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 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_constraints_get_ctx(
527 __isl_keep isl_schedule_constraints *sc);
529 #include <isl/band.h>
530 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
532 #include <isl/ast_build.h>
533 isl_ctx *isl_ast_build_get_ctx(
534 __isl_keep isl_ast_build *build);
537 isl_ctx *isl_ast_expr_get_ctx(
538 __isl_keep isl_ast_expr *expr);
539 isl_ctx *isl_ast_node_get_ctx(
540 __isl_keep isl_ast_node *node);
544 An C<isl_val> represents an integer value, a rational value
545 or one of three special values, infinity, negative infinity and NaN.
546 Some predefined values can be created using the following functions.
549 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
550 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
551 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
552 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
553 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
554 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
556 Specific integer values can be created using the following functions.
559 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
561 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
563 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
564 size_t n, size_t size, const void *chunks);
566 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
567 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
568 The least significant digit is assumed to be stored first.
570 Value objects can be copied and freed using the following functions.
573 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
574 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
576 They can be inspected using the following functions.
579 long isl_val_get_num_si(__isl_keep isl_val *v);
580 long isl_val_get_den_si(__isl_keep isl_val *v);
581 double isl_val_get_d(__isl_keep isl_val *v);
582 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
584 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
585 size_t size, void *chunks);
587 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
588 of C<size> bytes needed to store the absolute value of the
590 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
591 which is assumed to have been preallocated by the caller.
592 The least significant digit is stored first.
593 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
594 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
595 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
597 An C<isl_val> can be modified using the following function.
600 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
603 The following unary properties are defined on C<isl_val>s.
606 int isl_val_sgn(__isl_keep isl_val *v);
607 int isl_val_is_zero(__isl_keep isl_val *v);
608 int isl_val_is_one(__isl_keep isl_val *v);
609 int isl_val_is_negone(__isl_keep isl_val *v);
610 int isl_val_is_nonneg(__isl_keep isl_val *v);
611 int isl_val_is_nonpos(__isl_keep isl_val *v);
612 int isl_val_is_pos(__isl_keep isl_val *v);
613 int isl_val_is_neg(__isl_keep isl_val *v);
614 int isl_val_is_int(__isl_keep isl_val *v);
615 int isl_val_is_rat(__isl_keep isl_val *v);
616 int isl_val_is_nan(__isl_keep isl_val *v);
617 int isl_val_is_infty(__isl_keep isl_val *v);
618 int isl_val_is_neginfty(__isl_keep isl_val *v);
620 Note that the sign of NaN is undefined.
622 The following binary properties are defined on pairs of C<isl_val>s.
625 int isl_val_lt(__isl_keep isl_val *v1,
626 __isl_keep isl_val *v2);
627 int isl_val_le(__isl_keep isl_val *v1,
628 __isl_keep isl_val *v2);
629 int isl_val_gt(__isl_keep isl_val *v1,
630 __isl_keep isl_val *v2);
631 int isl_val_ge(__isl_keep isl_val *v1,
632 __isl_keep isl_val *v2);
633 int isl_val_eq(__isl_keep isl_val *v1,
634 __isl_keep isl_val *v2);
635 int isl_val_ne(__isl_keep isl_val *v1,
636 __isl_keep isl_val *v2);
637 int isl_val_abs_eq(__isl_keep isl_val *v1,
638 __isl_keep isl_val *v2);
640 The function C<isl_val_abs_eq> checks whether its two arguments
641 are equal in absolute value.
643 For integer C<isl_val>s we additionally have the following binary property.
646 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
647 __isl_keep isl_val *v2);
649 An C<isl_val> can also be compared to an integer using the following
650 function. The result is undefined for NaN.
653 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
655 The following unary operations are available on C<isl_val>s.
658 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
659 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
660 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
661 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
662 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
663 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
664 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
666 The following binary operations are available on C<isl_val>s.
669 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
670 __isl_take isl_val *v2);
671 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
672 __isl_take isl_val *v2);
673 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
674 __isl_take isl_val *v2);
675 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
677 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
678 __isl_take isl_val *v2);
679 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
681 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
682 __isl_take isl_val *v2);
683 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
685 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
686 __isl_take isl_val *v2);
688 On integer values, we additionally have the following operations.
691 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
692 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
693 __isl_take isl_val *v2);
694 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
695 __isl_take isl_val *v2);
696 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
697 __isl_take isl_val *v2, __isl_give isl_val **x,
698 __isl_give isl_val **y);
700 The function C<isl_val_gcdext> returns the greatest common divisor g
701 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
702 that C<*x> * C<v1> + C<*y> * C<v2> = g.
704 =head3 GMP specific functions
706 These functions are only available if C<isl> has been compiled with C<GMP>
709 Specific integer and rational values can be created from C<GMP> values using
710 the following functions.
712 #include <isl/val_gmp.h>
713 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
715 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
716 const mpz_t n, const mpz_t d);
718 The numerator and denominator of a rational value can be extracted as
719 C<GMP> values using the following functions.
721 #include <isl/val_gmp.h>
722 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
723 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
725 =head2 Sets and Relations
727 C<isl> uses six types of objects for representing sets and relations,
728 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
729 C<isl_union_set> and C<isl_union_map>.
730 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
731 can be described as a conjunction of affine constraints, while
732 C<isl_set> and C<isl_map> represent unions of
733 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
734 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
735 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
736 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
737 where spaces are considered different if they have a different number
738 of dimensions and/or different names (see L<"Spaces">).
739 The difference between sets and relations (maps) is that sets have
740 one set of variables, while relations have two sets of variables,
741 input variables and output variables.
743 =head2 Error Handling
745 C<isl> supports different ways to react in case a runtime error is triggered.
746 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
747 with two maps that have incompatible spaces. There are three possible ways
748 to react on error: to warn, to continue or to abort.
750 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
751 the last error in the corresponding C<isl_ctx> and the function in which the
752 error was triggered returns C<NULL>. An error does not corrupt internal state,
753 such that isl can continue to be used. C<isl> also provides functions to
754 read the last error and to reset the memory that stores the last error. The
755 last error is only stored for information purposes. Its presence does not
756 change the behavior of C<isl>. Hence, resetting an error is not required to
757 continue to use isl, but only to observe new errors.
760 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
761 void isl_ctx_reset_error(isl_ctx *ctx);
763 Another option is to continue on error. This is similar to warn on error mode,
764 except that C<isl> does not print any warning. This allows a program to
765 implement its own error reporting.
767 The last option is to directly abort the execution of the program from within
768 the isl library. This makes it obviously impossible to recover from an error,
769 but it allows to directly spot the error location. By aborting on error,
770 debuggers break at the location the error occurred and can provide a stack
771 trace. Other tools that automatically provide stack traces on abort or that do
772 not want to continue execution after an error was triggered may also prefer to
775 The on error behavior of isl can be specified by calling
776 C<isl_options_set_on_error> or by setting the command line option
777 C<--isl-on-error>. Valid arguments for the function call are
778 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
779 choices for the command line option are C<warn>, C<continue> and C<abort>.
780 It is also possible to query the current error mode.
782 #include <isl/options.h>
783 int isl_options_set_on_error(isl_ctx *ctx, int val);
784 int isl_options_get_on_error(isl_ctx *ctx);
788 Identifiers are used to identify both individual dimensions
789 and tuples of dimensions. They consist of an optional name and an optional
790 user pointer. The name and the user pointer cannot both be C<NULL>, however.
791 Identifiers with the same name but different pointer values
792 are considered to be distinct.
793 Similarly, identifiers with different names but the same pointer value
794 are also considered to be distinct.
795 Equal identifiers are represented using the same object.
796 Pairs of identifiers can therefore be tested for equality using the
798 Identifiers can be constructed, copied, freed, inspected and printed
799 using the following functions.
802 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
803 __isl_keep const char *name, void *user);
804 __isl_give isl_id *isl_id_set_free_user(
805 __isl_take isl_id *id,
806 __isl_give void (*free_user)(void *user));
807 __isl_give isl_id *isl_id_copy(isl_id *id);
808 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
810 void *isl_id_get_user(__isl_keep isl_id *id);
811 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
813 __isl_give isl_printer *isl_printer_print_id(
814 __isl_take isl_printer *p, __isl_keep isl_id *id);
816 The callback set by C<isl_id_set_free_user> is called on the user
817 pointer when the last reference to the C<isl_id> is freed.
818 Note that C<isl_id_get_name> returns a pointer to some internal
819 data structure, so the result can only be used while the
820 corresponding C<isl_id> is alive.
824 Whenever a new set, relation or similar object is created from scratch,
825 the space in which it lives needs to be specified using an C<isl_space>.
826 Each space involves zero or more parameters and zero, one or two
827 tuples of set or input/output dimensions. The parameters and dimensions
828 are identified by an C<isl_dim_type> and a position.
829 The type C<isl_dim_param> refers to parameters,
830 the type C<isl_dim_set> refers to set dimensions (for spaces
831 with a single tuple of dimensions) and the types C<isl_dim_in>
832 and C<isl_dim_out> refer to input and output dimensions
833 (for spaces with two tuples of dimensions).
834 Local spaces (see L</"Local Spaces">) also contain dimensions
835 of type C<isl_dim_div>.
836 Note that parameters are only identified by their position within
837 a given object. Across different objects, parameters are (usually)
838 identified by their names or identifiers. Only unnamed parameters
839 are identified by their positions across objects. The use of unnamed
840 parameters is discouraged.
842 #include <isl/space.h>
843 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
844 unsigned nparam, unsigned n_in, unsigned n_out);
845 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
847 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
848 unsigned nparam, unsigned dim);
849 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
850 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
852 The space used for creating a parameter domain
853 needs to be created using C<isl_space_params_alloc>.
854 For other sets, the space
855 needs to be created using C<isl_space_set_alloc>, while
856 for a relation, the space
857 needs to be created using C<isl_space_alloc>.
859 To check whether a given space is that of a set or a map
860 or whether it is a parameter space, use these functions:
862 #include <isl/space.h>
863 int isl_space_is_params(__isl_keep isl_space *space);
864 int isl_space_is_set(__isl_keep isl_space *space);
865 int isl_space_is_map(__isl_keep isl_space *space);
867 Spaces can be compared using the following functions:
869 #include <isl/space.h>
870 int isl_space_is_equal(__isl_keep isl_space *space1,
871 __isl_keep isl_space *space2);
872 int isl_space_is_domain(__isl_keep isl_space *space1,
873 __isl_keep isl_space *space2);
874 int isl_space_is_range(__isl_keep isl_space *space1,
875 __isl_keep isl_space *space2);
876 int isl_space_tuple_is_equal(
877 __isl_keep isl_space *space1,
878 enum isl_dim_type type1,
879 __isl_keep isl_space *space2,
880 enum isl_dim_type type2);
882 C<isl_space_is_domain> checks whether the first argument is equal
883 to the domain of the second argument. This requires in particular that
884 the first argument is a set space and that the second argument
885 is a map space. C<isl_space_tuple_is_equal> checks whether the given
886 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
887 spaces are the same. That is, it checks if they have the same
888 identifier (if any), the same dimension and the same internal structure
891 It is often useful to create objects that live in the
892 same space as some other object. This can be accomplished
893 by creating the new objects
894 (see L</"Creating New Sets and Relations"> or
895 L</"Functions">) based on the space
896 of the original object.
899 __isl_give isl_space *isl_basic_set_get_space(
900 __isl_keep isl_basic_set *bset);
901 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
903 #include <isl/union_set.h>
904 __isl_give isl_space *isl_union_set_get_space(
905 __isl_keep isl_union_set *uset);
908 __isl_give isl_space *isl_basic_map_get_space(
909 __isl_keep isl_basic_map *bmap);
910 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
912 #include <isl/union_map.h>
913 __isl_give isl_space *isl_union_map_get_space(
914 __isl_keep isl_union_map *umap);
916 #include <isl/constraint.h>
917 __isl_give isl_space *isl_constraint_get_space(
918 __isl_keep isl_constraint *constraint);
920 #include <isl/polynomial.h>
921 __isl_give isl_space *isl_qpolynomial_get_domain_space(
922 __isl_keep isl_qpolynomial *qp);
923 __isl_give isl_space *isl_qpolynomial_get_space(
924 __isl_keep isl_qpolynomial *qp);
925 __isl_give isl_space *isl_qpolynomial_fold_get_space(
926 __isl_keep isl_qpolynomial_fold *fold);
927 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
928 __isl_keep isl_pw_qpolynomial *pwqp);
929 __isl_give isl_space *isl_pw_qpolynomial_get_space(
930 __isl_keep isl_pw_qpolynomial *pwqp);
931 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
932 __isl_keep isl_pw_qpolynomial_fold *pwf);
933 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
934 __isl_keep isl_pw_qpolynomial_fold *pwf);
935 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
936 __isl_keep isl_union_pw_qpolynomial *upwqp);
937 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
938 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
941 __isl_give isl_space *isl_multi_val_get_space(
942 __isl_keep isl_multi_val *mv);
945 __isl_give isl_space *isl_aff_get_domain_space(
946 __isl_keep isl_aff *aff);
947 __isl_give isl_space *isl_aff_get_space(
948 __isl_keep isl_aff *aff);
949 __isl_give isl_space *isl_pw_aff_get_domain_space(
950 __isl_keep isl_pw_aff *pwaff);
951 __isl_give isl_space *isl_pw_aff_get_space(
952 __isl_keep isl_pw_aff *pwaff);
953 __isl_give isl_space *isl_multi_aff_get_domain_space(
954 __isl_keep isl_multi_aff *maff);
955 __isl_give isl_space *isl_multi_aff_get_space(
956 __isl_keep isl_multi_aff *maff);
957 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
958 __isl_keep isl_pw_multi_aff *pma);
959 __isl_give isl_space *isl_pw_multi_aff_get_space(
960 __isl_keep isl_pw_multi_aff *pma);
961 __isl_give isl_space *isl_union_pw_aff_get_space(
962 __isl_keep isl_union_pw_aff *upa);
963 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
964 __isl_keep isl_union_pw_multi_aff *upma);
965 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
966 __isl_keep isl_multi_pw_aff *mpa);
967 __isl_give isl_space *isl_multi_pw_aff_get_space(
968 __isl_keep isl_multi_pw_aff *mpa);
969 __isl_give isl_space *
970 isl_multi_union_pw_aff_get_domain_space(
971 __isl_keep isl_multi_union_pw_aff *mupa);
972 __isl_give isl_space *
973 isl_multi_union_pw_aff_get_space(
974 __isl_keep isl_multi_union_pw_aff *mupa);
976 #include <isl/point.h>
977 __isl_give isl_space *isl_point_get_space(
978 __isl_keep isl_point *pnt);
980 The number of dimensions of a given type of space
981 may be read off from a space or an object that lives
982 in a space using the following functions.
983 In case of C<isl_space_dim>, type may be
984 C<isl_dim_param>, C<isl_dim_in> (only for relations),
985 C<isl_dim_out> (only for relations), C<isl_dim_set>
986 (only for sets) or C<isl_dim_all>.
988 #include <isl/space.h>
989 unsigned isl_space_dim(__isl_keep isl_space *space,
990 enum isl_dim_type type);
992 #include <isl/local_space.h>
993 int isl_local_space_dim(__isl_keep isl_local_space *ls,
994 enum isl_dim_type type);
997 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
998 enum isl_dim_type type);
999 unsigned isl_set_dim(__isl_keep isl_set *set,
1000 enum isl_dim_type type);
1002 #include <isl/union_set.h>
1003 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1004 enum isl_dim_type type);
1006 #include <isl/map.h>
1007 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1008 enum isl_dim_type type);
1009 unsigned isl_map_dim(__isl_keep isl_map *map,
1010 enum isl_dim_type type);
1012 #include <isl/union_map.h>
1013 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1014 enum isl_dim_type type);
1016 #include <isl/val.h>
1017 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1018 enum isl_dim_type type);
1020 #include <isl/aff.h>
1021 int isl_aff_dim(__isl_keep isl_aff *aff,
1022 enum isl_dim_type type);
1023 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1024 enum isl_dim_type type);
1025 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1026 enum isl_dim_type type);
1027 unsigned isl_pw_multi_aff_dim(
1028 __isl_keep isl_pw_multi_aff *pma,
1029 enum isl_dim_type type);
1030 unsigned isl_multi_pw_aff_dim(
1031 __isl_keep isl_multi_pw_aff *mpa,
1032 enum isl_dim_type type);
1033 unsigned isl_union_pw_aff_dim(
1034 __isl_keep isl_union_pw_aff *upa,
1035 enum isl_dim_type type);
1036 unsigned isl_union_pw_multi_aff_dim(
1037 __isl_keep isl_union_pw_multi_aff *upma,
1038 enum isl_dim_type type);
1039 unsigned isl_multi_union_pw_aff_dim(
1040 __isl_keep isl_multi_union_pw_aff *mupa,
1041 enum isl_dim_type type);
1043 #include <isl/polynomial.h>
1044 unsigned isl_union_pw_qpolynomial_dim(
1045 __isl_keep isl_union_pw_qpolynomial *upwqp,
1046 enum isl_dim_type type);
1047 unsigned isl_union_pw_qpolynomial_fold_dim(
1048 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1049 enum isl_dim_type type);
1051 Note that an C<isl_union_set>, an C<isl_union_map>,
1052 an C<isl_union_pw_multi_aff>,
1053 an C<isl_union_pw_qpolynomial> and
1054 an C<isl_union_pw_qpolynomial_fold>
1055 only have parameters.
1057 The identifiers or names of the individual dimensions of spaces
1058 may be set or read off using the following functions on spaces
1059 or objects that live in spaces.
1060 These functions are mostly useful to obtain the identifiers, positions
1061 or names of the parameters. Identifiers of individual dimensions are
1062 essentially only useful for printing. They are ignored by all other
1063 operations and may not be preserved across those operations.
1065 #include <isl/space.h>
1066 __isl_give isl_space *isl_space_set_dim_id(
1067 __isl_take isl_space *space,
1068 enum isl_dim_type type, unsigned pos,
1069 __isl_take isl_id *id);
1070 int isl_space_has_dim_id(__isl_keep isl_space *space,
1071 enum isl_dim_type type, unsigned pos);
1072 __isl_give isl_id *isl_space_get_dim_id(
1073 __isl_keep isl_space *space,
1074 enum isl_dim_type type, unsigned pos);
1075 __isl_give isl_space *isl_space_set_dim_name(
1076 __isl_take isl_space *space,
1077 enum isl_dim_type type, unsigned pos,
1078 __isl_keep const char *name);
1079 int isl_space_has_dim_name(__isl_keep isl_space *space,
1080 enum isl_dim_type type, unsigned pos);
1081 __isl_keep const char *isl_space_get_dim_name(
1082 __isl_keep isl_space *space,
1083 enum isl_dim_type type, unsigned pos);
1085 #include <isl/local_space.h>
1086 __isl_give isl_local_space *isl_local_space_set_dim_id(
1087 __isl_take isl_local_space *ls,
1088 enum isl_dim_type type, unsigned pos,
1089 __isl_take isl_id *id);
1090 int isl_local_space_has_dim_id(
1091 __isl_keep isl_local_space *ls,
1092 enum isl_dim_type type, unsigned pos);
1093 __isl_give isl_id *isl_local_space_get_dim_id(
1094 __isl_keep isl_local_space *ls,
1095 enum isl_dim_type type, unsigned pos);
1096 __isl_give isl_local_space *isl_local_space_set_dim_name(
1097 __isl_take isl_local_space *ls,
1098 enum isl_dim_type type, unsigned pos, const char *s);
1099 int isl_local_space_has_dim_name(
1100 __isl_keep isl_local_space *ls,
1101 enum isl_dim_type type, unsigned pos)
1102 const char *isl_local_space_get_dim_name(
1103 __isl_keep isl_local_space *ls,
1104 enum isl_dim_type type, unsigned pos);
1106 #include <isl/constraint.h>
1107 const char *isl_constraint_get_dim_name(
1108 __isl_keep isl_constraint *constraint,
1109 enum isl_dim_type type, unsigned pos);
1111 #include <isl/set.h>
1112 __isl_give isl_id *isl_basic_set_get_dim_id(
1113 __isl_keep isl_basic_set *bset,
1114 enum isl_dim_type type, unsigned pos);
1115 __isl_give isl_set *isl_set_set_dim_id(
1116 __isl_take isl_set *set, enum isl_dim_type type,
1117 unsigned pos, __isl_take isl_id *id);
1118 int isl_set_has_dim_id(__isl_keep isl_set *set,
1119 enum isl_dim_type type, unsigned pos);
1120 __isl_give isl_id *isl_set_get_dim_id(
1121 __isl_keep isl_set *set, enum isl_dim_type type,
1123 const char *isl_basic_set_get_dim_name(
1124 __isl_keep isl_basic_set *bset,
1125 enum isl_dim_type type, unsigned pos);
1126 int isl_set_has_dim_name(__isl_keep isl_set *set,
1127 enum isl_dim_type type, unsigned pos);
1128 const char *isl_set_get_dim_name(
1129 __isl_keep isl_set *set,
1130 enum isl_dim_type type, unsigned pos);
1132 #include <isl/map.h>
1133 __isl_give isl_map *isl_map_set_dim_id(
1134 __isl_take isl_map *map, enum isl_dim_type type,
1135 unsigned pos, __isl_take isl_id *id);
1136 int isl_basic_map_has_dim_id(
1137 __isl_keep isl_basic_map *bmap,
1138 enum isl_dim_type type, unsigned pos);
1139 int isl_map_has_dim_id(__isl_keep isl_map *map,
1140 enum isl_dim_type type, unsigned pos);
1141 __isl_give isl_id *isl_map_get_dim_id(
1142 __isl_keep isl_map *map, enum isl_dim_type type,
1144 __isl_give isl_id *isl_union_map_get_dim_id(
1145 __isl_keep isl_union_map *umap,
1146 enum isl_dim_type type, unsigned pos);
1147 const char *isl_basic_map_get_dim_name(
1148 __isl_keep isl_basic_map *bmap,
1149 enum isl_dim_type type, unsigned pos);
1150 int isl_map_has_dim_name(__isl_keep isl_map *map,
1151 enum isl_dim_type type, unsigned pos);
1152 const char *isl_map_get_dim_name(
1153 __isl_keep isl_map *map,
1154 enum isl_dim_type type, unsigned pos);
1156 #include <isl/val.h>
1157 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1158 __isl_take isl_multi_val *mv,
1159 enum isl_dim_type type, unsigned pos,
1160 __isl_take isl_id *id);
1161 __isl_give isl_id *isl_multi_val_get_dim_id(
1162 __isl_keep isl_multi_val *mv,
1163 enum isl_dim_type type, unsigned pos);
1164 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1165 __isl_take isl_multi_val *mv,
1166 enum isl_dim_type type, unsigned pos, const char *s);
1168 #include <isl/aff.h>
1169 __isl_give isl_aff *isl_aff_set_dim_id(
1170 __isl_take isl_aff *aff, enum isl_dim_type type,
1171 unsigned pos, __isl_take isl_id *id);
1172 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1173 __isl_take isl_multi_aff *maff,
1174 enum isl_dim_type type, unsigned pos,
1175 __isl_take isl_id *id);
1176 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1177 __isl_take isl_pw_aff *pma,
1178 enum isl_dim_type type, unsigned pos,
1179 __isl_take isl_id *id);
1180 __isl_give isl_multi_pw_aff *
1181 isl_multi_pw_aff_set_dim_id(
1182 __isl_take isl_multi_pw_aff *mpa,
1183 enum isl_dim_type type, unsigned pos,
1184 __isl_take isl_id *id);
1185 __isl_give isl_multi_union_pw_aff *
1186 isl_multi_union_pw_aff_set_dim_id(
1187 __isl_take isl_multi_union_pw_aff *mupa,
1188 enum isl_dim_type type, unsigned pos,
1189 __isl_take isl_id *id);
1190 __isl_give isl_id *isl_multi_aff_get_dim_id(
1191 __isl_keep isl_multi_aff *ma,
1192 enum isl_dim_type type, unsigned pos);
1193 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1194 enum isl_dim_type type, unsigned pos);
1195 __isl_give isl_id *isl_pw_aff_get_dim_id(
1196 __isl_keep isl_pw_aff *pa,
1197 enum isl_dim_type type, unsigned pos);
1198 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1199 __isl_keep isl_pw_multi_aff *pma,
1200 enum isl_dim_type type, unsigned pos);
1201 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1202 __isl_keep isl_multi_pw_aff *mpa,
1203 enum isl_dim_type type, unsigned pos);
1204 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1205 __isl_keep isl_multi_union_pw_aff *mupa,
1206 enum isl_dim_type type, unsigned pos);
1207 __isl_give isl_aff *isl_aff_set_dim_name(
1208 __isl_take isl_aff *aff, enum isl_dim_type type,
1209 unsigned pos, const char *s);
1210 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1211 __isl_take isl_multi_aff *maff,
1212 enum isl_dim_type type, unsigned pos, const char *s);
1213 __isl_give isl_multi_pw_aff *
1214 isl_multi_pw_aff_set_dim_name(
1215 __isl_take isl_multi_pw_aff *mpa,
1216 enum isl_dim_type type, unsigned pos, const char *s);
1217 __isl_give isl_union_pw_aff *
1218 isl_union_pw_aff_set_dim_name(
1219 __isl_take isl_union_pw_aff *upa,
1220 enum isl_dim_type type, unsigned pos,
1222 __isl_give isl_union_pw_multi_aff *
1223 isl_union_pw_multi_aff_set_dim_name(
1224 __isl_take isl_union_pw_multi_aff *upma,
1225 enum isl_dim_type type, unsigned pos,
1227 __isl_give isl_multi_union_pw_aff *
1228 isl_multi_union_pw_aff_set_dim_name(
1229 __isl_take isl_multi_union_pw_aff *mupa,
1230 enum isl_dim_type type, unsigned pos,
1231 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1232 enum isl_dim_type type, unsigned pos);
1233 const char *isl_pw_aff_get_dim_name(
1234 __isl_keep isl_pw_aff *pa,
1235 enum isl_dim_type type, unsigned pos);
1236 const char *isl_pw_multi_aff_get_dim_name(
1237 __isl_keep isl_pw_multi_aff *pma,
1238 enum isl_dim_type type, unsigned pos);
1240 #include <isl/polynomial.h>
1241 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1242 __isl_take isl_qpolynomial *qp,
1243 enum isl_dim_type type, unsigned pos,
1245 __isl_give isl_pw_qpolynomial *
1246 isl_pw_qpolynomial_set_dim_name(
1247 __isl_take isl_pw_qpolynomial *pwqp,
1248 enum isl_dim_type type, unsigned pos,
1250 __isl_give isl_pw_qpolynomial_fold *
1251 isl_pw_qpolynomial_fold_set_dim_name(
1252 __isl_take isl_pw_qpolynomial_fold *pwf,
1253 enum isl_dim_type type, unsigned pos,
1255 __isl_give isl_union_pw_qpolynomial *
1256 isl_union_pw_qpolynomial_set_dim_name(
1257 __isl_take isl_union_pw_qpolynomial *upwqp,
1258 enum isl_dim_type type, unsigned pos,
1260 __isl_give isl_union_pw_qpolynomial_fold *
1261 isl_union_pw_qpolynomial_fold_set_dim_name(
1262 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1263 enum isl_dim_type type, unsigned pos,
1266 Note that C<isl_space_get_name> returns a pointer to some internal
1267 data structure, so the result can only be used while the
1268 corresponding C<isl_space> is alive.
1269 Also note that every function that operates on two sets or relations
1270 requires that both arguments have the same parameters. This also
1271 means that if one of the arguments has named parameters, then the
1272 other needs to have named parameters too and the names need to match.
1273 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1274 arguments may have different parameters (as long as they are named),
1275 in which case the result will have as parameters the union of the parameters of
1278 Given the identifier or name of a dimension (typically a parameter),
1279 its position can be obtained from the following functions.
1281 #include <isl/space.h>
1282 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1283 enum isl_dim_type type, __isl_keep isl_id *id);
1284 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1285 enum isl_dim_type type, const char *name);
1287 #include <isl/local_space.h>
1288 int isl_local_space_find_dim_by_name(
1289 __isl_keep isl_local_space *ls,
1290 enum isl_dim_type type, const char *name);
1292 #include <isl/val.h>
1293 int isl_multi_val_find_dim_by_id(
1294 __isl_keep isl_multi_val *mv,
1295 enum isl_dim_type type, __isl_keep isl_id *id);
1296 int isl_multi_val_find_dim_by_name(
1297 __isl_keep isl_multi_val *mv,
1298 enum isl_dim_type type, const char *name);
1300 #include <isl/set.h>
1301 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1302 enum isl_dim_type type, __isl_keep isl_id *id);
1303 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1304 enum isl_dim_type type, const char *name);
1306 #include <isl/map.h>
1307 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1308 enum isl_dim_type type, __isl_keep isl_id *id);
1309 int isl_basic_map_find_dim_by_name(
1310 __isl_keep isl_basic_map *bmap,
1311 enum isl_dim_type type, const char *name);
1312 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1313 enum isl_dim_type type, const char *name);
1314 int isl_union_map_find_dim_by_name(
1315 __isl_keep isl_union_map *umap,
1316 enum isl_dim_type type, const char *name);
1318 #include <isl/aff.h>
1319 int isl_multi_aff_find_dim_by_id(
1320 __isl_keep isl_multi_aff *ma,
1321 enum isl_dim_type type, __isl_keep isl_id *id);
1322 int isl_multi_pw_aff_find_dim_by_id(
1323 __isl_keep isl_multi_pw_aff *mpa,
1324 enum isl_dim_type type, __isl_keep isl_id *id);
1325 int isl_multi_union_pw_aff_find_dim_by_id(
1326 __isl_keep isl_union_multi_pw_aff *mupa,
1327 enum isl_dim_type type, __isl_keep isl_id *id);
1328 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1329 enum isl_dim_type type, const char *name);
1330 int isl_multi_aff_find_dim_by_name(
1331 __isl_keep isl_multi_aff *ma,
1332 enum isl_dim_type type, const char *name);
1333 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1334 enum isl_dim_type type, const char *name);
1335 int isl_multi_pw_aff_find_dim_by_name(
1336 __isl_keep isl_multi_pw_aff *mpa,
1337 enum isl_dim_type type, const char *name);
1338 int isl_pw_multi_aff_find_dim_by_name(
1339 __isl_keep isl_pw_multi_aff *pma,
1340 enum isl_dim_type type, const char *name);
1341 int isl_union_pw_aff_find_dim_by_name(
1342 __isl_keep isl_union_pw_aff *upa,
1343 enum isl_dim_type type, const char *name);
1344 int isl_union_pw_multi_aff_find_dim_by_name(
1345 __isl_keep isl_union_pw_multi_aff *upma,
1346 enum isl_dim_type type, const char *name);
1347 int isl_multi_union_pw_aff_find_dim_by_name(
1348 __isl_keep isl_multi_union_pw_aff *mupa,
1349 enum isl_dim_type type, const char *name);
1351 #include <isl/polynomial.h>
1352 int isl_pw_qpolynomial_find_dim_by_name(
1353 __isl_keep isl_pw_qpolynomial *pwqp,
1354 enum isl_dim_type type, const char *name);
1355 int isl_pw_qpolynomial_fold_find_dim_by_name(
1356 __isl_keep isl_pw_qpolynomial_fold *pwf,
1357 enum isl_dim_type type, const char *name);
1358 int isl_union_pw_qpolynomial_find_dim_by_name(
1359 __isl_keep isl_union_pw_qpolynomial *upwqp,
1360 enum isl_dim_type type, const char *name);
1361 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1362 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1363 enum isl_dim_type type, const char *name);
1365 The identifiers or names of entire spaces may be set or read off
1366 using the following functions.
1368 #include <isl/space.h>
1369 __isl_give isl_space *isl_space_set_tuple_id(
1370 __isl_take isl_space *space,
1371 enum isl_dim_type type, __isl_take isl_id *id);
1372 __isl_give isl_space *isl_space_reset_tuple_id(
1373 __isl_take isl_space *space, enum isl_dim_type type);
1374 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1375 enum isl_dim_type type);
1376 __isl_give isl_id *isl_space_get_tuple_id(
1377 __isl_keep isl_space *space, enum isl_dim_type type);
1378 __isl_give isl_space *isl_space_set_tuple_name(
1379 __isl_take isl_space *space,
1380 enum isl_dim_type type, const char *s);
1381 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1382 enum isl_dim_type type);
1383 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1384 enum isl_dim_type type);
1386 #include <isl/local_space.h>
1387 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1388 __isl_take isl_local_space *ls,
1389 enum isl_dim_type type, __isl_take isl_id *id);
1391 #include <isl/set.h>
1392 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1393 __isl_take isl_basic_set *bset,
1394 __isl_take isl_id *id);
1395 __isl_give isl_set *isl_set_set_tuple_id(
1396 __isl_take isl_set *set, __isl_take isl_id *id);
1397 __isl_give isl_set *isl_set_reset_tuple_id(
1398 __isl_take isl_set *set);
1399 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1400 __isl_give isl_id *isl_set_get_tuple_id(
1401 __isl_keep isl_set *set);
1402 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1403 __isl_take isl_basic_set *set, const char *s);
1404 __isl_give isl_set *isl_set_set_tuple_name(
1405 __isl_take isl_set *set, const char *s);
1406 const char *isl_basic_set_get_tuple_name(
1407 __isl_keep isl_basic_set *bset);
1408 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1409 const char *isl_set_get_tuple_name(
1410 __isl_keep isl_set *set);
1412 #include <isl/map.h>
1413 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1414 __isl_take isl_basic_map *bmap,
1415 enum isl_dim_type type, __isl_take isl_id *id);
1416 __isl_give isl_map *isl_map_set_tuple_id(
1417 __isl_take isl_map *map, enum isl_dim_type type,
1418 __isl_take isl_id *id);
1419 __isl_give isl_map *isl_map_reset_tuple_id(
1420 __isl_take isl_map *map, enum isl_dim_type type);
1421 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1422 enum isl_dim_type type);
1423 __isl_give isl_id *isl_map_get_tuple_id(
1424 __isl_keep isl_map *map, enum isl_dim_type type);
1425 __isl_give isl_map *isl_map_set_tuple_name(
1426 __isl_take isl_map *map,
1427 enum isl_dim_type type, const char *s);
1428 const char *isl_basic_map_get_tuple_name(
1429 __isl_keep isl_basic_map *bmap,
1430 enum isl_dim_type type);
1431 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1432 __isl_take isl_basic_map *bmap,
1433 enum isl_dim_type type, const char *s);
1434 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1435 enum isl_dim_type type);
1436 const char *isl_map_get_tuple_name(
1437 __isl_keep isl_map *map,
1438 enum isl_dim_type type);
1440 #include <isl/val.h>
1441 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1442 __isl_take isl_multi_val *mv,
1443 enum isl_dim_type type, __isl_take isl_id *id);
1444 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1445 __isl_take isl_multi_val *mv,
1446 enum isl_dim_type type);
1447 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1448 enum isl_dim_type type);
1449 __isl_give isl_id *isl_multi_val_get_tuple_id(
1450 __isl_keep isl_multi_val *mv,
1451 enum isl_dim_type type);
1452 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1453 __isl_take isl_multi_val *mv,
1454 enum isl_dim_type type, const char *s);
1455 const char *isl_multi_val_get_tuple_name(
1456 __isl_keep isl_multi_val *mv,
1457 enum isl_dim_type type);
1459 #include <isl/aff.h>
1460 __isl_give isl_aff *isl_aff_set_tuple_id(
1461 __isl_take isl_aff *aff,
1462 enum isl_dim_type type, __isl_take isl_id *id);
1463 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1464 __isl_take isl_multi_aff *maff,
1465 enum isl_dim_type type, __isl_take isl_id *id);
1466 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1467 __isl_take isl_pw_aff *pwaff,
1468 enum isl_dim_type type, __isl_take isl_id *id);
1469 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1470 __isl_take isl_pw_multi_aff *pma,
1471 enum isl_dim_type type, __isl_take isl_id *id);
1472 __isl_give isl_multi_union_pw_aff *
1473 isl_multi_union_pw_aff_set_tuple_id(
1474 __isl_take isl_multi_union_pw_aff *mupa,
1475 enum isl_dim_type type, __isl_take isl_id *id);
1476 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1477 __isl_take isl_multi_aff *ma,
1478 enum isl_dim_type type);
1479 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1480 __isl_take isl_pw_aff *pa,
1481 enum isl_dim_type type);
1482 __isl_give isl_multi_pw_aff *
1483 isl_multi_pw_aff_reset_tuple_id(
1484 __isl_take isl_multi_pw_aff *mpa,
1485 enum isl_dim_type type);
1486 __isl_give isl_pw_multi_aff *
1487 isl_pw_multi_aff_reset_tuple_id(
1488 __isl_take isl_pw_multi_aff *pma,
1489 enum isl_dim_type type);
1490 __isl_give isl_multi_union_pw_aff *
1491 isl_multi_union_pw_aff_reset_tuple_id(
1492 __isl_take isl_multi_union_pw_aff *mupa,
1493 enum isl_dim_type type);
1494 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1495 enum isl_dim_type type);
1496 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1497 __isl_keep isl_multi_aff *ma,
1498 enum isl_dim_type type);
1499 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1500 enum isl_dim_type type);
1501 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1502 __isl_keep isl_pw_aff *pa,
1503 enum isl_dim_type type);
1504 int isl_pw_multi_aff_has_tuple_id(
1505 __isl_keep isl_pw_multi_aff *pma,
1506 enum isl_dim_type type);
1507 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1508 __isl_keep isl_pw_multi_aff *pma,
1509 enum isl_dim_type type);
1510 int isl_multi_pw_aff_has_tuple_id(
1511 __isl_keep isl_multi_pw_aff *mpa,
1512 enum isl_dim_type type);
1513 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1514 __isl_keep isl_multi_pw_aff *mpa,
1515 enum isl_dim_type type);
1516 int isl_multi_union_pw_aff_has_tuple_id(
1517 __isl_keep isl_multi_union_pw_aff *mupa,
1518 enum isl_dim_type type);
1519 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1520 __isl_keep isl_multi_union_pw_aff *mupa,
1521 enum isl_dim_type type);
1522 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1523 __isl_take isl_multi_aff *maff,
1524 enum isl_dim_type type, const char *s);
1525 __isl_give isl_multi_pw_aff *
1526 isl_multi_pw_aff_set_tuple_name(
1527 __isl_take isl_multi_pw_aff *mpa,
1528 enum isl_dim_type type, const char *s);
1529 __isl_give isl_multi_union_pw_aff *
1530 isl_multi_union_pw_aff_set_tuple_name(
1531 __isl_take isl_multi_union_pw_aff *mupa,
1532 enum isl_dim_type type, const char *s);
1533 const char *isl_multi_aff_get_tuple_name(
1534 __isl_keep isl_multi_aff *multi,
1535 enum isl_dim_type type);
1536 int isl_pw_multi_aff_has_tuple_name(
1537 __isl_keep isl_pw_multi_aff *pma,
1538 enum isl_dim_type type);
1539 const char *isl_pw_multi_aff_get_tuple_name(
1540 __isl_keep isl_pw_multi_aff *pma,
1541 enum isl_dim_type type);
1542 const char *isl_multi_union_pw_aff_get_tuple_name(
1543 __isl_keep isl_multi_union_pw_aff *mupa,
1544 enum isl_dim_type type);
1546 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1547 or C<isl_dim_set>. As with C<isl_space_get_name>,
1548 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1550 Binary operations require the corresponding spaces of their arguments
1551 to have the same name.
