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);
1965 __isl_give isl_union_map *
1966 isl_union_map_from_multi_union_pw_aff(
1967 __isl_take isl_multi_union_pw_aff *mupa);
1969 The C<domain_space> argument describes the domain of the resulting
1970 basic relation. It is required because the C<list> may consist
1971 of zero affine expressions.
1972 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
1973 is not allowed to be zero-dimensional. The domain of the result
1974 is the shared domain of the union piecewise affine elements.
1976 =head2 Inspecting Sets and Relations
1978 Usually, the user should not have to care about the actual constraints
1979 of the sets and maps, but should instead apply the abstract operations
1980 explained in the following sections.
1981 Occasionally, however, it may be required to inspect the individual
1982 coefficients of the constraints. This section explains how to do so.
1983 In these cases, it may also be useful to have C<isl> compute
1984 an explicit representation of the existentially quantified variables.
1986 __isl_give isl_set *isl_set_compute_divs(
1987 __isl_take isl_set *set);
1988 __isl_give isl_map *isl_map_compute_divs(
1989 __isl_take isl_map *map);
1990 __isl_give isl_union_set *isl_union_set_compute_divs(
1991 __isl_take isl_union_set *uset);
1992 __isl_give isl_union_map *isl_union_map_compute_divs(
1993 __isl_take isl_union_map *umap);
1995 This explicit representation defines the existentially quantified
1996 variables as integer divisions of the other variables, possibly
1997 including earlier existentially quantified variables.
1998 An explicitly represented existentially quantified variable therefore
1999 has a unique value when the values of the other variables are known.
2000 If, furthermore, the same existentials, i.e., existentials
2001 with the same explicit representations, should appear in the
2002 same order in each of the disjuncts of a set or map, then the user should call
2003 either of the following functions.
2005 __isl_give isl_set *isl_set_align_divs(
2006 __isl_take isl_set *set);
2007 __isl_give isl_map *isl_map_align_divs(
2008 __isl_take isl_map *map);
2010 Alternatively, the existentially quantified variables can be removed
2011 using the following functions, which compute an overapproximation.
2013 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2014 __isl_take isl_basic_set *bset);
2015 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2016 __isl_take isl_basic_map *bmap);
2017 __isl_give isl_set *isl_set_remove_divs(
2018 __isl_take isl_set *set);
2019 __isl_give isl_map *isl_map_remove_divs(
2020 __isl_take isl_map *map);
2022 It is also possible to only remove those divs that are defined
2023 in terms of a given range of dimensions or only those for which
2024 no explicit representation is known.
2026 __isl_give isl_basic_set *
2027 isl_basic_set_remove_divs_involving_dims(
2028 __isl_take isl_basic_set *bset,
2029 enum isl_dim_type type,
2030 unsigned first, unsigned n);
2031 __isl_give isl_basic_map *
2032 isl_basic_map_remove_divs_involving_dims(
2033 __isl_take isl_basic_map *bmap,
2034 enum isl_dim_type type,
2035 unsigned first, unsigned n);
2036 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2037 __isl_take isl_set *set, enum isl_dim_type type,
2038 unsigned first, unsigned n);
2039 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2040 __isl_take isl_map *map, enum isl_dim_type type,
2041 unsigned first, unsigned n);
2043 __isl_give isl_basic_set *
2044 isl_basic_set_remove_unknown_divs(
2045 __isl_take isl_basic_set *bset);
2046 __isl_give isl_set *isl_set_remove_unknown_divs(
2047 __isl_take isl_set *set);
2048 __isl_give isl_map *isl_map_remove_unknown_divs(
2049 __isl_take isl_map *map);
2051 To iterate over all the sets or maps in a union set or map, use
2053 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
2054 int (*fn)(__isl_take isl_set *set, void *user),
2056 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
2057 int (*fn)(__isl_take isl_map *map, void *user),
2060 The number of sets or maps in a union set or map can be obtained
2063 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2064 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2066 To extract the set or map in a given space from a union, use
2068 __isl_give isl_set *isl_union_set_extract_set(
2069 __isl_keep isl_union_set *uset,
2070 __isl_take isl_space *space);
2071 __isl_give isl_map *isl_union_map_extract_map(
2072 __isl_keep isl_union_map *umap,
2073 __isl_take isl_space *space);
2075 To iterate over all the basic sets or maps in a set or map, use
2077 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
2078 int (*fn)(__isl_take isl_basic_set *bset, void *user),
2080 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
2081 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
2084 The callback function C<fn> should return 0 if successful and
2085 -1 if an error occurs. In the latter case, or if any other error
2086 occurs, the above functions will return -1.
2088 It should be noted that C<isl> does not guarantee that
2089 the basic sets or maps passed to C<fn> are disjoint.
2090 If this is required, then the user should call one of
2091 the following functions first.
2093 __isl_give isl_set *isl_set_make_disjoint(
2094 __isl_take isl_set *set);
2095 __isl_give isl_map *isl_map_make_disjoint(
2096 __isl_take isl_map *map);
2098 The number of basic sets in a set can be obtained
2099 or the number of basic maps in a map can be obtained
2102 #include <isl/set.h>
2103 int isl_set_n_basic_set(__isl_keep isl_set *set);
2105 #include <isl/map.h>
2106 int isl_map_n_basic_map(__isl_keep isl_map *map);
2108 To iterate over the constraints of a basic set or map, use
2110 #include <isl/constraint.h>
2112 int isl_basic_set_n_constraint(
2113 __isl_keep isl_basic_set *bset);
2114 int isl_basic_set_foreach_constraint(
2115 __isl_keep isl_basic_set *bset,
2116 int (*fn)(__isl_take isl_constraint *c, void *user),
2118 int isl_basic_map_n_constraint(
2119 __isl_keep isl_basic_map *bmap);
2120 int isl_basic_map_foreach_constraint(
2121 __isl_keep isl_basic_map *bmap,
2122 int (*fn)(__isl_take isl_constraint *c, void *user),
2124 __isl_null isl_constraint *isl_constraint_free(
2125 __isl_take isl_constraint *c);
2127 Again, the callback function C<fn> should return 0 if successful and
2128 -1 if an error occurs. In the latter case, or if any other error
2129 occurs, the above functions will return -1.
2130 The constraint C<c> represents either an equality or an inequality.
2131 Use the following function to find out whether a constraint
2132 represents an equality. If not, it represents an inequality.
2134 int isl_constraint_is_equality(
2135 __isl_keep isl_constraint *constraint);
2137 It is also possible to obtain a list of constraints from a basic
2140 #include <isl/constraint.h>
2141 __isl_give isl_constraint_list *
2142 isl_basic_map_get_constraint_list(
2143 __isl_keep isl_basic_map *bmap);
2144 __isl_give isl_constraint_list *
2145 isl_basic_set_get_constraint_list(
2146 __isl_keep isl_basic_set *bset);
2148 These functions require that all existentially quantified variables
2149 have an explicit representation.
2150 The returned list can be manipulated using the functions in L<"Lists">.
2152 The coefficients of the constraints can be inspected using
2153 the following functions.
2155 int isl_constraint_is_lower_bound(
2156 __isl_keep isl_constraint *constraint,
2157 enum isl_dim_type type, unsigned pos);
2158 int isl_constraint_is_upper_bound(
2159 __isl_keep isl_constraint *constraint,
2160 enum isl_dim_type type, unsigned pos);
2161 __isl_give isl_val *isl_constraint_get_constant_val(
2162 __isl_keep isl_constraint *constraint);
2163 __isl_give isl_val *isl_constraint_get_coefficient_val(
2164 __isl_keep isl_constraint *constraint,
2165 enum isl_dim_type type, int pos);
2167 The explicit representations of the existentially quantified
2168 variables can be inspected using the following function.
2169 Note that the user is only allowed to use this function
2170 if the inspected set or map is the result of a call
2171 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2172 The existentially quantified variable is equal to the floor
2173 of the returned affine expression. The affine expression
2174 itself can be inspected using the functions in
2177 __isl_give isl_aff *isl_constraint_get_div(
2178 __isl_keep isl_constraint *constraint, int pos);
2180 To obtain the constraints of a basic set or map in matrix
2181 form, use the following functions.
2183 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2184 __isl_keep isl_basic_set *bset,
2185 enum isl_dim_type c1, enum isl_dim_type c2,
2186 enum isl_dim_type c3, enum isl_dim_type c4);
2187 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2188 __isl_keep isl_basic_set *bset,
2189 enum isl_dim_type c1, enum isl_dim_type c2,
2190 enum isl_dim_type c3, enum isl_dim_type c4);
2191 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2192 __isl_keep isl_basic_map *bmap,
2193 enum isl_dim_type c1,
2194 enum isl_dim_type c2, enum isl_dim_type c3,
2195 enum isl_dim_type c4, enum isl_dim_type c5);
2196 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2197 __isl_keep isl_basic_map *bmap,
2198 enum isl_dim_type c1,
2199 enum isl_dim_type c2, enum isl_dim_type c3,
2200 enum isl_dim_type c4, enum isl_dim_type c5);
2202 The C<isl_dim_type> arguments dictate the order in which
2203 different kinds of variables appear in the resulting matrix.
2204 For set inputs, they should be a permutation of
2205 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2206 For map inputs, they should be a permutation of
2207 C<isl_dim_cst>, C<isl_dim_param>,
2208 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2212 Points are elements of a set. They can be used to construct
2213 simple sets (boxes) or they can be used to represent the
2214 individual elements of a set.
2215 The zero point (the origin) can be created using
2217 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2219 The coordinates of a point can be inspected, set and changed
2222 __isl_give isl_val *isl_point_get_coordinate_val(
2223 __isl_keep isl_point *pnt,
2224 enum isl_dim_type type, int pos);
2225 __isl_give isl_point *isl_point_set_coordinate_val(
2226 __isl_take isl_point *pnt,
2227 enum isl_dim_type type, int pos,
2228 __isl_take isl_val *v);
2230 __isl_give isl_point *isl_point_add_ui(
2231 __isl_take isl_point *pnt,
2232 enum isl_dim_type type, int pos, unsigned val);
2233 __isl_give isl_point *isl_point_sub_ui(
2234 __isl_take isl_point *pnt,
2235 enum isl_dim_type type, int pos, unsigned val);
2237 Points can be copied or freed using
2239 __isl_give isl_point *isl_point_copy(
2240 __isl_keep isl_point *pnt);
2241 void isl_point_free(__isl_take isl_point *pnt);
2243 A singleton set can be created from a point using
2245 __isl_give isl_basic_set *isl_basic_set_from_point(
2246 __isl_take isl_point *pnt);
2247 __isl_give isl_set *isl_set_from_point(
2248 __isl_take isl_point *pnt);
2250 and a box can be created from two opposite extremal points using
2252 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2253 __isl_take isl_point *pnt1,
2254 __isl_take isl_point *pnt2);
2255 __isl_give isl_set *isl_set_box_from_points(
2256 __isl_take isl_point *pnt1,
2257 __isl_take isl_point *pnt2);
2259 All elements of a B<bounded> (union) set can be enumerated using
2260 the following functions.
2262 int isl_set_foreach_point(__isl_keep isl_set *set,
2263 int (*fn)(__isl_take isl_point *pnt, void *user),
2265 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2266 int (*fn)(__isl_take isl_point *pnt, void *user),
2269 The function C<fn> is called for each integer point in
2270 C<set> with as second argument the last argument of
2271 the C<isl_set_foreach_point> call. The function C<fn>
2272 should return C<0> on success and C<-1> on failure.
2273 In the latter case, C<isl_set_foreach_point> will stop
2274 enumerating and return C<-1> as well.
2275 If the enumeration is performed successfully and to completion,
2276 then C<isl_set_foreach_point> returns C<0>.
2278 To obtain a single point of a (basic) set, use
2280 __isl_give isl_point *isl_basic_set_sample_point(
2281 __isl_take isl_basic_set *bset);
2282 __isl_give isl_point *isl_set_sample_point(
2283 __isl_take isl_set *set);
2285 If C<set> does not contain any (integer) points, then the
2286 resulting point will be ``void'', a property that can be
2289 int isl_point_is_void(__isl_keep isl_point *pnt);
2293 Besides sets and relation, C<isl> also supports various types of functions.
2294 Each of these types is derived from the value type (see L</"Values">)
2295 or from one of two primitive function types
2296 through the application of zero or more type constructors.
2297 We first describe the primitive type and then we describe
2298 the types derived from these primitive types.
2300 =head3 Primitive Functions
2302 C<isl> support two primitive function types, quasi-affine
2303 expressions and quasipolynomials.
2304 A quasi-affine expression is defined either over a parameter
2305 space or over a set and is composed of integer constants,
2306 parameters and set variables, addition, subtraction and
2307 integer division by an integer constant.
2308 For example, the quasi-affine expression
2310 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2312 maps C<x> to C<2*floor((4 n + x)/9>.
2313 A quasipolynomial is a polynomial expression in quasi-affine
2314 expression. That is, it additionally allows for multiplication.
2315 Note, though, that it is not allowed to construct an integer
2316 division of an expression involving multiplications.
2317 Here is an example of a quasipolynomial that is not
2318 quasi-affine expression
2320 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2322 Note that the external representations of quasi-affine expressions
2323 and quasipolynomials are different. Quasi-affine expressions
2324 use a notation with square brackets just like binary relations,
2325 while quasipolynomials do not. This might change at some point.
2327 If a primitive function is defined over a parameter space,
2328 then the space of the function itself is that of a set.
2329 If it is defined over a set, then the space of the function
2330 is that of a relation. In both cases, the set space (or
2331 the output space) is single-dimensional, anonymous and unstructured.
2332 To create functions with multiple dimensions or with other kinds
2333 of set or output spaces, use multiple expressions
2334 (see L</"Multiple Expressions">).
2338 =item * Quasi-affine Expressions
2340 Besides the expressions described above, a quasi-affine
2341 expression can also be set to NaN. Such expressions
2342 typically represent a failure to represent a result
2343 as a quasi-affine expression.
2345 The zero quasi affine expression or the quasi affine expression
2346 that is equal to a given value or
2347 a specified dimension on a given domain can be created using
2349 #include <isl/aff.h>
2350 __isl_give isl_aff *isl_aff_zero_on_domain(
2351 __isl_take isl_local_space *ls);
2352 __isl_give isl_aff *isl_aff_val_on_domain(
2353 __isl_take isl_local_space *ls,
2354 __isl_take isl_val *val);
2355 __isl_give isl_aff *isl_aff_var_on_domain(
2356 __isl_take isl_local_space *ls,
2357 enum isl_dim_type type, unsigned pos);
2358 __isl_give isl_aff *isl_aff_nan_on_domain(
2359 __isl_take isl_local_space *ls);
2361 Quasi affine expressions can be copied and freed using
2363 #include <isl/aff.h>
2364 __isl_give isl_aff *isl_aff_copy(
2365 __isl_keep isl_aff *aff);
2366 __isl_null isl_aff *isl_aff_free(
2367 __isl_take isl_aff *aff);
2369 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2370 using the following function. The constraint is required to have
2371 a non-zero coefficient for the specified dimension.
2373 #include <isl/constraint.h>
2374 __isl_give isl_aff *isl_constraint_get_bound(
2375 __isl_keep isl_constraint *constraint,
2376 enum isl_dim_type type, int pos);
2378 The entire affine expression of the constraint can also be extracted
2379 using the following function.
2381 #include <isl/constraint.h>
2382 __isl_give isl_aff *isl_constraint_get_aff(
2383 __isl_keep isl_constraint *constraint);
2385 Conversely, an equality constraint equating
2386 the affine expression to zero or an inequality constraint enforcing
2387 the affine expression to be non-negative, can be constructed using
2389 __isl_give isl_constraint *isl_equality_from_aff(
2390 __isl_take isl_aff *aff);
2391 __isl_give isl_constraint *isl_inequality_from_aff(
2392 __isl_take isl_aff *aff);
2394 The coefficients and the integer divisions of an affine expression
2395 can be inspected using the following functions.
2397 #include <isl/aff.h>
2398 __isl_give isl_val *isl_aff_get_constant_val(
2399 __isl_keep isl_aff *aff);
2400 __isl_give isl_val *isl_aff_get_coefficient_val(
2401 __isl_keep isl_aff *aff,
2402 enum isl_dim_type type, int pos);
2403 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2404 enum isl_dim_type type, int pos);
2405 __isl_give isl_val *isl_aff_get_denominator_val(
2406 __isl_keep isl_aff *aff);
2407 __isl_give isl_aff *isl_aff_get_div(
2408 __isl_keep isl_aff *aff, int pos);
2410 They can be modified using the following functions.
2412 #include <isl/aff.h>
2413 __isl_give isl_aff *isl_aff_set_constant_si(
2414 __isl_take isl_aff *aff, int v);
2415 __isl_give isl_aff *isl_aff_set_constant_val(
2416 __isl_take isl_aff *aff, __isl_take isl_val *v);
2417 __isl_give isl_aff *isl_aff_set_coefficient_si(
2418 __isl_take isl_aff *aff,
2419 enum isl_dim_type type, int pos, int v);
2420 __isl_give isl_aff *isl_aff_set_coefficient_val(
2421 __isl_take isl_aff *aff,
2422 enum isl_dim_type type, int pos,
2423 __isl_take isl_val *v);
2425 __isl_give isl_aff *isl_aff_add_constant_si(
2426 __isl_take isl_aff *aff, int v);
2427 __isl_give isl_aff *isl_aff_add_constant_val(
2428 __isl_take isl_aff *aff, __isl_take isl_val *v);
2429 __isl_give isl_aff *isl_aff_add_constant_num_si(
2430 __isl_take isl_aff *aff, int v);
2431 __isl_give isl_aff *isl_aff_add_coefficient_si(
2432 __isl_take isl_aff *aff,
2433 enum isl_dim_type type, int pos, int v);
2434 __isl_give isl_aff *isl_aff_add_coefficient_val(
2435 __isl_take isl_aff *aff,
2436 enum isl_dim_type type, int pos,
2437 __isl_take isl_val *v);
2439 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2440 set the I<numerator> of the constant or coefficient, while
2441 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2442 the constant or coefficient as a whole.
2443 The C<add_constant> and C<add_coefficient> functions add an integer
2444 or rational value to
2445 the possibly rational constant or coefficient.
2446 The C<add_constant_num> functions add an integer value to
2449 =item * Quasipolynomials
2451 Some simple quasipolynomials can be created using the following functions.
2453 #include <isl/polynomial.h>
2454 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2455 __isl_take isl_space *domain);
2456 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2457 __isl_take isl_space *domain);
2458 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2459 __isl_take isl_space *domain);
2460 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2461 __isl_take isl_space *domain);
2462 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2463 __isl_take isl_space *domain);
2464 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2465 __isl_take isl_space *domain,
2466 __isl_take isl_val *val);
2467 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2468 __isl_take isl_space *domain,
2469 enum isl_dim_type type, unsigned pos);
2470 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2471 __isl_take isl_aff *aff);
2473 Recall that the space in which a quasipolynomial lives is a map space
2474 with a one-dimensional range. The C<domain> argument in some of
2475 the functions above corresponds to the domain of this map space.
2477 Quasipolynomials can be copied and freed again using the following
2480 #include <isl/polynomial.h>
2481 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2482 __isl_keep isl_qpolynomial *qp);
2483 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2484 __isl_take isl_qpolynomial *qp);
2486 The constant term of a quasipolynomial can be extracted using
2488 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2489 __isl_keep isl_qpolynomial *qp);
2491 To iterate over all terms in a quasipolynomial,
2494 int isl_qpolynomial_foreach_term(
2495 __isl_keep isl_qpolynomial *qp,
2496 int (*fn)(__isl_take isl_term *term,
2497 void *user), void *user);
2499 The terms themselves can be inspected and freed using
2502 unsigned isl_term_dim(__isl_keep isl_term *term,
2503 enum isl_dim_type type);
2504 __isl_give isl_val *isl_term_get_coefficient_val(
2505 __isl_keep isl_term *term);
2506 int isl_term_get_exp(__isl_keep isl_term *term,
2507 enum isl_dim_type type, unsigned pos);
2508 __isl_give isl_aff *isl_term_get_div(
2509 __isl_keep isl_term *term, unsigned pos);
2510 void isl_term_free(__isl_take isl_term *term);
2512 Each term is a product of parameters, set variables and
2513 integer divisions. The function C<isl_term_get_exp>
2514 returns the exponent of a given dimensions in the given term.
2520 A reduction represents a maximum or a minimum of its
2522 The only reduction type defined by C<isl> is
2523 C<isl_qpolynomial_fold>.
2525 There are currently no functions to directly create such
2526 objects, but they do appear in the piecewise quasipolynomial
2527 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2529 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2531 Reductions can be copied and freed using
2532 the following functions.
2534 #include <isl/polynomial.h>
2535 __isl_give isl_qpolynomial_fold *
2536 isl_qpolynomial_fold_copy(
2537 __isl_keep isl_qpolynomial_fold *fold);
2538 void isl_qpolynomial_fold_free(
2539 __isl_take isl_qpolynomial_fold *fold);
2541 To iterate over all quasipolynomials in a reduction, use
2543 int isl_qpolynomial_fold_foreach_qpolynomial(
2544 __isl_keep isl_qpolynomial_fold *fold,
2545 int (*fn)(__isl_take isl_qpolynomial *qp,
2546 void *user), void *user);
2548 =head3 Multiple Expressions
2550 A multiple expression represents a sequence of zero or
2551 more base expressions, all defined on the same domain space.
2552 The domain space of the multiple expression is the same
2553 as that of the base expressions, but the range space
2554 can be any space. In case the base expressions have
2555 a set space, the corresponding multiple expression
2556 also has a set space.
2557 Objects of the value type do not have an associated space.
2558 The space of a multiple value is therefore always a set space.
2559 Similarly, the space of a multiple union piecewise
2560 affine expression is always a set space.
2562 The multiple expression types defined by C<isl>
2563 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2564 C<isl_multi_union_pw_aff>.
2566 A multiple expression with the value zero for
2567 each output (or set) dimension can be created
2568 using the following functions.
2570 #include <isl/val.h>
2571 __isl_give isl_multi_val *isl_multi_val_zero(
2572 __isl_take isl_space *space);
2574 #include <isl/aff.h>
2575 __isl_give isl_multi_aff *isl_multi_aff_zero(
2576 __isl_take isl_space *space);
2577 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2578 __isl_take isl_space *space);
2579 __isl_give isl_multi_union_pw_aff *
2580 isl_multi_union_pw_aff_zero(
2581 __isl_take isl_space *space);
2583 Since there is no canonical way of representing a zero
2584 value of type C<isl_union_pw_aff>, the space passed
2585 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2587 An identity function can be created using the following
2588 functions. The space needs to be that of a relation
2589 with the same number of input and output dimensions.
2591 #include <isl/aff.h>
2592 __isl_give isl_multi_aff *isl_multi_aff_identity(
2593 __isl_take isl_space *space);
2594 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2595 __isl_take isl_space *space);
2597 A function that performs a projection on a universe
2598 relation or set can be created using the following functions.
2599 See also the corresponding
2600 projection operations in L</"Unary Operations">.
2602 #include <isl/aff.h>
2603 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2604 __isl_take isl_space *space);
2605 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2606 __isl_take isl_space *space);
2607 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2608 __isl_take isl_space *space,
2609 enum isl_dim_type type,
2610 unsigned first, unsigned n);
2612 A multiple expression can be created from a single
2613 base expression using the following functions.
2614 The space of the created multiple expression is the same
2615 as that of the base expression, except for
2616 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2617 lives in a parameter space and the output lives
2618 in a single-dimensional set space.
2620 #include <isl/aff.h>
2621 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2622 __isl_take isl_aff *aff);
2623 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2624 __isl_take isl_pw_aff *pa);
2625 __isl_give isl_multi_union_pw_aff *
2626 isl_multi_union_pw_aff_from_union_pw_aff(
2627 __isl_take isl_union_pw_aff *upa);
2629 A multiple expression can be created from a list
2630 of base expression in a specified space.
2631 The domain of this space needs to be the same
2632 as the domains of the base expressions in the list.
2633 If the base expressions have a set space (or no associated space),
2634 then this space also needs to be a set space.
2636 #include <isl/val.h>
2637 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2638 __isl_take isl_space *space,
2639 __isl_take isl_val_list *list);
2641 #include <isl/aff.h>
2642 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2643 __isl_take isl_space *space,
2644 __isl_take isl_aff_list *list);
2645 __isl_give isl_multi_union_pw_aff *
2646 isl_multi_union_pw_aff_from_union_pw_aff_list(
2647 __isl_take isl_space *space,
2648 __isl_take isl_union_pw_aff_list *list);
2650 As a convenience, a multiple piecewise expression can
2651 also be created from a multiple expression.
2652 Each piecewise expression in the result has a single
2655 #include <isl/aff.h>
2656 __isl_give isl_multi_pw_aff *
2657 isl_multi_pw_aff_from_multi_aff(
2658 __isl_take isl_multi_aff *ma);
2660 Similarly, a multiple union expression can be
2661 created from a multiple expression.
2663 #include <isl/aff.h>
2664 __isl_give isl_multi_union_pw_aff *
2665 isl_multi_union_pw_aff_from_multi_aff(
2666 __isl_take isl_multi_aff *ma);
2667 __isl_give isl_multi_union_pw_aff *
2668 isl_multi_union_pw_aff_from_multi_pw_aff(
2669 __isl_take isl_multi_pw_aff *mpa);
2671 A multiple quasi-affine expression can be created from
2672 a multiple value with a given domain space using the following
2675 #include <isl/aff.h>
2676 __isl_give isl_multi_aff *
2677 isl_multi_aff_multi_val_on_space(
2678 __isl_take isl_space *space,
2679 __isl_take isl_multi_val *mv);
2682 a multiple union piecewise affine expression can be created from
2683 a multiple value with a given domain or
2684 a multiple affine expression with a given domain
2685 using the following functions.
2687 #include <isl/aff.h>
2688 __isl_give isl_multi_union_pw_aff *
2689 isl_multi_union_pw_aff_multi_val_on_domain(
2690 __isl_take isl_union_set *domain,
2691 __isl_take isl_multi_val *mv);
2692 __isl_give isl_multi_union_pw_aff *
2693 isl_multi_union_pw_aff_multi_aff_on_domain(
2694 __isl_take isl_union_set *domain,
2695 __isl_take isl_multi_aff *ma);
2697 Multiple expressions can be copied and freed using
2698 the following functions.
2700 #include <isl/val.h>
2701 __isl_give isl_multi_val *isl_multi_val_copy(
2702 __isl_keep isl_multi_val *mv);
2703 __isl_null isl_multi_val *isl_multi_val_free(
2704 __isl_take isl_multi_val *mv);
2706 #include <isl/aff.h>
2707 __isl_give isl_multi_aff *isl_multi_aff_copy(
2708 __isl_keep isl_multi_aff *maff);
2709 __isl_null isl_multi_aff *isl_multi_aff_free(
2710 __isl_take isl_multi_aff *maff);
2711 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2712 __isl_keep isl_multi_pw_aff *mpa);
2713 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2714 __isl_take isl_multi_pw_aff *mpa);
2715 __isl_give isl_multi_union_pw_aff *
2716 isl_multi_union_pw_aff_copy(
2717 __isl_keep isl_multi_union_pw_aff *mupa);
2718 __isl_null isl_multi_union_pw_aff *
2719 isl_multi_union_pw_aff_free(
2720 __isl_take isl_multi_union_pw_aff *mupa);
2722 The base expression at a given position of a multiple
2723 expression can be extracted using the following functions.
2725 #include <isl/val.h>
2726 __isl_give isl_val *isl_multi_val_get_val(
2727 __isl_keep isl_multi_val *mv, int pos);
2729 #include <isl/aff.h>
2730 __isl_give isl_aff *isl_multi_aff_get_aff(
2731 __isl_keep isl_multi_aff *multi, int pos);
2732 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2733 __isl_keep isl_multi_pw_aff *mpa, int pos);
2734 __isl_give isl_union_pw_aff *
2735 isl_multi_union_pw_aff_get_union_pw_aff(
2736 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2738 It can be replaced using the following functions.
2740 #include <isl/val.h>
2741 __isl_give isl_multi_val *isl_multi_val_set_val(
2742 __isl_take isl_multi_val *mv, int pos,
2743 __isl_take isl_val *val);
2745 #include <isl/aff.h>
2746 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2747 __isl_take isl_multi_aff *multi, int pos,
2748 __isl_take isl_aff *aff);
2749 __isl_give isl_multi_union_pw_aff *
2750 isl_multi_union_pw_aff_set_union_pw_aff(
2751 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2752 __isl_take isl_union_pw_aff *upa);
2754 Note that there is a difference between C<isl_multi_union_pw_aff>
2755 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2756 of unions of piecewise expressions, while the second is a union
2757 of piecewise sequences. In particular, multiple affine expressions
2758 in an C<isl_union_pw_multi_aff> may live in different spaces,
2759 while there is only a single multiple expression in
2760 an C<isl_multi_union_pw_aff>, which can therefore only live
2761 in a single space. This means that not every
2762 C<isl_union_pw_multi_aff> can be converted to
2763 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2764 C<isl_multi_union_pw_aff> carries no information
2765 about any possible domain and therefore cannot be converted
2766 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2767 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2768 while each multiple expression inside an C<isl_union_pw_multi_aff>
2769 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2770 of dimension greater than one may therefore not be exact.
2771 The following functions can
2772 be used to perform these conversions when they are possible.
2774 #include <isl/aff.h>
2775 __isl_give isl_multi_union_pw_aff *
2776 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2777 __isl_take isl_union_pw_multi_aff *upma);
2778 __isl_give isl_union_pw_multi_aff *
2779 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2780 __isl_take isl_multi_union_pw_aff *mupa);
2782 =head3 Piecewise Expressions
2784 A piecewise expression is an expression that is described
2785 using zero or more base expression defined over the same
2786 number of cells in the domain space of the base expressions.
2787 All base expressions are defined over the same
2788 domain space and the cells are disjoint.
2789 The space of a piecewise expression is the same as
2790 that of the base expressions.
2791 If the union of the cells is a strict subset of the domain
2792 space, then the value of the piecewise expression outside
2793 this union is different for types derived from quasi-affine
2794 expressions and those derived from quasipolynomials.
2795 Piecewise expressions derived from quasi-affine expressions
2796 are considered to be undefined outside the union of their cells.
2797 Piecewise expressions derived from quasipolynomials
2798 are considered to be zero outside the union of their cells.
2800 Piecewise quasipolynomials are mainly used by the C<barvinok>
2801 library for representing the number of elements in a parametric set or map.
2802 For example, the piecewise quasipolynomial
2804 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2806 represents the number of points in the map
2808 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2810 The piecewise expression types defined by C<isl>
2811 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2812 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2814 A piecewise expression with no cells can be created using
2815 the following functions.
2817 #include <isl/aff.h>
2818 __isl_give isl_pw_aff *isl_pw_aff_empty(
2819 __isl_take isl_space *space);
2820 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2821 __isl_take isl_space *space);
2823 A piecewise expression with a single universe cell can be
2824 created using the following functions.
2826 #include <isl/aff.h>
2827 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2828 __isl_take isl_aff *aff);
2829 __isl_give isl_pw_multi_aff *
2830 isl_pw_multi_aff_from_multi_aff(
2831 __isl_take isl_multi_aff *ma);
2833 #include <isl/polynomial.h>
2834 __isl_give isl_pw_qpolynomial *
2835 isl_pw_qpolynomial_from_qpolynomial(
2836 __isl_take isl_qpolynomial *qp);
2838 A piecewise expression with a single specified cell can be
2839 created using the following functions.
2841 #include <isl/aff.h>
2842 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2843 __isl_take isl_set *set, __isl_take isl_aff *aff);
2844 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2845 __isl_take isl_set *set,
2846 __isl_take isl_multi_aff *maff);
2848 #include <isl/polynomial.h>
2849 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2850 __isl_take isl_set *set,
2851 __isl_take isl_qpolynomial *qp);
2853 The following convenience functions first create a base expression and
2854 then create a piecewise expression over a universe domain.
