2770 #include <isl/aff.h>
2771 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2772 __isl_take isl_multi_aff *multi, int pos,
2773 __isl_take isl_aff *aff);
2774 __isl_give isl_multi_union_pw_aff *
2775 isl_multi_union_pw_aff_set_union_pw_aff(
2776 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2777 __isl_take isl_union_pw_aff *upa);
2779 As a convenience, a sequence of base expressions that have
2780 their domains in a given space can be extracted from a sequence
2781 of union expressions using the following function.
2783 #include <isl/aff.h>
2784 __isl_give isl_multi_pw_aff *
2785 isl_multi_union_pw_aff_extract_multi_pw_aff(
2786 __isl_keep isl_multi_union_pw_aff *mupa,
2787 __isl_take isl_space *space);
2789 Note that there is a difference between C<isl_multi_union_pw_aff>
2790 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2791 of unions of piecewise expressions, while the second is a union
2792 of piecewise sequences. In particular, multiple affine expressions
2793 in an C<isl_union_pw_multi_aff> may live in different spaces,
2794 while there is only a single multiple expression in
2795 an C<isl_multi_union_pw_aff>, which can therefore only live
2796 in a single space. This means that not every
2797 C<isl_union_pw_multi_aff> can be converted to
2798 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2799 C<isl_multi_union_pw_aff> carries no information
2800 about any possible domain and therefore cannot be converted
2801 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2802 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2803 while each multiple expression inside an C<isl_union_pw_multi_aff>
2804 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2805 of dimension greater than one may therefore not be exact.
2806 The following functions can
2807 be used to perform these conversions when they are possible.
2809 #include <isl/aff.h>
2810 __isl_give isl_multi_union_pw_aff *
2811 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2812 __isl_take isl_union_pw_multi_aff *upma);
2813 __isl_give isl_union_pw_multi_aff *
2814 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2815 __isl_take isl_multi_union_pw_aff *mupa);
2817 =head3 Piecewise Expressions
2819 A piecewise expression is an expression that is described
2820 using zero or more base expression defined over the same
2821 number of cells in the domain space of the base expressions.
2822 All base expressions are defined over the same
2823 domain space and the cells are disjoint.
2824 The space of a piecewise expression is the same as
2825 that of the base expressions.
2826 If the union of the cells is a strict subset of the domain
2827 space, then the value of the piecewise expression outside
2828 this union is different for types derived from quasi-affine
2829 expressions and those derived from quasipolynomials.
2830 Piecewise expressions derived from quasi-affine expressions
2831 are considered to be undefined outside the union of their cells.
2832 Piecewise expressions derived from quasipolynomials
2833 are considered to be zero outside the union of their cells.
2835 Piecewise quasipolynomials are mainly used by the C<barvinok>
2836 library for representing the number of elements in a parametric set or map.
2837 For example, the piecewise quasipolynomial
2839 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2841 represents the number of points in the map
2843 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2845 The piecewise expression types defined by C<isl>
2846 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2847 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2849 A piecewise expression with no cells can be created using
2850 the following functions.
2852 #include <isl/aff.h>
2853 __isl_give isl_pw_aff *isl_pw_aff_empty(
2854 __isl_take isl_space *space);
2855 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2856 __isl_take isl_space *space);
2858 A piecewise expression with a single universe cell can be
2859 created using the following functions.
2861 #include <isl/aff.h>
2862 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2863 __isl_take isl_aff *aff);
2864 __isl_give isl_pw_multi_aff *
2865 isl_pw_multi_aff_from_multi_aff(
2866 __isl_take isl_multi_aff *ma);
2868 #include <isl/polynomial.h>
2869 __isl_give isl_pw_qpolynomial *
2870 isl_pw_qpolynomial_from_qpolynomial(
2871 __isl_take isl_qpolynomial *qp);
2873 A piecewise expression with a single specified cell can be
2874 created using the following functions.
2876 #include <isl/aff.h>
2877 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2878 __isl_take isl_set *set, __isl_take isl_aff *aff);
2879 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2880 __isl_take isl_set *set,
2881 __isl_take isl_multi_aff *maff);
2883 #include <isl/polynomial.h>
2884 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2885 __isl_take isl_set *set,
2886 __isl_take isl_qpolynomial *qp);
2888 The following convenience functions first create a base expression and
2889 then create a piecewise expression over a universe domain.
2891 #include <isl/aff.h>
2892 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2893 __isl_take isl_local_space *ls);
2894 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2895 __isl_take isl_local_space *ls,
2896 enum isl_dim_type type, unsigned pos);
2897 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2898 __isl_take isl_local_space *ls);
2899 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2900 __isl_take isl_space *space);
2901 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2902 __isl_take isl_space *space);
2903 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2904 __isl_take isl_space *space);
2905 __isl_give isl_pw_multi_aff *
2906 isl_pw_multi_aff_project_out_map(
2907 __isl_take isl_space *space,
2908 enum isl_dim_type type,
2909 unsigned first, unsigned n);
2911 #include <isl/polynomial.h>
2912 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2913 __isl_take isl_space *space);
2915 The following convenience functions first create a base expression and
2916 then create a piecewise expression over a given domain.
2918 #include <isl/aff.h>
2919 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2920 __isl_take isl_set *domain,
2921 __isl_take isl_val *v);
2922 __isl_give isl_pw_multi_aff *
2923 isl_pw_multi_aff_multi_val_on_domain(
2924 __isl_take isl_set *domain,
2925 __isl_take isl_multi_val *mv);
2927 As a convenience, a piecewise multiple expression can
2928 also be created from a piecewise expression.
2929 Each multiple expression in the result is derived
2930 from the corresponding base expression.
2932 #include <isl/aff.h>
2933 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2934 __isl_take isl_pw_aff *pa);
2936 Similarly, a piecewise quasipolynomial can be
2937 created from a piecewise quasi-affine expression using
2938 the following function.
2940 #include <isl/polynomial.h>
2941 __isl_give isl_pw_qpolynomial *
2942 isl_pw_qpolynomial_from_pw_aff(
2943 __isl_take isl_pw_aff *pwaff);
2945 Piecewise expressions can be copied and freed using the following functions.
2947 #include <isl/aff.h>
2948 __isl_give isl_pw_aff *isl_pw_aff_copy(
2949 __isl_keep isl_pw_aff *pwaff);
2950 __isl_null isl_pw_aff *isl_pw_aff_free(
2951 __isl_take isl_pw_aff *pwaff);
2952 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2953 __isl_keep isl_pw_multi_aff *pma);
2954 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2955 __isl_take isl_pw_multi_aff *pma);
2957 #include <isl/polynomial.h>
2958 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2959 __isl_keep isl_pw_qpolynomial *pwqp);
2960 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2961 __isl_take isl_pw_qpolynomial *pwqp);
2962 __isl_give isl_pw_qpolynomial_fold *
2963 isl_pw_qpolynomial_fold_copy(
2964 __isl_keep isl_pw_qpolynomial_fold *pwf);
2965 __isl_null isl_pw_qpolynomial_fold *
2966 isl_pw_qpolynomial_fold_free(
2967 __isl_take isl_pw_qpolynomial_fold *pwf);
2969 To iterate over the different cells of a piecewise expression,
2970 use the following functions.
2972 #include <isl/aff.h>
2973 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2974 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2975 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2976 int (*fn)(__isl_take isl_set *set,
2977 __isl_take isl_aff *aff,
2978 void *user), void *user);
2979 int isl_pw_multi_aff_foreach_piece(
2980 __isl_keep isl_pw_multi_aff *pma,
2981 int (*fn)(__isl_take isl_set *set,
2982 __isl_take isl_multi_aff *maff,
2983 void *user), void *user);
2985 #include <isl/polynomial.h>
2986 int isl_pw_qpolynomial_foreach_piece(
2987 __isl_keep isl_pw_qpolynomial *pwqp,
2988 int (*fn)(__isl_take isl_set *set,
2989 __isl_take isl_qpolynomial *qp,
2990 void *user), void *user);
2991 int isl_pw_qpolynomial_foreach_lifted_piece(
2992 __isl_keep isl_pw_qpolynomial *pwqp,
2993 int (*fn)(__isl_take isl_set *set,
2994 __isl_take isl_qpolynomial *qp,
2995 void *user), void *user);
2996 int isl_pw_qpolynomial_fold_foreach_piece(
2997 __isl_keep isl_pw_qpolynomial_fold *pwf,
2998 int (*fn)(__isl_take isl_set *set,
2999 __isl_take isl_qpolynomial_fold *fold,
3000 void *user), void *user);
3001 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
3002 __isl_keep isl_pw_qpolynomial_fold *pwf,
3003 int (*fn)(__isl_take isl_set *set,
3004 __isl_take isl_qpolynomial_fold *fold,
3005 void *user), void *user);
3007 As usual, the function C<fn> should return C<0> on success
3008 and C<-1> on failure. The difference between
3009 C<isl_pw_qpolynomial_foreach_piece> and
3010 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3011 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3012 compute unique representations for all existentially quantified
3013 variables and then turn these existentially quantified variables
3014 into extra set variables, adapting the associated quasipolynomial
3015 accordingly. This means that the C<set> passed to C<fn>
3016 will not have any existentially quantified variables, but that
3017 the dimensions of the sets may be different for different
3018 invocations of C<fn>.
3019 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3020 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3022 A piecewise expression consisting of the expressions at a given
3023 position of a piecewise multiple expression can be extracted
3024 using the following function.
3026 #include <isl/aff.h>
3027 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3028 __isl_keep isl_pw_multi_aff *pma, int pos);
3030 These expressions can be replaced using the following function.
3032 #include <isl/aff.h>
3033 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3034 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3035 __isl_take isl_pw_aff *pa);
3037 Note that there is a difference between C<isl_multi_pw_aff> and
3038 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3039 affine expressions, while the second is a piecewise sequence
3040 of affine expressions. In particular, each of the piecewise
3041 affine expressions in an C<isl_multi_pw_aff> may have a different
3042 domain, while all multiple expressions associated to a cell
3043 in an C<isl_pw_multi_aff> have the same domain.
3044 It is possible to convert between the two, but when converting
3045 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3046 of the result is the intersection of the domains of the input.
3047 The reverse conversion is exact.
3049 #include <isl/aff.h>
3050 __isl_give isl_pw_multi_aff *
3051 isl_pw_multi_aff_from_multi_pw_aff(
3052 __isl_take isl_multi_pw_aff *mpa);
3053 __isl_give isl_multi_pw_aff *
3054 isl_multi_pw_aff_from_pw_multi_aff(
3055 __isl_take isl_pw_multi_aff *pma);
3057 =head3 Union Expressions
3059 A union expression collects base expressions defined
3060 over different domains. The space of a union expression
3061 is that of the shared parameter space.
3063 The union expression types defined by C<isl>
3064 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3065 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3067 An empty union expression can be created using the following functions.
3069 #include <isl/aff.h>
3070 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3071 __isl_take isl_space *space);
3072 __isl_give isl_union_pw_multi_aff *
3073 isl_union_pw_multi_aff_empty(
3074 __isl_take isl_space *space);
3076 #include <isl/polynomial.h>
3077 __isl_give isl_union_pw_qpolynomial *
3078 isl_union_pw_qpolynomial_zero(
3079 __isl_take isl_space *space);
3081 A union expression containing a single base expression
3082 can be created using the following functions.
3084 #include <isl/aff.h>
3085 __isl_give isl_union_pw_aff *
3086 isl_union_pw_aff_from_pw_aff(
3087 __isl_take isl_pw_aff *pa);
3088 __isl_give isl_union_pw_multi_aff *
3089 isl_union_pw_multi_aff_from_aff(
3090 __isl_take isl_aff *aff);
3091 __isl_give isl_union_pw_multi_aff *
3092 isl_union_pw_multi_aff_from_pw_multi_aff(
3093 __isl_take isl_pw_multi_aff *pma);
3095 #include <isl/polynomial.h>
3096 __isl_give isl_union_pw_qpolynomial *
3097 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3098 __isl_take isl_pw_qpolynomial *pwqp);
3100 The following functions create a base expression on each
3101 of the sets in the union set and collect the results.
3103 #include <isl/aff.h>
3104 __isl_give isl_union_pw_multi_aff *
3105 isl_union_pw_multi_aff_from_union_pw_aff(
3106 __isl_take isl_union_pw_aff *upa);
3107 __isl_give isl_union_pw_aff *
3108 isl_union_pw_multi_aff_get_union_pw_aff(
3109 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3110 __isl_give isl_union_pw_aff *
3111 isl_union_pw_aff_val_on_domain(
3112 __isl_take isl_union_set *domain,
3113 __isl_take isl_val *v);
3114 __isl_give isl_union_pw_multi_aff *
3115 isl_union_pw_multi_aff_multi_val_on_domain(
3116 __isl_take isl_union_set *domain,
3117 __isl_take isl_multi_val *mv);
3119 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3120 expression on a given domain can be created using the following
3123 #include <isl/aff.h>
3124 __isl_give isl_union_pw_aff *
3125 isl_union_pw_aff_aff_on_domain(
3126 __isl_take isl_union_set *domain,
3127 __isl_take isl_aff *aff);
3129 A base expression can be added to a union expression using
3130 the following functions.
3132 #include <isl/aff.h>
3133 __isl_give isl_union_pw_aff *
3134 isl_union_pw_aff_add_pw_aff(
3135 __isl_take isl_union_pw_aff *upa,
3136 __isl_take isl_pw_aff *pa);
3137 __isl_give isl_union_pw_multi_aff *
3138 isl_union_pw_multi_aff_add_pw_multi_aff(
3139 __isl_take isl_union_pw_multi_aff *upma,
3140 __isl_take isl_pw_multi_aff *pma);
3142 #include <isl/polynomial.h>
3143 __isl_give isl_union_pw_qpolynomial *
3144 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3145 __isl_take isl_union_pw_qpolynomial *upwqp,
3146 __isl_take isl_pw_qpolynomial *pwqp);
3148 Union expressions can be copied and freed using
3149 the following functions.
3151 #include <isl/aff.h>
3152 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3153 __isl_keep isl_union_pw_aff *upa);
3154 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3155 __isl_take isl_union_pw_aff *upa);
3156 __isl_give isl_union_pw_multi_aff *
3157 isl_union_pw_multi_aff_copy(
3158 __isl_keep isl_union_pw_multi_aff *upma);
3159 __isl_null isl_union_pw_multi_aff *
3160 isl_union_pw_multi_aff_free(
3161 __isl_take isl_union_pw_multi_aff *upma);
3163 #include <isl/polynomial.h>
3164 __isl_give isl_union_pw_qpolynomial *
3165 isl_union_pw_qpolynomial_copy(
3166 __isl_keep isl_union_pw_qpolynomial *upwqp);
3167 __isl_null isl_union_pw_qpolynomial *
3168 isl_union_pw_qpolynomial_free(
3169 __isl_take isl_union_pw_qpolynomial *upwqp);
3170 __isl_give isl_union_pw_qpolynomial_fold *
3171 isl_union_pw_qpolynomial_fold_copy(
3172 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3173 __isl_null isl_union_pw_qpolynomial_fold *
3174 isl_union_pw_qpolynomial_fold_free(
3175 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3177 To iterate over the base expressions in a union expression,
3178 use the following functions.
3180 #include <isl/aff.h>
3181 int isl_union_pw_aff_n_pw_aff(
3182 __isl_keep isl_union_pw_aff *upa);
3183 int isl_union_pw_aff_foreach_pw_aff(
3184 __isl_keep isl_union_pw_aff *upa,
3185 int (*fn)(__isl_take isl_pw_aff *ma, void *user),
3187 int isl_union_pw_multi_aff_n_pw_multi_aff(
3188 __isl_keep isl_union_pw_multi_aff *upma);
3189 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3190 __isl_keep isl_union_pw_multi_aff *upma,
3191 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3192 void *user), void *user);
3194 #include <isl/polynomial.h>
3195 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3196 __isl_keep isl_union_pw_qpolynomial *upwqp);
3197 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3198 __isl_keep isl_union_pw_qpolynomial *upwqp,
3199 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3200 void *user), void *user);
3201 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3202 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3203 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3204 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3205 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3206 void *user), void *user);
3208 To extract the base expression in a given space from a union, use
3209 the following functions.
3211 #include <isl/aff.h>
3212 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3213 __isl_keep isl_union_pw_aff *upa,
3214 __isl_take isl_space *space);
3215 __isl_give isl_pw_multi_aff *
3216 isl_union_pw_multi_aff_extract_pw_multi_aff(
3217 __isl_keep isl_union_pw_multi_aff *upma,
3218 __isl_take isl_space *space);
3220 #include <isl/polynomial.h>
3221 __isl_give isl_pw_qpolynomial *
3222 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3223 __isl_keep isl_union_pw_qpolynomial *upwqp,
3224 __isl_take isl_space *space);
3226 =head2 Input and Output
3228 For set and relation,
3229 C<isl> supports its own input/output format, which is similar
3230 to the C<Omega> format, but also supports the C<PolyLib> format
3232 For other object types, typically only an C<isl> format is supported.
3234 =head3 C<isl> format
3236 The C<isl> format is similar to that of C<Omega>, but has a different
3237 syntax for describing the parameters and allows for the definition
3238 of an existentially quantified variable as the integer division
3239 of an affine expression.
3240 For example, the set of integers C<i> between C<0> and C<n>
3241 such that C<i % 10 <= 6> can be described as
3243 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3246 A set or relation can have several disjuncts, separated
3247 by the keyword C<or>. Each disjunct is either a conjunction
3248 of constraints or a projection (C<exists>) of a conjunction
3249 of constraints. The constraints are separated by the keyword
3252 =head3 C<PolyLib> format
3254 If the represented set is a union, then the first line
3255 contains a single number representing the number of disjuncts.
3256 Otherwise, a line containing the number C<1> is optional.
3258 Each disjunct is represented by a matrix of constraints.
3259 The first line contains two numbers representing
3260 the number of rows and columns,
3261 where the number of rows is equal to the number of constraints
3262 and the number of columns is equal to two plus the number of variables.
3263 The following lines contain the actual rows of the constraint matrix.
3264 In each row, the first column indicates whether the constraint
3265 is an equality (C<0>) or inequality (C<1>). The final column
3266 corresponds to the constant term.
3268 If the set is parametric, then the coefficients of the parameters
3269 appear in the last columns before the constant column.
3270 The coefficients of any existentially quantified variables appear
3271 between those of the set variables and those of the parameters.
3273 =head3 Extended C<PolyLib> format
3275 The extended C<PolyLib> format is nearly identical to the
3276 C<PolyLib> format. The only difference is that the line
3277 containing the number of rows and columns of a constraint matrix
3278 also contains four additional numbers:
3279 the number of output dimensions, the number of input dimensions,
3280 the number of local dimensions (i.e., the number of existentially
3281 quantified variables) and the number of parameters.
3282 For sets, the number of ``output'' dimensions is equal
3283 to the number of set dimensions, while the number of ``input''
3288 Objects can be read from input using the following functions.
3290 #include <isl/val.h>
3291 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3293 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3294 isl_ctx *ctx, const char *str);
3296 #include <isl/set.h>
3297 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3298 isl_ctx *ctx, FILE *input);
3299 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3300 isl_ctx *ctx, const char *str);
3301 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3303 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3306 #include <isl/map.h>
3307 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3308 isl_ctx *ctx, FILE *input);
3309 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3310 isl_ctx *ctx, const char *str);
3311 __isl_give isl_map *isl_map_read_from_file(
3312 isl_ctx *ctx, FILE *input);
3313 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3316 #include <isl/union_set.h>
3317 __isl_give isl_union_set *isl_union_set_read_from_file(
3318 isl_ctx *ctx, FILE *input);
3319 __isl_give isl_union_set *isl_union_set_read_from_str(
3320 isl_ctx *ctx, const char *str);
3322 #include <isl/union_map.h>
3323 __isl_give isl_union_map *isl_union_map_read_from_file(
3324 isl_ctx *ctx, FILE *input);
3325 __isl_give isl_union_map *isl_union_map_read_from_str(
3326 isl_ctx *ctx, const char *str);
3328 #include <isl/aff.h>
3329 __isl_give isl_aff *isl_aff_read_from_str(
3330 isl_ctx *ctx, const char *str);
3331 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3332 isl_ctx *ctx, const char *str);
3333 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3334 isl_ctx *ctx, const char *str);
3335 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3336 isl_ctx *ctx, const char *str);
3337 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3338 isl_ctx *ctx, const char *str);
3339 __isl_give isl_union_pw_multi_aff *
3340 isl_union_pw_multi_aff_read_from_str(
3341 isl_ctx *ctx, const char *str);
3342 __isl_give isl_multi_union_pw_aff *
3343 isl_multi_union_pw_aff_read_from_str(
3344 isl_ctx *ctx, const char *str);
3346 #include <isl/polynomial.h>
3347 __isl_give isl_union_pw_qpolynomial *
3348 isl_union_pw_qpolynomial_read_from_str(
3349 isl_ctx *ctx, const char *str);
3351 For sets and relations,
3352 the input format is autodetected and may be either the C<PolyLib> format
3353 or the C<isl> format.
3357 Before anything can be printed, an C<isl_printer> needs to
3360 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3362 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3363 __isl_null isl_printer *isl_printer_free(
3364 __isl_take isl_printer *printer);
3365 __isl_give char *isl_printer_get_str(
3366 __isl_keep isl_printer *printer);
3368 The printer can be inspected using the following functions.
3370 FILE *isl_printer_get_file(
3371 __isl_keep isl_printer *printer);
3372 int isl_printer_get_output_format(
3373 __isl_keep isl_printer *p);
3374 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3376 The behavior of the printer can be modified in various ways
3378 __isl_give isl_printer *isl_printer_set_output_format(
3379 __isl_take isl_printer *p, int output_format);
3380 __isl_give isl_printer *isl_printer_set_indent(
3381 __isl_take isl_printer *p, int indent);
3382 __isl_give isl_printer *isl_printer_set_indent_prefix(
3383 __isl_take isl_printer *p, const char *prefix);
3384 __isl_give isl_printer *isl_printer_indent(
3385 __isl_take isl_printer *p, int indent);
3386 __isl_give isl_printer *isl_printer_set_prefix(
3387 __isl_take isl_printer *p, const char *prefix);
3388 __isl_give isl_printer *isl_printer_set_suffix(
3389 __isl_take isl_printer *p, const char *suffix);
3390 __isl_give isl_printer *isl_printer_set_yaml_style(
3391 __isl_take isl_printer *p, int yaml_style);
3393 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3394 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3395 and defaults to C<ISL_FORMAT_ISL>.
3396 Each line in the output is prefixed by C<indent_prefix>,
3397 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3398 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3399 In the C<PolyLib> format output,
3400 the coefficients of the existentially quantified variables
3401 appear between those of the set variables and those
3403 The function C<isl_printer_indent> increases the indentation
3404 by the specified amount (which may be negative).
3405 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3406 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3409 To actually print something, use
3411 #include <isl/printer.h>
3412 __isl_give isl_printer *isl_printer_print_double(
3413 __isl_take isl_printer *p, double d);
3415 #include <isl/val.h>
3416 __isl_give isl_printer *isl_printer_print_val(
3417 __isl_take isl_printer *p, __isl_keep isl_val *v);
3419 #include <isl/set.h>
3420 __isl_give isl_printer *isl_printer_print_basic_set(
3421 __isl_take isl_printer *printer,
3422 __isl_keep isl_basic_set *bset);
3423 __isl_give isl_printer *isl_printer_print_set(
3424 __isl_take isl_printer *printer,
3425 __isl_keep isl_set *set);
3427 #include <isl/map.h>
3428 __isl_give isl_printer *isl_printer_print_basic_map(
3429 __isl_take isl_printer *printer,
3430 __isl_keep isl_basic_map *bmap);
3431 __isl_give isl_printer *isl_printer_print_map(
3432 __isl_take isl_printer *printer,
3433 __isl_keep isl_map *map);
3435 #include <isl/union_set.h>
3436 __isl_give isl_printer *isl_printer_print_union_set(
3437 __isl_take isl_printer *p,
3438 __isl_keep isl_union_set *uset);
3440 #include <isl/union_map.h>
3441 __isl_give isl_printer *isl_printer_print_union_map(
3442 __isl_take isl_printer *p,
3443 __isl_keep isl_union_map *umap);
3445 #include <isl/val.h>
3446 __isl_give isl_printer *isl_printer_print_multi_val(
3447 __isl_take isl_printer *p,
3448 __isl_keep isl_multi_val *mv);
3450 #include <isl/aff.h>
3451 __isl_give isl_printer *isl_printer_print_aff(
3452 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3453 __isl_give isl_printer *isl_printer_print_multi_aff(
3454 __isl_take isl_printer *p,
3455 __isl_keep isl_multi_aff *maff);
3456 __isl_give isl_printer *isl_printer_print_pw_aff(
3457 __isl_take isl_printer *p,
3458 __isl_keep isl_pw_aff *pwaff);
3459 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3460 __isl_take isl_printer *p,
3461 __isl_keep isl_pw_multi_aff *pma);
3462 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3463 __isl_take isl_printer *p,
3464 __isl_keep isl_multi_pw_aff *mpa);
3465 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3466 __isl_take isl_printer *p,
3467 __isl_keep isl_union_pw_aff *upa);
3468 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3469 __isl_take isl_printer *p,
3470 __isl_keep isl_union_pw_multi_aff *upma);
3471 __isl_give isl_printer *
3472 isl_printer_print_multi_union_pw_aff(
3473 __isl_take isl_printer *p,
3474 __isl_keep isl_multi_union_pw_aff *mupa);
3476 #include <isl/polynomial.h>
3477 __isl_give isl_printer *isl_printer_print_qpolynomial(
3478 __isl_take isl_printer *p,
3479 __isl_keep isl_qpolynomial *qp);
3480 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3481 __isl_take isl_printer *p,
3482 __isl_keep isl_pw_qpolynomial *pwqp);
3483 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3484 __isl_take isl_printer *p,
3485 __isl_keep isl_union_pw_qpolynomial *upwqp);
3487 __isl_give isl_printer *
3488 isl_printer_print_pw_qpolynomial_fold(
3489 __isl_take isl_printer *p,
3490 __isl_keep isl_pw_qpolynomial_fold *pwf);
3491 __isl_give isl_printer *
3492 isl_printer_print_union_pw_qpolynomial_fold(
3493 __isl_take isl_printer *p,
3494 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3496 For C<isl_printer_print_qpolynomial>,
3497 C<isl_printer_print_pw_qpolynomial> and
3498 C<isl_printer_print_pw_qpolynomial_fold>,
3499 the output format of the printer
3500 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3501 For C<isl_printer_print_union_pw_qpolynomial> and
3502 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3504 In case of printing in C<ISL_FORMAT_C>, the user may want
3505 to set the names of all dimensions first.
3507 C<isl> also provides limited support for printing YAML documents,
3508 just enough for the internal use for printing such documents.
3510 #include <isl/printer.h>
3511 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3512 __isl_take isl_printer *p);
3513 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3514 __isl_take isl_printer *p);
3515 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3516 __isl_take isl_printer *p);
3517 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3518 __isl_take isl_printer *p);
3519 __isl_give isl_printer *isl_printer_yaml_next(
3520 __isl_take isl_printer *p);
3522 A document is started by a call to either
3523 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3524 Anything printed to the printer after such a call belong to the
3525 first key of the mapping or the first element in the sequence.
3526 The function C<isl_printer_yaml_next> moves to the value if
3527 we are currently printing a mapping key, the next key if we
3528 are printing a value or the next element if we are printing
3529 an element in a sequence.
3530 Nested mappings and sequences are initiated by the same
3531 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3532 Each call to these functions needs to have a corresponding call to
3533 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3535 When called on a file printer, the following function flushes
3536 the file. When called on a string printer, the buffer is cleared.
3538 __isl_give isl_printer *isl_printer_flush(
3539 __isl_take isl_printer *p);
3541 Alternatively, a string representation can be obtained
3542 directly using the following functions, which always print
3545 #include <isl/space.h>
3546 __isl_give char *isl_space_to_str(
3547 __isl_keep isl_space *space);
3549 #include <isl/val.h>
3550 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3551 __isl_give char *isl_multi_val_to_str(
3552 __isl_keep isl_multi_val *mv);
3554 #include <isl/set.h>
3555 __isl_give char *isl_set_to_str(
3556 __isl_keep isl_set *set);
3558 #include <isl/union_set.h>
3559 __isl_give char *isl_union_set_to_str(
3560 __isl_keep isl_union_set *uset);
3562 #include <isl/map.h>
3563 __isl_give char *isl_map_to_str(
3564 __isl_keep isl_map *map);
3566 #include <isl/union_map.h>
3567 __isl_give char *isl_union_map_to_str(
3568 __isl_keep isl_union_map *umap);
3570 #include <isl/aff.h>
3571 __isl_give char *isl_multi_aff_to_str(
3572 __isl_keep isl_multi_aff *aff);
3573 __isl_give char *isl_union_pw_aff_to_str(
3574 __isl_keep isl_union_pw_aff *upa);
3575 __isl_give char *isl_union_pw_multi_aff_to_str(
3576 __isl_keep isl_union_pw_multi_aff *upma);
3577 __isl_give char *isl_multi_union_pw_aff_to_str(
3578 __isl_keep isl_multi_union_pw_aff *mupa);
3582 =head3 Unary Properties
3588 The following functions test whether the given set or relation
3589 contains any integer points. The ``plain'' variants do not perform
3590 any computations, but simply check if the given set or relation
3591 is already known to be empty.
3593 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3594 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3595 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3596 int isl_set_is_empty(__isl_keep isl_set *set);
3597 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3598 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3599 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3600 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3601 int isl_map_is_empty(__isl_keep isl_map *map);
3602 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3604 =item * Universality
3606 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3607 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3608 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3609 int isl_map_plain_is_universe(__isl_keep isl_map *map);
3611 =item * Single-valuedness
3613 #include <isl/set.h>
3614 int isl_set_is_singleton(__isl_keep isl_set *set);
3616 #include <isl/map.h>
3617 int isl_basic_map_is_single_valued(
3618 __isl_keep isl_basic_map *bmap);
3619 int isl_map_plain_is_single_valued(
3620 __isl_keep isl_map *map);
3621 int isl_map_is_single_valued(__isl_keep isl_map *map);
3623 #include <isl/union_map.h>
3624 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3628 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3629 int isl_map_is_injective(__isl_keep isl_map *map);
3630 int isl_union_map_plain_is_injective(
3631 __isl_keep isl_union_map *umap);
3632 int isl_union_map_is_injective(
3633 __isl_keep isl_union_map *umap);
3637 int isl_map_is_bijective(__isl_keep isl_map *map);
3638 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3642 __isl_give isl_val *
3643 isl_basic_map_plain_get_val_if_fixed(
3644 __isl_keep isl_basic_map *bmap,
3645 enum isl_dim_type type, unsigned pos);
3646 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3647 __isl_keep isl_set *set,
3648 enum isl_dim_type type, unsigned pos);
3649 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3650 __isl_keep isl_map *map,
3651 enum isl_dim_type type, unsigned pos);
3653 If the set or relation obviously lies on a hyperplane where the given dimension
3654 has a fixed value, then return that value.
3655 Otherwise return NaN.
3659 int isl_set_dim_residue_class_val(
3660 __isl_keep isl_set *set,
3661 int pos, __isl_give isl_val **modulo,
3662 __isl_give isl_val **residue);
3664 Check if the values of the given set dimension are equal to a fixed
3665 value modulo some integer value. If so, assign the modulo to C<*modulo>
3666 and the fixed value to C<*residue>. If the given dimension attains only
3667 a single value, then assign C<0> to C<*modulo> and the fixed value to
3669 If the dimension does not attain only a single value and if no modulo
3670 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3674 To check whether the description of a set, relation or function depends
3675 on one or more given dimensions,
3676 the following functions can be used.
3678 #include <isl/constraint.h>
3679 int isl_constraint_involves_dims(
3680 __isl_keep isl_constraint *constraint,
3681 enum isl_dim_type type, unsigned first, unsigned n);
3683 #include <isl/set.h>
3684 int isl_basic_set_involves_dims(
3685 __isl_keep isl_basic_set *bset,
3686 enum isl_dim_type type, unsigned first, unsigned n);
3687 int isl_set_involves_dims(__isl_keep isl_set *set,
3688 enum isl_dim_type type, unsigned first, unsigned n);
3690 #include <isl/map.h>
3691 int isl_basic_map_involves_dims(
3692 __isl_keep isl_basic_map *bmap,
3693 enum isl_dim_type type, unsigned first, unsigned n);
3694 int isl_map_involves_dims(__isl_keep isl_map *map,
3695 enum isl_dim_type type, unsigned first, unsigned n);
3697 #include <isl/union_map.h>
3698 int isl_union_map_involves_dims(
3699 __isl_keep isl_union_map *umap,
3700 enum isl_dim_type type, unsigned first, unsigned n);
3702 #include <isl/aff.h>
3703 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3704 enum isl_dim_type type, unsigned first, unsigned n);
3705 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3706 enum isl_dim_type type, unsigned first, unsigned n);
3707 int isl_multi_aff_involves_dims(
3708 __isl_keep isl_multi_aff *ma,
3709 enum isl_dim_type type, unsigned first, unsigned n);
3710 int isl_multi_pw_aff_involves_dims(
3711 __isl_keep isl_multi_pw_aff *mpa,
3712 enum isl_dim_type type, unsigned first, unsigned n);
3714 Similarly, the following functions can be used to check whether
3715 a given dimension is involved in any lower or upper bound.
3717 #include <isl/set.h>
3718 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3719 enum isl_dim_type type, unsigned pos);
3720 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3721 enum isl_dim_type type, unsigned pos);
3723 Note that these functions return true even if there is a bound on
3724 the dimension on only some of the basic sets of C<set>.
3725 To check if they have a bound for all of the basic sets in C<set>,
3726 use the following functions instead.
3728 #include <isl/set.h>
3729 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3730 enum isl_dim_type type, unsigned pos);
3731 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3732 enum isl_dim_type type, unsigned pos);
3736 To check whether a set is a parameter domain, use this function:
3738 int isl_set_is_params(__isl_keep isl_set *set);
3739 int isl_union_set_is_params(
3740 __isl_keep isl_union_set *uset);
3744 The following functions check whether the space of the given
3745 (basic) set or relation range is a wrapped relation.