1553 To keep the names of all parameters and tuples, but reset the user pointers
1554 of all the corresponding identifiers, use the following function.
1556 #include <isl/space.h>
1557 __isl_give isl_space *isl_space_reset_user(
1558 __isl_take isl_space *space);
1560 #include <isl/set.h>
1561 __isl_give isl_set *isl_set_reset_user(
1562 __isl_take isl_set *set);
1564 #include <isl/map.h>
1565 __isl_give isl_map *isl_map_reset_user(
1566 __isl_take isl_map *map);
1568 #include <isl/union_set.h>
1569 __isl_give isl_union_set *isl_union_set_reset_user(
1570 __isl_take isl_union_set *uset);
1572 #include <isl/union_map.h>
1573 __isl_give isl_union_map *isl_union_map_reset_user(
1574 __isl_take isl_union_map *umap);
1576 #include <isl/val.h>
1577 __isl_give isl_multi_val *isl_multi_val_reset_user(
1578 __isl_take isl_multi_val *mv);
1580 #include <isl/aff.h>
1581 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1582 __isl_take isl_multi_aff *ma);
1583 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1584 __isl_take isl_pw_aff *pa);
1585 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1586 __isl_take isl_multi_pw_aff *mpa);
1587 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1588 __isl_take isl_pw_multi_aff *pma);
1589 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1590 __isl_take isl_union_pw_aff *upa);
1591 __isl_give isl_multi_union_pw_aff *
1592 isl_multi_union_pw_aff_reset_user(
1593 __isl_take isl_multi_union_pw_aff *mupa);
1594 __isl_give isl_union_pw_multi_aff *
1595 isl_union_pw_multi_aff_reset_user(
1596 __isl_take isl_union_pw_multi_aff *upma);
1598 #include <isl/polynomial.h>
1599 __isl_give isl_pw_qpolynomial *
1600 isl_pw_qpolynomial_reset_user(
1601 __isl_take isl_pw_qpolynomial *pwqp);
1602 __isl_give isl_union_pw_qpolynomial *
1603 isl_union_pw_qpolynomial_reset_user(
1604 __isl_take isl_union_pw_qpolynomial *upwqp);
1605 __isl_give isl_pw_qpolynomial_fold *
1606 isl_pw_qpolynomial_fold_reset_user(
1607 __isl_take isl_pw_qpolynomial_fold *pwf);
1608 __isl_give isl_union_pw_qpolynomial_fold *
1609 isl_union_pw_qpolynomial_fold_reset_user(
1610 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1612 Spaces can be nested. In particular, the domain of a set or
1613 the domain or range of a relation can be a nested relation.
1614 This process is also called I<wrapping>.
1615 The functions for detecting, constructing and deconstructing
1616 such nested spaces can be found in the wrapping properties
1617 of L</"Unary Properties">, the wrapping operations
1618 of L</"Unary Operations"> and the Cartesian product operations
1619 of L</"Basic Operations">.
1621 Spaces can be created from other spaces
1622 using the functions described in L</"Unary Operations">
1623 and L</"Binary Operations">.
1627 A local space is essentially a space with
1628 zero or more existentially quantified variables.
1629 The local space of various objects can be obtained
1630 using the following functions.
1632 #include <isl/constraint.h>
1633 __isl_give isl_local_space *isl_constraint_get_local_space(
1634 __isl_keep isl_constraint *constraint);
1636 #include <isl/set.h>
1637 __isl_give isl_local_space *isl_basic_set_get_local_space(
1638 __isl_keep isl_basic_set *bset);
1640 #include <isl/map.h>
1641 __isl_give isl_local_space *isl_basic_map_get_local_space(
1642 __isl_keep isl_basic_map *bmap);
1644 #include <isl/aff.h>
1645 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1646 __isl_keep isl_aff *aff);
1647 __isl_give isl_local_space *isl_aff_get_local_space(
1648 __isl_keep isl_aff *aff);
1650 A new local space can be created from a space using
1652 #include <isl/local_space.h>
1653 __isl_give isl_local_space *isl_local_space_from_space(
1654 __isl_take isl_space *space);
1656 They can be inspected, modified, copied and freed using the following functions.
1658 #include <isl/local_space.h>
1659 int isl_local_space_is_params(
1660 __isl_keep isl_local_space *ls);
1661 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1662 __isl_give isl_space *isl_local_space_get_space(
1663 __isl_keep isl_local_space *ls);
1664 __isl_give isl_aff *isl_local_space_get_div(
1665 __isl_keep isl_local_space *ls, int pos);
1666 __isl_give isl_local_space *isl_local_space_copy(
1667 __isl_keep isl_local_space *ls);
1668 __isl_null isl_local_space *isl_local_space_free(
1669 __isl_take isl_local_space *ls);
1671 Note that C<isl_local_space_get_div> can only be used on local spaces
1674 Two local spaces can be compared using
1676 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1677 __isl_keep isl_local_space *ls2);
1679 Local spaces can be created from other local spaces
1680 using the functions described in L</"Unary Operations">
1681 and L</"Binary Operations">.
1683 =head2 Creating New Sets and Relations
1685 C<isl> has functions for creating some standard sets and relations.
1689 =item * Empty sets and relations
1691 __isl_give isl_basic_set *isl_basic_set_empty(
1692 __isl_take isl_space *space);
1693 __isl_give isl_basic_map *isl_basic_map_empty(
1694 __isl_take isl_space *space);
1695 __isl_give isl_set *isl_set_empty(
1696 __isl_take isl_space *space);
1697 __isl_give isl_map *isl_map_empty(
1698 __isl_take isl_space *space);
1699 __isl_give isl_union_set *isl_union_set_empty(
1700 __isl_take isl_space *space);
1701 __isl_give isl_union_map *isl_union_map_empty(
1702 __isl_take isl_space *space);
1704 For C<isl_union_set>s and C<isl_union_map>s, the space
1705 is only used to specify the parameters.
1707 =item * Universe sets and relations
1709 __isl_give isl_basic_set *isl_basic_set_universe(
1710 __isl_take isl_space *space);
1711 __isl_give isl_basic_map *isl_basic_map_universe(
1712 __isl_take isl_space *space);
1713 __isl_give isl_set *isl_set_universe(
1714 __isl_take isl_space *space);
1715 __isl_give isl_map *isl_map_universe(
1716 __isl_take isl_space *space);
1717 __isl_give isl_union_set *isl_union_set_universe(
1718 __isl_take isl_union_set *uset);
1719 __isl_give isl_union_map *isl_union_map_universe(
1720 __isl_take isl_union_map *umap);
1722 The sets and relations constructed by the functions above
1723 contain all integer values, while those constructed by the
1724 functions below only contain non-negative values.
1726 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1727 __isl_take isl_space *space);
1728 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1729 __isl_take isl_space *space);
1730 __isl_give isl_set *isl_set_nat_universe(
1731 __isl_take isl_space *space);
1732 __isl_give isl_map *isl_map_nat_universe(
1733 __isl_take isl_space *space);
1735 =item * Identity relations
1737 __isl_give isl_basic_map *isl_basic_map_identity(
1738 __isl_take isl_space *space);
1739 __isl_give isl_map *isl_map_identity(
1740 __isl_take isl_space *space);
1742 The number of input and output dimensions in C<space> needs
1745 =item * Lexicographic order
1747 __isl_give isl_map *isl_map_lex_lt(
1748 __isl_take isl_space *set_space);
1749 __isl_give isl_map *isl_map_lex_le(
1750 __isl_take isl_space *set_space);
1751 __isl_give isl_map *isl_map_lex_gt(
1752 __isl_take isl_space *set_space);
1753 __isl_give isl_map *isl_map_lex_ge(
1754 __isl_take isl_space *set_space);
1755 __isl_give isl_map *isl_map_lex_lt_first(
1756 __isl_take isl_space *space, unsigned n);
1757 __isl_give isl_map *isl_map_lex_le_first(
1758 __isl_take isl_space *space, unsigned n);
1759 __isl_give isl_map *isl_map_lex_gt_first(
1760 __isl_take isl_space *space, unsigned n);
1761 __isl_give isl_map *isl_map_lex_ge_first(
1762 __isl_take isl_space *space, unsigned n);
1764 The first four functions take a space for a B<set>
1765 and return relations that express that the elements in the domain
1766 are lexicographically less
1767 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1768 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1769 than the elements in the range.
1770 The last four functions take a space for a map
1771 and return relations that express that the first C<n> dimensions
1772 in the domain are lexicographically less
1773 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1774 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1775 than the first C<n> dimensions in the range.
1779 A basic set or relation can be converted to a set or relation
1780 using the following functions.
1782 __isl_give isl_set *isl_set_from_basic_set(
1783 __isl_take isl_basic_set *bset);
1784 __isl_give isl_map *isl_map_from_basic_map(
1785 __isl_take isl_basic_map *bmap);
1787 Sets and relations can be converted to union sets and relations
1788 using the following functions.
1790 __isl_give isl_union_set *isl_union_set_from_basic_set(
1791 __isl_take isl_basic_set *bset);
1792 __isl_give isl_union_map *isl_union_map_from_basic_map(
1793 __isl_take isl_basic_map *bmap);
1794 __isl_give isl_union_set *isl_union_set_from_set(
1795 __isl_take isl_set *set);
1796 __isl_give isl_union_map *isl_union_map_from_map(
1797 __isl_take isl_map *map);
1799 The inverse conversions below can only be used if the input
1800 union set or relation is known to contain elements in exactly one
1803 __isl_give isl_set *isl_set_from_union_set(
1804 __isl_take isl_union_set *uset);
1805 __isl_give isl_map *isl_map_from_union_map(
1806 __isl_take isl_union_map *umap);
1808 Sets and relations can be copied and freed again using the following
1811 __isl_give isl_basic_set *isl_basic_set_copy(
1812 __isl_keep isl_basic_set *bset);
1813 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1814 __isl_give isl_union_set *isl_union_set_copy(
1815 __isl_keep isl_union_set *uset);
1816 __isl_give isl_basic_map *isl_basic_map_copy(
1817 __isl_keep isl_basic_map *bmap);
1818 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1819 __isl_give isl_union_map *isl_union_map_copy(
1820 __isl_keep isl_union_map *umap);
1821 __isl_null isl_basic_set *isl_basic_set_free(
1822 __isl_take isl_basic_set *bset);
1823 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1824 __isl_null isl_union_set *isl_union_set_free(
1825 __isl_take isl_union_set *uset);
1826 __isl_null isl_basic_map *isl_basic_map_free(
1827 __isl_take isl_basic_map *bmap);
1828 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1829 __isl_null isl_union_map *isl_union_map_free(
1830 __isl_take isl_union_map *umap);
1832 Other sets and relations can be constructed by starting
1833 from a universe set or relation, adding equality and/or
1834 inequality constraints and then projecting out the
1835 existentially quantified variables, if any.
1836 Constraints can be constructed, manipulated and
1837 added to (or removed from) (basic) sets and relations
1838 using the following functions.
1840 #include <isl/constraint.h>
1841 __isl_give isl_constraint *isl_equality_alloc(
1842 __isl_take isl_local_space *ls);
1843 __isl_give isl_constraint *isl_inequality_alloc(
1844 __isl_take isl_local_space *ls);
1845 __isl_give isl_constraint *isl_constraint_set_constant_si(
1846 __isl_take isl_constraint *constraint, int v);
1847 __isl_give isl_constraint *isl_constraint_set_constant_val(
1848 __isl_take isl_constraint *constraint,
1849 __isl_take isl_val *v);
1850 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1851 __isl_take isl_constraint *constraint,
1852 enum isl_dim_type type, int pos, int v);
1853 __isl_give isl_constraint *
1854 isl_constraint_set_coefficient_val(
1855 __isl_take isl_constraint *constraint,
1856 enum isl_dim_type type, int pos,
1857 __isl_take isl_val *v);
1858 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1859 __isl_take isl_basic_map *bmap,
1860 __isl_take isl_constraint *constraint);
1861 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1862 __isl_take isl_basic_set *bset,
1863 __isl_take isl_constraint *constraint);
1864 __isl_give isl_map *isl_map_add_constraint(
1865 __isl_take isl_map *map,
1866 __isl_take isl_constraint *constraint);
1867 __isl_give isl_set *isl_set_add_constraint(
1868 __isl_take isl_set *set,
1869 __isl_take isl_constraint *constraint);
1870 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1871 __isl_take isl_basic_set *bset,
1872 __isl_take isl_constraint *constraint);
1874 For example, to create a set containing the even integers
1875 between 10 and 42, you would use the following code.
1878 isl_local_space *ls;
1880 isl_basic_set *bset;
1882 space = isl_space_set_alloc(ctx, 0, 2);
1883 bset = isl_basic_set_universe(isl_space_copy(space));
1884 ls = isl_local_space_from_space(space);
1886 c = isl_equality_alloc(isl_local_space_copy(ls));
1887 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1888 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1889 bset = isl_basic_set_add_constraint(bset, c);
1891 c = isl_inequality_alloc(isl_local_space_copy(ls));
1892 c = isl_constraint_set_constant_si(c, -10);
1893 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1894 bset = isl_basic_set_add_constraint(bset, c);
1896 c = isl_inequality_alloc(ls);
1897 c = isl_constraint_set_constant_si(c, 42);
1898 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1899 bset = isl_basic_set_add_constraint(bset, c);
1901 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1905 isl_basic_set *bset;
1906 bset = isl_basic_set_read_from_str(ctx,
1907 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1909 A basic set or relation can also be constructed from two matrices
1910 describing the equalities and the inequalities.
1912 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1913 __isl_take isl_space *space,
1914 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1915 enum isl_dim_type c1,
1916 enum isl_dim_type c2, enum isl_dim_type c3,
1917 enum isl_dim_type c4);
1918 __isl_give isl_basic_map *isl_basic_map_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, enum isl_dim_type c5);
1925 The C<isl_dim_type> arguments indicate the order in which
1926 different kinds of variables appear in the input matrices
1927 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1928 C<isl_dim_set> and C<isl_dim_div> for sets and
1929 of C<isl_dim_cst>, C<isl_dim_param>,
1930 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1932 A (basic or union) set or relation can also be constructed from a
1933 (union) (piecewise) (multiple) affine expression
1934 or a list of affine expressions
1935 (See L</"Functions">).
1937 __isl_give isl_basic_map *isl_basic_map_from_aff(
1938 __isl_take isl_aff *aff);
1939 __isl_give isl_map *isl_map_from_aff(
1940 __isl_take isl_aff *aff);
1941 __isl_give isl_set *isl_set_from_pw_aff(
1942 __isl_take isl_pw_aff *pwaff);
1943 __isl_give isl_map *isl_map_from_pw_aff(
1944 __isl_take isl_pw_aff *pwaff);
1945 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1946 __isl_take isl_space *domain_space,
1947 __isl_take isl_aff_list *list);
1948 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1949 __isl_take isl_multi_aff *maff)
1950 __isl_give isl_map *isl_map_from_multi_aff(
1951 __isl_take isl_multi_aff *maff)
1952 __isl_give isl_set *isl_set_from_pw_multi_aff(
1953 __isl_take isl_pw_multi_aff *pma);
1954 __isl_give isl_map *isl_map_from_pw_multi_aff(
1955 __isl_take isl_pw_multi_aff *pma);
1956 __isl_give isl_set *isl_set_from_multi_pw_aff(
1957 __isl_take isl_multi_pw_aff *mpa);
1958 __isl_give isl_map *isl_map_from_multi_pw_aff(
1959 __isl_take isl_multi_pw_aff *mpa);
1960 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
1961 __isl_take isl_union_pw_aff *upa);
1962 __isl_give isl_union_map *
1963 isl_union_map_from_union_pw_multi_aff(
1964 __isl_take isl_union_pw_multi_aff *upma);
1966 The C<domain_space> argument describes the domain of the resulting
1967 basic relation. It is required because the C<list> may consist
1968 of zero affine expressions.
1970 =head2 Inspecting Sets and Relations
1972 Usually, the user should not have to care about the actual constraints
1973 of the sets and maps, but should instead apply the abstract operations
1974 explained in the following sections.
1975 Occasionally, however, it may be required to inspect the individual
1976 coefficients of the constraints. This section explains how to do so.
1977 In these cases, it may also be useful to have C<isl> compute
1978 an explicit representation of the existentially quantified variables.
1980 __isl_give isl_set *isl_set_compute_divs(
1981 __isl_take isl_set *set);
1982 __isl_give isl_map *isl_map_compute_divs(
1983 __isl_take isl_map *map);
1984 __isl_give isl_union_set *isl_union_set_compute_divs(
1985 __isl_take isl_union_set *uset);
1986 __isl_give isl_union_map *isl_union_map_compute_divs(
1987 __isl_take isl_union_map *umap);
1989 This explicit representation defines the existentially quantified
1990 variables as integer divisions of the other variables, possibly
1991 including earlier existentially quantified variables.
1992 An explicitly represented existentially quantified variable therefore
1993 has a unique value when the values of the other variables are known.
1994 If, furthermore, the same existentials, i.e., existentials
1995 with the same explicit representations, should appear in the
1996 same order in each of the disjuncts of a set or map, then the user should call
1997 either of the following functions.
1999 __isl_give isl_set *isl_set_align_divs(
2000 __isl_take isl_set *set);
2001 __isl_give isl_map *isl_map_align_divs(
2002 __isl_take isl_map *map);
2004 Alternatively, the existentially quantified variables can be removed
2005 using the following functions, which compute an overapproximation.
2007 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2008 __isl_take isl_basic_set *bset);
2009 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2010 __isl_take isl_basic_map *bmap);
2011 __isl_give isl_set *isl_set_remove_divs(
2012 __isl_take isl_set *set);
2013 __isl_give isl_map *isl_map_remove_divs(
2014 __isl_take isl_map *map);
2016 It is also possible to only remove those divs that are defined
2017 in terms of a given range of dimensions or only those for which
2018 no explicit representation is known.
2020 __isl_give isl_basic_set *
2021 isl_basic_set_remove_divs_involving_dims(
2022 __isl_take isl_basic_set *bset,
2023 enum isl_dim_type type,
2024 unsigned first, unsigned n);
2025 __isl_give isl_basic_map *
2026 isl_basic_map_remove_divs_involving_dims(
2027 __isl_take isl_basic_map *bmap,
2028 enum isl_dim_type type,
2029 unsigned first, unsigned n);
2030 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2031 __isl_take isl_set *set, enum isl_dim_type type,
2032 unsigned first, unsigned n);
2033 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2034 __isl_take isl_map *map, enum isl_dim_type type,
2035 unsigned first, unsigned n);
2037 __isl_give isl_basic_set *
2038 isl_basic_set_remove_unknown_divs(
2039 __isl_take isl_basic_set *bset);
2040 __isl_give isl_set *isl_set_remove_unknown_divs(
2041 __isl_take isl_set *set);
2042 __isl_give isl_map *isl_map_remove_unknown_divs(
2043 __isl_take isl_map *map);
2045 To iterate over all the sets or maps in a union set or map, use
2047 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
2048 int (*fn)(__isl_take isl_set *set, void *user),
2050 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
2051 int (*fn)(__isl_take isl_map *map, void *user),
2054 The number of sets or maps in a union set or map can be obtained
2057 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2058 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2060 To extract the set or map in a given space from a union, use
2062 __isl_give isl_set *isl_union_set_extract_set(
2063 __isl_keep isl_union_set *uset,
2064 __isl_take isl_space *space);
2065 __isl_give isl_map *isl_union_map_extract_map(
2066 __isl_keep isl_union_map *umap,
2067 __isl_take isl_space *space);
2069 To iterate over all the basic sets or maps in a set or map, use
2071 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
2072 int (*fn)(__isl_take isl_basic_set *bset, void *user),
2074 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
2075 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
2078 The callback function C<fn> should return 0 if successful and
2079 -1 if an error occurs. In the latter case, or if any other error
2080 occurs, the above functions will return -1.
2082 It should be noted that C<isl> does not guarantee that
2083 the basic sets or maps passed to C<fn> are disjoint.
2084 If this is required, then the user should call one of
2085 the following functions first.
2087 __isl_give isl_set *isl_set_make_disjoint(
2088 __isl_take isl_set *set);
2089 __isl_give isl_map *isl_map_make_disjoint(
2090 __isl_take isl_map *map);
2092 The number of basic sets in a set can be obtained
2093 or the number of basic maps in a map can be obtained
2096 #include <isl/set.h>
2097 int isl_set_n_basic_set(__isl_keep isl_set *set);
2099 #include <isl/map.h>
2100 int isl_map_n_basic_map(__isl_keep isl_map *map);
2102 To iterate over the constraints of a basic set or map, use
2104 #include <isl/constraint.h>
2106 int isl_basic_set_n_constraint(
2107 __isl_keep isl_basic_set *bset);
2108 int isl_basic_set_foreach_constraint(
2109 __isl_keep isl_basic_set *bset,
2110 int (*fn)(__isl_take isl_constraint *c, void *user),
2112 int isl_basic_map_n_constraint(
2113 __isl_keep isl_basic_map *bmap);
2114 int isl_basic_map_foreach_constraint(
2115 __isl_keep isl_basic_map *bmap,
2116 int (*fn)(__isl_take isl_constraint *c, void *user),
2118 __isl_null isl_constraint *isl_constraint_free(
2119 __isl_take isl_constraint *c);
2121 Again, the callback function C<fn> should return 0 if successful and
2122 -1 if an error occurs. In the latter case, or if any other error
2123 occurs, the above functions will return -1.
2124 The constraint C<c> represents either an equality or an inequality.
2125 Use the following function to find out whether a constraint
2126 represents an equality. If not, it represents an inequality.
2128 int isl_constraint_is_equality(
2129 __isl_keep isl_constraint *constraint);
2131 It is also possible to obtain a list of constraints from a basic
2134 #include <isl/constraint.h>
2135 __isl_give isl_constraint_list *
2136 isl_basic_map_get_constraint_list(
2137 __isl_keep isl_basic_map *bmap);
2138 __isl_give isl_constraint_list *
2139 isl_basic_set_get_constraint_list(
2140 __isl_keep isl_basic_set *bset);
2142 These functions require that all existentially quantified variables
2143 have an explicit representation.
2144 The returned list can be manipulated using the functions in L<"Lists">.
2146 The coefficients of the constraints can be inspected using
2147 the following functions.
2149 int isl_constraint_is_lower_bound(
2150 __isl_keep isl_constraint *constraint,
2151 enum isl_dim_type type, unsigned pos);
2152 int isl_constraint_is_upper_bound(
2153 __isl_keep isl_constraint *constraint,
2154 enum isl_dim_type type, unsigned pos);
2155 __isl_give isl_val *isl_constraint_get_constant_val(
2156 __isl_keep isl_constraint *constraint);
2157 __isl_give isl_val *isl_constraint_get_coefficient_val(
2158 __isl_keep isl_constraint *constraint,
2159 enum isl_dim_type type, int pos);
2161 The explicit representations of the existentially quantified
2162 variables can be inspected using the following function.
2163 Note that the user is only allowed to use this function
2164 if the inspected set or map is the result of a call
2165 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2166 The existentially quantified variable is equal to the floor
2167 of the returned affine expression. The affine expression
2168 itself can be inspected using the functions in
2171 __isl_give isl_aff *isl_constraint_get_div(
2172 __isl_keep isl_constraint *constraint, int pos);
2174 To obtain the constraints of a basic set or map in matrix
2175 form, use the following functions.
2177 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2178 __isl_keep isl_basic_set *bset,
2179 enum isl_dim_type c1, enum isl_dim_type c2,
2180 enum isl_dim_type c3, enum isl_dim_type c4);
2181 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2182 __isl_keep isl_basic_set *bset,
2183 enum isl_dim_type c1, enum isl_dim_type c2,
2184 enum isl_dim_type c3, enum isl_dim_type c4);
2185 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2186 __isl_keep isl_basic_map *bmap,
2187 enum isl_dim_type c1,
2188 enum isl_dim_type c2, enum isl_dim_type c3,
2189 enum isl_dim_type c4, enum isl_dim_type c5);
2190 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2191 __isl_keep isl_basic_map *bmap,
2192 enum isl_dim_type c1,
2193 enum isl_dim_type c2, enum isl_dim_type c3,
2194 enum isl_dim_type c4, enum isl_dim_type c5);
2196 The C<isl_dim_type> arguments dictate the order in which
2197 different kinds of variables appear in the resulting matrix.
2198 For set inputs, they should be a permutation of
2199 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2200 For map inputs, they should be a permutation of
2201 C<isl_dim_cst>, C<isl_dim_param>,
2202 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2206 Points are elements of a set. They can be used to construct
2207 simple sets (boxes) or they can be used to represent the
2208 individual elements of a set.
2209 The zero point (the origin) can be created using
2211 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2213 The coordinates of a point can be inspected, set and changed
2216 __isl_give isl_val *isl_point_get_coordinate_val(
2217 __isl_keep isl_point *pnt,
2218 enum isl_dim_type type, int pos);
2219 __isl_give isl_point *isl_point_set_coordinate_val(
2220 __isl_take isl_point *pnt,
2221 enum isl_dim_type type, int pos,
2222 __isl_take isl_val *v);
2224 __isl_give isl_point *isl_point_add_ui(
2225 __isl_take isl_point *pnt,
2226 enum isl_dim_type type, int pos, unsigned val);
2227 __isl_give isl_point *isl_point_sub_ui(
2228 __isl_take isl_point *pnt,
2229 enum isl_dim_type type, int pos, unsigned val);
2231 Points can be copied or freed using
2233 __isl_give isl_point *isl_point_copy(
2234 __isl_keep isl_point *pnt);
2235 void isl_point_free(__isl_take isl_point *pnt);
2237 A singleton set can be created from a point using
2239 __isl_give isl_basic_set *isl_basic_set_from_point(
2240 __isl_take isl_point *pnt);
2241 __isl_give isl_set *isl_set_from_point(
2242 __isl_take isl_point *pnt);
2244 and a box can be created from two opposite extremal points using
2246 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2247 __isl_take isl_point *pnt1,
2248 __isl_take isl_point *pnt2);
2249 __isl_give isl_set *isl_set_box_from_points(
2250 __isl_take isl_point *pnt1,
2251 __isl_take isl_point *pnt2);
2253 All elements of a B<bounded> (union) set can be enumerated using
2254 the following functions.
2256 int isl_set_foreach_point(__isl_keep isl_set *set,
2257 int (*fn)(__isl_take isl_point *pnt, void *user),
2259 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2260 int (*fn)(__isl_take isl_point *pnt, void *user),
2263 The function C<fn> is called for each integer point in
2264 C<set> with as second argument the last argument of
2265 the C<isl_set_foreach_point> call. The function C<fn>
2266 should return C<0> on success and C<-1> on failure.
2267 In the latter case, C<isl_set_foreach_point> will stop
2268 enumerating and return C<-1> as well.
2269 If the enumeration is performed successfully and to completion,
2270 then C<isl_set_foreach_point> returns C<0>.
2272 To obtain a single point of a (basic) set, use
2274 __isl_give isl_point *isl_basic_set_sample_point(
2275 __isl_take isl_basic_set *bset);
2276 __isl_give isl_point *isl_set_sample_point(
2277 __isl_take isl_set *set);
2279 If C<set> does not contain any (integer) points, then the
2280 resulting point will be ``void'', a property that can be
2283 int isl_point_is_void(__isl_keep isl_point *pnt);
2287 Besides sets and relation, C<isl> also supports various types of functions.
2288 Each of these types is derived from the value type (see L</"Values">)
2289 or from one of two primitive function types
2290 through the application of zero or more type constructors.
2291 We first describe the primitive type and then we describe
2292 the types derived from these primitive types.
2294 =head3 Primitive Functions
2296 C<isl> support two primitive function types, quasi-affine
2297 expressions and quasipolynomials.
2298 A quasi-affine expression is defined either over a parameter
2299 space or over a set and is composed of integer constants,
2300 parameters and set variables, addition, subtraction and
2301 integer division by an integer constant.
2302 For example, the quasi-affine expression
2304 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2306 maps C<x> to C<2*floor((4 n + x)/9>.
2307 A quasipolynomial is a polynomial expression in quasi-affine
2308 expression. That is, it additionally allows for multiplication.
2309 Note, though, that it is not allowed to construct an integer
2310 division of an expression involving multiplications.
2311 Here is an example of a quasipolynomial that is not
2312 quasi-affine expression
2314 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2316 Note that the external representations of quasi-affine expressions
2317 and quasipolynomials are different. Quasi-affine expressions
2318 use a notation with square brackets just like binary relations,
2319 while quasipolynomials do not. This might change at some point.
2321 If a primitive function is defined over a parameter space,
2322 then the space of the function itself is that of a set.
2323 If it is defined over a set, then the space of the function
2324 is that of a relation. In both cases, the set space (or
2325 the output space) is single-dimensional, anonymous and unstructured.
2326 To create functions with multiple dimensions or with other kinds
2327 of set or output spaces, use multiple expressions
2328 (see L</"Multiple Expressions">).
2332 =item * Quasi-affine Expressions
2334 Besides the expressions described above, a quasi-affine
2335 expression can also be set to NaN. Such expressions
2336 typically represent a failure to represent a result
2337 as a quasi-affine expression.
2339 The zero quasi affine expression or the quasi affine expression
2340 that is equal to a given value or
2341 a specified dimension on a given domain can be created using
2343 #include <isl/aff.h>
2344 __isl_give isl_aff *isl_aff_zero_on_domain(
2345 __isl_take isl_local_space *ls);
2346 __isl_give isl_aff *isl_aff_val_on_domain(
2347 __isl_take isl_local_space *ls,
2348 __isl_take isl_val *val);
2349 __isl_give isl_aff *isl_aff_var_on_domain(
2350 __isl_take isl_local_space *ls,
2351 enum isl_dim_type type, unsigned pos);
2352 __isl_give isl_aff *isl_aff_nan_on_domain(
2353 __isl_take isl_local_space *ls);
2355 Quasi affine expressions can be copied and freed using
2357 #include <isl/aff.h>
2358 __isl_give isl_aff *isl_aff_copy(
2359 __isl_keep isl_aff *aff);
2360 __isl_null isl_aff *isl_aff_free(
2361 __isl_take isl_aff *aff);
2363 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2364 using the following function. The constraint is required to have
2365 a non-zero coefficient for the specified dimension.
2367 #include <isl/constraint.h>
2368 __isl_give isl_aff *isl_constraint_get_bound(
2369 __isl_keep isl_constraint *constraint,
2370 enum isl_dim_type type, int pos);
2372 The entire affine expression of the constraint can also be extracted
2373 using the following function.
2375 #include <isl/constraint.h>
2376 __isl_give isl_aff *isl_constraint_get_aff(
2377 __isl_keep isl_constraint *constraint);
2379 Conversely, an equality constraint equating
2380 the affine expression to zero or an inequality constraint enforcing
2381 the affine expression to be non-negative, can be constructed using
2383 __isl_give isl_constraint *isl_equality_from_aff(
2384 __isl_take isl_aff *aff);
2385 __isl_give isl_constraint *isl_inequality_from_aff(
2386 __isl_take isl_aff *aff);
2388 The coefficients and the integer divisions of an affine expression
2389 can be inspected using the following functions.
2391 #include <isl/aff.h>
2392 __isl_give isl_val *isl_aff_get_constant_val(
2393 __isl_keep isl_aff *aff);
2394 __isl_give isl_val *isl_aff_get_coefficient_val(
2395 __isl_keep isl_aff *aff,
2396 enum isl_dim_type type, int pos);
2397 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2398 enum isl_dim_type type, int pos);
2399 __isl_give isl_val *isl_aff_get_denominator_val(
2400 __isl_keep isl_aff *aff);
2401 __isl_give isl_aff *isl_aff_get_div(
2402 __isl_keep isl_aff *aff, int pos);
2404 They can be modified using the following functions.
2406 #include <isl/aff.h>
2407 __isl_give isl_aff *isl_aff_set_constant_si(
2408 __isl_take isl_aff *aff, int v);
2409 __isl_give isl_aff *isl_aff_set_constant_val(
2410 __isl_take isl_aff *aff, __isl_take isl_val *v);
2411 __isl_give isl_aff *isl_aff_set_coefficient_si(
2412 __isl_take isl_aff *aff,
2413 enum isl_dim_type type, int pos, int v);
2414 __isl_give isl_aff *isl_aff_set_coefficient_val(
2415 __isl_take isl_aff *aff,
2416 enum isl_dim_type type, int pos,
2417 __isl_take isl_val *v);
2419 __isl_give isl_aff *isl_aff_add_constant_si(
2420 __isl_take isl_aff *aff, int v);
2421 __isl_give isl_aff *isl_aff_add_constant_val(
2422 __isl_take isl_aff *aff, __isl_take isl_val *v);
2423 __isl_give isl_aff *isl_aff_add_constant_num_si(
2424 __isl_take isl_aff *aff, int v);
2425 __isl_give isl_aff *isl_aff_add_coefficient_si(
2426 __isl_take isl_aff *aff,
2427 enum isl_dim_type type, int pos, int v);
2428 __isl_give isl_aff *isl_aff_add_coefficient_val(
2429 __isl_take isl_aff *aff,
2430 enum isl_dim_type type, int pos,
2431 __isl_take isl_val *v);
2433 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2434 set the I<numerator> of the constant or coefficient, while
2435 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2436 the constant or coefficient as a whole.
2437 The C<add_constant> and C<add_coefficient> functions add an integer
2438 or rational value to
2439 the possibly rational constant or coefficient.
2440 The C<add_constant_num> functions add an integer value to
2443 =item * Quasipolynomials
2445 Some simple quasipolynomials can be created using the following functions.
2447 #include <isl/polynomial.h>
2448 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2449 __isl_take isl_space *domain);
2450 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2451 __isl_take isl_space *domain);
2452 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2453 __isl_take isl_space *domain);
2454 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2455 __isl_take isl_space *domain);
2456 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2457 __isl_take isl_space *domain);
2458 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2459 __isl_take isl_space *domain,
2460 __isl_take isl_val *val);
2461 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2462 __isl_take isl_space *domain,
2463 enum isl_dim_type type, unsigned pos);
2464 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2465 __isl_take isl_aff *aff);
2467 Recall that the space in which a quasipolynomial lives is a map space
2468 with a one-dimensional range. The C<domain> argument in some of
2469 the functions above corresponds to the domain of this map space.
2471 Quasipolynomials can be copied and freed again using the following
2474 #include <isl/polynomial.h>
2475 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2476 __isl_keep isl_qpolynomial *qp);
2477 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2478 __isl_take isl_qpolynomial *qp);
2480 The constant term of a quasipolynomial can be extracted using
2482 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2483 __isl_keep isl_qpolynomial *qp);
2485 To iterate over all terms in a quasipolynomial,
2488 int isl_qpolynomial_foreach_term(
2489 __isl_keep isl_qpolynomial *qp,
2490 int (*fn)(__isl_take isl_term *term,
2491 void *user), void *user);
2493 The terms themselves can be inspected and freed using
2496 unsigned isl_term_dim(__isl_keep isl_term *term,
2497 enum isl_dim_type type);
2498 __isl_give isl_val *isl_term_get_coefficient_val(
2499 __isl_keep isl_term *term);
2500 int isl_term_get_exp(__isl_keep isl_term *term,
2501 enum isl_dim_type type, unsigned pos);
2502 __isl_give isl_aff *isl_term_get_div(
2503 __isl_keep isl_term *term, unsigned pos);
2504 void isl_term_free(__isl_take isl_term *term);
2506 Each term is a product of parameters, set variables and
2507 integer divisions. The function C<isl_term_get_exp>
2508 returns the exponent of a given dimensions in the given term.
2514 A reduction represents a maximum or a minimum of its
2516 The only reduction type defined by C<isl> is
2517 C<isl_qpolynomial_fold>.
2519 There are currently no functions to directly create such
2520 objects, but they do appear in the piecewise quasipolynomial
2521 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2523 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2525 Reductions can be copied and freed using
2526 the following functions.
2528 #include <isl/polynomial.h>
2529 __isl_give isl_qpolynomial_fold *
2530 isl_qpolynomial_fold_copy(
2531 __isl_keep isl_qpolynomial_fold *fold);
2532 void isl_qpolynomial_fold_free(
2533 __isl_take isl_qpolynomial_fold *fold);
2535 To iterate over all quasipolynomials in a reduction, use
2537 int isl_qpolynomial_fold_foreach_qpolynomial(
2538 __isl_keep isl_qpolynomial_fold *fold,
2539 int (*fn)(__isl_take isl_qpolynomial *qp,
2540 void *user), void *user);
2542 =head3 Multiple Expressions
2544 A multiple expression represents a sequence of zero or
2545 more base expressions, all defined on the same domain space.
2546 The domain space of the multiple expression is the same
2547 as that of the base expressions, but the range space
2548 can be any space. In case the base expressions have
2549 a set space, the corresponding multiple expression
2550 also has a set space.
2551 Objects of the value type do not have an associated space.
2552 The space of a multiple value is therefore always a set space.
2553 Similarly, the space of a multiple union piecewise
2554 affine expression is always a set space.
2556 The multiple expression types defined by C<isl>
2557 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2558 C<isl_multi_union_pw_aff>.
2560 A multiple expression with the value zero for
2561 each output (or set) dimension can be created
2562 using the following functions.
2564 #include <isl/val.h>
2565 __isl_give isl_multi_val *isl_multi_val_zero(
2566 __isl_take isl_space *space);
2568 #include <isl/aff.h>
2569 __isl_give isl_multi_aff *isl_multi_aff_zero(
2570 __isl_take isl_space *space);
2571 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2572 __isl_take isl_space *space);
2573 __isl_give isl_multi_union_pw_aff *
2574 isl_multi_union_pw_aff_zero(
2575 __isl_take isl_space *space);
2577 Since there is no canonical way of representing a zero
2578 value of type C<isl_union_pw_aff>, the space passed
2579 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2581 An identity function can be created using the following
2582 functions. The space needs to be that of a relation
2583 with the same number of input and output dimensions.