2856 #include <isl/aff.h>
2857 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2858 __isl_take isl_local_space *ls);
2859 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2860 __isl_take isl_local_space *ls,
2861 enum isl_dim_type type, unsigned pos);
2862 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2863 __isl_take isl_local_space *ls);
2864 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2865 __isl_take isl_space *space);
2866 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2867 __isl_take isl_space *space);
2868 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2869 __isl_take isl_space *space);
2870 __isl_give isl_pw_multi_aff *
2871 isl_pw_multi_aff_project_out_map(
2872 __isl_take isl_space *space,
2873 enum isl_dim_type type,
2874 unsigned first, unsigned n);
2876 #include <isl/polynomial.h>
2877 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2878 __isl_take isl_space *space);
2880 The following convenience functions first create a base expression and
2881 then create a piecewise expression over a given domain.
2883 #include <isl/aff.h>
2884 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2885 __isl_take isl_set *domain,
2886 __isl_take isl_val *v);
2887 __isl_give isl_pw_multi_aff *
2888 isl_pw_multi_aff_multi_val_on_domain(
2889 __isl_take isl_set *domain,
2890 __isl_take isl_multi_val *mv);
2892 As a convenience, a piecewise multiple expression can
2893 also be created from a piecewise expression.
2894 Each multiple expression in the result is derived
2895 from the corresponding base expression.
2897 #include <isl/aff.h>
2898 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2899 __isl_take isl_pw_aff *pa);
2901 Similarly, a piecewise quasipolynomial can be
2902 created from a piecewise quasi-affine expression using
2903 the following function.
2905 #include <isl/polynomial.h>
2906 __isl_give isl_pw_qpolynomial *
2907 isl_pw_qpolynomial_from_pw_aff(
2908 __isl_take isl_pw_aff *pwaff);
2910 Piecewise expressions can be copied and freed using the following functions.
2912 #include <isl/aff.h>
2913 __isl_give isl_pw_aff *isl_pw_aff_copy(
2914 __isl_keep isl_pw_aff *pwaff);
2915 __isl_null isl_pw_aff *isl_pw_aff_free(
2916 __isl_take isl_pw_aff *pwaff);
2917 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2918 __isl_keep isl_pw_multi_aff *pma);
2919 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2920 __isl_take isl_pw_multi_aff *pma);
2922 #include <isl/polynomial.h>
2923 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2924 __isl_keep isl_pw_qpolynomial *pwqp);
2925 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2926 __isl_take isl_pw_qpolynomial *pwqp);
2927 __isl_give isl_pw_qpolynomial_fold *
2928 isl_pw_qpolynomial_fold_copy(
2929 __isl_keep isl_pw_qpolynomial_fold *pwf);
2930 __isl_null isl_pw_qpolynomial_fold *
2931 isl_pw_qpolynomial_fold_free(
2932 __isl_take isl_pw_qpolynomial_fold *pwf);
2934 To iterate over the different cells of a piecewise expression,
2935 use the following functions.
2937 #include <isl/aff.h>
2938 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2939 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2940 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2941 int (*fn)(__isl_take isl_set *set,
2942 __isl_take isl_aff *aff,
2943 void *user), void *user);
2944 int isl_pw_multi_aff_foreach_piece(
2945 __isl_keep isl_pw_multi_aff *pma,
2946 int (*fn)(__isl_take isl_set *set,
2947 __isl_take isl_multi_aff *maff,
2948 void *user), void *user);
2950 #include <isl/polynomial.h>
2951 int isl_pw_qpolynomial_foreach_piece(
2952 __isl_keep isl_pw_qpolynomial *pwqp,
2953 int (*fn)(__isl_take isl_set *set,
2954 __isl_take isl_qpolynomial *qp,
2955 void *user), void *user);
2956 int isl_pw_qpolynomial_foreach_lifted_piece(
2957 __isl_keep isl_pw_qpolynomial *pwqp,
2958 int (*fn)(__isl_take isl_set *set,
2959 __isl_take isl_qpolynomial *qp,
2960 void *user), void *user);
2961 int isl_pw_qpolynomial_fold_foreach_piece(
2962 __isl_keep isl_pw_qpolynomial_fold *pwf,
2963 int (*fn)(__isl_take isl_set *set,
2964 __isl_take isl_qpolynomial_fold *fold,
2965 void *user), void *user);
2966 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2967 __isl_keep isl_pw_qpolynomial_fold *pwf,
2968 int (*fn)(__isl_take isl_set *set,
2969 __isl_take isl_qpolynomial_fold *fold,
2970 void *user), void *user);
2972 As usual, the function C<fn> should return C<0> on success
2973 and C<-1> on failure. The difference between
2974 C<isl_pw_qpolynomial_foreach_piece> and
2975 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2976 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2977 compute unique representations for all existentially quantified
2978 variables and then turn these existentially quantified variables
2979 into extra set variables, adapting the associated quasipolynomial
2980 accordingly. This means that the C<set> passed to C<fn>
2981 will not have any existentially quantified variables, but that
2982 the dimensions of the sets may be different for different
2983 invocations of C<fn>.
2984 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2985 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2987 A piecewise expression consisting of the expressions at a given
2988 position of a piecewise multiple expression can be extracted
2989 using the following function.
2991 #include <isl/aff.h>
2992 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2993 __isl_keep isl_pw_multi_aff *pma, int pos);
2995 These expressions can be replaced using the following function.
2997 #include <isl/aff.h>
2998 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2999 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3000 __isl_take isl_pw_aff *pa);
3002 Note that there is a difference between C<isl_multi_pw_aff> and
3003 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3004 affine expressions, while the second is a piecewise sequence
3005 of affine expressions. In particular, each of the piecewise
3006 affine expressions in an C<isl_multi_pw_aff> may have a different
3007 domain, while all multiple expressions associated to a cell
3008 in an C<isl_pw_multi_aff> have the same domain.
3009 It is possible to convert between the two, but when converting
3010 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3011 of the result is the intersection of the domains of the input.
3012 The reverse conversion is exact.
3014 #include <isl/aff.h>
3015 __isl_give isl_pw_multi_aff *
3016 isl_pw_multi_aff_from_multi_pw_aff(
3017 __isl_take isl_multi_pw_aff *mpa);
3018 __isl_give isl_multi_pw_aff *
3019 isl_multi_pw_aff_from_pw_multi_aff(
3020 __isl_take isl_pw_multi_aff *pma);
3022 =head3 Union Expressions
3024 A union expression collects base expressions defined
3025 over different domains. The space of a union expression
3026 is that of the shared parameter space.
3028 The union expression types defined by C<isl>
3029 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3030 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3032 An empty union expression can be created using the following functions.
3034 #include <isl/aff.h>
3035 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3036 __isl_take isl_space *space);
3037 __isl_give isl_union_pw_multi_aff *
3038 isl_union_pw_multi_aff_empty(
3039 __isl_take isl_space *space);
3041 #include <isl/polynomial.h>
3042 __isl_give isl_union_pw_qpolynomial *
3043 isl_union_pw_qpolynomial_zero(
3044 __isl_take isl_space *space);
3046 A union expression containing a single base expression
3047 can be created using the following functions.
3049 #include <isl/aff.h>
3050 __isl_give isl_union_pw_aff *
3051 isl_union_pw_aff_from_pw_aff(
3052 __isl_take isl_pw_aff *pa);
3053 __isl_give isl_union_pw_multi_aff *
3054 isl_union_pw_multi_aff_from_aff(
3055 __isl_take isl_aff *aff);
3056 __isl_give isl_union_pw_multi_aff *
3057 isl_union_pw_multi_aff_from_pw_multi_aff(
3058 __isl_take isl_pw_multi_aff *pma);
3060 #include <isl/polynomial.h>
3061 __isl_give isl_union_pw_qpolynomial *
3062 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3063 __isl_take isl_pw_qpolynomial *pwqp);
3065 The following functions create a base expression on each
3066 of the sets in the union set and collect the results.
3068 #include <isl/aff.h>
3069 __isl_give isl_union_pw_multi_aff *
3070 isl_union_pw_multi_aff_from_union_pw_aff(
3071 __isl_take isl_union_pw_aff *upa);
3072 __isl_give isl_union_pw_aff *
3073 isl_union_pw_multi_aff_get_union_pw_aff(
3074 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3075 __isl_give isl_union_pw_aff *
3076 isl_union_pw_aff_val_on_domain(
3077 __isl_take isl_union_set *domain,
3078 __isl_take isl_val *v);
3079 __isl_give isl_union_pw_multi_aff *
3080 isl_union_pw_multi_aff_multi_val_on_domain(
3081 __isl_take isl_union_set *domain,
3082 __isl_take isl_multi_val *mv);
3084 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3085 expression on a given domain can be created using the following
3088 #include <isl/aff.h>
3089 __isl_give isl_union_pw_aff *
3090 isl_union_pw_aff_aff_on_domain(
3091 __isl_take isl_union_set *domain,
3092 __isl_take isl_aff *aff);
3094 A base expression can be added to a union expression using
3095 the following functions.
3097 #include <isl/aff.h>
3098 __isl_give isl_union_pw_aff *
3099 isl_union_pw_aff_add_pw_aff(
3100 __isl_take isl_union_pw_aff *upa,
3101 __isl_take isl_pw_aff *pa);
3102 __isl_give isl_union_pw_multi_aff *
3103 isl_union_pw_multi_aff_add_pw_multi_aff(
3104 __isl_take isl_union_pw_multi_aff *upma,
3105 __isl_take isl_pw_multi_aff *pma);
3107 #include <isl/polynomial.h>
3108 __isl_give isl_union_pw_qpolynomial *
3109 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3110 __isl_take isl_union_pw_qpolynomial *upwqp,
3111 __isl_take isl_pw_qpolynomial *pwqp);
3113 Union expressions can be copied and freed using
3114 the following functions.
3116 #include <isl/aff.h>
3117 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3118 __isl_keep isl_union_pw_aff *upa);
3119 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3120 __isl_take isl_union_pw_aff *upa);
3121 __isl_give isl_union_pw_multi_aff *
3122 isl_union_pw_multi_aff_copy(
3123 __isl_keep isl_union_pw_multi_aff *upma);
3124 __isl_null isl_union_pw_multi_aff *
3125 isl_union_pw_multi_aff_free(
3126 __isl_take isl_union_pw_multi_aff *upma);
3128 #include <isl/polynomial.h>
3129 __isl_give isl_union_pw_qpolynomial *
3130 isl_union_pw_qpolynomial_copy(
3131 __isl_keep isl_union_pw_qpolynomial *upwqp);
3132 __isl_null isl_union_pw_qpolynomial *
3133 isl_union_pw_qpolynomial_free(
3134 __isl_take isl_union_pw_qpolynomial *upwqp);
3135 __isl_give isl_union_pw_qpolynomial_fold *
3136 isl_union_pw_qpolynomial_fold_copy(
3137 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3138 __isl_null isl_union_pw_qpolynomial_fold *
3139 isl_union_pw_qpolynomial_fold_free(
3140 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3142 To iterate over the base expressions in a union expression,
3143 use the following functions.
3145 #include <isl/aff.h>
3146 int isl_union_pw_aff_n_pw_multi_aff(
3147 __isl_keep isl_union_pw_aff *upa);
3148 int isl_union_pw_aff_foreach_pw_aff(
3149 __isl_keep isl_union_pw_aff *upa,
3150 int (*fn)(__isl_take isl_pw_aff *ma, void *user),
3152 int isl_union_pw_multi_aff_n_pw_multi_aff(
3153 __isl_keep isl_union_pw_multi_aff *upma);
3154 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3155 __isl_keep isl_union_pw_multi_aff *upma,
3156 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3157 void *user), void *user);
3159 #include <isl/polynomial.h>
3160 int isl_union_pw_qplynomial_n_pw_qpolynomial(
3161 __isl_keep isl_union_pw_qpolynomial *upwqp);
3162 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3163 __isl_keep isl_union_pw_qpolynomial *upwqp,
3164 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3165 void *user), void *user);
3166 int isl_union_pw_qplynomial_fold_n_pw_qpolynomial_fold(
3167 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3168 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3169 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3170 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3171 void *user), void *user);
3173 To extract the base expression in a given space from a union, use
3174 the following functions.
3176 #include <isl/aff.h>
3177 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3178 __isl_keep isl_union_pw_aff *upa,
3179 __isl_take isl_space *space);
3180 __isl_give isl_pw_multi_aff *
3181 isl_union_pw_multi_aff_extract_pw_multi_aff(
3182 __isl_keep isl_union_pw_multi_aff *upma,
3183 __isl_take isl_space *space);
3185 #include <isl/polynomial.h>
3186 __isl_give isl_pw_qpolynomial *
3187 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3188 __isl_keep isl_union_pw_qpolynomial *upwqp,
3189 __isl_take isl_space *space);
3191 =head2 Input and Output
3193 For set and relation,
3194 C<isl> supports its own input/output format, which is similar
3195 to the C<Omega> format, but also supports the C<PolyLib> format
3197 For other object types, typically only an C<isl> format is supported.
3199 =head3 C<isl> format
3201 The C<isl> format is similar to that of C<Omega>, but has a different
3202 syntax for describing the parameters and allows for the definition
3203 of an existentially quantified variable as the integer division
3204 of an affine expression.
3205 For example, the set of integers C<i> between C<0> and C<n>
3206 such that C<i % 10 <= 6> can be described as
3208 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3211 A set or relation can have several disjuncts, separated
3212 by the keyword C<or>. Each disjunct is either a conjunction
3213 of constraints or a projection (C<exists>) of a conjunction
3214 of constraints. The constraints are separated by the keyword
3217 =head3 C<PolyLib> format
3219 If the represented set is a union, then the first line
3220 contains a single number representing the number of disjuncts.
3221 Otherwise, a line containing the number C<1> is optional.
3223 Each disjunct is represented by a matrix of constraints.
3224 The first line contains two numbers representing
3225 the number of rows and columns,
3226 where the number of rows is equal to the number of constraints
3227 and the number of columns is equal to two plus the number of variables.
3228 The following lines contain the actual rows of the constraint matrix.
3229 In each row, the first column indicates whether the constraint
3230 is an equality (C<0>) or inequality (C<1>). The final column
3231 corresponds to the constant term.
3233 If the set is parametric, then the coefficients of the parameters
3234 appear in the last columns before the constant column.
3235 The coefficients of any existentially quantified variables appear
3236 between those of the set variables and those of the parameters.
3238 =head3 Extended C<PolyLib> format
3240 The extended C<PolyLib> format is nearly identical to the
3241 C<PolyLib> format. The only difference is that the line
3242 containing the number of rows and columns of a constraint matrix
3243 also contains four additional numbers:
3244 the number of output dimensions, the number of input dimensions,
3245 the number of local dimensions (i.e., the number of existentially
3246 quantified variables) and the number of parameters.
3247 For sets, the number of ``output'' dimensions is equal
3248 to the number of set dimensions, while the number of ``input''
3253 Objects can be read from input using the following functions.
3255 #include <isl/val.h>
3256 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3258 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3259 isl_ctx *ctx, const char *str);
3261 #include <isl/set.h>
3262 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3263 isl_ctx *ctx, FILE *input);
3264 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3265 isl_ctx *ctx, const char *str);
3266 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3268 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3271 #include <isl/map.h>
3272 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3273 isl_ctx *ctx, FILE *input);
3274 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3275 isl_ctx *ctx, const char *str);
3276 __isl_give isl_map *isl_map_read_from_file(
3277 isl_ctx *ctx, FILE *input);
3278 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3281 #include <isl/union_set.h>
3282 __isl_give isl_union_set *isl_union_set_read_from_file(
3283 isl_ctx *ctx, FILE *input);
3284 __isl_give isl_union_set *isl_union_set_read_from_str(
3285 isl_ctx *ctx, const char *str);
3287 #include <isl/union_map.h>
3288 __isl_give isl_union_map *isl_union_map_read_from_file(
3289 isl_ctx *ctx, FILE *input);
3290 __isl_give isl_union_map *isl_union_map_read_from_str(
3291 isl_ctx *ctx, const char *str);
3293 #include <isl/aff.h>
3294 __isl_give isl_aff *isl_aff_read_from_str(
3295 isl_ctx *ctx, const char *str);
3296 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3297 isl_ctx *ctx, const char *str);
3298 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3299 isl_ctx *ctx, const char *str);
3300 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3301 isl_ctx *ctx, const char *str);
3302 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3303 isl_ctx *ctx, const char *str);
3304 __isl_give isl_union_pw_multi_aff *
3305 isl_union_pw_multi_aff_read_from_str(
3306 isl_ctx *ctx, const char *str);
3307 __isl_give isl_multi_union_pw_aff *
3308 isl_multi_union_pw_aff_read_from_str(
3309 isl_ctx *ctx, const char *str);
3311 #include <isl/polynomial.h>
3312 __isl_give isl_union_pw_qpolynomial *
3313 isl_union_pw_qpolynomial_read_from_str(
3314 isl_ctx *ctx, const char *str);
3316 For sets and relations,
3317 the input format is autodetected and may be either the C<PolyLib> format
3318 or the C<isl> format.
3322 Before anything can be printed, an C<isl_printer> needs to
3325 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3327 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3328 __isl_null isl_printer *isl_printer_free(
3329 __isl_take isl_printer *printer);
3330 __isl_give char *isl_printer_get_str(
3331 __isl_keep isl_printer *printer);
3333 The printer can be inspected using the following functions.
3335 FILE *isl_printer_get_file(
3336 __isl_keep isl_printer *printer);
3337 int isl_printer_get_output_format(
3338 __isl_keep isl_printer *p);
3340 The behavior of the printer can be modified in various ways
3342 __isl_give isl_printer *isl_printer_set_output_format(
3343 __isl_take isl_printer *p, int output_format);
3344 __isl_give isl_printer *isl_printer_set_indent(
3345 __isl_take isl_printer *p, int indent);
3346 __isl_give isl_printer *isl_printer_set_indent_prefix(
3347 __isl_take isl_printer *p, const char *prefix);
3348 __isl_give isl_printer *isl_printer_indent(
3349 __isl_take isl_printer *p, int indent);
3350 __isl_give isl_printer *isl_printer_set_prefix(
3351 __isl_take isl_printer *p, const char *prefix);
3352 __isl_give isl_printer *isl_printer_set_suffix(
3353 __isl_take isl_printer *p, const char *suffix);
3355 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3356 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3357 and defaults to C<ISL_FORMAT_ISL>.
3358 Each line in the output is prefixed by C<indent_prefix>,
3359 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3360 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3361 In the C<PolyLib> format output,
3362 the coefficients of the existentially quantified variables
3363 appear between those of the set variables and those
3365 The function C<isl_printer_indent> increases the indentation
3366 by the specified amount (which may be negative).
3368 To actually print something, use
3370 #include <isl/printer.h>
3371 __isl_give isl_printer *isl_printer_print_double(
3372 __isl_take isl_printer *p, double d);
3374 #include <isl/val.h>
3375 __isl_give isl_printer *isl_printer_print_val(
3376 __isl_take isl_printer *p, __isl_keep isl_val *v);
3378 #include <isl/set.h>
3379 __isl_give isl_printer *isl_printer_print_basic_set(
3380 __isl_take isl_printer *printer,
3381 __isl_keep isl_basic_set *bset);
3382 __isl_give isl_printer *isl_printer_print_set(
3383 __isl_take isl_printer *printer,
3384 __isl_keep isl_set *set);
3386 #include <isl/map.h>
3387 __isl_give isl_printer *isl_printer_print_basic_map(
3388 __isl_take isl_printer *printer,
3389 __isl_keep isl_basic_map *bmap);
3390 __isl_give isl_printer *isl_printer_print_map(
3391 __isl_take isl_printer *printer,
3392 __isl_keep isl_map *map);
3394 #include <isl/union_set.h>
3395 __isl_give isl_printer *isl_printer_print_union_set(
3396 __isl_take isl_printer *p,
3397 __isl_keep isl_union_set *uset);
3399 #include <isl/union_map.h>
3400 __isl_give isl_printer *isl_printer_print_union_map(
3401 __isl_take isl_printer *p,
3402 __isl_keep isl_union_map *umap);
3404 #include <isl/val.h>
3405 __isl_give isl_printer *isl_printer_print_multi_val(
3406 __isl_take isl_printer *p,
3407 __isl_keep isl_multi_val *mv);
3409 #include <isl/aff.h>
3410 __isl_give isl_printer *isl_printer_print_aff(
3411 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3412 __isl_give isl_printer *isl_printer_print_multi_aff(
3413 __isl_take isl_printer *p,
3414 __isl_keep isl_multi_aff *maff);
3415 __isl_give isl_printer *isl_printer_print_pw_aff(
3416 __isl_take isl_printer *p,
3417 __isl_keep isl_pw_aff *pwaff);
3418 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3419 __isl_take isl_printer *p,
3420 __isl_keep isl_pw_multi_aff *pma);
3421 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3422 __isl_take isl_printer *p,
3423 __isl_keep isl_multi_pw_aff *mpa);
3424 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3425 __isl_take isl_printer *p,
3426 __isl_keep isl_union_pw_aff *upa);
3427 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3428 __isl_take isl_printer *p,
3429 __isl_keep isl_union_pw_multi_aff *upma);
3430 __isl_give isl_printer *
3431 isl_printer_print_multi_union_pw_aff(
3432 __isl_take isl_printer *p,
3433 __isl_keep isl_multi_union_pw_aff *mupa);
3435 #include <isl/polynomial.h>
3436 __isl_give isl_printer *isl_printer_print_qpolynomial(
3437 __isl_take isl_printer *p,
3438 __isl_keep isl_qpolynomial *qp);
3439 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3440 __isl_take isl_printer *p,
3441 __isl_keep isl_pw_qpolynomial *pwqp);
3442 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3443 __isl_take isl_printer *p,
3444 __isl_keep isl_union_pw_qpolynomial *upwqp);
3446 __isl_give isl_printer *
3447 isl_printer_print_pw_qpolynomial_fold(
3448 __isl_take isl_printer *p,
3449 __isl_keep isl_pw_qpolynomial_fold *pwf);
3450 __isl_give isl_printer *
3451 isl_printer_print_union_pw_qpolynomial_fold(
3452 __isl_take isl_printer *p,
3453 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3455 For C<isl_printer_print_qpolynomial>,
3456 C<isl_printer_print_pw_qpolynomial> and
3457 C<isl_printer_print_pw_qpolynomial_fold>,
3458 the output format of the printer
3459 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3460 For C<isl_printer_print_union_pw_qpolynomial> and
3461 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3463 In case of printing in C<ISL_FORMAT_C>, the user may want
3464 to set the names of all dimensions first.
3466 When called on a file printer, the following function flushes
3467 the file. When called on a string printer, the buffer is cleared.
3469 __isl_give isl_printer *isl_printer_flush(
3470 __isl_take isl_printer *p);
3472 Alternatively, a string representation can be obtained
3473 directly using the following functions, which always print
3476 #include <isl/space.h>
3477 __isl_give char *isl_space_to_str(
3478 __isl_keep isl_space *space);
3480 #include <isl/val.h>
3481 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3482 __isl_give char *isl_multi_val_to_str(
3483 __isl_keep isl_multi_val *mv);
3485 #include <isl/set.h>
3486 __isl_give char *isl_set_to_str(
3487 __isl_keep isl_set *set);
3489 #include <isl/union_set.h>
3490 __isl_give char *isl_union_set_to_str(
3491 __isl_keep isl_union_set *uset);
3493 #include <isl/map.h>
3494 __isl_give char *isl_map_to_str(
3495 __isl_keep isl_map *map);
3497 #include <isl/union_map.h>
3498 __isl_give char *isl_union_map_to_str(
3499 __isl_keep isl_union_map *umap);
3501 #include <isl/aff.h>
3502 __isl_give char *isl_multi_aff_to_str(
3503 __isl_keep isl_multi_aff *aff);
3504 __isl_give char *isl_union_pw_aff_to_str(
3505 __isl_keep isl_union_pw_aff *upa);
3506 __isl_give char *isl_union_pw_multi_aff_to_str(
3507 __isl_keep isl_union_pw_multi_aff *upma);
3508 __isl_give char *isl_multi_union_pw_aff_to_str(
3509 __isl_keep isl_multi_union_pw_aff *mupa);
3513 =head3 Unary Properties
3519 The following functions test whether the given set or relation
3520 contains any integer points. The ``plain'' variants do not perform
3521 any computations, but simply check if the given set or relation
3522 is already known to be empty.
3524 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3525 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3526 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3527 int isl_set_is_empty(__isl_keep isl_set *set);
3528 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3529 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3530 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3531 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3532 int isl_map_is_empty(__isl_keep isl_map *map);
3533 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3535 =item * Universality
3537 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3538 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3539 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3541 =item * Single-valuedness
3543 #include <isl/set.h>
3544 int isl_set_is_singleton(__isl_keep isl_set *set);
3546 #include <isl/map.h>
3547 int isl_basic_map_is_single_valued(
3548 __isl_keep isl_basic_map *bmap);
3549 int isl_map_plain_is_single_valued(
3550 __isl_keep isl_map *map);
3551 int isl_map_is_single_valued(__isl_keep isl_map *map);
3553 #include <isl/union_map.h>
3554 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3558 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3559 int isl_map_is_injective(__isl_keep isl_map *map);
3560 int isl_union_map_plain_is_injective(
3561 __isl_keep isl_union_map *umap);
3562 int isl_union_map_is_injective(
3563 __isl_keep isl_union_map *umap);
3567 int isl_map_is_bijective(__isl_keep isl_map *map);
3568 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3572 __isl_give isl_val *
3573 isl_basic_map_plain_get_val_if_fixed(
3574 __isl_keep isl_basic_map *bmap,
3575 enum isl_dim_type type, unsigned pos);
3576 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3577 __isl_keep isl_set *set,
3578 enum isl_dim_type type, unsigned pos);
3579 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3580 __isl_keep isl_map *map,
3581 enum isl_dim_type type, unsigned pos);
3583 If the set or relation obviously lies on a hyperplane where the given dimension
3584 has a fixed value, then return that value.
3585 Otherwise return NaN.
3589 int isl_set_dim_residue_class_val(
3590 __isl_keep isl_set *set,
3591 int pos, __isl_give isl_val **modulo,
3592 __isl_give isl_val **residue);
3594 Check if the values of the given set dimension are equal to a fixed
3595 value modulo some integer value. If so, assign the modulo to C<*modulo>
3596 and the fixed value to C<*residue>. If the given dimension attains only
3597 a single value, then assign C<0> to C<*modulo> and the fixed value to
3599 If the dimension does not attain only a single value and if no modulo
3600 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3604 To check whether the description of a set, relation or function depends
3605 on one or more given dimensions,
3606 the following functions can be used.
3608 #include <isl/constraint.h>
3609 int isl_constraint_involves_dims(
3610 __isl_keep isl_constraint *constraint,
3611 enum isl_dim_type type, unsigned first, unsigned n);
3613 #include <isl/set.h>
3614 int isl_basic_set_involves_dims(
3615 __isl_keep isl_basic_set *bset,
3616 enum isl_dim_type type, unsigned first, unsigned n);
3617 int isl_set_involves_dims(__isl_keep isl_set *set,
3618 enum isl_dim_type type, unsigned first, unsigned n);
3620 #include <isl/map.h>
3621 int isl_basic_map_involves_dims(
3622 __isl_keep isl_basic_map *bmap,
3623 enum isl_dim_type type, unsigned first, unsigned n);
3624 int isl_map_involves_dims(__isl_keep isl_map *map,
3625 enum isl_dim_type type, unsigned first, unsigned n);
3627 #include <isl/union_map.h>
3628 int isl_union_map_involves_dims(
3629 __isl_keep isl_union_map *umap,
3630 enum isl_dim_type type, unsigned first, unsigned n);
3632 #include <isl/aff.h>
3633 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3634 enum isl_dim_type type, unsigned first, unsigned n);
3635 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3636 enum isl_dim_type type, unsigned first, unsigned n);
3637 int isl_multi_aff_involves_dims(
3638 __isl_keep isl_multi_aff *ma,
3639 enum isl_dim_type type, unsigned first, unsigned n);
3640 int isl_multi_pw_aff_involves_dims(
3641 __isl_keep isl_multi_pw_aff *mpa,
3642 enum isl_dim_type type, unsigned first, unsigned n);
3644 Similarly, the following functions can be used to check whether
3645 a given dimension is involved in any lower or upper bound.
3647 #include <isl/set.h>
3648 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3649 enum isl_dim_type type, unsigned pos);
3650 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3651 enum isl_dim_type type, unsigned pos);
3653 Note that these functions return true even if there is a bound on
3654 the dimension on only some of the basic sets of C<set>.
3655 To check if they have a bound for all of the basic sets in C<set>,
3656 use the following functions instead.
3658 #include <isl/set.h>
3659 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3660 enum isl_dim_type type, unsigned pos);
3661 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3662 enum isl_dim_type type, unsigned pos);
3666 To check whether a set is a parameter domain, use this function:
3668 int isl_set_is_params(__isl_keep isl_set *set);
3669 int isl_union_set_is_params(
3670 __isl_keep isl_union_set *uset);
3674 The following functions check whether the space of the given
3675 (basic) set or relation range is a wrapped relation.
3677 #include <isl/space.h>
3678 int isl_space_is_wrapping(
3679 __isl_keep isl_space *space);
3680 int isl_space_domain_is_wrapping(
3681 __isl_keep isl_space *space);
3682 int isl_space_range_is_wrapping(
3683 __isl_keep isl_space *space);
3685 #include <isl/set.h>
3686 int isl_basic_set_is_wrapping(
3687 __isl_keep isl_basic_set *bset);
3688 int isl_set_is_wrapping(__isl_keep isl_set *set);
3690 #include <isl/map.h>
3691 int isl_map_domain_is_wrapping(
3692 __isl_keep isl_map *map);
3693 int isl_map_range_is_wrapping(
3694 __isl_keep isl_map *map);
3696 #include <isl/val.h>
3697 int isl_multi_val_range_is_wrapping(
3698 __isl_keep isl_multi_val *mv);
3700 #include <isl/aff.h>
3701 int isl_multi_aff_range_is_wrapping(
3702 __isl_keep isl_multi_aff *ma);
3703 int isl_multi_pw_aff_range_is_wrapping(
3704 __isl_keep isl_multi_pw_aff *mpa);
3705 int isl_multi_union_pw_aff_range_is_wrapping(
3706 __isl_keep isl_multi_union_pw_aff *mupa);
3708 The input to C<isl_space_is_wrapping> should
3709 be the space of a set, while that of
3710 C<isl_space_domain_is_wrapping> and
3711 C<isl_space_range_is_wrapping> should be the space of a relation.
3713 =item * Internal Product
3715 int isl_basic_map_can_zip(
3716 __isl_keep isl_basic_map *bmap);
3717 int isl_map_can_zip(__isl_keep isl_map *map);
3719 Check whether the product of domain and range of the given relation
3721 i.e., whether both domain and range are nested relations.
3725 int isl_basic_map_can_curry(
3726 __isl_keep isl_basic_map *bmap);
3727 int isl_map_can_curry(__isl_keep isl_map *map);
3729 Check whether the domain of the (basic) relation is a wrapped relation.
3731 int isl_basic_map_can_uncurry(
3732 __isl_keep isl_basic_map *bmap);
3733 int isl_map_can_uncurry(__isl_keep isl_map *map);
3735 Check whether the range of the (basic) relation is a wrapped relation.
3737 =item * Special Values
3739 #include <isl/aff.h>
3740 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3741 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3743 Check whether the given expression is a constant.
3745 #include <isl/aff.h>
3746 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3747 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3749 Check whether the given expression is equal to or involves NaN.
3751 #include <isl/aff.h>
3752 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3754 Check whether the affine expression is obviously zero.
3758 =head3 Binary Properties
3764 The following functions check whether two objects
3765 represent the same set, relation or function.
3766 The C<plain> variants only return true if the objects
3767 are obviously the same. That is, they may return false
3768 even if the objects are the same, but they will never
3769 return true if the objects are not the same.
