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 As a convenience, a sequence of base expressions that have
2755 their domains in a given space can be extracted from a sequence
2756 of union expressions using the following function.
2758 #include <isl/aff.h>
2759 __isl_give isl_multi_pw_aff *
2760 isl_multi_union_pw_aff_extract_multi_pw_aff(
2761 __isl_keep isl_multi_union_pw_aff *mupa,
2762 __isl_take isl_space *space);
2764 Note that there is a difference between C<isl_multi_union_pw_aff>
2765 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2766 of unions of piecewise expressions, while the second is a union
2767 of piecewise sequences. In particular, multiple affine expressions
2768 in an C<isl_union_pw_multi_aff> may live in different spaces,
2769 while there is only a single multiple expression in
2770 an C<isl_multi_union_pw_aff>, which can therefore only live
2771 in a single space. This means that not every
2772 C<isl_union_pw_multi_aff> can be converted to
2773 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2774 C<isl_multi_union_pw_aff> carries no information
2775 about any possible domain and therefore cannot be converted
2776 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2777 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2778 while each multiple expression inside an C<isl_union_pw_multi_aff>
2779 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2780 of dimension greater than one may therefore not be exact.
2781 The following functions can
2782 be used to perform these conversions when they are possible.
2784 #include <isl/aff.h>
2785 __isl_give isl_multi_union_pw_aff *
2786 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2787 __isl_take isl_union_pw_multi_aff *upma);
2788 __isl_give isl_union_pw_multi_aff *
2789 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2790 __isl_take isl_multi_union_pw_aff *mupa);
2792 =head3 Piecewise Expressions
2794 A piecewise expression is an expression that is described
2795 using zero or more base expression defined over the same
2796 number of cells in the domain space of the base expressions.
2797 All base expressions are defined over the same
2798 domain space and the cells are disjoint.
2799 The space of a piecewise expression is the same as
2800 that of the base expressions.
2801 If the union of the cells is a strict subset of the domain
2802 space, then the value of the piecewise expression outside
2803 this union is different for types derived from quasi-affine
2804 expressions and those derived from quasipolynomials.
2805 Piecewise expressions derived from quasi-affine expressions
2806 are considered to be undefined outside the union of their cells.
2807 Piecewise expressions derived from quasipolynomials
2808 are considered to be zero outside the union of their cells.
2810 Piecewise quasipolynomials are mainly used by the C<barvinok>
2811 library for representing the number of elements in a parametric set or map.
2812 For example, the piecewise quasipolynomial
2814 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2816 represents the number of points in the map
2818 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2820 The piecewise expression types defined by C<isl>
2821 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2822 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2824 A piecewise expression with no cells can be created using
2825 the following functions.
2827 #include <isl/aff.h>
2828 __isl_give isl_pw_aff *isl_pw_aff_empty(
2829 __isl_take isl_space *space);
2830 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2831 __isl_take isl_space *space);
2833 A piecewise expression with a single universe cell can be
2834 created using the following functions.
2836 #include <isl/aff.h>
2837 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2838 __isl_take isl_aff *aff);
2839 __isl_give isl_pw_multi_aff *
2840 isl_pw_multi_aff_from_multi_aff(
2841 __isl_take isl_multi_aff *ma);
2843 #include <isl/polynomial.h>
2844 __isl_give isl_pw_qpolynomial *
2845 isl_pw_qpolynomial_from_qpolynomial(
2846 __isl_take isl_qpolynomial *qp);
2848 A piecewise expression with a single specified cell can be
2849 created using the following functions.
2851 #include <isl/aff.h>
2852 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2853 __isl_take isl_set *set, __isl_take isl_aff *aff);
2854 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2855 __isl_take isl_set *set,
2856 __isl_take isl_multi_aff *maff);
2858 #include <isl/polynomial.h>
2859 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2860 __isl_take isl_set *set,
2861 __isl_take isl_qpolynomial *qp);
2863 The following convenience functions first create a base expression and
2864 then create a piecewise expression over a universe domain.
2866 #include <isl/aff.h>
2867 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2868 __isl_take isl_local_space *ls);
2869 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2870 __isl_take isl_local_space *ls,
2871 enum isl_dim_type type, unsigned pos);
2872 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2873 __isl_take isl_local_space *ls);
2874 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2875 __isl_take isl_space *space);
2876 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2877 __isl_take isl_space *space);
2878 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2879 __isl_take isl_space *space);
2880 __isl_give isl_pw_multi_aff *
2881 isl_pw_multi_aff_project_out_map(
2882 __isl_take isl_space *space,
2883 enum isl_dim_type type,
2884 unsigned first, unsigned n);
2886 #include <isl/polynomial.h>
2887 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2888 __isl_take isl_space *space);
2890 The following convenience functions first create a base expression and
2891 then create a piecewise expression over a given domain.
2893 #include <isl/aff.h>
2894 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2895 __isl_take isl_set *domain,
2896 __isl_take isl_val *v);
2897 __isl_give isl_pw_multi_aff *
2898 isl_pw_multi_aff_multi_val_on_domain(
2899 __isl_take isl_set *domain,
2900 __isl_take isl_multi_val *mv);
2902 As a convenience, a piecewise multiple expression can
2903 also be created from a piecewise expression.
2904 Each multiple expression in the result is derived
2905 from the corresponding base expression.
2907 #include <isl/aff.h>
2908 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2909 __isl_take isl_pw_aff *pa);
2911 Similarly, a piecewise quasipolynomial can be
2912 created from a piecewise quasi-affine expression using
2913 the following function.
2915 #include <isl/polynomial.h>
2916 __isl_give isl_pw_qpolynomial *
2917 isl_pw_qpolynomial_from_pw_aff(
2918 __isl_take isl_pw_aff *pwaff);
2920 Piecewise expressions can be copied and freed using the following functions.
2922 #include <isl/aff.h>
2923 __isl_give isl_pw_aff *isl_pw_aff_copy(
2924 __isl_keep isl_pw_aff *pwaff);
2925 __isl_null isl_pw_aff *isl_pw_aff_free(
2926 __isl_take isl_pw_aff *pwaff);
2927 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2928 __isl_keep isl_pw_multi_aff *pma);
2929 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2930 __isl_take isl_pw_multi_aff *pma);
2932 #include <isl/polynomial.h>
2933 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2934 __isl_keep isl_pw_qpolynomial *pwqp);
2935 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2936 __isl_take isl_pw_qpolynomial *pwqp);
2937 __isl_give isl_pw_qpolynomial_fold *
2938 isl_pw_qpolynomial_fold_copy(
2939 __isl_keep isl_pw_qpolynomial_fold *pwf);
2940 __isl_null isl_pw_qpolynomial_fold *
2941 isl_pw_qpolynomial_fold_free(
2942 __isl_take isl_pw_qpolynomial_fold *pwf);
2944 To iterate over the different cells of a piecewise expression,
2945 use the following functions.
2947 #include <isl/aff.h>
2948 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2949 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2950 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2951 int (*fn)(__isl_take isl_set *set,
2952 __isl_take isl_aff *aff,
2953 void *user), void *user);
2954 int isl_pw_multi_aff_foreach_piece(
2955 __isl_keep isl_pw_multi_aff *pma,
2956 int (*fn)(__isl_take isl_set *set,
2957 __isl_take isl_multi_aff *maff,
2958 void *user), void *user);
2960 #include <isl/polynomial.h>
2961 int isl_pw_qpolynomial_foreach_piece(
2962 __isl_keep isl_pw_qpolynomial *pwqp,
2963 int (*fn)(__isl_take isl_set *set,
2964 __isl_take isl_qpolynomial *qp,
2965 void *user), void *user);
2966 int isl_pw_qpolynomial_foreach_lifted_piece(
2967 __isl_keep isl_pw_qpolynomial *pwqp,
2968 int (*fn)(__isl_take isl_set *set,
2969 __isl_take isl_qpolynomial *qp,
2970 void *user), void *user);
2971 int isl_pw_qpolynomial_fold_foreach_piece(
2972 __isl_keep isl_pw_qpolynomial_fold *pwf,
2973 int (*fn)(__isl_take isl_set *set,
2974 __isl_take isl_qpolynomial_fold *fold,
2975 void *user), void *user);
2976 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2977 __isl_keep isl_pw_qpolynomial_fold *pwf,
2978 int (*fn)(__isl_take isl_set *set,
2979 __isl_take isl_qpolynomial_fold *fold,
2980 void *user), void *user);
2982 As usual, the function C<fn> should return C<0> on success
2983 and C<-1> on failure. The difference between
2984 C<isl_pw_qpolynomial_foreach_piece> and
2985 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2986 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2987 compute unique representations for all existentially quantified
2988 variables and then turn these existentially quantified variables
2989 into extra set variables, adapting the associated quasipolynomial
2990 accordingly. This means that the C<set> passed to C<fn>
2991 will not have any existentially quantified variables, but that
2992 the dimensions of the sets may be different for different
2993 invocations of C<fn>.
2994 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2995 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2997 A piecewise expression consisting of the expressions at a given
2998 position of a piecewise multiple expression can be extracted
2999 using the following function.
3001 #include <isl/aff.h>
3002 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3003 __isl_keep isl_pw_multi_aff *pma, int pos);
3005 These expressions can be replaced using the following function.
3007 #include <isl/aff.h>
3008 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3009 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3010 __isl_take isl_pw_aff *pa);
3012 Note that there is a difference between C<isl_multi_pw_aff> and
3013 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3014 affine expressions, while the second is a piecewise sequence
3015 of affine expressions. In particular, each of the piecewise
3016 affine expressions in an C<isl_multi_pw_aff> may have a different
3017 domain, while all multiple expressions associated to a cell
3018 in an C<isl_pw_multi_aff> have the same domain.
3019 It is possible to convert between the two, but when converting
3020 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3021 of the result is the intersection of the domains of the input.
3022 The reverse conversion is exact.
3024 #include <isl/aff.h>
3025 __isl_give isl_pw_multi_aff *
3026 isl_pw_multi_aff_from_multi_pw_aff(
3027 __isl_take isl_multi_pw_aff *mpa);
3028 __isl_give isl_multi_pw_aff *
3029 isl_multi_pw_aff_from_pw_multi_aff(
3030 __isl_take isl_pw_multi_aff *pma);
3032 =head3 Union Expressions
3034 A union expression collects base expressions defined
3035 over different domains. The space of a union expression
3036 is that of the shared parameter space.
3038 The union expression types defined by C<isl>
3039 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3040 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3042 An empty union expression can be created using the following functions.
3044 #include <isl/aff.h>
3045 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3046 __isl_take isl_space *space);
3047 __isl_give isl_union_pw_multi_aff *
3048 isl_union_pw_multi_aff_empty(
3049 __isl_take isl_space *space);
3051 #include <isl/polynomial.h>
3052 __isl_give isl_union_pw_qpolynomial *
3053 isl_union_pw_qpolynomial_zero(
3054 __isl_take isl_space *space);
3056 A union expression containing a single base expression
3057 can be created using the following functions.
3059 #include <isl/aff.h>
3060 __isl_give isl_union_pw_aff *
3061 isl_union_pw_aff_from_pw_aff(
3062 __isl_take isl_pw_aff *pa);
3063 __isl_give isl_union_pw_multi_aff *
3064 isl_union_pw_multi_aff_from_aff(
3065 __isl_take isl_aff *aff);
3066 __isl_give isl_union_pw_multi_aff *
3067 isl_union_pw_multi_aff_from_pw_multi_aff(
3068 __isl_take isl_pw_multi_aff *pma);
3070 #include <isl/polynomial.h>
3071 __isl_give isl_union_pw_qpolynomial *
3072 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3073 __isl_take isl_pw_qpolynomial *pwqp);
3075 The following functions create a base expression on each
3076 of the sets in the union set and collect the results.
3078 #include <isl/aff.h>
3079 __isl_give isl_union_pw_multi_aff *
3080 isl_union_pw_multi_aff_from_union_pw_aff(
3081 __isl_take isl_union_pw_aff *upa);
3082 __isl_give isl_union_pw_aff *
3083 isl_union_pw_multi_aff_get_union_pw_aff(
3084 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3085 __isl_give isl_union_pw_aff *
3086 isl_union_pw_aff_val_on_domain(
3087 __isl_take isl_union_set *domain,
3088 __isl_take isl_val *v);
3089 __isl_give isl_union_pw_multi_aff *
3090 isl_union_pw_multi_aff_multi_val_on_domain(
3091 __isl_take isl_union_set *domain,
3092 __isl_take isl_multi_val *mv);
3094 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3095 expression on a given domain can be created using the following
3098 #include <isl/aff.h>
3099 __isl_give isl_union_pw_aff *
3100 isl_union_pw_aff_aff_on_domain(
3101 __isl_take isl_union_set *domain,
3102 __isl_take isl_aff *aff);
3104 A base expression can be added to a union expression using
3105 the following functions.
3107 #include <isl/aff.h>
3108 __isl_give isl_union_pw_aff *
3109 isl_union_pw_aff_add_pw_aff(
3110 __isl_take isl_union_pw_aff *upa,
3111 __isl_take isl_pw_aff *pa);
3112 __isl_give isl_union_pw_multi_aff *
3113 isl_union_pw_multi_aff_add_pw_multi_aff(
3114 __isl_take isl_union_pw_multi_aff *upma,
3115 __isl_take isl_pw_multi_aff *pma);
3117 #include <isl/polynomial.h>
3118 __isl_give isl_union_pw_qpolynomial *
3119 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3120 __isl_take isl_union_pw_qpolynomial *upwqp,
3121 __isl_take isl_pw_qpolynomial *pwqp);
3123 Union expressions can be copied and freed using
3124 the following functions.
3126 #include <isl/aff.h>
3127 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3128 __isl_keep isl_union_pw_aff *upa);
3129 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3130 __isl_take isl_union_pw_aff *upa);
3131 __isl_give isl_union_pw_multi_aff *
3132 isl_union_pw_multi_aff_copy(
3133 __isl_keep isl_union_pw_multi_aff *upma);
3134 __isl_null isl_union_pw_multi_aff *
3135 isl_union_pw_multi_aff_free(
3136 __isl_take isl_union_pw_multi_aff *upma);
3138 #include <isl/polynomial.h>
3139 __isl_give isl_union_pw_qpolynomial *
3140 isl_union_pw_qpolynomial_copy(
3141 __isl_keep isl_union_pw_qpolynomial *upwqp);
3142 __isl_null isl_union_pw_qpolynomial *
3143 isl_union_pw_qpolynomial_free(
3144 __isl_take isl_union_pw_qpolynomial *upwqp);
3145 __isl_give isl_union_pw_qpolynomial_fold *
3146 isl_union_pw_qpolynomial_fold_copy(
3147 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3148 __isl_null isl_union_pw_qpolynomial_fold *
3149 isl_union_pw_qpolynomial_fold_free(
3150 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3152 To iterate over the base expressions in a union expression,
3153 use the following functions.
3155 #include <isl/aff.h>
3156 int isl_union_pw_aff_n_pw_multi_aff(
3157 __isl_keep isl_union_pw_aff *upa);
3158 int isl_union_pw_aff_foreach_pw_aff(
3159 __isl_keep isl_union_pw_aff *upa,
3160 int (*fn)(__isl_take isl_pw_aff *ma, void *user),
3162 int isl_union_pw_multi_aff_n_pw_multi_aff(
3163 __isl_keep isl_union_pw_multi_aff *upma);
3164 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3165 __isl_keep isl_union_pw_multi_aff *upma,
3166 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3167 void *user), void *user);
3169 #include <isl/polynomial.h>
3170 int isl_union_pw_qplynomial_n_pw_qpolynomial(
3171 __isl_keep isl_union_pw_qpolynomial *upwqp);
3172 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3173 __isl_keep isl_union_pw_qpolynomial *upwqp,
3174 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3175 void *user), void *user);
3176 int isl_union_pw_qplynomial_fold_n_pw_qpolynomial_fold(
3177 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3178 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3179 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3180 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3181 void *user), void *user);
3183 To extract the base expression in a given space from a union, use
3184 the following functions.
3186 #include <isl/aff.h>
3187 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3188 __isl_keep isl_union_pw_aff *upa,
3189 __isl_take isl_space *space);
3190 __isl_give isl_pw_multi_aff *
3191 isl_union_pw_multi_aff_extract_pw_multi_aff(
3192 __isl_keep isl_union_pw_multi_aff *upma,
3193 __isl_take isl_space *space);
3195 #include <isl/polynomial.h>
3196 __isl_give isl_pw_qpolynomial *
3197 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3198 __isl_keep isl_union_pw_qpolynomial *upwqp,
3199 __isl_take isl_space *space);
3201 =head2 Input and Output
3203 For set and relation,
3204 C<isl> supports its own input/output format, which is similar
3205 to the C<Omega> format, but also supports the C<PolyLib> format
3207 For other object types, typically only an C<isl> format is supported.
3209 =head3 C<isl> format
3211 The C<isl> format is similar to that of C<Omega>, but has a different
3212 syntax for describing the parameters and allows for the definition
3213 of an existentially quantified variable as the integer division
3214 of an affine expression.
3215 For example, the set of integers C<i> between C<0> and C<n>
3216 such that C<i % 10 <= 6> can be described as
3218 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3221 A set or relation can have several disjuncts, separated
3222 by the keyword C<or>. Each disjunct is either a conjunction
3223 of constraints or a projection (C<exists>) of a conjunction
3224 of constraints. The constraints are separated by the keyword
3227 =head3 C<PolyLib> format
3229 If the represented set is a union, then the first line
3230 contains a single number representing the number of disjuncts.
3231 Otherwise, a line containing the number C<1> is optional.
3233 Each disjunct is represented by a matrix of constraints.
3234 The first line contains two numbers representing
3235 the number of rows and columns,
3236 where the number of rows is equal to the number of constraints
3237 and the number of columns is equal to two plus the number of variables.
3238 The following lines contain the actual rows of the constraint matrix.
3239 In each row, the first column indicates whether the constraint
3240 is an equality (C<0>) or inequality (C<1>). The final column
3241 corresponds to the constant term.
3243 If the set is parametric, then the coefficients of the parameters
3244 appear in the last columns before the constant column.
3245 The coefficients of any existentially quantified variables appear
3246 between those of the set variables and those of the parameters.
3248 =head3 Extended C<PolyLib> format
3250 The extended C<PolyLib> format is nearly identical to the
3251 C<PolyLib> format. The only difference is that the line
3252 containing the number of rows and columns of a constraint matrix
3253 also contains four additional numbers:
3254 the number of output dimensions, the number of input dimensions,
3255 the number of local dimensions (i.e., the number of existentially
3256 quantified variables) and the number of parameters.
3257 For sets, the number of ``output'' dimensions is equal
3258 to the number of set dimensions, while the number of ``input''
3263 Objects can be read from input using the following functions.
3265 #include <isl/val.h>
3266 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3268 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3269 isl_ctx *ctx, const char *str);
3271 #include <isl/set.h>
3272 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3273 isl_ctx *ctx, FILE *input);
3274 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3275 isl_ctx *ctx, const char *str);
3276 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3278 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3281 #include <isl/map.h>
3282 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3283 isl_ctx *ctx, FILE *input);
3284 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3285 isl_ctx *ctx, const char *str);
3286 __isl_give isl_map *isl_map_read_from_file(
3287 isl_ctx *ctx, FILE *input);
3288 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3291 #include <isl/union_set.h>
3292 __isl_give isl_union_set *isl_union_set_read_from_file(
3293 isl_ctx *ctx, FILE *input);
3294 __isl_give isl_union_set *isl_union_set_read_from_str(
3295 isl_ctx *ctx, const char *str);
3297 #include <isl/union_map.h>
3298 __isl_give isl_union_map *isl_union_map_read_from_file(
3299 isl_ctx *ctx, FILE *input);
3300 __isl_give isl_union_map *isl_union_map_read_from_str(
3301 isl_ctx *ctx, const char *str);
3303 #include <isl/aff.h>
3304 __isl_give isl_aff *isl_aff_read_from_str(
3305 isl_ctx *ctx, const char *str);
3306 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3307 isl_ctx *ctx, const char *str);
3308 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3309 isl_ctx *ctx, const char *str);
3310 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3311 isl_ctx *ctx, const char *str);
3312 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3313 isl_ctx *ctx, const char *str);
3314 __isl_give isl_union_pw_multi_aff *
3315 isl_union_pw_multi_aff_read_from_str(
3316 isl_ctx *ctx, const char *str);
3317 __isl_give isl_multi_union_pw_aff *
3318 isl_multi_union_pw_aff_read_from_str(
3319 isl_ctx *ctx, const char *str);
3321 #include <isl/polynomial.h>
3322 __isl_give isl_union_pw_qpolynomial *
3323 isl_union_pw_qpolynomial_read_from_str(
3324 isl_ctx *ctx, const char *str);
3326 For sets and relations,
3327 the input format is autodetected and may be either the C<PolyLib> format
3328 or the C<isl> format.
3332 Before anything can be printed, an C<isl_printer> needs to
3335 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3337 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3338 __isl_null isl_printer *isl_printer_free(
3339 __isl_take isl_printer *printer);
3340 __isl_give char *isl_printer_get_str(
3341 __isl_keep isl_printer *printer);
3343 The printer can be inspected using the following functions.
3345 FILE *isl_printer_get_file(
3346 __isl_keep isl_printer *printer);
3347 int isl_printer_get_output_format(
3348 __isl_keep isl_printer *p);
3350 The behavior of the printer can be modified in various ways
3352 __isl_give isl_printer *isl_printer_set_output_format(
3353 __isl_take isl_printer *p, int output_format);
3354 __isl_give isl_printer *isl_printer_set_indent(
3355 __isl_take isl_printer *p, int indent);
3356 __isl_give isl_printer *isl_printer_set_indent_prefix(
3357 __isl_take isl_printer *p, const char *prefix);
3358 __isl_give isl_printer *isl_printer_indent(
3359 __isl_take isl_printer *p, int indent);
3360 __isl_give isl_printer *isl_printer_set_prefix(
3361 __isl_take isl_printer *p, const char *prefix);
3362 __isl_give isl_printer *isl_printer_set_suffix(
3363 __isl_take isl_printer *p, const char *suffix);
3365 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3366 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3367 and defaults to C<ISL_FORMAT_ISL>.
3368 Each line in the output is prefixed by C<indent_prefix>,
3369 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3370 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3371 In the C<PolyLib> format output,
3372 the coefficients of the existentially quantified variables
3373 appear between those of the set variables and those
3375 The function C<isl_printer_indent> increases the indentation
3376 by the specified amount (which may be negative).
3378 To actually print something, use
3380 #include <isl/printer.h>
3381 __isl_give isl_printer *isl_printer_print_double(
3382 __isl_take isl_printer *p, double d);
3384 #include <isl/val.h>
3385 __isl_give isl_printer *isl_printer_print_val(
3386 __isl_take isl_printer *p, __isl_keep isl_val *v);
3388 #include <isl/set.h>
3389 __isl_give isl_printer *isl_printer_print_basic_set(
3390 __isl_take isl_printer *printer,
3391 __isl_keep isl_basic_set *bset);
3392 __isl_give isl_printer *isl_printer_print_set(
3393 __isl_take isl_printer *printer,
3394 __isl_keep isl_set *set);
3396 #include <isl/map.h>
3397 __isl_give isl_printer *isl_printer_print_basic_map(
3398 __isl_take isl_printer *printer,
3399 __isl_keep isl_basic_map *bmap);
3400 __isl_give isl_printer *isl_printer_print_map(
3401 __isl_take isl_printer *printer,
3402 __isl_keep isl_map *map);
3404 #include <isl/union_set.h>
3405 __isl_give isl_printer *isl_printer_print_union_set(
3406 __isl_take isl_printer *p,
3407 __isl_keep isl_union_set *uset);
3409 #include <isl/union_map.h>
3410 __isl_give isl_printer *isl_printer_print_union_map(
3411 __isl_take isl_printer *p,
3412 __isl_keep isl_union_map *umap);
3414 #include <isl/val.h>
3415 __isl_give isl_printer *isl_printer_print_multi_val(
3416 __isl_take isl_printer *p,
3417 __isl_keep isl_multi_val *mv);
3419 #include <isl/aff.h>
3420 __isl_give isl_printer *isl_printer_print_aff(
3421 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3422 __isl_give isl_printer *isl_printer_print_multi_aff(
3423 __isl_take isl_printer *p,
3424 __isl_keep isl_multi_aff *maff);
3425 __isl_give isl_printer *isl_printer_print_pw_aff(
3426 __isl_take isl_printer *p,
3427 __isl_keep isl_pw_aff *pwaff);
3428 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3429 __isl_take isl_printer *p,
3430 __isl_keep isl_pw_multi_aff *pma);
3431 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3432 __isl_take isl_printer *p,
3433 __isl_keep isl_multi_pw_aff *mpa);
3434 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3435 __isl_take isl_printer *p,
3436 __isl_keep isl_union_pw_aff *upa);
3437 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3438 __isl_take isl_printer *p,
3439 __isl_keep isl_union_pw_multi_aff *upma);
3440 __isl_give isl_printer *
3441 isl_printer_print_multi_union_pw_aff(
3442 __isl_take isl_printer *p,
3443 __isl_keep isl_multi_union_pw_aff *mupa);
3445 #include <isl/polynomial.h>
3446 __isl_give isl_printer *isl_printer_print_qpolynomial(
3447 __isl_take isl_printer *p,
3448 __isl_keep isl_qpolynomial *qp);
3449 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3450 __isl_take isl_printer *p,
3451 __isl_keep isl_pw_qpolynomial *pwqp);
3452 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3453 __isl_take isl_printer *p,
3454 __isl_keep isl_union_pw_qpolynomial *upwqp);
3456 __isl_give isl_printer *
3457 isl_printer_print_pw_qpolynomial_fold(
3458 __isl_take isl_printer *p,
3459 __isl_keep isl_pw_qpolynomial_fold *pwf);
3460 __isl_give isl_printer *
3461 isl_printer_print_union_pw_qpolynomial_fold(
3462 __isl_take isl_printer *p,
3463 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3465 For C<isl_printer_print_qpolynomial>,
3466 C<isl_printer_print_pw_qpolynomial> and
3467 C<isl_printer_print_pw_qpolynomial_fold>,
3468 the output format of the printer
3469 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3470 For C<isl_printer_print_union_pw_qpolynomial> and
3471 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3473 In case of printing in C<ISL_FORMAT_C>, the user may want
3474 to set the names of all dimensions first.
3476 When called on a file printer, the following function flushes
3477 the file. When called on a string printer, the buffer is cleared.
3479 __isl_give isl_printer *isl_printer_flush(
3480 __isl_take isl_printer *p);
3482 Alternatively, a string representation can be obtained
3483 directly using the following functions, which always print
3486 #include <isl/space.h>
3487 __isl_give char *isl_space_to_str(
3488 __isl_keep isl_space *space);
3490 #include <isl/val.h>
3491 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3492 __isl_give char *isl_multi_val_to_str(
3493 __isl_keep isl_multi_val *mv);
3495 #include <isl/set.h>
3496 __isl_give char *isl_set_to_str(
3497 __isl_keep isl_set *set);
3499 #include <isl/union_set.h>
3500 __isl_give char *isl_union_set_to_str(
3501 __isl_keep isl_union_set *uset);
3503 #include <isl/map.h>
3504 __isl_give char *isl_map_to_str(
3505 __isl_keep isl_map *map);
3507 #include <isl/union_map.h>
3508 __isl_give char *isl_union_map_to_str(
3509 __isl_keep isl_union_map *umap);
3511 #include <isl/aff.h>
3512 __isl_give char *isl_multi_aff_to_str(
3513 __isl_keep isl_multi_aff *aff);
3514 __isl_give char *isl_union_pw_aff_to_str(
3515 __isl_keep isl_union_pw_aff *upa);
3516 __isl_give char *isl_union_pw_multi_aff_to_str(
3517 __isl_keep isl_union_pw_multi_aff *upma);
3518 __isl_give char *isl_multi_union_pw_aff_to_str(
3519 __isl_keep isl_multi_union_pw_aff *mupa);
3523 =head3 Unary Properties
3529 The following functions test whether the given set or relation
3530 contains any integer points. The ``plain'' variants do not perform
3531 any computations, but simply check if the given set or relation
3532 is already known to be empty.