2585 #include <isl/aff.h>
2586 __isl_give isl_multi_aff *isl_multi_aff_identity(
2587 __isl_take isl_space *space);
2588 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2589 __isl_take isl_space *space);
2591 A function that performs a projection on a universe
2592 relation or set can be created using the following functions.
2593 See also the corresponding
2594 projection operations in L</"Unary Operations">.
2596 #include <isl/aff.h>
2597 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2598 __isl_take isl_space *space);
2599 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2600 __isl_take isl_space *space);
2601 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2602 __isl_take isl_space *space,
2603 enum isl_dim_type type,
2604 unsigned first, unsigned n);
2606 A multiple expression can be created from a single
2607 base expression using the following functions.
2608 The space of the created multiple expression is the same
2609 as that of the base expression, except for
2610 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2611 lives in a parameter space and the output lives
2612 in a single-dimensional set space.
2614 #include <isl/aff.h>
2615 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2616 __isl_take isl_aff *aff);
2617 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2618 __isl_take isl_pw_aff *pa);
2619 __isl_give isl_multi_union_pw_aff *
2620 isl_multi_union_pw_aff_from_union_pw_aff(
2621 __isl_take isl_union_pw_aff *upa);
2623 A multiple expression can be created from a list
2624 of base expression in a specified space.
2625 The domain of this space needs to be the same
2626 as the domains of the base expressions in the list.
2627 If the base expressions have a set space (or no associated space),
2628 then this space also needs to be a set space.
2630 #include <isl/val.h>
2631 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2632 __isl_take isl_space *space,
2633 __isl_take isl_val_list *list);
2635 #include <isl/aff.h>
2636 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2637 __isl_take isl_space *space,
2638 __isl_take isl_aff_list *list);
2639 __isl_give isl_multi_union_pw_aff *
2640 isl_multi_union_pw_aff_from_union_pw_aff_list(
2641 __isl_take isl_space *space,
2642 __isl_take isl_union_pw_aff_list *list);
2644 As a convenience, a multiple piecewise expression can
2645 also be created from a multiple expression.
2646 Each piecewise expression in the result has a single
2649 #include <isl/aff.h>
2650 __isl_give isl_multi_pw_aff *
2651 isl_multi_pw_aff_from_multi_aff(
2652 __isl_take isl_multi_aff *ma);
2654 Similarly, a multiple union expression can be
2655 created from a multiple expression.
2657 #include <isl/aff.h>
2658 __isl_give isl_multi_union_pw_aff *
2659 isl_multi_union_pw_aff_from_multi_aff(
2660 __isl_take isl_multi_aff *ma);
2661 __isl_give isl_multi_union_pw_aff *
2662 isl_multi_union_pw_aff_from_multi_pw_aff(
2663 __isl_take isl_multi_pw_aff *mpa);
2665 A multiple quasi-affine expression can be created from
2666 a multiple value with a given domain space using the following
2669 #include <isl/aff.h>
2670 __isl_give isl_multi_aff *
2671 isl_multi_aff_multi_val_on_space(
2672 __isl_take isl_space *space,
2673 __isl_take isl_multi_val *mv);
2676 a multiple union piecewise affine expression can be created from
2677 a multiple value with a given domain or
2678 a multiple affine expression with a given domain
2679 using the following functions.
2681 #include <isl/aff.h>
2682 __isl_give isl_multi_union_pw_aff *
2683 isl_multi_union_pw_aff_multi_val_on_domain(
2684 __isl_take isl_union_set *domain,
2685 __isl_take isl_multi_val *mv);
2686 __isl_give isl_multi_union_pw_aff *
2687 isl_multi_union_pw_aff_multi_aff_on_domain(
2688 __isl_take isl_union_set *domain,
2689 __isl_take isl_multi_aff *ma);
2691 Multiple expressions can be copied and freed using
2692 the following functions.
2694 #include <isl/val.h>
2695 __isl_give isl_multi_val *isl_multi_val_copy(
2696 __isl_keep isl_multi_val *mv);
2697 __isl_null isl_multi_val *isl_multi_val_free(
2698 __isl_take isl_multi_val *mv);
2700 #include <isl/aff.h>
2701 __isl_give isl_multi_aff *isl_multi_aff_copy(
2702 __isl_keep isl_multi_aff *maff);
2703 __isl_null isl_multi_aff *isl_multi_aff_free(
2704 __isl_take isl_multi_aff *maff);
2705 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2706 __isl_keep isl_multi_pw_aff *mpa);
2707 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2708 __isl_take isl_multi_pw_aff *mpa);
2709 __isl_give isl_multi_union_pw_aff *
2710 isl_multi_union_pw_aff_copy(
2711 __isl_keep isl_multi_union_pw_aff *mupa);
2712 __isl_null isl_multi_union_pw_aff *
2713 isl_multi_union_pw_aff_free(
2714 __isl_take isl_multi_union_pw_aff *mupa);
2716 The base expression at a given position of a multiple
2717 expression can be extracted using the following functions.
2719 #include <isl/val.h>
2720 __isl_give isl_val *isl_multi_val_get_val(
2721 __isl_keep isl_multi_val *mv, int pos);
2723 #include <isl/aff.h>
2724 __isl_give isl_aff *isl_multi_aff_get_aff(
2725 __isl_keep isl_multi_aff *multi, int pos);
2726 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2727 __isl_keep isl_multi_pw_aff *mpa, int pos);
2728 __isl_give isl_union_pw_aff *
2729 isl_multi_union_pw_aff_get_union_pw_aff(
2730 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2732 It can be replaced using the following functions.
2734 #include <isl/val.h>
2735 __isl_give isl_multi_val *isl_multi_val_set_val(
2736 __isl_take isl_multi_val *mv, int pos,
2737 __isl_take isl_val *val);
2739 #include <isl/aff.h>
2740 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2741 __isl_take isl_multi_aff *multi, int pos,
2742 __isl_take isl_aff *aff);
2743 __isl_give isl_multi_union_pw_aff *
2744 isl_multi_union_pw_aff_set_union_pw_aff(
2745 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2746 __isl_take isl_union_pw_aff *upa);
2748 Note that there is a difference between C<isl_multi_union_pw_aff>
2749 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2750 of unions of piecewise expressions, while the second is a union
2751 of piecewise sequences. In particular, multiple affine expressions
2752 in an C<isl_union_pw_multi_aff> may live in different spaces,
2753 while there is only a single multiple expression in
2754 an C<isl_multi_union_pw_aff>, which can therefore only live
2755 in a single space. This means that not every
2756 C<isl_union_pw_multi_aff> can be converted to
2757 an C<isl_multi_union_pw_aff>. The following function can
2758 be used to perform this conversion when it is possible.
2760 #include <isl/aff.h>
2761 __isl_give isl_multi_union_pw_aff *
2762 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2763 __isl_take isl_union_pw_multi_aff *upma);
2765 =head3 Piecewise Expressions
2767 A piecewise expression is an expression that is described
2768 using zero or more base expression defined over the same
2769 number of cells in the domain space of the base expressions.
2770 All base expressions are defined over the same
2771 domain space and the cells are disjoint.
2772 The space of a piecewise expression is the same as
2773 that of the base expressions.
2774 If the union of the cells is a strict subset of the domain
2775 space, then the value of the piecewise expression outside
2776 this union is different for types derived from quasi-affine
2777 expressions and those derived from quasipolynomials.
2778 Piecewise expressions derived from quasi-affine expressions
2779 are considered to be undefined outside the union of their cells.
2780 Piecewise expressions derived from quasipolynomials
2781 are considered to be zero outside the union of their cells.
2783 Piecewise quasipolynomials are mainly used by the C<barvinok>
2784 library for representing the number of elements in a parametric set or map.
2785 For example, the piecewise quasipolynomial
2787 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2789 represents the number of points in the map
2791 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2793 The piecewise expression types defined by C<isl>
2794 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2795 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2797 A piecewise expression with no cells can be created using
2798 the following functions.
2800 #include <isl/aff.h>
2801 __isl_give isl_pw_aff *isl_pw_aff_empty(
2802 __isl_take isl_space *space);
2803 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2804 __isl_take isl_space *space);
2806 A piecewise expression with a single universe cell can be
2807 created using the following functions.
2809 #include <isl/aff.h>
2810 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2811 __isl_take isl_aff *aff);
2812 __isl_give isl_pw_multi_aff *
2813 isl_pw_multi_aff_from_multi_aff(
2814 __isl_take isl_multi_aff *ma);
2816 #include <isl/polynomial.h>
2817 __isl_give isl_pw_qpolynomial *
2818 isl_pw_qpolynomial_from_qpolynomial(
2819 __isl_take isl_qpolynomial *qp);
2821 A piecewise expression with a single specified cell can be
2822 created using the following functions.
2824 #include <isl/aff.h>
2825 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2826 __isl_take isl_set *set, __isl_take isl_aff *aff);
2827 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2828 __isl_take isl_set *set,
2829 __isl_take isl_multi_aff *maff);
2831 #include <isl/polynomial.h>
2832 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2833 __isl_take isl_set *set,
2834 __isl_take isl_qpolynomial *qp);
2836 The following convenience functions first create a base expression and
2837 then create a piecewise expression over a universe domain.
2839 #include <isl/aff.h>
2840 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2841 __isl_take isl_local_space *ls);
2842 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2843 __isl_take isl_local_space *ls,
2844 enum isl_dim_type type, unsigned pos);
2845 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2846 __isl_take isl_local_space *ls);
2847 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2848 __isl_take isl_space *space);
2849 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2850 __isl_take isl_space *space);
2851 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2852 __isl_take isl_space *space);
2853 __isl_give isl_pw_multi_aff *
2854 isl_pw_multi_aff_project_out_map(
2855 __isl_take isl_space *space,
2856 enum isl_dim_type type,
2857 unsigned first, unsigned n);
2859 #include <isl/polynomial.h>
2860 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2861 __isl_take isl_space *space);
2863 The following convenience functions first create a base expression and
2864 then create a piecewise expression over a given domain.
2866 #include <isl/aff.h>
2867 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2868 __isl_take isl_set *domain,
2869 __isl_take isl_val *v);
2870 __isl_give isl_pw_multi_aff *
2871 isl_pw_multi_aff_multi_val_on_domain(
2872 __isl_take isl_set *domain,
2873 __isl_take isl_multi_val *mv);
2875 As a convenience, a piecewise multiple expression can
2876 also be created from a piecewise expression.
2877 Each multiple expression in the result is derived
2878 from the corresponding base expression.
2880 #include <isl/aff.h>
2881 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2882 __isl_take isl_pw_aff *pa);
2884 Similarly, a piecewise quasipolynomial can be
2885 created from a piecewise quasi-affine expression using
2886 the following function.
2888 #include <isl/polynomial.h>
2889 __isl_give isl_pw_qpolynomial *
2890 isl_pw_qpolynomial_from_pw_aff(
2891 __isl_take isl_pw_aff *pwaff);
2893 Piecewise expressions can be copied and freed using the following functions.
2895 #include <isl/aff.h>
2896 __isl_give isl_pw_aff *isl_pw_aff_copy(
2897 __isl_keep isl_pw_aff *pwaff);
2898 __isl_null isl_pw_aff *isl_pw_aff_free(
2899 __isl_take isl_pw_aff *pwaff);
2900 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2901 __isl_keep isl_pw_multi_aff *pma);
2902 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2903 __isl_take isl_pw_multi_aff *pma);
2905 #include <isl/polynomial.h>
2906 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2907 __isl_keep isl_pw_qpolynomial *pwqp);
2908 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2909 __isl_take isl_pw_qpolynomial *pwqp);
2910 __isl_give isl_pw_qpolynomial_fold *
2911 isl_pw_qpolynomial_fold_copy(
2912 __isl_keep isl_pw_qpolynomial_fold *pwf);
2913 __isl_null isl_pw_qpolynomial_fold *
2914 isl_pw_qpolynomial_fold_free(
2915 __isl_take isl_pw_qpolynomial_fold *pwf);
2917 To iterate over the different cells of a piecewise expression,
2918 use the following functions.
2920 #include <isl/aff.h>
2921 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2922 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2923 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2924 int (*fn)(__isl_take isl_set *set,
2925 __isl_take isl_aff *aff,
2926 void *user), void *user);
2927 int isl_pw_multi_aff_foreach_piece(
2928 __isl_keep isl_pw_multi_aff *pma,
2929 int (*fn)(__isl_take isl_set *set,
2930 __isl_take isl_multi_aff *maff,
2931 void *user), void *user);
2933 #include <isl/polynomial.h>
2934 int isl_pw_qpolynomial_foreach_piece(
2935 __isl_keep isl_pw_qpolynomial *pwqp,
2936 int (*fn)(__isl_take isl_set *set,
2937 __isl_take isl_qpolynomial *qp,
2938 void *user), void *user);
2939 int isl_pw_qpolynomial_foreach_lifted_piece(
2940 __isl_keep isl_pw_qpolynomial *pwqp,
2941 int (*fn)(__isl_take isl_set *set,
2942 __isl_take isl_qpolynomial *qp,
2943 void *user), void *user);
2944 int isl_pw_qpolynomial_fold_foreach_piece(
2945 __isl_keep isl_pw_qpolynomial_fold *pwf,
2946 int (*fn)(__isl_take isl_set *set,
2947 __isl_take isl_qpolynomial_fold *fold,
2948 void *user), void *user);
2949 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2950 __isl_keep isl_pw_qpolynomial_fold *pwf,
2951 int (*fn)(__isl_take isl_set *set,
2952 __isl_take isl_qpolynomial_fold *fold,
2953 void *user), void *user);
2955 As usual, the function C<fn> should return C<0> on success
2956 and C<-1> on failure. The difference between
2957 C<isl_pw_qpolynomial_foreach_piece> and
2958 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2959 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2960 compute unique representations for all existentially quantified
2961 variables and then turn these existentially quantified variables
2962 into extra set variables, adapting the associated quasipolynomial
2963 accordingly. This means that the C<set> passed to C<fn>
2964 will not have any existentially quantified variables, but that
2965 the dimensions of the sets may be different for different
2966 invocations of C<fn>.
2967 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2968 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2970 A piecewise expression consisting of the expressions at a given
2971 position of a piecewise multiple expression can be extracted
2972 using the following function.
2974 #include <isl/aff.h>
2975 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2976 __isl_keep isl_pw_multi_aff *pma, int pos);
2978 These expressions can be replaced using the following function.
2980 #include <isl/aff.h>
2981 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2982 __isl_take isl_pw_multi_aff *pma, unsigned pos,
2983 __isl_take isl_pw_aff *pa);
2985 Note that there is a difference between C<isl_multi_pw_aff> and
2986 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
2987 affine expressions, while the second is a piecewise sequence
2988 of affine expressions. In particular, each of the piecewise
2989 affine expressions in an C<isl_multi_pw_aff> may have a different
2990 domain, while all multiple expressions associated to a cell
2991 in an C<isl_pw_multi_aff> have the same domain.
2992 It is possible to convert between the two, but when converting
2993 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
2994 of the result is the intersection of the domains of the input.
2995 The reverse conversion is exact.
2997 #include <isl/aff.h>
2998 __isl_give isl_pw_multi_aff *
2999 isl_pw_multi_aff_from_multi_pw_aff(
3000 __isl_take isl_multi_pw_aff *mpa);
3001 __isl_give isl_multi_pw_aff *
3002 isl_multi_pw_aff_from_pw_multi_aff(
3003 __isl_take isl_pw_multi_aff *pma);
3005 =head3 Union Expressions
3007 A union expression collects base expressions defined
3008 over different domains. The space of a union expression
3009 is that of the shared parameter space.
3011 The union expression types defined by C<isl>
3012 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3013 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3015 An empty union expression can be created using the following functions.
3017 #include <isl/aff.h>
3018 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3019 __isl_take isl_space *space);
3020 __isl_give isl_union_pw_multi_aff *
3021 isl_union_pw_multi_aff_empty(
3022 __isl_take isl_space *space);
3024 #include <isl/polynomial.h>
3025 __isl_give isl_union_pw_qpolynomial *
3026 isl_union_pw_qpolynomial_zero(
3027 __isl_take isl_space *space);
3029 A union expression containing a single base expression
3030 can be created using the following functions.
3032 #include <isl/aff.h>
3033 __isl_give isl_union_pw_aff *
3034 isl_union_pw_aff_from_pw_aff(
3035 __isl_take isl_pw_aff *pa);
3036 __isl_give isl_union_pw_multi_aff *
3037 isl_union_pw_multi_aff_from_aff(
3038 __isl_take isl_aff *aff);
3039 __isl_give isl_union_pw_multi_aff *
3040 isl_union_pw_multi_aff_from_pw_multi_aff(
3041 __isl_take isl_pw_multi_aff *pma);
3043 #include <isl/polynomial.h>
3044 __isl_give isl_union_pw_qpolynomial *
3045 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3046 __isl_take isl_pw_qpolynomial *pwqp);
3048 The following functions create a base expression on each
3049 of the sets in the union set and collect the results.
3051 #include <isl/aff.h>
3052 __isl_give isl_union_pw_multi_aff *
3053 isl_union_pw_multi_aff_from_union_pw_aff(
3054 __isl_take isl_union_pw_aff *upa);
3055 __isl_give isl_union_pw_aff *
3056 isl_union_pw_multi_aff_get_union_pw_aff(
3057 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3058 __isl_give isl_union_pw_aff *
3059 isl_union_pw_aff_val_on_domain(
3060 __isl_take isl_union_set *domain,
3061 __isl_take isl_val *v);
3062 __isl_give isl_union_pw_multi_aff *
3063 isl_union_pw_multi_aff_multi_val_on_domain(
3064 __isl_take isl_union_set *domain,
3065 __isl_take isl_multi_val *mv);
3067 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3068 expression on a given domain can be created using the following
3071 #include <isl/aff.h>
3072 __isl_give isl_union_pw_aff *
3073 isl_union_pw_aff_aff_on_domain(
3074 __isl_take isl_union_set *domain,
3075 __isl_take isl_aff *aff);
3077 A base expression can be added to a union expression using
3078 the following functions.
3080 #include <isl/aff.h>
3081 __isl_give isl_union_pw_aff *
3082 isl_union_pw_aff_add_pw_aff(
3083 __isl_take isl_union_pw_aff *upa,
3084 __isl_take isl_pw_aff *pa);
3085 __isl_give isl_union_pw_multi_aff *
3086 isl_union_pw_multi_aff_add_pw_multi_aff(
3087 __isl_take isl_union_pw_multi_aff *upma,
3088 __isl_take isl_pw_multi_aff *pma);
3090 #include <isl/polynomial.h>
3091 __isl_give isl_union_pw_qpolynomial *
3092 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3093 __isl_take isl_union_pw_qpolynomial *upwqp,
3094 __isl_take isl_pw_qpolynomial *pwqp);
3096 Union expressions can be copied and freed using
3097 the following functions.
3099 #include <isl/aff.h>
3100 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3101 __isl_keep isl_union_pw_aff *upa);
3102 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3103 __isl_take isl_union_pw_aff *upa);
3104 __isl_give isl_union_pw_multi_aff *
3105 isl_union_pw_multi_aff_copy(
3106 __isl_keep isl_union_pw_multi_aff *upma);
3107 __isl_null isl_union_pw_multi_aff *
3108 isl_union_pw_multi_aff_free(
3109 __isl_take isl_union_pw_multi_aff *upma);
3111 #include <isl/polynomial.h>
3112 __isl_give isl_union_pw_qpolynomial *
3113 isl_union_pw_qpolynomial_copy(
3114 __isl_keep isl_union_pw_qpolynomial *upwqp);
3115 __isl_null isl_union_pw_qpolynomial *
3116 isl_union_pw_qpolynomial_free(
3117 __isl_take isl_union_pw_qpolynomial *upwqp);
3118 __isl_give isl_union_pw_qpolynomial_fold *
3119 isl_union_pw_qpolynomial_fold_copy(
3120 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3121 __isl_null isl_union_pw_qpolynomial_fold *
3122 isl_union_pw_qpolynomial_fold_free(
3123 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3125 To iterate over the base expressions in a union expression,
3126 use the following functions.
3128 #include <isl/aff.h>
3129 int isl_union_pw_aff_n_pw_multi_aff(
3130 __isl_keep isl_union_pw_aff *upa);
3131 int isl_union_pw_aff_foreach_pw_aff(
3132 __isl_keep isl_union_pw_aff *upa,
3133 int (*fn)(__isl_take isl_pw_aff *ma, void *user),
3135 int isl_union_pw_multi_aff_n_pw_multi_aff(
3136 __isl_keep isl_union_pw_multi_aff *upma);
3137 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3138 __isl_keep isl_union_pw_multi_aff *upma,
3139 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3140 void *user), void *user);
3142 #include <isl/polynomial.h>
3143 int isl_union_pw_qplynomial_n_pw_qpolynomial(
3144 __isl_keep isl_union_pw_qpolynomial *upwqp);
3145 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3146 __isl_keep isl_union_pw_qpolynomial *upwqp,
3147 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3148 void *user), void *user);
3149 int isl_union_pw_qplynomial_fold_n_pw_qpolynomial_fold(
3150 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3151 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3152 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3153 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3154 void *user), void *user);
3156 To extract the base expression in a given space from a union, use
3157 the following functions.
3159 #include <isl/aff.h>
3160 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3161 __isl_keep isl_union_pw_aff *upa,
3162 __isl_take isl_space *space);
3163 __isl_give isl_pw_multi_aff *
3164 isl_union_pw_multi_aff_extract_pw_multi_aff(
3165 __isl_keep isl_union_pw_multi_aff *upma,
3166 __isl_take isl_space *space);
3168 #include <isl/polynomial.h>
3169 __isl_give isl_pw_qpolynomial *
3170 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3171 __isl_keep isl_union_pw_qpolynomial *upwqp,
3172 __isl_take isl_space *space);
3174 =head2 Input and Output
3176 For set and relation,
3177 C<isl> supports its own input/output format, which is similar
3178 to the C<Omega> format, but also supports the C<PolyLib> format
3180 For other object types, typically only an C<isl> format is supported.
3182 =head3 C<isl> format
3184 The C<isl> format is similar to that of C<Omega>, but has a different
3185 syntax for describing the parameters and allows for the definition
3186 of an existentially quantified variable as the integer division
3187 of an affine expression.
3188 For example, the set of integers C<i> between C<0> and C<n>
3189 such that C<i % 10 <= 6> can be described as
3191 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3194 A set or relation can have several disjuncts, separated
3195 by the keyword C<or>. Each disjunct is either a conjunction
3196 of constraints or a projection (C<exists>) of a conjunction
3197 of constraints. The constraints are separated by the keyword
3200 =head3 C<PolyLib> format
3202 If the represented set is a union, then the first line
3203 contains a single number representing the number of disjuncts.
3204 Otherwise, a line containing the number C<1> is optional.
3206 Each disjunct is represented by a matrix of constraints.
3207 The first line contains two numbers representing
3208 the number of rows and columns,
3209 where the number of rows is equal to the number of constraints
3210 and the number of columns is equal to two plus the number of variables.
3211 The following lines contain the actual rows of the constraint matrix.
3212 In each row, the first column indicates whether the constraint
3213 is an equality (C<0>) or inequality (C<1>). The final column
3214 corresponds to the constant term.
3216 If the set is parametric, then the coefficients of the parameters
3217 appear in the last columns before the constant column.
3218 The coefficients of any existentially quantified variables appear
3219 between those of the set variables and those of the parameters.
3221 =head3 Extended C<PolyLib> format
3223 The extended C<PolyLib> format is nearly identical to the
3224 C<PolyLib> format. The only difference is that the line
3225 containing the number of rows and columns of a constraint matrix
3226 also contains four additional numbers:
3227 the number of output dimensions, the number of input dimensions,
3228 the number of local dimensions (i.e., the number of existentially
3229 quantified variables) and the number of parameters.
3230 For sets, the number of ``output'' dimensions is equal
3231 to the number of set dimensions, while the number of ``input''
3236 Objects can be read from input using the following functions.
3238 #include <isl/val.h>
3239 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3241 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3242 isl_ctx *ctx, const char *str);
3244 #include <isl/set.h>
3245 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3246 isl_ctx *ctx, FILE *input);
3247 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3248 isl_ctx *ctx, const char *str);
3249 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3251 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3254 #include <isl/map.h>
3255 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3256 isl_ctx *ctx, FILE *input);
3257 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3258 isl_ctx *ctx, const char *str);
3259 __isl_give isl_map *isl_map_read_from_file(
3260 isl_ctx *ctx, FILE *input);
3261 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3264 #include <isl/union_set.h>
3265 __isl_give isl_union_set *isl_union_set_read_from_file(
3266 isl_ctx *ctx, FILE *input);
3267 __isl_give isl_union_set *isl_union_set_read_from_str(
3268 isl_ctx *ctx, const char *str);
3270 #include <isl/union_map.h>
3271 __isl_give isl_union_map *isl_union_map_read_from_file(
3272 isl_ctx *ctx, FILE *input);
3273 __isl_give isl_union_map *isl_union_map_read_from_str(
3274 isl_ctx *ctx, const char *str);
3276 #include <isl/aff.h>
3277 __isl_give isl_aff *isl_aff_read_from_str(
3278 isl_ctx *ctx, const char *str);
3279 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3280 isl_ctx *ctx, const char *str);
3281 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3282 isl_ctx *ctx, const char *str);
3283 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3284 isl_ctx *ctx, const char *str);
3285 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3286 isl_ctx *ctx, const char *str);
3287 __isl_give isl_union_pw_multi_aff *
3288 isl_union_pw_multi_aff_read_from_str(
3289 isl_ctx *ctx, const char *str);
3291 #include <isl/polynomial.h>
3292 __isl_give isl_union_pw_qpolynomial *
3293 isl_union_pw_qpolynomial_read_from_str(
3294 isl_ctx *ctx, const char *str);
3296 For sets and relations,
3297 the input format is autodetected and may be either the C<PolyLib> format
3298 or the C<isl> format.
3302 Before anything can be printed, an C<isl_printer> needs to
3305 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3307 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3308 __isl_null isl_printer *isl_printer_free(
3309 __isl_take isl_printer *printer);
3310 __isl_give char *isl_printer_get_str(
3311 __isl_keep isl_printer *printer);
3313 The printer can be inspected using the following functions.
3315 FILE *isl_printer_get_file(
3316 __isl_keep isl_printer *printer);
3317 int isl_printer_get_output_format(
3318 __isl_keep isl_printer *p);
3320 The behavior of the printer can be modified in various ways
3322 __isl_give isl_printer *isl_printer_set_output_format(
3323 __isl_take isl_printer *p, int output_format);
3324 __isl_give isl_printer *isl_printer_set_indent(
3325 __isl_take isl_printer *p, int indent);
3326 __isl_give isl_printer *isl_printer_set_indent_prefix(
3327 __isl_take isl_printer *p, const char *prefix);
3328 __isl_give isl_printer *isl_printer_indent(
3329 __isl_take isl_printer *p, int indent);
3330 __isl_give isl_printer *isl_printer_set_prefix(
3331 __isl_take isl_printer *p, const char *prefix);
3332 __isl_give isl_printer *isl_printer_set_suffix(
3333 __isl_take isl_printer *p, const char *suffix);
3335 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3336 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3337 and defaults to C<ISL_FORMAT_ISL>.
3338 Each line in the output is prefixed by C<indent_prefix>,
3339 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3340 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3341 In the C<PolyLib> format output,
3342 the coefficients of the existentially quantified variables
3343 appear between those of the set variables and those
3345 The function C<isl_printer_indent> increases the indentation
3346 by the specified amount (which may be negative).
3348 To actually print something, use
3350 #include <isl/printer.h>
3351 __isl_give isl_printer *isl_printer_print_double(
3352 __isl_take isl_printer *p, double d);
3354 #include <isl/val.h>
3355 __isl_give isl_printer *isl_printer_print_val(
3356 __isl_take isl_printer *p, __isl_keep isl_val *v);
3358 #include <isl/set.h>
3359 __isl_give isl_printer *isl_printer_print_basic_set(
3360 __isl_take isl_printer *printer,
3361 __isl_keep isl_basic_set *bset);
3362 __isl_give isl_printer *isl_printer_print_set(
3363 __isl_take isl_printer *printer,
3364 __isl_keep isl_set *set);
3366 #include <isl/map.h>
3367 __isl_give isl_printer *isl_printer_print_basic_map(
3368 __isl_take isl_printer *printer,
3369 __isl_keep isl_basic_map *bmap);
3370 __isl_give isl_printer *isl_printer_print_map(
3371 __isl_take isl_printer *printer,
3372 __isl_keep isl_map *map);
3374 #include <isl/union_set.h>
3375 __isl_give isl_printer *isl_printer_print_union_set(
3376 __isl_take isl_printer *p,
3377 __isl_keep isl_union_set *uset);
3379 #include <isl/union_map.h>
3380 __isl_give isl_printer *isl_printer_print_union_map(
3381 __isl_take isl_printer *p,
3382 __isl_keep isl_union_map *umap);
3384 #include <isl/val.h>
3385 __isl_give isl_printer *isl_printer_print_multi_val(
3386 __isl_take isl_printer *p,
3387 __isl_keep isl_multi_val *mv);
3389 #include <isl/aff.h>
3390 __isl_give isl_printer *isl_printer_print_aff(
3391 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3392 __isl_give isl_printer *isl_printer_print_multi_aff(
3393 __isl_take isl_printer *p,
3394 __isl_keep isl_multi_aff *maff);
3395 __isl_give isl_printer *isl_printer_print_pw_aff(
3396 __isl_take isl_printer *p,
3397 __isl_keep isl_pw_aff *pwaff);
3398 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3399 __isl_take isl_printer *p,
3400 __isl_keep isl_pw_multi_aff *pma);
3401 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3402 __isl_take isl_printer *p,
3403 __isl_keep isl_multi_pw_aff *mpa);
3404 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3405 __isl_take isl_printer *p,
3406 __isl_keep isl_union_pw_aff *upa);
3407 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3408 __isl_take isl_printer *p,
3409 __isl_keep isl_union_pw_multi_aff *upma);
3410 __isl_give isl_printer *
3411 isl_printer_print_multi_union_pw_aff(
3412 __isl_take isl_printer *p,
3413 __isl_keep isl_multi_union_pw_aff *mupa);
3415 #include <isl/polynomial.h>
3416 __isl_give isl_printer *isl_printer_print_qpolynomial(
3417 __isl_take isl_printer *p,
3418 __isl_keep isl_qpolynomial *qp);
3419 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3420 __isl_take isl_printer *p,
3421 __isl_keep isl_pw_qpolynomial *pwqp);
3422 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3423 __isl_take isl_printer *p,
3424 __isl_keep isl_union_pw_qpolynomial *upwqp);
3426 __isl_give isl_printer *
3427 isl_printer_print_pw_qpolynomial_fold(
3428 __isl_take isl_printer *p,
3429 __isl_keep isl_pw_qpolynomial_fold *pwf);
3430 __isl_give isl_printer *
3431 isl_printer_print_union_pw_qpolynomial_fold(
3432 __isl_take isl_printer *p,
3433 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3435 For C<isl_printer_print_qpolynomial>,
3436 C<isl_printer_print_pw_qpolynomial> and
3437 C<isl_printer_print_pw_qpolynomial_fold>,
3438 the output format of the printer
3439 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3440 For C<isl_printer_print_union_pw_qpolynomial> and
3441 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3443 In case of printing in C<ISL_FORMAT_C>, the user may want
3444 to set the names of all dimensions first.
3446 When called on a file printer, the following function flushes
3447 the file. When called on a string printer, the buffer is cleared.
3449 __isl_give isl_printer *isl_printer_flush(
3450 __isl_take isl_printer *p);
3452 Alternatively, a string representation can be obtained
3453 directly using the following functions, which always print
3456 #include <isl/space.h>
3457 __isl_give char *isl_space_to_str(
3458 __isl_keep isl_space *space);
3460 #include <isl/val.h>
3461 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3462 __isl_give char *isl_multi_val_to_str(
3463 __isl_keep isl_multi_val *mv);
3465 #include <isl/set.h>
3466 __isl_give char *isl_set_to_str(
3467 __isl_keep isl_set *set);
3469 #include <isl/union_set.h>
3470 __isl_give char *isl_union_set_to_str(
3471 __isl_keep isl_union_set *uset);
3473 #include <isl/map.h>
3474 __isl_give char *isl_map_to_str(
3475 __isl_keep isl_map *map);
3477 #include <isl/union_map.h>
3478 __isl_give char *isl_union_map_to_str(
3479 __isl_keep isl_union_map *umap);
3481 #include <isl/aff.h>
3482 __isl_give char *isl_multi_aff_to_str(
3483 __isl_keep isl_multi_aff *aff);
3484 __isl_give char *isl_union_pw_aff_to_str(
3485 __isl_keep isl_union_pw_aff *upa);
3486 __isl_give char *isl_union_pw_multi_aff_to_str(
3487 __isl_keep isl_union_pw_multi_aff *upma);
3488 __isl_give char *isl_multi_union_pw_aff_to_str(
3489 __isl_keep isl_multi_union_pw_aff *mupa);
3493 =head3 Unary Properties
3499 The following functions test whether the given set or relation
3500 contains any integer points. The ``plain'' variants do not perform
3501 any computations, but simply check if the given set or relation
3502 is already known to be empty.
3504 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3505 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3506 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3507 int isl_set_is_empty(__isl_keep isl_set *set);
3508 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3509 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3510 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3511 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3512 int isl_map_is_empty(__isl_keep isl_map *map);
3513 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3515 =item * Universality
3517 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3518 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3519 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3521 =item * Single-valuedness
3523 #include <isl/set.h>
3524 int isl_set_is_singleton(__isl_keep isl_set *set);
3526 #include <isl/map.h>
3527 int isl_basic_map_is_single_valued(
3528 __isl_keep isl_basic_map *bmap);
3529 int isl_map_plain_is_single_valued(
3530 __isl_keep isl_map *map);
3531 int isl_map_is_single_valued(__isl_keep isl_map *map);
3533 #include <isl/union_map.h>
3534 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3538 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3539 int isl_map_is_injective(__isl_keep isl_map *map);
3540 int isl_union_map_plain_is_injective(
3541 __isl_keep isl_union_map *umap);
3542 int isl_union_map_is_injective(
3543 __isl_keep isl_union_map *umap);
3547 int isl_map_is_bijective(__isl_keep isl_map *map);
3548 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3552 __isl_give isl_val *
3553 isl_basic_map_plain_get_val_if_fixed(
3554 __isl_keep isl_basic_map *bmap,
3555 enum isl_dim_type type, unsigned pos);
3556 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3557 __isl_keep isl_set *set,
3558 enum isl_dim_type type, unsigned pos);
3559 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3560 __isl_keep isl_map *map,
3561 enum isl_dim_type type, unsigned pos);
3563 If the set or relation obviously lies on a hyperplane where the given dimension
3564 has a fixed value, then return that value.
3565 Otherwise return NaN.
3569 int isl_set_dim_residue_class_val(
3570 __isl_keep isl_set *set,
3571 int pos, __isl_give isl_val **modulo,
3572 __isl_give isl_val **residue);
3574 Check if the values of the given set dimension are equal to a fixed
3575 value modulo some integer value. If so, assign the modulo to C<*modulo>
3576 and the fixed value to C<*residue>. If the given dimension attains only
3577 a single value, then assign C<0> to C<*modulo> and the fixed value to
3579 If the dimension does not attain only a single value and if no modulo
3580 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3584 To check whether the description of a set, relation or function depends
3585 on one or more given dimensions,
3586 the following functions can be used.
3588 #include <isl/constraint.h>
3589 int isl_constraint_involves_dims(
3590 __isl_keep isl_constraint *constraint,
3591 enum isl_dim_type type, unsigned first, unsigned n);
3593 #include <isl/set.h>
3594 int isl_basic_set_involves_dims(
3595 __isl_keep isl_basic_set *bset,
3596 enum isl_dim_type type, unsigned first, unsigned n);
3597 int isl_set_involves_dims(__isl_keep isl_set *set,
3598 enum isl_dim_type type, unsigned first, unsigned n);
3600 #include <isl/map.h>
3601 int isl_basic_map_involves_dims(
3602 __isl_keep isl_basic_map *bmap,
3603 enum isl_dim_type type, unsigned first, unsigned n);
3604 int isl_map_involves_dims(__isl_keep isl_map *map,
3605 enum isl_dim_type type, unsigned first, unsigned n);
3607 #include <isl/union_map.h>
3608 int isl_union_map_involves_dims(
3609 __isl_keep isl_union_map *umap,
3610 enum isl_dim_type type, unsigned first, unsigned n);
3612 #include <isl/aff.h>
3613 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3614 enum isl_dim_type type, unsigned first, unsigned n);
3615 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3616 enum isl_dim_type type, unsigned first, unsigned n);
3617 int isl_multi_aff_involves_dims(
3618 __isl_keep isl_multi_aff *ma,
3619 enum isl_dim_type type, unsigned first, unsigned n);
3620 int isl_multi_pw_aff_involves_dims(
3621 __isl_keep isl_multi_pw_aff *mpa,
3622 enum isl_dim_type type, unsigned first, unsigned n);
3624 Similarly, the following functions can be used to check whether
3625 a given dimension is involved in any lower or upper bound.
3627 #include <isl/set.h>
3628 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3629 enum isl_dim_type type, unsigned pos);
3630 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3631 enum isl_dim_type type, unsigned pos);
3633 Note that these functions return true even if there is a bound on
3634 the dimension on only some of the basic sets of C<set>.
3635 To check if they have a bound for all of the basic sets in C<set>,
3636 use the following functions instead.
3638 #include <isl/set.h>
3639 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3640 enum isl_dim_type type, unsigned pos);
3641 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3642 enum isl_dim_type type, unsigned pos);
3646 To check whether a set is a parameter domain, use this function:
3648 int isl_set_is_params(__isl_keep isl_set *set);
3649 int isl_union_set_is_params(
3650 __isl_keep isl_union_set *uset);
3654 The following functions check whether the space of the given
3655 (basic) set or relation range is a wrapped relation.
