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.
229 C<isl> is released under the MIT license.
233 Permission is hereby granted, free of charge, to any person obtaining a copy of
234 this software and associated documentation files (the "Software"), to deal in
235 the Software without restriction, including without limitation the rights to
236 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
237 of the Software, and to permit persons to whom the Software is furnished to do
238 so, subject to the following conditions:
240 The above copyright notice and this permission notice shall be included in all
241 copies or substantial portions of the Software.
243 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
244 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
245 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
246 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
247 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
248 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
253 Note that by default C<isl> requires C<GMP>, which is released
254 under the GNU Lesser General Public License (LGPL). This means
255 that code linked against C<isl> is also linked against LGPL code.
257 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
258 library for exact integer arithmetic released under the MIT license.
262 The source of C<isl> can be obtained either as a tarball
263 or from the git repository. Both are available from
264 L<http://freshmeat.net/projects/isl/>.
265 The installation process depends on how you obtained
268 =head2 Installation from the git repository
272 =item 1 Clone or update the repository
274 The first time the source is obtained, you need to clone
277 git clone git://repo.or.cz/isl.git
279 To obtain updates, you need to pull in the latest changes
283 =item 2 Optionally get C<imath> submodule
285 To build C<isl> with C<imath>, you need to obtain the C<imath>
286 submodule by running in the git source tree of C<isl>
291 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
293 =item 2 Generate C<configure>
299 After performing the above steps, continue
300 with the L<Common installation instructions>.
302 =head2 Common installation instructions
306 =item 1 Obtain C<GMP>
308 By default, building C<isl> requires C<GMP>, including its headers files.
309 Your distribution may not provide these header files by default
310 and you may need to install a package called C<gmp-devel> or something
311 similar. Alternatively, C<GMP> can be built from
312 source, available from L<http://gmplib.org/>.
313 C<GMP> is not needed if you build C<isl> with C<imath>.
317 C<isl> uses the standard C<autoconf> C<configure> script.
322 optionally followed by some configure options.
323 A complete list of options can be obtained by running
327 Below we discuss some of the more common options.
333 Installation prefix for C<isl>
335 =item C<--with-int=[gmp|imath]>
337 Select the integer library to be used by C<isl>, the default is C<gmp>.
338 Note that C<isl> may run significantly slower if you use C<imath>.
340 =item C<--with-gmp-prefix>
342 Installation prefix for C<GMP> (architecture-independent files).
344 =item C<--with-gmp-exec-prefix>
346 Installation prefix for C<GMP> (architecture-dependent files).
354 =item 4 Install (optional)
360 =head1 Integer Set Library
362 =head2 Memory Management
364 Since a high-level operation on isl objects usually involves
365 several substeps and since the user is usually not interested in
366 the intermediate results, most functions that return a new object
367 will also release all the objects passed as arguments.
368 If the user still wants to use one or more of these arguments
369 after the function call, she should pass along a copy of the
370 object rather than the object itself.
371 The user is then responsible for making sure that the original
372 object gets used somewhere else or is explicitly freed.
374 The arguments and return values of all documented functions are
375 annotated to make clear which arguments are released and which
376 arguments are preserved. In particular, the following annotations
383 C<__isl_give> means that a new object is returned.
384 The user should make sure that the returned pointer is
385 used exactly once as a value for an C<__isl_take> argument.
386 In between, it can be used as a value for as many
387 C<__isl_keep> arguments as the user likes.
388 There is one exception, and that is the case where the
389 pointer returned is C<NULL>. Is this case, the user
390 is free to use it as an C<__isl_take> argument or not.
391 When applied to a C<char *>, the returned pointer needs to be
396 C<__isl_null> means that a C<NULL> value is returned.
400 C<__isl_take> means that the object the argument points to
401 is taken over by the function and may no longer be used
402 by the user as an argument to any other function.
403 The pointer value must be one returned by a function
404 returning an C<__isl_give> pointer.
405 If the user passes in a C<NULL> value, then this will
406 be treated as an error in the sense that the function will
407 not perform its usual operation. However, it will still
408 make sure that all the other C<__isl_take> arguments
413 C<__isl_keep> means that the function will only use the object
414 temporarily. After the function has finished, the user
415 can still use it as an argument to other functions.
416 A C<NULL> value will be treated in the same way as
417 a C<NULL> value for an C<__isl_take> argument.
418 This annotation may also be used on return values of
419 type C<const char *>, in which case the returned pointer should
420 not be freed by the user and is only valid until the object
421 from which it was derived is updated or freed.
425 =head2 Initialization
427 All manipulations of integer sets and relations occur within
428 the context of an C<isl_ctx>.
429 A given C<isl_ctx> can only be used within a single thread.
430 All arguments of a function are required to have been allocated
431 within the same context.
432 There are currently no functions available for moving an object
433 from one C<isl_ctx> to another C<isl_ctx>. This means that
434 there is currently no way of safely moving an object from one
435 thread to another, unless the whole C<isl_ctx> is moved.
437 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
438 freed using C<isl_ctx_free>.
439 All objects allocated within an C<isl_ctx> should be freed
440 before the C<isl_ctx> itself is freed.
442 isl_ctx *isl_ctx_alloc();
443 void isl_ctx_free(isl_ctx *ctx);
445 The user can impose a bound on the number of low-level I<operations>
446 that can be performed by an C<isl_ctx>. This bound can be set and
447 retrieved using the following functions. A bound of zero means that
448 no bound is imposed. The number of operations performed can be
449 reset using C<isl_ctx_reset_operations>. Note that the number
450 of low-level operations needed to perform a high-level computation
451 may differ significantly across different versions
452 of C<isl>, but it should be the same across different platforms
453 for the same version of C<isl>.
455 Warning: This feature is experimental. C<isl> has good support to abort and
456 bail out during the computation, but this feature may exercise error code paths
457 that are normally not used that much. Consequently, it is not unlikely that
458 hidden bugs will be exposed.
460 void isl_ctx_set_max_operations(isl_ctx *ctx,
461 unsigned long max_operations);
462 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
463 void isl_ctx_reset_operations(isl_ctx *ctx);
465 In order to be able to create an object in the same context
466 as another object, most object types (described later in
467 this document) provide a function to obtain the context
468 in which the object was created.
471 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
472 isl_ctx *isl_multi_val_get_ctx(
473 __isl_keep isl_multi_val *mv);
476 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
478 #include <isl/local_space.h>
479 isl_ctx *isl_local_space_get_ctx(
480 __isl_keep isl_local_space *ls);
483 isl_ctx *isl_set_list_get_ctx(
484 __isl_keep isl_set_list *list);
487 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
488 isl_ctx *isl_multi_aff_get_ctx(
489 __isl_keep isl_multi_aff *maff);
490 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
491 isl_ctx *isl_pw_multi_aff_get_ctx(
492 __isl_keep isl_pw_multi_aff *pma);
493 isl_ctx *isl_multi_pw_aff_get_ctx(
494 __isl_keep isl_multi_pw_aff *mpa);
495 isl_ctx *isl_union_pw_aff_get_ctx(
496 __isl_keep isl_union_pw_aff *upa);
497 isl_ctx *isl_union_pw_multi_aff_get_ctx(
498 __isl_keep isl_union_pw_multi_aff *upma);
499 isl_ctx *isl_multi_union_pw_aff_get_ctx(
500 __isl_keep isl_multi_union_pw_aff *mupa);
502 #include <isl/id_to_ast_expr.h>
503 isl_ctx *isl_id_to_ast_expr_get_ctx(
504 __isl_keep isl_id_to_ast_expr *id2expr);
506 #include <isl/point.h>
507 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
510 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
513 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
515 #include <isl/vertices.h>
516 isl_ctx *isl_vertices_get_ctx(
517 __isl_keep isl_vertices *vertices);
518 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
519 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
521 #include <isl/flow.h>
522 isl_ctx *isl_restriction_get_ctx(
523 __isl_keep isl_restriction *restr);
525 #include <isl/schedule.h>
526 isl_ctx *isl_schedule_get_ctx(
527 __isl_keep isl_schedule *sched);
528 isl_ctx *isl_schedule_constraints_get_ctx(
529 __isl_keep isl_schedule_constraints *sc);
531 #include <isl/schedule_node.h>
532 isl_ctx *isl_schedule_node_get_ctx(
533 __isl_keep isl_schedule_node *node);
535 #include <isl/band.h>
536 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
538 #include <isl/ast_build.h>
539 isl_ctx *isl_ast_build_get_ctx(
540 __isl_keep isl_ast_build *build);
543 isl_ctx *isl_ast_expr_get_ctx(
544 __isl_keep isl_ast_expr *expr);
545 isl_ctx *isl_ast_node_get_ctx(
546 __isl_keep isl_ast_node *node);
550 An C<isl_val> represents an integer value, a rational value
551 or one of three special values, infinity, negative infinity and NaN.
552 Some predefined values can be created using the following functions.
555 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
556 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
557 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
558 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
559 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
560 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
562 Specific integer values can be created using the following functions.
565 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
567 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
569 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
570 size_t n, size_t size, const void *chunks);
572 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
573 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
574 The least significant digit is assumed to be stored first.
576 Value objects can be copied and freed using the following functions.
579 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
580 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
582 They can be inspected using the following functions.
585 long isl_val_get_num_si(__isl_keep isl_val *v);
586 long isl_val_get_den_si(__isl_keep isl_val *v);
587 double isl_val_get_d(__isl_keep isl_val *v);
588 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
590 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
591 size_t size, void *chunks);
593 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
594 of C<size> bytes needed to store the absolute value of the
596 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
597 which is assumed to have been preallocated by the caller.
598 The least significant digit is stored first.
599 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
600 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
601 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
603 An C<isl_val> can be modified using the following function.
606 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
609 The following unary properties are defined on C<isl_val>s.
612 int isl_val_sgn(__isl_keep isl_val *v);
613 int isl_val_is_zero(__isl_keep isl_val *v);
614 int isl_val_is_one(__isl_keep isl_val *v);
615 int isl_val_is_negone(__isl_keep isl_val *v);
616 int isl_val_is_nonneg(__isl_keep isl_val *v);
617 int isl_val_is_nonpos(__isl_keep isl_val *v);
618 int isl_val_is_pos(__isl_keep isl_val *v);
619 int isl_val_is_neg(__isl_keep isl_val *v);
620 int isl_val_is_int(__isl_keep isl_val *v);
621 int isl_val_is_rat(__isl_keep isl_val *v);
622 int isl_val_is_nan(__isl_keep isl_val *v);
623 int isl_val_is_infty(__isl_keep isl_val *v);
624 int isl_val_is_neginfty(__isl_keep isl_val *v);
626 Note that the sign of NaN is undefined.
628 The following binary properties are defined on pairs of C<isl_val>s.
631 int isl_val_lt(__isl_keep isl_val *v1,
632 __isl_keep isl_val *v2);
633 int isl_val_le(__isl_keep isl_val *v1,
634 __isl_keep isl_val *v2);
635 int isl_val_gt(__isl_keep isl_val *v1,
636 __isl_keep isl_val *v2);
637 int isl_val_ge(__isl_keep isl_val *v1,
638 __isl_keep isl_val *v2);
639 int isl_val_eq(__isl_keep isl_val *v1,
640 __isl_keep isl_val *v2);
641 int isl_val_ne(__isl_keep isl_val *v1,
642 __isl_keep isl_val *v2);
643 int isl_val_abs_eq(__isl_keep isl_val *v1,
644 __isl_keep isl_val *v2);
646 The function C<isl_val_abs_eq> checks whether its two arguments
647 are equal in absolute value.
649 For integer C<isl_val>s we additionally have the following binary property.
652 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
653 __isl_keep isl_val *v2);
655 An C<isl_val> can also be compared to an integer using the following
656 function. The result is undefined for NaN.
659 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
661 The following unary operations are available on C<isl_val>s.
664 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
665 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
666 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
667 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
668 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
669 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
670 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
672 The following binary operations are available on C<isl_val>s.
675 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
676 __isl_take isl_val *v2);
677 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
678 __isl_take isl_val *v2);
679 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
680 __isl_take isl_val *v2);
681 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
683 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
684 __isl_take isl_val *v2);
685 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
687 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
688 __isl_take isl_val *v2);
689 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
691 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
692 __isl_take isl_val *v2);
694 On integer values, we additionally have the following operations.
697 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
698 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
699 __isl_take isl_val *v2);
700 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
701 __isl_take isl_val *v2);
702 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
703 __isl_take isl_val *v2, __isl_give isl_val **x,
704 __isl_give isl_val **y);
706 The function C<isl_val_gcdext> returns the greatest common divisor g
707 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
708 that C<*x> * C<v1> + C<*y> * C<v2> = g.
710 =head3 GMP specific functions
712 These functions are only available if C<isl> has been compiled with C<GMP>
715 Specific integer and rational values can be created from C<GMP> values using
716 the following functions.
718 #include <isl/val_gmp.h>
719 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
721 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
722 const mpz_t n, const mpz_t d);
724 The numerator and denominator of a rational value can be extracted as
725 C<GMP> values using the following functions.
727 #include <isl/val_gmp.h>
728 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
729 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
731 =head2 Sets and Relations
733 C<isl> uses six types of objects for representing sets and relations,
734 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
735 C<isl_union_set> and C<isl_union_map>.
736 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
737 can be described as a conjunction of affine constraints, while
738 C<isl_set> and C<isl_map> represent unions of
739 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
740 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
741 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
742 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
743 where spaces are considered different if they have a different number
744 of dimensions and/or different names (see L<"Spaces">).
745 The difference between sets and relations (maps) is that sets have
746 one set of variables, while relations have two sets of variables,
747 input variables and output variables.
749 =head2 Error Handling
751 C<isl> supports different ways to react in case a runtime error is triggered.
752 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
753 with two maps that have incompatible spaces. There are three possible ways
754 to react on error: to warn, to continue or to abort.
756 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
757 the last error in the corresponding C<isl_ctx> and the function in which the
758 error was triggered returns C<NULL>. An error does not corrupt internal state,
759 such that isl can continue to be used. C<isl> also provides functions to
760 read the last error and to reset the memory that stores the last error. The
761 last error is only stored for information purposes. Its presence does not
762 change the behavior of C<isl>. Hence, resetting an error is not required to
763 continue to use isl, but only to observe new errors.
766 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
767 void isl_ctx_reset_error(isl_ctx *ctx);
769 Another option is to continue on error. This is similar to warn on error mode,
770 except that C<isl> does not print any warning. This allows a program to
771 implement its own error reporting.
773 The last option is to directly abort the execution of the program from within
774 the isl library. This makes it obviously impossible to recover from an error,
775 but it allows to directly spot the error location. By aborting on error,
776 debuggers break at the location the error occurred and can provide a stack
777 trace. Other tools that automatically provide stack traces on abort or that do
778 not want to continue execution after an error was triggered may also prefer to
781 The on error behavior of isl can be specified by calling
782 C<isl_options_set_on_error> or by setting the command line option
783 C<--isl-on-error>. Valid arguments for the function call are
784 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
785 choices for the command line option are C<warn>, C<continue> and C<abort>.
786 It is also possible to query the current error mode.
788 #include <isl/options.h>
789 int isl_options_set_on_error(isl_ctx *ctx, int val);
790 int isl_options_get_on_error(isl_ctx *ctx);
794 Identifiers are used to identify both individual dimensions
795 and tuples of dimensions. They consist of an optional name and an optional
796 user pointer. The name and the user pointer cannot both be C<NULL>, however.
797 Identifiers with the same name but different pointer values
798 are considered to be distinct.
799 Similarly, identifiers with different names but the same pointer value
800 are also considered to be distinct.
801 Equal identifiers are represented using the same object.
802 Pairs of identifiers can therefore be tested for equality using the
804 Identifiers can be constructed, copied, freed, inspected and printed
805 using the following functions.
808 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
809 __isl_keep const char *name, void *user);
810 __isl_give isl_id *isl_id_set_free_user(
811 __isl_take isl_id *id,
812 __isl_give void (*free_user)(void *user));
813 __isl_give isl_id *isl_id_copy(isl_id *id);
814 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
816 void *isl_id_get_user(__isl_keep isl_id *id);
817 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
819 __isl_give isl_printer *isl_printer_print_id(
820 __isl_take isl_printer *p, __isl_keep isl_id *id);
822 The callback set by C<isl_id_set_free_user> is called on the user
823 pointer when the last reference to the C<isl_id> is freed.
824 Note that C<isl_id_get_name> returns a pointer to some internal
825 data structure, so the result can only be used while the
826 corresponding C<isl_id> is alive.
830 Whenever a new set, relation or similar object is created from scratch,
831 the space in which it lives needs to be specified using an C<isl_space>.
832 Each space involves zero or more parameters and zero, one or two
833 tuples of set or input/output dimensions. The parameters and dimensions
834 are identified by an C<isl_dim_type> and a position.
835 The type C<isl_dim_param> refers to parameters,
836 the type C<isl_dim_set> refers to set dimensions (for spaces
837 with a single tuple of dimensions) and the types C<isl_dim_in>
838 and C<isl_dim_out> refer to input and output dimensions
839 (for spaces with two tuples of dimensions).
840 Local spaces (see L</"Local Spaces">) also contain dimensions
841 of type C<isl_dim_div>.
842 Note that parameters are only identified by their position within
843 a given object. Across different objects, parameters are (usually)
844 identified by their names or identifiers. Only unnamed parameters
845 are identified by their positions across objects. The use of unnamed
846 parameters is discouraged.
848 #include <isl/space.h>
849 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
850 unsigned nparam, unsigned n_in, unsigned n_out);
851 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
853 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
854 unsigned nparam, unsigned dim);
855 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
856 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
858 The space used for creating a parameter domain
859 needs to be created using C<isl_space_params_alloc>.
860 For other sets, the space
861 needs to be created using C<isl_space_set_alloc>, while
862 for a relation, the space
863 needs to be created using C<isl_space_alloc>.
865 To check whether a given space is that of a set or a map
866 or whether it is a parameter space, use these functions:
868 #include <isl/space.h>
869 int isl_space_is_params(__isl_keep isl_space *space);
870 int isl_space_is_set(__isl_keep isl_space *space);
871 int isl_space_is_map(__isl_keep isl_space *space);
873 Spaces can be compared using the following functions:
875 #include <isl/space.h>
876 int isl_space_is_equal(__isl_keep isl_space *space1,
877 __isl_keep isl_space *space2);
878 int isl_space_is_domain(__isl_keep isl_space *space1,
879 __isl_keep isl_space *space2);
880 int isl_space_is_range(__isl_keep isl_space *space1,
881 __isl_keep isl_space *space2);
882 int isl_space_tuple_is_equal(
883 __isl_keep isl_space *space1,
884 enum isl_dim_type type1,
885 __isl_keep isl_space *space2,
886 enum isl_dim_type type2);
888 C<isl_space_is_domain> checks whether the first argument is equal
889 to the domain of the second argument. This requires in particular that
890 the first argument is a set space and that the second argument
891 is a map space. C<isl_space_tuple_is_equal> checks whether the given
892 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
893 spaces are the same. That is, it checks if they have the same
894 identifier (if any), the same dimension and the same internal structure
897 It is often useful to create objects that live in the
898 same space as some other object. This can be accomplished
899 by creating the new objects
900 (see L</"Creating New Sets and Relations"> or
901 L</"Functions">) based on the space
902 of the original object.
905 __isl_give isl_space *isl_basic_set_get_space(
906 __isl_keep isl_basic_set *bset);
907 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
909 #include <isl/union_set.h>
910 __isl_give isl_space *isl_union_set_get_space(
911 __isl_keep isl_union_set *uset);
914 __isl_give isl_space *isl_basic_map_get_space(
915 __isl_keep isl_basic_map *bmap);
916 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
918 #include <isl/union_map.h>
919 __isl_give isl_space *isl_union_map_get_space(
920 __isl_keep isl_union_map *umap);
922 #include <isl/constraint.h>
923 __isl_give isl_space *isl_constraint_get_space(
924 __isl_keep isl_constraint *constraint);
926 #include <isl/polynomial.h>
927 __isl_give isl_space *isl_qpolynomial_get_domain_space(
928 __isl_keep isl_qpolynomial *qp);
929 __isl_give isl_space *isl_qpolynomial_get_space(
930 __isl_keep isl_qpolynomial *qp);
931 __isl_give isl_space *isl_qpolynomial_fold_get_space(
932 __isl_keep isl_qpolynomial_fold *fold);
933 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
934 __isl_keep isl_pw_qpolynomial *pwqp);
935 __isl_give isl_space *isl_pw_qpolynomial_get_space(
936 __isl_keep isl_pw_qpolynomial *pwqp);
937 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
938 __isl_keep isl_pw_qpolynomial_fold *pwf);
939 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
940 __isl_keep isl_pw_qpolynomial_fold *pwf);
941 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
942 __isl_keep isl_union_pw_qpolynomial *upwqp);
943 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
944 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
947 __isl_give isl_space *isl_multi_val_get_space(
948 __isl_keep isl_multi_val *mv);
951 __isl_give isl_space *isl_aff_get_domain_space(
952 __isl_keep isl_aff *aff);
953 __isl_give isl_space *isl_aff_get_space(
954 __isl_keep isl_aff *aff);
955 __isl_give isl_space *isl_pw_aff_get_domain_space(
956 __isl_keep isl_pw_aff *pwaff);
957 __isl_give isl_space *isl_pw_aff_get_space(
958 __isl_keep isl_pw_aff *pwaff);
959 __isl_give isl_space *isl_multi_aff_get_domain_space(
960 __isl_keep isl_multi_aff *maff);
961 __isl_give isl_space *isl_multi_aff_get_space(
962 __isl_keep isl_multi_aff *maff);
963 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
964 __isl_keep isl_pw_multi_aff *pma);
965 __isl_give isl_space *isl_pw_multi_aff_get_space(
966 __isl_keep isl_pw_multi_aff *pma);
967 __isl_give isl_space *isl_union_pw_aff_get_space(
968 __isl_keep isl_union_pw_aff *upa);
969 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
970 __isl_keep isl_union_pw_multi_aff *upma);
971 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
972 __isl_keep isl_multi_pw_aff *mpa);
973 __isl_give isl_space *isl_multi_pw_aff_get_space(
974 __isl_keep isl_multi_pw_aff *mpa);
975 __isl_give isl_space *
976 isl_multi_union_pw_aff_get_domain_space(
977 __isl_keep isl_multi_union_pw_aff *mupa);
978 __isl_give isl_space *
979 isl_multi_union_pw_aff_get_space(
980 __isl_keep isl_multi_union_pw_aff *mupa);
982 #include <isl/point.h>
983 __isl_give isl_space *isl_point_get_space(
984 __isl_keep isl_point *pnt);
986 The number of dimensions of a given type of space
987 may be read off from a space or an object that lives
988 in a space using the following functions.
989 In case of C<isl_space_dim>, type may be
990 C<isl_dim_param>, C<isl_dim_in> (only for relations),
991 C<isl_dim_out> (only for relations), C<isl_dim_set>
992 (only for sets) or C<isl_dim_all>.
994 #include <isl/space.h>
995 unsigned isl_space_dim(__isl_keep isl_space *space,
996 enum isl_dim_type type);
998 #include <isl/local_space.h>
999 int isl_local_space_dim(__isl_keep isl_local_space *ls,
1000 enum isl_dim_type type);
1002 #include <isl/set.h>
1003 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1004 enum isl_dim_type type);
1005 unsigned isl_set_dim(__isl_keep isl_set *set,
1006 enum isl_dim_type type);
1008 #include <isl/union_set.h>
1009 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1010 enum isl_dim_type type);
1012 #include <isl/map.h>
1013 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1014 enum isl_dim_type type);
1015 unsigned isl_map_dim(__isl_keep isl_map *map,
1016 enum isl_dim_type type);
1018 #include <isl/union_map.h>
1019 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1020 enum isl_dim_type type);
1022 #include <isl/val.h>
1023 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1024 enum isl_dim_type type);
1026 #include <isl/aff.h>
1027 int isl_aff_dim(__isl_keep isl_aff *aff,
1028 enum isl_dim_type type);
1029 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1030 enum isl_dim_type type);
1031 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1032 enum isl_dim_type type);
1033 unsigned isl_pw_multi_aff_dim(
1034 __isl_keep isl_pw_multi_aff *pma,
1035 enum isl_dim_type type);
1036 unsigned isl_multi_pw_aff_dim(
1037 __isl_keep isl_multi_pw_aff *mpa,
1038 enum isl_dim_type type);
1039 unsigned isl_union_pw_aff_dim(
1040 __isl_keep isl_union_pw_aff *upa,
1041 enum isl_dim_type type);
1042 unsigned isl_union_pw_multi_aff_dim(
1043 __isl_keep isl_union_pw_multi_aff *upma,
1044 enum isl_dim_type type);
1045 unsigned isl_multi_union_pw_aff_dim(
1046 __isl_keep isl_multi_union_pw_aff *mupa,
1047 enum isl_dim_type type);
1049 #include <isl/polynomial.h>
1050 unsigned isl_union_pw_qpolynomial_dim(
1051 __isl_keep isl_union_pw_qpolynomial *upwqp,
1052 enum isl_dim_type type);
1053 unsigned isl_union_pw_qpolynomial_fold_dim(
1054 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1055 enum isl_dim_type type);
1057 Note that an C<isl_union_set>, an C<isl_union_map>,
1058 an C<isl_union_pw_multi_aff>,
1059 an C<isl_union_pw_qpolynomial> and
1060 an C<isl_union_pw_qpolynomial_fold>
1061 only have parameters.
1063 The identifiers or names of the individual dimensions of spaces
1064 may be set or read off using the following functions on spaces
1065 or objects that live in spaces.
1066 These functions are mostly useful to obtain the identifiers, positions
1067 or names of the parameters. Identifiers of individual dimensions are
1068 essentially only useful for printing. They are ignored by all other
1069 operations and may not be preserved across those operations.
1071 #include <isl/space.h>
1072 __isl_give isl_space *isl_space_set_dim_id(
1073 __isl_take isl_space *space,
1074 enum isl_dim_type type, unsigned pos,
1075 __isl_take isl_id *id);
1076 int isl_space_has_dim_id(__isl_keep isl_space *space,
1077 enum isl_dim_type type, unsigned pos);
1078 __isl_give isl_id *isl_space_get_dim_id(
1079 __isl_keep isl_space *space,
1080 enum isl_dim_type type, unsigned pos);
1081 __isl_give isl_space *isl_space_set_dim_name(
1082 __isl_take isl_space *space,
1083 enum isl_dim_type type, unsigned pos,
1084 __isl_keep const char *name);
1085 int isl_space_has_dim_name(__isl_keep isl_space *space,
1086 enum isl_dim_type type, unsigned pos);
1087 __isl_keep const char *isl_space_get_dim_name(
1088 __isl_keep isl_space *space,
1089 enum isl_dim_type type, unsigned pos);
1091 #include <isl/local_space.h>
1092 __isl_give isl_local_space *isl_local_space_set_dim_id(
1093 __isl_take isl_local_space *ls,
1094 enum isl_dim_type type, unsigned pos,
1095 __isl_take isl_id *id);
1096 int isl_local_space_has_dim_id(
1097 __isl_keep isl_local_space *ls,
1098 enum isl_dim_type type, unsigned pos);
1099 __isl_give isl_id *isl_local_space_get_dim_id(
1100 __isl_keep isl_local_space *ls,
1101 enum isl_dim_type type, unsigned pos);
1102 __isl_give isl_local_space *isl_local_space_set_dim_name(
1103 __isl_take isl_local_space *ls,
1104 enum isl_dim_type type, unsigned pos, const char *s);
1105 int isl_local_space_has_dim_name(
1106 __isl_keep isl_local_space *ls,
1107 enum isl_dim_type type, unsigned pos)
1108 const char *isl_local_space_get_dim_name(
1109 __isl_keep isl_local_space *ls,
1110 enum isl_dim_type type, unsigned pos);
1112 #include <isl/constraint.h>
1113 const char *isl_constraint_get_dim_name(
1114 __isl_keep isl_constraint *constraint,
1115 enum isl_dim_type type, unsigned pos);
1117 #include <isl/set.h>
1118 __isl_give isl_id *isl_basic_set_get_dim_id(
1119 __isl_keep isl_basic_set *bset,
1120 enum isl_dim_type type, unsigned pos);
1121 __isl_give isl_set *isl_set_set_dim_id(
1122 __isl_take isl_set *set, enum isl_dim_type type,
1123 unsigned pos, __isl_take isl_id *id);
1124 int isl_set_has_dim_id(__isl_keep isl_set *set,
1125 enum isl_dim_type type, unsigned pos);
1126 __isl_give isl_id *isl_set_get_dim_id(
1127 __isl_keep isl_set *set, enum isl_dim_type type,
1129 const char *isl_basic_set_get_dim_name(
1130 __isl_keep isl_basic_set *bset,
1131 enum isl_dim_type type, unsigned pos);
1132 int isl_set_has_dim_name(__isl_keep isl_set *set,
1133 enum isl_dim_type type, unsigned pos);
1134 const char *isl_set_get_dim_name(
1135 __isl_keep isl_set *set,
1136 enum isl_dim_type type, unsigned pos);
1138 #include <isl/map.h>
1139 __isl_give isl_map *isl_map_set_dim_id(
1140 __isl_take isl_map *map, enum isl_dim_type type,
1141 unsigned pos, __isl_take isl_id *id);
1142 int isl_basic_map_has_dim_id(
1143 __isl_keep isl_basic_map *bmap,
1144 enum isl_dim_type type, unsigned pos);
1145 int isl_map_has_dim_id(__isl_keep isl_map *map,
1146 enum isl_dim_type type, unsigned pos);
1147 __isl_give isl_id *isl_map_get_dim_id(
1148 __isl_keep isl_map *map, enum isl_dim_type type,
1150 __isl_give isl_id *isl_union_map_get_dim_id(
1151 __isl_keep isl_union_map *umap,
1152 enum isl_dim_type type, unsigned pos);
1153 const char *isl_basic_map_get_dim_name(
1154 __isl_keep isl_basic_map *bmap,
1155 enum isl_dim_type type, unsigned pos);
1156 int isl_map_has_dim_name(__isl_keep isl_map *map,
1157 enum isl_dim_type type, unsigned pos);
1158 const char *isl_map_get_dim_name(
1159 __isl_keep isl_map *map,
1160 enum isl_dim_type type, unsigned pos);
1162 #include <isl/val.h>
1163 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1164 __isl_take isl_multi_val *mv,
1165 enum isl_dim_type type, unsigned pos,
1166 __isl_take isl_id *id);
1167 __isl_give isl_id *isl_multi_val_get_dim_id(
1168 __isl_keep isl_multi_val *mv,
1169 enum isl_dim_type type, unsigned pos);
1170 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1171 __isl_take isl_multi_val *mv,
1172 enum isl_dim_type type, unsigned pos, const char *s);
1174 #include <isl/aff.h>
1175 __isl_give isl_aff *isl_aff_set_dim_id(
1176 __isl_take isl_aff *aff, enum isl_dim_type type,
1177 unsigned pos, __isl_take isl_id *id);
1178 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1179 __isl_take isl_multi_aff *maff,
1180 enum isl_dim_type type, unsigned pos,
1181 __isl_take isl_id *id);
1182 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1183 __isl_take isl_pw_aff *pma,
1184 enum isl_dim_type type, unsigned pos,
1185 __isl_take isl_id *id);
1186 __isl_give isl_multi_pw_aff *
1187 isl_multi_pw_aff_set_dim_id(
1188 __isl_take isl_multi_pw_aff *mpa,
1189 enum isl_dim_type type, unsigned pos,
1190 __isl_take isl_id *id);
1191 __isl_give isl_multi_union_pw_aff *
1192 isl_multi_union_pw_aff_set_dim_id(
1193 __isl_take isl_multi_union_pw_aff *mupa,
1194 enum isl_dim_type type, unsigned pos,
1195 __isl_take isl_id *id);
1196 __isl_give isl_id *isl_multi_aff_get_dim_id(
1197 __isl_keep isl_multi_aff *ma,
1198 enum isl_dim_type type, unsigned pos);
1199 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1200 enum isl_dim_type type, unsigned pos);
1201 __isl_give isl_id *isl_pw_aff_get_dim_id(
1202 __isl_keep isl_pw_aff *pa,
1203 enum isl_dim_type type, unsigned pos);
1204 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1205 __isl_keep isl_pw_multi_aff *pma,
1206 enum isl_dim_type type, unsigned pos);
1207 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1208 __isl_keep isl_multi_pw_aff *mpa,
1209 enum isl_dim_type type, unsigned pos);
1210 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1211 __isl_keep isl_multi_union_pw_aff *mupa,
1212 enum isl_dim_type type, unsigned pos);
1213 __isl_give isl_aff *isl_aff_set_dim_name(
1214 __isl_take isl_aff *aff, enum isl_dim_type type,
1215 unsigned pos, const char *s);
1216 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1217 __isl_take isl_multi_aff *maff,
1218 enum isl_dim_type type, unsigned pos, const char *s);
1219 __isl_give isl_multi_pw_aff *
1220 isl_multi_pw_aff_set_dim_name(
1221 __isl_take isl_multi_pw_aff *mpa,
1222 enum isl_dim_type type, unsigned pos, const char *s);
1223 __isl_give isl_union_pw_aff *
1224 isl_union_pw_aff_set_dim_name(
1225 __isl_take isl_union_pw_aff *upa,
1226 enum isl_dim_type type, unsigned pos,
1228 __isl_give isl_union_pw_multi_aff *
1229 isl_union_pw_multi_aff_set_dim_name(
1230 __isl_take isl_union_pw_multi_aff *upma,
1231 enum isl_dim_type type, unsigned pos,
1233 __isl_give isl_multi_union_pw_aff *
1234 isl_multi_union_pw_aff_set_dim_name(
1235 __isl_take isl_multi_union_pw_aff *mupa,
1236 enum isl_dim_type type, unsigned pos,
1237 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1238 enum isl_dim_type type, unsigned pos);
1239 const char *isl_pw_aff_get_dim_name(
1240 __isl_keep isl_pw_aff *pa,
1241 enum isl_dim_type type, unsigned pos);
1242 const char *isl_pw_multi_aff_get_dim_name(
1243 __isl_keep isl_pw_multi_aff *pma,
1244 enum isl_dim_type type, unsigned pos);
1246 #include <isl/polynomial.h>
1247 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1248 __isl_take isl_qpolynomial *qp,
1249 enum isl_dim_type type, unsigned pos,
1251 __isl_give isl_pw_qpolynomial *
1252 isl_pw_qpolynomial_set_dim_name(
1253 __isl_take isl_pw_qpolynomial *pwqp,
1254 enum isl_dim_type type, unsigned pos,
1256 __isl_give isl_pw_qpolynomial_fold *
1257 isl_pw_qpolynomial_fold_set_dim_name(
1258 __isl_take isl_pw_qpolynomial_fold *pwf,
1259 enum isl_dim_type type, unsigned pos,
1261 __isl_give isl_union_pw_qpolynomial *
1262 isl_union_pw_qpolynomial_set_dim_name(
1263 __isl_take isl_union_pw_qpolynomial *upwqp,
1264 enum isl_dim_type type, unsigned pos,
1266 __isl_give isl_union_pw_qpolynomial_fold *
1267 isl_union_pw_qpolynomial_fold_set_dim_name(
1268 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1269 enum isl_dim_type type, unsigned pos,
1272 Note that C<isl_space_get_name> returns a pointer to some internal
1273 data structure, so the result can only be used while the
1274 corresponding C<isl_space> is alive.
1275 Also note that every function that operates on two sets or relations
1276 requires that both arguments have the same parameters. This also
1277 means that if one of the arguments has named parameters, then the
1278 other needs to have named parameters too and the names need to match.
1279 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1280 arguments may have different parameters (as long as they are named),
1281 in which case the result will have as parameters the union of the parameters of
1284 Given the identifier or name of a dimension (typically a parameter),
1285 its position can be obtained from the following functions.
1287 #include <isl/space.h>
1288 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1289 enum isl_dim_type type, __isl_keep isl_id *id);
1290 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1291 enum isl_dim_type type, const char *name);
1293 #include <isl/local_space.h>
1294 int isl_local_space_find_dim_by_name(
1295 __isl_keep isl_local_space *ls,
1296 enum isl_dim_type type, const char *name);
1298 #include <isl/val.h>
1299 int isl_multi_val_find_dim_by_id(
1300 __isl_keep isl_multi_val *mv,
1301 enum isl_dim_type type, __isl_keep isl_id *id);
1302 int isl_multi_val_find_dim_by_name(
1303 __isl_keep isl_multi_val *mv,
1304 enum isl_dim_type type, const char *name);
1306 #include <isl/set.h>
1307 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1308 enum isl_dim_type type, __isl_keep isl_id *id);
1309 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1310 enum isl_dim_type type, const char *name);
1312 #include <isl/map.h>
1313 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1314 enum isl_dim_type type, __isl_keep isl_id *id);
1315 int isl_basic_map_find_dim_by_name(
1316 __isl_keep isl_basic_map *bmap,
1317 enum isl_dim_type type, const char *name);
1318 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1319 enum isl_dim_type type, const char *name);
1320 int isl_union_map_find_dim_by_name(
1321 __isl_keep isl_union_map *umap,
1322 enum isl_dim_type type, const char *name);
1324 #include <isl/aff.h>
1325 int isl_multi_aff_find_dim_by_id(
1326 __isl_keep isl_multi_aff *ma,
1327 enum isl_dim_type type, __isl_keep isl_id *id);
1328 int isl_multi_pw_aff_find_dim_by_id(
1329 __isl_keep isl_multi_pw_aff *mpa,
1330 enum isl_dim_type type, __isl_keep isl_id *id);
1331 int isl_multi_union_pw_aff_find_dim_by_id(
1332 __isl_keep isl_union_multi_pw_aff *mupa,
1333 enum isl_dim_type type, __isl_keep isl_id *id);
1334 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1335 enum isl_dim_type type, const char *name);
1336 int isl_multi_aff_find_dim_by_name(
1337 __isl_keep isl_multi_aff *ma,
1338 enum isl_dim_type type, const char *name);
1339 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1340 enum isl_dim_type type, const char *name);
1341 int isl_multi_pw_aff_find_dim_by_name(
1342 __isl_keep isl_multi_pw_aff *mpa,
1343 enum isl_dim_type type, const char *name);
1344 int isl_pw_multi_aff_find_dim_by_name(
1345 __isl_keep isl_pw_multi_aff *pma,
1346 enum isl_dim_type type, const char *name);
1347 int isl_union_pw_aff_find_dim_by_name(
1348 __isl_keep isl_union_pw_aff *upa,
1349 enum isl_dim_type type, const char *name);
1350 int isl_union_pw_multi_aff_find_dim_by_name(
1351 __isl_keep isl_union_pw_multi_aff *upma,
1352 enum isl_dim_type type, const char *name);
1353 int isl_multi_union_pw_aff_find_dim_by_name(
1354 __isl_keep isl_multi_union_pw_aff *mupa,
1355 enum isl_dim_type type, const char *name);
1357 #include <isl/polynomial.h>
1358 int isl_pw_qpolynomial_find_dim_by_name(
1359 __isl_keep isl_pw_qpolynomial *pwqp,
1360 enum isl_dim_type type, const char *name);
1361 int isl_pw_qpolynomial_fold_find_dim_by_name(
1362 __isl_keep isl_pw_qpolynomial_fold *pwf,
1363 enum isl_dim_type type, const char *name);
1364 int isl_union_pw_qpolynomial_find_dim_by_name(
1365 __isl_keep isl_union_pw_qpolynomial *upwqp,
1366 enum isl_dim_type type, const char *name);
1367 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1368 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1369 enum isl_dim_type type, const char *name);
1371 The identifiers or names of entire spaces may be set or read off
1372 using the following functions.