3747 #include <isl/space.h>
3748 int isl_space_is_wrapping(
3749 __isl_keep isl_space *space);
3750 int isl_space_domain_is_wrapping(
3751 __isl_keep isl_space *space);
3752 int isl_space_range_is_wrapping(
3753 __isl_keep isl_space *space);
3755 #include <isl/set.h>
3756 int isl_basic_set_is_wrapping(
3757 __isl_keep isl_basic_set *bset);
3758 int isl_set_is_wrapping(__isl_keep isl_set *set);
3760 #include <isl/map.h>
3761 int isl_map_domain_is_wrapping(
3762 __isl_keep isl_map *map);
3763 int isl_map_range_is_wrapping(
3764 __isl_keep isl_map *map);
3766 #include <isl/val.h>
3767 int isl_multi_val_range_is_wrapping(
3768 __isl_keep isl_multi_val *mv);
3770 #include <isl/aff.h>
3771 int isl_multi_aff_range_is_wrapping(
3772 __isl_keep isl_multi_aff *ma);
3773 int isl_multi_pw_aff_range_is_wrapping(
3774 __isl_keep isl_multi_pw_aff *mpa);
3775 int isl_multi_union_pw_aff_range_is_wrapping(
3776 __isl_keep isl_multi_union_pw_aff *mupa);
3778 The input to C<isl_space_is_wrapping> should
3779 be the space of a set, while that of
3780 C<isl_space_domain_is_wrapping> and
3781 C<isl_space_range_is_wrapping> should be the space of a relation.
3783 =item * Internal Product
3785 int isl_basic_map_can_zip(
3786 __isl_keep isl_basic_map *bmap);
3787 int isl_map_can_zip(__isl_keep isl_map *map);
3789 Check whether the product of domain and range of the given relation
3791 i.e., whether both domain and range are nested relations.
3795 int isl_basic_map_can_curry(
3796 __isl_keep isl_basic_map *bmap);
3797 int isl_map_can_curry(__isl_keep isl_map *map);
3799 Check whether the domain of the (basic) relation is a wrapped relation.
3801 int isl_basic_map_can_uncurry(
3802 __isl_keep isl_basic_map *bmap);
3803 int isl_map_can_uncurry(__isl_keep isl_map *map);
3805 Check whether the range of the (basic) relation is a wrapped relation.
3807 =item * Special Values
3809 #include <isl/aff.h>
3810 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3811 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3813 Check whether the given expression is a constant.
3815 #include <isl/aff.h>
3816 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3817 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3819 #include <isl/polynomial.h>
3820 int isl_qpolynomial_fold_is_nan(
3821 __isl_keep isl_qpolynomial_fold *fold);
3823 Check whether the given expression is equal to or involves NaN.
3825 #include <isl/aff.h>
3826 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3828 Check whether the affine expression is obviously zero.
3832 =head3 Binary Properties
3838 The following functions check whether two objects
3839 represent the same set, relation or function.
3840 The C<plain> variants only return true if the objects
3841 are obviously the same. That is, they may return false
3842 even if the objects are the same, but they will never
3843 return true if the objects are not the same.
3845 #include <isl/set.h>
3846 int isl_basic_set_plain_is_equal(
3847 __isl_keep isl_basic_set *bset1,
3848 __isl_keep isl_basic_set *bset2);
3849 int isl_basic_set_is_equal(
3850 __isl_keep isl_basic_set *bset1,
3851 __isl_keep isl_basic_set *bset2);
3852 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3853 __isl_keep isl_set *set2);
3854 int isl_set_is_equal(__isl_keep isl_set *set1,
3855 __isl_keep isl_set *set2);
3857 #include <isl/map.h>
3858 int isl_basic_map_is_equal(
3859 __isl_keep isl_basic_map *bmap1,
3860 __isl_keep isl_basic_map *bmap2);
3861 int isl_map_is_equal(__isl_keep isl_map *map1,
3862 __isl_keep isl_map *map2);
3863 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3864 __isl_keep isl_map *map2);
3866 #include <isl/union_set.h>
3867 int isl_union_set_is_equal(
3868 __isl_keep isl_union_set *uset1,
3869 __isl_keep isl_union_set *uset2);
3871 #include <isl/union_map.h>
3872 int isl_union_map_is_equal(
3873 __isl_keep isl_union_map *umap1,
3874 __isl_keep isl_union_map *umap2);
3876 #include <isl/aff.h>
3877 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3878 __isl_keep isl_aff *aff2);
3879 int isl_multi_aff_plain_is_equal(
3880 __isl_keep isl_multi_aff *maff1,
3881 __isl_keep isl_multi_aff *maff2);
3882 int isl_pw_aff_plain_is_equal(
3883 __isl_keep isl_pw_aff *pwaff1,
3884 __isl_keep isl_pw_aff *pwaff2);
3885 int isl_pw_multi_aff_plain_is_equal(
3886 __isl_keep isl_pw_multi_aff *pma1,
3887 __isl_keep isl_pw_multi_aff *pma2);
3888 int isl_multi_pw_aff_plain_is_equal(
3889 __isl_keep isl_multi_pw_aff *mpa1,
3890 __isl_keep isl_multi_pw_aff *mpa2);
3891 int isl_multi_pw_aff_is_equal(
3892 __isl_keep isl_multi_pw_aff *mpa1,
3893 __isl_keep isl_multi_pw_aff *mpa2);
3894 int isl_union_pw_aff_plain_is_equal(
3895 __isl_keep isl_union_pw_aff *upa1,
3896 __isl_keep isl_union_pw_aff *upa2);
3897 int isl_union_pw_multi_aff_plain_is_equal(
3898 __isl_keep isl_union_pw_multi_aff *upma1,
3899 __isl_keep isl_union_pw_multi_aff *upma2);
3900 int isl_multi_union_pw_aff_plain_is_equal(
3901 __isl_keep isl_multi_union_pw_aff *mupa1,
3902 __isl_keep isl_multi_union_pw_aff *mupa2);
3904 #include <isl/polynomial.h>
3905 int isl_union_pw_qpolynomial_plain_is_equal(
3906 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3907 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3908 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3909 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3910 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3912 =item * Disjointness
3914 #include <isl/set.h>
3915 int isl_basic_set_is_disjoint(
3916 __isl_keep isl_basic_set *bset1,
3917 __isl_keep isl_basic_set *bset2);
3918 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3919 __isl_keep isl_set *set2);
3920 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3921 __isl_keep isl_set *set2);
3923 #include <isl/map.h>
3924 int isl_basic_map_is_disjoint(
3925 __isl_keep isl_basic_map *bmap1,
3926 __isl_keep isl_basic_map *bmap2);
3927 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3928 __isl_keep isl_map *map2);
3930 #include <isl/union_set.h>
3931 int isl_union_set_is_disjoint(
3932 __isl_keep isl_union_set *uset1,
3933 __isl_keep isl_union_set *uset2);
3935 #include <isl/union_map.h>
3936 int isl_union_map_is_disjoint(
3937 __isl_keep isl_union_map *umap1,
3938 __isl_keep isl_union_map *umap2);
3942 int isl_basic_set_is_subset(
3943 __isl_keep isl_basic_set *bset1,
3944 __isl_keep isl_basic_set *bset2);
3945 int isl_set_is_subset(__isl_keep isl_set *set1,
3946 __isl_keep isl_set *set2);
3947 int isl_set_is_strict_subset(
3948 __isl_keep isl_set *set1,
3949 __isl_keep isl_set *set2);
3950 int isl_union_set_is_subset(
3951 __isl_keep isl_union_set *uset1,
3952 __isl_keep isl_union_set *uset2);
3953 int isl_union_set_is_strict_subset(
3954 __isl_keep isl_union_set *uset1,
3955 __isl_keep isl_union_set *uset2);
3956 int isl_basic_map_is_subset(
3957 __isl_keep isl_basic_map *bmap1,
3958 __isl_keep isl_basic_map *bmap2);
3959 int isl_basic_map_is_strict_subset(
3960 __isl_keep isl_basic_map *bmap1,
3961 __isl_keep isl_basic_map *bmap2);
3962 int isl_map_is_subset(
3963 __isl_keep isl_map *map1,
3964 __isl_keep isl_map *map2);
3965 int isl_map_is_strict_subset(
3966 __isl_keep isl_map *map1,
3967 __isl_keep isl_map *map2);
3968 int isl_union_map_is_subset(
3969 __isl_keep isl_union_map *umap1,
3970 __isl_keep isl_union_map *umap2);
3971 int isl_union_map_is_strict_subset(
3972 __isl_keep isl_union_map *umap1,
3973 __isl_keep isl_union_map *umap2);
3975 Check whether the first argument is a (strict) subset of the
3980 Every comparison function returns a negative value if the first
3981 argument is considered smaller than the second, a positive value
3982 if the first argument is considered greater and zero if the two
3983 constraints are considered the same by the comparison criterion.
3985 #include <isl/constraint.h>
3986 int isl_constraint_plain_cmp(
3987 __isl_keep isl_constraint *c1,
3988 __isl_keep isl_constraint *c2);
3990 This function is useful for sorting C<isl_constraint>s.
3991 The order depends on the internal representation of the inputs.
3992 The order is fixed over different calls to the function (assuming
3993 the internal representation of the inputs has not changed), but may
3994 change over different versions of C<isl>.
3996 #include <isl/constraint.h>
3997 int isl_constraint_cmp_last_non_zero(
3998 __isl_keep isl_constraint *c1,
3999 __isl_keep isl_constraint *c2);
4001 This function can be used to sort constraints that live in the same
4002 local space. Constraints that involve ``earlier'' dimensions or
4003 that have a smaller coefficient for the shared latest dimension
4004 are considered smaller than other constraints.
4005 This function only defines a B<partial> order.
4007 #include <isl/set.h>
4008 int isl_set_plain_cmp(__isl_keep isl_set *set1,
4009 __isl_keep isl_set *set2);
4011 This function is useful for sorting C<isl_set>s.
4012 The order depends on the internal representation of the inputs.
4013 The order is fixed over different calls to the function (assuming
4014 the internal representation of the inputs has not changed), but may
4015 change over different versions of C<isl>.
4017 #include <isl/aff.h>
4018 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
4019 __isl_keep isl_pw_aff *pa2);
4021 The function C<isl_pw_aff_plain_cmp> can be used to sort
4022 C<isl_pw_aff>s. The order is not strictly defined.
4023 The current order sorts expressions that only involve
4024 earlier dimensions before those that involve later dimensions.
4028 =head2 Unary Operations
4034 __isl_give isl_set *isl_set_complement(
4035 __isl_take isl_set *set);
4036 __isl_give isl_map *isl_map_complement(
4037 __isl_take isl_map *map);
4041 #include <isl/space.h>
4042 __isl_give isl_space *isl_space_reverse(
4043 __isl_take isl_space *space);
4045 #include <isl/map.h>
4046 __isl_give isl_basic_map *isl_basic_map_reverse(
4047 __isl_take isl_basic_map *bmap);
4048 __isl_give isl_map *isl_map_reverse(
4049 __isl_take isl_map *map);
4051 #include <isl/union_map.h>
4052 __isl_give isl_union_map *isl_union_map_reverse(
4053 __isl_take isl_union_map *umap);
4057 #include <isl/space.h>
4058 __isl_give isl_space *isl_space_domain(
4059 __isl_take isl_space *space);
4060 __isl_give isl_space *isl_space_range(
4061 __isl_take isl_space *space);
4062 __isl_give isl_space *isl_space_params(
4063 __isl_take isl_space *space);
4065 #include <isl/local_space.h>
4066 __isl_give isl_local_space *isl_local_space_domain(
4067 __isl_take isl_local_space *ls);
4068 __isl_give isl_local_space *isl_local_space_range(
4069 __isl_take isl_local_space *ls);
4071 #include <isl/set.h>
4072 __isl_give isl_basic_set *isl_basic_set_project_out(
4073 __isl_take isl_basic_set *bset,
4074 enum isl_dim_type type, unsigned first, unsigned n);
4075 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4076 enum isl_dim_type type, unsigned first, unsigned n);
4077 __isl_give isl_basic_set *isl_basic_set_params(
4078 __isl_take isl_basic_set *bset);
4079 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4081 #include <isl/map.h>
4082 __isl_give isl_basic_map *isl_basic_map_project_out(
4083 __isl_take isl_basic_map *bmap,
4084 enum isl_dim_type type, unsigned first, unsigned n);
4085 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4086 enum isl_dim_type type, unsigned first, unsigned n);
4087 __isl_give isl_basic_set *isl_basic_map_domain(
4088 __isl_take isl_basic_map *bmap);
4089 __isl_give isl_basic_set *isl_basic_map_range(
4090 __isl_take isl_basic_map *bmap);
4091 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4092 __isl_give isl_set *isl_map_domain(
4093 __isl_take isl_map *bmap);
4094 __isl_give isl_set *isl_map_range(
4095 __isl_take isl_map *map);
4097 #include <isl/union_set.h>
4098 __isl_give isl_union_set *isl_union_set_project_out(
4099 __isl_take isl_union_set *uset,
4100 enum isl_dim_type type,
4101 unsigned first, unsigned n);
4102 __isl_give isl_set *isl_union_set_params(
4103 __isl_take isl_union_set *uset);
4105 The function C<isl_union_set_project_out> can only project out
4108 #include <isl/union_map.h>
4109 __isl_give isl_union_map *isl_union_map_project_out(
4110 __isl_take isl_union_map *umap,
4111 enum isl_dim_type type, unsigned first, unsigned n);
4112 __isl_give isl_set *isl_union_map_params(
4113 __isl_take isl_union_map *umap);
4114 __isl_give isl_union_set *isl_union_map_domain(
4115 __isl_take isl_union_map *umap);
4116 __isl_give isl_union_set *isl_union_map_range(
4117 __isl_take isl_union_map *umap);
4119 The function C<isl_union_map_project_out> can only project out
4122 #include <isl/aff.h>
4123 __isl_give isl_aff *isl_aff_project_domain_on_params(
4124 __isl_take isl_aff *aff);
4125 __isl_give isl_pw_multi_aff *
4126 isl_pw_multi_aff_project_domain_on_params(
4127 __isl_take isl_pw_multi_aff *pma);
4128 __isl_give isl_set *isl_pw_aff_domain(
4129 __isl_take isl_pw_aff *pwaff);
4130 __isl_give isl_set *isl_pw_multi_aff_domain(
4131 __isl_take isl_pw_multi_aff *pma);
4132 __isl_give isl_set *isl_multi_pw_aff_domain(
4133 __isl_take isl_multi_pw_aff *mpa);
4134 __isl_give isl_union_set *isl_union_pw_aff_domain(
4135 __isl_take isl_union_pw_aff *upa);
4136 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4137 __isl_take isl_union_pw_multi_aff *upma);
4138 __isl_give isl_union_set *
4139 isl_multi_union_pw_aff_domain(
4140 __isl_take isl_multi_union_pw_aff *mupa);
4141 __isl_give isl_set *isl_pw_aff_params(
4142 __isl_take isl_pw_aff *pwa);
4144 The function C<isl_multi_union_pw_aff_domain> requires its
4145 input to have at least one set dimension.
4147 #include <isl/polynomial.h>
4148 __isl_give isl_qpolynomial *
4149 isl_qpolynomial_project_domain_on_params(
4150 __isl_take isl_qpolynomial *qp);
4151 __isl_give isl_pw_qpolynomial *
4152 isl_pw_qpolynomial_project_domain_on_params(
4153 __isl_take isl_pw_qpolynomial *pwqp);
4154 __isl_give isl_pw_qpolynomial_fold *
4155 isl_pw_qpolynomial_fold_project_domain_on_params(
4156 __isl_take isl_pw_qpolynomial_fold *pwf);
4157 __isl_give isl_set *isl_pw_qpolynomial_domain(
4158 __isl_take isl_pw_qpolynomial *pwqp);
4159 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4160 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4161 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4162 __isl_take isl_union_pw_qpolynomial *upwqp);
4164 #include <isl/space.h>
4165 __isl_give isl_space *isl_space_domain_map(
4166 __isl_take isl_space *space);
4167 __isl_give isl_space *isl_space_range_map(
4168 __isl_take isl_space *space);
4170 #include <isl/map.h>
4171 __isl_give isl_map *isl_set_wrapped_domain_map(
4172 __isl_take isl_set *set);
4173 __isl_give isl_basic_map *isl_basic_map_domain_map(
4174 __isl_take isl_basic_map *bmap);
4175 __isl_give isl_basic_map *isl_basic_map_range_map(
4176 __isl_take isl_basic_map *bmap);
4177 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4178 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4180 #include <isl/union_map.h>
4181 __isl_give isl_union_map *isl_union_map_domain_map(
4182 __isl_take isl_union_map *umap);
4183 __isl_give isl_union_pw_multi_aff *
4184 isl_union_map_domain_map_union_pw_multi_aff(
4185 __isl_take isl_union_map *umap);
4186 __isl_give isl_union_map *isl_union_map_range_map(
4187 __isl_take isl_union_map *umap);
4188 __isl_give isl_union_map *
4189 isl_union_set_wrapped_domain_map(
4190 __isl_take isl_union_set *uset);
4192 The functions above construct a (basic, regular or union) relation
4193 that maps (a wrapped version of) the input relation to its domain or range.
4194 C<isl_set_wrapped_domain_map> maps the input set to the domain
4195 of its wrapped relation.
4199 __isl_give isl_basic_set *isl_basic_set_eliminate(
4200 __isl_take isl_basic_set *bset,
4201 enum isl_dim_type type,
4202 unsigned first, unsigned n);
4203 __isl_give isl_set *isl_set_eliminate(
4204 __isl_take isl_set *set, enum isl_dim_type type,
4205 unsigned first, unsigned n);
4206 __isl_give isl_basic_map *isl_basic_map_eliminate(
4207 __isl_take isl_basic_map *bmap,
4208 enum isl_dim_type type,
4209 unsigned first, unsigned n);
4210 __isl_give isl_map *isl_map_eliminate(
4211 __isl_take isl_map *map, enum isl_dim_type type,
4212 unsigned first, unsigned n);
4214 Eliminate the coefficients for the given dimensions from the constraints,
4215 without removing the dimensions.
4217 =item * Constructing a set from a parameter domain
4219 A zero-dimensional space or (basic) set can be constructed
4220 on a given parameter domain using the following functions.
4222 #include <isl/space.h>
4223 __isl_give isl_space *isl_space_set_from_params(
4224 __isl_take isl_space *space);
4226 #include <isl/set.h>
4227 __isl_give isl_basic_set *isl_basic_set_from_params(
4228 __isl_take isl_basic_set *bset);
4229 __isl_give isl_set *isl_set_from_params(
4230 __isl_take isl_set *set);
4232 =item * Constructing a relation from a set
4234 Create a relation with the given set as domain or range.
4235 The range or domain of the created relation is a zero-dimensional
4236 flat anonymous space.
4238 #include <isl/space.h>
4239 __isl_give isl_space *isl_space_from_domain(
4240 __isl_take isl_space *space);
4241 __isl_give isl_space *isl_space_from_range(
4242 __isl_take isl_space *space);
4243 __isl_give isl_space *isl_space_map_from_set(
4244 __isl_take isl_space *space);
4245 __isl_give isl_space *isl_space_map_from_domain_and_range(
4246 __isl_take isl_space *domain,
4247 __isl_take isl_space *range);
4249 #include <isl/local_space.h>
4250 __isl_give isl_local_space *isl_local_space_from_domain(
4251 __isl_take isl_local_space *ls);
4253 #include <isl/map.h>
4254 __isl_give isl_map *isl_map_from_domain(
4255 __isl_take isl_set *set);
4256 __isl_give isl_map *isl_map_from_range(
4257 __isl_take isl_set *set);
4259 #include <isl/val.h>
4260 __isl_give isl_multi_val *isl_multi_val_from_range(
4261 __isl_take isl_multi_val *mv);
4263 #include <isl/aff.h>
4264 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4265 __isl_take isl_multi_aff *ma);
4266 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4267 __isl_take isl_pw_aff *pwa);
4268 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4269 __isl_take isl_multi_pw_aff *mpa);
4270 __isl_give isl_multi_union_pw_aff *
4271 isl_multi_union_pw_aff_from_range(
4272 __isl_take isl_multi_union_pw_aff *mupa);
4273 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4274 __isl_take isl_set *set);
4275 __isl_give isl_union_pw_multi_aff *
4276 isl_union_pw_multi_aff_from_domain(
4277 __isl_take isl_union_set *uset);
4281 #include <isl/set.h>
4282 __isl_give isl_basic_set *isl_basic_set_fix_si(
4283 __isl_take isl_basic_set *bset,
4284 enum isl_dim_type type, unsigned pos, int value);
4285 __isl_give isl_basic_set *isl_basic_set_fix_val(
4286 __isl_take isl_basic_set *bset,
4287 enum isl_dim_type type, unsigned pos,
4288 __isl_take isl_val *v);
4289 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4290 enum isl_dim_type type, unsigned pos, int value);
4291 __isl_give isl_set *isl_set_fix_val(
4292 __isl_take isl_set *set,
4293 enum isl_dim_type type, unsigned pos,
4294 __isl_take isl_val *v);
4296 #include <isl/map.h>
4297 __isl_give isl_basic_map *isl_basic_map_fix_si(
4298 __isl_take isl_basic_map *bmap,
4299 enum isl_dim_type type, unsigned pos, int value);
4300 __isl_give isl_basic_map *isl_basic_map_fix_val(
4301 __isl_take isl_basic_map *bmap,
4302 enum isl_dim_type type, unsigned pos,
4303 __isl_take isl_val *v);
4304 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4305 enum isl_dim_type type, unsigned pos, int value);
4306 __isl_give isl_map *isl_map_fix_val(
4307 __isl_take isl_map *map,
4308 enum isl_dim_type type, unsigned pos,
4309 __isl_take isl_val *v);
4311 #include <isl/aff.h>
4312 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4313 __isl_take isl_pw_multi_aff *pma,
4314 enum isl_dim_type type, unsigned pos, int value);
4316 #include <isl/polynomial.h>
4317 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4318 __isl_take isl_pw_qpolynomial *pwqp,
4319 enum isl_dim_type type, unsigned n,
4320 __isl_take isl_val *v);
4322 Intersect the set, relation or function domain
4323 with the hyperplane where the given
4324 dimension has the fixed given value.
4326 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4327 __isl_take isl_basic_map *bmap,
4328 enum isl_dim_type type, unsigned pos, int value);
4329 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4330 __isl_take isl_basic_map *bmap,
4331 enum isl_dim_type type, unsigned pos, int value);
4332 __isl_give isl_set *isl_set_lower_bound_si(
4333 __isl_take isl_set *set,
4334 enum isl_dim_type type, unsigned pos, int value);
4335 __isl_give isl_set *isl_set_lower_bound_val(
4336 __isl_take isl_set *set,
4337 enum isl_dim_type type, unsigned pos,
4338 __isl_take isl_val *value);
4339 __isl_give isl_map *isl_map_lower_bound_si(
4340 __isl_take isl_map *map,
4341 enum isl_dim_type type, unsigned pos, int value);
4342 __isl_give isl_set *isl_set_upper_bound_si(
4343 __isl_take isl_set *set,
4344 enum isl_dim_type type, unsigned pos, int value);
4345 __isl_give isl_set *isl_set_upper_bound_val(
4346 __isl_take isl_set *set,
4347 enum isl_dim_type type, unsigned pos,
4348 __isl_take isl_val *value);
4349 __isl_give isl_map *isl_map_upper_bound_si(
4350 __isl_take isl_map *map,
4351 enum isl_dim_type type, unsigned pos, int value);
4353 Intersect the set or relation with the half-space where the given
4354 dimension has a value bounded by the fixed given integer value.
4356 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4357 enum isl_dim_type type1, int pos1,
4358 enum isl_dim_type type2, int pos2);
4359 __isl_give isl_basic_map *isl_basic_map_equate(
4360 __isl_take isl_basic_map *bmap,
4361 enum isl_dim_type type1, int pos1,
4362 enum isl_dim_type type2, int pos2);
4363 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4364 enum isl_dim_type type1, int pos1,
4365 enum isl_dim_type type2, int pos2);
4367 Intersect the set or relation with the hyperplane where the given
4368 dimensions are equal to each other.
4370 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4371 enum isl_dim_type type1, int pos1,
4372 enum isl_dim_type type2, int pos2);
4374 Intersect the relation with the hyperplane where the given
4375 dimensions have opposite values.
4377 __isl_give isl_map *isl_map_order_le(
4378 __isl_take isl_map *map,
4379 enum isl_dim_type type1, int pos1,
4380 enum isl_dim_type type2, int pos2);
4381 __isl_give isl_basic_map *isl_basic_map_order_ge(
4382 __isl_take isl_basic_map *bmap,
4383 enum isl_dim_type type1, int pos1,
4384 enum isl_dim_type type2, int pos2);
4385 __isl_give isl_map *isl_map_order_ge(
4386 __isl_take isl_map *map,
4387 enum isl_dim_type type1, int pos1,
4388 enum isl_dim_type type2, int pos2);
4389 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4390 enum isl_dim_type type1, int pos1,
4391 enum isl_dim_type type2, int pos2);
4392 __isl_give isl_basic_map *isl_basic_map_order_gt(
4393 __isl_take isl_basic_map *bmap,
4394 enum isl_dim_type type1, int pos1,
4395 enum isl_dim_type type2, int pos2);
4396 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4397 enum isl_dim_type type1, int pos1,
4398 enum isl_dim_type type2, int pos2);
4400 Intersect the relation with the half-space where the given
4401 dimensions satisfy the given ordering.
4405 #include <isl/aff.h>
4406 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4407 __isl_take isl_aff *aff);
4408 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4409 __isl_take isl_aff *aff);
4410 __isl_give isl_set *isl_pw_aff_pos_set(
4411 __isl_take isl_pw_aff *pa);
4412 __isl_give isl_set *isl_pw_aff_nonneg_set(
4413 __isl_take isl_pw_aff *pwaff);
4414 __isl_give isl_set *isl_pw_aff_zero_set(
4415 __isl_take isl_pw_aff *pwaff);
4416 __isl_give isl_set *isl_pw_aff_non_zero_set(
4417 __isl_take isl_pw_aff *pwaff);
4418 __isl_give isl_union_set *
4419 isl_union_pw_aff_zero_union_set(
4420 __isl_take isl_union_pw_aff *upa);
4421 __isl_give isl_union_set *
4422 isl_multi_union_pw_aff_zero_union_set(
4423 __isl_take isl_multi_union_pw_aff *mupa);
4425 The function C<isl_aff_neg_basic_set> returns a basic set
4426 containing those elements in the domain space
4427 of C<aff> where C<aff> is negative.
4428 The function C<isl_pw_aff_nonneg_set> returns a set
4429 containing those elements in the domain
4430 of C<pwaff> where C<pwaff> is non-negative.
4431 The function C<isl_multi_union_pw_aff_zero_union_set>
4432 returns a union set containing those elements
4433 in the domains of its elements where they are all zero.
4437 __isl_give isl_map *isl_set_identity(
4438 __isl_take isl_set *set);
4439 __isl_give isl_union_map *isl_union_set_identity(
4440 __isl_take isl_union_set *uset);
4441 __isl_give isl_union_pw_multi_aff *
4442 isl_union_set_identity_union_pw_multi_aff(
4443 __isl_take isl_union_set *uset);
4445 Construct an identity relation on the given (union) set.
4447 =item * Function Extraction
4449 A piecewise quasi affine expression that is equal to 1 on a set
4450 and 0 outside the set can be created using the following function.
4452 #include <isl/aff.h>
4453 __isl_give isl_pw_aff *isl_set_indicator_function(
4454 __isl_take isl_set *set);
4456 A piecewise multiple quasi affine expression can be extracted
4457 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4458 and the C<isl_map> is single-valued.
4459 In case of a conversion from an C<isl_union_map>
4460 to an C<isl_union_pw_multi_aff>, these properties need to hold
4461 in each domain space.
4462 A conversion to a C<isl_multi_union_pw_aff> additionally
4463 requires that the input is non-empty and involves only a single
4466 #include <isl/aff.h>
4467 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4468 __isl_take isl_set *set);
4469 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4470 __isl_take isl_map *map);
4472 __isl_give isl_union_pw_multi_aff *
4473 isl_union_pw_multi_aff_from_union_set(
4474 __isl_take isl_union_set *uset);
4475 __isl_give isl_union_pw_multi_aff *
4476 isl_union_pw_multi_aff_from_union_map(
4477 __isl_take isl_union_map *umap);
4479 __isl_give isl_multi_union_pw_aff *
4480 isl_multi_union_pw_aff_from_union_map(
4481 __isl_take isl_union_map *umap);
4485 __isl_give isl_basic_set *isl_basic_map_deltas(
4486 __isl_take isl_basic_map *bmap);
4487 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4488 __isl_give isl_union_set *isl_union_map_deltas(
4489 __isl_take isl_union_map *umap);
4491 These functions return a (basic) set containing the differences
4492 between image elements and corresponding domain elements in the input.
4494 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4495 __isl_take isl_basic_map *bmap);
4496 __isl_give isl_map *isl_map_deltas_map(
4497 __isl_take isl_map *map);
4498 __isl_give isl_union_map *isl_union_map_deltas_map(
4499 __isl_take isl_union_map *umap);
4501 The functions above construct a (basic, regular or union) relation
4502 that maps (a wrapped version of) the input relation to its delta set.
4506 Simplify the representation of a set, relation or functions by trying
4507 to combine pairs of basic sets or relations into a single
4508 basic set or relation.
4510 #include <isl/set.h>
4511 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4513 #include <isl/map.h>
4514 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4516 #include <isl/union_set.h>
4517 __isl_give isl_union_set *isl_union_set_coalesce(
4518 __isl_take isl_union_set *uset);
4520 #include <isl/union_map.h>
4521 __isl_give isl_union_map *isl_union_map_coalesce(
4522 __isl_take isl_union_map *umap);
4524 #include <isl/aff.h>
4525 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4526 __isl_take isl_pw_aff *pwqp);
4527 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4528 __isl_take isl_pw_multi_aff *pma);
4529 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4530 __isl_take isl_multi_pw_aff *mpa);
4531 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4532 __isl_take isl_union_pw_aff *upa);
4533 __isl_give isl_union_pw_multi_aff *
4534 isl_union_pw_multi_aff_coalesce(
4535 __isl_take isl_union_pw_multi_aff *upma);
4537 #include <isl/polynomial.h>
4538 __isl_give isl_pw_qpolynomial_fold *
4539 isl_pw_qpolynomial_fold_coalesce(
4540 __isl_take isl_pw_qpolynomial_fold *pwf);
4541 __isl_give isl_union_pw_qpolynomial *
4542 isl_union_pw_qpolynomial_coalesce(
4543 __isl_take isl_union_pw_qpolynomial *upwqp);
4544 __isl_give isl_union_pw_qpolynomial_fold *
4545 isl_union_pw_qpolynomial_fold_coalesce(
4546 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4548 One of the methods for combining pairs of basic sets or relations
4549 can result in coefficients that are much larger than those that appear
4550 in the constraints of the input. By default, the coefficients are
4551 not allowed to grow larger, but this can be changed by unsetting
4552 the following option.
4554 int isl_options_set_coalesce_bounded_wrapping(
4555 isl_ctx *ctx, int val);
4556 int isl_options_get_coalesce_bounded_wrapping(
4559 =item * Detecting equalities
4561 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4562 __isl_take isl_basic_set *bset);
4563 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4564 __isl_take isl_basic_map *bmap);
4565 __isl_give isl_set *isl_set_detect_equalities(
4566 __isl_take isl_set *set);
4567 __isl_give isl_map *isl_map_detect_equalities(
4568 __isl_take isl_map *map);
4569 __isl_give isl_union_set *isl_union_set_detect_equalities(
4570 __isl_take isl_union_set *uset);
4571 __isl_give isl_union_map *isl_union_map_detect_equalities(
4572 __isl_take isl_union_map *umap);
4574 Simplify the representation of a set or relation by detecting implicit
4577 =item * Removing redundant constraints
4579 #include <isl/set.h>
4580 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4581 __isl_take isl_basic_set *bset);
4582 __isl_give isl_set *isl_set_remove_redundancies(
4583 __isl_take isl_set *set);
4585 #include <isl/union_set.h>
4586 __isl_give isl_union_set *
4587 isl_union_set_remove_redundancies(
4588 __isl_take isl_union_set *uset);
4590 #include <isl/map.h>
4591 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4592 __isl_take isl_basic_map *bmap);
4593 __isl_give isl_map *isl_map_remove_redundancies(
4594 __isl_take isl_map *map);
4596 #include <isl/union_map.h>
4597 __isl_give isl_union_map *
4598 isl_union_map_remove_redundancies(
4599 __isl_take isl_union_map *umap);
4603 __isl_give isl_basic_set *isl_set_convex_hull(
4604 __isl_take isl_set *set);
4605 __isl_give isl_basic_map *isl_map_convex_hull(
4606 __isl_take isl_map *map);
4608 If the input set or relation has any existentially quantified
4609 variables, then the result of these operations is currently undefined.
4613 #include <isl/set.h>
4614 __isl_give isl_basic_set *
4615 isl_set_unshifted_simple_hull(
4616 __isl_take isl_set *set);
4617 __isl_give isl_basic_set *isl_set_simple_hull(
4618 __isl_take isl_set *set);
4619 __isl_give isl_basic_set *
4620 isl_set_unshifted_simple_hull_from_set_list(
4621 __isl_take isl_set *set,
4622 __isl_take isl_set_list *list);
4624 #include <isl/map.h>
4625 __isl_give isl_basic_map *
4626 isl_map_unshifted_simple_hull(
4627 __isl_take isl_map *map);
4628 __isl_give isl_basic_map *isl_map_simple_hull(
4629 __isl_take isl_map *map);
4630 __isl_give isl_basic_map *
4631 isl_map_unshifted_simple_hull_from_map_list(
4632 __isl_take isl_map *map,
4633 __isl_take isl_map_list *list);
4635 #include <isl/union_map.h>
4636 __isl_give isl_union_map *isl_union_map_simple_hull(
4637 __isl_take isl_union_map *umap);
4639 These functions compute a single basic set or relation
4640 that contains the whole input set or relation.
4641 In particular, the output is described by translates
4642 of the constraints describing the basic sets or relations in the input.
4643 In case of C<isl_set_unshifted_simple_hull>, only the original
4644 constraints are used, without any translation.
4645 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4646 C<isl_map_unshifted_simple_hull_from_map_list>, the
4647 constraints are taken from the elements of the second argument.
4651 (See \autoref{s:simple hull}.)
4657 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4658 __isl_take isl_basic_set *bset);
4659 __isl_give isl_basic_set *isl_set_affine_hull(
4660 __isl_take isl_set *set);
4661 __isl_give isl_union_set *isl_union_set_affine_hull(
4662 __isl_take isl_union_set *uset);
4663 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4664 __isl_take isl_basic_map *bmap);
4665 __isl_give isl_basic_map *isl_map_affine_hull(
4666 __isl_take isl_map *map);
4667 __isl_give isl_union_map *isl_union_map_affine_hull(
4668 __isl_take isl_union_map *umap);
4670 In case of union sets and relations, the affine hull is computed
4673 =item * Polyhedral hull
4675 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4676 __isl_take isl_set *set);
4677 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4678 __isl_take isl_map *map);
4679 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4680 __isl_take isl_union_set *uset);
4681 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4682 __isl_take isl_union_map *umap);
4684 These functions compute a single basic set or relation
4685 not involving any existentially quantified variables
4686 that contains the whole input set or relation.