3771 #include <isl/set.h>
3772 int isl_basic_set_plain_is_equal(
3773 __isl_keep isl_basic_set *bset1,
3774 __isl_keep isl_basic_set *bset2);
3775 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3776 __isl_keep isl_set *set2);
3777 int isl_set_is_equal(__isl_keep isl_set *set1,
3778 __isl_keep isl_set *set2);
3780 #include <isl/map.h>
3781 int isl_basic_map_is_equal(
3782 __isl_keep isl_basic_map *bmap1,
3783 __isl_keep isl_basic_map *bmap2);
3784 int isl_map_is_equal(__isl_keep isl_map *map1,
3785 __isl_keep isl_map *map2);
3786 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3787 __isl_keep isl_map *map2);
3789 #include <isl/union_set.h>
3790 int isl_union_set_is_equal(
3791 __isl_keep isl_union_set *uset1,
3792 __isl_keep isl_union_set *uset2);
3794 #include <isl/union_map.h>
3795 int isl_union_map_is_equal(
3796 __isl_keep isl_union_map *umap1,
3797 __isl_keep isl_union_map *umap2);
3799 #include <isl/aff.h>
3800 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3801 __isl_keep isl_aff *aff2);
3802 int isl_multi_aff_plain_is_equal(
3803 __isl_keep isl_multi_aff *maff1,
3804 __isl_keep isl_multi_aff *maff2);
3805 int isl_pw_aff_plain_is_equal(
3806 __isl_keep isl_pw_aff *pwaff1,
3807 __isl_keep isl_pw_aff *pwaff2);
3808 int isl_pw_multi_aff_plain_is_equal(
3809 __isl_keep isl_pw_multi_aff *pma1,
3810 __isl_keep isl_pw_multi_aff *pma2);
3811 int isl_multi_pw_aff_plain_is_equal(
3812 __isl_keep isl_multi_pw_aff *mpa1,
3813 __isl_keep isl_multi_pw_aff *mpa2);
3814 int isl_multi_pw_aff_is_equal(
3815 __isl_keep isl_multi_pw_aff *mpa1,
3816 __isl_keep isl_multi_pw_aff *mpa2);
3817 int isl_union_pw_aff_plain_is_equal(
3818 __isl_keep isl_union_pw_aff *upa1,
3819 __isl_keep isl_union_pw_aff *upa2);
3820 int isl_union_pw_multi_aff_plain_is_equal(
3821 __isl_keep isl_union_pw_multi_aff *upma1,
3822 __isl_keep isl_union_pw_multi_aff *upma2);
3823 int isl_multi_union_pw_aff_plain_is_equal(
3824 __isl_keep isl_multi_union_pw_aff *mupa1,
3825 __isl_keep isl_multi_union_pw_aff *mupa2);
3827 #include <isl/polynomial.h>
3828 int isl_union_pw_qpolynomial_plain_is_equal(
3829 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3830 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3831 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3832 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3833 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3835 =item * Disjointness
3837 #include <isl/set.h>
3838 int isl_basic_set_is_disjoint(
3839 __isl_keep isl_basic_set *bset1,
3840 __isl_keep isl_basic_set *bset2);
3841 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3842 __isl_keep isl_set *set2);
3843 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3844 __isl_keep isl_set *set2);
3846 #include <isl/map.h>
3847 int isl_basic_map_is_disjoint(
3848 __isl_keep isl_basic_map *bmap1,
3849 __isl_keep isl_basic_map *bmap2);
3850 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3851 __isl_keep isl_map *map2);
3853 #include <isl/union_set.h>
3854 int isl_union_set_is_disjoint(
3855 __isl_keep isl_union_set *uset1,
3856 __isl_keep isl_union_set *uset2);
3858 #include <isl/union_map.h>
3859 int isl_union_map_is_disjoint(
3860 __isl_keep isl_union_map *umap1,
3861 __isl_keep isl_union_map *umap2);
3865 int isl_basic_set_is_subset(
3866 __isl_keep isl_basic_set *bset1,
3867 __isl_keep isl_basic_set *bset2);
3868 int isl_set_is_subset(__isl_keep isl_set *set1,
3869 __isl_keep isl_set *set2);
3870 int isl_set_is_strict_subset(
3871 __isl_keep isl_set *set1,
3872 __isl_keep isl_set *set2);
3873 int isl_union_set_is_subset(
3874 __isl_keep isl_union_set *uset1,
3875 __isl_keep isl_union_set *uset2);
3876 int isl_union_set_is_strict_subset(
3877 __isl_keep isl_union_set *uset1,
3878 __isl_keep isl_union_set *uset2);
3879 int isl_basic_map_is_subset(
3880 __isl_keep isl_basic_map *bmap1,
3881 __isl_keep isl_basic_map *bmap2);
3882 int isl_basic_map_is_strict_subset(
3883 __isl_keep isl_basic_map *bmap1,
3884 __isl_keep isl_basic_map *bmap2);
3885 int isl_map_is_subset(
3886 __isl_keep isl_map *map1,
3887 __isl_keep isl_map *map2);
3888 int isl_map_is_strict_subset(
3889 __isl_keep isl_map *map1,
3890 __isl_keep isl_map *map2);
3891 int isl_union_map_is_subset(
3892 __isl_keep isl_union_map *umap1,
3893 __isl_keep isl_union_map *umap2);
3894 int isl_union_map_is_strict_subset(
3895 __isl_keep isl_union_map *umap1,
3896 __isl_keep isl_union_map *umap2);
3898 Check whether the first argument is a (strict) subset of the
3903 Every comparison function returns a negative value if the first
3904 argument is considered smaller than the second, a positive value
3905 if the first argument is considered greater and zero if the two
3906 constraints are considered the same by the comparison criterion.
3908 #include <isl/constraint.h>
3909 int isl_constraint_plain_cmp(
3910 __isl_keep isl_constraint *c1,
3911 __isl_keep isl_constraint *c2);
3913 This function is useful for sorting C<isl_constraint>s.
3914 The order depends on the internal representation of the inputs.
3915 The order is fixed over different calls to the function (assuming
3916 the internal representation of the inputs has not changed), but may
3917 change over different versions of C<isl>.
3919 #include <isl/constraint.h>
3920 int isl_constraint_cmp_last_non_zero(
3921 __isl_keep isl_constraint *c1,
3922 __isl_keep isl_constraint *c2);
3924 This function can be used to sort constraints that live in the same
3925 local space. Constraints that involve ``earlier'' dimensions or
3926 that have a smaller coefficient for the shared latest dimension
3927 are considered smaller than other constraints.
3928 This function only defines a B<partial> order.
3930 #include <isl/set.h>
3931 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3932 __isl_keep isl_set *set2);
3934 This function is useful for sorting C<isl_set>s.
3935 The order depends on the internal representation of the inputs.
3936 The order is fixed over different calls to the function (assuming
3937 the internal representation of the inputs has not changed), but may
3938 change over different versions of C<isl>.
3940 #include <isl/aff.h>
3941 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3942 __isl_keep isl_pw_aff *pa2);
3944 The function C<isl_pw_aff_plain_cmp> can be used to sort
3945 C<isl_pw_aff>s. The order is not strictly defined.
3946 The current order sorts expressions that only involve
3947 earlier dimensions before those that involve later dimensions.
3951 =head2 Unary Operations
3957 __isl_give isl_set *isl_set_complement(
3958 __isl_take isl_set *set);
3959 __isl_give isl_map *isl_map_complement(
3960 __isl_take isl_map *map);
3964 #include <isl/space.h>
3965 __isl_give isl_space *isl_space_reverse(
3966 __isl_take isl_space *space);
3968 #include <isl/map.h>
3969 __isl_give isl_basic_map *isl_basic_map_reverse(
3970 __isl_take isl_basic_map *bmap);
3971 __isl_give isl_map *isl_map_reverse(
3972 __isl_take isl_map *map);
3974 #include <isl/union_map.h>
3975 __isl_give isl_union_map *isl_union_map_reverse(
3976 __isl_take isl_union_map *umap);
3980 #include <isl/space.h>
3981 __isl_give isl_space *isl_space_domain(
3982 __isl_take isl_space *space);
3983 __isl_give isl_space *isl_space_range(
3984 __isl_take isl_space *space);
3985 __isl_give isl_space *isl_space_params(
3986 __isl_take isl_space *space);
3988 #include <isl/local_space.h>
3989 __isl_give isl_local_space *isl_local_space_domain(
3990 __isl_take isl_local_space *ls);
3991 __isl_give isl_local_space *isl_local_space_range(
3992 __isl_take isl_local_space *ls);
3994 #include <isl/set.h>
3995 __isl_give isl_basic_set *isl_basic_set_project_out(
3996 __isl_take isl_basic_set *bset,
3997 enum isl_dim_type type, unsigned first, unsigned n);
3998 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3999 enum isl_dim_type type, unsigned first, unsigned n);
4000 __isl_give isl_basic_set *isl_basic_set_params(
4001 __isl_take isl_basic_set *bset);
4002 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4004 #include <isl/map.h>
4005 __isl_give isl_basic_map *isl_basic_map_project_out(
4006 __isl_take isl_basic_map *bmap,
4007 enum isl_dim_type type, unsigned first, unsigned n);
4008 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4009 enum isl_dim_type type, unsigned first, unsigned n);
4010 __isl_give isl_basic_set *isl_basic_map_domain(
4011 __isl_take isl_basic_map *bmap);
4012 __isl_give isl_basic_set *isl_basic_map_range(
4013 __isl_take isl_basic_map *bmap);
4014 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4015 __isl_give isl_set *isl_map_domain(
4016 __isl_take isl_map *bmap);
4017 __isl_give isl_set *isl_map_range(
4018 __isl_take isl_map *map);
4020 #include <isl/union_set.h>
4021 __isl_give isl_union_set *isl_union_set_project_out(
4022 __isl_take isl_union_set *uset,
4023 enum isl_dim_type type,
4024 unsigned first, unsigned n);
4025 __isl_give isl_set *isl_union_set_params(
4026 __isl_take isl_union_set *uset);
4028 The function C<isl_union_set_project_out> can only project out
4031 #include <isl/union_map.h>
4032 __isl_give isl_union_map *isl_union_map_project_out(
4033 __isl_take isl_union_map *umap,
4034 enum isl_dim_type type, unsigned first, unsigned n);
4035 __isl_give isl_set *isl_union_map_params(
4036 __isl_take isl_union_map *umap);
4037 __isl_give isl_union_set *isl_union_map_domain(
4038 __isl_take isl_union_map *umap);
4039 __isl_give isl_union_set *isl_union_map_range(
4040 __isl_take isl_union_map *umap);
4042 The function C<isl_union_map_project_out> can only project out
4045 #include <isl/aff.h>
4046 __isl_give isl_aff *isl_aff_project_domain_on_params(
4047 __isl_take isl_aff *aff);
4048 __isl_give isl_pw_multi_aff *
4049 isl_pw_multi_aff_project_domain_on_params(
4050 __isl_take isl_pw_multi_aff *pma);
4051 __isl_give isl_set *isl_pw_aff_domain(
4052 __isl_take isl_pw_aff *pwaff);
4053 __isl_give isl_set *isl_pw_multi_aff_domain(
4054 __isl_take isl_pw_multi_aff *pma);
4055 __isl_give isl_set *isl_multi_pw_aff_domain(
4056 __isl_take isl_multi_pw_aff *mpa);
4057 __isl_give isl_union_set *isl_union_pw_aff_domain(
4058 __isl_take isl_union_pw_aff *upa);
4059 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4060 __isl_take isl_union_pw_multi_aff *upma);
4061 __isl_give isl_union_set *
4062 isl_multi_union_pw_aff_domain(
4063 __isl_take isl_multi_union_pw_aff *mupa);
4064 __isl_give isl_set *isl_pw_aff_params(
4065 __isl_take isl_pw_aff *pwa);
4067 The function C<isl_multi_union_pw_aff_domain> requires its
4068 input to have at least one set dimension.
4070 #include <isl/polynomial.h>
4071 __isl_give isl_qpolynomial *
4072 isl_qpolynomial_project_domain_on_params(
4073 __isl_take isl_qpolynomial *qp);
4074 __isl_give isl_pw_qpolynomial *
4075 isl_pw_qpolynomial_project_domain_on_params(
4076 __isl_take isl_pw_qpolynomial *pwqp);
4077 __isl_give isl_pw_qpolynomial_fold *
4078 isl_pw_qpolynomial_fold_project_domain_on_params(
4079 __isl_take isl_pw_qpolynomial_fold *pwf);
4080 __isl_give isl_set *isl_pw_qpolynomial_domain(
4081 __isl_take isl_pw_qpolynomial *pwqp);
4082 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4083 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4084 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4085 __isl_take isl_union_pw_qpolynomial *upwqp);
4087 #include <isl/space.h>
4088 __isl_give isl_space *isl_space_domain_map(
4089 __isl_take isl_space *space);
4090 __isl_give isl_space *isl_space_range_map(
4091 __isl_take isl_space *space);
4093 #include <isl/map.h>
4094 __isl_give isl_map *isl_set_wrapped_domain_map(
4095 __isl_take isl_set *set);
4096 __isl_give isl_basic_map *isl_basic_map_domain_map(
4097 __isl_take isl_basic_map *bmap);
4098 __isl_give isl_basic_map *isl_basic_map_range_map(
4099 __isl_take isl_basic_map *bmap);
4100 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4101 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4103 #include <isl/union_map.h>
4104 __isl_give isl_union_map *isl_union_map_domain_map(
4105 __isl_take isl_union_map *umap);
4106 __isl_give isl_union_pw_multi_aff *
4107 isl_union_map_domain_map_union_pw_multi_aff(
4108 __isl_take isl_union_map *umap);
4109 __isl_give isl_union_map *isl_union_map_range_map(
4110 __isl_take isl_union_map *umap);
4111 __isl_give isl_union_map *
4112 isl_union_set_wrapped_domain_map(
4113 __isl_take isl_union_set *uset);
4115 The functions above construct a (basic, regular or union) relation
4116 that maps (a wrapped version of) the input relation to its domain or range.
4117 C<isl_set_wrapped_domain_map> maps the input set to the domain
4118 of its wrapped relation.
4122 __isl_give isl_basic_set *isl_basic_set_eliminate(
4123 __isl_take isl_basic_set *bset,
4124 enum isl_dim_type type,
4125 unsigned first, unsigned n);
4126 __isl_give isl_set *isl_set_eliminate(
4127 __isl_take isl_set *set, enum isl_dim_type type,
4128 unsigned first, unsigned n);
4129 __isl_give isl_basic_map *isl_basic_map_eliminate(
4130 __isl_take isl_basic_map *bmap,
4131 enum isl_dim_type type,
4132 unsigned first, unsigned n);
4133 __isl_give isl_map *isl_map_eliminate(
4134 __isl_take isl_map *map, enum isl_dim_type type,
4135 unsigned first, unsigned n);
4137 Eliminate the coefficients for the given dimensions from the constraints,
4138 without removing the dimensions.
4140 =item * Constructing a set from a parameter domain
4142 A zero-dimensional space or (basic) set can be constructed
4143 on a given parameter domain using the following functions.
4145 #include <isl/space.h>
4146 __isl_give isl_space *isl_space_set_from_params(
4147 __isl_take isl_space *space);
4149 #include <isl/set.h>
4150 __isl_give isl_basic_set *isl_basic_set_from_params(
4151 __isl_take isl_basic_set *bset);
4152 __isl_give isl_set *isl_set_from_params(
4153 __isl_take isl_set *set);
4155 =item * Constructing a relation from a set
4157 Create a relation with the given set as domain or range.
4158 The range or domain of the created relation is a zero-dimensional
4159 flat anonymous space.
4161 #include <isl/space.h>
4162 __isl_give isl_space *isl_space_from_domain(
4163 __isl_take isl_space *space);
4164 __isl_give isl_space *isl_space_from_range(
4165 __isl_take isl_space *space);
4166 __isl_give isl_space *isl_space_map_from_set(
4167 __isl_take isl_space *space);
4168 __isl_give isl_space *isl_space_map_from_domain_and_range(
4169 __isl_take isl_space *domain,
4170 __isl_take isl_space *range);
4172 #include <isl/local_space.h>
4173 __isl_give isl_local_space *isl_local_space_from_domain(
4174 __isl_take isl_local_space *ls);
4176 #include <isl/map.h>
4177 __isl_give isl_map *isl_map_from_domain(
4178 __isl_take isl_set *set);
4179 __isl_give isl_map *isl_map_from_range(
4180 __isl_take isl_set *set);
4182 #include <isl/val.h>
4183 __isl_give isl_multi_val *isl_multi_val_from_range(
4184 __isl_take isl_multi_val *mv);
4186 #include <isl/aff.h>
4187 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4188 __isl_take isl_multi_aff *ma);
4189 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4190 __isl_take isl_pw_aff *pwa);
4191 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4192 __isl_take isl_multi_pw_aff *mpa);
4193 __isl_give isl_multi_union_pw_aff *
4194 isl_multi_union_pw_aff_from_range(
4195 __isl_take isl_multi_union_pw_aff *mupa);
4196 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4197 __isl_take isl_set *set);
4198 __isl_give isl_union_pw_multi_aff *
4199 isl_union_pw_multi_aff_from_domain(
4200 __isl_take isl_union_set *uset);
4204 #include <isl/set.h>
4205 __isl_give isl_basic_set *isl_basic_set_fix_si(
4206 __isl_take isl_basic_set *bset,
4207 enum isl_dim_type type, unsigned pos, int value);
4208 __isl_give isl_basic_set *isl_basic_set_fix_val(
4209 __isl_take isl_basic_set *bset,
4210 enum isl_dim_type type, unsigned pos,
4211 __isl_take isl_val *v);
4212 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4213 enum isl_dim_type type, unsigned pos, int value);
4214 __isl_give isl_set *isl_set_fix_val(
4215 __isl_take isl_set *set,
4216 enum isl_dim_type type, unsigned pos,
4217 __isl_take isl_val *v);
4219 #include <isl/map.h>
4220 __isl_give isl_basic_map *isl_basic_map_fix_si(
4221 __isl_take isl_basic_map *bmap,
4222 enum isl_dim_type type, unsigned pos, int value);
4223 __isl_give isl_basic_map *isl_basic_map_fix_val(
4224 __isl_take isl_basic_map *bmap,
4225 enum isl_dim_type type, unsigned pos,
4226 __isl_take isl_val *v);
4227 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4228 enum isl_dim_type type, unsigned pos, int value);
4229 __isl_give isl_map *isl_map_fix_val(
4230 __isl_take isl_map *map,
4231 enum isl_dim_type type, unsigned pos,
4232 __isl_take isl_val *v);
4234 #include <isl/aff.h>
4235 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4236 __isl_take isl_pw_multi_aff *pma,
4237 enum isl_dim_type type, unsigned pos, int value);
4239 #include <isl/polynomial.h>
4240 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4241 __isl_take isl_pw_qpolynomial *pwqp,
4242 enum isl_dim_type type, unsigned n,
4243 __isl_take isl_val *v);
4245 Intersect the set, relation or function domain
4246 with the hyperplane where the given
4247 dimension has the fixed given value.
4249 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4250 __isl_take isl_basic_map *bmap,
4251 enum isl_dim_type type, unsigned pos, int value);
4252 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4253 __isl_take isl_basic_map *bmap,
4254 enum isl_dim_type type, unsigned pos, int value);
4255 __isl_give isl_set *isl_set_lower_bound_si(
4256 __isl_take isl_set *set,
4257 enum isl_dim_type type, unsigned pos, int value);
4258 __isl_give isl_set *isl_set_lower_bound_val(
4259 __isl_take isl_set *set,
4260 enum isl_dim_type type, unsigned pos,
4261 __isl_take isl_val *value);
4262 __isl_give isl_map *isl_map_lower_bound_si(
4263 __isl_take isl_map *map,
4264 enum isl_dim_type type, unsigned pos, int value);
4265 __isl_give isl_set *isl_set_upper_bound_si(
4266 __isl_take isl_set *set,
4267 enum isl_dim_type type, unsigned pos, int value);
4268 __isl_give isl_set *isl_set_upper_bound_val(
4269 __isl_take isl_set *set,
4270 enum isl_dim_type type, unsigned pos,
4271 __isl_take isl_val *value);
4272 __isl_give isl_map *isl_map_upper_bound_si(
4273 __isl_take isl_map *map,
4274 enum isl_dim_type type, unsigned pos, int value);
4276 Intersect the set or relation with the half-space where the given
4277 dimension has a value bounded by the fixed given integer value.
4279 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4280 enum isl_dim_type type1, int pos1,
4281 enum isl_dim_type type2, int pos2);
4282 __isl_give isl_basic_map *isl_basic_map_equate(
4283 __isl_take isl_basic_map *bmap,
4284 enum isl_dim_type type1, int pos1,
4285 enum isl_dim_type type2, int pos2);
4286 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4287 enum isl_dim_type type1, int pos1,
4288 enum isl_dim_type type2, int pos2);
4290 Intersect the set or relation with the hyperplane where the given
4291 dimensions are equal to each other.
4293 __isl_give isl_map *isl_map_oppose(__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 hyperplane where the given
4298 dimensions have opposite values.
4300 __isl_give isl_map *isl_map_order_le(
4301 __isl_take isl_map *map,
4302 enum isl_dim_type type1, int pos1,
4303 enum isl_dim_type type2, int pos2);
4304 __isl_give isl_basic_map *isl_basic_map_order_ge(
4305 __isl_take isl_basic_map *bmap,
4306 enum isl_dim_type type1, int pos1,
4307 enum isl_dim_type type2, int pos2);
4308 __isl_give isl_map *isl_map_order_ge(
4309 __isl_take isl_map *map,
4310 enum isl_dim_type type1, int pos1,
4311 enum isl_dim_type type2, int pos2);
4312 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4313 enum isl_dim_type type1, int pos1,
4314 enum isl_dim_type type2, int pos2);
4315 __isl_give isl_basic_map *isl_basic_map_order_gt(
4316 __isl_take isl_basic_map *bmap,
4317 enum isl_dim_type type1, int pos1,
4318 enum isl_dim_type type2, int pos2);
4319 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4320 enum isl_dim_type type1, int pos1,
4321 enum isl_dim_type type2, int pos2);
4323 Intersect the relation with the half-space where the given
4324 dimensions satisfy the given ordering.
4328 #include <isl/aff.h>
4329 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4330 __isl_take isl_aff *aff);
4331 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4332 __isl_take isl_aff *aff);
4333 __isl_give isl_set *isl_pw_aff_pos_set(
4334 __isl_take isl_pw_aff *pa);
4335 __isl_give isl_set *isl_pw_aff_nonneg_set(
4336 __isl_take isl_pw_aff *pwaff);
4337 __isl_give isl_set *isl_pw_aff_zero_set(
4338 __isl_take isl_pw_aff *pwaff);
4339 __isl_give isl_set *isl_pw_aff_non_zero_set(
4340 __isl_take isl_pw_aff *pwaff);
4341 __isl_give isl_union_set *
4342 isl_union_pw_aff_zero_union_set(
4343 __isl_take isl_union_pw_aff *upa);
4344 __isl_give isl_union_set *
4345 isl_multi_union_pw_aff_zero_union_set(
4346 __isl_take isl_multi_union_pw_aff *mupa);
4348 The function C<isl_aff_neg_basic_set> returns a basic set
4349 containing those elements in the domain space
4350 of C<aff> where C<aff> is negative.
4351 The function C<isl_pw_aff_nonneg_set> returns a set
4352 containing those elements in the domain
4353 of C<pwaff> where C<pwaff> is non-negative.
4354 The function C<isl_multi_union_pw_aff_zero_union_set>
4355 returns a union set containing those elements
4356 in the domains of its elements where they are all zero.
4360 __isl_give isl_map *isl_set_identity(
4361 __isl_take isl_set *set);
4362 __isl_give isl_union_map *isl_union_set_identity(
4363 __isl_take isl_union_set *uset);
4364 __isl_give isl_union_pw_multi_aff *
4365 isl_union_set_identity_union_pw_multi_aff(
4366 __isl_take isl_union_set *uset);
4368 Construct an identity relation on the given (union) set.
4370 =item * Function Extraction
4372 A piecewise quasi affine expression that is equal to 1 on a set
4373 and 0 outside the set can be created using the following function.
4375 #include <isl/aff.h>
4376 __isl_give isl_pw_aff *isl_set_indicator_function(
4377 __isl_take isl_set *set);
4379 A piecewise multiple quasi affine expression can be extracted
4380 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4381 and the C<isl_map> is single-valued.
4382 In case of a conversion from an C<isl_union_map>
4383 to an C<isl_union_pw_multi_aff>, these properties need to hold
4384 in each domain space.
4385 A conversion to a C<isl_multi_union_pw_aff> additionally
4386 requires that the input is non-empty and involves only a single
4389 #include <isl/aff.h>
4390 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4391 __isl_take isl_set *set);
4392 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4393 __isl_take isl_map *map);
4395 __isl_give isl_union_pw_multi_aff *
4396 isl_union_pw_multi_aff_from_union_set(
4397 __isl_take isl_union_set *uset);
4398 __isl_give isl_union_pw_multi_aff *
4399 isl_union_pw_multi_aff_from_union_map(
4400 __isl_take isl_union_map *umap);
4402 __isl_give isl_multi_union_pw_aff *
4403 isl_multi_union_pw_aff_from_union_map(
4404 __isl_take isl_union_map *umap);
4408 __isl_give isl_basic_set *isl_basic_map_deltas(
4409 __isl_take isl_basic_map *bmap);
4410 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4411 __isl_give isl_union_set *isl_union_map_deltas(
4412 __isl_take isl_union_map *umap);
4414 These functions return a (basic) set containing the differences
4415 between image elements and corresponding domain elements in the input.
4417 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4418 __isl_take isl_basic_map *bmap);
4419 __isl_give isl_map *isl_map_deltas_map(
4420 __isl_take isl_map *map);
4421 __isl_give isl_union_map *isl_union_map_deltas_map(
4422 __isl_take isl_union_map *umap);
4424 The functions above construct a (basic, regular or union) relation
4425 that maps (a wrapped version of) the input relation to its delta set.
4429 Simplify the representation of a set, relation or functions by trying
4430 to combine pairs of basic sets or relations into a single
4431 basic set or relation.
4433 #include <isl/set.h>
4434 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4436 #include <isl/map.h>
4437 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4439 #include <isl/union_set.h>
4440 __isl_give isl_union_set *isl_union_set_coalesce(
4441 __isl_take isl_union_set *uset);
4443 #include <isl/union_map.h>
4444 __isl_give isl_union_map *isl_union_map_coalesce(
4445 __isl_take isl_union_map *umap);
4447 #include <isl/aff.h>
4448 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4449 __isl_take isl_pw_aff *pwqp);
4450 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4451 __isl_take isl_pw_multi_aff *pma);
4452 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4453 __isl_take isl_multi_pw_aff *mpa);
4454 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4455 __isl_take isl_union_pw_aff *upa);
4456 __isl_give isl_union_pw_multi_aff *
4457 isl_union_pw_multi_aff_coalesce(
4458 __isl_take isl_union_pw_multi_aff *upma);
4460 #include <isl/polynomial.h>
4461 __isl_give isl_pw_qpolynomial_fold *
4462 isl_pw_qpolynomial_fold_coalesce(
4463 __isl_take isl_pw_qpolynomial_fold *pwf);
4464 __isl_give isl_union_pw_qpolynomial *
4465 isl_union_pw_qpolynomial_coalesce(
4466 __isl_take isl_union_pw_qpolynomial *upwqp);
4467 __isl_give isl_union_pw_qpolynomial_fold *
4468 isl_union_pw_qpolynomial_fold_coalesce(
4469 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4471 One of the methods for combining pairs of basic sets or relations
4472 can result in coefficients that are much larger than those that appear
4473 in the constraints of the input. By default, the coefficients are
4474 not allowed to grow larger, but this can be changed by unsetting
4475 the following option.
4477 int isl_options_set_coalesce_bounded_wrapping(
4478 isl_ctx *ctx, int val);
4479 int isl_options_get_coalesce_bounded_wrapping(
4482 =item * Detecting equalities
4484 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4485 __isl_take isl_basic_set *bset);
4486 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4487 __isl_take isl_basic_map *bmap);
4488 __isl_give isl_set *isl_set_detect_equalities(
4489 __isl_take isl_set *set);
4490 __isl_give isl_map *isl_map_detect_equalities(
4491 __isl_take isl_map *map);
4492 __isl_give isl_union_set *isl_union_set_detect_equalities(
4493 __isl_take isl_union_set *uset);
4494 __isl_give isl_union_map *isl_union_map_detect_equalities(
4495 __isl_take isl_union_map *umap);
4497 Simplify the representation of a set or relation by detecting implicit
4500 =item * Removing redundant constraints
4502 #include <isl/set.h>
4503 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4504 __isl_take isl_basic_set *bset);
4505 __isl_give isl_set *isl_set_remove_redundancies(
4506 __isl_take isl_set *set);
4508 #include <isl/union_set.h>
4509 __isl_give isl_union_set *
4510 isl_union_set_remove_redundancies(
4511 __isl_take isl_union_set *uset);
4513 #include <isl/map.h>
4514 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4515 __isl_take isl_basic_map *bmap);
4516 __isl_give isl_map *isl_map_remove_redundancies(
4517 __isl_take isl_map *map);
4519 #include <isl/union_map.h>
4520 __isl_give isl_union_map *
4521 isl_union_map_remove_redundancies(
4522 __isl_take isl_union_map *umap);
4526 __isl_give isl_basic_set *isl_set_convex_hull(
4527 __isl_take isl_set *set);
4528 __isl_give isl_basic_map *isl_map_convex_hull(
4529 __isl_take isl_map *map);
4531 If the input set or relation has any existentially quantified
4532 variables, then the result of these operations is currently undefined.
4536 #include <isl/set.h>
4537 __isl_give isl_basic_set *
4538 isl_set_unshifted_simple_hull(
4539 __isl_take isl_set *set);
4540 __isl_give isl_basic_set *isl_set_simple_hull(
4541 __isl_take isl_set *set);
4542 __isl_give isl_basic_set *
4543 isl_set_unshifted_simple_hull_from_set_list(
4544 __isl_take isl_set *set,
4545 __isl_take isl_set_list *list);
4547 #include <isl/map.h>
4548 __isl_give isl_basic_map *
4549 isl_map_unshifted_simple_hull(
4550 __isl_take isl_map *map);
4551 __isl_give isl_basic_map *isl_map_simple_hull(
4552 __isl_take isl_map *map);
4553 __isl_give isl_basic_map *
4554 isl_map_unshifted_simple_hull_from_map_list(
4555 __isl_take isl_map *map,
4556 __isl_take isl_map_list *list);
4558 #include <isl/union_map.h>
4559 __isl_give isl_union_map *isl_union_map_simple_hull(
4560 __isl_take isl_union_map *umap);
4562 These functions compute a single basic set or relation
4563 that contains the whole input set or relation.
4564 In particular, the output is described by translates
4565 of the constraints describing the basic sets or relations in the input.
4566 In case of C<isl_set_unshifted_simple_hull>, only the original
4567 constraints are used, without any translation.
4568 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4569 C<isl_map_unshifted_simple_hull_from_map_list>, the
4570 constraints are taken from the elements of the second argument.
4574 (See \autoref{s:simple hull}.)
4580 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4581 __isl_take isl_basic_set *bset);
4582 __isl_give isl_basic_set *isl_set_affine_hull(
4583 __isl_take isl_set *set);
4584 __isl_give isl_union_set *isl_union_set_affine_hull(
4585 __isl_take isl_union_set *uset);
4586 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4587 __isl_take isl_basic_map *bmap);
4588 __isl_give isl_basic_map *isl_map_affine_hull(
4589 __isl_take isl_map *map);
4590 __isl_give isl_union_map *isl_union_map_affine_hull(
4591 __isl_take isl_union_map *umap);
4593 In case of union sets and relations, the affine hull is computed
4596 =item * Polyhedral hull
4598 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4599 __isl_take isl_set *set);
4600 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4601 __isl_take isl_map *map);
4602 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4603 __isl_take isl_union_set *uset);
4604 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4605 __isl_take isl_union_map *umap);
4607 These functions compute a single basic set or relation
4608 not involving any existentially quantified variables
4609 that contains the whole input set or relation.
