3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * Objects of type C<isl_union_pw_multi_aff> can no longer contain
216 two or more C<isl_pw_multi_aff> objects with the same domain space.
218 =item * The function C<isl_union_pw_multi_aff_add> now consistently
219 computes the sum on the shared definition domain.
220 The function C<isl_union_pw_multi_aff_union_add> has been added
221 to compute the sum on the union of definition domains.
222 The original behavior of C<isl_union_pw_multi_aff_add> was
223 confused and is no longer available.
229 C<isl> is released under the MIT license.
233 Permission is hereby granted, free of charge, to any person obtaining a copy of
234 this software and associated documentation files (the "Software"), to deal in
235 the Software without restriction, including without limitation the rights to
236 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
237 of the Software, and to permit persons to whom the Software is furnished to do
238 so, subject to the following conditions:
240 The above copyright notice and this permission notice shall be included in all
241 copies or substantial portions of the Software.
243 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
244 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
245 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
246 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
247 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
248 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
253 Note that by default C<isl> requires C<GMP>, which is released
254 under the GNU Lesser General Public License (LGPL). This means
255 that code linked against C<isl> is also linked against LGPL code.
257 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
258 library for exact integer arithmetic released under the MIT license.
262 The source of C<isl> can be obtained either as a tarball
263 or from the git repository. Both are available from
264 L<http://freshmeat.net/projects/isl/>.
265 The installation process depends on how you obtained
268 =head2 Installation from the git repository
272 =item 1 Clone or update the repository
274 The first time the source is obtained, you need to clone
277 git clone git://repo.or.cz/isl.git
279 To obtain updates, you need to pull in the latest changes
283 =item 2 Optionally get C<imath> submodule
285 To build C<isl> with C<imath>, you need to obtain the C<imath>
286 submodule by running in the git source tree of C<isl>
291 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
293 =item 2 Generate C<configure>
299 After performing the above steps, continue
300 with the L<Common installation instructions>.
302 =head2 Common installation instructions
306 =item 1 Obtain C<GMP>
308 By default, building C<isl> requires C<GMP>, including its headers files.
309 Your distribution may not provide these header files by default
310 and you may need to install a package called C<gmp-devel> or something
311 similar. Alternatively, C<GMP> can be built from
312 source, available from L<http://gmplib.org/>.
313 C<GMP> is not needed if you build C<isl> with C<imath>.
317 C<isl> uses the standard C<autoconf> C<configure> script.
322 optionally followed by some configure options.
323 A complete list of options can be obtained by running
327 Below we discuss some of the more common options.
333 Installation prefix for C<isl>
335 =item C<--with-int=[gmp|imath]>
337 Select the integer library to be used by C<isl>, the default is C<gmp>.
338 Note that C<isl> may run significantly slower if you use C<imath>.
340 =item C<--with-gmp-prefix>
342 Installation prefix for C<GMP> (architecture-independent files).
344 =item C<--with-gmp-exec-prefix>
346 Installation prefix for C<GMP> (architecture-dependent files).
354 =item 4 Install (optional)
360 =head1 Integer Set Library
362 =head2 Memory Management
364 Since a high-level operation on isl objects usually involves
365 several substeps and since the user is usually not interested in
366 the intermediate results, most functions that return a new object
367 will also release all the objects passed as arguments.
368 If the user still wants to use one or more of these arguments
369 after the function call, she should pass along a copy of the
370 object rather than the object itself.
371 The user is then responsible for making sure that the original
372 object gets used somewhere else or is explicitly freed.
374 The arguments and return values of all documented functions are
375 annotated to make clear which arguments are released and which
376 arguments are preserved. In particular, the following annotations
383 C<__isl_give> means that a new object is returned.
384 The user should make sure that the returned pointer is
385 used exactly once as a value for an C<__isl_take> argument.
386 In between, it can be used as a value for as many
387 C<__isl_keep> arguments as the user likes.
388 There is one exception, and that is the case where the
389 pointer returned is C<NULL>. Is this case, the user
390 is free to use it as an C<__isl_take> argument or not.
391 When applied to a C<char *>, the returned pointer needs to be
396 C<__isl_null> means that a C<NULL> value is returned.
400 C<__isl_take> means that the object the argument points to
401 is taken over by the function and may no longer be used
402 by the user as an argument to any other function.
403 The pointer value must be one returned by a function
404 returning an C<__isl_give> pointer.