4687 In case of union sets and relations, the polyhedral hull is computed
4690 =item * Other approximations
4692 #include <isl/set.h>
4693 __isl_give isl_basic_set *
4694 isl_basic_set_drop_constraints_involving_dims(
4695 __isl_take isl_basic_set *bset,
4696 enum isl_dim_type type,
4697 unsigned first, unsigned n);
4698 __isl_give isl_basic_set *
4699 isl_basic_set_drop_constraints_not_involving_dims(
4700 __isl_take isl_basic_set *bset,
4701 enum isl_dim_type type,
4702 unsigned first, unsigned n);
4703 __isl_give isl_set *
4704 isl_set_drop_constraints_involving_dims(
4705 __isl_take isl_set *set,
4706 enum isl_dim_type type,
4707 unsigned first, unsigned n);
4709 #include <isl/map.h>
4710 __isl_give isl_basic_map *
4711 isl_basic_map_drop_constraints_involving_dims(
4712 __isl_take isl_basic_map *bmap,
4713 enum isl_dim_type type,
4714 unsigned first, unsigned n);
4715 __isl_give isl_map *
4716 isl_map_drop_constraints_involving_dims(
4717 __isl_take isl_map *map,
4718 enum isl_dim_type type,
4719 unsigned first, unsigned n);
4721 These functions drop any constraints (not) involving the specified dimensions.
4722 Note that the result depends on the representation of the input.
4724 #include <isl/polynomial.h>
4725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4726 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4727 __isl_give isl_union_pw_qpolynomial *
4728 isl_union_pw_qpolynomial_to_polynomial(
4729 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4731 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4732 the polynomial will be an overapproximation. If C<sign> is negative,
4733 it will be an underapproximation. If C<sign> is zero, the approximation
4734 will lie somewhere in between.
4738 __isl_give isl_basic_set *isl_basic_set_sample(
4739 __isl_take isl_basic_set *bset);
4740 __isl_give isl_basic_set *isl_set_sample(
4741 __isl_take isl_set *set);
4742 __isl_give isl_basic_map *isl_basic_map_sample(
4743 __isl_take isl_basic_map *bmap);
4744 __isl_give isl_basic_map *isl_map_sample(
4745 __isl_take isl_map *map);
4747 If the input (basic) set or relation is non-empty, then return
4748 a singleton subset of the input. Otherwise, return an empty set.
4750 =item * Optimization
4752 #include <isl/ilp.h>
4753 __isl_give isl_val *isl_basic_set_max_val(
4754 __isl_keep isl_basic_set *bset,
4755 __isl_keep isl_aff *obj);
4756 __isl_give isl_val *isl_set_min_val(
4757 __isl_keep isl_set *set,
4758 __isl_keep isl_aff *obj);
4759 __isl_give isl_val *isl_set_max_val(
4760 __isl_keep isl_set *set,
4761 __isl_keep isl_aff *obj);
4763 Compute the minimum or maximum of the integer affine expression C<obj>
4764 over the points in C<set>, returning the result in C<opt>.
4765 The result is C<NULL> in case of an error, the optimal value in case
4766 there is one, negative infinity or infinity if the problem is unbounded and
4767 NaN if the problem is empty.
4769 =item * Parametric optimization
4771 __isl_give isl_pw_aff *isl_set_dim_min(
4772 __isl_take isl_set *set, int pos);
4773 __isl_give isl_pw_aff *isl_set_dim_max(
4774 __isl_take isl_set *set, int pos);
4775 __isl_give isl_pw_aff *isl_map_dim_max(
4776 __isl_take isl_map *map, int pos);
4778 Compute the minimum or maximum of the given set or output dimension
4779 as a function of the parameters (and input dimensions), but independently
4780 of the other set or output dimensions.
4781 For lexicographic optimization, see L<"Lexicographic Optimization">.
4785 The following functions compute either the set of (rational) coefficient
4786 values of valid constraints for the given set or the set of (rational)
4787 values satisfying the constraints with coefficients from the given set.
4788 Internally, these two sets of functions perform essentially the
4789 same operations, except that the set of coefficients is assumed to
4790 be a cone, while the set of values may be any polyhedron.
4791 The current implementation is based on the Farkas lemma and
4792 Fourier-Motzkin elimination, but this may change or be made optional
4793 in future. In particular, future implementations may use different
4794 dualization algorithms or skip the elimination step.
4796 __isl_give isl_basic_set *isl_basic_set_coefficients(
4797 __isl_take isl_basic_set *bset);
4798 __isl_give isl_basic_set *isl_set_coefficients(
4799 __isl_take isl_set *set);
4800 __isl_give isl_union_set *isl_union_set_coefficients(
4801 __isl_take isl_union_set *bset);
4802 __isl_give isl_basic_set *isl_basic_set_solutions(
4803 __isl_take isl_basic_set *bset);
4804 __isl_give isl_basic_set *isl_set_solutions(
4805 __isl_take isl_set *set);
4806 __isl_give isl_union_set *isl_union_set_solutions(
4807 __isl_take isl_union_set *bset);
4811 __isl_give isl_map *isl_map_fixed_power_val(
4812 __isl_take isl_map *map,
4813 __isl_take isl_val *exp);
4814 __isl_give isl_union_map *
4815 isl_union_map_fixed_power_val(
4816 __isl_take isl_union_map *umap,
4817 __isl_take isl_val *exp);
4819 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4820 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4821 of C<map> is computed.
4823 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4825 __isl_give isl_union_map *isl_union_map_power(
4826 __isl_take isl_union_map *umap, int *exact);
4828 Compute a parametric representation for all positive powers I<k> of C<map>.
4829 The result maps I<k> to a nested relation corresponding to the
4830 I<k>th power of C<map>.
4831 The result may be an overapproximation. If the result is known to be exact,
4832 then C<*exact> is set to C<1>.
4834 =item * Transitive closure
4836 __isl_give isl_map *isl_map_transitive_closure(
4837 __isl_take isl_map *map, int *exact);
4838 __isl_give isl_union_map *isl_union_map_transitive_closure(
4839 __isl_take isl_union_map *umap, int *exact);
4841 Compute the transitive closure of C<map>.
4842 The result may be an overapproximation. If the result is known to be exact,
4843 then C<*exact> is set to C<1>.
4845 =item * Reaching path lengths
4847 __isl_give isl_map *isl_map_reaching_path_lengths(
4848 __isl_take isl_map *map, int *exact);
4850 Compute a relation that maps each element in the range of C<map>
4851 to the lengths of all paths composed of edges in C<map> that
4852 end up in the given element.
4853 The result may be an overapproximation. If the result is known to be exact,
4854 then C<*exact> is set to C<1>.
4855 To compute the I<maximal> path length, the resulting relation
4856 should be postprocessed by C<isl_map_lexmax>.
4857 In particular, if the input relation is a dependence relation
4858 (mapping sources to sinks), then the maximal path length corresponds
4859 to the free schedule.
4860 Note, however, that C<isl_map_lexmax> expects the maximum to be
4861 finite, so if the path lengths are unbounded (possibly due to
4862 the overapproximation), then you will get an error message.
4866 #include <isl/space.h>
4867 __isl_give isl_space *isl_space_wrap(
4868 __isl_take isl_space *space);
4869 __isl_give isl_space *isl_space_unwrap(
4870 __isl_take isl_space *space);
4872 #include <isl/local_space.h>
4873 __isl_give isl_local_space *isl_local_space_wrap(
4874 __isl_take isl_local_space *ls);
4876 #include <isl/set.h>
4877 __isl_give isl_basic_map *isl_basic_set_unwrap(
4878 __isl_take isl_basic_set *bset);
4879 __isl_give isl_map *isl_set_unwrap(
4880 __isl_take isl_set *set);
4882 #include <isl/map.h>
4883 __isl_give isl_basic_set *isl_basic_map_wrap(
4884 __isl_take isl_basic_map *bmap);
4885 __isl_give isl_set *isl_map_wrap(
4886 __isl_take isl_map *map);
4888 #include <isl/union_set.h>
4889 __isl_give isl_union_map *isl_union_set_unwrap(
4890 __isl_take isl_union_set *uset);
4892 #include <isl/union_map.h>
4893 __isl_give isl_union_set *isl_union_map_wrap(
4894 __isl_take isl_union_map *umap);
4896 The input to C<isl_space_unwrap> should
4897 be the space of a set, while that of
4898 C<isl_space_wrap> should be the space of a relation.
4899 Conversely, the output of C<isl_space_unwrap> is the space
4900 of a relation, while that of C<isl_space_wrap> is the space of a set.
4904 Remove any internal structure of domain (and range) of the given
4905 set or relation. If there is any such internal structure in the input,
4906 then the name of the space is also removed.
4908 #include <isl/local_space.h>
4909 __isl_give isl_local_space *
4910 isl_local_space_flatten_domain(
4911 __isl_take isl_local_space *ls);
4912 __isl_give isl_local_space *
4913 isl_local_space_flatten_range(
4914 __isl_take isl_local_space *ls);
4916 #include <isl/set.h>
4917 __isl_give isl_basic_set *isl_basic_set_flatten(
4918 __isl_take isl_basic_set *bset);
4919 __isl_give isl_set *isl_set_flatten(
4920 __isl_take isl_set *set);
4922 #include <isl/map.h>
4923 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4924 __isl_take isl_basic_map *bmap);
4925 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4926 __isl_take isl_basic_map *bmap);
4927 __isl_give isl_map *isl_map_flatten_range(
4928 __isl_take isl_map *map);
4929 __isl_give isl_map *isl_map_flatten_domain(
4930 __isl_take isl_map *map);
4931 __isl_give isl_basic_map *isl_basic_map_flatten(
4932 __isl_take isl_basic_map *bmap);
4933 __isl_give isl_map *isl_map_flatten(
4934 __isl_take isl_map *map);
4936 #include <isl/val.h>
4937 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4938 __isl_take isl_multi_val *mv);
4940 #include <isl/aff.h>
4941 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4942 __isl_take isl_multi_aff *ma);
4943 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4944 __isl_take isl_multi_aff *ma);
4945 __isl_give isl_multi_pw_aff *
4946 isl_multi_pw_aff_flatten_range(
4947 __isl_take isl_multi_pw_aff *mpa);
4948 __isl_give isl_multi_union_pw_aff *
4949 isl_multi_union_pw_aff_flatten_range(
4950 __isl_take isl_multi_union_pw_aff *mupa);
4952 #include <isl/map.h>
4953 __isl_give isl_map *isl_set_flatten_map(
4954 __isl_take isl_set *set);
4956 The function above constructs a relation
4957 that maps the input set to a flattened version of the set.
4961 Lift the input set to a space with extra dimensions corresponding
4962 to the existentially quantified variables in the input.
4963 In particular, the result lives in a wrapped map where the domain
4964 is the original space and the range corresponds to the original
4965 existentially quantified variables.
4967 #include <isl/set.h>
4968 __isl_give isl_basic_set *isl_basic_set_lift(
4969 __isl_take isl_basic_set *bset);
4970 __isl_give isl_set *isl_set_lift(
4971 __isl_take isl_set *set);
4972 __isl_give isl_union_set *isl_union_set_lift(
4973 __isl_take isl_union_set *uset);
4975 Given a local space that contains the existentially quantified
4976 variables of a set, a basic relation that, when applied to
4977 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4978 can be constructed using the following function.
4980 #include <isl/local_space.h>
4981 __isl_give isl_basic_map *isl_local_space_lifting(
4982 __isl_take isl_local_space *ls);
4984 #include <isl/aff.h>
4985 __isl_give isl_multi_aff *isl_multi_aff_lift(
4986 __isl_take isl_multi_aff *maff,
4987 __isl_give isl_local_space **ls);
4989 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4990 then it is assigned the local space that lies at the basis of
4991 the lifting applied.
4993 =item * Internal Product
4995 #include <isl/space.h>
4996 __isl_give isl_space *isl_space_zip(
4997 __isl_take isl_space *space);
4999 #include <isl/map.h>
5000 __isl_give isl_basic_map *isl_basic_map_zip(
5001 __isl_take isl_basic_map *bmap);
5002 __isl_give isl_map *isl_map_zip(
5003 __isl_take isl_map *map);
5005 #include <isl/union_map.h>
5006 __isl_give isl_union_map *isl_union_map_zip(
5007 __isl_take isl_union_map *umap);
5009 Given a relation with nested relations for domain and range,
5010 interchange the range of the domain with the domain of the range.
5014 #include <isl/space.h>
5015 __isl_give isl_space *isl_space_curry(
5016 __isl_take isl_space *space);
5017 __isl_give isl_space *isl_space_uncurry(
5018 __isl_take isl_space *space);
5020 #include <isl/map.h>
5021 __isl_give isl_basic_map *isl_basic_map_curry(
5022 __isl_take isl_basic_map *bmap);
5023 __isl_give isl_basic_map *isl_basic_map_uncurry(
5024 __isl_take isl_basic_map *bmap);
5025 __isl_give isl_map *isl_map_curry(
5026 __isl_take isl_map *map);
5027 __isl_give isl_map *isl_map_uncurry(
5028 __isl_take isl_map *map);
5030 #include <isl/union_map.h>
5031 __isl_give isl_union_map *isl_union_map_curry(
5032 __isl_take isl_union_map *umap);
5033 __isl_give isl_union_map *isl_union_map_uncurry(
5034 __isl_take isl_union_map *umap);
5036 Given a relation with a nested relation for domain,
5037 the C<curry> functions
5038 move the range of the nested relation out of the domain
5039 and use it as the domain of a nested relation in the range,
5040 with the original range as range of this nested relation.
5041 The C<uncurry> functions perform the inverse operation.
5043 =item * Aligning parameters
5045 Change the order of the parameters of the given set, relation
5047 such that the first parameters match those of C<model>.
5048 This may involve the introduction of extra parameters.
5049 All parameters need to be named.
5051 #include <isl/space.h>
5052 __isl_give isl_space *isl_space_align_params(
5053 __isl_take isl_space *space1,
5054 __isl_take isl_space *space2)
5056 #include <isl/set.h>
5057 __isl_give isl_basic_set *isl_basic_set_align_params(
5058 __isl_take isl_basic_set *bset,
5059 __isl_take isl_space *model);
5060 __isl_give isl_set *isl_set_align_params(
5061 __isl_take isl_set *set,
5062 __isl_take isl_space *model);
5064 #include <isl/map.h>
5065 __isl_give isl_basic_map *isl_basic_map_align_params(
5066 __isl_take isl_basic_map *bmap,
5067 __isl_take isl_space *model);
5068 __isl_give isl_map *isl_map_align_params(
5069 __isl_take isl_map *map,
5070 __isl_take isl_space *model);
5072 #include <isl/val.h>
5073 __isl_give isl_multi_val *isl_multi_val_align_params(
5074 __isl_take isl_multi_val *mv,
5075 __isl_take isl_space *model);
5077 #include <isl/aff.h>
5078 __isl_give isl_aff *isl_aff_align_params(
5079 __isl_take isl_aff *aff,
5080 __isl_take isl_space *model);
5081 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5082 __isl_take isl_multi_aff *multi,
5083 __isl_take isl_space *model);
5084 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5085 __isl_take isl_pw_aff *pwaff,
5086 __isl_take isl_space *model);
5087 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5088 __isl_take isl_pw_multi_aff *pma,
5089 __isl_take isl_space *model);
5090 __isl_give isl_union_pw_aff *
5091 isl_union_pw_aff_align_params(
5092 __isl_take isl_union_pw_aff *upa,
5093 __isl_take isl_space *model);
5094 __isl_give isl_union_pw_multi_aff *
5095 isl_union_pw_multi_aff_align_params(
5096 __isl_take isl_union_pw_multi_aff *upma,
5097 __isl_take isl_space *model);
5098 __isl_give isl_multi_union_pw_aff *
5099 isl_multi_union_pw_aff_align_params(
5100 __isl_take isl_multi_union_pw_aff *mupa,
5101 __isl_take isl_space *model);
5103 #include <isl/polynomial.h>
5104 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5105 __isl_take isl_qpolynomial *qp,
5106 __isl_take isl_space *model);
5108 =item * Unary Arithmethic Operations
5110 #include <isl/val.h>
5111 __isl_give isl_multi_val *isl_multi_val_neg(
5112 __isl_take isl_multi_val *mv);
5114 #include <isl/aff.h>
5115 __isl_give isl_aff *isl_aff_neg(
5116 __isl_take isl_aff *aff);
5117 __isl_give isl_multi_aff *isl_multi_aff_neg(
5118 __isl_take isl_multi_aff *ma);
5119 __isl_give isl_pw_aff *isl_pw_aff_neg(
5120 __isl_take isl_pw_aff *pwaff);
5121 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5122 __isl_take isl_pw_multi_aff *pma);
5123 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5124 __isl_take isl_multi_pw_aff *mpa);
5125 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5126 __isl_take isl_union_pw_aff *upa);
5127 __isl_give isl_union_pw_multi_aff *
5128 isl_union_pw_multi_aff_neg(
5129 __isl_take isl_union_pw_multi_aff *upma);
5130 __isl_give isl_multi_union_pw_aff *
5131 isl_multi_union_pw_aff_neg(
5132 __isl_take isl_multi_union_pw_aff *mupa);
5133 __isl_give isl_aff *isl_aff_ceil(
5134 __isl_take isl_aff *aff);
5135 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5136 __isl_take isl_pw_aff *pwaff);
5137 __isl_give isl_aff *isl_aff_floor(
5138 __isl_take isl_aff *aff);
5139 __isl_give isl_multi_aff *isl_multi_aff_floor(
5140 __isl_take isl_multi_aff *ma);
5141 __isl_give isl_pw_aff *isl_pw_aff_floor(
5142 __isl_take isl_pw_aff *pwaff);
5143 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5144 __isl_take isl_union_pw_aff *upa);
5145 __isl_give isl_multi_union_pw_aff *
5146 isl_multi_union_pw_aff_floor(
5147 __isl_take isl_multi_union_pw_aff *mupa);
5149 #include <isl/aff.h>
5150 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5151 __isl_take isl_pw_aff_list *list);
5152 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5153 __isl_take isl_pw_aff_list *list);
5155 #include <isl/polynomial.h>
5156 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5157 __isl_take isl_qpolynomial *qp);
5158 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5159 __isl_take isl_pw_qpolynomial *pwqp);
5160 __isl_give isl_union_pw_qpolynomial *
5161 isl_union_pw_qpolynomial_neg(
5162 __isl_take isl_union_pw_qpolynomial *upwqp);
5163 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5164 __isl_take isl_qpolynomial *qp,
5166 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5167 __isl_take isl_pw_qpolynomial *pwqp,
5172 The following functions evaluate a function in a point.
5174 #include <isl/polynomial.h>
5175 __isl_give isl_val *isl_pw_qpolynomial_eval(
5176 __isl_take isl_pw_qpolynomial *pwqp,
5177 __isl_take isl_point *pnt);
5178 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5179 __isl_take isl_pw_qpolynomial_fold *pwf,
5180 __isl_take isl_point *pnt);
5181 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5182 __isl_take isl_union_pw_qpolynomial *upwqp,
5183 __isl_take isl_point *pnt);
5184 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5185 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5186 __isl_take isl_point *pnt);
5188 =item * Dimension manipulation
5190 It is usually not advisable to directly change the (input or output)
5191 space of a set or a relation as this removes the name and the internal
5192 structure of the space. However, the functions below can be useful
5193 to add new parameters, assuming
5194 C<isl_set_align_params> and C<isl_map_align_params>
5197 #include <isl/space.h>
5198 __isl_give isl_space *isl_space_add_dims(
5199 __isl_take isl_space *space,
5200 enum isl_dim_type type, unsigned n);
5201 __isl_give isl_space *isl_space_insert_dims(
5202 __isl_take isl_space *space,
5203 enum isl_dim_type type, unsigned pos, unsigned n);
5204 __isl_give isl_space *isl_space_drop_dims(
5205 __isl_take isl_space *space,
5206 enum isl_dim_type type, unsigned first, unsigned n);
5207 __isl_give isl_space *isl_space_move_dims(
5208 __isl_take isl_space *space,
5209 enum isl_dim_type dst_type, unsigned dst_pos,
5210 enum isl_dim_type src_type, unsigned src_pos,
5213 #include <isl/local_space.h>
5214 __isl_give isl_local_space *isl_local_space_add_dims(
5215 __isl_take isl_local_space *ls,
5216 enum isl_dim_type type, unsigned n);
5217 __isl_give isl_local_space *isl_local_space_insert_dims(
5218 __isl_take isl_local_space *ls,
5219 enum isl_dim_type type, unsigned first, unsigned n);
5220 __isl_give isl_local_space *isl_local_space_drop_dims(
5221 __isl_take isl_local_space *ls,
5222 enum isl_dim_type type, unsigned first, unsigned n);
5224 #include <isl/set.h>
5225 __isl_give isl_basic_set *isl_basic_set_add_dims(
5226 __isl_take isl_basic_set *bset,
5227 enum isl_dim_type type, unsigned n);
5228 __isl_give isl_set *isl_set_add_dims(
5229 __isl_take isl_set *set,
5230 enum isl_dim_type type, unsigned n);
5231 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5232 __isl_take isl_basic_set *bset,
5233 enum isl_dim_type type, unsigned pos,
5235 __isl_give isl_set *isl_set_insert_dims(
5236 __isl_take isl_set *set,
5237 enum isl_dim_type type, unsigned pos, unsigned n);
5238 __isl_give isl_basic_set *isl_basic_set_move_dims(
5239 __isl_take isl_basic_set *bset,
5240 enum isl_dim_type dst_type, unsigned dst_pos,
5241 enum isl_dim_type src_type, unsigned src_pos,
5243 __isl_give isl_set *isl_set_move_dims(
5244 __isl_take isl_set *set,
5245 enum isl_dim_type dst_type, unsigned dst_pos,
5246 enum isl_dim_type src_type, unsigned src_pos,
5249 #include <isl/map.h>
5250 __isl_give isl_basic_map *isl_basic_map_add_dims(
5251 __isl_take isl_basic_map *bmap,
5252 enum isl_dim_type type, unsigned n);
5253 __isl_give isl_map *isl_map_add_dims(
5254 __isl_take isl_map *map,
5255 enum isl_dim_type type, unsigned n);
5256 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5257 __isl_take isl_basic_map *bmap,
5258 enum isl_dim_type type, unsigned pos,
5260 __isl_give isl_map *isl_map_insert_dims(
5261 __isl_take isl_map *map,
5262 enum isl_dim_type type, unsigned pos, unsigned n);
5263 __isl_give isl_basic_map *isl_basic_map_move_dims(
5264 __isl_take isl_basic_map *bmap,
5265 enum isl_dim_type dst_type, unsigned dst_pos,
5266 enum isl_dim_type src_type, unsigned src_pos,
5268 __isl_give isl_map *isl_map_move_dims(
5269 __isl_take isl_map *map,
5270 enum isl_dim_type dst_type, unsigned dst_pos,
5271 enum isl_dim_type src_type, unsigned src_pos,
5274 #include <isl/val.h>
5275 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5276 __isl_take isl_multi_val *mv,
5277 enum isl_dim_type type, unsigned first, unsigned n);
5278 __isl_give isl_multi_val *isl_multi_val_add_dims(
5279 __isl_take isl_multi_val *mv,
5280 enum isl_dim_type type, unsigned n);
5281 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5282 __isl_take isl_multi_val *mv,
5283 enum isl_dim_type type, unsigned first, unsigned n);
5285 #include <isl/aff.h>
5286 __isl_give isl_aff *isl_aff_insert_dims(
5287 __isl_take isl_aff *aff,
5288 enum isl_dim_type type, unsigned first, unsigned n);
5289 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5290 __isl_take isl_multi_aff *ma,
5291 enum isl_dim_type type, unsigned first, unsigned n);
5292 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5293 __isl_take isl_pw_aff *pwaff,
5294 enum isl_dim_type type, unsigned first, unsigned n);
5295 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5296 __isl_take isl_multi_pw_aff *mpa,
5297 enum isl_dim_type type, unsigned first, unsigned n);
5298 __isl_give isl_aff *isl_aff_add_dims(
5299 __isl_take isl_aff *aff,
5300 enum isl_dim_type type, unsigned n);
5301 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5302 __isl_take isl_multi_aff *ma,
5303 enum isl_dim_type type, unsigned n);
5304 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5305 __isl_take isl_pw_aff *pwaff,
5306 enum isl_dim_type type, unsigned n);
5307 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5308 __isl_take isl_multi_pw_aff *mpa,
5309 enum isl_dim_type type, unsigned n);
5310 __isl_give isl_aff *isl_aff_drop_dims(
5311 __isl_take isl_aff *aff,
5312 enum isl_dim_type type, unsigned first, unsigned n);
5313 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5314 __isl_take isl_multi_aff *maff,
5315 enum isl_dim_type type, unsigned first, unsigned n);
5316 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5317 __isl_take isl_pw_aff *pwaff,
5318 enum isl_dim_type type, unsigned first, unsigned n);
5319 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5320 __isl_take isl_pw_multi_aff *pma,
5321 enum isl_dim_type type, unsigned first, unsigned n);
5322 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5323 __isl_take isl_union_pw_aff *upa,
5324 enum isl_dim_type type, unsigned first, unsigned n);
5325 __isl_give isl_union_pw_multi_aff *
5326 isl_union_pw_multi_aff_drop_dims(
5327 __isl_take isl_union_pw_multi_aff *upma,
5328 enum isl_dim_type type,
5329 unsigned first, unsigned n);
5330 __isl_give isl_multi_union_pw_aff *
5331 isl_multi_union_pw_aff_drop_dims(
5332 __isl_take isl_multi_union_pw_aff *mupa,
5333 enum isl_dim_type type, unsigned first,
5335 __isl_give isl_aff *isl_aff_move_dims(
5336 __isl_take isl_aff *aff,
5337 enum isl_dim_type dst_type, unsigned dst_pos,
5338 enum isl_dim_type src_type, unsigned src_pos,
5340 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5341 __isl_take isl_multi_aff *ma,
5342 enum isl_dim_type dst_type, unsigned dst_pos,
5343 enum isl_dim_type src_type, unsigned src_pos,
5345 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5346 __isl_take isl_pw_aff *pa,
5347 enum isl_dim_type dst_type, unsigned dst_pos,
5348 enum isl_dim_type src_type, unsigned src_pos,
5350 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5351 __isl_take isl_multi_pw_aff *pma,
5352 enum isl_dim_type dst_type, unsigned dst_pos,
5353 enum isl_dim_type src_type, unsigned src_pos,
5356 #include <isl/polynomial.h>
5357 __isl_give isl_union_pw_qpolynomial *
5358 isl_union_pw_qpolynomial_drop_dims(
5359 __isl_take isl_union_pw_qpolynomial *upwqp,
5360 enum isl_dim_type type,
5361 unsigned first, unsigned n);
5362 __isl_give isl_union_pw_qpolynomial_fold *
5363 isl_union_pw_qpolynomial_fold_drop_dims(
5364 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5365 enum isl_dim_type type,
5366 unsigned first, unsigned n);
5368 The operations on union expressions can only manipulate parameters.
5372 =head2 Binary Operations
5374 The two arguments of a binary operation not only need to live
5375 in the same C<isl_ctx>, they currently also need to have
5376 the same (number of) parameters.
5378 =head3 Basic Operations
5382 =item * Intersection
5384 #include <isl/local_space.h>
5385 __isl_give isl_local_space *isl_local_space_intersect(
5386 __isl_take isl_local_space *ls1,
5387 __isl_take isl_local_space *ls2);
5389 #include <isl/set.h>
5390 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5391 __isl_take isl_basic_set *bset1,
5392 __isl_take isl_basic_set *bset2);
5393 __isl_give isl_basic_set *isl_basic_set_intersect(
5394 __isl_take isl_basic_set *bset1,
5395 __isl_take isl_basic_set *bset2);
5396 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5397 __isl_take struct isl_basic_set_list *list);
5398 __isl_give isl_set *isl_set_intersect_params(
5399 __isl_take isl_set *set,
5400 __isl_take isl_set *params);
5401 __isl_give isl_set *isl_set_intersect(
5402 __isl_take isl_set *set1,
5403 __isl_take isl_set *set2);
5405 #include <isl/map.h>
5406 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5407 __isl_take isl_basic_map *bmap,
5408 __isl_take isl_basic_set *bset);
5409 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5410 __isl_take isl_basic_map *bmap,
5411 __isl_take isl_basic_set *bset);
5412 __isl_give isl_basic_map *isl_basic_map_intersect(
5413 __isl_take isl_basic_map *bmap1,
5414 __isl_take isl_basic_map *bmap2);
5415 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5416 __isl_take isl_basic_map_list *list);
5417 __isl_give isl_map *isl_map_intersect_params(
5418 __isl_take isl_map *map,
5419 __isl_take isl_set *params);
5420 __isl_give isl_map *isl_map_intersect_domain(
5421 __isl_take isl_map *map,
5422 __isl_take isl_set *set);
5423 __isl_give isl_map *isl_map_intersect_range(
5424 __isl_take isl_map *map,
5425 __isl_take isl_set *set);
5426 __isl_give isl_map *isl_map_intersect(
5427 __isl_take isl_map *map1,
5428 __isl_take isl_map *map2);
5430 #include <isl/union_set.h>
5431 __isl_give isl_union_set *isl_union_set_intersect_params(
5432 __isl_take isl_union_set *uset,
5433 __isl_take isl_set *set);
5434 __isl_give isl_union_set *isl_union_set_intersect(
5435 __isl_take isl_union_set *uset1,
5436 __isl_take isl_union_set *uset2);
5438 #include <isl/union_map.h>
5439 __isl_give isl_union_map *isl_union_map_intersect_params(
5440 __isl_take isl_union_map *umap,
5441 __isl_take isl_set *set);
5442 __isl_give isl_union_map *isl_union_map_intersect_domain(
5443 __isl_take isl_union_map *umap,
5444 __isl_take isl_union_set *uset);
5445 __isl_give isl_union_map *isl_union_map_intersect_range(
5446 __isl_take isl_union_map *umap,
5447 __isl_take isl_union_set *uset);
5448 __isl_give isl_union_map *isl_union_map_intersect(
5449 __isl_take isl_union_map *umap1,
5450 __isl_take isl_union_map *umap2);
5452 #include <isl/aff.h>
5453 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5454 __isl_take isl_pw_aff *pa,
5455 __isl_take isl_set *set);
5456 __isl_give isl_multi_pw_aff *
5457 isl_multi_pw_aff_intersect_domain(
5458 __isl_take isl_multi_pw_aff *mpa,
5459 __isl_take isl_set *domain);
5460 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5461 __isl_take isl_pw_multi_aff *pma,
5462 __isl_take isl_set *set);
5463 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5464 __isl_take isl_union_pw_aff *upa,
5465 __isl_take isl_union_set *uset);
5466 __isl_give isl_union_pw_multi_aff *
5467 isl_union_pw_multi_aff_intersect_domain(
5468 __isl_take isl_union_pw_multi_aff *upma,
5469 __isl_take isl_union_set *uset);
5470 __isl_give isl_multi_union_pw_aff *
5471 isl_multi_union_pw_aff_intersect_domain(
5472 __isl_take isl_multi_union_pw_aff *mupa,
5473 __isl_take isl_union_set *uset);
5474 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5475 __isl_take isl_pw_aff *pa,
5476 __isl_take isl_set *set);
5477 __isl_give isl_multi_pw_aff *
5478 isl_multi_pw_aff_intersect_params(
5479 __isl_take isl_multi_pw_aff *mpa,
5480 __isl_take isl_set *set);
5481 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5482 __isl_take isl_pw_multi_aff *pma,
5483 __isl_take isl_set *set);
5484 __isl_give isl_union_pw_aff *
5485 isl_union_pw_aff_intersect_params(
5486 __isl_take isl_union_pw_aff *upa,
5487 __isl_give isl_union_pw_multi_aff *
5488 isl_union_pw_multi_aff_intersect_params(
5489 __isl_take isl_union_pw_multi_aff *upma,
5490 __isl_take isl_set *set);
5491 __isl_give isl_multi_union_pw_aff *
5492 isl_multi_union_pw_aff_intersect_params(
5493 __isl_take isl_multi_union_pw_aff *mupa,
5494 __isl_take isl_set *params);
5495 isl_multi_union_pw_aff_intersect_range(
5496 __isl_take isl_multi_union_pw_aff *mupa,
5497 __isl_take isl_set *set);
5499 #include <isl/polynomial.h>
5500 __isl_give isl_pw_qpolynomial *
5501 isl_pw_qpolynomial_intersect_domain(
5502 __isl_take isl_pw_qpolynomial *pwpq,
5503 __isl_take isl_set *set);
5504 __isl_give isl_union_pw_qpolynomial *
5505 isl_union_pw_qpolynomial_intersect_domain(
5506 __isl_take isl_union_pw_qpolynomial *upwpq,
5507 __isl_take isl_union_set *uset);
5508 __isl_give isl_union_pw_qpolynomial_fold *
5509 isl_union_pw_qpolynomial_fold_intersect_domain(
5510 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5511 __isl_take isl_union_set *uset);
5512 __isl_give isl_pw_qpolynomial *
5513 isl_pw_qpolynomial_intersect_params(
5514 __isl_take isl_pw_qpolynomial *pwpq,
5515 __isl_take isl_set *set);
5516 __isl_give isl_pw_qpolynomial_fold *
5517 isl_pw_qpolynomial_fold_intersect_params(
5518 __isl_take isl_pw_qpolynomial_fold *pwf,
5519 __isl_take isl_set *set);
5520 __isl_give isl_union_pw_qpolynomial *
5521 isl_union_pw_qpolynomial_intersect_params(
5522 __isl_take isl_union_pw_qpolynomial *upwpq,
5523 __isl_take isl_set *set);
5524 __isl_give isl_union_pw_qpolynomial_fold *
5525 isl_union_pw_qpolynomial_fold_intersect_params(
5526 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5527 __isl_take isl_set *set);
5529 The second argument to the C<_params> functions needs to be
5530 a parametric (basic) set. For the other functions, a parametric set
5531 for either argument is only allowed if the other argument is
5532 a parametric set as well.
5533 The list passed to C<isl_basic_set_list_intersect> needs to have
5534 at least one element and all elements need to live in the same space.
5535 The function C<isl_multi_union_pw_aff_intersect_range>
5536 restricts the input function to those shared domain elements
5537 that map to the specified range.