4610 In case of union sets and relations, the polyhedral hull is computed
4613 =item * Other approximations
4615 #include <isl/set.h>
4616 __isl_give isl_basic_set *
4617 isl_basic_set_drop_constraints_involving_dims(
4618 __isl_take isl_basic_set *bset,
4619 enum isl_dim_type type,
4620 unsigned first, unsigned n);
4621 __isl_give isl_basic_set *
4622 isl_basic_set_drop_constraints_not_involving_dims(
4623 __isl_take isl_basic_set *bset,
4624 enum isl_dim_type type,
4625 unsigned first, unsigned n);
4626 __isl_give isl_set *
4627 isl_set_drop_constraints_involving_dims(
4628 __isl_take isl_set *set,
4629 enum isl_dim_type type,
4630 unsigned first, unsigned n);
4632 #include <isl/map.h>
4633 __isl_give isl_basic_map *
4634 isl_basic_map_drop_constraints_involving_dims(
4635 __isl_take isl_basic_map *bmap,
4636 enum isl_dim_type type,
4637 unsigned first, unsigned n);
4638 __isl_give isl_map *
4639 isl_map_drop_constraints_involving_dims(
4640 __isl_take isl_map *map,
4641 enum isl_dim_type type,
4642 unsigned first, unsigned n);
4644 These functions drop any constraints (not) involving the specified dimensions.
4645 Note that the result depends on the representation of the input.
4647 #include <isl/polynomial.h>
4648 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4649 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4650 __isl_give isl_union_pw_qpolynomial *
4651 isl_union_pw_qpolynomial_to_polynomial(
4652 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4654 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4655 the polynomial will be an overapproximation. If C<sign> is negative,
4656 it will be an underapproximation. If C<sign> is zero, the approximation
4657 will lie somewhere in between.
4661 __isl_give isl_basic_set *isl_basic_set_sample(
4662 __isl_take isl_basic_set *bset);
4663 __isl_give isl_basic_set *isl_set_sample(
4664 __isl_take isl_set *set);
4665 __isl_give isl_basic_map *isl_basic_map_sample(
4666 __isl_take isl_basic_map *bmap);
4667 __isl_give isl_basic_map *isl_map_sample(
4668 __isl_take isl_map *map);
4670 If the input (basic) set or relation is non-empty, then return
4671 a singleton subset of the input. Otherwise, return an empty set.
4673 =item * Optimization
4675 #include <isl/ilp.h>
4676 __isl_give isl_val *isl_basic_set_max_val(
4677 __isl_keep isl_basic_set *bset,
4678 __isl_keep isl_aff *obj);
4679 __isl_give isl_val *isl_set_min_val(
4680 __isl_keep isl_set *set,
4681 __isl_keep isl_aff *obj);
4682 __isl_give isl_val *isl_set_max_val(
4683 __isl_keep isl_set *set,
4684 __isl_keep isl_aff *obj);
4686 Compute the minimum or maximum of the integer affine expression C<obj>
4687 over the points in C<set>, returning the result in C<opt>.
4688 The result is C<NULL> in case of an error, the optimal value in case
4689 there is one, negative infinity or infinity if the problem is unbounded and
4690 NaN if the problem is empty.
4692 =item * Parametric optimization
4694 __isl_give isl_pw_aff *isl_set_dim_min(
4695 __isl_take isl_set *set, int pos);
4696 __isl_give isl_pw_aff *isl_set_dim_max(
4697 __isl_take isl_set *set, int pos);
4698 __isl_give isl_pw_aff *isl_map_dim_max(
4699 __isl_take isl_map *map, int pos);
4701 Compute the minimum or maximum of the given set or output dimension
4702 as a function of the parameters (and input dimensions), but independently
4703 of the other set or output dimensions.
4704 For lexicographic optimization, see L<"Lexicographic Optimization">.
4708 The following functions compute either the set of (rational) coefficient
4709 values of valid constraints for the given set or the set of (rational)
4710 values satisfying the constraints with coefficients from the given set.
4711 Internally, these two sets of functions perform essentially the
4712 same operations, except that the set of coefficients is assumed to
4713 be a cone, while the set of values may be any polyhedron.
4714 The current implementation is based on the Farkas lemma and
4715 Fourier-Motzkin elimination, but this may change or be made optional
4716 in future. In particular, future implementations may use different
4717 dualization algorithms or skip the elimination step.
4719 __isl_give isl_basic_set *isl_basic_set_coefficients(
4720 __isl_take isl_basic_set *bset);
4721 __isl_give isl_basic_set *isl_set_coefficients(
4722 __isl_take isl_set *set);
4723 __isl_give isl_union_set *isl_union_set_coefficients(
4724 __isl_take isl_union_set *bset);
4725 __isl_give isl_basic_set *isl_basic_set_solutions(
4726 __isl_take isl_basic_set *bset);
4727 __isl_give isl_basic_set *isl_set_solutions(
4728 __isl_take isl_set *set);
4729 __isl_give isl_union_set *isl_union_set_solutions(
4730 __isl_take isl_union_set *bset);
4734 __isl_give isl_map *isl_map_fixed_power_val(
4735 __isl_take isl_map *map,
4736 __isl_take isl_val *exp);
4737 __isl_give isl_union_map *
4738 isl_union_map_fixed_power_val(
4739 __isl_take isl_union_map *umap,
4740 __isl_take isl_val *exp);
4742 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4743 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4744 of C<map> is computed.
4746 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4748 __isl_give isl_union_map *isl_union_map_power(
4749 __isl_take isl_union_map *umap, int *exact);
4751 Compute a parametric representation for all positive powers I<k> of C<map>.
4752 The result maps I<k> to a nested relation corresponding to the
4753 I<k>th power of C<map>.
4754 The result may be an overapproximation. If the result is known to be exact,
4755 then C<*exact> is set to C<1>.
4757 =item * Transitive closure
4759 __isl_give isl_map *isl_map_transitive_closure(
4760 __isl_take isl_map *map, int *exact);
4761 __isl_give isl_union_map *isl_union_map_transitive_closure(
4762 __isl_take isl_union_map *umap, int *exact);
4764 Compute the transitive closure of C<map>.
4765 The result may be an overapproximation. If the result is known to be exact,
4766 then C<*exact> is set to C<1>.
4768 =item * Reaching path lengths
4770 __isl_give isl_map *isl_map_reaching_path_lengths(
4771 __isl_take isl_map *map, int *exact);
4773 Compute a relation that maps each element in the range of C<map>
4774 to the lengths of all paths composed of edges in C<map> that
4775 end up in the given element.
4776 The result may be an overapproximation. If the result is known to be exact,
4777 then C<*exact> is set to C<1>.
4778 To compute the I<maximal> path length, the resulting relation
4779 should be postprocessed by C<isl_map_lexmax>.
4780 In particular, if the input relation is a dependence relation
4781 (mapping sources to sinks), then the maximal path length corresponds
4782 to the free schedule.
4783 Note, however, that C<isl_map_lexmax> expects the maximum to be
4784 finite, so if the path lengths are unbounded (possibly due to
4785 the overapproximation), then you will get an error message.
4789 #include <isl/space.h>
4790 __isl_give isl_space *isl_space_wrap(
4791 __isl_take isl_space *space);
4792 __isl_give isl_space *isl_space_unwrap(
4793 __isl_take isl_space *space);
4795 #include <isl/local_space.h>
4796 __isl_give isl_local_space *isl_local_space_wrap(
4797 __isl_take isl_local_space *ls);
4799 #include <isl/set.h>
4800 __isl_give isl_basic_map *isl_basic_set_unwrap(
4801 __isl_take isl_basic_set *bset);
4802 __isl_give isl_map *isl_set_unwrap(
4803 __isl_take isl_set *set);
4805 #include <isl/map.h>
4806 __isl_give isl_basic_set *isl_basic_map_wrap(
4807 __isl_take isl_basic_map *bmap);
4808 __isl_give isl_set *isl_map_wrap(
4809 __isl_take isl_map *map);
4811 #include <isl/union_set.h>
4812 __isl_give isl_union_map *isl_union_set_unwrap(
4813 __isl_take isl_union_set *uset);
4815 #include <isl/union_map.h>
4816 __isl_give isl_union_set *isl_union_map_wrap(
4817 __isl_take isl_union_map *umap);
4819 The input to C<isl_space_unwrap> should
4820 be the space of a set, while that of
4821 C<isl_space_wrap> should be the space of a relation.
4822 Conversely, the output of C<isl_space_unwrap> is the space
4823 of a relation, while that of C<isl_space_wrap> is the space of a set.
4827 Remove any internal structure of domain (and range) of the given
4828 set or relation. If there is any such internal structure in the input,
4829 then the name of the space is also removed.
4831 #include <isl/local_space.h>
4832 __isl_give isl_local_space *
4833 isl_local_space_flatten_domain(
4834 __isl_take isl_local_space *ls);
4835 __isl_give isl_local_space *
4836 isl_local_space_flatten_range(
4837 __isl_take isl_local_space *ls);
4839 #include <isl/set.h>
4840 __isl_give isl_basic_set *isl_basic_set_flatten(
4841 __isl_take isl_basic_set *bset);
4842 __isl_give isl_set *isl_set_flatten(
4843 __isl_take isl_set *set);
4845 #include <isl/map.h>
4846 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4847 __isl_take isl_basic_map *bmap);
4848 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4849 __isl_take isl_basic_map *bmap);
4850 __isl_give isl_map *isl_map_flatten_range(
4851 __isl_take isl_map *map);
4852 __isl_give isl_map *isl_map_flatten_domain(
4853 __isl_take isl_map *map);
4854 __isl_give isl_basic_map *isl_basic_map_flatten(
4855 __isl_take isl_basic_map *bmap);
4856 __isl_give isl_map *isl_map_flatten(
4857 __isl_take isl_map *map);
4859 #include <isl/val.h>
4860 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4861 __isl_take isl_multi_val *mv);
4863 #include <isl/aff.h>
4864 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4865 __isl_take isl_multi_aff *ma);
4866 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4867 __isl_take isl_multi_aff *ma);
4868 __isl_give isl_multi_pw_aff *
4869 isl_multi_pw_aff_flatten_range(
4870 __isl_take isl_multi_pw_aff *mpa);
4871 __isl_give isl_multi_union_pw_aff *
4872 isl_multi_union_pw_aff_flatten_range(
4873 __isl_take isl_multi_union_pw_aff *mupa);
4875 #include <isl/map.h>
4876 __isl_give isl_map *isl_set_flatten_map(
4877 __isl_take isl_set *set);
4879 The function above constructs a relation
4880 that maps the input set to a flattened version of the set.
4884 Lift the input set to a space with extra dimensions corresponding
4885 to the existentially quantified variables in the input.
4886 In particular, the result lives in a wrapped map where the domain
4887 is the original space and the range corresponds to the original
4888 existentially quantified variables.
4890 #include <isl/set.h>
4891 __isl_give isl_basic_set *isl_basic_set_lift(
4892 __isl_take isl_basic_set *bset);
4893 __isl_give isl_set *isl_set_lift(
4894 __isl_take isl_set *set);
4895 __isl_give isl_union_set *isl_union_set_lift(
4896 __isl_take isl_union_set *uset);
4898 Given a local space that contains the existentially quantified
4899 variables of a set, a basic relation that, when applied to
4900 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4901 can be constructed using the following function.
4903 #include <isl/local_space.h>
4904 __isl_give isl_basic_map *isl_local_space_lifting(
4905 __isl_take isl_local_space *ls);
4907 #include <isl/aff.h>
4908 __isl_give isl_multi_aff *isl_multi_aff_lift(
4909 __isl_take isl_multi_aff *maff,
4910 __isl_give isl_local_space **ls);
4912 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4913 then it is assigned the local space that lies at the basis of
4914 the lifting applied.
4916 =item * Internal Product
4918 #include <isl/space.h>
4919 __isl_give isl_space *isl_space_zip(
4920 __isl_take isl_space *space);
4922 #include <isl/map.h>
4923 __isl_give isl_basic_map *isl_basic_map_zip(
4924 __isl_take isl_basic_map *bmap);
4925 __isl_give isl_map *isl_map_zip(
4926 __isl_take isl_map *map);
4928 #include <isl/union_map.h>
4929 __isl_give isl_union_map *isl_union_map_zip(
4930 __isl_take isl_union_map *umap);
4932 Given a relation with nested relations for domain and range,
4933 interchange the range of the domain with the domain of the range.
4937 #include <isl/space.h>
4938 __isl_give isl_space *isl_space_curry(
4939 __isl_take isl_space *space);
4940 __isl_give isl_space *isl_space_uncurry(
4941 __isl_take isl_space *space);
4943 #include <isl/map.h>
4944 __isl_give isl_basic_map *isl_basic_map_curry(
4945 __isl_take isl_basic_map *bmap);
4946 __isl_give isl_basic_map *isl_basic_map_uncurry(
4947 __isl_take isl_basic_map *bmap);
4948 __isl_give isl_map *isl_map_curry(
4949 __isl_take isl_map *map);
4950 __isl_give isl_map *isl_map_uncurry(
4951 __isl_take isl_map *map);
4953 #include <isl/union_map.h>
4954 __isl_give isl_union_map *isl_union_map_curry(
4955 __isl_take isl_union_map *umap);
4956 __isl_give isl_union_map *isl_union_map_uncurry(
4957 __isl_take isl_union_map *umap);
4959 Given a relation with a nested relation for domain,
4960 the C<curry> functions
4961 move the range of the nested relation out of the domain
4962 and use it as the domain of a nested relation in the range,
4963 with the original range as range of this nested relation.
4964 The C<uncurry> functions perform the inverse operation.
4966 =item * Aligning parameters
4968 Change the order of the parameters of the given set, relation
4970 such that the first parameters match those of C<model>.
4971 This may involve the introduction of extra parameters.
4972 All parameters need to be named.
4974 #include <isl/space.h>
4975 __isl_give isl_space *isl_space_align_params(
4976 __isl_take isl_space *space1,
4977 __isl_take isl_space *space2)
4979 #include <isl/set.h>
4980 __isl_give isl_basic_set *isl_basic_set_align_params(
4981 __isl_take isl_basic_set *bset,
4982 __isl_take isl_space *model);
4983 __isl_give isl_set *isl_set_align_params(
4984 __isl_take isl_set *set,
4985 __isl_take isl_space *model);
4987 #include <isl/map.h>
4988 __isl_give isl_basic_map *isl_basic_map_align_params(
4989 __isl_take isl_basic_map *bmap,
4990 __isl_take isl_space *model);
4991 __isl_give isl_map *isl_map_align_params(
4992 __isl_take isl_map *map,
4993 __isl_take isl_space *model);
4995 #include <isl/val.h>
4996 __isl_give isl_multi_val *isl_multi_val_align_params(
4997 __isl_take isl_multi_val *mv,
4998 __isl_take isl_space *model);
5000 #include <isl/aff.h>
5001 __isl_give isl_aff *isl_aff_align_params(
5002 __isl_take isl_aff *aff,
5003 __isl_take isl_space *model);
5004 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5005 __isl_take isl_multi_aff *multi,
5006 __isl_take isl_space *model);
5007 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5008 __isl_take isl_pw_aff *pwaff,
5009 __isl_take isl_space *model);
5010 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5011 __isl_take isl_pw_multi_aff *pma,
5012 __isl_take isl_space *model);
5013 __isl_give isl_union_pw_aff *
5014 isl_union_pw_aff_align_params(
5015 __isl_take isl_union_pw_aff *upa,
5016 __isl_take isl_space *model);
5017 __isl_give isl_union_pw_multi_aff *
5018 isl_union_pw_multi_aff_align_params(
5019 __isl_take isl_union_pw_multi_aff *upma,
5020 __isl_take isl_space *model);
5021 __isl_give isl_multi_union_pw_aff *
5022 isl_multi_union_pw_aff_align_params(
5023 __isl_take isl_multi_union_pw_aff *mupa,
5024 __isl_take isl_space *model);
5026 #include <isl/polynomial.h>
5027 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5028 __isl_take isl_qpolynomial *qp,
5029 __isl_take isl_space *model);
5031 =item * Unary Arithmethic Operations
5033 #include <isl/val.h>
5034 __isl_give isl_multi_val *isl_multi_val_neg(
5035 __isl_take isl_multi_val *mv);
5037 #include <isl/aff.h>
5038 __isl_give isl_aff *isl_aff_neg(
5039 __isl_take isl_aff *aff);
5040 __isl_give isl_multi_aff *isl_multi_aff_neg(
5041 __isl_take isl_multi_aff *ma);
5042 __isl_give isl_pw_aff *isl_pw_aff_neg(
5043 __isl_take isl_pw_aff *pwaff);
5044 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5045 __isl_take isl_pw_multi_aff *pma);
5046 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5047 __isl_take isl_multi_pw_aff *mpa);
5048 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5049 __isl_take isl_union_pw_aff *upa);
5050 __isl_give isl_union_pw_multi_aff *
5051 isl_union_pw_multi_aff_neg(
5052 __isl_take isl_union_pw_multi_aff *upma);
5053 __isl_give isl_multi_union_pw_aff *
5054 isl_multi_union_pw_aff_neg(
5055 __isl_take isl_multi_union_pw_aff *mupa);
5056 __isl_give isl_aff *isl_aff_ceil(
5057 __isl_take isl_aff *aff);
5058 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5059 __isl_take isl_pw_aff *pwaff);
5060 __isl_give isl_aff *isl_aff_floor(
5061 __isl_take isl_aff *aff);
5062 __isl_give isl_multi_aff *isl_multi_aff_floor(
5063 __isl_take isl_multi_aff *ma);
5064 __isl_give isl_pw_aff *isl_pw_aff_floor(
5065 __isl_take isl_pw_aff *pwaff);
5066 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5067 __isl_take isl_union_pw_aff *upa);
5069 #include <isl/aff.h>
5070 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5071 __isl_take isl_pw_aff_list *list);
5072 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5073 __isl_take isl_pw_aff_list *list);
5075 #include <isl/polynomial.h>
5076 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5077 __isl_take isl_qpolynomial *qp);
5078 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5079 __isl_take isl_pw_qpolynomial *pwqp);
5080 __isl_give isl_union_pw_qpolynomial *
5081 isl_union_pw_qpolynomial_neg(
5082 __isl_take isl_union_pw_qpolynomial *upwqp);
5083 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5084 __isl_take isl_qpolynomial *qp,
5086 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5087 __isl_take isl_pw_qpolynomial *pwqp,
5092 The following functions evaluate a function in a point.
5094 #include <isl/polynomial.h>
5095 __isl_give isl_val *isl_pw_qpolynomial_eval(
5096 __isl_take isl_pw_qpolynomial *pwqp,
5097 __isl_take isl_point *pnt);
5098 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5099 __isl_take isl_pw_qpolynomial_fold *pwf,
5100 __isl_take isl_point *pnt);
5101 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5102 __isl_take isl_union_pw_qpolynomial *upwqp,
5103 __isl_take isl_point *pnt);
5104 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5105 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5106 __isl_take isl_point *pnt);
5108 =item * Dimension manipulation
5110 It is usually not advisable to directly change the (input or output)
5111 space of a set or a relation as this removes the name and the internal
5112 structure of the space. However, the functions below can be useful
5113 to add new parameters, assuming
5114 C<isl_set_align_params> and C<isl_map_align_params>
5117 #include <isl/space.h>
5118 __isl_give isl_space *isl_space_add_dims(
5119 __isl_take isl_space *space,
5120 enum isl_dim_type type, unsigned n);
5121 __isl_give isl_space *isl_space_insert_dims(
5122 __isl_take isl_space *space,
5123 enum isl_dim_type type, unsigned pos, unsigned n);
5124 __isl_give isl_space *isl_space_drop_dims(
5125 __isl_take isl_space *space,
5126 enum isl_dim_type type, unsigned first, unsigned n);
5127 __isl_give isl_space *isl_space_move_dims(
5128 __isl_take isl_space *space,
5129 enum isl_dim_type dst_type, unsigned dst_pos,
5130 enum isl_dim_type src_type, unsigned src_pos,
5133 #include <isl/local_space.h>
5134 __isl_give isl_local_space *isl_local_space_add_dims(
5135 __isl_take isl_local_space *ls,
5136 enum isl_dim_type type, unsigned n);
5137 __isl_give isl_local_space *isl_local_space_insert_dims(
5138 __isl_take isl_local_space *ls,
5139 enum isl_dim_type type, unsigned first, unsigned n);
5140 __isl_give isl_local_space *isl_local_space_drop_dims(
5141 __isl_take isl_local_space *ls,
5142 enum isl_dim_type type, unsigned first, unsigned n);
5144 #include <isl/set.h>
5145 __isl_give isl_basic_set *isl_basic_set_add_dims(
5146 __isl_take isl_basic_set *bset,
5147 enum isl_dim_type type, unsigned n);
5148 __isl_give isl_set *isl_set_add_dims(
5149 __isl_take isl_set *set,
5150 enum isl_dim_type type, unsigned n);
5151 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5152 __isl_take isl_basic_set *bset,
5153 enum isl_dim_type type, unsigned pos,
5155 __isl_give isl_set *isl_set_insert_dims(
5156 __isl_take isl_set *set,
5157 enum isl_dim_type type, unsigned pos, unsigned n);
5158 __isl_give isl_basic_set *isl_basic_set_move_dims(
5159 __isl_take isl_basic_set *bset,
5160 enum isl_dim_type dst_type, unsigned dst_pos,
5161 enum isl_dim_type src_type, unsigned src_pos,
5163 __isl_give isl_set *isl_set_move_dims(
5164 __isl_take isl_set *set,
5165 enum isl_dim_type dst_type, unsigned dst_pos,
5166 enum isl_dim_type src_type, unsigned src_pos,
5169 #include <isl/map.h>
5170 __isl_give isl_map *isl_map_add_dims(
5171 __isl_take isl_map *map,
5172 enum isl_dim_type type, unsigned n);
5173 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5174 __isl_take isl_basic_map *bmap,
5175 enum isl_dim_type type, unsigned pos,
5177 __isl_give isl_map *isl_map_insert_dims(
5178 __isl_take isl_map *map,
5179 enum isl_dim_type type, unsigned pos, unsigned n);
5180 __isl_give isl_basic_map *isl_basic_map_move_dims(
5181 __isl_take isl_basic_map *bmap,
5182 enum isl_dim_type dst_type, unsigned dst_pos,
5183 enum isl_dim_type src_type, unsigned src_pos,
5185 __isl_give isl_map *isl_map_move_dims(
5186 __isl_take isl_map *map,
5187 enum isl_dim_type dst_type, unsigned dst_pos,
5188 enum isl_dim_type src_type, unsigned src_pos,
5191 #include <isl/val.h>
5192 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5193 __isl_take isl_multi_val *mv,
5194 enum isl_dim_type type, unsigned first, unsigned n);
5195 __isl_give isl_multi_val *isl_multi_val_add_dims(
5196 __isl_take isl_multi_val *mv,
5197 enum isl_dim_type type, unsigned n);
5198 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5199 __isl_take isl_multi_val *mv,
5200 enum isl_dim_type type, unsigned first, unsigned n);
5202 #include <isl/aff.h>
5203 __isl_give isl_aff *isl_aff_insert_dims(
5204 __isl_take isl_aff *aff,
5205 enum isl_dim_type type, unsigned first, unsigned n);
5206 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5207 __isl_take isl_multi_aff *ma,
5208 enum isl_dim_type type, unsigned first, unsigned n);
5209 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5210 __isl_take isl_pw_aff *pwaff,
5211 enum isl_dim_type type, unsigned first, unsigned n);
5212 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5213 __isl_take isl_multi_pw_aff *mpa,
5214 enum isl_dim_type type, unsigned first, unsigned n);
5215 __isl_give isl_aff *isl_aff_add_dims(
5216 __isl_take isl_aff *aff,
5217 enum isl_dim_type type, unsigned n);
5218 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5219 __isl_take isl_multi_aff *ma,
5220 enum isl_dim_type type, unsigned n);
5221 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5222 __isl_take isl_pw_aff *pwaff,
5223 enum isl_dim_type type, unsigned n);
5224 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5225 __isl_take isl_multi_pw_aff *mpa,
5226 enum isl_dim_type type, unsigned n);
5227 __isl_give isl_aff *isl_aff_drop_dims(
5228 __isl_take isl_aff *aff,
5229 enum isl_dim_type type, unsigned first, unsigned n);
5230 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5231 __isl_take isl_multi_aff *maff,
5232 enum isl_dim_type type, unsigned first, unsigned n);
5233 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5234 __isl_take isl_pw_aff *pwaff,
5235 enum isl_dim_type type, unsigned first, unsigned n);
5236 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5237 __isl_take isl_pw_multi_aff *pma,
5238 enum isl_dim_type type, unsigned first, unsigned n);
5239 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5240 __isl_take isl_union_pw_aff *upa,
5241 enum isl_dim_type type, unsigned first, unsigned n);
5242 __isl_give isl_union_pw_multi_aff *
5243 isl_union_pw_multi_aff_drop_dims(
5244 __isl_take isl_union_pw_multi_aff *upma,
5245 enum isl_dim_type type,
5246 unsigned first, unsigned n);
5247 __isl_give isl_multi_union_pw_aff *
5248 isl_multi_union_pw_aff_drop_dims(
5249 __isl_take isl_multi_union_pw_aff *mupa,
5250 enum isl_dim_type type, unsigned first,
5252 __isl_give isl_aff *isl_aff_move_dims(
5253 __isl_take isl_aff *aff,
5254 enum isl_dim_type dst_type, unsigned dst_pos,
5255 enum isl_dim_type src_type, unsigned src_pos,
5257 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5258 __isl_take isl_multi_aff *ma,
5259 enum isl_dim_type dst_type, unsigned dst_pos,
5260 enum isl_dim_type src_type, unsigned src_pos,
5262 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5263 __isl_take isl_pw_aff *pa,
5264 enum isl_dim_type dst_type, unsigned dst_pos,
5265 enum isl_dim_type src_type, unsigned src_pos,
5267 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5268 __isl_take isl_multi_pw_aff *pma,
5269 enum isl_dim_type dst_type, unsigned dst_pos,
5270 enum isl_dim_type src_type, unsigned src_pos,
5273 #include <isl/polynomial.h>
5274 __isl_give isl_union_pw_qpolynomial *
5275 isl_union_pw_qpolynomial_drop_dims(
5276 __isl_take isl_union_pw_qpolynomial *upwqp,
5277 enum isl_dim_type type,
5278 unsigned first, unsigned n);
5279 __isl_give isl_union_pw_qpolynomial_fold *
5280 isl_union_pw_qpolynomial_fold_drop_dims(
5281 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5282 enum isl_dim_type type,
5283 unsigned first, unsigned n);
5285 The operations on union expressions can only manipulate parameters.
5289 =head2 Binary Operations
5291 The two arguments of a binary operation not only need to live
5292 in the same C<isl_ctx>, they currently also need to have
5293 the same (number of) parameters.
5295 =head3 Basic Operations
5299 =item * Intersection
5301 #include <isl/local_space.h>
5302 __isl_give isl_local_space *isl_local_space_intersect(
5303 __isl_take isl_local_space *ls1,
5304 __isl_take isl_local_space *ls2);
5306 #include <isl/set.h>
5307 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5308 __isl_take isl_basic_set *bset1,
5309 __isl_take isl_basic_set *bset2);
5310 __isl_give isl_basic_set *isl_basic_set_intersect(
5311 __isl_take isl_basic_set *bset1,
5312 __isl_take isl_basic_set *bset2);
5313 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5314 __isl_take struct isl_basic_set_list *list);
5315 __isl_give isl_set *isl_set_intersect_params(
5316 __isl_take isl_set *set,
5317 __isl_take isl_set *params);
5318 __isl_give isl_set *isl_set_intersect(
5319 __isl_take isl_set *set1,
5320 __isl_take isl_set *set2);
5322 #include <isl/map.h>
5323 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5324 __isl_take isl_basic_map *bmap,
5325 __isl_take isl_basic_set *bset);
5326 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5327 __isl_take isl_basic_map *bmap,
5328 __isl_take isl_basic_set *bset);
5329 __isl_give isl_basic_map *isl_basic_map_intersect(
5330 __isl_take isl_basic_map *bmap1,
5331 __isl_take isl_basic_map *bmap2);
5332 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5333 __isl_take isl_basic_map_list *list);
5334 __isl_give isl_map *isl_map_intersect_params(
5335 __isl_take isl_map *map,
5336 __isl_take isl_set *params);
5337 __isl_give isl_map *isl_map_intersect_domain(
5338 __isl_take isl_map *map,
5339 __isl_take isl_set *set);
5340 __isl_give isl_map *isl_map_intersect_range(
5341 __isl_take isl_map *map,
5342 __isl_take isl_set *set);
5343 __isl_give isl_map *isl_map_intersect(
5344 __isl_take isl_map *map1,
5345 __isl_take isl_map *map2);
5347 #include <isl/union_set.h>
5348 __isl_give isl_union_set *isl_union_set_intersect_params(
5349 __isl_take isl_union_set *uset,
5350 __isl_take isl_set *set);
5351 __isl_give isl_union_set *isl_union_set_intersect(
5352 __isl_take isl_union_set *uset1,
5353 __isl_take isl_union_set *uset2);
5355 #include <isl/union_map.h>
5356 __isl_give isl_union_map *isl_union_map_intersect_params(
5357 __isl_take isl_union_map *umap,
5358 __isl_take isl_set *set);
5359 __isl_give isl_union_map *isl_union_map_intersect_domain(
5360 __isl_take isl_union_map *umap,
5361 __isl_take isl_union_set *uset);
5362 __isl_give isl_union_map *isl_union_map_intersect_range(
5363 __isl_take isl_union_map *umap,
5364 __isl_take isl_union_set *uset);
5365 __isl_give isl_union_map *isl_union_map_intersect(
5366 __isl_take isl_union_map *umap1,
5367 __isl_take isl_union_map *umap2);
5369 #include <isl/aff.h>
5370 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5371 __isl_take isl_pw_aff *pa,
5372 __isl_take isl_set *set);
5373 __isl_give isl_multi_pw_aff *
5374 isl_multi_pw_aff_intersect_domain(
5375 __isl_take isl_multi_pw_aff *mpa,
5376 __isl_take isl_set *domain);
5377 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5378 __isl_take isl_pw_multi_aff *pma,
5379 __isl_take isl_set *set);
5380 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5381 __isl_take isl_union_pw_aff *upa,
5382 __isl_take isl_union_set *uset);
5383 __isl_give isl_union_pw_multi_aff *
5384 isl_union_pw_multi_aff_intersect_domain(
5385 __isl_take isl_union_pw_multi_aff *upma,
5386 __isl_take isl_union_set *uset);
5387 __isl_give isl_multi_union_pw_aff *
5388 isl_multi_union_pw_aff_intersect_domain(
5389 __isl_take isl_multi_union_pw_aff *mupa,
5390 __isl_take isl_union_set *uset);
5391 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5392 __isl_take isl_pw_aff *pa,
5393 __isl_take isl_set *set);
5394 __isl_give isl_multi_pw_aff *
5395 isl_multi_pw_aff_intersect_params(
5396 __isl_take isl_multi_pw_aff *mpa,
5397 __isl_take isl_set *set);
5398 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5399 __isl_take isl_pw_multi_aff *pma,
5400 __isl_take isl_set *set);
5401 __isl_give isl_union_pw_aff *
5402 isl_union_pw_aff_intersect_params(
5403 __isl_take isl_union_pw_aff *upa,
5404 __isl_give isl_union_pw_multi_aff *
5405 isl_union_pw_multi_aff_intersect_params(
5406 __isl_take isl_union_pw_multi_aff *upma,
5407 __isl_take isl_set *set);
5408 __isl_give isl_multi_union_pw_aff *
5409 isl_multi_union_pw_aff_intersect_params(
5410 __isl_take isl_multi_union_pw_aff *mupa,
5411 __isl_take isl_set *params);
5412 isl_multi_union_pw_aff_intersect_range(
5413 __isl_take isl_multi_union_pw_aff *mupa,
5414 __isl_take isl_set *set);
5416 #include <isl/polynomial.h>
5417 __isl_give isl_pw_qpolynomial *
5418 isl_pw_qpolynomial_intersect_domain(
5419 __isl_take isl_pw_qpolynomial *pwpq,
5420 __isl_take isl_set *set);
5421 __isl_give isl_union_pw_qpolynomial *
5422 isl_union_pw_qpolynomial_intersect_domain(
5423 __isl_take isl_union_pw_qpolynomial *upwpq,
5424 __isl_take isl_union_set *uset);
5425 __isl_give isl_union_pw_qpolynomial_fold *
5426 isl_union_pw_qpolynomial_fold_intersect_domain(
5427 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5428 __isl_take isl_union_set *uset);
5429 __isl_give isl_pw_qpolynomial *
5430 isl_pw_qpolynomial_intersect_params(
5431 __isl_take isl_pw_qpolynomial *pwpq,
5432 __isl_take isl_set *set);
5433 __isl_give isl_pw_qpolynomial_fold *
5434 isl_pw_qpolynomial_fold_intersect_params(
5435 __isl_take isl_pw_qpolynomial_fold *pwf,
5436 __isl_take isl_set *set);
5437 __isl_give isl_union_pw_qpolynomial *
5438 isl_union_pw_qpolynomial_intersect_params(
5439 __isl_take isl_union_pw_qpolynomial *upwpq,
5440 __isl_take isl_set *set);
5441 __isl_give isl_union_pw_qpolynomial_fold *
5442 isl_union_pw_qpolynomial_fold_intersect_params(
5443 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5444 __isl_take isl_set *set);
5446 The second argument to the C<_params> functions needs to be
5447 a parametric (basic) set. For the other functions, a parametric set
5448 for either argument is only allowed if the other argument is
5449 a parametric set as well.