3657 #include <isl/space.h>
3658 int isl_space_is_wrapping(
3659 __isl_keep isl_space *space);
3660 int isl_space_domain_is_wrapping(
3661 __isl_keep isl_space *space);
3662 int isl_space_range_is_wrapping(
3663 __isl_keep isl_space *space);
3665 #include <isl/set.h>
3666 int isl_basic_set_is_wrapping(
3667 __isl_keep isl_basic_set *bset);
3668 int isl_set_is_wrapping(__isl_keep isl_set *set);
3670 #include <isl/map.h>
3671 int isl_map_domain_is_wrapping(
3672 __isl_keep isl_map *map);
3673 int isl_map_range_is_wrapping(
3674 __isl_keep isl_map *map);
3676 #include <isl/val.h>
3677 int isl_multi_val_range_is_wrapping(
3678 __isl_keep isl_multi_val *mv);
3680 #include <isl/aff.h>
3681 int isl_multi_aff_range_is_wrapping(
3682 __isl_keep isl_multi_aff *ma);
3683 int isl_multi_pw_aff_range_is_wrapping(
3684 __isl_keep isl_multi_pw_aff *mpa);
3685 int isl_multi_union_pw_aff_range_is_wrapping(
3686 __isl_keep isl_multi_union_pw_aff *mupa);
3688 The input to C<isl_space_is_wrapping> should
3689 be the space of a set, while that of
3690 C<isl_space_domain_is_wrapping> and
3691 C<isl_space_range_is_wrapping> should be the space of a relation.
3693 =item * Internal Product
3695 int isl_basic_map_can_zip(
3696 __isl_keep isl_basic_map *bmap);
3697 int isl_map_can_zip(__isl_keep isl_map *map);
3699 Check whether the product of domain and range of the given relation
3701 i.e., whether both domain and range are nested relations.
3705 int isl_basic_map_can_curry(
3706 __isl_keep isl_basic_map *bmap);
3707 int isl_map_can_curry(__isl_keep isl_map *map);
3709 Check whether the domain of the (basic) relation is a wrapped relation.
3711 int isl_basic_map_can_uncurry(
3712 __isl_keep isl_basic_map *bmap);
3713 int isl_map_can_uncurry(__isl_keep isl_map *map);
3715 Check whether the range of the (basic) relation is a wrapped relation.
3717 =item * Special Values
3719 #include <isl/aff.h>
3720 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3721 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3723 Check whether the given expression is a constant.
3725 #include <isl/aff.h>
3726 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3727 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3729 Check whether the given expression is equal to or involves NaN.
3731 #include <isl/aff.h>
3732 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3734 Check whether the affine expression is obviously zero.
3738 =head3 Binary Properties
3744 The following functions check whether two objects
3745 represent the same set, relation or function.
3746 The C<plain> variants only return true if the objects
3747 are obviously the same. That is, they may return false
3748 even if the objects are the same, but they will never
3749 return true if the objects are not the same.
3751 #include <isl/set.h>
3752 int isl_basic_set_plain_is_equal(
3753 __isl_keep isl_basic_set *bset1,
3754 __isl_keep isl_basic_set *bset2);
3755 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3756 __isl_keep isl_set *set2);
3757 int isl_set_is_equal(__isl_keep isl_set *set1,
3758 __isl_keep isl_set *set2);
3760 #include <isl/map.h>
3761 int isl_basic_map_is_equal(
3762 __isl_keep isl_basic_map *bmap1,
3763 __isl_keep isl_basic_map *bmap2);
3764 int isl_map_is_equal(__isl_keep isl_map *map1,
3765 __isl_keep isl_map *map2);
3766 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3767 __isl_keep isl_map *map2);
3769 #include <isl/union_set.h>
3770 int isl_union_set_is_equal(
3771 __isl_keep isl_union_set *uset1,
3772 __isl_keep isl_union_set *uset2);
3774 #include <isl/union_map.h>
3775 int isl_union_map_is_equal(
3776 __isl_keep isl_union_map *umap1,
3777 __isl_keep isl_union_map *umap2);
3779 #include <isl/aff.h>
3780 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3781 __isl_keep isl_aff *aff2);
3782 int isl_multi_aff_plain_is_equal(
3783 __isl_keep isl_multi_aff *maff1,
3784 __isl_keep isl_multi_aff *maff2);
3785 int isl_pw_aff_plain_is_equal(
3786 __isl_keep isl_pw_aff *pwaff1,
3787 __isl_keep isl_pw_aff *pwaff2);
3788 int isl_pw_multi_aff_plain_is_equal(
3789 __isl_keep isl_pw_multi_aff *pma1,
3790 __isl_keep isl_pw_multi_aff *pma2);
3791 int isl_multi_pw_aff_plain_is_equal(
3792 __isl_keep isl_multi_pw_aff *mpa1,
3793 __isl_keep isl_multi_pw_aff *mpa2);
3794 int isl_multi_pw_aff_is_equal(
3795 __isl_keep isl_multi_pw_aff *mpa1,
3796 __isl_keep isl_multi_pw_aff *mpa2);
3797 int isl_union_pw_aff_plain_is_equal(
3798 __isl_keep isl_union_pw_aff *upa1,
3799 __isl_keep isl_union_pw_aff *upa2);
3800 int isl_union_pw_multi_aff_plain_is_equal(
3801 __isl_keep isl_union_pw_multi_aff *upma1,
3802 __isl_keep isl_union_pw_multi_aff *upma2);
3803 int isl_multi_union_pw_aff_plain_is_equal(
3804 __isl_keep isl_multi_union_pw_aff *mupa1,
3805 __isl_keep isl_multi_union_pw_aff *mupa2);
3807 #include <isl/polynomial.h>
3808 int isl_union_pw_qpolynomial_plain_is_equal(
3809 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3810 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3811 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3812 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3813 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3815 =item * Disjointness
3817 #include <isl/set.h>
3818 int isl_basic_set_is_disjoint(
3819 __isl_keep isl_basic_set *bset1,
3820 __isl_keep isl_basic_set *bset2);
3821 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3822 __isl_keep isl_set *set2);
3823 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3824 __isl_keep isl_set *set2);
3826 #include <isl/map.h>
3827 int isl_basic_map_is_disjoint(
3828 __isl_keep isl_basic_map *bmap1,
3829 __isl_keep isl_basic_map *bmap2);
3830 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3831 __isl_keep isl_map *map2);
3833 #include <isl/union_set.h>
3834 int isl_union_set_is_disjoint(
3835 __isl_keep isl_union_set *uset1,
3836 __isl_keep isl_union_set *uset2);
3838 #include <isl/union_map.h>
3839 int isl_union_map_is_disjoint(
3840 __isl_keep isl_union_map *umap1,
3841 __isl_keep isl_union_map *umap2);
3845 int isl_basic_set_is_subset(
3846 __isl_keep isl_basic_set *bset1,
3847 __isl_keep isl_basic_set *bset2);
3848 int isl_set_is_subset(__isl_keep isl_set *set1,
3849 __isl_keep isl_set *set2);
3850 int isl_set_is_strict_subset(
3851 __isl_keep isl_set *set1,
3852 __isl_keep isl_set *set2);
3853 int isl_union_set_is_subset(
3854 __isl_keep isl_union_set *uset1,
3855 __isl_keep isl_union_set *uset2);
3856 int isl_union_set_is_strict_subset(
3857 __isl_keep isl_union_set *uset1,
3858 __isl_keep isl_union_set *uset2);
3859 int isl_basic_map_is_subset(
3860 __isl_keep isl_basic_map *bmap1,
3861 __isl_keep isl_basic_map *bmap2);
3862 int isl_basic_map_is_strict_subset(
3863 __isl_keep isl_basic_map *bmap1,
3864 __isl_keep isl_basic_map *bmap2);
3865 int isl_map_is_subset(
3866 __isl_keep isl_map *map1,
3867 __isl_keep isl_map *map2);
3868 int isl_map_is_strict_subset(
3869 __isl_keep isl_map *map1,
3870 __isl_keep isl_map *map2);
3871 int isl_union_map_is_subset(
3872 __isl_keep isl_union_map *umap1,
3873 __isl_keep isl_union_map *umap2);
3874 int isl_union_map_is_strict_subset(
3875 __isl_keep isl_union_map *umap1,
3876 __isl_keep isl_union_map *umap2);
3878 Check whether the first argument is a (strict) subset of the
3883 Every comparison function returns a negative value if the first
3884 argument is considered smaller than the second, a positive value
3885 if the first argument is considered greater and zero if the two
3886 constraints are considered the same by the comparison criterion.
3888 #include <isl/constraint.h>
3889 int isl_constraint_plain_cmp(
3890 __isl_keep isl_constraint *c1,
3891 __isl_keep isl_constraint *c2);
3893 This function is useful for sorting C<isl_constraint>s.
3894 The order depends on the internal representation of the inputs.
3895 The order is fixed over different calls to the function (assuming
3896 the internal representation of the inputs has not changed), but may
3897 change over different versions of C<isl>.
3899 #include <isl/constraint.h>
3900 int isl_constraint_cmp_last_non_zero(
3901 __isl_keep isl_constraint *c1,
3902 __isl_keep isl_constraint *c2);
3904 This function can be used to sort constraints that live in the same
3905 local space. Constraints that involve ``earlier'' dimensions or
3906 that have a smaller coefficient for the shared latest dimension
3907 are considered smaller than other constraints.
3908 This function only defines a B<partial> order.
3910 #include <isl/set.h>
3911 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3912 __isl_keep isl_set *set2);
3914 This function is useful for sorting C<isl_set>s.
3915 The order depends on the internal representation of the inputs.
3916 The order is fixed over different calls to the function (assuming
3917 the internal representation of the inputs has not changed), but may
3918 change over different versions of C<isl>.
3920 #include <isl/aff.h>
3921 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3922 __isl_keep isl_pw_aff *pa2);
3924 The function C<isl_pw_aff_plain_cmp> can be used to sort
3925 C<isl_pw_aff>s. The order is not strictly defined.
3926 The current order sorts expressions that only involve
3927 earlier dimensions before those that involve later dimensions.
3931 =head2 Unary Operations
3937 __isl_give isl_set *isl_set_complement(
3938 __isl_take isl_set *set);
3939 __isl_give isl_map *isl_map_complement(
3940 __isl_take isl_map *map);
3944 #include <isl/space.h>
3945 __isl_give isl_space *isl_space_reverse(
3946 __isl_take isl_space *space);
3948 #include <isl/map.h>
3949 __isl_give isl_basic_map *isl_basic_map_reverse(
3950 __isl_take isl_basic_map *bmap);
3951 __isl_give isl_map *isl_map_reverse(
3952 __isl_take isl_map *map);
3954 #include <isl/union_map.h>
3955 __isl_give isl_union_map *isl_union_map_reverse(
3956 __isl_take isl_union_map *umap);
3960 #include <isl/space.h>
3961 __isl_give isl_space *isl_space_domain(
3962 __isl_take isl_space *space);
3963 __isl_give isl_space *isl_space_range(
3964 __isl_take isl_space *space);
3965 __isl_give isl_space *isl_space_params(
3966 __isl_take isl_space *space);
3968 #include <isl/local_space.h>
3969 __isl_give isl_local_space *isl_local_space_domain(
3970 __isl_take isl_local_space *ls);
3971 __isl_give isl_local_space *isl_local_space_range(
3972 __isl_take isl_local_space *ls);
3974 #include <isl/set.h>
3975 __isl_give isl_basic_set *isl_basic_set_project_out(
3976 __isl_take isl_basic_set *bset,
3977 enum isl_dim_type type, unsigned first, unsigned n);
3978 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3979 enum isl_dim_type type, unsigned first, unsigned n);
3980 __isl_give isl_basic_set *isl_basic_set_params(
3981 __isl_take isl_basic_set *bset);
3982 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
3984 #include <isl/map.h>
3985 __isl_give isl_basic_map *isl_basic_map_project_out(
3986 __isl_take isl_basic_map *bmap,
3987 enum isl_dim_type type, unsigned first, unsigned n);
3988 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3989 enum isl_dim_type type, unsigned first, unsigned n);
3990 __isl_give isl_basic_set *isl_basic_map_domain(
3991 __isl_take isl_basic_map *bmap);
3992 __isl_give isl_basic_set *isl_basic_map_range(
3993 __isl_take isl_basic_map *bmap);
3994 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
3995 __isl_give isl_set *isl_map_domain(
3996 __isl_take isl_map *bmap);
3997 __isl_give isl_set *isl_map_range(
3998 __isl_take isl_map *map);
4000 #include <isl/union_set.h>
4001 __isl_give isl_union_set *isl_union_set_project_out(
4002 __isl_take isl_union_set *uset,
4003 enum isl_dim_type type,
4004 unsigned first, unsigned n);
4005 __isl_give isl_set *isl_union_set_params(
4006 __isl_take isl_union_set *uset);
4008 The function C<isl_union_set_project_out> can only project out
4011 #include <isl/union_map.h>
4012 __isl_give isl_union_map *isl_union_map_project_out(
4013 __isl_take isl_union_map *umap,
4014 enum isl_dim_type type, unsigned first, unsigned n);
4015 __isl_give isl_set *isl_union_map_params(
4016 __isl_take isl_union_map *umap);
4017 __isl_give isl_union_set *isl_union_map_domain(
4018 __isl_take isl_union_map *umap);
4019 __isl_give isl_union_set *isl_union_map_range(
4020 __isl_take isl_union_map *umap);
4022 The function C<isl_union_map_project_out> can only project out
4025 #include <isl/aff.h>
4026 __isl_give isl_aff *isl_aff_project_domain_on_params(
4027 __isl_take isl_aff *aff);
4028 __isl_give isl_pw_multi_aff *
4029 isl_pw_multi_aff_project_domain_on_params(
4030 __isl_take isl_pw_multi_aff *pma);
4031 __isl_give isl_set *isl_pw_aff_domain(
4032 __isl_take isl_pw_aff *pwaff);
4033 __isl_give isl_set *isl_pw_multi_aff_domain(
4034 __isl_take isl_pw_multi_aff *pma);
4035 __isl_give isl_set *isl_multi_pw_aff_domain(
4036 __isl_take isl_multi_pw_aff *mpa);
4037 __isl_give isl_union_set *isl_union_pw_aff_domain(
4038 __isl_take isl_union_pw_aff *upa);
4039 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4040 __isl_take isl_union_pw_multi_aff *upma);
4041 __isl_give isl_set *isl_pw_aff_params(
4042 __isl_take isl_pw_aff *pwa);
4044 #include <isl/polynomial.h>
4045 __isl_give isl_qpolynomial *
4046 isl_qpolynomial_project_domain_on_params(
4047 __isl_take isl_qpolynomial *qp);
4048 __isl_give isl_pw_qpolynomial *
4049 isl_pw_qpolynomial_project_domain_on_params(
4050 __isl_take isl_pw_qpolynomial *pwqp);
4051 __isl_give isl_pw_qpolynomial_fold *
4052 isl_pw_qpolynomial_fold_project_domain_on_params(
4053 __isl_take isl_pw_qpolynomial_fold *pwf);
4054 __isl_give isl_set *isl_pw_qpolynomial_domain(
4055 __isl_take isl_pw_qpolynomial *pwqp);
4056 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4057 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4058 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4059 __isl_take isl_union_pw_qpolynomial *upwqp);
4061 #include <isl/space.h>
4062 __isl_give isl_space *isl_space_domain_map(
4063 __isl_take isl_space *space);
4064 __isl_give isl_space *isl_space_range_map(
4065 __isl_take isl_space *space);
4067 #include <isl/map.h>
4068 __isl_give isl_map *isl_set_wrapped_domain_map(
4069 __isl_take isl_set *set);
4070 __isl_give isl_basic_map *isl_basic_map_domain_map(
4071 __isl_take isl_basic_map *bmap);
4072 __isl_give isl_basic_map *isl_basic_map_range_map(
4073 __isl_take isl_basic_map *bmap);
4074 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4075 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4077 #include <isl/union_map.h>
4078 __isl_give isl_union_map *isl_union_map_domain_map(
4079 __isl_take isl_union_map *umap);
4080 __isl_give isl_union_pw_multi_aff *
4081 isl_union_map_domain_map_union_pw_multi_aff(
4082 __isl_take isl_union_map *umap);
4083 __isl_give isl_union_map *isl_union_map_range_map(
4084 __isl_take isl_union_map *umap);
4085 __isl_give isl_union_map *
4086 isl_union_set_wrapped_domain_map(
4087 __isl_take isl_union_set *uset);
4089 The functions above construct a (basic, regular or union) relation
4090 that maps (a wrapped version of) the input relation to its domain or range.
4091 C<isl_set_wrapped_domain_map> maps the input set to the domain
4092 of its wrapped relation.
4096 __isl_give isl_basic_set *isl_basic_set_eliminate(
4097 __isl_take isl_basic_set *bset,
4098 enum isl_dim_type type,
4099 unsigned first, unsigned n);
4100 __isl_give isl_set *isl_set_eliminate(
4101 __isl_take isl_set *set, enum isl_dim_type type,
4102 unsigned first, unsigned n);
4103 __isl_give isl_basic_map *isl_basic_map_eliminate(
4104 __isl_take isl_basic_map *bmap,
4105 enum isl_dim_type type,
4106 unsigned first, unsigned n);
4107 __isl_give isl_map *isl_map_eliminate(
4108 __isl_take isl_map *map, enum isl_dim_type type,
4109 unsigned first, unsigned n);
4111 Eliminate the coefficients for the given dimensions from the constraints,
4112 without removing the dimensions.
4114 =item * Constructing a set from a parameter domain
4116 A zero-dimensional space or (basic) set can be constructed
4117 on a given parameter domain using the following functions.
4119 #include <isl/space.h>
4120 __isl_give isl_space *isl_space_set_from_params(
4121 __isl_take isl_space *space);
4123 #include <isl/set.h>
4124 __isl_give isl_basic_set *isl_basic_set_from_params(
4125 __isl_take isl_basic_set *bset);
4126 __isl_give isl_set *isl_set_from_params(
4127 __isl_take isl_set *set);
4129 =item * Constructing a relation from a set
4131 Create a relation with the given set as domain or range.
4132 The range or domain of the created relation is a zero-dimensional
4133 flat anonymous space.
4135 #include <isl/space.h>
4136 __isl_give isl_space *isl_space_from_domain(
4137 __isl_take isl_space *space);
4138 __isl_give isl_space *isl_space_from_range(
4139 __isl_take isl_space *space);
4140 __isl_give isl_space *isl_space_map_from_set(
4141 __isl_take isl_space *space);
4142 __isl_give isl_space *isl_space_map_from_domain_and_range(
4143 __isl_take isl_space *domain,
4144 __isl_take isl_space *range);
4146 #include <isl/local_space.h>
4147 __isl_give isl_local_space *isl_local_space_from_domain(
4148 __isl_take isl_local_space *ls);
4150 #include <isl/map.h>
4151 __isl_give isl_map *isl_map_from_domain(
4152 __isl_take isl_set *set);
4153 __isl_give isl_map *isl_map_from_range(
4154 __isl_take isl_set *set);
4156 #include <isl/val.h>
4157 __isl_give isl_multi_val *isl_multi_val_from_range(
4158 __isl_take isl_multi_val *mv);
4160 #include <isl/aff.h>
4161 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4162 __isl_take isl_multi_aff *ma);
4163 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4164 __isl_take isl_pw_aff *pwa);
4165 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4166 __isl_take isl_multi_pw_aff *mpa);
4167 __isl_give isl_multi_union_pw_aff *
4168 isl_multi_union_pw_aff_from_range(
4169 __isl_take isl_multi_union_pw_aff *mupa);
4170 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4171 __isl_take isl_set *set);
4172 __isl_give isl_union_pw_multi_aff *
4173 isl_union_pw_multi_aff_from_domain(
4174 __isl_take isl_union_set *uset);
4178 #include <isl/set.h>
4179 __isl_give isl_basic_set *isl_basic_set_fix_si(
4180 __isl_take isl_basic_set *bset,
4181 enum isl_dim_type type, unsigned pos, int value);
4182 __isl_give isl_basic_set *isl_basic_set_fix_val(
4183 __isl_take isl_basic_set *bset,
4184 enum isl_dim_type type, unsigned pos,
4185 __isl_take isl_val *v);
4186 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4187 enum isl_dim_type type, unsigned pos, int value);
4188 __isl_give isl_set *isl_set_fix_val(
4189 __isl_take isl_set *set,
4190 enum isl_dim_type type, unsigned pos,
4191 __isl_take isl_val *v);
4193 #include <isl/map.h>
4194 __isl_give isl_basic_map *isl_basic_map_fix_si(
4195 __isl_take isl_basic_map *bmap,
4196 enum isl_dim_type type, unsigned pos, int value);
4197 __isl_give isl_basic_map *isl_basic_map_fix_val(
4198 __isl_take isl_basic_map *bmap,
4199 enum isl_dim_type type, unsigned pos,
4200 __isl_take isl_val *v);
4201 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4202 enum isl_dim_type type, unsigned pos, int value);
4203 __isl_give isl_map *isl_map_fix_val(
4204 __isl_take isl_map *map,
4205 enum isl_dim_type type, unsigned pos,
4206 __isl_take isl_val *v);
4208 #include <isl/aff.h>
4209 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4210 __isl_take isl_pw_multi_aff *pma,
4211 enum isl_dim_type type, unsigned pos, int value);
4213 #include <isl/polynomial.h>
4214 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4215 __isl_take isl_pw_qpolynomial *pwqp,
4216 enum isl_dim_type type, unsigned n,
4217 __isl_take isl_val *v);
4219 Intersect the set, relation or function domain
4220 with the hyperplane where the given
4221 dimension has the fixed given value.
4223 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4224 __isl_take isl_basic_map *bmap,
4225 enum isl_dim_type type, unsigned pos, int value);
4226 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4227 __isl_take isl_basic_map *bmap,
4228 enum isl_dim_type type, unsigned pos, int value);
4229 __isl_give isl_set *isl_set_lower_bound_si(
4230 __isl_take isl_set *set,
4231 enum isl_dim_type type, unsigned pos, int value);
4232 __isl_give isl_set *isl_set_lower_bound_val(
4233 __isl_take isl_set *set,
4234 enum isl_dim_type type, unsigned pos,
4235 __isl_take isl_val *value);
4236 __isl_give isl_map *isl_map_lower_bound_si(
4237 __isl_take isl_map *map,
4238 enum isl_dim_type type, unsigned pos, int value);
4239 __isl_give isl_set *isl_set_upper_bound_si(
4240 __isl_take isl_set *set,
4241 enum isl_dim_type type, unsigned pos, int value);
4242 __isl_give isl_set *isl_set_upper_bound_val(
4243 __isl_take isl_set *set,
4244 enum isl_dim_type type, unsigned pos,
4245 __isl_take isl_val *value);
4246 __isl_give isl_map *isl_map_upper_bound_si(
4247 __isl_take isl_map *map,
4248 enum isl_dim_type type, unsigned pos, int value);
4250 Intersect the set or relation with the half-space where the given
4251 dimension has a value bounded by the fixed given integer value.
4253 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4254 enum isl_dim_type type1, int pos1,
4255 enum isl_dim_type type2, int pos2);
4256 __isl_give isl_basic_map *isl_basic_map_equate(
4257 __isl_take isl_basic_map *bmap,
4258 enum isl_dim_type type1, int pos1,
4259 enum isl_dim_type type2, int pos2);
4260 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4261 enum isl_dim_type type1, int pos1,
4262 enum isl_dim_type type2, int pos2);
4264 Intersect the set or relation with the hyperplane where the given
4265 dimensions are equal to each other.
4267 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4268 enum isl_dim_type type1, int pos1,
4269 enum isl_dim_type type2, int pos2);
4271 Intersect the relation with the hyperplane where the given
4272 dimensions have opposite values.
4274 __isl_give isl_map *isl_map_order_le(
4275 __isl_take isl_map *map,
4276 enum isl_dim_type type1, int pos1,
4277 enum isl_dim_type type2, int pos2);
4278 __isl_give isl_basic_map *isl_basic_map_order_ge(
4279 __isl_take isl_basic_map *bmap,
4280 enum isl_dim_type type1, int pos1,
4281 enum isl_dim_type type2, int pos2);
4282 __isl_give isl_map *isl_map_order_ge(
4283 __isl_take isl_map *map,
4284 enum isl_dim_type type1, int pos1,
4285 enum isl_dim_type type2, int pos2);
4286 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4287 enum isl_dim_type type1, int pos1,
4288 enum isl_dim_type type2, int pos2);
4289 __isl_give isl_basic_map *isl_basic_map_order_gt(
4290 __isl_take isl_basic_map *bmap,
4291 enum isl_dim_type type1, int pos1,
4292 enum isl_dim_type type2, int pos2);
4293 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4294 enum isl_dim_type type1, int pos1,
4295 enum isl_dim_type type2, int pos2);
4297 Intersect the relation with the half-space where the given
4298 dimensions satisfy the given ordering.
4302 #include <isl/aff.h>
4303 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4304 __isl_take isl_aff *aff);
4305 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4306 __isl_take isl_aff *aff);
4307 __isl_give isl_set *isl_pw_aff_pos_set(
4308 __isl_take isl_pw_aff *pa);
4309 __isl_give isl_set *isl_pw_aff_nonneg_set(
4310 __isl_take isl_pw_aff *pwaff);
4311 __isl_give isl_set *isl_pw_aff_zero_set(
4312 __isl_take isl_pw_aff *pwaff);
4313 __isl_give isl_set *isl_pw_aff_non_zero_set(
4314 __isl_take isl_pw_aff *pwaff);
4315 __isl_give isl_union_set *
4316 isl_union_pw_aff_zero_union_set(
4317 __isl_take isl_union_pw_aff *upa);
4319 The function C<isl_aff_neg_basic_set> returns a basic set
4320 containing those elements in the domain space
4321 of C<aff> where C<aff> is negative.
4322 The function C<isl_pw_aff_nonneg_set> returns a set
4323 containing those elements in the domain
4324 of C<pwaff> where C<pwaff> is non-negative.
4328 __isl_give isl_map *isl_set_identity(
4329 __isl_take isl_set *set);
4330 __isl_give isl_union_map *isl_union_set_identity(
4331 __isl_take isl_union_set *uset);
4332 __isl_give isl_union_pw_multi_aff *
4333 isl_union_set_identity_union_pw_multi_aff(
4334 __isl_take isl_union_set *uset);
4336 Construct an identity relation on the given (union) set.
4338 =item * Function Extraction
4340 A piecewise quasi affine expression that is equal to 1 on a set
4341 and 0 outside the set can be created using the following function.
4343 #include <isl/aff.h>
4344 __isl_give isl_pw_aff *isl_set_indicator_function(
4345 __isl_take isl_set *set);
4347 A piecewise multiple quasi affine expression can be extracted
4348 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4349 and the C<isl_map> is single-valued.
4350 In case of a conversion from an C<isl_union_map>
4351 to an C<isl_union_pw_multi_aff>, these properties need to hold
4352 in each domain space.
4353 A conversion to a C<isl_multi_union_pw_aff> additionally
4354 requires that the input is non-empty and involves only a single
4357 #include <isl/aff.h>
4358 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4359 __isl_take isl_set *set);
4360 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4361 __isl_take isl_map *map);
4363 __isl_give isl_union_pw_multi_aff *
4364 isl_union_pw_multi_aff_from_union_set(
4365 __isl_take isl_union_set *uset);
4366 __isl_give isl_union_pw_multi_aff *
4367 isl_union_pw_multi_aff_from_union_map(
4368 __isl_take isl_union_map *umap);
4370 __isl_give isl_multi_union_pw_aff *
4371 isl_multi_union_pw_aff_from_union_map(
4372 __isl_take isl_union_map *umap);
4376 __isl_give isl_basic_set *isl_basic_map_deltas(
4377 __isl_take isl_basic_map *bmap);
4378 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4379 __isl_give isl_union_set *isl_union_map_deltas(
4380 __isl_take isl_union_map *umap);
4382 These functions return a (basic) set containing the differences
4383 between image elements and corresponding domain elements in the input.
4385 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4386 __isl_take isl_basic_map *bmap);
4387 __isl_give isl_map *isl_map_deltas_map(
4388 __isl_take isl_map *map);
4389 __isl_give isl_union_map *isl_union_map_deltas_map(
4390 __isl_take isl_union_map *umap);
4392 The functions above construct a (basic, regular or union) relation
4393 that maps (a wrapped version of) the input relation to its delta set.
4397 Simplify the representation of a set, relation or functions by trying
4398 to combine pairs of basic sets or relations into a single
4399 basic set or relation.
4401 #include <isl/set.h>
4402 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4404 #include <isl/map.h>
4405 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4407 #include <isl/union_set.h>
4408 __isl_give isl_union_set *isl_union_set_coalesce(
4409 __isl_take isl_union_set *uset);
4411 #include <isl/union_map.h>
4412 __isl_give isl_union_map *isl_union_map_coalesce(
4413 __isl_take isl_union_map *umap);
4415 #include <isl/aff.h>
4416 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4417 __isl_take isl_pw_aff *pwqp);
4418 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4419 __isl_take isl_pw_multi_aff *pma);
4420 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4421 __isl_take isl_multi_pw_aff *mpa);
4422 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4423 __isl_take isl_union_pw_aff *upa);
4424 __isl_give isl_union_pw_multi_aff *
4425 isl_union_pw_multi_aff_coalesce(
4426 __isl_take isl_union_pw_multi_aff *upma);
4428 #include <isl/polynomial.h>
4429 __isl_give isl_pw_qpolynomial_fold *
4430 isl_pw_qpolynomial_fold_coalesce(
4431 __isl_take isl_pw_qpolynomial_fold *pwf);
4432 __isl_give isl_union_pw_qpolynomial *
4433 isl_union_pw_qpolynomial_coalesce(
4434 __isl_take isl_union_pw_qpolynomial *upwqp);
4435 __isl_give isl_union_pw_qpolynomial_fold *
4436 isl_union_pw_qpolynomial_fold_coalesce(
4437 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4439 One of the methods for combining pairs of basic sets or relations
4440 can result in coefficients that are much larger than those that appear
4441 in the constraints of the input. By default, the coefficients are
4442 not allowed to grow larger, but this can be changed by unsetting
4443 the following option.
4445 int isl_options_set_coalesce_bounded_wrapping(
4446 isl_ctx *ctx, int val);
4447 int isl_options_get_coalesce_bounded_wrapping(
4450 =item * Detecting equalities
4452 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4453 __isl_take isl_basic_set *bset);
4454 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4455 __isl_take isl_basic_map *bmap);
4456 __isl_give isl_set *isl_set_detect_equalities(
4457 __isl_take isl_set *set);
4458 __isl_give isl_map *isl_map_detect_equalities(
4459 __isl_take isl_map *map);
4460 __isl_give isl_union_set *isl_union_set_detect_equalities(
4461 __isl_take isl_union_set *uset);
4462 __isl_give isl_union_map *isl_union_map_detect_equalities(
4463 __isl_take isl_union_map *umap);
4465 Simplify the representation of a set or relation by detecting implicit
4468 =item * Removing redundant constraints
4470 #include <isl/set.h>
4471 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4472 __isl_take isl_basic_set *bset);
4473 __isl_give isl_set *isl_set_remove_redundancies(
4474 __isl_take isl_set *set);
4476 #include <isl/union_set.h>
4477 __isl_give isl_union_set *
4478 isl_union_set_remove_redundancies(
4479 __isl_take isl_union_set *uset);
4481 #include <isl/map.h>
4482 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4483 __isl_take isl_basic_map *bmap);
4484 __isl_give isl_map *isl_map_remove_redundancies(
4485 __isl_take isl_map *map);
4487 #include <isl/union_map.h>
4488 __isl_give isl_union_map *
4489 isl_union_map_remove_redundancies(
4490 __isl_take isl_union_map *umap);
4494 __isl_give isl_basic_set *isl_set_convex_hull(
4495 __isl_take isl_set *set);
4496 __isl_give isl_basic_map *isl_map_convex_hull(
4497 __isl_take isl_map *map);
4499 If the input set or relation has any existentially quantified
4500 variables, then the result of these operations is currently undefined.
4504 #include <isl/set.h>
4505 __isl_give isl_basic_set *
4506 isl_set_unshifted_simple_hull(
4507 __isl_take isl_set *set);
4508 __isl_give isl_basic_set *isl_set_simple_hull(
4509 __isl_take isl_set *set);
4510 __isl_give isl_basic_set *
4511 isl_set_unshifted_simple_hull_from_set_list(
4512 __isl_take isl_set *set,
4513 __isl_take isl_set_list *list);
4515 #include <isl/map.h>
4516 __isl_give isl_basic_map *
4517 isl_map_unshifted_simple_hull(
4518 __isl_take isl_map *map);
4519 __isl_give isl_basic_map *isl_map_simple_hull(
4520 __isl_take isl_map *map);
4521 __isl_give isl_basic_map *
4522 isl_map_unshifted_simple_hull_from_map_list(
4523 __isl_take isl_map *map,
4524 __isl_take isl_map_list *list);
4526 #include <isl/union_map.h>
4527 __isl_give isl_union_map *isl_union_map_simple_hull(
4528 __isl_take isl_union_map *umap);
4530 These functions compute a single basic set or relation
4531 that contains the whole input set or relation.
4532 In particular, the output is described by translates
4533 of the constraints describing the basic sets or relations in the input.
4534 In case of C<isl_set_unshifted_simple_hull>, only the original
4535 constraints are used, without any translation.
4536 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4537 C<isl_map_unshifted_simple_hull_from_map_list>, the
4538 constraints are taken from the elements of the second argument.
4542 (See \autoref{s:simple hull}.)
4548 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4549 __isl_take isl_basic_set *bset);
4550 __isl_give isl_basic_set *isl_set_affine_hull(
4551 __isl_take isl_set *set);
4552 __isl_give isl_union_set *isl_union_set_affine_hull(
4553 __isl_take isl_union_set *uset);
4554 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4555 __isl_take isl_basic_map *bmap);
4556 __isl_give isl_basic_map *isl_map_affine_hull(
4557 __isl_take isl_map *map);
4558 __isl_give isl_union_map *isl_union_map_affine_hull(
4559 __isl_take isl_union_map *umap);
4561 In case of union sets and relations, the affine hull is computed
4564 =item * Polyhedral hull
4566 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4567 __isl_take isl_set *set);
4568 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4569 __isl_take isl_map *map);
4570 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4571 __isl_take isl_union_set *uset);
4572 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4573 __isl_take isl_union_map *umap);
4575 These functions compute a single basic set or relation
4576 not involving any existentially quantified variables
4577 that contains the whole input set or relation.
4578 In case of union sets and relations, the polyhedral hull is computed
4581 =item * Other approximations
4583 #include <isl/set.h>
4584 __isl_give isl_basic_set *
4585 isl_basic_set_drop_constraints_involving_dims(
4586 __isl_take isl_basic_set *bset,
4587 enum isl_dim_type type,
4588 unsigned first, unsigned n);
4589 __isl_give isl_basic_set *
4590 isl_basic_set_drop_constraints_not_involving_dims(
4591 __isl_take isl_basic_set *bset,
4592 enum isl_dim_type type,
4593 unsigned first, unsigned n);
4594 __isl_give isl_set *
4595 isl_set_drop_constraints_involving_dims(
4596 __isl_take isl_set *set,
4597 enum isl_dim_type type,
4598 unsigned first, unsigned n);
4600 #include <isl/map.h>
4601 __isl_give isl_basic_map *
4602 isl_basic_map_drop_constraints_involving_dims(
4603 __isl_take isl_basic_map *bmap,
4604 enum isl_dim_type type,
4605 unsigned first, unsigned n);
4606 __isl_give isl_map *
4607 isl_map_drop_constraints_involving_dims(
4608 __isl_take isl_map *map,
4609 enum isl_dim_type type,
4610 unsigned first, unsigned n);
4612 These functions drop any constraints (not) involving the specified dimensions.
4613 Note that the result depends on the representation of the input.
4615 #include <isl/polynomial.h>
4616 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4617 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4618 __isl_give isl_union_pw_qpolynomial *
4619 isl_union_pw_qpolynomial_to_polynomial(
4620 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4622 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4623 the polynomial will be an overapproximation. If C<sign> is negative,
4624 it will be an underapproximation. If C<sign> is zero, the approximation
4625 will lie somewhere in between.
4629 __isl_give isl_basic_set *isl_basic_set_sample(
4630 __isl_take isl_basic_set *bset);
4631 __isl_give isl_basic_set *isl_set_sample(
4632 __isl_take isl_set *set);
4633 __isl_give isl_basic_map *isl_basic_map_sample(
4634 __isl_take isl_basic_map *bmap);
4635 __isl_give isl_basic_map *isl_map_sample(
4636 __isl_take isl_map *map);
4638 If the input (basic) set or relation is non-empty, then return
4639 a singleton subset of the input. Otherwise, return an empty set.
4641 =item * Optimization
4643 #include <isl/ilp.h>
4644 __isl_give isl_val *isl_basic_set_max_val(
4645 __isl_keep isl_basic_set *bset,
4646 __isl_keep isl_aff *obj);
4647 __isl_give isl_val *isl_set_min_val(
4648 __isl_keep isl_set *set,
4649 __isl_keep isl_aff *obj);
4650 __isl_give isl_val *isl_set_max_val(
4651 __isl_keep isl_set *set,
4652 __isl_keep isl_aff *obj);
4654 Compute the minimum or maximum of the integer affine expression C<obj>
4655 over the points in C<set>, returning the result in C<opt>.
4656 The result is C<NULL> in case of an error, the optimal value in case
4657 there is one, negative infinity or infinity if the problem is unbounded and
4658 NaN if the problem is empty.
4660 =item * Parametric optimization
4662 __isl_give isl_pw_aff *isl_set_dim_min(
4663 __isl_take isl_set *set, int pos);
4664 __isl_give isl_pw_aff *isl_set_dim_max(
4665 __isl_take isl_set *set, int pos);
4666 __isl_give isl_pw_aff *isl_map_dim_max(
4667 __isl_take isl_map *map, int pos);
4669 Compute the minimum or maximum of the given set or output dimension
4670 as a function of the parameters (and input dimensions), but independently
4671 of the other set or output dimensions.
4672 For lexicographic optimization, see L<"Lexicographic Optimization">.
4676 The following functions compute either the set of (rational) coefficient
4677 values of valid constraints for the given set or the set of (rational)
4678 values satisfying the constraints with coefficients from the given set.
4679 Internally, these two sets of functions perform essentially the
4680 same operations, except that the set of coefficients is assumed to
4681 be a cone, while the set of values may be any polyhedron.
4682 The current implementation is based on the Farkas lemma and
4683 Fourier-Motzkin elimination, but this may change or be made optional
4684 in future. In particular, future implementations may use different
4685 dualization algorithms or skip the elimination step.