1374 #include <isl/space.h>
1375 __isl_give isl_space *isl_space_set_tuple_id(
1376 __isl_take isl_space *space,
1377 enum isl_dim_type type, __isl_take isl_id *id);
1378 __isl_give isl_space *isl_space_reset_tuple_id(
1379 __isl_take isl_space *space, enum isl_dim_type type);
1380 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1381 enum isl_dim_type type);
1382 __isl_give isl_id *isl_space_get_tuple_id(
1383 __isl_keep isl_space *space, enum isl_dim_type type);
1384 __isl_give isl_space *isl_space_set_tuple_name(
1385 __isl_take isl_space *space,
1386 enum isl_dim_type type, const char *s);
1387 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1388 enum isl_dim_type type);
1389 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1390 enum isl_dim_type type);
1392 #include <isl/local_space.h>
1393 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1394 __isl_take isl_local_space *ls,
1395 enum isl_dim_type type, __isl_take isl_id *id);
1397 #include <isl/set.h>
1398 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1399 __isl_take isl_basic_set *bset,
1400 __isl_take isl_id *id);
1401 __isl_give isl_set *isl_set_set_tuple_id(
1402 __isl_take isl_set *set, __isl_take isl_id *id);
1403 __isl_give isl_set *isl_set_reset_tuple_id(
1404 __isl_take isl_set *set);
1405 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1406 __isl_give isl_id *isl_set_get_tuple_id(
1407 __isl_keep isl_set *set);
1408 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1409 __isl_take isl_basic_set *set, const char *s);
1410 __isl_give isl_set *isl_set_set_tuple_name(
1411 __isl_take isl_set *set, const char *s);
1412 const char *isl_basic_set_get_tuple_name(
1413 __isl_keep isl_basic_set *bset);
1414 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1415 const char *isl_set_get_tuple_name(
1416 __isl_keep isl_set *set);
1418 #include <isl/map.h>
1419 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1420 __isl_take isl_basic_map *bmap,
1421 enum isl_dim_type type, __isl_take isl_id *id);
1422 __isl_give isl_map *isl_map_set_tuple_id(
1423 __isl_take isl_map *map, enum isl_dim_type type,
1424 __isl_take isl_id *id);
1425 __isl_give isl_map *isl_map_reset_tuple_id(
1426 __isl_take isl_map *map, enum isl_dim_type type);
1427 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1428 enum isl_dim_type type);
1429 __isl_give isl_id *isl_map_get_tuple_id(
1430 __isl_keep isl_map *map, enum isl_dim_type type);
1431 __isl_give isl_map *isl_map_set_tuple_name(
1432 __isl_take isl_map *map,
1433 enum isl_dim_type type, const char *s);
1434 const char *isl_basic_map_get_tuple_name(
1435 __isl_keep isl_basic_map *bmap,
1436 enum isl_dim_type type);
1437 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1438 __isl_take isl_basic_map *bmap,
1439 enum isl_dim_type type, const char *s);
1440 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1441 enum isl_dim_type type);
1442 const char *isl_map_get_tuple_name(
1443 __isl_keep isl_map *map,
1444 enum isl_dim_type type);
1446 #include <isl/val.h>
1447 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1448 __isl_take isl_multi_val *mv,
1449 enum isl_dim_type type, __isl_take isl_id *id);
1450 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1451 __isl_take isl_multi_val *mv,
1452 enum isl_dim_type type);
1453 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1454 enum isl_dim_type type);
1455 __isl_give isl_id *isl_multi_val_get_tuple_id(
1456 __isl_keep isl_multi_val *mv,
1457 enum isl_dim_type type);
1458 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1459 __isl_take isl_multi_val *mv,
1460 enum isl_dim_type type, const char *s);
1461 const char *isl_multi_val_get_tuple_name(
1462 __isl_keep isl_multi_val *mv,
1463 enum isl_dim_type type);
1465 #include <isl/aff.h>
1466 __isl_give isl_aff *isl_aff_set_tuple_id(
1467 __isl_take isl_aff *aff,
1468 enum isl_dim_type type, __isl_take isl_id *id);
1469 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1470 __isl_take isl_multi_aff *maff,
1471 enum isl_dim_type type, __isl_take isl_id *id);
1472 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1473 __isl_take isl_pw_aff *pwaff,
1474 enum isl_dim_type type, __isl_take isl_id *id);
1475 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1476 __isl_take isl_pw_multi_aff *pma,
1477 enum isl_dim_type type, __isl_take isl_id *id);
1478 __isl_give isl_multi_union_pw_aff *
1479 isl_multi_union_pw_aff_set_tuple_id(
1480 __isl_take isl_multi_union_pw_aff *mupa,
1481 enum isl_dim_type type, __isl_take isl_id *id);
1482 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1483 __isl_take isl_multi_aff *ma,
1484 enum isl_dim_type type);
1485 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1486 __isl_take isl_pw_aff *pa,
1487 enum isl_dim_type type);
1488 __isl_give isl_multi_pw_aff *
1489 isl_multi_pw_aff_reset_tuple_id(
1490 __isl_take isl_multi_pw_aff *mpa,
1491 enum isl_dim_type type);
1492 __isl_give isl_pw_multi_aff *
1493 isl_pw_multi_aff_reset_tuple_id(
1494 __isl_take isl_pw_multi_aff *pma,
1495 enum isl_dim_type type);
1496 __isl_give isl_multi_union_pw_aff *
1497 isl_multi_union_pw_aff_reset_tuple_id(
1498 __isl_take isl_multi_union_pw_aff *mupa,
1499 enum isl_dim_type type);
1500 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1501 enum isl_dim_type type);
1502 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1503 __isl_keep isl_multi_aff *ma,
1504 enum isl_dim_type type);
1505 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1506 enum isl_dim_type type);
1507 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1508 __isl_keep isl_pw_aff *pa,
1509 enum isl_dim_type type);
1510 int isl_pw_multi_aff_has_tuple_id(
1511 __isl_keep isl_pw_multi_aff *pma,
1512 enum isl_dim_type type);
1513 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1514 __isl_keep isl_pw_multi_aff *pma,
1515 enum isl_dim_type type);
1516 int isl_multi_pw_aff_has_tuple_id(
1517 __isl_keep isl_multi_pw_aff *mpa,
1518 enum isl_dim_type type);
1519 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1520 __isl_keep isl_multi_pw_aff *mpa,
1521 enum isl_dim_type type);
1522 int isl_multi_union_pw_aff_has_tuple_id(
1523 __isl_keep isl_multi_union_pw_aff *mupa,
1524 enum isl_dim_type type);
1525 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1526 __isl_keep isl_multi_union_pw_aff *mupa,
1527 enum isl_dim_type type);
1528 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1529 __isl_take isl_multi_aff *maff,
1530 enum isl_dim_type type, const char *s);
1531 __isl_give isl_multi_pw_aff *
1532 isl_multi_pw_aff_set_tuple_name(
1533 __isl_take isl_multi_pw_aff *mpa,
1534 enum isl_dim_type type, const char *s);
1535 __isl_give isl_multi_union_pw_aff *
1536 isl_multi_union_pw_aff_set_tuple_name(
1537 __isl_take isl_multi_union_pw_aff *mupa,
1538 enum isl_dim_type type, const char *s);
1539 const char *isl_multi_aff_get_tuple_name(
1540 __isl_keep isl_multi_aff *multi,
1541 enum isl_dim_type type);
1542 int isl_pw_multi_aff_has_tuple_name(
1543 __isl_keep isl_pw_multi_aff *pma,
1544 enum isl_dim_type type);
1545 const char *isl_pw_multi_aff_get_tuple_name(
1546 __isl_keep isl_pw_multi_aff *pma,
1547 enum isl_dim_type type);
1548 const char *isl_multi_union_pw_aff_get_tuple_name(
1549 __isl_keep isl_multi_union_pw_aff *mupa,
1550 enum isl_dim_type type);
1552 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1553 or C<isl_dim_set>. As with C<isl_space_get_name>,
1554 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1556 Binary operations require the corresponding spaces of their arguments
1557 to have the same name.
1559 To keep the names of all parameters and tuples, but reset the user pointers
1560 of all the corresponding identifiers, use the following function.
1562 #include <isl/space.h>
1563 __isl_give isl_space *isl_space_reset_user(
1564 __isl_take isl_space *space);
1566 #include <isl/set.h>
1567 __isl_give isl_set *isl_set_reset_user(
1568 __isl_take isl_set *set);
1570 #include <isl/map.h>
1571 __isl_give isl_map *isl_map_reset_user(
1572 __isl_take isl_map *map);
1574 #include <isl/union_set.h>
1575 __isl_give isl_union_set *isl_union_set_reset_user(
1576 __isl_take isl_union_set *uset);
1578 #include <isl/union_map.h>
1579 __isl_give isl_union_map *isl_union_map_reset_user(
1580 __isl_take isl_union_map *umap);
1582 #include <isl/val.h>
1583 __isl_give isl_multi_val *isl_multi_val_reset_user(
1584 __isl_take isl_multi_val *mv);
1586 #include <isl/aff.h>
1587 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1588 __isl_take isl_multi_aff *ma);
1589 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1590 __isl_take isl_pw_aff *pa);
1591 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1592 __isl_take isl_multi_pw_aff *mpa);
1593 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1594 __isl_take isl_pw_multi_aff *pma);
1595 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1596 __isl_take isl_union_pw_aff *upa);
1597 __isl_give isl_multi_union_pw_aff *
1598 isl_multi_union_pw_aff_reset_user(
1599 __isl_take isl_multi_union_pw_aff *mupa);
1600 __isl_give isl_union_pw_multi_aff *
1601 isl_union_pw_multi_aff_reset_user(
1602 __isl_take isl_union_pw_multi_aff *upma);
1604 #include <isl/polynomial.h>
1605 __isl_give isl_pw_qpolynomial *
1606 isl_pw_qpolynomial_reset_user(
1607 __isl_take isl_pw_qpolynomial *pwqp);
1608 __isl_give isl_union_pw_qpolynomial *
1609 isl_union_pw_qpolynomial_reset_user(
1610 __isl_take isl_union_pw_qpolynomial *upwqp);
1611 __isl_give isl_pw_qpolynomial_fold *
1612 isl_pw_qpolynomial_fold_reset_user(
1613 __isl_take isl_pw_qpolynomial_fold *pwf);
1614 __isl_give isl_union_pw_qpolynomial_fold *
1615 isl_union_pw_qpolynomial_fold_reset_user(
1616 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1618 Spaces can be nested. In particular, the domain of a set or
1619 the domain or range of a relation can be a nested relation.
1620 This process is also called I<wrapping>.
1621 The functions for detecting, constructing and deconstructing
1622 such nested spaces can be found in the wrapping properties
1623 of L</"Unary Properties">, the wrapping operations
1624 of L</"Unary Operations"> and the Cartesian product operations
1625 of L</"Basic Operations">.
1627 Spaces can be created from other spaces
1628 using the functions described in L</"Unary Operations">
1629 and L</"Binary Operations">.
1633 A local space is essentially a space with
1634 zero or more existentially quantified variables.
1635 The local space of various objects can be obtained
1636 using the following functions.
1638 #include <isl/constraint.h>
1639 __isl_give isl_local_space *isl_constraint_get_local_space(
1640 __isl_keep isl_constraint *constraint);
1642 #include <isl/set.h>
1643 __isl_give isl_local_space *isl_basic_set_get_local_space(
1644 __isl_keep isl_basic_set *bset);
1646 #include <isl/map.h>
1647 __isl_give isl_local_space *isl_basic_map_get_local_space(
1648 __isl_keep isl_basic_map *bmap);
1650 #include <isl/aff.h>
1651 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1652 __isl_keep isl_aff *aff);
1653 __isl_give isl_local_space *isl_aff_get_local_space(
1654 __isl_keep isl_aff *aff);
1656 A new local space can be created from a space using
1658 #include <isl/local_space.h>
1659 __isl_give isl_local_space *isl_local_space_from_space(
1660 __isl_take isl_space *space);
1662 They can be inspected, modified, copied and freed using the following functions.
1664 #include <isl/local_space.h>
1665 int isl_local_space_is_params(
1666 __isl_keep isl_local_space *ls);
1667 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1668 __isl_give isl_space *isl_local_space_get_space(
1669 __isl_keep isl_local_space *ls);
1670 __isl_give isl_aff *isl_local_space_get_div(
1671 __isl_keep isl_local_space *ls, int pos);
1672 __isl_give isl_local_space *isl_local_space_copy(
1673 __isl_keep isl_local_space *ls);
1674 __isl_null isl_local_space *isl_local_space_free(
1675 __isl_take isl_local_space *ls);
1677 Note that C<isl_local_space_get_div> can only be used on local spaces
1680 Two local spaces can be compared using
1682 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1683 __isl_keep isl_local_space *ls2);
1685 Local spaces can be created from other local spaces
1686 using the functions described in L</"Unary Operations">
1687 and L</"Binary Operations">.
1689 =head2 Creating New Sets and Relations
1691 C<isl> has functions for creating some standard sets and relations.
1695 =item * Empty sets and relations
1697 __isl_give isl_basic_set *isl_basic_set_empty(
1698 __isl_take isl_space *space);
1699 __isl_give isl_basic_map *isl_basic_map_empty(
1700 __isl_take isl_space *space);
1701 __isl_give isl_set *isl_set_empty(
1702 __isl_take isl_space *space);
1703 __isl_give isl_map *isl_map_empty(
1704 __isl_take isl_space *space);
1705 __isl_give isl_union_set *isl_union_set_empty(
1706 __isl_take isl_space *space);
1707 __isl_give isl_union_map *isl_union_map_empty(
1708 __isl_take isl_space *space);
1710 For C<isl_union_set>s and C<isl_union_map>s, the space
1711 is only used to specify the parameters.
1713 =item * Universe sets and relations
1715 __isl_give isl_basic_set *isl_basic_set_universe(
1716 __isl_take isl_space *space);
1717 __isl_give isl_basic_map *isl_basic_map_universe(
1718 __isl_take isl_space *space);
1719 __isl_give isl_set *isl_set_universe(
1720 __isl_take isl_space *space);
1721 __isl_give isl_map *isl_map_universe(
1722 __isl_take isl_space *space);
1723 __isl_give isl_union_set *isl_union_set_universe(
1724 __isl_take isl_union_set *uset);
1725 __isl_give isl_union_map *isl_union_map_universe(
1726 __isl_take isl_union_map *umap);
1728 The sets and relations constructed by the functions above
1729 contain all integer values, while those constructed by the
1730 functions below only contain non-negative values.
1732 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1733 __isl_take isl_space *space);
1734 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1735 __isl_take isl_space *space);
1736 __isl_give isl_set *isl_set_nat_universe(
1737 __isl_take isl_space *space);
1738 __isl_give isl_map *isl_map_nat_universe(
1739 __isl_take isl_space *space);
1741 =item * Identity relations
1743 __isl_give isl_basic_map *isl_basic_map_identity(
1744 __isl_take isl_space *space);
1745 __isl_give isl_map *isl_map_identity(
1746 __isl_take isl_space *space);
1748 The number of input and output dimensions in C<space> needs
1751 =item * Lexicographic order
1753 __isl_give isl_map *isl_map_lex_lt(
1754 __isl_take isl_space *set_space);
1755 __isl_give isl_map *isl_map_lex_le(
1756 __isl_take isl_space *set_space);
1757 __isl_give isl_map *isl_map_lex_gt(
1758 __isl_take isl_space *set_space);
1759 __isl_give isl_map *isl_map_lex_ge(
1760 __isl_take isl_space *set_space);
1761 __isl_give isl_map *isl_map_lex_lt_first(
1762 __isl_take isl_space *space, unsigned n);
1763 __isl_give isl_map *isl_map_lex_le_first(
1764 __isl_take isl_space *space, unsigned n);
1765 __isl_give isl_map *isl_map_lex_gt_first(
1766 __isl_take isl_space *space, unsigned n);
1767 __isl_give isl_map *isl_map_lex_ge_first(
1768 __isl_take isl_space *space, unsigned n);
1770 The first four functions take a space for a B<set>
1771 and return relations that express that the elements in the domain
1772 are lexicographically less
1773 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1774 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1775 than the elements in the range.
1776 The last four functions take a space for a map
1777 and return relations that express that the first C<n> dimensions
1778 in the domain are lexicographically less
1779 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1780 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1781 than the first C<n> dimensions in the range.
1785 A basic set or relation can be converted to a set or relation
1786 using the following functions.
1788 __isl_give isl_set *isl_set_from_basic_set(
1789 __isl_take isl_basic_set *bset);
1790 __isl_give isl_map *isl_map_from_basic_map(
1791 __isl_take isl_basic_map *bmap);
1793 Sets and relations can be converted to union sets and relations
1794 using the following functions.
1796 __isl_give isl_union_set *isl_union_set_from_basic_set(
1797 __isl_take isl_basic_set *bset);
1798 __isl_give isl_union_map *isl_union_map_from_basic_map(
1799 __isl_take isl_basic_map *bmap);
1800 __isl_give isl_union_set *isl_union_set_from_set(
1801 __isl_take isl_set *set);
1802 __isl_give isl_union_map *isl_union_map_from_map(
1803 __isl_take isl_map *map);
1805 The inverse conversions below can only be used if the input
1806 union set or relation is known to contain elements in exactly one
1809 __isl_give isl_set *isl_set_from_union_set(
1810 __isl_take isl_union_set *uset);
1811 __isl_give isl_map *isl_map_from_union_map(
1812 __isl_take isl_union_map *umap);
1814 Sets and relations can be copied and freed again using the following
1817 __isl_give isl_basic_set *isl_basic_set_copy(
1818 __isl_keep isl_basic_set *bset);
1819 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1820 __isl_give isl_union_set *isl_union_set_copy(
1821 __isl_keep isl_union_set *uset);
1822 __isl_give isl_basic_map *isl_basic_map_copy(
1823 __isl_keep isl_basic_map *bmap);
1824 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1825 __isl_give isl_union_map *isl_union_map_copy(
1826 __isl_keep isl_union_map *umap);
1827 __isl_null isl_basic_set *isl_basic_set_free(
1828 __isl_take isl_basic_set *bset);
1829 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1830 __isl_null isl_union_set *isl_union_set_free(
1831 __isl_take isl_union_set *uset);
1832 __isl_null isl_basic_map *isl_basic_map_free(
1833 __isl_take isl_basic_map *bmap);
1834 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1835 __isl_null isl_union_map *isl_union_map_free(
1836 __isl_take isl_union_map *umap);
1838 Other sets and relations can be constructed by starting
1839 from a universe set or relation, adding equality and/or
1840 inequality constraints and then projecting out the
1841 existentially quantified variables, if any.
1842 Constraints can be constructed, manipulated and
1843 added to (or removed from) (basic) sets and relations
1844 using the following functions.
1846 #include <isl/constraint.h>
1847 __isl_give isl_constraint *isl_equality_alloc(
1848 __isl_take isl_local_space *ls);
1849 __isl_give isl_constraint *isl_inequality_alloc(
1850 __isl_take isl_local_space *ls);
1851 __isl_give isl_constraint *isl_constraint_set_constant_si(
1852 __isl_take isl_constraint *constraint, int v);
1853 __isl_give isl_constraint *isl_constraint_set_constant_val(
1854 __isl_take isl_constraint *constraint,
1855 __isl_take isl_val *v);
1856 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1857 __isl_take isl_constraint *constraint,
1858 enum isl_dim_type type, int pos, int v);
1859 __isl_give isl_constraint *
1860 isl_constraint_set_coefficient_val(
1861 __isl_take isl_constraint *constraint,
1862 enum isl_dim_type type, int pos,
1863 __isl_take isl_val *v);
1864 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1865 __isl_take isl_basic_map *bmap,
1866 __isl_take isl_constraint *constraint);
1867 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1868 __isl_take isl_basic_set *bset,
1869 __isl_take isl_constraint *constraint);
1870 __isl_give isl_map *isl_map_add_constraint(
1871 __isl_take isl_map *map,
1872 __isl_take isl_constraint *constraint);
1873 __isl_give isl_set *isl_set_add_constraint(
1874 __isl_take isl_set *set,
1875 __isl_take isl_constraint *constraint);
1876 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1877 __isl_take isl_basic_set *bset,
1878 __isl_take isl_constraint *constraint);
1880 For example, to create a set containing the even integers
1881 between 10 and 42, you would use the following code.
1884 isl_local_space *ls;
1886 isl_basic_set *bset;
1888 space = isl_space_set_alloc(ctx, 0, 2);
1889 bset = isl_basic_set_universe(isl_space_copy(space));
1890 ls = isl_local_space_from_space(space);
1892 c = isl_equality_alloc(isl_local_space_copy(ls));
1893 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1894 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1895 bset = isl_basic_set_add_constraint(bset, c);
1897 c = isl_inequality_alloc(isl_local_space_copy(ls));
1898 c = isl_constraint_set_constant_si(c, -10);
1899 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1900 bset = isl_basic_set_add_constraint(bset, c);
1902 c = isl_inequality_alloc(ls);
1903 c = isl_constraint_set_constant_si(c, 42);
1904 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1905 bset = isl_basic_set_add_constraint(bset, c);
1907 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1911 isl_basic_set *bset;
1912 bset = isl_basic_set_read_from_str(ctx,
1913 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1915 A basic set or relation can also be constructed from two matrices
1916 describing the equalities and the inequalities.
1918 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1919 __isl_take isl_space *space,
1920 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1921 enum isl_dim_type c1,
1922 enum isl_dim_type c2, enum isl_dim_type c3,
1923 enum isl_dim_type c4);
1924 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1925 __isl_take isl_space *space,
1926 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1927 enum isl_dim_type c1,
1928 enum isl_dim_type c2, enum isl_dim_type c3,
1929 enum isl_dim_type c4, enum isl_dim_type c5);
1931 The C<isl_dim_type> arguments indicate the order in which
1932 different kinds of variables appear in the input matrices
1933 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1934 C<isl_dim_set> and C<isl_dim_div> for sets and
1935 of C<isl_dim_cst>, C<isl_dim_param>,
1936 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1938 A (basic or union) set or relation can also be constructed from a
1939 (union) (piecewise) (multiple) affine expression
1940 or a list of affine expressions
1941 (See L</"Functions">).
1943 __isl_give isl_basic_map *isl_basic_map_from_aff(
1944 __isl_take isl_aff *aff);
1945 __isl_give isl_map *isl_map_from_aff(
1946 __isl_take isl_aff *aff);
1947 __isl_give isl_set *isl_set_from_pw_aff(
1948 __isl_take isl_pw_aff *pwaff);
1949 __isl_give isl_map *isl_map_from_pw_aff(
1950 __isl_take isl_pw_aff *pwaff);
1951 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1952 __isl_take isl_space *domain_space,
1953 __isl_take isl_aff_list *list);
1954 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1955 __isl_take isl_multi_aff *maff)
1956 __isl_give isl_map *isl_map_from_multi_aff(
1957 __isl_take isl_multi_aff *maff)
1958 __isl_give isl_set *isl_set_from_pw_multi_aff(
1959 __isl_take isl_pw_multi_aff *pma);
1960 __isl_give isl_map *isl_map_from_pw_multi_aff(
1961 __isl_take isl_pw_multi_aff *pma);
1962 __isl_give isl_set *isl_set_from_multi_pw_aff(
1963 __isl_take isl_multi_pw_aff *mpa);
1964 __isl_give isl_map *isl_map_from_multi_pw_aff(
1965 __isl_take isl_multi_pw_aff *mpa);
1966 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
1967 __isl_take isl_union_pw_aff *upa);
1968 __isl_give isl_union_map *
1969 isl_union_map_from_union_pw_multi_aff(
1970 __isl_take isl_union_pw_multi_aff *upma);
1971 __isl_give isl_union_map *
1972 isl_union_map_from_multi_union_pw_aff(
1973 __isl_take isl_multi_union_pw_aff *mupa);
1975 The C<domain_space> argument describes the domain of the resulting
1976 basic relation. It is required because the C<list> may consist
1977 of zero affine expressions.
1978 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
1979 is not allowed to be zero-dimensional. The domain of the result
1980 is the shared domain of the union piecewise affine elements.
1982 =head2 Inspecting Sets and Relations
1984 Usually, the user should not have to care about the actual constraints
1985 of the sets and maps, but should instead apply the abstract operations
1986 explained in the following sections.
1987 Occasionally, however, it may be required to inspect the individual
1988 coefficients of the constraints. This section explains how to do so.
1989 In these cases, it may also be useful to have C<isl> compute
1990 an explicit representation of the existentially quantified variables.
1992 __isl_give isl_set *isl_set_compute_divs(
1993 __isl_take isl_set *set);
1994 __isl_give isl_map *isl_map_compute_divs(
1995 __isl_take isl_map *map);
1996 __isl_give isl_union_set *isl_union_set_compute_divs(
1997 __isl_take isl_union_set *uset);
1998 __isl_give isl_union_map *isl_union_map_compute_divs(
1999 __isl_take isl_union_map *umap);
2001 This explicit representation defines the existentially quantified
2002 variables as integer divisions of the other variables, possibly
2003 including earlier existentially quantified variables.
2004 An explicitly represented existentially quantified variable therefore
2005 has a unique value when the values of the other variables are known.
2006 If, furthermore, the same existentials, i.e., existentials
2007 with the same explicit representations, should appear in the
2008 same order in each of the disjuncts of a set or map, then the user should call
2009 either of the following functions.
2011 __isl_give isl_set *isl_set_align_divs(
2012 __isl_take isl_set *set);
2013 __isl_give isl_map *isl_map_align_divs(
2014 __isl_take isl_map *map);
2016 Alternatively, the existentially quantified variables can be removed
2017 using the following functions, which compute an overapproximation.
2019 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2020 __isl_take isl_basic_set *bset);
2021 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2022 __isl_take isl_basic_map *bmap);
2023 __isl_give isl_set *isl_set_remove_divs(
2024 __isl_take isl_set *set);
2025 __isl_give isl_map *isl_map_remove_divs(
2026 __isl_take isl_map *map);
2028 It is also possible to only remove those divs that are defined
2029 in terms of a given range of dimensions or only those for which
2030 no explicit representation is known.
2032 __isl_give isl_basic_set *
2033 isl_basic_set_remove_divs_involving_dims(
2034 __isl_take isl_basic_set *bset,
2035 enum isl_dim_type type,
2036 unsigned first, unsigned n);
2037 __isl_give isl_basic_map *
2038 isl_basic_map_remove_divs_involving_dims(
2039 __isl_take isl_basic_map *bmap,
2040 enum isl_dim_type type,
2041 unsigned first, unsigned n);
2042 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2043 __isl_take isl_set *set, enum isl_dim_type type,
2044 unsigned first, unsigned n);
2045 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2046 __isl_take isl_map *map, enum isl_dim_type type,
2047 unsigned first, unsigned n);
2049 __isl_give isl_basic_set *
2050 isl_basic_set_remove_unknown_divs(
2051 __isl_take isl_basic_set *bset);
2052 __isl_give isl_set *isl_set_remove_unknown_divs(
2053 __isl_take isl_set *set);
2054 __isl_give isl_map *isl_map_remove_unknown_divs(
2055 __isl_take isl_map *map);
2057 To iterate over all the sets or maps in a union set or map, use
2059 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
2060 int (*fn)(__isl_take isl_set *set, void *user),
2062 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
2063 int (*fn)(__isl_take isl_map *map, void *user),
2066 The number of sets or maps in a union set or map can be obtained
2069 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2070 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2072 To extract the set or map in a given space from a union, use
2074 __isl_give isl_set *isl_union_set_extract_set(
2075 __isl_keep isl_union_set *uset,
2076 __isl_take isl_space *space);
2077 __isl_give isl_map *isl_union_map_extract_map(
2078 __isl_keep isl_union_map *umap,
2079 __isl_take isl_space *space);
2081 To iterate over all the basic sets or maps in a set or map, use
2083 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
2084 int (*fn)(__isl_take isl_basic_set *bset, void *user),
2086 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
2087 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
2090 The callback function C<fn> should return 0 if successful and
2091 -1 if an error occurs. In the latter case, or if any other error
2092 occurs, the above functions will return -1.
2094 It should be noted that C<isl> does not guarantee that
2095 the basic sets or maps passed to C<fn> are disjoint.
2096 If this is required, then the user should call one of
2097 the following functions first.
2099 __isl_give isl_set *isl_set_make_disjoint(
2100 __isl_take isl_set *set);
2101 __isl_give isl_map *isl_map_make_disjoint(
2102 __isl_take isl_map *map);
2104 The number of basic sets in a set can be obtained
2105 or the number of basic maps in a map can be obtained
2108 #include <isl/set.h>
2109 int isl_set_n_basic_set(__isl_keep isl_set *set);
2111 #include <isl/map.h>
2112 int isl_map_n_basic_map(__isl_keep isl_map *map);
2114 To iterate over the constraints of a basic set or map, use
2116 #include <isl/constraint.h>
2118 int isl_basic_set_n_constraint(
2119 __isl_keep isl_basic_set *bset);
2120 int isl_basic_set_foreach_constraint(
2121 __isl_keep isl_basic_set *bset,
2122 int (*fn)(__isl_take isl_constraint *c, void *user),
2124 int isl_basic_map_n_constraint(
2125 __isl_keep isl_basic_map *bmap);
2126 int isl_basic_map_foreach_constraint(
2127 __isl_keep isl_basic_map *bmap,
2128 int (*fn)(__isl_take isl_constraint *c, void *user),
2130 __isl_null isl_constraint *isl_constraint_free(
2131 __isl_take isl_constraint *c);
2133 Again, the callback function C<fn> should return 0 if successful and
2134 -1 if an error occurs. In the latter case, or if any other error
2135 occurs, the above functions will return -1.
2136 The constraint C<c> represents either an equality or an inequality.
2137 Use the following function to find out whether a constraint
2138 represents an equality. If not, it represents an inequality.
2140 int isl_constraint_is_equality(
2141 __isl_keep isl_constraint *constraint);
2143 It is also possible to obtain a list of constraints from a basic
2146 #include <isl/constraint.h>
2147 __isl_give isl_constraint_list *
2148 isl_basic_map_get_constraint_list(
2149 __isl_keep isl_basic_map *bmap);
2150 __isl_give isl_constraint_list *
2151 isl_basic_set_get_constraint_list(
2152 __isl_keep isl_basic_set *bset);
2154 These functions require that all existentially quantified variables
2155 have an explicit representation.
2156 The returned list can be manipulated using the functions in L<"Lists">.
2158 The coefficients of the constraints can be inspected using
2159 the following functions.
2161 int isl_constraint_is_lower_bound(
2162 __isl_keep isl_constraint *constraint,
2163 enum isl_dim_type type, unsigned pos);
2164 int isl_constraint_is_upper_bound(
2165 __isl_keep isl_constraint *constraint,
2166 enum isl_dim_type type, unsigned pos);
2167 __isl_give isl_val *isl_constraint_get_constant_val(
2168 __isl_keep isl_constraint *constraint);
2169 __isl_give isl_val *isl_constraint_get_coefficient_val(
2170 __isl_keep isl_constraint *constraint,
2171 enum isl_dim_type type, int pos);
2173 The explicit representations of the existentially quantified
2174 variables can be inspected using the following function.
2175 Note that the user is only allowed to use this function
2176 if the inspected set or map is the result of a call
2177 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2178 The existentially quantified variable is equal to the floor
2179 of the returned affine expression. The affine expression
2180 itself can be inspected using the functions in
2183 __isl_give isl_aff *isl_constraint_get_div(
2184 __isl_keep isl_constraint *constraint, int pos);
2186 To obtain the constraints of a basic set or map in matrix
2187 form, use the following functions.
2189 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2190 __isl_keep isl_basic_set *bset,
2191 enum isl_dim_type c1, enum isl_dim_type c2,
2192 enum isl_dim_type c3, enum isl_dim_type c4);
2193 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2194 __isl_keep isl_basic_set *bset,
2195 enum isl_dim_type c1, enum isl_dim_type c2,
2196 enum isl_dim_type c3, enum isl_dim_type c4);
2197 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2198 __isl_keep isl_basic_map *bmap,
2199 enum isl_dim_type c1,
2200 enum isl_dim_type c2, enum isl_dim_type c3,
2201 enum isl_dim_type c4, enum isl_dim_type c5);
2202 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2203 __isl_keep isl_basic_map *bmap,
2204 enum isl_dim_type c1,
2205 enum isl_dim_type c2, enum isl_dim_type c3,
2206 enum isl_dim_type c4, enum isl_dim_type c5);
2208 The C<isl_dim_type> arguments dictate the order in which
2209 different kinds of variables appear in the resulting matrix.
2210 For set inputs, they should be a permutation of
2211 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2212 For map inputs, they should be a permutation of
2213 C<isl_dim_cst>, C<isl_dim_param>,
2214 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2218 Points are elements of a set. They can be used to construct
2219 simple sets (boxes) or they can be used to represent the
2220 individual elements of a set.
2221 The zero point (the origin) can be created using
2223 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2225 The coordinates of a point can be inspected, set and changed
2228 __isl_give isl_val *isl_point_get_coordinate_val(
2229 __isl_keep isl_point *pnt,
2230 enum isl_dim_type type, int pos);
2231 __isl_give isl_point *isl_point_set_coordinate_val(
2232 __isl_take isl_point *pnt,
2233 enum isl_dim_type type, int pos,
2234 __isl_take isl_val *v);
2236 __isl_give isl_point *isl_point_add_ui(
2237 __isl_take isl_point *pnt,
2238 enum isl_dim_type type, int pos, unsigned val);
2239 __isl_give isl_point *isl_point_sub_ui(
2240 __isl_take isl_point *pnt,
2241 enum isl_dim_type type, int pos, unsigned val);
2243 Points can be copied or freed using
2245 __isl_give isl_point *isl_point_copy(
2246 __isl_keep isl_point *pnt);
2247 void isl_point_free(__isl_take isl_point *pnt);
2249 A singleton set can be created from a point using
2251 __isl_give isl_basic_set *isl_basic_set_from_point(
2252 __isl_take isl_point *pnt);
2253 __isl_give isl_set *isl_set_from_point(
2254 __isl_take isl_point *pnt);
2256 and a box can be created from two opposite extremal points using
2258 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2259 __isl_take isl_point *pnt1,
2260 __isl_take isl_point *pnt2);
2261 __isl_give isl_set *isl_set_box_from_points(
2262 __isl_take isl_point *pnt1,
2263 __isl_take isl_point *pnt2);
2265 All elements of a B<bounded> (union) set can be enumerated using
2266 the following functions.
2268 int isl_set_foreach_point(__isl_keep isl_set *set,
2269 int (*fn)(__isl_take isl_point *pnt, void *user),
2271 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2272 int (*fn)(__isl_take isl_point *pnt, void *user),
2275 The function C<fn> is called for each integer point in
2276 C<set> with as second argument the last argument of
2277 the C<isl_set_foreach_point> call. The function C<fn>
2278 should return C<0> on success and C<-1> on failure.
2279 In the latter case, C<isl_set_foreach_point> will stop
2280 enumerating and return C<-1> as well.
2281 If the enumeration is performed successfully and to completion,
2282 then C<isl_set_foreach_point> returns C<0>.
2284 To obtain a single point of a (basic) set, use
2286 __isl_give isl_point *isl_basic_set_sample_point(
2287 __isl_take isl_basic_set *bset);
2288 __isl_give isl_point *isl_set_sample_point(
2289 __isl_take isl_set *set);
2291 If C<set> does not contain any (integer) points, then the
2292 resulting point will be ``void'', a property that can be
2295 int isl_point_is_void(__isl_keep isl_point *pnt);
2299 Besides sets and relation, C<isl> also supports various types of functions.
2300 Each of these types is derived from the value type (see L</"Values">)
2301 or from one of two primitive function types
2302 through the application of zero or more type constructors.
2303 We first describe the primitive type and then we describe
2304 the types derived from these primitive types.
2306 =head3 Primitive Functions
2308 C<isl> support two primitive function types, quasi-affine
2309 expressions and quasipolynomials.
2310 A quasi-affine expression is defined either over a parameter
2311 space or over a set and is composed of integer constants,
2312 parameters and set variables, addition, subtraction and
2313 integer division by an integer constant.
2314 For example, the quasi-affine expression
2316 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2318 maps C<x> to C<2*floor((4 n + x)/9>.
2319 A quasipolynomial is a polynomial expression in quasi-affine
2320 expression. That is, it additionally allows for multiplication.
2321 Note, though, that it is not allowed to construct an integer
2322 division of an expression involving multiplications.
2323 Here is an example of a quasipolynomial that is not
2324 quasi-affine expression
2326 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2328 Note that the external representations of quasi-affine expressions
2329 and quasipolynomials are different. Quasi-affine expressions
2330 use a notation with square brackets just like binary relations,
2331 while quasipolynomials do not. This might change at some point.
2333 If a primitive function is defined over a parameter space,
2334 then the space of the function itself is that of a set.
2335 If it is defined over a set, then the space of the function
2336 is that of a relation. In both cases, the set space (or
2337 the output space) is single-dimensional, anonymous and unstructured.
2338 To create functions with multiple dimensions or with other kinds
2339 of set or output spaces, use multiple expressions
2340 (see L</"Multiple Expressions">).
2344 =item * Quasi-affine Expressions
2346 Besides the expressions described above, a quasi-affine
2347 expression can also be set to NaN. Such expressions
2348 typically represent a failure to represent a result
2349 as a quasi-affine expression.
2351 The zero quasi affine expression or the quasi affine expression
2352 that is equal to a given value or
2353 a specified dimension on a given domain can be created using
2355 #include <isl/aff.h>
2356 __isl_give isl_aff *isl_aff_zero_on_domain(
2357 __isl_take isl_local_space *ls);
2358 __isl_give isl_aff *isl_aff_val_on_domain(
2359 __isl_take isl_local_space *ls,
2360 __isl_take isl_val *val);
2361 __isl_give isl_aff *isl_aff_var_on_domain(
2362 __isl_take isl_local_space *ls,
2363 enum isl_dim_type type, unsigned pos);
2364 __isl_give isl_aff *isl_aff_nan_on_domain(
2365 __isl_take isl_local_space *ls);
2367 Quasi affine expressions can be copied and freed using
2369 #include <isl/aff.h>
2370 __isl_give isl_aff *isl_aff_copy(
2371 __isl_keep isl_aff *aff);
2372 __isl_null isl_aff *isl_aff_free(
2373 __isl_take isl_aff *aff);
2375 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2376 using the following function. The constraint is required to have
2377 a non-zero coefficient for the specified dimension.
2379 #include <isl/constraint.h>
2380 __isl_give isl_aff *isl_constraint_get_bound(
2381 __isl_keep isl_constraint *constraint,
2382 enum isl_dim_type type, int pos);
2384 The entire affine expression of the constraint can also be extracted
2385 using the following function.
2387 #include <isl/constraint.h>
2388 __isl_give isl_aff *isl_constraint_get_aff(
2389 __isl_keep isl_constraint *constraint);
2391 Conversely, an equality constraint equating
2392 the affine expression to zero or an inequality constraint enforcing
2393 the affine expression to be non-negative, can be constructed using
2395 __isl_give isl_constraint *isl_equality_from_aff(
2396 __isl_take isl_aff *aff);
2397 __isl_give isl_constraint *isl_inequality_from_aff(
2398 __isl_take isl_aff *aff);
2400 The coefficients and the integer divisions of an affine expression
2401 can be inspected using the following functions.
2403 #include <isl/aff.h>
2404 __isl_give isl_val *isl_aff_get_constant_val(
2405 __isl_keep isl_aff *aff);
2406 __isl_give isl_val *isl_aff_get_coefficient_val(
2407 __isl_keep isl_aff *aff,
2408 enum isl_dim_type type, int pos);
2409 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2410 enum isl_dim_type type, int pos);
2411 __isl_give isl_val *isl_aff_get_denominator_val(
2412 __isl_keep isl_aff *aff);
2413 __isl_give isl_aff *isl_aff_get_div(
2414 __isl_keep isl_aff *aff, int pos);
2416 They can be modified using the following functions.
2418 #include <isl/aff.h>
2419 __isl_give isl_aff *isl_aff_set_constant_si(
2420 __isl_take isl_aff *aff, int v);
2421 __isl_give isl_aff *isl_aff_set_constant_val(
2422 __isl_take isl_aff *aff, __isl_take isl_val *v);
2423 __isl_give isl_aff *isl_aff_set_coefficient_si(
2424 __isl_take isl_aff *aff,
2425 enum isl_dim_type type, int pos, int v);
2426 __isl_give isl_aff *isl_aff_set_coefficient_val(
2427 __isl_take isl_aff *aff,
2428 enum isl_dim_type type, int pos,
2429 __isl_take isl_val *v);
2431 __isl_give isl_aff *isl_aff_add_constant_si(
2432 __isl_take isl_aff *aff, int v);
2433 __isl_give isl_aff *isl_aff_add_constant_val(
2434 __isl_take isl_aff *aff, __isl_take isl_val *v);
2435 __isl_give isl_aff *isl_aff_add_constant_num_si(
2436 __isl_take isl_aff *aff, int v);
2437 __isl_give isl_aff *isl_aff_add_coefficient_si(
2438 __isl_take isl_aff *aff,
2439 enum isl_dim_type type, int pos, int v);
2440 __isl_give isl_aff *isl_aff_add_coefficient_val(
2441 __isl_take isl_aff *aff,
2442 enum isl_dim_type type, int pos,
2443 __isl_take isl_val *v);
2445 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2446 set the I<numerator> of the constant or coefficient, while
2447 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2448 the constant or coefficient as a whole.
2449 The C<add_constant> and C<add_coefficient> functions add an integer
2450 or rational value to
2451 the possibly rational constant or coefficient.
2452 The C<add_constant_num> functions add an integer value to
2455 =item * Quasipolynomials
2457 Some simple quasipolynomials can be created using the following functions.
2459 #include <isl/polynomial.h>
2460 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2461 __isl_take isl_space *domain);
2462 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2463 __isl_take isl_space *domain);
2464 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2465 __isl_take isl_space *domain);
2466 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2467 __isl_take isl_space *domain);
2468 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2469 __isl_take isl_space *domain);
2470 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2471 __isl_take isl_space *domain,
2472 __isl_take isl_val *val);
2473 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2474 __isl_take isl_space *domain,
2475 enum isl_dim_type type, unsigned pos);
2476 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2477 __isl_take isl_aff *aff);
2479 Recall that the space in which a quasipolynomial lives is a map space
2480 with a one-dimensional range. The C<domain> argument in some of
2481 the functions above corresponds to the domain of this map space.
2483 Quasipolynomials can be copied and freed again using the following
2486 #include <isl/polynomial.h>
2487 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2488 __isl_keep isl_qpolynomial *qp);
2489 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2490 __isl_take isl_qpolynomial *qp);
2492 The constant term of a quasipolynomial can be extracted using
2494 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2495 __isl_keep isl_qpolynomial *qp);
2497 To iterate over all terms in a quasipolynomial,
2500 int isl_qpolynomial_foreach_term(
2501 __isl_keep isl_qpolynomial *qp,
2502 int (*fn)(__isl_take isl_term *term,
2503 void *user), void *user);
2505 The terms themselves can be inspected and freed using
2508 unsigned isl_term_dim(__isl_keep isl_term *term,
2509 enum isl_dim_type type);
2510 __isl_give isl_val *isl_term_get_coefficient_val(
2511 __isl_keep isl_term *term);
2512 int isl_term_get_exp(__isl_keep isl_term *term,
2513 enum isl_dim_type type, unsigned pos);
2514 __isl_give isl_aff *isl_term_get_div(
2515 __isl_keep isl_term *term, unsigned pos);
2516 void isl_term_free(__isl_take isl_term *term);
2518 Each term is a product of parameters, set variables and
2519 integer divisions. The function C<isl_term_get_exp>
2520 returns the exponent of a given dimensions in the given term.
2526 A reduction represents a maximum or a minimum of its
2528 The only reduction type defined by C<isl> is
2529 C<isl_qpolynomial_fold>.
2531 There are currently no functions to directly create such
2532 objects, but they do appear in the piecewise quasipolynomial
2533 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2535 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2537 Reductions can be copied and freed using
2538 the following functions.
2540 #include <isl/polynomial.h>
2541 __isl_give isl_qpolynomial_fold *
2542 isl_qpolynomial_fold_copy(
2543 __isl_keep isl_qpolynomial_fold *fold);
2544 void isl_qpolynomial_fold_free(
2545 __isl_take isl_qpolynomial_fold *fold);
2547 To iterate over all quasipolynomials in a reduction, use
2549 int isl_qpolynomial_fold_foreach_qpolynomial(
2550 __isl_keep isl_qpolynomial_fold *fold,
2551 int (*fn)(__isl_take isl_qpolynomial *qp,
2552 void *user), void *user);
2554 =head3 Multiple Expressions
2556 A multiple expression represents a sequence of zero or
2557 more base expressions, all defined on the same domain space.
2558 The domain space of the multiple expression is the same
2559 as that of the base expressions, but the range space
2560 can be any space. In case the base expressions have
2561 a set space, the corresponding multiple expression
2562 also has a set space.
2563 Objects of the value type do not have an associated space.
2564 The space of a multiple value is therefore always a set space.
2565 Similarly, the space of a multiple union piecewise
2566 affine expression is always a set space.
2568 The multiple expression types defined by C<isl>
2569 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2570 C<isl_multi_union_pw_aff>.