5450 The list passed to C<isl_basic_set_list_intersect> needs to have
5451 at least one element and all elements need to live in the same space.
5452 The function C<isl_multi_union_pw_aff_intersect_range>
5453 restricts the input function to those shared domain elements
5454 that map to the specified range.
5458 #include <isl/set.h>
5459 __isl_give isl_set *isl_basic_set_union(
5460 __isl_take isl_basic_set *bset1,
5461 __isl_take isl_basic_set *bset2);
5462 __isl_give isl_set *isl_set_union(
5463 __isl_take isl_set *set1,
5464 __isl_take isl_set *set2);
5466 #include <isl/map.h>
5467 __isl_give isl_map *isl_basic_map_union(
5468 __isl_take isl_basic_map *bmap1,
5469 __isl_take isl_basic_map *bmap2);
5470 __isl_give isl_map *isl_map_union(
5471 __isl_take isl_map *map1,
5472 __isl_take isl_map *map2);
5474 #include <isl/union_set.h>
5475 __isl_give isl_union_set *isl_union_set_union(
5476 __isl_take isl_union_set *uset1,
5477 __isl_take isl_union_set *uset2);
5478 __isl_give isl_union_set *isl_union_set_list_union(
5479 __isl_take isl_union_set_list *list);
5481 #include <isl/union_map.h>
5482 __isl_give isl_union_map *isl_union_map_union(
5483 __isl_take isl_union_map *umap1,
5484 __isl_take isl_union_map *umap2);
5486 =item * Set difference
5488 #include <isl/set.h>
5489 __isl_give isl_set *isl_set_subtract(
5490 __isl_take isl_set *set1,
5491 __isl_take isl_set *set2);
5493 #include <isl/map.h>
5494 __isl_give isl_map *isl_map_subtract(
5495 __isl_take isl_map *map1,
5496 __isl_take isl_map *map2);
5497 __isl_give isl_map *isl_map_subtract_domain(
5498 __isl_take isl_map *map,
5499 __isl_take isl_set *dom);
5500 __isl_give isl_map *isl_map_subtract_range(
5501 __isl_take isl_map *map,
5502 __isl_take isl_set *dom);
5504 #include <isl/union_set.h>
5505 __isl_give isl_union_set *isl_union_set_subtract(
5506 __isl_take isl_union_set *uset1,
5507 __isl_take isl_union_set *uset2);
5509 #include <isl/union_map.h>
5510 __isl_give isl_union_map *isl_union_map_subtract(
5511 __isl_take isl_union_map *umap1,
5512 __isl_take isl_union_map *umap2);
5513 __isl_give isl_union_map *isl_union_map_subtract_domain(
5514 __isl_take isl_union_map *umap,
5515 __isl_take isl_union_set *dom);
5516 __isl_give isl_union_map *isl_union_map_subtract_range(
5517 __isl_take isl_union_map *umap,
5518 __isl_take isl_union_set *dom);
5520 #include <isl/aff.h>
5521 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5522 __isl_take isl_pw_aff *pa,
5523 __isl_take isl_set *set);
5524 __isl_give isl_pw_multi_aff *
5525 isl_pw_multi_aff_subtract_domain(
5526 __isl_take isl_pw_multi_aff *pma,
5527 __isl_take isl_set *set);
5528 __isl_give isl_union_pw_aff *
5529 isl_union_pw_aff_subtract_domain(
5530 __isl_take isl_union_pw_aff *upa,
5531 __isl_take isl_union_set *uset);
5532 __isl_give isl_union_pw_multi_aff *
5533 isl_union_pw_multi_aff_subtract_domain(
5534 __isl_take isl_union_pw_multi_aff *upma,
5535 __isl_take isl_set *set);
5537 #include <isl/polynomial.h>
5538 __isl_give isl_pw_qpolynomial *
5539 isl_pw_qpolynomial_subtract_domain(
5540 __isl_take isl_pw_qpolynomial *pwpq,
5541 __isl_take isl_set *set);
5542 __isl_give isl_pw_qpolynomial_fold *
5543 isl_pw_qpolynomial_fold_subtract_domain(
5544 __isl_take isl_pw_qpolynomial_fold *pwf,
5545 __isl_take isl_set *set);
5546 __isl_give isl_union_pw_qpolynomial *
5547 isl_union_pw_qpolynomial_subtract_domain(
5548 __isl_take isl_union_pw_qpolynomial *upwpq,
5549 __isl_take isl_union_set *uset);
5550 __isl_give isl_union_pw_qpolynomial_fold *
5551 isl_union_pw_qpolynomial_fold_subtract_domain(
5552 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5553 __isl_take isl_union_set *uset);
5557 #include <isl/space.h>
5558 __isl_give isl_space *isl_space_join(
5559 __isl_take isl_space *left,
5560 __isl_take isl_space *right);
5562 #include <isl/map.h>
5563 __isl_give isl_basic_set *isl_basic_set_apply(
5564 __isl_take isl_basic_set *bset,
5565 __isl_take isl_basic_map *bmap);
5566 __isl_give isl_set *isl_set_apply(
5567 __isl_take isl_set *set,
5568 __isl_take isl_map *map);
5569 __isl_give isl_union_set *isl_union_set_apply(
5570 __isl_take isl_union_set *uset,
5571 __isl_take isl_union_map *umap);
5572 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5573 __isl_take isl_basic_map *bmap1,
5574 __isl_take isl_basic_map *bmap2);
5575 __isl_give isl_basic_map *isl_basic_map_apply_range(
5576 __isl_take isl_basic_map *bmap1,
5577 __isl_take isl_basic_map *bmap2);
5578 __isl_give isl_map *isl_map_apply_domain(
5579 __isl_take isl_map *map1,
5580 __isl_take isl_map *map2);
5581 __isl_give isl_map *isl_map_apply_range(
5582 __isl_take isl_map *map1,
5583 __isl_take isl_map *map2);
5585 #include <isl/union_map.h>
5586 __isl_give isl_union_map *isl_union_map_apply_domain(
5587 __isl_take isl_union_map *umap1,
5588 __isl_take isl_union_map *umap2);
5589 __isl_give isl_union_map *isl_union_map_apply_range(
5590 __isl_take isl_union_map *umap1,
5591 __isl_take isl_union_map *umap2);
5593 #include <isl/aff.h>
5594 __isl_give isl_union_pw_aff *
5595 isl_multi_union_pw_aff_apply_aff(
5596 __isl_take isl_multi_union_pw_aff *mupa,
5597 __isl_take isl_aff *aff);
5598 __isl_give isl_union_pw_aff *
5599 isl_multi_union_pw_aff_apply_pw_aff(
5600 __isl_take isl_multi_union_pw_aff *mupa,
5601 __isl_take isl_pw_aff *pa);
5602 __isl_give isl_multi_union_pw_aff *
5603 isl_multi_union_pw_aff_apply_multi_aff(
5604 __isl_take isl_multi_union_pw_aff *mupa,
5605 __isl_take isl_multi_aff *ma);
5606 __isl_give isl_multi_union_pw_aff *
5607 isl_multi_union_pw_aff_apply_pw_multi_aff(
5608 __isl_take isl_multi_union_pw_aff *mupa,
5609 __isl_take isl_pw_multi_aff *pma);
5611 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5612 over the shared domain of the elements of the input. The dimension is
5613 required to be greater than zero.
5614 The C<isl_multi_union_pw_aff> argument of
5615 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5616 but only if the range of the C<isl_multi_aff> argument
5617 is also zero-dimensional.
5618 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5620 #include <isl/polynomial.h>
5621 __isl_give isl_pw_qpolynomial_fold *
5622 isl_set_apply_pw_qpolynomial_fold(
5623 __isl_take isl_set *set,
5624 __isl_take isl_pw_qpolynomial_fold *pwf,
5626 __isl_give isl_pw_qpolynomial_fold *
5627 isl_map_apply_pw_qpolynomial_fold(
5628 __isl_take isl_map *map,
5629 __isl_take isl_pw_qpolynomial_fold *pwf,
5631 __isl_give isl_union_pw_qpolynomial_fold *
5632 isl_union_set_apply_union_pw_qpolynomial_fold(
5633 __isl_take isl_union_set *uset,
5634 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5636 __isl_give isl_union_pw_qpolynomial_fold *
5637 isl_union_map_apply_union_pw_qpolynomial_fold(
5638 __isl_take isl_union_map *umap,
5639 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5642 The functions taking a map
5643 compose the given map with the given piecewise quasipolynomial reduction.
5644 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5645 over all elements in the intersection of the range of the map
5646 and the domain of the piecewise quasipolynomial reduction
5647 as a function of an element in the domain of the map.
5648 The functions taking a set compute a bound over all elements in the
5649 intersection of the set and the domain of the
5650 piecewise quasipolynomial reduction.
5654 #include <isl/set.h>
5655 __isl_give isl_basic_set *
5656 isl_basic_set_preimage_multi_aff(
5657 __isl_take isl_basic_set *bset,
5658 __isl_take isl_multi_aff *ma);
5659 __isl_give isl_set *isl_set_preimage_multi_aff(
5660 __isl_take isl_set *set,
5661 __isl_take isl_multi_aff *ma);
5662 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5663 __isl_take isl_set *set,
5664 __isl_take isl_pw_multi_aff *pma);
5665 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5666 __isl_take isl_set *set,
5667 __isl_take isl_multi_pw_aff *mpa);
5669 #include <isl/union_set.h>
5670 __isl_give isl_union_set *
5671 isl_union_set_preimage_multi_aff(
5672 __isl_take isl_union_set *uset,
5673 __isl_take isl_multi_aff *ma);
5674 __isl_give isl_union_set *
5675 isl_union_set_preimage_pw_multi_aff(
5676 __isl_take isl_union_set *uset,
5677 __isl_take isl_pw_multi_aff *pma);
5678 __isl_give isl_union_set *
5679 isl_union_set_preimage_union_pw_multi_aff(
5680 __isl_take isl_union_set *uset,
5681 __isl_take isl_union_pw_multi_aff *upma);
5683 #include <isl/map.h>
5684 __isl_give isl_basic_map *
5685 isl_basic_map_preimage_domain_multi_aff(
5686 __isl_take isl_basic_map *bmap,
5687 __isl_take isl_multi_aff *ma);
5688 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5689 __isl_take isl_map *map,
5690 __isl_take isl_multi_aff *ma);
5691 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5692 __isl_take isl_map *map,
5693 __isl_take isl_multi_aff *ma);
5694 __isl_give isl_map *
5695 isl_map_preimage_domain_pw_multi_aff(
5696 __isl_take isl_map *map,
5697 __isl_take isl_pw_multi_aff *pma);
5698 __isl_give isl_map *
5699 isl_map_preimage_range_pw_multi_aff(
5700 __isl_take isl_map *map,
5701 __isl_take isl_pw_multi_aff *pma);
5702 __isl_give isl_map *
5703 isl_map_preimage_domain_multi_pw_aff(
5704 __isl_take isl_map *map,
5705 __isl_take isl_multi_pw_aff *mpa);
5706 __isl_give isl_basic_map *
5707 isl_basic_map_preimage_range_multi_aff(
5708 __isl_take isl_basic_map *bmap,
5709 __isl_take isl_multi_aff *ma);
5711 #include <isl/union_map.h>
5712 __isl_give isl_union_map *
5713 isl_union_map_preimage_domain_multi_aff(
5714 __isl_take isl_union_map *umap,
5715 __isl_take isl_multi_aff *ma);
5716 __isl_give isl_union_map *
5717 isl_union_map_preimage_range_multi_aff(
5718 __isl_take isl_union_map *umap,
5719 __isl_take isl_multi_aff *ma);
5720 __isl_give isl_union_map *
5721 isl_union_map_preimage_domain_pw_multi_aff(
5722 __isl_take isl_union_map *umap,
5723 __isl_take isl_pw_multi_aff *pma);
5724 __isl_give isl_union_map *
5725 isl_union_map_preimage_range_pw_multi_aff(
5726 __isl_take isl_union_map *umap,
5727 __isl_take isl_pw_multi_aff *pma);
5728 __isl_give isl_union_map *
5729 isl_union_map_preimage_domain_union_pw_multi_aff(
5730 __isl_take isl_union_map *umap,
5731 __isl_take isl_union_pw_multi_aff *upma);
5732 __isl_give isl_union_map *
5733 isl_union_map_preimage_range_union_pw_multi_aff(
5734 __isl_take isl_union_map *umap,
5735 __isl_take isl_union_pw_multi_aff *upma);
5737 These functions compute the preimage of the given set or map domain/range under
5738 the given function. In other words, the expression is plugged
5739 into the set description or into the domain/range of the map.
5743 #include <isl/aff.h>
5744 __isl_give isl_aff *isl_aff_pullback_aff(
5745 __isl_take isl_aff *aff1,
5746 __isl_take isl_aff *aff2);
5747 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5748 __isl_take isl_aff *aff,
5749 __isl_take isl_multi_aff *ma);
5750 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5751 __isl_take isl_pw_aff *pa,
5752 __isl_take isl_multi_aff *ma);
5753 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5754 __isl_take isl_pw_aff *pa,
5755 __isl_take isl_pw_multi_aff *pma);
5756 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5757 __isl_take isl_pw_aff *pa,
5758 __isl_take isl_multi_pw_aff *mpa);
5759 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5760 __isl_take isl_multi_aff *ma1,
5761 __isl_take isl_multi_aff *ma2);
5762 __isl_give isl_pw_multi_aff *
5763 isl_pw_multi_aff_pullback_multi_aff(
5764 __isl_take isl_pw_multi_aff *pma,
5765 __isl_take isl_multi_aff *ma);
5766 __isl_give isl_multi_pw_aff *
5767 isl_multi_pw_aff_pullback_multi_aff(
5768 __isl_take isl_multi_pw_aff *mpa,
5769 __isl_take isl_multi_aff *ma);
5770 __isl_give isl_pw_multi_aff *
5771 isl_pw_multi_aff_pullback_pw_multi_aff(
5772 __isl_take isl_pw_multi_aff *pma1,
5773 __isl_take isl_pw_multi_aff *pma2);
5774 __isl_give isl_multi_pw_aff *
5775 isl_multi_pw_aff_pullback_pw_multi_aff(
5776 __isl_take isl_multi_pw_aff *mpa,
5777 __isl_take isl_pw_multi_aff *pma);
5778 __isl_give isl_multi_pw_aff *
5779 isl_multi_pw_aff_pullback_multi_pw_aff(
5780 __isl_take isl_multi_pw_aff *mpa1,
5781 __isl_take isl_multi_pw_aff *mpa2);
5782 __isl_give isl_union_pw_aff *
5783 isl_union_pw_aff_pullback_union_pw_multi_aff(
5784 __isl_take isl_union_pw_aff *upa,
5785 __isl_take isl_union_pw_multi_aff *upma);
5786 __isl_give isl_union_pw_multi_aff *
5787 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5788 __isl_take isl_union_pw_multi_aff *upma1,
5789 __isl_take isl_union_pw_multi_aff *upma2);
5790 __isl_give isl_multi_union_pw_aff *
5791 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
5792 __isl_take isl_multi_union_pw_aff *mupa,
5793 __isl_take isl_union_pw_multi_aff *upma);
5795 These functions precompose the first expression by the second function.
5796 In other words, the second function is plugged
5797 into the first expression.
5801 #include <isl/aff.h>
5802 __isl_give isl_basic_set *isl_aff_le_basic_set(
5803 __isl_take isl_aff *aff1,
5804 __isl_take isl_aff *aff2);
5805 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5806 __isl_take isl_aff *aff1,
5807 __isl_take isl_aff *aff2);
5808 __isl_give isl_set *isl_pw_aff_eq_set(
5809 __isl_take isl_pw_aff *pwaff1,
5810 __isl_take isl_pw_aff *pwaff2);
5811 __isl_give isl_set *isl_pw_aff_ne_set(
5812 __isl_take isl_pw_aff *pwaff1,
5813 __isl_take isl_pw_aff *pwaff2);
5814 __isl_give isl_set *isl_pw_aff_le_set(
5815 __isl_take isl_pw_aff *pwaff1,
5816 __isl_take isl_pw_aff *pwaff2);
5817 __isl_give isl_set *isl_pw_aff_lt_set(
5818 __isl_take isl_pw_aff *pwaff1,
5819 __isl_take isl_pw_aff *pwaff2);
5820 __isl_give isl_set *isl_pw_aff_ge_set(
5821 __isl_take isl_pw_aff *pwaff1,
5822 __isl_take isl_pw_aff *pwaff2);
5823 __isl_give isl_set *isl_pw_aff_gt_set(
5824 __isl_take isl_pw_aff *pwaff1,
5825 __isl_take isl_pw_aff *pwaff2);
5827 __isl_give isl_set *isl_multi_aff_lex_le_set(
5828 __isl_take isl_multi_aff *ma1,
5829 __isl_take isl_multi_aff *ma2);
5830 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5831 __isl_take isl_multi_aff *ma1,
5832 __isl_take isl_multi_aff *ma2);
5834 __isl_give isl_set *isl_pw_aff_list_eq_set(
5835 __isl_take isl_pw_aff_list *list1,
5836 __isl_take isl_pw_aff_list *list2);
5837 __isl_give isl_set *isl_pw_aff_list_ne_set(
5838 __isl_take isl_pw_aff_list *list1,
5839 __isl_take isl_pw_aff_list *list2);
5840 __isl_give isl_set *isl_pw_aff_list_le_set(
5841 __isl_take isl_pw_aff_list *list1,
5842 __isl_take isl_pw_aff_list *list2);
5843 __isl_give isl_set *isl_pw_aff_list_lt_set(
5844 __isl_take isl_pw_aff_list *list1,
5845 __isl_take isl_pw_aff_list *list2);
5846 __isl_give isl_set *isl_pw_aff_list_ge_set(
5847 __isl_take isl_pw_aff_list *list1,
5848 __isl_take isl_pw_aff_list *list2);
5849 __isl_give isl_set *isl_pw_aff_list_gt_set(
5850 __isl_take isl_pw_aff_list *list1,
5851 __isl_take isl_pw_aff_list *list2);
5853 The function C<isl_aff_ge_basic_set> returns a basic set
5854 containing those elements in the shared space
5855 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5856 The function C<isl_pw_aff_ge_set> returns a set
5857 containing those elements in the shared domain
5858 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5859 greater than or equal to C<pwaff2>.
5860 The function C<isl_multi_aff_lex_le_set> returns a set
5861 containing those elements in the shared domain space
5862 where C<ma1> is lexicographically smaller than or
5864 The functions operating on C<isl_pw_aff_list> apply the corresponding
5865 C<isl_pw_aff> function to each pair of elements in the two lists.
5867 =item * Cartesian Product
5869 #include <isl/space.h>
5870 __isl_give isl_space *isl_space_product(
5871 __isl_take isl_space *space1,
5872 __isl_take isl_space *space2);
5873 __isl_give isl_space *isl_space_domain_product(
5874 __isl_take isl_space *space1,
5875 __isl_take isl_space *space2);
5876 __isl_give isl_space *isl_space_range_product(
5877 __isl_take isl_space *space1,
5878 __isl_take isl_space *space2);
5881 C<isl_space_product>, C<isl_space_domain_product>
5882 and C<isl_space_range_product> take pairs or relation spaces and
5883 produce a single relations space, where either the domain, the range
5884 or both domain and range are wrapped spaces of relations between
5885 the domains and/or ranges of the input spaces.
5886 If the product is only constructed over the domain or the range
5887 then the ranges or the domains of the inputs should be the same.
5888 The function C<isl_space_product> also accepts a pair of set spaces,
5889 in which case it returns a wrapped space of a relation between the
5892 #include <isl/set.h>
5893 __isl_give isl_set *isl_set_product(
5894 __isl_take isl_set *set1,
5895 __isl_take isl_set *set2);
5897 #include <isl/map.h>
5898 __isl_give isl_basic_map *isl_basic_map_domain_product(
5899 __isl_take isl_basic_map *bmap1,
5900 __isl_take isl_basic_map *bmap2);
5901 __isl_give isl_basic_map *isl_basic_map_range_product(
5902 __isl_take isl_basic_map *bmap1,
5903 __isl_take isl_basic_map *bmap2);
5904 __isl_give isl_basic_map *isl_basic_map_product(
5905 __isl_take isl_basic_map *bmap1,
5906 __isl_take isl_basic_map *bmap2);
5907 __isl_give isl_map *isl_map_domain_product(
5908 __isl_take isl_map *map1,
5909 __isl_take isl_map *map2);
5910 __isl_give isl_map *isl_map_range_product(
5911 __isl_take isl_map *map1,
5912 __isl_take isl_map *map2);
5913 __isl_give isl_map *isl_map_product(
5914 __isl_take isl_map *map1,
5915 __isl_take isl_map *map2);
5917 #include <isl/union_set.h>
5918 __isl_give isl_union_set *isl_union_set_product(
5919 __isl_take isl_union_set *uset1,
5920 __isl_take isl_union_set *uset2);
5922 #include <isl/union_map.h>
5923 __isl_give isl_union_map *isl_union_map_domain_product(
5924 __isl_take isl_union_map *umap1,
5925 __isl_take isl_union_map *umap2);
5926 __isl_give isl_union_map *isl_union_map_range_product(
5927 __isl_take isl_union_map *umap1,
5928 __isl_take isl_union_map *umap2);
5929 __isl_give isl_union_map *isl_union_map_product(
5930 __isl_take isl_union_map *umap1,
5931 __isl_take isl_union_map *umap2);
5933 #include <isl/val.h>
5934 __isl_give isl_multi_val *isl_multi_val_range_product(
5935 __isl_take isl_multi_val *mv1,
5936 __isl_take isl_multi_val *mv2);
5937 __isl_give isl_multi_val *isl_multi_val_product(
5938 __isl_take isl_multi_val *mv1,
5939 __isl_take isl_multi_val *mv2);
5941 #include <isl/aff.h>
5942 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5943 __isl_take isl_multi_aff *ma1,
5944 __isl_take isl_multi_aff *ma2);
5945 __isl_give isl_multi_aff *isl_multi_aff_product(
5946 __isl_take isl_multi_aff *ma1,
5947 __isl_take isl_multi_aff *ma2);
5948 __isl_give isl_multi_pw_aff *
5949 isl_multi_pw_aff_range_product(
5950 __isl_take isl_multi_pw_aff *mpa1,
5951 __isl_take isl_multi_pw_aff *mpa2);
5952 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5953 __isl_take isl_multi_pw_aff *mpa1,
5954 __isl_take isl_multi_pw_aff *mpa2);
5955 __isl_give isl_pw_multi_aff *
5956 isl_pw_multi_aff_range_product(
5957 __isl_take isl_pw_multi_aff *pma1,
5958 __isl_take isl_pw_multi_aff *pma2);
5959 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5960 __isl_take isl_pw_multi_aff *pma1,
5961 __isl_take isl_pw_multi_aff *pma2);
5962 __isl_give isl_multi_union_pw_aff *
5963 isl_multi_union_pw_aff_range_product(
5964 __isl_take isl_multi_union_pw_aff *mupa1,
5965 __isl_take isl_multi_union_pw_aff *mupa2);
5967 The above functions compute the cross product of the given
5968 sets, relations or functions. The domains and ranges of the results
5969 are wrapped maps between domains and ranges of the inputs.
5970 To obtain a ``flat'' product, use the following functions
5973 #include <isl/set.h>
5974 __isl_give isl_basic_set *isl_basic_set_flat_product(
5975 __isl_take isl_basic_set *bset1,
5976 __isl_take isl_basic_set *bset2);
5977 __isl_give isl_set *isl_set_flat_product(
5978 __isl_take isl_set *set1,
5979 __isl_take isl_set *set2);
5981 #include <isl/map.h>
5982 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5983 __isl_take isl_basic_map *bmap1,
5984 __isl_take isl_basic_map *bmap2);
5985 __isl_give isl_map *isl_map_flat_domain_product(
5986 __isl_take isl_map *map1,
5987 __isl_take isl_map *map2);
5988 __isl_give isl_map *isl_map_flat_range_product(
5989 __isl_take isl_map *map1,
5990 __isl_take isl_map *map2);
5991 __isl_give isl_basic_map *isl_basic_map_flat_product(
5992 __isl_take isl_basic_map *bmap1,
5993 __isl_take isl_basic_map *bmap2);
5994 __isl_give isl_map *isl_map_flat_product(
5995 __isl_take isl_map *map1,
5996 __isl_take isl_map *map2);
5998 #include <isl/union_map.h>
5999 __isl_give isl_union_map *
6000 isl_union_map_flat_domain_product(
6001 __isl_take isl_union_map *umap1,
6002 __isl_take isl_union_map *umap2);
6003 __isl_give isl_union_map *
6004 isl_union_map_flat_range_product(
6005 __isl_take isl_union_map *umap1,
6006 __isl_take isl_union_map *umap2);
6008 #include <isl/val.h>
6009 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6010 __isl_take isl_multi_val *mv1,
6011 __isl_take isl_multi_aff *mv2);
6013 #include <isl/aff.h>
6014 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6015 __isl_take isl_multi_aff *ma1,
6016 __isl_take isl_multi_aff *ma2);
6017 __isl_give isl_pw_multi_aff *
6018 isl_pw_multi_aff_flat_range_product(
6019 __isl_take isl_pw_multi_aff *pma1,
6020 __isl_take isl_pw_multi_aff *pma2);
6021 __isl_give isl_multi_pw_aff *
6022 isl_multi_pw_aff_flat_range_product(
6023 __isl_take isl_multi_pw_aff *mpa1,
6024 __isl_take isl_multi_pw_aff *mpa2);
6025 __isl_give isl_union_pw_multi_aff *
6026 isl_union_pw_multi_aff_flat_range_product(
6027 __isl_take isl_union_pw_multi_aff *upma1,
6028 __isl_take isl_union_pw_multi_aff *upma2);
6029 __isl_give isl_multi_union_pw_aff *
6030 isl_multi_union_pw_aff_flat_range_product(
6031 __isl_take isl_multi_union_pw_aff *mupa1,
6032 __isl_take isl_multi_union_pw_aff *mupa2);
6034 #include <isl/space.h>
6035 __isl_give isl_space *isl_space_factor_domain(
6036 __isl_take isl_space *space);
6037 __isl_give isl_space *isl_space_factor_range(
6038 __isl_take isl_space *space);
6039 __isl_give isl_space *isl_space_domain_factor_domain(
6040 __isl_take isl_space *space);
6041 __isl_give isl_space *isl_space_domain_factor_range(
6042 __isl_take isl_space *space);
6043 __isl_give isl_space *isl_space_range_factor_domain(
6044 __isl_take isl_space *space);
6045 __isl_give isl_space *isl_space_range_factor_range(
6046 __isl_take isl_space *space);
6048 The functions C<isl_space_range_factor_domain> and
6049 C<isl_space_range_factor_range> extract the two arguments from
6050 the result of a call to C<isl_space_range_product>.
6052 The arguments of a call to C<isl_map_range_product> can be extracted
6053 from the result using the following functions.
6055 #include <isl/map.h>
6056 __isl_give isl_map *isl_map_factor_domain(
6057 __isl_take isl_map *map);
6058 __isl_give isl_map *isl_map_factor_range(
6059 __isl_take isl_map *map);
6060 __isl_give isl_map *isl_map_domain_factor_domain(
6061 __isl_take isl_map *map);
6062 __isl_give isl_map *isl_map_domain_factor_range(
6063 __isl_take isl_map *map);
6064 __isl_give isl_map *isl_map_range_factor_domain(
6065 __isl_take isl_map *map);
6066 __isl_give isl_map *isl_map_range_factor_range(
6067 __isl_take isl_map *map);
6069 #include <isl/union_map.h>
6070 __isl_give isl_union_map *isl_union_map_factor_domain(
6071 __isl_take isl_union_map *umap);
6072 __isl_give isl_union_map *isl_union_map_factor_range(
6073 __isl_take isl_union_map *umap);
6074 __isl_give isl_union_map *
6075 isl_union_map_domain_factor_domain(
6076 __isl_take isl_union_map *umap);
6077 __isl_give isl_union_map *
6078 isl_union_map_domain_factor_range(
6079 __isl_take isl_union_map *umap);
6080 __isl_give isl_union_map *
6081 isl_union_map_range_factor_range(
6082 __isl_take isl_union_map *umap);
6084 #include <isl/val.h>
6085 __isl_give isl_multi_val *
6086 isl_multi_val_range_factor_domain(
6087 __isl_take isl_multi_val *mv);
6088 __isl_give isl_multi_val *
6089 isl_multi_val_range_factor_range(
6090 __isl_take isl_multi_val *mv);
6092 #include <isl/aff.h>
6093 __isl_give isl_multi_aff *
6094 isl_multi_aff_range_factor_domain(
6095 __isl_take isl_multi_aff *ma);
6096 __isl_give isl_multi_aff *
6097 isl_multi_aff_range_factor_range(
6098 __isl_take isl_multi_aff *ma);
6099 __isl_give isl_multi_pw_aff *
6100 isl_multi_pw_aff_range_factor_domain(
6101 __isl_take isl_multi_pw_aff *mpa);
6102 __isl_give isl_multi_pw_aff *
6103 isl_multi_pw_aff_range_factor_range(
6104 __isl_take isl_multi_pw_aff *mpa);
6105 __isl_give isl_multi_union_pw_aff *
6106 isl_multi_union_pw_aff_range_factor_domain(
6107 __isl_take isl_multi_union_pw_aff *mupa);
6108 __isl_give isl_multi_union_pw_aff *
6109 isl_multi_union_pw_aff_range_factor_range(
6110 __isl_take isl_multi_union_pw_aff *mupa);
6112 The splice functions are a generalization of the flat product functions,
6113 where the second argument may be inserted at any position inside
6114 the first argument rather than being placed at the end.
6116 #include <isl/val.h>
6117 __isl_give isl_multi_val *isl_multi_val_range_splice(
6118 __isl_take isl_multi_val *mv1, unsigned pos,
6119 __isl_take isl_multi_val *mv2);
6121 #include <isl/aff.h>
6122 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6123 __isl_take isl_multi_aff *ma1, unsigned pos,
6124 __isl_take isl_multi_aff *ma2);
6125 __isl_give isl_multi_aff *isl_multi_aff_splice(
6126 __isl_take isl_multi_aff *ma1,
6127 unsigned in_pos, unsigned out_pos,
6128 __isl_take isl_multi_aff *ma2);
6129 __isl_give isl_multi_pw_aff *
6130 isl_multi_pw_aff_range_splice(
6131 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6132 __isl_take isl_multi_pw_aff *mpa2);
6133 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6134 __isl_take isl_multi_pw_aff *mpa1,
6135 unsigned in_pos, unsigned out_pos,
6136 __isl_take isl_multi_pw_aff *mpa2);
6137 __isl_give isl_multi_union_pw_aff *
6138 isl_multi_union_pw_aff_range_splice(
6139 __isl_take isl_multi_union_pw_aff *mupa1,
6141 __isl_take isl_multi_union_pw_aff *mupa2);
6143 =item * Simplification
6145 When applied to a set or relation,
6146 the gist operation returns a set or relation that has the
6147 same intersection with the context as the input set or relation.