5541 #include <isl/set.h>
5542 __isl_give isl_set *isl_basic_set_union(
5543 __isl_take isl_basic_set *bset1,
5544 __isl_take isl_basic_set *bset2);
5545 __isl_give isl_set *isl_set_union(
5546 __isl_take isl_set *set1,
5547 __isl_take isl_set *set2);
5549 #include <isl/map.h>
5550 __isl_give isl_map *isl_basic_map_union(
5551 __isl_take isl_basic_map *bmap1,
5552 __isl_take isl_basic_map *bmap2);
5553 __isl_give isl_map *isl_map_union(
5554 __isl_take isl_map *map1,
5555 __isl_take isl_map *map2);
5557 #include <isl/union_set.h>
5558 __isl_give isl_union_set *isl_union_set_union(
5559 __isl_take isl_union_set *uset1,
5560 __isl_take isl_union_set *uset2);
5561 __isl_give isl_union_set *isl_union_set_list_union(
5562 __isl_take isl_union_set_list *list);
5564 #include <isl/union_map.h>
5565 __isl_give isl_union_map *isl_union_map_union(
5566 __isl_take isl_union_map *umap1,
5567 __isl_take isl_union_map *umap2);
5569 =item * Set difference
5571 #include <isl/set.h>
5572 __isl_give isl_set *isl_set_subtract(
5573 __isl_take isl_set *set1,
5574 __isl_take isl_set *set2);
5576 #include <isl/map.h>
5577 __isl_give isl_map *isl_map_subtract(
5578 __isl_take isl_map *map1,
5579 __isl_take isl_map *map2);
5580 __isl_give isl_map *isl_map_subtract_domain(
5581 __isl_take isl_map *map,
5582 __isl_take isl_set *dom);
5583 __isl_give isl_map *isl_map_subtract_range(
5584 __isl_take isl_map *map,
5585 __isl_take isl_set *dom);
5587 #include <isl/union_set.h>
5588 __isl_give isl_union_set *isl_union_set_subtract(
5589 __isl_take isl_union_set *uset1,
5590 __isl_take isl_union_set *uset2);
5592 #include <isl/union_map.h>
5593 __isl_give isl_union_map *isl_union_map_subtract(
5594 __isl_take isl_union_map *umap1,
5595 __isl_take isl_union_map *umap2);
5596 __isl_give isl_union_map *isl_union_map_subtract_domain(
5597 __isl_take isl_union_map *umap,
5598 __isl_take isl_union_set *dom);
5599 __isl_give isl_union_map *isl_union_map_subtract_range(
5600 __isl_take isl_union_map *umap,
5601 __isl_take isl_union_set *dom);
5603 #include <isl/aff.h>
5604 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5605 __isl_take isl_pw_aff *pa,
5606 __isl_take isl_set *set);
5607 __isl_give isl_pw_multi_aff *
5608 isl_pw_multi_aff_subtract_domain(
5609 __isl_take isl_pw_multi_aff *pma,
5610 __isl_take isl_set *set);
5611 __isl_give isl_union_pw_aff *
5612 isl_union_pw_aff_subtract_domain(
5613 __isl_take isl_union_pw_aff *upa,
5614 __isl_take isl_union_set *uset);
5615 __isl_give isl_union_pw_multi_aff *
5616 isl_union_pw_multi_aff_subtract_domain(
5617 __isl_take isl_union_pw_multi_aff *upma,
5618 __isl_take isl_set *set);
5620 #include <isl/polynomial.h>
5621 __isl_give isl_pw_qpolynomial *
5622 isl_pw_qpolynomial_subtract_domain(
5623 __isl_take isl_pw_qpolynomial *pwpq,
5624 __isl_take isl_set *set);
5625 __isl_give isl_pw_qpolynomial_fold *
5626 isl_pw_qpolynomial_fold_subtract_domain(
5627 __isl_take isl_pw_qpolynomial_fold *pwf,
5628 __isl_take isl_set *set);
5629 __isl_give isl_union_pw_qpolynomial *
5630 isl_union_pw_qpolynomial_subtract_domain(
5631 __isl_take isl_union_pw_qpolynomial *upwpq,
5632 __isl_take isl_union_set *uset);
5633 __isl_give isl_union_pw_qpolynomial_fold *
5634 isl_union_pw_qpolynomial_fold_subtract_domain(
5635 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5636 __isl_take isl_union_set *uset);
5640 #include <isl/space.h>
5641 __isl_give isl_space *isl_space_join(
5642 __isl_take isl_space *left,
5643 __isl_take isl_space *right);
5645 #include <isl/map.h>
5646 __isl_give isl_basic_set *isl_basic_set_apply(
5647 __isl_take isl_basic_set *bset,
5648 __isl_take isl_basic_map *bmap);
5649 __isl_give isl_set *isl_set_apply(
5650 __isl_take isl_set *set,
5651 __isl_take isl_map *map);
5652 __isl_give isl_union_set *isl_union_set_apply(
5653 __isl_take isl_union_set *uset,
5654 __isl_take isl_union_map *umap);
5655 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5656 __isl_take isl_basic_map *bmap1,
5657 __isl_take isl_basic_map *bmap2);
5658 __isl_give isl_basic_map *isl_basic_map_apply_range(
5659 __isl_take isl_basic_map *bmap1,
5660 __isl_take isl_basic_map *bmap2);
5661 __isl_give isl_map *isl_map_apply_domain(
5662 __isl_take isl_map *map1,
5663 __isl_take isl_map *map2);
5664 __isl_give isl_map *isl_map_apply_range(
5665 __isl_take isl_map *map1,
5666 __isl_take isl_map *map2);
5668 #include <isl/union_map.h>
5669 __isl_give isl_union_map *isl_union_map_apply_domain(
5670 __isl_take isl_union_map *umap1,
5671 __isl_take isl_union_map *umap2);
5672 __isl_give isl_union_map *isl_union_map_apply_range(
5673 __isl_take isl_union_map *umap1,
5674 __isl_take isl_union_map *umap2);
5676 #include <isl/aff.h>
5677 __isl_give isl_union_pw_aff *
5678 isl_multi_union_pw_aff_apply_aff(
5679 __isl_take isl_multi_union_pw_aff *mupa,
5680 __isl_take isl_aff *aff);
5681 __isl_give isl_union_pw_aff *
5682 isl_multi_union_pw_aff_apply_pw_aff(
5683 __isl_take isl_multi_union_pw_aff *mupa,
5684 __isl_take isl_pw_aff *pa);
5685 __isl_give isl_multi_union_pw_aff *
5686 isl_multi_union_pw_aff_apply_multi_aff(
5687 __isl_take isl_multi_union_pw_aff *mupa,
5688 __isl_take isl_multi_aff *ma);
5689 __isl_give isl_multi_union_pw_aff *
5690 isl_multi_union_pw_aff_apply_pw_multi_aff(
5691 __isl_take isl_multi_union_pw_aff *mupa,
5692 __isl_take isl_pw_multi_aff *pma);
5694 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5695 over the shared domain of the elements of the input. The dimension is
5696 required to be greater than zero.
5697 The C<isl_multi_union_pw_aff> argument of
5698 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5699 but only if the range of the C<isl_multi_aff> argument
5700 is also zero-dimensional.
5701 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5703 #include <isl/polynomial.h>
5704 __isl_give isl_pw_qpolynomial_fold *
5705 isl_set_apply_pw_qpolynomial_fold(
5706 __isl_take isl_set *set,
5707 __isl_take isl_pw_qpolynomial_fold *pwf,
5709 __isl_give isl_pw_qpolynomial_fold *
5710 isl_map_apply_pw_qpolynomial_fold(
5711 __isl_take isl_map *map,
5712 __isl_take isl_pw_qpolynomial_fold *pwf,
5714 __isl_give isl_union_pw_qpolynomial_fold *
5715 isl_union_set_apply_union_pw_qpolynomial_fold(
5716 __isl_take isl_union_set *uset,
5717 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5719 __isl_give isl_union_pw_qpolynomial_fold *
5720 isl_union_map_apply_union_pw_qpolynomial_fold(
5721 __isl_take isl_union_map *umap,
5722 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5725 The functions taking a map
5726 compose the given map with the given piecewise quasipolynomial reduction.
5727 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5728 over all elements in the intersection of the range of the map
5729 and the domain of the piecewise quasipolynomial reduction
5730 as a function of an element in the domain of the map.
5731 The functions taking a set compute a bound over all elements in the
5732 intersection of the set and the domain of the
5733 piecewise quasipolynomial reduction.
5737 #include <isl/set.h>
5738 __isl_give isl_basic_set *
5739 isl_basic_set_preimage_multi_aff(
5740 __isl_take isl_basic_set *bset,
5741 __isl_take isl_multi_aff *ma);
5742 __isl_give isl_set *isl_set_preimage_multi_aff(
5743 __isl_take isl_set *set,
5744 __isl_take isl_multi_aff *ma);
5745 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5746 __isl_take isl_set *set,
5747 __isl_take isl_pw_multi_aff *pma);
5748 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5749 __isl_take isl_set *set,
5750 __isl_take isl_multi_pw_aff *mpa);
5752 #include <isl/union_set.h>
5753 __isl_give isl_union_set *
5754 isl_union_set_preimage_multi_aff(
5755 __isl_take isl_union_set *uset,
5756 __isl_take isl_multi_aff *ma);
5757 __isl_give isl_union_set *
5758 isl_union_set_preimage_pw_multi_aff(
5759 __isl_take isl_union_set *uset,
5760 __isl_take isl_pw_multi_aff *pma);
5761 __isl_give isl_union_set *
5762 isl_union_set_preimage_union_pw_multi_aff(
5763 __isl_take isl_union_set *uset,
5764 __isl_take isl_union_pw_multi_aff *upma);
5766 #include <isl/map.h>
5767 __isl_give isl_basic_map *
5768 isl_basic_map_preimage_domain_multi_aff(
5769 __isl_take isl_basic_map *bmap,
5770 __isl_take isl_multi_aff *ma);
5771 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5772 __isl_take isl_map *map,
5773 __isl_take isl_multi_aff *ma);
5774 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5775 __isl_take isl_map *map,
5776 __isl_take isl_multi_aff *ma);
5777 __isl_give isl_map *
5778 isl_map_preimage_domain_pw_multi_aff(
5779 __isl_take isl_map *map,
5780 __isl_take isl_pw_multi_aff *pma);
5781 __isl_give isl_map *
5782 isl_map_preimage_range_pw_multi_aff(
5783 __isl_take isl_map *map,
5784 __isl_take isl_pw_multi_aff *pma);
5785 __isl_give isl_map *
5786 isl_map_preimage_domain_multi_pw_aff(
5787 __isl_take isl_map *map,
5788 __isl_take isl_multi_pw_aff *mpa);
5789 __isl_give isl_basic_map *
5790 isl_basic_map_preimage_range_multi_aff(
5791 __isl_take isl_basic_map *bmap,
5792 __isl_take isl_multi_aff *ma);
5794 #include <isl/union_map.h>
5795 __isl_give isl_union_map *
5796 isl_union_map_preimage_domain_multi_aff(
5797 __isl_take isl_union_map *umap,
5798 __isl_take isl_multi_aff *ma);
5799 __isl_give isl_union_map *
5800 isl_union_map_preimage_range_multi_aff(
5801 __isl_take isl_union_map *umap,
5802 __isl_take isl_multi_aff *ma);
5803 __isl_give isl_union_map *
5804 isl_union_map_preimage_domain_pw_multi_aff(
5805 __isl_take isl_union_map *umap,
5806 __isl_take isl_pw_multi_aff *pma);
5807 __isl_give isl_union_map *
5808 isl_union_map_preimage_range_pw_multi_aff(
5809 __isl_take isl_union_map *umap,
5810 __isl_take isl_pw_multi_aff *pma);
5811 __isl_give isl_union_map *
5812 isl_union_map_preimage_domain_union_pw_multi_aff(
5813 __isl_take isl_union_map *umap,
5814 __isl_take isl_union_pw_multi_aff *upma);
5815 __isl_give isl_union_map *
5816 isl_union_map_preimage_range_union_pw_multi_aff(
5817 __isl_take isl_union_map *umap,
5818 __isl_take isl_union_pw_multi_aff *upma);
5820 These functions compute the preimage of the given set or map domain/range under
5821 the given function. In other words, the expression is plugged
5822 into the set description or into the domain/range of the map.
5826 #include <isl/aff.h>
5827 __isl_give isl_aff *isl_aff_pullback_aff(
5828 __isl_take isl_aff *aff1,
5829 __isl_take isl_aff *aff2);
5830 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5831 __isl_take isl_aff *aff,
5832 __isl_take isl_multi_aff *ma);
5833 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5834 __isl_take isl_pw_aff *pa,
5835 __isl_take isl_multi_aff *ma);
5836 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5837 __isl_take isl_pw_aff *pa,
5838 __isl_take isl_pw_multi_aff *pma);
5839 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5840 __isl_take isl_pw_aff *pa,
5841 __isl_take isl_multi_pw_aff *mpa);
5842 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5843 __isl_take isl_multi_aff *ma1,
5844 __isl_take isl_multi_aff *ma2);
5845 __isl_give isl_pw_multi_aff *
5846 isl_pw_multi_aff_pullback_multi_aff(
5847 __isl_take isl_pw_multi_aff *pma,
5848 __isl_take isl_multi_aff *ma);
5849 __isl_give isl_multi_pw_aff *
5850 isl_multi_pw_aff_pullback_multi_aff(
5851 __isl_take isl_multi_pw_aff *mpa,
5852 __isl_take isl_multi_aff *ma);
5853 __isl_give isl_pw_multi_aff *
5854 isl_pw_multi_aff_pullback_pw_multi_aff(
5855 __isl_take isl_pw_multi_aff *pma1,
5856 __isl_take isl_pw_multi_aff *pma2);
5857 __isl_give isl_multi_pw_aff *
5858 isl_multi_pw_aff_pullback_pw_multi_aff(
5859 __isl_take isl_multi_pw_aff *mpa,
5860 __isl_take isl_pw_multi_aff *pma);
5861 __isl_give isl_multi_pw_aff *
5862 isl_multi_pw_aff_pullback_multi_pw_aff(
5863 __isl_take isl_multi_pw_aff *mpa1,
5864 __isl_take isl_multi_pw_aff *mpa2);
5865 __isl_give isl_union_pw_aff *
5866 isl_union_pw_aff_pullback_union_pw_multi_aff(
5867 __isl_take isl_union_pw_aff *upa,
5868 __isl_take isl_union_pw_multi_aff *upma);
5869 __isl_give isl_union_pw_multi_aff *
5870 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5871 __isl_take isl_union_pw_multi_aff *upma1,
5872 __isl_take isl_union_pw_multi_aff *upma2);
5873 __isl_give isl_multi_union_pw_aff *
5874 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
5875 __isl_take isl_multi_union_pw_aff *mupa,
5876 __isl_take isl_union_pw_multi_aff *upma);
5878 These functions precompose the first expression by the second function.
5879 In other words, the second function is plugged
5880 into the first expression.
5884 #include <isl/aff.h>
5885 __isl_give isl_basic_set *isl_aff_le_basic_set(
5886 __isl_take isl_aff *aff1,
5887 __isl_take isl_aff *aff2);
5888 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5889 __isl_take isl_aff *aff1,
5890 __isl_take isl_aff *aff2);
5891 __isl_give isl_set *isl_pw_aff_eq_set(
5892 __isl_take isl_pw_aff *pwaff1,
5893 __isl_take isl_pw_aff *pwaff2);
5894 __isl_give isl_set *isl_pw_aff_ne_set(
5895 __isl_take isl_pw_aff *pwaff1,
5896 __isl_take isl_pw_aff *pwaff2);
5897 __isl_give isl_set *isl_pw_aff_le_set(
5898 __isl_take isl_pw_aff *pwaff1,
5899 __isl_take isl_pw_aff *pwaff2);
5900 __isl_give isl_set *isl_pw_aff_lt_set(
5901 __isl_take isl_pw_aff *pwaff1,
5902 __isl_take isl_pw_aff *pwaff2);
5903 __isl_give isl_set *isl_pw_aff_ge_set(
5904 __isl_take isl_pw_aff *pwaff1,
5905 __isl_take isl_pw_aff *pwaff2);
5906 __isl_give isl_set *isl_pw_aff_gt_set(
5907 __isl_take isl_pw_aff *pwaff1,
5908 __isl_take isl_pw_aff *pwaff2);
5910 __isl_give isl_set *isl_multi_aff_lex_le_set(
5911 __isl_take isl_multi_aff *ma1,
5912 __isl_take isl_multi_aff *ma2);
5913 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5914 __isl_take isl_multi_aff *ma1,
5915 __isl_take isl_multi_aff *ma2);
5917 __isl_give isl_set *isl_pw_aff_list_eq_set(
5918 __isl_take isl_pw_aff_list *list1,
5919 __isl_take isl_pw_aff_list *list2);
5920 __isl_give isl_set *isl_pw_aff_list_ne_set(
5921 __isl_take isl_pw_aff_list *list1,
5922 __isl_take isl_pw_aff_list *list2);
5923 __isl_give isl_set *isl_pw_aff_list_le_set(
5924 __isl_take isl_pw_aff_list *list1,
5925 __isl_take isl_pw_aff_list *list2);
5926 __isl_give isl_set *isl_pw_aff_list_lt_set(
5927 __isl_take isl_pw_aff_list *list1,
5928 __isl_take isl_pw_aff_list *list2);
5929 __isl_give isl_set *isl_pw_aff_list_ge_set(
5930 __isl_take isl_pw_aff_list *list1,
5931 __isl_take isl_pw_aff_list *list2);
5932 __isl_give isl_set *isl_pw_aff_list_gt_set(
5933 __isl_take isl_pw_aff_list *list1,
5934 __isl_take isl_pw_aff_list *list2);
5936 The function C<isl_aff_ge_basic_set> returns a basic set
5937 containing those elements in the shared space
5938 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5939 The function C<isl_pw_aff_ge_set> returns a set
5940 containing those elements in the shared domain
5941 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5942 greater than or equal to C<pwaff2>.
5943 The function C<isl_multi_aff_lex_le_set> returns a set
5944 containing those elements in the shared domain space
5945 where C<ma1> is lexicographically smaller than or
5947 The functions operating on C<isl_pw_aff_list> apply the corresponding
5948 C<isl_pw_aff> function to each pair of elements in the two lists.
5950 #include <isl/aff.h>
5951 __isl_give isl_map *isl_pw_aff_eq_map(
5952 __isl_take isl_pw_aff *pa1,
5953 __isl_take isl_pw_aff *pa2);
5954 __isl_give isl_map *isl_pw_aff_lt_map(
5955 __isl_take isl_pw_aff *pa1,
5956 __isl_take isl_pw_aff *pa2);
5957 __isl_give isl_map *isl_pw_aff_gt_map(
5958 __isl_take isl_pw_aff *pa1,
5959 __isl_take isl_pw_aff *pa2);
5961 __isl_give isl_map *isl_multi_pw_aff_eq_map(
5962 __isl_take isl_multi_pw_aff *mpa1,
5963 __isl_take isl_multi_pw_aff *mpa2);
5964 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
5965 __isl_take isl_multi_pw_aff *mpa1,
5966 __isl_take isl_multi_pw_aff *mpa2);
5967 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
5968 __isl_take isl_multi_pw_aff *mpa1,
5969 __isl_take isl_multi_pw_aff *mpa2);
5971 These functions return a map between domain elements of the arguments
5972 where the function values satisfy the given relation.
5974 #include <isl/union_map.h>
5975 __isl_give isl_union_map *
5976 isl_union_map_eq_at_multi_union_pw_aff(
5977 __isl_take isl_union_map *umap,
5978 __isl_take isl_multi_union_pw_aff *mupa);
5979 __isl_give isl_union_map *
5980 isl_union_map_lex_lt_at_multi_union_pw_aff(
5981 __isl_take isl_union_map *umap,
5982 __isl_take isl_multi_union_pw_aff *mupa);
5983 __isl_give isl_union_map *
5984 isl_union_map_lex_gt_at_multi_union_pw_aff(
5985 __isl_take isl_union_map *umap,
5986 __isl_take isl_multi_union_pw_aff *mupa);
5988 These functions select the subset of elements in the union map
5989 that have an equal or lexicographically smaller function value.
5991 =item * Cartesian Product
5993 #include <isl/space.h>
5994 __isl_give isl_space *isl_space_product(
5995 __isl_take isl_space *space1,
5996 __isl_take isl_space *space2);
5997 __isl_give isl_space *isl_space_domain_product(
5998 __isl_take isl_space *space1,
5999 __isl_take isl_space *space2);
6000 __isl_give isl_space *isl_space_range_product(
6001 __isl_take isl_space *space1,
6002 __isl_take isl_space *space2);
6005 C<isl_space_product>, C<isl_space_domain_product>
6006 and C<isl_space_range_product> take pairs or relation spaces and
6007 produce a single relations space, where either the domain, the range
6008 or both domain and range are wrapped spaces of relations between
6009 the domains and/or ranges of the input spaces.
6010 If the product is only constructed over the domain or the range
6011 then the ranges or the domains of the inputs should be the same.
6012 The function C<isl_space_product> also accepts a pair of set spaces,
6013 in which case it returns a wrapped space of a relation between the
6016 #include <isl/set.h>
6017 __isl_give isl_set *isl_set_product(
6018 __isl_take isl_set *set1,
6019 __isl_take isl_set *set2);
6021 #include <isl/map.h>
6022 __isl_give isl_basic_map *isl_basic_map_domain_product(
6023 __isl_take isl_basic_map *bmap1,
6024 __isl_take isl_basic_map *bmap2);
6025 __isl_give isl_basic_map *isl_basic_map_range_product(
6026 __isl_take isl_basic_map *bmap1,
6027 __isl_take isl_basic_map *bmap2);
6028 __isl_give isl_basic_map *isl_basic_map_product(
6029 __isl_take isl_basic_map *bmap1,
6030 __isl_take isl_basic_map *bmap2);
6031 __isl_give isl_map *isl_map_domain_product(
6032 __isl_take isl_map *map1,
6033 __isl_take isl_map *map2);
6034 __isl_give isl_map *isl_map_range_product(
6035 __isl_take isl_map *map1,
6036 __isl_take isl_map *map2);
6037 __isl_give isl_map *isl_map_product(
6038 __isl_take isl_map *map1,
6039 __isl_take isl_map *map2);
6041 #include <isl/union_set.h>
6042 __isl_give isl_union_set *isl_union_set_product(
6043 __isl_take isl_union_set *uset1,
6044 __isl_take isl_union_set *uset2);
6046 #include <isl/union_map.h>
6047 __isl_give isl_union_map *isl_union_map_domain_product(
6048 __isl_take isl_union_map *umap1,
6049 __isl_take isl_union_map *umap2);
6050 __isl_give isl_union_map *isl_union_map_range_product(
6051 __isl_take isl_union_map *umap1,
6052 __isl_take isl_union_map *umap2);
6053 __isl_give isl_union_map *isl_union_map_product(
6054 __isl_take isl_union_map *umap1,
6055 __isl_take isl_union_map *umap2);
6057 #include <isl/val.h>
6058 __isl_give isl_multi_val *isl_multi_val_range_product(
6059 __isl_take isl_multi_val *mv1,
6060 __isl_take isl_multi_val *mv2);
6061 __isl_give isl_multi_val *isl_multi_val_product(
6062 __isl_take isl_multi_val *mv1,
6063 __isl_take isl_multi_val *mv2);
6065 #include <isl/aff.h>
6066 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6067 __isl_take isl_multi_aff *ma1,
6068 __isl_take isl_multi_aff *ma2);
6069 __isl_give isl_multi_aff *isl_multi_aff_product(
6070 __isl_take isl_multi_aff *ma1,
6071 __isl_take isl_multi_aff *ma2);
6072 __isl_give isl_multi_pw_aff *
6073 isl_multi_pw_aff_range_product(
6074 __isl_take isl_multi_pw_aff *mpa1,
6075 __isl_take isl_multi_pw_aff *mpa2);
6076 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6077 __isl_take isl_multi_pw_aff *mpa1,
6078 __isl_take isl_multi_pw_aff *mpa2);
6079 __isl_give isl_pw_multi_aff *
6080 isl_pw_multi_aff_range_product(
6081 __isl_take isl_pw_multi_aff *pma1,
6082 __isl_take isl_pw_multi_aff *pma2);
6083 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6084 __isl_take isl_pw_multi_aff *pma1,
6085 __isl_take isl_pw_multi_aff *pma2);
6086 __isl_give isl_multi_union_pw_aff *
6087 isl_multi_union_pw_aff_range_product(
6088 __isl_take isl_multi_union_pw_aff *mupa1,
6089 __isl_take isl_multi_union_pw_aff *mupa2);
6091 The above functions compute the cross product of the given
6092 sets, relations or functions. The domains and ranges of the results
6093 are wrapped maps between domains and ranges of the inputs.
6094 To obtain a ``flat'' product, use the following functions
6097 #include <isl/set.h>
6098 __isl_give isl_basic_set *isl_basic_set_flat_product(
6099 __isl_take isl_basic_set *bset1,
6100 __isl_take isl_basic_set *bset2);
6101 __isl_give isl_set *isl_set_flat_product(
6102 __isl_take isl_set *set1,
6103 __isl_take isl_set *set2);
6105 #include <isl/map.h>
6106 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6107 __isl_take isl_basic_map *bmap1,
6108 __isl_take isl_basic_map *bmap2);
6109 __isl_give isl_map *isl_map_flat_domain_product(
6110 __isl_take isl_map *map1,
6111 __isl_take isl_map *map2);
6112 __isl_give isl_map *isl_map_flat_range_product(
6113 __isl_take isl_map *map1,
6114 __isl_take isl_map *map2);
6115 __isl_give isl_basic_map *isl_basic_map_flat_product(
6116 __isl_take isl_basic_map *bmap1,
6117 __isl_take isl_basic_map *bmap2);
6118 __isl_give isl_map *isl_map_flat_product(
6119 __isl_take isl_map *map1,
6120 __isl_take isl_map *map2);
6122 #include <isl/union_map.h>
6123 __isl_give isl_union_map *
6124 isl_union_map_flat_domain_product(
6125 __isl_take isl_union_map *umap1,
6126 __isl_take isl_union_map *umap2);
6127 __isl_give isl_union_map *
6128 isl_union_map_flat_range_product(
6129 __isl_take isl_union_map *umap1,
6130 __isl_take isl_union_map *umap2);
6132 #include <isl/val.h>
6133 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6134 __isl_take isl_multi_val *mv1,
6135 __isl_take isl_multi_aff *mv2);
6137 #include <isl/aff.h>
6138 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6139 __isl_take isl_multi_aff *ma1,
6140 __isl_take isl_multi_aff *ma2);
6141 __isl_give isl_pw_multi_aff *
6142 isl_pw_multi_aff_flat_range_product(
6143 __isl_take isl_pw_multi_aff *pma1,
6144 __isl_take isl_pw_multi_aff *pma2);
6145 __isl_give isl_multi_pw_aff *
6146 isl_multi_pw_aff_flat_range_product(
6147 __isl_take isl_multi_pw_aff *mpa1,
6148 __isl_take isl_multi_pw_aff *mpa2);
6149 __isl_give isl_union_pw_multi_aff *
6150 isl_union_pw_multi_aff_flat_range_product(
6151 __isl_take isl_union_pw_multi_aff *upma1,
6152 __isl_take isl_union_pw_multi_aff *upma2);
6153 __isl_give isl_multi_union_pw_aff *
6154 isl_multi_union_pw_aff_flat_range_product(
6155 __isl_take isl_multi_union_pw_aff *mupa1,
6156 __isl_take isl_multi_union_pw_aff *mupa2);
6158 #include <isl/space.h>
6159 __isl_give isl_space *isl_space_factor_domain(
6160 __isl_take isl_space *space);
6161 __isl_give isl_space *isl_space_factor_range(
6162 __isl_take isl_space *space);
6163 __isl_give isl_space *isl_space_domain_factor_domain(
6164 __isl_take isl_space *space);
6165 __isl_give isl_space *isl_space_domain_factor_range(
6166 __isl_take isl_space *space);
6167 __isl_give isl_space *isl_space_range_factor_domain(
6168 __isl_take isl_space *space);
6169 __isl_give isl_space *isl_space_range_factor_range(
6170 __isl_take isl_space *space);
6172 The functions C<isl_space_range_factor_domain> and
6173 C<isl_space_range_factor_range> extract the two arguments from
6174 the result of a call to C<isl_space_range_product>.
6176 The arguments of a call to C<isl_map_range_product> can be extracted
6177 from the result using the following functions.
6179 #include <isl/map.h>
6180 __isl_give isl_map *isl_map_factor_domain(
6181 __isl_take isl_map *map);
6182 __isl_give isl_map *isl_map_factor_range(
6183 __isl_take isl_map *map);
6184 __isl_give isl_map *isl_map_domain_factor_domain(
6185 __isl_take isl_map *map);
6186 __isl_give isl_map *isl_map_domain_factor_range(
6187 __isl_take isl_map *map);
6188 __isl_give isl_map *isl_map_range_factor_domain(
6189 __isl_take isl_map *map);
6190 __isl_give isl_map *isl_map_range_factor_range(
6191 __isl_take isl_map *map);
6193 #include <isl/union_map.h>
6194 __isl_give isl_union_map *isl_union_map_factor_domain(
6195 __isl_take isl_union_map *umap);
6196 __isl_give isl_union_map *isl_union_map_factor_range(
6197 __isl_take isl_union_map *umap);
6198 __isl_give isl_union_map *
6199 isl_union_map_domain_factor_domain(
6200 __isl_take isl_union_map *umap);
6201 __isl_give isl_union_map *
6202 isl_union_map_domain_factor_range(
6203 __isl_take isl_union_map *umap);
6204 __isl_give isl_union_map *
6205 isl_union_map_range_factor_range(
6206 __isl_take isl_union_map *umap);
6208 #include <isl/val.h>
6209 __isl_give isl_multi_val *
6210 isl_multi_val_range_factor_domain(
6211 __isl_take isl_multi_val *mv);
6212 __isl_give isl_multi_val *
6213 isl_multi_val_range_factor_range(
6214 __isl_take isl_multi_val *mv);
6216 #include <isl/aff.h>
6217 __isl_give isl_multi_aff *
6218 isl_multi_aff_range_factor_domain(
6219 __isl_take isl_multi_aff *ma);
6220 __isl_give isl_multi_aff *
6221 isl_multi_aff_range_factor_range(
6222 __isl_take isl_multi_aff *ma);
6223 __isl_give isl_multi_pw_aff *
6224 isl_multi_pw_aff_range_factor_domain(
6225 __isl_take isl_multi_pw_aff *mpa);
6226 __isl_give isl_multi_pw_aff *
6227 isl_multi_pw_aff_range_factor_range(
6228 __isl_take isl_multi_pw_aff *mpa);
6229 __isl_give isl_multi_union_pw_aff *
6230 isl_multi_union_pw_aff_range_factor_domain(
6231 __isl_take isl_multi_union_pw_aff *mupa);
6232 __isl_give isl_multi_union_pw_aff *
6233 isl_multi_union_pw_aff_range_factor_range(
6234 __isl_take isl_multi_union_pw_aff *mupa);
6236 The splice functions are a generalization of the flat product functions,
6237 where the second argument may be inserted at any position inside
6238 the first argument rather than being placed at the end.
6240 #include <isl/val.h>
6241 __isl_give isl_multi_val *isl_multi_val_range_splice(
6242 __isl_take isl_multi_val *mv1, unsigned pos,
6243 __isl_take isl_multi_val *mv2);
6245 #include <isl/aff.h>
6246 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6247 __isl_take isl_multi_aff *ma1, unsigned pos,
6248 __isl_take isl_multi_aff *ma2);
6249 __isl_give isl_multi_aff *isl_multi_aff_splice(
6250 __isl_take isl_multi_aff *ma1,
6251 unsigned in_pos, unsigned out_pos,
6252 __isl_take isl_multi_aff *ma2);
6253 __isl_give isl_multi_pw_aff *
6254 isl_multi_pw_aff_range_splice(
6255 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6256 __isl_take isl_multi_pw_aff *mpa2);
6257 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6258 __isl_take isl_multi_pw_aff *mpa1,
6259 unsigned in_pos, unsigned out_pos,
6260 __isl_take isl_multi_pw_aff *mpa2);
6261 __isl_give isl_multi_union_pw_aff *
6262 isl_multi_union_pw_aff_range_splice(
6263 __isl_take isl_multi_union_pw_aff *mupa1,
6265 __isl_take isl_multi_union_pw_aff *mupa2);
6267 =item * Simplification
6269 When applied to a set or relation,
6270 the gist operation returns a set or relation that has the
6271 same intersection with the context as the input set or relation.
6272 Any implicit equality in the intersection is made explicit in the result,
6273 while all inequalities that are redundant with respect to the intersection
6275 In case of union sets and relations, the gist operation is performed
6278 When applied to a function,
6279 the gist operation applies the set gist operation to each of
6280 the cells in the domain of the input piecewise expression.
6281 The context is also exploited
6282 to simplify the expression associated to each cell.