2572 A multiple expression with the value zero for
2573 each output (or set) dimension can be created
2574 using the following functions.
2576 #include <isl/val.h>
2577 __isl_give isl_multi_val *isl_multi_val_zero(
2578 __isl_take isl_space *space);
2580 #include <isl/aff.h>
2581 __isl_give isl_multi_aff *isl_multi_aff_zero(
2582 __isl_take isl_space *space);
2583 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2584 __isl_take isl_space *space);
2585 __isl_give isl_multi_union_pw_aff *
2586 isl_multi_union_pw_aff_zero(
2587 __isl_take isl_space *space);
2589 Since there is no canonical way of representing a zero
2590 value of type C<isl_union_pw_aff>, the space passed
2591 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2593 An identity function can be created using the following
2594 functions. The space needs to be that of a relation
2595 with the same number of input and output dimensions.
2597 #include <isl/aff.h>
2598 __isl_give isl_multi_aff *isl_multi_aff_identity(
2599 __isl_take isl_space *space);
2600 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2601 __isl_take isl_space *space);
2603 A function that performs a projection on a universe
2604 relation or set can be created using the following functions.
2605 See also the corresponding
2606 projection operations in L</"Unary Operations">.
2608 #include <isl/aff.h>
2609 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2610 __isl_take isl_space *space);
2611 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2612 __isl_take isl_space *space);
2613 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2614 __isl_take isl_space *space,
2615 enum isl_dim_type type,
2616 unsigned first, unsigned n);
2618 A multiple expression can be created from a single
2619 base expression using the following functions.
2620 The space of the created multiple expression is the same
2621 as that of the base expression, except for
2622 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2623 lives in a parameter space and the output lives
2624 in a single-dimensional set space.
2626 #include <isl/aff.h>
2627 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2628 __isl_take isl_aff *aff);
2629 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2630 __isl_take isl_pw_aff *pa);
2631 __isl_give isl_multi_union_pw_aff *
2632 isl_multi_union_pw_aff_from_union_pw_aff(
2633 __isl_take isl_union_pw_aff *upa);
2635 A multiple expression can be created from a list
2636 of base expression in a specified space.
2637 The domain of this space needs to be the same
2638 as the domains of the base expressions in the list.
2639 If the base expressions have a set space (or no associated space),
2640 then this space also needs to be a set space.
2642 #include <isl/val.h>
2643 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2644 __isl_take isl_space *space,
2645 __isl_take isl_val_list *list);
2647 #include <isl/aff.h>
2648 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2649 __isl_take isl_space *space,
2650 __isl_take isl_aff_list *list);
2651 __isl_give isl_multi_union_pw_aff *
2652 isl_multi_union_pw_aff_from_union_pw_aff_list(
2653 __isl_take isl_space *space,
2654 __isl_take isl_union_pw_aff_list *list);
2656 As a convenience, a multiple piecewise expression can
2657 also be created from a multiple expression.
2658 Each piecewise expression in the result has a single
2661 #include <isl/aff.h>
2662 __isl_give isl_multi_pw_aff *
2663 isl_multi_pw_aff_from_multi_aff(
2664 __isl_take isl_multi_aff *ma);
2666 Similarly, a multiple union expression can be
2667 created from a multiple expression.
2669 #include <isl/aff.h>
2670 __isl_give isl_multi_union_pw_aff *
2671 isl_multi_union_pw_aff_from_multi_aff(
2672 __isl_take isl_multi_aff *ma);
2673 __isl_give isl_multi_union_pw_aff *
2674 isl_multi_union_pw_aff_from_multi_pw_aff(
2675 __isl_take isl_multi_pw_aff *mpa);
2677 A multiple quasi-affine expression can be created from
2678 a multiple value with a given domain space using the following
2681 #include <isl/aff.h>
2682 __isl_give isl_multi_aff *
2683 isl_multi_aff_multi_val_on_space(
2684 __isl_take isl_space *space,
2685 __isl_take isl_multi_val *mv);
2688 a multiple union piecewise affine expression can be created from
2689 a multiple value with a given domain or
2690 a multiple affine expression with a given domain
2691 using the following functions.
2693 #include <isl/aff.h>
2694 __isl_give isl_multi_union_pw_aff *
2695 isl_multi_union_pw_aff_multi_val_on_domain(
2696 __isl_take isl_union_set *domain,
2697 __isl_take isl_multi_val *mv);
2698 __isl_give isl_multi_union_pw_aff *
2699 isl_multi_union_pw_aff_multi_aff_on_domain(
2700 __isl_take isl_union_set *domain,
2701 __isl_take isl_multi_aff *ma);
2703 Multiple expressions can be copied and freed using
2704 the following functions.
2706 #include <isl/val.h>
2707 __isl_give isl_multi_val *isl_multi_val_copy(
2708 __isl_keep isl_multi_val *mv);
2709 __isl_null isl_multi_val *isl_multi_val_free(
2710 __isl_take isl_multi_val *mv);
2712 #include <isl/aff.h>
2713 __isl_give isl_multi_aff *isl_multi_aff_copy(
2714 __isl_keep isl_multi_aff *maff);
2715 __isl_null isl_multi_aff *isl_multi_aff_free(
2716 __isl_take isl_multi_aff *maff);
2717 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2718 __isl_keep isl_multi_pw_aff *mpa);
2719 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2720 __isl_take isl_multi_pw_aff *mpa);
2721 __isl_give isl_multi_union_pw_aff *
2722 isl_multi_union_pw_aff_copy(
2723 __isl_keep isl_multi_union_pw_aff *mupa);
2724 __isl_null isl_multi_union_pw_aff *
2725 isl_multi_union_pw_aff_free(
2726 __isl_take isl_multi_union_pw_aff *mupa);
2728 The base expression at a given position of a multiple
2729 expression can be extracted using the following functions.
2731 #include <isl/val.h>
2732 __isl_give isl_val *isl_multi_val_get_val(
2733 __isl_keep isl_multi_val *mv, int pos);
2735 #include <isl/aff.h>
2736 __isl_give isl_aff *isl_multi_aff_get_aff(
2737 __isl_keep isl_multi_aff *multi, int pos);
2738 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2739 __isl_keep isl_multi_pw_aff *mpa, int pos);
2740 __isl_give isl_union_pw_aff *
2741 isl_multi_union_pw_aff_get_union_pw_aff(
2742 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2744 It can be replaced using the following functions.
2746 #include <isl/val.h>
2747 __isl_give isl_multi_val *isl_multi_val_set_val(
2748 __isl_take isl_multi_val *mv, int pos,
2749 __isl_take isl_val *val);
2751 #include <isl/aff.h>
2752 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2753 __isl_take isl_multi_aff *multi, int pos,
2754 __isl_take isl_aff *aff);
2755 __isl_give isl_multi_union_pw_aff *
2756 isl_multi_union_pw_aff_set_union_pw_aff(
2757 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2758 __isl_take isl_union_pw_aff *upa);
2760 As a convenience, a sequence of base expressions that have
2761 their domains in a given space can be extracted from a sequence
2762 of union expressions using the following function.
2764 #include <isl/aff.h>
2765 __isl_give isl_multi_pw_aff *
2766 isl_multi_union_pw_aff_extract_multi_pw_aff(
2767 __isl_keep isl_multi_union_pw_aff *mupa,
2768 __isl_take isl_space *space);
2770 Note that there is a difference between C<isl_multi_union_pw_aff>
2771 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2772 of unions of piecewise expressions, while the second is a union
2773 of piecewise sequences. In particular, multiple affine expressions
2774 in an C<isl_union_pw_multi_aff> may live in different spaces,
2775 while there is only a single multiple expression in
2776 an C<isl_multi_union_pw_aff>, which can therefore only live
2777 in a single space. This means that not every
2778 C<isl_union_pw_multi_aff> can be converted to
2779 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2780 C<isl_multi_union_pw_aff> carries no information
2781 about any possible domain and therefore cannot be converted
2782 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2783 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2784 while each multiple expression inside an C<isl_union_pw_multi_aff>
2785 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2786 of dimension greater than one may therefore not be exact.
2787 The following functions can
2788 be used to perform these conversions when they are possible.
2790 #include <isl/aff.h>
2791 __isl_give isl_multi_union_pw_aff *
2792 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2793 __isl_take isl_union_pw_multi_aff *upma);
2794 __isl_give isl_union_pw_multi_aff *
2795 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2796 __isl_take isl_multi_union_pw_aff *mupa);
2798 =head3 Piecewise Expressions
2800 A piecewise expression is an expression that is described
2801 using zero or more base expression defined over the same
2802 number of cells in the domain space of the base expressions.
2803 All base expressions are defined over the same
2804 domain space and the cells are disjoint.
2805 The space of a piecewise expression is the same as
2806 that of the base expressions.
2807 If the union of the cells is a strict subset of the domain
2808 space, then the value of the piecewise expression outside
2809 this union is different for types derived from quasi-affine
2810 expressions and those derived from quasipolynomials.
2811 Piecewise expressions derived from quasi-affine expressions
2812 are considered to be undefined outside the union of their cells.
2813 Piecewise expressions derived from quasipolynomials
2814 are considered to be zero outside the union of their cells.
2816 Piecewise quasipolynomials are mainly used by the C<barvinok>
2817 library for representing the number of elements in a parametric set or map.
2818 For example, the piecewise quasipolynomial
2820 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2822 represents the number of points in the map
2824 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2826 The piecewise expression types defined by C<isl>
2827 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2828 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2830 A piecewise expression with no cells can be created using
2831 the following functions.
2833 #include <isl/aff.h>
2834 __isl_give isl_pw_aff *isl_pw_aff_empty(
2835 __isl_take isl_space *space);
2836 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2837 __isl_take isl_space *space);
2839 A piecewise expression with a single universe cell can be
2840 created using the following functions.
2842 #include <isl/aff.h>
2843 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2844 __isl_take isl_aff *aff);
2845 __isl_give isl_pw_multi_aff *
2846 isl_pw_multi_aff_from_multi_aff(
2847 __isl_take isl_multi_aff *ma);
2849 #include <isl/polynomial.h>
2850 __isl_give isl_pw_qpolynomial *
2851 isl_pw_qpolynomial_from_qpolynomial(
2852 __isl_take isl_qpolynomial *qp);
2854 A piecewise expression with a single specified cell can be
2855 created using the following functions.
2857 #include <isl/aff.h>
2858 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2859 __isl_take isl_set *set, __isl_take isl_aff *aff);
2860 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2861 __isl_take isl_set *set,
2862 __isl_take isl_multi_aff *maff);
2864 #include <isl/polynomial.h>
2865 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2866 __isl_take isl_set *set,
2867 __isl_take isl_qpolynomial *qp);
2869 The following convenience functions first create a base expression and
2870 then create a piecewise expression over a universe domain.
2872 #include <isl/aff.h>
2873 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2874 __isl_take isl_local_space *ls);
2875 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2876 __isl_take isl_local_space *ls,
2877 enum isl_dim_type type, unsigned pos);
2878 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2879 __isl_take isl_local_space *ls);
2880 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2881 __isl_take isl_space *space);
2882 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2883 __isl_take isl_space *space);
2884 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2885 __isl_take isl_space *space);
2886 __isl_give isl_pw_multi_aff *
2887 isl_pw_multi_aff_project_out_map(
2888 __isl_take isl_space *space,
2889 enum isl_dim_type type,
2890 unsigned first, unsigned n);
2892 #include <isl/polynomial.h>
2893 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2894 __isl_take isl_space *space);
2896 The following convenience functions first create a base expression and
2897 then create a piecewise expression over a given domain.
2899 #include <isl/aff.h>
2900 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2901 __isl_take isl_set *domain,
2902 __isl_take isl_val *v);
2903 __isl_give isl_pw_multi_aff *
2904 isl_pw_multi_aff_multi_val_on_domain(
2905 __isl_take isl_set *domain,
2906 __isl_take isl_multi_val *mv);
2908 As a convenience, a piecewise multiple expression can
2909 also be created from a piecewise expression.
2910 Each multiple expression in the result is derived
2911 from the corresponding base expression.
2913 #include <isl/aff.h>
2914 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2915 __isl_take isl_pw_aff *pa);
2917 Similarly, a piecewise quasipolynomial can be
2918 created from a piecewise quasi-affine expression using
2919 the following function.
2921 #include <isl/polynomial.h>
2922 __isl_give isl_pw_qpolynomial *
2923 isl_pw_qpolynomial_from_pw_aff(
2924 __isl_take isl_pw_aff *pwaff);
2926 Piecewise expressions can be copied and freed using the following functions.
2928 #include <isl/aff.h>
2929 __isl_give isl_pw_aff *isl_pw_aff_copy(
2930 __isl_keep isl_pw_aff *pwaff);
2931 __isl_null isl_pw_aff *isl_pw_aff_free(
2932 __isl_take isl_pw_aff *pwaff);
2933 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2934 __isl_keep isl_pw_multi_aff *pma);
2935 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2936 __isl_take isl_pw_multi_aff *pma);
2938 #include <isl/polynomial.h>
2939 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2940 __isl_keep isl_pw_qpolynomial *pwqp);
2941 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2942 __isl_take isl_pw_qpolynomial *pwqp);
2943 __isl_give isl_pw_qpolynomial_fold *
2944 isl_pw_qpolynomial_fold_copy(
2945 __isl_keep isl_pw_qpolynomial_fold *pwf);
2946 __isl_null isl_pw_qpolynomial_fold *
2947 isl_pw_qpolynomial_fold_free(
2948 __isl_take isl_pw_qpolynomial_fold *pwf);
2950 To iterate over the different cells of a piecewise expression,
2951 use the following functions.
2953 #include <isl/aff.h>
2954 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2955 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2956 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2957 int (*fn)(__isl_take isl_set *set,
2958 __isl_take isl_aff *aff,
2959 void *user), void *user);
2960 int isl_pw_multi_aff_foreach_piece(
2961 __isl_keep isl_pw_multi_aff *pma,
2962 int (*fn)(__isl_take isl_set *set,
2963 __isl_take isl_multi_aff *maff,
2964 void *user), void *user);
2966 #include <isl/polynomial.h>
2967 int isl_pw_qpolynomial_foreach_piece(
2968 __isl_keep isl_pw_qpolynomial *pwqp,
2969 int (*fn)(__isl_take isl_set *set,
2970 __isl_take isl_qpolynomial *qp,
2971 void *user), void *user);
2972 int isl_pw_qpolynomial_foreach_lifted_piece(
2973 __isl_keep isl_pw_qpolynomial *pwqp,
2974 int (*fn)(__isl_take isl_set *set,
2975 __isl_take isl_qpolynomial *qp,
2976 void *user), void *user);
2977 int isl_pw_qpolynomial_fold_foreach_piece(
2978 __isl_keep isl_pw_qpolynomial_fold *pwf,
2979 int (*fn)(__isl_take isl_set *set,
2980 __isl_take isl_qpolynomial_fold *fold,
2981 void *user), void *user);
2982 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2983 __isl_keep isl_pw_qpolynomial_fold *pwf,
2984 int (*fn)(__isl_take isl_set *set,
2985 __isl_take isl_qpolynomial_fold *fold,
2986 void *user), void *user);
2988 As usual, the function C<fn> should return C<0> on success
2989 and C<-1> on failure. The difference between
2990 C<isl_pw_qpolynomial_foreach_piece> and
2991 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2992 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2993 compute unique representations for all existentially quantified
2994 variables and then turn these existentially quantified variables
2995 into extra set variables, adapting the associated quasipolynomial
2996 accordingly. This means that the C<set> passed to C<fn>
2997 will not have any existentially quantified variables, but that
2998 the dimensions of the sets may be different for different
2999 invocations of C<fn>.
3000 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
3001 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
3003 A piecewise expression consisting of the expressions at a given
3004 position of a piecewise multiple expression can be extracted
3005 using the following function.
3007 #include <isl/aff.h>
3008 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3009 __isl_keep isl_pw_multi_aff *pma, int pos);
3011 These expressions can be replaced using the following function.
3013 #include <isl/aff.h>
3014 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3015 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3016 __isl_take isl_pw_aff *pa);
3018 Note that there is a difference between C<isl_multi_pw_aff> and
3019 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3020 affine expressions, while the second is a piecewise sequence
3021 of affine expressions. In particular, each of the piecewise
3022 affine expressions in an C<isl_multi_pw_aff> may have a different
3023 domain, while all multiple expressions associated to a cell
3024 in an C<isl_pw_multi_aff> have the same domain.
3025 It is possible to convert between the two, but when converting
3026 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3027 of the result is the intersection of the domains of the input.
3028 The reverse conversion is exact.
3030 #include <isl/aff.h>
3031 __isl_give isl_pw_multi_aff *
3032 isl_pw_multi_aff_from_multi_pw_aff(
3033 __isl_take isl_multi_pw_aff *mpa);
3034 __isl_give isl_multi_pw_aff *
3035 isl_multi_pw_aff_from_pw_multi_aff(
3036 __isl_take isl_pw_multi_aff *pma);
3038 =head3 Union Expressions
3040 A union expression collects base expressions defined
3041 over different domains. The space of a union expression
3042 is that of the shared parameter space.
3044 The union expression types defined by C<isl>
3045 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3046 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3048 An empty union expression can be created using the following functions.
3050 #include <isl/aff.h>
3051 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3052 __isl_take isl_space *space);
3053 __isl_give isl_union_pw_multi_aff *
3054 isl_union_pw_multi_aff_empty(
3055 __isl_take isl_space *space);
3057 #include <isl/polynomial.h>
3058 __isl_give isl_union_pw_qpolynomial *
3059 isl_union_pw_qpolynomial_zero(
3060 __isl_take isl_space *space);
3062 A union expression containing a single base expression
3063 can be created using the following functions.
3065 #include <isl/aff.h>
3066 __isl_give isl_union_pw_aff *
3067 isl_union_pw_aff_from_pw_aff(
3068 __isl_take isl_pw_aff *pa);
3069 __isl_give isl_union_pw_multi_aff *
3070 isl_union_pw_multi_aff_from_aff(
3071 __isl_take isl_aff *aff);
3072 __isl_give isl_union_pw_multi_aff *
3073 isl_union_pw_multi_aff_from_pw_multi_aff(
3074 __isl_take isl_pw_multi_aff *pma);
3076 #include <isl/polynomial.h>
3077 __isl_give isl_union_pw_qpolynomial *
3078 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3079 __isl_take isl_pw_qpolynomial *pwqp);
3081 The following functions create a base expression on each
3082 of the sets in the union set and collect the results.
3084 #include <isl/aff.h>
3085 __isl_give isl_union_pw_multi_aff *
3086 isl_union_pw_multi_aff_from_union_pw_aff(
3087 __isl_take isl_union_pw_aff *upa);
3088 __isl_give isl_union_pw_aff *
3089 isl_union_pw_multi_aff_get_union_pw_aff(
3090 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3091 __isl_give isl_union_pw_aff *
3092 isl_union_pw_aff_val_on_domain(
3093 __isl_take isl_union_set *domain,
3094 __isl_take isl_val *v);
3095 __isl_give isl_union_pw_multi_aff *
3096 isl_union_pw_multi_aff_multi_val_on_domain(
3097 __isl_take isl_union_set *domain,
3098 __isl_take isl_multi_val *mv);
3100 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3101 expression on a given domain can be created using the following
3104 #include <isl/aff.h>
3105 __isl_give isl_union_pw_aff *
3106 isl_union_pw_aff_aff_on_domain(
3107 __isl_take isl_union_set *domain,
3108 __isl_take isl_aff *aff);
3110 A base expression can be added to a union expression using
3111 the following functions.
3113 #include <isl/aff.h>
3114 __isl_give isl_union_pw_aff *
3115 isl_union_pw_aff_add_pw_aff(
3116 __isl_take isl_union_pw_aff *upa,
3117 __isl_take isl_pw_aff *pa);
3118 __isl_give isl_union_pw_multi_aff *
3119 isl_union_pw_multi_aff_add_pw_multi_aff(
3120 __isl_take isl_union_pw_multi_aff *upma,
3121 __isl_take isl_pw_multi_aff *pma);
3123 #include <isl/polynomial.h>
3124 __isl_give isl_union_pw_qpolynomial *
3125 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3126 __isl_take isl_union_pw_qpolynomial *upwqp,
3127 __isl_take isl_pw_qpolynomial *pwqp);
3129 Union expressions can be copied and freed using
3130 the following functions.
3132 #include <isl/aff.h>
3133 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3134 __isl_keep isl_union_pw_aff *upa);
3135 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3136 __isl_take isl_union_pw_aff *upa);
3137 __isl_give isl_union_pw_multi_aff *
3138 isl_union_pw_multi_aff_copy(
3139 __isl_keep isl_union_pw_multi_aff *upma);
3140 __isl_null isl_union_pw_multi_aff *
3141 isl_union_pw_multi_aff_free(
3142 __isl_take isl_union_pw_multi_aff *upma);
3144 #include <isl/polynomial.h>
3145 __isl_give isl_union_pw_qpolynomial *
3146 isl_union_pw_qpolynomial_copy(
3147 __isl_keep isl_union_pw_qpolynomial *upwqp);
3148 __isl_null isl_union_pw_qpolynomial *
3149 isl_union_pw_qpolynomial_free(
3150 __isl_take isl_union_pw_qpolynomial *upwqp);
3151 __isl_give isl_union_pw_qpolynomial_fold *
3152 isl_union_pw_qpolynomial_fold_copy(
3153 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3154 __isl_null isl_union_pw_qpolynomial_fold *
3155 isl_union_pw_qpolynomial_fold_free(
3156 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3158 To iterate over the base expressions in a union expression,
3159 use the following functions.
3161 #include <isl/aff.h>
3162 int isl_union_pw_aff_n_pw_aff(
3163 __isl_keep isl_union_pw_aff *upa);
3164 int isl_union_pw_aff_foreach_pw_aff(
3165 __isl_keep isl_union_pw_aff *upa,
3166 int (*fn)(__isl_take isl_pw_aff *ma, void *user),
3168 int isl_union_pw_multi_aff_n_pw_multi_aff(
3169 __isl_keep isl_union_pw_multi_aff *upma);
3170 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3171 __isl_keep isl_union_pw_multi_aff *upma,
3172 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3173 void *user), void *user);
3175 #include <isl/polynomial.h>
3176 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3177 __isl_keep isl_union_pw_qpolynomial *upwqp);
3178 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3179 __isl_keep isl_union_pw_qpolynomial *upwqp,
3180 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3181 void *user), void *user);
3182 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3183 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3184 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3185 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3186 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3187 void *user), void *user);
3189 To extract the base expression in a given space from a union, use
3190 the following functions.
3192 #include <isl/aff.h>
3193 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3194 __isl_keep isl_union_pw_aff *upa,
3195 __isl_take isl_space *space);
3196 __isl_give isl_pw_multi_aff *
3197 isl_union_pw_multi_aff_extract_pw_multi_aff(
3198 __isl_keep isl_union_pw_multi_aff *upma,
3199 __isl_take isl_space *space);
3201 #include <isl/polynomial.h>
3202 __isl_give isl_pw_qpolynomial *
3203 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3204 __isl_keep isl_union_pw_qpolynomial *upwqp,
3205 __isl_take isl_space *space);
3207 =head2 Input and Output
3209 For set and relation,
3210 C<isl> supports its own input/output format, which is similar
3211 to the C<Omega> format, but also supports the C<PolyLib> format
3213 For other object types, typically only an C<isl> format is supported.
3215 =head3 C<isl> format
3217 The C<isl> format is similar to that of C<Omega>, but has a different
3218 syntax for describing the parameters and allows for the definition
3219 of an existentially quantified variable as the integer division
3220 of an affine expression.
3221 For example, the set of integers C<i> between C<0> and C<n>
3222 such that C<i % 10 <= 6> can be described as
3224 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3227 A set or relation can have several disjuncts, separated
3228 by the keyword C<or>. Each disjunct is either a conjunction
3229 of constraints or a projection (C<exists>) of a conjunction
3230 of constraints. The constraints are separated by the keyword
3233 =head3 C<PolyLib> format
3235 If the represented set is a union, then the first line
3236 contains a single number representing the number of disjuncts.
3237 Otherwise, a line containing the number C<1> is optional.
3239 Each disjunct is represented by a matrix of constraints.
3240 The first line contains two numbers representing
3241 the number of rows and columns,
3242 where the number of rows is equal to the number of constraints
3243 and the number of columns is equal to two plus the number of variables.
3244 The following lines contain the actual rows of the constraint matrix.
3245 In each row, the first column indicates whether the constraint
3246 is an equality (C<0>) or inequality (C<1>). The final column
3247 corresponds to the constant term.
3249 If the set is parametric, then the coefficients of the parameters
3250 appear in the last columns before the constant column.
3251 The coefficients of any existentially quantified variables appear
3252 between those of the set variables and those of the parameters.
3254 =head3 Extended C<PolyLib> format
3256 The extended C<PolyLib> format is nearly identical to the
3257 C<PolyLib> format. The only difference is that the line
3258 containing the number of rows and columns of a constraint matrix
3259 also contains four additional numbers:
3260 the number of output dimensions, the number of input dimensions,
3261 the number of local dimensions (i.e., the number of existentially
3262 quantified variables) and the number of parameters.
3263 For sets, the number of ``output'' dimensions is equal
3264 to the number of set dimensions, while the number of ``input''
3269 Objects can be read from input using the following functions.
3271 #include <isl/val.h>
3272 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3274 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3275 isl_ctx *ctx, const char *str);
3277 #include <isl/set.h>
3278 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3279 isl_ctx *ctx, FILE *input);
3280 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3281 isl_ctx *ctx, const char *str);
3282 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3284 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3287 #include <isl/map.h>
3288 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3289 isl_ctx *ctx, FILE *input);
3290 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3291 isl_ctx *ctx, const char *str);
3292 __isl_give isl_map *isl_map_read_from_file(
3293 isl_ctx *ctx, FILE *input);
3294 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3297 #include <isl/union_set.h>
3298 __isl_give isl_union_set *isl_union_set_read_from_file(
3299 isl_ctx *ctx, FILE *input);
3300 __isl_give isl_union_set *isl_union_set_read_from_str(
3301 isl_ctx *ctx, const char *str);
3303 #include <isl/union_map.h>
3304 __isl_give isl_union_map *isl_union_map_read_from_file(
3305 isl_ctx *ctx, FILE *input);
3306 __isl_give isl_union_map *isl_union_map_read_from_str(
3307 isl_ctx *ctx, const char *str);
3309 #include <isl/aff.h>
3310 __isl_give isl_aff *isl_aff_read_from_str(
3311 isl_ctx *ctx, const char *str);
3312 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3313 isl_ctx *ctx, const char *str);
3314 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3315 isl_ctx *ctx, const char *str);
3316 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3317 isl_ctx *ctx, const char *str);
3318 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3319 isl_ctx *ctx, const char *str);
3320 __isl_give isl_union_pw_multi_aff *
3321 isl_union_pw_multi_aff_read_from_str(
3322 isl_ctx *ctx, const char *str);
3323 __isl_give isl_multi_union_pw_aff *
3324 isl_multi_union_pw_aff_read_from_str(
3325 isl_ctx *ctx, const char *str);
3327 #include <isl/polynomial.h>
3328 __isl_give isl_union_pw_qpolynomial *
3329 isl_union_pw_qpolynomial_read_from_str(
3330 isl_ctx *ctx, const char *str);
3332 For sets and relations,
3333 the input format is autodetected and may be either the C<PolyLib> format
3334 or the C<isl> format.
3338 Before anything can be printed, an C<isl_printer> needs to
3341 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3343 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3344 __isl_null isl_printer *isl_printer_free(
3345 __isl_take isl_printer *printer);
3346 __isl_give char *isl_printer_get_str(
3347 __isl_keep isl_printer *printer);
3349 The printer can be inspected using the following functions.
3351 FILE *isl_printer_get_file(
3352 __isl_keep isl_printer *printer);
3353 int isl_printer_get_output_format(
3354 __isl_keep isl_printer *p);
3355 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3357 The behavior of the printer can be modified in various ways
3359 __isl_give isl_printer *isl_printer_set_output_format(
3360 __isl_take isl_printer *p, int output_format);
3361 __isl_give isl_printer *isl_printer_set_indent(
3362 __isl_take isl_printer *p, int indent);
3363 __isl_give isl_printer *isl_printer_set_indent_prefix(
3364 __isl_take isl_printer *p, const char *prefix);
3365 __isl_give isl_printer *isl_printer_indent(
3366 __isl_take isl_printer *p, int indent);
3367 __isl_give isl_printer *isl_printer_set_prefix(
3368 __isl_take isl_printer *p, const char *prefix);
3369 __isl_give isl_printer *isl_printer_set_suffix(
3370 __isl_take isl_printer *p, const char *suffix);
3371 __isl_give isl_printer *isl_printer_set_yaml_style(
3372 __isl_take isl_printer *p, int yaml_style);
3374 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3375 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3376 and defaults to C<ISL_FORMAT_ISL>.
3377 Each line in the output is prefixed by C<indent_prefix>,
3378 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3379 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3380 In the C<PolyLib> format output,
3381 the coefficients of the existentially quantified variables
3382 appear between those of the set variables and those
3384 The function C<isl_printer_indent> increases the indentation
3385 by the specified amount (which may be negative).
3386 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3387 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3390 To actually print something, use
3392 #include <isl/printer.h>
3393 __isl_give isl_printer *isl_printer_print_double(
3394 __isl_take isl_printer *p, double d);
3396 #include <isl/val.h>
3397 __isl_give isl_printer *isl_printer_print_val(
3398 __isl_take isl_printer *p, __isl_keep isl_val *v);
3400 #include <isl/set.h>
3401 __isl_give isl_printer *isl_printer_print_basic_set(
3402 __isl_take isl_printer *printer,
3403 __isl_keep isl_basic_set *bset);
3404 __isl_give isl_printer *isl_printer_print_set(
3405 __isl_take isl_printer *printer,
3406 __isl_keep isl_set *set);
3408 #include <isl/map.h>
3409 __isl_give isl_printer *isl_printer_print_basic_map(
3410 __isl_take isl_printer *printer,
3411 __isl_keep isl_basic_map *bmap);
3412 __isl_give isl_printer *isl_printer_print_map(
3413 __isl_take isl_printer *printer,
3414 __isl_keep isl_map *map);
3416 #include <isl/union_set.h>
3417 __isl_give isl_printer *isl_printer_print_union_set(
3418 __isl_take isl_printer *p,
3419 __isl_keep isl_union_set *uset);
3421 #include <isl/union_map.h>
3422 __isl_give isl_printer *isl_printer_print_union_map(
3423 __isl_take isl_printer *p,
3424 __isl_keep isl_union_map *umap);
3426 #include <isl/val.h>
3427 __isl_give isl_printer *isl_printer_print_multi_val(
3428 __isl_take isl_printer *p,
3429 __isl_keep isl_multi_val *mv);
3431 #include <isl/aff.h>
3432 __isl_give isl_printer *isl_printer_print_aff(
3433 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3434 __isl_give isl_printer *isl_printer_print_multi_aff(
3435 __isl_take isl_printer *p,
3436 __isl_keep isl_multi_aff *maff);
3437 __isl_give isl_printer *isl_printer_print_pw_aff(
3438 __isl_take isl_printer *p,
3439 __isl_keep isl_pw_aff *pwaff);
3440 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3441 __isl_take isl_printer *p,
3442 __isl_keep isl_pw_multi_aff *pma);
3443 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3444 __isl_take isl_printer *p,
3445 __isl_keep isl_multi_pw_aff *mpa);
3446 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3447 __isl_take isl_printer *p,
3448 __isl_keep isl_union_pw_aff *upa);
3449 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3450 __isl_take isl_printer *p,
3451 __isl_keep isl_union_pw_multi_aff *upma);
3452 __isl_give isl_printer *
3453 isl_printer_print_multi_union_pw_aff(
3454 __isl_take isl_printer *p,
3455 __isl_keep isl_multi_union_pw_aff *mupa);
3457 #include <isl/polynomial.h>
3458 __isl_give isl_printer *isl_printer_print_qpolynomial(
3459 __isl_take isl_printer *p,
3460 __isl_keep isl_qpolynomial *qp);
3461 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3462 __isl_take isl_printer *p,
3463 __isl_keep isl_pw_qpolynomial *pwqp);
3464 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3465 __isl_take isl_printer *p,
3466 __isl_keep isl_union_pw_qpolynomial *upwqp);
3468 __isl_give isl_printer *
3469 isl_printer_print_pw_qpolynomial_fold(
3470 __isl_take isl_printer *p,
3471 __isl_keep isl_pw_qpolynomial_fold *pwf);
3472 __isl_give isl_printer *
3473 isl_printer_print_union_pw_qpolynomial_fold(
3474 __isl_take isl_printer *p,
3475 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3477 For C<isl_printer_print_qpolynomial>,
3478 C<isl_printer_print_pw_qpolynomial> and
3479 C<isl_printer_print_pw_qpolynomial_fold>,
3480 the output format of the printer
3481 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3482 For C<isl_printer_print_union_pw_qpolynomial> and
3483 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3485 In case of printing in C<ISL_FORMAT_C>, the user may want
3486 to set the names of all dimensions first.
3488 C<isl> also provides limited support for printing YAML documents,
3489 just enough for the internal use for printing such documents.
3491 #include <isl/printer.h>
3492 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3493 __isl_take isl_printer *p);
3494 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3495 __isl_take isl_printer *p);
3496 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3497 __isl_take isl_printer *p);
3498 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3499 __isl_take isl_printer *p);
3500 __isl_give isl_printer *isl_printer_yaml_next(
3501 __isl_take isl_printer *p);
3503 A document is started by a call to either
3504 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3505 Anything printed to the printer after such a call belong to the
3506 first key of the mapping or the first element in the sequence.
3507 The function C<isl_printer_yaml_next> moves to the value if
3508 we are currently printing a mapping key, the next key if we
3509 are printing a value or the next element if we are printing
3510 an element in a sequence.
3511 Nested mappings and sequences are initiated by the same
3512 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3513 Each call to these functions needs to have a corresponding call to
3514 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3516 When called on a file printer, the following function flushes
3517 the file. When called on a string printer, the buffer is cleared.
3519 __isl_give isl_printer *isl_printer_flush(
3520 __isl_take isl_printer *p);
3522 Alternatively, a string representation can be obtained
3523 directly using the following functions, which always print
3526 #include <isl/space.h>
3527 __isl_give char *isl_space_to_str(
3528 __isl_keep isl_space *space);
3530 #include <isl/val.h>
3531 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3532 __isl_give char *isl_multi_val_to_str(
3533 __isl_keep isl_multi_val *mv);
3535 #include <isl/set.h>
3536 __isl_give char *isl_set_to_str(
3537 __isl_keep isl_set *set);
3539 #include <isl/union_set.h>
3540 __isl_give char *isl_union_set_to_str(
3541 __isl_keep isl_union_set *uset);
3543 #include <isl/map.h>
3544 __isl_give char *isl_map_to_str(
3545 __isl_keep isl_map *map);
3547 #include <isl/union_map.h>
3548 __isl_give char *isl_union_map_to_str(
3549 __isl_keep isl_union_map *umap);
3551 #include <isl/aff.h>
3552 __isl_give char *isl_multi_aff_to_str(
3553 __isl_keep isl_multi_aff *aff);
3554 __isl_give char *isl_union_pw_aff_to_str(
3555 __isl_keep isl_union_pw_aff *upa);
3556 __isl_give char *isl_union_pw_multi_aff_to_str(
3557 __isl_keep isl_union_pw_multi_aff *upma);
3558 __isl_give char *isl_multi_union_pw_aff_to_str(
3559 __isl_keep isl_multi_union_pw_aff *mupa);
3563 =head3 Unary Properties
3569 The following functions test whether the given set or relation
3570 contains any integer points. The ``plain'' variants do not perform
3571 any computations, but simply check if the given set or relation
3572 is already known to be empty.
3574 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3575 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3576 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3577 int isl_set_is_empty(__isl_keep isl_set *set);
3578 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3579 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3580 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3581 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3582 int isl_map_is_empty(__isl_keep isl_map *map);
3583 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3585 =item * Universality
3587 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3588 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3589 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3591 =item * Single-valuedness
3593 #include <isl/set.h>
3594 int isl_set_is_singleton(__isl_keep isl_set *set);
3596 #include <isl/map.h>
3597 int isl_basic_map_is_single_valued(
3598 __isl_keep isl_basic_map *bmap);
3599 int isl_map_plain_is_single_valued(
3600 __isl_keep isl_map *map);
3601 int isl_map_is_single_valued(__isl_keep isl_map *map);
3603 #include <isl/union_map.h>
3604 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3608 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3609 int isl_map_is_injective(__isl_keep isl_map *map);
3610 int isl_union_map_plain_is_injective(
3611 __isl_keep isl_union_map *umap);
3612 int isl_union_map_is_injective(
3613 __isl_keep isl_union_map *umap);
3617 int isl_map_is_bijective(__isl_keep isl_map *map);
3618 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3622 __isl_give isl_val *
3623 isl_basic_map_plain_get_val_if_fixed(
3624 __isl_keep isl_basic_map *bmap,
3625 enum isl_dim_type type, unsigned pos);
3626 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3627 __isl_keep isl_set *set,
3628 enum isl_dim_type type, unsigned pos);
3629 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3630 __isl_keep isl_map *map,
3631 enum isl_dim_type type, unsigned pos);
3633 If the set or relation obviously lies on a hyperplane where the given dimension
3634 has a fixed value, then return that value.
3635 Otherwise return NaN.
3639 int isl_set_dim_residue_class_val(
3640 __isl_keep isl_set *set,
3641 int pos, __isl_give isl_val **modulo,
3642 __isl_give isl_val **residue);
3644 Check if the values of the given set dimension are equal to a fixed
3645 value modulo some integer value. If so, assign the modulo to C<*modulo>
3646 and the fixed value to C<*residue>. If the given dimension attains only
3647 a single value, then assign C<0> to C<*modulo> and the fixed value to
3649 If the dimension does not attain only a single value and if no modulo
3650 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3654 To check whether the description of a set, relation or function depends
3655 on one or more given dimensions,
3656 the following functions can be used.
3658 #include <isl/constraint.h>
3659 int isl_constraint_involves_dims(
3660 __isl_keep isl_constraint *constraint,
3661 enum isl_dim_type type, unsigned first, unsigned n);
3663 #include <isl/set.h>
3664 int isl_basic_set_involves_dims(
3665 __isl_keep isl_basic_set *bset,
3666 enum isl_dim_type type, unsigned first, unsigned n);
3667 int isl_set_involves_dims(__isl_keep isl_set *set,
3668 enum isl_dim_type type, unsigned first, unsigned n);
3670 #include <isl/map.h>
3671 int isl_basic_map_involves_dims(
3672 __isl_keep isl_basic_map *bmap,
3673 enum isl_dim_type type, unsigned first, unsigned n);
3674 int isl_map_involves_dims(__isl_keep isl_map *map,
3675 enum isl_dim_type type, unsigned first, unsigned n);
3677 #include <isl/union_map.h>
3678 int isl_union_map_involves_dims(
3679 __isl_keep isl_union_map *umap,
3680 enum isl_dim_type type, unsigned first, unsigned n);
3682 #include <isl/aff.h>
3683 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3684 enum isl_dim_type type, unsigned first, unsigned n);
3685 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3686 enum isl_dim_type type, unsigned first, unsigned n);
3687 int isl_multi_aff_involves_dims(
3688 __isl_keep isl_multi_aff *ma,
3689 enum isl_dim_type type, unsigned first, unsigned n);
3690 int isl_multi_pw_aff_involves_dims(
3691 __isl_keep isl_multi_pw_aff *mpa,
3692 enum isl_dim_type type, unsigned first, unsigned n);
3694 Similarly, the following functions can be used to check whether
3695 a given dimension is involved in any lower or upper bound.
3697 #include <isl/set.h>
3698 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3699 enum isl_dim_type type, unsigned pos);
3700 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3701 enum isl_dim_type type, unsigned pos);
3703 Note that these functions return true even if there is a bound on
3704 the dimension on only some of the basic sets of C<set>.
3705 To check if they have a bound for all of the basic sets in C<set>,
3706 use the following functions instead.
3708 #include <isl/set.h>
3709 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3710 enum isl_dim_type type, unsigned pos);
3711 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3712 enum isl_dim_type type, unsigned pos);
3716 To check whether a set is a parameter domain, use this function:
3718 int isl_set_is_params(__isl_keep isl_set *set);
3719 int isl_union_set_is_params(
3720 __isl_keep isl_union_set *uset);
3724 The following functions check whether the space of the given
3725 (basic) set or relation range is a wrapped relation.
3727 #include <isl/space.h>
3728 int isl_space_is_wrapping(
3729 __isl_keep isl_space *space);
3730 int isl_space_domain_is_wrapping(
3731 __isl_keep isl_space *space);
3732 int isl_space_range_is_wrapping(
3733 __isl_keep isl_space *space);
3735 #include <isl/set.h>
3736 int isl_basic_set_is_wrapping(
3737 __isl_keep isl_basic_set *bset);
3738 int isl_set_is_wrapping(__isl_keep isl_set *set);
3740 #include <isl/map.h>
3741 int isl_map_domain_is_wrapping(
3742 __isl_keep isl_map *map);
3743 int isl_map_range_is_wrapping(
3744 __isl_keep isl_map *map);
3746 #include <isl/val.h>
3747 int isl_multi_val_range_is_wrapping(
3748 __isl_keep isl_multi_val *mv);
3750 #include <isl/aff.h>
3751 int isl_multi_aff_range_is_wrapping(
3752 __isl_keep isl_multi_aff *ma);
3753 int isl_multi_pw_aff_range_is_wrapping(
3754 __isl_keep isl_multi_pw_aff *mpa);
3755 int isl_multi_union_pw_aff_range_is_wrapping(
3756 __isl_keep isl_multi_union_pw_aff *mupa);
3758 The input to C<isl_space_is_wrapping> should
3759 be the space of a set, while that of
3760 C<isl_space_domain_is_wrapping> and
3761 C<isl_space_range_is_wrapping> should be the space of a relation.
3763 =item * Internal Product
3765 int isl_basic_map_can_zip(
3766 __isl_keep isl_basic_map *bmap);
3767 int isl_map_can_zip(__isl_keep isl_map *map);
3769 Check whether the product of domain and range of the given relation
3771 i.e., whether both domain and range are nested relations.