3534 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3535 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3536 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3537 int isl_set_is_empty(__isl_keep isl_set *set);
3538 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3539 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3540 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3541 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3542 int isl_map_is_empty(__isl_keep isl_map *map);
3543 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3545 =item * Universality
3547 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3548 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3549 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3551 =item * Single-valuedness
3553 #include <isl/set.h>
3554 int isl_set_is_singleton(__isl_keep isl_set *set);
3556 #include <isl/map.h>
3557 int isl_basic_map_is_single_valued(
3558 __isl_keep isl_basic_map *bmap);
3559 int isl_map_plain_is_single_valued(
3560 __isl_keep isl_map *map);
3561 int isl_map_is_single_valued(__isl_keep isl_map *map);
3563 #include <isl/union_map.h>
3564 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3568 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3569 int isl_map_is_injective(__isl_keep isl_map *map);
3570 int isl_union_map_plain_is_injective(
3571 __isl_keep isl_union_map *umap);
3572 int isl_union_map_is_injective(
3573 __isl_keep isl_union_map *umap);
3577 int isl_map_is_bijective(__isl_keep isl_map *map);
3578 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3582 __isl_give isl_val *
3583 isl_basic_map_plain_get_val_if_fixed(
3584 __isl_keep isl_basic_map *bmap,
3585 enum isl_dim_type type, unsigned pos);
3586 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3587 __isl_keep isl_set *set,
3588 enum isl_dim_type type, unsigned pos);
3589 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3590 __isl_keep isl_map *map,
3591 enum isl_dim_type type, unsigned pos);
3593 If the set or relation obviously lies on a hyperplane where the given dimension
3594 has a fixed value, then return that value.
3595 Otherwise return NaN.
3599 int isl_set_dim_residue_class_val(
3600 __isl_keep isl_set *set,
3601 int pos, __isl_give isl_val **modulo,
3602 __isl_give isl_val **residue);
3604 Check if the values of the given set dimension are equal to a fixed
3605 value modulo some integer value. If so, assign the modulo to C<*modulo>
3606 and the fixed value to C<*residue>. If the given dimension attains only
3607 a single value, then assign C<0> to C<*modulo> and the fixed value to
3609 If the dimension does not attain only a single value and if no modulo
3610 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3614 To check whether the description of a set, relation or function depends
3615 on one or more given dimensions,
3616 the following functions can be used.
3618 #include <isl/constraint.h>
3619 int isl_constraint_involves_dims(
3620 __isl_keep isl_constraint *constraint,
3621 enum isl_dim_type type, unsigned first, unsigned n);
3623 #include <isl/set.h>
3624 int isl_basic_set_involves_dims(
3625 __isl_keep isl_basic_set *bset,
3626 enum isl_dim_type type, unsigned first, unsigned n);
3627 int isl_set_involves_dims(__isl_keep isl_set *set,
3628 enum isl_dim_type type, unsigned first, unsigned n);
3630 #include <isl/map.h>
3631 int isl_basic_map_involves_dims(
3632 __isl_keep isl_basic_map *bmap,
3633 enum isl_dim_type type, unsigned first, unsigned n);
3634 int isl_map_involves_dims(__isl_keep isl_map *map,
3635 enum isl_dim_type type, unsigned first, unsigned n);
3637 #include <isl/union_map.h>
3638 int isl_union_map_involves_dims(
3639 __isl_keep isl_union_map *umap,
3640 enum isl_dim_type type, unsigned first, unsigned n);
3642 #include <isl/aff.h>
3643 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3644 enum isl_dim_type type, unsigned first, unsigned n);
3645 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3646 enum isl_dim_type type, unsigned first, unsigned n);
3647 int isl_multi_aff_involves_dims(
3648 __isl_keep isl_multi_aff *ma,
3649 enum isl_dim_type type, unsigned first, unsigned n);
3650 int isl_multi_pw_aff_involves_dims(
3651 __isl_keep isl_multi_pw_aff *mpa,
3652 enum isl_dim_type type, unsigned first, unsigned n);
3654 Similarly, the following functions can be used to check whether
3655 a given dimension is involved in any lower or upper bound.
3657 #include <isl/set.h>
3658 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3659 enum isl_dim_type type, unsigned pos);
3660 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3661 enum isl_dim_type type, unsigned pos);
3663 Note that these functions return true even if there is a bound on
3664 the dimension on only some of the basic sets of C<set>.
3665 To check if they have a bound for all of the basic sets in C<set>,
3666 use the following functions instead.
3668 #include <isl/set.h>
3669 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3670 enum isl_dim_type type, unsigned pos);
3671 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3672 enum isl_dim_type type, unsigned pos);
3676 To check whether a set is a parameter domain, use this function:
3678 int isl_set_is_params(__isl_keep isl_set *set);
3679 int isl_union_set_is_params(
3680 __isl_keep isl_union_set *uset);
3684 The following functions check whether the space of the given
3685 (basic) set or relation range is a wrapped relation.
3687 #include <isl/space.h>
3688 int isl_space_is_wrapping(
3689 __isl_keep isl_space *space);
3690 int isl_space_domain_is_wrapping(
3691 __isl_keep isl_space *space);
3692 int isl_space_range_is_wrapping(
3693 __isl_keep isl_space *space);
3695 #include <isl/set.h>
3696 int isl_basic_set_is_wrapping(
3697 __isl_keep isl_basic_set *bset);
3698 int isl_set_is_wrapping(__isl_keep isl_set *set);
3700 #include <isl/map.h>
3701 int isl_map_domain_is_wrapping(
3702 __isl_keep isl_map *map);
3703 int isl_map_range_is_wrapping(
3704 __isl_keep isl_map *map);
3706 #include <isl/val.h>
3707 int isl_multi_val_range_is_wrapping(
3708 __isl_keep isl_multi_val *mv);
3710 #include <isl/aff.h>
3711 int isl_multi_aff_range_is_wrapping(
3712 __isl_keep isl_multi_aff *ma);
3713 int isl_multi_pw_aff_range_is_wrapping(
3714 __isl_keep isl_multi_pw_aff *mpa);
3715 int isl_multi_union_pw_aff_range_is_wrapping(
3716 __isl_keep isl_multi_union_pw_aff *mupa);
3718 The input to C<isl_space_is_wrapping> should
3719 be the space of a set, while that of
3720 C<isl_space_domain_is_wrapping> and
3721 C<isl_space_range_is_wrapping> should be the space of a relation.
3723 =item * Internal Product
3725 int isl_basic_map_can_zip(
3726 __isl_keep isl_basic_map *bmap);
3727 int isl_map_can_zip(__isl_keep isl_map *map);
3729 Check whether the product of domain and range of the given relation
3731 i.e., whether both domain and range are nested relations.
3735 int isl_basic_map_can_curry(
3736 __isl_keep isl_basic_map *bmap);
3737 int isl_map_can_curry(__isl_keep isl_map *map);
3739 Check whether the domain of the (basic) relation is a wrapped relation.
3741 int isl_basic_map_can_uncurry(
3742 __isl_keep isl_basic_map *bmap);
3743 int isl_map_can_uncurry(__isl_keep isl_map *map);
3745 Check whether the range of the (basic) relation is a wrapped relation.
3747 =item * Special Values
3749 #include <isl/aff.h>
3750 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3751 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3753 Check whether the given expression is a constant.
3755 #include <isl/aff.h>
3756 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3757 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3759 Check whether the given expression is equal to or involves NaN.
3761 #include <isl/aff.h>
3762 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3764 Check whether the affine expression is obviously zero.
3768 =head3 Binary Properties
3774 The following functions check whether two objects
3775 represent the same set, relation or function.
3776 The C<plain> variants only return true if the objects
3777 are obviously the same. That is, they may return false
3778 even if the objects are the same, but they will never
3779 return true if the objects are not the same.
3781 #include <isl/set.h>
3782 int isl_basic_set_plain_is_equal(
3783 __isl_keep isl_basic_set *bset1,
3784 __isl_keep isl_basic_set *bset2);
3785 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3786 __isl_keep isl_set *set2);
3787 int isl_set_is_equal(__isl_keep isl_set *set1,
3788 __isl_keep isl_set *set2);
3790 #include <isl/map.h>
3791 int isl_basic_map_is_equal(
3792 __isl_keep isl_basic_map *bmap1,
3793 __isl_keep isl_basic_map *bmap2);
3794 int isl_map_is_equal(__isl_keep isl_map *map1,
3795 __isl_keep isl_map *map2);
3796 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3797 __isl_keep isl_map *map2);
3799 #include <isl/union_set.h>
3800 int isl_union_set_is_equal(
3801 __isl_keep isl_union_set *uset1,
3802 __isl_keep isl_union_set *uset2);
3804 #include <isl/union_map.h>
3805 int isl_union_map_is_equal(
3806 __isl_keep isl_union_map *umap1,
3807 __isl_keep isl_union_map *umap2);
3809 #include <isl/aff.h>
3810 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3811 __isl_keep isl_aff *aff2);
3812 int isl_multi_aff_plain_is_equal(
3813 __isl_keep isl_multi_aff *maff1,
3814 __isl_keep isl_multi_aff *maff2);
3815 int isl_pw_aff_plain_is_equal(
3816 __isl_keep isl_pw_aff *pwaff1,
3817 __isl_keep isl_pw_aff *pwaff2);
3818 int isl_pw_multi_aff_plain_is_equal(
3819 __isl_keep isl_pw_multi_aff *pma1,
3820 __isl_keep isl_pw_multi_aff *pma2);
3821 int isl_multi_pw_aff_plain_is_equal(
3822 __isl_keep isl_multi_pw_aff *mpa1,
3823 __isl_keep isl_multi_pw_aff *mpa2);
3824 int isl_multi_pw_aff_is_equal(
3825 __isl_keep isl_multi_pw_aff *mpa1,
3826 __isl_keep isl_multi_pw_aff *mpa2);
3827 int isl_union_pw_aff_plain_is_equal(
3828 __isl_keep isl_union_pw_aff *upa1,
3829 __isl_keep isl_union_pw_aff *upa2);
3830 int isl_union_pw_multi_aff_plain_is_equal(
3831 __isl_keep isl_union_pw_multi_aff *upma1,
3832 __isl_keep isl_union_pw_multi_aff *upma2);
3833 int isl_multi_union_pw_aff_plain_is_equal(
3834 __isl_keep isl_multi_union_pw_aff *mupa1,
3835 __isl_keep isl_multi_union_pw_aff *mupa2);
3837 #include <isl/polynomial.h>
3838 int isl_union_pw_qpolynomial_plain_is_equal(
3839 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3840 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3841 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3842 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3843 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3845 =item * Disjointness
3847 #include <isl/set.h>
3848 int isl_basic_set_is_disjoint(
3849 __isl_keep isl_basic_set *bset1,
3850 __isl_keep isl_basic_set *bset2);
3851 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3852 __isl_keep isl_set *set2);
3853 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3854 __isl_keep isl_set *set2);
3856 #include <isl/map.h>
3857 int isl_basic_map_is_disjoint(
3858 __isl_keep isl_basic_map *bmap1,
3859 __isl_keep isl_basic_map *bmap2);
3860 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3861 __isl_keep isl_map *map2);
3863 #include <isl/union_set.h>
3864 int isl_union_set_is_disjoint(
3865 __isl_keep isl_union_set *uset1,
3866 __isl_keep isl_union_set *uset2);
3868 #include <isl/union_map.h>
3869 int isl_union_map_is_disjoint(
3870 __isl_keep isl_union_map *umap1,
3871 __isl_keep isl_union_map *umap2);
3875 int isl_basic_set_is_subset(
3876 __isl_keep isl_basic_set *bset1,
3877 __isl_keep isl_basic_set *bset2);
3878 int isl_set_is_subset(__isl_keep isl_set *set1,
3879 __isl_keep isl_set *set2);
3880 int isl_set_is_strict_subset(
3881 __isl_keep isl_set *set1,
3882 __isl_keep isl_set *set2);
3883 int isl_union_set_is_subset(
3884 __isl_keep isl_union_set *uset1,
3885 __isl_keep isl_union_set *uset2);
3886 int isl_union_set_is_strict_subset(
3887 __isl_keep isl_union_set *uset1,
3888 __isl_keep isl_union_set *uset2);
3889 int isl_basic_map_is_subset(
3890 __isl_keep isl_basic_map *bmap1,
3891 __isl_keep isl_basic_map *bmap2);
3892 int isl_basic_map_is_strict_subset(
3893 __isl_keep isl_basic_map *bmap1,
3894 __isl_keep isl_basic_map *bmap2);
3895 int isl_map_is_subset(
3896 __isl_keep isl_map *map1,
3897 __isl_keep isl_map *map2);
3898 int isl_map_is_strict_subset(
3899 __isl_keep isl_map *map1,
3900 __isl_keep isl_map *map2);
3901 int isl_union_map_is_subset(
3902 __isl_keep isl_union_map *umap1,
3903 __isl_keep isl_union_map *umap2);
3904 int isl_union_map_is_strict_subset(
3905 __isl_keep isl_union_map *umap1,
3906 __isl_keep isl_union_map *umap2);
3908 Check whether the first argument is a (strict) subset of the
3913 Every comparison function returns a negative value if the first
3914 argument is considered smaller than the second, a positive value
3915 if the first argument is considered greater and zero if the two
3916 constraints are considered the same by the comparison criterion.
3918 #include <isl/constraint.h>
3919 int isl_constraint_plain_cmp(
3920 __isl_keep isl_constraint *c1,
3921 __isl_keep isl_constraint *c2);
3923 This function is useful for sorting C<isl_constraint>s.
3924 The order depends on the internal representation of the inputs.
3925 The order is fixed over different calls to the function (assuming
3926 the internal representation of the inputs has not changed), but may
3927 change over different versions of C<isl>.
3929 #include <isl/constraint.h>
3930 int isl_constraint_cmp_last_non_zero(
3931 __isl_keep isl_constraint *c1,
3932 __isl_keep isl_constraint *c2);
3934 This function can be used to sort constraints that live in the same
3935 local space. Constraints that involve ``earlier'' dimensions or
3936 that have a smaller coefficient for the shared latest dimension
3937 are considered smaller than other constraints.
3938 This function only defines a B<partial> order.
3940 #include <isl/set.h>
3941 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3942 __isl_keep isl_set *set2);
3944 This function is useful for sorting C<isl_set>s.
3945 The order depends on the internal representation of the inputs.
3946 The order is fixed over different calls to the function (assuming
3947 the internal representation of the inputs has not changed), but may
3948 change over different versions of C<isl>.
3950 #include <isl/aff.h>
3951 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3952 __isl_keep isl_pw_aff *pa2);
3954 The function C<isl_pw_aff_plain_cmp> can be used to sort
3955 C<isl_pw_aff>s. The order is not strictly defined.
3956 The current order sorts expressions that only involve
3957 earlier dimensions before those that involve later dimensions.
3961 =head2 Unary Operations
3967 __isl_give isl_set *isl_set_complement(
3968 __isl_take isl_set *set);
3969 __isl_give isl_map *isl_map_complement(
3970 __isl_take isl_map *map);
3974 #include <isl/space.h>
3975 __isl_give isl_space *isl_space_reverse(
3976 __isl_take isl_space *space);
3978 #include <isl/map.h>
3979 __isl_give isl_basic_map *isl_basic_map_reverse(
3980 __isl_take isl_basic_map *bmap);
3981 __isl_give isl_map *isl_map_reverse(
3982 __isl_take isl_map *map);
3984 #include <isl/union_map.h>
3985 __isl_give isl_union_map *isl_union_map_reverse(
3986 __isl_take isl_union_map *umap);
3990 #include <isl/space.h>
3991 __isl_give isl_space *isl_space_domain(
3992 __isl_take isl_space *space);
3993 __isl_give isl_space *isl_space_range(
3994 __isl_take isl_space *space);
3995 __isl_give isl_space *isl_space_params(
3996 __isl_take isl_space *space);
3998 #include <isl/local_space.h>
3999 __isl_give isl_local_space *isl_local_space_domain(
4000 __isl_take isl_local_space *ls);
4001 __isl_give isl_local_space *isl_local_space_range(
4002 __isl_take isl_local_space *ls);
4004 #include <isl/set.h>
4005 __isl_give isl_basic_set *isl_basic_set_project_out(
4006 __isl_take isl_basic_set *bset,
4007 enum isl_dim_type type, unsigned first, unsigned n);
4008 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4009 enum isl_dim_type type, unsigned first, unsigned n);
4010 __isl_give isl_basic_set *isl_basic_set_params(
4011 __isl_take isl_basic_set *bset);
4012 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4014 #include <isl/map.h>
4015 __isl_give isl_basic_map *isl_basic_map_project_out(
4016 __isl_take isl_basic_map *bmap,
4017 enum isl_dim_type type, unsigned first, unsigned n);
4018 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4019 enum isl_dim_type type, unsigned first, unsigned n);
4020 __isl_give isl_basic_set *isl_basic_map_domain(
4021 __isl_take isl_basic_map *bmap);
4022 __isl_give isl_basic_set *isl_basic_map_range(
4023 __isl_take isl_basic_map *bmap);
4024 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4025 __isl_give isl_set *isl_map_domain(
4026 __isl_take isl_map *bmap);
4027 __isl_give isl_set *isl_map_range(
4028 __isl_take isl_map *map);
4030 #include <isl/union_set.h>
4031 __isl_give isl_union_set *isl_union_set_project_out(
4032 __isl_take isl_union_set *uset,
4033 enum isl_dim_type type,
4034 unsigned first, unsigned n);
4035 __isl_give isl_set *isl_union_set_params(
4036 __isl_take isl_union_set *uset);
4038 The function C<isl_union_set_project_out> can only project out
4041 #include <isl/union_map.h>
4042 __isl_give isl_union_map *isl_union_map_project_out(
4043 __isl_take isl_union_map *umap,
4044 enum isl_dim_type type, unsigned first, unsigned n);
4045 __isl_give isl_set *isl_union_map_params(
4046 __isl_take isl_union_map *umap);
4047 __isl_give isl_union_set *isl_union_map_domain(
4048 __isl_take isl_union_map *umap);
4049 __isl_give isl_union_set *isl_union_map_range(
4050 __isl_take isl_union_map *umap);
4052 The function C<isl_union_map_project_out> can only project out
4055 #include <isl/aff.h>
4056 __isl_give isl_aff *isl_aff_project_domain_on_params(
4057 __isl_take isl_aff *aff);
4058 __isl_give isl_pw_multi_aff *
4059 isl_pw_multi_aff_project_domain_on_params(
4060 __isl_take isl_pw_multi_aff *pma);
4061 __isl_give isl_set *isl_pw_aff_domain(
4062 __isl_take isl_pw_aff *pwaff);
4063 __isl_give isl_set *isl_pw_multi_aff_domain(
4064 __isl_take isl_pw_multi_aff *pma);
4065 __isl_give isl_set *isl_multi_pw_aff_domain(
4066 __isl_take isl_multi_pw_aff *mpa);
4067 __isl_give isl_union_set *isl_union_pw_aff_domain(
4068 __isl_take isl_union_pw_aff *upa);
4069 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4070 __isl_take isl_union_pw_multi_aff *upma);
4071 __isl_give isl_union_set *
4072 isl_multi_union_pw_aff_domain(
4073 __isl_take isl_multi_union_pw_aff *mupa);
4074 __isl_give isl_set *isl_pw_aff_params(
4075 __isl_take isl_pw_aff *pwa);
4077 The function C<isl_multi_union_pw_aff_domain> requires its
4078 input to have at least one set dimension.
4080 #include <isl/polynomial.h>
4081 __isl_give isl_qpolynomial *
4082 isl_qpolynomial_project_domain_on_params(
4083 __isl_take isl_qpolynomial *qp);
4084 __isl_give isl_pw_qpolynomial *
4085 isl_pw_qpolynomial_project_domain_on_params(
4086 __isl_take isl_pw_qpolynomial *pwqp);
4087 __isl_give isl_pw_qpolynomial_fold *
4088 isl_pw_qpolynomial_fold_project_domain_on_params(
4089 __isl_take isl_pw_qpolynomial_fold *pwf);
4090 __isl_give isl_set *isl_pw_qpolynomial_domain(
4091 __isl_take isl_pw_qpolynomial *pwqp);
4092 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4093 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4094 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4095 __isl_take isl_union_pw_qpolynomial *upwqp);
4097 #include <isl/space.h>
4098 __isl_give isl_space *isl_space_domain_map(
4099 __isl_take isl_space *space);
4100 __isl_give isl_space *isl_space_range_map(
4101 __isl_take isl_space *space);
4103 #include <isl/map.h>
4104 __isl_give isl_map *isl_set_wrapped_domain_map(
4105 __isl_take isl_set *set);
4106 __isl_give isl_basic_map *isl_basic_map_domain_map(
4107 __isl_take isl_basic_map *bmap);
4108 __isl_give isl_basic_map *isl_basic_map_range_map(
4109 __isl_take isl_basic_map *bmap);
4110 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4111 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4113 #include <isl/union_map.h>
4114 __isl_give isl_union_map *isl_union_map_domain_map(
4115 __isl_take isl_union_map *umap);
4116 __isl_give isl_union_pw_multi_aff *
4117 isl_union_map_domain_map_union_pw_multi_aff(
4118 __isl_take isl_union_map *umap);
4119 __isl_give isl_union_map *isl_union_map_range_map(
4120 __isl_take isl_union_map *umap);
4121 __isl_give isl_union_map *
4122 isl_union_set_wrapped_domain_map(
4123 __isl_take isl_union_set *uset);
4125 The functions above construct a (basic, regular or union) relation
4126 that maps (a wrapped version of) the input relation to its domain or range.
4127 C<isl_set_wrapped_domain_map> maps the input set to the domain
4128 of its wrapped relation.
4132 __isl_give isl_basic_set *isl_basic_set_eliminate(
4133 __isl_take isl_basic_set *bset,
4134 enum isl_dim_type type,
4135 unsigned first, unsigned n);
4136 __isl_give isl_set *isl_set_eliminate(
4137 __isl_take isl_set *set, enum isl_dim_type type,
4138 unsigned first, unsigned n);
4139 __isl_give isl_basic_map *isl_basic_map_eliminate(
4140 __isl_take isl_basic_map *bmap,
4141 enum isl_dim_type type,
4142 unsigned first, unsigned n);
4143 __isl_give isl_map *isl_map_eliminate(
4144 __isl_take isl_map *map, enum isl_dim_type type,
4145 unsigned first, unsigned n);
4147 Eliminate the coefficients for the given dimensions from the constraints,
4148 without removing the dimensions.
4150 =item * Constructing a set from a parameter domain
4152 A zero-dimensional space or (basic) set can be constructed
4153 on a given parameter domain using the following functions.
4155 #include <isl/space.h>
4156 __isl_give isl_space *isl_space_set_from_params(
4157 __isl_take isl_space *space);
4159 #include <isl/set.h>
4160 __isl_give isl_basic_set *isl_basic_set_from_params(
4161 __isl_take isl_basic_set *bset);
4162 __isl_give isl_set *isl_set_from_params(
4163 __isl_take isl_set *set);
4165 =item * Constructing a relation from a set
4167 Create a relation with the given set as domain or range.
4168 The range or domain of the created relation is a zero-dimensional
4169 flat anonymous space.
4171 #include <isl/space.h>
4172 __isl_give isl_space *isl_space_from_domain(
4173 __isl_take isl_space *space);
4174 __isl_give isl_space *isl_space_from_range(
4175 __isl_take isl_space *space);
4176 __isl_give isl_space *isl_space_map_from_set(
4177 __isl_take isl_space *space);
4178 __isl_give isl_space *isl_space_map_from_domain_and_range(
4179 __isl_take isl_space *domain,
4180 __isl_take isl_space *range);
4182 #include <isl/local_space.h>
4183 __isl_give isl_local_space *isl_local_space_from_domain(
4184 __isl_take isl_local_space *ls);
4186 #include <isl/map.h>
4187 __isl_give isl_map *isl_map_from_domain(
4188 __isl_take isl_set *set);
4189 __isl_give isl_map *isl_map_from_range(
4190 __isl_take isl_set *set);
4192 #include <isl/val.h>
4193 __isl_give isl_multi_val *isl_multi_val_from_range(
4194 __isl_take isl_multi_val *mv);
4196 #include <isl/aff.h>
4197 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4198 __isl_take isl_multi_aff *ma);
4199 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4200 __isl_take isl_pw_aff *pwa);
4201 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4202 __isl_take isl_multi_pw_aff *mpa);
4203 __isl_give isl_multi_union_pw_aff *
4204 isl_multi_union_pw_aff_from_range(
4205 __isl_take isl_multi_union_pw_aff *mupa);
4206 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4207 __isl_take isl_set *set);
4208 __isl_give isl_union_pw_multi_aff *
4209 isl_union_pw_multi_aff_from_domain(
4210 __isl_take isl_union_set *uset);
4214 #include <isl/set.h>
4215 __isl_give isl_basic_set *isl_basic_set_fix_si(
4216 __isl_take isl_basic_set *bset,
4217 enum isl_dim_type type, unsigned pos, int value);
4218 __isl_give isl_basic_set *isl_basic_set_fix_val(
4219 __isl_take isl_basic_set *bset,
4220 enum isl_dim_type type, unsigned pos,
4221 __isl_take isl_val *v);
4222 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4223 enum isl_dim_type type, unsigned pos, int value);
4224 __isl_give isl_set *isl_set_fix_val(
4225 __isl_take isl_set *set,
4226 enum isl_dim_type type, unsigned pos,
4227 __isl_take isl_val *v);
4229 #include <isl/map.h>
4230 __isl_give isl_basic_map *isl_basic_map_fix_si(
4231 __isl_take isl_basic_map *bmap,
4232 enum isl_dim_type type, unsigned pos, int value);
4233 __isl_give isl_basic_map *isl_basic_map_fix_val(
4234 __isl_take isl_basic_map *bmap,
4235 enum isl_dim_type type, unsigned pos,
4236 __isl_take isl_val *v);
4237 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4238 enum isl_dim_type type, unsigned pos, int value);
4239 __isl_give isl_map *isl_map_fix_val(
4240 __isl_take isl_map *map,
4241 enum isl_dim_type type, unsigned pos,
4242 __isl_take isl_val *v);
4244 #include <isl/aff.h>
4245 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4246 __isl_take isl_pw_multi_aff *pma,
4247 enum isl_dim_type type, unsigned pos, int value);
4249 #include <isl/polynomial.h>
4250 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4251 __isl_take isl_pw_qpolynomial *pwqp,
4252 enum isl_dim_type type, unsigned n,
4253 __isl_take isl_val *v);
4255 Intersect the set, relation or function domain
4256 with the hyperplane where the given
4257 dimension has the fixed given value.
4259 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4260 __isl_take isl_basic_map *bmap,
4261 enum isl_dim_type type, unsigned pos, int value);
4262 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4263 __isl_take isl_basic_map *bmap,
4264 enum isl_dim_type type, unsigned pos, int value);
4265 __isl_give isl_set *isl_set_lower_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_lower_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_lower_bound_si(
4273 __isl_take isl_map *map,
4274 enum isl_dim_type type, unsigned pos, int value);
4275 __isl_give isl_set *isl_set_upper_bound_si(
4276 __isl_take isl_set *set,
4277 enum isl_dim_type type, unsigned pos, int value);
4278 __isl_give isl_set *isl_set_upper_bound_val(
4279 __isl_take isl_set *set,
4280 enum isl_dim_type type, unsigned pos,
4281 __isl_take isl_val *value);
4282 __isl_give isl_map *isl_map_upper_bound_si(
4283 __isl_take isl_map *map,
4284 enum isl_dim_type type, unsigned pos, int value);
4286 Intersect the set or relation with the half-space where the given
4287 dimension has a value bounded by the fixed given integer value.
4289 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4290 enum isl_dim_type type1, int pos1,
4291 enum isl_dim_type type2, int pos2);
4292 __isl_give isl_basic_map *isl_basic_map_equate(
4293 __isl_take isl_basic_map *bmap,
4294 enum isl_dim_type type1, int pos1,
4295 enum isl_dim_type type2, int pos2);
4296 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4297 enum isl_dim_type type1, int pos1,
4298 enum isl_dim_type type2, int pos2);
4300 Intersect the set or relation with the hyperplane where the given
4301 dimensions are equal to each other.
4303 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4304 enum isl_dim_type type1, int pos1,
4305 enum isl_dim_type type2, int pos2);
4307 Intersect the relation with the hyperplane where the given
4308 dimensions have opposite values.