6284 #include <isl/set.h>
6285 __isl_give isl_basic_set *isl_basic_set_gist(
6286 __isl_take isl_basic_set *bset,
6287 __isl_take isl_basic_set *context);
6288 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6289 __isl_take isl_set *context);
6290 __isl_give isl_set *isl_set_gist_params(
6291 __isl_take isl_set *set,
6292 __isl_take isl_set *context);
6294 #include <isl/map.h>
6295 __isl_give isl_basic_map *isl_basic_map_gist(
6296 __isl_take isl_basic_map *bmap,
6297 __isl_take isl_basic_map *context);
6298 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6299 __isl_take isl_basic_map *bmap,
6300 __isl_take isl_basic_set *context);
6301 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6302 __isl_take isl_map *context);
6303 __isl_give isl_map *isl_map_gist_params(
6304 __isl_take isl_map *map,
6305 __isl_take isl_set *context);
6306 __isl_give isl_map *isl_map_gist_domain(
6307 __isl_take isl_map *map,
6308 __isl_take isl_set *context);
6309 __isl_give isl_map *isl_map_gist_range(
6310 __isl_take isl_map *map,
6311 __isl_take isl_set *context);
6313 #include <isl/union_set.h>
6314 __isl_give isl_union_set *isl_union_set_gist(
6315 __isl_take isl_union_set *uset,
6316 __isl_take isl_union_set *context);
6317 __isl_give isl_union_set *isl_union_set_gist_params(
6318 __isl_take isl_union_set *uset,
6319 __isl_take isl_set *set);
6321 #include <isl/union_map.h>
6322 __isl_give isl_union_map *isl_union_map_gist(
6323 __isl_take isl_union_map *umap,
6324 __isl_take isl_union_map *context);
6325 __isl_give isl_union_map *isl_union_map_gist_params(
6326 __isl_take isl_union_map *umap,
6327 __isl_take isl_set *set);
6328 __isl_give isl_union_map *isl_union_map_gist_domain(
6329 __isl_take isl_union_map *umap,
6330 __isl_take isl_union_set *uset);
6331 __isl_give isl_union_map *isl_union_map_gist_range(
6332 __isl_take isl_union_map *umap,
6333 __isl_take isl_union_set *uset);
6335 #include <isl/aff.h>
6336 __isl_give isl_aff *isl_aff_gist_params(
6337 __isl_take isl_aff *aff,
6338 __isl_take isl_set *context);
6339 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6340 __isl_take isl_set *context);
6341 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6342 __isl_take isl_multi_aff *maff,
6343 __isl_take isl_set *context);
6344 __isl_give isl_multi_aff *isl_multi_aff_gist(
6345 __isl_take isl_multi_aff *maff,
6346 __isl_take isl_set *context);
6347 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6348 __isl_take isl_pw_aff *pwaff,
6349 __isl_take isl_set *context);
6350 __isl_give isl_pw_aff *isl_pw_aff_gist(
6351 __isl_take isl_pw_aff *pwaff,
6352 __isl_take isl_set *context);
6353 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6354 __isl_take isl_pw_multi_aff *pma,
6355 __isl_take isl_set *set);
6356 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6357 __isl_take isl_pw_multi_aff *pma,
6358 __isl_take isl_set *set);
6359 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6360 __isl_take isl_multi_pw_aff *mpa,
6361 __isl_take isl_set *set);
6362 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6363 __isl_take isl_multi_pw_aff *mpa,
6364 __isl_take isl_set *set);
6365 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6366 __isl_take isl_union_pw_aff *upa,
6367 __isl_take isl_union_set *context);
6368 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6369 __isl_take isl_union_pw_aff *upa,
6370 __isl_take isl_set *context);
6371 __isl_give isl_union_pw_multi_aff *
6372 isl_union_pw_multi_aff_gist_params(
6373 __isl_take isl_union_pw_multi_aff *upma,
6374 __isl_take isl_set *context);
6375 __isl_give isl_union_pw_multi_aff *
6376 isl_union_pw_multi_aff_gist(
6377 __isl_take isl_union_pw_multi_aff *upma,
6378 __isl_take isl_union_set *context);
6379 __isl_give isl_multi_union_pw_aff *
6380 isl_multi_union_pw_aff_gist_params(
6381 __isl_take isl_multi_union_pw_aff *aff,
6382 __isl_take isl_set *context);
6383 __isl_give isl_multi_union_pw_aff *
6384 isl_multi_union_pw_aff_gist(
6385 __isl_take isl_multi_union_pw_aff *aff,
6386 __isl_take isl_union_set *context);
6388 #include <isl/polynomial.h>
6389 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6390 __isl_take isl_qpolynomial *qp,
6391 __isl_take isl_set *context);
6392 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6393 __isl_take isl_qpolynomial *qp,
6394 __isl_take isl_set *context);
6395 __isl_give isl_qpolynomial_fold *
6396 isl_qpolynomial_fold_gist_params(
6397 __isl_take isl_qpolynomial_fold *fold,
6398 __isl_take isl_set *context);
6399 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6400 __isl_take isl_qpolynomial_fold *fold,
6401 __isl_take isl_set *context);
6402 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6403 __isl_take isl_pw_qpolynomial *pwqp,
6404 __isl_take isl_set *context);
6405 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6406 __isl_take isl_pw_qpolynomial *pwqp,
6407 __isl_take isl_set *context);
6408 __isl_give isl_pw_qpolynomial_fold *
6409 isl_pw_qpolynomial_fold_gist(
6410 __isl_take isl_pw_qpolynomial_fold *pwf,
6411 __isl_take isl_set *context);
6412 __isl_give isl_pw_qpolynomial_fold *
6413 isl_pw_qpolynomial_fold_gist_params(
6414 __isl_take isl_pw_qpolynomial_fold *pwf,
6415 __isl_take isl_set *context);
6416 __isl_give isl_union_pw_qpolynomial *
6417 isl_union_pw_qpolynomial_gist_params(
6418 __isl_take isl_union_pw_qpolynomial *upwqp,
6419 __isl_take isl_set *context);
6420 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6421 __isl_take isl_union_pw_qpolynomial *upwqp,
6422 __isl_take isl_union_set *context);
6423 __isl_give isl_union_pw_qpolynomial_fold *
6424 isl_union_pw_qpolynomial_fold_gist(
6425 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6426 __isl_take isl_union_set *context);
6427 __isl_give isl_union_pw_qpolynomial_fold *
6428 isl_union_pw_qpolynomial_fold_gist_params(
6429 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6430 __isl_take isl_set *context);
6432 =item * Binary Arithmethic Operations
6434 #include <isl/val.h>
6435 __isl_give isl_multi_val *isl_multi_val_sub(
6436 __isl_take isl_multi_val *mv1,
6437 __isl_take isl_multi_val *mv2);
6439 #include <isl/aff.h>
6440 __isl_give isl_aff *isl_aff_add(
6441 __isl_take isl_aff *aff1,
6442 __isl_take isl_aff *aff2);
6443 __isl_give isl_multi_aff *isl_multi_aff_add(
6444 __isl_take isl_multi_aff *maff1,
6445 __isl_take isl_multi_aff *maff2);
6446 __isl_give isl_pw_aff *isl_pw_aff_add(
6447 __isl_take isl_pw_aff *pwaff1,
6448 __isl_take isl_pw_aff *pwaff2);
6449 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6450 __isl_take isl_pw_multi_aff *pma1,
6451 __isl_take isl_pw_multi_aff *pma2);
6452 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6453 __isl_take isl_union_pw_aff *upa1,
6454 __isl_take isl_union_pw_aff *upa2);
6455 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6456 __isl_take isl_union_pw_multi_aff *upma1,
6457 __isl_take isl_union_pw_multi_aff *upma2);
6458 __isl_give isl_pw_aff *isl_pw_aff_min(
6459 __isl_take isl_pw_aff *pwaff1,
6460 __isl_take isl_pw_aff *pwaff2);
6461 __isl_give isl_pw_aff *isl_pw_aff_max(
6462 __isl_take isl_pw_aff *pwaff1,
6463 __isl_take isl_pw_aff *pwaff2);
6464 __isl_give isl_aff *isl_aff_sub(
6465 __isl_take isl_aff *aff1,
6466 __isl_take isl_aff *aff2);
6467 __isl_give isl_multi_aff *isl_multi_aff_sub(
6468 __isl_take isl_multi_aff *ma1,
6469 __isl_take isl_multi_aff *ma2);
6470 __isl_give isl_pw_aff *isl_pw_aff_sub(
6471 __isl_take isl_pw_aff *pwaff1,
6472 __isl_take isl_pw_aff *pwaff2);
6473 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6474 __isl_take isl_multi_pw_aff *mpa1,
6475 __isl_take isl_multi_pw_aff *mpa2);
6476 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6477 __isl_take isl_pw_multi_aff *pma1,
6478 __isl_take isl_pw_multi_aff *pma2);
6479 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6480 __isl_take isl_union_pw_aff *upa1,
6481 __isl_take isl_union_pw_aff *upa2);
6482 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6483 __isl_take isl_union_pw_multi_aff *upma1,
6484 __isl_take isl_union_pw_multi_aff *upma2);
6485 __isl_give isl_multi_union_pw_aff *
6486 isl_multi_union_pw_aff_sub(
6487 __isl_take isl_multi_union_pw_aff *mupa1,
6488 __isl_take isl_multi_union_pw_aff *mupa2);
6490 C<isl_aff_sub> subtracts the second argument from the first.
6492 #include <isl/polynomial.h>
6493 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6494 __isl_take isl_qpolynomial *qp1,
6495 __isl_take isl_qpolynomial *qp2);
6496 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6497 __isl_take isl_pw_qpolynomial *pwqp1,
6498 __isl_take isl_pw_qpolynomial *pwqp2);
6499 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6500 __isl_take isl_pw_qpolynomial *pwqp1,
6501 __isl_take isl_pw_qpolynomial *pwqp2);
6502 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6503 __isl_take isl_pw_qpolynomial_fold *pwf1,
6504 __isl_take isl_pw_qpolynomial_fold *pwf2);
6505 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6506 __isl_take isl_union_pw_qpolynomial *upwqp1,
6507 __isl_take isl_union_pw_qpolynomial *upwqp2);
6508 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6509 __isl_take isl_qpolynomial *qp1,
6510 __isl_take isl_qpolynomial *qp2);
6511 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6512 __isl_take isl_pw_qpolynomial *pwqp1,
6513 __isl_take isl_pw_qpolynomial *pwqp2);
6514 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6515 __isl_take isl_union_pw_qpolynomial *upwqp1,
6516 __isl_take isl_union_pw_qpolynomial *upwqp2);
6517 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6518 __isl_take isl_pw_qpolynomial_fold *pwf1,
6519 __isl_take isl_pw_qpolynomial_fold *pwf2);
6520 __isl_give isl_union_pw_qpolynomial_fold *
6521 isl_union_pw_qpolynomial_fold_fold(
6522 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6523 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6525 #include <isl/aff.h>
6526 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6527 __isl_take isl_pw_aff *pwaff1,
6528 __isl_take isl_pw_aff *pwaff2);
6529 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6530 __isl_take isl_pw_multi_aff *pma1,
6531 __isl_take isl_pw_multi_aff *pma2);
6532 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6533 __isl_take isl_union_pw_aff *upa1,
6534 __isl_take isl_union_pw_aff *upa2);
6535 __isl_give isl_union_pw_multi_aff *
6536 isl_union_pw_multi_aff_union_add(
6537 __isl_take isl_union_pw_multi_aff *upma1,
6538 __isl_take isl_union_pw_multi_aff *upma2);
6539 __isl_give isl_multi_union_pw_aff *
6540 isl_multi_union_pw_aff_union_add(
6541 __isl_take isl_multi_union_pw_aff *mupa1,
6542 __isl_take isl_multi_union_pw_aff *mupa2);
6543 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6544 __isl_take isl_pw_aff *pwaff1,
6545 __isl_take isl_pw_aff *pwaff2);
6546 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6547 __isl_take isl_pw_aff *pwaff1,
6548 __isl_take isl_pw_aff *pwaff2);
6550 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6551 expression with a domain that is the union of those of C<pwaff1> and
6552 C<pwaff2> and such that on each cell, the quasi-affine expression is
6553 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6554 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6555 associated expression is the defined one.
6556 This in contrast to the C<isl_pw_aff_max> function, which is
6557 only defined on the shared definition domain of the arguments.
6559 #include <isl/val.h>
6560 __isl_give isl_multi_val *isl_multi_val_add_val(
6561 __isl_take isl_multi_val *mv,
6562 __isl_take isl_val *v);
6563 __isl_give isl_multi_val *isl_multi_val_mod_val(
6564 __isl_take isl_multi_val *mv,
6565 __isl_take isl_val *v);
6566 __isl_give isl_multi_val *isl_multi_val_scale_val(
6567 __isl_take isl_multi_val *mv,
6568 __isl_take isl_val *v);
6569 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6570 __isl_take isl_multi_val *mv,
6571 __isl_take isl_val *v);
6573 #include <isl/aff.h>
6574 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6575 __isl_take isl_val *mod);
6576 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6577 __isl_take isl_pw_aff *pa,
6578 __isl_take isl_val *mod);
6579 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6580 __isl_take isl_union_pw_aff *upa,
6581 __isl_take isl_val *f);
6582 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6583 __isl_take isl_val *v);
6584 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6585 __isl_take isl_multi_aff *ma,
6586 __isl_take isl_val *v);
6587 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6588 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6589 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6590 __isl_take isl_multi_pw_aff *mpa,
6591 __isl_take isl_val *v);
6592 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6593 __isl_take isl_pw_multi_aff *pma,
6594 __isl_take isl_val *v);
6595 __isl_give isl_union_pw_multi_aff *
6596 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6597 __isl_take isl_union_pw_aff *upa,
6598 __isl_take isl_val *f);
6599 isl_union_pw_multi_aff_scale_val(
6600 __isl_take isl_union_pw_multi_aff *upma,
6601 __isl_take isl_val *val);
6602 __isl_give isl_multi_union_pw_aff *
6603 isl_multi_union_pw_aff_scale_val(
6604 __isl_take isl_multi_union_pw_aff *mupa,
6605 __isl_take isl_val *v);
6606 __isl_give isl_aff *isl_aff_scale_down_ui(
6607 __isl_take isl_aff *aff, unsigned f);
6608 __isl_give isl_aff *isl_aff_scale_down_val(
6609 __isl_take isl_aff *aff, __isl_take isl_val *v);
6610 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6611 __isl_take isl_multi_aff *ma,
6612 __isl_take isl_val *v);
6613 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6614 __isl_take isl_pw_aff *pa,
6615 __isl_take isl_val *f);
6616 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6617 __isl_take isl_multi_pw_aff *mpa,
6618 __isl_take isl_val *v);
6619 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6620 __isl_take isl_pw_multi_aff *pma,
6621 __isl_take isl_val *v);
6622 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6623 __isl_take isl_union_pw_aff *upa,
6624 __isl_take isl_val *v);
6625 __isl_give isl_union_pw_multi_aff *
6626 isl_union_pw_multi_aff_scale_down_val(
6627 __isl_take isl_union_pw_multi_aff *upma,
6628 __isl_take isl_val *val);
6629 __isl_give isl_multi_union_pw_aff *
6630 isl_multi_union_pw_aff_scale_down_val(
6631 __isl_take isl_multi_union_pw_aff *mupa,
6632 __isl_take isl_val *v);
6634 #include <isl/polynomial.h>
6635 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6636 __isl_take isl_qpolynomial *qp,
6637 __isl_take isl_val *v);
6638 __isl_give isl_qpolynomial_fold *
6639 isl_qpolynomial_fold_scale_val(
6640 __isl_take isl_qpolynomial_fold *fold,
6641 __isl_take isl_val *v);
6642 __isl_give isl_pw_qpolynomial *
6643 isl_pw_qpolynomial_scale_val(
6644 __isl_take isl_pw_qpolynomial *pwqp,
6645 __isl_take isl_val *v);
6646 __isl_give isl_pw_qpolynomial_fold *
6647 isl_pw_qpolynomial_fold_scale_val(
6648 __isl_take isl_pw_qpolynomial_fold *pwf,
6649 __isl_take isl_val *v);
6650 __isl_give isl_union_pw_qpolynomial *
6651 isl_union_pw_qpolynomial_scale_val(
6652 __isl_take isl_union_pw_qpolynomial *upwqp,
6653 __isl_take isl_val *v);
6654 __isl_give isl_union_pw_qpolynomial_fold *
6655 isl_union_pw_qpolynomial_fold_scale_val(
6656 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6657 __isl_take isl_val *v);
6658 __isl_give isl_qpolynomial *
6659 isl_qpolynomial_scale_down_val(
6660 __isl_take isl_qpolynomial *qp,
6661 __isl_take isl_val *v);
6662 __isl_give isl_qpolynomial_fold *
6663 isl_qpolynomial_fold_scale_down_val(
6664 __isl_take isl_qpolynomial_fold *fold,
6665 __isl_take isl_val *v);
6666 __isl_give isl_pw_qpolynomial *
6667 isl_pw_qpolynomial_scale_down_val(
6668 __isl_take isl_pw_qpolynomial *pwqp,
6669 __isl_take isl_val *v);
6670 __isl_give isl_pw_qpolynomial_fold *
6671 isl_pw_qpolynomial_fold_scale_down_val(
6672 __isl_take isl_pw_qpolynomial_fold *pwf,
6673 __isl_take isl_val *v);
6674 __isl_give isl_union_pw_qpolynomial *
6675 isl_union_pw_qpolynomial_scale_down_val(
6676 __isl_take isl_union_pw_qpolynomial *upwqp,
6677 __isl_take isl_val *v);
6678 __isl_give isl_union_pw_qpolynomial_fold *
6679 isl_union_pw_qpolynomial_fold_scale_down_val(
6680 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6681 __isl_take isl_val *v);
6683 #include <isl/val.h>
6684 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6685 __isl_take isl_multi_val *mv1,
6686 __isl_take isl_multi_val *mv2);
6687 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6688 __isl_take isl_multi_val *mv1,
6689 __isl_take isl_multi_val *mv2);
6690 __isl_give isl_multi_val *
6691 isl_multi_val_scale_down_multi_val(
6692 __isl_take isl_multi_val *mv1,
6693 __isl_take isl_multi_val *mv2);
6695 #include <isl/aff.h>
6696 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6697 __isl_take isl_multi_aff *ma,
6698 __isl_take isl_multi_val *mv);
6699 __isl_give isl_multi_union_pw_aff *
6700 isl_multi_union_pw_aff_mod_multi_val(
6701 __isl_take isl_multi_union_pw_aff *upma,
6702 __isl_take isl_multi_val *mv);
6703 __isl_give isl_multi_pw_aff *
6704 isl_multi_pw_aff_mod_multi_val(
6705 __isl_take isl_multi_pw_aff *mpa,
6706 __isl_take isl_multi_val *mv);
6707 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6708 __isl_take isl_multi_aff *ma,
6709 __isl_take isl_multi_val *mv);
6710 __isl_give isl_pw_multi_aff *
6711 isl_pw_multi_aff_scale_multi_val(
6712 __isl_take isl_pw_multi_aff *pma,
6713 __isl_take isl_multi_val *mv);
6714 __isl_give isl_multi_pw_aff *
6715 isl_multi_pw_aff_scale_multi_val(
6716 __isl_take isl_multi_pw_aff *mpa,
6717 __isl_take isl_multi_val *mv);
6718 __isl_give isl_multi_union_pw_aff *
6719 isl_multi_union_pw_aff_scale_multi_val(
6720 __isl_take isl_multi_union_pw_aff *mupa,
6721 __isl_take isl_multi_val *mv);
6722 __isl_give isl_union_pw_multi_aff *
6723 isl_union_pw_multi_aff_scale_multi_val(
6724 __isl_take isl_union_pw_multi_aff *upma,
6725 __isl_take isl_multi_val *mv);
6726 __isl_give isl_multi_aff *
6727 isl_multi_aff_scale_down_multi_val(
6728 __isl_take isl_multi_aff *ma,
6729 __isl_take isl_multi_val *mv);
6730 __isl_give isl_multi_pw_aff *
6731 isl_multi_pw_aff_scale_down_multi_val(
6732 __isl_take isl_multi_pw_aff *mpa,
6733 __isl_take isl_multi_val *mv);
6734 __isl_give isl_multi_union_pw_aff *
6735 isl_multi_union_pw_aff_scale_down_multi_val(
6736 __isl_take isl_multi_union_pw_aff *mupa,
6737 __isl_take isl_multi_val *mv);
6739 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6740 by the corresponding elements of C<mv>.
6742 #include <isl/aff.h>
6743 __isl_give isl_aff *isl_aff_mul(
6744 __isl_take isl_aff *aff1,
6745 __isl_take isl_aff *aff2);
6746 __isl_give isl_aff *isl_aff_div(
6747 __isl_take isl_aff *aff1,
6748 __isl_take isl_aff *aff2);
6749 __isl_give isl_pw_aff *isl_pw_aff_mul(
6750 __isl_take isl_pw_aff *pwaff1,
6751 __isl_take isl_pw_aff *pwaff2);
6752 __isl_give isl_pw_aff *isl_pw_aff_div(
6753 __isl_take isl_pw_aff *pa1,
6754 __isl_take isl_pw_aff *pa2);
6755 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6756 __isl_take isl_pw_aff *pa1,
6757 __isl_take isl_pw_aff *pa2);
6758 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6759 __isl_take isl_pw_aff *pa1,
6760 __isl_take isl_pw_aff *pa2);
6762 When multiplying two affine expressions, at least one of the two needs
6763 to be a constant. Similarly, when dividing an affine expression by another,
6764 the second expression needs to be a constant.
6765 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6766 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6769 #include <isl/polynomial.h>
6770 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6771 __isl_take isl_qpolynomial *qp1,
6772 __isl_take isl_qpolynomial *qp2);
6773 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6774 __isl_take isl_pw_qpolynomial *pwqp1,
6775 __isl_take isl_pw_qpolynomial *pwqp2);
6776 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6777 __isl_take isl_union_pw_qpolynomial *upwqp1,
6778 __isl_take isl_union_pw_qpolynomial *upwqp2);
6782 =head3 Lexicographic Optimization
6784 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6785 the following functions
6786 compute a set that contains the lexicographic minimum or maximum
6787 of the elements in C<set> (or C<bset>) for those values of the parameters
6788 that satisfy C<dom>.
6789 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6790 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6792 In other words, the union of the parameter values
6793 for which the result is non-empty and of C<*empty>
6796 #include <isl/set.h>
6797 __isl_give isl_set *isl_basic_set_partial_lexmin(
6798 __isl_take isl_basic_set *bset,
6799 __isl_take isl_basic_set *dom,
6800 __isl_give isl_set **empty);
6801 __isl_give isl_set *isl_basic_set_partial_lexmax(
6802 __isl_take isl_basic_set *bset,
6803 __isl_take isl_basic_set *dom,
6804 __isl_give isl_set **empty);
6805 __isl_give isl_set *isl_set_partial_lexmin(
6806 __isl_take isl_set *set, __isl_take isl_set *dom,
6807 __isl_give isl_set **empty);
6808 __isl_give isl_set *isl_set_partial_lexmax(
6809 __isl_take isl_set *set, __isl_take isl_set *dom,
6810 __isl_give isl_set **empty);
6812 Given a (basic) set C<set> (or C<bset>), the following functions simply
6813 return a set containing the lexicographic minimum or maximum
6814 of the elements in C<set> (or C<bset>).
6815 In case of union sets, the optimum is computed per space.
6817 #include <isl/set.h>
6818 __isl_give isl_set *isl_basic_set_lexmin(
6819 __isl_take isl_basic_set *bset);
6820 __isl_give isl_set *isl_basic_set_lexmax(
6821 __isl_take isl_basic_set *bset);
6822 __isl_give isl_set *isl_set_lexmin(
6823 __isl_take isl_set *set);
6824 __isl_give isl_set *isl_set_lexmax(
6825 __isl_take isl_set *set);
6826 __isl_give isl_union_set *isl_union_set_lexmin(
6827 __isl_take isl_union_set *uset);
6828 __isl_give isl_union_set *isl_union_set_lexmax(
6829 __isl_take isl_union_set *uset);
6831 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6832 the following functions
6833 compute a relation that maps each element of C<dom>
6834 to the single lexicographic minimum or maximum
6835 of the elements that are associated to that same
6836 element in C<map> (or C<bmap>).
6837 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6838 that contains the elements in C<dom> that do not map
6839 to any elements in C<map> (or C<bmap>).
6840 In other words, the union of the domain of the result and of C<*empty>
6843 #include <isl/map.h>
6844 __isl_give isl_map *isl_basic_map_partial_lexmax(
6845 __isl_take isl_basic_map *bmap,
6846 __isl_take isl_basic_set *dom,
6847 __isl_give isl_set **empty);
6848 __isl_give isl_map *isl_basic_map_partial_lexmin(
6849 __isl_take isl_basic_map *bmap,
6850 __isl_take isl_basic_set *dom,
6851 __isl_give isl_set **empty);
6852 __isl_give isl_map *isl_map_partial_lexmax(
6853 __isl_take isl_map *map, __isl_take isl_set *dom,
6854 __isl_give isl_set **empty);
6855 __isl_give isl_map *isl_map_partial_lexmin(
6856 __isl_take isl_map *map, __isl_take isl_set *dom,
6857 __isl_give isl_set **empty);
6859 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6860 return a map mapping each element in the domain of
6861 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6862 of all elements associated to that element.
6863 In case of union relations, the optimum is computed per space.
6865 #include <isl/map.h>
6866 __isl_give isl_map *isl_basic_map_lexmin(
6867 __isl_take isl_basic_map *bmap);
6868 __isl_give isl_map *isl_basic_map_lexmax(
6869 __isl_take isl_basic_map *bmap);
6870 __isl_give isl_map *isl_map_lexmin(
6871 __isl_take isl_map *map);
6872 __isl_give isl_map *isl_map_lexmax(
6873 __isl_take isl_map *map);
6874 __isl_give isl_union_map *isl_union_map_lexmin(
6875 __isl_take isl_union_map *umap);
6876 __isl_give isl_union_map *isl_union_map_lexmax(
6877 __isl_take isl_union_map *umap);
6879 The following functions return their result in the form of
6880 a piecewise multi-affine expression,
6881 but are otherwise equivalent to the corresponding functions
6882 returning a basic set or relation.
6884 #include <isl/set.h>
6885 __isl_give isl_pw_multi_aff *
6886 isl_basic_set_partial_lexmin_pw_multi_aff(
6887 __isl_take isl_basic_set *bset,
6888 __isl_take isl_basic_set *dom,
6889 __isl_give isl_set **empty);
6890 __isl_give isl_pw_multi_aff *
6891 isl_basic_set_partial_lexmax_pw_multi_aff(
6892 __isl_take isl_basic_set *bset,
6893 __isl_take isl_basic_set *dom,
6894 __isl_give isl_set **empty);
6895 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6896 __isl_take isl_set *set);
6897 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6898 __isl_take isl_set *set);
6900 #include <isl/map.h>
6901 __isl_give isl_pw_multi_aff *
6902 isl_basic_map_lexmin_pw_multi_aff(
6903 __isl_take isl_basic_map *bmap);
6904 __isl_give isl_pw_multi_aff *
6905 isl_basic_map_partial_lexmin_pw_multi_aff(
6906 __isl_take isl_basic_map *bmap,
6907 __isl_take isl_basic_set *dom,
6908 __isl_give isl_set **empty);
6909 __isl_give isl_pw_multi_aff *
6910 isl_basic_map_partial_lexmax_pw_multi_aff(
6911 __isl_take isl_basic_map *bmap,
6912 __isl_take isl_basic_set *dom,
6913 __isl_give isl_set **empty);
6914 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6915 __isl_take isl_map *map);
6916 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6917 __isl_take isl_map *map);
6919 The following functions return the lexicographic minimum or maximum
6920 on the shared domain of the inputs and the single defined function
6921 on those parts of the domain where only a single function is defined.
6923 #include <isl/aff.h>
6924 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6925 __isl_take isl_pw_multi_aff *pma1,
6926 __isl_take isl_pw_multi_aff *pma2);
6927 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6928 __isl_take isl_pw_multi_aff *pma1,
6929 __isl_take isl_pw_multi_aff *pma2);
6931 =head2 Ternary Operations
6933 #include <isl/aff.h>
6934 __isl_give isl_pw_aff *isl_pw_aff_cond(
6935 __isl_take isl_pw_aff *cond,
6936 __isl_take isl_pw_aff *pwaff_true,
6937 __isl_take isl_pw_aff *pwaff_false);
6939 The function C<isl_pw_aff_cond> performs a conditional operator
6940 and returns an expression that is equal to C<pwaff_true>
6941 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6942 where C<cond> is zero.
6946 Lists are defined over several element types, including
6947 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
6948 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6949 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6950 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6951 Here we take lists of C<isl_set>s as an example.
6952 Lists can be created, copied, modified and freed using the following functions.
6954 #include <isl/set.h>
6955 __isl_give isl_set_list *isl_set_list_from_set(
6956 __isl_take isl_set *el);
6957 __isl_give isl_set_list *isl_set_list_alloc(
6958 isl_ctx *ctx, int n);
6959 __isl_give isl_set_list *isl_set_list_copy(
6960 __isl_keep isl_set_list *list);
6961 __isl_give isl_set_list *isl_set_list_insert(
6962 __isl_take isl_set_list *list, unsigned pos,
6963 __isl_take isl_set *el);
6964 __isl_give isl_set_list *isl_set_list_add(
6965 __isl_take isl_set_list *list,
6966 __isl_take isl_set *el);
6967 __isl_give isl_set_list *isl_set_list_drop(
6968 __isl_take isl_set_list *list,
6969 unsigned first, unsigned n);
6970 __isl_give isl_set_list *isl_set_list_set_set(
6971 __isl_take isl_set_list *list, int index,
6972 __isl_take isl_set *set);
6973 __isl_give isl_set_list *isl_set_list_concat(
6974 __isl_take isl_set_list *list1,
6975 __isl_take isl_set_list *list2);
6976 __isl_give isl_set_list *isl_set_list_sort(
6977 __isl_take isl_set_list *list,
6978 int (*cmp)(__isl_keep isl_set *a,
6979 __isl_keep isl_set *b, void *user),
6981 __isl_null isl_set_list *isl_set_list_free(
6982 __isl_take isl_set_list *list);
6984 C<isl_set_list_alloc> creates an empty list with an initial capacity
6985 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
6986 add elements to a list, increasing its capacity as needed.
6987 C<isl_set_list_from_set> creates a list with a single element.
6989 Lists can be inspected using the following functions.
6991 #include <isl/set.h>
6992 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6993 __isl_give isl_set *isl_set_list_get_set(
6994 __isl_keep isl_set_list *list, int index);
6995 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6996 int (*fn)(__isl_take isl_set *el, void *user),
6998 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6999 int (*follows)(__isl_keep isl_set *a,
7000 __isl_keep isl_set *b, void *user),
7002 int (*fn)(__isl_take isl_set *el, void *user),
7005 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
7006 strongly connected components of the graph with as vertices the elements
7007 of C<list> and a directed edge from vertex C<b> to vertex C<a>
7008 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
7009 should return C<-1> on error.
7011 Lists can be printed using
7013 #include <isl/set.h>
7014 __isl_give isl_printer *isl_printer_print_set_list(
7015 __isl_take isl_printer *p,
7016 __isl_keep isl_set_list *list);
7018 =head2 Associative arrays
7020 Associative arrays map isl objects of a specific type to isl objects
7021 of some (other) specific type. They are defined for several pairs
7022 of types, including (C<isl_map>, C<isl_basic_set>),
7023 (C<isl_id>, C<isl_ast_expr>) and.
7024 (C<isl_id>, C<isl_pw_aff>).
7025 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
7028 Associative arrays can be created, copied and freed using
7029 the following functions.
7031 #include <isl/id_to_ast_expr.h>
7032 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7033 isl_ctx *ctx, int min_size);
7034 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7035 __isl_keep isl_id_to_ast_expr *id2expr);
7036 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7037 __isl_take isl_id_to_ast_expr *id2expr);
7039 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7040 to specify the expected size of the associative array.
7041 The associative array will be grown automatically as needed.
7043 Associative arrays can be inspected using the following functions.
7045 #include <isl/id_to_ast_expr.h>
7046 int isl_id_to_ast_expr_has(
7047 __isl_keep isl_id_to_ast_expr *id2expr,
7048 __isl_keep isl_id *key);
7049 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7050 __isl_keep isl_id_to_ast_expr *id2expr,
7051 __isl_take isl_id *key);
7052 int isl_id_to_ast_expr_foreach(
7053 __isl_keep isl_id_to_ast_expr *id2expr,
7054 int (*fn)(__isl_take isl_id *key,
7055 __isl_take isl_ast_expr *val, void *user),
7058 They can be modified using the following function.
7060 #include <isl/id_to_ast_expr.h>
7061 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7062 __isl_take isl_id_to_ast_expr *id2expr,
7063 __isl_take isl_id *key,
7064 __isl_take isl_ast_expr *val);
7065 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7066 __isl_take isl_id_to_ast_expr *id2expr,
7067 __isl_take isl_id *key);
7069 Associative arrays can be printed using the following function.
7071 #include <isl/id_to_ast_expr.h>
7072 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7073 __isl_take isl_printer *p,
7074 __isl_keep isl_id_to_ast_expr *id2expr);
7078 Vectors can be created, copied and freed using the following functions.
7080 #include <isl/vec.h>
7081 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7083 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7084 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7086 Note that the elements of a newly created vector may have arbitrary values.
7087 The elements can be changed and inspected using the following functions.
7089 int isl_vec_size(__isl_keep isl_vec *vec);
7090 __isl_give isl_val *isl_vec_get_element_val(
7091 __isl_keep isl_vec *vec, int pos);
7092 __isl_give isl_vec *isl_vec_set_element_si(
7093 __isl_take isl_vec *vec, int pos, int v);
7094 __isl_give isl_vec *isl_vec_set_element_val(
7095 __isl_take isl_vec *vec, int pos,
7096 __isl_take isl_val *v);
7097 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7099 __isl_give isl_vec *isl_vec_set_val(
7100 __isl_take isl_vec *vec, __isl_take isl_val *v);
7101 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7102 __isl_keep isl_vec *vec2, int pos);
7104 C<isl_vec_get_element> will return a negative value if anything went wrong.
7105 In that case, the value of C<*v> is undefined.
7107 The following function can be used to concatenate two vectors.
7109 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7110 __isl_take isl_vec *vec2);
7114 Matrices can be created, copied and freed using the following functions.
7116 #include <isl/mat.h>
7117 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7118 unsigned n_row, unsigned n_col);
7119 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7120 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7122 Note that the elements of a newly created matrix may have arbitrary values.
7123 The elements can be changed and inspected using the following functions.
7125 int isl_mat_rows(__isl_keep isl_mat *mat);
7126 int isl_mat_cols(__isl_keep isl_mat *mat);
7127 __isl_give isl_val *isl_mat_get_element_val(
7128 __isl_keep isl_mat *mat, int row, int col);
7129 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7130 int row, int col, int v);
7131 __isl_give isl_mat *isl_mat_set_element_val(
7132 __isl_take isl_mat *mat, int row, int col,
7133 __isl_take isl_val *v);
7135 C<isl_mat_get_element> will return a negative value if anything went wrong.
7136 In that case, the value of C<*v> is undefined.
7138 The following function can be used to compute the (right) inverse
7139 of a matrix, i.e., a matrix such that the product of the original
7140 and the inverse (in that order) is a multiple of the identity matrix.
7141 The input matrix is assumed to be of full row-rank.
7143 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7145 The following function can be used to compute the (right) kernel
7146 (or null space) of a matrix, i.e., a matrix such that the product of
7147 the original and the kernel (in that order) is the zero matrix.
7149 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7151 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7153 The following functions determine
7154 an upper or lower bound on a quasipolynomial over its domain.
7156 __isl_give isl_pw_qpolynomial_fold *
7157 isl_pw_qpolynomial_bound(
7158 __isl_take isl_pw_qpolynomial *pwqp,
7159 enum isl_fold type, int *tight);
7161 __isl_give isl_union_pw_qpolynomial_fold *
7162 isl_union_pw_qpolynomial_bound(
7163 __isl_take isl_union_pw_qpolynomial *upwqp,
7164 enum isl_fold type, int *tight);
7166 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7167 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7168 is the returned bound is known be tight, i.e., for each value
7169 of the parameters there is at least
7170 one element in the domain that reaches the bound.
7171 If the domain of C<pwqp> is not wrapping, then the bound is computed
7172 over all elements in that domain and the result has a purely parametric
7173 domain. If the domain of C<pwqp> is wrapping, then the bound is
7174 computed over the range of the wrapped relation. The domain of the
7175 wrapped relation becomes the domain of the result.
7177 =head2 Parametric Vertex Enumeration
7179 The parametric vertex enumeration described in this section
7180 is mainly intended to be used internally and by the C<barvinok>
7183 #include <isl/vertices.h>
7184 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7185 __isl_keep isl_basic_set *bset);
7187 The function C<isl_basic_set_compute_vertices> performs the
7188 actual computation of the parametric vertices and the chamber
7189 decomposition and store the result in an C<isl_vertices> object.
7190 This information can be queried by either iterating over all
7191 the vertices or iterating over all the chambers or cells
7192 and then iterating over all vertices that are active on the chamber.