3775 int isl_basic_map_can_curry(
3776 __isl_keep isl_basic_map *bmap);
3777 int isl_map_can_curry(__isl_keep isl_map *map);
3779 Check whether the domain of the (basic) relation is a wrapped relation.
3781 int isl_basic_map_can_uncurry(
3782 __isl_keep isl_basic_map *bmap);
3783 int isl_map_can_uncurry(__isl_keep isl_map *map);
3785 Check whether the range of the (basic) relation is a wrapped relation.
3787 =item * Special Values
3789 #include <isl/aff.h>
3790 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3791 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3793 Check whether the given expression is a constant.
3795 #include <isl/aff.h>
3796 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3797 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3799 Check whether the given expression is equal to or involves NaN.
3801 #include <isl/aff.h>
3802 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3804 Check whether the affine expression is obviously zero.
3808 =head3 Binary Properties
3814 The following functions check whether two objects
3815 represent the same set, relation or function.
3816 The C<plain> variants only return true if the objects
3817 are obviously the same. That is, they may return false
3818 even if the objects are the same, but they will never
3819 return true if the objects are not the same.
3821 #include <isl/set.h>
3822 int isl_basic_set_plain_is_equal(
3823 __isl_keep isl_basic_set *bset1,
3824 __isl_keep isl_basic_set *bset2);
3825 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3826 __isl_keep isl_set *set2);
3827 int isl_set_is_equal(__isl_keep isl_set *set1,
3828 __isl_keep isl_set *set2);
3830 #include <isl/map.h>
3831 int isl_basic_map_is_equal(
3832 __isl_keep isl_basic_map *bmap1,
3833 __isl_keep isl_basic_map *bmap2);
3834 int isl_map_is_equal(__isl_keep isl_map *map1,
3835 __isl_keep isl_map *map2);
3836 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3837 __isl_keep isl_map *map2);
3839 #include <isl/union_set.h>
3840 int isl_union_set_is_equal(
3841 __isl_keep isl_union_set *uset1,
3842 __isl_keep isl_union_set *uset2);
3844 #include <isl/union_map.h>
3845 int isl_union_map_is_equal(
3846 __isl_keep isl_union_map *umap1,
3847 __isl_keep isl_union_map *umap2);
3849 #include <isl/aff.h>
3850 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3851 __isl_keep isl_aff *aff2);
3852 int isl_multi_aff_plain_is_equal(
3853 __isl_keep isl_multi_aff *maff1,
3854 __isl_keep isl_multi_aff *maff2);
3855 int isl_pw_aff_plain_is_equal(
3856 __isl_keep isl_pw_aff *pwaff1,
3857 __isl_keep isl_pw_aff *pwaff2);
3858 int isl_pw_multi_aff_plain_is_equal(
3859 __isl_keep isl_pw_multi_aff *pma1,
3860 __isl_keep isl_pw_multi_aff *pma2);
3861 int isl_multi_pw_aff_plain_is_equal(
3862 __isl_keep isl_multi_pw_aff *mpa1,
3863 __isl_keep isl_multi_pw_aff *mpa2);
3864 int isl_multi_pw_aff_is_equal(
3865 __isl_keep isl_multi_pw_aff *mpa1,
3866 __isl_keep isl_multi_pw_aff *mpa2);
3867 int isl_union_pw_aff_plain_is_equal(
3868 __isl_keep isl_union_pw_aff *upa1,
3869 __isl_keep isl_union_pw_aff *upa2);
3870 int isl_union_pw_multi_aff_plain_is_equal(
3871 __isl_keep isl_union_pw_multi_aff *upma1,
3872 __isl_keep isl_union_pw_multi_aff *upma2);
3873 int isl_multi_union_pw_aff_plain_is_equal(
3874 __isl_keep isl_multi_union_pw_aff *mupa1,
3875 __isl_keep isl_multi_union_pw_aff *mupa2);
3877 #include <isl/polynomial.h>
3878 int isl_union_pw_qpolynomial_plain_is_equal(
3879 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3880 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3881 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3882 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3883 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3885 =item * Disjointness
3887 #include <isl/set.h>
3888 int isl_basic_set_is_disjoint(
3889 __isl_keep isl_basic_set *bset1,
3890 __isl_keep isl_basic_set *bset2);
3891 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3892 __isl_keep isl_set *set2);
3893 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3894 __isl_keep isl_set *set2);
3896 #include <isl/map.h>
3897 int isl_basic_map_is_disjoint(
3898 __isl_keep isl_basic_map *bmap1,
3899 __isl_keep isl_basic_map *bmap2);
3900 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3901 __isl_keep isl_map *map2);
3903 #include <isl/union_set.h>
3904 int isl_union_set_is_disjoint(
3905 __isl_keep isl_union_set *uset1,
3906 __isl_keep isl_union_set *uset2);
3908 #include <isl/union_map.h>
3909 int isl_union_map_is_disjoint(
3910 __isl_keep isl_union_map *umap1,
3911 __isl_keep isl_union_map *umap2);
3915 int isl_basic_set_is_subset(
3916 __isl_keep isl_basic_set *bset1,
3917 __isl_keep isl_basic_set *bset2);
3918 int isl_set_is_subset(__isl_keep isl_set *set1,
3919 __isl_keep isl_set *set2);
3920 int isl_set_is_strict_subset(
3921 __isl_keep isl_set *set1,
3922 __isl_keep isl_set *set2);
3923 int isl_union_set_is_subset(
3924 __isl_keep isl_union_set *uset1,
3925 __isl_keep isl_union_set *uset2);
3926 int isl_union_set_is_strict_subset(
3927 __isl_keep isl_union_set *uset1,
3928 __isl_keep isl_union_set *uset2);
3929 int isl_basic_map_is_subset(
3930 __isl_keep isl_basic_map *bmap1,
3931 __isl_keep isl_basic_map *bmap2);
3932 int isl_basic_map_is_strict_subset(
3933 __isl_keep isl_basic_map *bmap1,
3934 __isl_keep isl_basic_map *bmap2);
3935 int isl_map_is_subset(
3936 __isl_keep isl_map *map1,
3937 __isl_keep isl_map *map2);
3938 int isl_map_is_strict_subset(
3939 __isl_keep isl_map *map1,
3940 __isl_keep isl_map *map2);
3941 int isl_union_map_is_subset(
3942 __isl_keep isl_union_map *umap1,
3943 __isl_keep isl_union_map *umap2);
3944 int isl_union_map_is_strict_subset(
3945 __isl_keep isl_union_map *umap1,
3946 __isl_keep isl_union_map *umap2);
3948 Check whether the first argument is a (strict) subset of the
3953 Every comparison function returns a negative value if the first
3954 argument is considered smaller than the second, a positive value
3955 if the first argument is considered greater and zero if the two
3956 constraints are considered the same by the comparison criterion.
3958 #include <isl/constraint.h>
3959 int isl_constraint_plain_cmp(
3960 __isl_keep isl_constraint *c1,
3961 __isl_keep isl_constraint *c2);
3963 This function is useful for sorting C<isl_constraint>s.
3964 The order depends on the internal representation of the inputs.
3965 The order is fixed over different calls to the function (assuming
3966 the internal representation of the inputs has not changed), but may
3967 change over different versions of C<isl>.
3969 #include <isl/constraint.h>
3970 int isl_constraint_cmp_last_non_zero(
3971 __isl_keep isl_constraint *c1,
3972 __isl_keep isl_constraint *c2);
3974 This function can be used to sort constraints that live in the same
3975 local space. Constraints that involve ``earlier'' dimensions or
3976 that have a smaller coefficient for the shared latest dimension
3977 are considered smaller than other constraints.
3978 This function only defines a B<partial> order.
3980 #include <isl/set.h>
3981 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3982 __isl_keep isl_set *set2);
3984 This function is useful for sorting C<isl_set>s.
3985 The order depends on the internal representation of the inputs.
3986 The order is fixed over different calls to the function (assuming
3987 the internal representation of the inputs has not changed), but may
3988 change over different versions of C<isl>.
3990 #include <isl/aff.h>
3991 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3992 __isl_keep isl_pw_aff *pa2);
3994 The function C<isl_pw_aff_plain_cmp> can be used to sort
3995 C<isl_pw_aff>s. The order is not strictly defined.
3996 The current order sorts expressions that only involve
3997 earlier dimensions before those that involve later dimensions.
4001 =head2 Unary Operations
4007 __isl_give isl_set *isl_set_complement(
4008 __isl_take isl_set *set);
4009 __isl_give isl_map *isl_map_complement(
4010 __isl_take isl_map *map);
4014 #include <isl/space.h>
4015 __isl_give isl_space *isl_space_reverse(
4016 __isl_take isl_space *space);
4018 #include <isl/map.h>
4019 __isl_give isl_basic_map *isl_basic_map_reverse(
4020 __isl_take isl_basic_map *bmap);
4021 __isl_give isl_map *isl_map_reverse(
4022 __isl_take isl_map *map);
4024 #include <isl/union_map.h>
4025 __isl_give isl_union_map *isl_union_map_reverse(
4026 __isl_take isl_union_map *umap);
4030 #include <isl/space.h>
4031 __isl_give isl_space *isl_space_domain(
4032 __isl_take isl_space *space);
4033 __isl_give isl_space *isl_space_range(
4034 __isl_take isl_space *space);
4035 __isl_give isl_space *isl_space_params(
4036 __isl_take isl_space *space);
4038 #include <isl/local_space.h>
4039 __isl_give isl_local_space *isl_local_space_domain(
4040 __isl_take isl_local_space *ls);
4041 __isl_give isl_local_space *isl_local_space_range(
4042 __isl_take isl_local_space *ls);
4044 #include <isl/set.h>
4045 __isl_give isl_basic_set *isl_basic_set_project_out(
4046 __isl_take isl_basic_set *bset,
4047 enum isl_dim_type type, unsigned first, unsigned n);
4048 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4049 enum isl_dim_type type, unsigned first, unsigned n);
4050 __isl_give isl_basic_set *isl_basic_set_params(
4051 __isl_take isl_basic_set *bset);
4052 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4054 #include <isl/map.h>
4055 __isl_give isl_basic_map *isl_basic_map_project_out(
4056 __isl_take isl_basic_map *bmap,
4057 enum isl_dim_type type, unsigned first, unsigned n);
4058 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4059 enum isl_dim_type type, unsigned first, unsigned n);
4060 __isl_give isl_basic_set *isl_basic_map_domain(
4061 __isl_take isl_basic_map *bmap);
4062 __isl_give isl_basic_set *isl_basic_map_range(
4063 __isl_take isl_basic_map *bmap);
4064 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4065 __isl_give isl_set *isl_map_domain(
4066 __isl_take isl_map *bmap);
4067 __isl_give isl_set *isl_map_range(
4068 __isl_take isl_map *map);
4070 #include <isl/union_set.h>
4071 __isl_give isl_union_set *isl_union_set_project_out(
4072 __isl_take isl_union_set *uset,
4073 enum isl_dim_type type,
4074 unsigned first, unsigned n);
4075 __isl_give isl_set *isl_union_set_params(
4076 __isl_take isl_union_set *uset);
4078 The function C<isl_union_set_project_out> can only project out
4081 #include <isl/union_map.h>
4082 __isl_give isl_union_map *isl_union_map_project_out(
4083 __isl_take isl_union_map *umap,
4084 enum isl_dim_type type, unsigned first, unsigned n);
4085 __isl_give isl_set *isl_union_map_params(
4086 __isl_take isl_union_map *umap);
4087 __isl_give isl_union_set *isl_union_map_domain(
4088 __isl_take isl_union_map *umap);
4089 __isl_give isl_union_set *isl_union_map_range(
4090 __isl_take isl_union_map *umap);
4092 The function C<isl_union_map_project_out> can only project out
4095 #include <isl/aff.h>
4096 __isl_give isl_aff *isl_aff_project_domain_on_params(
4097 __isl_take isl_aff *aff);
4098 __isl_give isl_pw_multi_aff *
4099 isl_pw_multi_aff_project_domain_on_params(
4100 __isl_take isl_pw_multi_aff *pma);
4101 __isl_give isl_set *isl_pw_aff_domain(
4102 __isl_take isl_pw_aff *pwaff);
4103 __isl_give isl_set *isl_pw_multi_aff_domain(
4104 __isl_take isl_pw_multi_aff *pma);
4105 __isl_give isl_set *isl_multi_pw_aff_domain(
4106 __isl_take isl_multi_pw_aff *mpa);
4107 __isl_give isl_union_set *isl_union_pw_aff_domain(
4108 __isl_take isl_union_pw_aff *upa);
4109 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4110 __isl_take isl_union_pw_multi_aff *upma);
4111 __isl_give isl_union_set *
4112 isl_multi_union_pw_aff_domain(
4113 __isl_take isl_multi_union_pw_aff *mupa);
4114 __isl_give isl_set *isl_pw_aff_params(
4115 __isl_take isl_pw_aff *pwa);
4117 The function C<isl_multi_union_pw_aff_domain> requires its
4118 input to have at least one set dimension.
4120 #include <isl/polynomial.h>
4121 __isl_give isl_qpolynomial *
4122 isl_qpolynomial_project_domain_on_params(
4123 __isl_take isl_qpolynomial *qp);
4124 __isl_give isl_pw_qpolynomial *
4125 isl_pw_qpolynomial_project_domain_on_params(
4126 __isl_take isl_pw_qpolynomial *pwqp);
4127 __isl_give isl_pw_qpolynomial_fold *
4128 isl_pw_qpolynomial_fold_project_domain_on_params(
4129 __isl_take isl_pw_qpolynomial_fold *pwf);
4130 __isl_give isl_set *isl_pw_qpolynomial_domain(
4131 __isl_take isl_pw_qpolynomial *pwqp);
4132 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4133 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4134 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4135 __isl_take isl_union_pw_qpolynomial *upwqp);
4137 #include <isl/space.h>
4138 __isl_give isl_space *isl_space_domain_map(
4139 __isl_take isl_space *space);
4140 __isl_give isl_space *isl_space_range_map(
4141 __isl_take isl_space *space);
4143 #include <isl/map.h>
4144 __isl_give isl_map *isl_set_wrapped_domain_map(
4145 __isl_take isl_set *set);
4146 __isl_give isl_basic_map *isl_basic_map_domain_map(
4147 __isl_take isl_basic_map *bmap);
4148 __isl_give isl_basic_map *isl_basic_map_range_map(
4149 __isl_take isl_basic_map *bmap);
4150 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4151 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4153 #include <isl/union_map.h>
4154 __isl_give isl_union_map *isl_union_map_domain_map(
4155 __isl_take isl_union_map *umap);
4156 __isl_give isl_union_pw_multi_aff *
4157 isl_union_map_domain_map_union_pw_multi_aff(
4158 __isl_take isl_union_map *umap);
4159 __isl_give isl_union_map *isl_union_map_range_map(
4160 __isl_take isl_union_map *umap);
4161 __isl_give isl_union_map *
4162 isl_union_set_wrapped_domain_map(
4163 __isl_take isl_union_set *uset);
4165 The functions above construct a (basic, regular or union) relation
4166 that maps (a wrapped version of) the input relation to its domain or range.
4167 C<isl_set_wrapped_domain_map> maps the input set to the domain
4168 of its wrapped relation.
4172 __isl_give isl_basic_set *isl_basic_set_eliminate(
4173 __isl_take isl_basic_set *bset,
4174 enum isl_dim_type type,
4175 unsigned first, unsigned n);
4176 __isl_give isl_set *isl_set_eliminate(
4177 __isl_take isl_set *set, enum isl_dim_type type,
4178 unsigned first, unsigned n);
4179 __isl_give isl_basic_map *isl_basic_map_eliminate(
4180 __isl_take isl_basic_map *bmap,
4181 enum isl_dim_type type,
4182 unsigned first, unsigned n);
4183 __isl_give isl_map *isl_map_eliminate(
4184 __isl_take isl_map *map, enum isl_dim_type type,
4185 unsigned first, unsigned n);
4187 Eliminate the coefficients for the given dimensions from the constraints,
4188 without removing the dimensions.
4190 =item * Constructing a set from a parameter domain
4192 A zero-dimensional space or (basic) set can be constructed
4193 on a given parameter domain using the following functions.
4195 #include <isl/space.h>
4196 __isl_give isl_space *isl_space_set_from_params(
4197 __isl_take isl_space *space);
4199 #include <isl/set.h>
4200 __isl_give isl_basic_set *isl_basic_set_from_params(
4201 __isl_take isl_basic_set *bset);
4202 __isl_give isl_set *isl_set_from_params(
4203 __isl_take isl_set *set);
4205 =item * Constructing a relation from a set
4207 Create a relation with the given set as domain or range.
4208 The range or domain of the created relation is a zero-dimensional
4209 flat anonymous space.
4211 #include <isl/space.h>
4212 __isl_give isl_space *isl_space_from_domain(
4213 __isl_take isl_space *space);
4214 __isl_give isl_space *isl_space_from_range(
4215 __isl_take isl_space *space);
4216 __isl_give isl_space *isl_space_map_from_set(
4217 __isl_take isl_space *space);
4218 __isl_give isl_space *isl_space_map_from_domain_and_range(
4219 __isl_take isl_space *domain,
4220 __isl_take isl_space *range);
4222 #include <isl/local_space.h>
4223 __isl_give isl_local_space *isl_local_space_from_domain(
4224 __isl_take isl_local_space *ls);
4226 #include <isl/map.h>
4227 __isl_give isl_map *isl_map_from_domain(
4228 __isl_take isl_set *set);
4229 __isl_give isl_map *isl_map_from_range(
4230 __isl_take isl_set *set);
4232 #include <isl/val.h>
4233 __isl_give isl_multi_val *isl_multi_val_from_range(
4234 __isl_take isl_multi_val *mv);
4236 #include <isl/aff.h>
4237 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4238 __isl_take isl_multi_aff *ma);
4239 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4240 __isl_take isl_pw_aff *pwa);
4241 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4242 __isl_take isl_multi_pw_aff *mpa);
4243 __isl_give isl_multi_union_pw_aff *
4244 isl_multi_union_pw_aff_from_range(
4245 __isl_take isl_multi_union_pw_aff *mupa);
4246 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4247 __isl_take isl_set *set);
4248 __isl_give isl_union_pw_multi_aff *
4249 isl_union_pw_multi_aff_from_domain(
4250 __isl_take isl_union_set *uset);
4254 #include <isl/set.h>
4255 __isl_give isl_basic_set *isl_basic_set_fix_si(
4256 __isl_take isl_basic_set *bset,
4257 enum isl_dim_type type, unsigned pos, int value);
4258 __isl_give isl_basic_set *isl_basic_set_fix_val(
4259 __isl_take isl_basic_set *bset,
4260 enum isl_dim_type type, unsigned pos,
4261 __isl_take isl_val *v);
4262 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4263 enum isl_dim_type type, unsigned pos, int value);
4264 __isl_give isl_set *isl_set_fix_val(
4265 __isl_take isl_set *set,
4266 enum isl_dim_type type, unsigned pos,
4267 __isl_take isl_val *v);
4269 #include <isl/map.h>
4270 __isl_give isl_basic_map *isl_basic_map_fix_si(
4271 __isl_take isl_basic_map *bmap,
4272 enum isl_dim_type type, unsigned pos, int value);
4273 __isl_give isl_basic_map *isl_basic_map_fix_val(
4274 __isl_take isl_basic_map *bmap,
4275 enum isl_dim_type type, unsigned pos,
4276 __isl_take isl_val *v);
4277 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4278 enum isl_dim_type type, unsigned pos, int value);
4279 __isl_give isl_map *isl_map_fix_val(
4280 __isl_take isl_map *map,
4281 enum isl_dim_type type, unsigned pos,
4282 __isl_take isl_val *v);
4284 #include <isl/aff.h>
4285 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4286 __isl_take isl_pw_multi_aff *pma,
4287 enum isl_dim_type type, unsigned pos, int value);
4289 #include <isl/polynomial.h>
4290 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4291 __isl_take isl_pw_qpolynomial *pwqp,
4292 enum isl_dim_type type, unsigned n,
4293 __isl_take isl_val *v);
4295 Intersect the set, relation or function domain
4296 with the hyperplane where the given
4297 dimension has the fixed given value.
4299 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4300 __isl_take isl_basic_map *bmap,
4301 enum isl_dim_type type, unsigned pos, int value);
4302 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4303 __isl_take isl_basic_map *bmap,
4304 enum isl_dim_type type, unsigned pos, int value);
4305 __isl_give isl_set *isl_set_lower_bound_si(
4306 __isl_take isl_set *set,
4307 enum isl_dim_type type, unsigned pos, int value);
4308 __isl_give isl_set *isl_set_lower_bound_val(
4309 __isl_take isl_set *set,
4310 enum isl_dim_type type, unsigned pos,
4311 __isl_take isl_val *value);
4312 __isl_give isl_map *isl_map_lower_bound_si(
4313 __isl_take isl_map *map,
4314 enum isl_dim_type type, unsigned pos, int value);
4315 __isl_give isl_set *isl_set_upper_bound_si(
4316 __isl_take isl_set *set,
4317 enum isl_dim_type type, unsigned pos, int value);
4318 __isl_give isl_set *isl_set_upper_bound_val(
4319 __isl_take isl_set *set,
4320 enum isl_dim_type type, unsigned pos,
4321 __isl_take isl_val *value);
4322 __isl_give isl_map *isl_map_upper_bound_si(
4323 __isl_take isl_map *map,
4324 enum isl_dim_type type, unsigned pos, int value);
4326 Intersect the set or relation with the half-space where the given
4327 dimension has a value bounded by the fixed given integer value.
4329 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4330 enum isl_dim_type type1, int pos1,
4331 enum isl_dim_type type2, int pos2);
4332 __isl_give isl_basic_map *isl_basic_map_equate(
4333 __isl_take isl_basic_map *bmap,
4334 enum isl_dim_type type1, int pos1,
4335 enum isl_dim_type type2, int pos2);
4336 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4337 enum isl_dim_type type1, int pos1,
4338 enum isl_dim_type type2, int pos2);
4340 Intersect the set or relation with the hyperplane where the given
4341 dimensions are equal to each other.
4343 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4344 enum isl_dim_type type1, int pos1,
4345 enum isl_dim_type type2, int pos2);
4347 Intersect the relation with the hyperplane where the given
4348 dimensions have opposite values.
4350 __isl_give isl_map *isl_map_order_le(
4351 __isl_take isl_map *map,
4352 enum isl_dim_type type1, int pos1,
4353 enum isl_dim_type type2, int pos2);
4354 __isl_give isl_basic_map *isl_basic_map_order_ge(
4355 __isl_take isl_basic_map *bmap,
4356 enum isl_dim_type type1, int pos1,
4357 enum isl_dim_type type2, int pos2);
4358 __isl_give isl_map *isl_map_order_ge(
4359 __isl_take isl_map *map,
4360 enum isl_dim_type type1, int pos1,
4361 enum isl_dim_type type2, int pos2);
4362 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4363 enum isl_dim_type type1, int pos1,
4364 enum isl_dim_type type2, int pos2);
4365 __isl_give isl_basic_map *isl_basic_map_order_gt(
4366 __isl_take isl_basic_map *bmap,
4367 enum isl_dim_type type1, int pos1,
4368 enum isl_dim_type type2, int pos2);
4369 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4370 enum isl_dim_type type1, int pos1,
4371 enum isl_dim_type type2, int pos2);
4373 Intersect the relation with the half-space where the given
4374 dimensions satisfy the given ordering.
4378 #include <isl/aff.h>
4379 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4380 __isl_take isl_aff *aff);
4381 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4382 __isl_take isl_aff *aff);
4383 __isl_give isl_set *isl_pw_aff_pos_set(
4384 __isl_take isl_pw_aff *pa);
4385 __isl_give isl_set *isl_pw_aff_nonneg_set(
4386 __isl_take isl_pw_aff *pwaff);
4387 __isl_give isl_set *isl_pw_aff_zero_set(
4388 __isl_take isl_pw_aff *pwaff);
4389 __isl_give isl_set *isl_pw_aff_non_zero_set(
4390 __isl_take isl_pw_aff *pwaff);
4391 __isl_give isl_union_set *
4392 isl_union_pw_aff_zero_union_set(
4393 __isl_take isl_union_pw_aff *upa);
4394 __isl_give isl_union_set *
4395 isl_multi_union_pw_aff_zero_union_set(
4396 __isl_take isl_multi_union_pw_aff *mupa);
4398 The function C<isl_aff_neg_basic_set> returns a basic set
4399 containing those elements in the domain space
4400 of C<aff> where C<aff> is negative.
4401 The function C<isl_pw_aff_nonneg_set> returns a set
4402 containing those elements in the domain
4403 of C<pwaff> where C<pwaff> is non-negative.
4404 The function C<isl_multi_union_pw_aff_zero_union_set>
4405 returns a union set containing those elements
4406 in the domains of its elements where they are all zero.
4410 __isl_give isl_map *isl_set_identity(
4411 __isl_take isl_set *set);
4412 __isl_give isl_union_map *isl_union_set_identity(
4413 __isl_take isl_union_set *uset);
4414 __isl_give isl_union_pw_multi_aff *
4415 isl_union_set_identity_union_pw_multi_aff(
4416 __isl_take isl_union_set *uset);
4418 Construct an identity relation on the given (union) set.
4420 =item * Function Extraction
4422 A piecewise quasi affine expression that is equal to 1 on a set
4423 and 0 outside the set can be created using the following function.
4425 #include <isl/aff.h>
4426 __isl_give isl_pw_aff *isl_set_indicator_function(
4427 __isl_take isl_set *set);
4429 A piecewise multiple quasi affine expression can be extracted
4430 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4431 and the C<isl_map> is single-valued.
4432 In case of a conversion from an C<isl_union_map>
4433 to an C<isl_union_pw_multi_aff>, these properties need to hold
4434 in each domain space.
4435 A conversion to a C<isl_multi_union_pw_aff> additionally
4436 requires that the input is non-empty and involves only a single
4439 #include <isl/aff.h>
4440 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4441 __isl_take isl_set *set);
4442 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4443 __isl_take isl_map *map);
4445 __isl_give isl_union_pw_multi_aff *
4446 isl_union_pw_multi_aff_from_union_set(
4447 __isl_take isl_union_set *uset);
4448 __isl_give isl_union_pw_multi_aff *
4449 isl_union_pw_multi_aff_from_union_map(
4450 __isl_take isl_union_map *umap);
4452 __isl_give isl_multi_union_pw_aff *
4453 isl_multi_union_pw_aff_from_union_map(
4454 __isl_take isl_union_map *umap);
4458 __isl_give isl_basic_set *isl_basic_map_deltas(
4459 __isl_take isl_basic_map *bmap);
4460 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4461 __isl_give isl_union_set *isl_union_map_deltas(
4462 __isl_take isl_union_map *umap);
4464 These functions return a (basic) set containing the differences
4465 between image elements and corresponding domain elements in the input.
4467 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4468 __isl_take isl_basic_map *bmap);
4469 __isl_give isl_map *isl_map_deltas_map(
4470 __isl_take isl_map *map);
4471 __isl_give isl_union_map *isl_union_map_deltas_map(
4472 __isl_take isl_union_map *umap);
4474 The functions above construct a (basic, regular or union) relation
4475 that maps (a wrapped version of) the input relation to its delta set.
4479 Simplify the representation of a set, relation or functions by trying
4480 to combine pairs of basic sets or relations into a single
4481 basic set or relation.
4483 #include <isl/set.h>
4484 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4486 #include <isl/map.h>
4487 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4489 #include <isl/union_set.h>
4490 __isl_give isl_union_set *isl_union_set_coalesce(
4491 __isl_take isl_union_set *uset);
4493 #include <isl/union_map.h>
4494 __isl_give isl_union_map *isl_union_map_coalesce(
4495 __isl_take isl_union_map *umap);
4497 #include <isl/aff.h>
4498 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4499 __isl_take isl_pw_aff *pwqp);
4500 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4501 __isl_take isl_pw_multi_aff *pma);
4502 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4503 __isl_take isl_multi_pw_aff *mpa);
4504 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4505 __isl_take isl_union_pw_aff *upa);
4506 __isl_give isl_union_pw_multi_aff *
4507 isl_union_pw_multi_aff_coalesce(
4508 __isl_take isl_union_pw_multi_aff *upma);
4510 #include <isl/polynomial.h>
4511 __isl_give isl_pw_qpolynomial_fold *
4512 isl_pw_qpolynomial_fold_coalesce(
4513 __isl_take isl_pw_qpolynomial_fold *pwf);
4514 __isl_give isl_union_pw_qpolynomial *
4515 isl_union_pw_qpolynomial_coalesce(
4516 __isl_take isl_union_pw_qpolynomial *upwqp);
4517 __isl_give isl_union_pw_qpolynomial_fold *
4518 isl_union_pw_qpolynomial_fold_coalesce(
4519 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4521 One of the methods for combining pairs of basic sets or relations
4522 can result in coefficients that are much larger than those that appear
4523 in the constraints of the input. By default, the coefficients are
4524 not allowed to grow larger, but this can be changed by unsetting
4525 the following option.
4527 int isl_options_set_coalesce_bounded_wrapping(
4528 isl_ctx *ctx, int val);
4529 int isl_options_get_coalesce_bounded_wrapping(
4532 =item * Detecting equalities
4534 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4535 __isl_take isl_basic_set *bset);
4536 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4537 __isl_take isl_basic_map *bmap);
4538 __isl_give isl_set *isl_set_detect_equalities(
4539 __isl_take isl_set *set);
4540 __isl_give isl_map *isl_map_detect_equalities(
4541 __isl_take isl_map *map);
4542 __isl_give isl_union_set *isl_union_set_detect_equalities(
4543 __isl_take isl_union_set *uset);
4544 __isl_give isl_union_map *isl_union_map_detect_equalities(
4545 __isl_take isl_union_map *umap);
4547 Simplify the representation of a set or relation by detecting implicit
4550 =item * Removing redundant constraints
4552 #include <isl/set.h>
4553 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4554 __isl_take isl_basic_set *bset);
4555 __isl_give isl_set *isl_set_remove_redundancies(
4556 __isl_take isl_set *set);
4558 #include <isl/union_set.h>
4559 __isl_give isl_union_set *
4560 isl_union_set_remove_redundancies(
4561 __isl_take isl_union_set *uset);
4563 #include <isl/map.h>
4564 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4565 __isl_take isl_basic_map *bmap);
4566 __isl_give isl_map *isl_map_remove_redundancies(
4567 __isl_take isl_map *map);
4569 #include <isl/union_map.h>
4570 __isl_give isl_union_map *
4571 isl_union_map_remove_redundancies(
4572 __isl_take isl_union_map *umap);
4576 __isl_give isl_basic_set *isl_set_convex_hull(
4577 __isl_take isl_set *set);
4578 __isl_give isl_basic_map *isl_map_convex_hull(
4579 __isl_take isl_map *map);
4581 If the input set or relation has any existentially quantified
4582 variables, then the result of these operations is currently undefined.
4586 #include <isl/set.h>
4587 __isl_give isl_basic_set *
4588 isl_set_unshifted_simple_hull(
4589 __isl_take isl_set *set);
4590 __isl_give isl_basic_set *isl_set_simple_hull(
4591 __isl_take isl_set *set);
4592 __isl_give isl_basic_set *
4593 isl_set_unshifted_simple_hull_from_set_list(
4594 __isl_take isl_set *set,
4595 __isl_take isl_set_list *list);
4597 #include <isl/map.h>
4598 __isl_give isl_basic_map *
4599 isl_map_unshifted_simple_hull(
4600 __isl_take isl_map *map);
4601 __isl_give isl_basic_map *isl_map_simple_hull(
4602 __isl_take isl_map *map);
4603 __isl_give isl_basic_map *
4604 isl_map_unshifted_simple_hull_from_map_list(
4605 __isl_take isl_map *map,
4606 __isl_take isl_map_list *list);
4608 #include <isl/union_map.h>
4609 __isl_give isl_union_map *isl_union_map_simple_hull(
4610 __isl_take isl_union_map *umap);
4612 These functions compute a single basic set or relation
4613 that contains the whole input set or relation.
4614 In particular, the output is described by translates
4615 of the constraints describing the basic sets or relations in the input.
4616 In case of C<isl_set_unshifted_simple_hull>, only the original
4617 constraints are used, without any translation.
4618 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4619 C<isl_map_unshifted_simple_hull_from_map_list>, the
4620 constraints are taken from the elements of the second argument.
4624 (See \autoref{s:simple hull}.)
4630 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4631 __isl_take isl_basic_set *bset);
4632 __isl_give isl_basic_set *isl_set_affine_hull(
4633 __isl_take isl_set *set);
4634 __isl_give isl_union_set *isl_union_set_affine_hull(
4635 __isl_take isl_union_set *uset);
4636 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4637 __isl_take isl_basic_map *bmap);
4638 __isl_give isl_basic_map *isl_map_affine_hull(
4639 __isl_take isl_map *map);
4640 __isl_give isl_union_map *isl_union_map_affine_hull(
4641 __isl_take isl_union_map *umap);
4643 In case of union sets and relations, the affine hull is computed
4646 =item * Polyhedral hull
4648 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4649 __isl_take isl_set *set);
4650 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4651 __isl_take isl_map *map);
4652 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4653 __isl_take isl_union_set *uset);
4654 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4655 __isl_take isl_union_map *umap);
4657 These functions compute a single basic set or relation
4658 not involving any existentially quantified variables
4659 that contains the whole input set or relation.
4660 In case of union sets and relations, the polyhedral hull is computed
4663 =item * Other approximations
4665 #include <isl/set.h>
4666 __isl_give isl_basic_set *
4667 isl_basic_set_drop_constraints_involving_dims(
4668 __isl_take isl_basic_set *bset,
4669 enum isl_dim_type type,
4670 unsigned first, unsigned n);
4671 __isl_give isl_basic_set *
4672 isl_basic_set_drop_constraints_not_involving_dims(
4673 __isl_take isl_basic_set *bset,
4674 enum isl_dim_type type,
4675 unsigned first, unsigned n);
4676 __isl_give isl_set *
4677 isl_set_drop_constraints_involving_dims(
4678 __isl_take isl_set *set,
4679 enum isl_dim_type type,
4680 unsigned first, unsigned n);
4682 #include <isl/map.h>
4683 __isl_give isl_basic_map *
4684 isl_basic_map_drop_constraints_involving_dims(
4685 __isl_take isl_basic_map *bmap,
4686 enum isl_dim_type type,
4687 unsigned first, unsigned n);
4688 __isl_give isl_map *
4689 isl_map_drop_constraints_involving_dims(
4690 __isl_take isl_map *map,
4691 enum isl_dim_type type,
4692 unsigned first, unsigned n);
4694 These functions drop any constraints (not) involving the specified dimensions.
4695 Note that the result depends on the representation of the input.
4697 #include <isl/polynomial.h>
4698 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4699 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4700 __isl_give isl_union_pw_qpolynomial *
4701 isl_union_pw_qpolynomial_to_polynomial(
4702 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4704 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4705 the polynomial will be an overapproximation. If C<sign> is negative,
4706 it will be an underapproximation. If C<sign> is zero, the approximation
4707 will lie somewhere in between.
4711 __isl_give isl_basic_set *isl_basic_set_sample(
4712 __isl_take isl_basic_set *bset);
4713 __isl_give isl_basic_set *isl_set_sample(
4714 __isl_take isl_set *set);
4715 __isl_give isl_basic_map *isl_basic_map_sample(
4716 __isl_take isl_basic_map *bmap);
4717 __isl_give isl_basic_map *isl_map_sample(
4718 __isl_take isl_map *map);
4720 If the input (basic) set or relation is non-empty, then return
4721 a singleton subset of the input. Otherwise, return an empty set.
4723 =item * Optimization
4725 #include <isl/ilp.h>
4726 __isl_give isl_val *isl_basic_set_max_val(
4727 __isl_keep isl_basic_set *bset,
4728 __isl_keep isl_aff *obj);
4729 __isl_give isl_val *isl_set_min_val(
4730 __isl_keep isl_set *set,
4731 __isl_keep isl_aff *obj);
4732 __isl_give isl_val *isl_set_max_val(
4733 __isl_keep isl_set *set,
4734 __isl_keep isl_aff *obj);
4736 Compute the minimum or maximum of the integer affine expression C<obj>
4737 over the points in C<set>, returning the result in C<opt>.
4738 The result is C<NULL> in case of an error, the optimal value in case
4739 there is one, negative infinity or infinity if the problem is unbounded and
4740 NaN if the problem is empty.
4742 =item * Parametric optimization
4744 __isl_give isl_pw_aff *isl_set_dim_min(
4745 __isl_take isl_set *set, int pos);
4746 __isl_give isl_pw_aff *isl_set_dim_max(
4747 __isl_take isl_set *set, int pos);
4748 __isl_give isl_pw_aff *isl_map_dim_max(
4749 __isl_take isl_map *map, int pos);
4751 Compute the minimum or maximum of the given set or output dimension
4752 as a function of the parameters (and input dimensions), but independently
4753 of the other set or output dimensions.
4754 For lexicographic optimization, see L<"Lexicographic Optimization">.
4758 The following functions compute either the set of (rational) coefficient
4759 values of valid constraints for the given set or the set of (rational)
4760 values satisfying the constraints with coefficients from the given set.
4761 Internally, these two sets of functions perform essentially the
4762 same operations, except that the set of coefficients is assumed to
4763 be a cone, while the set of values may be any polyhedron.
4764 The current implementation is based on the Farkas lemma and
4765 Fourier-Motzkin elimination, but this may change or be made optional
4766 in future. In particular, future implementations may use different
4767 dualization algorithms or skip the elimination step.
4769 __isl_give isl_basic_set *isl_basic_set_coefficients(
4770 __isl_take isl_basic_set *bset);
4771 __isl_give isl_basic_set *isl_set_coefficients(
4772 __isl_take isl_set *set);
4773 __isl_give isl_union_set *isl_union_set_coefficients(
4774 __isl_take isl_union_set *bset);
4775 __isl_give isl_basic_set *isl_basic_set_solutions(
4776 __isl_take isl_basic_set *bset);
4777 __isl_give isl_basic_set *isl_set_solutions(
4778 __isl_take isl_set *set);
4779 __isl_give isl_union_set *isl_union_set_solutions(
4780 __isl_take isl_union_set *bset);
4784 __isl_give isl_map *isl_map_fixed_power_val(
4785 __isl_take isl_map *map,
4786 __isl_take isl_val *exp);
4787 __isl_give isl_union_map *
4788 isl_union_map_fixed_power_val(
4789 __isl_take isl_union_map *umap,
4790 __isl_take isl_val *exp);
4792 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4793 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4794 of C<map> is computed.
4796 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4798 __isl_give isl_union_map *isl_union_map_power(
4799 __isl_take isl_union_map *umap, int *exact);
4801 Compute a parametric representation for all positive powers I<k> of C<map>.
4802 The result maps I<k> to a nested relation corresponding to the
4803 I<k>th power of C<map>.
4804 The result may be an overapproximation. If the result is known to be exact,
4805 then C<*exact> is set to C<1>.
4807 =item * Transitive closure
4809 __isl_give isl_map *isl_map_transitive_closure(
4810 __isl_take isl_map *map, int *exact);
4811 __isl_give isl_union_map *isl_union_map_transitive_closure(
4812 __isl_take isl_union_map *umap, int *exact);
4814 Compute the transitive closure of C<map>.
4815 The result may be an overapproximation. If the result is known to be exact,
4816 then C<*exact> is set to C<1>.
4818 =item * Reaching path lengths
4820 __isl_give isl_map *isl_map_reaching_path_lengths(
4821 __isl_take isl_map *map, int *exact);
4823 Compute a relation that maps each element in the range of C<map>
4824 to the lengths of all paths composed of edges in C<map> that
4825 end up in the given element.
4826 The result may be an overapproximation. If the result is known to be exact,
4827 then C<*exact> is set to C<1>.
4828 To compute the I<maximal> path length, the resulting relation
4829 should be postprocessed by C<isl_map_lexmax>.
4830 In particular, if the input relation is a dependence relation
4831 (mapping sources to sinks), then the maximal path length corresponds
4832 to the free schedule.
4833 Note, however, that C<isl_map_lexmax> expects the maximum to be
4834 finite, so if the path lengths are unbounded (possibly due to
4835 the overapproximation), then you will get an error message.
4839 #include <isl/space.h>
4840 __isl_give isl_space *isl_space_wrap(
4841 __isl_take isl_space *space);
4842 __isl_give isl_space *isl_space_unwrap(
4843 __isl_take isl_space *space);
4845 #include <isl/local_space.h>
4846 __isl_give isl_local_space *isl_local_space_wrap(
4847 __isl_take isl_local_space *ls);
4849 #include <isl/set.h>
4850 __isl_give isl_basic_map *isl_basic_set_unwrap(
4851 __isl_take isl_basic_set *bset);
4852 __isl_give isl_map *isl_set_unwrap(
4853 __isl_take isl_set *set);
4855 #include <isl/map.h>
4856 __isl_give isl_basic_set *isl_basic_map_wrap(
4857 __isl_take isl_basic_map *bmap);
4858 __isl_give isl_set *isl_map_wrap(
4859 __isl_take isl_map *map);
4861 #include <isl/union_set.h>
4862 __isl_give isl_union_map *isl_union_set_unwrap(
4863 __isl_take isl_union_set *uset);
4865 #include <isl/union_map.h>
4866 __isl_give isl_union_set *isl_union_map_wrap(
4867 __isl_take isl_union_map *umap);
4869 The input to C<isl_space_unwrap> should
4870 be the space of a set, while that of
4871 C<isl_space_wrap> should be the space of a relation.
4872 Conversely, the output of C<isl_space_unwrap> is the space
4873 of a relation, while that of C<isl_space_wrap> is the space of a set.
4877 Remove any internal structure of domain (and range) of the given
4878 set or relation. If there is any such internal structure in the input,
4879 then the name of the space is also removed.