4310 __isl_give isl_map *isl_map_order_le(
4311 __isl_take isl_map *map,
4312 enum isl_dim_type type1, int pos1,
4313 enum isl_dim_type type2, int pos2);
4314 __isl_give isl_basic_map *isl_basic_map_order_ge(
4315 __isl_take isl_basic_map *bmap,
4316 enum isl_dim_type type1, int pos1,
4317 enum isl_dim_type type2, int pos2);
4318 __isl_give isl_map *isl_map_order_ge(
4319 __isl_take isl_map *map,
4320 enum isl_dim_type type1, int pos1,
4321 enum isl_dim_type type2, int pos2);
4322 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4323 enum isl_dim_type type1, int pos1,
4324 enum isl_dim_type type2, int pos2);
4325 __isl_give isl_basic_map *isl_basic_map_order_gt(
4326 __isl_take isl_basic_map *bmap,
4327 enum isl_dim_type type1, int pos1,
4328 enum isl_dim_type type2, int pos2);
4329 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4330 enum isl_dim_type type1, int pos1,
4331 enum isl_dim_type type2, int pos2);
4333 Intersect the relation with the half-space where the given
4334 dimensions satisfy the given ordering.
4338 #include <isl/aff.h>
4339 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4340 __isl_take isl_aff *aff);
4341 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4342 __isl_take isl_aff *aff);
4343 __isl_give isl_set *isl_pw_aff_pos_set(
4344 __isl_take isl_pw_aff *pa);
4345 __isl_give isl_set *isl_pw_aff_nonneg_set(
4346 __isl_take isl_pw_aff *pwaff);
4347 __isl_give isl_set *isl_pw_aff_zero_set(
4348 __isl_take isl_pw_aff *pwaff);
4349 __isl_give isl_set *isl_pw_aff_non_zero_set(
4350 __isl_take isl_pw_aff *pwaff);
4351 __isl_give isl_union_set *
4352 isl_union_pw_aff_zero_union_set(
4353 __isl_take isl_union_pw_aff *upa);
4354 __isl_give isl_union_set *
4355 isl_multi_union_pw_aff_zero_union_set(
4356 __isl_take isl_multi_union_pw_aff *mupa);
4358 The function C<isl_aff_neg_basic_set> returns a basic set
4359 containing those elements in the domain space
4360 of C<aff> where C<aff> is negative.
4361 The function C<isl_pw_aff_nonneg_set> returns a set
4362 containing those elements in the domain
4363 of C<pwaff> where C<pwaff> is non-negative.
4364 The function C<isl_multi_union_pw_aff_zero_union_set>
4365 returns a union set containing those elements
4366 in the domains of its elements where they are all zero.
4370 __isl_give isl_map *isl_set_identity(
4371 __isl_take isl_set *set);
4372 __isl_give isl_union_map *isl_union_set_identity(
4373 __isl_take isl_union_set *uset);
4374 __isl_give isl_union_pw_multi_aff *
4375 isl_union_set_identity_union_pw_multi_aff(
4376 __isl_take isl_union_set *uset);
4378 Construct an identity relation on the given (union) set.
4380 =item * Function Extraction
4382 A piecewise quasi affine expression that is equal to 1 on a set
4383 and 0 outside the set can be created using the following function.
4385 #include <isl/aff.h>
4386 __isl_give isl_pw_aff *isl_set_indicator_function(
4387 __isl_take isl_set *set);
4389 A piecewise multiple quasi affine expression can be extracted
4390 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4391 and the C<isl_map> is single-valued.
4392 In case of a conversion from an C<isl_union_map>
4393 to an C<isl_union_pw_multi_aff>, these properties need to hold
4394 in each domain space.
4395 A conversion to a C<isl_multi_union_pw_aff> additionally
4396 requires that the input is non-empty and involves only a single
4399 #include <isl/aff.h>
4400 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4401 __isl_take isl_set *set);
4402 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4403 __isl_take isl_map *map);
4405 __isl_give isl_union_pw_multi_aff *
4406 isl_union_pw_multi_aff_from_union_set(
4407 __isl_take isl_union_set *uset);
4408 __isl_give isl_union_pw_multi_aff *
4409 isl_union_pw_multi_aff_from_union_map(
4410 __isl_take isl_union_map *umap);
4412 __isl_give isl_multi_union_pw_aff *
4413 isl_multi_union_pw_aff_from_union_map(
4414 __isl_take isl_union_map *umap);
4418 __isl_give isl_basic_set *isl_basic_map_deltas(
4419 __isl_take isl_basic_map *bmap);
4420 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4421 __isl_give isl_union_set *isl_union_map_deltas(
4422 __isl_take isl_union_map *umap);
4424 These functions return a (basic) set containing the differences
4425 between image elements and corresponding domain elements in the input.
4427 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4428 __isl_take isl_basic_map *bmap);
4429 __isl_give isl_map *isl_map_deltas_map(
4430 __isl_take isl_map *map);
4431 __isl_give isl_union_map *isl_union_map_deltas_map(
4432 __isl_take isl_union_map *umap);
4434 The functions above construct a (basic, regular or union) relation
4435 that maps (a wrapped version of) the input relation to its delta set.
4439 Simplify the representation of a set, relation or functions by trying
4440 to combine pairs of basic sets or relations into a single
4441 basic set or relation.
4443 #include <isl/set.h>
4444 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4446 #include <isl/map.h>
4447 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4449 #include <isl/union_set.h>
4450 __isl_give isl_union_set *isl_union_set_coalesce(
4451 __isl_take isl_union_set *uset);
4453 #include <isl/union_map.h>
4454 __isl_give isl_union_map *isl_union_map_coalesce(
4455 __isl_take isl_union_map *umap);
4457 #include <isl/aff.h>
4458 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4459 __isl_take isl_pw_aff *pwqp);
4460 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4461 __isl_take isl_pw_multi_aff *pma);
4462 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4463 __isl_take isl_multi_pw_aff *mpa);
4464 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4465 __isl_take isl_union_pw_aff *upa);
4466 __isl_give isl_union_pw_multi_aff *
4467 isl_union_pw_multi_aff_coalesce(
4468 __isl_take isl_union_pw_multi_aff *upma);
4470 #include <isl/polynomial.h>
4471 __isl_give isl_pw_qpolynomial_fold *
4472 isl_pw_qpolynomial_fold_coalesce(
4473 __isl_take isl_pw_qpolynomial_fold *pwf);
4474 __isl_give isl_union_pw_qpolynomial *
4475 isl_union_pw_qpolynomial_coalesce(
4476 __isl_take isl_union_pw_qpolynomial *upwqp);
4477 __isl_give isl_union_pw_qpolynomial_fold *
4478 isl_union_pw_qpolynomial_fold_coalesce(
4479 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4481 One of the methods for combining pairs of basic sets or relations
4482 can result in coefficients that are much larger than those that appear
4483 in the constraints of the input. By default, the coefficients are
4484 not allowed to grow larger, but this can be changed by unsetting
4485 the following option.
4487 int isl_options_set_coalesce_bounded_wrapping(
4488 isl_ctx *ctx, int val);
4489 int isl_options_get_coalesce_bounded_wrapping(
4492 =item * Detecting equalities
4494 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4495 __isl_take isl_basic_set *bset);
4496 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4497 __isl_take isl_basic_map *bmap);
4498 __isl_give isl_set *isl_set_detect_equalities(
4499 __isl_take isl_set *set);
4500 __isl_give isl_map *isl_map_detect_equalities(
4501 __isl_take isl_map *map);
4502 __isl_give isl_union_set *isl_union_set_detect_equalities(
4503 __isl_take isl_union_set *uset);
4504 __isl_give isl_union_map *isl_union_map_detect_equalities(
4505 __isl_take isl_union_map *umap);
4507 Simplify the representation of a set or relation by detecting implicit
4510 =item * Removing redundant constraints
4512 #include <isl/set.h>
4513 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4514 __isl_take isl_basic_set *bset);
4515 __isl_give isl_set *isl_set_remove_redundancies(
4516 __isl_take isl_set *set);
4518 #include <isl/union_set.h>
4519 __isl_give isl_union_set *
4520 isl_union_set_remove_redundancies(
4521 __isl_take isl_union_set *uset);
4523 #include <isl/map.h>
4524 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4525 __isl_take isl_basic_map *bmap);
4526 __isl_give isl_map *isl_map_remove_redundancies(
4527 __isl_take isl_map *map);
4529 #include <isl/union_map.h>
4530 __isl_give isl_union_map *
4531 isl_union_map_remove_redundancies(
4532 __isl_take isl_union_map *umap);
4536 __isl_give isl_basic_set *isl_set_convex_hull(
4537 __isl_take isl_set *set);
4538 __isl_give isl_basic_map *isl_map_convex_hull(
4539 __isl_take isl_map *map);
4541 If the input set or relation has any existentially quantified
4542 variables, then the result of these operations is currently undefined.
4546 #include <isl/set.h>
4547 __isl_give isl_basic_set *
4548 isl_set_unshifted_simple_hull(
4549 __isl_take isl_set *set);
4550 __isl_give isl_basic_set *isl_set_simple_hull(
4551 __isl_take isl_set *set);
4552 __isl_give isl_basic_set *
4553 isl_set_unshifted_simple_hull_from_set_list(
4554 __isl_take isl_set *set,
4555 __isl_take isl_set_list *list);
4557 #include <isl/map.h>
4558 __isl_give isl_basic_map *
4559 isl_map_unshifted_simple_hull(
4560 __isl_take isl_map *map);
4561 __isl_give isl_basic_map *isl_map_simple_hull(
4562 __isl_take isl_map *map);
4563 __isl_give isl_basic_map *
4564 isl_map_unshifted_simple_hull_from_map_list(
4565 __isl_take isl_map *map,
4566 __isl_take isl_map_list *list);
4568 #include <isl/union_map.h>
4569 __isl_give isl_union_map *isl_union_map_simple_hull(
4570 __isl_take isl_union_map *umap);
4572 These functions compute a single basic set or relation
4573 that contains the whole input set or relation.
4574 In particular, the output is described by translates
4575 of the constraints describing the basic sets or relations in the input.
4576 In case of C<isl_set_unshifted_simple_hull>, only the original
4577 constraints are used, without any translation.
4578 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4579 C<isl_map_unshifted_simple_hull_from_map_list>, the
4580 constraints are taken from the elements of the second argument.
4584 (See \autoref{s:simple hull}.)
4590 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4591 __isl_take isl_basic_set *bset);
4592 __isl_give isl_basic_set *isl_set_affine_hull(
4593 __isl_take isl_set *set);
4594 __isl_give isl_union_set *isl_union_set_affine_hull(
4595 __isl_take isl_union_set *uset);
4596 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4597 __isl_take isl_basic_map *bmap);
4598 __isl_give isl_basic_map *isl_map_affine_hull(
4599 __isl_take isl_map *map);
4600 __isl_give isl_union_map *isl_union_map_affine_hull(
4601 __isl_take isl_union_map *umap);
4603 In case of union sets and relations, the affine hull is computed
4606 =item * Polyhedral hull
4608 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4609 __isl_take isl_set *set);
4610 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4611 __isl_take isl_map *map);
4612 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4613 __isl_take isl_union_set *uset);
4614 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4615 __isl_take isl_union_map *umap);
4617 These functions compute a single basic set or relation
4618 not involving any existentially quantified variables
4619 that contains the whole input set or relation.
4620 In case of union sets and relations, the polyhedral hull is computed
4623 =item * Other approximations
4625 #include <isl/set.h>
4626 __isl_give isl_basic_set *
4627 isl_basic_set_drop_constraints_involving_dims(
4628 __isl_take isl_basic_set *bset,
4629 enum isl_dim_type type,
4630 unsigned first, unsigned n);
4631 __isl_give isl_basic_set *
4632 isl_basic_set_drop_constraints_not_involving_dims(
4633 __isl_take isl_basic_set *bset,
4634 enum isl_dim_type type,
4635 unsigned first, unsigned n);
4636 __isl_give isl_set *
4637 isl_set_drop_constraints_involving_dims(
4638 __isl_take isl_set *set,
4639 enum isl_dim_type type,
4640 unsigned first, unsigned n);
4642 #include <isl/map.h>
4643 __isl_give isl_basic_map *
4644 isl_basic_map_drop_constraints_involving_dims(
4645 __isl_take isl_basic_map *bmap,
4646 enum isl_dim_type type,
4647 unsigned first, unsigned n);
4648 __isl_give isl_map *
4649 isl_map_drop_constraints_involving_dims(
4650 __isl_take isl_map *map,
4651 enum isl_dim_type type,
4652 unsigned first, unsigned n);
4654 These functions drop any constraints (not) involving the specified dimensions.
4655 Note that the result depends on the representation of the input.
4657 #include <isl/polynomial.h>
4658 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4659 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4660 __isl_give isl_union_pw_qpolynomial *
4661 isl_union_pw_qpolynomial_to_polynomial(
4662 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4664 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4665 the polynomial will be an overapproximation. If C<sign> is negative,
4666 it will be an underapproximation. If C<sign> is zero, the approximation
4667 will lie somewhere in between.
4671 __isl_give isl_basic_set *isl_basic_set_sample(
4672 __isl_take isl_basic_set *bset);
4673 __isl_give isl_basic_set *isl_set_sample(
4674 __isl_take isl_set *set);
4675 __isl_give isl_basic_map *isl_basic_map_sample(
4676 __isl_take isl_basic_map *bmap);
4677 __isl_give isl_basic_map *isl_map_sample(
4678 __isl_take isl_map *map);
4680 If the input (basic) set or relation is non-empty, then return
4681 a singleton subset of the input. Otherwise, return an empty set.
4683 =item * Optimization
4685 #include <isl/ilp.h>
4686 __isl_give isl_val *isl_basic_set_max_val(
4687 __isl_keep isl_basic_set *bset,
4688 __isl_keep isl_aff *obj);
4689 __isl_give isl_val *isl_set_min_val(
4690 __isl_keep isl_set *set,
4691 __isl_keep isl_aff *obj);
4692 __isl_give isl_val *isl_set_max_val(
4693 __isl_keep isl_set *set,
4694 __isl_keep isl_aff *obj);
4696 Compute the minimum or maximum of the integer affine expression C<obj>
4697 over the points in C<set>, returning the result in C<opt>.
4698 The result is C<NULL> in case of an error, the optimal value in case
4699 there is one, negative infinity or infinity if the problem is unbounded and
4700 NaN if the problem is empty.
4702 =item * Parametric optimization
4704 __isl_give isl_pw_aff *isl_set_dim_min(
4705 __isl_take isl_set *set, int pos);
4706 __isl_give isl_pw_aff *isl_set_dim_max(
4707 __isl_take isl_set *set, int pos);
4708 __isl_give isl_pw_aff *isl_map_dim_max(
4709 __isl_take isl_map *map, int pos);
4711 Compute the minimum or maximum of the given set or output dimension
4712 as a function of the parameters (and input dimensions), but independently
4713 of the other set or output dimensions.
4714 For lexicographic optimization, see L<"Lexicographic Optimization">.
4718 The following functions compute either the set of (rational) coefficient
4719 values of valid constraints for the given set or the set of (rational)
4720 values satisfying the constraints with coefficients from the given set.
4721 Internally, these two sets of functions perform essentially the
4722 same operations, except that the set of coefficients is assumed to
4723 be a cone, while the set of values may be any polyhedron.
4724 The current implementation is based on the Farkas lemma and
4725 Fourier-Motzkin elimination, but this may change or be made optional
4726 in future. In particular, future implementations may use different
4727 dualization algorithms or skip the elimination step.
4729 __isl_give isl_basic_set *isl_basic_set_coefficients(
4730 __isl_take isl_basic_set *bset);
4731 __isl_give isl_basic_set *isl_set_coefficients(
4732 __isl_take isl_set *set);
4733 __isl_give isl_union_set *isl_union_set_coefficients(
4734 __isl_take isl_union_set *bset);
4735 __isl_give isl_basic_set *isl_basic_set_solutions(
4736 __isl_take isl_basic_set *bset);
4737 __isl_give isl_basic_set *isl_set_solutions(
4738 __isl_take isl_set *set);
4739 __isl_give isl_union_set *isl_union_set_solutions(
4740 __isl_take isl_union_set *bset);
4744 __isl_give isl_map *isl_map_fixed_power_val(
4745 __isl_take isl_map *map,
4746 __isl_take isl_val *exp);
4747 __isl_give isl_union_map *
4748 isl_union_map_fixed_power_val(
4749 __isl_take isl_union_map *umap,
4750 __isl_take isl_val *exp);
4752 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4753 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4754 of C<map> is computed.
4756 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4758 __isl_give isl_union_map *isl_union_map_power(
4759 __isl_take isl_union_map *umap, int *exact);
4761 Compute a parametric representation for all positive powers I<k> of C<map>.
4762 The result maps I<k> to a nested relation corresponding to the
4763 I<k>th power of C<map>.
4764 The result may be an overapproximation. If the result is known to be exact,
4765 then C<*exact> is set to C<1>.
4767 =item * Transitive closure
4769 __isl_give isl_map *isl_map_transitive_closure(
4770 __isl_take isl_map *map, int *exact);
4771 __isl_give isl_union_map *isl_union_map_transitive_closure(
4772 __isl_take isl_union_map *umap, int *exact);
4774 Compute the transitive closure of C<map>.
4775 The result may be an overapproximation. If the result is known to be exact,
4776 then C<*exact> is set to C<1>.
4778 =item * Reaching path lengths
4780 __isl_give isl_map *isl_map_reaching_path_lengths(
4781 __isl_take isl_map *map, int *exact);
4783 Compute a relation that maps each element in the range of C<map>
4784 to the lengths of all paths composed of edges in C<map> that
4785 end up in the given element.
4786 The result may be an overapproximation. If the result is known to be exact,
4787 then C<*exact> is set to C<1>.
4788 To compute the I<maximal> path length, the resulting relation
4789 should be postprocessed by C<isl_map_lexmax>.
4790 In particular, if the input relation is a dependence relation
4791 (mapping sources to sinks), then the maximal path length corresponds
4792 to the free schedule.
4793 Note, however, that C<isl_map_lexmax> expects the maximum to be
4794 finite, so if the path lengths are unbounded (possibly due to
4795 the overapproximation), then you will get an error message.
4799 #include <isl/space.h>
4800 __isl_give isl_space *isl_space_wrap(
4801 __isl_take isl_space *space);
4802 __isl_give isl_space *isl_space_unwrap(
4803 __isl_take isl_space *space);
4805 #include <isl/local_space.h>
4806 __isl_give isl_local_space *isl_local_space_wrap(
4807 __isl_take isl_local_space *ls);
4809 #include <isl/set.h>
4810 __isl_give isl_basic_map *isl_basic_set_unwrap(
4811 __isl_take isl_basic_set *bset);
4812 __isl_give isl_map *isl_set_unwrap(
4813 __isl_take isl_set *set);
4815 #include <isl/map.h>
4816 __isl_give isl_basic_set *isl_basic_map_wrap(
4817 __isl_take isl_basic_map *bmap);
4818 __isl_give isl_set *isl_map_wrap(
4819 __isl_take isl_map *map);
4821 #include <isl/union_set.h>
4822 __isl_give isl_union_map *isl_union_set_unwrap(
4823 __isl_take isl_union_set *uset);
4825 #include <isl/union_map.h>
4826 __isl_give isl_union_set *isl_union_map_wrap(
4827 __isl_take isl_union_map *umap);
4829 The input to C<isl_space_unwrap> should
4830 be the space of a set, while that of
4831 C<isl_space_wrap> should be the space of a relation.
4832 Conversely, the output of C<isl_space_unwrap> is the space
4833 of a relation, while that of C<isl_space_wrap> is the space of a set.
4837 Remove any internal structure of domain (and range) of the given
4838 set or relation. If there is any such internal structure in the input,
4839 then the name of the space is also removed.
4841 #include <isl/local_space.h>
4842 __isl_give isl_local_space *
4843 isl_local_space_flatten_domain(
4844 __isl_take isl_local_space *ls);
4845 __isl_give isl_local_space *
4846 isl_local_space_flatten_range(
4847 __isl_take isl_local_space *ls);
4849 #include <isl/set.h>
4850 __isl_give isl_basic_set *isl_basic_set_flatten(
4851 __isl_take isl_basic_set *bset);
4852 __isl_give isl_set *isl_set_flatten(
4853 __isl_take isl_set *set);
4855 #include <isl/map.h>
4856 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4857 __isl_take isl_basic_map *bmap);
4858 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4859 __isl_take isl_basic_map *bmap);
4860 __isl_give isl_map *isl_map_flatten_range(
4861 __isl_take isl_map *map);
4862 __isl_give isl_map *isl_map_flatten_domain(
4863 __isl_take isl_map *map);
4864 __isl_give isl_basic_map *isl_basic_map_flatten(
4865 __isl_take isl_basic_map *bmap);
4866 __isl_give isl_map *isl_map_flatten(
4867 __isl_take isl_map *map);
4869 #include <isl/val.h>
4870 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4871 __isl_take isl_multi_val *mv);
4873 #include <isl/aff.h>
4874 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4875 __isl_take isl_multi_aff *ma);
4876 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4877 __isl_take isl_multi_aff *ma);
4878 __isl_give isl_multi_pw_aff *
4879 isl_multi_pw_aff_flatten_range(
4880 __isl_take isl_multi_pw_aff *mpa);
4881 __isl_give isl_multi_union_pw_aff *
4882 isl_multi_union_pw_aff_flatten_range(
4883 __isl_take isl_multi_union_pw_aff *mupa);
4885 #include <isl/map.h>
4886 __isl_give isl_map *isl_set_flatten_map(
4887 __isl_take isl_set *set);
4889 The function above constructs a relation
4890 that maps the input set to a flattened version of the set.
4894 Lift the input set to a space with extra dimensions corresponding
4895 to the existentially quantified variables in the input.
4896 In particular, the result lives in a wrapped map where the domain
4897 is the original space and the range corresponds to the original
4898 existentially quantified variables.
4900 #include <isl/set.h>
4901 __isl_give isl_basic_set *isl_basic_set_lift(
4902 __isl_take isl_basic_set *bset);
4903 __isl_give isl_set *isl_set_lift(
4904 __isl_take isl_set *set);
4905 __isl_give isl_union_set *isl_union_set_lift(
4906 __isl_take isl_union_set *uset);
4908 Given a local space that contains the existentially quantified
4909 variables of a set, a basic relation that, when applied to
4910 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4911 can be constructed using the following function.
4913 #include <isl/local_space.h>
4914 __isl_give isl_basic_map *isl_local_space_lifting(
4915 __isl_take isl_local_space *ls);
4917 #include <isl/aff.h>
4918 __isl_give isl_multi_aff *isl_multi_aff_lift(
4919 __isl_take isl_multi_aff *maff,
4920 __isl_give isl_local_space **ls);
4922 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4923 then it is assigned the local space that lies at the basis of
4924 the lifting applied.
4926 =item * Internal Product
4928 #include <isl/space.h>
4929 __isl_give isl_space *isl_space_zip(
4930 __isl_take isl_space *space);
4932 #include <isl/map.h>
4933 __isl_give isl_basic_map *isl_basic_map_zip(
4934 __isl_take isl_basic_map *bmap);
4935 __isl_give isl_map *isl_map_zip(
4936 __isl_take isl_map *map);
4938 #include <isl/union_map.h>
4939 __isl_give isl_union_map *isl_union_map_zip(
4940 __isl_take isl_union_map *umap);
4942 Given a relation with nested relations for domain and range,
4943 interchange the range of the domain with the domain of the range.
4947 #include <isl/space.h>
4948 __isl_give isl_space *isl_space_curry(
4949 __isl_take isl_space *space);
4950 __isl_give isl_space *isl_space_uncurry(
4951 __isl_take isl_space *space);
4953 #include <isl/map.h>
4954 __isl_give isl_basic_map *isl_basic_map_curry(
4955 __isl_take isl_basic_map *bmap);
4956 __isl_give isl_basic_map *isl_basic_map_uncurry(
4957 __isl_take isl_basic_map *bmap);
4958 __isl_give isl_map *isl_map_curry(
4959 __isl_take isl_map *map);
4960 __isl_give isl_map *isl_map_uncurry(
4961 __isl_take isl_map *map);
4963 #include <isl/union_map.h>
4964 __isl_give isl_union_map *isl_union_map_curry(
4965 __isl_take isl_union_map *umap);
4966 __isl_give isl_union_map *isl_union_map_uncurry(
4967 __isl_take isl_union_map *umap);
4969 Given a relation with a nested relation for domain,
4970 the C<curry> functions
4971 move the range of the nested relation out of the domain
4972 and use it as the domain of a nested relation in the range,
4973 with the original range as range of this nested relation.
4974 The C<uncurry> functions perform the inverse operation.
4976 =item * Aligning parameters
4978 Change the order of the parameters of the given set, relation
4980 such that the first parameters match those of C<model>.
4981 This may involve the introduction of extra parameters.
4982 All parameters need to be named.
4984 #include <isl/space.h>
4985 __isl_give isl_space *isl_space_align_params(
4986 __isl_take isl_space *space1,
4987 __isl_take isl_space *space2)
4989 #include <isl/set.h>
4990 __isl_give isl_basic_set *isl_basic_set_align_params(
4991 __isl_take isl_basic_set *bset,
4992 __isl_take isl_space *model);
4993 __isl_give isl_set *isl_set_align_params(
4994 __isl_take isl_set *set,
4995 __isl_take isl_space *model);
4997 #include <isl/map.h>
4998 __isl_give isl_basic_map *isl_basic_map_align_params(
4999 __isl_take isl_basic_map *bmap,
5000 __isl_take isl_space *model);
5001 __isl_give isl_map *isl_map_align_params(
5002 __isl_take isl_map *map,
5003 __isl_take isl_space *model);
5005 #include <isl/val.h>
5006 __isl_give isl_multi_val *isl_multi_val_align_params(
5007 __isl_take isl_multi_val *mv,
5008 __isl_take isl_space *model);
5010 #include <isl/aff.h>
5011 __isl_give isl_aff *isl_aff_align_params(
5012 __isl_take isl_aff *aff,
5013 __isl_take isl_space *model);
5014 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5015 __isl_take isl_multi_aff *multi,
5016 __isl_take isl_space *model);
5017 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5018 __isl_take isl_pw_aff *pwaff,
5019 __isl_take isl_space *model);
5020 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5021 __isl_take isl_pw_multi_aff *pma,
5022 __isl_take isl_space *model);
5023 __isl_give isl_union_pw_aff *
5024 isl_union_pw_aff_align_params(
5025 __isl_take isl_union_pw_aff *upa,
5026 __isl_take isl_space *model);
5027 __isl_give isl_union_pw_multi_aff *
5028 isl_union_pw_multi_aff_align_params(
5029 __isl_take isl_union_pw_multi_aff *upma,
5030 __isl_take isl_space *model);
5031 __isl_give isl_multi_union_pw_aff *
5032 isl_multi_union_pw_aff_align_params(
5033 __isl_take isl_multi_union_pw_aff *mupa,
5034 __isl_take isl_space *model);
5036 #include <isl/polynomial.h>
5037 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5038 __isl_take isl_qpolynomial *qp,
5039 __isl_take isl_space *model);
5041 =item * Unary Arithmethic Operations
5043 #include <isl/val.h>
5044 __isl_give isl_multi_val *isl_multi_val_neg(
5045 __isl_take isl_multi_val *mv);
5047 #include <isl/aff.h>
5048 __isl_give isl_aff *isl_aff_neg(
5049 __isl_take isl_aff *aff);
5050 __isl_give isl_multi_aff *isl_multi_aff_neg(
5051 __isl_take isl_multi_aff *ma);
5052 __isl_give isl_pw_aff *isl_pw_aff_neg(
5053 __isl_take isl_pw_aff *pwaff);
5054 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5055 __isl_take isl_pw_multi_aff *pma);
5056 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5057 __isl_take isl_multi_pw_aff *mpa);
5058 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5059 __isl_take isl_union_pw_aff *upa);
5060 __isl_give isl_union_pw_multi_aff *
5061 isl_union_pw_multi_aff_neg(
5062 __isl_take isl_union_pw_multi_aff *upma);
5063 __isl_give isl_multi_union_pw_aff *
5064 isl_multi_union_pw_aff_neg(
5065 __isl_take isl_multi_union_pw_aff *mupa);
5066 __isl_give isl_aff *isl_aff_ceil(
5067 __isl_take isl_aff *aff);
5068 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5069 __isl_take isl_pw_aff *pwaff);
5070 __isl_give isl_aff *isl_aff_floor(
5071 __isl_take isl_aff *aff);
5072 __isl_give isl_multi_aff *isl_multi_aff_floor(
5073 __isl_take isl_multi_aff *ma);
5074 __isl_give isl_pw_aff *isl_pw_aff_floor(
5075 __isl_take isl_pw_aff *pwaff);
5076 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5077 __isl_take isl_union_pw_aff *upa);
5078 __isl_give isl_multi_union_pw_aff *
5079 isl_multi_union_pw_aff_floor(
5080 __isl_take isl_multi_union_pw_aff *mupa);
5082 #include <isl/aff.h>
5083 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5084 __isl_take isl_pw_aff_list *list);
5085 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5086 __isl_take isl_pw_aff_list *list);
5088 #include <isl/polynomial.h>
5089 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5090 __isl_take isl_qpolynomial *qp);
5091 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5092 __isl_take isl_pw_qpolynomial *pwqp);
5093 __isl_give isl_union_pw_qpolynomial *
5094 isl_union_pw_qpolynomial_neg(
5095 __isl_take isl_union_pw_qpolynomial *upwqp);
5096 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5097 __isl_take isl_qpolynomial *qp,
5099 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5100 __isl_take isl_pw_qpolynomial *pwqp,