7194 int isl_vertices_foreach_vertex(
7195 __isl_keep isl_vertices *vertices,
7196 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7199 int isl_vertices_foreach_cell(
7200 __isl_keep isl_vertices *vertices,
7201 int (*fn)(__isl_take isl_cell *cell, void *user),
7203 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7204 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7207 Other operations that can be performed on an C<isl_vertices> object are
7210 int isl_vertices_get_n_vertices(
7211 __isl_keep isl_vertices *vertices);
7212 void isl_vertices_free(__isl_take isl_vertices *vertices);
7214 Vertices can be inspected and destroyed using the following functions.
7216 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7217 __isl_give isl_basic_set *isl_vertex_get_domain(
7218 __isl_keep isl_vertex *vertex);
7219 __isl_give isl_multi_aff *isl_vertex_get_expr(
7220 __isl_keep isl_vertex *vertex);
7221 void isl_vertex_free(__isl_take isl_vertex *vertex);
7223 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7224 describing the vertex in terms of the parameters,
7225 while C<isl_vertex_get_domain> returns the activity domain
7228 Chambers can be inspected and destroyed using the following functions.
7230 __isl_give isl_basic_set *isl_cell_get_domain(
7231 __isl_keep isl_cell *cell);
7232 void isl_cell_free(__isl_take isl_cell *cell);
7234 =head1 Polyhedral Compilation Library
7236 This section collects functionality in C<isl> that has been specifically
7237 designed for use during polyhedral compilation.
7239 =head2 Schedule Trees
7241 A schedule tree is a structured representation of a schedule,
7242 assigning a relative order to a set of domain elements.
7243 The relative order expressed by the schedule tree is
7244 defined recursively. In particular, the order between
7245 two domain elements is determined by the node that is closest
7246 to the root that refers to both elements and that orders them apart.
7247 Each node in the tree is of one of several types.
7248 The root node is always of type C<isl_schedule_node_domain>
7249 (or C<isl_schedule_node_extension>)
7250 and it describes the (extra) domain elements to which the schedule applies.
7251 The other types of nodes are as follows.
7255 =item C<isl_schedule_node_band>
7257 A band of schedule dimensions. Each schedule dimension is represented
7258 by a union piecewise quasi-affine expression. If this expression
7259 assigns a different value to two domain elements, while all previous
7260 schedule dimensions in the same band assign them the same value,
7261 then the two domain elements are ordered according to these two
7264 =item C<isl_schedule_node_expansion>
7266 An expansion node maps each of the domain elements that reach the node
7267 to one or more domain elements. The image of this mapping forms
7268 the set of domain elements that reach the child of the expansion node.
7269 The function that maps each of the expanded domain elements
7270 to the original domain element from which it was expanded
7271 is called the contraction.
7273 =item C<isl_schedule_node_filter>
7275 A filter node does not impose any ordering, but rather intersects
7276 the set of domain elements that the current subtree refers to
7277 with a given union set. The subtree of the filter node only
7278 refers to domain elements in the intersection.
7279 A filter node is typically only used a child of a sequence or
7282 =item C<isl_schedule_node_leaf>
7284 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7286 =item C<isl_schedule_node_mark>
7288 A mark node can be used to attach any kind of information to a subtree
7289 of the schedule tree.
7291 =item C<isl_schedule_node_sequence>
7293 A sequence node has one or more children, each of which is a filter node.
7294 The filters on these filter nodes form a partition of
7295 the domain elements that the current subtree refers to.
7296 If two domain elements appear in distinct filters then the sequence
7297 node orders them according to the child positions of the corresponding
7300 =item C<isl_schedule_node_set>
7302 A set node is similar to a sequence node, except that
7303 it expresses that domain elements appearing in distinct filters
7304 may have any order. The order of the children of a set node
7305 is therefore also immaterial.
7309 The following node types are only supported by the AST generator.
7313 =item C<isl_schedule_node_context>
7315 The context describes constraints on the parameters and
7316 the schedule dimensions of outer
7317 bands that the AST generator may assume to hold. It is also the only
7318 kind of node that may introduce additional parameters.
7319 The space of the context is that of the flat product of the outer
7320 band nodes. In particular, if there are no outer band nodes, then
7321 this space is the unnamed zero-dimensional space.
7322 Since a context node references the outer band nodes, any tree
7323 containing a context node is considered to be anchored.
7325 =item C<isl_schedule_node_extension>
7327 An extension node instructs the AST generator to add additional
7328 domain elements that need to be scheduled.
7329 The additional domain elements are described by the range of
7330 the extension map in terms of the outer schedule dimensions,
7331 i.e., the flat product of the outer band nodes.
7332 Note that domain elements are added whenever the AST generator
7333 reaches the extension node, meaning that there are still some
7334 active domain elements for which an AST needs to be generated.
7335 The conditions under which some domain elements are still active
7336 may however not be completely described by the outer AST nodes
7337 generated at that point.
7339 An extension node may also appear as the root of a schedule tree,
7340 when it is intended to be inserted into another tree
7341 using C<isl_schedule_node_graft_before> or C<isl_schedule_node_graft_after>.
7342 In this case, the domain of the extension node should
7343 correspond to the flat product of the outer band nodes
7344 in this other schedule tree at the point where the extension tree
7347 =item C<isl_schedule_node_guard>
7349 The guard describes constraints on the parameters and
7350 the schedule dimensions of outer
7351 bands that need to be enforced by the outer nodes
7352 in the generated AST.
7353 The space of the guard is that of the flat product of the outer
7354 band nodes. In particular, if there are no outer band nodes, then
7355 this space is the unnamed zero-dimensional space.
7356 Since a guard node references the outer band nodes, any tree
7357 containing a guard node is considered to be anchored.
7361 Except for the C<isl_schedule_node_context> nodes,
7362 none of the nodes may introduce any parameters that were not
7363 already present in the root domain node.
7365 A schedule tree is encapsulated in an C<isl_schedule> object.
7366 The simplest such objects, those with a tree consisting of single domain node,
7367 can be created using the following functions with either an empty
7368 domain or a given domain.
7370 #include <isl/schedule.h>
7371 __isl_give isl_schedule *isl_schedule_empty(
7372 __isl_take isl_space *space);
7373 __isl_give isl_schedule *isl_schedule_from_domain(
7374 __isl_take isl_union_set *domain);
7376 The function C<isl_schedule_constraints_compute_schedule> described
7377 in L</"Scheduling"> can also be used to construct schedules.
7379 C<isl_schedule> objects may be copied and freed using the following functions.
7381 #include <isl/schedule.h>
7382 __isl_give isl_schedule *isl_schedule_copy(
7383 __isl_keep isl_schedule *sched);
7384 __isl_null isl_schedule *isl_schedule_free(
7385 __isl_take isl_schedule *sched);
7387 The following functions checks whether two C<isl_schedule> objects
7388 are obviously the same.
7390 #include <isl/schedule.h>
7391 int isl_schedule_plain_is_equal(
7392 __isl_keep isl_schedule *schedule1,
7393 __isl_keep isl_schedule *schedule2);
7395 The domain of the schedule, i.e., the domain described by the root node,
7396 can be obtained using the following function.
7398 #include <isl/schedule.h>
7399 __isl_give isl_union_set *isl_schedule_get_domain(
7400 __isl_keep isl_schedule *schedule);
7402 An extra top-level band node (right underneath the domain node) can
7403 be introduced into the schedule using the following function.
7404 The schedule tree is assumed not to have any anchored nodes.
7406 #include <isl/schedule.h>
7407 __isl_give isl_schedule *
7408 isl_schedule_insert_partial_schedule(
7409 __isl_take isl_schedule *schedule,
7410 __isl_take isl_multi_union_pw_aff *partial);
7412 A top-level context node (right underneath the domain node) can
7413 be introduced into the schedule using the following function.
7415 #include <isl/schedule.h>
7416 __isl_give isl_schedule *isl_schedule_insert_context(
7417 __isl_take isl_schedule *schedule,
7418 __isl_take isl_set *context)
7420 A top-level guard node (right underneath the domain node) can
7421 be introduced into the schedule using the following function.
7423 #include <isl/schedule.h>
7424 __isl_give isl_schedule *isl_schedule_insert_guard(
7425 __isl_take isl_schedule *schedule,
7426 __isl_take isl_set *guard)
7428 A schedule that combines two schedules either in the given
7429 order or in an arbitrary order, i.e., with an C<isl_schedule_node_sequence>
7430 or an C<isl_schedule_node_set> node,
7431 can be created using the following functions.
7433 #include <isl/schedule.h>
7434 __isl_give isl_schedule *isl_schedule_sequence(
7435 __isl_take isl_schedule *schedule1,
7436 __isl_take isl_schedule *schedule2);
7437 __isl_give isl_schedule *isl_schedule_set(
7438 __isl_take isl_schedule *schedule1,
7439 __isl_take isl_schedule *schedule2);
7441 The domains of the two input schedules need to be disjoint.
7443 The following function can be used to restrict the domain
7444 of a schedule with a domain node as root to be a subset of the given union set.
7445 This operation may remove nodes in the tree that have become
7448 #include <isl/schedule.h>
7449 __isl_give isl_schedule *isl_schedule_intersect_domain(
7450 __isl_take isl_schedule *schedule,
7451 __isl_take isl_union_set *domain);
7453 The following function resets the user pointers on all parameter
7454 and tuple identifiers referenced by the nodes of the given schedule.
7456 #include <isl/schedule.h>
7457 __isl_give isl_schedule *isl_schedule_reset_user(
7458 __isl_take isl_schedule *schedule);
7460 The following function aligns the parameters of all nodes
7461 in the given schedule to the given space.
7463 #include <isl/schedule.h>
7464 __isl_give isl_schedule *isl_schedule_align_params(
7465 __isl_take isl_schedule *schedule,
7466 __isl_take isl_space *space);
7468 The following function allows the user to plug in a given function
7469 in the iteration domains. The input schedule is not allowed to contain
7470 any expansion nodes.
7472 #include <isl/schedule.h>
7473 __isl_give isl_schedule *
7474 isl_schedule_pullback_union_pw_multi_aff(
7475 __isl_take isl_schedule *schedule,
7476 __isl_take isl_union_pw_multi_aff *upma);
7478 An C<isl_union_map> representation of the schedule can be obtained
7479 from an C<isl_schedule> using the following function.
7481 #include <isl/schedule.h>
7482 __isl_give isl_union_map *isl_schedule_get_map(
7483 __isl_keep isl_schedule *sched);
7485 The resulting relation encodes the same relative ordering as
7486 the schedule by mapping the domain elements to a common schedule space.
7487 If the schedule_separate_components option is set, then the order
7488 of the children of a set node is explicitly encoded in the result.
7489 If the tree contains any expansion nodes, then the relation
7490 is formulated in terms of the expanded domain elements.
7492 Schedules can be read from input using the following functions.
7494 #include <isl/schedule.h>
7495 __isl_give isl_schedule *isl_schedule_read_from_file(
7496 isl_ctx *ctx, FILE *input);
7497 __isl_give isl_schedule *isl_schedule_read_from_str(
7498 isl_ctx *ctx, const char *str);
7500 A representation of the schedule can be printed using
7502 #include <isl/schedule.h>
7503 __isl_give isl_printer *isl_printer_print_schedule(
7504 __isl_take isl_printer *p,
7505 __isl_keep isl_schedule *schedule);
7507 The schedule tree can be traversed through the use of
7508 C<isl_schedule_node> objects that point to a particular
7509 position in the schedule tree. Whenever a C<isl_schedule_node>
7510 is use to modify a node in the schedule tree, the original schedule
7511 tree is left untouched and the modifications are performed to a copy
7512 of the tree. The returned C<isl_schedule_node> then points to
7513 this modified copy of the tree.
7515 The root of the schedule tree can be obtained using the following function.
7517 #include <isl/schedule.h>
7518 __isl_give isl_schedule_node *isl_schedule_get_root(
7519 __isl_keep isl_schedule *schedule);
7521 A pointer to a newly created schedule tree with a single domain
7522 node can be created using the following functions.
7524 #include <isl/schedule_node.h>
7525 __isl_give isl_schedule_node *
7526 isl_schedule_node_from_domain(
7527 __isl_take isl_union_set *domain);
7528 __isl_give isl_schedule_node *
7529 isl_schedule_node_from_extension(
7530 __isl_take isl_union_map *extension);
7532 C<isl_schedule_node_from_extension> creates a tree with an extension
7535 Schedule nodes can be copied and freed using the following functions.
7537 #include <isl/schedule_node.h>
7538 __isl_give isl_schedule_node *isl_schedule_node_copy(
7539 __isl_keep isl_schedule_node *node);
7540 __isl_null isl_schedule_node *isl_schedule_node_free(
7541 __isl_take isl_schedule_node *node);
7543 The following functions can be used to check if two schedule
7544 nodes point to the same position in the same schedule.
7546 #include <isl/schedule_node.h>
7547 int isl_schedule_node_is_equal(
7548 __isl_keep isl_schedule_node *node1,
7549 __isl_keep isl_schedule_node *node2);
7551 The following properties can be obtained from a schedule node.
7553 #include <isl/schedule_node.h>
7554 enum isl_schedule_node_type isl_schedule_node_get_type(
7555 __isl_keep isl_schedule_node *node);
7556 enum isl_schedule_node_type
7557 isl_schedule_node_get_parent_type(
7558 __isl_keep isl_schedule_node *node);
7559 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7560 __isl_keep isl_schedule_node *node);
7562 The function C<isl_schedule_node_get_type> returns the type of
7563 the node, while C<isl_schedule_node_get_parent_type> returns
7564 type of the parent of the node, which is required to exist.
7565 The function C<isl_schedule_node_get_schedule> returns a copy
7566 to the schedule to which the node belongs.
7568 The following functions can be used to move the schedule node
7569 to a different position in the tree or to check if such a position
7572 #include <isl/schedule_node.h>
7573 int isl_schedule_node_has_parent(
7574 __isl_keep isl_schedule_node *node);
7575 __isl_give isl_schedule_node *isl_schedule_node_parent(
7576 __isl_take isl_schedule_node *node);
7577 __isl_give isl_schedule_node *isl_schedule_node_root(
7578 __isl_take isl_schedule_node *node);
7579 __isl_give isl_schedule_node *isl_schedule_node_ancestor(
7580 __isl_take isl_schedule_node *node,
7582 int isl_schedule_node_n_children(
7583 __isl_keep isl_schedule_node *node);
7584 __isl_give isl_schedule_node *isl_schedule_node_child(
7585 __isl_take isl_schedule_node *node, int pos);
7586 int isl_schedule_node_has_children(
7587 __isl_keep isl_schedule_node *node);
7588 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7589 __isl_take isl_schedule_node *node);
7590 int isl_schedule_node_has_previous_sibling(
7591 __isl_keep isl_schedule_node *node);
7592 __isl_give isl_schedule_node *
7593 isl_schedule_node_previous_sibling(
7594 __isl_take isl_schedule_node *node);
7595 int isl_schedule_node_has_next_sibling(
7596 __isl_keep isl_schedule_node *node);
7597 __isl_give isl_schedule_node *
7598 isl_schedule_node_next_sibling(
7599 __isl_take isl_schedule_node *node);
7601 For C<isl_schedule_node_ancestor>, the ancestor of generation 0
7602 is the node itself, the ancestor of generation 1 is its parent and so on.
7604 It is also possible to query the number of ancestors of a node,
7605 the position of the current node
7606 within the children of its parent, the position of the subtree
7607 containing a node within the children of an ancestor
7608 or to obtain a copy of a given
7609 child without destroying the current node.
7610 Given two nodes that point to the same schedule, their closest
7611 shared ancestor can be obtained using
7612 C<isl_schedule_node_get_shared_ancestor>.
7614 #include <isl/schedule_node.h>
7615 int isl_schedule_node_get_tree_depth(
7616 __isl_keep isl_schedule_node *node);
7617 int isl_schedule_node_get_child_position(
7618 __isl_keep isl_schedule_node *node);
7619 int isl_schedule_node_get_ancestor_child_position(
7620 __isl_keep isl_schedule_node *node,
7621 __isl_keep isl_schedule_node *ancestor);
7622 __isl_give isl_schedule_node *isl_schedule_node_get_child(
7623 __isl_keep isl_schedule_node *node, int pos);
7624 __isl_give isl_schedule_node *
7625 isl_schedule_node_get_shared_ancestor(
7626 __isl_keep isl_schedule_node *node1,
7627 __isl_keep isl_schedule_node *node2);
7629 All nodes in a schedule tree or
7630 all descendants of a specific node (including the node) can be visited
7631 in depth-first pre-order using the following functions.
7633 #include <isl/schedule.h>
7634 int isl_schedule_foreach_schedule_node(
7635 __isl_keep isl_schedule *sched,
7636 int (*fn)(__isl_keep isl_schedule_node *node,
7637 void *user), void *user);
7639 #include <isl/schedule_node.h>
7640 int isl_schedule_node_foreach_descendant(
7641 __isl_keep isl_schedule_node *node,
7642 int (*fn)(__isl_keep isl_schedule_node *node,
7643 void *user), void *user);
7645 The callback function is slightly different from the usual
7646 callbacks in that it not only indicates success (non-negative result)
7647 or failure (negative result), but also indicates whether the children
7648 of the given node should be visited. In particular, if the callback
7649 returns a positive value, then the children are visited, but if
7650 the callback returns zero, then the children are not visited.
7652 The ancestors of a node in a schedule tree can be visited from
7653 the root down to and including the parent of the node using
7654 the following function.
7656 #include <isl/schedule_node.h>
7657 int isl_schedule_node_foreach_ancestor_top_down(
7658 __isl_keep isl_schedule_node *node,
7659 int (*fn)(__isl_keep isl_schedule_node *node,
7660 void *user), void *user);
7662 The following functions allows for a depth-first post-order
7663 traversal of the nodes in a schedule tree or
7664 of the descendants of a specific node (including the node
7665 itself), where the user callback is allowed to modify the
7668 #include <isl/schedule.h>
7669 __isl_give isl_schedule *isl_schedule_map_schedule_node(
7670 __isl_take isl_schedule *schedule,
7671 __isl_give isl_schedule_node *(*fn)(
7672 __isl_take isl_schedule_node *node,
7673 void *user), void *user);
7675 #include <isl/schedule_node.h>
7676 __isl_give isl_schedule_node *
7677 isl_schedule_node_map_descendant(
7678 __isl_take isl_schedule_node *node,
7679 __isl_give isl_schedule_node *(*fn)(
7680 __isl_take isl_schedule_node *node,
7681 void *user), void *user);
7683 The traversal continues from the node returned by the callback function.
7684 It is the responsibility of the user to ensure that this does not
7685 lead to an infinite loop. It is safest to always return a pointer
7686 to the same position (same ancestors and child positions) as the input node.
7688 The following function removes a node (along with its descendants)
7689 from a schedule tree and returns a pointer to the leaf at the
7690 same position in the updated tree.
7691 It is not allowed to remove the root of a schedule tree or
7692 a child of a set or sequence node.
7694 #include <isl/schedule_node.h>
7695 __isl_give isl_schedule_node *isl_schedule_node_cut(
7696 __isl_take isl_schedule_node *node);
7698 The following function removes a single node
7699 from a schedule tree and returns a pointer to the child
7700 of the node, now located at the position of the original node
7701 or to a leaf node at that position if there was no child.
7702 It is not allowed to remove the root of a schedule tree,
7703 a set or sequence node, a child of a set or sequence node or
7704 a band node with an anchored subtree.
7706 #include <isl/schedule_node.h>
7707 __isl_give isl_schedule_node *isl_schedule_node_delete(
7708 __isl_take isl_schedule_node *node);
7710 Most nodes in a schedule tree only contain local information.
7711 In some cases, however, a node may also refer to outer band nodes.
7712 This means that the position of the node within the tree should
7713 not be changed, or at least that no changes are performed to the
7714 outer band nodes. The following function can be used to test
7715 whether the subtree rooted at a given node contains any such nodes.
7717 #include <isl/schedule_node.h>
7718 int isl_schedule_node_is_subtree_anchored(
7719 __isl_keep isl_schedule_node *node);
7721 The following function resets the user pointers on all parameter
7722 and tuple identifiers referenced by the given schedule node.
7724 #include <isl/schedule_node.h>
7725 __isl_give isl_schedule_node *isl_schedule_node_reset_user(
7726 __isl_take isl_schedule_node *node);
7728 The following function aligns the parameters of the given schedule
7729 node to the given space.
7731 #include <isl/schedule_node.h>
7732 __isl_give isl_schedule_node *
7733 isl_schedule_node_align_params(
7734 __isl_take isl_schedule_node *node,
7735 __isl_take isl_space *space);
7737 Several node types have their own functions for querying
7738 (and in some cases setting) some node type specific properties.
7740 #include <isl/schedule_node.h>
7741 __isl_give isl_space *isl_schedule_node_band_get_space(
7742 __isl_keep isl_schedule_node *node);
7743 __isl_give isl_multi_union_pw_aff *
7744 isl_schedule_node_band_get_partial_schedule(
7745 __isl_keep isl_schedule_node *node);
7746 __isl_give isl_union_map *
7747 isl_schedule_node_band_get_partial_schedule_union_map(
7748 __isl_keep isl_schedule_node *node);
7749 unsigned isl_schedule_node_band_n_member(
7750 __isl_keep isl_schedule_node *node);
7751 int isl_schedule_node_band_member_get_coincident(
7752 __isl_keep isl_schedule_node *node, int pos);
7753 __isl_give isl_schedule_node *
7754 isl_schedule_node_band_member_set_coincident(
7755 __isl_take isl_schedule_node *node, int pos,
7757 int isl_schedule_node_band_get_permutable(
7758 __isl_keep isl_schedule_node *node);
7759 __isl_give isl_schedule_node *
7760 isl_schedule_node_band_set_permutable(
7761 __isl_take isl_schedule_node *node, int permutable);
7762 enum isl_ast_loop_type
7763 isl_schedule_node_band_member_get_ast_loop_type(
7764 __isl_keep isl_schedule_node *node, int pos);
7765 __isl_give isl_schedule_node *
7766 isl_schedule_node_band_member_set_ast_loop_type(
7767 __isl_take isl_schedule_node *node, int pos,
7768 enum isl_ast_loop_type type);
7769 __isl_give isl_union_set *
7770 enum isl_ast_loop_type
7771 isl_schedule_node_band_member_get_isolate_ast_loop_type(
7772 __isl_keep isl_schedule_node *node, int pos);
7773 __isl_give isl_schedule_node *
7774 isl_schedule_node_band_member_set_isolate_ast_loop_type(
7775 __isl_take isl_schedule_node *node, int pos,
7776 enum isl_ast_loop_type type);
7777 isl_schedule_node_band_get_ast_build_options(
7778 __isl_keep isl_schedule_node *node);
7779 __isl_give isl_schedule_node *
7780 isl_schedule_node_band_set_ast_build_options(
7781 __isl_take isl_schedule_node *node,
7782 __isl_take isl_union_set *options);
7784 The function C<isl_schedule_node_band_get_space> returns the space
7785 of the partial schedule of the band.
7786 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
7787 returns a representation of the partial schedule of the band node
7788 in the form of an C<isl_union_map>.
7789 The coincident and permutable properties are set by
7790 C<isl_schedule_constraints_compute_schedule> on the schedule tree
7792 A scheduling dimension is considered to be ``coincident''
7793 if it satisfies the coincidence constraints within its band.
7794 That is, if the dependence distances of the coincidence
7795 constraints are all zero in that direction (for fixed
7796 iterations of outer bands).
7797 A band is marked permutable if it was produced using the Pluto-like scheduler.
7798 Note that the scheduler may have to resort to a Feautrier style scheduling
7799 step even if the default scheduler is used.
7800 An C<isl_ast_loop_type> is one of C<isl_ast_loop_default>,
7801 C<isl_ast_loop_atomic>, C<isl_ast_loop_unroll> or C<isl_ast_loop_separate>.
7802 For the meaning of these loop AST generation types and the difference
7803 between the regular loop AST generation type and the isolate
7804 loop AST generation type, see L</"AST Generation Options (Schedule Tree)">.
7805 The functions C<isl_schedule_node_band_member_get_ast_loop_type>
7806 and C<isl_schedule_node_band_member_get_isolate_ast_loop_type>
7807 may return C<isl_ast_loop_error> if an error occurs.
7808 The AST build options govern how an AST is generated for
7809 the individual schedule dimensions during AST generation.
7810 See L</"AST Generation Options (Schedule Tree)">.
7812 #include <isl/schedule_node.h>
7813 __isl_give isl_set *
7814 isl_schedule_node_context_get_context(
7815 __isl_keep isl_schedule_node *node);
7817 #include <isl/schedule_node.h>
7818 __isl_give isl_union_set *
7819 isl_schedule_node_domain_get_domain(
7820 __isl_keep isl_schedule_node *node);
7822 #include <isl/schedule_node.h>
7823 __isl_give isl_union_map *
7824 isl_schedule_node_expansion_get_expansion(
7825 __isl_keep isl_schedule_node *node);
7826 __isl_give isl_union_pw_multi_aff *
7827 isl_schedule_node_expansion_get_contraction(
7828 __isl_keep isl_schedule_node *node);
7830 #include <isl/schedule_node.h>
7831 __isl_give isl_union_map *
7832 isl_schedule_node_extension_get_extension(
7833 __isl_keep isl_schedule_node *node);
7835 #include <isl/schedule_node.h>
7836 __isl_give isl_union_set *
7837 isl_schedule_node_filter_get_filter(
7838 __isl_keep isl_schedule_node *node);
7840 #include <isl/schedule_node.h>
7841 __isl_give isl_set *isl_schedule_node_guard_get_guard(
7842 __isl_keep isl_schedule_node *node);
7844 #include <isl/schedule_node.h>
7845 __isl_give isl_id *isl_schedule_node_mark_get_id(
7846 __isl_keep isl_schedule_node *node);
7848 The following functions can be used to obtain an C<isl_multi_union_pw_aff>,
7849 an C<isl_union_pw_multi_aff> or C<isl_union_map> representation of
7850 partial schedules related to the node.
7852 #include <isl/schedule_node.h>
7853 __isl_give isl_multi_union_pw_aff *
7854 isl_schedule_node_get_prefix_schedule_multi_union_pw_aff(
7855 __isl_keep isl_schedule_node *node);
7856 __isl_give isl_union_pw_multi_aff *
7857 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
7858 __isl_keep isl_schedule_node *node);
7859 __isl_give isl_union_map *
7860 isl_schedule_node_get_prefix_schedule_union_map(
7861 __isl_keep isl_schedule_node *node);
7862 __isl_give isl_union_map *
7863 isl_schedule_node_get_prefix_schedule_relation(
7864 __isl_keep isl_schedule_node *node);
7865 __isl_give isl_union_map *
7866 isl_schedule_node_get_subtree_schedule_union_map(
7867 __isl_keep isl_schedule_node *node);
7869 In particular, the functions
7870 C<isl_schedule_node_get_prefix_schedule_multi_union_pw_aff>,
7871 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
7872 and C<isl_schedule_node_get_prefix_schedule_union_map>
7873 return a relative ordering on the domain elements that reach the given
7874 node determined by its ancestors.
7875 The function C<isl_schedule_node_get_prefix_schedule_relation>
7876 additionally includes the domain constraints in the result.
7877 The function C<isl_schedule_node_get_subtree_schedule_union_map>
7878 returns a representation of the partial schedule defined by the
7879 subtree rooted at the given node.
7880 If the tree contains any expansion nodes, then the subtree schedule
7881 is formulated in terms of the expanded domain elements.
7882 The tree passed to functions returning a prefix schedule
7883 may only contain extension nodes if these would not affect
7884 the result of these functions. That is, if one of the ancestors
7885 is an extension node, then all of the domain elements that were
7886 added by the extension node need to have been filtered out
7887 by filter nodes between the extension node and the input node.
7888 The tree passed to C<isl_schedule_node_get_subtree_schedule_union_map>
7889 may not contain in extension nodes in the selected subtree.
7891 The expansion/contraction defined by an entire subtree, combining
7892 the expansions/contractions
7893 on the expansion nodes in the subtree, can be obtained using
7894 the following functions.
7896 #include <isl/schedule_node.h>
7897 __isl_give isl_union_map *
7898 isl_schedule_node_get_subtree_expansion(
7899 __isl_keep isl_schedule_node *node);
7900 __isl_give isl_union_pw_multi_aff *
7901 isl_schedule_node_get_subtree_contraction(
7902 __isl_keep isl_schedule_node *node);
7904 The total number of outer band members of given node, i.e.,
7905 the shared output dimension of the maps in the result
7906 of C<isl_schedule_node_get_prefix_schedule_union_map> can be obtained
7907 using the following function.
7909 #include <isl/schedule_node.h>
7910 int isl_schedule_node_get_schedule_depth(
7911 __isl_keep isl_schedule_node *node);
7913 The following functions return the elements that reach the given node
7914 or the union of universes in the spaces that contain these elements.
7916 #include <isl/schedule_node.h>
7917 __isl_give isl_union_set *
7918 isl_schedule_node_get_domain(
7919 __isl_keep isl_schedule_node *node);
7920 __isl_give isl_union_set *
7921 isl_schedule_node_get_universe_domain(
7922 __isl_keep isl_schedule_node *node);
7924 The input tree of C<isl_schedule_node_get_domain>
7925 may only contain extension nodes if these would not affect
7926 the result of this function. That is, if one of the ancestors
7927 is an extension node, then all of the domain elements that were
7928 added by the extension node need to have been filtered out
7929 by filter nodes between the extension node and the input node.
7931 The following functions can be used to introduce additional nodes
7932 in the schedule tree. The new node is introduced at the point
7933 in the tree where the C<isl_schedule_node> points to and
7934 the results points to the new node.
7936 #include <isl/schedule_node.h>
7937 __isl_give isl_schedule_node *
7938 isl_schedule_node_insert_partial_schedule(
7939 __isl_take isl_schedule_node *node,
7940 __isl_take isl_multi_union_pw_aff *schedule);
7942 This function inserts a new band node with (the greatest integer
7943 part of) the given partial schedule.
7944 The subtree rooted at the given node is assumed not to have
7947 #include <isl/schedule_node.h>
7948 __isl_give isl_schedule_node *
7949 isl_schedule_node_insert_context(
7950 __isl_take isl_schedule_node *node,
7951 __isl_take isl_set *context);
7953 This function inserts a new context node with the given context constraints.
7955 #include <isl/schedule_node.h>
7956 __isl_give isl_schedule_node *
7957 isl_schedule_node_insert_filter(
7958 __isl_take isl_schedule_node *node,
7959 __isl_take isl_union_set *filter);
7961 This function inserts a new filter node with the given filter.
7962 If the original node already pointed to a filter node, then the
7963 two filter nodes are merged into one.
7965 #include <isl/schedule_node.h>
7966 __isl_give isl_schedule_node *
7967 isl_schedule_node_insert_guard(
7968 __isl_take isl_schedule_node *node,
7969 __isl_take isl_set *guard);
7971 This function inserts a new guard node with the given guard constraints.
7973 #include <isl/schedule_node.h>
7974 __isl_give isl_schedule_node *
7975 isl_schedule_node_insert_mark(
7976 __isl_take isl_schedule_node *node,
7977 __isl_take isl_id *mark);
7979 This function inserts a new mark node with the give mark identifier.
7981 #include <isl/schedule_node.h>
7982 __isl_give isl_schedule_node *
7983 isl_schedule_node_insert_sequence(
7984 __isl_take isl_schedule_node *node,
7985 __isl_take isl_union_set_list *filters);
7986 __isl_give isl_schedule_node *
7987 isl_schedule_node_insert_set(
7988 __isl_take isl_schedule_node *node,
7989 __isl_take isl_union_set_list *filters);
7991 These functions insert a new sequence or set node with the given
7992 filters as children.
7994 #include <isl/schedule_node.h>
7995 __isl_give isl_schedule_node *isl_schedule_node_group(
7996 __isl_take isl_schedule_node *node,
7997 __isl_take isl_id *group_id);
7999 This function introduces an expansion node in between the current
8000 node and its parent that expands instances of a space with tuple
8001 identifier C<group_id> to the original domain elements that reach
8002 the node. The group instances are identified by the prefix schedule
8003 of those domain elements. The ancestors of the node are adjusted
8004 to refer to the group instances instead of the original domain
8005 elements. The return value points to the same node in the updated
8006 schedule tree as the input node, i.e., to the child of the newly
8007 introduced expansion node. Grouping instances of different statements
8008 ensures that they will be treated as a single statement by the
8009 AST generator up to the point of the expansion node.
8011 The partial schedule of a band node can be scaled (down) using
8012 the following functions.
8014 #include <isl/schedule_node.h>
8015 __isl_give isl_schedule_node *
8016 isl_schedule_node_band_scale(
8017 __isl_take isl_schedule_node *node,
8018 __isl_take isl_multi_val *mv);
8019 __isl_give isl_schedule_node *
8020 isl_schedule_node_band_scale_down(
8021 __isl_take isl_schedule_node *node,
8022 __isl_take isl_multi_val *mv);
8024 The spaces of the two arguments need to match.
8025 After scaling, the partial schedule is replaced by its greatest
8026 integer part to ensure that the schedule remains integral.
8028 A band node can be tiled using the following function.
8030 #include <isl/schedule_node.h>
8031 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
8032 __isl_take isl_schedule_node *node,
8033 __isl_take isl_multi_val *sizes);
8035 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8037 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8038 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8040 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8042 The C<isl_schedule_node_band_tile> function tiles
8043 the band using the given tile sizes inside its schedule.
8044 A new child band node is created to represent the point loops and it is
8045 inserted between the modified band and its children.
8046 The subtree rooted at the given node is assumed not to have
8048 The C<tile_scale_tile_loops> option specifies whether the tile
8049 loops iterators should be scaled by the tile sizes.
8050 If the C<tile_shift_point_loops> option is set, then the point loops
8051 are shifted to start at zero.
8053 A band node can be split into two nested band nodes
8054 using the following function.
8056 #include <isl/schedule_node.h>
8057 __isl_give isl_schedule_node *isl_schedule_node_band_split(
8058 __isl_take isl_schedule_node *node, int pos);
8060 The resulting outer band node contains the first C<pos> dimensions of
8061 the schedule of C<node> while the inner band contains the remaining dimensions.
8062 The schedules of the two band nodes live in anonymous spaces.
8064 A band node can be moved down to the leaves of the subtree rooted
8065 at the band node using the following function.
8067 #include <isl/schedule_node.h>
8068 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
8069 __isl_take isl_schedule_node *node);
8071 The subtree rooted at the given node is assumed not to have
8073 The result points to the node in the resulting tree that is in the same
8074 position as the node pointed to by C<node> in the original tree.
8076 #include <isl/schedule_node.h>
8077 __isl_give isl_schedule_node *
8078 isl_schedule_node_order_after(
8079 __isl_take isl_schedule_node *node,
8080 __isl_take isl_union_set *filter);
8082 This function splits the domain elements that reach C<node>
8083 into those that satisfy C<filter> and those that do not and
8084 arranges for the elements that do satisfy the filter to be
8085 executed after those that do not. The order is imposed by
8086 a sequence node, possibly reusing the grandparent of C<node>
8087 on two copies of the subtree attached to the original C<node>.