4687 __isl_give isl_basic_set *isl_basic_set_coefficients(
4688 __isl_take isl_basic_set *bset);
4689 __isl_give isl_basic_set *isl_set_coefficients(
4690 __isl_take isl_set *set);
4691 __isl_give isl_union_set *isl_union_set_coefficients(
4692 __isl_take isl_union_set *bset);
4693 __isl_give isl_basic_set *isl_basic_set_solutions(
4694 __isl_take isl_basic_set *bset);
4695 __isl_give isl_basic_set *isl_set_solutions(
4696 __isl_take isl_set *set);
4697 __isl_give isl_union_set *isl_union_set_solutions(
4698 __isl_take isl_union_set *bset);
4702 __isl_give isl_map *isl_map_fixed_power_val(
4703 __isl_take isl_map *map,
4704 __isl_take isl_val *exp);
4705 __isl_give isl_union_map *
4706 isl_union_map_fixed_power_val(
4707 __isl_take isl_union_map *umap,
4708 __isl_take isl_val *exp);
4710 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4711 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4712 of C<map> is computed.
4714 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4716 __isl_give isl_union_map *isl_union_map_power(
4717 __isl_take isl_union_map *umap, int *exact);
4719 Compute a parametric representation for all positive powers I<k> of C<map>.
4720 The result maps I<k> to a nested relation corresponding to the
4721 I<k>th power of C<map>.
4722 The result may be an overapproximation. If the result is known to be exact,
4723 then C<*exact> is set to C<1>.
4725 =item * Transitive closure
4727 __isl_give isl_map *isl_map_transitive_closure(
4728 __isl_take isl_map *map, int *exact);
4729 __isl_give isl_union_map *isl_union_map_transitive_closure(
4730 __isl_take isl_union_map *umap, int *exact);
4732 Compute the transitive closure of C<map>.
4733 The result may be an overapproximation. If the result is known to be exact,
4734 then C<*exact> is set to C<1>.
4736 =item * Reaching path lengths
4738 __isl_give isl_map *isl_map_reaching_path_lengths(
4739 __isl_take isl_map *map, int *exact);
4741 Compute a relation that maps each element in the range of C<map>
4742 to the lengths of all paths composed of edges in C<map> that
4743 end up in the given element.
4744 The result may be an overapproximation. If the result is known to be exact,
4745 then C<*exact> is set to C<1>.
4746 To compute the I<maximal> path length, the resulting relation
4747 should be postprocessed by C<isl_map_lexmax>.
4748 In particular, if the input relation is a dependence relation
4749 (mapping sources to sinks), then the maximal path length corresponds
4750 to the free schedule.
4751 Note, however, that C<isl_map_lexmax> expects the maximum to be
4752 finite, so if the path lengths are unbounded (possibly due to
4753 the overapproximation), then you will get an error message.
4757 #include <isl/space.h>
4758 __isl_give isl_space *isl_space_wrap(
4759 __isl_take isl_space *space);
4760 __isl_give isl_space *isl_space_unwrap(
4761 __isl_take isl_space *space);
4763 #include <isl/local_space.h>
4764 __isl_give isl_local_space *isl_local_space_wrap(
4765 __isl_take isl_local_space *ls);
4767 #include <isl/set.h>
4768 __isl_give isl_basic_map *isl_basic_set_unwrap(
4769 __isl_take isl_basic_set *bset);
4770 __isl_give isl_map *isl_set_unwrap(
4771 __isl_take isl_set *set);
4773 #include <isl/map.h>
4774 __isl_give isl_basic_set *isl_basic_map_wrap(
4775 __isl_take isl_basic_map *bmap);
4776 __isl_give isl_set *isl_map_wrap(
4777 __isl_take isl_map *map);
4779 #include <isl/union_set.h>
4780 __isl_give isl_union_map *isl_union_set_unwrap(
4781 __isl_take isl_union_set *uset);
4783 #include <isl/union_map.h>
4784 __isl_give isl_union_set *isl_union_map_wrap(
4785 __isl_take isl_union_map *umap);
4787 The input to C<isl_space_unwrap> should
4788 be the space of a set, while that of
4789 C<isl_space_wrap> should be the space of a relation.
4790 Conversely, the output of C<isl_space_unwrap> is the space
4791 of a relation, while that of C<isl_space_wrap> is the space of a set.
4795 Remove any internal structure of domain (and range) of the given
4796 set or relation. If there is any such internal structure in the input,
4797 then the name of the space is also removed.
4799 #include <isl/local_space.h>
4800 __isl_give isl_local_space *
4801 isl_local_space_flatten_domain(
4802 __isl_take isl_local_space *ls);
4803 __isl_give isl_local_space *
4804 isl_local_space_flatten_range(
4805 __isl_take isl_local_space *ls);
4807 #include <isl/set.h>
4808 __isl_give isl_basic_set *isl_basic_set_flatten(
4809 __isl_take isl_basic_set *bset);
4810 __isl_give isl_set *isl_set_flatten(
4811 __isl_take isl_set *set);
4813 #include <isl/map.h>
4814 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4815 __isl_take isl_basic_map *bmap);
4816 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4817 __isl_take isl_basic_map *bmap);
4818 __isl_give isl_map *isl_map_flatten_range(
4819 __isl_take isl_map *map);
4820 __isl_give isl_map *isl_map_flatten_domain(
4821 __isl_take isl_map *map);
4822 __isl_give isl_basic_map *isl_basic_map_flatten(
4823 __isl_take isl_basic_map *bmap);
4824 __isl_give isl_map *isl_map_flatten(
4825 __isl_take isl_map *map);
4827 #include <isl/val.h>
4828 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4829 __isl_take isl_multi_val *mv);
4831 #include <isl/aff.h>
4832 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4833 __isl_take isl_multi_aff *ma);
4834 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4835 __isl_take isl_multi_aff *ma);
4836 __isl_give isl_multi_pw_aff *
4837 isl_multi_pw_aff_flatten_range(
4838 __isl_take isl_multi_pw_aff *mpa);
4839 __isl_give isl_multi_union_pw_aff *
4840 isl_multi_union_pw_aff_flatten_range(
4841 __isl_take isl_multi_union_pw_aff *mupa);
4843 #include <isl/map.h>
4844 __isl_give isl_map *isl_set_flatten_map(
4845 __isl_take isl_set *set);
4847 The function above constructs a relation
4848 that maps the input set to a flattened version of the set.
4852 Lift the input set to a space with extra dimensions corresponding
4853 to the existentially quantified variables in the input.
4854 In particular, the result lives in a wrapped map where the domain
4855 is the original space and the range corresponds to the original
4856 existentially quantified variables.
4858 #include <isl/set.h>
4859 __isl_give isl_basic_set *isl_basic_set_lift(
4860 __isl_take isl_basic_set *bset);
4861 __isl_give isl_set *isl_set_lift(
4862 __isl_take isl_set *set);
4863 __isl_give isl_union_set *isl_union_set_lift(
4864 __isl_take isl_union_set *uset);
4866 Given a local space that contains the existentially quantified
4867 variables of a set, a basic relation that, when applied to
4868 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4869 can be constructed using the following function.
4871 #include <isl/local_space.h>
4872 __isl_give isl_basic_map *isl_local_space_lifting(
4873 __isl_take isl_local_space *ls);
4875 #include <isl/aff.h>
4876 __isl_give isl_multi_aff *isl_multi_aff_lift(
4877 __isl_take isl_multi_aff *maff,
4878 __isl_give isl_local_space **ls);
4880 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4881 then it is assigned the local space that lies at the basis of
4882 the lifting applied.
4884 =item * Internal Product
4886 #include <isl/space.h>
4887 __isl_give isl_space *isl_space_zip(
4888 __isl_take isl_space *space);
4890 #include <isl/map.h>
4891 __isl_give isl_basic_map *isl_basic_map_zip(
4892 __isl_take isl_basic_map *bmap);
4893 __isl_give isl_map *isl_map_zip(
4894 __isl_take isl_map *map);
4896 #include <isl/union_map.h>
4897 __isl_give isl_union_map *isl_union_map_zip(
4898 __isl_take isl_union_map *umap);
4900 Given a relation with nested relations for domain and range,
4901 interchange the range of the domain with the domain of the range.
4905 #include <isl/space.h>
4906 __isl_give isl_space *isl_space_curry(
4907 __isl_take isl_space *space);
4908 __isl_give isl_space *isl_space_uncurry(
4909 __isl_take isl_space *space);
4911 #include <isl/map.h>
4912 __isl_give isl_basic_map *isl_basic_map_curry(
4913 __isl_take isl_basic_map *bmap);
4914 __isl_give isl_basic_map *isl_basic_map_uncurry(
4915 __isl_take isl_basic_map *bmap);
4916 __isl_give isl_map *isl_map_curry(
4917 __isl_take isl_map *map);
4918 __isl_give isl_map *isl_map_uncurry(
4919 __isl_take isl_map *map);
4921 #include <isl/union_map.h>
4922 __isl_give isl_union_map *isl_union_map_curry(
4923 __isl_take isl_union_map *umap);
4924 __isl_give isl_union_map *isl_union_map_uncurry(
4925 __isl_take isl_union_map *umap);
4927 Given a relation with a nested relation for domain,
4928 the C<curry> functions
4929 move the range of the nested relation out of the domain
4930 and use it as the domain of a nested relation in the range,
4931 with the original range as range of this nested relation.
4932 The C<uncurry> functions perform the inverse operation.
4934 =item * Aligning parameters
4936 Change the order of the parameters of the given set, relation
4938 such that the first parameters match those of C<model>.
4939 This may involve the introduction of extra parameters.
4940 All parameters need to be named.
4942 #include <isl/space.h>
4943 __isl_give isl_space *isl_space_align_params(
4944 __isl_take isl_space *space1,
4945 __isl_take isl_space *space2)
4947 #include <isl/set.h>
4948 __isl_give isl_basic_set *isl_basic_set_align_params(
4949 __isl_take isl_basic_set *bset,
4950 __isl_take isl_space *model);
4951 __isl_give isl_set *isl_set_align_params(
4952 __isl_take isl_set *set,
4953 __isl_take isl_space *model);
4955 #include <isl/map.h>
4956 __isl_give isl_basic_map *isl_basic_map_align_params(
4957 __isl_take isl_basic_map *bmap,
4958 __isl_take isl_space *model);
4959 __isl_give isl_map *isl_map_align_params(
4960 __isl_take isl_map *map,
4961 __isl_take isl_space *model);
4963 #include <isl/val.h>
4964 __isl_give isl_multi_val *isl_multi_val_align_params(
4965 __isl_take isl_multi_val *mv,
4966 __isl_take isl_space *model);
4968 #include <isl/aff.h>
4969 __isl_give isl_aff *isl_aff_align_params(
4970 __isl_take isl_aff *aff,
4971 __isl_take isl_space *model);
4972 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4973 __isl_take isl_multi_aff *multi,
4974 __isl_take isl_space *model);
4975 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4976 __isl_take isl_pw_aff *pwaff,
4977 __isl_take isl_space *model);
4978 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4979 __isl_take isl_pw_multi_aff *pma,
4980 __isl_take isl_space *model);
4981 __isl_give isl_union_pw_aff *
4982 isl_union_pw_aff_align_params(
4983 __isl_take isl_union_pw_aff *upa,
4984 __isl_take isl_space *model);
4985 __isl_give isl_union_pw_multi_aff *
4986 isl_union_pw_multi_aff_align_params(
4987 __isl_take isl_union_pw_multi_aff *upma,
4988 __isl_take isl_space *model);
4989 __isl_give isl_multi_union_pw_aff *
4990 isl_multi_union_pw_aff_align_params(
4991 __isl_take isl_multi_union_pw_aff *mupa,
4992 __isl_take isl_space *model);
4994 #include <isl/polynomial.h>
4995 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4996 __isl_take isl_qpolynomial *qp,
4997 __isl_take isl_space *model);
4999 =item * Unary Arithmethic Operations
5001 #include <isl/val.h>
5002 __isl_give isl_multi_val *isl_multi_val_neg(
5003 __isl_take isl_multi_val *mv);
5005 #include <isl/aff.h>
5006 __isl_give isl_aff *isl_aff_neg(
5007 __isl_take isl_aff *aff);
5008 __isl_give isl_multi_aff *isl_multi_aff_neg(
5009 __isl_take isl_multi_aff *ma);
5010 __isl_give isl_pw_aff *isl_pw_aff_neg(
5011 __isl_take isl_pw_aff *pwaff);
5012 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5013 __isl_take isl_pw_multi_aff *pma);
5014 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5015 __isl_take isl_multi_pw_aff *mpa);
5016 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5017 __isl_take isl_union_pw_aff *upa);
5018 __isl_give isl_union_pw_multi_aff *
5019 isl_union_pw_multi_aff_neg(
5020 __isl_take isl_union_pw_multi_aff *upma);
5021 __isl_give isl_multi_union_pw_aff *
5022 isl_multi_union_pw_aff_neg(
5023 __isl_take isl_multi_union_pw_aff *mupa);
5024 __isl_give isl_aff *isl_aff_ceil(
5025 __isl_take isl_aff *aff);
5026 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5027 __isl_take isl_pw_aff *pwaff);
5028 __isl_give isl_aff *isl_aff_floor(
5029 __isl_take isl_aff *aff);
5030 __isl_give isl_multi_aff *isl_multi_aff_floor(
5031 __isl_take isl_multi_aff *ma);
5032 __isl_give isl_pw_aff *isl_pw_aff_floor(
5033 __isl_take isl_pw_aff *pwaff);
5034 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5035 __isl_take isl_union_pw_aff *upa);
5037 #include <isl/aff.h>
5038 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5039 __isl_take isl_pw_aff_list *list);
5040 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5041 __isl_take isl_pw_aff_list *list);
5043 #include <isl/polynomial.h>
5044 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5045 __isl_take isl_qpolynomial *qp);
5046 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5047 __isl_take isl_pw_qpolynomial *pwqp);
5048 __isl_give isl_union_pw_qpolynomial *
5049 isl_union_pw_qpolynomial_neg(
5050 __isl_take isl_union_pw_qpolynomial *upwqp);
5051 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5052 __isl_take isl_qpolynomial *qp,
5054 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5055 __isl_take isl_pw_qpolynomial *pwqp,
5060 The following functions evaluate a function in a point.
5062 #include <isl/polynomial.h>
5063 __isl_give isl_val *isl_pw_qpolynomial_eval(
5064 __isl_take isl_pw_qpolynomial *pwqp,
5065 __isl_take isl_point *pnt);
5066 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5067 __isl_take isl_pw_qpolynomial_fold *pwf,
5068 __isl_take isl_point *pnt);
5069 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5070 __isl_take isl_union_pw_qpolynomial *upwqp,
5071 __isl_take isl_point *pnt);
5072 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5073 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5074 __isl_take isl_point *pnt);
5076 =item * Dimension manipulation
5078 It is usually not advisable to directly change the (input or output)
5079 space of a set or a relation as this removes the name and the internal
5080 structure of the space. However, the functions below can be useful
5081 to add new parameters, assuming
5082 C<isl_set_align_params> and C<isl_map_align_params>
5085 #include <isl/space.h>
5086 __isl_give isl_space *isl_space_add_dims(
5087 __isl_take isl_space *space,
5088 enum isl_dim_type type, unsigned n);
5089 __isl_give isl_space *isl_space_insert_dims(
5090 __isl_take isl_space *space,
5091 enum isl_dim_type type, unsigned pos, unsigned n);
5092 __isl_give isl_space *isl_space_drop_dims(
5093 __isl_take isl_space *space,
5094 enum isl_dim_type type, unsigned first, unsigned n);
5095 __isl_give isl_space *isl_space_move_dims(
5096 __isl_take isl_space *space,
5097 enum isl_dim_type dst_type, unsigned dst_pos,
5098 enum isl_dim_type src_type, unsigned src_pos,
5101 #include <isl/local_space.h>
5102 __isl_give isl_local_space *isl_local_space_add_dims(
5103 __isl_take isl_local_space *ls,
5104 enum isl_dim_type type, unsigned n);
5105 __isl_give isl_local_space *isl_local_space_insert_dims(
5106 __isl_take isl_local_space *ls,
5107 enum isl_dim_type type, unsigned first, unsigned n);
5108 __isl_give isl_local_space *isl_local_space_drop_dims(
5109 __isl_take isl_local_space *ls,
5110 enum isl_dim_type type, unsigned first, unsigned n);
5112 #include <isl/set.h>
5113 __isl_give isl_basic_set *isl_basic_set_add_dims(
5114 __isl_take isl_basic_set *bset,
5115 enum isl_dim_type type, unsigned n);
5116 __isl_give isl_set *isl_set_add_dims(
5117 __isl_take isl_set *set,
5118 enum isl_dim_type type, unsigned n);
5119 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5120 __isl_take isl_basic_set *bset,
5121 enum isl_dim_type type, unsigned pos,
5123 __isl_give isl_set *isl_set_insert_dims(
5124 __isl_take isl_set *set,
5125 enum isl_dim_type type, unsigned pos, unsigned n);
5126 __isl_give isl_basic_set *isl_basic_set_move_dims(
5127 __isl_take isl_basic_set *bset,
5128 enum isl_dim_type dst_type, unsigned dst_pos,
5129 enum isl_dim_type src_type, unsigned src_pos,
5131 __isl_give isl_set *isl_set_move_dims(
5132 __isl_take isl_set *set,
5133 enum isl_dim_type dst_type, unsigned dst_pos,
5134 enum isl_dim_type src_type, unsigned src_pos,
5137 #include <isl/map.h>
5138 __isl_give isl_map *isl_map_add_dims(
5139 __isl_take isl_map *map,
5140 enum isl_dim_type type, unsigned n);
5141 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5142 __isl_take isl_basic_map *bmap,
5143 enum isl_dim_type type, unsigned pos,
5145 __isl_give isl_map *isl_map_insert_dims(
5146 __isl_take isl_map *map,
5147 enum isl_dim_type type, unsigned pos, unsigned n);
5148 __isl_give isl_basic_map *isl_basic_map_move_dims(
5149 __isl_take isl_basic_map *bmap,
5150 enum isl_dim_type dst_type, unsigned dst_pos,
5151 enum isl_dim_type src_type, unsigned src_pos,
5153 __isl_give isl_map *isl_map_move_dims(
5154 __isl_take isl_map *map,
5155 enum isl_dim_type dst_type, unsigned dst_pos,
5156 enum isl_dim_type src_type, unsigned src_pos,
5159 #include <isl/val.h>
5160 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5161 __isl_take isl_multi_val *mv,
5162 enum isl_dim_type type, unsigned first, unsigned n);
5163 __isl_give isl_multi_val *isl_multi_val_add_dims(
5164 __isl_take isl_multi_val *mv,
5165 enum isl_dim_type type, unsigned n);
5166 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5167 __isl_take isl_multi_val *mv,
5168 enum isl_dim_type type, unsigned first, unsigned n);
5170 #include <isl/aff.h>
5171 __isl_give isl_aff *isl_aff_insert_dims(
5172 __isl_take isl_aff *aff,
5173 enum isl_dim_type type, unsigned first, unsigned n);
5174 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5175 __isl_take isl_multi_aff *ma,
5176 enum isl_dim_type type, unsigned first, unsigned n);
5177 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5178 __isl_take isl_pw_aff *pwaff,
5179 enum isl_dim_type type, unsigned first, unsigned n);
5180 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5181 __isl_take isl_multi_pw_aff *mpa,
5182 enum isl_dim_type type, unsigned first, unsigned n);
5183 __isl_give isl_aff *isl_aff_add_dims(
5184 __isl_take isl_aff *aff,
5185 enum isl_dim_type type, unsigned n);
5186 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5187 __isl_take isl_multi_aff *ma,
5188 enum isl_dim_type type, unsigned n);
5189 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5190 __isl_take isl_pw_aff *pwaff,
5191 enum isl_dim_type type, unsigned n);
5192 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5193 __isl_take isl_multi_pw_aff *mpa,
5194 enum isl_dim_type type, unsigned n);
5195 __isl_give isl_aff *isl_aff_drop_dims(
5196 __isl_take isl_aff *aff,
5197 enum isl_dim_type type, unsigned first, unsigned n);
5198 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5199 __isl_take isl_multi_aff *maff,
5200 enum isl_dim_type type, unsigned first, unsigned n);
5201 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5202 __isl_take isl_pw_aff *pwaff,
5203 enum isl_dim_type type, unsigned first, unsigned n);
5204 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5205 __isl_take isl_pw_multi_aff *pma,
5206 enum isl_dim_type type, unsigned first, unsigned n);
5207 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5208 __isl_take isl_union_pw_aff *upa,
5209 enum isl_dim_type type, unsigned first, unsigned n);
5210 __isl_give isl_union_pw_multi_aff *
5211 isl_union_pw_multi_aff_drop_dims(
5212 __isl_take isl_union_pw_multi_aff *upma,
5213 enum isl_dim_type type,
5214 unsigned first, unsigned n);
5215 __isl_give isl_multi_union_pw_aff *
5216 isl_multi_union_pw_aff_drop_dims(
5217 __isl_take isl_multi_union_pw_aff *mupa,
5218 enum isl_dim_type type, unsigned first,
5220 __isl_give isl_aff *isl_aff_move_dims(
5221 __isl_take isl_aff *aff,
5222 enum isl_dim_type dst_type, unsigned dst_pos,
5223 enum isl_dim_type src_type, unsigned src_pos,
5225 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5226 __isl_take isl_multi_aff *ma,
5227 enum isl_dim_type dst_type, unsigned dst_pos,
5228 enum isl_dim_type src_type, unsigned src_pos,
5230 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5231 __isl_take isl_pw_aff *pa,
5232 enum isl_dim_type dst_type, unsigned dst_pos,
5233 enum isl_dim_type src_type, unsigned src_pos,
5235 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5236 __isl_take isl_multi_pw_aff *pma,
5237 enum isl_dim_type dst_type, unsigned dst_pos,
5238 enum isl_dim_type src_type, unsigned src_pos,
5241 #include <isl/polynomial.h>
5242 __isl_give isl_union_pw_qpolynomial *
5243 isl_union_pw_qpolynomial_drop_dims(
5244 __isl_take isl_union_pw_qpolynomial *upwqp,
5245 enum isl_dim_type type,
5246 unsigned first, unsigned n);
5247 __isl_give isl_union_pw_qpolynomial_fold *
5248 isl_union_pw_qpolynomial_fold_drop_dims(
5249 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5250 enum isl_dim_type type,
5251 unsigned first, unsigned n);
5253 The operations on union expressions can only manipulate parameters.
5257 =head2 Binary Operations
5259 The two arguments of a binary operation not only need to live
5260 in the same C<isl_ctx>, they currently also need to have
5261 the same (number of) parameters.
5263 =head3 Basic Operations
5267 =item * Intersection
5269 #include <isl/local_space.h>
5270 __isl_give isl_local_space *isl_local_space_intersect(
5271 __isl_take isl_local_space *ls1,
5272 __isl_take isl_local_space *ls2);
5274 #include <isl/set.h>
5275 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5276 __isl_take isl_basic_set *bset1,
5277 __isl_take isl_basic_set *bset2);
5278 __isl_give isl_basic_set *isl_basic_set_intersect(
5279 __isl_take isl_basic_set *bset1,
5280 __isl_take isl_basic_set *bset2);
5281 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5282 __isl_take struct isl_basic_set_list *list);
5283 __isl_give isl_set *isl_set_intersect_params(
5284 __isl_take isl_set *set,
5285 __isl_take isl_set *params);
5286 __isl_give isl_set *isl_set_intersect(
5287 __isl_take isl_set *set1,
5288 __isl_take isl_set *set2);
5290 #include <isl/map.h>
5291 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5292 __isl_take isl_basic_map *bmap,
5293 __isl_take isl_basic_set *bset);
5294 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5295 __isl_take isl_basic_map *bmap,
5296 __isl_take isl_basic_set *bset);
5297 __isl_give isl_basic_map *isl_basic_map_intersect(
5298 __isl_take isl_basic_map *bmap1,
5299 __isl_take isl_basic_map *bmap2);
5300 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5301 __isl_take isl_basic_map_list *list);
5302 __isl_give isl_map *isl_map_intersect_params(
5303 __isl_take isl_map *map,
5304 __isl_take isl_set *params);
5305 __isl_give isl_map *isl_map_intersect_domain(
5306 __isl_take isl_map *map,
5307 __isl_take isl_set *set);
5308 __isl_give isl_map *isl_map_intersect_range(
5309 __isl_take isl_map *map,
5310 __isl_take isl_set *set);
5311 __isl_give isl_map *isl_map_intersect(
5312 __isl_take isl_map *map1,
5313 __isl_take isl_map *map2);
5315 #include <isl/union_set.h>
5316 __isl_give isl_union_set *isl_union_set_intersect_params(
5317 __isl_take isl_union_set *uset,
5318 __isl_take isl_set *set);
5319 __isl_give isl_union_set *isl_union_set_intersect(
5320 __isl_take isl_union_set *uset1,
5321 __isl_take isl_union_set *uset2);
5323 #include <isl/union_map.h>
5324 __isl_give isl_union_map *isl_union_map_intersect_params(
5325 __isl_take isl_union_map *umap,
5326 __isl_take isl_set *set);
5327 __isl_give isl_union_map *isl_union_map_intersect_domain(
5328 __isl_take isl_union_map *umap,
5329 __isl_take isl_union_set *uset);
5330 __isl_give isl_union_map *isl_union_map_intersect_range(
5331 __isl_take isl_union_map *umap,
5332 __isl_take isl_union_set *uset);
5333 __isl_give isl_union_map *isl_union_map_intersect(
5334 __isl_take isl_union_map *umap1,
5335 __isl_take isl_union_map *umap2);
5337 #include <isl/aff.h>
5338 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5339 __isl_take isl_pw_aff *pa,
5340 __isl_take isl_set *set);
5341 __isl_give isl_multi_pw_aff *
5342 isl_multi_pw_aff_intersect_domain(
5343 __isl_take isl_multi_pw_aff *mpa,
5344 __isl_take isl_set *domain);
5345 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5346 __isl_take isl_pw_multi_aff *pma,
5347 __isl_take isl_set *set);
5348 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5349 __isl_take isl_union_pw_aff *upa,
5350 __isl_take isl_union_set *uset);
5351 __isl_give isl_union_pw_multi_aff *
5352 isl_union_pw_multi_aff_intersect_domain(
5353 __isl_take isl_union_pw_multi_aff *upma,
5354 __isl_take isl_union_set *uset);
5355 __isl_give isl_multi_union_pw_aff *
5356 isl_multi_union_pw_aff_intersect_domain(
5357 __isl_take isl_multi_union_pw_aff *mupa,
5358 __isl_take isl_union_set *uset);
5359 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5360 __isl_take isl_pw_aff *pa,
5361 __isl_take isl_set *set);
5362 __isl_give isl_multi_pw_aff *
5363 isl_multi_pw_aff_intersect_params(
5364 __isl_take isl_multi_pw_aff *mpa,
5365 __isl_take isl_set *set);
5366 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5367 __isl_take isl_pw_multi_aff *pma,
5368 __isl_take isl_set *set);
5369 __isl_give isl_union_pw_aff *
5370 isl_union_pw_aff_intersect_params(
5371 __isl_take isl_union_pw_aff *upa,
5372 __isl_give isl_union_pw_multi_aff *
5373 isl_union_pw_multi_aff_intersect_params(
5374 __isl_take isl_union_pw_multi_aff *upma,
5375 __isl_take isl_set *set);
5376 __isl_give isl_multi_union_pw_aff *
5377 isl_multi_union_pw_aff_intersect_params(
5378 __isl_take isl_multi_union_pw_aff *mupa,
5379 __isl_take isl_set *params);
5381 #include <isl/polynomial.h>
5382 __isl_give isl_pw_qpolynomial *
5383 isl_pw_qpolynomial_intersect_domain(
5384 __isl_take isl_pw_qpolynomial *pwpq,
5385 __isl_take isl_set *set);
5386 __isl_give isl_union_pw_qpolynomial *
5387 isl_union_pw_qpolynomial_intersect_domain(
5388 __isl_take isl_union_pw_qpolynomial *upwpq,
5389 __isl_take isl_union_set *uset);
5390 __isl_give isl_union_pw_qpolynomial_fold *
5391 isl_union_pw_qpolynomial_fold_intersect_domain(
5392 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5393 __isl_take isl_union_set *uset);
5394 __isl_give isl_pw_qpolynomial *
5395 isl_pw_qpolynomial_intersect_params(
5396 __isl_take isl_pw_qpolynomial *pwpq,
5397 __isl_take isl_set *set);
5398 __isl_give isl_pw_qpolynomial_fold *
5399 isl_pw_qpolynomial_fold_intersect_params(
5400 __isl_take isl_pw_qpolynomial_fold *pwf,
5401 __isl_take isl_set *set);
5402 __isl_give isl_union_pw_qpolynomial *
5403 isl_union_pw_qpolynomial_intersect_params(
5404 __isl_take isl_union_pw_qpolynomial *upwpq,
5405 __isl_take isl_set *set);
5406 __isl_give isl_union_pw_qpolynomial_fold *
5407 isl_union_pw_qpolynomial_fold_intersect_params(
5408 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5409 __isl_take isl_set *set);
5411 The second argument to the C<_params> functions needs to be
5412 a parametric (basic) set. For the other functions, a parametric set
5413 for either argument is only allowed if the other argument is
5414 a parametric set as well.
5415 The list passed to C<isl_basic_set_list_intersect> needs to have
5416 at least one element and all elements need to live in the same space.
5420 #include <isl/set.h>
5421 __isl_give isl_set *isl_basic_set_union(
5422 __isl_take isl_basic_set *bset1,
5423 __isl_take isl_basic_set *bset2);
5424 __isl_give isl_set *isl_set_union(
5425 __isl_take isl_set *set1,
5426 __isl_take isl_set *set2);
5428 #include <isl/map.h>
5429 __isl_give isl_map *isl_basic_map_union(
5430 __isl_take isl_basic_map *bmap1,
5431 __isl_take isl_basic_map *bmap2);
5432 __isl_give isl_map *isl_map_union(
5433 __isl_take isl_map *map1,
5434 __isl_take isl_map *map2);
5436 #include <isl/union_set.h>
5437 __isl_give isl_union_set *isl_union_set_union(
5438 __isl_take isl_union_set *uset1,
5439 __isl_take isl_union_set *uset2);
5440 __isl_give isl_union_set *isl_union_set_list_union(
5441 __isl_take isl_union_set_list *list);
5443 #include <isl/union_map.h>
5444 __isl_give isl_union_map *isl_union_map_union(
5445 __isl_take isl_union_map *umap1,
5446 __isl_take isl_union_map *umap2);
5448 =item * Set difference
5450 #include <isl/set.h>
5451 __isl_give isl_set *isl_set_subtract(
5452 __isl_take isl_set *set1,
5453 __isl_take isl_set *set2);
5455 #include <isl/map.h>
5456 __isl_give isl_map *isl_map_subtract(
5457 __isl_take isl_map *map1,
5458 __isl_take isl_map *map2);
5459 __isl_give isl_map *isl_map_subtract_domain(
5460 __isl_take isl_map *map,
5461 __isl_take isl_set *dom);
5462 __isl_give isl_map *isl_map_subtract_range(
5463 __isl_take isl_map *map,
5464 __isl_take isl_set *dom);
5466 #include <isl/union_set.h>
5467 __isl_give isl_union_set *isl_union_set_subtract(
5468 __isl_take isl_union_set *uset1,
5469 __isl_take isl_union_set *uset2);
5471 #include <isl/union_map.h>
5472 __isl_give isl_union_map *isl_union_map_subtract(
5473 __isl_take isl_union_map *umap1,
5474 __isl_take isl_union_map *umap2);
5475 __isl_give isl_union_map *isl_union_map_subtract_domain(
5476 __isl_take isl_union_map *umap,
5477 __isl_take isl_union_set *dom);
5478 __isl_give isl_union_map *isl_union_map_subtract_range(
5479 __isl_take isl_union_map *umap,
5480 __isl_take isl_union_set *dom);
5482 #include <isl/aff.h>
5483 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5484 __isl_take isl_pw_aff *pa,
5485 __isl_take isl_set *set);
5486 __isl_give isl_pw_multi_aff *
5487 isl_pw_multi_aff_subtract_domain(
5488 __isl_take isl_pw_multi_aff *pma,
5489 __isl_take isl_set *set);
5490 __isl_give isl_union_pw_aff *
5491 isl_union_pw_aff_subtract_domain(
5492 __isl_take isl_union_pw_aff *upa,
5493 __isl_take isl_union_set *uset);
5494 __isl_give isl_union_pw_multi_aff *
5495 isl_union_pw_multi_aff_subtract_domain(
5496 __isl_take isl_union_pw_multi_aff *upma,
5497 __isl_take isl_set *set);
5499 #include <isl/polynomial.h>
5500 __isl_give isl_pw_qpolynomial *
5501 isl_pw_qpolynomial_subtract_domain(
5502 __isl_take isl_pw_qpolynomial *pwpq,
5503 __isl_take isl_set *set);
5504 __isl_give isl_pw_qpolynomial_fold *
5505 isl_pw_qpolynomial_fold_subtract_domain(
5506 __isl_take isl_pw_qpolynomial_fold *pwf,
5507 __isl_take isl_set *set);
5508 __isl_give isl_union_pw_qpolynomial *
5509 isl_union_pw_qpolynomial_subtract_domain(
5510 __isl_take isl_union_pw_qpolynomial *upwpq,
5511 __isl_take isl_union_set *uset);
5512 __isl_give isl_union_pw_qpolynomial_fold *
5513 isl_union_pw_qpolynomial_fold_subtract_domain(
5514 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5515 __isl_take isl_union_set *uset);
5519 #include <isl/space.h>
5520 __isl_give isl_space *isl_space_join(
5521 __isl_take isl_space *left,
5522 __isl_take isl_space *right);
5524 #include <isl/map.h>
5525 __isl_give isl_basic_set *isl_basic_set_apply(
5526 __isl_take isl_basic_set *bset,
5527 __isl_take isl_basic_map *bmap);
5528 __isl_give isl_set *isl_set_apply(
5529 __isl_take isl_set *set,
5530 __isl_take isl_map *map);
5531 __isl_give isl_union_set *isl_union_set_apply(
5532 __isl_take isl_union_set *uset,
5533 __isl_take isl_union_map *umap);
5534 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5535 __isl_take isl_basic_map *bmap1,
5536 __isl_take isl_basic_map *bmap2);
5537 __isl_give isl_basic_map *isl_basic_map_apply_range(
5538 __isl_take isl_basic_map *bmap1,
5539 __isl_take isl_basic_map *bmap2);
5540 __isl_give isl_map *isl_map_apply_domain(
5541 __isl_take isl_map *map1,
5542 __isl_take isl_map *map2);
5543 __isl_give isl_map *isl_map_apply_range(
5544 __isl_take isl_map *map1,
5545 __isl_take isl_map *map2);
5547 #include <isl/union_map.h>
5548 __isl_give isl_union_map *isl_union_map_apply_domain(
5549 __isl_take isl_union_map *umap1,
5550 __isl_take isl_union_map *umap2);
5551 __isl_give isl_union_map *isl_union_map_apply_range(
5552 __isl_take isl_union_map *umap1,
5553 __isl_take isl_union_map *umap2);
5555 #include <isl/polynomial.h>
5556 __isl_give isl_pw_qpolynomial_fold *
5557 isl_set_apply_pw_qpolynomial_fold(
5558 __isl_take isl_set *set,
5559 __isl_take isl_pw_qpolynomial_fold *pwf,
5561 __isl_give isl_pw_qpolynomial_fold *
5562 isl_map_apply_pw_qpolynomial_fold(
5563 __isl_take isl_map *map,
5564 __isl_take isl_pw_qpolynomial_fold *pwf,
5566 __isl_give isl_union_pw_qpolynomial_fold *
5567 isl_union_set_apply_union_pw_qpolynomial_fold(
5568 __isl_take isl_union_set *uset,
5569 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5571 __isl_give isl_union_pw_qpolynomial_fold *
5572 isl_union_map_apply_union_pw_qpolynomial_fold(
5573 __isl_take isl_union_map *umap,
5574 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5577 The functions taking a map
5578 compose the given map with the given piecewise quasipolynomial reduction.
5579 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5580 over all elements in the intersection of the range of the map
5581 and the domain of the piecewise quasipolynomial reduction
5582 as a function of an element in the domain of the map.
5583 The functions taking a set compute a bound over all elements in the
5584 intersection of the set and the domain of the
5585 piecewise quasipolynomial reduction.
5589 #include <isl/set.h>
5590 __isl_give isl_basic_set *
5591 isl_basic_set_preimage_multi_aff(
5592 __isl_take isl_basic_set *bset,
5593 __isl_take isl_multi_aff *ma);
5594 __isl_give isl_set *isl_set_preimage_multi_aff(
5595 __isl_take isl_set *set,
5596 __isl_take isl_multi_aff *ma);
5597 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5598 __isl_take isl_set *set,
5599 __isl_take isl_pw_multi_aff *pma);
5600 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5601 __isl_take isl_set *set,
5602 __isl_take isl_multi_pw_aff *mpa);
5604 #include <isl/union_set.h>
5605 __isl_give isl_union_set *
5606 isl_union_set_preimage_multi_aff(
5607 __isl_take isl_union_set *uset,
5608 __isl_take isl_multi_aff *ma);
5609 __isl_give isl_union_set *
5610 isl_union_set_preimage_pw_multi_aff(
5611 __isl_take isl_union_set *uset,
5612 __isl_take isl_pw_multi_aff *pma);
5613 __isl_give isl_union_set *
5614 isl_union_set_preimage_union_pw_multi_aff(
5615 __isl_take isl_union_set *uset,
5616 __isl_take isl_union_pw_multi_aff *upma);
5618 #include <isl/map.h>
5619 __isl_give isl_basic_map *
5620 isl_basic_map_preimage_domain_multi_aff(
5621 __isl_take isl_basic_map *bmap,
5622 __isl_take isl_multi_aff *ma);
5623 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5624 __isl_take isl_map *map,
5625 __isl_take isl_multi_aff *ma);
5626 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5627 __isl_take isl_map *map,
5628 __isl_take isl_multi_aff *ma);
5629 __isl_give isl_map *
5630 isl_map_preimage_domain_pw_multi_aff(
5631 __isl_take isl_map *map,
5632 __isl_take isl_pw_multi_aff *pma);
5633 __isl_give isl_map *
5634 isl_map_preimage_range_pw_multi_aff(
5635 __isl_take isl_map *map,
5636 __isl_take isl_pw_multi_aff *pma);
5637 __isl_give isl_map *
5638 isl_map_preimage_domain_multi_pw_aff(
5639 __isl_take isl_map *map,
5640 __isl_take isl_multi_pw_aff *mpa);
5641 __isl_give isl_basic_map *
5642 isl_basic_map_preimage_range_multi_aff(
5643 __isl_take isl_basic_map *bmap,
5644 __isl_take isl_multi_aff *ma);
5646 #include <isl/union_map.h>
5647 __isl_give isl_union_map *
5648 isl_union_map_preimage_domain_multi_aff(
5649 __isl_take isl_union_map *umap,
5650 __isl_take isl_multi_aff *ma);
5651 __isl_give isl_union_map *
5652 isl_union_map_preimage_range_multi_aff(
5653 __isl_take isl_union_map *umap,
5654 __isl_take isl_multi_aff *ma);
5655 __isl_give isl_union_map *
5656 isl_union_map_preimage_domain_pw_multi_aff(
5657 __isl_take isl_union_map *umap,
5658 __isl_take isl_pw_multi_aff *pma);
5659 __isl_give isl_union_map *
5660 isl_union_map_preimage_range_pw_multi_aff(
5661 __isl_take isl_union_map *umap,
5662 __isl_take isl_pw_multi_aff *pma);
5663 __isl_give isl_union_map *
5664 isl_union_map_preimage_domain_union_pw_multi_aff(
5665 __isl_take isl_union_map *umap,
5666 __isl_take isl_union_pw_multi_aff *upma);
5667 __isl_give isl_union_map *
5668 isl_union_map_preimage_range_union_pw_multi_aff(
5669 __isl_take isl_union_map *umap,
5670 __isl_take isl_union_pw_multi_aff *upma);
5672 These functions compute the preimage of the given set or map domain/range under
5673 the given function. In other words, the expression is plugged
5674 into the set description or into the domain/range of the map.