5105 The following functions evaluate a function in a point.
5107 #include <isl/polynomial.h>
5108 __isl_give isl_val *isl_pw_qpolynomial_eval(
5109 __isl_take isl_pw_qpolynomial *pwqp,
5110 __isl_take isl_point *pnt);
5111 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5112 __isl_take isl_pw_qpolynomial_fold *pwf,
5113 __isl_take isl_point *pnt);
5114 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5115 __isl_take isl_union_pw_qpolynomial *upwqp,
5116 __isl_take isl_point *pnt);
5117 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5118 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5119 __isl_take isl_point *pnt);
5121 =item * Dimension manipulation
5123 It is usually not advisable to directly change the (input or output)
5124 space of a set or a relation as this removes the name and the internal
5125 structure of the space. However, the functions below can be useful
5126 to add new parameters, assuming
5127 C<isl_set_align_params> and C<isl_map_align_params>
5130 #include <isl/space.h>
5131 __isl_give isl_space *isl_space_add_dims(
5132 __isl_take isl_space *space,
5133 enum isl_dim_type type, unsigned n);
5134 __isl_give isl_space *isl_space_insert_dims(
5135 __isl_take isl_space *space,
5136 enum isl_dim_type type, unsigned pos, unsigned n);
5137 __isl_give isl_space *isl_space_drop_dims(
5138 __isl_take isl_space *space,
5139 enum isl_dim_type type, unsigned first, unsigned n);
5140 __isl_give isl_space *isl_space_move_dims(
5141 __isl_take isl_space *space,
5142 enum isl_dim_type dst_type, unsigned dst_pos,
5143 enum isl_dim_type src_type, unsigned src_pos,
5146 #include <isl/local_space.h>
5147 __isl_give isl_local_space *isl_local_space_add_dims(
5148 __isl_take isl_local_space *ls,
5149 enum isl_dim_type type, unsigned n);
5150 __isl_give isl_local_space *isl_local_space_insert_dims(
5151 __isl_take isl_local_space *ls,
5152 enum isl_dim_type type, unsigned first, unsigned n);
5153 __isl_give isl_local_space *isl_local_space_drop_dims(
5154 __isl_take isl_local_space *ls,
5155 enum isl_dim_type type, unsigned first, unsigned n);
5157 #include <isl/set.h>
5158 __isl_give isl_basic_set *isl_basic_set_add_dims(
5159 __isl_take isl_basic_set *bset,
5160 enum isl_dim_type type, unsigned n);
5161 __isl_give isl_set *isl_set_add_dims(
5162 __isl_take isl_set *set,
5163 enum isl_dim_type type, unsigned n);
5164 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5165 __isl_take isl_basic_set *bset,
5166 enum isl_dim_type type, unsigned pos,
5168 __isl_give isl_set *isl_set_insert_dims(
5169 __isl_take isl_set *set,
5170 enum isl_dim_type type, unsigned pos, unsigned n);
5171 __isl_give isl_basic_set *isl_basic_set_move_dims(
5172 __isl_take isl_basic_set *bset,
5173 enum isl_dim_type dst_type, unsigned dst_pos,
5174 enum isl_dim_type src_type, unsigned src_pos,
5176 __isl_give isl_set *isl_set_move_dims(
5177 __isl_take isl_set *set,
5178 enum isl_dim_type dst_type, unsigned dst_pos,
5179 enum isl_dim_type src_type, unsigned src_pos,
5182 #include <isl/map.h>
5183 __isl_give isl_map *isl_map_add_dims(
5184 __isl_take isl_map *map,
5185 enum isl_dim_type type, unsigned n);
5186 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5187 __isl_take isl_basic_map *bmap,
5188 enum isl_dim_type type, unsigned pos,
5190 __isl_give isl_map *isl_map_insert_dims(
5191 __isl_take isl_map *map,
5192 enum isl_dim_type type, unsigned pos, unsigned n);
5193 __isl_give isl_basic_map *isl_basic_map_move_dims(
5194 __isl_take isl_basic_map *bmap,
5195 enum isl_dim_type dst_type, unsigned dst_pos,
5196 enum isl_dim_type src_type, unsigned src_pos,
5198 __isl_give isl_map *isl_map_move_dims(
5199 __isl_take isl_map *map,
5200 enum isl_dim_type dst_type, unsigned dst_pos,
5201 enum isl_dim_type src_type, unsigned src_pos,
5204 #include <isl/val.h>
5205 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5206 __isl_take isl_multi_val *mv,
5207 enum isl_dim_type type, unsigned first, unsigned n);
5208 __isl_give isl_multi_val *isl_multi_val_add_dims(
5209 __isl_take isl_multi_val *mv,
5210 enum isl_dim_type type, unsigned n);
5211 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5212 __isl_take isl_multi_val *mv,
5213 enum isl_dim_type type, unsigned first, unsigned n);
5215 #include <isl/aff.h>
5216 __isl_give isl_aff *isl_aff_insert_dims(
5217 __isl_take isl_aff *aff,
5218 enum isl_dim_type type, unsigned first, unsigned n);
5219 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5220 __isl_take isl_multi_aff *ma,
5221 enum isl_dim_type type, unsigned first, unsigned n);
5222 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5223 __isl_take isl_pw_aff *pwaff,
5224 enum isl_dim_type type, unsigned first, unsigned n);
5225 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5226 __isl_take isl_multi_pw_aff *mpa,
5227 enum isl_dim_type type, unsigned first, unsigned n);
5228 __isl_give isl_aff *isl_aff_add_dims(
5229 __isl_take isl_aff *aff,
5230 enum isl_dim_type type, unsigned n);
5231 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5232 __isl_take isl_multi_aff *ma,
5233 enum isl_dim_type type, unsigned n);
5234 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5235 __isl_take isl_pw_aff *pwaff,
5236 enum isl_dim_type type, unsigned n);
5237 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5238 __isl_take isl_multi_pw_aff *mpa,
5239 enum isl_dim_type type, unsigned n);
5240 __isl_give isl_aff *isl_aff_drop_dims(
5241 __isl_take isl_aff *aff,
5242 enum isl_dim_type type, unsigned first, unsigned n);
5243 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5244 __isl_take isl_multi_aff *maff,
5245 enum isl_dim_type type, unsigned first, unsigned n);
5246 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5247 __isl_take isl_pw_aff *pwaff,
5248 enum isl_dim_type type, unsigned first, unsigned n);
5249 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5250 __isl_take isl_pw_multi_aff *pma,
5251 enum isl_dim_type type, unsigned first, unsigned n);
5252 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5253 __isl_take isl_union_pw_aff *upa,
5254 enum isl_dim_type type, unsigned first, unsigned n);
5255 __isl_give isl_union_pw_multi_aff *
5256 isl_union_pw_multi_aff_drop_dims(
5257 __isl_take isl_union_pw_multi_aff *upma,
5258 enum isl_dim_type type,
5259 unsigned first, unsigned n);
5260 __isl_give isl_multi_union_pw_aff *
5261 isl_multi_union_pw_aff_drop_dims(
5262 __isl_take isl_multi_union_pw_aff *mupa,
5263 enum isl_dim_type type, unsigned first,
5265 __isl_give isl_aff *isl_aff_move_dims(
5266 __isl_take isl_aff *aff,
5267 enum isl_dim_type dst_type, unsigned dst_pos,
5268 enum isl_dim_type src_type, unsigned src_pos,
5270 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5271 __isl_take isl_multi_aff *ma,
5272 enum isl_dim_type dst_type, unsigned dst_pos,
5273 enum isl_dim_type src_type, unsigned src_pos,
5275 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5276 __isl_take isl_pw_aff *pa,
5277 enum isl_dim_type dst_type, unsigned dst_pos,
5278 enum isl_dim_type src_type, unsigned src_pos,
5280 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5281 __isl_take isl_multi_pw_aff *pma,
5282 enum isl_dim_type dst_type, unsigned dst_pos,
5283 enum isl_dim_type src_type, unsigned src_pos,
5286 #include <isl/polynomial.h>
5287 __isl_give isl_union_pw_qpolynomial *
5288 isl_union_pw_qpolynomial_drop_dims(
5289 __isl_take isl_union_pw_qpolynomial *upwqp,
5290 enum isl_dim_type type,
5291 unsigned first, unsigned n);
5292 __isl_give isl_union_pw_qpolynomial_fold *
5293 isl_union_pw_qpolynomial_fold_drop_dims(
5294 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5295 enum isl_dim_type type,
5296 unsigned first, unsigned n);
5298 The operations on union expressions can only manipulate parameters.
5302 =head2 Binary Operations
5304 The two arguments of a binary operation not only need to live
5305 in the same C<isl_ctx>, they currently also need to have
5306 the same (number of) parameters.
5308 =head3 Basic Operations
5312 =item * Intersection
5314 #include <isl/local_space.h>
5315 __isl_give isl_local_space *isl_local_space_intersect(
5316 __isl_take isl_local_space *ls1,
5317 __isl_take isl_local_space *ls2);
5319 #include <isl/set.h>
5320 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5321 __isl_take isl_basic_set *bset1,
5322 __isl_take isl_basic_set *bset2);
5323 __isl_give isl_basic_set *isl_basic_set_intersect(
5324 __isl_take isl_basic_set *bset1,
5325 __isl_take isl_basic_set *bset2);
5326 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5327 __isl_take struct isl_basic_set_list *list);
5328 __isl_give isl_set *isl_set_intersect_params(
5329 __isl_take isl_set *set,
5330 __isl_take isl_set *params);
5331 __isl_give isl_set *isl_set_intersect(
5332 __isl_take isl_set *set1,
5333 __isl_take isl_set *set2);
5335 #include <isl/map.h>
5336 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5337 __isl_take isl_basic_map *bmap,
5338 __isl_take isl_basic_set *bset);
5339 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5340 __isl_take isl_basic_map *bmap,
5341 __isl_take isl_basic_set *bset);
5342 __isl_give isl_basic_map *isl_basic_map_intersect(
5343 __isl_take isl_basic_map *bmap1,
5344 __isl_take isl_basic_map *bmap2);
5345 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5346 __isl_take isl_basic_map_list *list);
5347 __isl_give isl_map *isl_map_intersect_params(
5348 __isl_take isl_map *map,
5349 __isl_take isl_set *params);
5350 __isl_give isl_map *isl_map_intersect_domain(
5351 __isl_take isl_map *map,
5352 __isl_take isl_set *set);
5353 __isl_give isl_map *isl_map_intersect_range(
5354 __isl_take isl_map *map,
5355 __isl_take isl_set *set);
5356 __isl_give isl_map *isl_map_intersect(
5357 __isl_take isl_map *map1,
5358 __isl_take isl_map *map2);
5360 #include <isl/union_set.h>
5361 __isl_give isl_union_set *isl_union_set_intersect_params(
5362 __isl_take isl_union_set *uset,
5363 __isl_take isl_set *set);
5364 __isl_give isl_union_set *isl_union_set_intersect(
5365 __isl_take isl_union_set *uset1,
5366 __isl_take isl_union_set *uset2);
5368 #include <isl/union_map.h>
5369 __isl_give isl_union_map *isl_union_map_intersect_params(
5370 __isl_take isl_union_map *umap,
5371 __isl_take isl_set *set);
5372 __isl_give isl_union_map *isl_union_map_intersect_domain(
5373 __isl_take isl_union_map *umap,
5374 __isl_take isl_union_set *uset);
5375 __isl_give isl_union_map *isl_union_map_intersect_range(
5376 __isl_take isl_union_map *umap,
5377 __isl_take isl_union_set *uset);
5378 __isl_give isl_union_map *isl_union_map_intersect(
5379 __isl_take isl_union_map *umap1,
5380 __isl_take isl_union_map *umap2);
5382 #include <isl/aff.h>
5383 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5384 __isl_take isl_pw_aff *pa,
5385 __isl_take isl_set *set);
5386 __isl_give isl_multi_pw_aff *
5387 isl_multi_pw_aff_intersect_domain(
5388 __isl_take isl_multi_pw_aff *mpa,
5389 __isl_take isl_set *domain);
5390 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5391 __isl_take isl_pw_multi_aff *pma,
5392 __isl_take isl_set *set);
5393 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5394 __isl_take isl_union_pw_aff *upa,
5395 __isl_take isl_union_set *uset);
5396 __isl_give isl_union_pw_multi_aff *
5397 isl_union_pw_multi_aff_intersect_domain(
5398 __isl_take isl_union_pw_multi_aff *upma,
5399 __isl_take isl_union_set *uset);
5400 __isl_give isl_multi_union_pw_aff *
5401 isl_multi_union_pw_aff_intersect_domain(
5402 __isl_take isl_multi_union_pw_aff *mupa,
5403 __isl_take isl_union_set *uset);
5404 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5405 __isl_take isl_pw_aff *pa,
5406 __isl_take isl_set *set);
5407 __isl_give isl_multi_pw_aff *
5408 isl_multi_pw_aff_intersect_params(
5409 __isl_take isl_multi_pw_aff *mpa,
5410 __isl_take isl_set *set);
5411 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5412 __isl_take isl_pw_multi_aff *pma,
5413 __isl_take isl_set *set);
5414 __isl_give isl_union_pw_aff *
5415 isl_union_pw_aff_intersect_params(
5416 __isl_take isl_union_pw_aff *upa,
5417 __isl_give isl_union_pw_multi_aff *
5418 isl_union_pw_multi_aff_intersect_params(
5419 __isl_take isl_union_pw_multi_aff *upma,
5420 __isl_take isl_set *set);
5421 __isl_give isl_multi_union_pw_aff *
5422 isl_multi_union_pw_aff_intersect_params(
5423 __isl_take isl_multi_union_pw_aff *mupa,
5424 __isl_take isl_set *params);
5425 isl_multi_union_pw_aff_intersect_range(
5426 __isl_take isl_multi_union_pw_aff *mupa,
5427 __isl_take isl_set *set);
5429 #include <isl/polynomial.h>
5430 __isl_give isl_pw_qpolynomial *
5431 isl_pw_qpolynomial_intersect_domain(
5432 __isl_take isl_pw_qpolynomial *pwpq,
5433 __isl_take isl_set *set);
5434 __isl_give isl_union_pw_qpolynomial *
5435 isl_union_pw_qpolynomial_intersect_domain(
5436 __isl_take isl_union_pw_qpolynomial *upwpq,
5437 __isl_take isl_union_set *uset);
5438 __isl_give isl_union_pw_qpolynomial_fold *
5439 isl_union_pw_qpolynomial_fold_intersect_domain(
5440 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5441 __isl_take isl_union_set *uset);
5442 __isl_give isl_pw_qpolynomial *
5443 isl_pw_qpolynomial_intersect_params(
5444 __isl_take isl_pw_qpolynomial *pwpq,
5445 __isl_take isl_set *set);
5446 __isl_give isl_pw_qpolynomial_fold *
5447 isl_pw_qpolynomial_fold_intersect_params(
5448 __isl_take isl_pw_qpolynomial_fold *pwf,
5449 __isl_take isl_set *set);
5450 __isl_give isl_union_pw_qpolynomial *
5451 isl_union_pw_qpolynomial_intersect_params(
5452 __isl_take isl_union_pw_qpolynomial *upwpq,
5453 __isl_take isl_set *set);
5454 __isl_give isl_union_pw_qpolynomial_fold *
5455 isl_union_pw_qpolynomial_fold_intersect_params(
5456 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5457 __isl_take isl_set *set);
5459 The second argument to the C<_params> functions needs to be
5460 a parametric (basic) set. For the other functions, a parametric set
5461 for either argument is only allowed if the other argument is
5462 a parametric set as well.
5463 The list passed to C<isl_basic_set_list_intersect> needs to have
5464 at least one element and all elements need to live in the same space.
5465 The function C<isl_multi_union_pw_aff_intersect_range>
5466 restricts the input function to those shared domain elements
5467 that map to the specified range.
5471 #include <isl/set.h>
5472 __isl_give isl_set *isl_basic_set_union(
5473 __isl_take isl_basic_set *bset1,
5474 __isl_take isl_basic_set *bset2);
5475 __isl_give isl_set *isl_set_union(
5476 __isl_take isl_set *set1,
5477 __isl_take isl_set *set2);
5479 #include <isl/map.h>
5480 __isl_give isl_map *isl_basic_map_union(
5481 __isl_take isl_basic_map *bmap1,
5482 __isl_take isl_basic_map *bmap2);
5483 __isl_give isl_map *isl_map_union(
5484 __isl_take isl_map *map1,
5485 __isl_take isl_map *map2);
5487 #include <isl/union_set.h>
5488 __isl_give isl_union_set *isl_union_set_union(
5489 __isl_take isl_union_set *uset1,
5490 __isl_take isl_union_set *uset2);
5491 __isl_give isl_union_set *isl_union_set_list_union(
5492 __isl_take isl_union_set_list *list);
5494 #include <isl/union_map.h>
5495 __isl_give isl_union_map *isl_union_map_union(
5496 __isl_take isl_union_map *umap1,
5497 __isl_take isl_union_map *umap2);
5499 =item * Set difference
5501 #include <isl/set.h>
5502 __isl_give isl_set *isl_set_subtract(
5503 __isl_take isl_set *set1,
5504 __isl_take isl_set *set2);
5506 #include <isl/map.h>
5507 __isl_give isl_map *isl_map_subtract(
5508 __isl_take isl_map *map1,
5509 __isl_take isl_map *map2);
5510 __isl_give isl_map *isl_map_subtract_domain(
5511 __isl_take isl_map *map,
5512 __isl_take isl_set *dom);
5513 __isl_give isl_map *isl_map_subtract_range(
5514 __isl_take isl_map *map,
5515 __isl_take isl_set *dom);
5517 #include <isl/union_set.h>
5518 __isl_give isl_union_set *isl_union_set_subtract(
5519 __isl_take isl_union_set *uset1,
5520 __isl_take isl_union_set *uset2);
5522 #include <isl/union_map.h>
5523 __isl_give isl_union_map *isl_union_map_subtract(
5524 __isl_take isl_union_map *umap1,
5525 __isl_take isl_union_map *umap2);
5526 __isl_give isl_union_map *isl_union_map_subtract_domain(
5527 __isl_take isl_union_map *umap,
5528 __isl_take isl_union_set *dom);
5529 __isl_give isl_union_map *isl_union_map_subtract_range(
5530 __isl_take isl_union_map *umap,
5531 __isl_take isl_union_set *dom);
5533 #include <isl/aff.h>
5534 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5535 __isl_take isl_pw_aff *pa,
5536 __isl_take isl_set *set);
5537 __isl_give isl_pw_multi_aff *
5538 isl_pw_multi_aff_subtract_domain(
5539 __isl_take isl_pw_multi_aff *pma,
5540 __isl_take isl_set *set);
5541 __isl_give isl_union_pw_aff *
5542 isl_union_pw_aff_subtract_domain(
5543 __isl_take isl_union_pw_aff *upa,
5544 __isl_take isl_union_set *uset);
5545 __isl_give isl_union_pw_multi_aff *
5546 isl_union_pw_multi_aff_subtract_domain(
5547 __isl_take isl_union_pw_multi_aff *upma,
5548 __isl_take isl_set *set);
5550 #include <isl/polynomial.h>
5551 __isl_give isl_pw_qpolynomial *
5552 isl_pw_qpolynomial_subtract_domain(
5553 __isl_take isl_pw_qpolynomial *pwpq,
5554 __isl_take isl_set *set);
5555 __isl_give isl_pw_qpolynomial_fold *
5556 isl_pw_qpolynomial_fold_subtract_domain(
5557 __isl_take isl_pw_qpolynomial_fold *pwf,
5558 __isl_take isl_set *set);
5559 __isl_give isl_union_pw_qpolynomial *
5560 isl_union_pw_qpolynomial_subtract_domain(
5561 __isl_take isl_union_pw_qpolynomial *upwpq,
5562 __isl_take isl_union_set *uset);
5563 __isl_give isl_union_pw_qpolynomial_fold *
5564 isl_union_pw_qpolynomial_fold_subtract_domain(
5565 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5566 __isl_take isl_union_set *uset);
5570 #include <isl/space.h>
5571 __isl_give isl_space *isl_space_join(
5572 __isl_take isl_space *left,
5573 __isl_take isl_space *right);
5575 #include <isl/map.h>
5576 __isl_give isl_basic_set *isl_basic_set_apply(
5577 __isl_take isl_basic_set *bset,
5578 __isl_take isl_basic_map *bmap);
5579 __isl_give isl_set *isl_set_apply(
5580 __isl_take isl_set *set,
5581 __isl_take isl_map *map);
5582 __isl_give isl_union_set *isl_union_set_apply(
5583 __isl_take isl_union_set *uset,
5584 __isl_take isl_union_map *umap);
5585 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5586 __isl_take isl_basic_map *bmap1,
5587 __isl_take isl_basic_map *bmap2);
5588 __isl_give isl_basic_map *isl_basic_map_apply_range(
5589 __isl_take isl_basic_map *bmap1,
5590 __isl_take isl_basic_map *bmap2);
5591 __isl_give isl_map *isl_map_apply_domain(
5592 __isl_take isl_map *map1,
5593 __isl_take isl_map *map2);
5594 __isl_give isl_map *isl_map_apply_range(
5595 __isl_take isl_map *map1,
5596 __isl_take isl_map *map2);
5598 #include <isl/union_map.h>
5599 __isl_give isl_union_map *isl_union_map_apply_domain(
5600 __isl_take isl_union_map *umap1,
5601 __isl_take isl_union_map *umap2);
5602 __isl_give isl_union_map *isl_union_map_apply_range(
5603 __isl_take isl_union_map *umap1,
5604 __isl_take isl_union_map *umap2);
5606 #include <isl/aff.h>
5607 __isl_give isl_union_pw_aff *
5608 isl_multi_union_pw_aff_apply_aff(
5609 __isl_take isl_multi_union_pw_aff *mupa,
5610 __isl_take isl_aff *aff);
5611 __isl_give isl_union_pw_aff *
5612 isl_multi_union_pw_aff_apply_pw_aff(
5613 __isl_take isl_multi_union_pw_aff *mupa,
5614 __isl_take isl_pw_aff *pa);
5615 __isl_give isl_multi_union_pw_aff *
5616 isl_multi_union_pw_aff_apply_multi_aff(
5617 __isl_take isl_multi_union_pw_aff *mupa,
5618 __isl_take isl_multi_aff *ma);
5619 __isl_give isl_multi_union_pw_aff *
5620 isl_multi_union_pw_aff_apply_pw_multi_aff(
5621 __isl_take isl_multi_union_pw_aff *mupa,
5622 __isl_take isl_pw_multi_aff *pma);
5624 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5625 over the shared domain of the elements of the input. The dimension is
5626 required to be greater than zero.
5627 The C<isl_multi_union_pw_aff> argument of
5628 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5629 but only if the range of the C<isl_multi_aff> argument
5630 is also zero-dimensional.
5631 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5633 #include <isl/polynomial.h>
5634 __isl_give isl_pw_qpolynomial_fold *
5635 isl_set_apply_pw_qpolynomial_fold(
5636 __isl_take isl_set *set,
5637 __isl_take isl_pw_qpolynomial_fold *pwf,
5639 __isl_give isl_pw_qpolynomial_fold *
5640 isl_map_apply_pw_qpolynomial_fold(
5641 __isl_take isl_map *map,
5642 __isl_take isl_pw_qpolynomial_fold *pwf,
5644 __isl_give isl_union_pw_qpolynomial_fold *
5645 isl_union_set_apply_union_pw_qpolynomial_fold(
5646 __isl_take isl_union_set *uset,
5647 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5649 __isl_give isl_union_pw_qpolynomial_fold *
5650 isl_union_map_apply_union_pw_qpolynomial_fold(
5651 __isl_take isl_union_map *umap,
5652 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5655 The functions taking a map
5656 compose the given map with the given piecewise quasipolynomial reduction.
5657 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5658 over all elements in the intersection of the range of the map
5659 and the domain of the piecewise quasipolynomial reduction
5660 as a function of an element in the domain of the map.
5661 The functions taking a set compute a bound over all elements in the
5662 intersection of the set and the domain of the
5663 piecewise quasipolynomial reduction.
5667 #include <isl/set.h>
5668 __isl_give isl_basic_set *
5669 isl_basic_set_preimage_multi_aff(
5670 __isl_take isl_basic_set *bset,
5671 __isl_take isl_multi_aff *ma);
5672 __isl_give isl_set *isl_set_preimage_multi_aff(
5673 __isl_take isl_set *set,
5674 __isl_take isl_multi_aff *ma);
5675 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5676 __isl_take isl_set *set,
5677 __isl_take isl_pw_multi_aff *pma);
5678 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5679 __isl_take isl_set *set,
5680 __isl_take isl_multi_pw_aff *mpa);
5682 #include <isl/union_set.h>
5683 __isl_give isl_union_set *
5684 isl_union_set_preimage_multi_aff(
5685 __isl_take isl_union_set *uset,
5686 __isl_take isl_multi_aff *ma);
5687 __isl_give isl_union_set *
5688 isl_union_set_preimage_pw_multi_aff(
5689 __isl_take isl_union_set *uset,
5690 __isl_take isl_pw_multi_aff *pma);
5691 __isl_give isl_union_set *
5692 isl_union_set_preimage_union_pw_multi_aff(
5693 __isl_take isl_union_set *uset,
5694 __isl_take isl_union_pw_multi_aff *upma);
5696 #include <isl/map.h>
5697 __isl_give isl_basic_map *
5698 isl_basic_map_preimage_domain_multi_aff(
5699 __isl_take isl_basic_map *bmap,
5700 __isl_take isl_multi_aff *ma);
5701 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5702 __isl_take isl_map *map,
5703 __isl_take isl_multi_aff *ma);
5704 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5705 __isl_take isl_map *map,
5706 __isl_take isl_multi_aff *ma);
5707 __isl_give isl_map *
5708 isl_map_preimage_domain_pw_multi_aff(
5709 __isl_take isl_map *map,
5710 __isl_take isl_pw_multi_aff *pma);
5711 __isl_give isl_map *
5712 isl_map_preimage_range_pw_multi_aff(
5713 __isl_take isl_map *map,
5714 __isl_take isl_pw_multi_aff *pma);
5715 __isl_give isl_map *
5716 isl_map_preimage_domain_multi_pw_aff(
5717 __isl_take isl_map *map,
5718 __isl_take isl_multi_pw_aff *mpa);
5719 __isl_give isl_basic_map *
5720 isl_basic_map_preimage_range_multi_aff(
5721 __isl_take isl_basic_map *bmap,
5722 __isl_take isl_multi_aff *ma);
5724 #include <isl/union_map.h>
5725 __isl_give isl_union_map *
5726 isl_union_map_preimage_domain_multi_aff(
5727 __isl_take isl_union_map *umap,
5728 __isl_take isl_multi_aff *ma);
5729 __isl_give isl_union_map *
5730 isl_union_map_preimage_range_multi_aff(
5731 __isl_take isl_union_map *umap,
5732 __isl_take isl_multi_aff *ma);
5733 __isl_give isl_union_map *
5734 isl_union_map_preimage_domain_pw_multi_aff(
5735 __isl_take isl_union_map *umap,
5736 __isl_take isl_pw_multi_aff *pma);
5737 __isl_give isl_union_map *
5738 isl_union_map_preimage_range_pw_multi_aff(
5739 __isl_take isl_union_map *umap,
5740 __isl_take isl_pw_multi_aff *pma);
5741 __isl_give isl_union_map *
5742 isl_union_map_preimage_domain_union_pw_multi_aff(
5743 __isl_take isl_union_map *umap,
5744 __isl_take isl_union_pw_multi_aff *upma);
5745 __isl_give isl_union_map *
5746 isl_union_map_preimage_range_union_pw_multi_aff(
5747 __isl_take isl_union_map *umap,
5748 __isl_take isl_union_pw_multi_aff *upma);
5750 These functions compute the preimage of the given set or map domain/range under
5751 the given function. In other words, the expression is plugged
5752 into the set description or into the domain/range of the map.