6148 Any implicit equality in the intersection is made explicit in the result,
6149 while all inequalities that are redundant with respect to the intersection
6151 In case of union sets and relations, the gist operation is performed
6154 When applied to a function,
6155 the gist operation applies the set gist operation to each of
6156 the cells in the domain of the input piecewise expression.
6157 The context is also exploited
6158 to simplify the expression associated to each cell.
6160 #include <isl/set.h>
6161 __isl_give isl_basic_set *isl_basic_set_gist(
6162 __isl_take isl_basic_set *bset,
6163 __isl_take isl_basic_set *context);
6164 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6165 __isl_take isl_set *context);
6166 __isl_give isl_set *isl_set_gist_params(
6167 __isl_take isl_set *set,
6168 __isl_take isl_set *context);
6170 #include <isl/map.h>
6171 __isl_give isl_basic_map *isl_basic_map_gist(
6172 __isl_take isl_basic_map *bmap,
6173 __isl_take isl_basic_map *context);
6174 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6175 __isl_take isl_basic_map *bmap,
6176 __isl_take isl_basic_set *context);
6177 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6178 __isl_take isl_map *context);
6179 __isl_give isl_map *isl_map_gist_params(
6180 __isl_take isl_map *map,
6181 __isl_take isl_set *context);
6182 __isl_give isl_map *isl_map_gist_domain(
6183 __isl_take isl_map *map,
6184 __isl_take isl_set *context);
6185 __isl_give isl_map *isl_map_gist_range(
6186 __isl_take isl_map *map,
6187 __isl_take isl_set *context);
6189 #include <isl/union_set.h>
6190 __isl_give isl_union_set *isl_union_set_gist(
6191 __isl_take isl_union_set *uset,
6192 __isl_take isl_union_set *context);
6193 __isl_give isl_union_set *isl_union_set_gist_params(
6194 __isl_take isl_union_set *uset,
6195 __isl_take isl_set *set);
6197 #include <isl/union_map.h>
6198 __isl_give isl_union_map *isl_union_map_gist(
6199 __isl_take isl_union_map *umap,
6200 __isl_take isl_union_map *context);
6201 __isl_give isl_union_map *isl_union_map_gist_params(
6202 __isl_take isl_union_map *umap,
6203 __isl_take isl_set *set);
6204 __isl_give isl_union_map *isl_union_map_gist_domain(
6205 __isl_take isl_union_map *umap,
6206 __isl_take isl_union_set *uset);
6207 __isl_give isl_union_map *isl_union_map_gist_range(
6208 __isl_take isl_union_map *umap,
6209 __isl_take isl_union_set *uset);
6211 #include <isl/aff.h>
6212 __isl_give isl_aff *isl_aff_gist_params(
6213 __isl_take isl_aff *aff,
6214 __isl_take isl_set *context);
6215 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6216 __isl_take isl_set *context);
6217 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6218 __isl_take isl_multi_aff *maff,
6219 __isl_take isl_set *context);
6220 __isl_give isl_multi_aff *isl_multi_aff_gist(
6221 __isl_take isl_multi_aff *maff,
6222 __isl_take isl_set *context);
6223 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6224 __isl_take isl_pw_aff *pwaff,
6225 __isl_take isl_set *context);
6226 __isl_give isl_pw_aff *isl_pw_aff_gist(
6227 __isl_take isl_pw_aff *pwaff,
6228 __isl_take isl_set *context);
6229 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6230 __isl_take isl_pw_multi_aff *pma,
6231 __isl_take isl_set *set);
6232 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6233 __isl_take isl_pw_multi_aff *pma,
6234 __isl_take isl_set *set);
6235 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6236 __isl_take isl_multi_pw_aff *mpa,
6237 __isl_take isl_set *set);
6238 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6239 __isl_take isl_multi_pw_aff *mpa,
6240 __isl_take isl_set *set);
6241 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6242 __isl_take isl_union_pw_aff *upa,
6243 __isl_take isl_union_set *context);
6244 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6245 __isl_take isl_union_pw_aff *upa,
6246 __isl_take isl_set *context);
6247 __isl_give isl_union_pw_multi_aff *
6248 isl_union_pw_multi_aff_gist_params(
6249 __isl_take isl_union_pw_multi_aff *upma,
6250 __isl_take isl_set *context);
6251 __isl_give isl_union_pw_multi_aff *
6252 isl_union_pw_multi_aff_gist(
6253 __isl_take isl_union_pw_multi_aff *upma,
6254 __isl_take isl_union_set *context);
6255 __isl_give isl_multi_union_pw_aff *
6256 isl_multi_union_pw_aff_gist_params(
6257 __isl_take isl_multi_union_pw_aff *aff,
6258 __isl_take isl_set *context);
6259 __isl_give isl_multi_union_pw_aff *
6260 isl_multi_union_pw_aff_gist(
6261 __isl_take isl_multi_union_pw_aff *aff,
6262 __isl_take isl_union_set *context);
6264 #include <isl/polynomial.h>
6265 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6266 __isl_take isl_qpolynomial *qp,
6267 __isl_take isl_set *context);
6268 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6269 __isl_take isl_qpolynomial *qp,
6270 __isl_take isl_set *context);
6271 __isl_give isl_qpolynomial_fold *
6272 isl_qpolynomial_fold_gist_params(
6273 __isl_take isl_qpolynomial_fold *fold,
6274 __isl_take isl_set *context);
6275 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6276 __isl_take isl_qpolynomial_fold *fold,
6277 __isl_take isl_set *context);
6278 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6279 __isl_take isl_pw_qpolynomial *pwqp,
6280 __isl_take isl_set *context);
6281 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6282 __isl_take isl_pw_qpolynomial *pwqp,
6283 __isl_take isl_set *context);
6284 __isl_give isl_pw_qpolynomial_fold *
6285 isl_pw_qpolynomial_fold_gist(
6286 __isl_take isl_pw_qpolynomial_fold *pwf,
6287 __isl_take isl_set *context);
6288 __isl_give isl_pw_qpolynomial_fold *
6289 isl_pw_qpolynomial_fold_gist_params(
6290 __isl_take isl_pw_qpolynomial_fold *pwf,
6291 __isl_take isl_set *context);
6292 __isl_give isl_union_pw_qpolynomial *
6293 isl_union_pw_qpolynomial_gist_params(
6294 __isl_take isl_union_pw_qpolynomial *upwqp,
6295 __isl_take isl_set *context);
6296 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6297 __isl_take isl_union_pw_qpolynomial *upwqp,
6298 __isl_take isl_union_set *context);
6299 __isl_give isl_union_pw_qpolynomial_fold *
6300 isl_union_pw_qpolynomial_fold_gist(
6301 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6302 __isl_take isl_union_set *context);
6303 __isl_give isl_union_pw_qpolynomial_fold *
6304 isl_union_pw_qpolynomial_fold_gist_params(
6305 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6306 __isl_take isl_set *context);
6308 =item * Binary Arithmethic Operations
6310 #include <isl/val.h>
6311 __isl_give isl_multi_val *isl_multi_val_sub(
6312 __isl_take isl_multi_val *mv1,
6313 __isl_take isl_multi_val *mv2);
6315 #include <isl/aff.h>
6316 __isl_give isl_aff *isl_aff_add(
6317 __isl_take isl_aff *aff1,
6318 __isl_take isl_aff *aff2);
6319 __isl_give isl_multi_aff *isl_multi_aff_add(
6320 __isl_take isl_multi_aff *maff1,
6321 __isl_take isl_multi_aff *maff2);
6322 __isl_give isl_pw_aff *isl_pw_aff_add(
6323 __isl_take isl_pw_aff *pwaff1,
6324 __isl_take isl_pw_aff *pwaff2);
6325 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6326 __isl_take isl_pw_multi_aff *pma1,
6327 __isl_take isl_pw_multi_aff *pma2);
6328 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6329 __isl_take isl_union_pw_aff *upa1,
6330 __isl_take isl_union_pw_aff *upa2);
6331 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6332 __isl_take isl_union_pw_multi_aff *upma1,
6333 __isl_take isl_union_pw_multi_aff *upma2);
6334 __isl_give isl_pw_aff *isl_pw_aff_min(
6335 __isl_take isl_pw_aff *pwaff1,
6336 __isl_take isl_pw_aff *pwaff2);
6337 __isl_give isl_pw_aff *isl_pw_aff_max(
6338 __isl_take isl_pw_aff *pwaff1,
6339 __isl_take isl_pw_aff *pwaff2);
6340 __isl_give isl_aff *isl_aff_sub(
6341 __isl_take isl_aff *aff1,
6342 __isl_take isl_aff *aff2);
6343 __isl_give isl_multi_aff *isl_multi_aff_sub(
6344 __isl_take isl_multi_aff *ma1,
6345 __isl_take isl_multi_aff *ma2);
6346 __isl_give isl_pw_aff *isl_pw_aff_sub(
6347 __isl_take isl_pw_aff *pwaff1,
6348 __isl_take isl_pw_aff *pwaff2);
6349 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6350 __isl_take isl_multi_pw_aff *mpa1,
6351 __isl_take isl_multi_pw_aff *mpa2);
6352 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6353 __isl_take isl_pw_multi_aff *pma1,
6354 __isl_take isl_pw_multi_aff *pma2);
6355 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6356 __isl_take isl_union_pw_aff *upa1,
6357 __isl_take isl_union_pw_aff *upa2);
6358 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6359 __isl_take isl_union_pw_multi_aff *upma1,
6360 __isl_take isl_union_pw_multi_aff *upma2);
6361 __isl_give isl_multi_union_pw_aff *
6362 isl_multi_union_pw_aff_sub(
6363 __isl_take isl_multi_union_pw_aff *mupa1,
6364 __isl_take isl_multi_union_pw_aff *mupa2);
6366 C<isl_aff_sub> subtracts the second argument from the first.
6368 #include <isl/polynomial.h>
6369 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6370 __isl_take isl_qpolynomial *qp1,
6371 __isl_take isl_qpolynomial *qp2);
6372 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6373 __isl_take isl_pw_qpolynomial *pwqp1,
6374 __isl_take isl_pw_qpolynomial *pwqp2);
6375 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6376 __isl_take isl_pw_qpolynomial *pwqp1,
6377 __isl_take isl_pw_qpolynomial *pwqp2);
6378 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6379 __isl_take isl_pw_qpolynomial_fold *pwf1,
6380 __isl_take isl_pw_qpolynomial_fold *pwf2);
6381 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6382 __isl_take isl_union_pw_qpolynomial *upwqp1,
6383 __isl_take isl_union_pw_qpolynomial *upwqp2);
6384 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6385 __isl_take isl_qpolynomial *qp1,
6386 __isl_take isl_qpolynomial *qp2);
6387 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6388 __isl_take isl_pw_qpolynomial *pwqp1,
6389 __isl_take isl_pw_qpolynomial *pwqp2);
6390 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6391 __isl_take isl_union_pw_qpolynomial *upwqp1,
6392 __isl_take isl_union_pw_qpolynomial *upwqp2);
6393 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6394 __isl_take isl_pw_qpolynomial_fold *pwf1,
6395 __isl_take isl_pw_qpolynomial_fold *pwf2);
6396 __isl_give isl_union_pw_qpolynomial_fold *
6397 isl_union_pw_qpolynomial_fold_fold(
6398 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6399 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6401 #include <isl/aff.h>
6402 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6403 __isl_take isl_pw_aff *pwaff1,
6404 __isl_take isl_pw_aff *pwaff2);
6405 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6406 __isl_take isl_pw_multi_aff *pma1,
6407 __isl_take isl_pw_multi_aff *pma2);
6408 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6409 __isl_take isl_union_pw_aff *upa1,
6410 __isl_take isl_union_pw_aff *upa2);
6411 __isl_give isl_union_pw_multi_aff *
6412 isl_union_pw_multi_aff_union_add(
6413 __isl_take isl_union_pw_multi_aff *upma1,
6414 __isl_take isl_union_pw_multi_aff *upma2);
6415 __isl_give isl_multi_union_pw_aff *
6416 isl_multi_union_pw_aff_union_add(
6417 __isl_take isl_multi_union_pw_aff *mupa1,
6418 __isl_take isl_multi_union_pw_aff *mupa2);
6419 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6420 __isl_take isl_pw_aff *pwaff1,
6421 __isl_take isl_pw_aff *pwaff2);
6422 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6423 __isl_take isl_pw_aff *pwaff1,
6424 __isl_take isl_pw_aff *pwaff2);
6426 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6427 expression with a domain that is the union of those of C<pwaff1> and
6428 C<pwaff2> and such that on each cell, the quasi-affine expression is
6429 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6430 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6431 associated expression is the defined one.
6432 This in contrast to the C<isl_pw_aff_max> function, which is
6433 only defined on the shared definition domain of the arguments.
6435 #include <isl/val.h>
6436 __isl_give isl_multi_val *isl_multi_val_add_val(
6437 __isl_take isl_multi_val *mv,
6438 __isl_take isl_val *v);
6439 __isl_give isl_multi_val *isl_multi_val_mod_val(
6440 __isl_take isl_multi_val *mv,
6441 __isl_take isl_val *v);
6442 __isl_give isl_multi_val *isl_multi_val_scale_val(
6443 __isl_take isl_multi_val *mv,
6444 __isl_take isl_val *v);
6445 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6446 __isl_take isl_multi_val *mv,
6447 __isl_take isl_val *v);
6449 #include <isl/aff.h>
6450 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6451 __isl_take isl_val *mod);
6452 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6453 __isl_take isl_pw_aff *pa,
6454 __isl_take isl_val *mod);
6455 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6456 __isl_take isl_union_pw_aff *upa,
6457 __isl_take isl_val *f);
6458 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6459 __isl_take isl_val *v);
6460 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6461 __isl_take isl_multi_aff *ma,
6462 __isl_take isl_val *v);
6463 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6464 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6465 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6466 __isl_take isl_multi_pw_aff *mpa,
6467 __isl_take isl_val *v);
6468 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6469 __isl_take isl_pw_multi_aff *pma,
6470 __isl_take isl_val *v);
6471 __isl_give isl_union_pw_multi_aff *
6472 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6473 __isl_take isl_union_pw_aff *upa,
6474 __isl_take isl_val *f);
6475 isl_union_pw_multi_aff_scale_val(
6476 __isl_take isl_union_pw_multi_aff *upma,
6477 __isl_take isl_val *val);
6478 __isl_give isl_multi_union_pw_aff *
6479 isl_multi_union_pw_aff_scale_val(
6480 __isl_take isl_multi_union_pw_aff *mupa,
6481 __isl_take isl_val *v);
6482 __isl_give isl_aff *isl_aff_scale_down_ui(
6483 __isl_take isl_aff *aff, unsigned f);
6484 __isl_give isl_aff *isl_aff_scale_down_val(
6485 __isl_take isl_aff *aff, __isl_take isl_val *v);
6486 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6487 __isl_take isl_multi_aff *ma,
6488 __isl_take isl_val *v);
6489 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6490 __isl_take isl_pw_aff *pa,
6491 __isl_take isl_val *f);
6492 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6493 __isl_take isl_multi_pw_aff *mpa,
6494 __isl_take isl_val *v);
6495 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6496 __isl_take isl_pw_multi_aff *pma,
6497 __isl_take isl_val *v);
6498 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6499 __isl_take isl_union_pw_aff *upa,
6500 __isl_take isl_val *v);
6501 __isl_give isl_union_pw_multi_aff *
6502 isl_union_pw_multi_aff_scale_down_val(
6503 __isl_take isl_union_pw_multi_aff *upma,
6504 __isl_take isl_val *val);
6505 __isl_give isl_multi_union_pw_aff *
6506 isl_multi_union_pw_aff_scale_down_val(
6507 __isl_take isl_multi_union_pw_aff *mupa,
6508 __isl_take isl_val *v);
6510 #include <isl/polynomial.h>
6511 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6512 __isl_take isl_qpolynomial *qp,
6513 __isl_take isl_val *v);
6514 __isl_give isl_qpolynomial_fold *
6515 isl_qpolynomial_fold_scale_val(
6516 __isl_take isl_qpolynomial_fold *fold,
6517 __isl_take isl_val *v);
6518 __isl_give isl_pw_qpolynomial *
6519 isl_pw_qpolynomial_scale_val(
6520 __isl_take isl_pw_qpolynomial *pwqp,
6521 __isl_take isl_val *v);
6522 __isl_give isl_pw_qpolynomial_fold *
6523 isl_pw_qpolynomial_fold_scale_val(
6524 __isl_take isl_pw_qpolynomial_fold *pwf,
6525 __isl_take isl_val *v);
6526 __isl_give isl_union_pw_qpolynomial *
6527 isl_union_pw_qpolynomial_scale_val(
6528 __isl_take isl_union_pw_qpolynomial *upwqp,
6529 __isl_take isl_val *v);
6530 __isl_give isl_union_pw_qpolynomial_fold *
6531 isl_union_pw_qpolynomial_fold_scale_val(
6532 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6533 __isl_take isl_val *v);
6534 __isl_give isl_qpolynomial *
6535 isl_qpolynomial_scale_down_val(
6536 __isl_take isl_qpolynomial *qp,
6537 __isl_take isl_val *v);
6538 __isl_give isl_qpolynomial_fold *
6539 isl_qpolynomial_fold_scale_down_val(
6540 __isl_take isl_qpolynomial_fold *fold,
6541 __isl_take isl_val *v);
6542 __isl_give isl_pw_qpolynomial *
6543 isl_pw_qpolynomial_scale_down_val(
6544 __isl_take isl_pw_qpolynomial *pwqp,
6545 __isl_take isl_val *v);
6546 __isl_give isl_pw_qpolynomial_fold *
6547 isl_pw_qpolynomial_fold_scale_down_val(
6548 __isl_take isl_pw_qpolynomial_fold *pwf,
6549 __isl_take isl_val *v);
6550 __isl_give isl_union_pw_qpolynomial *
6551 isl_union_pw_qpolynomial_scale_down_val(
6552 __isl_take isl_union_pw_qpolynomial *upwqp,
6553 __isl_take isl_val *v);
6554 __isl_give isl_union_pw_qpolynomial_fold *
6555 isl_union_pw_qpolynomial_fold_scale_down_val(
6556 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6557 __isl_take isl_val *v);
6559 #include <isl/val.h>
6560 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6561 __isl_take isl_multi_val *mv1,
6562 __isl_take isl_multi_val *mv2);
6563 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6564 __isl_take isl_multi_val *mv1,
6565 __isl_take isl_multi_val *mv2);
6566 __isl_give isl_multi_val *
6567 isl_multi_val_scale_down_multi_val(
6568 __isl_take isl_multi_val *mv1,
6569 __isl_take isl_multi_val *mv2);
6571 #include <isl/aff.h>
6572 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6573 __isl_take isl_multi_aff *ma,
6574 __isl_take isl_multi_val *mv);
6575 __isl_give isl_multi_union_pw_aff *
6576 isl_multi_union_pw_aff_mod_multi_val(
6577 __isl_take isl_multi_union_pw_aff *upma,
6578 __isl_take isl_multi_val *mv);
6579 __isl_give isl_multi_pw_aff *
6580 isl_multi_pw_aff_mod_multi_val(
6581 __isl_take isl_multi_pw_aff *mpa,
6582 __isl_take isl_multi_val *mv);
6583 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6584 __isl_take isl_multi_aff *ma,
6585 __isl_take isl_multi_val *mv);
6586 __isl_give isl_pw_multi_aff *
6587 isl_pw_multi_aff_scale_multi_val(
6588 __isl_take isl_pw_multi_aff *pma,
6589 __isl_take isl_multi_val *mv);
6590 __isl_give isl_multi_pw_aff *
6591 isl_multi_pw_aff_scale_multi_val(
6592 __isl_take isl_multi_pw_aff *mpa,
6593 __isl_take isl_multi_val *mv);
6594 __isl_give isl_multi_union_pw_aff *
6595 isl_multi_union_pw_aff_scale_multi_val(
6596 __isl_take isl_multi_union_pw_aff *mupa,
6597 __isl_take isl_multi_val *mv);
6598 __isl_give isl_union_pw_multi_aff *
6599 isl_union_pw_multi_aff_scale_multi_val(
6600 __isl_take isl_union_pw_multi_aff *upma,
6601 __isl_take isl_multi_val *mv);
6602 __isl_give isl_multi_aff *
6603 isl_multi_aff_scale_down_multi_val(
6604 __isl_take isl_multi_aff *ma,
6605 __isl_take isl_multi_val *mv);
6606 __isl_give isl_multi_pw_aff *
6607 isl_multi_pw_aff_scale_down_multi_val(
6608 __isl_take isl_multi_pw_aff *mpa,
6609 __isl_take isl_multi_val *mv);
6610 __isl_give isl_multi_union_pw_aff *
6611 isl_multi_union_pw_aff_scale_down_multi_val(
6612 __isl_take isl_multi_union_pw_aff *mupa,
6613 __isl_take isl_multi_val *mv);
6615 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6616 by the corresponding elements of C<mv>.
6618 #include <isl/aff.h>
6619 __isl_give isl_aff *isl_aff_mul(
6620 __isl_take isl_aff *aff1,
6621 __isl_take isl_aff *aff2);
6622 __isl_give isl_aff *isl_aff_div(
6623 __isl_take isl_aff *aff1,
6624 __isl_take isl_aff *aff2);
6625 __isl_give isl_pw_aff *isl_pw_aff_mul(
6626 __isl_take isl_pw_aff *pwaff1,
6627 __isl_take isl_pw_aff *pwaff2);
6628 __isl_give isl_pw_aff *isl_pw_aff_div(
6629 __isl_take isl_pw_aff *pa1,
6630 __isl_take isl_pw_aff *pa2);
6631 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6632 __isl_take isl_pw_aff *pa1,
6633 __isl_take isl_pw_aff *pa2);
6634 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6635 __isl_take isl_pw_aff *pa1,
6636 __isl_take isl_pw_aff *pa2);
6638 When multiplying two affine expressions, at least one of the two needs
6639 to be a constant. Similarly, when dividing an affine expression by another,
6640 the second expression needs to be a constant.
6641 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6642 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6645 #include <isl/polynomial.h>
6646 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6647 __isl_take isl_qpolynomial *qp1,
6648 __isl_take isl_qpolynomial *qp2);
6649 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6650 __isl_take isl_pw_qpolynomial *pwqp1,
6651 __isl_take isl_pw_qpolynomial *pwqp2);
6652 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6653 __isl_take isl_union_pw_qpolynomial *upwqp1,
6654 __isl_take isl_union_pw_qpolynomial *upwqp2);
6658 =head3 Lexicographic Optimization
6660 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6661 the following functions
6662 compute a set that contains the lexicographic minimum or maximum
6663 of the elements in C<set> (or C<bset>) for those values of the parameters
6664 that satisfy C<dom>.
6665 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6666 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6668 In other words, the union of the parameter values
6669 for which the result is non-empty and of C<*empty>
6672 #include <isl/set.h>
6673 __isl_give isl_set *isl_basic_set_partial_lexmin(
6674 __isl_take isl_basic_set *bset,
6675 __isl_take isl_basic_set *dom,
6676 __isl_give isl_set **empty);
6677 __isl_give isl_set *isl_basic_set_partial_lexmax(
6678 __isl_take isl_basic_set *bset,
6679 __isl_take isl_basic_set *dom,
6680 __isl_give isl_set **empty);
6681 __isl_give isl_set *isl_set_partial_lexmin(
6682 __isl_take isl_set *set, __isl_take isl_set *dom,
6683 __isl_give isl_set **empty);
6684 __isl_give isl_set *isl_set_partial_lexmax(
6685 __isl_take isl_set *set, __isl_take isl_set *dom,
6686 __isl_give isl_set **empty);
6688 Given a (basic) set C<set> (or C<bset>), the following functions simply
6689 return a set containing the lexicographic minimum or maximum
6690 of the elements in C<set> (or C<bset>).
6691 In case of union sets, the optimum is computed per space.
6693 #include <isl/set.h>
6694 __isl_give isl_set *isl_basic_set_lexmin(
6695 __isl_take isl_basic_set *bset);
6696 __isl_give isl_set *isl_basic_set_lexmax(
6697 __isl_take isl_basic_set *bset);
6698 __isl_give isl_set *isl_set_lexmin(
6699 __isl_take isl_set *set);
6700 __isl_give isl_set *isl_set_lexmax(
6701 __isl_take isl_set *set);
6702 __isl_give isl_union_set *isl_union_set_lexmin(
6703 __isl_take isl_union_set *uset);
6704 __isl_give isl_union_set *isl_union_set_lexmax(
6705 __isl_take isl_union_set *uset);
6707 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6708 the following functions
6709 compute a relation that maps each element of C<dom>
6710 to the single lexicographic minimum or maximum
6711 of the elements that are associated to that same
6712 element in C<map> (or C<bmap>).
6713 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6714 that contains the elements in C<dom> that do not map
6715 to any elements in C<map> (or C<bmap>).
6716 In other words, the union of the domain of the result and of C<*empty>
6719 #include <isl/map.h>
6720 __isl_give isl_map *isl_basic_map_partial_lexmax(
6721 __isl_take isl_basic_map *bmap,
6722 __isl_take isl_basic_set *dom,
6723 __isl_give isl_set **empty);
6724 __isl_give isl_map *isl_basic_map_partial_lexmin(
6725 __isl_take isl_basic_map *bmap,
6726 __isl_take isl_basic_set *dom,
6727 __isl_give isl_set **empty);
6728 __isl_give isl_map *isl_map_partial_lexmax(
6729 __isl_take isl_map *map, __isl_take isl_set *dom,
6730 __isl_give isl_set **empty);
6731 __isl_give isl_map *isl_map_partial_lexmin(
6732 __isl_take isl_map *map, __isl_take isl_set *dom,
6733 __isl_give isl_set **empty);
6735 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6736 return a map mapping each element in the domain of
6737 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6738 of all elements associated to that element.
6739 In case of union relations, the optimum is computed per space.
6741 #include <isl/map.h>
6742 __isl_give isl_map *isl_basic_map_lexmin(
6743 __isl_take isl_basic_map *bmap);
6744 __isl_give isl_map *isl_basic_map_lexmax(
6745 __isl_take isl_basic_map *bmap);
6746 __isl_give isl_map *isl_map_lexmin(
6747 __isl_take isl_map *map);
6748 __isl_give isl_map *isl_map_lexmax(
6749 __isl_take isl_map *map);
6750 __isl_give isl_union_map *isl_union_map_lexmin(
6751 __isl_take isl_union_map *umap);
6752 __isl_give isl_union_map *isl_union_map_lexmax(
6753 __isl_take isl_union_map *umap);
6755 The following functions return their result in the form of
6756 a piecewise multi-affine expression,
6757 but are otherwise equivalent to the corresponding functions
6758 returning a basic set or relation.
6760 #include <isl/set.h>
6761 __isl_give isl_pw_multi_aff *
6762 isl_basic_set_partial_lexmin_pw_multi_aff(
6763 __isl_take isl_basic_set *bset,
6764 __isl_take isl_basic_set *dom,
6765 __isl_give isl_set **empty);
6766 __isl_give isl_pw_multi_aff *
6767 isl_basic_set_partial_lexmax_pw_multi_aff(
6768 __isl_take isl_basic_set *bset,
6769 __isl_take isl_basic_set *dom,
6770 __isl_give isl_set **empty);
6771 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6772 __isl_take isl_set *set);
6773 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6774 __isl_take isl_set *set);
6776 #include <isl/map.h>
6777 __isl_give isl_pw_multi_aff *
6778 isl_basic_map_lexmin_pw_multi_aff(
6779 __isl_take isl_basic_map *bmap);
6780 __isl_give isl_pw_multi_aff *
6781 isl_basic_map_partial_lexmin_pw_multi_aff(
6782 __isl_take isl_basic_map *bmap,
6783 __isl_take isl_basic_set *dom,
6784 __isl_give isl_set **empty);
6785 __isl_give isl_pw_multi_aff *
6786 isl_basic_map_partial_lexmax_pw_multi_aff(
6787 __isl_take isl_basic_map *bmap,
6788 __isl_take isl_basic_set *dom,
6789 __isl_give isl_set **empty);
6790 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6791 __isl_take isl_map *map);
6792 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6793 __isl_take isl_map *map);
6795 The following functions return the lexicographic minimum or maximum
6796 on the shared domain of the inputs and the single defined function
6797 on those parts of the domain where only a single function is defined.
6799 #include <isl/aff.h>
6800 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6801 __isl_take isl_pw_multi_aff *pma1,
6802 __isl_take isl_pw_multi_aff *pma2);
6803 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6804 __isl_take isl_pw_multi_aff *pma1,
6805 __isl_take isl_pw_multi_aff *pma2);
6807 =head2 Ternary Operations
6809 #include <isl/aff.h>
6810 __isl_give isl_pw_aff *isl_pw_aff_cond(
6811 __isl_take isl_pw_aff *cond,
6812 __isl_take isl_pw_aff *pwaff_true,
6813 __isl_take isl_pw_aff *pwaff_false);
6815 The function C<isl_pw_aff_cond> performs a conditional operator
6816 and returns an expression that is equal to C<pwaff_true>
6817 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6818 where C<cond> is zero.
6822 Lists are defined over several element types, including
6823 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
6824 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6825 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6826 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6827 Here we take lists of C<isl_set>s as an example.
6828 Lists can be created, copied, modified and freed using the following functions.
6830 #include <isl/set.h>
6831 __isl_give isl_set_list *isl_set_list_from_set(
6832 __isl_take isl_set *el);
6833 __isl_give isl_set_list *isl_set_list_alloc(
6834 isl_ctx *ctx, int n);
6835 __isl_give isl_set_list *isl_set_list_copy(
6836 __isl_keep isl_set_list *list);
6837 __isl_give isl_set_list *isl_set_list_insert(
6838 __isl_take isl_set_list *list, unsigned pos,
6839 __isl_take isl_set *el);
6840 __isl_give isl_set_list *isl_set_list_add(
6841 __isl_take isl_set_list *list,
6842 __isl_take isl_set *el);
6843 __isl_give isl_set_list *isl_set_list_drop(
6844 __isl_take isl_set_list *list,
6845 unsigned first, unsigned n);
6846 __isl_give isl_set_list *isl_set_list_set_set(
6847 __isl_take isl_set_list *list, int index,
6848 __isl_take isl_set *set);
6849 __isl_give isl_set_list *isl_set_list_concat(
6850 __isl_take isl_set_list *list1,
6851 __isl_take isl_set_list *list2);
6852 __isl_give isl_set_list *isl_set_list_sort(
6853 __isl_take isl_set_list *list,
6854 int (*cmp)(__isl_keep isl_set *a,
6855 __isl_keep isl_set *b, void *user),
6857 __isl_null isl_set_list *isl_set_list_free(
6858 __isl_take isl_set_list *list);
6860 C<isl_set_list_alloc> creates an empty list with an initial capacity
6861 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
6862 add elements to a list, increasing its capacity as needed.
6863 C<isl_set_list_from_set> creates a list with a single element.
6865 Lists can be inspected using the following functions.
6867 #include <isl/set.h>
6868 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6869 __isl_give isl_set *isl_set_list_get_set(
6870 __isl_keep isl_set_list *list, int index);
6871 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6872 int (*fn)(__isl_take isl_set *el, void *user),
6874 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6875 int (*follows)(__isl_keep isl_set *a,
6876 __isl_keep isl_set *b, void *user),
6878 int (*fn)(__isl_take isl_set *el, void *user),
6881 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6882 strongly connected components of the graph with as vertices the elements
6883 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6884 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6885 should return C<-1> on error.