5678 #include <isl/aff.h>
5679 __isl_give isl_aff *isl_aff_pullback_aff(
5680 __isl_take isl_aff *aff1,
5681 __isl_take isl_aff *aff2);
5682 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5683 __isl_take isl_aff *aff,
5684 __isl_take isl_multi_aff *ma);
5685 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5686 __isl_take isl_pw_aff *pa,
5687 __isl_take isl_multi_aff *ma);
5688 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5689 __isl_take isl_pw_aff *pa,
5690 __isl_take isl_pw_multi_aff *pma);
5691 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5692 __isl_take isl_pw_aff *pa,
5693 __isl_take isl_multi_pw_aff *mpa);
5694 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5695 __isl_take isl_multi_aff *ma1,
5696 __isl_take isl_multi_aff *ma2);
5697 __isl_give isl_pw_multi_aff *
5698 isl_pw_multi_aff_pullback_multi_aff(
5699 __isl_take isl_pw_multi_aff *pma,
5700 __isl_take isl_multi_aff *ma);
5701 __isl_give isl_multi_pw_aff *
5702 isl_multi_pw_aff_pullback_multi_aff(
5703 __isl_take isl_multi_pw_aff *mpa,
5704 __isl_take isl_multi_aff *ma);
5705 __isl_give isl_pw_multi_aff *
5706 isl_pw_multi_aff_pullback_pw_multi_aff(
5707 __isl_take isl_pw_multi_aff *pma1,
5708 __isl_take isl_pw_multi_aff *pma2);
5709 __isl_give isl_multi_pw_aff *
5710 isl_multi_pw_aff_pullback_pw_multi_aff(
5711 __isl_take isl_multi_pw_aff *mpa,
5712 __isl_take isl_pw_multi_aff *pma);
5713 __isl_give isl_multi_pw_aff *
5714 isl_multi_pw_aff_pullback_multi_pw_aff(
5715 __isl_take isl_multi_pw_aff *mpa1,
5716 __isl_take isl_multi_pw_aff *mpa2);
5717 __isl_give isl_union_pw_aff *
5718 isl_union_pw_aff_pullback_union_pw_multi_aff(
5719 __isl_take isl_union_pw_aff *upa,
5720 __isl_take isl_union_pw_multi_aff *upma);
5721 __isl_give isl_union_pw_multi_aff *
5722 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5723 __isl_take isl_union_pw_multi_aff *upma1,
5724 __isl_take isl_union_pw_multi_aff *upma2);
5726 These functions precompose the first expression by the second function.
5727 In other words, the second function is plugged
5728 into the first expression.
5732 #include <isl/aff.h>
5733 __isl_give isl_basic_set *isl_aff_le_basic_set(
5734 __isl_take isl_aff *aff1,
5735 __isl_take isl_aff *aff2);
5736 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5737 __isl_take isl_aff *aff1,
5738 __isl_take isl_aff *aff2);
5739 __isl_give isl_set *isl_pw_aff_eq_set(
5740 __isl_take isl_pw_aff *pwaff1,
5741 __isl_take isl_pw_aff *pwaff2);
5742 __isl_give isl_set *isl_pw_aff_ne_set(
5743 __isl_take isl_pw_aff *pwaff1,
5744 __isl_take isl_pw_aff *pwaff2);
5745 __isl_give isl_set *isl_pw_aff_le_set(
5746 __isl_take isl_pw_aff *pwaff1,
5747 __isl_take isl_pw_aff *pwaff2);
5748 __isl_give isl_set *isl_pw_aff_lt_set(
5749 __isl_take isl_pw_aff *pwaff1,
5750 __isl_take isl_pw_aff *pwaff2);
5751 __isl_give isl_set *isl_pw_aff_ge_set(
5752 __isl_take isl_pw_aff *pwaff1,
5753 __isl_take isl_pw_aff *pwaff2);
5754 __isl_give isl_set *isl_pw_aff_gt_set(
5755 __isl_take isl_pw_aff *pwaff1,
5756 __isl_take isl_pw_aff *pwaff2);
5758 __isl_give isl_set *isl_multi_aff_lex_le_set(
5759 __isl_take isl_multi_aff *ma1,
5760 __isl_take isl_multi_aff *ma2);
5761 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5762 __isl_take isl_multi_aff *ma1,
5763 __isl_take isl_multi_aff *ma2);
5765 __isl_give isl_set *isl_pw_aff_list_eq_set(
5766 __isl_take isl_pw_aff_list *list1,
5767 __isl_take isl_pw_aff_list *list2);
5768 __isl_give isl_set *isl_pw_aff_list_ne_set(
5769 __isl_take isl_pw_aff_list *list1,
5770 __isl_take isl_pw_aff_list *list2);
5771 __isl_give isl_set *isl_pw_aff_list_le_set(
5772 __isl_take isl_pw_aff_list *list1,
5773 __isl_take isl_pw_aff_list *list2);
5774 __isl_give isl_set *isl_pw_aff_list_lt_set(
5775 __isl_take isl_pw_aff_list *list1,
5776 __isl_take isl_pw_aff_list *list2);
5777 __isl_give isl_set *isl_pw_aff_list_ge_set(
5778 __isl_take isl_pw_aff_list *list1,
5779 __isl_take isl_pw_aff_list *list2);
5780 __isl_give isl_set *isl_pw_aff_list_gt_set(
5781 __isl_take isl_pw_aff_list *list1,
5782 __isl_take isl_pw_aff_list *list2);
5784 The function C<isl_aff_ge_basic_set> returns a basic set
5785 containing those elements in the shared space
5786 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5787 The function C<isl_pw_aff_ge_set> returns a set
5788 containing those elements in the shared domain
5789 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5790 greater than or equal to C<pwaff2>.
5791 The function C<isl_multi_aff_lex_le_set> returns a set
5792 containing those elements in the shared domain space
5793 where C<ma1> is lexicographically smaller than or
5795 The functions operating on C<isl_pw_aff_list> apply the corresponding
5796 C<isl_pw_aff> function to each pair of elements in the two lists.
5798 =item * Cartesian Product
5800 #include <isl/space.h>
5801 __isl_give isl_space *isl_space_product(
5802 __isl_take isl_space *space1,
5803 __isl_take isl_space *space2);
5804 __isl_give isl_space *isl_space_domain_product(
5805 __isl_take isl_space *space1,
5806 __isl_take isl_space *space2);
5807 __isl_give isl_space *isl_space_range_product(
5808 __isl_take isl_space *space1,
5809 __isl_take isl_space *space2);
5812 C<isl_space_product>, C<isl_space_domain_product>
5813 and C<isl_space_range_product> take pairs or relation spaces and
5814 produce a single relations space, where either the domain, the range
5815 or both domain and range are wrapped spaces of relations between
5816 the domains and/or ranges of the input spaces.
5817 If the product is only constructed over the domain or the range
5818 then the ranges or the domains of the inputs should be the same.
5819 The function C<isl_space_product> also accepts a pair of set spaces,
5820 in which case it returns a wrapped space of a relation between the
5823 #include <isl/set.h>
5824 __isl_give isl_set *isl_set_product(
5825 __isl_take isl_set *set1,
5826 __isl_take isl_set *set2);
5828 #include <isl/map.h>
5829 __isl_give isl_basic_map *isl_basic_map_domain_product(
5830 __isl_take isl_basic_map *bmap1,
5831 __isl_take isl_basic_map *bmap2);
5832 __isl_give isl_basic_map *isl_basic_map_range_product(
5833 __isl_take isl_basic_map *bmap1,
5834 __isl_take isl_basic_map *bmap2);
5835 __isl_give isl_basic_map *isl_basic_map_product(
5836 __isl_take isl_basic_map *bmap1,
5837 __isl_take isl_basic_map *bmap2);
5838 __isl_give isl_map *isl_map_domain_product(
5839 __isl_take isl_map *map1,
5840 __isl_take isl_map *map2);
5841 __isl_give isl_map *isl_map_range_product(
5842 __isl_take isl_map *map1,
5843 __isl_take isl_map *map2);
5844 __isl_give isl_map *isl_map_product(
5845 __isl_take isl_map *map1,
5846 __isl_take isl_map *map2);
5848 #include <isl/union_set.h>
5849 __isl_give isl_union_set *isl_union_set_product(
5850 __isl_take isl_union_set *uset1,
5851 __isl_take isl_union_set *uset2);
5853 #include <isl/union_map.h>
5854 __isl_give isl_union_map *isl_union_map_domain_product(
5855 __isl_take isl_union_map *umap1,
5856 __isl_take isl_union_map *umap2);
5857 __isl_give isl_union_map *isl_union_map_range_product(
5858 __isl_take isl_union_map *umap1,
5859 __isl_take isl_union_map *umap2);
5860 __isl_give isl_union_map *isl_union_map_product(
5861 __isl_take isl_union_map *umap1,
5862 __isl_take isl_union_map *umap2);
5864 #include <isl/val.h>
5865 __isl_give isl_multi_val *isl_multi_val_range_product(
5866 __isl_take isl_multi_val *mv1,
5867 __isl_take isl_multi_val *mv2);
5868 __isl_give isl_multi_val *isl_multi_val_product(
5869 __isl_take isl_multi_val *mv1,
5870 __isl_take isl_multi_val *mv2);
5872 #include <isl/aff.h>
5873 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5874 __isl_take isl_multi_aff *ma1,
5875 __isl_take isl_multi_aff *ma2);
5876 __isl_give isl_multi_aff *isl_multi_aff_product(
5877 __isl_take isl_multi_aff *ma1,
5878 __isl_take isl_multi_aff *ma2);
5879 __isl_give isl_multi_pw_aff *
5880 isl_multi_pw_aff_range_product(
5881 __isl_take isl_multi_pw_aff *mpa1,
5882 __isl_take isl_multi_pw_aff *mpa2);
5883 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5884 __isl_take isl_multi_pw_aff *mpa1,
5885 __isl_take isl_multi_pw_aff *mpa2);
5886 __isl_give isl_pw_multi_aff *
5887 isl_pw_multi_aff_range_product(
5888 __isl_take isl_pw_multi_aff *pma1,
5889 __isl_take isl_pw_multi_aff *pma2);
5890 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5891 __isl_take isl_pw_multi_aff *pma1,
5892 __isl_take isl_pw_multi_aff *pma2);
5893 __isl_give isl_multi_union_pw_aff *
5894 isl_multi_union_pw_aff_range_product(
5895 __isl_take isl_multi_union_pw_aff *mupa1,
5896 __isl_take isl_multi_union_pw_aff *mupa2);
5898 The above functions compute the cross product of the given
5899 sets, relations or functions. The domains and ranges of the results
5900 are wrapped maps between domains and ranges of the inputs.
5901 To obtain a ``flat'' product, use the following functions
5904 #include <isl/set.h>
5905 __isl_give isl_basic_set *isl_basic_set_flat_product(
5906 __isl_take isl_basic_set *bset1,
5907 __isl_take isl_basic_set *bset2);
5908 __isl_give isl_set *isl_set_flat_product(
5909 __isl_take isl_set *set1,
5910 __isl_take isl_set *set2);
5912 #include <isl/map.h>
5913 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5914 __isl_take isl_basic_map *bmap1,
5915 __isl_take isl_basic_map *bmap2);
5916 __isl_give isl_map *isl_map_flat_domain_product(
5917 __isl_take isl_map *map1,
5918 __isl_take isl_map *map2);
5919 __isl_give isl_map *isl_map_flat_range_product(
5920 __isl_take isl_map *map1,
5921 __isl_take isl_map *map2);
5922 __isl_give isl_basic_map *isl_basic_map_flat_product(
5923 __isl_take isl_basic_map *bmap1,
5924 __isl_take isl_basic_map *bmap2);
5925 __isl_give isl_map *isl_map_flat_product(
5926 __isl_take isl_map *map1,
5927 __isl_take isl_map *map2);
5929 #include <isl/union_map.h>
5930 __isl_give isl_union_map *
5931 isl_union_map_flat_domain_product(
5932 __isl_take isl_union_map *umap1,
5933 __isl_take isl_union_map *umap2);
5934 __isl_give isl_union_map *
5935 isl_union_map_flat_range_product(
5936 __isl_take isl_union_map *umap1,
5937 __isl_take isl_union_map *umap2);
5939 #include <isl/val.h>
5940 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
5941 __isl_take isl_multi_val *mv1,
5942 __isl_take isl_multi_aff *mv2);
5944 #include <isl/aff.h>
5945 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
5946 __isl_take isl_multi_aff *ma1,
5947 __isl_take isl_multi_aff *ma2);
5948 __isl_give isl_pw_multi_aff *
5949 isl_pw_multi_aff_flat_range_product(
5950 __isl_take isl_pw_multi_aff *pma1,
5951 __isl_take isl_pw_multi_aff *pma2);
5952 __isl_give isl_multi_pw_aff *
5953 isl_multi_pw_aff_flat_range_product(
5954 __isl_take isl_multi_pw_aff *mpa1,
5955 __isl_take isl_multi_pw_aff *mpa2);
5956 __isl_give isl_union_pw_multi_aff *
5957 isl_union_pw_multi_aff_flat_range_product(
5958 __isl_take isl_union_pw_multi_aff *upma1,
5959 __isl_take isl_union_pw_multi_aff *upma2);
5960 __isl_give isl_multi_union_pw_aff *
5961 isl_multi_union_pw_aff_flat_range_product(
5962 __isl_take isl_multi_union_pw_aff *mupa1,
5963 __isl_take isl_multi_union_pw_aff *mupa2);
5965 #include <isl/space.h>
5966 __isl_give isl_space *isl_space_factor_domain(
5967 __isl_take isl_space *space);
5968 __isl_give isl_space *isl_space_factor_range(
5969 __isl_take isl_space *space);
5970 __isl_give isl_space *isl_space_domain_factor_domain(
5971 __isl_take isl_space *space);
5972 __isl_give isl_space *isl_space_domain_factor_range(
5973 __isl_take isl_space *space);
5974 __isl_give isl_space *isl_space_range_factor_domain(
5975 __isl_take isl_space *space);
5976 __isl_give isl_space *isl_space_range_factor_range(
5977 __isl_take isl_space *space);
5979 The functions C<isl_space_range_factor_domain> and
5980 C<isl_space_range_factor_range> extract the two arguments from
5981 the result of a call to C<isl_space_range_product>.
5983 The arguments of a call to C<isl_map_range_product> can be extracted
5984 from the result using the following functions.
5986 #include <isl/map.h>
5987 __isl_give isl_map *isl_map_factor_domain(
5988 __isl_take isl_map *map);
5989 __isl_give isl_map *isl_map_factor_range(
5990 __isl_take isl_map *map);
5991 __isl_give isl_map *isl_map_domain_factor_domain(
5992 __isl_take isl_map *map);
5993 __isl_give isl_map *isl_map_domain_factor_range(
5994 __isl_take isl_map *map);
5995 __isl_give isl_map *isl_map_range_factor_domain(
5996 __isl_take isl_map *map);
5997 __isl_give isl_map *isl_map_range_factor_range(
5998 __isl_take isl_map *map);
6000 #include <isl/union_map.h>
6001 __isl_give isl_union_map *isl_union_map_factor_domain(
6002 __isl_take isl_union_map *umap);
6003 __isl_give isl_union_map *isl_union_map_factor_range(
6004 __isl_take isl_union_map *umap);
6005 __isl_give isl_union_map *
6006 isl_union_map_domain_factor_domain(
6007 __isl_take isl_union_map *umap);
6008 __isl_give isl_union_map *
6009 isl_union_map_domain_factor_range(
6010 __isl_take isl_union_map *umap);
6011 __isl_give isl_union_map *
6012 isl_union_map_range_factor_range(
6013 __isl_take isl_union_map *umap);
6015 #include <isl/val.h>
6016 __isl_give isl_multi_val *
6017 isl_multi_val_range_factor_domain(
6018 __isl_take isl_multi_val *mv);
6019 __isl_give isl_multi_val *
6020 isl_multi_val_range_factor_range(
6021 __isl_take isl_multi_val *mv);
6023 #include <isl/aff.h>
6024 __isl_give isl_multi_aff *
6025 isl_multi_aff_range_factor_domain(
6026 __isl_take isl_multi_aff *ma);
6027 __isl_give isl_multi_aff *
6028 isl_multi_aff_range_factor_range(
6029 __isl_take isl_multi_aff *ma);
6030 __isl_give isl_multi_pw_aff *
6031 isl_multi_pw_aff_range_factor_domain(
6032 __isl_take isl_multi_pw_aff *mpa);
6033 __isl_give isl_multi_pw_aff *
6034 isl_multi_pw_aff_range_factor_range(
6035 __isl_take isl_multi_pw_aff *mpa);
6036 __isl_give isl_multi_union_pw_aff *
6037 isl_multi_union_pw_aff_range_factor_domain(
6038 __isl_take isl_multi_union_pw_aff *mupa);
6039 __isl_give isl_multi_union_pw_aff *
6040 isl_multi_union_pw_aff_range_factor_range(
6041 __isl_take isl_multi_union_pw_aff *mupa);
6043 The splice functions are a generalization of the flat product functions,
6044 where the second argument may be inserted at any position inside
6045 the first argument rather than being placed at the end.
6047 #include <isl/val.h>
6048 __isl_give isl_multi_val *isl_multi_val_range_splice(
6049 __isl_take isl_multi_val *mv1, unsigned pos,
6050 __isl_take isl_multi_val *mv2);
6052 #include <isl/aff.h>
6053 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6054 __isl_take isl_multi_aff *ma1, unsigned pos,
6055 __isl_take isl_multi_aff *ma2);
6056 __isl_give isl_multi_aff *isl_multi_aff_splice(
6057 __isl_take isl_multi_aff *ma1,
6058 unsigned in_pos, unsigned out_pos,
6059 __isl_take isl_multi_aff *ma2);
6060 __isl_give isl_multi_pw_aff *
6061 isl_multi_pw_aff_range_splice(
6062 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6063 __isl_take isl_multi_pw_aff *mpa2);
6064 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6065 __isl_take isl_multi_pw_aff *mpa1,
6066 unsigned in_pos, unsigned out_pos,
6067 __isl_take isl_multi_pw_aff *mpa2);
6068 __isl_give isl_multi_union_pw_aff *
6069 isl_multi_union_pw_aff_range_splice(
6070 __isl_take isl_multi_union_pw_aff *mupa1,
6072 __isl_take isl_multi_union_pw_aff *mupa2);
6074 =item * Simplification
6076 When applied to a set or relation,
6077 the gist operation returns a set or relation that has the
6078 same intersection with the context as the input set or relation.
6079 Any implicit equality in the intersection is made explicit in the result,
6080 while all inequalities that are redundant with respect to the intersection
6082 In case of union sets and relations, the gist operation is performed
6085 When applied to a function,
6086 the gist operation applies the set gist operation to each of
6087 the cells in the domain of the input piecewise expression.
6088 The context is also exploited
6089 to simplify the expression associated to each cell.
6091 #include <isl/set.h>
6092 __isl_give isl_basic_set *isl_basic_set_gist(
6093 __isl_take isl_basic_set *bset,
6094 __isl_take isl_basic_set *context);
6095 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6096 __isl_take isl_set *context);
6097 __isl_give isl_set *isl_set_gist_params(
6098 __isl_take isl_set *set,
6099 __isl_take isl_set *context);
6101 #include <isl/map.h>
6102 __isl_give isl_basic_map *isl_basic_map_gist(
6103 __isl_take isl_basic_map *bmap,
6104 __isl_take isl_basic_map *context);
6105 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6106 __isl_take isl_basic_map *bmap,
6107 __isl_take isl_basic_set *context);
6108 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6109 __isl_take isl_map *context);
6110 __isl_give isl_map *isl_map_gist_params(
6111 __isl_take isl_map *map,
6112 __isl_take isl_set *context);
6113 __isl_give isl_map *isl_map_gist_domain(
6114 __isl_take isl_map *map,
6115 __isl_take isl_set *context);
6116 __isl_give isl_map *isl_map_gist_range(
6117 __isl_take isl_map *map,
6118 __isl_take isl_set *context);
6120 #include <isl/union_set.h>
6121 __isl_give isl_union_set *isl_union_set_gist(
6122 __isl_take isl_union_set *uset,
6123 __isl_take isl_union_set *context);
6124 __isl_give isl_union_set *isl_union_set_gist_params(
6125 __isl_take isl_union_set *uset,
6126 __isl_take isl_set *set);
6128 #include <isl/union_map.h>
6129 __isl_give isl_union_map *isl_union_map_gist(
6130 __isl_take isl_union_map *umap,
6131 __isl_take isl_union_map *context);
6132 __isl_give isl_union_map *isl_union_map_gist_params(
6133 __isl_take isl_union_map *umap,
6134 __isl_take isl_set *set);
6135 __isl_give isl_union_map *isl_union_map_gist_domain(
6136 __isl_take isl_union_map *umap,
6137 __isl_take isl_union_set *uset);
6138 __isl_give isl_union_map *isl_union_map_gist_range(
6139 __isl_take isl_union_map *umap,
6140 __isl_take isl_union_set *uset);
6142 #include <isl/aff.h>
6143 __isl_give isl_aff *isl_aff_gist_params(
6144 __isl_take isl_aff *aff,
6145 __isl_take isl_set *context);
6146 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6147 __isl_take isl_set *context);
6148 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6149 __isl_take isl_multi_aff *maff,
6150 __isl_take isl_set *context);
6151 __isl_give isl_multi_aff *isl_multi_aff_gist(
6152 __isl_take isl_multi_aff *maff,
6153 __isl_take isl_set *context);
6154 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6155 __isl_take isl_pw_aff *pwaff,
6156 __isl_take isl_set *context);
6157 __isl_give isl_pw_aff *isl_pw_aff_gist(
6158 __isl_take isl_pw_aff *pwaff,
6159 __isl_take isl_set *context);
6160 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6161 __isl_take isl_pw_multi_aff *pma,
6162 __isl_take isl_set *set);
6163 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6164 __isl_take isl_pw_multi_aff *pma,
6165 __isl_take isl_set *set);
6166 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6167 __isl_take isl_multi_pw_aff *mpa,
6168 __isl_take isl_set *set);
6169 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6170 __isl_take isl_multi_pw_aff *mpa,
6171 __isl_take isl_set *set);
6172 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6173 __isl_take isl_union_pw_aff *upa,
6174 __isl_take isl_union_set *context);
6175 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6176 __isl_take isl_union_pw_aff *upa,
6177 __isl_take isl_set *context);
6178 __isl_give isl_union_pw_multi_aff *
6179 isl_union_pw_multi_aff_gist_params(
6180 __isl_take isl_union_pw_multi_aff *upma,
6181 __isl_take isl_set *context);
6182 __isl_give isl_union_pw_multi_aff *
6183 isl_union_pw_multi_aff_gist(
6184 __isl_take isl_union_pw_multi_aff *upma,
6185 __isl_take isl_union_set *context);
6186 __isl_give isl_multi_union_pw_aff *
6187 isl_multi_union_pw_aff_gist_params(
6188 __isl_take isl_multi_union_pw_aff *aff,
6189 __isl_take isl_set *context);
6190 __isl_give isl_multi_union_pw_aff *
6191 isl_multi_union_pw_aff_gist(
6192 __isl_take isl_multi_union_pw_aff *aff,
6193 __isl_take isl_union_set *context);
6195 #include <isl/polynomial.h>
6196 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6197 __isl_take isl_qpolynomial *qp,
6198 __isl_take isl_set *context);
6199 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6200 __isl_take isl_qpolynomial *qp,
6201 __isl_take isl_set *context);
6202 __isl_give isl_qpolynomial_fold *
6203 isl_qpolynomial_fold_gist_params(
6204 __isl_take isl_qpolynomial_fold *fold,
6205 __isl_take isl_set *context);
6206 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6207 __isl_take isl_qpolynomial_fold *fold,
6208 __isl_take isl_set *context);
6209 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6210 __isl_take isl_pw_qpolynomial *pwqp,
6211 __isl_take isl_set *context);
6212 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6213 __isl_take isl_pw_qpolynomial *pwqp,
6214 __isl_take isl_set *context);
6215 __isl_give isl_pw_qpolynomial_fold *
6216 isl_pw_qpolynomial_fold_gist(
6217 __isl_take isl_pw_qpolynomial_fold *pwf,
6218 __isl_take isl_set *context);
6219 __isl_give isl_pw_qpolynomial_fold *
6220 isl_pw_qpolynomial_fold_gist_params(
6221 __isl_take isl_pw_qpolynomial_fold *pwf,
6222 __isl_take isl_set *context);
6223 __isl_give isl_union_pw_qpolynomial *
6224 isl_union_pw_qpolynomial_gist_params(
6225 __isl_take isl_union_pw_qpolynomial *upwqp,
6226 __isl_take isl_set *context);
6227 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6228 __isl_take isl_union_pw_qpolynomial *upwqp,
6229 __isl_take isl_union_set *context);
6230 __isl_give isl_union_pw_qpolynomial_fold *
6231 isl_union_pw_qpolynomial_fold_gist(
6232 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6233 __isl_take isl_union_set *context);
6234 __isl_give isl_union_pw_qpolynomial_fold *
6235 isl_union_pw_qpolynomial_fold_gist_params(
6236 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6237 __isl_take isl_set *context);
6239 =item * Binary Arithmethic Operations
6241 #include <isl/val.h>
6242 __isl_give isl_multi_val *isl_multi_val_sub(
6243 __isl_take isl_multi_val *mv1,
6244 __isl_take isl_multi_val *mv2);
6246 #include <isl/aff.h>
6247 __isl_give isl_aff *isl_aff_add(
6248 __isl_take isl_aff *aff1,
6249 __isl_take isl_aff *aff2);
6250 __isl_give isl_multi_aff *isl_multi_aff_add(
6251 __isl_take isl_multi_aff *maff1,
6252 __isl_take isl_multi_aff *maff2);
6253 __isl_give isl_pw_aff *isl_pw_aff_add(
6254 __isl_take isl_pw_aff *pwaff1,
6255 __isl_take isl_pw_aff *pwaff2);
6256 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6257 __isl_take isl_pw_multi_aff *pma1,
6258 __isl_take isl_pw_multi_aff *pma2);
6259 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6260 __isl_take isl_union_pw_aff *upa1,
6261 __isl_take isl_union_pw_aff *upa2);
6262 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6263 __isl_take isl_union_pw_multi_aff *upma1,
6264 __isl_take isl_union_pw_multi_aff *upma2);
6265 __isl_give isl_pw_aff *isl_pw_aff_min(
6266 __isl_take isl_pw_aff *pwaff1,
6267 __isl_take isl_pw_aff *pwaff2);
6268 __isl_give isl_pw_aff *isl_pw_aff_max(
6269 __isl_take isl_pw_aff *pwaff1,
6270 __isl_take isl_pw_aff *pwaff2);
6271 __isl_give isl_aff *isl_aff_sub(
6272 __isl_take isl_aff *aff1,
6273 __isl_take isl_aff *aff2);
6274 __isl_give isl_multi_aff *isl_multi_aff_sub(
6275 __isl_take isl_multi_aff *ma1,
6276 __isl_take isl_multi_aff *ma2);
6277 __isl_give isl_pw_aff *isl_pw_aff_sub(
6278 __isl_take isl_pw_aff *pwaff1,
6279 __isl_take isl_pw_aff *pwaff2);
6280 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6281 __isl_take isl_multi_pw_aff *mpa1,
6282 __isl_take isl_multi_pw_aff *mpa2);
6283 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6284 __isl_take isl_pw_multi_aff *pma1,
6285 __isl_take isl_pw_multi_aff *pma2);
6286 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6287 __isl_take isl_union_pw_aff *upa1,
6288 __isl_take isl_union_pw_aff *upa2);
6289 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6290 __isl_take isl_union_pw_multi_aff *upma1,
6291 __isl_take isl_union_pw_multi_aff *upma2);
6292 __isl_give isl_multi_union_pw_aff *
6293 isl_multi_union_pw_aff_sub(
6294 __isl_take isl_multi_union_pw_aff *mupa1,
6295 __isl_take isl_multi_union_pw_aff *mupa2);
6297 C<isl_aff_sub> subtracts the second argument from the first.
6299 #include <isl/polynomial.h>
6300 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6301 __isl_take isl_qpolynomial *qp1,
6302 __isl_take isl_qpolynomial *qp2);
6303 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6304 __isl_take isl_pw_qpolynomial *pwqp1,
6305 __isl_take isl_pw_qpolynomial *pwqp2);
6306 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6307 __isl_take isl_pw_qpolynomial *pwqp1,
6308 __isl_take isl_pw_qpolynomial *pwqp2);
6309 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6310 __isl_take isl_pw_qpolynomial_fold *pwf1,
6311 __isl_take isl_pw_qpolynomial_fold *pwf2);
6312 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6313 __isl_take isl_union_pw_qpolynomial *upwqp1,
6314 __isl_take isl_union_pw_qpolynomial *upwqp2);
6315 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6316 __isl_take isl_qpolynomial *qp1,
6317 __isl_take isl_qpolynomial *qp2);
6318 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6319 __isl_take isl_pw_qpolynomial *pwqp1,
6320 __isl_take isl_pw_qpolynomial *pwqp2);
6321 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6322 __isl_take isl_union_pw_qpolynomial *upwqp1,
6323 __isl_take isl_union_pw_qpolynomial *upwqp2);
6324 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6325 __isl_take isl_pw_qpolynomial_fold *pwf1,
6326 __isl_take isl_pw_qpolynomial_fold *pwf2);
6327 __isl_give isl_union_pw_qpolynomial_fold *
6328 isl_union_pw_qpolynomial_fold_fold(
6329 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6330 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6332 #include <isl/aff.h>
6333 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6334 __isl_take isl_pw_aff *pwaff1,
6335 __isl_take isl_pw_aff *pwaff2);
6336 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6337 __isl_take isl_pw_multi_aff *pma1,
6338 __isl_take isl_pw_multi_aff *pma2);
6339 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6340 __isl_take isl_union_pw_aff *upa1,
6341 __isl_take isl_union_pw_aff *upa2);
6342 __isl_give isl_union_pw_multi_aff *
6343 isl_union_pw_multi_aff_union_add(
6344 __isl_take isl_union_pw_multi_aff *upma1,
6345 __isl_take isl_union_pw_multi_aff *upma2);
6346 __isl_give isl_multi_union_pw_aff *
6347 isl_multi_union_pw_aff_union_add(
6348 __isl_take isl_multi_union_pw_aff *mupa1,
6349 __isl_take isl_multi_union_pw_aff *mupa2);
6350 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6351 __isl_take isl_pw_aff *pwaff1,
6352 __isl_take isl_pw_aff *pwaff2);
6353 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6354 __isl_take isl_pw_aff *pwaff1,
6355 __isl_take isl_pw_aff *pwaff2);
6357 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6358 expression with a domain that is the union of those of C<pwaff1> and
6359 C<pwaff2> and such that on each cell, the quasi-affine expression is
6360 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6361 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6362 associated expression is the defined one.
6363 This in contrast to the C<isl_pw_aff_max> function, which is
6364 only defined on the shared definition domain of the arguments.
6366 #include <isl/val.h>
6367 __isl_give isl_multi_val *isl_multi_val_add_val(
6368 __isl_take isl_multi_val *mv,
6369 __isl_take isl_val *v);
6370 __isl_give isl_multi_val *isl_multi_val_mod_val(
6371 __isl_take isl_multi_val *mv,
6372 __isl_take isl_val *v);
6373 __isl_give isl_multi_val *isl_multi_val_scale_val(
6374 __isl_take isl_multi_val *mv,
6375 __isl_take isl_val *v);
6376 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6377 __isl_take isl_multi_val *mv,
6378 __isl_take isl_val *v);
6380 #include <isl/aff.h>
6381 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6382 __isl_take isl_val *mod);
6383 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6384 __isl_take isl_pw_aff *pa,
6385 __isl_take isl_val *mod);
6386 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6387 __isl_take isl_union_pw_aff *upa,
6388 __isl_take isl_val *f);
6389 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6390 __isl_take isl_val *v);
6391 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6392 __isl_take isl_multi_aff *ma,
6393 __isl_take isl_val *v);
6394 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6395 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6396 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6397 __isl_take isl_multi_pw_aff *mpa,
6398 __isl_take isl_val *v);
6399 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6400 __isl_take isl_pw_multi_aff *pma,
6401 __isl_take isl_val *v);
6402 __isl_give isl_union_pw_multi_aff *
6403 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6404 __isl_take isl_union_pw_aff *upa,
6405 __isl_take isl_val *f);
6406 isl_union_pw_multi_aff_scale_val(
6407 __isl_take isl_union_pw_multi_aff *upma,
6408 __isl_take isl_val *val);
6409 __isl_give isl_multi_union_pw_aff *
6410 isl_multi_union_pw_aff_scale_val(
6411 __isl_take isl_multi_union_pw_aff *mupa,
6412 __isl_take isl_val *v);
6413 __isl_give isl_aff *isl_aff_scale_down_ui(
6414 __isl_take isl_aff *aff, unsigned f);
6415 __isl_give isl_aff *isl_aff_scale_down_val(
6416 __isl_take isl_aff *aff, __isl_take isl_val *v);
6417 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6418 __isl_take isl_multi_aff *ma,
6419 __isl_take isl_val *v);
6420 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6421 __isl_take isl_pw_aff *pa,
6422 __isl_take isl_val *f);
6423 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6424 __isl_take isl_multi_pw_aff *mpa,
6425 __isl_take isl_val *v);
6426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6427 __isl_take isl_pw_multi_aff *pma,
6428 __isl_take isl_val *v);
6429 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6430 __isl_take isl_union_pw_aff *upa,
6431 __isl_take isl_val *v);
6432 __isl_give isl_union_pw_multi_aff *
6433 isl_union_pw_multi_aff_scale_down_val(
6434 __isl_take isl_union_pw_multi_aff *upma,
6435 __isl_take isl_val *val);
6436 __isl_give isl_multi_union_pw_aff *
6437 isl_multi_union_pw_aff_scale_down_val(
6438 __isl_take isl_multi_union_pw_aff *mupa,
6439 __isl_take isl_val *v);
6441 #include <isl/polynomial.h>
6442 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6443 __isl_take isl_qpolynomial *qp,
6444 __isl_take isl_val *v);
6445 __isl_give isl_qpolynomial_fold *
6446 isl_qpolynomial_fold_scale_val(
6447 __isl_take isl_qpolynomial_fold *fold,
6448 __isl_take isl_val *v);
6449 __isl_give isl_pw_qpolynomial *
6450 isl_pw_qpolynomial_scale_val(
6451 __isl_take isl_pw_qpolynomial *pwqp,
6452 __isl_take isl_val *v);
6453 __isl_give isl_pw_qpolynomial_fold *
6454 isl_pw_qpolynomial_fold_scale_val(
6455 __isl_take isl_pw_qpolynomial_fold *pwf,
6456 __isl_take isl_val *v);
6457 __isl_give isl_union_pw_qpolynomial *
6458 isl_union_pw_qpolynomial_scale_val(
6459 __isl_take isl_union_pw_qpolynomial *upwqp,
6460 __isl_take isl_val *v);
6461 __isl_give isl_union_pw_qpolynomial_fold *
6462 isl_union_pw_qpolynomial_fold_scale_val(
6463 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6464 __isl_take isl_val *v);
6465 __isl_give isl_qpolynomial *
6466 isl_qpolynomial_scale_down_val(
6467 __isl_take isl_qpolynomial *qp,
6468 __isl_take isl_val *v);
6469 __isl_give isl_qpolynomial_fold *
6470 isl_qpolynomial_fold_scale_down_val(
6471 __isl_take isl_qpolynomial_fold *fold,
6472 __isl_take isl_val *v);
6473 __isl_give isl_pw_qpolynomial *
6474 isl_pw_qpolynomial_scale_down_val(
6475 __isl_take isl_pw_qpolynomial *pwqp,
6476 __isl_take isl_val *v);
6477 __isl_give isl_pw_qpolynomial_fold *
6478 isl_pw_qpolynomial_fold_scale_down_val(
6479 __isl_take isl_pw_qpolynomial_fold *pwf,
6480 __isl_take isl_val *v);
6481 __isl_give isl_union_pw_qpolynomial *
6482 isl_union_pw_qpolynomial_scale_down_val(
6483 __isl_take isl_union_pw_qpolynomial *upwqp,
6484 __isl_take isl_val *v);
6485 __isl_give isl_union_pw_qpolynomial_fold *
6486 isl_union_pw_qpolynomial_fold_scale_down_val(
6487 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6488 __isl_take isl_val *v);
6490 #include <isl/val.h>
6491 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6492 __isl_take isl_multi_val *mv1,
6493 __isl_take isl_multi_val *mv2);
6494 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6495 __isl_take isl_multi_val *mv1,
6496 __isl_take isl_multi_val *mv2);
6497 __isl_give isl_multi_val *
6498 isl_multi_val_scale_down_multi_val(
6499 __isl_take isl_multi_val *mv1,
6500 __isl_take isl_multi_val *mv2);
6502 #include <isl/aff.h>
6503 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6504 __isl_take isl_multi_aff *ma,
6505 __isl_take isl_multi_val *mv);
6506 __isl_give isl_multi_union_pw_aff *
6507 isl_multi_union_pw_aff_mod_multi_val(
6508 __isl_take isl_multi_union_pw_aff *upma,
6509 __isl_take isl_multi_val *mv);
6510 __isl_give isl_multi_pw_aff *
6511 isl_multi_pw_aff_mod_multi_val(
6512 __isl_take isl_multi_pw_aff *mpa,
6513 __isl_take isl_multi_val *mv);
6514 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6515 __isl_take isl_multi_aff *ma,
6516 __isl_take isl_multi_val *mv);
6517 __isl_give isl_pw_multi_aff *
6518 isl_pw_multi_aff_scale_multi_val(
6519 __isl_take isl_pw_multi_aff *pma,
6520 __isl_take isl_multi_val *mv);
6521 __isl_give isl_multi_pw_aff *
6522 isl_multi_pw_aff_scale_multi_val(
6523 __isl_take isl_multi_pw_aff *mpa,
6524 __isl_take isl_multi_val *mv);
6525 __isl_give isl_multi_union_pw_aff *
6526 isl_multi_union_pw_aff_scale_multi_val(
6527 __isl_take isl_multi_union_pw_aff *mupa,
6528 __isl_take isl_multi_val *mv);
6529 __isl_give isl_union_pw_multi_aff *
6530 isl_union_pw_multi_aff_scale_multi_val(
6531 __isl_take isl_union_pw_multi_aff *upma,
6532 __isl_take isl_multi_val *mv);
6533 __isl_give isl_multi_aff *
6534 isl_multi_aff_scale_down_multi_val(
6535 __isl_take isl_multi_aff *ma,
6536 __isl_take isl_multi_val *mv);
6537 __isl_give isl_multi_pw_aff *
6538 isl_multi_pw_aff_scale_down_multi_val(
6539 __isl_take isl_multi_pw_aff *mpa,
6540 __isl_take isl_multi_val *mv);
6541 __isl_give isl_multi_union_pw_aff *
6542 isl_multi_union_pw_aff_scale_down_multi_val(
6543 __isl_take isl_multi_union_pw_aff *mupa,
6544 __isl_take isl_multi_val *mv);
6546 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6547 by the corresponding elements of C<mv>.