8088 Both copies are simplified with respect to their filter.
8090 Return a pointer to the copy of the subtree that does not
8091 satisfy C<filter>. If there is no such copy (because all
8092 reaching domain elements satisfy the filter), then return
8093 the original pointer.
8095 #include <isl/schedule_node.h>
8096 __isl_give isl_schedule_node *
8097 isl_schedule_node_graft_before(
8098 __isl_take isl_schedule_node *node,
8099 __isl_take isl_schedule_node *graft);
8100 __isl_give isl_schedule_node *
8101 isl_schedule_node_graft_after(
8102 __isl_take isl_schedule_node *node,
8103 __isl_take isl_schedule_node *graft);
8105 This function inserts the C<graft> tree into the tree containing C<node>
8106 such that it is executed before (in case of C<isl_schedule_node_graft_before>)
8107 or after (in case of C<isl_schedule_node_graft_after>) C<node>.
8108 The root node of C<graft>
8109 should be an extension node where the domain of the extension
8110 is the flat product of all outer band nodes of C<node>.
8111 The root node may also be a domain node.
8112 The elements of the domain or the range of the extension may not
8113 intersect with the domain elements that reach "node".
8114 The schedule tree of C<graft> may not be anchored.
8116 The schedule tree of C<node> is modified to include an extension node
8117 corresponding to the root node of C<graft> as a child of the original
8118 parent of C<node>. The original node that C<node> points to and the
8119 child of the root node of C<graft> are attached to this extension node
8120 through a sequence, with appropriate filters and with the child
8121 of C<graft> appearing before or after the original C<node>.
8123 If C<node> already appears inside a sequence that is the child of
8124 an extension node and if the spaces of the new domain elements
8125 do not overlap with those of the original domain elements,
8126 then that extension node is extended with the new extension
8127 rather than introducing a new segment of extension and sequence nodes.
8129 Return a pointer to the same node in the modified tree that
8130 C<node> pointed to in the original tree.
8132 A representation of the schedule node can be printed using
8134 #include <isl/schedule_node.h>
8135 __isl_give isl_printer *isl_printer_print_schedule_node(
8136 __isl_take isl_printer *p,
8137 __isl_keep isl_schedule_node *node);
8139 =head2 Dependence Analysis
8141 C<isl> contains specialized functionality for performing
8142 array dataflow analysis. That is, given a I<sink> access relation
8143 and a collection of possible I<source> access relations,
8144 C<isl> can compute relations that describe
8145 for each iteration of the sink access, which iteration
8146 of which of the source access relations was the last
8147 to access the same data element before the given iteration
8149 The resulting dependence relations map source iterations
8150 to the corresponding sink iterations.
8151 To compute standard flow dependences, the sink should be
8152 a read, while the sources should be writes.
8153 If any of the source accesses are marked as being I<may>
8154 accesses, then there will be a dependence from the last
8155 I<must> access B<and> from any I<may> access that follows
8156 this last I<must> access.
8157 In particular, if I<all> sources are I<may> accesses,
8158 then memory based dependence analysis is performed.
8159 If, on the other hand, all sources are I<must> accesses,
8160 then value based dependence analysis is performed.
8162 =head3 High-level Interface
8164 A high-level interface to dependence analysis is provided
8165 by the following function.
8167 #include <isl/flow.h>
8168 __isl_give isl_union_flow *
8169 isl_union_access_info_compute_flow(
8170 __isl_take isl_union_access_info *access);
8172 The input C<isl_union_access_info> object describes the sink
8173 access relations, the source access relations and a schedule,
8174 while the output C<isl_union_flow> object describes
8175 the resulting dependence relations and the subsets of the
8176 sink relations for which no source was found.
8178 An C<isl_union_access_info> is created, modified and freed using
8179 the following functions.
8181 #include <isl/flow.h>
8182 __isl_give isl_union_access_info *
8183 isl_union_access_info_from_sink(
8184 __isl_take isl_union_map *sink);
8185 __isl_give isl_union_access_info *
8186 isl_union_access_info_set_must_source(
8187 __isl_take isl_union_access_info *access,
8188 __isl_take isl_union_map *must_source);
8189 __isl_give isl_union_access_info *
8190 isl_union_access_info_set_may_source(
8191 __isl_take isl_union_access_info *access,
8192 __isl_take isl_union_map *may_source);
8193 __isl_give isl_union_access_info *
8194 isl_union_access_info_set_schedule(
8195 __isl_take isl_union_access_info *access,
8196 __isl_take isl_schedule *schedule);
8197 __isl_give isl_union_access_info *
8198 isl_union_access_info_set_schedule_map(
8199 __isl_take isl_union_access_info *access,
8200 __isl_take isl_union_map *schedule_map);
8201 __isl_null isl_union_access_info *
8202 isl_union_access_info_free(
8203 __isl_take isl_union_access_info *access);
8205 The may sources set by C<isl_union_access_info_set_may_source>
8206 do not need to include the must sources set by
8207 C<isl_union_access_info_set_must_source> as a subset.
8208 The user is free not to call one (or both) of these functions,
8209 in which case the corresponding set is kept to its empty default.
8210 Similarly, the default schedule initialized by
8211 C<isl_union_access_info_from_sink> is empty.
8212 The current schedule is determined by the last call to either
8213 C<isl_union_access_info_set_schedule> or
8214 C<isl_union_access_info_set_schedule_map>.
8215 The domain of the schedule corresponds to the domains of
8216 the access relations. In particular, the domains of the access
8217 relations are effectively intersected with the domain of the schedule
8218 and only the resulting accesses are considered by the dependence analysis.
8220 The output of C<isl_union_access_info_compute_flow> can be examined
8221 and freed using the following functions.
8223 #include <isl/flow.h>
8224 __isl_give isl_union_map *isl_union_flow_get_must_dependence(
8225 __isl_keep isl_union_flow *flow);
8226 __isl_give isl_union_map *isl_union_flow_get_may_dependence(
8227 __isl_keep isl_union_flow *flow);
8228 __isl_give isl_union_map *isl_union_flow_get_must_no_source(
8229 __isl_keep isl_union_flow *flow);
8230 __isl_give isl_union_map *isl_union_flow_get_may_no_source(
8231 __isl_keep isl_union_flow *flow);
8232 __isl_null isl_union_flow *isl_union_flow_free(
8233 __isl_take isl_union_flow *flow);
8235 The relation returned by C<isl_union_flow_get_must_dependence>
8236 relates domain elements of must sources to domain elements of the sink.
8237 The relation returned by C<isl_union_flow_get_may_dependence>
8238 relates domain elements of must or may sources to domain elements of the sink
8239 and includes the previous relation as a subset.
8240 The relation returned by C<isl_union_flow_get_must_no_source> is the subset
8241 of the sink relation for which no dependences have been found.
8242 The relation returned by C<isl_union_flow_get_may_no_source> is the subset
8243 of the sink relation for which no definite dependences have been found.
8244 That is, it contains those sink access that do not contribute to any
8245 of the elements in the relation returned
8246 by C<isl_union_flow_get_must_dependence>.
8248 =head3 Low-level Interface
8250 A lower-level interface is provided by the following functions.
8252 #include <isl/flow.h>
8254 typedef int (*isl_access_level_before)(void *first, void *second);
8256 __isl_give isl_access_info *isl_access_info_alloc(
8257 __isl_take isl_map *sink,
8258 void *sink_user, isl_access_level_before fn,
8260 __isl_give isl_access_info *isl_access_info_add_source(
8261 __isl_take isl_access_info *acc,
8262 __isl_take isl_map *source, int must,
8264 __isl_null isl_access_info *isl_access_info_free(
8265 __isl_take isl_access_info *acc);
8267 __isl_give isl_flow *isl_access_info_compute_flow(
8268 __isl_take isl_access_info *acc);
8270 int isl_flow_foreach(__isl_keep isl_flow *deps,
8271 int (*fn)(__isl_take isl_map *dep, int must,
8272 void *dep_user, void *user),
8274 __isl_give isl_map *isl_flow_get_no_source(
8275 __isl_keep isl_flow *deps, int must);
8276 void isl_flow_free(__isl_take isl_flow *deps);
8278 The function C<isl_access_info_compute_flow> performs the actual
8279 dependence analysis. The other functions are used to construct
8280 the input for this function or to read off the output.
8282 The input is collected in an C<isl_access_info>, which can
8283 be created through a call to C<isl_access_info_alloc>.
8284 The arguments to this functions are the sink access relation
8285 C<sink>, a token C<sink_user> used to identify the sink
8286 access to the user, a callback function for specifying the
8287 relative order of source and sink accesses, and the number
8288 of source access relations that will be added.
8289 The callback function has type C<int (*)(void *first, void *second)>.
8290 The function is called with two user supplied tokens identifying
8291 either a source or the sink and it should return the shared nesting
8292 level and the relative order of the two accesses.
8293 In particular, let I<n> be the number of loops shared by
8294 the two accesses. If C<first> precedes C<second> textually,
8295 then the function should return I<2 * n + 1>; otherwise,
8296 it should return I<2 * n>.
8297 The sources can be added to the C<isl_access_info> by performing
8298 (at most) C<max_source> calls to C<isl_access_info_add_source>.
8299 C<must> indicates whether the source is a I<must> access
8300 or a I<may> access. Note that a multi-valued access relation
8301 should only be marked I<must> if every iteration in the domain
8302 of the relation accesses I<all> elements in its image.
8303 The C<source_user> token is again used to identify
8304 the source access. The range of the source access relation
8305 C<source> should have the same dimension as the range
8306 of the sink access relation.
8307 The C<isl_access_info_free> function should usually not be
8308 called explicitly, because it is called implicitly by
8309 C<isl_access_info_compute_flow>.
8311 The result of the dependence analysis is collected in an
8312 C<isl_flow>. There may be elements of
8313 the sink access for which no preceding source access could be
8314 found or for which all preceding sources are I<may> accesses.
8315 The relations containing these elements can be obtained through
8316 calls to C<isl_flow_get_no_source>, the first with C<must> set
8317 and the second with C<must> unset.
8318 In the case of standard flow dependence analysis,
8319 with the sink a read and the sources I<must> writes,
8320 the first relation corresponds to the reads from uninitialized
8321 array elements and the second relation is empty.
8322 The actual flow dependences can be extracted using
8323 C<isl_flow_foreach>. This function will call the user-specified
8324 callback function C<fn> for each B<non-empty> dependence between
8325 a source and the sink. The callback function is called
8326 with four arguments, the actual flow dependence relation
8327 mapping source iterations to sink iterations, a boolean that
8328 indicates whether it is a I<must> or I<may> dependence, a token
8329 identifying the source and an additional C<void *> with value
8330 equal to the third argument of the C<isl_flow_foreach> call.
8331 A dependence is marked I<must> if it originates from a I<must>
8332 source and if it is not followed by any I<may> sources.
8334 After finishing with an C<isl_flow>, the user should call
8335 C<isl_flow_free> to free all associated memory.
8337 =head3 Interaction with the Low-level Interface
8339 During the dependence analysis, we frequently need to perform
8340 the following operation. Given a relation between sink iterations
8341 and potential source iterations from a particular source domain,
8342 what is the last potential source iteration corresponding to each
8343 sink iteration. It can sometimes be convenient to adjust
8344 the set of potential source iterations before or after each such operation.
8345 The prototypical example is fuzzy array dataflow analysis,
8346 where we need to analyze if, based on data-dependent constraints,
8347 the sink iteration can ever be executed without one or more of
8348 the corresponding potential source iterations being executed.
8349 If so, we can introduce extra parameters and select an unknown
8350 but fixed source iteration from the potential source iterations.
8351 To be able to perform such manipulations, C<isl> provides the following
8354 #include <isl/flow.h>
8356 typedef __isl_give isl_restriction *(*isl_access_restrict)(
8357 __isl_keep isl_map *source_map,
8358 __isl_keep isl_set *sink, void *source_user,
8360 __isl_give isl_access_info *isl_access_info_set_restrict(
8361 __isl_take isl_access_info *acc,
8362 isl_access_restrict fn, void *user);
8364 The function C<isl_access_info_set_restrict> should be called
8365 before calling C<isl_access_info_compute_flow> and registers a callback function
8366 that will be called any time C<isl> is about to compute the last
8367 potential source. The first argument is the (reverse) proto-dependence,
8368 mapping sink iterations to potential source iterations.
8369 The second argument represents the sink iterations for which
8370 we want to compute the last source iteration.
8371 The third argument is the token corresponding to the source
8372 and the final argument is the token passed to C<isl_access_info_set_restrict>.
8373 The callback is expected to return a restriction on either the input or
8374 the output of the operation computing the last potential source.
8375 If the input needs to be restricted then restrictions are needed
8376 for both the source and the sink iterations. The sink iterations
8377 and the potential source iterations will be intersected with these sets.
8378 If the output needs to be restricted then only a restriction on the source
8379 iterations is required.
8380 If any error occurs, the callback should return C<NULL>.
8381 An C<isl_restriction> object can be created, freed and inspected
8382 using the following functions.
8384 #include <isl/flow.h>
8386 __isl_give isl_restriction *isl_restriction_input(
8387 __isl_take isl_set *source_restr,
8388 __isl_take isl_set *sink_restr);
8389 __isl_give isl_restriction *isl_restriction_output(
8390 __isl_take isl_set *source_restr);
8391 __isl_give isl_restriction *isl_restriction_none(
8392 __isl_take isl_map *source_map);
8393 __isl_give isl_restriction *isl_restriction_empty(
8394 __isl_take isl_map *source_map);
8395 __isl_null isl_restriction *isl_restriction_free(
8396 __isl_take isl_restriction *restr);
8398 C<isl_restriction_none> and C<isl_restriction_empty> are special
8399 cases of C<isl_restriction_input>. C<isl_restriction_none>
8400 is essentially equivalent to
8402 isl_restriction_input(isl_set_universe(
8403 isl_space_range(isl_map_get_space(source_map))),
8405 isl_space_domain(isl_map_get_space(source_map))));
8407 whereas C<isl_restriction_empty> is essentially equivalent to
8409 isl_restriction_input(isl_set_empty(
8410 isl_space_range(isl_map_get_space(source_map))),
8412 isl_space_domain(isl_map_get_space(source_map))));
8416 B<The functionality described in this section is fairly new
8417 and may be subject to change.>
8419 #include <isl/schedule.h>
8420 __isl_give isl_schedule *
8421 isl_schedule_constraints_compute_schedule(
8422 __isl_take isl_schedule_constraints *sc);
8424 The function C<isl_schedule_constraints_compute_schedule> can be
8425 used to compute a schedule that satisfies the given schedule constraints.
8426 These schedule constraints include the iteration domain for which
8427 a schedule should be computed and dependences between pairs of
8428 iterations. In particular, these dependences include
8429 I<validity> dependences and I<proximity> dependences.
8430 By default, the algorithm used to construct the schedule is similar
8431 to that of C<Pluto>.
8432 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
8434 The generated schedule respects all validity dependences.
8435 That is, all dependence distances over these dependences in the
8436 scheduled space are lexicographically positive.
8438 The default algorithm tries to ensure that the dependence distances
8439 over coincidence constraints are zero and to minimize the
8440 dependence distances over proximity dependences.
8441 Moreover, it tries to obtain sequences (bands) of schedule dimensions
8442 for groups of domains where the dependence distances over validity
8443 dependences have only non-negative values.
8444 Note that when minimizing the maximal dependence distance
8445 over proximity dependences, a single affine expression in the parameters
8446 is constructed that bounds all dependence distances. If no such expression
8447 exists, then the algorithm will fail and resort to an alternative
8448 scheduling algorithm. In particular, this means that adding proximity
8449 dependences may eliminate valid solutions. A typical example where this
8450 phenomenon may occur is when some subset of the proximity dependences
8451 has no restriction on some parameter, forcing the coefficient of that
8452 parameter to be zero, while some other subset forces the dependence
8453 distance to depend on that parameter, requiring the same coefficient
8455 When using Feautrier's algorithm, the coincidence and proximity constraints
8456 are only taken into account during the extension to a
8457 full-dimensional schedule.
8459 An C<isl_schedule_constraints> object can be constructed
8460 and manipulated using the following functions.
8462 #include <isl/schedule.h>
8463 __isl_give isl_schedule_constraints *
8464 isl_schedule_constraints_copy(
8465 __isl_keep isl_schedule_constraints *sc);
8466 __isl_give isl_schedule_constraints *
8467 isl_schedule_constraints_on_domain(
8468 __isl_take isl_union_set *domain);
8469 __isl_give isl_schedule_constraints *
8470 isl_schedule_constraints_set_context(
8471 __isl_take isl_schedule_constraints *sc,
8472 __isl_take isl_set *context);
8473 __isl_give isl_schedule_constraints *
8474 isl_schedule_constraints_set_validity(
8475 __isl_take isl_schedule_constraints *sc,
8476 __isl_take isl_union_map *validity);
8477 __isl_give isl_schedule_constraints *
8478 isl_schedule_constraints_set_coincidence(
8479 __isl_take isl_schedule_constraints *sc,
8480 __isl_take isl_union_map *coincidence);
8481 __isl_give isl_schedule_constraints *
8482 isl_schedule_constraints_set_proximity(
8483 __isl_take isl_schedule_constraints *sc,
8484 __isl_take isl_union_map *proximity);
8485 __isl_give isl_schedule_constraints *
8486 isl_schedule_constraints_set_conditional_validity(
8487 __isl_take isl_schedule_constraints *sc,
8488 __isl_take isl_union_map *condition,
8489 __isl_take isl_union_map *validity);
8490 __isl_null isl_schedule_constraints *
8491 isl_schedule_constraints_free(
8492 __isl_take isl_schedule_constraints *sc);
8494 The initial C<isl_schedule_constraints> object created by
8495 C<isl_schedule_constraints_on_domain> does not impose any constraints.
8496 That is, it has an empty set of dependences.
8497 The function C<isl_schedule_constraints_set_context> allows the user
8498 to specify additional constraints on the parameters that may
8499 be assumed to hold during the construction of the schedule.
8500 The function C<isl_schedule_constraints_set_validity> replaces the
8501 validity dependences, mapping domain elements I<i> to domain
8502 elements that should be scheduled after I<i>.
8503 The function C<isl_schedule_constraints_set_coincidence> replaces the
8504 coincidence dependences, mapping domain elements I<i> to domain
8505 elements that should be scheduled together with I<I>, if possible.
8506 The function C<isl_schedule_constraints_set_proximity> replaces the
8507 proximity dependences, mapping domain elements I<i> to domain
8508 elements that should be scheduled either before I<I>
8509 or as early as possible after I<i>.
8511 The function C<isl_schedule_constraints_set_conditional_validity>
8512 replaces the conditional validity constraints.
8513 A conditional validity constraint is only imposed when any of the corresponding
8514 conditions is satisfied, i.e., when any of them is non-zero.
8515 That is, the scheduler ensures that within each band if the dependence
8516 distances over the condition constraints are not all zero
8517 then all corresponding conditional validity constraints are respected.
8518 A conditional validity constraint corresponds to a condition
8519 if the two are adjacent, i.e., if the domain of one relation intersect
8520 the range of the other relation.
8521 The typical use case of conditional validity constraints is
8522 to allow order constraints between live ranges to be violated
8523 as long as the live ranges themselves are local to the band.
8524 To allow more fine-grained control over which conditions correspond
8525 to which conditional validity constraints, the domains and ranges
8526 of these relations may include I<tags>. That is, the domains and
8527 ranges of those relation may themselves be wrapped relations
8528 where the iteration domain appears in the domain of those wrapped relations
8529 and the range of the wrapped relations can be arbitrarily chosen
8530 by the user. Conditions and conditional validity constraints are only
8531 considered adjacent to each other if the entire wrapped relation matches.
8532 In particular, a relation with a tag will never be considered adjacent
8533 to a relation without a tag.
8535 An C<isl_schedule_constraints> object can be inspected
8536 using the following functions.
8538 #include <isl/schedule.h>
8539 __isl_give isl_union_map *
8540 isl_schedule_constraints_get_validity(
8541 __isl_keep isl_schedule_constraints *sc);
8542 __isl_give isl_union_map *
8543 isl_schedule_constraints_get_coincidence(
8544 __isl_keep isl_schedule_constraints *sc);
8545 __isl_give isl_union_map *
8546 isl_schedule_constraints_get_conditional_validity(
8547 __isl_keep isl_schedule_constraints *sc);
8548 __isl_give isl_union_map *
8549 isl_schedule_constraints_get_conditional_validity_condition(
8550 __isl_keep isl_schedule_constraints *sc);
8552 The following function computes a schedule directly from
8553 an iteration domain and validity and proximity dependences
8554 and is implemented in terms of the functions described above.
8555 The use of C<isl_union_set_compute_schedule> is discouraged.
8557 #include <isl/schedule.h>
8558 __isl_give isl_schedule *isl_union_set_compute_schedule(
8559 __isl_take isl_union_set *domain,
8560 __isl_take isl_union_map *validity,
8561 __isl_take isl_union_map *proximity);
8563 The generated schedule represents a schedule tree.
8564 For more information on schedule trees, see
8565 L</"Schedule Trees">.
8569 #include <isl/schedule.h>
8570 int isl_options_set_schedule_max_coefficient(
8571 isl_ctx *ctx, int val);
8572 int isl_options_get_schedule_max_coefficient(
8574 int isl_options_set_schedule_max_constant_term(
8575 isl_ctx *ctx, int val);
8576 int isl_options_get_schedule_max_constant_term(
8578 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
8579 int isl_options_get_schedule_fuse(isl_ctx *ctx);
8580 int isl_options_set_schedule_maximize_band_depth(
8581 isl_ctx *ctx, int val);
8582 int isl_options_get_schedule_maximize_band_depth(
8584 int isl_options_set_schedule_outer_coincidence(
8585 isl_ctx *ctx, int val);
8586 int isl_options_get_schedule_outer_coincidence(
8588 int isl_options_set_schedule_split_scaled(
8589 isl_ctx *ctx, int val);
8590 int isl_options_get_schedule_split_scaled(
8592 int isl_options_set_schedule_algorithm(
8593 isl_ctx *ctx, int val);
8594 int isl_options_get_schedule_algorithm(
8596 int isl_options_set_schedule_separate_components(
8597 isl_ctx *ctx, int val);
8598 int isl_options_get_schedule_separate_components(
8603 =item * schedule_max_coefficient
8605 This option enforces that the coefficients for variable and parameter
8606 dimensions in the calculated schedule are not larger than the specified value.
8607 This option can significantly increase the speed of the scheduling calculation
8608 and may also prevent fusing of unrelated dimensions. A value of -1 means that
8609 this option does not introduce bounds on the variable or parameter
8612 =item * schedule_max_constant_term
8614 This option enforces that the constant coefficients in the calculated schedule
8615 are not larger than the maximal constant term. This option can significantly
8616 increase the speed of the scheduling calculation and may also prevent fusing of
8617 unrelated dimensions. A value of -1 means that this option does not introduce
8618 bounds on the constant coefficients.
8620 =item * schedule_fuse
8622 This option controls the level of fusion.
8623 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
8624 resulting schedule will be distributed as much as possible.
8625 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
8626 try to fuse loops in the resulting schedule.
8628 =item * schedule_maximize_band_depth
8630 If this option is set, we do not split bands at the point
8631 where we detect splitting is necessary. Instead, we
8632 backtrack and split bands as early as possible. This
8633 reduces the number of splits and maximizes the width of
8634 the bands. Wider bands give more possibilities for tiling.
8635 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
8636 then bands will be split as early as possible, even if there is no need.
8637 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
8639 =item * schedule_outer_coincidence
8641 If this option is set, then we try to construct schedules
8642 where the outermost scheduling dimension in each band
8643 satisfies the coincidence constraints.
8645 =item * schedule_split_scaled
8647 If this option is set, then we try to construct schedules in which the
8648 constant term is split off from the linear part if the linear parts of
8649 the scheduling rows for all nodes in the graphs have a common non-trivial
8651 The constant term is then placed in a separate band and the linear
8654 =item * schedule_algorithm
8656 Selects the scheduling algorithm to be used.
8657 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
8658 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
8660 =item * schedule_separate_components
8662 If this option is set then the function C<isl_schedule_get_map>
8663 will treat set nodes in the same way as sequence nodes.
8667 =head2 AST Generation
8669 This section describes the C<isl> functionality for generating
8670 ASTs that visit all the elements
8671 in a domain in an order specified by a schedule tree or
8673 In case the schedule given as a C<isl_union_map>, an AST is generated
8674 that visits all the elements in the domain of the C<isl_union_map>
8675 according to the lexicographic order of the corresponding image
8676 element(s). If the range of the C<isl_union_map> consists of
8677 elements in more than one space, then each of these spaces is handled
8678 separately in an arbitrary order.
8679 It should be noted that the schedule tree or the image elements
8680 in a schedule map only specify the I<order>
8681 in which the corresponding domain elements should be visited.
8682 No direct relation between the partial schedule values
8683 or the image elements on the one hand and the loop iterators
8684 in the generated AST on the other hand should be assumed.
8686 Each AST is generated within a build. The initial build
8687 simply specifies the constraints on the parameters (if any)
8688 and can be created, inspected, copied and freed using the following functions.
8690 #include <isl/ast_build.h>
8691 __isl_give isl_ast_build *isl_ast_build_alloc(
8693 __isl_give isl_ast_build *isl_ast_build_from_context(
8694 __isl_take isl_set *set);
8695 __isl_give isl_ast_build *isl_ast_build_copy(
8696 __isl_keep isl_ast_build *build);
8697 __isl_null isl_ast_build *isl_ast_build_free(
8698 __isl_take isl_ast_build *build);
8700 The C<set> argument is usually a parameter set with zero or more parameters.
8701 In fact, when creating an AST using C<isl_ast_build_node_from_schedule>,
8702 this set is required to be a parameter set.
8703 An C<isl_ast_build> created using C<isl_ast_build_alloc> does not
8704 specify any parameter constraints.
8705 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
8706 and L</"Fine-grained Control over AST Generation">.
8707 Finally, the AST itself can be constructed using one of the following
8710 #include <isl/ast_build.h>
8711 __isl_give isl_ast_node *isl_ast_build_node_from_schedule(
8712 __isl_keep isl_ast_build *build,
8713 __isl_take isl_schedule *schedule);
8714 __isl_give isl_ast_node *
8715 isl_ast_build_node_from_schedule_map(
8716 __isl_keep isl_ast_build *build,
8717 __isl_take isl_union_map *schedule);
8719 =head3 Inspecting the AST
8721 The basic properties of an AST node can be obtained as follows.
8723 #include <isl/ast.h>
8724 enum isl_ast_node_type isl_ast_node_get_type(
8725 __isl_keep isl_ast_node *node);
8727 The type of an AST node is one of
8728 C<isl_ast_node_for>,
8730 C<isl_ast_node_block>,
8731 C<isl_ast_node_mark> or
8732 C<isl_ast_node_user>.
8733 An C<isl_ast_node_for> represents a for node.
8734 An C<isl_ast_node_if> represents an if node.
8735 An C<isl_ast_node_block> represents a compound node.
8736 An C<isl_ast_node_mark> introduces a mark in the AST.
8737 An C<isl_ast_node_user> represents an expression statement.
8738 An expression statement typically corresponds to a domain element, i.e.,
8739 one of the elements that is visited by the AST.
8741 Each type of node has its own additional properties.
8743 #include <isl/ast.h>
8744 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
8745 __isl_keep isl_ast_node *node);
8746 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
8747 __isl_keep isl_ast_node *node);
8748 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
8749 __isl_keep isl_ast_node *node);
8750 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
8751 __isl_keep isl_ast_node *node);
8752 __isl_give isl_ast_node *isl_ast_node_for_get_body(
8753 __isl_keep isl_ast_node *node);
8754 int isl_ast_node_for_is_degenerate(
8755 __isl_keep isl_ast_node *node);
8757 An C<isl_ast_for> is considered degenerate if it is known to execute
8760 #include <isl/ast.h>
8761 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
8762 __isl_keep isl_ast_node *node);
8763 __isl_give isl_ast_node *isl_ast_node_if_get_then(
8764 __isl_keep isl_ast_node *node);
8765 int isl_ast_node_if_has_else(
8766 __isl_keep isl_ast_node *node);
8767 __isl_give isl_ast_node *isl_ast_node_if_get_else(
8768 __isl_keep isl_ast_node *node);
8770 __isl_give isl_ast_node_list *
8771 isl_ast_node_block_get_children(
8772 __isl_keep isl_ast_node *node);
8774 __isl_give isl_id *isl_ast_node_mark_get_id(
8775 __isl_keep isl_ast_node *node);
8776 __isl_give isl_ast_node *isl_ast_node_mark_get_node(
8777 __isl_keep isl_ast_node *node);
8779 C<isl_ast_node_mark_get_id> returns the identifier of the mark.
8780 C<isl_ast_node_mark_get_node> returns the child node that is being marked.
8782 #include <isl/ast.h>
8783 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
8784 __isl_keep isl_ast_node *node);
8786 Each of the returned C<isl_ast_expr>s can in turn be inspected using
8787 the following functions.
8789 #include <isl/ast.h>
8790 enum isl_ast_expr_type isl_ast_expr_get_type(
8791 __isl_keep isl_ast_expr *expr);
8793 The type of an AST expression is one of
8795 C<isl_ast_expr_id> or
8796 C<isl_ast_expr_int>.
8797 An C<isl_ast_expr_op> represents the result of an operation.
8798 An C<isl_ast_expr_id> represents an identifier.
8799 An C<isl_ast_expr_int> represents an integer value.
8801 Each type of expression has its own additional properties.
8803 #include <isl/ast.h>
8804 enum isl_ast_op_type isl_ast_expr_get_op_type(
8805 __isl_keep isl_ast_expr *expr);
8806 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
8807 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
8808 __isl_keep isl_ast_expr *expr, int pos);
8809 int isl_ast_node_foreach_ast_op_type(
8810 __isl_keep isl_ast_node *node,
8811 int (*fn)(enum isl_ast_op_type type, void *user),
8814 C<isl_ast_expr_get_op_type> returns the type of the operation
8815 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
8816 arguments. C<isl_ast_expr_get_op_arg> returns the specified
8818 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
8819 C<isl_ast_op_type> that appears in C<node>.
8820 The operation type is one of the following.
8824 =item C<isl_ast_op_and>
8826 Logical I<and> of two arguments.
8827 Both arguments can be evaluated.
8829 =item C<isl_ast_op_and_then>
8831 Logical I<and> of two arguments.
8832 The second argument can only be evaluated if the first evaluates to true.
8834 =item C<isl_ast_op_or>
8836 Logical I<or> of two arguments.
8837 Both arguments can be evaluated.
8839 =item C<isl_ast_op_or_else>
8841 Logical I<or> of two arguments.
8842 The second argument can only be evaluated if the first evaluates to false.
8844 =item C<isl_ast_op_max>
8846 Maximum of two or more arguments.
8848 =item C<isl_ast_op_min>
8850 Minimum of two or more arguments.
8852 =item C<isl_ast_op_minus>
8856 =item C<isl_ast_op_add>
8858 Sum of two arguments.
8860 =item C<isl_ast_op_sub>
8862 Difference of two arguments.
8864 =item C<isl_ast_op_mul>
8866 Product of two arguments.
8868 =item C<isl_ast_op_div>
8870 Exact division. That is, the result is known to be an integer.
8872 =item C<isl_ast_op_fdiv_q>
8874 Result of integer division, rounded towards negative
8877 =item C<isl_ast_op_pdiv_q>
8879 Result of integer division, where dividend is known to be non-negative.
8881 =item C<isl_ast_op_pdiv_r>
8883 Remainder of integer division, where dividend is known to be non-negative.
8885 =item C<isl_ast_op_zdiv_r>
8887 Equal to zero iff the remainder on integer division is zero.
8889 =item C<isl_ast_op_cond>
8891 Conditional operator defined on three arguments.
8892 If the first argument evaluates to true, then the result
8893 is equal to the second argument. Otherwise, the result
8894 is equal to the third argument.
8895 The second and third argument may only be evaluated if
8896 the first argument evaluates to true and false, respectively.
8897 Corresponds to C<a ? b : c> in C.
8899 =item C<isl_ast_op_select>
8901 Conditional operator defined on three arguments.
8902 If the first argument evaluates to true, then the result
8903 is equal to the second argument. Otherwise, the result
8904 is equal to the third argument.
8905 The second and third argument may be evaluated independently
8906 of the value of the first argument.
8907 Corresponds to C<a * b + (1 - a) * c> in C.
8909 =item C<isl_ast_op_eq>
8913 =item C<isl_ast_op_le>
8915 Less than or equal relation.
8917 =item C<isl_ast_op_lt>
8921 =item C<isl_ast_op_ge>
8923 Greater than or equal relation.
8925 =item C<isl_ast_op_gt>
8927 Greater than relation.
8929 =item C<isl_ast_op_call>
8932 The number of arguments of the C<isl_ast_expr> is one more than
8933 the number of arguments in the function call, the first argument
8934 representing the function being called.
8936 =item C<isl_ast_op_access>
8939 The number of arguments of the C<isl_ast_expr> is one more than
8940 the number of index expressions in the array access, the first argument
8941 representing the array being accessed.
8943 =item C<isl_ast_op_member>
8946 This operation has two arguments, a structure and the name of
8947 the member of the structure being accessed.
8951 #include <isl/ast.h>
8952 __isl_give isl_id *isl_ast_expr_get_id(
8953 __isl_keep isl_ast_expr *expr);
8955 Return the identifier represented by the AST expression.
8957 #include <isl/ast.h>
8958 __isl_give isl_val *isl_ast_expr_get_val(
8959 __isl_keep isl_ast_expr *expr);
8961 Return the integer represented by the AST expression.
8963 =head3 Properties of ASTs
8965 #include <isl/ast.h>
8966 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
8967 __isl_keep isl_ast_expr *expr2);
8969 Check if two C<isl_ast_expr>s are equal to each other.
8971 =head3 Manipulating and printing the AST
8973 AST nodes can be copied and freed using the following functions.
8975 #include <isl/ast.h>
8976 __isl_give isl_ast_node *isl_ast_node_copy(
8977 __isl_keep isl_ast_node *node);
8978 __isl_null isl_ast_node *isl_ast_node_free(
8979 __isl_take isl_ast_node *node);
8981 AST expressions can be copied and freed using the following functions.
8983 #include <isl/ast.h>
8984 __isl_give isl_ast_expr *isl_ast_expr_copy(
8985 __isl_keep isl_ast_expr *expr);
8986 __isl_null isl_ast_expr *isl_ast_expr_free(
8987 __isl_take isl_ast_expr *expr);
8989 New AST expressions can be created either directly or within
8990 the context of an C<isl_ast_build>.