6887 Lists can be printed using
6889 #include <isl/set.h>
6890 __isl_give isl_printer *isl_printer_print_set_list(
6891 __isl_take isl_printer *p,
6892 __isl_keep isl_set_list *list);
6894 =head2 Associative arrays
6896 Associative arrays map isl objects of a specific type to isl objects
6897 of some (other) specific type. They are defined for several pairs
6898 of types, including (C<isl_map>, C<isl_basic_set>),
6899 (C<isl_id>, C<isl_ast_expr>) and.
6900 (C<isl_id>, C<isl_pw_aff>).
6901 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6904 Associative arrays can be created, copied and freed using
6905 the following functions.
6907 #include <isl/id_to_ast_expr.h>
6908 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6909 isl_ctx *ctx, int min_size);
6910 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6911 __isl_keep id_to_ast_expr *id2expr);
6912 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6913 __isl_take id_to_ast_expr *id2expr);
6915 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6916 to specify the expected size of the associative array.
6917 The associative array will be grown automatically as needed.
6919 Associative arrays can be inspected using the following functions.
6921 #include <isl/id_to_ast_expr.h>
6922 int isl_id_to_ast_expr_has(
6923 __isl_keep id_to_ast_expr *id2expr,
6924 __isl_keep isl_id *key);
6925 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6926 __isl_keep id_to_ast_expr *id2expr,
6927 __isl_take isl_id *key);
6928 int isl_id_to_ast_expr_foreach(
6929 __isl_keep id_to_ast_expr *id2expr,
6930 int (*fn)(__isl_take isl_id *key,
6931 __isl_take isl_ast_expr *val, void *user),
6934 They can be modified using the following function.
6936 #include <isl/id_to_ast_expr.h>
6937 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6938 __isl_take id_to_ast_expr *id2expr,
6939 __isl_take isl_id *key,
6940 __isl_take isl_ast_expr *val);
6941 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6942 __isl_take id_to_ast_expr *id2expr,
6943 __isl_take isl_id *key);
6945 Associative arrays can be printed using the following function.
6947 #include <isl/id_to_ast_expr.h>
6948 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6949 __isl_take isl_printer *p,
6950 __isl_keep id_to_ast_expr *id2expr);
6954 Vectors can be created, copied and freed using the following functions.
6956 #include <isl/vec.h>
6957 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6959 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6960 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6962 Note that the elements of a newly created vector may have arbitrary values.
6963 The elements can be changed and inspected using the following functions.
6965 int isl_vec_size(__isl_keep isl_vec *vec);
6966 __isl_give isl_val *isl_vec_get_element_val(
6967 __isl_keep isl_vec *vec, int pos);
6968 __isl_give isl_vec *isl_vec_set_element_si(
6969 __isl_take isl_vec *vec, int pos, int v);
6970 __isl_give isl_vec *isl_vec_set_element_val(
6971 __isl_take isl_vec *vec, int pos,
6972 __isl_take isl_val *v);
6973 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6975 __isl_give isl_vec *isl_vec_set_val(
6976 __isl_take isl_vec *vec, __isl_take isl_val *v);
6977 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6978 __isl_keep isl_vec *vec2, int pos);
6980 C<isl_vec_get_element> will return a negative value if anything went wrong.
6981 In that case, the value of C<*v> is undefined.
6983 The following function can be used to concatenate two vectors.
6985 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6986 __isl_take isl_vec *vec2);
6990 Matrices can be created, copied and freed using the following functions.
6992 #include <isl/mat.h>
6993 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6994 unsigned n_row, unsigned n_col);
6995 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6996 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6998 Note that the elements of a newly created matrix may have arbitrary values.
6999 The elements can be changed and inspected using the following functions.
7001 int isl_mat_rows(__isl_keep isl_mat *mat);
7002 int isl_mat_cols(__isl_keep isl_mat *mat);
7003 __isl_give isl_val *isl_mat_get_element_val(
7004 __isl_keep isl_mat *mat, int row, int col);
7005 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7006 int row, int col, int v);
7007 __isl_give isl_mat *isl_mat_set_element_val(
7008 __isl_take isl_mat *mat, int row, int col,
7009 __isl_take isl_val *v);
7011 C<isl_mat_get_element> will return a negative value if anything went wrong.
7012 In that case, the value of C<*v> is undefined.
7014 The following function can be used to compute the (right) inverse
7015 of a matrix, i.e., a matrix such that the product of the original
7016 and the inverse (in that order) is a multiple of the identity matrix.
7017 The input matrix is assumed to be of full row-rank.
7019 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7021 The following function can be used to compute the (right) kernel
7022 (or null space) of a matrix, i.e., a matrix such that the product of
7023 the original and the kernel (in that order) is the zero matrix.
7025 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7027 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7029 The following functions determine
7030 an upper or lower bound on a quasipolynomial over its domain.
7032 __isl_give isl_pw_qpolynomial_fold *
7033 isl_pw_qpolynomial_bound(
7034 __isl_take isl_pw_qpolynomial *pwqp,
7035 enum isl_fold type, int *tight);
7037 __isl_give isl_union_pw_qpolynomial_fold *
7038 isl_union_pw_qpolynomial_bound(
7039 __isl_take isl_union_pw_qpolynomial *upwqp,
7040 enum isl_fold type, int *tight);
7042 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7043 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7044 is the returned bound is known be tight, i.e., for each value
7045 of the parameters there is at least
7046 one element in the domain that reaches the bound.
7047 If the domain of C<pwqp> is not wrapping, then the bound is computed
7048 over all elements in that domain and the result has a purely parametric
7049 domain. If the domain of C<pwqp> is wrapping, then the bound is
7050 computed over the range of the wrapped relation. The domain of the
7051 wrapped relation becomes the domain of the result.
7053 =head2 Parametric Vertex Enumeration
7055 The parametric vertex enumeration described in this section
7056 is mainly intended to be used internally and by the C<barvinok>
7059 #include <isl/vertices.h>
7060 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7061 __isl_keep isl_basic_set *bset);
7063 The function C<isl_basic_set_compute_vertices> performs the
7064 actual computation of the parametric vertices and the chamber
7065 decomposition and store the result in an C<isl_vertices> object.
7066 This information can be queried by either iterating over all
7067 the vertices or iterating over all the chambers or cells
7068 and then iterating over all vertices that are active on the chamber.
7070 int isl_vertices_foreach_vertex(
7071 __isl_keep isl_vertices *vertices,
7072 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7075 int isl_vertices_foreach_cell(
7076 __isl_keep isl_vertices *vertices,
7077 int (*fn)(__isl_take isl_cell *cell, void *user),
7079 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7080 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7083 Other operations that can be performed on an C<isl_vertices> object are
7086 int isl_vertices_get_n_vertices(
7087 __isl_keep isl_vertices *vertices);
7088 void isl_vertices_free(__isl_take isl_vertices *vertices);
7090 Vertices can be inspected and destroyed using the following functions.
7092 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7093 __isl_give isl_basic_set *isl_vertex_get_domain(
7094 __isl_keep isl_vertex *vertex);
7095 __isl_give isl_multi_aff *isl_vertex_get_expr(
7096 __isl_keep isl_vertex *vertex);
7097 void isl_vertex_free(__isl_take isl_vertex *vertex);
7099 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7100 describing the vertex in terms of the parameters,
7101 while C<isl_vertex_get_domain> returns the activity domain
7104 Chambers can be inspected and destroyed using the following functions.
7106 __isl_give isl_basic_set *isl_cell_get_domain(
7107 __isl_keep isl_cell *cell);
7108 void isl_cell_free(__isl_take isl_cell *cell);
7110 =head1 Polyhedral Compilation Library
7112 This section collects functionality in C<isl> that has been specifically
7113 designed for use during polyhedral compilation.
7115 =head2 Dependence Analysis
7117 C<isl> contains specialized functionality for performing
7118 array dataflow analysis. That is, given a I<sink> access relation
7119 and a collection of possible I<source> access relations,
7120 C<isl> can compute relations that describe
7121 for each iteration of the sink access, which iteration
7122 of which of the source access relations was the last
7123 to access the same data element before the given iteration
7125 The resulting dependence relations map source iterations
7126 to the corresponding sink iterations.
7127 To compute standard flow dependences, the sink should be
7128 a read, while the sources should be writes.
7129 If any of the source accesses are marked as being I<may>
7130 accesses, then there will be a dependence from the last
7131 I<must> access B<and> from any I<may> access that follows
7132 this last I<must> access.
7133 In particular, if I<all> sources are I<may> accesses,
7134 then memory based dependence analysis is performed.
7135 If, on the other hand, all sources are I<must> accesses,
7136 then value based dependence analysis is performed.
7138 #include <isl/flow.h>
7140 typedef int (*isl_access_level_before)(void *first, void *second);
7142 __isl_give isl_access_info *isl_access_info_alloc(
7143 __isl_take isl_map *sink,
7144 void *sink_user, isl_access_level_before fn,
7146 __isl_give isl_access_info *isl_access_info_add_source(
7147 __isl_take isl_access_info *acc,
7148 __isl_take isl_map *source, int must,
7150 __isl_null isl_access_info *isl_access_info_free(
7151 __isl_take isl_access_info *acc);
7153 __isl_give isl_flow *isl_access_info_compute_flow(
7154 __isl_take isl_access_info *acc);
7156 int isl_flow_foreach(__isl_keep isl_flow *deps,
7157 int (*fn)(__isl_take isl_map *dep, int must,
7158 void *dep_user, void *user),
7160 __isl_give isl_map *isl_flow_get_no_source(
7161 __isl_keep isl_flow *deps, int must);
7162 void isl_flow_free(__isl_take isl_flow *deps);
7164 The function C<isl_access_info_compute_flow> performs the actual
7165 dependence analysis. The other functions are used to construct
7166 the input for this function or to read off the output.
7168 The input is collected in an C<isl_access_info>, which can
7169 be created through a call to C<isl_access_info_alloc>.
7170 The arguments to this functions are the sink access relation
7171 C<sink>, a token C<sink_user> used to identify the sink
7172 access to the user, a callback function for specifying the
7173 relative order of source and sink accesses, and the number
7174 of source access relations that will be added.
7175 The callback function has type C<int (*)(void *first, void *second)>.
7176 The function is called with two user supplied tokens identifying
7177 either a source or the sink and it should return the shared nesting
7178 level and the relative order of the two accesses.
7179 In particular, let I<n> be the number of loops shared by
7180 the two accesses. If C<first> precedes C<second> textually,
7181 then the function should return I<2 * n + 1>; otherwise,
7182 it should return I<2 * n>.
7183 The sources can be added to the C<isl_access_info> by performing
7184 (at most) C<max_source> calls to C<isl_access_info_add_source>.
7185 C<must> indicates whether the source is a I<must> access
7186 or a I<may> access. Note that a multi-valued access relation
7187 should only be marked I<must> if every iteration in the domain
7188 of the relation accesses I<all> elements in its image.
7189 The C<source_user> token is again used to identify
7190 the source access. The range of the source access relation
7191 C<source> should have the same dimension as the range
7192 of the sink access relation.
7193 The C<isl_access_info_free> function should usually not be
7194 called explicitly, because it is called implicitly by
7195 C<isl_access_info_compute_flow>.
7197 The result of the dependence analysis is collected in an
7198 C<isl_flow>. There may be elements of
7199 the sink access for which no preceding source access could be
7200 found or for which all preceding sources are I<may> accesses.
7201 The relations containing these elements can be obtained through
7202 calls to C<isl_flow_get_no_source>, the first with C<must> set
7203 and the second with C<must> unset.
7204 In the case of standard flow dependence analysis,
7205 with the sink a read and the sources I<must> writes,
7206 the first relation corresponds to the reads from uninitialized
7207 array elements and the second relation is empty.
7208 The actual flow dependences can be extracted using
7209 C<isl_flow_foreach>. This function will call the user-specified
7210 callback function C<fn> for each B<non-empty> dependence between
7211 a source and the sink. The callback function is called
7212 with four arguments, the actual flow dependence relation
7213 mapping source iterations to sink iterations, a boolean that
7214 indicates whether it is a I<must> or I<may> dependence, a token
7215 identifying the source and an additional C<void *> with value
7216 equal to the third argument of the C<isl_flow_foreach> call.
7217 A dependence is marked I<must> if it originates from a I<must>
7218 source and if it is not followed by any I<may> sources.
7220 After finishing with an C<isl_flow>, the user should call
7221 C<isl_flow_free> to free all associated memory.
7223 A higher-level interface to dependence analysis is provided
7224 by the following function.
7226 #include <isl/flow.h>
7228 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
7229 __isl_take isl_union_map *must_source,
7230 __isl_take isl_union_map *may_source,
7231 __isl_take isl_union_map *schedule,
7232 __isl_give isl_union_map **must_dep,
7233 __isl_give isl_union_map **may_dep,
7234 __isl_give isl_union_map **must_no_source,
7235 __isl_give isl_union_map **may_no_source);
7237 The arrays are identified by the tuple names of the ranges
7238 of the accesses. The iteration domains by the tuple names
7239 of the domains of the accesses and of the schedule.
7240 The relative order of the iteration domains is given by the
7241 schedule. The relations returned through C<must_no_source>
7242 and C<may_no_source> are subsets of C<sink>.
7243 Any of C<must_dep>, C<may_dep>, C<must_no_source>
7244 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
7245 any of the other arguments is treated as an error.
7247 =head3 Interaction with Dependence Analysis
7249 During the dependence analysis, we frequently need to perform
7250 the following operation. Given a relation between sink iterations
7251 and potential source iterations from a particular source domain,
7252 what is the last potential source iteration corresponding to each
7253 sink iteration. It can sometimes be convenient to adjust
7254 the set of potential source iterations before or after each such operation.
7255 The prototypical example is fuzzy array dataflow analysis,
7256 where we need to analyze if, based on data-dependent constraints,
7257 the sink iteration can ever be executed without one or more of
7258 the corresponding potential source iterations being executed.
7259 If so, we can introduce extra parameters and select an unknown
7260 but fixed source iteration from the potential source iterations.
7261 To be able to perform such manipulations, C<isl> provides the following
7264 #include <isl/flow.h>
7266 typedef __isl_give isl_restriction *(*isl_access_restrict)(
7267 __isl_keep isl_map *source_map,
7268 __isl_keep isl_set *sink, void *source_user,
7270 __isl_give isl_access_info *isl_access_info_set_restrict(
7271 __isl_take isl_access_info *acc,
7272 isl_access_restrict fn, void *user);
7274 The function C<isl_access_info_set_restrict> should be called
7275 before calling C<isl_access_info_compute_flow> and registers a callback function
7276 that will be called any time C<isl> is about to compute the last
7277 potential source. The first argument is the (reverse) proto-dependence,
7278 mapping sink iterations to potential source iterations.
7279 The second argument represents the sink iterations for which
7280 we want to compute the last source iteration.
7281 The third argument is the token corresponding to the source
7282 and the final argument is the token passed to C<isl_access_info_set_restrict>.
7283 The callback is expected to return a restriction on either the input or
7284 the output of the operation computing the last potential source.
7285 If the input needs to be restricted then restrictions are needed
7286 for both the source and the sink iterations. The sink iterations
7287 and the potential source iterations will be intersected with these sets.
7288 If the output needs to be restricted then only a restriction on the source
7289 iterations is required.
7290 If any error occurs, the callback should return C<NULL>.
7291 An C<isl_restriction> object can be created, freed and inspected
7292 using the following functions.
7294 #include <isl/flow.h>
7296 __isl_give isl_restriction *isl_restriction_input(
7297 __isl_take isl_set *source_restr,
7298 __isl_take isl_set *sink_restr);
7299 __isl_give isl_restriction *isl_restriction_output(
7300 __isl_take isl_set *source_restr);
7301 __isl_give isl_restriction *isl_restriction_none(
7302 __isl_take isl_map *source_map);
7303 __isl_give isl_restriction *isl_restriction_empty(
7304 __isl_take isl_map *source_map);
7305 __isl_null isl_restriction *isl_restriction_free(
7306 __isl_take isl_restriction *restr);
7308 C<isl_restriction_none> and C<isl_restriction_empty> are special
7309 cases of C<isl_restriction_input>. C<isl_restriction_none>
7310 is essentially equivalent to
7312 isl_restriction_input(isl_set_universe(
7313 isl_space_range(isl_map_get_space(source_map))),
7315 isl_space_domain(isl_map_get_space(source_map))));
7317 whereas C<isl_restriction_empty> is essentially equivalent to
7319 isl_restriction_input(isl_set_empty(
7320 isl_space_range(isl_map_get_space(source_map))),
7322 isl_space_domain(isl_map_get_space(source_map))));
7326 B<The functionality described in this section is fairly new
7327 and may be subject to change.>
7329 #include <isl/schedule.h>
7330 __isl_give isl_schedule *
7331 isl_schedule_constraints_compute_schedule(
7332 __isl_take isl_schedule_constraints *sc);
7333 __isl_null isl_schedule *isl_schedule_free(
7334 __isl_take isl_schedule *sched);
7336 The function C<isl_schedule_constraints_compute_schedule> can be
7337 used to compute a schedule that satisfies the given schedule constraints.
7338 These schedule constraints include the iteration domain for which
7339 a schedule should be computed and dependences between pairs of
7340 iterations. In particular, these dependences include
7341 I<validity> dependences and I<proximity> dependences.
7342 By default, the algorithm used to construct the schedule is similar
7343 to that of C<Pluto>.
7344 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
7346 The generated schedule respects all validity dependences.
7347 That is, all dependence distances over these dependences in the
7348 scheduled space are lexicographically positive.
7349 The default algorithm tries to ensure that the dependence distances
7350 over coincidence constraints are zero and to minimize the
7351 dependence distances over proximity dependences.
7352 Moreover, it tries to obtain sequences (bands) of schedule dimensions
7353 for groups of domains where the dependence distances over validity
7354 dependences have only non-negative values.
7355 When using Feautrier's algorithm, the coincidence and proximity constraints
7356 are only taken into account during the extension to a
7357 full-dimensional schedule.
7359 An C<isl_schedule_constraints> object can be constructed
7360 and manipulated using the following functions.
7362 #include <isl/schedule.h>
7363 __isl_give isl_schedule_constraints *
7364 isl_schedule_constraints_copy(
7365 __isl_keep isl_schedule_constraints *sc);
7366 __isl_give isl_schedule_constraints *
7367 isl_schedule_constraints_on_domain(
7368 __isl_take isl_union_set *domain);
7369 __isl_give isl_schedule_constraints *
7370 isl_schedule_constraints_set_validity(
7371 __isl_take isl_schedule_constraints *sc,
7372 __isl_take isl_union_map *validity);
7373 __isl_give isl_schedule_constraints *
7374 isl_schedule_constraints_set_coincidence(
7375 __isl_take isl_schedule_constraints *sc,
7376 __isl_take isl_union_map *coincidence);
7377 __isl_give isl_schedule_constraints *
7378 isl_schedule_constraints_set_proximity(
7379 __isl_take isl_schedule_constraints *sc,
7380 __isl_take isl_union_map *proximity);
7381 __isl_give isl_schedule_constraints *
7382 isl_schedule_constraints_set_conditional_validity(
7383 __isl_take isl_schedule_constraints *sc,
7384 __isl_take isl_union_map *condition,
7385 __isl_take isl_union_map *validity);
7386 __isl_null isl_schedule_constraints *
7387 isl_schedule_constraints_free(
7388 __isl_take isl_schedule_constraints *sc);
7390 The initial C<isl_schedule_constraints> object created by
7391 C<isl_schedule_constraints_on_domain> does not impose any constraints.
7392 That is, it has an empty set of dependences.
7393 The function C<isl_schedule_constraints_set_validity> replaces the
7394 validity dependences, mapping domain elements I<i> to domain
7395 elements that should be scheduled after I<i>.
7396 The function C<isl_schedule_constraints_set_coincidence> replaces the
7397 coincidence dependences, mapping domain elements I<i> to domain
7398 elements that should be scheduled together with I<I>, if possible.
7399 The function C<isl_schedule_constraints_set_proximity> replaces the
7400 proximity dependences, mapping domain elements I<i> to domain
7401 elements that should be scheduled either before I<I>
7402 or as early as possible after I<i>.
7404 The function C<isl_schedule_constraints_set_conditional_validity>
7405 replaces the conditional validity constraints.
7406 A conditional validity constraint is only imposed when any of the corresponding
7407 conditions is satisfied, i.e., when any of them is non-zero.
7408 That is, the scheduler ensures that within each band if the dependence
7409 distances over the condition constraints are not all zero
7410 then all corresponding conditional validity constraints are respected.
7411 A conditional validity constraint corresponds to a condition
7412 if the two are adjacent, i.e., if the domain of one relation intersect
7413 the range of the other relation.
7414 The typical use case of conditional validity constraints is
7415 to allow order constraints between live ranges to be violated
7416 as long as the live ranges themselves are local to the band.
7417 To allow more fine-grained control over which conditions correspond
7418 to which conditional validity constraints, the domains and ranges
7419 of these relations may include I<tags>. That is, the domains and
7420 ranges of those relation may themselves be wrapped relations
7421 where the iteration domain appears in the domain of those wrapped relations
7422 and the range of the wrapped relations can be arbitrarily chosen
7423 by the user. Conditions and conditional validity constraints are only
7424 considered adjacent to each other if the entire wrapped relation matches.
7425 In particular, a relation with a tag will never be considered adjacent
7426 to a relation without a tag.
7428 The following function computes a schedule directly from
7429 an iteration domain and validity and proximity dependences
7430 and is implemented in terms of the functions described above.
7431 The use of C<isl_union_set_compute_schedule> is discouraged.
7433 #include <isl/schedule.h>
7434 __isl_give isl_schedule *isl_union_set_compute_schedule(
7435 __isl_take isl_union_set *domain,
7436 __isl_take isl_union_map *validity,
7437 __isl_take isl_union_map *proximity);
7439 A mapping from the domains to the scheduled space can be obtained
7440 from an C<isl_schedule> using the following function.
7442 __isl_give isl_union_map *isl_schedule_get_map(
7443 __isl_keep isl_schedule *sched);
7445 A representation of the schedule can be printed using
7447 __isl_give isl_printer *isl_printer_print_schedule(
7448 __isl_take isl_printer *p,
7449 __isl_keep isl_schedule *schedule);
7451 A representation of the schedule as a forest of bands can be obtained
7452 using the following function.
7454 __isl_give isl_band_list *isl_schedule_get_band_forest(
7455 __isl_keep isl_schedule *schedule);
7457 The individual bands can be visited in depth-first post-order
7458 using the following function.
7460 #include <isl/schedule.h>
7461 int isl_schedule_foreach_band(
7462 __isl_keep isl_schedule *sched,
7463 int (*fn)(__isl_keep isl_band *band, void *user),
7466 The list can be manipulated as explained in L<"Lists">.
7467 The bands inside the list can be copied and freed using the following
7470 #include <isl/band.h>
7471 __isl_give isl_band *isl_band_copy(
7472 __isl_keep isl_band *band);
7473 __isl_null isl_band *isl_band_free(
7474 __isl_take isl_band *band);
7476 Each band contains zero or more scheduling dimensions.
7477 These are referred to as the members of the band.
7478 The section of the schedule that corresponds to the band is
7479 referred to as the partial schedule of the band.
7480 For those nodes that participate in a band, the outer scheduling
7481 dimensions form the prefix schedule, while the inner scheduling
7482 dimensions form the suffix schedule.
7483 That is, if we take a cut of the band forest, then the union of
7484 the concatenations of the prefix, partial and suffix schedules of
7485 each band in the cut is equal to the entire schedule (modulo
7486 some possible padding at the end with zero scheduling dimensions).
7487 The properties of a band can be inspected using the following functions.
7489 #include <isl/band.h>
7490 int isl_band_has_children(__isl_keep isl_band *band);
7491 __isl_give isl_band_list *isl_band_get_children(
7492 __isl_keep isl_band *band);
7494 __isl_give isl_union_map *isl_band_get_prefix_schedule(
7495 __isl_keep isl_band *band);
7496 __isl_give isl_union_map *isl_band_get_partial_schedule(
7497 __isl_keep isl_band *band);
7498 __isl_give isl_union_map *isl_band_get_suffix_schedule(
7499 __isl_keep isl_band *band);
7501 int isl_band_n_member(__isl_keep isl_band *band);
7502 int isl_band_member_is_coincident(
7503 __isl_keep isl_band *band, int pos);
7505 int isl_band_list_foreach_band(
7506 __isl_keep isl_band_list *list,
7507 int (*fn)(__isl_keep isl_band *band, void *user),
7510 Note that a scheduling dimension is considered to be ``coincident''
7511 if it satisfies the coincidence constraints within its band.
7512 That is, if the dependence distances of the coincidence
7513 constraints are all zero in that direction (for fixed
7514 iterations of outer bands).
7515 Like C<isl_schedule_foreach_band>,
7516 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
7517 in depth-first post-order.
7519 A band can be tiled using the following function.
7521 #include <isl/band.h>
7522 int isl_band_tile(__isl_keep isl_band *band,
7523 __isl_take isl_vec *sizes);
7525 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
7527 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
7528 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
7530 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
7532 The C<isl_band_tile> function tiles the band using the given tile sizes
7533 inside its schedule.
7534 A new child band is created to represent the point loops and it is
7535 inserted between the modified band and its children.
7536 The C<tile_scale_tile_loops> option specifies whether the tile
7537 loops iterators should be scaled by the tile sizes.
7538 If the C<tile_shift_point_loops> option is set, then the point loops
7539 are shifted to start at zero.
7541 A band can be split into two nested bands using the following function.
7543 int isl_band_split(__isl_keep isl_band *band, int pos);
7545 The resulting outer band contains the first C<pos> dimensions of C<band>
7546 while the inner band contains the remaining dimensions.
7548 A representation of the band can be printed using
7550 #include <isl/band.h>
7551 __isl_give isl_printer *isl_printer_print_band(
7552 __isl_take isl_printer *p,
7553 __isl_keep isl_band *band);
7557 #include <isl/schedule.h>
7558 int isl_options_set_schedule_max_coefficient(
7559 isl_ctx *ctx, int val);
7560 int isl_options_get_schedule_max_coefficient(
7562 int isl_options_set_schedule_max_constant_term(
7563 isl_ctx *ctx, int val);
7564 int isl_options_get_schedule_max_constant_term(
7566 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
7567 int isl_options_get_schedule_fuse(isl_ctx *ctx);
7568 int isl_options_set_schedule_maximize_band_depth(
7569 isl_ctx *ctx, int val);
7570 int isl_options_get_schedule_maximize_band_depth(
7572 int isl_options_set_schedule_outer_coincidence(
7573 isl_ctx *ctx, int val);
7574 int isl_options_get_schedule_outer_coincidence(
7576 int isl_options_set_schedule_split_scaled(
7577 isl_ctx *ctx, int val);
7578 int isl_options_get_schedule_split_scaled(
7580 int isl_options_set_schedule_algorithm(
7581 isl_ctx *ctx, int val);
7582 int isl_options_get_schedule_algorithm(
7584 int isl_options_set_schedule_separate_components(
7585 isl_ctx *ctx, int val);
7586 int isl_options_get_schedule_separate_components(
7591 =item * schedule_max_coefficient
7593 This option enforces that the coefficients for variable and parameter
7594 dimensions in the calculated schedule are not larger than the specified value.
7595 This option can significantly increase the speed of the scheduling calculation
7596 and may also prevent fusing of unrelated dimensions. A value of -1 means that
7597 this option does not introduce bounds on the variable or parameter
7600 =item * schedule_max_constant_term
7602 This option enforces that the constant coefficients in the calculated schedule
7603 are not larger than the maximal constant term. This option can significantly
7604 increase the speed of the scheduling calculation and may also prevent fusing of
7605 unrelated dimensions. A value of -1 means that this option does not introduce
7606 bounds on the constant coefficients.
7608 =item * schedule_fuse
7610 This option controls the level of fusion.
7611 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
7612 resulting schedule will be distributed as much as possible.
7613 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
7614 try to fuse loops in the resulting schedule.
7616 =item * schedule_maximize_band_depth
7618 If this option is set, we do not split bands at the point
7619 where we detect splitting is necessary. Instead, we
7620 backtrack and split bands as early as possible. This
7621 reduces the number of splits and maximizes the width of
7622 the bands. Wider bands give more possibilities for tiling.
7623 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
7624 then bands will be split as early as possible, even if there is no need.
7625 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
7627 =item * schedule_outer_coincidence
7629 If this option is set, then we try to construct schedules
7630 where the outermost scheduling dimension in each band
7631 satisfies the coincidence constraints.
7633 =item * schedule_split_scaled
7635 If this option is set, then we try to construct schedules in which the
7636 constant term is split off from the linear part if the linear parts of
7637 the scheduling rows for all nodes in the graphs have a common non-trivial
7639 The constant term is then placed in a separate band and the linear
7642 =item * schedule_algorithm
7644 Selects the scheduling algorithm to be used.
7645 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
7646 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
7648 =item * schedule_separate_components
7650 If at any point the dependence graph contains any (weakly connected) components,
7651 then these components are scheduled separately.
7652 If this option is not set, then some iterations of the domains
7653 in these components may be scheduled together.
7654 If this option is set, then the components are given consecutive
7659 =head2 AST Generation
7661 This section describes the C<isl> functionality for generating
7662 ASTs that visit all the elements
7663 in a domain in an order specified by a schedule.
7664 In particular, given a C<isl_union_map>, an AST is generated
7665 that visits all the elements in the domain of the C<isl_union_map>
7666 according to the lexicographic order of the corresponding image
7667 element(s). If the range of the C<isl_union_map> consists of
7668 elements in more than one space, then each of these spaces is handled
7669 separately in an arbitrary order.
7670 It should be noted that the image elements only specify the I<order>
7671 in which the corresponding domain elements should be visited.
7672 No direct relation between the image elements and the loop iterators
7673 in the generated AST should be assumed.
7675 Each AST is generated within a build. The initial build
7676 simply specifies the constraints on the parameters (if any)
7677 and can be created, inspected, copied and freed using the following functions.
7679 #include <isl/ast_build.h>
7680 __isl_give isl_ast_build *isl_ast_build_from_context(
7681 __isl_take isl_set *set);
7682 __isl_give isl_ast_build *isl_ast_build_copy(
7683 __isl_keep isl_ast_build *build);
7684 __isl_null isl_ast_build *isl_ast_build_free(
7685 __isl_take isl_ast_build *build);
7687 The C<set> argument is usually a parameter set with zero or more parameters.
7688 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
7689 and L</"Fine-grained Control over AST Generation">.
7690 Finally, the AST itself can be constructed using the following
7693 #include <isl/ast_build.h>
7694 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
7695 __isl_keep isl_ast_build *build,
7696 __isl_take isl_union_map *schedule);
7698 =head3 Inspecting the AST
7700 The basic properties of an AST node can be obtained as follows.
7702 #include <isl/ast.h>
7703 enum isl_ast_node_type isl_ast_node_get_type(
7704 __isl_keep isl_ast_node *node);
7706 The type of an AST node is one of
7707 C<isl_ast_node_for>,
7709 C<isl_ast_node_block> or
7710 C<isl_ast_node_user>.
7711 An C<isl_ast_node_for> represents a for node.
7712 An C<isl_ast_node_if> represents an if node.
7713 An C<isl_ast_node_block> represents a compound node.
7714 An C<isl_ast_node_user> represents an expression statement.
7715 An expression statement typically corresponds to a domain element, i.e.,
7716 one of the elements that is visited by the AST.
7718 Each type of node has its own additional properties.
7720 #include <isl/ast.h>
7721 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7722 __isl_keep isl_ast_node *node);
7723 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7724 __isl_keep isl_ast_node *node);
7725 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7726 __isl_keep isl_ast_node *node);
7727 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7728 __isl_keep isl_ast_node *node);
7729 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7730 __isl_keep isl_ast_node *node);
7731 int isl_ast_node_for_is_degenerate(
7732 __isl_keep isl_ast_node *node);
7734 An C<isl_ast_for> is considered degenerate if it is known to execute
7737 #include <isl/ast.h>
7738 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7739 __isl_keep isl_ast_node *node);
7740 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7741 __isl_keep isl_ast_node *node);
7742 int isl_ast_node_if_has_else(
7743 __isl_keep isl_ast_node *node);
7744 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7745 __isl_keep isl_ast_node *node);
7747 __isl_give isl_ast_node_list *
7748 isl_ast_node_block_get_children(
7749 __isl_keep isl_ast_node *node);
7751 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7752 __isl_keep isl_ast_node *node);
7754 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7755 the following functions.