4881 #include <isl/local_space.h>
4882 __isl_give isl_local_space *
4883 isl_local_space_flatten_domain(
4884 __isl_take isl_local_space *ls);
4885 __isl_give isl_local_space *
4886 isl_local_space_flatten_range(
4887 __isl_take isl_local_space *ls);
4889 #include <isl/set.h>
4890 __isl_give isl_basic_set *isl_basic_set_flatten(
4891 __isl_take isl_basic_set *bset);
4892 __isl_give isl_set *isl_set_flatten(
4893 __isl_take isl_set *set);
4895 #include <isl/map.h>
4896 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4897 __isl_take isl_basic_map *bmap);
4898 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4899 __isl_take isl_basic_map *bmap);
4900 __isl_give isl_map *isl_map_flatten_range(
4901 __isl_take isl_map *map);
4902 __isl_give isl_map *isl_map_flatten_domain(
4903 __isl_take isl_map *map);
4904 __isl_give isl_basic_map *isl_basic_map_flatten(
4905 __isl_take isl_basic_map *bmap);
4906 __isl_give isl_map *isl_map_flatten(
4907 __isl_take isl_map *map);
4909 #include <isl/val.h>
4910 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4911 __isl_take isl_multi_val *mv);
4913 #include <isl/aff.h>
4914 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4915 __isl_take isl_multi_aff *ma);
4916 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4917 __isl_take isl_multi_aff *ma);
4918 __isl_give isl_multi_pw_aff *
4919 isl_multi_pw_aff_flatten_range(
4920 __isl_take isl_multi_pw_aff *mpa);
4921 __isl_give isl_multi_union_pw_aff *
4922 isl_multi_union_pw_aff_flatten_range(
4923 __isl_take isl_multi_union_pw_aff *mupa);
4925 #include <isl/map.h>
4926 __isl_give isl_map *isl_set_flatten_map(
4927 __isl_take isl_set *set);
4929 The function above constructs a relation
4930 that maps the input set to a flattened version of the set.
4934 Lift the input set to a space with extra dimensions corresponding
4935 to the existentially quantified variables in the input.
4936 In particular, the result lives in a wrapped map where the domain
4937 is the original space and the range corresponds to the original
4938 existentially quantified variables.
4940 #include <isl/set.h>
4941 __isl_give isl_basic_set *isl_basic_set_lift(
4942 __isl_take isl_basic_set *bset);
4943 __isl_give isl_set *isl_set_lift(
4944 __isl_take isl_set *set);
4945 __isl_give isl_union_set *isl_union_set_lift(
4946 __isl_take isl_union_set *uset);
4948 Given a local space that contains the existentially quantified
4949 variables of a set, a basic relation that, when applied to
4950 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4951 can be constructed using the following function.
4953 #include <isl/local_space.h>
4954 __isl_give isl_basic_map *isl_local_space_lifting(
4955 __isl_take isl_local_space *ls);
4957 #include <isl/aff.h>
4958 __isl_give isl_multi_aff *isl_multi_aff_lift(
4959 __isl_take isl_multi_aff *maff,
4960 __isl_give isl_local_space **ls);
4962 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4963 then it is assigned the local space that lies at the basis of
4964 the lifting applied.
4966 =item * Internal Product
4968 #include <isl/space.h>
4969 __isl_give isl_space *isl_space_zip(
4970 __isl_take isl_space *space);
4972 #include <isl/map.h>
4973 __isl_give isl_basic_map *isl_basic_map_zip(
4974 __isl_take isl_basic_map *bmap);
4975 __isl_give isl_map *isl_map_zip(
4976 __isl_take isl_map *map);
4978 #include <isl/union_map.h>
4979 __isl_give isl_union_map *isl_union_map_zip(
4980 __isl_take isl_union_map *umap);
4982 Given a relation with nested relations for domain and range,
4983 interchange the range of the domain with the domain of the range.
4987 #include <isl/space.h>
4988 __isl_give isl_space *isl_space_curry(
4989 __isl_take isl_space *space);
4990 __isl_give isl_space *isl_space_uncurry(
4991 __isl_take isl_space *space);
4993 #include <isl/map.h>
4994 __isl_give isl_basic_map *isl_basic_map_curry(
4995 __isl_take isl_basic_map *bmap);
4996 __isl_give isl_basic_map *isl_basic_map_uncurry(
4997 __isl_take isl_basic_map *bmap);
4998 __isl_give isl_map *isl_map_curry(
4999 __isl_take isl_map *map);
5000 __isl_give isl_map *isl_map_uncurry(
5001 __isl_take isl_map *map);
5003 #include <isl/union_map.h>
5004 __isl_give isl_union_map *isl_union_map_curry(
5005 __isl_take isl_union_map *umap);
5006 __isl_give isl_union_map *isl_union_map_uncurry(
5007 __isl_take isl_union_map *umap);
5009 Given a relation with a nested relation for domain,
5010 the C<curry> functions
5011 move the range of the nested relation out of the domain
5012 and use it as the domain of a nested relation in the range,
5013 with the original range as range of this nested relation.
5014 The C<uncurry> functions perform the inverse operation.
5016 =item * Aligning parameters
5018 Change the order of the parameters of the given set, relation
5020 such that the first parameters match those of C<model>.
5021 This may involve the introduction of extra parameters.
5022 All parameters need to be named.
5024 #include <isl/space.h>
5025 __isl_give isl_space *isl_space_align_params(
5026 __isl_take isl_space *space1,
5027 __isl_take isl_space *space2)
5029 #include <isl/set.h>
5030 __isl_give isl_basic_set *isl_basic_set_align_params(
5031 __isl_take isl_basic_set *bset,
5032 __isl_take isl_space *model);
5033 __isl_give isl_set *isl_set_align_params(
5034 __isl_take isl_set *set,
5035 __isl_take isl_space *model);
5037 #include <isl/map.h>
5038 __isl_give isl_basic_map *isl_basic_map_align_params(
5039 __isl_take isl_basic_map *bmap,
5040 __isl_take isl_space *model);
5041 __isl_give isl_map *isl_map_align_params(
5042 __isl_take isl_map *map,
5043 __isl_take isl_space *model);
5045 #include <isl/val.h>
5046 __isl_give isl_multi_val *isl_multi_val_align_params(
5047 __isl_take isl_multi_val *mv,
5048 __isl_take isl_space *model);
5050 #include <isl/aff.h>
5051 __isl_give isl_aff *isl_aff_align_params(
5052 __isl_take isl_aff *aff,
5053 __isl_take isl_space *model);
5054 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5055 __isl_take isl_multi_aff *multi,
5056 __isl_take isl_space *model);
5057 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5058 __isl_take isl_pw_aff *pwaff,
5059 __isl_take isl_space *model);
5060 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5061 __isl_take isl_pw_multi_aff *pma,
5062 __isl_take isl_space *model);
5063 __isl_give isl_union_pw_aff *
5064 isl_union_pw_aff_align_params(
5065 __isl_take isl_union_pw_aff *upa,
5066 __isl_take isl_space *model);
5067 __isl_give isl_union_pw_multi_aff *
5068 isl_union_pw_multi_aff_align_params(
5069 __isl_take isl_union_pw_multi_aff *upma,
5070 __isl_take isl_space *model);
5071 __isl_give isl_multi_union_pw_aff *
5072 isl_multi_union_pw_aff_align_params(
5073 __isl_take isl_multi_union_pw_aff *mupa,
5074 __isl_take isl_space *model);
5076 #include <isl/polynomial.h>
5077 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5078 __isl_take isl_qpolynomial *qp,
5079 __isl_take isl_space *model);
5081 =item * Unary Arithmethic Operations
5083 #include <isl/val.h>
5084 __isl_give isl_multi_val *isl_multi_val_neg(
5085 __isl_take isl_multi_val *mv);
5087 #include <isl/aff.h>
5088 __isl_give isl_aff *isl_aff_neg(
5089 __isl_take isl_aff *aff);
5090 __isl_give isl_multi_aff *isl_multi_aff_neg(
5091 __isl_take isl_multi_aff *ma);
5092 __isl_give isl_pw_aff *isl_pw_aff_neg(
5093 __isl_take isl_pw_aff *pwaff);
5094 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5095 __isl_take isl_pw_multi_aff *pma);
5096 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5097 __isl_take isl_multi_pw_aff *mpa);
5098 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5099 __isl_take isl_union_pw_aff *upa);
5100 __isl_give isl_union_pw_multi_aff *
5101 isl_union_pw_multi_aff_neg(
5102 __isl_take isl_union_pw_multi_aff *upma);
5103 __isl_give isl_multi_union_pw_aff *
5104 isl_multi_union_pw_aff_neg(
5105 __isl_take isl_multi_union_pw_aff *mupa);
5106 __isl_give isl_aff *isl_aff_ceil(
5107 __isl_take isl_aff *aff);
5108 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5109 __isl_take isl_pw_aff *pwaff);
5110 __isl_give isl_aff *isl_aff_floor(
5111 __isl_take isl_aff *aff);
5112 __isl_give isl_multi_aff *isl_multi_aff_floor(
5113 __isl_take isl_multi_aff *ma);
5114 __isl_give isl_pw_aff *isl_pw_aff_floor(
5115 __isl_take isl_pw_aff *pwaff);
5116 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5117 __isl_take isl_union_pw_aff *upa);
5118 __isl_give isl_multi_union_pw_aff *
5119 isl_multi_union_pw_aff_floor(
5120 __isl_take isl_multi_union_pw_aff *mupa);
5122 #include <isl/aff.h>
5123 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5124 __isl_take isl_pw_aff_list *list);
5125 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5126 __isl_take isl_pw_aff_list *list);
5128 #include <isl/polynomial.h>
5129 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5130 __isl_take isl_qpolynomial *qp);
5131 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5132 __isl_take isl_pw_qpolynomial *pwqp);
5133 __isl_give isl_union_pw_qpolynomial *
5134 isl_union_pw_qpolynomial_neg(
5135 __isl_take isl_union_pw_qpolynomial *upwqp);
5136 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5137 __isl_take isl_qpolynomial *qp,
5139 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5140 __isl_take isl_pw_qpolynomial *pwqp,
5145 The following functions evaluate a function in a point.
5147 #include <isl/polynomial.h>
5148 __isl_give isl_val *isl_pw_qpolynomial_eval(
5149 __isl_take isl_pw_qpolynomial *pwqp,
5150 __isl_take isl_point *pnt);
5151 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5152 __isl_take isl_pw_qpolynomial_fold *pwf,
5153 __isl_take isl_point *pnt);
5154 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5155 __isl_take isl_union_pw_qpolynomial *upwqp,
5156 __isl_take isl_point *pnt);
5157 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5158 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5159 __isl_take isl_point *pnt);
5161 =item * Dimension manipulation
5163 It is usually not advisable to directly change the (input or output)
5164 space of a set or a relation as this removes the name and the internal
5165 structure of the space. However, the functions below can be useful
5166 to add new parameters, assuming
5167 C<isl_set_align_params> and C<isl_map_align_params>
5170 #include <isl/space.h>
5171 __isl_give isl_space *isl_space_add_dims(
5172 __isl_take isl_space *space,
5173 enum isl_dim_type type, unsigned n);
5174 __isl_give isl_space *isl_space_insert_dims(
5175 __isl_take isl_space *space,
5176 enum isl_dim_type type, unsigned pos, unsigned n);
5177 __isl_give isl_space *isl_space_drop_dims(
5178 __isl_take isl_space *space,
5179 enum isl_dim_type type, unsigned first, unsigned n);
5180 __isl_give isl_space *isl_space_move_dims(
5181 __isl_take isl_space *space,
5182 enum isl_dim_type dst_type, unsigned dst_pos,
5183 enum isl_dim_type src_type, unsigned src_pos,
5186 #include <isl/local_space.h>
5187 __isl_give isl_local_space *isl_local_space_add_dims(
5188 __isl_take isl_local_space *ls,
5189 enum isl_dim_type type, unsigned n);
5190 __isl_give isl_local_space *isl_local_space_insert_dims(
5191 __isl_take isl_local_space *ls,
5192 enum isl_dim_type type, unsigned first, unsigned n);
5193 __isl_give isl_local_space *isl_local_space_drop_dims(
5194 __isl_take isl_local_space *ls,
5195 enum isl_dim_type type, unsigned first, unsigned n);
5197 #include <isl/set.h>
5198 __isl_give isl_basic_set *isl_basic_set_add_dims(
5199 __isl_take isl_basic_set *bset,
5200 enum isl_dim_type type, unsigned n);
5201 __isl_give isl_set *isl_set_add_dims(
5202 __isl_take isl_set *set,
5203 enum isl_dim_type type, unsigned n);
5204 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5205 __isl_take isl_basic_set *bset,
5206 enum isl_dim_type type, unsigned pos,
5208 __isl_give isl_set *isl_set_insert_dims(
5209 __isl_take isl_set *set,
5210 enum isl_dim_type type, unsigned pos, unsigned n);
5211 __isl_give isl_basic_set *isl_basic_set_move_dims(
5212 __isl_take isl_basic_set *bset,
5213 enum isl_dim_type dst_type, unsigned dst_pos,
5214 enum isl_dim_type src_type, unsigned src_pos,
5216 __isl_give isl_set *isl_set_move_dims(
5217 __isl_take isl_set *set,
5218 enum isl_dim_type dst_type, unsigned dst_pos,
5219 enum isl_dim_type src_type, unsigned src_pos,
5222 #include <isl/map.h>
5223 __isl_give isl_map *isl_map_add_dims(
5224 __isl_take isl_map *map,
5225 enum isl_dim_type type, unsigned n);
5226 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5227 __isl_take isl_basic_map *bmap,
5228 enum isl_dim_type type, unsigned pos,
5230 __isl_give isl_map *isl_map_insert_dims(
5231 __isl_take isl_map *map,
5232 enum isl_dim_type type, unsigned pos, unsigned n);
5233 __isl_give isl_basic_map *isl_basic_map_move_dims(
5234 __isl_take isl_basic_map *bmap,
5235 enum isl_dim_type dst_type, unsigned dst_pos,
5236 enum isl_dim_type src_type, unsigned src_pos,
5238 __isl_give isl_map *isl_map_move_dims(
5239 __isl_take isl_map *map,
5240 enum isl_dim_type dst_type, unsigned dst_pos,
5241 enum isl_dim_type src_type, unsigned src_pos,
5244 #include <isl/val.h>
5245 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5246 __isl_take isl_multi_val *mv,
5247 enum isl_dim_type type, unsigned first, unsigned n);
5248 __isl_give isl_multi_val *isl_multi_val_add_dims(
5249 __isl_take isl_multi_val *mv,
5250 enum isl_dim_type type, unsigned n);
5251 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5252 __isl_take isl_multi_val *mv,
5253 enum isl_dim_type type, unsigned first, unsigned n);
5255 #include <isl/aff.h>
5256 __isl_give isl_aff *isl_aff_insert_dims(
5257 __isl_take isl_aff *aff,
5258 enum isl_dim_type type, unsigned first, unsigned n);
5259 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5260 __isl_take isl_multi_aff *ma,
5261 enum isl_dim_type type, unsigned first, unsigned n);
5262 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5263 __isl_take isl_pw_aff *pwaff,
5264 enum isl_dim_type type, unsigned first, unsigned n);
5265 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5266 __isl_take isl_multi_pw_aff *mpa,
5267 enum isl_dim_type type, unsigned first, unsigned n);
5268 __isl_give isl_aff *isl_aff_add_dims(
5269 __isl_take isl_aff *aff,
5270 enum isl_dim_type type, unsigned n);
5271 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5272 __isl_take isl_multi_aff *ma,
5273 enum isl_dim_type type, unsigned n);
5274 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5275 __isl_take isl_pw_aff *pwaff,
5276 enum isl_dim_type type, unsigned n);
5277 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5278 __isl_take isl_multi_pw_aff *mpa,
5279 enum isl_dim_type type, unsigned n);
5280 __isl_give isl_aff *isl_aff_drop_dims(
5281 __isl_take isl_aff *aff,
5282 enum isl_dim_type type, unsigned first, unsigned n);
5283 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5284 __isl_take isl_multi_aff *maff,
5285 enum isl_dim_type type, unsigned first, unsigned n);
5286 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5287 __isl_take isl_pw_aff *pwaff,
5288 enum isl_dim_type type, unsigned first, unsigned n);
5289 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5290 __isl_take isl_pw_multi_aff *pma,
5291 enum isl_dim_type type, unsigned first, unsigned n);
5292 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5293 __isl_take isl_union_pw_aff *upa,
5294 enum isl_dim_type type, unsigned first, unsigned n);
5295 __isl_give isl_union_pw_multi_aff *
5296 isl_union_pw_multi_aff_drop_dims(
5297 __isl_take isl_union_pw_multi_aff *upma,
5298 enum isl_dim_type type,
5299 unsigned first, unsigned n);
5300 __isl_give isl_multi_union_pw_aff *
5301 isl_multi_union_pw_aff_drop_dims(
5302 __isl_take isl_multi_union_pw_aff *mupa,
5303 enum isl_dim_type type, unsigned first,
5305 __isl_give isl_aff *isl_aff_move_dims(
5306 __isl_take isl_aff *aff,
5307 enum isl_dim_type dst_type, unsigned dst_pos,
5308 enum isl_dim_type src_type, unsigned src_pos,
5310 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5311 __isl_take isl_multi_aff *ma,
5312 enum isl_dim_type dst_type, unsigned dst_pos,
5313 enum isl_dim_type src_type, unsigned src_pos,
5315 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5316 __isl_take isl_pw_aff *pa,
5317 enum isl_dim_type dst_type, unsigned dst_pos,
5318 enum isl_dim_type src_type, unsigned src_pos,
5320 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5321 __isl_take isl_multi_pw_aff *pma,
5322 enum isl_dim_type dst_type, unsigned dst_pos,
5323 enum isl_dim_type src_type, unsigned src_pos,
5326 #include <isl/polynomial.h>
5327 __isl_give isl_union_pw_qpolynomial *
5328 isl_union_pw_qpolynomial_drop_dims(
5329 __isl_take isl_union_pw_qpolynomial *upwqp,
5330 enum isl_dim_type type,
5331 unsigned first, unsigned n);
5332 __isl_give isl_union_pw_qpolynomial_fold *
5333 isl_union_pw_qpolynomial_fold_drop_dims(
5334 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5335 enum isl_dim_type type,
5336 unsigned first, unsigned n);
5338 The operations on union expressions can only manipulate parameters.
5342 =head2 Binary Operations
5344 The two arguments of a binary operation not only need to live
5345 in the same C<isl_ctx>, they currently also need to have
5346 the same (number of) parameters.
5348 =head3 Basic Operations
5352 =item * Intersection
5354 #include <isl/local_space.h>
5355 __isl_give isl_local_space *isl_local_space_intersect(
5356 __isl_take isl_local_space *ls1,
5357 __isl_take isl_local_space *ls2);
5359 #include <isl/set.h>
5360 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5361 __isl_take isl_basic_set *bset1,
5362 __isl_take isl_basic_set *bset2);
5363 __isl_give isl_basic_set *isl_basic_set_intersect(
5364 __isl_take isl_basic_set *bset1,
5365 __isl_take isl_basic_set *bset2);
5366 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5367 __isl_take struct isl_basic_set_list *list);
5368 __isl_give isl_set *isl_set_intersect_params(
5369 __isl_take isl_set *set,
5370 __isl_take isl_set *params);
5371 __isl_give isl_set *isl_set_intersect(
5372 __isl_take isl_set *set1,
5373 __isl_take isl_set *set2);
5375 #include <isl/map.h>
5376 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5377 __isl_take isl_basic_map *bmap,
5378 __isl_take isl_basic_set *bset);
5379 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5380 __isl_take isl_basic_map *bmap,
5381 __isl_take isl_basic_set *bset);
5382 __isl_give isl_basic_map *isl_basic_map_intersect(
5383 __isl_take isl_basic_map *bmap1,
5384 __isl_take isl_basic_map *bmap2);
5385 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5386 __isl_take isl_basic_map_list *list);
5387 __isl_give isl_map *isl_map_intersect_params(
5388 __isl_take isl_map *map,
5389 __isl_take isl_set *params);
5390 __isl_give isl_map *isl_map_intersect_domain(
5391 __isl_take isl_map *map,
5392 __isl_take isl_set *set);
5393 __isl_give isl_map *isl_map_intersect_range(
5394 __isl_take isl_map *map,
5395 __isl_take isl_set *set);
5396 __isl_give isl_map *isl_map_intersect(
5397 __isl_take isl_map *map1,
5398 __isl_take isl_map *map2);
5400 #include <isl/union_set.h>
5401 __isl_give isl_union_set *isl_union_set_intersect_params(
5402 __isl_take isl_union_set *uset,
5403 __isl_take isl_set *set);
5404 __isl_give isl_union_set *isl_union_set_intersect(
5405 __isl_take isl_union_set *uset1,
5406 __isl_take isl_union_set *uset2);
5408 #include <isl/union_map.h>
5409 __isl_give isl_union_map *isl_union_map_intersect_params(
5410 __isl_take isl_union_map *umap,
5411 __isl_take isl_set *set);
5412 __isl_give isl_union_map *isl_union_map_intersect_domain(
5413 __isl_take isl_union_map *umap,
5414 __isl_take isl_union_set *uset);
5415 __isl_give isl_union_map *isl_union_map_intersect_range(
5416 __isl_take isl_union_map *umap,
5417 __isl_take isl_union_set *uset);
5418 __isl_give isl_union_map *isl_union_map_intersect(
5419 __isl_take isl_union_map *umap1,
5420 __isl_take isl_union_map *umap2);
5422 #include <isl/aff.h>
5423 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5424 __isl_take isl_pw_aff *pa,
5425 __isl_take isl_set *set);
5426 __isl_give isl_multi_pw_aff *
5427 isl_multi_pw_aff_intersect_domain(
5428 __isl_take isl_multi_pw_aff *mpa,
5429 __isl_take isl_set *domain);
5430 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5431 __isl_take isl_pw_multi_aff *pma,
5432 __isl_take isl_set *set);
5433 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5434 __isl_take isl_union_pw_aff *upa,
5435 __isl_take isl_union_set *uset);
5436 __isl_give isl_union_pw_multi_aff *
5437 isl_union_pw_multi_aff_intersect_domain(
5438 __isl_take isl_union_pw_multi_aff *upma,
5439 __isl_take isl_union_set *uset);
5440 __isl_give isl_multi_union_pw_aff *
5441 isl_multi_union_pw_aff_intersect_domain(
5442 __isl_take isl_multi_union_pw_aff *mupa,
5443 __isl_take isl_union_set *uset);
5444 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5445 __isl_take isl_pw_aff *pa,
5446 __isl_take isl_set *set);
5447 __isl_give isl_multi_pw_aff *
5448 isl_multi_pw_aff_intersect_params(
5449 __isl_take isl_multi_pw_aff *mpa,
5450 __isl_take isl_set *set);
5451 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5452 __isl_take isl_pw_multi_aff *pma,
5453 __isl_take isl_set *set);
5454 __isl_give isl_union_pw_aff *
5455 isl_union_pw_aff_intersect_params(
5456 __isl_take isl_union_pw_aff *upa,
5457 __isl_give isl_union_pw_multi_aff *
5458 isl_union_pw_multi_aff_intersect_params(
5459 __isl_take isl_union_pw_multi_aff *upma,
5460 __isl_take isl_set *set);
5461 __isl_give isl_multi_union_pw_aff *
5462 isl_multi_union_pw_aff_intersect_params(
5463 __isl_take isl_multi_union_pw_aff *mupa,
5464 __isl_take isl_set *params);
5465 isl_multi_union_pw_aff_intersect_range(
5466 __isl_take isl_multi_union_pw_aff *mupa,
5467 __isl_take isl_set *set);
5469 #include <isl/polynomial.h>
5470 __isl_give isl_pw_qpolynomial *
5471 isl_pw_qpolynomial_intersect_domain(
5472 __isl_take isl_pw_qpolynomial *pwpq,
5473 __isl_take isl_set *set);
5474 __isl_give isl_union_pw_qpolynomial *
5475 isl_union_pw_qpolynomial_intersect_domain(
5476 __isl_take isl_union_pw_qpolynomial *upwpq,
5477 __isl_take isl_union_set *uset);
5478 __isl_give isl_union_pw_qpolynomial_fold *
5479 isl_union_pw_qpolynomial_fold_intersect_domain(
5480 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5481 __isl_take isl_union_set *uset);
5482 __isl_give isl_pw_qpolynomial *
5483 isl_pw_qpolynomial_intersect_params(
5484 __isl_take isl_pw_qpolynomial *pwpq,
5485 __isl_take isl_set *set);
5486 __isl_give isl_pw_qpolynomial_fold *
5487 isl_pw_qpolynomial_fold_intersect_params(
5488 __isl_take isl_pw_qpolynomial_fold *pwf,
5489 __isl_take isl_set *set);
5490 __isl_give isl_union_pw_qpolynomial *
5491 isl_union_pw_qpolynomial_intersect_params(
5492 __isl_take isl_union_pw_qpolynomial *upwpq,
5493 __isl_take isl_set *set);
5494 __isl_give isl_union_pw_qpolynomial_fold *
5495 isl_union_pw_qpolynomial_fold_intersect_params(
5496 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5497 __isl_take isl_set *set);
5499 The second argument to the C<_params> functions needs to be
5500 a parametric (basic) set. For the other functions, a parametric set
5501 for either argument is only allowed if the other argument is
5502 a parametric set as well.
5503 The list passed to C<isl_basic_set_list_intersect> needs to have
5504 at least one element and all elements need to live in the same space.
5505 The function C<isl_multi_union_pw_aff_intersect_range>
5506 restricts the input function to those shared domain elements
5507 that map to the specified range.
5511 #include <isl/set.h>
5512 __isl_give isl_set *isl_basic_set_union(
5513 __isl_take isl_basic_set *bset1,
5514 __isl_take isl_basic_set *bset2);
5515 __isl_give isl_set *isl_set_union(
5516 __isl_take isl_set *set1,
5517 __isl_take isl_set *set2);
5519 #include <isl/map.h>
5520 __isl_give isl_map *isl_basic_map_union(
5521 __isl_take isl_basic_map *bmap1,
5522 __isl_take isl_basic_map *bmap2);
5523 __isl_give isl_map *isl_map_union(
5524 __isl_take isl_map *map1,
5525 __isl_take isl_map *map2);
5527 #include <isl/union_set.h>
5528 __isl_give isl_union_set *isl_union_set_union(
5529 __isl_take isl_union_set *uset1,
5530 __isl_take isl_union_set *uset2);
5531 __isl_give isl_union_set *isl_union_set_list_union(
5532 __isl_take isl_union_set_list *list);
5534 #include <isl/union_map.h>
5535 __isl_give isl_union_map *isl_union_map_union(
5536 __isl_take isl_union_map *umap1,
5537 __isl_take isl_union_map *umap2);
5539 =item * Set difference
5541 #include <isl/set.h>
5542 __isl_give isl_set *isl_set_subtract(
5543 __isl_take isl_set *set1,
5544 __isl_take isl_set *set2);
5546 #include <isl/map.h>
5547 __isl_give isl_map *isl_map_subtract(
5548 __isl_take isl_map *map1,
5549 __isl_take isl_map *map2);
5550 __isl_give isl_map *isl_map_subtract_domain(
5551 __isl_take isl_map *map,
5552 __isl_take isl_set *dom);
5553 __isl_give isl_map *isl_map_subtract_range(
5554 __isl_take isl_map *map,
5555 __isl_take isl_set *dom);
5557 #include <isl/union_set.h>
5558 __isl_give isl_union_set *isl_union_set_subtract(
5559 __isl_take isl_union_set *uset1,
5560 __isl_take isl_union_set *uset2);
5562 #include <isl/union_map.h>
5563 __isl_give isl_union_map *isl_union_map_subtract(
5564 __isl_take isl_union_map *umap1,
5565 __isl_take isl_union_map *umap2);
5566 __isl_give isl_union_map *isl_union_map_subtract_domain(
5567 __isl_take isl_union_map *umap,
5568 __isl_take isl_union_set *dom);
5569 __isl_give isl_union_map *isl_union_map_subtract_range(
5570 __isl_take isl_union_map *umap,
5571 __isl_take isl_union_set *dom);
5573 #include <isl/aff.h>
5574 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5575 __isl_take isl_pw_aff *pa,
5576 __isl_take isl_set *set);
5577 __isl_give isl_pw_multi_aff *
5578 isl_pw_multi_aff_subtract_domain(
5579 __isl_take isl_pw_multi_aff *pma,
5580 __isl_take isl_set *set);
5581 __isl_give isl_union_pw_aff *
5582 isl_union_pw_aff_subtract_domain(
5583 __isl_take isl_union_pw_aff *upa,
5584 __isl_take isl_union_set *uset);
5585 __isl_give isl_union_pw_multi_aff *
5586 isl_union_pw_multi_aff_subtract_domain(
5587 __isl_take isl_union_pw_multi_aff *upma,
5588 __isl_take isl_set *set);
5590 #include <isl/polynomial.h>
5591 __isl_give isl_pw_qpolynomial *
5592 isl_pw_qpolynomial_subtract_domain(
5593 __isl_take isl_pw_qpolynomial *pwpq,
5594 __isl_take isl_set *set);
5595 __isl_give isl_pw_qpolynomial_fold *
5596 isl_pw_qpolynomial_fold_subtract_domain(
5597 __isl_take isl_pw_qpolynomial_fold *pwf,
5598 __isl_take isl_set *set);
5599 __isl_give isl_union_pw_qpolynomial *
5600 isl_union_pw_qpolynomial_subtract_domain(
5601 __isl_take isl_union_pw_qpolynomial *upwpq,
5602 __isl_take isl_union_set *uset);
5603 __isl_give isl_union_pw_qpolynomial_fold *
5604 isl_union_pw_qpolynomial_fold_subtract_domain(
5605 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5606 __isl_take isl_union_set *uset);
5610 #include <isl/space.h>
5611 __isl_give isl_space *isl_space_join(
5612 __isl_take isl_space *left,
5613 __isl_take isl_space *right);
5615 #include <isl/map.h>
5616 __isl_give isl_basic_set *isl_basic_set_apply(
5617 __isl_take isl_basic_set *bset,
5618 __isl_take isl_basic_map *bmap);
5619 __isl_give isl_set *isl_set_apply(
5620 __isl_take isl_set *set,
5621 __isl_take isl_map *map);
5622 __isl_give isl_union_set *isl_union_set_apply(
5623 __isl_take isl_union_set *uset,
5624 __isl_take isl_union_map *umap);
5625 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5626 __isl_take isl_basic_map *bmap1,
5627 __isl_take isl_basic_map *bmap2);
5628 __isl_give isl_basic_map *isl_basic_map_apply_range(
5629 __isl_take isl_basic_map *bmap1,
5630 __isl_take isl_basic_map *bmap2);
5631 __isl_give isl_map *isl_map_apply_domain(
5632 __isl_take isl_map *map1,
5633 __isl_take isl_map *map2);
5634 __isl_give isl_map *isl_map_apply_range(
5635 __isl_take isl_map *map1,
5636 __isl_take isl_map *map2);
5638 #include <isl/union_map.h>
5639 __isl_give isl_union_map *isl_union_map_apply_domain(
5640 __isl_take isl_union_map *umap1,
5641 __isl_take isl_union_map *umap2);
5642 __isl_give isl_union_map *isl_union_map_apply_range(
5643 __isl_take isl_union_map *umap1,
5644 __isl_take isl_union_map *umap2);
5646 #include <isl/aff.h>
5647 __isl_give isl_union_pw_aff *
5648 isl_multi_union_pw_aff_apply_aff(
5649 __isl_take isl_multi_union_pw_aff *mupa,
5650 __isl_take isl_aff *aff);
5651 __isl_give isl_union_pw_aff *
5652 isl_multi_union_pw_aff_apply_pw_aff(
5653 __isl_take isl_multi_union_pw_aff *mupa,
5654 __isl_take isl_pw_aff *pa);
5655 __isl_give isl_multi_union_pw_aff *
5656 isl_multi_union_pw_aff_apply_multi_aff(
5657 __isl_take isl_multi_union_pw_aff *mupa,
5658 __isl_take isl_multi_aff *ma);
5659 __isl_give isl_multi_union_pw_aff *
5660 isl_multi_union_pw_aff_apply_pw_multi_aff(
5661 __isl_take isl_multi_union_pw_aff *mupa,
5662 __isl_take isl_pw_multi_aff *pma);
5664 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5665 over the shared domain of the elements of the input. The dimension is
5666 required to be greater than zero.
5667 The C<isl_multi_union_pw_aff> argument of
5668 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5669 but only if the range of the C<isl_multi_aff> argument
5670 is also zero-dimensional.
5671 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5673 #include <isl/polynomial.h>
5674 __isl_give isl_pw_qpolynomial_fold *
5675 isl_set_apply_pw_qpolynomial_fold(
5676 __isl_take isl_set *set,
5677 __isl_take isl_pw_qpolynomial_fold *pwf,
5679 __isl_give isl_pw_qpolynomial_fold *
5680 isl_map_apply_pw_qpolynomial_fold(
5681 __isl_take isl_map *map,
5682 __isl_take isl_pw_qpolynomial_fold *pwf,
5684 __isl_give isl_union_pw_qpolynomial_fold *
5685 isl_union_set_apply_union_pw_qpolynomial_fold(
5686 __isl_take isl_union_set *uset,
5687 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5689 __isl_give isl_union_pw_qpolynomial_fold *
5690 isl_union_map_apply_union_pw_qpolynomial_fold(
5691 __isl_take isl_union_map *umap,
5692 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5695 The functions taking a map
5696 compose the given map with the given piecewise quasipolynomial reduction.
5697 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5698 over all elements in the intersection of the range of the map
5699 and the domain of the piecewise quasipolynomial reduction
5700 as a function of an element in the domain of the map.
5701 The functions taking a set compute a bound over all elements in the
5702 intersection of the set and the domain of the
5703 piecewise quasipolynomial reduction.
5707 #include <isl/set.h>
5708 __isl_give isl_basic_set *
5709 isl_basic_set_preimage_multi_aff(
5710 __isl_take isl_basic_set *bset,
5711 __isl_take isl_multi_aff *ma);
5712 __isl_give isl_set *isl_set_preimage_multi_aff(
5713 __isl_take isl_set *set,
5714 __isl_take isl_multi_aff *ma);
5715 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5716 __isl_take isl_set *set,
5717 __isl_take isl_pw_multi_aff *pma);
5718 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5719 __isl_take isl_set *set,
5720 __isl_take isl_multi_pw_aff *mpa);
5722 #include <isl/union_set.h>
5723 __isl_give isl_union_set *
5724 isl_union_set_preimage_multi_aff(
5725 __isl_take isl_union_set *uset,
5726 __isl_take isl_multi_aff *ma);
5727 __isl_give isl_union_set *
5728 isl_union_set_preimage_pw_multi_aff(
5729 __isl_take isl_union_set *uset,
5730 __isl_take isl_pw_multi_aff *pma);
5731 __isl_give isl_union_set *
5732 isl_union_set_preimage_union_pw_multi_aff(
5733 __isl_take isl_union_set *uset,
5734 __isl_take isl_union_pw_multi_aff *upma);
5736 #include <isl/map.h>
5737 __isl_give isl_basic_map *
5738 isl_basic_map_preimage_domain_multi_aff(
5739 __isl_take isl_basic_map *bmap,
5740 __isl_take isl_multi_aff *ma);
5741 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5742 __isl_take isl_map *map,
5743 __isl_take isl_multi_aff *ma);
5744 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5745 __isl_take isl_map *map,
5746 __isl_take isl_multi_aff *ma);
5747 __isl_give isl_map *
5748 isl_map_preimage_domain_pw_multi_aff(
5749 __isl_take isl_map *map,
5750 __isl_take isl_pw_multi_aff *pma);
5751 __isl_give isl_map *
5752 isl_map_preimage_range_pw_multi_aff(
5753 __isl_take isl_map *map,
5754 __isl_take isl_pw_multi_aff *pma);
5755 __isl_give isl_map *
5756 isl_map_preimage_domain_multi_pw_aff(
5757 __isl_take isl_map *map,
5758 __isl_take isl_multi_pw_aff *mpa);
5759 __isl_give isl_basic_map *
5760 isl_basic_map_preimage_range_multi_aff(
5761 __isl_take isl_basic_map *bmap,
5762 __isl_take isl_multi_aff *ma);
5764 #include <isl/union_map.h>
5765 __isl_give isl_union_map *
5766 isl_union_map_preimage_domain_multi_aff(
5767 __isl_take isl_union_map *umap,
5768 __isl_take isl_multi_aff *ma);
5769 __isl_give isl_union_map *
5770 isl_union_map_preimage_range_multi_aff(
5771 __isl_take isl_union_map *umap,
5772 __isl_take isl_multi_aff *ma);
5773 __isl_give isl_union_map *
5774 isl_union_map_preimage_domain_pw_multi_aff(
5775 __isl_take isl_union_map *umap,
5776 __isl_take isl_pw_multi_aff *pma);
5777 __isl_give isl_union_map *
5778 isl_union_map_preimage_range_pw_multi_aff(
5779 __isl_take isl_union_map *umap,
5780 __isl_take isl_pw_multi_aff *pma);
5781 __isl_give isl_union_map *
5782 isl_union_map_preimage_domain_union_pw_multi_aff(
5783 __isl_take isl_union_map *umap,
5784 __isl_take isl_union_pw_multi_aff *upma);
5785 __isl_give isl_union_map *
5786 isl_union_map_preimage_range_union_pw_multi_aff(
5787 __isl_take isl_union_map *umap,
5788 __isl_take isl_union_pw_multi_aff *upma);
5790 These functions compute the preimage of the given set or map domain/range under
5791 the given function. In other words, the expression is plugged
5792 into the set description or into the domain/range of the map.
5796 #include <isl/aff.h>
5797 __isl_give isl_aff *isl_aff_pullback_aff(
5798 __isl_take isl_aff *aff1,
5799 __isl_take isl_aff *aff2);
5800 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5801 __isl_take isl_aff *aff,
5802 __isl_take isl_multi_aff *ma);
5803 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5804 __isl_take isl_pw_aff *pa,
5805 __isl_take isl_multi_aff *ma);
5806 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5807 __isl_take isl_pw_aff *pa,
5808 __isl_take isl_pw_multi_aff *pma);
5809 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5810 __isl_take isl_pw_aff *pa,
5811 __isl_take isl_multi_pw_aff *mpa);
5812 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5813 __isl_take isl_multi_aff *ma1,
5814 __isl_take isl_multi_aff *ma2);
5815 __isl_give isl_pw_multi_aff *
5816 isl_pw_multi_aff_pullback_multi_aff(
5817 __isl_take isl_pw_multi_aff *pma,
5818 __isl_take isl_multi_aff *ma);
5819 __isl_give isl_multi_pw_aff *
5820 isl_multi_pw_aff_pullback_multi_aff(
5821 __isl_take isl_multi_pw_aff *mpa,
5822 __isl_take isl_multi_aff *ma);
5823 __isl_give isl_pw_multi_aff *
5824 isl_pw_multi_aff_pullback_pw_multi_aff(
5825 __isl_take isl_pw_multi_aff *pma1,
5826 __isl_take isl_pw_multi_aff *pma2);
5827 __isl_give isl_multi_pw_aff *
5828 isl_multi_pw_aff_pullback_pw_multi_aff(
5829 __isl_take isl_multi_pw_aff *mpa,
5830 __isl_take isl_pw_multi_aff *pma);
5831 __isl_give isl_multi_pw_aff *
5832 isl_multi_pw_aff_pullback_multi_pw_aff(
5833 __isl_take isl_multi_pw_aff *mpa1,
5834 __isl_take isl_multi_pw_aff *mpa2);
5835 __isl_give isl_union_pw_aff *
5836 isl_union_pw_aff_pullback_union_pw_multi_aff(
5837 __isl_take isl_union_pw_aff *upa,
5838 __isl_take isl_union_pw_multi_aff *upma);
5839 __isl_give isl_union_pw_multi_aff *
5840 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5841 __isl_take isl_union_pw_multi_aff *upma1,
5842 __isl_take isl_union_pw_multi_aff *upma2);
5843 __isl_give isl_multi_union_pw_aff *
5844 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
5845 __isl_take isl_multi_union_pw_aff *mupa,
5846 __isl_take isl_union_pw_multi_aff *upma);
5848 These functions precompose the first expression by the second function.
5849 In other words, the second function is plugged
5850 into the first expression.
5854 #include <isl/aff.h>
5855 __isl_give isl_basic_set *isl_aff_le_basic_set(
5856 __isl_take isl_aff *aff1,
5857 __isl_take isl_aff *aff2);
5858 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5859 __isl_take isl_aff *aff1,
5860 __isl_take isl_aff *aff2);
5861 __isl_give isl_set *isl_pw_aff_eq_set(
5862 __isl_take isl_pw_aff *pwaff1,
5863 __isl_take isl_pw_aff *pwaff2);
5864 __isl_give isl_set *isl_pw_aff_ne_set(
5865 __isl_take isl_pw_aff *pwaff1,
5866 __isl_take isl_pw_aff *pwaff2);
5867 __isl_give isl_set *isl_pw_aff_le_set(
5868 __isl_take isl_pw_aff *pwaff1,
5869 __isl_take isl_pw_aff *pwaff2);
5870 __isl_give isl_set *isl_pw_aff_lt_set(
5871 __isl_take isl_pw_aff *pwaff1,
5872 __isl_take isl_pw_aff *pwaff2);
5873 __isl_give isl_set *isl_pw_aff_ge_set(
5874 __isl_take isl_pw_aff *pwaff1,
5875 __isl_take isl_pw_aff *pwaff2);
5876 __isl_give isl_set *isl_pw_aff_gt_set(
5877 __isl_take isl_pw_aff *pwaff1,
5878 __isl_take isl_pw_aff *pwaff2);
5880 __isl_give isl_set *isl_multi_aff_lex_le_set(
5881 __isl_take isl_multi_aff *ma1,
5882 __isl_take isl_multi_aff *ma2);
5883 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5884 __isl_take isl_multi_aff *ma1,
5885 __isl_take isl_multi_aff *ma2);
5887 __isl_give isl_set *isl_pw_aff_list_eq_set(
5888 __isl_take isl_pw_aff_list *list1,
5889 __isl_take isl_pw_aff_list *list2);
5890 __isl_give isl_set *isl_pw_aff_list_ne_set(
5891 __isl_take isl_pw_aff_list *list1,
5892 __isl_take isl_pw_aff_list *list2);
5893 __isl_give isl_set *isl_pw_aff_list_le_set(
5894 __isl_take isl_pw_aff_list *list1,
5895 __isl_take isl_pw_aff_list *list2);
5896 __isl_give isl_set *isl_pw_aff_list_lt_set(
5897 __isl_take isl_pw_aff_list *list1,
5898 __isl_take isl_pw_aff_list *list2);
5899 __isl_give isl_set *isl_pw_aff_list_ge_set(
5900 __isl_take isl_pw_aff_list *list1,
5901 __isl_take isl_pw_aff_list *list2);
5902 __isl_give isl_set *isl_pw_aff_list_gt_set(
5903 __isl_take isl_pw_aff_list *list1,
5904 __isl_take isl_pw_aff_list *list2);
5906 The function C<isl_aff_ge_basic_set> returns a basic set
5907 containing those elements in the shared space
5908 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5909 The function C<isl_pw_aff_ge_set> returns a set
5910 containing those elements in the shared domain
5911 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5912 greater than or equal to C<pwaff2>.