405 If the user passes in a C<NULL> value, then this will
406 be treated as an error in the sense that the function will
407 not perform its usual operation. However, it will still
408 make sure that all the other C<__isl_take> arguments
413 C<__isl_keep> means that the function will only use the object
414 temporarily. After the function has finished, the user
415 can still use it as an argument to other functions.
416 A C<NULL> value will be treated in the same way as
417 a C<NULL> value for an C<__isl_take> argument.
418 This annotation may also be used on return values of
419 type C<const char *>, in which case the returned pointer should
420 not be freed by the user and is only valid until the object
421 from which it was derived is updated or freed.
425 =head2 Initialization
427 All manipulations of integer sets and relations occur within
428 the context of an C<isl_ctx>.
429 A given C<isl_ctx> can only be used within a single thread.
430 All arguments of a function are required to have been allocated
431 within the same context.
432 There are currently no functions available for moving an object
433 from one C<isl_ctx> to another C<isl_ctx>. This means that
434 there is currently no way of safely moving an object from one
435 thread to another, unless the whole C<isl_ctx> is moved.
437 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
438 freed using C<isl_ctx_free>.
439 All objects allocated within an C<isl_ctx> should be freed
440 before the C<isl_ctx> itself is freed.
442 isl_ctx *isl_ctx_alloc();
443 void isl_ctx_free(isl_ctx *ctx);
445 The user can impose a bound on the number of low-level I<operations>
446 that can be performed by an C<isl_ctx>. This bound can be set and
447 retrieved using the following functions. A bound of zero means that
448 no bound is imposed. The number of operations performed can be
449 reset using C<isl_ctx_reset_operations>. Note that the number
450 of low-level operations needed to perform a high-level computation
451 may differ significantly across different versions
452 of C<isl>, but it should be the same across different platforms
453 for the same version of C<isl>.
455 Warning: This feature is experimental. C<isl> has good support to abort and
456 bail out during the computation, but this feature may exercise error code paths
457 that are normally not used that much. Consequently, it is not unlikely that
458 hidden bugs will be exposed.
460 void isl_ctx_set_max_operations(isl_ctx *ctx,
461 unsigned long max_operations);
462 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
463 void isl_ctx_reset_operations(isl_ctx *ctx);
465 In order to be able to create an object in the same context
466 as another object, most object types (described later in
467 this document) provide a function to obtain the context
468 in which the object was created.
471 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
472 isl_ctx *isl_multi_val_get_ctx(
473 __isl_keep isl_multi_val *mv);
476 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
478 #include <isl/local_space.h>
479 isl_ctx *isl_local_space_get_ctx(
480 __isl_keep isl_local_space *ls);
483 isl_ctx *isl_set_list_get_ctx(
484 __isl_keep isl_set_list *list);
487 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
488 isl_ctx *isl_multi_aff_get_ctx(
489 __isl_keep isl_multi_aff *maff);
490 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
491 isl_ctx *isl_pw_multi_aff_get_ctx(
492 __isl_keep isl_pw_multi_aff *pma);
493 isl_ctx *isl_multi_pw_aff_get_ctx(
494 __isl_keep isl_multi_pw_aff *mpa);
495 isl_ctx *isl_union_pw_aff_get_ctx(
496 __isl_keep isl_union_pw_aff *upa);
497 isl_ctx *isl_union_pw_multi_aff_get_ctx(
498 __isl_keep isl_union_pw_multi_aff *upma);
499 isl_ctx *isl_multi_union_pw_aff_get_ctx(
500 __isl_keep isl_multi_union_pw_aff *mupa);
502 #include <isl/id_to_ast_expr.h>
503 isl_ctx *isl_id_to_ast_expr_get_ctx(
504 __isl_keep id_to_ast_expr *id2expr);
506 #include <isl/point.h>
507 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
510 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
513 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
515 #include <isl/vertices.h>
516 isl_ctx *isl_vertices_get_ctx(
517 __isl_keep isl_vertices *vertices);
518 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
519 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
521 #include <isl/flow.h>
522 isl_ctx *isl_restriction_get_ctx(
523 __isl_keep isl_restriction *restr);
525 #include <isl/schedule.h>
526 isl_ctx *isl_schedule_constraints_get_ctx(
527 __isl_keep isl_schedule_constraints *sc);
529 #include <isl/band.h>
530 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
532 #include <isl/ast_build.h>
533 isl_ctx *isl_ast_build_get_ctx(
534 __isl_keep isl_ast_build *build);
537 isl_ctx *isl_ast_expr_get_ctx(
538 __isl_keep isl_ast_expr *expr);
539 isl_ctx *isl_ast_node_get_ctx(
540 __isl_keep isl_ast_node *node);
544 An C<isl_val> represents an integer value, a rational value
545 or one of three special values, infinity, negative infinity and NaN.