5756 #include <isl/aff.h>
5757 __isl_give isl_aff *isl_aff_pullback_aff(
5758 __isl_take isl_aff *aff1,
5759 __isl_take isl_aff *aff2);
5760 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5761 __isl_take isl_aff *aff,
5762 __isl_take isl_multi_aff *ma);
5763 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5764 __isl_take isl_pw_aff *pa,
5765 __isl_take isl_multi_aff *ma);
5766 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5767 __isl_take isl_pw_aff *pa,
5768 __isl_take isl_pw_multi_aff *pma);
5769 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5770 __isl_take isl_pw_aff *pa,
5771 __isl_take isl_multi_pw_aff *mpa);
5772 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5773 __isl_take isl_multi_aff *ma1,
5774 __isl_take isl_multi_aff *ma2);
5775 __isl_give isl_pw_multi_aff *
5776 isl_pw_multi_aff_pullback_multi_aff(
5777 __isl_take isl_pw_multi_aff *pma,
5778 __isl_take isl_multi_aff *ma);
5779 __isl_give isl_multi_pw_aff *
5780 isl_multi_pw_aff_pullback_multi_aff(
5781 __isl_take isl_multi_pw_aff *mpa,
5782 __isl_take isl_multi_aff *ma);
5783 __isl_give isl_pw_multi_aff *
5784 isl_pw_multi_aff_pullback_pw_multi_aff(
5785 __isl_take isl_pw_multi_aff *pma1,
5786 __isl_take isl_pw_multi_aff *pma2);
5787 __isl_give isl_multi_pw_aff *
5788 isl_multi_pw_aff_pullback_pw_multi_aff(
5789 __isl_take isl_multi_pw_aff *mpa,
5790 __isl_take isl_pw_multi_aff *pma);
5791 __isl_give isl_multi_pw_aff *
5792 isl_multi_pw_aff_pullback_multi_pw_aff(
5793 __isl_take isl_multi_pw_aff *mpa1,
5794 __isl_take isl_multi_pw_aff *mpa2);
5795 __isl_give isl_union_pw_aff *
5796 isl_union_pw_aff_pullback_union_pw_multi_aff(
5797 __isl_take isl_union_pw_aff *upa,
5798 __isl_take isl_union_pw_multi_aff *upma);
5799 __isl_give isl_union_pw_multi_aff *
5800 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5801 __isl_take isl_union_pw_multi_aff *upma1,
5802 __isl_take isl_union_pw_multi_aff *upma2);
5803 __isl_give isl_multi_union_pw_aff *
5804 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
5805 __isl_take isl_multi_union_pw_aff *mupa,
5806 __isl_take isl_union_pw_multi_aff *upma);
5808 These functions precompose the first expression by the second function.
5809 In other words, the second function is plugged
5810 into the first expression.
5814 #include <isl/aff.h>
5815 __isl_give isl_basic_set *isl_aff_le_basic_set(
5816 __isl_take isl_aff *aff1,
5817 __isl_take isl_aff *aff2);
5818 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5819 __isl_take isl_aff *aff1,
5820 __isl_take isl_aff *aff2);
5821 __isl_give isl_set *isl_pw_aff_eq_set(
5822 __isl_take isl_pw_aff *pwaff1,
5823 __isl_take isl_pw_aff *pwaff2);
5824 __isl_give isl_set *isl_pw_aff_ne_set(
5825 __isl_take isl_pw_aff *pwaff1,
5826 __isl_take isl_pw_aff *pwaff2);
5827 __isl_give isl_set *isl_pw_aff_le_set(
5828 __isl_take isl_pw_aff *pwaff1,
5829 __isl_take isl_pw_aff *pwaff2);
5830 __isl_give isl_set *isl_pw_aff_lt_set(
5831 __isl_take isl_pw_aff *pwaff1,
5832 __isl_take isl_pw_aff *pwaff2);
5833 __isl_give isl_set *isl_pw_aff_ge_set(
5834 __isl_take isl_pw_aff *pwaff1,
5835 __isl_take isl_pw_aff *pwaff2);
5836 __isl_give isl_set *isl_pw_aff_gt_set(
5837 __isl_take isl_pw_aff *pwaff1,
5838 __isl_take isl_pw_aff *pwaff2);
5840 __isl_give isl_set *isl_multi_aff_lex_le_set(
5841 __isl_take isl_multi_aff *ma1,
5842 __isl_take isl_multi_aff *ma2);
5843 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5844 __isl_take isl_multi_aff *ma1,
5845 __isl_take isl_multi_aff *ma2);
5847 __isl_give isl_set *isl_pw_aff_list_eq_set(
5848 __isl_take isl_pw_aff_list *list1,
5849 __isl_take isl_pw_aff_list *list2);
5850 __isl_give isl_set *isl_pw_aff_list_ne_set(
5851 __isl_take isl_pw_aff_list *list1,
5852 __isl_take isl_pw_aff_list *list2);
5853 __isl_give isl_set *isl_pw_aff_list_le_set(
5854 __isl_take isl_pw_aff_list *list1,
5855 __isl_take isl_pw_aff_list *list2);
5856 __isl_give isl_set *isl_pw_aff_list_lt_set(
5857 __isl_take isl_pw_aff_list *list1,
5858 __isl_take isl_pw_aff_list *list2);
5859 __isl_give isl_set *isl_pw_aff_list_ge_set(
5860 __isl_take isl_pw_aff_list *list1,
5861 __isl_take isl_pw_aff_list *list2);
5862 __isl_give isl_set *isl_pw_aff_list_gt_set(
5863 __isl_take isl_pw_aff_list *list1,
5864 __isl_take isl_pw_aff_list *list2);
5866 The function C<isl_aff_ge_basic_set> returns a basic set
5867 containing those elements in the shared space
5868 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5869 The function C<isl_pw_aff_ge_set> returns a set
5870 containing those elements in the shared domain
5871 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5872 greater than or equal to C<pwaff2>.
5873 The function C<isl_multi_aff_lex_le_set> returns a set
5874 containing those elements in the shared domain space
5875 where C<ma1> is lexicographically smaller than or
5877 The functions operating on C<isl_pw_aff_list> apply the corresponding
5878 C<isl_pw_aff> function to each pair of elements in the two lists.
5880 #include <isl/aff.h>
5881 __isl_give isl_map *isl_pw_aff_eq_map(
5882 __isl_take isl_pw_aff *pa1,
5883 __isl_take isl_pw_aff *pa2);
5885 This function returns a map between domain elements of the arguments
5886 where the function values satisfy the given relation.
5888 =item * Cartesian Product
5890 #include <isl/space.h>
5891 __isl_give isl_space *isl_space_product(
5892 __isl_take isl_space *space1,
5893 __isl_take isl_space *space2);
5894 __isl_give isl_space *isl_space_domain_product(
5895 __isl_take isl_space *space1,
5896 __isl_take isl_space *space2);
5897 __isl_give isl_space *isl_space_range_product(
5898 __isl_take isl_space *space1,
5899 __isl_take isl_space *space2);
5902 C<isl_space_product>, C<isl_space_domain_product>
5903 and C<isl_space_range_product> take pairs or relation spaces and
5904 produce a single relations space, where either the domain, the range
5905 or both domain and range are wrapped spaces of relations between
5906 the domains and/or ranges of the input spaces.
5907 If the product is only constructed over the domain or the range
5908 then the ranges or the domains of the inputs should be the same.
5909 The function C<isl_space_product> also accepts a pair of set spaces,
5910 in which case it returns a wrapped space of a relation between the
5913 #include <isl/set.h>
5914 __isl_give isl_set *isl_set_product(
5915 __isl_take isl_set *set1,
5916 __isl_take isl_set *set2);
5918 #include <isl/map.h>
5919 __isl_give isl_basic_map *isl_basic_map_domain_product(
5920 __isl_take isl_basic_map *bmap1,
5921 __isl_take isl_basic_map *bmap2);
5922 __isl_give isl_basic_map *isl_basic_map_range_product(
5923 __isl_take isl_basic_map *bmap1,
5924 __isl_take isl_basic_map *bmap2);
5925 __isl_give isl_basic_map *isl_basic_map_product(
5926 __isl_take isl_basic_map *bmap1,
5927 __isl_take isl_basic_map *bmap2);
5928 __isl_give isl_map *isl_map_domain_product(
5929 __isl_take isl_map *map1,
5930 __isl_take isl_map *map2);
5931 __isl_give isl_map *isl_map_range_product(
5932 __isl_take isl_map *map1,
5933 __isl_take isl_map *map2);
5934 __isl_give isl_map *isl_map_product(
5935 __isl_take isl_map *map1,
5936 __isl_take isl_map *map2);
5938 #include <isl/union_set.h>
5939 __isl_give isl_union_set *isl_union_set_product(
5940 __isl_take isl_union_set *uset1,
5941 __isl_take isl_union_set *uset2);
5943 #include <isl/union_map.h>
5944 __isl_give isl_union_map *isl_union_map_domain_product(
5945 __isl_take isl_union_map *umap1,
5946 __isl_take isl_union_map *umap2);
5947 __isl_give isl_union_map *isl_union_map_range_product(
5948 __isl_take isl_union_map *umap1,
5949 __isl_take isl_union_map *umap2);
5950 __isl_give isl_union_map *isl_union_map_product(
5951 __isl_take isl_union_map *umap1,
5952 __isl_take isl_union_map *umap2);
5954 #include <isl/val.h>
5955 __isl_give isl_multi_val *isl_multi_val_range_product(
5956 __isl_take isl_multi_val *mv1,
5957 __isl_take isl_multi_val *mv2);
5958 __isl_give isl_multi_val *isl_multi_val_product(
5959 __isl_take isl_multi_val *mv1,
5960 __isl_take isl_multi_val *mv2);
5962 #include <isl/aff.h>
5963 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5964 __isl_take isl_multi_aff *ma1,
5965 __isl_take isl_multi_aff *ma2);
5966 __isl_give isl_multi_aff *isl_multi_aff_product(
5967 __isl_take isl_multi_aff *ma1,
5968 __isl_take isl_multi_aff *ma2);
5969 __isl_give isl_multi_pw_aff *
5970 isl_multi_pw_aff_range_product(
5971 __isl_take isl_multi_pw_aff *mpa1,
5972 __isl_take isl_multi_pw_aff *mpa2);
5973 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5974 __isl_take isl_multi_pw_aff *mpa1,
5975 __isl_take isl_multi_pw_aff *mpa2);
5976 __isl_give isl_pw_multi_aff *
5977 isl_pw_multi_aff_range_product(
5978 __isl_take isl_pw_multi_aff *pma1,
5979 __isl_take isl_pw_multi_aff *pma2);
5980 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5981 __isl_take isl_pw_multi_aff *pma1,
5982 __isl_take isl_pw_multi_aff *pma2);
5983 __isl_give isl_multi_union_pw_aff *
5984 isl_multi_union_pw_aff_range_product(
5985 __isl_take isl_multi_union_pw_aff *mupa1,
5986 __isl_take isl_multi_union_pw_aff *mupa2);
5988 The above functions compute the cross product of the given
5989 sets, relations or functions. The domains and ranges of the results
5990 are wrapped maps between domains and ranges of the inputs.
5991 To obtain a ``flat'' product, use the following functions
5994 #include <isl/set.h>
5995 __isl_give isl_basic_set *isl_basic_set_flat_product(
5996 __isl_take isl_basic_set *bset1,
5997 __isl_take isl_basic_set *bset2);
5998 __isl_give isl_set *isl_set_flat_product(
5999 __isl_take isl_set *set1,
6000 __isl_take isl_set *set2);
6002 #include <isl/map.h>
6003 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6004 __isl_take isl_basic_map *bmap1,
6005 __isl_take isl_basic_map *bmap2);
6006 __isl_give isl_map *isl_map_flat_domain_product(
6007 __isl_take isl_map *map1,
6008 __isl_take isl_map *map2);
6009 __isl_give isl_map *isl_map_flat_range_product(
6010 __isl_take isl_map *map1,
6011 __isl_take isl_map *map2);
6012 __isl_give isl_basic_map *isl_basic_map_flat_product(
6013 __isl_take isl_basic_map *bmap1,
6014 __isl_take isl_basic_map *bmap2);
6015 __isl_give isl_map *isl_map_flat_product(
6016 __isl_take isl_map *map1,
6017 __isl_take isl_map *map2);
6019 #include <isl/union_map.h>
6020 __isl_give isl_union_map *
6021 isl_union_map_flat_domain_product(
6022 __isl_take isl_union_map *umap1,
6023 __isl_take isl_union_map *umap2);
6024 __isl_give isl_union_map *
6025 isl_union_map_flat_range_product(
6026 __isl_take isl_union_map *umap1,
6027 __isl_take isl_union_map *umap2);
6029 #include <isl/val.h>
6030 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6031 __isl_take isl_multi_val *mv1,
6032 __isl_take isl_multi_aff *mv2);
6034 #include <isl/aff.h>
6035 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6036 __isl_take isl_multi_aff *ma1,
6037 __isl_take isl_multi_aff *ma2);
6038 __isl_give isl_pw_multi_aff *
6039 isl_pw_multi_aff_flat_range_product(
6040 __isl_take isl_pw_multi_aff *pma1,
6041 __isl_take isl_pw_multi_aff *pma2);
6042 __isl_give isl_multi_pw_aff *
6043 isl_multi_pw_aff_flat_range_product(
6044 __isl_take isl_multi_pw_aff *mpa1,
6045 __isl_take isl_multi_pw_aff *mpa2);
6046 __isl_give isl_union_pw_multi_aff *
6047 isl_union_pw_multi_aff_flat_range_product(
6048 __isl_take isl_union_pw_multi_aff *upma1,
6049 __isl_take isl_union_pw_multi_aff *upma2);
6050 __isl_give isl_multi_union_pw_aff *
6051 isl_multi_union_pw_aff_flat_range_product(
6052 __isl_take isl_multi_union_pw_aff *mupa1,
6053 __isl_take isl_multi_union_pw_aff *mupa2);
6055 #include <isl/space.h>
6056 __isl_give isl_space *isl_space_factor_domain(
6057 __isl_take isl_space *space);
6058 __isl_give isl_space *isl_space_factor_range(
6059 __isl_take isl_space *space);
6060 __isl_give isl_space *isl_space_domain_factor_domain(
6061 __isl_take isl_space *space);
6062 __isl_give isl_space *isl_space_domain_factor_range(
6063 __isl_take isl_space *space);
6064 __isl_give isl_space *isl_space_range_factor_domain(
6065 __isl_take isl_space *space);
6066 __isl_give isl_space *isl_space_range_factor_range(
6067 __isl_take isl_space *space);
6069 The functions C<isl_space_range_factor_domain> and
6070 C<isl_space_range_factor_range> extract the two arguments from
6071 the result of a call to C<isl_space_range_product>.
6073 The arguments of a call to C<isl_map_range_product> can be extracted
6074 from the result using the following functions.
6076 #include <isl/map.h>
6077 __isl_give isl_map *isl_map_factor_domain(
6078 __isl_take isl_map *map);
6079 __isl_give isl_map *isl_map_factor_range(
6080 __isl_take isl_map *map);
6081 __isl_give isl_map *isl_map_domain_factor_domain(
6082 __isl_take isl_map *map);
6083 __isl_give isl_map *isl_map_domain_factor_range(
6084 __isl_take isl_map *map);
6085 __isl_give isl_map *isl_map_range_factor_domain(
6086 __isl_take isl_map *map);
6087 __isl_give isl_map *isl_map_range_factor_range(
6088 __isl_take isl_map *map);
6090 #include <isl/union_map.h>
6091 __isl_give isl_union_map *isl_union_map_factor_domain(
6092 __isl_take isl_union_map *umap);
6093 __isl_give isl_union_map *isl_union_map_factor_range(
6094 __isl_take isl_union_map *umap);
6095 __isl_give isl_union_map *
6096 isl_union_map_domain_factor_domain(
6097 __isl_take isl_union_map *umap);
6098 __isl_give isl_union_map *
6099 isl_union_map_domain_factor_range(
6100 __isl_take isl_union_map *umap);
6101 __isl_give isl_union_map *
6102 isl_union_map_range_factor_range(
6103 __isl_take isl_union_map *umap);
6105 #include <isl/val.h>
6106 __isl_give isl_multi_val *
6107 isl_multi_val_range_factor_domain(
6108 __isl_take isl_multi_val *mv);
6109 __isl_give isl_multi_val *
6110 isl_multi_val_range_factor_range(
6111 __isl_take isl_multi_val *mv);
6113 #include <isl/aff.h>
6114 __isl_give isl_multi_aff *
6115 isl_multi_aff_range_factor_domain(
6116 __isl_take isl_multi_aff *ma);
6117 __isl_give isl_multi_aff *
6118 isl_multi_aff_range_factor_range(
6119 __isl_take isl_multi_aff *ma);
6120 __isl_give isl_multi_pw_aff *
6121 isl_multi_pw_aff_range_factor_domain(
6122 __isl_take isl_multi_pw_aff *mpa);
6123 __isl_give isl_multi_pw_aff *
6124 isl_multi_pw_aff_range_factor_range(
6125 __isl_take isl_multi_pw_aff *mpa);
6126 __isl_give isl_multi_union_pw_aff *
6127 isl_multi_union_pw_aff_range_factor_domain(
6128 __isl_take isl_multi_union_pw_aff *mupa);
6129 __isl_give isl_multi_union_pw_aff *
6130 isl_multi_union_pw_aff_range_factor_range(
6131 __isl_take isl_multi_union_pw_aff *mupa);
6133 The splice functions are a generalization of the flat product functions,
6134 where the second argument may be inserted at any position inside
6135 the first argument rather than being placed at the end.
6137 #include <isl/val.h>
6138 __isl_give isl_multi_val *isl_multi_val_range_splice(
6139 __isl_take isl_multi_val *mv1, unsigned pos,
6140 __isl_take isl_multi_val *mv2);
6142 #include <isl/aff.h>
6143 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6144 __isl_take isl_multi_aff *ma1, unsigned pos,
6145 __isl_take isl_multi_aff *ma2);
6146 __isl_give isl_multi_aff *isl_multi_aff_splice(
6147 __isl_take isl_multi_aff *ma1,
6148 unsigned in_pos, unsigned out_pos,
6149 __isl_take isl_multi_aff *ma2);
6150 __isl_give isl_multi_pw_aff *
6151 isl_multi_pw_aff_range_splice(
6152 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6153 __isl_take isl_multi_pw_aff *mpa2);
6154 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6155 __isl_take isl_multi_pw_aff *mpa1,
6156 unsigned in_pos, unsigned out_pos,
6157 __isl_take isl_multi_pw_aff *mpa2);
6158 __isl_give isl_multi_union_pw_aff *
6159 isl_multi_union_pw_aff_range_splice(
6160 __isl_take isl_multi_union_pw_aff *mupa1,
6162 __isl_take isl_multi_union_pw_aff *mupa2);
6164 =item * Simplification
6166 When applied to a set or relation,
6167 the gist operation returns a set or relation that has the
6168 same intersection with the context as the input set or relation.
6169 Any implicit equality in the intersection is made explicit in the result,
6170 while all inequalities that are redundant with respect to the intersection
6172 In case of union sets and relations, the gist operation is performed
6175 When applied to a function,
6176 the gist operation applies the set gist operation to each of
6177 the cells in the domain of the input piecewise expression.
6178 The context is also exploited
6179 to simplify the expression associated to each cell.
6181 #include <isl/set.h>
6182 __isl_give isl_basic_set *isl_basic_set_gist(
6183 __isl_take isl_basic_set *bset,
6184 __isl_take isl_basic_set *context);
6185 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6186 __isl_take isl_set *context);
6187 __isl_give isl_set *isl_set_gist_params(
6188 __isl_take isl_set *set,
6189 __isl_take isl_set *context);
6191 #include <isl/map.h>
6192 __isl_give isl_basic_map *isl_basic_map_gist(
6193 __isl_take isl_basic_map *bmap,
6194 __isl_take isl_basic_map *context);
6195 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6196 __isl_take isl_basic_map *bmap,
6197 __isl_take isl_basic_set *context);
6198 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6199 __isl_take isl_map *context);
6200 __isl_give isl_map *isl_map_gist_params(
6201 __isl_take isl_map *map,
6202 __isl_take isl_set *context);
6203 __isl_give isl_map *isl_map_gist_domain(
6204 __isl_take isl_map *map,
6205 __isl_take isl_set *context);
6206 __isl_give isl_map *isl_map_gist_range(
6207 __isl_take isl_map *map,
6208 __isl_take isl_set *context);
6210 #include <isl/union_set.h>
6211 __isl_give isl_union_set *isl_union_set_gist(
6212 __isl_take isl_union_set *uset,
6213 __isl_take isl_union_set *context);
6214 __isl_give isl_union_set *isl_union_set_gist_params(
6215 __isl_take isl_union_set *uset,
6216 __isl_take isl_set *set);
6218 #include <isl/union_map.h>
6219 __isl_give isl_union_map *isl_union_map_gist(
6220 __isl_take isl_union_map *umap,
6221 __isl_take isl_union_map *context);
6222 __isl_give isl_union_map *isl_union_map_gist_params(
6223 __isl_take isl_union_map *umap,
6224 __isl_take isl_set *set);
6225 __isl_give isl_union_map *isl_union_map_gist_domain(
6226 __isl_take isl_union_map *umap,
6227 __isl_take isl_union_set *uset);
6228 __isl_give isl_union_map *isl_union_map_gist_range(
6229 __isl_take isl_union_map *umap,
6230 __isl_take isl_union_set *uset);
6232 #include <isl/aff.h>
6233 __isl_give isl_aff *isl_aff_gist_params(
6234 __isl_take isl_aff *aff,
6235 __isl_take isl_set *context);
6236 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6237 __isl_take isl_set *context);
6238 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6239 __isl_take isl_multi_aff *maff,
6240 __isl_take isl_set *context);
6241 __isl_give isl_multi_aff *isl_multi_aff_gist(
6242 __isl_take isl_multi_aff *maff,
6243 __isl_take isl_set *context);
6244 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6245 __isl_take isl_pw_aff *pwaff,
6246 __isl_take isl_set *context);
6247 __isl_give isl_pw_aff *isl_pw_aff_gist(
6248 __isl_take isl_pw_aff *pwaff,
6249 __isl_take isl_set *context);
6250 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6251 __isl_take isl_pw_multi_aff *pma,
6252 __isl_take isl_set *set);
6253 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6254 __isl_take isl_pw_multi_aff *pma,
6255 __isl_take isl_set *set);
6256 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6257 __isl_take isl_multi_pw_aff *mpa,
6258 __isl_take isl_set *set);
6259 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6260 __isl_take isl_multi_pw_aff *mpa,
6261 __isl_take isl_set *set);
6262 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6263 __isl_take isl_union_pw_aff *upa,
6264 __isl_take isl_union_set *context);
6265 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6266 __isl_take isl_union_pw_aff *upa,
6267 __isl_take isl_set *context);
6268 __isl_give isl_union_pw_multi_aff *
6269 isl_union_pw_multi_aff_gist_params(
6270 __isl_take isl_union_pw_multi_aff *upma,
6271 __isl_take isl_set *context);
6272 __isl_give isl_union_pw_multi_aff *
6273 isl_union_pw_multi_aff_gist(
6274 __isl_take isl_union_pw_multi_aff *upma,
6275 __isl_take isl_union_set *context);
6276 __isl_give isl_multi_union_pw_aff *
6277 isl_multi_union_pw_aff_gist_params(
6278 __isl_take isl_multi_union_pw_aff *aff,
6279 __isl_take isl_set *context);
6280 __isl_give isl_multi_union_pw_aff *
6281 isl_multi_union_pw_aff_gist(
6282 __isl_take isl_multi_union_pw_aff *aff,
6283 __isl_take isl_union_set *context);
6285 #include <isl/polynomial.h>
6286 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6287 __isl_take isl_qpolynomial *qp,
6288 __isl_take isl_set *context);
6289 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6290 __isl_take isl_qpolynomial *qp,
6291 __isl_take isl_set *context);
6292 __isl_give isl_qpolynomial_fold *
6293 isl_qpolynomial_fold_gist_params(
6294 __isl_take isl_qpolynomial_fold *fold,
6295 __isl_take isl_set *context);
6296 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6297 __isl_take isl_qpolynomial_fold *fold,
6298 __isl_take isl_set *context);
6299 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6300 __isl_take isl_pw_qpolynomial *pwqp,
6301 __isl_take isl_set *context);
6302 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6303 __isl_take isl_pw_qpolynomial *pwqp,
6304 __isl_take isl_set *context);
6305 __isl_give isl_pw_qpolynomial_fold *
6306 isl_pw_qpolynomial_fold_gist(
6307 __isl_take isl_pw_qpolynomial_fold *pwf,
6308 __isl_take isl_set *context);
6309 __isl_give isl_pw_qpolynomial_fold *
6310 isl_pw_qpolynomial_fold_gist_params(
6311 __isl_take isl_pw_qpolynomial_fold *pwf,
6312 __isl_take isl_set *context);
6313 __isl_give isl_union_pw_qpolynomial *
6314 isl_union_pw_qpolynomial_gist_params(
6315 __isl_take isl_union_pw_qpolynomial *upwqp,
6316 __isl_take isl_set *context);
6317 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6318 __isl_take isl_union_pw_qpolynomial *upwqp,
6319 __isl_take isl_union_set *context);
6320 __isl_give isl_union_pw_qpolynomial_fold *
6321 isl_union_pw_qpolynomial_fold_gist(
6322 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6323 __isl_take isl_union_set *context);
6324 __isl_give isl_union_pw_qpolynomial_fold *
6325 isl_union_pw_qpolynomial_fold_gist_params(
6326 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6327 __isl_take isl_set *context);
6329 =item * Binary Arithmethic Operations
6331 #include <isl/val.h>
6332 __isl_give isl_multi_val *isl_multi_val_sub(
6333 __isl_take isl_multi_val *mv1,
6334 __isl_take isl_multi_val *mv2);
6336 #include <isl/aff.h>
6337 __isl_give isl_aff *isl_aff_add(
6338 __isl_take isl_aff *aff1,
6339 __isl_take isl_aff *aff2);
6340 __isl_give isl_multi_aff *isl_multi_aff_add(
6341 __isl_take isl_multi_aff *maff1,
6342 __isl_take isl_multi_aff *maff2);
6343 __isl_give isl_pw_aff *isl_pw_aff_add(
6344 __isl_take isl_pw_aff *pwaff1,
6345 __isl_take isl_pw_aff *pwaff2);
6346 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6347 __isl_take isl_pw_multi_aff *pma1,
6348 __isl_take isl_pw_multi_aff *pma2);
6349 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6350 __isl_take isl_union_pw_aff *upa1,
6351 __isl_take isl_union_pw_aff *upa2);
6352 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6353 __isl_take isl_union_pw_multi_aff *upma1,
6354 __isl_take isl_union_pw_multi_aff *upma2);
6355 __isl_give isl_pw_aff *isl_pw_aff_min(
6356 __isl_take isl_pw_aff *pwaff1,
6357 __isl_take isl_pw_aff *pwaff2);
6358 __isl_give isl_pw_aff *isl_pw_aff_max(
6359 __isl_take isl_pw_aff *pwaff1,
6360 __isl_take isl_pw_aff *pwaff2);
6361 __isl_give isl_aff *isl_aff_sub(
6362 __isl_take isl_aff *aff1,
6363 __isl_take isl_aff *aff2);
6364 __isl_give isl_multi_aff *isl_multi_aff_sub(
6365 __isl_take isl_multi_aff *ma1,
6366 __isl_take isl_multi_aff *ma2);
6367 __isl_give isl_pw_aff *isl_pw_aff_sub(
6368 __isl_take isl_pw_aff *pwaff1,
6369 __isl_take isl_pw_aff *pwaff2);
6370 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6371 __isl_take isl_multi_pw_aff *mpa1,
6372 __isl_take isl_multi_pw_aff *mpa2);
6373 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6374 __isl_take isl_pw_multi_aff *pma1,
6375 __isl_take isl_pw_multi_aff *pma2);
6376 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6377 __isl_take isl_union_pw_aff *upa1,
6378 __isl_take isl_union_pw_aff *upa2);
6379 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6380 __isl_take isl_union_pw_multi_aff *upma1,
6381 __isl_take isl_union_pw_multi_aff *upma2);
6382 __isl_give isl_multi_union_pw_aff *
6383 isl_multi_union_pw_aff_sub(
6384 __isl_take isl_multi_union_pw_aff *mupa1,
6385 __isl_take isl_multi_union_pw_aff *mupa2);
6387 C<isl_aff_sub> subtracts the second argument from the first.
6389 #include <isl/polynomial.h>
6390 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6391 __isl_take isl_qpolynomial *qp1,
6392 __isl_take isl_qpolynomial *qp2);
6393 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6394 __isl_take isl_pw_qpolynomial *pwqp1,
6395 __isl_take isl_pw_qpolynomial *pwqp2);
6396 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6397 __isl_take isl_pw_qpolynomial *pwqp1,
6398 __isl_take isl_pw_qpolynomial *pwqp2);
6399 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6400 __isl_take isl_pw_qpolynomial_fold *pwf1,
6401 __isl_take isl_pw_qpolynomial_fold *pwf2);
6402 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6403 __isl_take isl_union_pw_qpolynomial *upwqp1,
6404 __isl_take isl_union_pw_qpolynomial *upwqp2);
6405 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6406 __isl_take isl_qpolynomial *qp1,
6407 __isl_take isl_qpolynomial *qp2);
6408 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6409 __isl_take isl_pw_qpolynomial *pwqp1,
6410 __isl_take isl_pw_qpolynomial *pwqp2);
6411 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6412 __isl_take isl_union_pw_qpolynomial *upwqp1,
6413 __isl_take isl_union_pw_qpolynomial *upwqp2);
6414 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6415 __isl_take isl_pw_qpolynomial_fold *pwf1,
6416 __isl_take isl_pw_qpolynomial_fold *pwf2);
6417 __isl_give isl_union_pw_qpolynomial_fold *
6418 isl_union_pw_qpolynomial_fold_fold(
6419 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6420 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6422 #include <isl/aff.h>
6423 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6424 __isl_take isl_pw_aff *pwaff1,
6425 __isl_take isl_pw_aff *pwaff2);
6426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6427 __isl_take isl_pw_multi_aff *pma1,
6428 __isl_take isl_pw_multi_aff *pma2);
6429 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6430 __isl_take isl_union_pw_aff *upa1,
6431 __isl_take isl_union_pw_aff *upa2);
6432 __isl_give isl_union_pw_multi_aff *
6433 isl_union_pw_multi_aff_union_add(
6434 __isl_take isl_union_pw_multi_aff *upma1,
6435 __isl_take isl_union_pw_multi_aff *upma2);
6436 __isl_give isl_multi_union_pw_aff *
6437 isl_multi_union_pw_aff_union_add(
6438 __isl_take isl_multi_union_pw_aff *mupa1,
6439 __isl_take isl_multi_union_pw_aff *mupa2);
6440 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6441 __isl_take isl_pw_aff *pwaff1,
6442 __isl_take isl_pw_aff *pwaff2);
6443 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6444 __isl_take isl_pw_aff *pwaff1,
6445 __isl_take isl_pw_aff *pwaff2);
6447 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6448 expression with a domain that is the union of those of C<pwaff1> and
6449 C<pwaff2> and such that on each cell, the quasi-affine expression is
6450 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6451 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6452 associated expression is the defined one.