6549 #include <isl/aff.h>
6550 __isl_give isl_aff *isl_aff_mul(
6551 __isl_take isl_aff *aff1,
6552 __isl_take isl_aff *aff2);
6553 __isl_give isl_aff *isl_aff_div(
6554 __isl_take isl_aff *aff1,
6555 __isl_take isl_aff *aff2);
6556 __isl_give isl_pw_aff *isl_pw_aff_mul(
6557 __isl_take isl_pw_aff *pwaff1,
6558 __isl_take isl_pw_aff *pwaff2);
6559 __isl_give isl_pw_aff *isl_pw_aff_div(
6560 __isl_take isl_pw_aff *pa1,
6561 __isl_take isl_pw_aff *pa2);
6562 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6563 __isl_take isl_pw_aff *pa1,
6564 __isl_take isl_pw_aff *pa2);
6565 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6566 __isl_take isl_pw_aff *pa1,
6567 __isl_take isl_pw_aff *pa2);
6569 When multiplying two affine expressions, at least one of the two needs
6570 to be a constant. Similarly, when dividing an affine expression by another,
6571 the second expression needs to be a constant.
6572 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6573 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6576 #include <isl/polynomial.h>
6577 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6578 __isl_take isl_qpolynomial *qp1,
6579 __isl_take isl_qpolynomial *qp2);
6580 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6581 __isl_take isl_pw_qpolynomial *pwqp1,
6582 __isl_take isl_pw_qpolynomial *pwqp2);
6583 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6584 __isl_take isl_union_pw_qpolynomial *upwqp1,
6585 __isl_take isl_union_pw_qpolynomial *upwqp2);
6589 =head3 Lexicographic Optimization
6591 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6592 the following functions
6593 compute a set that contains the lexicographic minimum or maximum
6594 of the elements in C<set> (or C<bset>) for those values of the parameters
6595 that satisfy C<dom>.
6596 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6597 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6599 In other words, the union of the parameter values
6600 for which the result is non-empty and of C<*empty>
6603 #include <isl/set.h>
6604 __isl_give isl_set *isl_basic_set_partial_lexmin(
6605 __isl_take isl_basic_set *bset,
6606 __isl_take isl_basic_set *dom,
6607 __isl_give isl_set **empty);
6608 __isl_give isl_set *isl_basic_set_partial_lexmax(
6609 __isl_take isl_basic_set *bset,
6610 __isl_take isl_basic_set *dom,
6611 __isl_give isl_set **empty);
6612 __isl_give isl_set *isl_set_partial_lexmin(
6613 __isl_take isl_set *set, __isl_take isl_set *dom,
6614 __isl_give isl_set **empty);
6615 __isl_give isl_set *isl_set_partial_lexmax(
6616 __isl_take isl_set *set, __isl_take isl_set *dom,
6617 __isl_give isl_set **empty);
6619 Given a (basic) set C<set> (or C<bset>), the following functions simply
6620 return a set containing the lexicographic minimum or maximum
6621 of the elements in C<set> (or C<bset>).
6622 In case of union sets, the optimum is computed per space.
6624 #include <isl/set.h>
6625 __isl_give isl_set *isl_basic_set_lexmin(
6626 __isl_take isl_basic_set *bset);
6627 __isl_give isl_set *isl_basic_set_lexmax(
6628 __isl_take isl_basic_set *bset);
6629 __isl_give isl_set *isl_set_lexmin(
6630 __isl_take isl_set *set);
6631 __isl_give isl_set *isl_set_lexmax(
6632 __isl_take isl_set *set);
6633 __isl_give isl_union_set *isl_union_set_lexmin(
6634 __isl_take isl_union_set *uset);
6635 __isl_give isl_union_set *isl_union_set_lexmax(
6636 __isl_take isl_union_set *uset);
6638 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6639 the following functions
6640 compute a relation that maps each element of C<dom>
6641 to the single lexicographic minimum or maximum
6642 of the elements that are associated to that same
6643 element in C<map> (or C<bmap>).
6644 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6645 that contains the elements in C<dom> that do not map
6646 to any elements in C<map> (or C<bmap>).
6647 In other words, the union of the domain of the result and of C<*empty>
6650 #include <isl/map.h>
6651 __isl_give isl_map *isl_basic_map_partial_lexmax(
6652 __isl_take isl_basic_map *bmap,
6653 __isl_take isl_basic_set *dom,
6654 __isl_give isl_set **empty);
6655 __isl_give isl_map *isl_basic_map_partial_lexmin(
6656 __isl_take isl_basic_map *bmap,
6657 __isl_take isl_basic_set *dom,
6658 __isl_give isl_set **empty);
6659 __isl_give isl_map *isl_map_partial_lexmax(
6660 __isl_take isl_map *map, __isl_take isl_set *dom,
6661 __isl_give isl_set **empty);
6662 __isl_give isl_map *isl_map_partial_lexmin(
6663 __isl_take isl_map *map, __isl_take isl_set *dom,
6664 __isl_give isl_set **empty);
6666 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6667 return a map mapping each element in the domain of
6668 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6669 of all elements associated to that element.
6670 In case of union relations, the optimum is computed per space.
6672 #include <isl/map.h>
6673 __isl_give isl_map *isl_basic_map_lexmin(
6674 __isl_take isl_basic_map *bmap);
6675 __isl_give isl_map *isl_basic_map_lexmax(
6676 __isl_take isl_basic_map *bmap);
6677 __isl_give isl_map *isl_map_lexmin(
6678 __isl_take isl_map *map);
6679 __isl_give isl_map *isl_map_lexmax(
6680 __isl_take isl_map *map);
6681 __isl_give isl_union_map *isl_union_map_lexmin(
6682 __isl_take isl_union_map *umap);
6683 __isl_give isl_union_map *isl_union_map_lexmax(
6684 __isl_take isl_union_map *umap);
6686 The following functions return their result in the form of
6687 a piecewise multi-affine expression,
6688 but are otherwise equivalent to the corresponding functions
6689 returning a basic set or relation.
6691 #include <isl/set.h>
6692 __isl_give isl_pw_multi_aff *
6693 isl_basic_set_partial_lexmin_pw_multi_aff(
6694 __isl_take isl_basic_set *bset,
6695 __isl_take isl_basic_set *dom,
6696 __isl_give isl_set **empty);
6697 __isl_give isl_pw_multi_aff *
6698 isl_basic_set_partial_lexmax_pw_multi_aff(
6699 __isl_take isl_basic_set *bset,
6700 __isl_take isl_basic_set *dom,
6701 __isl_give isl_set **empty);
6702 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6703 __isl_take isl_set *set);
6704 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6705 __isl_take isl_set *set);
6707 #include <isl/map.h>
6708 __isl_give isl_pw_multi_aff *
6709 isl_basic_map_lexmin_pw_multi_aff(
6710 __isl_take isl_basic_map *bmap);
6711 __isl_give isl_pw_multi_aff *
6712 isl_basic_map_partial_lexmin_pw_multi_aff(
6713 __isl_take isl_basic_map *bmap,
6714 __isl_take isl_basic_set *dom,
6715 __isl_give isl_set **empty);
6716 __isl_give isl_pw_multi_aff *
6717 isl_basic_map_partial_lexmax_pw_multi_aff(
6718 __isl_take isl_basic_map *bmap,
6719 __isl_take isl_basic_set *dom,
6720 __isl_give isl_set **empty);
6721 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6722 __isl_take isl_map *map);
6723 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6724 __isl_take isl_map *map);
6726 The following functions return the lexicographic minimum or maximum
6727 on the shared domain of the inputs and the single defined function
6728 on those parts of the domain where only a single function is defined.
6730 #include <isl/aff.h>
6731 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6732 __isl_take isl_pw_multi_aff *pma1,
6733 __isl_take isl_pw_multi_aff *pma2);
6734 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6735 __isl_take isl_pw_multi_aff *pma1,
6736 __isl_take isl_pw_multi_aff *pma2);
6738 =head2 Ternary Operations
6740 #include <isl/aff.h>
6741 __isl_give isl_pw_aff *isl_pw_aff_cond(
6742 __isl_take isl_pw_aff *cond,
6743 __isl_take isl_pw_aff *pwaff_true,
6744 __isl_take isl_pw_aff *pwaff_false);
6746 The function C<isl_pw_aff_cond> performs a conditional operator
6747 and returns an expression that is equal to C<pwaff_true>
6748 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6749 where C<cond> is zero.
6753 Lists are defined over several element types, including
6754 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
6755 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6756 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6757 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6758 Here we take lists of C<isl_set>s as an example.
6759 Lists can be created, copied, modified and freed using the following functions.
6761 #include <isl/set.h>
6762 __isl_give isl_set_list *isl_set_list_from_set(
6763 __isl_take isl_set *el);
6764 __isl_give isl_set_list *isl_set_list_alloc(
6765 isl_ctx *ctx, int n);
6766 __isl_give isl_set_list *isl_set_list_copy(
6767 __isl_keep isl_set_list *list);
6768 __isl_give isl_set_list *isl_set_list_insert(
6769 __isl_take isl_set_list *list, unsigned pos,
6770 __isl_take isl_set *el);
6771 __isl_give isl_set_list *isl_set_list_add(
6772 __isl_take isl_set_list *list,
6773 __isl_take isl_set *el);
6774 __isl_give isl_set_list *isl_set_list_drop(
6775 __isl_take isl_set_list *list,
6776 unsigned first, unsigned n);
6777 __isl_give isl_set_list *isl_set_list_set_set(
6778 __isl_take isl_set_list *list, int index,
6779 __isl_take isl_set *set);
6780 __isl_give isl_set_list *isl_set_list_concat(
6781 __isl_take isl_set_list *list1,
6782 __isl_take isl_set_list *list2);
6783 __isl_give isl_set_list *isl_set_list_sort(
6784 __isl_take isl_set_list *list,
6785 int (*cmp)(__isl_keep isl_set *a,
6786 __isl_keep isl_set *b, void *user),
6788 __isl_null isl_set_list *isl_set_list_free(
6789 __isl_take isl_set_list *list);
6791 C<isl_set_list_alloc> creates an empty list with an initial capacity
6792 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
6793 add elements to a list, increasing its capacity as needed.
6794 C<isl_set_list_from_set> creates a list with a single element.
6796 Lists can be inspected using the following functions.
6798 #include <isl/set.h>
6799 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6800 __isl_give isl_set *isl_set_list_get_set(
6801 __isl_keep isl_set_list *list, int index);
6802 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6803 int (*fn)(__isl_take isl_set *el, void *user),
6805 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6806 int (*follows)(__isl_keep isl_set *a,
6807 __isl_keep isl_set *b, void *user),
6809 int (*fn)(__isl_take isl_set *el, void *user),
6812 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6813 strongly connected components of the graph with as vertices the elements
6814 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6815 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6816 should return C<-1> on error.
6818 Lists can be printed using
6820 #include <isl/set.h>
6821 __isl_give isl_printer *isl_printer_print_set_list(
6822 __isl_take isl_printer *p,
6823 __isl_keep isl_set_list *list);
6825 =head2 Associative arrays
6827 Associative arrays map isl objects of a specific type to isl objects
6828 of some (other) specific type. They are defined for several pairs
6829 of types, including (C<isl_map>, C<isl_basic_set>),
6830 (C<isl_id>, C<isl_ast_expr>) and.
6831 (C<isl_id>, C<isl_pw_aff>).
6832 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6835 Associative arrays can be created, copied and freed using
6836 the following functions.
6838 #include <isl/id_to_ast_expr.h>
6839 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6840 isl_ctx *ctx, int min_size);
6841 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6842 __isl_keep id_to_ast_expr *id2expr);
6843 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6844 __isl_take id_to_ast_expr *id2expr);
6846 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6847 to specify the expected size of the associative array.
6848 The associative array will be grown automatically as needed.
6850 Associative arrays can be inspected using the following functions.
6852 #include <isl/id_to_ast_expr.h>
6853 int isl_id_to_ast_expr_has(
6854 __isl_keep id_to_ast_expr *id2expr,
6855 __isl_keep isl_id *key);
6856 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6857 __isl_keep id_to_ast_expr *id2expr,
6858 __isl_take isl_id *key);
6859 int isl_id_to_ast_expr_foreach(
6860 __isl_keep id_to_ast_expr *id2expr,
6861 int (*fn)(__isl_take isl_id *key,
6862 __isl_take isl_ast_expr *val, void *user),
6865 They can be modified using the following function.
6867 #include <isl/id_to_ast_expr.h>
6868 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6869 __isl_take id_to_ast_expr *id2expr,
6870 __isl_take isl_id *key,
6871 __isl_take isl_ast_expr *val);
6872 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6873 __isl_take id_to_ast_expr *id2expr,
6874 __isl_take isl_id *key);
6876 Associative arrays can be printed using the following function.
6878 #include <isl/id_to_ast_expr.h>
6879 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6880 __isl_take isl_printer *p,
6881 __isl_keep id_to_ast_expr *id2expr);
6885 Vectors can be created, copied and freed using the following functions.
6887 #include <isl/vec.h>
6888 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6890 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6891 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6893 Note that the elements of a newly created vector may have arbitrary values.
6894 The elements can be changed and inspected using the following functions.
6896 int isl_vec_size(__isl_keep isl_vec *vec);
6897 __isl_give isl_val *isl_vec_get_element_val(
6898 __isl_keep isl_vec *vec, int pos);
6899 __isl_give isl_vec *isl_vec_set_element_si(
6900 __isl_take isl_vec *vec, int pos, int v);
6901 __isl_give isl_vec *isl_vec_set_element_val(
6902 __isl_take isl_vec *vec, int pos,
6903 __isl_take isl_val *v);
6904 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6906 __isl_give isl_vec *isl_vec_set_val(
6907 __isl_take isl_vec *vec, __isl_take isl_val *v);
6908 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6909 __isl_keep isl_vec *vec2, int pos);
6911 C<isl_vec_get_element> will return a negative value if anything went wrong.
6912 In that case, the value of C<*v> is undefined.
6914 The following function can be used to concatenate two vectors.
6916 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6917 __isl_take isl_vec *vec2);
6921 Matrices can be created, copied and freed using the following functions.
6923 #include <isl/mat.h>
6924 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6925 unsigned n_row, unsigned n_col);
6926 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6927 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6929 Note that the elements of a newly created matrix may have arbitrary values.
6930 The elements can be changed and inspected using the following functions.
6932 int isl_mat_rows(__isl_keep isl_mat *mat);
6933 int isl_mat_cols(__isl_keep isl_mat *mat);
6934 __isl_give isl_val *isl_mat_get_element_val(
6935 __isl_keep isl_mat *mat, int row, int col);
6936 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
6937 int row, int col, int v);
6938 __isl_give isl_mat *isl_mat_set_element_val(
6939 __isl_take isl_mat *mat, int row, int col,
6940 __isl_take isl_val *v);
6942 C<isl_mat_get_element> will return a negative value if anything went wrong.
6943 In that case, the value of C<*v> is undefined.
6945 The following function can be used to compute the (right) inverse
6946 of a matrix, i.e., a matrix such that the product of the original
6947 and the inverse (in that order) is a multiple of the identity matrix.
6948 The input matrix is assumed to be of full row-rank.
6950 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
6952 The following function can be used to compute the (right) kernel
6953 (or null space) of a matrix, i.e., a matrix such that the product of
6954 the original and the kernel (in that order) is the zero matrix.
6956 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
6958 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
6960 The following functions determine
6961 an upper or lower bound on a quasipolynomial over its domain.
6963 __isl_give isl_pw_qpolynomial_fold *
6964 isl_pw_qpolynomial_bound(
6965 __isl_take isl_pw_qpolynomial *pwqp,
6966 enum isl_fold type, int *tight);
6968 __isl_give isl_union_pw_qpolynomial_fold *
6969 isl_union_pw_qpolynomial_bound(
6970 __isl_take isl_union_pw_qpolynomial *upwqp,
6971 enum isl_fold type, int *tight);
6973 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
6974 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
6975 is the returned bound is known be tight, i.e., for each value
6976 of the parameters there is at least
6977 one element in the domain that reaches the bound.
6978 If the domain of C<pwqp> is not wrapping, then the bound is computed
6979 over all elements in that domain and the result has a purely parametric
6980 domain. If the domain of C<pwqp> is wrapping, then the bound is
6981 computed over the range of the wrapped relation. The domain of the
6982 wrapped relation becomes the domain of the result.
6984 =head2 Parametric Vertex Enumeration
6986 The parametric vertex enumeration described in this section
6987 is mainly intended to be used internally and by the C<barvinok>
6990 #include <isl/vertices.h>
6991 __isl_give isl_vertices *isl_basic_set_compute_vertices(
6992 __isl_keep isl_basic_set *bset);
6994 The function C<isl_basic_set_compute_vertices> performs the
6995 actual computation of the parametric vertices and the chamber
6996 decomposition and store the result in an C<isl_vertices> object.
6997 This information can be queried by either iterating over all
6998 the vertices or iterating over all the chambers or cells
6999 and then iterating over all vertices that are active on the chamber.
7001 int isl_vertices_foreach_vertex(
7002 __isl_keep isl_vertices *vertices,
7003 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7006 int isl_vertices_foreach_cell(
7007 __isl_keep isl_vertices *vertices,
7008 int (*fn)(__isl_take isl_cell *cell, void *user),
7010 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7011 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7014 Other operations that can be performed on an C<isl_vertices> object are
7017 int isl_vertices_get_n_vertices(
7018 __isl_keep isl_vertices *vertices);
7019 void isl_vertices_free(__isl_take isl_vertices *vertices);
7021 Vertices can be inspected and destroyed using the following functions.
7023 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7024 __isl_give isl_basic_set *isl_vertex_get_domain(
7025 __isl_keep isl_vertex *vertex);
7026 __isl_give isl_multi_aff *isl_vertex_get_expr(
7027 __isl_keep isl_vertex *vertex);
7028 void isl_vertex_free(__isl_take isl_vertex *vertex);
7030 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7031 describing the vertex in terms of the parameters,
7032 while C<isl_vertex_get_domain> returns the activity domain
7035 Chambers can be inspected and destroyed using the following functions.
7037 __isl_give isl_basic_set *isl_cell_get_domain(
7038 __isl_keep isl_cell *cell);
7039 void isl_cell_free(__isl_take isl_cell *cell);
7041 =head1 Polyhedral Compilation Library
7043 This section collects functionality in C<isl> that has been specifically
7044 designed for use during polyhedral compilation.
7046 =head2 Dependence Analysis
7048 C<isl> contains specialized functionality for performing
7049 array dataflow analysis. That is, given a I<sink> access relation
7050 and a collection of possible I<source> access relations,
7051 C<isl> can compute relations that describe
7052 for each iteration of the sink access, which iteration
7053 of which of the source access relations was the last
7054 to access the same data element before the given iteration
7056 The resulting dependence relations map source iterations
7057 to the corresponding sink iterations.
7058 To compute standard flow dependences, the sink should be
7059 a read, while the sources should be writes.
7060 If any of the source accesses are marked as being I<may>
7061 accesses, then there will be a dependence from the last
7062 I<must> access B<and> from any I<may> access that follows
7063 this last I<must> access.
7064 In particular, if I<all> sources are I<may> accesses,
7065 then memory based dependence analysis is performed.
7066 If, on the other hand, all sources are I<must> accesses,
7067 then value based dependence analysis is performed.
7069 #include <isl/flow.h>
7071 typedef int (*isl_access_level_before)(void *first, void *second);
7073 __isl_give isl_access_info *isl_access_info_alloc(
7074 __isl_take isl_map *sink,
7075 void *sink_user, isl_access_level_before fn,
7077 __isl_give isl_access_info *isl_access_info_add_source(
7078 __isl_take isl_access_info *acc,
7079 __isl_take isl_map *source, int must,
7081 __isl_null isl_access_info *isl_access_info_free(
7082 __isl_take isl_access_info *acc);
7084 __isl_give isl_flow *isl_access_info_compute_flow(
7085 __isl_take isl_access_info *acc);
7087 int isl_flow_foreach(__isl_keep isl_flow *deps,
7088 int (*fn)(__isl_take isl_map *dep, int must,
7089 void *dep_user, void *user),
7091 __isl_give isl_map *isl_flow_get_no_source(
7092 __isl_keep isl_flow *deps, int must);
7093 void isl_flow_free(__isl_take isl_flow *deps);
7095 The function C<isl_access_info_compute_flow> performs the actual
7096 dependence analysis. The other functions are used to construct
7097 the input for this function or to read off the output.
7099 The input is collected in an C<isl_access_info>, which can
7100 be created through a call to C<isl_access_info_alloc>.
7101 The arguments to this functions are the sink access relation
7102 C<sink>, a token C<sink_user> used to identify the sink
7103 access to the user, a callback function for specifying the
7104 relative order of source and sink accesses, and the number
7105 of source access relations that will be added.
7106 The callback function has type C<int (*)(void *first, void *second)>.
7107 The function is called with two user supplied tokens identifying
7108 either a source or the sink and it should return the shared nesting
7109 level and the relative order of the two accesses.
7110 In particular, let I<n> be the number of loops shared by
7111 the two accesses. If C<first> precedes C<second> textually,
7112 then the function should return I<2 * n + 1>; otherwise,
7113 it should return I<2 * n>.
7114 The sources can be added to the C<isl_access_info> by performing
7115 (at most) C<max_source> calls to C<isl_access_info_add_source>.
7116 C<must> indicates whether the source is a I<must> access
7117 or a I<may> access. Note that a multi-valued access relation
7118 should only be marked I<must> if every iteration in the domain
7119 of the relation accesses I<all> elements in its image.
7120 The C<source_user> token is again used to identify
7121 the source access. The range of the source access relation
7122 C<source> should have the same dimension as the range
7123 of the sink access relation.
7124 The C<isl_access_info_free> function should usually not be
7125 called explicitly, because it is called implicitly by
7126 C<isl_access_info_compute_flow>.
7128 The result of the dependence analysis is collected in an
7129 C<isl_flow>. There may be elements of
7130 the sink access for which no preceding source access could be
7131 found or for which all preceding sources are I<may> accesses.
7132 The relations containing these elements can be obtained through
7133 calls to C<isl_flow_get_no_source>, the first with C<must> set
7134 and the second with C<must> unset.
7135 In the case of standard flow dependence analysis,
7136 with the sink a read and the sources I<must> writes,
7137 the first relation corresponds to the reads from uninitialized
7138 array elements and the second relation is empty.
7139 The actual flow dependences can be extracted using
7140 C<isl_flow_foreach>. This function will call the user-specified
7141 callback function C<fn> for each B<non-empty> dependence between
7142 a source and the sink. The callback function is called
7143 with four arguments, the actual flow dependence relation
7144 mapping source iterations to sink iterations, a boolean that
7145 indicates whether it is a I<must> or I<may> dependence, a token
7146 identifying the source and an additional C<void *> with value
7147 equal to the third argument of the C<isl_flow_foreach> call.
7148 A dependence is marked I<must> if it originates from a I<must>
7149 source and if it is not followed by any I<may> sources.
7151 After finishing with an C<isl_flow>, the user should call
7152 C<isl_flow_free> to free all associated memory.
7154 A higher-level interface to dependence analysis is provided
7155 by the following function.
7157 #include <isl/flow.h>
7159 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
7160 __isl_take isl_union_map *must_source,
7161 __isl_take isl_union_map *may_source,
7162 __isl_take isl_union_map *schedule,
7163 __isl_give isl_union_map **must_dep,
7164 __isl_give isl_union_map **may_dep,
7165 __isl_give isl_union_map **must_no_source,
7166 __isl_give isl_union_map **may_no_source);
7168 The arrays are identified by the tuple names of the ranges
7169 of the accesses. The iteration domains by the tuple names
7170 of the domains of the accesses and of the schedule.
7171 The relative order of the iteration domains is given by the
7172 schedule. The relations returned through C<must_no_source>
7173 and C<may_no_source> are subsets of C<sink>.
7174 Any of C<must_dep>, C<may_dep>, C<must_no_source>
7175 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
7176 any of the other arguments is treated as an error.
7178 =head3 Interaction with Dependence Analysis
7180 During the dependence analysis, we frequently need to perform
7181 the following operation. Given a relation between sink iterations
7182 and potential source iterations from a particular source domain,
7183 what is the last potential source iteration corresponding to each
7184 sink iteration. It can sometimes be convenient to adjust
7185 the set of potential source iterations before or after each such operation.
7186 The prototypical example is fuzzy array dataflow analysis,
7187 where we need to analyze if, based on data-dependent constraints,
7188 the sink iteration can ever be executed without one or more of
7189 the corresponding potential source iterations being executed.
7190 If so, we can introduce extra parameters and select an unknown
7191 but fixed source iteration from the potential source iterations.
7192 To be able to perform such manipulations, C<isl> provides the following
7195 #include <isl/flow.h>
7197 typedef __isl_give isl_restriction *(*isl_access_restrict)(
7198 __isl_keep isl_map *source_map,
7199 __isl_keep isl_set *sink, void *source_user,
7201 __isl_give isl_access_info *isl_access_info_set_restrict(
7202 __isl_take isl_access_info *acc,
7203 isl_access_restrict fn, void *user);
7205 The function C<isl_access_info_set_restrict> should be called
7206 before calling C<isl_access_info_compute_flow> and registers a callback function
7207 that will be called any time C<isl> is about to compute the last
7208 potential source. The first argument is the (reverse) proto-dependence,
7209 mapping sink iterations to potential source iterations.
7210 The second argument represents the sink iterations for which
7211 we want to compute the last source iteration.
7212 The third argument is the token corresponding to the source
7213 and the final argument is the token passed to C<isl_access_info_set_restrict>.
7214 The callback is expected to return a restriction on either the input or
7215 the output of the operation computing the last potential source.
7216 If the input needs to be restricted then restrictions are needed
7217 for both the source and the sink iterations. The sink iterations
7218 and the potential source iterations will be intersected with these sets.
7219 If the output needs to be restricted then only a restriction on the source
7220 iterations is required.
7221 If any error occurs, the callback should return C<NULL>.
7222 An C<isl_restriction> object can be created, freed and inspected
7223 using the following functions.
7225 #include <isl/flow.h>
7227 __isl_give isl_restriction *isl_restriction_input(
7228 __isl_take isl_set *source_restr,
7229 __isl_take isl_set *sink_restr);
7230 __isl_give isl_restriction *isl_restriction_output(
7231 __isl_take isl_set *source_restr);
7232 __isl_give isl_restriction *isl_restriction_none(
7233 __isl_take isl_map *source_map);
7234 __isl_give isl_restriction *isl_restriction_empty(
7235 __isl_take isl_map *source_map);
7236 __isl_null isl_restriction *isl_restriction_free(
7237 __isl_take isl_restriction *restr);
7239 C<isl_restriction_none> and C<isl_restriction_empty> are special
7240 cases of C<isl_restriction_input>. C<isl_restriction_none>
7241 is essentially equivalent to
7243 isl_restriction_input(isl_set_universe(
7244 isl_space_range(isl_map_get_space(source_map))),
7246 isl_space_domain(isl_map_get_space(source_map))));
7248 whereas C<isl_restriction_empty> is essentially equivalent to
7250 isl_restriction_input(isl_set_empty(
7251 isl_space_range(isl_map_get_space(source_map))),
7253 isl_space_domain(isl_map_get_space(source_map))));
7257 B<The functionality described in this section is fairly new
7258 and may be subject to change.>
7260 #include <isl/schedule.h>
7261 __isl_give isl_schedule *
7262 isl_schedule_constraints_compute_schedule(
7263 __isl_take isl_schedule_constraints *sc);
7264 __isl_null isl_schedule *isl_schedule_free(
7265 __isl_take isl_schedule *sched);
7267 The function C<isl_schedule_constraints_compute_schedule> can be
7268 used to compute a schedule that satisfies the given schedule constraints.
7269 These schedule constraints include the iteration domain for which
7270 a schedule should be computed and dependences between pairs of
7271 iterations. In particular, these dependences include
7272 I<validity> dependences and I<proximity> dependences.
7273 By default, the algorithm used to construct the schedule is similar
7274 to that of C<Pluto>.
7275 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
7277 The generated schedule respects all validity dependences.
7278 That is, all dependence distances over these dependences in the
7279 scheduled space are lexicographically positive.
7280 The default algorithm tries to ensure that the dependence distances
7281 over coincidence constraints are zero and to minimize the
7282 dependence distances over proximity dependences.
7283 Moreover, it tries to obtain sequences (bands) of schedule dimensions
7284 for groups of domains where the dependence distances over validity
7285 dependences have only non-negative values.
7286 When using Feautrier's algorithm, the coincidence and proximity constraints
7287 are only taken into account during the extension to a
7288 full-dimensional schedule.
7290 An C<isl_schedule_constraints> object can be constructed
7291 and manipulated using the following functions.
7293 #include <isl/schedule.h>
7294 __isl_give isl_schedule_constraints *
7295 isl_schedule_constraints_copy(
7296 __isl_keep isl_schedule_constraints *sc);
7297 __isl_give isl_schedule_constraints *
7298 isl_schedule_constraints_on_domain(
7299 __isl_take isl_union_set *domain);
7300 __isl_give isl_schedule_constraints *
7301 isl_schedule_constraints_set_validity(
7302 __isl_take isl_schedule_constraints *sc,
7303 __isl_take isl_union_map *validity);
7304 __isl_give isl_schedule_constraints *
7305 isl_schedule_constraints_set_coincidence(
7306 __isl_take isl_schedule_constraints *sc,
7307 __isl_take isl_union_map *coincidence);
7308 __isl_give isl_schedule_constraints *
7309 isl_schedule_constraints_set_proximity(
7310 __isl_take isl_schedule_constraints *sc,
7311 __isl_take isl_union_map *proximity);
7312 __isl_give isl_schedule_constraints *
7313 isl_schedule_constraints_set_conditional_validity(
7314 __isl_take isl_schedule_constraints *sc,
7315 __isl_take isl_union_map *condition,
7316 __isl_take isl_union_map *validity);
7317 __isl_null isl_schedule_constraints *
7318 isl_schedule_constraints_free(
7319 __isl_take isl_schedule_constraints *sc);
7321 The initial C<isl_schedule_constraints> object created by
7322 C<isl_schedule_constraints_on_domain> does not impose any constraints.
7323 That is, it has an empty set of dependences.
7324 The function C<isl_schedule_constraints_set_validity> replaces the
7325 validity dependences, mapping domain elements I<i> to domain
7326 elements that should be scheduled after I<i>.
7327 The function C<isl_schedule_constraints_set_coincidence> replaces the
7328 coincidence dependences, mapping domain elements I<i> to domain
7329 elements that should be scheduled together with I<I>, if possible.
7330 The function C<isl_schedule_constraints_set_proximity> replaces the
7331 proximity dependences, mapping domain elements I<i> to domain
7332 elements that should be scheduled either before I<I>
7333 or as early as possible after I<i>.
7335 The function C<isl_schedule_constraints_set_conditional_validity>
7336 replaces the conditional validity constraints.
7337 A conditional validity constraint is only imposed when any of the corresponding
7338 conditions is satisfied, i.e., when any of them is non-zero.
7339 That is, the scheduler ensures that within each band if the dependence
7340 distances over the condition constraints are not all zero
7341 then all corresponding conditional validity constraints are respected.
7342 A conditional validity constraint corresponds to a condition
7343 if the two are adjacent, i.e., if the domain of one relation intersect
7344 the range of the other relation.
7345 The typical use case of conditional validity constraints is
7346 to allow order constraints between live ranges to be violated
7347 as long as the live ranges themselves are local to the band.
7348 To allow more fine-grained control over which conditions correspond
7349 to which conditional validity constraints, the domains and ranges
7350 of these relations may include I<tags>. That is, the domains and
7351 ranges of those relation may themselves be wrapped relations
7352 where the iteration domain appears in the domain of those wrapped relations
7353 and the range of the wrapped relations can be arbitrarily chosen
7354 by the user. Conditions and conditional validity constraints are only
7355 considered adjacent to each other if the entire wrapped relation matches.
7356 In particular, a relation with a tag will never be considered adjacent
7357 to a relation without a tag.
7359 The following function computes a schedule directly from
7360 an iteration domain and validity and proximity dependences
7361 and is implemented in terms of the functions described above.
7362 The use of C<isl_union_set_compute_schedule> is discouraged.
7364 #include <isl/schedule.h>
7365 __isl_give isl_schedule *isl_union_set_compute_schedule(
7366 __isl_take isl_union_set *domain,
7367 __isl_take isl_union_map *validity,
7368 __isl_take isl_union_map *proximity);
7370 A mapping from the domains to the scheduled space can be obtained
7371 from an C<isl_schedule> using the following function.
7373 __isl_give isl_union_map *isl_schedule_get_map(
7374 __isl_keep isl_schedule *sched);
7376 A representation of the schedule can be printed using
7378 __isl_give isl_printer *isl_printer_print_schedule(
7379 __isl_take isl_printer *p,
7380 __isl_keep isl_schedule *schedule);
7382 A representation of the schedule as a forest of bands can be obtained
7383 using the following function.
7385 __isl_give isl_band_list *isl_schedule_get_band_forest(
7386 __isl_keep isl_schedule *schedule);
7388 The individual bands can be visited in depth-first post-order
7389 using the following function.
7391 #include <isl/schedule.h>
7392 int isl_schedule_foreach_band(
7393 __isl_keep isl_schedule *sched,
7394 int (*fn)(__isl_keep isl_band *band, void *user),
7397 The list can be manipulated as explained in L<"Lists">.
7398 The bands inside the list can be copied and freed using the following
7401 #include <isl/band.h>
7402 __isl_give isl_band *isl_band_copy(
7403 __isl_keep isl_band *band);
7404 __isl_null isl_band *isl_band_free(
7405 __isl_take isl_band *band);
7407 Each band contains zero or more scheduling dimensions.
7408 These are referred to as the members of the band.
7409 The section of the schedule that corresponds to the band is
7410 referred to as the partial schedule of the band.
7411 For those nodes that participate in a band, the outer scheduling
7412 dimensions form the prefix schedule, while the inner scheduling
7413 dimensions form the suffix schedule.
7414 That is, if we take a cut of the band forest, then the union of
7415 the concatenations of the prefix, partial and suffix schedules of
7416 each band in the cut is equal to the entire schedule (modulo
7417 some possible padding at the end with zero scheduling dimensions).
7418 The properties of a band can be inspected using the following functions.
7420 #include <isl/band.h>
7421 int isl_band_has_children(__isl_keep isl_band *band);
7422 __isl_give isl_band_list *isl_band_get_children(
7423 __isl_keep isl_band *band);
7425 __isl_give isl_union_map *isl_band_get_prefix_schedule(
7426 __isl_keep isl_band *band);
7427 __isl_give isl_union_map *isl_band_get_partial_schedule(
7428 __isl_keep isl_band *band);
7429 __isl_give isl_union_map *isl_band_get_suffix_schedule(
7430 __isl_keep isl_band *band);
7432 int isl_band_n_member(__isl_keep isl_band *band);
7433 int isl_band_member_is_coincident(
7434 __isl_keep isl_band *band, int pos);
7436 int isl_band_list_foreach_band(
7437 __isl_keep isl_band_list *list,
7438 int (*fn)(__isl_keep isl_band *band, void *user),
7441 Note that a scheduling dimension is considered to be ``coincident''
7442 if it satisfies the coincidence constraints within its band.
7443 That is, if the dependence distances of the coincidence
7444 constraints are all zero in that direction (for fixed
7445 iterations of outer bands).
7446 Like C<isl_schedule_foreach_band>,
7447 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
7448 in depth-first post-order.
7450 A band can be tiled using the following function.
7452 #include <isl/band.h>
7453 int isl_band_tile(__isl_keep isl_band *band,
7454 __isl_take isl_vec *sizes);
7456 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
7458 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
7459 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
7461 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
7463 The C<isl_band_tile> function tiles the band using the given tile sizes
7464 inside its schedule.
7465 A new child band is created to represent the point loops and it is
7466 inserted between the modified band and its children.
7467 The C<tile_scale_tile_loops> option specifies whether the tile
7468 loops iterators should be scaled by the tile sizes.
7469 If the C<tile_shift_point_loops> option is set, then the point loops
7470 are shifted to start at zero.