546 Some predefined values can be created using the following functions.
549 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
550 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
551 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
552 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
553 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
554 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
556 Specific integer values can be created using the following functions.
559 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
561 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
563 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
564 size_t n, size_t size, const void *chunks);
566 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
567 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
568 The least significant digit is assumed to be stored first.
570 Value objects can be copied and freed using the following functions.
573 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
574 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
576 They can be inspected using the following functions.
579 long isl_val_get_num_si(__isl_keep isl_val *v);
580 long isl_val_get_den_si(__isl_keep isl_val *v);
581 double isl_val_get_d(__isl_keep isl_val *v);
582 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
584 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
585 size_t size, void *chunks);
587 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
588 of C<size> bytes needed to store the absolute value of the
590 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
591 which is assumed to have been preallocated by the caller.
592 The least significant digit is stored first.
593 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
594 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
595 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
597 An C<isl_val> can be modified using the following function.
600 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
603 The following unary properties are defined on C<isl_val>s.
606 int isl_val_sgn(__isl_keep isl_val *v);
607 int isl_val_is_zero(__isl_keep isl_val *v);
608 int isl_val_is_one(__isl_keep isl_val *v);
609 int isl_val_is_negone(__isl_keep isl_val *v);
610 int isl_val_is_nonneg(__isl_keep isl_val *v);
611 int isl_val_is_nonpos(__isl_keep isl_val *v);
612 int isl_val_is_pos(__isl_keep isl_val *v);
613 int isl_val_is_neg(__isl_keep isl_val *v);
614 int isl_val_is_int(__isl_keep isl_val *v);
615 int isl_val_is_rat(__isl_keep isl_val *v);
616 int isl_val_is_nan(__isl_keep isl_val *v);
617 int isl_val_is_infty(__isl_keep isl_val *v);
618 int isl_val_is_neginfty(__isl_keep isl_val *v);
620 Note that the sign of NaN is undefined.
622 The following binary properties are defined on pairs of C<isl_val>s.
625 int isl_val_lt(__isl_keep isl_val *v1,
626 __isl_keep isl_val *v2);
627 int isl_val_le(__isl_keep isl_val *v1,
628 __isl_keep isl_val *v2);
629 int isl_val_gt(__isl_keep isl_val *v1,
630 __isl_keep isl_val *v2);
631 int isl_val_ge(__isl_keep isl_val *v1,
632 __isl_keep isl_val *v2);
633 int isl_val_eq(__isl_keep isl_val *v1,
634 __isl_keep isl_val *v2);
635 int isl_val_ne(__isl_keep isl_val *v1,
636 __isl_keep isl_val *v2);
637 int isl_val_abs_eq(__isl_keep isl_val *v1,
638 __isl_keep isl_val *v2);
640 The function C<isl_val_abs_eq> checks whether its two arguments
641 are equal in absolute value.
643 For integer C<isl_val>s we additionally have the following binary property.
646 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
647 __isl_keep isl_val *v2);
649 An C<isl_val> can also be compared to an integer using the following
650 function. The result is undefined for NaN.
653 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
655 The following unary operations are available on C<isl_val>s.
658 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
659 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
660 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
661 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
662 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
663 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
664 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
666 The following binary operations are available on C<isl_val>s.
669 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
670 __isl_take isl_val *v2);
671 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
672 __isl_take isl_val *v2);
673 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
674 __isl_take isl_val *v2);
675 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
677 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
678 __isl_take isl_val *v2);
679 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
681 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
682 __isl_take isl_val *v2);
683 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
685 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
686 __isl_take isl_val *v2);
688 On integer values, we additionally have the following operations.
691 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
692 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
693 __isl_take isl_val *v2);
694 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
695 __isl_take isl_val *v2);
696 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
697 __isl_take isl_val *v2, __isl_give isl_val **x,
698 __isl_give isl_val **y);
700 The function C<isl_val_gcdext> returns the greatest common divisor g
701 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
702 that C<*x> * C<v1> + C<*y> * C<v2> = g.