6453 This in contrast to the C<isl_pw_aff_max> function, which is
6454 only defined on the shared definition domain of the arguments.
6456 #include <isl/val.h>
6457 __isl_give isl_multi_val *isl_multi_val_add_val(
6458 __isl_take isl_multi_val *mv,
6459 __isl_take isl_val *v);
6460 __isl_give isl_multi_val *isl_multi_val_mod_val(
6461 __isl_take isl_multi_val *mv,
6462 __isl_take isl_val *v);
6463 __isl_give isl_multi_val *isl_multi_val_scale_val(
6464 __isl_take isl_multi_val *mv,
6465 __isl_take isl_val *v);
6466 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6467 __isl_take isl_multi_val *mv,
6468 __isl_take isl_val *v);
6470 #include <isl/aff.h>
6471 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6472 __isl_take isl_val *mod);
6473 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6474 __isl_take isl_pw_aff *pa,
6475 __isl_take isl_val *mod);
6476 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6477 __isl_take isl_union_pw_aff *upa,
6478 __isl_take isl_val *f);
6479 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6480 __isl_take isl_val *v);
6481 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6482 __isl_take isl_multi_aff *ma,
6483 __isl_take isl_val *v);
6484 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6485 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6486 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6487 __isl_take isl_multi_pw_aff *mpa,
6488 __isl_take isl_val *v);
6489 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6490 __isl_take isl_pw_multi_aff *pma,
6491 __isl_take isl_val *v);
6492 __isl_give isl_union_pw_multi_aff *
6493 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6494 __isl_take isl_union_pw_aff *upa,
6495 __isl_take isl_val *f);
6496 isl_union_pw_multi_aff_scale_val(
6497 __isl_take isl_union_pw_multi_aff *upma,
6498 __isl_take isl_val *val);
6499 __isl_give isl_multi_union_pw_aff *
6500 isl_multi_union_pw_aff_scale_val(
6501 __isl_take isl_multi_union_pw_aff *mupa,
6502 __isl_take isl_val *v);
6503 __isl_give isl_aff *isl_aff_scale_down_ui(
6504 __isl_take isl_aff *aff, unsigned f);
6505 __isl_give isl_aff *isl_aff_scale_down_val(
6506 __isl_take isl_aff *aff, __isl_take isl_val *v);
6507 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6508 __isl_take isl_multi_aff *ma,
6509 __isl_take isl_val *v);
6510 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6511 __isl_take isl_pw_aff *pa,
6512 __isl_take isl_val *f);
6513 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6514 __isl_take isl_multi_pw_aff *mpa,
6515 __isl_take isl_val *v);
6516 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6517 __isl_take isl_pw_multi_aff *pma,
6518 __isl_take isl_val *v);
6519 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6520 __isl_take isl_union_pw_aff *upa,
6521 __isl_take isl_val *v);
6522 __isl_give isl_union_pw_multi_aff *
6523 isl_union_pw_multi_aff_scale_down_val(
6524 __isl_take isl_union_pw_multi_aff *upma,
6525 __isl_take isl_val *val);
6526 __isl_give isl_multi_union_pw_aff *
6527 isl_multi_union_pw_aff_scale_down_val(
6528 __isl_take isl_multi_union_pw_aff *mupa,
6529 __isl_take isl_val *v);
6531 #include <isl/polynomial.h>
6532 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6533 __isl_take isl_qpolynomial *qp,
6534 __isl_take isl_val *v);
6535 __isl_give isl_qpolynomial_fold *
6536 isl_qpolynomial_fold_scale_val(
6537 __isl_take isl_qpolynomial_fold *fold,
6538 __isl_take isl_val *v);
6539 __isl_give isl_pw_qpolynomial *
6540 isl_pw_qpolynomial_scale_val(
6541 __isl_take isl_pw_qpolynomial *pwqp,
6542 __isl_take isl_val *v);
6543 __isl_give isl_pw_qpolynomial_fold *
6544 isl_pw_qpolynomial_fold_scale_val(
6545 __isl_take isl_pw_qpolynomial_fold *pwf,
6546 __isl_take isl_val *v);
6547 __isl_give isl_union_pw_qpolynomial *
6548 isl_union_pw_qpolynomial_scale_val(
6549 __isl_take isl_union_pw_qpolynomial *upwqp,
6550 __isl_take isl_val *v);
6551 __isl_give isl_union_pw_qpolynomial_fold *
6552 isl_union_pw_qpolynomial_fold_scale_val(
6553 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6554 __isl_take isl_val *v);
6555 __isl_give isl_qpolynomial *
6556 isl_qpolynomial_scale_down_val(
6557 __isl_take isl_qpolynomial *qp,
6558 __isl_take isl_val *v);
6559 __isl_give isl_qpolynomial_fold *
6560 isl_qpolynomial_fold_scale_down_val(
6561 __isl_take isl_qpolynomial_fold *fold,
6562 __isl_take isl_val *v);
6563 __isl_give isl_pw_qpolynomial *
6564 isl_pw_qpolynomial_scale_down_val(
6565 __isl_take isl_pw_qpolynomial *pwqp,
6566 __isl_take isl_val *v);
6567 __isl_give isl_pw_qpolynomial_fold *
6568 isl_pw_qpolynomial_fold_scale_down_val(
6569 __isl_take isl_pw_qpolynomial_fold *pwf,
6570 __isl_take isl_val *v);
6571 __isl_give isl_union_pw_qpolynomial *
6572 isl_union_pw_qpolynomial_scale_down_val(
6573 __isl_take isl_union_pw_qpolynomial *upwqp,
6574 __isl_take isl_val *v);
6575 __isl_give isl_union_pw_qpolynomial_fold *
6576 isl_union_pw_qpolynomial_fold_scale_down_val(
6577 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6578 __isl_take isl_val *v);
6580 #include <isl/val.h>
6581 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6582 __isl_take isl_multi_val *mv1,
6583 __isl_take isl_multi_val *mv2);
6584 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6585 __isl_take isl_multi_val *mv1,
6586 __isl_take isl_multi_val *mv2);
6587 __isl_give isl_multi_val *
6588 isl_multi_val_scale_down_multi_val(
6589 __isl_take isl_multi_val *mv1,
6590 __isl_take isl_multi_val *mv2);
6592 #include <isl/aff.h>
6593 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6594 __isl_take isl_multi_aff *ma,
6595 __isl_take isl_multi_val *mv);
6596 __isl_give isl_multi_union_pw_aff *
6597 isl_multi_union_pw_aff_mod_multi_val(
6598 __isl_take isl_multi_union_pw_aff *upma,
6599 __isl_take isl_multi_val *mv);
6600 __isl_give isl_multi_pw_aff *
6601 isl_multi_pw_aff_mod_multi_val(
6602 __isl_take isl_multi_pw_aff *mpa,
6603 __isl_take isl_multi_val *mv);
6604 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6605 __isl_take isl_multi_aff *ma,
6606 __isl_take isl_multi_val *mv);
6607 __isl_give isl_pw_multi_aff *
6608 isl_pw_multi_aff_scale_multi_val(
6609 __isl_take isl_pw_multi_aff *pma,
6610 __isl_take isl_multi_val *mv);
6611 __isl_give isl_multi_pw_aff *
6612 isl_multi_pw_aff_scale_multi_val(
6613 __isl_take isl_multi_pw_aff *mpa,
6614 __isl_take isl_multi_val *mv);
6615 __isl_give isl_multi_union_pw_aff *
6616 isl_multi_union_pw_aff_scale_multi_val(
6617 __isl_take isl_multi_union_pw_aff *mupa,
6618 __isl_take isl_multi_val *mv);
6619 __isl_give isl_union_pw_multi_aff *
6620 isl_union_pw_multi_aff_scale_multi_val(
6621 __isl_take isl_union_pw_multi_aff *upma,
6622 __isl_take isl_multi_val *mv);
6623 __isl_give isl_multi_aff *
6624 isl_multi_aff_scale_down_multi_val(
6625 __isl_take isl_multi_aff *ma,
6626 __isl_take isl_multi_val *mv);
6627 __isl_give isl_multi_pw_aff *
6628 isl_multi_pw_aff_scale_down_multi_val(
6629 __isl_take isl_multi_pw_aff *mpa,
6630 __isl_take isl_multi_val *mv);
6631 __isl_give isl_multi_union_pw_aff *
6632 isl_multi_union_pw_aff_scale_down_multi_val(
6633 __isl_take isl_multi_union_pw_aff *mupa,
6634 __isl_take isl_multi_val *mv);
6636 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6637 by the corresponding elements of C<mv>.
6639 #include <isl/aff.h>
6640 __isl_give isl_aff *isl_aff_mul(
6641 __isl_take isl_aff *aff1,
6642 __isl_take isl_aff *aff2);
6643 __isl_give isl_aff *isl_aff_div(
6644 __isl_take isl_aff *aff1,
6645 __isl_take isl_aff *aff2);
6646 __isl_give isl_pw_aff *isl_pw_aff_mul(
6647 __isl_take isl_pw_aff *pwaff1,
6648 __isl_take isl_pw_aff *pwaff2);
6649 __isl_give isl_pw_aff *isl_pw_aff_div(
6650 __isl_take isl_pw_aff *pa1,
6651 __isl_take isl_pw_aff *pa2);
6652 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6653 __isl_take isl_pw_aff *pa1,
6654 __isl_take isl_pw_aff *pa2);
6655 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6656 __isl_take isl_pw_aff *pa1,
6657 __isl_take isl_pw_aff *pa2);
6659 When multiplying two affine expressions, at least one of the two needs
6660 to be a constant. Similarly, when dividing an affine expression by another,
6661 the second expression needs to be a constant.
6662 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6663 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6666 #include <isl/polynomial.h>
6667 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6668 __isl_take isl_qpolynomial *qp1,
6669 __isl_take isl_qpolynomial *qp2);
6670 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6671 __isl_take isl_pw_qpolynomial *pwqp1,
6672 __isl_take isl_pw_qpolynomial *pwqp2);
6673 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6674 __isl_take isl_union_pw_qpolynomial *upwqp1,
6675 __isl_take isl_union_pw_qpolynomial *upwqp2);
6679 =head3 Lexicographic Optimization
6681 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6682 the following functions
6683 compute a set that contains the lexicographic minimum or maximum
6684 of the elements in C<set> (or C<bset>) for those values of the parameters
6685 that satisfy C<dom>.
6686 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6687 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6689 In other words, the union of the parameter values
6690 for which the result is non-empty and of C<*empty>
6693 #include <isl/set.h>
6694 __isl_give isl_set *isl_basic_set_partial_lexmin(
6695 __isl_take isl_basic_set *bset,
6696 __isl_take isl_basic_set *dom,
6697 __isl_give isl_set **empty);
6698 __isl_give isl_set *isl_basic_set_partial_lexmax(
6699 __isl_take isl_basic_set *bset,
6700 __isl_take isl_basic_set *dom,
6701 __isl_give isl_set **empty);
6702 __isl_give isl_set *isl_set_partial_lexmin(
6703 __isl_take isl_set *set, __isl_take isl_set *dom,
6704 __isl_give isl_set **empty);
6705 __isl_give isl_set *isl_set_partial_lexmax(
6706 __isl_take isl_set *set, __isl_take isl_set *dom,
6707 __isl_give isl_set **empty);
6709 Given a (basic) set C<set> (or C<bset>), the following functions simply
6710 return a set containing the lexicographic minimum or maximum
6711 of the elements in C<set> (or C<bset>).
6712 In case of union sets, the optimum is computed per space.
6714 #include <isl/set.h>
6715 __isl_give isl_set *isl_basic_set_lexmin(
6716 __isl_take isl_basic_set *bset);
6717 __isl_give isl_set *isl_basic_set_lexmax(
6718 __isl_take isl_basic_set *bset);
6719 __isl_give isl_set *isl_set_lexmin(
6720 __isl_take isl_set *set);
6721 __isl_give isl_set *isl_set_lexmax(
6722 __isl_take isl_set *set);
6723 __isl_give isl_union_set *isl_union_set_lexmin(
6724 __isl_take isl_union_set *uset);
6725 __isl_give isl_union_set *isl_union_set_lexmax(
6726 __isl_take isl_union_set *uset);
6728 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6729 the following functions
6730 compute a relation that maps each element of C<dom>
6731 to the single lexicographic minimum or maximum
6732 of the elements that are associated to that same
6733 element in C<map> (or C<bmap>).
6734 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6735 that contains the elements in C<dom> that do not map
6736 to any elements in C<map> (or C<bmap>).
6737 In other words, the union of the domain of the result and of C<*empty>
6740 #include <isl/map.h>
6741 __isl_give isl_map *isl_basic_map_partial_lexmax(
6742 __isl_take isl_basic_map *bmap,
6743 __isl_take isl_basic_set *dom,
6744 __isl_give isl_set **empty);
6745 __isl_give isl_map *isl_basic_map_partial_lexmin(
6746 __isl_take isl_basic_map *bmap,
6747 __isl_take isl_basic_set *dom,
6748 __isl_give isl_set **empty);
6749 __isl_give isl_map *isl_map_partial_lexmax(
6750 __isl_take isl_map *map, __isl_take isl_set *dom,
6751 __isl_give isl_set **empty);
6752 __isl_give isl_map *isl_map_partial_lexmin(
6753 __isl_take isl_map *map, __isl_take isl_set *dom,
6754 __isl_give isl_set **empty);
6756 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6757 return a map mapping each element in the domain of
6758 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6759 of all elements associated to that element.
6760 In case of union relations, the optimum is computed per space.
6762 #include <isl/map.h>
6763 __isl_give isl_map *isl_basic_map_lexmin(
6764 __isl_take isl_basic_map *bmap);
6765 __isl_give isl_map *isl_basic_map_lexmax(
6766 __isl_take isl_basic_map *bmap);
6767 __isl_give isl_map *isl_map_lexmin(
6768 __isl_take isl_map *map);
6769 __isl_give isl_map *isl_map_lexmax(
6770 __isl_take isl_map *map);
6771 __isl_give isl_union_map *isl_union_map_lexmin(
6772 __isl_take isl_union_map *umap);
6773 __isl_give isl_union_map *isl_union_map_lexmax(
6774 __isl_take isl_union_map *umap);
6776 The following functions return their result in the form of
6777 a piecewise multi-affine expression,
6778 but are otherwise equivalent to the corresponding functions
6779 returning a basic set or relation.
6781 #include <isl/set.h>
6782 __isl_give isl_pw_multi_aff *
6783 isl_basic_set_partial_lexmin_pw_multi_aff(
6784 __isl_take isl_basic_set *bset,
6785 __isl_take isl_basic_set *dom,
6786 __isl_give isl_set **empty);
6787 __isl_give isl_pw_multi_aff *
6788 isl_basic_set_partial_lexmax_pw_multi_aff(
6789 __isl_take isl_basic_set *bset,
6790 __isl_take isl_basic_set *dom,
6791 __isl_give isl_set **empty);
6792 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6793 __isl_take isl_set *set);
6794 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6795 __isl_take isl_set *set);
6797 #include <isl/map.h>
6798 __isl_give isl_pw_multi_aff *
6799 isl_basic_map_lexmin_pw_multi_aff(
6800 __isl_take isl_basic_map *bmap);
6801 __isl_give isl_pw_multi_aff *
6802 isl_basic_map_partial_lexmin_pw_multi_aff(
6803 __isl_take isl_basic_map *bmap,
6804 __isl_take isl_basic_set *dom,
6805 __isl_give isl_set **empty);
6806 __isl_give isl_pw_multi_aff *
6807 isl_basic_map_partial_lexmax_pw_multi_aff(
6808 __isl_take isl_basic_map *bmap,
6809 __isl_take isl_basic_set *dom,
6810 __isl_give isl_set **empty);
6811 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6812 __isl_take isl_map *map);
6813 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6814 __isl_take isl_map *map);
6816 The following functions return the lexicographic minimum or maximum
6817 on the shared domain of the inputs and the single defined function
6818 on those parts of the domain where only a single function is defined.
6820 #include <isl/aff.h>
6821 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6822 __isl_take isl_pw_multi_aff *pma1,
6823 __isl_take isl_pw_multi_aff *pma2);
6824 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6825 __isl_take isl_pw_multi_aff *pma1,
6826 __isl_take isl_pw_multi_aff *pma2);
6828 =head2 Ternary Operations
6830 #include <isl/aff.h>
6831 __isl_give isl_pw_aff *isl_pw_aff_cond(
6832 __isl_take isl_pw_aff *cond,
6833 __isl_take isl_pw_aff *pwaff_true,
6834 __isl_take isl_pw_aff *pwaff_false);
6836 The function C<isl_pw_aff_cond> performs a conditional operator
6837 and returns an expression that is equal to C<pwaff_true>
6838 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6839 where C<cond> is zero.
6843 Lists are defined over several element types, including
6844 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
6845 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6846 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6847 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6848 Here we take lists of C<isl_set>s as an example.
6849 Lists can be created, copied, modified and freed using the following functions.
6851 #include <isl/set.h>
6852 __isl_give isl_set_list *isl_set_list_from_set(
6853 __isl_take isl_set *el);
6854 __isl_give isl_set_list *isl_set_list_alloc(
6855 isl_ctx *ctx, int n);
6856 __isl_give isl_set_list *isl_set_list_copy(
6857 __isl_keep isl_set_list *list);
6858 __isl_give isl_set_list *isl_set_list_insert(
6859 __isl_take isl_set_list *list, unsigned pos,
6860 __isl_take isl_set *el);
6861 __isl_give isl_set_list *isl_set_list_add(
6862 __isl_take isl_set_list *list,
6863 __isl_take isl_set *el);
6864 __isl_give isl_set_list *isl_set_list_drop(
6865 __isl_take isl_set_list *list,
6866 unsigned first, unsigned n);
6867 __isl_give isl_set_list *isl_set_list_set_set(
6868 __isl_take isl_set_list *list, int index,
6869 __isl_take isl_set *set);
6870 __isl_give isl_set_list *isl_set_list_concat(
6871 __isl_take isl_set_list *list1,
6872 __isl_take isl_set_list *list2);
6873 __isl_give isl_set_list *isl_set_list_sort(
6874 __isl_take isl_set_list *list,
6875 int (*cmp)(__isl_keep isl_set *a,
6876 __isl_keep isl_set *b, void *user),
6878 __isl_null isl_set_list *isl_set_list_free(
6879 __isl_take isl_set_list *list);
6881 C<isl_set_list_alloc> creates an empty list with an initial capacity
6882 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
6883 add elements to a list, increasing its capacity as needed.
6884 C<isl_set_list_from_set> creates a list with a single element.
6886 Lists can be inspected using the following functions.
6888 #include <isl/set.h>
6889 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6890 __isl_give isl_set *isl_set_list_get_set(
6891 __isl_keep isl_set_list *list, int index);
6892 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6893 int (*fn)(__isl_take isl_set *el, void *user),
6895 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6896 int (*follows)(__isl_keep isl_set *a,
6897 __isl_keep isl_set *b, void *user),
6899 int (*fn)(__isl_take isl_set *el, void *user),
6902 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6903 strongly connected components of the graph with as vertices the elements
6904 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6905 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6906 should return C<-1> on error.
6908 Lists can be printed using
6910 #include <isl/set.h>
6911 __isl_give isl_printer *isl_printer_print_set_list(
6912 __isl_take isl_printer *p,
6913 __isl_keep isl_set_list *list);
6915 =head2 Associative arrays
6917 Associative arrays map isl objects of a specific type to isl objects
6918 of some (other) specific type. They are defined for several pairs
6919 of types, including (C<isl_map>, C<isl_basic_set>),
6920 (C<isl_id>, C<isl_ast_expr>) and.
6921 (C<isl_id>, C<isl_pw_aff>).
6922 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6925 Associative arrays can be created, copied and freed using
6926 the following functions.
6928 #include <isl/id_to_ast_expr.h>
6929 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6930 isl_ctx *ctx, int min_size);
6931 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6932 __isl_keep id_to_ast_expr *id2expr);
6933 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6934 __isl_take id_to_ast_expr *id2expr);
6936 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6937 to specify the expected size of the associative array.
6938 The associative array will be grown automatically as needed.
6940 Associative arrays can be inspected using the following functions.
6942 #include <isl/id_to_ast_expr.h>
6943 int isl_id_to_ast_expr_has(
6944 __isl_keep id_to_ast_expr *id2expr,
6945 __isl_keep isl_id *key);
6946 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6947 __isl_keep id_to_ast_expr *id2expr,
6948 __isl_take isl_id *key);
6949 int isl_id_to_ast_expr_foreach(
6950 __isl_keep id_to_ast_expr *id2expr,
6951 int (*fn)(__isl_take isl_id *key,
6952 __isl_take isl_ast_expr *val, void *user),
6955 They can be modified using the following function.
6957 #include <isl/id_to_ast_expr.h>
6958 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6959 __isl_take id_to_ast_expr *id2expr,
6960 __isl_take isl_id *key,
6961 __isl_take isl_ast_expr *val);
6962 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6963 __isl_take id_to_ast_expr *id2expr,
6964 __isl_take isl_id *key);
6966 Associative arrays can be printed using the following function.
6968 #include <isl/id_to_ast_expr.h>
6969 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6970 __isl_take isl_printer *p,
6971 __isl_keep id_to_ast_expr *id2expr);
6975 Vectors can be created, copied and freed using the following functions.
6977 #include <isl/vec.h>
6978 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6980 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6981 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6983 Note that the elements of a newly created vector may have arbitrary values.
6984 The elements can be changed and inspected using the following functions.
6986 int isl_vec_size(__isl_keep isl_vec *vec);
6987 __isl_give isl_val *isl_vec_get_element_val(
6988 __isl_keep isl_vec *vec, int pos);
6989 __isl_give isl_vec *isl_vec_set_element_si(
6990 __isl_take isl_vec *vec, int pos, int v);
6991 __isl_give isl_vec *isl_vec_set_element_val(
6992 __isl_take isl_vec *vec, int pos,
6993 __isl_take isl_val *v);
6994 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6996 __isl_give isl_vec *isl_vec_set_val(
6997 __isl_take isl_vec *vec, __isl_take isl_val *v);
6998 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6999 __isl_keep isl_vec *vec2, int pos);
7001 C<isl_vec_get_element> will return a negative value if anything went wrong.
7002 In that case, the value of C<*v> is undefined.
7004 The following function can be used to concatenate two vectors.
7006 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7007 __isl_take isl_vec *vec2);
7011 Matrices can be created, copied and freed using the following functions.
7013 #include <isl/mat.h>
7014 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7015 unsigned n_row, unsigned n_col);
7016 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7017 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7019 Note that the elements of a newly created matrix may have arbitrary values.
7020 The elements can be changed and inspected using the following functions.
7022 int isl_mat_rows(__isl_keep isl_mat *mat);
7023 int isl_mat_cols(__isl_keep isl_mat *mat);
7024 __isl_give isl_val *isl_mat_get_element_val(
7025 __isl_keep isl_mat *mat, int row, int col);
7026 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7027 int row, int col, int v);
7028 __isl_give isl_mat *isl_mat_set_element_val(
7029 __isl_take isl_mat *mat, int row, int col,
7030 __isl_take isl_val *v);
7032 C<isl_mat_get_element> will return a negative value if anything went wrong.
7033 In that case, the value of C<*v> is undefined.
7035 The following function can be used to compute the (right) inverse
7036 of a matrix, i.e., a matrix such that the product of the original
7037 and the inverse (in that order) is a multiple of the identity matrix.
7038 The input matrix is assumed to be of full row-rank.
7040 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7042 The following function can be used to compute the (right) kernel
7043 (or null space) of a matrix, i.e., a matrix such that the product of
7044 the original and the kernel (in that order) is the zero matrix.
7046 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7048 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7050 The following functions determine
7051 an upper or lower bound on a quasipolynomial over its domain.
7053 __isl_give isl_pw_qpolynomial_fold *
7054 isl_pw_qpolynomial_bound(
7055 __isl_take isl_pw_qpolynomial *pwqp,
7056 enum isl_fold type, int *tight);
7058 __isl_give isl_union_pw_qpolynomial_fold *
7059 isl_union_pw_qpolynomial_bound(
7060 __isl_take isl_union_pw_qpolynomial *upwqp,
7061 enum isl_fold type, int *tight);
7063 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7064 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7065 is the returned bound is known be tight, i.e., for each value
7066 of the parameters there is at least
7067 one element in the domain that reaches the bound.
7068 If the domain of C<pwqp> is not wrapping, then the bound is computed
7069 over all elements in that domain and the result has a purely parametric
7070 domain. If the domain of C<pwqp> is wrapping, then the bound is
7071 computed over the range of the wrapped relation. The domain of the
7072 wrapped relation becomes the domain of the result.
7074 =head2 Parametric Vertex Enumeration
7076 The parametric vertex enumeration described in this section
7077 is mainly intended to be used internally and by the C<barvinok>
7080 #include <isl/vertices.h>
7081 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7082 __isl_keep isl_basic_set *bset);
7084 The function C<isl_basic_set_compute_vertices> performs the
7085 actual computation of the parametric vertices and the chamber
7086 decomposition and store the result in an C<isl_vertices> object.
7087 This information can be queried by either iterating over all
7088 the vertices or iterating over all the chambers or cells
7089 and then iterating over all vertices that are active on the chamber.
7091 int isl_vertices_foreach_vertex(
7092 __isl_keep isl_vertices *vertices,
7093 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7096 int isl_vertices_foreach_cell(
7097 __isl_keep isl_vertices *vertices,
7098 int (*fn)(__isl_take isl_cell *cell, void *user),
7100 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7101 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7104 Other operations that can be performed on an C<isl_vertices> object are
7107 int isl_vertices_get_n_vertices(
7108 __isl_keep isl_vertices *vertices);
7109 void isl_vertices_free(__isl_take isl_vertices *vertices);
7111 Vertices can be inspected and destroyed using the following functions.
7113 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7114 __isl_give isl_basic_set *isl_vertex_get_domain(
7115 __isl_keep isl_vertex *vertex);
7116 __isl_give isl_multi_aff *isl_vertex_get_expr(
7117 __isl_keep isl_vertex *vertex);
7118 void isl_vertex_free(__isl_take isl_vertex *vertex);
7120 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7121 describing the vertex in terms of the parameters,
7122 while C<isl_vertex_get_domain> returns the activity domain
7125 Chambers can be inspected and destroyed using the following functions.
7127 __isl_give isl_basic_set *isl_cell_get_domain(
7128 __isl_keep isl_cell *cell);
7129 void isl_cell_free(__isl_take isl_cell *cell);
7131 =head1 Polyhedral Compilation Library
7133 This section collects functionality in C<isl> that has been specifically
7134 designed for use during polyhedral compilation.