7472 A band can be split into two nested bands using the following function.
7474 int isl_band_split(__isl_keep isl_band *band, int pos);
7476 The resulting outer band contains the first C<pos> dimensions of C<band>
7477 while the inner band contains the remaining dimensions.
7479 A representation of the band can be printed using
7481 #include <isl/band.h>
7482 __isl_give isl_printer *isl_printer_print_band(
7483 __isl_take isl_printer *p,
7484 __isl_keep isl_band *band);
7488 #include <isl/schedule.h>
7489 int isl_options_set_schedule_max_coefficient(
7490 isl_ctx *ctx, int val);
7491 int isl_options_get_schedule_max_coefficient(
7493 int isl_options_set_schedule_max_constant_term(
7494 isl_ctx *ctx, int val);
7495 int isl_options_get_schedule_max_constant_term(
7497 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
7498 int isl_options_get_schedule_fuse(isl_ctx *ctx);
7499 int isl_options_set_schedule_maximize_band_depth(
7500 isl_ctx *ctx, int val);
7501 int isl_options_get_schedule_maximize_band_depth(
7503 int isl_options_set_schedule_outer_coincidence(
7504 isl_ctx *ctx, int val);
7505 int isl_options_get_schedule_outer_coincidence(
7507 int isl_options_set_schedule_split_scaled(
7508 isl_ctx *ctx, int val);
7509 int isl_options_get_schedule_split_scaled(
7511 int isl_options_set_schedule_algorithm(
7512 isl_ctx *ctx, int val);
7513 int isl_options_get_schedule_algorithm(
7515 int isl_options_set_schedule_separate_components(
7516 isl_ctx *ctx, int val);
7517 int isl_options_get_schedule_separate_components(
7522 =item * schedule_max_coefficient
7524 This option enforces that the coefficients for variable and parameter
7525 dimensions in the calculated schedule are not larger than the specified value.
7526 This option can significantly increase the speed of the scheduling calculation
7527 and may also prevent fusing of unrelated dimensions. A value of -1 means that
7528 this option does not introduce bounds on the variable or parameter
7531 =item * schedule_max_constant_term
7533 This option enforces that the constant coefficients in the calculated schedule
7534 are not larger than the maximal constant term. This option can significantly
7535 increase the speed of the scheduling calculation and may also prevent fusing of
7536 unrelated dimensions. A value of -1 means that this option does not introduce
7537 bounds on the constant coefficients.
7539 =item * schedule_fuse
7541 This option controls the level of fusion.
7542 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
7543 resulting schedule will be distributed as much as possible.
7544 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
7545 try to fuse loops in the resulting schedule.
7547 =item * schedule_maximize_band_depth
7549 If this option is set, we do not split bands at the point
7550 where we detect splitting is necessary. Instead, we
7551 backtrack and split bands as early as possible. This
7552 reduces the number of splits and maximizes the width of
7553 the bands. Wider bands give more possibilities for tiling.
7554 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
7555 then bands will be split as early as possible, even if there is no need.
7556 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
7558 =item * schedule_outer_coincidence
7560 If this option is set, then we try to construct schedules
7561 where the outermost scheduling dimension in each band
7562 satisfies the coincidence constraints.
7564 =item * schedule_split_scaled
7566 If this option is set, then we try to construct schedules in which the
7567 constant term is split off from the linear part if the linear parts of
7568 the scheduling rows for all nodes in the graphs have a common non-trivial
7570 The constant term is then placed in a separate band and the linear
7573 =item * schedule_algorithm
7575 Selects the scheduling algorithm to be used.
7576 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
7577 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
7579 =item * schedule_separate_components
7581 If at any point the dependence graph contains any (weakly connected) components,
7582 then these components are scheduled separately.
7583 If this option is not set, then some iterations of the domains
7584 in these components may be scheduled together.
7585 If this option is set, then the components are given consecutive
7590 =head2 AST Generation
7592 This section describes the C<isl> functionality for generating
7593 ASTs that visit all the elements
7594 in a domain in an order specified by a schedule.
7595 In particular, given a C<isl_union_map>, an AST is generated
7596 that visits all the elements in the domain of the C<isl_union_map>
7597 according to the lexicographic order of the corresponding image
7598 element(s). If the range of the C<isl_union_map> consists of
7599 elements in more than one space, then each of these spaces is handled
7600 separately in an arbitrary order.
7601 It should be noted that the image elements only specify the I<order>
7602 in which the corresponding domain elements should be visited.
7603 No direct relation between the image elements and the loop iterators
7604 in the generated AST should be assumed.
7606 Each AST is generated within a build. The initial build
7607 simply specifies the constraints on the parameters (if any)
7608 and can be created, inspected, copied and freed using the following functions.
7610 #include <isl/ast_build.h>
7611 __isl_give isl_ast_build *isl_ast_build_from_context(
7612 __isl_take isl_set *set);
7613 __isl_give isl_ast_build *isl_ast_build_copy(
7614 __isl_keep isl_ast_build *build);
7615 __isl_null isl_ast_build *isl_ast_build_free(
7616 __isl_take isl_ast_build *build);
7618 The C<set> argument is usually a parameter set with zero or more parameters.
7619 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
7620 and L</"Fine-grained Control over AST Generation">.
7621 Finally, the AST itself can be constructed using the following
7624 #include <isl/ast_build.h>
7625 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
7626 __isl_keep isl_ast_build *build,
7627 __isl_take isl_union_map *schedule);
7629 =head3 Inspecting the AST
7631 The basic properties of an AST node can be obtained as follows.
7633 #include <isl/ast.h>
7634 enum isl_ast_node_type isl_ast_node_get_type(
7635 __isl_keep isl_ast_node *node);
7637 The type of an AST node is one of
7638 C<isl_ast_node_for>,
7640 C<isl_ast_node_block> or
7641 C<isl_ast_node_user>.
7642 An C<isl_ast_node_for> represents a for node.
7643 An C<isl_ast_node_if> represents an if node.
7644 An C<isl_ast_node_block> represents a compound node.
7645 An C<isl_ast_node_user> represents an expression statement.
7646 An expression statement typically corresponds to a domain element, i.e.,
7647 one of the elements that is visited by the AST.
7649 Each type of node has its own additional properties.
7651 #include <isl/ast.h>
7652 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7653 __isl_keep isl_ast_node *node);
7654 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7655 __isl_keep isl_ast_node *node);
7656 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7657 __isl_keep isl_ast_node *node);
7658 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7659 __isl_keep isl_ast_node *node);
7660 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7661 __isl_keep isl_ast_node *node);
7662 int isl_ast_node_for_is_degenerate(
7663 __isl_keep isl_ast_node *node);
7665 An C<isl_ast_for> is considered degenerate if it is known to execute
7668 #include <isl/ast.h>
7669 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7670 __isl_keep isl_ast_node *node);
7671 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7672 __isl_keep isl_ast_node *node);
7673 int isl_ast_node_if_has_else(
7674 __isl_keep isl_ast_node *node);
7675 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7676 __isl_keep isl_ast_node *node);
7678 __isl_give isl_ast_node_list *
7679 isl_ast_node_block_get_children(
7680 __isl_keep isl_ast_node *node);
7682 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7683 __isl_keep isl_ast_node *node);
7685 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7686 the following functions.
7688 #include <isl/ast.h>
7689 enum isl_ast_expr_type isl_ast_expr_get_type(
7690 __isl_keep isl_ast_expr *expr);
7692 The type of an AST expression is one of
7694 C<isl_ast_expr_id> or
7695 C<isl_ast_expr_int>.
7696 An C<isl_ast_expr_op> represents the result of an operation.
7697 An C<isl_ast_expr_id> represents an identifier.
7698 An C<isl_ast_expr_int> represents an integer value.
7700 Each type of expression has its own additional properties.
7702 #include <isl/ast.h>
7703 enum isl_ast_op_type isl_ast_expr_get_op_type(
7704 __isl_keep isl_ast_expr *expr);
7705 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7706 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7707 __isl_keep isl_ast_expr *expr, int pos);
7708 int isl_ast_node_foreach_ast_op_type(
7709 __isl_keep isl_ast_node *node,
7710 int (*fn)(enum isl_ast_op_type type, void *user),
7713 C<isl_ast_expr_get_op_type> returns the type of the operation
7714 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7715 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7717 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7718 C<isl_ast_op_type> that appears in C<node>.
7719 The operation type is one of the following.
7723 =item C<isl_ast_op_and>
7725 Logical I<and> of two arguments.
7726 Both arguments can be evaluated.
7728 =item C<isl_ast_op_and_then>
7730 Logical I<and> of two arguments.
7731 The second argument can only be evaluated if the first evaluates to true.
7733 =item C<isl_ast_op_or>
7735 Logical I<or> of two arguments.
7736 Both arguments can be evaluated.
7738 =item C<isl_ast_op_or_else>
7740 Logical I<or> of two arguments.
7741 The second argument can only be evaluated if the first evaluates to false.
7743 =item C<isl_ast_op_max>
7745 Maximum of two or more arguments.
7747 =item C<isl_ast_op_min>
7749 Minimum of two or more arguments.
7751 =item C<isl_ast_op_minus>
7755 =item C<isl_ast_op_add>
7757 Sum of two arguments.
7759 =item C<isl_ast_op_sub>
7761 Difference of two arguments.
7763 =item C<isl_ast_op_mul>
7765 Product of two arguments.
7767 =item C<isl_ast_op_div>
7769 Exact division. That is, the result is known to be an integer.
7771 =item C<isl_ast_op_fdiv_q>
7773 Result of integer division, rounded towards negative
7776 =item C<isl_ast_op_pdiv_q>
7778 Result of integer division, where dividend is known to be non-negative.
7780 =item C<isl_ast_op_pdiv_r>
7782 Remainder of integer division, where dividend is known to be non-negative.
7784 =item C<isl_ast_op_zdiv_r>
7786 Equal to zero iff the remainder on integer division is zero.
7788 =item C<isl_ast_op_cond>
7790 Conditional operator defined on three arguments.
7791 If the first argument evaluates to true, then the result
7792 is equal to the second argument. Otherwise, the result
7793 is equal to the third argument.
7794 The second and third argument may only be evaluated if
7795 the first argument evaluates to true and false, respectively.
7796 Corresponds to C<a ? b : c> in C.
7798 =item C<isl_ast_op_select>
7800 Conditional operator defined on three arguments.
7801 If the first argument evaluates to true, then the result
7802 is equal to the second argument. Otherwise, the result
7803 is equal to the third argument.
7804 The second and third argument may be evaluated independently
7805 of the value of the first argument.
7806 Corresponds to C<a * b + (1 - a) * c> in C.
7808 =item C<isl_ast_op_eq>
7812 =item C<isl_ast_op_le>
7814 Less than or equal relation.
7816 =item C<isl_ast_op_lt>
7820 =item C<isl_ast_op_ge>
7822 Greater than or equal relation.
7824 =item C<isl_ast_op_gt>
7826 Greater than relation.
7828 =item C<isl_ast_op_call>
7831 The number of arguments of the C<isl_ast_expr> is one more than
7832 the number of arguments in the function call, the first argument
7833 representing the function being called.
7835 =item C<isl_ast_op_access>
7838 The number of arguments of the C<isl_ast_expr> is one more than
7839 the number of index expressions in the array access, the first argument
7840 representing the array being accessed.
7842 =item C<isl_ast_op_member>
7845 This operation has two arguments, a structure and the name of
7846 the member of the structure being accessed.
7850 #include <isl/ast.h>
7851 __isl_give isl_id *isl_ast_expr_get_id(
7852 __isl_keep isl_ast_expr *expr);
7854 Return the identifier represented by the AST expression.
7856 #include <isl/ast.h>
7857 __isl_give isl_val *isl_ast_expr_get_val(
7858 __isl_keep isl_ast_expr *expr);
7860 Return the integer represented by the AST expression.
7862 =head3 Properties of ASTs
7864 #include <isl/ast.h>
7865 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7866 __isl_keep isl_ast_expr *expr2);
7868 Check if two C<isl_ast_expr>s are equal to each other.
7870 =head3 Manipulating and printing the AST
7872 AST nodes can be copied and freed using the following functions.
7874 #include <isl/ast.h>
7875 __isl_give isl_ast_node *isl_ast_node_copy(
7876 __isl_keep isl_ast_node *node);
7877 __isl_null isl_ast_node *isl_ast_node_free(
7878 __isl_take isl_ast_node *node);
7880 AST expressions can be copied and freed using the following functions.
7882 #include <isl/ast.h>
7883 __isl_give isl_ast_expr *isl_ast_expr_copy(
7884 __isl_keep isl_ast_expr *expr);
7885 __isl_null isl_ast_expr *isl_ast_expr_free(
7886 __isl_take isl_ast_expr *expr);
7888 New AST expressions can be created either directly or within
7889 the context of an C<isl_ast_build>.
7891 #include <isl/ast.h>
7892 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7893 __isl_take isl_val *v);
7894 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7895 __isl_take isl_id *id);
7896 __isl_give isl_ast_expr *isl_ast_expr_neg(
7897 __isl_take isl_ast_expr *expr);
7898 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7899 __isl_take isl_ast_expr *expr);
7900 __isl_give isl_ast_expr *isl_ast_expr_add(
7901 __isl_take isl_ast_expr *expr1,
7902 __isl_take isl_ast_expr *expr2);
7903 __isl_give isl_ast_expr *isl_ast_expr_sub(
7904 __isl_take isl_ast_expr *expr1,
7905 __isl_take isl_ast_expr *expr2);
7906 __isl_give isl_ast_expr *isl_ast_expr_mul(
7907 __isl_take isl_ast_expr *expr1,
7908 __isl_take isl_ast_expr *expr2);
7909 __isl_give isl_ast_expr *isl_ast_expr_div(
7910 __isl_take isl_ast_expr *expr1,
7911 __isl_take isl_ast_expr *expr2);
7912 __isl_give isl_ast_expr *isl_ast_expr_and(
7913 __isl_take isl_ast_expr *expr1,
7914 __isl_take isl_ast_expr *expr2)
7915 __isl_give isl_ast_expr *isl_ast_expr_or(
7916 __isl_take isl_ast_expr *expr1,
7917 __isl_take isl_ast_expr *expr2)
7918 __isl_give isl_ast_expr *isl_ast_expr_eq(
7919 __isl_take isl_ast_expr *expr1,
7920 __isl_take isl_ast_expr *expr2);
7921 __isl_give isl_ast_expr *isl_ast_expr_le(
7922 __isl_take isl_ast_expr *expr1,
7923 __isl_take isl_ast_expr *expr2);
7924 __isl_give isl_ast_expr *isl_ast_expr_lt(
7925 __isl_take isl_ast_expr *expr1,
7926 __isl_take isl_ast_expr *expr2);
7927 __isl_give isl_ast_expr *isl_ast_expr_ge(
7928 __isl_take isl_ast_expr *expr1,
7929 __isl_take isl_ast_expr *expr2);
7930 __isl_give isl_ast_expr *isl_ast_expr_gt(
7931 __isl_take isl_ast_expr *expr1,
7932 __isl_take isl_ast_expr *expr2);
7933 __isl_give isl_ast_expr *isl_ast_expr_access(
7934 __isl_take isl_ast_expr *array,
7935 __isl_take isl_ast_expr_list *indices);
7937 The function C<isl_ast_expr_address_of> can be applied to an
7938 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
7939 to represent the address of the C<isl_ast_expr_access>.
7941 #include <isl/ast_build.h>
7942 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
7943 __isl_keep isl_ast_build *build,
7944 __isl_take isl_pw_aff *pa);
7945 __isl_give isl_ast_expr *
7946 isl_ast_build_access_from_pw_multi_aff(
7947 __isl_keep isl_ast_build *build,
7948 __isl_take isl_pw_multi_aff *pma);
7949 __isl_give isl_ast_expr *
7950 isl_ast_build_access_from_multi_pw_aff(
7951 __isl_keep isl_ast_build *build,
7952 __isl_take isl_multi_pw_aff *mpa);
7953 __isl_give isl_ast_expr *
7954 isl_ast_build_call_from_pw_multi_aff(
7955 __isl_keep isl_ast_build *build,
7956 __isl_take isl_pw_multi_aff *pma);
7957 __isl_give isl_ast_expr *
7958 isl_ast_build_call_from_multi_pw_aff(
7959 __isl_keep isl_ast_build *build,
7960 __isl_take isl_multi_pw_aff *mpa);
7962 The domains of C<pa>, C<mpa> and C<pma> should correspond
7963 to the schedule space of C<build>.
7964 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
7965 the function being called.
7966 If the accessed space is a nested relation, then it is taken
7967 to represent an access of the member specified by the range
7968 of this nested relation of the structure specified by the domain
7969 of the nested relation.
7971 The following functions can be used to modify an C<isl_ast_expr>.
7973 #include <isl/ast.h>
7974 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
7975 __isl_take isl_ast_expr *expr, int pos,
7976 __isl_take isl_ast_expr *arg);
7978 Replace the argument of C<expr> at position C<pos> by C<arg>.
7980 #include <isl/ast.h>
7981 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
7982 __isl_take isl_ast_expr *expr,
7983 __isl_take isl_id_to_ast_expr *id2expr);
7985 The function C<isl_ast_expr_substitute_ids> replaces the
7986 subexpressions of C<expr> of type C<isl_ast_expr_id>
7987 by the corresponding expression in C<id2expr>, if there is any.
7990 User specified data can be attached to an C<isl_ast_node> and obtained
7991 from the same C<isl_ast_node> using the following functions.
7993 #include <isl/ast.h>
7994 __isl_give isl_ast_node *isl_ast_node_set_annotation(
7995 __isl_take isl_ast_node *node,
7996 __isl_take isl_id *annotation);
7997 __isl_give isl_id *isl_ast_node_get_annotation(
7998 __isl_keep isl_ast_node *node);
8000 Basic printing can be performed using the following functions.
8002 #include <isl/ast.h>
8003 __isl_give isl_printer *isl_printer_print_ast_expr(
8004 __isl_take isl_printer *p,
8005 __isl_keep isl_ast_expr *expr);
8006 __isl_give isl_printer *isl_printer_print_ast_node(
8007 __isl_take isl_printer *p,
8008 __isl_keep isl_ast_node *node);
8009 __isl_give char *isl_ast_expr_to_str(
8010 __isl_keep isl_ast_expr *expr);
8012 More advanced printing can be performed using the following functions.
8014 #include <isl/ast.h>
8015 __isl_give isl_printer *isl_ast_op_type_print_macro(
8016 enum isl_ast_op_type type,
8017 __isl_take isl_printer *p);
8018 __isl_give isl_printer *isl_ast_node_print_macros(
8019 __isl_keep isl_ast_node *node,
8020 __isl_take isl_printer *p);
8021 __isl_give isl_printer *isl_ast_node_print(
8022 __isl_keep isl_ast_node *node,
8023 __isl_take isl_printer *p,
8024 __isl_take isl_ast_print_options *options);
8025 __isl_give isl_printer *isl_ast_node_for_print(
8026 __isl_keep isl_ast_node *node,
8027 __isl_take isl_printer *p,
8028 __isl_take isl_ast_print_options *options);
8029 __isl_give isl_printer *isl_ast_node_if_print(
8030 __isl_keep isl_ast_node *node,
8031 __isl_take isl_printer *p,
8032 __isl_take isl_ast_print_options *options);
8034 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
8035 C<isl> may print out an AST that makes use of macros such
8036 as C<floord>, C<min> and C<max>.
8037 C<isl_ast_op_type_print_macro> prints out the macro
8038 corresponding to a specific C<isl_ast_op_type>.
8039 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
8040 for expressions where these macros would be used and prints
8041 out the required macro definitions.
8042 Essentially, C<isl_ast_node_print_macros> calls
8043 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
8044 as function argument.
8045 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
8046 C<isl_ast_node_if_print> print an C<isl_ast_node>
8047 in C<ISL_FORMAT_C>, but allow for some extra control
8048 through an C<isl_ast_print_options> object.
8049 This object can be created using the following functions.
8051 #include <isl/ast.h>
8052 __isl_give isl_ast_print_options *
8053 isl_ast_print_options_alloc(isl_ctx *ctx);
8054 __isl_give isl_ast_print_options *
8055 isl_ast_print_options_copy(
8056 __isl_keep isl_ast_print_options *options);
8057 __isl_null isl_ast_print_options *
8058 isl_ast_print_options_free(
8059 __isl_take isl_ast_print_options *options);
8061 __isl_give isl_ast_print_options *
8062 isl_ast_print_options_set_print_user(
8063 __isl_take isl_ast_print_options *options,
8064 __isl_give isl_printer *(*print_user)(
8065 __isl_take isl_printer *p,
8066 __isl_take isl_ast_print_options *options,
8067 __isl_keep isl_ast_node *node, void *user),
8069 __isl_give isl_ast_print_options *
8070 isl_ast_print_options_set_print_for(
8071 __isl_take isl_ast_print_options *options,
8072 __isl_give isl_printer *(*print_for)(
8073 __isl_take isl_printer *p,
8074 __isl_take isl_ast_print_options *options,
8075 __isl_keep isl_ast_node *node, void *user),
8078 The callback set by C<isl_ast_print_options_set_print_user>
8079 is called whenever a node of type C<isl_ast_node_user> needs to
8081 The callback set by C<isl_ast_print_options_set_print_for>
8082 is called whenever a node of type C<isl_ast_node_for> needs to
8084 Note that C<isl_ast_node_for_print> will I<not> call the
8085 callback set by C<isl_ast_print_options_set_print_for> on the node
8086 on which C<isl_ast_node_for_print> is called, but only on nested
8087 nodes of type C<isl_ast_node_for>. It is therefore safe to
8088 call C<isl_ast_node_for_print> from within the callback set by
8089 C<isl_ast_print_options_set_print_for>.
8091 The following option determines the type to be used for iterators
8092 while printing the AST.
8094 int isl_options_set_ast_iterator_type(
8095 isl_ctx *ctx, const char *val);
8096 const char *isl_options_get_ast_iterator_type(
8099 The AST printer only prints body nodes as blocks if these
8100 blocks cannot be safely omitted.
8101 For example, a C<for> node with one body node will not be
8102 surrounded with braces in C<ISL_FORMAT_C>.
8103 A block will always be printed by setting the following option.
8105 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
8107 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
8111 #include <isl/ast_build.h>
8112 int isl_options_set_ast_build_atomic_upper_bound(
8113 isl_ctx *ctx, int val);
8114 int isl_options_get_ast_build_atomic_upper_bound(
8116 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
8118 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
8119 int isl_options_set_ast_build_exploit_nested_bounds(
8120 isl_ctx *ctx, int val);
8121 int isl_options_get_ast_build_exploit_nested_bounds(
8123 int isl_options_set_ast_build_group_coscheduled(
8124 isl_ctx *ctx, int val);
8125 int isl_options_get_ast_build_group_coscheduled(
8127 int isl_options_set_ast_build_scale_strides(
8128 isl_ctx *ctx, int val);
8129 int isl_options_get_ast_build_scale_strides(
8131 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
8133 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
8134 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
8136 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
8140 =item * ast_build_atomic_upper_bound
8142 Generate loop upper bounds that consist of the current loop iterator,
8143 an operator and an expression not involving the iterator.
8144 If this option is not set, then the current loop iterator may appear
8145 several times in the upper bound.
8146 For example, when this option is turned off, AST generation
8149 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
8153 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
8156 When the option is turned on, the following AST is generated
8158 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
8161 =item * ast_build_prefer_pdiv
8163 If this option is turned off, then the AST generation will
8164 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
8165 operators, but no C<isl_ast_op_pdiv_q> or
8166 C<isl_ast_op_pdiv_r> operators.
8167 If this options is turned on, then C<isl> will try to convert
8168 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
8169 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
8171 =item * ast_build_exploit_nested_bounds
8173 Simplify conditions based on bounds of nested for loops.
8174 In particular, remove conditions that are implied by the fact
8175 that one or more nested loops have at least one iteration,
8176 meaning that the upper bound is at least as large as the lower bound.
8177 For example, when this option is turned off, AST generation
8180 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
8186 for (int c0 = 0; c0 <= N; c0 += 1)
8187 for (int c1 = 0; c1 <= M; c1 += 1)
8190 When the option is turned on, the following AST is generated
8192 for (int c0 = 0; c0 <= N; c0 += 1)
8193 for (int c1 = 0; c1 <= M; c1 += 1)
8196 =item * ast_build_group_coscheduled
8198 If two domain elements are assigned the same schedule point, then
8199 they may be executed in any order and they may even appear in different
8200 loops. If this options is set, then the AST generator will make
8201 sure that coscheduled domain elements do not appear in separate parts
8202 of the AST. This is useful in case of nested AST generation
8203 if the outer AST generation is given only part of a schedule
8204 and the inner AST generation should handle the domains that are
8205 coscheduled by this initial part of the schedule together.
8206 For example if an AST is generated for a schedule
8208 { A[i] -> [0]; B[i] -> [0] }
8210 then the C<isl_ast_build_set_create_leaf> callback described
8211 below may get called twice, once for each domain.
8212 Setting this option ensures that the callback is only called once
8213 on both domains together.
8215 =item * ast_build_separation_bounds
8217 This option specifies which bounds to use during separation.
8218 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
8219 then all (possibly implicit) bounds on the current dimension will
8220 be used during separation.
8221 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
8222 then only those bounds that are explicitly available will
8223 be used during separation.
8225 =item * ast_build_scale_strides
8227 This option specifies whether the AST generator is allowed
8228 to scale down iterators of strided loops.
8230 =item * ast_build_allow_else
8232 This option specifies whether the AST generator is allowed
8233 to construct if statements with else branches.
8235 =item * ast_build_allow_or
8237 This option specifies whether the AST generator is allowed
8238 to construct if conditions with disjunctions.
8242 =head3 Fine-grained Control over AST Generation
8244 Besides specifying the constraints on the parameters,
8245 an C<isl_ast_build> object can be used to control
8246 various aspects of the AST generation process.
8247 The most prominent way of control is through ``options'',
8248 which can be set using the following function.
8250 #include <isl/ast_build.h>
8251 __isl_give isl_ast_build *
8252 isl_ast_build_set_options(
8253 __isl_take isl_ast_build *control,
8254 __isl_take isl_union_map *options);
8256 The options are encoded in an C<isl_union_map>.
8257 The domain of this union relation refers to the schedule domain,
8258 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
8259 In the case of nested AST generation (see L</"Nested AST Generation">),
8260 the domain of C<options> should refer to the extra piece of the schedule.
8261 That is, it should be equal to the range of the wrapped relation in the
8262 range of the schedule.
8263 The range of the options can consist of elements in one or more spaces,
8264 the names of which determine the effect of the option.
8265 The values of the range typically also refer to the schedule dimension
8266 to which the option applies. In case of nested AST generation
8267 (see L</"Nested AST Generation">), these values refer to the position
8268 of the schedule dimension within the innermost AST generation.
8269 The constraints on the domain elements of
8270 the option should only refer to this dimension and earlier dimensions.
8271 We consider the following spaces.
8275 =item C<separation_class>
8277 This space is a wrapped relation between two one dimensional spaces.
8278 The input space represents the schedule dimension to which the option
8279 applies and the output space represents the separation class.
8280 While constructing a loop corresponding to the specified schedule
8281 dimension(s), the AST generator will try to generate separate loops
8282 for domain elements that are assigned different classes.
8283 If only some of the elements are assigned a class, then those elements
8284 that are not assigned any class will be treated as belonging to a class
8285 that is separate from the explicitly assigned classes.
8286 The typical use case for this option is to separate full tiles from
8288 The other options, described below, are applied after the separation
8291 As an example, consider the separation into full and partial tiles
8292 of a tiling of a triangular domain.
8293 Take, for example, the domain
8295 { A[i,j] : 0 <= i,j and i + j <= 100 }
8297 and a tiling into tiles of 10 by 10. The input to the AST generator
8298 is then the schedule
8300 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
8303 Without any options, the following AST is generated
8305 for (int c0 = 0; c0 <= 10; c0 += 1)
8306 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8307 for (int c2 = 10 * c0;
8308 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8310 for (int c3 = 10 * c1;
8311 c3 <= min(10 * c1 + 9, -c2 + 100);
8315 Separation into full and partial tiles can be obtained by assigning
8316 a class, say C<0>, to the full tiles. The full tiles are represented by those
8317 values of the first and second schedule dimensions for which there are
8318 values of the third and fourth dimensions to cover an entire tile.
8319 That is, we need to specify the following option
8321 { [a,b,c,d] -> separation_class[[0]->[0]] :
8322 exists b': 0 <= 10a,10b' and
8323 10a+9+10b'+9 <= 100;
8324 [a,b,c,d] -> separation_class[[1]->[0]] :
8325 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
8329 { [a, b, c, d] -> separation_class[[1] -> [0]] :
8330 a >= 0 and b >= 0 and b <= 8 - a;
8331 [a, b, c, d] -> separation_class[[0] -> [0]] :
8334 With this option, the generated AST is as follows
8337 for (int c0 = 0; c0 <= 8; c0 += 1) {
8338 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
8339 for (int c2 = 10 * c0;
8340 c2 <= 10 * c0 + 9; c2 += 1)
8341 for (int c3 = 10 * c1;
8342 c3 <= 10 * c1 + 9; c3 += 1)
8344 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
8345 for (int c2 = 10 * c0;
8346 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8348 for (int c3 = 10 * c1;
8349 c3 <= min(-c2 + 100, 10 * c1 + 9);
8353 for (int c0 = 9; c0 <= 10; c0 += 1)
8354 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8355 for (int c2 = 10 * c0;
8356 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8358 for (int c3 = 10 * c1;
8359 c3 <= min(10 * c1 + 9, -c2 + 100);
8366 This is a single-dimensional space representing the schedule dimension(s)
8367 to which ``separation'' should be applied. Separation tries to split
8368 a loop into several pieces if this can avoid the generation of guards
8370 See also the C<atomic> option.
8374 This is a single-dimensional space representing the schedule dimension(s)
8375 for which the domains should be considered ``atomic''. That is, the
8376 AST generator will make sure that any given domain space will only appear
8377 in a single loop at the specified level.
8379 Consider the following schedule
8381 { a[i] -> [i] : 0 <= i < 10;
8382 b[i] -> [i+1] : 0 <= i < 10 }
8384 If the following option is specified
8386 { [i] -> separate[x] }
8388 then the following AST will be generated
8392 for (int c0 = 1; c0 <= 9; c0 += 1) {
8399 If, on the other hand, the following option is specified
8401 { [i] -> atomic[x] }
8403 then the following AST will be generated
8405 for (int c0 = 0; c0 <= 10; c0 += 1) {
8412 If neither C<atomic> nor C<separate> is specified, then the AST generator
8413 may produce either of these two results or some intermediate form.
8417 This is a single-dimensional space representing the schedule dimension(s)
8418 that should be I<completely> unrolled.
8419 To obtain a partial unrolling, the user should apply an additional
8420 strip-mining to the schedule and fully unroll the inner loop.
8424 Additional control is available through the following functions.
8426 #include <isl/ast_build.h>
8427 __isl_give isl_ast_build *
8428 isl_ast_build_set_iterators(
8429 __isl_take isl_ast_build *control,
8430 __isl_take isl_id_list *iterators);
8432 The function C<isl_ast_build_set_iterators> allows the user to
8433 specify a list of iterator C<isl_id>s to be used as iterators.
8434 If the input schedule is injective, then
8435 the number of elements in this list should be as large as the dimension
8436 of the schedule space, but no direct correspondence should be assumed
8437 between dimensions and elements.
8438 If the input schedule is not injective, then an additional number
8439 of C<isl_id>s equal to the largest dimension of the input domains
8441 If the number of provided C<isl_id>s is insufficient, then additional
8442 names are automatically generated.
8444 #include <isl/ast_build.h>
8445 __isl_give isl_ast_build *
8446 isl_ast_build_set_create_leaf(
8447 __isl_take isl_ast_build *control,
8448 __isl_give isl_ast_node *(*fn)(
8449 __isl_take isl_ast_build *build,
8450 void *user), void *user);
8453 C<isl_ast_build_set_create_leaf> function allows for the
8454 specification of a callback that should be called whenever the AST
8455 generator arrives at an element of the schedule domain.
8456 The callback should return an AST node that should be inserted
8457 at the corresponding position of the AST. The default action (when
8458 the callback is not set) is to continue generating parts of the AST to scan
8459 all the domain elements associated to the schedule domain element
8460 and to insert user nodes, ``calling'' the domain element, for each of them.
8461 The C<build> argument contains the current state of the C<isl_ast_build>.
8462 To ease nested AST generation (see L</"Nested AST Generation">),
8463 all control information that is
8464 specific to the current AST generation such as the options and
8465 the callbacks has been removed from this C<isl_ast_build>.
8466 The callback would typically return the result of a nested
8468 user defined node created using the following function.
8470 #include <isl/ast.h>
8471 __isl_give isl_ast_node *isl_ast_node_alloc_user(
8472 __isl_take isl_ast_expr *expr);
8474 #include <isl/ast_build.h>
8475 __isl_give isl_ast_build *
8476 isl_ast_build_set_at_each_domain(
8477 __isl_take isl_ast_build *build,
8478 __isl_give isl_ast_node *(*fn)(
8479 __isl_take isl_ast_node *node,
8480 __isl_keep isl_ast_build *build,
8481 void *user), void *user);
8482 __isl_give isl_ast_build *
8483 isl_ast_build_set_before_each_for(
8484 __isl_take isl_ast_build *build,
8485 __isl_give isl_id *(*fn)(
8486 __isl_keep isl_ast_build *build,
8487 void *user), void *user);
8488 __isl_give isl_ast_build *
8489 isl_ast_build_set_after_each_for(
8490 __isl_take isl_ast_build *build,
8491 __isl_give isl_ast_node *(*fn)(
8492 __isl_take isl_ast_node *node,
8493 __isl_keep isl_ast_build *build,
8494 void *user), void *user);
8496 The callback set by C<isl_ast_build_set_at_each_domain> will
8497 be called for each domain AST node.
8498 The callbacks set by C<isl_ast_build_set_before_each_for>
8499 and C<isl_ast_build_set_after_each_for> will be called
8500 for each for AST node. The first will be called in depth-first
8501 pre-order, while the second will be called in depth-first post-order.
8502 Since C<isl_ast_build_set_before_each_for> is called before the for
8503 node is actually constructed, it is only passed an C<isl_ast_build>.
8504 The returned C<isl_id> will be added as an annotation (using
8505 C<isl_ast_node_set_annotation>) to the constructed for node.
8506 In particular, if the user has also specified an C<after_each_for>
8507 callback, then the annotation can be retrieved from the node passed to
8508 that callback using C<isl_ast_node_get_annotation>.
8509 All callbacks should C<NULL> on failure.
8510 The given C<isl_ast_build> can be used to create new
8511 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
8512 or C<isl_ast_build_call_from_pw_multi_aff>.
8514 =head3 Nested AST Generation
8516 C<isl> allows the user to create an AST within the context
8517 of another AST. These nested ASTs are created using the
8518 same C<isl_ast_build_ast_from_schedule> function that is used to create the
8519 outer AST. The C<build> argument should be an C<isl_ast_build>
8520 passed to a callback set by
8521 C<isl_ast_build_set_create_leaf>.
8522 The space of the range of the C<schedule> argument should refer
8523 to this build. In particular, the space should be a wrapped
8524 relation and the domain of this wrapped relation should be the
8525 same as that of the range of the schedule returned by
8526 C<isl_ast_build_get_schedule> below.
8527 In practice, the new schedule is typically
8528 created by calling C<isl_union_map_range_product> on the old schedule
8529 and some extra piece of the schedule.
8530 The space of the schedule domain is also available from
8531 the C<isl_ast_build>.
8533 #include <isl/ast_build.h>
8534 __isl_give isl_union_map *isl_ast_build_get_schedule(
8535 __isl_keep isl_ast_build *build);
8536 __isl_give isl_space *isl_ast_build_get_schedule_space(
8537 __isl_keep isl_ast_build *build);
8538 __isl_give isl_ast_build *isl_ast_build_restrict(
8539 __isl_take isl_ast_build *build,
8540 __isl_take isl_set *set);
8542 The C<isl_ast_build_get_schedule> function returns a (partial)
8543 schedule for the domains elements for which part of the AST still needs to
8544 be generated in the current build.
8545 In particular, the domain elements are mapped to those iterations of the loops
8546 enclosing the current point of the AST generation inside which
8547 the domain elements are executed.
8548 No direct correspondence between
8549 the input schedule and this schedule should be assumed.
8550 The space obtained from C<isl_ast_build_get_schedule_space> can be used
8551 to create a set for C<isl_ast_build_restrict> to intersect
8552 with the current build. In particular, the set passed to
8553 C<isl_ast_build_restrict> can have additional parameters.
8554 The ids of the set dimensions in the space returned by
8555 C<isl_ast_build_get_schedule_space> correspond to the
8556 iterators of the already generated loops.
8557 The user should not rely on the ids of the output dimensions
8558 of the relations in the union relation returned by
8559 C<isl_ast_build_get_schedule> having any particular value.
8563 Although C<isl> is mainly meant to be used as a library,
8564 it also contains some basic applications that use some
8565 of the functionality of C<isl>.
8566 The input may be specified in either the L<isl format>
8567 or the L<PolyLib format>.
8569 =head2 C<isl_polyhedron_sample>
8571 C<isl_polyhedron_sample> takes a polyhedron as input and prints
8572 an integer element of the polyhedron, if there is any.
8573 The first column in the output is the denominator and is always
8574 equal to 1. If the polyhedron contains no integer points,
8575 then a vector of length zero is printed.
8579 C<isl_pip> takes the same input as the C<example> program
8580 from the C<piplib> distribution, i.e., a set of constraints
8581 on the parameters, a line containing only -1 and finally a set
8582 of constraints on a parametric polyhedron.
8583 The coefficients of the parameters appear in the last columns
8584 (but before the final constant column).
8585 The output is the lexicographic minimum of the parametric polyhedron.
8586 As C<isl> currently does not have its own output format, the output
8587 is just a dump of the internal state.
8589 =head2 C<isl_polyhedron_minimize>
8591 C<isl_polyhedron_minimize> computes the minimum of some linear
8592 or affine objective function over the integer points in a polyhedron.
8593 If an affine objective function
8594 is given, then the constant should appear in the last column.
8596 =head2 C<isl_polytope_scan>
8598 Given a polytope, C<isl_polytope_scan> prints
8599 all integer points in the polytope.
8601 =head2 C<isl_codegen>
8603 Given a schedule, a context set and an options relation,
8604 C<isl_codegen> prints out an AST that scans the domain elements
8605 of the schedule in the order of their image(s) taking into account
8606 the constraints in the context set.