8992 #include <isl/ast.h>
8993 __isl_give isl_ast_expr *isl_ast_expr_from_val(
8994 __isl_take isl_val *v);
8995 __isl_give isl_ast_expr *isl_ast_expr_from_id(
8996 __isl_take isl_id *id);
8997 __isl_give isl_ast_expr *isl_ast_expr_neg(
8998 __isl_take isl_ast_expr *expr);
8999 __isl_give isl_ast_expr *isl_ast_expr_address_of(
9000 __isl_take isl_ast_expr *expr);
9001 __isl_give isl_ast_expr *isl_ast_expr_add(
9002 __isl_take isl_ast_expr *expr1,
9003 __isl_take isl_ast_expr *expr2);
9004 __isl_give isl_ast_expr *isl_ast_expr_sub(
9005 __isl_take isl_ast_expr *expr1,
9006 __isl_take isl_ast_expr *expr2);
9007 __isl_give isl_ast_expr *isl_ast_expr_mul(
9008 __isl_take isl_ast_expr *expr1,
9009 __isl_take isl_ast_expr *expr2);
9010 __isl_give isl_ast_expr *isl_ast_expr_div(
9011 __isl_take isl_ast_expr *expr1,
9012 __isl_take isl_ast_expr *expr2);
9013 __isl_give isl_ast_expr *isl_ast_expr_pdiv_q(
9014 __isl_take isl_ast_expr *expr1,
9015 __isl_take isl_ast_expr *expr2);
9016 __isl_give isl_ast_expr *isl_ast_expr_pdiv_r(
9017 __isl_take isl_ast_expr *expr1,
9018 __isl_take isl_ast_expr *expr2);
9019 __isl_give isl_ast_expr *isl_ast_expr_and(
9020 __isl_take isl_ast_expr *expr1,
9021 __isl_take isl_ast_expr *expr2)
9022 __isl_give isl_ast_expr *isl_ast_expr_and_then(
9023 __isl_take isl_ast_expr *expr1,
9024 __isl_take isl_ast_expr *expr2)
9025 __isl_give isl_ast_expr *isl_ast_expr_or(
9026 __isl_take isl_ast_expr *expr1,
9027 __isl_take isl_ast_expr *expr2)
9028 __isl_give isl_ast_expr *isl_ast_expr_or_else(
9029 __isl_take isl_ast_expr *expr1,
9030 __isl_take isl_ast_expr *expr2)
9031 __isl_give isl_ast_expr *isl_ast_expr_eq(
9032 __isl_take isl_ast_expr *expr1,
9033 __isl_take isl_ast_expr *expr2);
9034 __isl_give isl_ast_expr *isl_ast_expr_le(
9035 __isl_take isl_ast_expr *expr1,
9036 __isl_take isl_ast_expr *expr2);
9037 __isl_give isl_ast_expr *isl_ast_expr_lt(
9038 __isl_take isl_ast_expr *expr1,
9039 __isl_take isl_ast_expr *expr2);
9040 __isl_give isl_ast_expr *isl_ast_expr_ge(
9041 __isl_take isl_ast_expr *expr1,
9042 __isl_take isl_ast_expr *expr2);
9043 __isl_give isl_ast_expr *isl_ast_expr_gt(
9044 __isl_take isl_ast_expr *expr1,
9045 __isl_take isl_ast_expr *expr2);
9046 __isl_give isl_ast_expr *isl_ast_expr_access(
9047 __isl_take isl_ast_expr *array,
9048 __isl_take isl_ast_expr_list *indices);
9049 __isl_give isl_ast_expr *isl_ast_expr_call(
9050 __isl_take isl_ast_expr *function,
9051 __isl_take isl_ast_expr_list *arguments);
9053 The function C<isl_ast_expr_address_of> can be applied to an
9054 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
9055 to represent the address of the C<isl_ast_expr_access>. The function
9056 C<isl_ast_expr_and_then> as well as C<isl_ast_expr_or_else> are short-circuit
9057 versions of C<isl_ast_expr_and> and C<isl_ast_expr_or>, respectively.
9059 #include <isl/ast_build.h>
9060 __isl_give isl_ast_expr *isl_ast_build_expr_from_set(
9061 __isl_keep isl_ast_build *build,
9062 __isl_take isl_set *set);
9063 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
9064 __isl_keep isl_ast_build *build,
9065 __isl_take isl_pw_aff *pa);
9066 __isl_give isl_ast_expr *
9067 isl_ast_build_access_from_pw_multi_aff(
9068 __isl_keep isl_ast_build *build,
9069 __isl_take isl_pw_multi_aff *pma);
9070 __isl_give isl_ast_expr *
9071 isl_ast_build_access_from_multi_pw_aff(
9072 __isl_keep isl_ast_build *build,
9073 __isl_take isl_multi_pw_aff *mpa);
9074 __isl_give isl_ast_expr *
9075 isl_ast_build_call_from_pw_multi_aff(
9076 __isl_keep isl_ast_build *build,
9077 __isl_take isl_pw_multi_aff *pma);
9078 __isl_give isl_ast_expr *
9079 isl_ast_build_call_from_multi_pw_aff(
9080 __isl_keep isl_ast_build *build,
9081 __isl_take isl_multi_pw_aff *mpa);
9084 the domains of C<pa>, C<mpa> and C<pma> should correspond
9085 to the schedule space of C<build>.
9086 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
9087 the function being called.
9088 If the accessed space is a nested relation, then it is taken
9089 to represent an access of the member specified by the range
9090 of this nested relation of the structure specified by the domain
9091 of the nested relation.
9093 The following functions can be used to modify an C<isl_ast_expr>.
9095 #include <isl/ast.h>
9096 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
9097 __isl_take isl_ast_expr *expr, int pos,
9098 __isl_take isl_ast_expr *arg);
9100 Replace the argument of C<expr> at position C<pos> by C<arg>.
9102 #include <isl/ast.h>
9103 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
9104 __isl_take isl_ast_expr *expr,
9105 __isl_take isl_id_to_ast_expr *id2expr);
9107 The function C<isl_ast_expr_substitute_ids> replaces the
9108 subexpressions of C<expr> of type C<isl_ast_expr_id>
9109 by the corresponding expression in C<id2expr>, if there is any.
9112 User specified data can be attached to an C<isl_ast_node> and obtained
9113 from the same C<isl_ast_node> using the following functions.
9115 #include <isl/ast.h>
9116 __isl_give isl_ast_node *isl_ast_node_set_annotation(
9117 __isl_take isl_ast_node *node,
9118 __isl_take isl_id *annotation);
9119 __isl_give isl_id *isl_ast_node_get_annotation(
9120 __isl_keep isl_ast_node *node);
9122 Basic printing can be performed using the following functions.
9124 #include <isl/ast.h>
9125 __isl_give isl_printer *isl_printer_print_ast_expr(
9126 __isl_take isl_printer *p,
9127 __isl_keep isl_ast_expr *expr);
9128 __isl_give isl_printer *isl_printer_print_ast_node(
9129 __isl_take isl_printer *p,
9130 __isl_keep isl_ast_node *node);
9131 __isl_give char *isl_ast_expr_to_str(
9132 __isl_keep isl_ast_expr *expr);
9134 More advanced printing can be performed using the following functions.
9136 #include <isl/ast.h>
9137 __isl_give isl_printer *isl_ast_op_type_print_macro(
9138 enum isl_ast_op_type type,
9139 __isl_take isl_printer *p);
9140 __isl_give isl_printer *isl_ast_node_print_macros(
9141 __isl_keep isl_ast_node *node,
9142 __isl_take isl_printer *p);
9143 __isl_give isl_printer *isl_ast_node_print(
9144 __isl_keep isl_ast_node *node,
9145 __isl_take isl_printer *p,
9146 __isl_take isl_ast_print_options *options);
9147 __isl_give isl_printer *isl_ast_node_for_print(
9148 __isl_keep isl_ast_node *node,
9149 __isl_take isl_printer *p,
9150 __isl_take isl_ast_print_options *options);
9151 __isl_give isl_printer *isl_ast_node_if_print(
9152 __isl_keep isl_ast_node *node,
9153 __isl_take isl_printer *p,
9154 __isl_take isl_ast_print_options *options);
9156 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
9157 C<isl> may print out an AST that makes use of macros such
9158 as C<floord>, C<min> and C<max>.
9159 C<isl_ast_op_type_print_macro> prints out the macro
9160 corresponding to a specific C<isl_ast_op_type>.
9161 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
9162 for expressions where these macros would be used and prints
9163 out the required macro definitions.
9164 Essentially, C<isl_ast_node_print_macros> calls
9165 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
9166 as function argument.
9167 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
9168 C<isl_ast_node_if_print> print an C<isl_ast_node>
9169 in C<ISL_FORMAT_C>, but allow for some extra control
9170 through an C<isl_ast_print_options> object.
9171 This object can be created using the following functions.
9173 #include <isl/ast.h>
9174 __isl_give isl_ast_print_options *
9175 isl_ast_print_options_alloc(isl_ctx *ctx);
9176 __isl_give isl_ast_print_options *
9177 isl_ast_print_options_copy(
9178 __isl_keep isl_ast_print_options *options);
9179 __isl_null isl_ast_print_options *
9180 isl_ast_print_options_free(
9181 __isl_take isl_ast_print_options *options);
9183 __isl_give isl_ast_print_options *
9184 isl_ast_print_options_set_print_user(
9185 __isl_take isl_ast_print_options *options,
9186 __isl_give isl_printer *(*print_user)(
9187 __isl_take isl_printer *p,
9188 __isl_take isl_ast_print_options *options,
9189 __isl_keep isl_ast_node *node, void *user),
9191 __isl_give isl_ast_print_options *
9192 isl_ast_print_options_set_print_for(
9193 __isl_take isl_ast_print_options *options,
9194 __isl_give isl_printer *(*print_for)(
9195 __isl_take isl_printer *p,
9196 __isl_take isl_ast_print_options *options,
9197 __isl_keep isl_ast_node *node, void *user),
9200 The callback set by C<isl_ast_print_options_set_print_user>
9201 is called whenever a node of type C<isl_ast_node_user> needs to
9203 The callback set by C<isl_ast_print_options_set_print_for>
9204 is called whenever a node of type C<isl_ast_node_for> needs to
9206 Note that C<isl_ast_node_for_print> will I<not> call the
9207 callback set by C<isl_ast_print_options_set_print_for> on the node
9208 on which C<isl_ast_node_for_print> is called, but only on nested
9209 nodes of type C<isl_ast_node_for>. It is therefore safe to
9210 call C<isl_ast_node_for_print> from within the callback set by
9211 C<isl_ast_print_options_set_print_for>.
9213 The following option determines the type to be used for iterators
9214 while printing the AST.
9216 int isl_options_set_ast_iterator_type(
9217 isl_ctx *ctx, const char *val);
9218 const char *isl_options_get_ast_iterator_type(
9221 The AST printer only prints body nodes as blocks if these
9222 blocks cannot be safely omitted.
9223 For example, a C<for> node with one body node will not be
9224 surrounded with braces in C<ISL_FORMAT_C>.
9225 A block will always be printed by setting the following option.
9227 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
9229 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
9233 #include <isl/ast_build.h>
9234 int isl_options_set_ast_build_atomic_upper_bound(
9235 isl_ctx *ctx, int val);
9236 int isl_options_get_ast_build_atomic_upper_bound(
9238 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
9240 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
9241 int isl_options_set_ast_build_exploit_nested_bounds(
9242 isl_ctx *ctx, int val);
9243 int isl_options_get_ast_build_exploit_nested_bounds(
9245 int isl_options_set_ast_build_group_coscheduled(
9246 isl_ctx *ctx, int val);
9247 int isl_options_get_ast_build_group_coscheduled(
9249 int isl_options_set_ast_build_scale_strides(
9250 isl_ctx *ctx, int val);
9251 int isl_options_get_ast_build_scale_strides(
9253 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
9255 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
9256 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
9258 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
9262 =item * ast_build_atomic_upper_bound
9264 Generate loop upper bounds that consist of the current loop iterator,
9265 an operator and an expression not involving the iterator.
9266 If this option is not set, then the current loop iterator may appear
9267 several times in the upper bound.
9268 For example, when this option is turned off, AST generation
9271 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
9275 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
9278 When the option is turned on, the following AST is generated
9280 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
9283 =item * ast_build_prefer_pdiv
9285 If this option is turned off, then the AST generation will
9286 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
9287 operators, but no C<isl_ast_op_pdiv_q> or
9288 C<isl_ast_op_pdiv_r> operators.
9289 If this options is turned on, then C<isl> will try to convert
9290 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
9291 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
9293 =item * ast_build_exploit_nested_bounds
9295 Simplify conditions based on bounds of nested for loops.
9296 In particular, remove conditions that are implied by the fact
9297 that one or more nested loops have at least one iteration,
9298 meaning that the upper bound is at least as large as the lower bound.
9299 For example, when this option is turned off, AST generation
9302 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
9308 for (int c0 = 0; c0 <= N; c0 += 1)
9309 for (int c1 = 0; c1 <= M; c1 += 1)
9312 When the option is turned on, the following AST is generated
9314 for (int c0 = 0; c0 <= N; c0 += 1)
9315 for (int c1 = 0; c1 <= M; c1 += 1)
9318 =item * ast_build_group_coscheduled
9320 If two domain elements are assigned the same schedule point, then
9321 they may be executed in any order and they may even appear in different
9322 loops. If this options is set, then the AST generator will make
9323 sure that coscheduled domain elements do not appear in separate parts
9324 of the AST. This is useful in case of nested AST generation
9325 if the outer AST generation is given only part of a schedule
9326 and the inner AST generation should handle the domains that are
9327 coscheduled by this initial part of the schedule together.
9328 For example if an AST is generated for a schedule
9330 { A[i] -> [0]; B[i] -> [0] }
9332 then the C<isl_ast_build_set_create_leaf> callback described
9333 below may get called twice, once for each domain.
9334 Setting this option ensures that the callback is only called once
9335 on both domains together.
9337 =item * ast_build_separation_bounds
9339 This option specifies which bounds to use during separation.
9340 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
9341 then all (possibly implicit) bounds on the current dimension will
9342 be used during separation.
9343 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
9344 then only those bounds that are explicitly available will
9345 be used during separation.
9347 =item * ast_build_scale_strides
9349 This option specifies whether the AST generator is allowed
9350 to scale down iterators of strided loops.
9352 =item * ast_build_allow_else
9354 This option specifies whether the AST generator is allowed
9355 to construct if statements with else branches.
9357 =item * ast_build_allow_or
9359 This option specifies whether the AST generator is allowed
9360 to construct if conditions with disjunctions.
9364 =head3 AST Generation Options (Schedule Tree)
9366 In case of AST construction from a schedule tree, the options
9367 that control how an AST is created from the individual schedule
9368 dimensions are stored in the band nodes of the tree
9369 (see L</"Schedule Trees">).
9371 In particular, a schedule dimension can be handled in four
9372 different ways, atomic, separate, unroll or the default.
9373 This loop AST generation type can be set using
9374 C<isl_schedule_node_band_member_set_ast_loop_type>.
9376 the first three can be selected by including a one-dimensional
9377 element with as value the position of the schedule dimension
9378 within the band and as name one of C<atomic>, C<separate>
9379 or C<unroll> in the options
9380 set by C<isl_schedule_node_band_set_ast_build_options>.
9381 Only one of these three may be specified for
9382 any given schedule dimension within a band node.
9383 If none of these is specified, then the default
9384 is used. The meaning of the options is as follows.
9390 When this option is specified, the AST generator will make
9391 sure that a given domains space only appears in a single
9392 loop at the specified level.
9394 For example, for the schedule tree
9396 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9398 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9399 options: "{ atomic[x] }"
9401 the following AST will be generated
9403 for (int c0 = 0; c0 <= 10; c0 += 1) {
9410 On the other hand, for the schedule tree
9412 domain: "{ a[i] : 0 <= i < 10; b[i] : 0 <= i < 10 }"
9414 schedule: "[{ a[i] -> [i]; b[i] -> [i+1] }]"
9415 options: "{ separate[x] }"
9417 the following AST will be generated
9421 for (int c0 = 1; c0 <= 9; c0 += 1) {
9428 If neither C<atomic> nor C<separate> is specified, then the AST generator
9429 may produce either of these two results or some intermediate form.
9433 When this option is specified, the AST generator will
9434 split the domain of the specified schedule dimension
9435 into pieces with a fixed set of statements for which
9436 instances need to be executed by the iterations in
9437 the schedule domain part. This option tends to avoid
9438 the generation of guards inside the corresponding loops.
9439 See also the C<atomic> option.
9443 When this option is specified, the AST generator will
9444 I<completely> unroll the corresponding schedule dimension.
9445 It is the responsibility of the user to ensure that such
9446 unrolling is possible.
9447 To obtain a partial unrolling, the user should apply an additional
9448 strip-mining to the schedule and fully unroll the inner schedule
9453 The C<isolate> option is a bit more involved. It allows the user
9454 to isolate a range of schedule dimension values from smaller and
9455 greater values. Additionally, the user may specify a different
9456 atomic/separate/unroll choice for the isolated part and the remaining
9457 parts. The typical use case of the C<isolate> option is to isolate
9458 full tiles from partial tiles.
9459 The part that needs to be isolated may depend on outer schedule dimensions.
9460 The option therefore needs to be able to reference those outer schedule
9461 dimensions. In particular, the space of the C<isolate> option is that
9462 of a wrapped map with as domain the flat product of all outer band nodes
9463 and as range the space of the current band node.
9464 The atomic/separate/unroll choice for the isolated part is determined
9465 by an option that lives in an unnamed wrapped space with as domain
9466 a zero-dimensional C<isolate> space and as range the regular
9467 C<atomic>, C<separate> or C<unroll> space.
9468 This option may also be set directly using
9469 C<isl_schedule_node_band_member_set_isolate_ast_loop_type>.
9470 The atomic/separate/unroll choice for the remaining part is determined
9471 by the regular C<atomic>, C<separate> or C<unroll> option.
9472 The use of the C<isolate> option causes any tree containing the node
9473 to be considered anchored.
9475 As an example, consider the isolation of full tiles from partial tiles
9476 in a tiling of a triangular domain. The original schedule is as follows.
9478 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9480 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9481 { A[i,j] -> [floor(j/10)] }, \
9482 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9486 for (int c0 = 0; c0 <= 10; c0 += 1)
9487 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9488 for (int c2 = 10 * c0;
9489 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9490 for (int c3 = 10 * c1;
9491 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9494 Isolating the full tiles, we have the following input
9496 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9498 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9499 { A[i,j] -> [floor(j/10)] }, \
9500 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9501 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9502 10a+9+10b+9 <= 100 }"
9507 for (int c0 = 0; c0 <= 8; c0 += 1) {
9508 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9509 for (int c2 = 10 * c0;
9510 c2 <= 10 * c0 + 9; c2 += 1)
9511 for (int c3 = 10 * c1;
9512 c3 <= 10 * c1 + 9; c3 += 1)
9514 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9515 for (int c2 = 10 * c0;
9516 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9517 for (int c3 = 10 * c1;
9518 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9521 for (int c0 = 9; c0 <= 10; c0 += 1)
9522 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9523 for (int c2 = 10 * c0;
9524 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9525 for (int c3 = 10 * c1;
9526 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9530 We may then additionally unroll the innermost loop of the isolated part
9532 domain: "{ A[i,j] : 0 <= i,j and i + j <= 100 }"
9534 schedule: "[{ A[i,j] -> [floor(i/10)] }, \
9535 { A[i,j] -> [floor(j/10)] }, \
9536 { A[i,j] -> [i] }, { A[i,j] -> [j] }]"
9537 options: "{ isolate[[] -> [a,b,c,d]] : 0 <= 10a,10b and \
9538 10a+9+10b+9 <= 100; [isolate[] -> unroll[3]] }"
9543 for (int c0 = 0; c0 <= 8; c0 += 1) {
9544 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9545 for (int c2 = 10 * c0; c2 <= 10 * c0 + 9; c2 += 1) {
9557 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9558 for (int c2 = 10 * c0;
9559 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9560 for (int c3 = 10 * c1;
9561 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9564 for (int c0 = 9; c0 <= 10; c0 += 1)
9565 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9566 for (int c2 = 10 * c0;
9567 c2 <= min(10 * c0 + 9, -10 * c1 + 100); c2 += 1)
9568 for (int c3 = 10 * c1;
9569 c3 <= min(10 * c1 + 9, -c2 + 100); c3 += 1)
9574 =head3 AST Generation Options (Schedule Map)
9576 In case of AST construction using
9577 C<isl_ast_build_node_from_schedule_map>, the options
9578 that control how an AST is created from the individual schedule
9579 dimensions are stored in the C<isl_ast_build>.
9580 They can be set using the following function.
9582 #include <isl/ast_build.h>
9583 __isl_give isl_ast_build *
9584 isl_ast_build_set_options(
9585 __isl_take isl_ast_build *control,
9586 __isl_take isl_union_map *options);
9588 The options are encoded in an C<isl_union_map>.
9589 The domain of this union relation refers to the schedule domain,
9590 i.e., the range of the schedule passed
9591 to C<isl_ast_build_node_from_schedule_map>.
9592 In the case of nested AST generation (see L</"Nested AST Generation">),
9593 the domain of C<options> should refer to the extra piece of the schedule.
9594 That is, it should be equal to the range of the wrapped relation in the
9595 range of the schedule.
9596 The range of the options can consist of elements in one or more spaces,
9597 the names of which determine the effect of the option.
9598 The values of the range typically also refer to the schedule dimension
9599 to which the option applies. In case of nested AST generation
9600 (see L</"Nested AST Generation">), these values refer to the position
9601 of the schedule dimension within the innermost AST generation.
9602 The constraints on the domain elements of
9603 the option should only refer to this dimension and earlier dimensions.
9604 We consider the following spaces.
9608 =item C<separation_class>
9610 B<This option has been deprecated. Use the isolate option on
9611 schedule trees instead.>
9613 This space is a wrapped relation between two one dimensional spaces.
9614 The input space represents the schedule dimension to which the option
9615 applies and the output space represents the separation class.
9616 While constructing a loop corresponding to the specified schedule
9617 dimension(s), the AST generator will try to generate separate loops
9618 for domain elements that are assigned different classes.
9619 If only some of the elements are assigned a class, then those elements
9620 that are not assigned any class will be treated as belonging to a class
9621 that is separate from the explicitly assigned classes.
9622 The typical use case for this option is to separate full tiles from
9624 The other options, described below, are applied after the separation
9627 As an example, consider the separation into full and partial tiles
9628 of a tiling of a triangular domain.
9629 Take, for example, the domain
9631 { A[i,j] : 0 <= i,j and i + j <= 100 }
9633 and a tiling into tiles of 10 by 10. The input to the AST generator
9634 is then the schedule
9636 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
9639 Without any options, the following AST is generated
9641 for (int c0 = 0; c0 <= 10; c0 += 1)
9642 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9643 for (int c2 = 10 * c0;
9644 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9646 for (int c3 = 10 * c1;
9647 c3 <= min(10 * c1 + 9, -c2 + 100);
9651 Separation into full and partial tiles can be obtained by assigning
9652 a class, say C<0>, to the full tiles. The full tiles are represented by those
9653 values of the first and second schedule dimensions for which there are
9654 values of the third and fourth dimensions to cover an entire tile.
9655 That is, we need to specify the following option
9657 { [a,b,c,d] -> separation_class[[0]->[0]] :
9658 exists b': 0 <= 10a,10b' and
9659 10a+9+10b'+9 <= 100;
9660 [a,b,c,d] -> separation_class[[1]->[0]] :
9661 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
9665 { [a, b, c, d] -> separation_class[[1] -> [0]] :
9666 a >= 0 and b >= 0 and b <= 8 - a;
9667 [a, b, c, d] -> separation_class[[0] -> [0]] :
9670 With this option, the generated AST is as follows
9673 for (int c0 = 0; c0 <= 8; c0 += 1) {
9674 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
9675 for (int c2 = 10 * c0;
9676 c2 <= 10 * c0 + 9; c2 += 1)
9677 for (int c3 = 10 * c1;
9678 c3 <= 10 * c1 + 9; c3 += 1)
9680 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
9681 for (int c2 = 10 * c0;
9682 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9684 for (int c3 = 10 * c1;
9685 c3 <= min(-c2 + 100, 10 * c1 + 9);
9689 for (int c0 = 9; c0 <= 10; c0 += 1)
9690 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
9691 for (int c2 = 10 * c0;
9692 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
9694 for (int c3 = 10 * c1;
9695 c3 <= min(10 * c1 + 9, -c2 + 100);
9702 This is a single-dimensional space representing the schedule dimension(s)
9703 to which ``separation'' should be applied. Separation tries to split
9704 a loop into several pieces if this can avoid the generation of guards
9706 See also the C<atomic> option.
9710 This is a single-dimensional space representing the schedule dimension(s)
9711 for which the domains should be considered ``atomic''. That is, the
9712 AST generator will make sure that any given domain space will only appear
9713 in a single loop at the specified level.
9715 Consider the following schedule
9717 { a[i] -> [i] : 0 <= i < 10;
9718 b[i] -> [i+1] : 0 <= i < 10 }
9720 If the following option is specified
9722 { [i] -> separate[x] }
9724 then the following AST will be generated
9728 for (int c0 = 1; c0 <= 9; c0 += 1) {
9735 If, on the other hand, the following option is specified
9737 { [i] -> atomic[x] }
9739 then the following AST will be generated
9741 for (int c0 = 0; c0 <= 10; c0 += 1) {
9748 If neither C<atomic> nor C<separate> is specified, then the AST generator
9749 may produce either of these two results or some intermediate form.
9753 This is a single-dimensional space representing the schedule dimension(s)
9754 that should be I<completely> unrolled.
9755 To obtain a partial unrolling, the user should apply an additional
9756 strip-mining to the schedule and fully unroll the inner loop.
9760 =head3 Fine-grained Control over AST Generation
9762 Besides specifying the constraints on the parameters,
9763 an C<isl_ast_build> object can be used to control
9764 various aspects of the AST generation process.
9765 In case of AST construction using
9766 C<isl_ast_build_node_from_schedule_map>,
9767 the most prominent way of control is through ``options'',
9770 Additional control is available through the following functions.
9772 #include <isl/ast_build.h>
9773 __isl_give isl_ast_build *
9774 isl_ast_build_set_iterators(
9775 __isl_take isl_ast_build *control,
9776 __isl_take isl_id_list *iterators);
9778 The function C<isl_ast_build_set_iterators> allows the user to
9779 specify a list of iterator C<isl_id>s to be used as iterators.
9780 If the input schedule is injective, then
9781 the number of elements in this list should be as large as the dimension
9782 of the schedule space, but no direct correspondence should be assumed
9783 between dimensions and elements.
9784 If the input schedule is not injective, then an additional number
9785 of C<isl_id>s equal to the largest dimension of the input domains
9787 If the number of provided C<isl_id>s is insufficient, then additional
9788 names are automatically generated.
9790 #include <isl/ast_build.h>
9791 __isl_give isl_ast_build *
9792 isl_ast_build_set_create_leaf(
9793 __isl_take isl_ast_build *control,
9794 __isl_give isl_ast_node *(*fn)(
9795 __isl_take isl_ast_build *build,
9796 void *user), void *user);
9799 C<isl_ast_build_set_create_leaf> function allows for the
9800 specification of a callback that should be called whenever the AST
9801 generator arrives at an element of the schedule domain.
9802 The callback should return an AST node that should be inserted
9803 at the corresponding position of the AST. The default action (when
9804 the callback is not set) is to continue generating parts of the AST to scan
9805 all the domain elements associated to the schedule domain element
9806 and to insert user nodes, ``calling'' the domain element, for each of them.
9807 The C<build> argument contains the current state of the C<isl_ast_build>.
9808 To ease nested AST generation (see L</"Nested AST Generation">),
9809 all control information that is
9810 specific to the current AST generation such as the options and
9811 the callbacks has been removed from this C<isl_ast_build>.
9812 The callback would typically return the result of a nested
9814 user defined node created using the following function.
9816 #include <isl/ast.h>
9817 __isl_give isl_ast_node *isl_ast_node_alloc_user(
9818 __isl_take isl_ast_expr *expr);
9820 #include <isl/ast_build.h>
9821 __isl_give isl_ast_build *
9822 isl_ast_build_set_at_each_domain(
9823 __isl_take isl_ast_build *build,
9824 __isl_give isl_ast_node *(*fn)(
9825 __isl_take isl_ast_node *node,
9826 __isl_keep isl_ast_build *build,
9827 void *user), void *user);
9828 __isl_give isl_ast_build *
9829 isl_ast_build_set_before_each_for(
9830 __isl_take isl_ast_build *build,
9831 __isl_give isl_id *(*fn)(
9832 __isl_keep isl_ast_build *build,
9833 void *user), void *user);
9834 __isl_give isl_ast_build *
9835 isl_ast_build_set_after_each_for(
9836 __isl_take isl_ast_build *build,
9837 __isl_give isl_ast_node *(*fn)(
9838 __isl_take isl_ast_node *node,
9839 __isl_keep isl_ast_build *build,
9840 void *user), void *user);
9841 __isl_give isl_ast_build *
9842 isl_ast_build_set_before_each_mark(
9843 __isl_take isl_ast_build *build,
9844 int (*fn)(__isl_keep isl_id *mark,
9845 __isl_keep isl_ast_build *build,
9846 void *user), void *user);
9847 __isl_give isl_ast_build *
9848 isl_ast_build_set_after_each_mark(
9849 __isl_take isl_ast_build *build,
9850 __isl_give isl_ast_node *(*fn)(
9851 __isl_take isl_ast_node *node,
9852 __isl_keep isl_ast_build *build,
9853 void *user), void *user);
9855 The callback set by C<isl_ast_build_set_at_each_domain> will
9856 be called for each domain AST node.
9857 The callbacks set by C<isl_ast_build_set_before_each_for>
9858 and C<isl_ast_build_set_after_each_for> will be called
9859 for each for AST node. The first will be called in depth-first
9860 pre-order, while the second will be called in depth-first post-order.
9861 Since C<isl_ast_build_set_before_each_for> is called before the for
9862 node is actually constructed, it is only passed an C<isl_ast_build>.
9863 The returned C<isl_id> will be added as an annotation (using
9864 C<isl_ast_node_set_annotation>) to the constructed for node.
9865 In particular, if the user has also specified an C<after_each_for>
9866 callback, then the annotation can be retrieved from the node passed to
9867 that callback using C<isl_ast_node_get_annotation>.
9868 The callbacks set by C<isl_ast_build_set_before_each_mark>
9869 and C<isl_ast_build_set_after_each_mark> will be called for each
9870 mark AST node that is created, i.e., for each mark schedule node
9871 in the input schedule tree. The first will be called in depth-first
9872 pre-order, while the second will be called in depth-first post-order.
9873 Since the callback set by C<isl_ast_build_set_before_each_mark>
9874 is called before the mark AST node is actually constructed, it is passed
9875 the identifier of the mark node.
9876 All callbacks should C<NULL> (or -1) on failure.
9877 The given C<isl_ast_build> can be used to create new
9878 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
9879 or C<isl_ast_build_call_from_pw_multi_aff>.
9881 =head3 Nested AST Generation
9883 C<isl> allows the user to create an AST within the context
9884 of another AST. These nested ASTs are created using the
9885 same C<isl_ast_build_node_from_schedule_map> function that is used to create
9886 the outer AST. The C<build> argument should be an C<isl_ast_build>
9887 passed to a callback set by
9888 C<isl_ast_build_set_create_leaf>.
9889 The space of the range of the C<schedule> argument should refer
9890 to this build. In particular, the space should be a wrapped
9891 relation and the domain of this wrapped relation should be the
9892 same as that of the range of the schedule returned by
9893 C<isl_ast_build_get_schedule> below.
9894 In practice, the new schedule is typically
9895 created by calling C<isl_union_map_range_product> on the old schedule
9896 and some extra piece of the schedule.
9897 The space of the schedule domain is also available from
9898 the C<isl_ast_build>.
9900 #include <isl/ast_build.h>
9901 __isl_give isl_union_map *isl_ast_build_get_schedule(
9902 __isl_keep isl_ast_build *build);
9903 __isl_give isl_space *isl_ast_build_get_schedule_space(
9904 __isl_keep isl_ast_build *build);
9905 __isl_give isl_ast_build *isl_ast_build_restrict(
9906 __isl_take isl_ast_build *build,
9907 __isl_take isl_set *set);
9909 The C<isl_ast_build_get_schedule> function returns a (partial)
9910 schedule for the domains elements for which part of the AST still needs to
9911 be generated in the current build.
9912 In particular, the domain elements are mapped to those iterations of the loops
9913 enclosing the current point of the AST generation inside which
9914 the domain elements are executed.
9915 No direct correspondence between
9916 the input schedule and this schedule should be assumed.
9917 The space obtained from C<isl_ast_build_get_schedule_space> can be used
9918 to create a set for C<isl_ast_build_restrict> to intersect
9919 with the current build. In particular, the set passed to
9920 C<isl_ast_build_restrict> can have additional parameters.
9921 The ids of the set dimensions in the space returned by
9922 C<isl_ast_build_get_schedule_space> correspond to the
9923 iterators of the already generated loops.
9924 The user should not rely on the ids of the output dimensions
9925 of the relations in the union relation returned by
9926 C<isl_ast_build_get_schedule> having any particular value.
9930 Although C<isl> is mainly meant to be used as a library,
9931 it also contains some basic applications that use some
9932 of the functionality of C<isl>.
9933 The input may be specified in either the L<isl format>
9934 or the L<PolyLib format>.
9936 =head2 C<isl_polyhedron_sample>
9938 C<isl_polyhedron_sample> takes a polyhedron as input and prints
9939 an integer element of the polyhedron, if there is any.
9940 The first column in the output is the denominator and is always
9941 equal to 1. If the polyhedron contains no integer points,
9942 then a vector of length zero is printed.
9946 C<isl_pip> takes the same input as the C<example> program
9947 from the C<piplib> distribution, i.e., a set of constraints
9948 on the parameters, a line containing only -1 and finally a set
9949 of constraints on a parametric polyhedron.
9950 The coefficients of the parameters appear in the last columns
9951 (but before the final constant column).
9952 The output is the lexicographic minimum of the parametric polyhedron.
9953 As C<isl> currently does not have its own output format, the output
9954 is just a dump of the internal state.
9956 =head2 C<isl_polyhedron_minimize>
9958 C<isl_polyhedron_minimize> computes the minimum of some linear
9959 or affine objective function over the integer points in a polyhedron.
9960 If an affine objective function
9961 is given, then the constant should appear in the last column.
9963 =head2 C<isl_polytope_scan>
9965 Given a polytope, C<isl_polytope_scan> prints
9966 all integer points in the polytope.
9968 =head2 C<isl_codegen>
9970 Given a schedule, a context set and an options relation,
9971 C<isl_codegen> prints out an AST that scans the domain elements
9972 of the schedule in the order of their image(s) taking into account
9973 the constraints in the context set.