5913 The function C<isl_multi_aff_lex_le_set> returns a set
5914 containing those elements in the shared domain space
5915 where C<ma1> is lexicographically smaller than or
5917 The functions operating on C<isl_pw_aff_list> apply the corresponding
5918 C<isl_pw_aff> function to each pair of elements in the two lists.
5920 #include <isl/aff.h>
5921 __isl_give isl_map *isl_pw_aff_eq_map(
5922 __isl_take isl_pw_aff *pa1,
5923 __isl_take isl_pw_aff *pa2);
5924 __isl_give isl_map *isl_pw_aff_lt_map(
5925 __isl_take isl_pw_aff *pa1,
5926 __isl_take isl_pw_aff *pa2);
5927 __isl_give isl_map *isl_pw_aff_gt_map(
5928 __isl_take isl_pw_aff *pa1,
5929 __isl_take isl_pw_aff *pa2);
5931 __isl_give isl_map *isl_multi_pw_aff_eq_map(
5932 __isl_take isl_multi_pw_aff *mpa1,
5933 __isl_take isl_multi_pw_aff *mpa2);
5934 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
5935 __isl_take isl_multi_pw_aff *mpa1,
5936 __isl_take isl_multi_pw_aff *mpa2);
5937 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
5938 __isl_take isl_multi_pw_aff *mpa1,
5939 __isl_take isl_multi_pw_aff *mpa2);
5941 These functions return a map between domain elements of the arguments
5942 where the function values satisfy the given relation.
5944 #include <isl/union_map.h>
5945 __isl_give isl_union_map *
5946 isl_union_map_eq_at_multi_union_pw_aff(
5947 __isl_take isl_union_map *umap,
5948 __isl_take isl_multi_union_pw_aff *mupa);
5949 __isl_give isl_union_map *
5950 isl_union_map_lex_lt_at_multi_union_pw_aff(
5951 __isl_take isl_union_map *umap,
5952 __isl_take isl_multi_union_pw_aff *mupa);
5953 __isl_give isl_union_map *
5954 isl_union_map_lex_gt_at_multi_union_pw_aff(
5955 __isl_take isl_union_map *umap,
5956 __isl_take isl_multi_union_pw_aff *mupa);
5958 These functions select the subset of elements in the union map
5959 that have an equal or lexicographically smaller function value.
5961 =item * Cartesian Product
5963 #include <isl/space.h>
5964 __isl_give isl_space *isl_space_product(
5965 __isl_take isl_space *space1,
5966 __isl_take isl_space *space2);
5967 __isl_give isl_space *isl_space_domain_product(
5968 __isl_take isl_space *space1,
5969 __isl_take isl_space *space2);
5970 __isl_give isl_space *isl_space_range_product(
5971 __isl_take isl_space *space1,
5972 __isl_take isl_space *space2);
5975 C<isl_space_product>, C<isl_space_domain_product>
5976 and C<isl_space_range_product> take pairs or relation spaces and
5977 produce a single relations space, where either the domain, the range
5978 or both domain and range are wrapped spaces of relations between
5979 the domains and/or ranges of the input spaces.
5980 If the product is only constructed over the domain or the range
5981 then the ranges or the domains of the inputs should be the same.
5982 The function C<isl_space_product> also accepts a pair of set spaces,
5983 in which case it returns a wrapped space of a relation between the
5986 #include <isl/set.h>
5987 __isl_give isl_set *isl_set_product(
5988 __isl_take isl_set *set1,
5989 __isl_take isl_set *set2);
5991 #include <isl/map.h>
5992 __isl_give isl_basic_map *isl_basic_map_domain_product(
5993 __isl_take isl_basic_map *bmap1,
5994 __isl_take isl_basic_map *bmap2);
5995 __isl_give isl_basic_map *isl_basic_map_range_product(
5996 __isl_take isl_basic_map *bmap1,
5997 __isl_take isl_basic_map *bmap2);
5998 __isl_give isl_basic_map *isl_basic_map_product(
5999 __isl_take isl_basic_map *bmap1,
6000 __isl_take isl_basic_map *bmap2);
6001 __isl_give isl_map *isl_map_domain_product(
6002 __isl_take isl_map *map1,
6003 __isl_take isl_map *map2);
6004 __isl_give isl_map *isl_map_range_product(
6005 __isl_take isl_map *map1,
6006 __isl_take isl_map *map2);
6007 __isl_give isl_map *isl_map_product(
6008 __isl_take isl_map *map1,
6009 __isl_take isl_map *map2);
6011 #include <isl/union_set.h>
6012 __isl_give isl_union_set *isl_union_set_product(
6013 __isl_take isl_union_set *uset1,
6014 __isl_take isl_union_set *uset2);
6016 #include <isl/union_map.h>
6017 __isl_give isl_union_map *isl_union_map_domain_product(
6018 __isl_take isl_union_map *umap1,
6019 __isl_take isl_union_map *umap2);
6020 __isl_give isl_union_map *isl_union_map_range_product(
6021 __isl_take isl_union_map *umap1,
6022 __isl_take isl_union_map *umap2);
6023 __isl_give isl_union_map *isl_union_map_product(
6024 __isl_take isl_union_map *umap1,
6025 __isl_take isl_union_map *umap2);
6027 #include <isl/val.h>
6028 __isl_give isl_multi_val *isl_multi_val_range_product(
6029 __isl_take isl_multi_val *mv1,
6030 __isl_take isl_multi_val *mv2);
6031 __isl_give isl_multi_val *isl_multi_val_product(
6032 __isl_take isl_multi_val *mv1,
6033 __isl_take isl_multi_val *mv2);
6035 #include <isl/aff.h>
6036 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6037 __isl_take isl_multi_aff *ma1,
6038 __isl_take isl_multi_aff *ma2);
6039 __isl_give isl_multi_aff *isl_multi_aff_product(
6040 __isl_take isl_multi_aff *ma1,
6041 __isl_take isl_multi_aff *ma2);
6042 __isl_give isl_multi_pw_aff *
6043 isl_multi_pw_aff_range_product(
6044 __isl_take isl_multi_pw_aff *mpa1,
6045 __isl_take isl_multi_pw_aff *mpa2);
6046 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6047 __isl_take isl_multi_pw_aff *mpa1,
6048 __isl_take isl_multi_pw_aff *mpa2);
6049 __isl_give isl_pw_multi_aff *
6050 isl_pw_multi_aff_range_product(
6051 __isl_take isl_pw_multi_aff *pma1,
6052 __isl_take isl_pw_multi_aff *pma2);
6053 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6054 __isl_take isl_pw_multi_aff *pma1,
6055 __isl_take isl_pw_multi_aff *pma2);
6056 __isl_give isl_multi_union_pw_aff *
6057 isl_multi_union_pw_aff_range_product(
6058 __isl_take isl_multi_union_pw_aff *mupa1,
6059 __isl_take isl_multi_union_pw_aff *mupa2);
6061 The above functions compute the cross product of the given
6062 sets, relations or functions. The domains and ranges of the results
6063 are wrapped maps between domains and ranges of the inputs.
6064 To obtain a ``flat'' product, use the following functions
6067 #include <isl/set.h>
6068 __isl_give isl_basic_set *isl_basic_set_flat_product(
6069 __isl_take isl_basic_set *bset1,
6070 __isl_take isl_basic_set *bset2);
6071 __isl_give isl_set *isl_set_flat_product(
6072 __isl_take isl_set *set1,
6073 __isl_take isl_set *set2);
6075 #include <isl/map.h>
6076 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6077 __isl_take isl_basic_map *bmap1,
6078 __isl_take isl_basic_map *bmap2);
6079 __isl_give isl_map *isl_map_flat_domain_product(
6080 __isl_take isl_map *map1,
6081 __isl_take isl_map *map2);
6082 __isl_give isl_map *isl_map_flat_range_product(
6083 __isl_take isl_map *map1,
6084 __isl_take isl_map *map2);
6085 __isl_give isl_basic_map *isl_basic_map_flat_product(
6086 __isl_take isl_basic_map *bmap1,
6087 __isl_take isl_basic_map *bmap2);
6088 __isl_give isl_map *isl_map_flat_product(
6089 __isl_take isl_map *map1,
6090 __isl_take isl_map *map2);
6092 #include <isl/union_map.h>
6093 __isl_give isl_union_map *
6094 isl_union_map_flat_domain_product(
6095 __isl_take isl_union_map *umap1,
6096 __isl_take isl_union_map *umap2);
6097 __isl_give isl_union_map *
6098 isl_union_map_flat_range_product(
6099 __isl_take isl_union_map *umap1,
6100 __isl_take isl_union_map *umap2);
6102 #include <isl/val.h>
6103 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6104 __isl_take isl_multi_val *mv1,
6105 __isl_take isl_multi_aff *mv2);
6107 #include <isl/aff.h>
6108 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6109 __isl_take isl_multi_aff *ma1,
6110 __isl_take isl_multi_aff *ma2);
6111 __isl_give isl_pw_multi_aff *
6112 isl_pw_multi_aff_flat_range_product(
6113 __isl_take isl_pw_multi_aff *pma1,
6114 __isl_take isl_pw_multi_aff *pma2);
6115 __isl_give isl_multi_pw_aff *
6116 isl_multi_pw_aff_flat_range_product(
6117 __isl_take isl_multi_pw_aff *mpa1,
6118 __isl_take isl_multi_pw_aff *mpa2);
6119 __isl_give isl_union_pw_multi_aff *
6120 isl_union_pw_multi_aff_flat_range_product(
6121 __isl_take isl_union_pw_multi_aff *upma1,
6122 __isl_take isl_union_pw_multi_aff *upma2);
6123 __isl_give isl_multi_union_pw_aff *
6124 isl_multi_union_pw_aff_flat_range_product(
6125 __isl_take isl_multi_union_pw_aff *mupa1,
6126 __isl_take isl_multi_union_pw_aff *mupa2);
6128 #include <isl/space.h>
6129 __isl_give isl_space *isl_space_factor_domain(
6130 __isl_take isl_space *space);
6131 __isl_give isl_space *isl_space_factor_range(
6132 __isl_take isl_space *space);
6133 __isl_give isl_space *isl_space_domain_factor_domain(
6134 __isl_take isl_space *space);
6135 __isl_give isl_space *isl_space_domain_factor_range(
6136 __isl_take isl_space *space);
6137 __isl_give isl_space *isl_space_range_factor_domain(
6138 __isl_take isl_space *space);
6139 __isl_give isl_space *isl_space_range_factor_range(
6140 __isl_take isl_space *space);
6142 The functions C<isl_space_range_factor_domain> and
6143 C<isl_space_range_factor_range> extract the two arguments from
6144 the result of a call to C<isl_space_range_product>.
6146 The arguments of a call to C<isl_map_range_product> can be extracted
6147 from the result using the following functions.
6149 #include <isl/map.h>
6150 __isl_give isl_map *isl_map_factor_domain(
6151 __isl_take isl_map *map);
6152 __isl_give isl_map *isl_map_factor_range(
6153 __isl_take isl_map *map);
6154 __isl_give isl_map *isl_map_domain_factor_domain(
6155 __isl_take isl_map *map);
6156 __isl_give isl_map *isl_map_domain_factor_range(
6157 __isl_take isl_map *map);
6158 __isl_give isl_map *isl_map_range_factor_domain(
6159 __isl_take isl_map *map);
6160 __isl_give isl_map *isl_map_range_factor_range(
6161 __isl_take isl_map *map);
6163 #include <isl/union_map.h>
6164 __isl_give isl_union_map *isl_union_map_factor_domain(
6165 __isl_take isl_union_map *umap);
6166 __isl_give isl_union_map *isl_union_map_factor_range(
6167 __isl_take isl_union_map *umap);
6168 __isl_give isl_union_map *
6169 isl_union_map_domain_factor_domain(
6170 __isl_take isl_union_map *umap);
6171 __isl_give isl_union_map *
6172 isl_union_map_domain_factor_range(
6173 __isl_take isl_union_map *umap);
6174 __isl_give isl_union_map *
6175 isl_union_map_range_factor_range(
6176 __isl_take isl_union_map *umap);
6178 #include <isl/val.h>
6179 __isl_give isl_multi_val *
6180 isl_multi_val_range_factor_domain(
6181 __isl_take isl_multi_val *mv);
6182 __isl_give isl_multi_val *
6183 isl_multi_val_range_factor_range(
6184 __isl_take isl_multi_val *mv);
6186 #include <isl/aff.h>
6187 __isl_give isl_multi_aff *
6188 isl_multi_aff_range_factor_domain(
6189 __isl_take isl_multi_aff *ma);
6190 __isl_give isl_multi_aff *
6191 isl_multi_aff_range_factor_range(
6192 __isl_take isl_multi_aff *ma);
6193 __isl_give isl_multi_pw_aff *
6194 isl_multi_pw_aff_range_factor_domain(
6195 __isl_take isl_multi_pw_aff *mpa);
6196 __isl_give isl_multi_pw_aff *
6197 isl_multi_pw_aff_range_factor_range(
6198 __isl_take isl_multi_pw_aff *mpa);
6199 __isl_give isl_multi_union_pw_aff *
6200 isl_multi_union_pw_aff_range_factor_domain(
6201 __isl_take isl_multi_union_pw_aff *mupa);
6202 __isl_give isl_multi_union_pw_aff *
6203 isl_multi_union_pw_aff_range_factor_range(
6204 __isl_take isl_multi_union_pw_aff *mupa);
6206 The splice functions are a generalization of the flat product functions,
6207 where the second argument may be inserted at any position inside
6208 the first argument rather than being placed at the end.
6210 #include <isl/val.h>
6211 __isl_give isl_multi_val *isl_multi_val_range_splice(
6212 __isl_take isl_multi_val *mv1, unsigned pos,
6213 __isl_take isl_multi_val *mv2);
6215 #include <isl/aff.h>
6216 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6217 __isl_take isl_multi_aff *ma1, unsigned pos,
6218 __isl_take isl_multi_aff *ma2);
6219 __isl_give isl_multi_aff *isl_multi_aff_splice(
6220 __isl_take isl_multi_aff *ma1,
6221 unsigned in_pos, unsigned out_pos,
6222 __isl_take isl_multi_aff *ma2);
6223 __isl_give isl_multi_pw_aff *
6224 isl_multi_pw_aff_range_splice(
6225 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6226 __isl_take isl_multi_pw_aff *mpa2);
6227 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6228 __isl_take isl_multi_pw_aff *mpa1,
6229 unsigned in_pos, unsigned out_pos,
6230 __isl_take isl_multi_pw_aff *mpa2);
6231 __isl_give isl_multi_union_pw_aff *
6232 isl_multi_union_pw_aff_range_splice(
6233 __isl_take isl_multi_union_pw_aff *mupa1,
6235 __isl_take isl_multi_union_pw_aff *mupa2);
6237 =item * Simplification
6239 When applied to a set or relation,
6240 the gist operation returns a set or relation that has the
6241 same intersection with the context as the input set or relation.
6242 Any implicit equality in the intersection is made explicit in the result,
6243 while all inequalities that are redundant with respect to the intersection
6245 In case of union sets and relations, the gist operation is performed
6248 When applied to a function,
6249 the gist operation applies the set gist operation to each of
6250 the cells in the domain of the input piecewise expression.
6251 The context is also exploited
6252 to simplify the expression associated to each cell.
6254 #include <isl/set.h>
6255 __isl_give isl_basic_set *isl_basic_set_gist(
6256 __isl_take isl_basic_set *bset,
6257 __isl_take isl_basic_set *context);
6258 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6259 __isl_take isl_set *context);
6260 __isl_give isl_set *isl_set_gist_params(
6261 __isl_take isl_set *set,
6262 __isl_take isl_set *context);
6264 #include <isl/map.h>
6265 __isl_give isl_basic_map *isl_basic_map_gist(
6266 __isl_take isl_basic_map *bmap,
6267 __isl_take isl_basic_map *context);
6268 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6269 __isl_take isl_basic_map *bmap,
6270 __isl_take isl_basic_set *context);
6271 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6272 __isl_take isl_map *context);
6273 __isl_give isl_map *isl_map_gist_params(
6274 __isl_take isl_map *map,
6275 __isl_take isl_set *context);
6276 __isl_give isl_map *isl_map_gist_domain(
6277 __isl_take isl_map *map,
6278 __isl_take isl_set *context);
6279 __isl_give isl_map *isl_map_gist_range(
6280 __isl_take isl_map *map,
6281 __isl_take isl_set *context);
6283 #include <isl/union_set.h>
6284 __isl_give isl_union_set *isl_union_set_gist(
6285 __isl_take isl_union_set *uset,
6286 __isl_take isl_union_set *context);
6287 __isl_give isl_union_set *isl_union_set_gist_params(
6288 __isl_take isl_union_set *uset,
6289 __isl_take isl_set *set);
6291 #include <isl/union_map.h>
6292 __isl_give isl_union_map *isl_union_map_gist(
6293 __isl_take isl_union_map *umap,
6294 __isl_take isl_union_map *context);
6295 __isl_give isl_union_map *isl_union_map_gist_params(
6296 __isl_take isl_union_map *umap,
6297 __isl_take isl_set *set);
6298 __isl_give isl_union_map *isl_union_map_gist_domain(
6299 __isl_take isl_union_map *umap,
6300 __isl_take isl_union_set *uset);
6301 __isl_give isl_union_map *isl_union_map_gist_range(
6302 __isl_take isl_union_map *umap,
6303 __isl_take isl_union_set *uset);
6305 #include <isl/aff.h>
6306 __isl_give isl_aff *isl_aff_gist_params(
6307 __isl_take isl_aff *aff,
6308 __isl_take isl_set *context);
6309 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6310 __isl_take isl_set *context);
6311 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6312 __isl_take isl_multi_aff *maff,
6313 __isl_take isl_set *context);
6314 __isl_give isl_multi_aff *isl_multi_aff_gist(
6315 __isl_take isl_multi_aff *maff,
6316 __isl_take isl_set *context);
6317 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6318 __isl_take isl_pw_aff *pwaff,
6319 __isl_take isl_set *context);
6320 __isl_give isl_pw_aff *isl_pw_aff_gist(
6321 __isl_take isl_pw_aff *pwaff,
6322 __isl_take isl_set *context);
6323 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6324 __isl_take isl_pw_multi_aff *pma,
6325 __isl_take isl_set *set);
6326 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6327 __isl_take isl_pw_multi_aff *pma,
6328 __isl_take isl_set *set);
6329 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6330 __isl_take isl_multi_pw_aff *mpa,
6331 __isl_take isl_set *set);
6332 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6333 __isl_take isl_multi_pw_aff *mpa,
6334 __isl_take isl_set *set);
6335 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6336 __isl_take isl_union_pw_aff *upa,
6337 __isl_take isl_union_set *context);
6338 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6339 __isl_take isl_union_pw_aff *upa,
6340 __isl_take isl_set *context);
6341 __isl_give isl_union_pw_multi_aff *
6342 isl_union_pw_multi_aff_gist_params(
6343 __isl_take isl_union_pw_multi_aff *upma,
6344 __isl_take isl_set *context);
6345 __isl_give isl_union_pw_multi_aff *
6346 isl_union_pw_multi_aff_gist(
6347 __isl_take isl_union_pw_multi_aff *upma,
6348 __isl_take isl_union_set *context);
6349 __isl_give isl_multi_union_pw_aff *
6350 isl_multi_union_pw_aff_gist_params(
6351 __isl_take isl_multi_union_pw_aff *aff,
6352 __isl_take isl_set *context);
6353 __isl_give isl_multi_union_pw_aff *
6354 isl_multi_union_pw_aff_gist(
6355 __isl_take isl_multi_union_pw_aff *aff,
6356 __isl_take isl_union_set *context);
6358 #include <isl/polynomial.h>
6359 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6360 __isl_take isl_qpolynomial *qp,
6361 __isl_take isl_set *context);
6362 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6363 __isl_take isl_qpolynomial *qp,
6364 __isl_take isl_set *context);
6365 __isl_give isl_qpolynomial_fold *
6366 isl_qpolynomial_fold_gist_params(
6367 __isl_take isl_qpolynomial_fold *fold,
6368 __isl_take isl_set *context);
6369 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6370 __isl_take isl_qpolynomial_fold *fold,
6371 __isl_take isl_set *context);
6372 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6373 __isl_take isl_pw_qpolynomial *pwqp,
6374 __isl_take isl_set *context);
6375 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6376 __isl_take isl_pw_qpolynomial *pwqp,
6377 __isl_take isl_set *context);
6378 __isl_give isl_pw_qpolynomial_fold *
6379 isl_pw_qpolynomial_fold_gist(
6380 __isl_take isl_pw_qpolynomial_fold *pwf,
6381 __isl_take isl_set *context);
6382 __isl_give isl_pw_qpolynomial_fold *
6383 isl_pw_qpolynomial_fold_gist_params(
6384 __isl_take isl_pw_qpolynomial_fold *pwf,
6385 __isl_take isl_set *context);
6386 __isl_give isl_union_pw_qpolynomial *
6387 isl_union_pw_qpolynomial_gist_params(
6388 __isl_take isl_union_pw_qpolynomial *upwqp,
6389 __isl_take isl_set *context);
6390 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6391 __isl_take isl_union_pw_qpolynomial *upwqp,
6392 __isl_take isl_union_set *context);
6393 __isl_give isl_union_pw_qpolynomial_fold *
6394 isl_union_pw_qpolynomial_fold_gist(
6395 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6396 __isl_take isl_union_set *context);
6397 __isl_give isl_union_pw_qpolynomial_fold *
6398 isl_union_pw_qpolynomial_fold_gist_params(
6399 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6400 __isl_take isl_set *context);
6402 =item * Binary Arithmethic Operations
6404 #include <isl/val.h>
6405 __isl_give isl_multi_val *isl_multi_val_sub(
6406 __isl_take isl_multi_val *mv1,
6407 __isl_take isl_multi_val *mv2);
6409 #include <isl/aff.h>
6410 __isl_give isl_aff *isl_aff_add(
6411 __isl_take isl_aff *aff1,
6412 __isl_take isl_aff *aff2);
6413 __isl_give isl_multi_aff *isl_multi_aff_add(
6414 __isl_take isl_multi_aff *maff1,
6415 __isl_take isl_multi_aff *maff2);
6416 __isl_give isl_pw_aff *isl_pw_aff_add(
6417 __isl_take isl_pw_aff *pwaff1,
6418 __isl_take isl_pw_aff *pwaff2);
6419 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6420 __isl_take isl_pw_multi_aff *pma1,
6421 __isl_take isl_pw_multi_aff *pma2);
6422 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6423 __isl_take isl_union_pw_aff *upa1,
6424 __isl_take isl_union_pw_aff *upa2);
6425 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6426 __isl_take isl_union_pw_multi_aff *upma1,
6427 __isl_take isl_union_pw_multi_aff *upma2);
6428 __isl_give isl_pw_aff *isl_pw_aff_min(
6429 __isl_take isl_pw_aff *pwaff1,
6430 __isl_take isl_pw_aff *pwaff2);
6431 __isl_give isl_pw_aff *isl_pw_aff_max(
6432 __isl_take isl_pw_aff *pwaff1,
6433 __isl_take isl_pw_aff *pwaff2);
6434 __isl_give isl_aff *isl_aff_sub(
6435 __isl_take isl_aff *aff1,
6436 __isl_take isl_aff *aff2);
6437 __isl_give isl_multi_aff *isl_multi_aff_sub(
6438 __isl_take isl_multi_aff *ma1,
6439 __isl_take isl_multi_aff *ma2);
6440 __isl_give isl_pw_aff *isl_pw_aff_sub(
6441 __isl_take isl_pw_aff *pwaff1,
6442 __isl_take isl_pw_aff *pwaff2);
6443 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6444 __isl_take isl_multi_pw_aff *mpa1,
6445 __isl_take isl_multi_pw_aff *mpa2);
6446 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6447 __isl_take isl_pw_multi_aff *pma1,
6448 __isl_take isl_pw_multi_aff *pma2);
6449 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6450 __isl_take isl_union_pw_aff *upa1,
6451 __isl_take isl_union_pw_aff *upa2);
6452 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6453 __isl_take isl_union_pw_multi_aff *upma1,
6454 __isl_take isl_union_pw_multi_aff *upma2);
6455 __isl_give isl_multi_union_pw_aff *
6456 isl_multi_union_pw_aff_sub(
6457 __isl_take isl_multi_union_pw_aff *mupa1,
6458 __isl_take isl_multi_union_pw_aff *mupa2);
6460 C<isl_aff_sub> subtracts the second argument from the first.
6462 #include <isl/polynomial.h>
6463 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6464 __isl_take isl_qpolynomial *qp1,
6465 __isl_take isl_qpolynomial *qp2);
6466 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6467 __isl_take isl_pw_qpolynomial *pwqp1,
6468 __isl_take isl_pw_qpolynomial *pwqp2);
6469 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6470 __isl_take isl_pw_qpolynomial *pwqp1,
6471 __isl_take isl_pw_qpolynomial *pwqp2);
6472 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6473 __isl_take isl_pw_qpolynomial_fold *pwf1,
6474 __isl_take isl_pw_qpolynomial_fold *pwf2);
6475 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6476 __isl_take isl_union_pw_qpolynomial *upwqp1,
6477 __isl_take isl_union_pw_qpolynomial *upwqp2);
6478 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6479 __isl_take isl_qpolynomial *qp1,
6480 __isl_take isl_qpolynomial *qp2);
6481 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6482 __isl_take isl_pw_qpolynomial *pwqp1,
6483 __isl_take isl_pw_qpolynomial *pwqp2);
6484 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6485 __isl_take isl_union_pw_qpolynomial *upwqp1,
6486 __isl_take isl_union_pw_qpolynomial *upwqp2);
6487 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6488 __isl_take isl_pw_qpolynomial_fold *pwf1,
6489 __isl_take isl_pw_qpolynomial_fold *pwf2);
6490 __isl_give isl_union_pw_qpolynomial_fold *
6491 isl_union_pw_qpolynomial_fold_fold(
6492 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6493 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6495 #include <isl/aff.h>
6496 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6497 __isl_take isl_pw_aff *pwaff1,
6498 __isl_take isl_pw_aff *pwaff2);
6499 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6500 __isl_take isl_pw_multi_aff *pma1,
6501 __isl_take isl_pw_multi_aff *pma2);
6502 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6503 __isl_take isl_union_pw_aff *upa1,
6504 __isl_take isl_union_pw_aff *upa2);
6505 __isl_give isl_union_pw_multi_aff *
6506 isl_union_pw_multi_aff_union_add(
6507 __isl_take isl_union_pw_multi_aff *upma1,
6508 __isl_take isl_union_pw_multi_aff *upma2);
6509 __isl_give isl_multi_union_pw_aff *
6510 isl_multi_union_pw_aff_union_add(
6511 __isl_take isl_multi_union_pw_aff *mupa1,
6512 __isl_take isl_multi_union_pw_aff *mupa2);
6513 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6514 __isl_take isl_pw_aff *pwaff1,
6515 __isl_take isl_pw_aff *pwaff2);
6516 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6517 __isl_take isl_pw_aff *pwaff1,
6518 __isl_take isl_pw_aff *pwaff2);
6520 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6521 expression with a domain that is the union of those of C<pwaff1> and
6522 C<pwaff2> and such that on each cell, the quasi-affine expression is
6523 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6524 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6525 associated expression is the defined one.
6526 This in contrast to the C<isl_pw_aff_max> function, which is
6527 only defined on the shared definition domain of the arguments.
6529 #include <isl/val.h>
6530 __isl_give isl_multi_val *isl_multi_val_add_val(
6531 __isl_take isl_multi_val *mv,
6532 __isl_take isl_val *v);
6533 __isl_give isl_multi_val *isl_multi_val_mod_val(
6534 __isl_take isl_multi_val *mv,
6535 __isl_take isl_val *v);
6536 __isl_give isl_multi_val *isl_multi_val_scale_val(
6537 __isl_take isl_multi_val *mv,
6538 __isl_take isl_val *v);
6539 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6540 __isl_take isl_multi_val *mv,
6541 __isl_take isl_val *v);
6543 #include <isl/aff.h>
6544 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6545 __isl_take isl_val *mod);
6546 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6547 __isl_take isl_pw_aff *pa,
6548 __isl_take isl_val *mod);
6549 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6550 __isl_take isl_union_pw_aff *upa,
6551 __isl_take isl_val *f);
6552 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6553 __isl_take isl_val *v);
6554 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6555 __isl_take isl_multi_aff *ma,
6556 __isl_take isl_val *v);
6557 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6558 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6559 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6560 __isl_take isl_multi_pw_aff *mpa,
6561 __isl_take isl_val *v);
6562 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6563 __isl_take isl_pw_multi_aff *pma,
6564 __isl_take isl_val *v);
6565 __isl_give isl_union_pw_multi_aff *
6566 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6567 __isl_take isl_union_pw_aff *upa,
6568 __isl_take isl_val *f);
6569 isl_union_pw_multi_aff_scale_val(
6570 __isl_take isl_union_pw_multi_aff *upma,
6571 __isl_take isl_val *val);
6572 __isl_give isl_multi_union_pw_aff *
6573 isl_multi_union_pw_aff_scale_val(
6574 __isl_take isl_multi_union_pw_aff *mupa,
6575 __isl_take isl_val *v);
6576 __isl_give isl_aff *isl_aff_scale_down_ui(
6577 __isl_take isl_aff *aff, unsigned f);
6578 __isl_give isl_aff *isl_aff_scale_down_val(
6579 __isl_take isl_aff *aff, __isl_take isl_val *v);
6580 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6581 __isl_take isl_multi_aff *ma,
6582 __isl_take isl_val *v);
6583 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6584 __isl_take isl_pw_aff *pa,
6585 __isl_take isl_val *f);
6586 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6587 __isl_take isl_multi_pw_aff *mpa,
6588 __isl_take isl_val *v);
6589 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6590 __isl_take isl_pw_multi_aff *pma,
6591 __isl_take isl_val *v);
6592 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6593 __isl_take isl_union_pw_aff *upa,
6594 __isl_take isl_val *v);
6595 __isl_give isl_union_pw_multi_aff *
6596 isl_union_pw_multi_aff_scale_down_val(
6597 __isl_take isl_union_pw_multi_aff *upma,
6598 __isl_take isl_val *val);
6599 __isl_give isl_multi_union_pw_aff *
6600 isl_multi_union_pw_aff_scale_down_val(
6601 __isl_take isl_multi_union_pw_aff *mupa,
6602 __isl_take isl_val *v);
6604 #include <isl/polynomial.h>
6605 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6606 __isl_take isl_qpolynomial *qp,
6607 __isl_take isl_val *v);
6608 __isl_give isl_qpolynomial_fold *
6609 isl_qpolynomial_fold_scale_val(
6610 __isl_take isl_qpolynomial_fold *fold,
6611 __isl_take isl_val *v);
6612 __isl_give isl_pw_qpolynomial *
6613 isl_pw_qpolynomial_scale_val(
6614 __isl_take isl_pw_qpolynomial *pwqp,
6615 __isl_take isl_val *v);
6616 __isl_give isl_pw_qpolynomial_fold *
6617 isl_pw_qpolynomial_fold_scale_val(
6618 __isl_take isl_pw_qpolynomial_fold *pwf,
6619 __isl_take isl_val *v);
6620 __isl_give isl_union_pw_qpolynomial *
6621 isl_union_pw_qpolynomial_scale_val(
6622 __isl_take isl_union_pw_qpolynomial *upwqp,
6623 __isl_take isl_val *v);
6624 __isl_give isl_union_pw_qpolynomial_fold *
6625 isl_union_pw_qpolynomial_fold_scale_val(
6626 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6627 __isl_take isl_val *v);
6628 __isl_give isl_qpolynomial *
6629 isl_qpolynomial_scale_down_val(
6630 __isl_take isl_qpolynomial *qp,
6631 __isl_take isl_val *v);
6632 __isl_give isl_qpolynomial_fold *
6633 isl_qpolynomial_fold_scale_down_val(
6634 __isl_take isl_qpolynomial_fold *fold,
6635 __isl_take isl_val *v);
6636 __isl_give isl_pw_qpolynomial *
6637 isl_pw_qpolynomial_scale_down_val(
6638 __isl_take isl_pw_qpolynomial *pwqp,
6639 __isl_take isl_val *v);
6640 __isl_give isl_pw_qpolynomial_fold *
6641 isl_pw_qpolynomial_fold_scale_down_val(
6642 __isl_take isl_pw_qpolynomial_fold *pwf,
6643 __isl_take isl_val *v);
6644 __isl_give isl_union_pw_qpolynomial *
6645 isl_union_pw_qpolynomial_scale_down_val(
6646 __isl_take isl_union_pw_qpolynomial *upwqp,
6647 __isl_take isl_val *v);
6648 __isl_give isl_union_pw_qpolynomial_fold *
6649 isl_union_pw_qpolynomial_fold_scale_down_val(
6650 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6651 __isl_take isl_val *v);
6653 #include <isl/val.h>
6654 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6655 __isl_take isl_multi_val *mv1,
6656 __isl_take isl_multi_val *mv2);
6657 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6658 __isl_take isl_multi_val *mv1,
6659 __isl_take isl_multi_val *mv2);
6660 __isl_give isl_multi_val *
6661 isl_multi_val_scale_down_multi_val(
6662 __isl_take isl_multi_val *mv1,
6663 __isl_take isl_multi_val *mv2);
6665 #include <isl/aff.h>
6666 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6667 __isl_take isl_multi_aff *ma,
6668 __isl_take isl_multi_val *mv);
6669 __isl_give isl_multi_union_pw_aff *
6670 isl_multi_union_pw_aff_mod_multi_val(
6671 __isl_take isl_multi_union_pw_aff *upma,
6672 __isl_take isl_multi_val *mv);
6673 __isl_give isl_multi_pw_aff *
6674 isl_multi_pw_aff_mod_multi_val(
6675 __isl_take isl_multi_pw_aff *mpa,
6676 __isl_take isl_multi_val *mv);
6677 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6678 __isl_take isl_multi_aff *ma,
6679 __isl_take isl_multi_val *mv);
6680 __isl_give isl_pw_multi_aff *
6681 isl_pw_multi_aff_scale_multi_val(
6682 __isl_take isl_pw_multi_aff *pma,
6683 __isl_take isl_multi_val *mv);
6684 __isl_give isl_multi_pw_aff *
6685 isl_multi_pw_aff_scale_multi_val(
6686 __isl_take isl_multi_pw_aff *mpa,
6687 __isl_take isl_multi_val *mv);
6688 __isl_give isl_multi_union_pw_aff *
6689 isl_multi_union_pw_aff_scale_multi_val(
6690 __isl_take isl_multi_union_pw_aff *mupa,
6691 __isl_take isl_multi_val *mv);
6692 __isl_give isl_union_pw_multi_aff *
6693 isl_union_pw_multi_aff_scale_multi_val(
6694 __isl_take isl_union_pw_multi_aff *upma,
6695 __isl_take isl_multi_val *mv);
6696 __isl_give isl_multi_aff *
6697 isl_multi_aff_scale_down_multi_val(
6698 __isl_take isl_multi_aff *ma,
6699 __isl_take isl_multi_val *mv);
6700 __isl_give isl_multi_pw_aff *
6701 isl_multi_pw_aff_scale_down_multi_val(
6702 __isl_take isl_multi_pw_aff *mpa,
6703 __isl_take isl_multi_val *mv);
6704 __isl_give isl_multi_union_pw_aff *
6705 isl_multi_union_pw_aff_scale_down_multi_val(
6706 __isl_take isl_multi_union_pw_aff *mupa,
6707 __isl_take isl_multi_val *mv);
6709 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6710 by the corresponding elements of C<mv>.
6712 #include <isl/aff.h>
6713 __isl_give isl_aff *isl_aff_mul(
6714 __isl_take isl_aff *aff1,
6715 __isl_take isl_aff *aff2);
6716 __isl_give isl_aff *isl_aff_div(
6717 __isl_take isl_aff *aff1,
6718 __isl_take isl_aff *aff2);
6719 __isl_give isl_pw_aff *isl_pw_aff_mul(
6720 __isl_take isl_pw_aff *pwaff1,
6721 __isl_take isl_pw_aff *pwaff2);
6722 __isl_give isl_pw_aff *isl_pw_aff_div(
6723 __isl_take isl_pw_aff *pa1,
6724 __isl_take isl_pw_aff *pa2);
6725 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6726 __isl_take isl_pw_aff *pa1,
6727 __isl_take isl_pw_aff *pa2);
6728 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6729 __isl_take isl_pw_aff *pa1,
6730 __isl_take isl_pw_aff *pa2);
6732 When multiplying two affine expressions, at least one of the two needs
6733 to be a constant. Similarly, when dividing an affine expression by another,
6734 the second expression needs to be a constant.
6735 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6736 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6739 #include <isl/polynomial.h>
6740 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6741 __isl_take isl_qpolynomial *qp1,
6742 __isl_take isl_qpolynomial *qp2);
6743 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6744 __isl_take isl_pw_qpolynomial *pwqp1,
6745 __isl_take isl_pw_qpolynomial *pwqp2);
6746 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6747 __isl_take isl_union_pw_qpolynomial *upwqp1,
6748 __isl_take isl_union_pw_qpolynomial *upwqp2);
6752 =head3 Lexicographic Optimization
6754 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6755 the following functions
6756 compute a set that contains the lexicographic minimum or maximum
6757 of the elements in C<set> (or C<bset>) for those values of the parameters
6758 that satisfy C<dom>.
6759 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6760 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6762 In other words, the union of the parameter values
6763 for which the result is non-empty and of C<*empty>
6766 #include <isl/set.h>
6767 __isl_give isl_set *isl_basic_set_partial_lexmin(
6768 __isl_take isl_basic_set *bset,
6769 __isl_take isl_basic_set *dom,
6770 __isl_give isl_set **empty);
6771 __isl_give isl_set *isl_basic_set_partial_lexmax(
6772 __isl_take isl_basic_set *bset,
6773 __isl_take isl_basic_set *dom,
6774 __isl_give isl_set **empty);
6775 __isl_give isl_set *isl_set_partial_lexmin(
6776 __isl_take isl_set *set, __isl_take isl_set *dom,
6777 __isl_give isl_set **empty);
6778 __isl_give isl_set *isl_set_partial_lexmax(
6779 __isl_take isl_set *set, __isl_take isl_set *dom,
6780 __isl_give isl_set **empty);
6782 Given a (basic) set C<set> (or C<bset>), the following functions simply
6783 return a set containing the lexicographic minimum or maximum
6784 of the elements in C<set> (or C<bset>).
6785 In case of union sets, the optimum is computed per space.
6787 #include <isl/set.h>
6788 __isl_give isl_set *isl_basic_set_lexmin(
6789 __isl_take isl_basic_set *bset);
6790 __isl_give isl_set *isl_basic_set_lexmax(
6791 __isl_take isl_basic_set *bset);
6792 __isl_give isl_set *isl_set_lexmin(
6793 __isl_take isl_set *set);
6794 __isl_give isl_set *isl_set_lexmax(
6795 __isl_take isl_set *set);
6796 __isl_give isl_union_set *isl_union_set_lexmin(
6797 __isl_take isl_union_set *uset);
6798 __isl_give isl_union_set *isl_union_set_lexmax(
6799 __isl_take isl_union_set *uset);
6801 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6802 the following functions
6803 compute a relation that maps each element of C<dom>
6804 to the single lexicographic minimum or maximum
6805 of the elements that are associated to that same
6806 element in C<map> (or C<bmap>).
6807 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6808 that contains the elements in C<dom> that do not map
6809 to any elements in C<map> (or C<bmap>).
6810 In other words, the union of the domain of the result and of C<*empty>
6813 #include <isl/map.h>
6814 __isl_give isl_map *isl_basic_map_partial_lexmax(
6815 __isl_take isl_basic_map *bmap,
6816 __isl_take isl_basic_set *dom,
6817 __isl_give isl_set **empty);
6818 __isl_give isl_map *isl_basic_map_partial_lexmin(
6819 __isl_take isl_basic_map *bmap,
6820 __isl_take isl_basic_set *dom,
6821 __isl_give isl_set **empty);
6822 __isl_give isl_map *isl_map_partial_lexmax(
6823 __isl_take isl_map *map, __isl_take isl_set *dom,
6824 __isl_give isl_set **empty);
6825 __isl_give isl_map *isl_map_partial_lexmin(
6826 __isl_take isl_map *map, __isl_take isl_set *dom,
6827 __isl_give isl_set **empty);
6829 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6830 return a map mapping each element in the domain of
6831 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6832 of all elements associated to that element.
6833 In case of union relations, the optimum is computed per space.
6835 #include <isl/map.h>
6836 __isl_give isl_map *isl_basic_map_lexmin(
6837 __isl_take isl_basic_map *bmap);
6838 __isl_give isl_map *isl_basic_map_lexmax(
6839 __isl_take isl_basic_map *bmap);
6840 __isl_give isl_map *isl_map_lexmin(
6841 __isl_take isl_map *map);
6842 __isl_give isl_map *isl_map_lexmax(
6843 __isl_take isl_map *map);
6844 __isl_give isl_union_map *isl_union_map_lexmin(
6845 __isl_take isl_union_map *umap);
6846 __isl_give isl_union_map *isl_union_map_lexmax(
6847 __isl_take isl_union_map *umap);
6849 The following functions return their result in the form of
6850 a piecewise multi-affine expression,
6851 but are otherwise equivalent to the corresponding functions
6852 returning a basic set or relation.
6854 #include <isl/set.h>
6855 __isl_give isl_pw_multi_aff *
6856 isl_basic_set_partial_lexmin_pw_multi_aff(
6857 __isl_take isl_basic_set *bset,
6858 __isl_take isl_basic_set *dom,
6859 __isl_give isl_set **empty);
6860 __isl_give isl_pw_multi_aff *
6861 isl_basic_set_partial_lexmax_pw_multi_aff(
6862 __isl_take isl_basic_set *bset,
6863 __isl_take isl_basic_set *dom,
6864 __isl_give isl_set **empty);
6865 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6866 __isl_take isl_set *set);
6867 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6868 __isl_take isl_set *set);
6870 #include <isl/map.h>
6871 __isl_give isl_pw_multi_aff *
6872 isl_basic_map_lexmin_pw_multi_aff(
6873 __isl_take isl_basic_map *bmap);
6874 __isl_give isl_pw_multi_aff *
6875 isl_basic_map_partial_lexmin_pw_multi_aff(
6876 __isl_take isl_basic_map *bmap,
6877 __isl_take isl_basic_set *dom,
6878 __isl_give isl_set **empty);
6879 __isl_give isl_pw_multi_aff *
6880 isl_basic_map_partial_lexmax_pw_multi_aff(
6881 __isl_take isl_basic_map *bmap,
6882 __isl_take isl_basic_set *dom,
6883 __isl_give isl_set **empty);
6884 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6885 __isl_take isl_map *map);
6886 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6887 __isl_take isl_map *map);
6889 The following functions return the lexicographic minimum or maximum
6890 on the shared domain of the inputs and the single defined function
6891 on those parts of the domain where only a single function is defined.