7136 =head2 Dependence Analysis
7138 C<isl> contains specialized functionality for performing
7139 array dataflow analysis. That is, given a I<sink> access relation
7140 and a collection of possible I<source> access relations,
7141 C<isl> can compute relations that describe
7142 for each iteration of the sink access, which iteration
7143 of which of the source access relations was the last
7144 to access the same data element before the given iteration
7146 The resulting dependence relations map source iterations
7147 to the corresponding sink iterations.
7148 To compute standard flow dependences, the sink should be
7149 a read, while the sources should be writes.
7150 If any of the source accesses are marked as being I<may>
7151 accesses, then there will be a dependence from the last
7152 I<must> access B<and> from any I<may> access that follows
7153 this last I<must> access.
7154 In particular, if I<all> sources are I<may> accesses,
7155 then memory based dependence analysis is performed.
7156 If, on the other hand, all sources are I<must> accesses,
7157 then value based dependence analysis is performed.
7159 #include <isl/flow.h>
7161 typedef int (*isl_access_level_before)(void *first, void *second);
7163 __isl_give isl_access_info *isl_access_info_alloc(
7164 __isl_take isl_map *sink,
7165 void *sink_user, isl_access_level_before fn,
7167 __isl_give isl_access_info *isl_access_info_add_source(
7168 __isl_take isl_access_info *acc,
7169 __isl_take isl_map *source, int must,
7171 __isl_null isl_access_info *isl_access_info_free(
7172 __isl_take isl_access_info *acc);
7174 __isl_give isl_flow *isl_access_info_compute_flow(
7175 __isl_take isl_access_info *acc);
7177 int isl_flow_foreach(__isl_keep isl_flow *deps,
7178 int (*fn)(__isl_take isl_map *dep, int must,
7179 void *dep_user, void *user),
7181 __isl_give isl_map *isl_flow_get_no_source(
7182 __isl_keep isl_flow *deps, int must);
7183 void isl_flow_free(__isl_take isl_flow *deps);
7185 The function C<isl_access_info_compute_flow> performs the actual
7186 dependence analysis. The other functions are used to construct
7187 the input for this function or to read off the output.
7189 The input is collected in an C<isl_access_info>, which can
7190 be created through a call to C<isl_access_info_alloc>.
7191 The arguments to this functions are the sink access relation
7192 C<sink>, a token C<sink_user> used to identify the sink
7193 access to the user, a callback function for specifying the
7194 relative order of source and sink accesses, and the number
7195 of source access relations that will be added.
7196 The callback function has type C<int (*)(void *first, void *second)>.
7197 The function is called with two user supplied tokens identifying
7198 either a source or the sink and it should return the shared nesting
7199 level and the relative order of the two accesses.
7200 In particular, let I<n> be the number of loops shared by
7201 the two accesses. If C<first> precedes C<second> textually,
7202 then the function should return I<2 * n + 1>; otherwise,
7203 it should return I<2 * n>.
7204 The sources can be added to the C<isl_access_info> by performing
7205 (at most) C<max_source> calls to C<isl_access_info_add_source>.
7206 C<must> indicates whether the source is a I<must> access
7207 or a I<may> access. Note that a multi-valued access relation
7208 should only be marked I<must> if every iteration in the domain
7209 of the relation accesses I<all> elements in its image.
7210 The C<source_user> token is again used to identify
7211 the source access. The range of the source access relation
7212 C<source> should have the same dimension as the range
7213 of the sink access relation.
7214 The C<isl_access_info_free> function should usually not be
7215 called explicitly, because it is called implicitly by
7216 C<isl_access_info_compute_flow>.
7218 The result of the dependence analysis is collected in an
7219 C<isl_flow>. There may be elements of
7220 the sink access for which no preceding source access could be
7221 found or for which all preceding sources are I<may> accesses.
7222 The relations containing these elements can be obtained through
7223 calls to C<isl_flow_get_no_source>, the first with C<must> set
7224 and the second with C<must> unset.
7225 In the case of standard flow dependence analysis,
7226 with the sink a read and the sources I<must> writes,
7227 the first relation corresponds to the reads from uninitialized
7228 array elements and the second relation is empty.
7229 The actual flow dependences can be extracted using
7230 C<isl_flow_foreach>. This function will call the user-specified
7231 callback function C<fn> for each B<non-empty> dependence between
7232 a source and the sink. The callback function is called
7233 with four arguments, the actual flow dependence relation
7234 mapping source iterations to sink iterations, a boolean that
7235 indicates whether it is a I<must> or I<may> dependence, a token
7236 identifying the source and an additional C<void *> with value
7237 equal to the third argument of the C<isl_flow_foreach> call.
7238 A dependence is marked I<must> if it originates from a I<must>
7239 source and if it is not followed by any I<may> sources.
7241 After finishing with an C<isl_flow>, the user should call
7242 C<isl_flow_free> to free all associated memory.
7244 A higher-level interface to dependence analysis is provided
7245 by the following function.
7247 #include <isl/flow.h>
7249 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
7250 __isl_take isl_union_map *must_source,
7251 __isl_take isl_union_map *may_source,
7252 __isl_take isl_union_map *schedule,
7253 __isl_give isl_union_map **must_dep,
7254 __isl_give isl_union_map **may_dep,
7255 __isl_give isl_union_map **must_no_source,
7256 __isl_give isl_union_map **may_no_source);
7258 The arrays are identified by the tuple names of the ranges
7259 of the accesses. The iteration domains by the tuple names
7260 of the domains of the accesses and of the schedule.
7261 The relative order of the iteration domains is given by the
7262 schedule. The relations returned through C<must_no_source>
7263 and C<may_no_source> are subsets of C<sink>.
7264 Any of C<must_dep>, C<may_dep>, C<must_no_source>
7265 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
7266 any of the other arguments is treated as an error.
7268 =head3 Interaction with Dependence Analysis
7270 During the dependence analysis, we frequently need to perform
7271 the following operation. Given a relation between sink iterations
7272 and potential source iterations from a particular source domain,
7273 what is the last potential source iteration corresponding to each
7274 sink iteration. It can sometimes be convenient to adjust
7275 the set of potential source iterations before or after each such operation.
7276 The prototypical example is fuzzy array dataflow analysis,
7277 where we need to analyze if, based on data-dependent constraints,
7278 the sink iteration can ever be executed without one or more of
7279 the corresponding potential source iterations being executed.
7280 If so, we can introduce extra parameters and select an unknown
7281 but fixed source iteration from the potential source iterations.
7282 To be able to perform such manipulations, C<isl> provides the following
7285 #include <isl/flow.h>
7287 typedef __isl_give isl_restriction *(*isl_access_restrict)(
7288 __isl_keep isl_map *source_map,
7289 __isl_keep isl_set *sink, void *source_user,
7291 __isl_give isl_access_info *isl_access_info_set_restrict(
7292 __isl_take isl_access_info *acc,
7293 isl_access_restrict fn, void *user);
7295 The function C<isl_access_info_set_restrict> should be called
7296 before calling C<isl_access_info_compute_flow> and registers a callback function
7297 that will be called any time C<isl> is about to compute the last
7298 potential source. The first argument is the (reverse) proto-dependence,
7299 mapping sink iterations to potential source iterations.
7300 The second argument represents the sink iterations for which
7301 we want to compute the last source iteration.
7302 The third argument is the token corresponding to the source
7303 and the final argument is the token passed to C<isl_access_info_set_restrict>.
7304 The callback is expected to return a restriction on either the input or
7305 the output of the operation computing the last potential source.
7306 If the input needs to be restricted then restrictions are needed
7307 for both the source and the sink iterations. The sink iterations
7308 and the potential source iterations will be intersected with these sets.
7309 If the output needs to be restricted then only a restriction on the source
7310 iterations is required.
7311 If any error occurs, the callback should return C<NULL>.
7312 An C<isl_restriction> object can be created, freed and inspected
7313 using the following functions.
7315 #include <isl/flow.h>
7317 __isl_give isl_restriction *isl_restriction_input(
7318 __isl_take isl_set *source_restr,
7319 __isl_take isl_set *sink_restr);
7320 __isl_give isl_restriction *isl_restriction_output(
7321 __isl_take isl_set *source_restr);
7322 __isl_give isl_restriction *isl_restriction_none(
7323 __isl_take isl_map *source_map);
7324 __isl_give isl_restriction *isl_restriction_empty(
7325 __isl_take isl_map *source_map);
7326 __isl_null isl_restriction *isl_restriction_free(
7327 __isl_take isl_restriction *restr);
7329 C<isl_restriction_none> and C<isl_restriction_empty> are special
7330 cases of C<isl_restriction_input>. C<isl_restriction_none>
7331 is essentially equivalent to
7333 isl_restriction_input(isl_set_universe(
7334 isl_space_range(isl_map_get_space(source_map))),
7336 isl_space_domain(isl_map_get_space(source_map))));
7338 whereas C<isl_restriction_empty> is essentially equivalent to
7340 isl_restriction_input(isl_set_empty(
7341 isl_space_range(isl_map_get_space(source_map))),
7343 isl_space_domain(isl_map_get_space(source_map))));
7347 B<The functionality described in this section is fairly new
7348 and may be subject to change.>
7350 #include <isl/schedule.h>
7351 __isl_give isl_schedule *
7352 isl_schedule_constraints_compute_schedule(
7353 __isl_take isl_schedule_constraints *sc);
7354 __isl_null isl_schedule *isl_schedule_free(
7355 __isl_take isl_schedule *sched);
7357 The function C<isl_schedule_constraints_compute_schedule> can be
7358 used to compute a schedule that satisfies the given schedule constraints.
7359 These schedule constraints include the iteration domain for which
7360 a schedule should be computed and dependences between pairs of
7361 iterations. In particular, these dependences include
7362 I<validity> dependences and I<proximity> dependences.
7363 By default, the algorithm used to construct the schedule is similar
7364 to that of C<Pluto>.
7365 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
7367 The generated schedule respects all validity dependences.
7368 That is, all dependence distances over these dependences in the
7369 scheduled space are lexicographically positive.
7370 The default algorithm tries to ensure that the dependence distances
7371 over coincidence constraints are zero and to minimize the
7372 dependence distances over proximity dependences.
7373 Moreover, it tries to obtain sequences (bands) of schedule dimensions
7374 for groups of domains where the dependence distances over validity
7375 dependences have only non-negative values.
7376 When using Feautrier's algorithm, the coincidence and proximity constraints
7377 are only taken into account during the extension to a
7378 full-dimensional schedule.
7380 An C<isl_schedule_constraints> object can be constructed
7381 and manipulated using the following functions.
7383 #include <isl/schedule.h>
7384 __isl_give isl_schedule_constraints *
7385 isl_schedule_constraints_copy(
7386 __isl_keep isl_schedule_constraints *sc);
7387 __isl_give isl_schedule_constraints *
7388 isl_schedule_constraints_on_domain(
7389 __isl_take isl_union_set *domain);
7390 __isl_give isl_schedule_constraints *
7391 isl_schedule_constraints_set_validity(
7392 __isl_take isl_schedule_constraints *sc,
7393 __isl_take isl_union_map *validity);
7394 __isl_give isl_schedule_constraints *
7395 isl_schedule_constraints_set_coincidence(
7396 __isl_take isl_schedule_constraints *sc,
7397 __isl_take isl_union_map *coincidence);
7398 __isl_give isl_schedule_constraints *
7399 isl_schedule_constraints_set_proximity(
7400 __isl_take isl_schedule_constraints *sc,
7401 __isl_take isl_union_map *proximity);
7402 __isl_give isl_schedule_constraints *
7403 isl_schedule_constraints_set_conditional_validity(
7404 __isl_take isl_schedule_constraints *sc,
7405 __isl_take isl_union_map *condition,
7406 __isl_take isl_union_map *validity);
7407 __isl_null isl_schedule_constraints *
7408 isl_schedule_constraints_free(
7409 __isl_take isl_schedule_constraints *sc);
7411 The initial C<isl_schedule_constraints> object created by
7412 C<isl_schedule_constraints_on_domain> does not impose any constraints.
7413 That is, it has an empty set of dependences.
7414 The function C<isl_schedule_constraints_set_validity> replaces the
7415 validity dependences, mapping domain elements I<i> to domain
7416 elements that should be scheduled after I<i>.
7417 The function C<isl_schedule_constraints_set_coincidence> replaces the
7418 coincidence dependences, mapping domain elements I<i> to domain
7419 elements that should be scheduled together with I<I>, if possible.
7420 The function C<isl_schedule_constraints_set_proximity> replaces the
7421 proximity dependences, mapping domain elements I<i> to domain
7422 elements that should be scheduled either before I<I>
7423 or as early as possible after I<i>.
7425 The function C<isl_schedule_constraints_set_conditional_validity>
7426 replaces the conditional validity constraints.
7427 A conditional validity constraint is only imposed when any of the corresponding
7428 conditions is satisfied, i.e., when any of them is non-zero.
7429 That is, the scheduler ensures that within each band if the dependence
7430 distances over the condition constraints are not all zero
7431 then all corresponding conditional validity constraints are respected.
7432 A conditional validity constraint corresponds to a condition
7433 if the two are adjacent, i.e., if the domain of one relation intersect
7434 the range of the other relation.
7435 The typical use case of conditional validity constraints is
7436 to allow order constraints between live ranges to be violated
7437 as long as the live ranges themselves are local to the band.
7438 To allow more fine-grained control over which conditions correspond
7439 to which conditional validity constraints, the domains and ranges
7440 of these relations may include I<tags>. That is, the domains and
7441 ranges of those relation may themselves be wrapped relations
7442 where the iteration domain appears in the domain of those wrapped relations
7443 and the range of the wrapped relations can be arbitrarily chosen
7444 by the user. Conditions and conditional validity constraints are only
7445 considered adjacent to each other if the entire wrapped relation matches.
7446 In particular, a relation with a tag will never be considered adjacent
7447 to a relation without a tag.
7449 The following function computes a schedule directly from
7450 an iteration domain and validity and proximity dependences
7451 and is implemented in terms of the functions described above.
7452 The use of C<isl_union_set_compute_schedule> is discouraged.
7454 #include <isl/schedule.h>
7455 __isl_give isl_schedule *isl_union_set_compute_schedule(
7456 __isl_take isl_union_set *domain,
7457 __isl_take isl_union_map *validity,
7458 __isl_take isl_union_map *proximity);
7460 A mapping from the domains to the scheduled space can be obtained
7461 from an C<isl_schedule> using the following function.
7463 __isl_give isl_union_map *isl_schedule_get_map(
7464 __isl_keep isl_schedule *sched);
7466 A representation of the schedule can be printed using
7468 __isl_give isl_printer *isl_printer_print_schedule(
7469 __isl_take isl_printer *p,
7470 __isl_keep isl_schedule *schedule);
7472 A representation of the schedule as a forest of bands can be obtained
7473 using the following function.
7475 __isl_give isl_band_list *isl_schedule_get_band_forest(
7476 __isl_keep isl_schedule *schedule);
7478 The individual bands can be visited in depth-first post-order
7479 using the following function.
7481 #include <isl/schedule.h>
7482 int isl_schedule_foreach_band(
7483 __isl_keep isl_schedule *sched,
7484 int (*fn)(__isl_keep isl_band *band, void *user),
7487 The list can be manipulated as explained in L<"Lists">.
7488 The bands inside the list can be copied and freed using the following
7491 #include <isl/band.h>
7492 __isl_give isl_band *isl_band_copy(
7493 __isl_keep isl_band *band);
7494 __isl_null isl_band *isl_band_free(
7495 __isl_take isl_band *band);
7497 Each band contains zero or more scheduling dimensions.
7498 These are referred to as the members of the band.
7499 The section of the schedule that corresponds to the band is
7500 referred to as the partial schedule of the band.
7501 For those nodes that participate in a band, the outer scheduling
7502 dimensions form the prefix schedule, while the inner scheduling
7503 dimensions form the suffix schedule.
7504 That is, if we take a cut of the band forest, then the union of
7505 the concatenations of the prefix, partial and suffix schedules of
7506 each band in the cut is equal to the entire schedule (modulo
7507 some possible padding at the end with zero scheduling dimensions).
7508 The properties of a band can be inspected using the following functions.
7510 #include <isl/band.h>
7511 int isl_band_has_children(__isl_keep isl_band *band);
7512 __isl_give isl_band_list *isl_band_get_children(
7513 __isl_keep isl_band *band);
7515 __isl_give isl_union_map *isl_band_get_prefix_schedule(
7516 __isl_keep isl_band *band);
7517 __isl_give isl_union_map *isl_band_get_partial_schedule(
7518 __isl_keep isl_band *band);
7519 __isl_give isl_union_map *isl_band_get_suffix_schedule(
7520 __isl_keep isl_band *band);
7522 int isl_band_n_member(__isl_keep isl_band *band);
7523 int isl_band_member_is_coincident(
7524 __isl_keep isl_band *band, int pos);
7526 int isl_band_list_foreach_band(
7527 __isl_keep isl_band_list *list,
7528 int (*fn)(__isl_keep isl_band *band, void *user),
7531 Note that a scheduling dimension is considered to be ``coincident''
7532 if it satisfies the coincidence constraints within its band.
7533 That is, if the dependence distances of the coincidence
7534 constraints are all zero in that direction (for fixed
7535 iterations of outer bands).
7536 Like C<isl_schedule_foreach_band>,
7537 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
7538 in depth-first post-order.
7540 A band can be tiled using the following function.
7542 #include <isl/band.h>
7543 int isl_band_tile(__isl_keep isl_band *band,
7544 __isl_take isl_vec *sizes);
7546 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
7548 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
7549 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
7551 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
7553 The C<isl_band_tile> function tiles the band using the given tile sizes
7554 inside its schedule.
7555 A new child band is created to represent the point loops and it is
7556 inserted between the modified band and its children.
7557 The C<tile_scale_tile_loops> option specifies whether the tile
7558 loops iterators should be scaled by the tile sizes.
7559 If the C<tile_shift_point_loops> option is set, then the point loops
7560 are shifted to start at zero.
7562 A band can be split into two nested bands using the following function.
7564 int isl_band_split(__isl_keep isl_band *band, int pos);
7566 The resulting outer band contains the first C<pos> dimensions of C<band>
7567 while the inner band contains the remaining dimensions.
7569 A representation of the band can be printed using
7571 #include <isl/band.h>
7572 __isl_give isl_printer *isl_printer_print_band(
7573 __isl_take isl_printer *p,
7574 __isl_keep isl_band *band);
7578 #include <isl/schedule.h>
7579 int isl_options_set_schedule_max_coefficient(
7580 isl_ctx *ctx, int val);
7581 int isl_options_get_schedule_max_coefficient(
7583 int isl_options_set_schedule_max_constant_term(
7584 isl_ctx *ctx, int val);
7585 int isl_options_get_schedule_max_constant_term(
7587 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
7588 int isl_options_get_schedule_fuse(isl_ctx *ctx);
7589 int isl_options_set_schedule_maximize_band_depth(
7590 isl_ctx *ctx, int val);
7591 int isl_options_get_schedule_maximize_band_depth(
7593 int isl_options_set_schedule_outer_coincidence(
7594 isl_ctx *ctx, int val);
7595 int isl_options_get_schedule_outer_coincidence(
7597 int isl_options_set_schedule_split_scaled(
7598 isl_ctx *ctx, int val);
7599 int isl_options_get_schedule_split_scaled(
7601 int isl_options_set_schedule_algorithm(
7602 isl_ctx *ctx, int val);
7603 int isl_options_get_schedule_algorithm(
7605 int isl_options_set_schedule_separate_components(
7606 isl_ctx *ctx, int val);
7607 int isl_options_get_schedule_separate_components(
7612 =item * schedule_max_coefficient
7614 This option enforces that the coefficients for variable and parameter
7615 dimensions in the calculated schedule are not larger than the specified value.
7616 This option can significantly increase the speed of the scheduling calculation
7617 and may also prevent fusing of unrelated dimensions. A value of -1 means that
7618 this option does not introduce bounds on the variable or parameter
7621 =item * schedule_max_constant_term
7623 This option enforces that the constant coefficients in the calculated schedule
7624 are not larger than the maximal constant term. This option can significantly
7625 increase the speed of the scheduling calculation and may also prevent fusing of
7626 unrelated dimensions. A value of -1 means that this option does not introduce
7627 bounds on the constant coefficients.
7629 =item * schedule_fuse
7631 This option controls the level of fusion.
7632 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
7633 resulting schedule will be distributed as much as possible.
7634 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
7635 try to fuse loops in the resulting schedule.
7637 =item * schedule_maximize_band_depth
7639 If this option is set, we do not split bands at the point
7640 where we detect splitting is necessary. Instead, we
7641 backtrack and split bands as early as possible. This
7642 reduces the number of splits and maximizes the width of
7643 the bands. Wider bands give more possibilities for tiling.
7644 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
7645 then bands will be split as early as possible, even if there is no need.
7646 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
7648 =item * schedule_outer_coincidence
7650 If this option is set, then we try to construct schedules
7651 where the outermost scheduling dimension in each band
7652 satisfies the coincidence constraints.
7654 =item * schedule_split_scaled
7656 If this option is set, then we try to construct schedules in which the
7657 constant term is split off from the linear part if the linear parts of
7658 the scheduling rows for all nodes in the graphs have a common non-trivial
7660 The constant term is then placed in a separate band and the linear
7663 =item * schedule_algorithm
7665 Selects the scheduling algorithm to be used.
7666 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
7667 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
7669 =item * schedule_separate_components
7671 If at any point the dependence graph contains any (weakly connected) components,
7672 then these components are scheduled separately.
7673 If this option is not set, then some iterations of the domains
7674 in these components may be scheduled together.
7675 If this option is set, then the components are given consecutive
7680 =head2 AST Generation
7682 This section describes the C<isl> functionality for generating
7683 ASTs that visit all the elements
7684 in a domain in an order specified by a schedule.
7685 In particular, given a C<isl_union_map>, an AST is generated
7686 that visits all the elements in the domain of the C<isl_union_map>
7687 according to the lexicographic order of the corresponding image
7688 element(s). If the range of the C<isl_union_map> consists of
7689 elements in more than one space, then each of these spaces is handled
7690 separately in an arbitrary order.
7691 It should be noted that the image elements only specify the I<order>
7692 in which the corresponding domain elements should be visited.
7693 No direct relation between the image elements and the loop iterators
7694 in the generated AST should be assumed.
7696 Each AST is generated within a build. The initial build
7697 simply specifies the constraints on the parameters (if any)
7698 and can be created, inspected, copied and freed using the following functions.
7700 #include <isl/ast_build.h>
7701 __isl_give isl_ast_build *isl_ast_build_from_context(
7702 __isl_take isl_set *set);
7703 __isl_give isl_ast_build *isl_ast_build_copy(
7704 __isl_keep isl_ast_build *build);
7705 __isl_null isl_ast_build *isl_ast_build_free(
7706 __isl_take isl_ast_build *build);
7708 The C<set> argument is usually a parameter set with zero or more parameters.
7709 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
7710 and L</"Fine-grained Control over AST Generation">.
7711 Finally, the AST itself can be constructed using the following
7714 #include <isl/ast_build.h>
7715 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
7716 __isl_keep isl_ast_build *build,
7717 __isl_take isl_union_map *schedule);
7719 =head3 Inspecting the AST
7721 The basic properties of an AST node can be obtained as follows.
7723 #include <isl/ast.h>
7724 enum isl_ast_node_type isl_ast_node_get_type(
7725 __isl_keep isl_ast_node *node);
7727 The type of an AST node is one of
7728 C<isl_ast_node_for>,
7730 C<isl_ast_node_block> or
7731 C<isl_ast_node_user>.
7732 An C<isl_ast_node_for> represents a for node.
7733 An C<isl_ast_node_if> represents an if node.
7734 An C<isl_ast_node_block> represents a compound node.
7735 An C<isl_ast_node_user> represents an expression statement.
7736 An expression statement typically corresponds to a domain element, i.e.,
7737 one of the elements that is visited by the AST.
7739 Each type of node has its own additional properties.
7741 #include <isl/ast.h>
7742 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7743 __isl_keep isl_ast_node *node);
7744 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7745 __isl_keep isl_ast_node *node);
7746 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7747 __isl_keep isl_ast_node *node);
7748 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7749 __isl_keep isl_ast_node *node);
7750 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7751 __isl_keep isl_ast_node *node);
7752 int isl_ast_node_for_is_degenerate(
7753 __isl_keep isl_ast_node *node);
7755 An C<isl_ast_for> is considered degenerate if it is known to execute
7758 #include <isl/ast.h>
7759 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7760 __isl_keep isl_ast_node *node);
7761 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7762 __isl_keep isl_ast_node *node);
7763 int isl_ast_node_if_has_else(
7764 __isl_keep isl_ast_node *node);
7765 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7766 __isl_keep isl_ast_node *node);
7768 __isl_give isl_ast_node_list *
7769 isl_ast_node_block_get_children(
7770 __isl_keep isl_ast_node *node);
7772 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7773 __isl_keep isl_ast_node *node);
7775 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7776 the following functions.
7778 #include <isl/ast.h>
7779 enum isl_ast_expr_type isl_ast_expr_get_type(
7780 __isl_keep isl_ast_expr *expr);
7782 The type of an AST expression is one of
7784 C<isl_ast_expr_id> or
7785 C<isl_ast_expr_int>.
7786 An C<isl_ast_expr_op> represents the result of an operation.
7787 An C<isl_ast_expr_id> represents an identifier.
7788 An C<isl_ast_expr_int> represents an integer value.
7790 Each type of expression has its own additional properties.
7792 #include <isl/ast.h>
7793 enum isl_ast_op_type isl_ast_expr_get_op_type(
7794 __isl_keep isl_ast_expr *expr);
7795 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7796 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7797 __isl_keep isl_ast_expr *expr, int pos);
7798 int isl_ast_node_foreach_ast_op_type(
7799 __isl_keep isl_ast_node *node,
7800 int (*fn)(enum isl_ast_op_type type, void *user),
7803 C<isl_ast_expr_get_op_type> returns the type of the operation
7804 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7805 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7807 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7808 C<isl_ast_op_type> that appears in C<node>.
7809 The operation type is one of the following.
7813 =item C<isl_ast_op_and>
7815 Logical I<and> of two arguments.
7816 Both arguments can be evaluated.
7818 =item C<isl_ast_op_and_then>
7820 Logical I<and> of two arguments.
7821 The second argument can only be evaluated if the first evaluates to true.
7823 =item C<isl_ast_op_or>
7825 Logical I<or> of two arguments.
7826 Both arguments can be evaluated.
7828 =item C<isl_ast_op_or_else>
7830 Logical I<or> of two arguments.
7831 The second argument can only be evaluated if the first evaluates to false.
7833 =item C<isl_ast_op_max>
7835 Maximum of two or more arguments.
7837 =item C<isl_ast_op_min>
7839 Minimum of two or more arguments.
7841 =item C<isl_ast_op_minus>
7845 =item C<isl_ast_op_add>
7847 Sum of two arguments.
7849 =item C<isl_ast_op_sub>
7851 Difference of two arguments.
7853 =item C<isl_ast_op_mul>
7855 Product of two arguments.
7857 =item C<isl_ast_op_div>
7859 Exact division. That is, the result is known to be an integer.
7861 =item C<isl_ast_op_fdiv_q>
7863 Result of integer division, rounded towards negative
7866 =item C<isl_ast_op_pdiv_q>
7868 Result of integer division, where dividend is known to be non-negative.
7870 =item C<isl_ast_op_pdiv_r>
7872 Remainder of integer division, where dividend is known to be non-negative.
7874 =item C<isl_ast_op_zdiv_r>
7876 Equal to zero iff the remainder on integer division is zero.
7878 =item C<isl_ast_op_cond>
7880 Conditional operator defined on three arguments.
7881 If the first argument evaluates to true, then the result
7882 is equal to the second argument. Otherwise, the result
7883 is equal to the third argument.
7884 The second and third argument may only be evaluated if
7885 the first argument evaluates to true and false, respectively.