704 =head3 GMP specific functions
706 These functions are only available if C<isl> has been compiled with C<GMP>
709 Specific integer and rational values can be created from C<GMP> values using
710 the following functions.
712 #include <isl/val_gmp.h>
713 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
715 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
716 const mpz_t n, const mpz_t d);
718 The numerator and denominator of a rational value can be extracted as
719 C<GMP> values using the following functions.
721 #include <isl/val_gmp.h>
722 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
723 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
725 =head2 Sets and Relations
727 C<isl> uses six types of objects for representing sets and relations,
728 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
729 C<isl_union_set> and C<isl_union_map>.
730 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
731 can be described as a conjunction of affine constraints, while
732 C<isl_set> and C<isl_map> represent unions of
733 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
734 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
735 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
736 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
737 where spaces are considered different if they have a different number
738 of dimensions and/or different names (see L<"Spaces">).
739 The difference between sets and relations (maps) is that sets have
740 one set of variables, while relations have two sets of variables,
741 input variables and output variables.
743 =head2 Error Handling
745 C<isl> supports different ways to react in case a runtime error is triggered.
746 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
747 with two maps that have incompatible spaces. There are three possible ways
748 to react on error: to warn, to continue or to abort.
750 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
751 the last error in the corresponding C<isl_ctx> and the function in which the
752 error was triggered returns C<NULL>. An error does not corrupt internal state,
753 such that isl can continue to be used. C<isl> also provides functions to
754 read the last error and to reset the memory that stores the last error. The
755 last error is only stored for information purposes. Its presence does not
756 change the behavior of C<isl>. Hence, resetting an error is not required to
757 continue to use isl, but only to observe new errors.
760 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
761 void isl_ctx_reset_error(isl_ctx *ctx);
763 Another option is to continue on error. This is similar to warn on error mode,
764 except that C<isl> does not print any warning. This allows a program to
765 implement its own error reporting.
767 The last option is to directly abort the execution of the program from within
768 the isl library. This makes it obviously impossible to recover from an error,
769 but it allows to directly spot the error location. By aborting on error,
770 debuggers break at the location the error occurred and can provide a stack
771 trace. Other tools that automatically provide stack traces on abort or that do
772 not want to continue execution after an error was triggered may also prefer to
775 The on error behavior of isl can be specified by calling
776 C<isl_options_set_on_error> or by setting the command line option
777 C<--isl-on-error>. Valid arguments for the function call are
778 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
779 choices for the command line option are C<warn>, C<continue> and C<abort>.
780 It is also possible to query the current error mode.
782 #include <isl/options.h>
783 int isl_options_set_on_error(isl_ctx *ctx, int val);
784 int isl_options_get_on_error(isl_ctx *ctx);
788 Identifiers are used to identify both individual dimensions
789 and tuples of dimensions. They consist of an optional name and an optional
790 user pointer. The name and the user pointer cannot both be C<NULL>, however.
791 Identifiers with the same name but different pointer values
792 are considered to be distinct.
793 Similarly, identifiers with different names but the same pointer value
794 are also considered to be distinct.
795 Equal identifiers are represented using the same object.
796 Pairs of identifiers can therefore be tested for equality using the
798 Identifiers can be constructed, copied, freed, inspected and printed
799 using the following functions.
802 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
803 __isl_keep const char *name, void *user);
804 __isl_give isl_id *isl_id_set_free_user(
805 __isl_take isl_id *id,
806 __isl_give void (*free_user)(void *user));
807 __isl_give isl_id *isl_id_copy(isl_id *id);
808 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
810 void *isl_id_get_user(__isl_keep isl_id *id);
811 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
813 __isl_give isl_printer *isl_printer_print_id(
814 __isl_take isl_printer *p, __isl_keep isl_id *id);
816 The callback set by C<isl_id_set_free_user> is called on the user
817 pointer when the last reference to the C<isl_id> is freed.
818 Note that C<isl_id_get_name> returns a pointer to some internal
819 data structure, so the result can only be used while the
820 corresponding C<isl_id> is alive.
824 Whenever a new set, relation or similar object is created from scratch,
825 the space in which it lives needs to be specified using an C<isl_space>.
826 Each space involves zero or more parameters and zero, one or two
827 tuples of set or input/output dimensions. The parameters and dimensions
828 are identified by an C<isl_dim_type> and a position.