6893 #include <isl/aff.h>
6894 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6895 __isl_take isl_pw_multi_aff *pma1,
6896 __isl_take isl_pw_multi_aff *pma2);
6897 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6898 __isl_take isl_pw_multi_aff *pma1,
6899 __isl_take isl_pw_multi_aff *pma2);
6901 =head2 Ternary Operations
6903 #include <isl/aff.h>
6904 __isl_give isl_pw_aff *isl_pw_aff_cond(
6905 __isl_take isl_pw_aff *cond,
6906 __isl_take isl_pw_aff *pwaff_true,
6907 __isl_take isl_pw_aff *pwaff_false);
6909 The function C<isl_pw_aff_cond> performs a conditional operator
6910 and returns an expression that is equal to C<pwaff_true>
6911 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6912 where C<cond> is zero.
6916 Lists are defined over several element types, including
6917 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
6918 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6919 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6920 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6921 Here we take lists of C<isl_set>s as an example.
6922 Lists can be created, copied, modified and freed using the following functions.
6924 #include <isl/set.h>
6925 __isl_give isl_set_list *isl_set_list_from_set(
6926 __isl_take isl_set *el);
6927 __isl_give isl_set_list *isl_set_list_alloc(
6928 isl_ctx *ctx, int n);
6929 __isl_give isl_set_list *isl_set_list_copy(
6930 __isl_keep isl_set_list *list);
6931 __isl_give isl_set_list *isl_set_list_insert(
6932 __isl_take isl_set_list *list, unsigned pos,
6933 __isl_take isl_set *el);
6934 __isl_give isl_set_list *isl_set_list_add(
6935 __isl_take isl_set_list *list,
6936 __isl_take isl_set *el);
6937 __isl_give isl_set_list *isl_set_list_drop(
6938 __isl_take isl_set_list *list,
6939 unsigned first, unsigned n);
6940 __isl_give isl_set_list *isl_set_list_set_set(
6941 __isl_take isl_set_list *list, int index,
6942 __isl_take isl_set *set);
6943 __isl_give isl_set_list *isl_set_list_concat(
6944 __isl_take isl_set_list *list1,
6945 __isl_take isl_set_list *list2);
6946 __isl_give isl_set_list *isl_set_list_sort(
6947 __isl_take isl_set_list *list,
6948 int (*cmp)(__isl_keep isl_set *a,
6949 __isl_keep isl_set *b, void *user),
6951 __isl_null isl_set_list *isl_set_list_free(
6952 __isl_take isl_set_list *list);
6954 C<isl_set_list_alloc> creates an empty list with an initial capacity
6955 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
6956 add elements to a list, increasing its capacity as needed.
6957 C<isl_set_list_from_set> creates a list with a single element.
6959 Lists can be inspected using the following functions.
6961 #include <isl/set.h>
6962 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6963 __isl_give isl_set *isl_set_list_get_set(
6964 __isl_keep isl_set_list *list, int index);
6965 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6966 int (*fn)(__isl_take isl_set *el, void *user),
6968 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6969 int (*follows)(__isl_keep isl_set *a,
6970 __isl_keep isl_set *b, void *user),
6972 int (*fn)(__isl_take isl_set *el, void *user),
6975 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6976 strongly connected components of the graph with as vertices the elements
6977 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6978 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6979 should return C<-1> on error.
6981 Lists can be printed using
6983 #include <isl/set.h>
6984 __isl_give isl_printer *isl_printer_print_set_list(
6985 __isl_take isl_printer *p,
6986 __isl_keep isl_set_list *list);
6988 =head2 Associative arrays
6990 Associative arrays map isl objects of a specific type to isl objects
6991 of some (other) specific type. They are defined for several pairs
6992 of types, including (C<isl_map>, C<isl_basic_set>),
6993 (C<isl_id>, C<isl_ast_expr>) and.
6994 (C<isl_id>, C<isl_pw_aff>).
6995 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6998 Associative arrays can be created, copied and freed using
6999 the following functions.
7001 #include <isl/id_to_ast_expr.h>
7002 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
7003 isl_ctx *ctx, int min_size);
7004 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7005 __isl_keep isl_id_to_ast_expr *id2expr);
7006 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7007 __isl_take isl_id_to_ast_expr *id2expr);
7009 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7010 to specify the expected size of the associative array.
7011 The associative array will be grown automatically as needed.
7013 Associative arrays can be inspected using the following functions.
7015 #include <isl/id_to_ast_expr.h>
7016 int isl_id_to_ast_expr_has(
7017 __isl_keep isl_id_to_ast_expr *id2expr,
7018 __isl_keep isl_id *key);
7019 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7020 __isl_keep isl_id_to_ast_expr *id2expr,
7021 __isl_take isl_id *key);
7022 int isl_id_to_ast_expr_foreach(
7023 __isl_keep isl_id_to_ast_expr *id2expr,
7024 int (*fn)(__isl_take isl_id *key,
7025 __isl_take isl_ast_expr *val, void *user),
7028 They can be modified using the following function.
7030 #include <isl/id_to_ast_expr.h>
7031 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7032 __isl_take isl_id_to_ast_expr *id2expr,
7033 __isl_take isl_id *key,
7034 __isl_take isl_ast_expr *val);
7035 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7036 __isl_take isl_id_to_ast_expr *id2expr,
7037 __isl_take isl_id *key);
7039 Associative arrays can be printed using the following function.
7041 #include <isl/id_to_ast_expr.h>
7042 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7043 __isl_take isl_printer *p,
7044 __isl_keep isl_id_to_ast_expr *id2expr);
7048 Vectors can be created, copied and freed using the following functions.
7050 #include <isl/vec.h>
7051 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7053 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7054 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7056 Note that the elements of a newly created vector may have arbitrary values.
7057 The elements can be changed and inspected using the following functions.
7059 int isl_vec_size(__isl_keep isl_vec *vec);
7060 __isl_give isl_val *isl_vec_get_element_val(
7061 __isl_keep isl_vec *vec, int pos);
7062 __isl_give isl_vec *isl_vec_set_element_si(
7063 __isl_take isl_vec *vec, int pos, int v);
7064 __isl_give isl_vec *isl_vec_set_element_val(
7065 __isl_take isl_vec *vec, int pos,
7066 __isl_take isl_val *v);
7067 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7069 __isl_give isl_vec *isl_vec_set_val(
7070 __isl_take isl_vec *vec, __isl_take isl_val *v);
7071 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7072 __isl_keep isl_vec *vec2, int pos);
7074 C<isl_vec_get_element> will return a negative value if anything went wrong.
7075 In that case, the value of C<*v> is undefined.
7077 The following function can be used to concatenate two vectors.
7079 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7080 __isl_take isl_vec *vec2);
7084 Matrices can be created, copied and freed using the following functions.
7086 #include <isl/mat.h>
7087 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7088 unsigned n_row, unsigned n_col);
7089 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7090 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7092 Note that the elements of a newly created matrix may have arbitrary values.
7093 The elements can be changed and inspected using the following functions.
7095 int isl_mat_rows(__isl_keep isl_mat *mat);
7096 int isl_mat_cols(__isl_keep isl_mat *mat);
7097 __isl_give isl_val *isl_mat_get_element_val(
7098 __isl_keep isl_mat *mat, int row, int col);
7099 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7100 int row, int col, int v);
7101 __isl_give isl_mat *isl_mat_set_element_val(
7102 __isl_take isl_mat *mat, int row, int col,
7103 __isl_take isl_val *v);
7105 C<isl_mat_get_element> will return a negative value if anything went wrong.
7106 In that case, the value of C<*v> is undefined.
7108 The following function can be used to compute the (right) inverse
7109 of a matrix, i.e., a matrix such that the product of the original
7110 and the inverse (in that order) is a multiple of the identity matrix.
7111 The input matrix is assumed to be of full row-rank.
7113 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7115 The following function can be used to compute the (right) kernel
7116 (or null space) of a matrix, i.e., a matrix such that the product of
7117 the original and the kernel (in that order) is the zero matrix.
7119 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7121 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7123 The following functions determine
7124 an upper or lower bound on a quasipolynomial over its domain.
7126 __isl_give isl_pw_qpolynomial_fold *
7127 isl_pw_qpolynomial_bound(
7128 __isl_take isl_pw_qpolynomial *pwqp,
7129 enum isl_fold type, int *tight);
7131 __isl_give isl_union_pw_qpolynomial_fold *
7132 isl_union_pw_qpolynomial_bound(
7133 __isl_take isl_union_pw_qpolynomial *upwqp,
7134 enum isl_fold type, int *tight);
7136 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7137 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7138 is the returned bound is known be tight, i.e., for each value
7139 of the parameters there is at least
7140 one element in the domain that reaches the bound.
7141 If the domain of C<pwqp> is not wrapping, then the bound is computed
7142 over all elements in that domain and the result has a purely parametric
7143 domain. If the domain of C<pwqp> is wrapping, then the bound is
7144 computed over the range of the wrapped relation. The domain of the
7145 wrapped relation becomes the domain of the result.
7147 =head2 Parametric Vertex Enumeration
7149 The parametric vertex enumeration described in this section
7150 is mainly intended to be used internally and by the C<barvinok>
7153 #include <isl/vertices.h>
7154 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7155 __isl_keep isl_basic_set *bset);
7157 The function C<isl_basic_set_compute_vertices> performs the
7158 actual computation of the parametric vertices and the chamber
7159 decomposition and store the result in an C<isl_vertices> object.
7160 This information can be queried by either iterating over all
7161 the vertices or iterating over all the chambers or cells
7162 and then iterating over all vertices that are active on the chamber.
7164 int isl_vertices_foreach_vertex(
7165 __isl_keep isl_vertices *vertices,
7166 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7169 int isl_vertices_foreach_cell(
7170 __isl_keep isl_vertices *vertices,
7171 int (*fn)(__isl_take isl_cell *cell, void *user),
7173 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7174 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7177 Other operations that can be performed on an C<isl_vertices> object are
7180 int isl_vertices_get_n_vertices(
7181 __isl_keep isl_vertices *vertices);
7182 void isl_vertices_free(__isl_take isl_vertices *vertices);
7184 Vertices can be inspected and destroyed using the following functions.
7186 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7187 __isl_give isl_basic_set *isl_vertex_get_domain(
7188 __isl_keep isl_vertex *vertex);
7189 __isl_give isl_multi_aff *isl_vertex_get_expr(
7190 __isl_keep isl_vertex *vertex);
7191 void isl_vertex_free(__isl_take isl_vertex *vertex);
7193 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7194 describing the vertex in terms of the parameters,
7195 while C<isl_vertex_get_domain> returns the activity domain
7198 Chambers can be inspected and destroyed using the following functions.
7200 __isl_give isl_basic_set *isl_cell_get_domain(
7201 __isl_keep isl_cell *cell);
7202 void isl_cell_free(__isl_take isl_cell *cell);
7204 =head1 Polyhedral Compilation Library
7206 This section collects functionality in C<isl> that has been specifically
7207 designed for use during polyhedral compilation.
7209 =head2 Schedule Trees
7211 A schedule tree is a structured representation of a schedule,
7212 assigning a relative order to a set of domain elements.
7213 The relative order expressed by the schedule tree is
7214 defined recursively. In particular, the order between
7215 two domain elements is determined by the node that is closest
7216 to the root that refers to both elements and that orders them apart.
7217 Each node in the tree is of one of several types.
7218 The root node is always of type C<isl_schedule_node_domain>
7219 and it describes the domain elements to which the schedule applies.
7220 The other types of nodes are as follows.
7224 =item C<isl_schedule_node_band>
7226 A band of schedule dimensions. Each schedule dimension is represented
7227 by a union piecewise quasi-affine expression. If this expression
7228 assigns a different value to two domain elements, while all previous
7229 schedule dimensions in the same band assign them the same value,
7230 then the two domain elements are ordered according to these two
7233 =item C<isl_schedule_node_filter>
7235 A filter node does not impose any ordering, but rather intersects
7236 the set of domain elements that the current subtree refers to
7237 with a given union set. The subtree of the filter node only
7238 refers to domain elements in the intersection.
7239 A filter node is typically only used a child of a sequence or
7242 =item C<isl_schedule_node_leaf>
7244 A leaf of the schedule tree. Leaf nodes do not impose any ordering.
7246 =item C<isl_schedule_node_sequence>
7248 A sequence node has one or more children, each of which is a filter node.
7249 The filters on these filter nodes form a partition of
7250 the domain elements that the current subtree refers to.
7251 If two domain elements appear in distinct filters then the sequence
7252 node orders them according to the child positions of the corresponding
7255 =item C<isl_schedule_node_set>
7257 A set node is similar to a sequence node, except that
7258 it expresses that domain elements appearing in distinct filters
7259 may have any order. The order of the children of a set node
7260 is therefore also immaterial.
7264 A schedule tree is encapsulated in an C<isl_schedule> object.
7265 The simplest such objects, those with a tree consisting of single domain node,
7266 can be created using the following functions with either an empty
7267 domain or a given domain.
7269 #include <isl/schedule.h>
7270 __isl_give isl_schedule *isl_schedule_empty(
7271 __isl_take isl_space *space);
7272 __isl_give isl_schedule *isl_schedule_from_domain(
7273 __isl_take isl_union_set *domain);
7275 The function C<isl_schedule_constraints_compute_schedule> described
7276 in L</"Scheduling"> can also be used to construct schedules.
7278 C<isl_schedule> objects may be copied and freed using the following functions.
7280 #include <isl/schedule.h>
7281 __isl_give isl_schedule *isl_schedule_copy(
7282 __isl_keep isl_schedule *sched);
7283 __isl_null isl_schedule *isl_schedule_free(
7284 __isl_take isl_schedule *sched);
7286 The domain of the schedule, i.e., the domain described by the root node,
7287 can be obtained using the following function.
7289 #include <isl/schedule.h>
7290 __isl_give isl_union_set *isl_schedule_get_domain(
7291 __isl_keep isl_schedule *schedule);
7293 An C<isl_union_map> representation of the schedule can be obtained
7294 from an C<isl_schedule> using the following function.
7296 #include <isl/schedule.h>
7297 __isl_give isl_union_map *isl_schedule_get_map(
7298 __isl_keep isl_schedule *sched);
7300 The resulting relation encodes the same relative ordering as
7301 the schedule by mapping the domain elements to a common schedule space.
7302 If the schedule_separate_components option is set, then the order
7303 of the children of a set node is explicitly encoded in the result.
7305 A representation of the schedule can be printed using
7307 #include <isl/schedule.h>
7308 __isl_give isl_printer *isl_printer_print_schedule(
7309 __isl_take isl_printer *p,
7310 __isl_keep isl_schedule *schedule);
7312 The schedule tree can be traversed through the use of
7313 C<isl_schedule_node> objects that point to a particular
7314 position in the schedule tree. Whenever a C<isl_schedule_node>
7315 is use to modify a node in the schedule tree, the original schedule
7316 tree is left untouched and the modifications are performed to a copy
7317 of the tree. The returned C<isl_schedule_node> then points to
7318 this modified copy of the tree.
7320 The root of the schedule tree can be obtained using the following function.
7322 #include <isl/schedule.h>
7323 __isl_give isl_schedule_node *isl_schedule_get_root(
7324 __isl_keep isl_schedule *schedule);
7326 A pointer to a newly created schedule tree with a single domain
7327 node can be created using the following function.
7329 #include <isl/schedule_node.h>
7330 __isl_give isl_schedule_node *
7331 isl_schedule_node_from_domain(
7332 __isl_take isl_union_set *domain);
7334 Schedule nodes can be copied and freed using the following functions.
7336 #include <isl/schedule_node.h>
7337 __isl_give isl_schedule_node *isl_schedule_node_copy(
7338 __isl_keep isl_schedule_node *node);
7339 __isl_null isl_schedule_node *isl_schedule_node_free(
7340 __isl_take isl_schedule_node *node);
7342 The following properties can be obtained from a schedule node.
7344 #include <isl/schedule_node.h>
7345 enum isl_schedule_node_type isl_schedule_node_get_type(
7346 __isl_keep isl_schedule_node *node);
7347 enum isl_schedule_node_type
7348 isl_schedule_node_get_parent_type(
7349 __isl_keep isl_schedule_node *node);
7350 __isl_give isl_schedule *isl_schedule_node_get_schedule(
7351 __isl_keep isl_schedule_node *node);
7353 The function C<isl_schedule_node_get_type> returns the type of
7354 the node, while C<isl_schedule_node_get_parent_type> returns
7355 type of the parent of the node, which is required to exist.
7356 The function C<isl_schedule_node_get_schedule> returns a copy
7357 to the schedule to which the node belongs.
7359 The following functions can be used to move the schedule node
7360 to a different position in the tree or to check if such a position
7363 #include <isl/schedule_node.h>
7364 int isl_schedule_node_has_parent(
7365 __isl_keep isl_schedule_node *node);
7366 __isl_give isl_schedule_node *isl_schedule_node_parent(
7367 __isl_take isl_schedule_node *node);
7368 int isl_schedule_node_n_children(
7369 __isl_keep isl_schedule_node *node);
7370 __isl_give isl_schedule_node *isl_schedule_node_child(
7371 __isl_take isl_schedule_node *node, int pos);
7372 int isl_schedule_node_has_children(
7373 __isl_keep isl_schedule_node *node);
7374 __isl_give isl_schedule_node *isl_schedule_node_first_child(
7375 __isl_take isl_schedule_node *node);
7376 int isl_schedule_node_has_previous_sibling(
7377 __isl_keep isl_schedule_node *node);
7378 __isl_give isl_schedule_node *
7379 isl_schedule_node_previous_sibling(
7380 __isl_take isl_schedule_node *node);
7381 int isl_schedule_node_has_next_sibling(
7382 __isl_keep isl_schedule_node *node);
7383 __isl_give isl_schedule_node *
7384 isl_schedule_node_next_sibling(
7385 __isl_take isl_schedule_node *node);
7387 It is also possible to query the number of ancestors of a node,
7388 the position of the current node
7389 within the children of its parent or to obtain a copy of a given
7390 child without destroying the current node.
7392 #include <isl/schedule_node.h>
7393 int isl_schedule_node_get_tree_depth(
7394 __isl_keep isl_schedule_node *node);
7395 int isl_schedule_node_get_child_position(
7396 __isl_keep isl_schedule_node *node);
7397 __isl_give isl_schedule_node *isl_schedule_node_get_child(
7398 __isl_keep isl_schedule_node *node, int pos);
7400 All nodes in a schedule tree or
7401 all descendants of a specific node (including the node) can be visited
7402 in depth-first pre-order using the following functions.
7404 #include <isl/schedule.h>
7405 int isl_schedule_foreach_schedule_node(
7406 __isl_keep isl_schedule *sched,
7407 int (*fn)(__isl_keep isl_schedule_node *node,
7408 void *user), void *user);
7410 #include <isl/schedule_node.h>
7411 int isl_schedule_node_foreach_descendant(
7412 __isl_keep isl_schedule_node *node,
7413 int (*fn)(__isl_keep isl_schedule_node *node,
7414 void *user), void *user);
7416 The callback function is slightly different from the usual
7417 callbacks in that it not only indicates success (non-negative result)
7418 or failure (negative result), but also indicates whether the children
7419 of the given node should be visited. In particular, if the callback
7420 returns a positive value, then the children are visited, but if
7421 the callback returns zero, then the children are not visited.
7423 The following function allows for a depth-first post-order
7424 traversal of the descendants of a specific node (including the node
7425 itself), where the user callback is allowed to modify the
7428 #include <isl/schedule_node.h>
7429 __isl_give isl_schedule_node *
7430 isl_schedule_node_map_descendant(
7431 __isl_take isl_schedule_node *node,
7432 __isl_give isl_schedule_node *(*fn)(
7433 __isl_take isl_schedule_node *node,
7434 void *user), void *user);
7436 The traversal continues from the node returned by the callback function.
7437 It is the responsibility of the user to ensure that this does not
7438 lead to an infinite loop. It is safest to always return a pointer
7439 to the same position (same ancestors and child positions) as the input node.
7441 Several node types have their own functions for querying
7442 (and in some cases setting) some node type specific properties.
7444 #include <isl/schedule_node.h>
7445 __isl_give isl_space *isl_schedule_node_band_get_space(
7446 __isl_keep isl_schedule_node *node);
7447 __isl_give isl_multi_union_pw_aff *
7448 isl_schedule_node_band_get_partial_schedule(
7449 __isl_keep isl_schedule_node *node);
7450 __isl_give isl_union_map *
7451 isl_schedule_node_band_get_partial_schedule_union_map(
7452 __isl_keep isl_schedule_node *node);
7453 unsigned isl_schedule_node_band_n_member(
7454 __isl_keep isl_schedule_node *node);
7455 int isl_schedule_node_band_member_get_coincident(
7456 __isl_keep isl_schedule_node *node, int pos);
7457 __isl_give isl_schedule_node *
7458 isl_schedule_node_band_member_set_coincident(
7459 __isl_take isl_schedule_node *node, int pos,
7461 int isl_schedule_node_band_get_permutable(
7462 __isl_keep isl_schedule_node *node);
7463 __isl_give isl_schedule_node *
7464 isl_schedule_node_band_set_permutable(
7465 __isl_take isl_schedule_node *node, int permutable);
7467 The function C<isl_schedule_node_band_get_space> returns the space
7468 of the partial schedule of the band.
7469 The function C<isl_schedule_node_band_get_partial_schedule_union_map>
7470 returns a representation of the partial schedule of the band node
7471 in the form of an C<isl_union_map>.
7472 The coincident and permutable properties are set by
7473 C<isl_schedule_constraints_compute_schedule> on the schedule tree
7475 A scheduling dimension is considered to be ``coincident''
7476 if it satisfies the coincidence constraints within its band.
7477 That is, if the dependence distances of the coincidence
7478 constraints are all zero in that direction (for fixed
7479 iterations of outer bands).
7480 A band is marked permutable if it was produced using the Pluto-like scheduler.
7481 Note that the scheduler may have to resort to a Feautrier style scheduling
7482 step even if the default scheduler is used.
7484 #include <isl/schedule_node.h>
7485 __isl_give isl_union_set *
7486 isl_schedule_node_domain_get_domain(
7487 __isl_keep isl_schedule_node *node);
7489 #include <isl/schedule_node.h>
7490 __isl_give isl_union_set *
7491 isl_schedule_node_filter_get_filter(
7492 __isl_keep isl_schedule_node *node);
7494 The following functions can be used to obtain an C<isl_union_pw_multi_aff>
7495 or C<isl_union_map> representation of partial schedules related to the node.
7497 #include <isl/schedule_node.h>
7498 __isl_give isl_union_pw_multi_aff *
7499 isl_schedule_node_get_prefix_schedule_union_pw_multi_aff(
7500 __isl_keep isl_schedule_node *node);
7501 __isl_give isl_union_map *
7502 isl_schedule_node_get_prefix_schedule_union_map(
7503 __isl_keep isl_schedule_node *node);
7504 __isl_give isl_union_map *
7505 isl_schedule_node_get_subtree_schedule_union_map(
7506 __isl_keep isl_schedule_node *node);
7508 In particular, the functions
7509 C<isl_schedule_node_get_prefix_schedule_union_pw_multi_aff>
7510 and C<isl_schedule_node_get_prefix_schedule_union_map>
7511 return a relative ordering on the domain elements that reach the given
7512 node determined by its ancestors.
7513 The function C<isl_schedule_node_get_subtree_schedule_union_map>
7514 returns a representation of the partial schedule defined by the
7515 subtree rooted at the given node.
7517 The following function returns the union of universes in the spaces that
7518 contain elements that reach the given node.
7520 #include <isl/schedule_node.h>
7521 __isl_give isl_union_set *
7522 isl_schedule_node_get_universe_domain(
7523 __isl_keep isl_schedule_node *node);
7525 The following functions can be used to introduce additional nodes
7526 in the schedule tree. The new node is introduced at the point
7527 in the tree where the C<isl_schedule_node> points to and
7528 the results points to the new node.
7530 #include <isl/schedule_node.h>
7531 __isl_give isl_schedule_node *
7532 isl_schedule_node_insert_partial_schedule(
7533 __isl_take isl_schedule_node *node,
7534 __isl_take isl_multi_union_pw_aff *schedule);
7536 This function inserts a new band node with (the greatest integer
7537 part of) the given partial schedule.
7539 #include <isl/schedule_node.h>
7540 __isl_give isl_schedule_node *
7541 isl_schedule_node_insert_filter(
7542 __isl_take isl_schedule_node *node,
7543 __isl_take isl_union_set *filter);
7545 This function inserts a new filter node with the given filter.
7546 If the original node already pointed to a filter node, then the
7547 two filter nodes are merged into one.
7549 #include <isl/schedule_node.h>
7550 __isl_give isl_schedule_node *
7551 isl_schedule_node_insert_sequence(
7552 __isl_take isl_schedule_node *node,
7553 __isl_take isl_union_set_list *filters);
7554 __isl_give isl_schedule_node *
7555 isl_schedule_node_insert_set(
7556 __isl_take isl_schedule_node *node,
7557 __isl_take isl_union_set_list *filters);
7559 These functions insert a new sequence or set node with the given
7560 filters as children.
7562 The partial schedule of a band node can be scaled (down) using
7563 the following functions.
7565 #include <isl/schedule_node.h>
7566 __isl_give isl_schedule_node *
7567 isl_schedule_node_band_scale(
7568 __isl_take isl_schedule_node *node,
7569 __isl_take isl_multi_val *mv);
7570 __isl_give isl_schedule_node *
7571 isl_schedule_node_band_scale_down(
7572 __isl_take isl_schedule_node *node,
7573 __isl_take isl_multi_val *mv);
7575 The spaces of the two arguments need to match.
7576 After scaling, the partial schedule is replaced by its greatest
7577 integer part to ensure that the schedule remains integral.
7579 A band node can be tiled using the following function.
7581 #include <isl/schedule_node.h>
7582 __isl_give isl_schedule_node *isl_schedule_node_band_tile(
7583 __isl_take isl_schedule_node *node,
7584 __isl_take isl_multi_val *sizes);
7586 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
7588 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
7589 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
7591 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
7593 The C<isl_schedule_node_band_tile> function tiles
7594 the band using the given tile sizes inside its schedule.
7595 A new child band node is created to represent the point loops and it is
7596 inserted between the modified band and its children.
7597 The C<tile_scale_tile_loops> option specifies whether the tile
7598 loops iterators should be scaled by the tile sizes.
7599 If the C<tile_shift_point_loops> option is set, then the point loops
7600 are shifted to start at zero.
7602 A band node can be split into two nested band nodes
7603 using the following function.
7605 #include <isl/schedule_node.h>
7606 __isl_give isl_schedule_node *isl_schedule_node_band_split(
7607 __isl_take isl_schedule_node *node, int pos);
7609 The resulting outer band node contains the first C<pos> dimensions of
7610 the schedule of C<node> while the inner band contains the remaining dimensions.
7611 The schedules of the two band nodes live in anonymous spaces.
7613 A band node can be moved down to the leaves of the subtree rooted
7614 at the band node using the following function.
7616 #include <isl/schedule_node.h>
7617 __isl_give isl_schedule_node *isl_schedule_node_band_sink(
7618 __isl_take isl_schedule_node *node);
7620 The result points to the node in the resulting tree that is in the same
7621 position as the node pointed to by C<node> in the original tree.
7623 A representation of the schedule node can be printed using
7625 #include <isl/schedule_node.h>
7626 __isl_give isl_printer *isl_printer_print_schedule_node(
7627 __isl_take isl_printer *p,
7628 __isl_keep isl_schedule_node *node);
7630 =head2 Dependence Analysis
7632 C<isl> contains specialized functionality for performing
7633 array dataflow analysis. That is, given a I<sink> access relation
7634 and a collection of possible I<source> access relations,
7635 C<isl> can compute relations that describe
7636 for each iteration of the sink access, which iteration
7637 of which of the source access relations was the last
7638 to access the same data element before the given iteration
7640 The resulting dependence relations map source iterations
7641 to the corresponding sink iterations.
7642 To compute standard flow dependences, the sink should be
7643 a read, while the sources should be writes.
7644 If any of the source accesses are marked as being I<may>
7645 accesses, then there will be a dependence from the last
7646 I<must> access B<and> from any I<may> access that follows
7647 this last I<must> access.
7648 In particular, if I<all> sources are I<may> accesses,
7649 then memory based dependence analysis is performed.
7650 If, on the other hand, all sources are I<must> accesses,
7651 then value based dependence analysis is performed.
7653 #include <isl/flow.h>
7655 typedef int (*isl_access_level_before)(void *first, void *second);
7657 __isl_give isl_access_info *isl_access_info_alloc(
7658 __isl_take isl_map *sink,
7659 void *sink_user, isl_access_level_before fn,
7661 __isl_give isl_access_info *isl_access_info_add_source(
7662 __isl_take isl_access_info *acc,
7663 __isl_take isl_map *source, int must,
7665 __isl_null isl_access_info *isl_access_info_free(
7666 __isl_take isl_access_info *acc);
7668 __isl_give isl_flow *isl_access_info_compute_flow(
7669 __isl_take isl_access_info *acc);
7671 int isl_flow_foreach(__isl_keep isl_flow *deps,
7672 int (*fn)(__isl_take isl_map *dep, int must,
7673 void *dep_user, void *user),
7675 __isl_give isl_map *isl_flow_get_no_source(
7676 __isl_keep isl_flow *deps, int must);
7677 void isl_flow_free(__isl_take isl_flow *deps);
7679 The function C<isl_access_info_compute_flow> performs the actual
7680 dependence analysis. The other functions are used to construct
7681 the input for this function or to read off the output.
7683 The input is collected in an C<isl_access_info>, which can
7684 be created through a call to C<isl_access_info_alloc>.
7685 The arguments to this functions are the sink access relation
7686 C<sink>, a token C<sink_user> used to identify the sink
7687 access to the user, a callback function for specifying the
7688 relative order of source and sink accesses, and the number
7689 of source access relations that will be added.
7690 The callback function has type C<int (*)(void *first, void *second)>.
7691 The function is called with two user supplied tokens identifying
7692 either a source or the sink and it should return the shared nesting
7693 level and the relative order of the two accesses.
7694 In particular, let I<n> be the number of loops shared by
7695 the two accesses. If C<first> precedes C<second> textually,
7696 then the function should return I<2 * n + 1>; otherwise,
7697 it should return I<2 * n>.
7698 The sources can be added to the C<isl_access_info> by performing
7699 (at most) C<max_source> calls to C<isl_access_info_add_source>.
7700 C<must> indicates whether the source is a I<must> access
7701 or a I<may> access. Note that a multi-valued access relation
7702 should only be marked I<must> if every iteration in the domain
7703 of the relation accesses I<all> elements in its image.
7704 The C<source_user> token is again used to identify
7705 the source access. The range of the source access relation
7706 C<source> should have the same dimension as the range
7707 of the sink access relation.
7708 The C<isl_access_info_free> function should usually not be
7709 called explicitly, because it is called implicitly by
7710 C<isl_access_info_compute_flow>.
7712 The result of the dependence analysis is collected in an
7713 C<isl_flow>. There may be elements of
7714 the sink access for which no preceding source access could be
7715 found or for which all preceding sources are I<may> accesses.
7716 The relations containing these elements can be obtained through
7717 calls to C<isl_flow_get_no_source>, the first with C<must> set
7718 and the second with C<must> unset.
7719 In the case of standard flow dependence analysis,
7720 with the sink a read and the sources I<must> writes,
7721 the first relation corresponds to the reads from uninitialized
7722 array elements and the second relation is empty.
7723 The actual flow dependences can be extracted using
7724 C<isl_flow_foreach>. This function will call the user-specified
7725 callback function C<fn> for each B<non-empty> dependence between
7726 a source and the sink. The callback function is called
7727 with four arguments, the actual flow dependence relation
7728 mapping source iterations to sink iterations, a boolean that
7729 indicates whether it is a I<must> or I<may> dependence, a token
7730 identifying the source and an additional C<void *> with value
7731 equal to the third argument of the C<isl_flow_foreach> call.
7732 A dependence is marked I<must> if it originates from a I<must>
7733 source and if it is not followed by any I<may> sources.
7735 After finishing with an C<isl_flow>, the user should call
7736 C<isl_flow_free> to free all associated memory.
7738 A higher-level interface to dependence analysis is provided
7739 by the following function.
7741 #include <isl/flow.h>
7743 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
7744 __isl_take isl_union_map *must_source,
7745 __isl_take isl_union_map *may_source,
7746 __isl_take isl_union_map *schedule,
7747 __isl_give isl_union_map **must_dep,
7748 __isl_give isl_union_map **may_dep,
7749 __isl_give isl_union_map **must_no_source,
7750 __isl_give isl_union_map **may_no_source);
7752 The arrays are identified by the tuple names of the ranges
7753 of the accesses. The iteration domains by the tuple names
7754 of the domains of the accesses and of the schedule.
7755 The relative order of the iteration domains is given by the
7756 schedule. The relations returned through C<must_no_source>
7757 and C<may_no_source> are subsets of C<sink>.
7758 Any of C<must_dep>, C<may_dep>, C<must_no_source>
7759 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
7760 any of the other arguments is treated as an error.
7762 =head3 Interaction with Dependence Analysis
7764 During the dependence analysis, we frequently need to perform
7765 the following operation. Given a relation between sink iterations
7766 and potential source iterations from a particular source domain,
7767 what is the last potential source iteration corresponding to each
7768 sink iteration. It can sometimes be convenient to adjust
7769 the set of potential source iterations before or after each such operation.
7770 The prototypical example is fuzzy array dataflow analysis,
7771 where we need to analyze if, based on data-dependent constraints,
7772 the sink iteration can ever be executed without one or more of
7773 the corresponding potential source iterations being executed.
7774 If so, we can introduce extra parameters and select an unknown
7775 but fixed source iteration from the potential source iterations.
7776 To be able to perform such manipulations, C<isl> provides the following
7779 #include <isl/flow.h>
7781 typedef __isl_give isl_restriction *(*isl_access_restrict)(
7782 __isl_keep isl_map *source_map,
7783 __isl_keep isl_set *sink, void *source_user,
7785 __isl_give isl_access_info *isl_access_info_set_restrict(
7786 __isl_take isl_access_info *acc,
7787 isl_access_restrict fn, void *user);
7789 The function C<isl_access_info_set_restrict> should be called
7790 before calling C<isl_access_info_compute_flow> and registers a callback function
7791 that will be called any time C<isl> is about to compute the last
7792 potential source. The first argument is the (reverse) proto-dependence,
7793 mapping sink iterations to potential source iterations.
7794 The second argument represents the sink iterations for which
7795 we want to compute the last source iteration.
7796 The third argument is the token corresponding to the source
7797 and the final argument is the token passed to C<isl_access_info_set_restrict>.
7798 The callback is expected to return a restriction on either the input or
7799 the output of the operation computing the last potential source.
7800 If the input needs to be restricted then restrictions are needed
7801 for both the source and the sink iterations. The sink iterations
7802 and the potential source iterations will be intersected with these sets.
7803 If the output needs to be restricted then only a restriction on the source
7804 iterations is required.
7805 If any error occurs, the callback should return C<NULL>.
7806 An C<isl_restriction> object can be created, freed and inspected
7807 using the following functions.
7809 #include <isl/flow.h>
7811 __isl_give isl_restriction *isl_restriction_input(
7812 __isl_take isl_set *source_restr,
7813 __isl_take isl_set *sink_restr);
7814 __isl_give isl_restriction *isl_restriction_output(
7815 __isl_take isl_set *source_restr);
7816 __isl_give isl_restriction *isl_restriction_none(
7817 __isl_take isl_map *source_map);
7818 __isl_give isl_restriction *isl_restriction_empty(
7819 __isl_take isl_map *source_map);
7820 __isl_null isl_restriction *isl_restriction_free(
7821 __isl_take isl_restriction *restr);
7823 C<isl_restriction_none> and C<isl_restriction_empty> are special
7824 cases of C<isl_restriction_input>. C<isl_restriction_none>
7825 is essentially equivalent to
7827 isl_restriction_input(isl_set_universe(
7828 isl_space_range(isl_map_get_space(source_map))),
7830 isl_space_domain(isl_map_get_space(source_map))));
7832 whereas C<isl_restriction_empty> is essentially equivalent to
7834 isl_restriction_input(isl_set_empty(
7835 isl_space_range(isl_map_get_space(source_map))),
7837 isl_space_domain(isl_map_get_space(source_map))));
7841 B<The functionality described in this section is fairly new
7842 and may be subject to change.>
7844 #include <isl/schedule.h>
7845 __isl_give isl_schedule *
7846 isl_schedule_constraints_compute_schedule(
7847 __isl_take isl_schedule_constraints *sc);
7849 The function C<isl_schedule_constraints_compute_schedule> can be
7850 used to compute a schedule that satisfies the given schedule constraints.
7851 These schedule constraints include the iteration domain for which
7852 a schedule should be computed and dependences between pairs of
7853 iterations. In particular, these dependences include
7854 I<validity> dependences and I<proximity> dependences.
7855 By default, the algorithm used to construct the schedule is similar
7856 to that of C<Pluto>.
7857 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
7859 The generated schedule respects all validity dependences.
7860 That is, all dependence distances over these dependences in the
7861 scheduled space are lexicographically positive.
7862 The default algorithm tries to ensure that the dependence distances
7863 over coincidence constraints are zero and to minimize the
7864 dependence distances over proximity dependences.
7865 Moreover, it tries to obtain sequences (bands) of schedule dimensions
7866 for groups of domains where the dependence distances over validity
7867 dependences have only non-negative values.
7868 When using Feautrier's algorithm, the coincidence and proximity constraints
7869 are only taken into account during the extension to a
7870 full-dimensional schedule.
7872 An C<isl_schedule_constraints> object can be constructed
7873 and manipulated using the following functions.
7875 #include <isl/schedule.h>
7876 __isl_give isl_schedule_constraints *
7877 isl_schedule_constraints_copy(
7878 __isl_keep isl_schedule_constraints *sc);
7879 __isl_give isl_schedule_constraints *
7880 isl_schedule_constraints_on_domain(
7881 __isl_take isl_union_set *domain);
7882 __isl_give isl_schedule_constraints *
7883 isl_schedule_constraints_set_context(
7884 __isl_take isl_schedule_constraints *sc,
7885 __isl_take isl_set *context);
7886 __isl_give isl_schedule_constraints *
7887 isl_schedule_constraints_set_validity(
7888 __isl_take isl_schedule_constraints *sc,
7889 __isl_take isl_union_map *validity);
7890 __isl_give isl_schedule_constraints *
7891 isl_schedule_constraints_set_coincidence(
7892 __isl_take isl_schedule_constraints *sc,
7893 __isl_take isl_union_map *coincidence);
7894 __isl_give isl_schedule_constraints *
7895 isl_schedule_constraints_set_proximity(
7896 __isl_take isl_schedule_constraints *sc,
7897 __isl_take isl_union_map *proximity);
7898 __isl_give isl_schedule_constraints *
7899 isl_schedule_constraints_set_conditional_validity(
7900 __isl_take isl_schedule_constraints *sc,
7901 __isl_take isl_union_map *condition,
7902 __isl_take isl_union_map *validity);
7903 __isl_null isl_schedule_constraints *
7904 isl_schedule_constraints_free(
7905 __isl_take isl_schedule_constraints *sc);
7907 The initial C<isl_schedule_constraints> object created by
7908 C<isl_schedule_constraints_on_domain> does not impose any constraints.
7909 That is, it has an empty set of dependences.
7910 The function C<isl_schedule_constraints_set_context> allows the user
7911 to specify additional constraints on the parameters that may
7912 be assumed to hold during the construction of the schedule.
7913 The function C<isl_schedule_constraints_set_validity> replaces the
7914 validity dependences, mapping domain elements I<i> to domain
7915 elements that should be scheduled after I<i>.
7916 The function C<isl_schedule_constraints_set_coincidence> replaces the
7917 coincidence dependences, mapping domain elements I<i> to domain
7918 elements that should be scheduled together with I<I>, if possible.
7919 The function C<isl_schedule_constraints_set_proximity> replaces the
7920 proximity dependences, mapping domain elements I<i> to domain
7921 elements that should be scheduled either before I<I>
7922 or as early as possible after I<i>.
7924 The function C<isl_schedule_constraints_set_conditional_validity>
7925 replaces the conditional validity constraints.
7926 A conditional validity constraint is only imposed when any of the corresponding
7927 conditions is satisfied, i.e., when any of them is non-zero.
7928 That is, the scheduler ensures that within each band if the dependence
7929 distances over the condition constraints are not all zero
7930 then all corresponding conditional validity constraints are respected.
7931 A conditional validity constraint corresponds to a condition
7932 if the two are adjacent, i.e., if the domain of one relation intersect
7933 the range of the other relation.
7934 The typical use case of conditional validity constraints is
7935 to allow order constraints between live ranges to be violated
7936 as long as the live ranges themselves are local to the band.
7937 To allow more fine-grained control over which conditions correspond
7938 to which conditional validity constraints, the domains and ranges
7939 of these relations may include I<tags>. That is, the domains and
7940 ranges of those relation may themselves be wrapped relations
7941 where the iteration domain appears in the domain of those wrapped relations
7942 and the range of the wrapped relations can be arbitrarily chosen
7943 by the user. Conditions and conditional validity constraints are only
7944 considered adjacent to each other if the entire wrapped relation matches.
7945 In particular, a relation with a tag will never be considered adjacent
7946 to a relation without a tag.
7948 The following function computes a schedule directly from
7949 an iteration domain and validity and proximity dependences
7950 and is implemented in terms of the functions described above.
7951 The use of C<isl_union_set_compute_schedule> is discouraged.
7953 #include <isl/schedule.h>
7954 __isl_give isl_schedule *isl_union_set_compute_schedule(
7955 __isl_take isl_union_set *domain,
7956 __isl_take isl_union_map *validity,
7957 __isl_take isl_union_map *proximity);
7959 The generated schedule represents a schedule tree.
7960 For more information on schedule trees, see
7961 L</"Schedule Trees">.
7963 A representation of the schedule as a forest of bands can be obtained
7964 using the following function.