7757 #include <isl/ast.h>
7758 enum isl_ast_expr_type isl_ast_expr_get_type(
7759 __isl_keep isl_ast_expr *expr);
7761 The type of an AST expression is one of
7763 C<isl_ast_expr_id> or
7764 C<isl_ast_expr_int>.
7765 An C<isl_ast_expr_op> represents the result of an operation.
7766 An C<isl_ast_expr_id> represents an identifier.
7767 An C<isl_ast_expr_int> represents an integer value.
7769 Each type of expression has its own additional properties.
7771 #include <isl/ast.h>
7772 enum isl_ast_op_type isl_ast_expr_get_op_type(
7773 __isl_keep isl_ast_expr *expr);
7774 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7775 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7776 __isl_keep isl_ast_expr *expr, int pos);
7777 int isl_ast_node_foreach_ast_op_type(
7778 __isl_keep isl_ast_node *node,
7779 int (*fn)(enum isl_ast_op_type type, void *user),
7782 C<isl_ast_expr_get_op_type> returns the type of the operation
7783 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7784 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7786 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7787 C<isl_ast_op_type> that appears in C<node>.
7788 The operation type is one of the following.
7792 =item C<isl_ast_op_and>
7794 Logical I<and> of two arguments.
7795 Both arguments can be evaluated.
7797 =item C<isl_ast_op_and_then>
7799 Logical I<and> of two arguments.
7800 The second argument can only be evaluated if the first evaluates to true.
7802 =item C<isl_ast_op_or>
7804 Logical I<or> of two arguments.
7805 Both arguments can be evaluated.
7807 =item C<isl_ast_op_or_else>
7809 Logical I<or> of two arguments.
7810 The second argument can only be evaluated if the first evaluates to false.
7812 =item C<isl_ast_op_max>
7814 Maximum of two or more arguments.
7816 =item C<isl_ast_op_min>
7818 Minimum of two or more arguments.
7820 =item C<isl_ast_op_minus>
7824 =item C<isl_ast_op_add>
7826 Sum of two arguments.
7828 =item C<isl_ast_op_sub>
7830 Difference of two arguments.
7832 =item C<isl_ast_op_mul>
7834 Product of two arguments.
7836 =item C<isl_ast_op_div>
7838 Exact division. That is, the result is known to be an integer.
7840 =item C<isl_ast_op_fdiv_q>
7842 Result of integer division, rounded towards negative
7845 =item C<isl_ast_op_pdiv_q>
7847 Result of integer division, where dividend is known to be non-negative.
7849 =item C<isl_ast_op_pdiv_r>
7851 Remainder of integer division, where dividend is known to be non-negative.
7853 =item C<isl_ast_op_zdiv_r>
7855 Equal to zero iff the remainder on integer division is zero.
7857 =item C<isl_ast_op_cond>
7859 Conditional operator defined on three arguments.
7860 If the first argument evaluates to true, then the result
7861 is equal to the second argument. Otherwise, the result
7862 is equal to the third argument.
7863 The second and third argument may only be evaluated if
7864 the first argument evaluates to true and false, respectively.
7865 Corresponds to C<a ? b : c> in C.
7867 =item C<isl_ast_op_select>
7869 Conditional operator defined on three arguments.
7870 If the first argument evaluates to true, then the result
7871 is equal to the second argument. Otherwise, the result
7872 is equal to the third argument.
7873 The second and third argument may be evaluated independently
7874 of the value of the first argument.
7875 Corresponds to C<a * b + (1 - a) * c> in C.
7877 =item C<isl_ast_op_eq>
7881 =item C<isl_ast_op_le>
7883 Less than or equal relation.
7885 =item C<isl_ast_op_lt>
7889 =item C<isl_ast_op_ge>
7891 Greater than or equal relation.
7893 =item C<isl_ast_op_gt>
7895 Greater than relation.
7897 =item C<isl_ast_op_call>
7900 The number of arguments of the C<isl_ast_expr> is one more than
7901 the number of arguments in the function call, the first argument
7902 representing the function being called.
7904 =item C<isl_ast_op_access>
7907 The number of arguments of the C<isl_ast_expr> is one more than
7908 the number of index expressions in the array access, the first argument
7909 representing the array being accessed.
7911 =item C<isl_ast_op_member>
7914 This operation has two arguments, a structure and the name of
7915 the member of the structure being accessed.
7919 #include <isl/ast.h>
7920 __isl_give isl_id *isl_ast_expr_get_id(
7921 __isl_keep isl_ast_expr *expr);
7923 Return the identifier represented by the AST expression.
7925 #include <isl/ast.h>
7926 __isl_give isl_val *isl_ast_expr_get_val(
7927 __isl_keep isl_ast_expr *expr);
7929 Return the integer represented by the AST expression.
7931 =head3 Properties of ASTs
7933 #include <isl/ast.h>
7934 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7935 __isl_keep isl_ast_expr *expr2);
7937 Check if two C<isl_ast_expr>s are equal to each other.
7939 =head3 Manipulating and printing the AST
7941 AST nodes can be copied and freed using the following functions.
7943 #include <isl/ast.h>
7944 __isl_give isl_ast_node *isl_ast_node_copy(
7945 __isl_keep isl_ast_node *node);
7946 __isl_null isl_ast_node *isl_ast_node_free(
7947 __isl_take isl_ast_node *node);
7949 AST expressions can be copied and freed using the following functions.
7951 #include <isl/ast.h>
7952 __isl_give isl_ast_expr *isl_ast_expr_copy(
7953 __isl_keep isl_ast_expr *expr);
7954 __isl_null isl_ast_expr *isl_ast_expr_free(
7955 __isl_take isl_ast_expr *expr);
7957 New AST expressions can be created either directly or within
7958 the context of an C<isl_ast_build>.
7960 #include <isl/ast.h>
7961 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7962 __isl_take isl_val *v);
7963 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7964 __isl_take isl_id *id);
7965 __isl_give isl_ast_expr *isl_ast_expr_neg(
7966 __isl_take isl_ast_expr *expr);
7967 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7968 __isl_take isl_ast_expr *expr);
7969 __isl_give isl_ast_expr *isl_ast_expr_add(
7970 __isl_take isl_ast_expr *expr1,
7971 __isl_take isl_ast_expr *expr2);
7972 __isl_give isl_ast_expr *isl_ast_expr_sub(
7973 __isl_take isl_ast_expr *expr1,
7974 __isl_take isl_ast_expr *expr2);
7975 __isl_give isl_ast_expr *isl_ast_expr_mul(
7976 __isl_take isl_ast_expr *expr1,
7977 __isl_take isl_ast_expr *expr2);
7978 __isl_give isl_ast_expr *isl_ast_expr_div(
7979 __isl_take isl_ast_expr *expr1,
7980 __isl_take isl_ast_expr *expr2);
7981 __isl_give isl_ast_expr *isl_ast_expr_and(
7982 __isl_take isl_ast_expr *expr1,
7983 __isl_take isl_ast_expr *expr2)
7984 __isl_give isl_ast_expr *isl_ast_expr_or(
7985 __isl_take isl_ast_expr *expr1,
7986 __isl_take isl_ast_expr *expr2)
7987 __isl_give isl_ast_expr *isl_ast_expr_eq(
7988 __isl_take isl_ast_expr *expr1,
7989 __isl_take isl_ast_expr *expr2);
7990 __isl_give isl_ast_expr *isl_ast_expr_le(
7991 __isl_take isl_ast_expr *expr1,
7992 __isl_take isl_ast_expr *expr2);
7993 __isl_give isl_ast_expr *isl_ast_expr_lt(
7994 __isl_take isl_ast_expr *expr1,
7995 __isl_take isl_ast_expr *expr2);
7996 __isl_give isl_ast_expr *isl_ast_expr_ge(
7997 __isl_take isl_ast_expr *expr1,
7998 __isl_take isl_ast_expr *expr2);
7999 __isl_give isl_ast_expr *isl_ast_expr_gt(
8000 __isl_take isl_ast_expr *expr1,
8001 __isl_take isl_ast_expr *expr2);
8002 __isl_give isl_ast_expr *isl_ast_expr_access(
8003 __isl_take isl_ast_expr *array,
8004 __isl_take isl_ast_expr_list *indices);
8006 The function C<isl_ast_expr_address_of> can be applied to an
8007 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
8008 to represent the address of the C<isl_ast_expr_access>.
8010 #include <isl/ast_build.h>
8011 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
8012 __isl_keep isl_ast_build *build,
8013 __isl_take isl_pw_aff *pa);
8014 __isl_give isl_ast_expr *
8015 isl_ast_build_access_from_pw_multi_aff(
8016 __isl_keep isl_ast_build *build,
8017 __isl_take isl_pw_multi_aff *pma);
8018 __isl_give isl_ast_expr *
8019 isl_ast_build_access_from_multi_pw_aff(
8020 __isl_keep isl_ast_build *build,
8021 __isl_take isl_multi_pw_aff *mpa);
8022 __isl_give isl_ast_expr *
8023 isl_ast_build_call_from_pw_multi_aff(
8024 __isl_keep isl_ast_build *build,
8025 __isl_take isl_pw_multi_aff *pma);
8026 __isl_give isl_ast_expr *
8027 isl_ast_build_call_from_multi_pw_aff(
8028 __isl_keep isl_ast_build *build,
8029 __isl_take isl_multi_pw_aff *mpa);
8031 The domains of C<pa>, C<mpa> and C<pma> should correspond
8032 to the schedule space of C<build>.
8033 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
8034 the function being called.
8035 If the accessed space is a nested relation, then it is taken
8036 to represent an access of the member specified by the range
8037 of this nested relation of the structure specified by the domain
8038 of the nested relation.
8040 The following functions can be used to modify an C<isl_ast_expr>.
8042 #include <isl/ast.h>
8043 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
8044 __isl_take isl_ast_expr *expr, int pos,
8045 __isl_take isl_ast_expr *arg);
8047 Replace the argument of C<expr> at position C<pos> by C<arg>.
8049 #include <isl/ast.h>
8050 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
8051 __isl_take isl_ast_expr *expr,
8052 __isl_take isl_id_to_ast_expr *id2expr);
8054 The function C<isl_ast_expr_substitute_ids> replaces the
8055 subexpressions of C<expr> of type C<isl_ast_expr_id>
8056 by the corresponding expression in C<id2expr>, if there is any.
8059 User specified data can be attached to an C<isl_ast_node> and obtained
8060 from the same C<isl_ast_node> using the following functions.
8062 #include <isl/ast.h>
8063 __isl_give isl_ast_node *isl_ast_node_set_annotation(
8064 __isl_take isl_ast_node *node,
8065 __isl_take isl_id *annotation);
8066 __isl_give isl_id *isl_ast_node_get_annotation(
8067 __isl_keep isl_ast_node *node);
8069 Basic printing can be performed using the following functions.
8071 #include <isl/ast.h>
8072 __isl_give isl_printer *isl_printer_print_ast_expr(
8073 __isl_take isl_printer *p,
8074 __isl_keep isl_ast_expr *expr);
8075 __isl_give isl_printer *isl_printer_print_ast_node(
8076 __isl_take isl_printer *p,
8077 __isl_keep isl_ast_node *node);
8078 __isl_give char *isl_ast_expr_to_str(
8079 __isl_keep isl_ast_expr *expr);
8081 More advanced printing can be performed using the following functions.
8083 #include <isl/ast.h>
8084 __isl_give isl_printer *isl_ast_op_type_print_macro(
8085 enum isl_ast_op_type type,
8086 __isl_take isl_printer *p);
8087 __isl_give isl_printer *isl_ast_node_print_macros(
8088 __isl_keep isl_ast_node *node,
8089 __isl_take isl_printer *p);
8090 __isl_give isl_printer *isl_ast_node_print(
8091 __isl_keep isl_ast_node *node,
8092 __isl_take isl_printer *p,
8093 __isl_take isl_ast_print_options *options);
8094 __isl_give isl_printer *isl_ast_node_for_print(
8095 __isl_keep isl_ast_node *node,
8096 __isl_take isl_printer *p,
8097 __isl_take isl_ast_print_options *options);
8098 __isl_give isl_printer *isl_ast_node_if_print(
8099 __isl_keep isl_ast_node *node,
8100 __isl_take isl_printer *p,
8101 __isl_take isl_ast_print_options *options);
8103 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
8104 C<isl> may print out an AST that makes use of macros such
8105 as C<floord>, C<min> and C<max>.
8106 C<isl_ast_op_type_print_macro> prints out the macro
8107 corresponding to a specific C<isl_ast_op_type>.
8108 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
8109 for expressions where these macros would be used and prints
8110 out the required macro definitions.
8111 Essentially, C<isl_ast_node_print_macros> calls
8112 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
8113 as function argument.
8114 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
8115 C<isl_ast_node_if_print> print an C<isl_ast_node>
8116 in C<ISL_FORMAT_C>, but allow for some extra control
8117 through an C<isl_ast_print_options> object.
8118 This object can be created using the following functions.
8120 #include <isl/ast.h>
8121 __isl_give isl_ast_print_options *
8122 isl_ast_print_options_alloc(isl_ctx *ctx);
8123 __isl_give isl_ast_print_options *
8124 isl_ast_print_options_copy(
8125 __isl_keep isl_ast_print_options *options);
8126 __isl_null isl_ast_print_options *
8127 isl_ast_print_options_free(
8128 __isl_take isl_ast_print_options *options);
8130 __isl_give isl_ast_print_options *
8131 isl_ast_print_options_set_print_user(
8132 __isl_take isl_ast_print_options *options,
8133 __isl_give isl_printer *(*print_user)(
8134 __isl_take isl_printer *p,
8135 __isl_take isl_ast_print_options *options,
8136 __isl_keep isl_ast_node *node, void *user),
8138 __isl_give isl_ast_print_options *
8139 isl_ast_print_options_set_print_for(
8140 __isl_take isl_ast_print_options *options,
8141 __isl_give isl_printer *(*print_for)(
8142 __isl_take isl_printer *p,
8143 __isl_take isl_ast_print_options *options,
8144 __isl_keep isl_ast_node *node, void *user),
8147 The callback set by C<isl_ast_print_options_set_print_user>
8148 is called whenever a node of type C<isl_ast_node_user> needs to
8150 The callback set by C<isl_ast_print_options_set_print_for>
8151 is called whenever a node of type C<isl_ast_node_for> needs to
8153 Note that C<isl_ast_node_for_print> will I<not> call the
8154 callback set by C<isl_ast_print_options_set_print_for> on the node
8155 on which C<isl_ast_node_for_print> is called, but only on nested
8156 nodes of type C<isl_ast_node_for>. It is therefore safe to
8157 call C<isl_ast_node_for_print> from within the callback set by
8158 C<isl_ast_print_options_set_print_for>.
8160 The following option determines the type to be used for iterators
8161 while printing the AST.
8163 int isl_options_set_ast_iterator_type(
8164 isl_ctx *ctx, const char *val);
8165 const char *isl_options_get_ast_iterator_type(
8168 The AST printer only prints body nodes as blocks if these
8169 blocks cannot be safely omitted.
8170 For example, a C<for> node with one body node will not be
8171 surrounded with braces in C<ISL_FORMAT_C>.
8172 A block will always be printed by setting the following option.
8174 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
8176 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
8180 #include <isl/ast_build.h>
8181 int isl_options_set_ast_build_atomic_upper_bound(
8182 isl_ctx *ctx, int val);
8183 int isl_options_get_ast_build_atomic_upper_bound(
8185 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
8187 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
8188 int isl_options_set_ast_build_exploit_nested_bounds(
8189 isl_ctx *ctx, int val);
8190 int isl_options_get_ast_build_exploit_nested_bounds(
8192 int isl_options_set_ast_build_group_coscheduled(
8193 isl_ctx *ctx, int val);
8194 int isl_options_get_ast_build_group_coscheduled(
8196 int isl_options_set_ast_build_scale_strides(
8197 isl_ctx *ctx, int val);
8198 int isl_options_get_ast_build_scale_strides(
8200 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
8202 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
8203 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
8205 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
8209 =item * ast_build_atomic_upper_bound
8211 Generate loop upper bounds that consist of the current loop iterator,
8212 an operator and an expression not involving the iterator.
8213 If this option is not set, then the current loop iterator may appear
8214 several times in the upper bound.
8215 For example, when this option is turned off, AST generation
8218 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
8222 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
8225 When the option is turned on, the following AST is generated
8227 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
8230 =item * ast_build_prefer_pdiv
8232 If this option is turned off, then the AST generation will
8233 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
8234 operators, but no C<isl_ast_op_pdiv_q> or
8235 C<isl_ast_op_pdiv_r> operators.
8236 If this options is turned on, then C<isl> will try to convert
8237 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
8238 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
8240 =item * ast_build_exploit_nested_bounds
8242 Simplify conditions based on bounds of nested for loops.
8243 In particular, remove conditions that are implied by the fact
8244 that one or more nested loops have at least one iteration,
8245 meaning that the upper bound is at least as large as the lower bound.
8246 For example, when this option is turned off, AST generation
8249 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
8255 for (int c0 = 0; c0 <= N; c0 += 1)
8256 for (int c1 = 0; c1 <= M; c1 += 1)
8259 When the option is turned on, the following AST is generated
8261 for (int c0 = 0; c0 <= N; c0 += 1)
8262 for (int c1 = 0; c1 <= M; c1 += 1)
8265 =item * ast_build_group_coscheduled
8267 If two domain elements are assigned the same schedule point, then
8268 they may be executed in any order and they may even appear in different
8269 loops. If this options is set, then the AST generator will make
8270 sure that coscheduled domain elements do not appear in separate parts
8271 of the AST. This is useful in case of nested AST generation
8272 if the outer AST generation is given only part of a schedule
8273 and the inner AST generation should handle the domains that are
8274 coscheduled by this initial part of the schedule together.
8275 For example if an AST is generated for a schedule
8277 { A[i] -> [0]; B[i] -> [0] }
8279 then the C<isl_ast_build_set_create_leaf> callback described
8280 below may get called twice, once for each domain.
8281 Setting this option ensures that the callback is only called once
8282 on both domains together.
8284 =item * ast_build_separation_bounds
8286 This option specifies which bounds to use during separation.
8287 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
8288 then all (possibly implicit) bounds on the current dimension will
8289 be used during separation.
8290 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
8291 then only those bounds that are explicitly available will
8292 be used during separation.
8294 =item * ast_build_scale_strides
8296 This option specifies whether the AST generator is allowed
8297 to scale down iterators of strided loops.
8299 =item * ast_build_allow_else
8301 This option specifies whether the AST generator is allowed
8302 to construct if statements with else branches.
8304 =item * ast_build_allow_or
8306 This option specifies whether the AST generator is allowed
8307 to construct if conditions with disjunctions.
8311 =head3 Fine-grained Control over AST Generation
8313 Besides specifying the constraints on the parameters,
8314 an C<isl_ast_build> object can be used to control
8315 various aspects of the AST generation process.
8316 The most prominent way of control is through ``options'',
8317 which can be set using the following function.
8319 #include <isl/ast_build.h>
8320 __isl_give isl_ast_build *
8321 isl_ast_build_set_options(
8322 __isl_take isl_ast_build *control,
8323 __isl_take isl_union_map *options);
8325 The options are encoded in an C<isl_union_map>.
8326 The domain of this union relation refers to the schedule domain,
8327 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
8328 In the case of nested AST generation (see L</"Nested AST Generation">),
8329 the domain of C<options> should refer to the extra piece of the schedule.
8330 That is, it should be equal to the range of the wrapped relation in the
8331 range of the schedule.
8332 The range of the options can consist of elements in one or more spaces,
8333 the names of which determine the effect of the option.
8334 The values of the range typically also refer to the schedule dimension
8335 to which the option applies. In case of nested AST generation
8336 (see L</"Nested AST Generation">), these values refer to the position
8337 of the schedule dimension within the innermost AST generation.
8338 The constraints on the domain elements of
8339 the option should only refer to this dimension and earlier dimensions.
8340 We consider the following spaces.
8344 =item C<separation_class>
8346 This space is a wrapped relation between two one dimensional spaces.
8347 The input space represents the schedule dimension to which the option
8348 applies and the output space represents the separation class.
8349 While constructing a loop corresponding to the specified schedule
8350 dimension(s), the AST generator will try to generate separate loops
8351 for domain elements that are assigned different classes.
8352 If only some of the elements are assigned a class, then those elements
8353 that are not assigned any class will be treated as belonging to a class
8354 that is separate from the explicitly assigned classes.
8355 The typical use case for this option is to separate full tiles from
8357 The other options, described below, are applied after the separation
8360 As an example, consider the separation into full and partial tiles
8361 of a tiling of a triangular domain.
8362 Take, for example, the domain
8364 { A[i,j] : 0 <= i,j and i + j <= 100 }
8366 and a tiling into tiles of 10 by 10. The input to the AST generator
8367 is then the schedule
8369 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
8372 Without any options, the following AST is generated
8374 for (int c0 = 0; c0 <= 10; c0 += 1)
8375 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8376 for (int c2 = 10 * c0;
8377 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8379 for (int c3 = 10 * c1;
8380 c3 <= min(10 * c1 + 9, -c2 + 100);
8384 Separation into full and partial tiles can be obtained by assigning
8385 a class, say C<0>, to the full tiles. The full tiles are represented by those
8386 values of the first and second schedule dimensions for which there are
8387 values of the third and fourth dimensions to cover an entire tile.
8388 That is, we need to specify the following option
8390 { [a,b,c,d] -> separation_class[[0]->[0]] :
8391 exists b': 0 <= 10a,10b' and
8392 10a+9+10b'+9 <= 100;
8393 [a,b,c,d] -> separation_class[[1]->[0]] :
8394 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
8398 { [a, b, c, d] -> separation_class[[1] -> [0]] :
8399 a >= 0 and b >= 0 and b <= 8 - a;
8400 [a, b, c, d] -> separation_class[[0] -> [0]] :
8403 With this option, the generated AST is as follows
8406 for (int c0 = 0; c0 <= 8; c0 += 1) {
8407 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
8408 for (int c2 = 10 * c0;
8409 c2 <= 10 * c0 + 9; c2 += 1)
8410 for (int c3 = 10 * c1;
8411 c3 <= 10 * c1 + 9; c3 += 1)
8413 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
8414 for (int c2 = 10 * c0;
8415 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8417 for (int c3 = 10 * c1;
8418 c3 <= min(-c2 + 100, 10 * c1 + 9);
8422 for (int c0 = 9; c0 <= 10; c0 += 1)
8423 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8424 for (int c2 = 10 * c0;
8425 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8427 for (int c3 = 10 * c1;
8428 c3 <= min(10 * c1 + 9, -c2 + 100);
8435 This is a single-dimensional space representing the schedule dimension(s)
8436 to which ``separation'' should be applied. Separation tries to split
8437 a loop into several pieces if this can avoid the generation of guards
8439 See also the C<atomic> option.
8443 This is a single-dimensional space representing the schedule dimension(s)
8444 for which the domains should be considered ``atomic''. That is, the
8445 AST generator will make sure that any given domain space will only appear
8446 in a single loop at the specified level.
8448 Consider the following schedule
8450 { a[i] -> [i] : 0 <= i < 10;
8451 b[i] -> [i+1] : 0 <= i < 10 }
8453 If the following option is specified
8455 { [i] -> separate[x] }
8457 then the following AST will be generated
8461 for (int c0 = 1; c0 <= 9; c0 += 1) {
8468 If, on the other hand, the following option is specified
8470 { [i] -> atomic[x] }
8472 then the following AST will be generated
8474 for (int c0 = 0; c0 <= 10; c0 += 1) {
8481 If neither C<atomic> nor C<separate> is specified, then the AST generator
8482 may produce either of these two results or some intermediate form.
8486 This is a single-dimensional space representing the schedule dimension(s)
8487 that should be I<completely> unrolled.
8488 To obtain a partial unrolling, the user should apply an additional
8489 strip-mining to the schedule and fully unroll the inner loop.
8493 Additional control is available through the following functions.
8495 #include <isl/ast_build.h>
8496 __isl_give isl_ast_build *
8497 isl_ast_build_set_iterators(
8498 __isl_take isl_ast_build *control,
8499 __isl_take isl_id_list *iterators);
8501 The function C<isl_ast_build_set_iterators> allows the user to
8502 specify a list of iterator C<isl_id>s to be used as iterators.
8503 If the input schedule is injective, then
8504 the number of elements in this list should be as large as the dimension
8505 of the schedule space, but no direct correspondence should be assumed
8506 between dimensions and elements.
8507 If the input schedule is not injective, then an additional number
8508 of C<isl_id>s equal to the largest dimension of the input domains
8510 If the number of provided C<isl_id>s is insufficient, then additional
8511 names are automatically generated.
8513 #include <isl/ast_build.h>
8514 __isl_give isl_ast_build *
8515 isl_ast_build_set_create_leaf(
8516 __isl_take isl_ast_build *control,
8517 __isl_give isl_ast_node *(*fn)(
8518 __isl_take isl_ast_build *build,
8519 void *user), void *user);
8522 C<isl_ast_build_set_create_leaf> function allows for the
8523 specification of a callback that should be called whenever the AST
8524 generator arrives at an element of the schedule domain.
8525 The callback should return an AST node that should be inserted
8526 at the corresponding position of the AST. The default action (when
8527 the callback is not set) is to continue generating parts of the AST to scan
8528 all the domain elements associated to the schedule domain element
8529 and to insert user nodes, ``calling'' the domain element, for each of them.
8530 The C<build> argument contains the current state of the C<isl_ast_build>.
8531 To ease nested AST generation (see L</"Nested AST Generation">),
8532 all control information that is
8533 specific to the current AST generation such as the options and
8534 the callbacks has been removed from this C<isl_ast_build>.
8535 The callback would typically return the result of a nested
8537 user defined node created using the following function.
8539 #include <isl/ast.h>
8540 __isl_give isl_ast_node *isl_ast_node_alloc_user(
8541 __isl_take isl_ast_expr *expr);
8543 #include <isl/ast_build.h>
8544 __isl_give isl_ast_build *
8545 isl_ast_build_set_at_each_domain(
8546 __isl_take isl_ast_build *build,
8547 __isl_give isl_ast_node *(*fn)(
8548 __isl_take isl_ast_node *node,
8549 __isl_keep isl_ast_build *build,
8550 void *user), void *user);
8551 __isl_give isl_ast_build *
8552 isl_ast_build_set_before_each_for(
8553 __isl_take isl_ast_build *build,
8554 __isl_give isl_id *(*fn)(
8555 __isl_keep isl_ast_build *build,
8556 void *user), void *user);
8557 __isl_give isl_ast_build *
8558 isl_ast_build_set_after_each_for(
8559 __isl_take isl_ast_build *build,
8560 __isl_give isl_ast_node *(*fn)(
8561 __isl_take isl_ast_node *node,
8562 __isl_keep isl_ast_build *build,
8563 void *user), void *user);
8565 The callback set by C<isl_ast_build_set_at_each_domain> will
8566 be called for each domain AST node.
8567 The callbacks set by C<isl_ast_build_set_before_each_for>
8568 and C<isl_ast_build_set_after_each_for> will be called
8569 for each for AST node. The first will be called in depth-first
8570 pre-order, while the second will be called in depth-first post-order.
8571 Since C<isl_ast_build_set_before_each_for> is called before the for
8572 node is actually constructed, it is only passed an C<isl_ast_build>.
8573 The returned C<isl_id> will be added as an annotation (using
8574 C<isl_ast_node_set_annotation>) to the constructed for node.
8575 In particular, if the user has also specified an C<after_each_for>
8576 callback, then the annotation can be retrieved from the node passed to
8577 that callback using C<isl_ast_node_get_annotation>.
8578 All callbacks should C<NULL> on failure.
8579 The given C<isl_ast_build> can be used to create new
8580 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
8581 or C<isl_ast_build_call_from_pw_multi_aff>.
8583 =head3 Nested AST Generation
8585 C<isl> allows the user to create an AST within the context
8586 of another AST. These nested ASTs are created using the
8587 same C<isl_ast_build_ast_from_schedule> function that is used to create the
8588 outer AST. The C<build> argument should be an C<isl_ast_build>
8589 passed to a callback set by
8590 C<isl_ast_build_set_create_leaf>.
8591 The space of the range of the C<schedule> argument should refer
8592 to this build. In particular, the space should be a wrapped
8593 relation and the domain of this wrapped relation should be the
8594 same as that of the range of the schedule returned by
8595 C<isl_ast_build_get_schedule> below.
8596 In practice, the new schedule is typically
8597 created by calling C<isl_union_map_range_product> on the old schedule
8598 and some extra piece of the schedule.
8599 The space of the schedule domain is also available from
8600 the C<isl_ast_build>.
8602 #include <isl/ast_build.h>
8603 __isl_give isl_union_map *isl_ast_build_get_schedule(
8604 __isl_keep isl_ast_build *build);
8605 __isl_give isl_space *isl_ast_build_get_schedule_space(
8606 __isl_keep isl_ast_build *build);
8607 __isl_give isl_ast_build *isl_ast_build_restrict(
8608 __isl_take isl_ast_build *build,
8609 __isl_take isl_set *set);
8611 The C<isl_ast_build_get_schedule> function returns a (partial)
8612 schedule for the domains elements for which part of the AST still needs to
8613 be generated in the current build.
8614 In particular, the domain elements are mapped to those iterations of the loops
8615 enclosing the current point of the AST generation inside which
8616 the domain elements are executed.
8617 No direct correspondence between
8618 the input schedule and this schedule should be assumed.
8619 The space obtained from C<isl_ast_build_get_schedule_space> can be used
8620 to create a set for C<isl_ast_build_restrict> to intersect
8621 with the current build. In particular, the set passed to
8622 C<isl_ast_build_restrict> can have additional parameters.
8623 The ids of the set dimensions in the space returned by
8624 C<isl_ast_build_get_schedule_space> correspond to the
8625 iterators of the already generated loops.
8626 The user should not rely on the ids of the output dimensions
8627 of the relations in the union relation returned by
8628 C<isl_ast_build_get_schedule> having any particular value.
8632 Although C<isl> is mainly meant to be used as a library,
8633 it also contains some basic applications that use some
8634 of the functionality of C<isl>.
8635 The input may be specified in either the L<isl format>
8636 or the L<PolyLib format>.
8638 =head2 C<isl_polyhedron_sample>
8640 C<isl_polyhedron_sample> takes a polyhedron as input and prints
8641 an integer element of the polyhedron, if there is any.
8642 The first column in the output is the denominator and is always
8643 equal to 1. If the polyhedron contains no integer points,
8644 then a vector of length zero is printed.
8648 C<isl_pip> takes the same input as the C<example> program
8649 from the C<piplib> distribution, i.e., a set of constraints
8650 on the parameters, a line containing only -1 and finally a set
8651 of constraints on a parametric polyhedron.
8652 The coefficients of the parameters appear in the last columns
8653 (but before the final constant column).
8654 The output is the lexicographic minimum of the parametric polyhedron.
8655 As C<isl> currently does not have its own output format, the output
8656 is just a dump of the internal state.
8658 =head2 C<isl_polyhedron_minimize>
8660 C<isl_polyhedron_minimize> computes the minimum of some linear
8661 or affine objective function over the integer points in a polyhedron.
8662 If an affine objective function
8663 is given, then the constant should appear in the last column.
8665 =head2 C<isl_polytope_scan>
8667 Given a polytope, C<isl_polytope_scan> prints
8668 all integer points in the polytope.
8670 =head2 C<isl_codegen>
8672 Given a schedule, a context set and an options relation,
8673 C<isl_codegen> prints out an AST that scans the domain elements
8674 of the schedule in the order of their image(s) taking into account
8675 the constraints in the context set.