7886 Corresponds to C<a ? b : c> in C.
7888 =item C<isl_ast_op_select>
7890 Conditional operator defined on three arguments.
7891 If the first argument evaluates to true, then the result
7892 is equal to the second argument. Otherwise, the result
7893 is equal to the third argument.
7894 The second and third argument may be evaluated independently
7895 of the value of the first argument.
7896 Corresponds to C<a * b + (1 - a) * c> in C.
7898 =item C<isl_ast_op_eq>
7902 =item C<isl_ast_op_le>
7904 Less than or equal relation.
7906 =item C<isl_ast_op_lt>
7910 =item C<isl_ast_op_ge>
7912 Greater than or equal relation.
7914 =item C<isl_ast_op_gt>
7916 Greater than relation.
7918 =item C<isl_ast_op_call>
7921 The number of arguments of the C<isl_ast_expr> is one more than
7922 the number of arguments in the function call, the first argument
7923 representing the function being called.
7925 =item C<isl_ast_op_access>
7928 The number of arguments of the C<isl_ast_expr> is one more than
7929 the number of index expressions in the array access, the first argument
7930 representing the array being accessed.
7932 =item C<isl_ast_op_member>
7935 This operation has two arguments, a structure and the name of
7936 the member of the structure being accessed.
7940 #include <isl/ast.h>
7941 __isl_give isl_id *isl_ast_expr_get_id(
7942 __isl_keep isl_ast_expr *expr);
7944 Return the identifier represented by the AST expression.
7946 #include <isl/ast.h>
7947 __isl_give isl_val *isl_ast_expr_get_val(
7948 __isl_keep isl_ast_expr *expr);
7950 Return the integer represented by the AST expression.
7952 =head3 Properties of ASTs
7954 #include <isl/ast.h>
7955 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7956 __isl_keep isl_ast_expr *expr2);
7958 Check if two C<isl_ast_expr>s are equal to each other.
7960 =head3 Manipulating and printing the AST
7962 AST nodes can be copied and freed using the following functions.
7964 #include <isl/ast.h>
7965 __isl_give isl_ast_node *isl_ast_node_copy(
7966 __isl_keep isl_ast_node *node);
7967 __isl_null isl_ast_node *isl_ast_node_free(
7968 __isl_take isl_ast_node *node);
7970 AST expressions can be copied and freed using the following functions.
7972 #include <isl/ast.h>
7973 __isl_give isl_ast_expr *isl_ast_expr_copy(
7974 __isl_keep isl_ast_expr *expr);
7975 __isl_null isl_ast_expr *isl_ast_expr_free(
7976 __isl_take isl_ast_expr *expr);
7978 New AST expressions can be created either directly or within
7979 the context of an C<isl_ast_build>.
7981 #include <isl/ast.h>
7982 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7983 __isl_take isl_val *v);
7984 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7985 __isl_take isl_id *id);
7986 __isl_give isl_ast_expr *isl_ast_expr_neg(
7987 __isl_take isl_ast_expr *expr);
7988 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7989 __isl_take isl_ast_expr *expr);
7990 __isl_give isl_ast_expr *isl_ast_expr_add(
7991 __isl_take isl_ast_expr *expr1,
7992 __isl_take isl_ast_expr *expr2);
7993 __isl_give isl_ast_expr *isl_ast_expr_sub(
7994 __isl_take isl_ast_expr *expr1,
7995 __isl_take isl_ast_expr *expr2);
7996 __isl_give isl_ast_expr *isl_ast_expr_mul(
7997 __isl_take isl_ast_expr *expr1,
7998 __isl_take isl_ast_expr *expr2);
7999 __isl_give isl_ast_expr *isl_ast_expr_div(
8000 __isl_take isl_ast_expr *expr1,
8001 __isl_take isl_ast_expr *expr2);
8002 __isl_give isl_ast_expr *isl_ast_expr_and(
8003 __isl_take isl_ast_expr *expr1,
8004 __isl_take isl_ast_expr *expr2)
8005 __isl_give isl_ast_expr *isl_ast_expr_or(
8006 __isl_take isl_ast_expr *expr1,
8007 __isl_take isl_ast_expr *expr2)
8008 __isl_give isl_ast_expr *isl_ast_expr_eq(
8009 __isl_take isl_ast_expr *expr1,
8010 __isl_take isl_ast_expr *expr2);
8011 __isl_give isl_ast_expr *isl_ast_expr_le(
8012 __isl_take isl_ast_expr *expr1,
8013 __isl_take isl_ast_expr *expr2);
8014 __isl_give isl_ast_expr *isl_ast_expr_lt(
8015 __isl_take isl_ast_expr *expr1,
8016 __isl_take isl_ast_expr *expr2);
8017 __isl_give isl_ast_expr *isl_ast_expr_ge(
8018 __isl_take isl_ast_expr *expr1,
8019 __isl_take isl_ast_expr *expr2);
8020 __isl_give isl_ast_expr *isl_ast_expr_gt(
8021 __isl_take isl_ast_expr *expr1,
8022 __isl_take isl_ast_expr *expr2);
8023 __isl_give isl_ast_expr *isl_ast_expr_access(
8024 __isl_take isl_ast_expr *array,
8025 __isl_take isl_ast_expr_list *indices);
8027 The function C<isl_ast_expr_address_of> can be applied to an
8028 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
8029 to represent the address of the C<isl_ast_expr_access>.
8031 #include <isl/ast_build.h>
8032 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
8033 __isl_keep isl_ast_build *build,
8034 __isl_take isl_pw_aff *pa);
8035 __isl_give isl_ast_expr *
8036 isl_ast_build_access_from_pw_multi_aff(
8037 __isl_keep isl_ast_build *build,
8038 __isl_take isl_pw_multi_aff *pma);
8039 __isl_give isl_ast_expr *
8040 isl_ast_build_access_from_multi_pw_aff(
8041 __isl_keep isl_ast_build *build,
8042 __isl_take isl_multi_pw_aff *mpa);
8043 __isl_give isl_ast_expr *
8044 isl_ast_build_call_from_pw_multi_aff(
8045 __isl_keep isl_ast_build *build,
8046 __isl_take isl_pw_multi_aff *pma);
8047 __isl_give isl_ast_expr *
8048 isl_ast_build_call_from_multi_pw_aff(
8049 __isl_keep isl_ast_build *build,
8050 __isl_take isl_multi_pw_aff *mpa);
8052 The domains of C<pa>, C<mpa> and C<pma> should correspond
8053 to the schedule space of C<build>.
8054 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
8055 the function being called.
8056 If the accessed space is a nested relation, then it is taken
8057 to represent an access of the member specified by the range
8058 of this nested relation of the structure specified by the domain
8059 of the nested relation.
8061 The following functions can be used to modify an C<isl_ast_expr>.
8063 #include <isl/ast.h>
8064 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
8065 __isl_take isl_ast_expr *expr, int pos,
8066 __isl_take isl_ast_expr *arg);
8068 Replace the argument of C<expr> at position C<pos> by C<arg>.
8070 #include <isl/ast.h>
8071 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
8072 __isl_take isl_ast_expr *expr,
8073 __isl_take isl_id_to_ast_expr *id2expr);
8075 The function C<isl_ast_expr_substitute_ids> replaces the
8076 subexpressions of C<expr> of type C<isl_ast_expr_id>
8077 by the corresponding expression in C<id2expr>, if there is any.
8080 User specified data can be attached to an C<isl_ast_node> and obtained
8081 from the same C<isl_ast_node> using the following functions.
8083 #include <isl/ast.h>
8084 __isl_give isl_ast_node *isl_ast_node_set_annotation(
8085 __isl_take isl_ast_node *node,
8086 __isl_take isl_id *annotation);
8087 __isl_give isl_id *isl_ast_node_get_annotation(
8088 __isl_keep isl_ast_node *node);
8090 Basic printing can be performed using the following functions.
8092 #include <isl/ast.h>
8093 __isl_give isl_printer *isl_printer_print_ast_expr(
8094 __isl_take isl_printer *p,
8095 __isl_keep isl_ast_expr *expr);
8096 __isl_give isl_printer *isl_printer_print_ast_node(
8097 __isl_take isl_printer *p,
8098 __isl_keep isl_ast_node *node);
8099 __isl_give char *isl_ast_expr_to_str(
8100 __isl_keep isl_ast_expr *expr);
8102 More advanced printing can be performed using the following functions.
8104 #include <isl/ast.h>
8105 __isl_give isl_printer *isl_ast_op_type_print_macro(
8106 enum isl_ast_op_type type,
8107 __isl_take isl_printer *p);
8108 __isl_give isl_printer *isl_ast_node_print_macros(
8109 __isl_keep isl_ast_node *node,
8110 __isl_take isl_printer *p);
8111 __isl_give isl_printer *isl_ast_node_print(
8112 __isl_keep isl_ast_node *node,
8113 __isl_take isl_printer *p,
8114 __isl_take isl_ast_print_options *options);
8115 __isl_give isl_printer *isl_ast_node_for_print(
8116 __isl_keep isl_ast_node *node,
8117 __isl_take isl_printer *p,
8118 __isl_take isl_ast_print_options *options);
8119 __isl_give isl_printer *isl_ast_node_if_print(
8120 __isl_keep isl_ast_node *node,
8121 __isl_take isl_printer *p,
8122 __isl_take isl_ast_print_options *options);
8124 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
8125 C<isl> may print out an AST that makes use of macros such
8126 as C<floord>, C<min> and C<max>.
8127 C<isl_ast_op_type_print_macro> prints out the macro
8128 corresponding to a specific C<isl_ast_op_type>.
8129 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
8130 for expressions where these macros would be used and prints
8131 out the required macro definitions.
8132 Essentially, C<isl_ast_node_print_macros> calls
8133 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
8134 as function argument.
8135 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
8136 C<isl_ast_node_if_print> print an C<isl_ast_node>
8137 in C<ISL_FORMAT_C>, but allow for some extra control
8138 through an C<isl_ast_print_options> object.
8139 This object can be created using the following functions.
8141 #include <isl/ast.h>
8142 __isl_give isl_ast_print_options *
8143 isl_ast_print_options_alloc(isl_ctx *ctx);
8144 __isl_give isl_ast_print_options *
8145 isl_ast_print_options_copy(
8146 __isl_keep isl_ast_print_options *options);
8147 __isl_null isl_ast_print_options *
8148 isl_ast_print_options_free(
8149 __isl_take isl_ast_print_options *options);
8151 __isl_give isl_ast_print_options *
8152 isl_ast_print_options_set_print_user(
8153 __isl_take isl_ast_print_options *options,
8154 __isl_give isl_printer *(*print_user)(
8155 __isl_take isl_printer *p,
8156 __isl_take isl_ast_print_options *options,
8157 __isl_keep isl_ast_node *node, void *user),
8159 __isl_give isl_ast_print_options *
8160 isl_ast_print_options_set_print_for(
8161 __isl_take isl_ast_print_options *options,
8162 __isl_give isl_printer *(*print_for)(
8163 __isl_take isl_printer *p,
8164 __isl_take isl_ast_print_options *options,
8165 __isl_keep isl_ast_node *node, void *user),
8168 The callback set by C<isl_ast_print_options_set_print_user>
8169 is called whenever a node of type C<isl_ast_node_user> needs to
8171 The callback set by C<isl_ast_print_options_set_print_for>
8172 is called whenever a node of type C<isl_ast_node_for> needs to
8174 Note that C<isl_ast_node_for_print> will I<not> call the
8175 callback set by C<isl_ast_print_options_set_print_for> on the node
8176 on which C<isl_ast_node_for_print> is called, but only on nested
8177 nodes of type C<isl_ast_node_for>. It is therefore safe to
8178 call C<isl_ast_node_for_print> from within the callback set by
8179 C<isl_ast_print_options_set_print_for>.
8181 The following option determines the type to be used for iterators
8182 while printing the AST.
8184 int isl_options_set_ast_iterator_type(
8185 isl_ctx *ctx, const char *val);
8186 const char *isl_options_get_ast_iterator_type(
8189 The AST printer only prints body nodes as blocks if these
8190 blocks cannot be safely omitted.
8191 For example, a C<for> node with one body node will not be
8192 surrounded with braces in C<ISL_FORMAT_C>.
8193 A block will always be printed by setting the following option.
8195 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
8197 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
8201 #include <isl/ast_build.h>
8202 int isl_options_set_ast_build_atomic_upper_bound(
8203 isl_ctx *ctx, int val);
8204 int isl_options_get_ast_build_atomic_upper_bound(
8206 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
8208 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
8209 int isl_options_set_ast_build_exploit_nested_bounds(
8210 isl_ctx *ctx, int val);
8211 int isl_options_get_ast_build_exploit_nested_bounds(
8213 int isl_options_set_ast_build_group_coscheduled(
8214 isl_ctx *ctx, int val);
8215 int isl_options_get_ast_build_group_coscheduled(
8217 int isl_options_set_ast_build_scale_strides(
8218 isl_ctx *ctx, int val);
8219 int isl_options_get_ast_build_scale_strides(
8221 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
8223 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
8224 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
8226 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
8230 =item * ast_build_atomic_upper_bound
8232 Generate loop upper bounds that consist of the current loop iterator,
8233 an operator and an expression not involving the iterator.
8234 If this option is not set, then the current loop iterator may appear
8235 several times in the upper bound.
8236 For example, when this option is turned off, AST generation
8239 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
8243 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
8246 When the option is turned on, the following AST is generated
8248 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
8251 =item * ast_build_prefer_pdiv
8253 If this option is turned off, then the AST generation will
8254 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
8255 operators, but no C<isl_ast_op_pdiv_q> or
8256 C<isl_ast_op_pdiv_r> operators.
8257 If this options is turned on, then C<isl> will try to convert
8258 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
8259 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
8261 =item * ast_build_exploit_nested_bounds
8263 Simplify conditions based on bounds of nested for loops.
8264 In particular, remove conditions that are implied by the fact
8265 that one or more nested loops have at least one iteration,
8266 meaning that the upper bound is at least as large as the lower bound.
8267 For example, when this option is turned off, AST generation
8270 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
8276 for (int c0 = 0; c0 <= N; c0 += 1)
8277 for (int c1 = 0; c1 <= M; c1 += 1)
8280 When the option is turned on, the following AST is generated
8282 for (int c0 = 0; c0 <= N; c0 += 1)
8283 for (int c1 = 0; c1 <= M; c1 += 1)
8286 =item * ast_build_group_coscheduled
8288 If two domain elements are assigned the same schedule point, then
8289 they may be executed in any order and they may even appear in different
8290 loops. If this options is set, then the AST generator will make
8291 sure that coscheduled domain elements do not appear in separate parts
8292 of the AST. This is useful in case of nested AST generation
8293 if the outer AST generation is given only part of a schedule
8294 and the inner AST generation should handle the domains that are
8295 coscheduled by this initial part of the schedule together.
8296 For example if an AST is generated for a schedule
8298 { A[i] -> [0]; B[i] -> [0] }
8300 then the C<isl_ast_build_set_create_leaf> callback described
8301 below may get called twice, once for each domain.
8302 Setting this option ensures that the callback is only called once
8303 on both domains together.
8305 =item * ast_build_separation_bounds
8307 This option specifies which bounds to use during separation.
8308 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
8309 then all (possibly implicit) bounds on the current dimension will
8310 be used during separation.
8311 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
8312 then only those bounds that are explicitly available will
8313 be used during separation.
8315 =item * ast_build_scale_strides
8317 This option specifies whether the AST generator is allowed
8318 to scale down iterators of strided loops.
8320 =item * ast_build_allow_else
8322 This option specifies whether the AST generator is allowed
8323 to construct if statements with else branches.
8325 =item * ast_build_allow_or
8327 This option specifies whether the AST generator is allowed
8328 to construct if conditions with disjunctions.
8332 =head3 Fine-grained Control over AST Generation
8334 Besides specifying the constraints on the parameters,
8335 an C<isl_ast_build> object can be used to control
8336 various aspects of the AST generation process.
8337 The most prominent way of control is through ``options'',
8338 which can be set using the following function.
8340 #include <isl/ast_build.h>
8341 __isl_give isl_ast_build *
8342 isl_ast_build_set_options(
8343 __isl_take isl_ast_build *control,
8344 __isl_take isl_union_map *options);
8346 The options are encoded in an C<isl_union_map>.
8347 The domain of this union relation refers to the schedule domain,
8348 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
8349 In the case of nested AST generation (see L</"Nested AST Generation">),
8350 the domain of C<options> should refer to the extra piece of the schedule.
8351 That is, it should be equal to the range of the wrapped relation in the
8352 range of the schedule.
8353 The range of the options can consist of elements in one or more spaces,
8354 the names of which determine the effect of the option.
8355 The values of the range typically also refer to the schedule dimension
8356 to which the option applies. In case of nested AST generation
8357 (see L</"Nested AST Generation">), these values refer to the position
8358 of the schedule dimension within the innermost AST generation.
8359 The constraints on the domain elements of
8360 the option should only refer to this dimension and earlier dimensions.
8361 We consider the following spaces.
8365 =item C<separation_class>
8367 This space is a wrapped relation between two one dimensional spaces.
8368 The input space represents the schedule dimension to which the option
8369 applies and the output space represents the separation class.
8370 While constructing a loop corresponding to the specified schedule
8371 dimension(s), the AST generator will try to generate separate loops
8372 for domain elements that are assigned different classes.
8373 If only some of the elements are assigned a class, then those elements
8374 that are not assigned any class will be treated as belonging to a class
8375 that is separate from the explicitly assigned classes.
8376 The typical use case for this option is to separate full tiles from
8378 The other options, described below, are applied after the separation
8381 As an example, consider the separation into full and partial tiles
8382 of a tiling of a triangular domain.
8383 Take, for example, the domain
8385 { A[i,j] : 0 <= i,j and i + j <= 100 }
8387 and a tiling into tiles of 10 by 10. The input to the AST generator
8388 is then the schedule
8390 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
8393 Without any options, the following AST is generated
8395 for (int c0 = 0; c0 <= 10; c0 += 1)
8396 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8397 for (int c2 = 10 * c0;
8398 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8400 for (int c3 = 10 * c1;
8401 c3 <= min(10 * c1 + 9, -c2 + 100);
8405 Separation into full and partial tiles can be obtained by assigning
8406 a class, say C<0>, to the full tiles. The full tiles are represented by those
8407 values of the first and second schedule dimensions for which there are
8408 values of the third and fourth dimensions to cover an entire tile.
8409 That is, we need to specify the following option
8411 { [a,b,c,d] -> separation_class[[0]->[0]] :
8412 exists b': 0 <= 10a,10b' and
8413 10a+9+10b'+9 <= 100;
8414 [a,b,c,d] -> separation_class[[1]->[0]] :
8415 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
8419 { [a, b, c, d] -> separation_class[[1] -> [0]] :
8420 a >= 0 and b >= 0 and b <= 8 - a;
8421 [a, b, c, d] -> separation_class[[0] -> [0]] :
8424 With this option, the generated AST is as follows
8427 for (int c0 = 0; c0 <= 8; c0 += 1) {
8428 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
8429 for (int c2 = 10 * c0;
8430 c2 <= 10 * c0 + 9; c2 += 1)
8431 for (int c3 = 10 * c1;
8432 c3 <= 10 * c1 + 9; c3 += 1)
8434 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
8435 for (int c2 = 10 * c0;
8436 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8438 for (int c3 = 10 * c1;
8439 c3 <= min(-c2 + 100, 10 * c1 + 9);
8443 for (int c0 = 9; c0 <= 10; c0 += 1)
8444 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8445 for (int c2 = 10 * c0;
8446 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8448 for (int c3 = 10 * c1;
8449 c3 <= min(10 * c1 + 9, -c2 + 100);
8456 This is a single-dimensional space representing the schedule dimension(s)
8457 to which ``separation'' should be applied. Separation tries to split
8458 a loop into several pieces if this can avoid the generation of guards
8460 See also the C<atomic> option.
8464 This is a single-dimensional space representing the schedule dimension(s)
8465 for which the domains should be considered ``atomic''. That is, the
8466 AST generator will make sure that any given domain space will only appear
8467 in a single loop at the specified level.
8469 Consider the following schedule
8471 { a[i] -> [i] : 0 <= i < 10;
8472 b[i] -> [i+1] : 0 <= i < 10 }
8474 If the following option is specified
8476 { [i] -> separate[x] }
8478 then the following AST will be generated
8482 for (int c0 = 1; c0 <= 9; c0 += 1) {
8489 If, on the other hand, the following option is specified
8491 { [i] -> atomic[x] }
8493 then the following AST will be generated
8495 for (int c0 = 0; c0 <= 10; c0 += 1) {
8502 If neither C<atomic> nor C<separate> is specified, then the AST generator
8503 may produce either of these two results or some intermediate form.
8507 This is a single-dimensional space representing the schedule dimension(s)
8508 that should be I<completely> unrolled.
8509 To obtain a partial unrolling, the user should apply an additional
8510 strip-mining to the schedule and fully unroll the inner loop.
8514 Additional control is available through the following functions.
8516 #include <isl/ast_build.h>
8517 __isl_give isl_ast_build *
8518 isl_ast_build_set_iterators(
8519 __isl_take isl_ast_build *control,
8520 __isl_take isl_id_list *iterators);
8522 The function C<isl_ast_build_set_iterators> allows the user to
8523 specify a list of iterator C<isl_id>s to be used as iterators.
8524 If the input schedule is injective, then
8525 the number of elements in this list should be as large as the dimension
8526 of the schedule space, but no direct correspondence should be assumed
8527 between dimensions and elements.
8528 If the input schedule is not injective, then an additional number
8529 of C<isl_id>s equal to the largest dimension of the input domains
8531 If the number of provided C<isl_id>s is insufficient, then additional
8532 names are automatically generated.
8534 #include <isl/ast_build.h>
8535 __isl_give isl_ast_build *
8536 isl_ast_build_set_create_leaf(
8537 __isl_take isl_ast_build *control,
8538 __isl_give isl_ast_node *(*fn)(
8539 __isl_take isl_ast_build *build,
8540 void *user), void *user);
8543 C<isl_ast_build_set_create_leaf> function allows for the
8544 specification of a callback that should be called whenever the AST
8545 generator arrives at an element of the schedule domain.
8546 The callback should return an AST node that should be inserted
8547 at the corresponding position of the AST. The default action (when
8548 the callback is not set) is to continue generating parts of the AST to scan
8549 all the domain elements associated to the schedule domain element
8550 and to insert user nodes, ``calling'' the domain element, for each of them.
8551 The C<build> argument contains the current state of the C<isl_ast_build>.
8552 To ease nested AST generation (see L</"Nested AST Generation">),
8553 all control information that is
8554 specific to the current AST generation such as the options and
8555 the callbacks has been removed from this C<isl_ast_build>.
8556 The callback would typically return the result of a nested
8558 user defined node created using the following function.
8560 #include <isl/ast.h>
8561 __isl_give isl_ast_node *isl_ast_node_alloc_user(
8562 __isl_take isl_ast_expr *expr);
8564 #include <isl/ast_build.h>
8565 __isl_give isl_ast_build *
8566 isl_ast_build_set_at_each_domain(
8567 __isl_take isl_ast_build *build,
8568 __isl_give isl_ast_node *(*fn)(
8569 __isl_take isl_ast_node *node,
8570 __isl_keep isl_ast_build *build,
8571 void *user), void *user);
8572 __isl_give isl_ast_build *
8573 isl_ast_build_set_before_each_for(
8574 __isl_take isl_ast_build *build,
8575 __isl_give isl_id *(*fn)(
8576 __isl_keep isl_ast_build *build,
8577 void *user), void *user);
8578 __isl_give isl_ast_build *
8579 isl_ast_build_set_after_each_for(
8580 __isl_take isl_ast_build *build,
8581 __isl_give isl_ast_node *(*fn)(
8582 __isl_take isl_ast_node *node,
8583 __isl_keep isl_ast_build *build,
8584 void *user), void *user);
8586 The callback set by C<isl_ast_build_set_at_each_domain> will
8587 be called for each domain AST node.
8588 The callbacks set by C<isl_ast_build_set_before_each_for>
8589 and C<isl_ast_build_set_after_each_for> will be called
8590 for each for AST node. The first will be called in depth-first
8591 pre-order, while the second will be called in depth-first post-order.
8592 Since C<isl_ast_build_set_before_each_for> is called before the for
8593 node is actually constructed, it is only passed an C<isl_ast_build>.
8594 The returned C<isl_id> will be added as an annotation (using
8595 C<isl_ast_node_set_annotation>) to the constructed for node.
8596 In particular, if the user has also specified an C<after_each_for>
8597 callback, then the annotation can be retrieved from the node passed to
8598 that callback using C<isl_ast_node_get_annotation>.
8599 All callbacks should C<NULL> on failure.
8600 The given C<isl_ast_build> can be used to create new
8601 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
8602 or C<isl_ast_build_call_from_pw_multi_aff>.
8604 =head3 Nested AST Generation
8606 C<isl> allows the user to create an AST within the context
8607 of another AST. These nested ASTs are created using the
8608 same C<isl_ast_build_ast_from_schedule> function that is used to create the
8609 outer AST. The C<build> argument should be an C<isl_ast_build>
8610 passed to a callback set by
8611 C<isl_ast_build_set_create_leaf>.
8612 The space of the range of the C<schedule> argument should refer
8613 to this build. In particular, the space should be a wrapped
8614 relation and the domain of this wrapped relation should be the
8615 same as that of the range of the schedule returned by
8616 C<isl_ast_build_get_schedule> below.
8617 In practice, the new schedule is typically
8618 created by calling C<isl_union_map_range_product> on the old schedule
8619 and some extra piece of the schedule.
8620 The space of the schedule domain is also available from
8621 the C<isl_ast_build>.
8623 #include <isl/ast_build.h>
8624 __isl_give isl_union_map *isl_ast_build_get_schedule(
8625 __isl_keep isl_ast_build *build);
8626 __isl_give isl_space *isl_ast_build_get_schedule_space(
8627 __isl_keep isl_ast_build *build);
8628 __isl_give isl_ast_build *isl_ast_build_restrict(
8629 __isl_take isl_ast_build *build,
8630 __isl_take isl_set *set);
8632 The C<isl_ast_build_get_schedule> function returns a (partial)
8633 schedule for the domains elements for which part of the AST still needs to
8634 be generated in the current build.
8635 In particular, the domain elements are mapped to those iterations of the loops
8636 enclosing the current point of the AST generation inside which
8637 the domain elements are executed.
8638 No direct correspondence between
8639 the input schedule and this schedule should be assumed.
8640 The space obtained from C<isl_ast_build_get_schedule_space> can be used
8641 to create a set for C<isl_ast_build_restrict> to intersect
8642 with the current build. In particular, the set passed to
8643 C<isl_ast_build_restrict> can have additional parameters.
8644 The ids of the set dimensions in the space returned by
8645 C<isl_ast_build_get_schedule_space> correspond to the
8646 iterators of the already generated loops.
8647 The user should not rely on the ids of the output dimensions
8648 of the relations in the union relation returned by
8649 C<isl_ast_build_get_schedule> having any particular value.
8653 Although C<isl> is mainly meant to be used as a library,
8654 it also contains some basic applications that use some
8655 of the functionality of C<isl>.
8656 The input may be specified in either the L<isl format>
8657 or the L<PolyLib format>.
8659 =head2 C<isl_polyhedron_sample>
8661 C<isl_polyhedron_sample> takes a polyhedron as input and prints
8662 an integer element of the polyhedron, if there is any.
8663 The first column in the output is the denominator and is always
8664 equal to 1. If the polyhedron contains no integer points,
8665 then a vector of length zero is printed.
8669 C<isl_pip> takes the same input as the C<example> program
8670 from the C<piplib> distribution, i.e., a set of constraints
8671 on the parameters, a line containing only -1 and finally a set
8672 of constraints on a parametric polyhedron.
8673 The coefficients of the parameters appear in the last columns
8674 (but before the final constant column).
8675 The output is the lexicographic minimum of the parametric polyhedron.
8676 As C<isl> currently does not have its own output format, the output
8677 is just a dump of the internal state.
8679 =head2 C<isl_polyhedron_minimize>
8681 C<isl_polyhedron_minimize> computes the minimum of some linear
8682 or affine objective function over the integer points in a polyhedron.
8683 If an affine objective function
8684 is given, then the constant should appear in the last column.
8686 =head2 C<isl_polytope_scan>
8688 Given a polytope, C<isl_polytope_scan> prints
8689 all integer points in the polytope.
8691 =head2 C<isl_codegen>
8693 Given a schedule, a context set and an options relation,
8694 C<isl_codegen> prints out an AST that scans the domain elements
8695 of the schedule in the order of their image(s) taking into account
8696 the constraints in the context set.