7966 __isl_give isl_band_list *isl_schedule_get_band_forest(
7967 __isl_keep isl_schedule *schedule);
7969 If the input schedule is represented by a schedule tree, then a call
7970 to C<isl_schedule_get_band_forest> replaces the internal schedule tree
7971 representation by a band forest representation.
7973 The individual bands can be visited in depth-first post-order
7974 using the following function.
7976 #include <isl/schedule.h>
7977 int isl_schedule_foreach_band(
7978 __isl_keep isl_schedule *sched,
7979 int (*fn)(__isl_keep isl_band *band, void *user),
7982 The list can be manipulated as explained in L<"Lists">.
7983 The bands inside the list can be copied and freed using the following
7986 #include <isl/band.h>
7987 __isl_give isl_band *isl_band_copy(
7988 __isl_keep isl_band *band);
7989 __isl_null isl_band *isl_band_free(
7990 __isl_take isl_band *band);
7992 Each band contains zero or more scheduling dimensions.
7993 These are referred to as the members of the band.
7994 The section of the schedule that corresponds to the band is
7995 referred to as the partial schedule of the band.
7996 For those nodes that participate in a band, the outer scheduling
7997 dimensions form the prefix schedule, while the inner scheduling
7998 dimensions form the suffix schedule.
7999 That is, if we take a cut of the band forest, then the union of
8000 the concatenations of the prefix, partial and suffix schedules of
8001 each band in the cut is equal to the entire schedule (modulo
8002 some possible padding at the end with zero scheduling dimensions).
8003 The properties of a band can be inspected using the following functions.
8005 #include <isl/band.h>
8006 int isl_band_has_children(__isl_keep isl_band *band);
8007 __isl_give isl_band_list *isl_band_get_children(
8008 __isl_keep isl_band *band);
8010 __isl_give isl_union_map *isl_band_get_prefix_schedule(
8011 __isl_keep isl_band *band);
8012 __isl_give isl_union_map *isl_band_get_partial_schedule(
8013 __isl_keep isl_band *band);
8014 __isl_give isl_union_map *isl_band_get_suffix_schedule(
8015 __isl_keep isl_band *band);
8017 int isl_band_n_member(__isl_keep isl_band *band);
8018 int isl_band_member_is_coincident(
8019 __isl_keep isl_band *band, int pos);
8021 int isl_band_list_foreach_band(
8022 __isl_keep isl_band_list *list,
8023 int (*fn)(__isl_keep isl_band *band, void *user),
8026 Note that a scheduling dimension is considered to be ``coincident''
8027 if it satisfies the coincidence constraints within its band.
8028 That is, if the dependence distances of the coincidence
8029 constraints are all zero in that direction (for fixed
8030 iterations of outer bands).
8031 Like C<isl_schedule_foreach_band>,
8032 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
8033 in depth-first post-order.
8035 A band can be tiled using the following function.
8037 #include <isl/band.h>
8038 int isl_band_tile(__isl_keep isl_band *band,
8039 __isl_take isl_vec *sizes);
8041 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
8043 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
8044 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
8046 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
8048 The C<isl_band_tile> function tiles the band using the given tile sizes
8049 inside its schedule.
8050 A new child band is created to represent the point loops and it is
8051 inserted between the modified band and its children.
8052 The C<tile_scale_tile_loops> option specifies whether the tile
8053 loops iterators should be scaled by the tile sizes.
8054 If the C<tile_shift_point_loops> option is set, then the point loops
8055 are shifted to start at zero.
8057 A band can be split into two nested bands using the following function.
8059 int isl_band_split(__isl_keep isl_band *band, int pos);
8061 The resulting outer band contains the first C<pos> dimensions of C<band>
8062 while the inner band contains the remaining dimensions.
8064 A representation of the band can be printed using
8066 #include <isl/band.h>
8067 __isl_give isl_printer *isl_printer_print_band(
8068 __isl_take isl_printer *p,
8069 __isl_keep isl_band *band);
8073 #include <isl/schedule.h>
8074 int isl_options_set_schedule_max_coefficient(
8075 isl_ctx *ctx, int val);
8076 int isl_options_get_schedule_max_coefficient(
8078 int isl_options_set_schedule_max_constant_term(
8079 isl_ctx *ctx, int val);
8080 int isl_options_get_schedule_max_constant_term(
8082 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
8083 int isl_options_get_schedule_fuse(isl_ctx *ctx);
8084 int isl_options_set_schedule_maximize_band_depth(
8085 isl_ctx *ctx, int val);
8086 int isl_options_get_schedule_maximize_band_depth(
8088 int isl_options_set_schedule_outer_coincidence(
8089 isl_ctx *ctx, int val);
8090 int isl_options_get_schedule_outer_coincidence(
8092 int isl_options_set_schedule_split_scaled(
8093 isl_ctx *ctx, int val);
8094 int isl_options_get_schedule_split_scaled(
8096 int isl_options_set_schedule_algorithm(
8097 isl_ctx *ctx, int val);
8098 int isl_options_get_schedule_algorithm(
8100 int isl_options_set_schedule_separate_components(
8101 isl_ctx *ctx, int val);
8102 int isl_options_get_schedule_separate_components(
8107 =item * schedule_max_coefficient
8109 This option enforces that the coefficients for variable and parameter
8110 dimensions in the calculated schedule are not larger than the specified value.
8111 This option can significantly increase the speed of the scheduling calculation
8112 and may also prevent fusing of unrelated dimensions. A value of -1 means that
8113 this option does not introduce bounds on the variable or parameter
8116 =item * schedule_max_constant_term
8118 This option enforces that the constant coefficients in the calculated schedule
8119 are not larger than the maximal constant term. This option can significantly
8120 increase the speed of the scheduling calculation and may also prevent fusing of
8121 unrelated dimensions. A value of -1 means that this option does not introduce
8122 bounds on the constant coefficients.
8124 =item * schedule_fuse
8126 This option controls the level of fusion.
8127 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
8128 resulting schedule will be distributed as much as possible.
8129 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
8130 try to fuse loops in the resulting schedule.
8132 =item * schedule_maximize_band_depth
8134 If this option is set, we do not split bands at the point
8135 where we detect splitting is necessary. Instead, we
8136 backtrack and split bands as early as possible. This
8137 reduces the number of splits and maximizes the width of
8138 the bands. Wider bands give more possibilities for tiling.
8139 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
8140 then bands will be split as early as possible, even if there is no need.
8141 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
8143 =item * schedule_outer_coincidence
8145 If this option is set, then we try to construct schedules
8146 where the outermost scheduling dimension in each band
8147 satisfies the coincidence constraints.
8149 =item * schedule_split_scaled
8151 If this option is set, then we try to construct schedules in which the
8152 constant term is split off from the linear part if the linear parts of
8153 the scheduling rows for all nodes in the graphs have a common non-trivial
8155 The constant term is then placed in a separate band and the linear
8158 =item * schedule_algorithm
8160 Selects the scheduling algorithm to be used.
8161 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
8162 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
8164 =item * schedule_separate_components
8166 If this option is set then the function C<isl_schedule_get_map>
8167 will treat set nodes in the same way as sequence nodes.
8171 =head2 AST Generation
8173 This section describes the C<isl> functionality for generating
8174 ASTs that visit all the elements
8175 in a domain in an order specified by a schedule.
8176 In particular, given a C<isl_union_map>, an AST is generated
8177 that visits all the elements in the domain of the C<isl_union_map>
8178 according to the lexicographic order of the corresponding image
8179 element(s). If the range of the C<isl_union_map> consists of
8180 elements in more than one space, then each of these spaces is handled
8181 separately in an arbitrary order.
8182 It should be noted that the image elements only specify the I<order>
8183 in which the corresponding domain elements should be visited.
8184 No direct relation between the image elements and the loop iterators
8185 in the generated AST should be assumed.
8187 Each AST is generated within a build. The initial build
8188 simply specifies the constraints on the parameters (if any)
8189 and can be created, inspected, copied and freed using the following functions.
8191 #include <isl/ast_build.h>
8192 __isl_give isl_ast_build *isl_ast_build_from_context(
8193 __isl_take isl_set *set);
8194 __isl_give isl_ast_build *isl_ast_build_copy(
8195 __isl_keep isl_ast_build *build);
8196 __isl_null isl_ast_build *isl_ast_build_free(
8197 __isl_take isl_ast_build *build);
8199 The C<set> argument is usually a parameter set with zero or more parameters.
8200 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
8201 and L</"Fine-grained Control over AST Generation">.
8202 Finally, the AST itself can be constructed using the following
8205 #include <isl/ast_build.h>
8206 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
8207 __isl_keep isl_ast_build *build,
8208 __isl_take isl_union_map *schedule);
8210 =head3 Inspecting the AST
8212 The basic properties of an AST node can be obtained as follows.
8214 #include <isl/ast.h>
8215 enum isl_ast_node_type isl_ast_node_get_type(
8216 __isl_keep isl_ast_node *node);
8218 The type of an AST node is one of
8219 C<isl_ast_node_for>,
8221 C<isl_ast_node_block> or
8222 C<isl_ast_node_user>.
8223 An C<isl_ast_node_for> represents a for node.
8224 An C<isl_ast_node_if> represents an if node.
8225 An C<isl_ast_node_block> represents a compound node.
8226 An C<isl_ast_node_user> represents an expression statement.
8227 An expression statement typically corresponds to a domain element, i.e.,
8228 one of the elements that is visited by the AST.
8230 Each type of node has its own additional properties.
8232 #include <isl/ast.h>
8233 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
8234 __isl_keep isl_ast_node *node);
8235 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
8236 __isl_keep isl_ast_node *node);
8237 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
8238 __isl_keep isl_ast_node *node);
8239 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
8240 __isl_keep isl_ast_node *node);
8241 __isl_give isl_ast_node *isl_ast_node_for_get_body(
8242 __isl_keep isl_ast_node *node);
8243 int isl_ast_node_for_is_degenerate(
8244 __isl_keep isl_ast_node *node);
8246 An C<isl_ast_for> is considered degenerate if it is known to execute
8249 #include <isl/ast.h>
8250 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
8251 __isl_keep isl_ast_node *node);
8252 __isl_give isl_ast_node *isl_ast_node_if_get_then(
8253 __isl_keep isl_ast_node *node);
8254 int isl_ast_node_if_has_else(
8255 __isl_keep isl_ast_node *node);
8256 __isl_give isl_ast_node *isl_ast_node_if_get_else(
8257 __isl_keep isl_ast_node *node);
8259 __isl_give isl_ast_node_list *
8260 isl_ast_node_block_get_children(
8261 __isl_keep isl_ast_node *node);
8263 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
8264 __isl_keep isl_ast_node *node);
8266 Each of the returned C<isl_ast_expr>s can in turn be inspected using
8267 the following functions.
8269 #include <isl/ast.h>
8270 enum isl_ast_expr_type isl_ast_expr_get_type(
8271 __isl_keep isl_ast_expr *expr);
8273 The type of an AST expression is one of
8275 C<isl_ast_expr_id> or
8276 C<isl_ast_expr_int>.
8277 An C<isl_ast_expr_op> represents the result of an operation.
8278 An C<isl_ast_expr_id> represents an identifier.
8279 An C<isl_ast_expr_int> represents an integer value.
8281 Each type of expression has its own additional properties.
8283 #include <isl/ast.h>
8284 enum isl_ast_op_type isl_ast_expr_get_op_type(
8285 __isl_keep isl_ast_expr *expr);
8286 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
8287 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
8288 __isl_keep isl_ast_expr *expr, int pos);
8289 int isl_ast_node_foreach_ast_op_type(
8290 __isl_keep isl_ast_node *node,
8291 int (*fn)(enum isl_ast_op_type type, void *user),
8294 C<isl_ast_expr_get_op_type> returns the type of the operation
8295 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
8296 arguments. C<isl_ast_expr_get_op_arg> returns the specified
8298 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
8299 C<isl_ast_op_type> that appears in C<node>.
8300 The operation type is one of the following.
8304 =item C<isl_ast_op_and>
8306 Logical I<and> of two arguments.
8307 Both arguments can be evaluated.
8309 =item C<isl_ast_op_and_then>
8311 Logical I<and> of two arguments.
8312 The second argument can only be evaluated if the first evaluates to true.
8314 =item C<isl_ast_op_or>
8316 Logical I<or> of two arguments.
8317 Both arguments can be evaluated.
8319 =item C<isl_ast_op_or_else>
8321 Logical I<or> of two arguments.
8322 The second argument can only be evaluated if the first evaluates to false.
8324 =item C<isl_ast_op_max>
8326 Maximum of two or more arguments.
8328 =item C<isl_ast_op_min>
8330 Minimum of two or more arguments.
8332 =item C<isl_ast_op_minus>
8336 =item C<isl_ast_op_add>
8338 Sum of two arguments.
8340 =item C<isl_ast_op_sub>
8342 Difference of two arguments.
8344 =item C<isl_ast_op_mul>
8346 Product of two arguments.
8348 =item C<isl_ast_op_div>
8350 Exact division. That is, the result is known to be an integer.
8352 =item C<isl_ast_op_fdiv_q>
8354 Result of integer division, rounded towards negative
8357 =item C<isl_ast_op_pdiv_q>
8359 Result of integer division, where dividend is known to be non-negative.
8361 =item C<isl_ast_op_pdiv_r>
8363 Remainder of integer division, where dividend is known to be non-negative.
8365 =item C<isl_ast_op_zdiv_r>
8367 Equal to zero iff the remainder on integer division is zero.
8369 =item C<isl_ast_op_cond>
8371 Conditional operator defined on three arguments.
8372 If the first argument evaluates to true, then the result
8373 is equal to the second argument. Otherwise, the result
8374 is equal to the third argument.
8375 The second and third argument may only be evaluated if
8376 the first argument evaluates to true and false, respectively.
8377 Corresponds to C<a ? b : c> in C.
8379 =item C<isl_ast_op_select>
8381 Conditional operator defined on three arguments.
8382 If the first argument evaluates to true, then the result
8383 is equal to the second argument. Otherwise, the result
8384 is equal to the third argument.
8385 The second and third argument may be evaluated independently
8386 of the value of the first argument.
8387 Corresponds to C<a * b + (1 - a) * c> in C.
8389 =item C<isl_ast_op_eq>
8393 =item C<isl_ast_op_le>
8395 Less than or equal relation.
8397 =item C<isl_ast_op_lt>
8401 =item C<isl_ast_op_ge>
8403 Greater than or equal relation.
8405 =item C<isl_ast_op_gt>
8407 Greater than relation.
8409 =item C<isl_ast_op_call>
8412 The number of arguments of the C<isl_ast_expr> is one more than
8413 the number of arguments in the function call, the first argument
8414 representing the function being called.
8416 =item C<isl_ast_op_access>
8419 The number of arguments of the C<isl_ast_expr> is one more than
8420 the number of index expressions in the array access, the first argument
8421 representing the array being accessed.
8423 =item C<isl_ast_op_member>
8426 This operation has two arguments, a structure and the name of
8427 the member of the structure being accessed.
8431 #include <isl/ast.h>
8432 __isl_give isl_id *isl_ast_expr_get_id(
8433 __isl_keep isl_ast_expr *expr);
8435 Return the identifier represented by the AST expression.
8437 #include <isl/ast.h>
8438 __isl_give isl_val *isl_ast_expr_get_val(
8439 __isl_keep isl_ast_expr *expr);
8441 Return the integer represented by the AST expression.
8443 =head3 Properties of ASTs
8445 #include <isl/ast.h>
8446 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
8447 __isl_keep isl_ast_expr *expr2);
8449 Check if two C<isl_ast_expr>s are equal to each other.
8451 =head3 Manipulating and printing the AST
8453 AST nodes can be copied and freed using the following functions.
8455 #include <isl/ast.h>
8456 __isl_give isl_ast_node *isl_ast_node_copy(
8457 __isl_keep isl_ast_node *node);
8458 __isl_null isl_ast_node *isl_ast_node_free(
8459 __isl_take isl_ast_node *node);
8461 AST expressions can be copied and freed using the following functions.
8463 #include <isl/ast.h>
8464 __isl_give isl_ast_expr *isl_ast_expr_copy(
8465 __isl_keep isl_ast_expr *expr);
8466 __isl_null isl_ast_expr *isl_ast_expr_free(
8467 __isl_take isl_ast_expr *expr);
8469 New AST expressions can be created either directly or within
8470 the context of an C<isl_ast_build>.
8472 #include <isl/ast.h>
8473 __isl_give isl_ast_expr *isl_ast_expr_from_val(
8474 __isl_take isl_val *v);
8475 __isl_give isl_ast_expr *isl_ast_expr_from_id(
8476 __isl_take isl_id *id);
8477 __isl_give isl_ast_expr *isl_ast_expr_neg(
8478 __isl_take isl_ast_expr *expr);
8479 __isl_give isl_ast_expr *isl_ast_expr_address_of(
8480 __isl_take isl_ast_expr *expr);
8481 __isl_give isl_ast_expr *isl_ast_expr_add(
8482 __isl_take isl_ast_expr *expr1,
8483 __isl_take isl_ast_expr *expr2);
8484 __isl_give isl_ast_expr *isl_ast_expr_sub(
8485 __isl_take isl_ast_expr *expr1,
8486 __isl_take isl_ast_expr *expr2);
8487 __isl_give isl_ast_expr *isl_ast_expr_mul(
8488 __isl_take isl_ast_expr *expr1,
8489 __isl_take isl_ast_expr *expr2);
8490 __isl_give isl_ast_expr *isl_ast_expr_div(
8491 __isl_take isl_ast_expr *expr1,
8492 __isl_take isl_ast_expr *expr2);
8493 __isl_give isl_ast_expr *isl_ast_expr_and(
8494 __isl_take isl_ast_expr *expr1,
8495 __isl_take isl_ast_expr *expr2)
8496 __isl_give isl_ast_expr *isl_ast_expr_or(
8497 __isl_take isl_ast_expr *expr1,
8498 __isl_take isl_ast_expr *expr2)
8499 __isl_give isl_ast_expr *isl_ast_expr_eq(
8500 __isl_take isl_ast_expr *expr1,
8501 __isl_take isl_ast_expr *expr2);
8502 __isl_give isl_ast_expr *isl_ast_expr_le(
8503 __isl_take isl_ast_expr *expr1,
8504 __isl_take isl_ast_expr *expr2);
8505 __isl_give isl_ast_expr *isl_ast_expr_lt(
8506 __isl_take isl_ast_expr *expr1,
8507 __isl_take isl_ast_expr *expr2);
8508 __isl_give isl_ast_expr *isl_ast_expr_ge(
8509 __isl_take isl_ast_expr *expr1,
8510 __isl_take isl_ast_expr *expr2);
8511 __isl_give isl_ast_expr *isl_ast_expr_gt(
8512 __isl_take isl_ast_expr *expr1,
8513 __isl_take isl_ast_expr *expr2);
8514 __isl_give isl_ast_expr *isl_ast_expr_access(
8515 __isl_take isl_ast_expr *array,
8516 __isl_take isl_ast_expr_list *indices);
8518 The function C<isl_ast_expr_address_of> can be applied to an
8519 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
8520 to represent the address of the C<isl_ast_expr_access>.
8522 #include <isl/ast_build.h>
8523 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
8524 __isl_keep isl_ast_build *build,
8525 __isl_take isl_pw_aff *pa);
8526 __isl_give isl_ast_expr *
8527 isl_ast_build_access_from_pw_multi_aff(
8528 __isl_keep isl_ast_build *build,
8529 __isl_take isl_pw_multi_aff *pma);
8530 __isl_give isl_ast_expr *
8531 isl_ast_build_access_from_multi_pw_aff(
8532 __isl_keep isl_ast_build *build,
8533 __isl_take isl_multi_pw_aff *mpa);
8534 __isl_give isl_ast_expr *
8535 isl_ast_build_call_from_pw_multi_aff(
8536 __isl_keep isl_ast_build *build,
8537 __isl_take isl_pw_multi_aff *pma);
8538 __isl_give isl_ast_expr *
8539 isl_ast_build_call_from_multi_pw_aff(
8540 __isl_keep isl_ast_build *build,
8541 __isl_take isl_multi_pw_aff *mpa);
8543 The domains of C<pa>, C<mpa> and C<pma> should correspond
8544 to the schedule space of C<build>.
8545 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
8546 the function being called.
8547 If the accessed space is a nested relation, then it is taken
8548 to represent an access of the member specified by the range
8549 of this nested relation of the structure specified by the domain
8550 of the nested relation.
8552 The following functions can be used to modify an C<isl_ast_expr>.
8554 #include <isl/ast.h>
8555 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
8556 __isl_take isl_ast_expr *expr, int pos,
8557 __isl_take isl_ast_expr *arg);
8559 Replace the argument of C<expr> at position C<pos> by C<arg>.
8561 #include <isl/ast.h>
8562 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
8563 __isl_take isl_ast_expr *expr,
8564 __isl_take isl_id_to_ast_expr *id2expr);
8566 The function C<isl_ast_expr_substitute_ids> replaces the
8567 subexpressions of C<expr> of type C<isl_ast_expr_id>
8568 by the corresponding expression in C<id2expr>, if there is any.
8571 User specified data can be attached to an C<isl_ast_node> and obtained
8572 from the same C<isl_ast_node> using the following functions.
8574 #include <isl/ast.h>
8575 __isl_give isl_ast_node *isl_ast_node_set_annotation(
8576 __isl_take isl_ast_node *node,
8577 __isl_take isl_id *annotation);
8578 __isl_give isl_id *isl_ast_node_get_annotation(
8579 __isl_keep isl_ast_node *node);
8581 Basic printing can be performed using the following functions.
8583 #include <isl/ast.h>
8584 __isl_give isl_printer *isl_printer_print_ast_expr(
8585 __isl_take isl_printer *p,
8586 __isl_keep isl_ast_expr *expr);
8587 __isl_give isl_printer *isl_printer_print_ast_node(
8588 __isl_take isl_printer *p,
8589 __isl_keep isl_ast_node *node);
8590 __isl_give char *isl_ast_expr_to_str(
8591 __isl_keep isl_ast_expr *expr);
8593 More advanced printing can be performed using the following functions.
8595 #include <isl/ast.h>
8596 __isl_give isl_printer *isl_ast_op_type_print_macro(
8597 enum isl_ast_op_type type,
8598 __isl_take isl_printer *p);
8599 __isl_give isl_printer *isl_ast_node_print_macros(
8600 __isl_keep isl_ast_node *node,
8601 __isl_take isl_printer *p);
8602 __isl_give isl_printer *isl_ast_node_print(
8603 __isl_keep isl_ast_node *node,
8604 __isl_take isl_printer *p,
8605 __isl_take isl_ast_print_options *options);
8606 __isl_give isl_printer *isl_ast_node_for_print(
8607 __isl_keep isl_ast_node *node,
8608 __isl_take isl_printer *p,
8609 __isl_take isl_ast_print_options *options);
8610 __isl_give isl_printer *isl_ast_node_if_print(
8611 __isl_keep isl_ast_node *node,
8612 __isl_take isl_printer *p,
8613 __isl_take isl_ast_print_options *options);
8615 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
8616 C<isl> may print out an AST that makes use of macros such
8617 as C<floord>, C<min> and C<max>.
8618 C<isl_ast_op_type_print_macro> prints out the macro
8619 corresponding to a specific C<isl_ast_op_type>.
8620 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
8621 for expressions where these macros would be used and prints
8622 out the required macro definitions.
8623 Essentially, C<isl_ast_node_print_macros> calls
8624 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
8625 as function argument.
8626 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
8627 C<isl_ast_node_if_print> print an C<isl_ast_node>
8628 in C<ISL_FORMAT_C>, but allow for some extra control
8629 through an C<isl_ast_print_options> object.
8630 This object can be created using the following functions.
8632 #include <isl/ast.h>
8633 __isl_give isl_ast_print_options *
8634 isl_ast_print_options_alloc(isl_ctx *ctx);
8635 __isl_give isl_ast_print_options *
8636 isl_ast_print_options_copy(
8637 __isl_keep isl_ast_print_options *options);
8638 __isl_null isl_ast_print_options *
8639 isl_ast_print_options_free(
8640 __isl_take isl_ast_print_options *options);
8642 __isl_give isl_ast_print_options *
8643 isl_ast_print_options_set_print_user(
8644 __isl_take isl_ast_print_options *options,
8645 __isl_give isl_printer *(*print_user)(
8646 __isl_take isl_printer *p,
8647 __isl_take isl_ast_print_options *options,
8648 __isl_keep isl_ast_node *node, void *user),
8650 __isl_give isl_ast_print_options *
8651 isl_ast_print_options_set_print_for(
8652 __isl_take isl_ast_print_options *options,
8653 __isl_give isl_printer *(*print_for)(
8654 __isl_take isl_printer *p,
8655 __isl_take isl_ast_print_options *options,
8656 __isl_keep isl_ast_node *node, void *user),
8659 The callback set by C<isl_ast_print_options_set_print_user>
8660 is called whenever a node of type C<isl_ast_node_user> needs to
8662 The callback set by C<isl_ast_print_options_set_print_for>
8663 is called whenever a node of type C<isl_ast_node_for> needs to
8665 Note that C<isl_ast_node_for_print> will I<not> call the
8666 callback set by C<isl_ast_print_options_set_print_for> on the node
8667 on which C<isl_ast_node_for_print> is called, but only on nested
8668 nodes of type C<isl_ast_node_for>. It is therefore safe to
8669 call C<isl_ast_node_for_print> from within the callback set by
8670 C<isl_ast_print_options_set_print_for>.
8672 The following option determines the type to be used for iterators
8673 while printing the AST.
8675 int isl_options_set_ast_iterator_type(
8676 isl_ctx *ctx, const char *val);
8677 const char *isl_options_get_ast_iterator_type(
8680 The AST printer only prints body nodes as blocks if these
8681 blocks cannot be safely omitted.
8682 For example, a C<for> node with one body node will not be
8683 surrounded with braces in C<ISL_FORMAT_C>.
8684 A block will always be printed by setting the following option.
8686 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
8688 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
8692 #include <isl/ast_build.h>
8693 int isl_options_set_ast_build_atomic_upper_bound(
8694 isl_ctx *ctx, int val);
8695 int isl_options_get_ast_build_atomic_upper_bound(
8697 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
8699 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
8700 int isl_options_set_ast_build_exploit_nested_bounds(
8701 isl_ctx *ctx, int val);
8702 int isl_options_get_ast_build_exploit_nested_bounds(
8704 int isl_options_set_ast_build_group_coscheduled(
8705 isl_ctx *ctx, int val);
8706 int isl_options_get_ast_build_group_coscheduled(
8708 int isl_options_set_ast_build_scale_strides(
8709 isl_ctx *ctx, int val);
8710 int isl_options_get_ast_build_scale_strides(
8712 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
8714 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
8715 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
8717 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
8721 =item * ast_build_atomic_upper_bound
8723 Generate loop upper bounds that consist of the current loop iterator,
8724 an operator and an expression not involving the iterator.
8725 If this option is not set, then the current loop iterator may appear
8726 several times in the upper bound.
8727 For example, when this option is turned off, AST generation
8730 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
8734 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
8737 When the option is turned on, the following AST is generated
8739 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
8742 =item * ast_build_prefer_pdiv
8744 If this option is turned off, then the AST generation will
8745 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
8746 operators, but no C<isl_ast_op_pdiv_q> or
8747 C<isl_ast_op_pdiv_r> operators.
8748 If this options is turned on, then C<isl> will try to convert
8749 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
8750 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
8752 =item * ast_build_exploit_nested_bounds
8754 Simplify conditions based on bounds of nested for loops.
8755 In particular, remove conditions that are implied by the fact
8756 that one or more nested loops have at least one iteration,
8757 meaning that the upper bound is at least as large as the lower bound.
8758 For example, when this option is turned off, AST generation
8761 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
8767 for (int c0 = 0; c0 <= N; c0 += 1)
8768 for (int c1 = 0; c1 <= M; c1 += 1)
8771 When the option is turned on, the following AST is generated
8773 for (int c0 = 0; c0 <= N; c0 += 1)
8774 for (int c1 = 0; c1 <= M; c1 += 1)
8777 =item * ast_build_group_coscheduled
8779 If two domain elements are assigned the same schedule point, then
8780 they may be executed in any order and they may even appear in different
8781 loops. If this options is set, then the AST generator will make
8782 sure that coscheduled domain elements do not appear in separate parts
8783 of the AST. This is useful in case of nested AST generation
8784 if the outer AST generation is given only part of a schedule
8785 and the inner AST generation should handle the domains that are
8786 coscheduled by this initial part of the schedule together.
8787 For example if an AST is generated for a schedule
8789 { A[i] -> [0]; B[i] -> [0] }
8791 then the C<isl_ast_build_set_create_leaf> callback described
8792 below may get called twice, once for each domain.
8793 Setting this option ensures that the callback is only called once
8794 on both domains together.
8796 =item * ast_build_separation_bounds
8798 This option specifies which bounds to use during separation.
8799 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
8800 then all (possibly implicit) bounds on the current dimension will
8801 be used during separation.
8802 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
8803 then only those bounds that are explicitly available will
8804 be used during separation.
8806 =item * ast_build_scale_strides
8808 This option specifies whether the AST generator is allowed
8809 to scale down iterators of strided loops.
8811 =item * ast_build_allow_else
8813 This option specifies whether the AST generator is allowed
8814 to construct if statements with else branches.
8816 =item * ast_build_allow_or
8818 This option specifies whether the AST generator is allowed
8819 to construct if conditions with disjunctions.
8823 =head3 Fine-grained Control over AST Generation
8825 Besides specifying the constraints on the parameters,
8826 an C<isl_ast_build> object can be used to control
8827 various aspects of the AST generation process.
8828 The most prominent way of control is through ``options'',
8829 which can be set using the following function.
8831 #include <isl/ast_build.h>
8832 __isl_give isl_ast_build *
8833 isl_ast_build_set_options(
8834 __isl_take isl_ast_build *control,
8835 __isl_take isl_union_map *options);
8837 The options are encoded in an C<isl_union_map>.
8838 The domain of this union relation refers to the schedule domain,
8839 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
8840 In the case of nested AST generation (see L</"Nested AST Generation">),
8841 the domain of C<options> should refer to the extra piece of the schedule.
8842 That is, it should be equal to the range of the wrapped relation in the
8843 range of the schedule.
8844 The range of the options can consist of elements in one or more spaces,
8845 the names of which determine the effect of the option.
8846 The values of the range typically also refer to the schedule dimension
8847 to which the option applies. In case of nested AST generation
8848 (see L</"Nested AST Generation">), these values refer to the position
8849 of the schedule dimension within the innermost AST generation.
8850 The constraints on the domain elements of
8851 the option should only refer to this dimension and earlier dimensions.
8852 We consider the following spaces.
8856 =item C<separation_class>
8858 This space is a wrapped relation between two one dimensional spaces.
8859 The input space represents the schedule dimension to which the option
8860 applies and the output space represents the separation class.
8861 While constructing a loop corresponding to the specified schedule
8862 dimension(s), the AST generator will try to generate separate loops
8863 for domain elements that are assigned different classes.
8864 If only some of the elements are assigned a class, then those elements
8865 that are not assigned any class will be treated as belonging to a class
8866 that is separate from the explicitly assigned classes.
8867 The typical use case for this option is to separate full tiles from
8869 The other options, described below, are applied after the separation
8872 As an example, consider the separation into full and partial tiles
8873 of a tiling of a triangular domain.
8874 Take, for example, the domain
8876 { A[i,j] : 0 <= i,j and i + j <= 100 }
8878 and a tiling into tiles of 10 by 10. The input to the AST generator
8879 is then the schedule
8881 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
8884 Without any options, the following AST is generated
8886 for (int c0 = 0; c0 <= 10; c0 += 1)
8887 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8888 for (int c2 = 10 * c0;
8889 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8891 for (int c3 = 10 * c1;
8892 c3 <= min(10 * c1 + 9, -c2 + 100);
8896 Separation into full and partial tiles can be obtained by assigning
8897 a class, say C<0>, to the full tiles. The full tiles are represented by those
8898 values of the first and second schedule dimensions for which there are
8899 values of the third and fourth dimensions to cover an entire tile.
8900 That is, we need to specify the following option
8902 { [a,b,c,d] -> separation_class[[0]->[0]] :
8903 exists b': 0 <= 10a,10b' and
8904 10a+9+10b'+9 <= 100;
8905 [a,b,c,d] -> separation_class[[1]->[0]] :
8906 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
8910 { [a, b, c, d] -> separation_class[[1] -> [0]] :
8911 a >= 0 and b >= 0 and b <= 8 - a;
8912 [a, b, c, d] -> separation_class[[0] -> [0]] :
8915 With this option, the generated AST is as follows
8918 for (int c0 = 0; c0 <= 8; c0 += 1) {
8919 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
8920 for (int c2 = 10 * c0;
8921 c2 <= 10 * c0 + 9; c2 += 1)
8922 for (int c3 = 10 * c1;
8923 c3 <= 10 * c1 + 9; c3 += 1)
8925 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
8926 for (int c2 = 10 * c0;
8927 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8929 for (int c3 = 10 * c1;
8930 c3 <= min(-c2 + 100, 10 * c1 + 9);
8934 for (int c0 = 9; c0 <= 10; c0 += 1)
8935 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8936 for (int c2 = 10 * c0;
8937 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8939 for (int c3 = 10 * c1;
8940 c3 <= min(10 * c1 + 9, -c2 + 100);
8947 This is a single-dimensional space representing the schedule dimension(s)
8948 to which ``separation'' should be applied. Separation tries to split
8949 a loop into several pieces if this can avoid the generation of guards
8951 See also the C<atomic> option.
8955 This is a single-dimensional space representing the schedule dimension(s)
8956 for which the domains should be considered ``atomic''. That is, the
8957 AST generator will make sure that any given domain space will only appear
8958 in a single loop at the specified level.
8960 Consider the following schedule
8962 { a[i] -> [i] : 0 <= i < 10;
8963 b[i] -> [i+1] : 0 <= i < 10 }
8965 If the following option is specified
8967 { [i] -> separate[x] }
8969 then the following AST will be generated
8973 for (int c0 = 1; c0 <= 9; c0 += 1) {
8980 If, on the other hand, the following option is specified
8982 { [i] -> atomic[x] }
8984 then the following AST will be generated
8986 for (int c0 = 0; c0 <= 10; c0 += 1) {
8993 If neither C<atomic> nor C<separate> is specified, then the AST generator
8994 may produce either of these two results or some intermediate form.
8998 This is a single-dimensional space representing the schedule dimension(s)
8999 that should be I<completely> unrolled.
9000 To obtain a partial unrolling, the user should apply an additional
9001 strip-mining to the schedule and fully unroll the inner loop.
9005 Additional control is available through the following functions.
9007 #include <isl/ast_build.h>
9008 __isl_give isl_ast_build *
9009 isl_ast_build_set_iterators(
9010 __isl_take isl_ast_build *control,
9011 __isl_take isl_id_list *iterators);
9013 The function C<isl_ast_build_set_iterators> allows the user to
9014 specify a list of iterator C<isl_id>s to be used as iterators.
9015 If the input schedule is injective, then
9016 the number of elements in this list should be as large as the dimension
9017 of the schedule space, but no direct correspondence should be assumed
9018 between dimensions and elements.
9019 If the input schedule is not injective, then an additional number
9020 of C<isl_id>s equal to the largest dimension of the input domains
9022 If the number of provided C<isl_id>s is insufficient, then additional
9023 names are automatically generated.
9025 #include <isl/ast_build.h>
9026 __isl_give isl_ast_build *
9027 isl_ast_build_set_create_leaf(
9028 __isl_take isl_ast_build *control,
9029 __isl_give isl_ast_node *(*fn)(
9030 __isl_take isl_ast_build *build,
9031 void *user), void *user);
9034 C<isl_ast_build_set_create_leaf> function allows for the
9035 specification of a callback that should be called whenever the AST
9036 generator arrives at an element of the schedule domain.
9037 The callback should return an AST node that should be inserted
9038 at the corresponding position of the AST. The default action (when
9039 the callback is not set) is to continue generating parts of the AST to scan
9040 all the domain elements associated to the schedule domain element
9041 and to insert user nodes, ``calling'' the domain element, for each of them.
9042 The C<build> argument contains the current state of the C<isl_ast_build>.
9043 To ease nested AST generation (see L</"Nested AST Generation">),
9044 all control information that is
9045 specific to the current AST generation such as the options and
9046 the callbacks has been removed from this C<isl_ast_build>.
9047 The callback would typically return the result of a nested
9049 user defined node created using the following function.
9051 #include <isl/ast.h>
9052 __isl_give isl_ast_node *isl_ast_node_alloc_user(
9053 __isl_take isl_ast_expr *expr);
9055 #include <isl/ast_build.h>
9056 __isl_give isl_ast_build *
9057 isl_ast_build_set_at_each_domain(
9058 __isl_take isl_ast_build *build,
9059 __isl_give isl_ast_node *(*fn)(
9060 __isl_take isl_ast_node *node,
9061 __isl_keep isl_ast_build *build,
9062 void *user), void *user);
9063 __isl_give isl_ast_build *
9064 isl_ast_build_set_before_each_for(
9065 __isl_take isl_ast_build *build,
9066 __isl_give isl_id *(*fn)(
9067 __isl_keep isl_ast_build *build,
9068 void *user), void *user);
9069 __isl_give isl_ast_build *
9070 isl_ast_build_set_after_each_for(
9071 __isl_take isl_ast_build *build,
9072 __isl_give isl_ast_node *(*fn)(
9073 __isl_take isl_ast_node *node,
9074 __isl_keep isl_ast_build *build,
9075 void *user), void *user);
9077 The callback set by C<isl_ast_build_set_at_each_domain> will
9078 be called for each domain AST node.
9079 The callbacks set by C<isl_ast_build_set_before_each_for>
9080 and C<isl_ast_build_set_after_each_for> will be called
9081 for each for AST node. The first will be called in depth-first
9082 pre-order, while the second will be called in depth-first post-order.
9083 Since C<isl_ast_build_set_before_each_for> is called before the for
9084 node is actually constructed, it is only passed an C<isl_ast_build>.
9085 The returned C<isl_id> will be added as an annotation (using
9086 C<isl_ast_node_set_annotation>) to the constructed for node.
9087 In particular, if the user has also specified an C<after_each_for>
9088 callback, then the annotation can be retrieved from the node passed to
9089 that callback using C<isl_ast_node_get_annotation>.
9090 All callbacks should C<NULL> on failure.
9091 The given C<isl_ast_build> can be used to create new
9092 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
9093 or C<isl_ast_build_call_from_pw_multi_aff>.
9095 =head3 Nested AST Generation
9097 C<isl> allows the user to create an AST within the context
9098 of another AST. These nested ASTs are created using the
9099 same C<isl_ast_build_ast_from_schedule> function that is used to create the
9100 outer AST. The C<build> argument should be an C<isl_ast_build>
9101 passed to a callback set by
9102 C<isl_ast_build_set_create_leaf>.
9103 The space of the range of the C<schedule> argument should refer
9104 to this build. In particular, the space should be a wrapped
9105 relation and the domain of this wrapped relation should be the
9106 same as that of the range of the schedule returned by
9107 C<isl_ast_build_get_schedule> below.
9108 In practice, the new schedule is typically
9109 created by calling C<isl_union_map_range_product> on the old schedule
9110 and some extra piece of the schedule.
9111 The space of the schedule domain is also available from
9112 the C<isl_ast_build>.
9114 #include <isl/ast_build.h>
9115 __isl_give isl_union_map *isl_ast_build_get_schedule(
9116 __isl_keep isl_ast_build *build);
9117 __isl_give isl_space *isl_ast_build_get_schedule_space(
9118 __isl_keep isl_ast_build *build);
9119 __isl_give isl_ast_build *isl_ast_build_restrict(
9120 __isl_take isl_ast_build *build,
9121 __isl_take isl_set *set);
9123 The C<isl_ast_build_get_schedule> function returns a (partial)
9124 schedule for the domains elements for which part of the AST still needs to
9125 be generated in the current build.
9126 In particular, the domain elements are mapped to those iterations of the loops
9127 enclosing the current point of the AST generation inside which
9128 the domain elements are executed.
9129 No direct correspondence between
9130 the input schedule and this schedule should be assumed.
9131 The space obtained from C<isl_ast_build_get_schedule_space> can be used
9132 to create a set for C<isl_ast_build_restrict> to intersect
9133 with the current build. In particular, the set passed to
9134 C<isl_ast_build_restrict> can have additional parameters.
9135 The ids of the set dimensions in the space returned by
9136 C<isl_ast_build_get_schedule_space> correspond to the
9137 iterators of the already generated loops.
9138 The user should not rely on the ids of the output dimensions
9139 of the relations in the union relation returned by
9140 C<isl_ast_build_get_schedule> having any particular value.
9144 Although C<isl> is mainly meant to be used as a library,
9145 it also contains some basic applications that use some
9146 of the functionality of C<isl>.
9147 The input may be specified in either the L<isl format>
9148 or the L<PolyLib format>.
9150 =head2 C<isl_polyhedron_sample>
9152 C<isl_polyhedron_sample> takes a polyhedron as input and prints
9153 an integer element of the polyhedron, if there is any.
9154 The first column in the output is the denominator and is always
9155 equal to 1. If the polyhedron contains no integer points,
9156 then a vector of length zero is printed.
9160 C<isl_pip> takes the same input as the C<example> program
9161 from the C<piplib> distribution, i.e., a set of constraints
9162 on the parameters, a line containing only -1 and finally a set
9163 of constraints on a parametric polyhedron.
9164 The coefficients of the parameters appear in the last columns
9165 (but before the final constant column).
9166 The output is the lexicographic minimum of the parametric polyhedron.
9167 As C<isl> currently does not have its own output format, the output
9168 is just a dump of the internal state.
9170 =head2 C<isl_polyhedron_minimize>
9172 C<isl_polyhedron_minimize> computes the minimum of some linear
9173 or affine objective function over the integer points in a polyhedron.
9174 If an affine objective function
9175 is given, then the constant should appear in the last column.
9177 =head2 C<isl_polytope_scan>
9179 Given a polytope, C<isl_polytope_scan> prints
9180 all integer points in the polytope.
9182 =head2 C<isl_codegen>
9184 Given a schedule, a context set and an options relation,
9185 C<isl_codegen> prints out an AST that scans the domain elements
9186 of the schedule in the order of their image(s) taking into account
9187 the constraints in the context set.