829 The type C<isl_dim_param> refers to parameters,
830 the type C<isl_dim_set> refers to set dimensions (for spaces
831 with a single tuple of dimensions) and the types C<isl_dim_in>
832 and C<isl_dim_out> refer to input and output dimensions
833 (for spaces with two tuples of dimensions).
834 Local spaces (see L</"Local Spaces">) also contain dimensions
835 of type C<isl_dim_div>.
836 Note that parameters are only identified by their position within
837 a given object. Across different objects, parameters are (usually)
838 identified by their names or identifiers. Only unnamed parameters
839 are identified by their positions across objects. The use of unnamed
840 parameters is discouraged.
842 #include <isl/space.h>
843 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
844 unsigned nparam, unsigned n_in, unsigned n_out);
845 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
847 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
848 unsigned nparam, unsigned dim);
849 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
850 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
852 The space used for creating a parameter domain
853 needs to be created using C<isl_space_params_alloc>.
854 For other sets, the space
855 needs to be created using C<isl_space_set_alloc>, while
856 for a relation, the space
857 needs to be created using C<isl_space_alloc>.
859 To check whether a given space is that of a set or a map
860 or whether it is a parameter space, use these functions:
862 #include <isl/space.h>
863 int isl_space_is_params(__isl_keep isl_space *space);
864 int isl_space_is_set(__isl_keep isl_space *space);
865 int isl_space_is_map(__isl_keep isl_space *space);
867 Spaces can be compared using the following functions:
869 #include <isl/space.h>
870 int isl_space_is_equal(__isl_keep isl_space *space1,
871 __isl_keep isl_space *space2);
872 int isl_space_is_domain(__isl_keep isl_space *space1,
873 __isl_keep isl_space *space2);
874 int isl_space_is_range(__isl_keep isl_space *space1,
875 __isl_keep isl_space *space2);
876 int isl_space_tuple_is_equal(
877 __isl_keep isl_space *space1,
878 enum isl_dim_type type1,
879 __isl_keep isl_space *space2,
880 enum isl_dim_type type2);
882 C<isl_space_is_domain> checks whether the first argument is equal
883 to the domain of the second argument. This requires in particular that
884 the first argument is a set space and that the second argument
885 is a map space. C<isl_space_tuple_is_equal> checks whether the given
886 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
887 spaces are the same. That is, it checks if they have the same
888 identifier (if any), the same dimension and the same internal structure
891 It is often useful to create objects that live in the
892 same space as some other object. This can be accomplished
893 by creating the new objects
894 (see L</"Creating New Sets and Relations"> or
895 L</"Functions">) based on the space
896 of the original object.
899 __isl_give isl_space *isl_basic_set_get_space(
900 __isl_keep isl_basic_set *bset);
901 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
903 #include <isl/union_set.h>
904 __isl_give isl_space *isl_union_set_get_space(
905 __isl_keep isl_union_set *uset);
908 __isl_give isl_space *isl_basic_map_get_space(
909 __isl_keep isl_basic_map *bmap);
910 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
912 #include <isl/union_map.h>
913 __isl_give isl_space *isl_union_map_get_space(
914 __isl_keep isl_union_map *umap);
916 #include <isl/constraint.h>
917 __isl_give isl_space *isl_constraint_get_space(
918 __isl_keep isl_constraint *constraint);
920 #include <isl/polynomial.h>
921 __isl_give isl_space *isl_qpolynomial_get_domain_space(
922 __isl_keep isl_qpolynomial *qp);
923 __isl_give isl_space *isl_qpolynomial_get_space(
924 __isl_keep isl_qpolynomial *qp);
925 __isl_give isl_space *isl_qpolynomial_fold_get_space(
926 __isl_keep isl_qpolynomial_fold *fold);
927 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
928 __isl_keep isl_pw_qpolynomial *pwqp);
929 __isl_give isl_space *isl_pw_qpolynomial_get_space(
930 __isl_keep isl_pw_qpolynomial *pwqp);
931 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
932 __isl_keep isl_pw_qpolynomial_fold *pwf);
933 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
934 __isl_keep isl_pw_qpolynomial_fold *pwf);
935 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
936 __isl_keep isl_union_pw_qpolynomial *upwqp);
937 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
938 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
941 __isl_give isl_space *isl_multi_val_get_space(
942 __isl_keep isl_multi_val *mv);
945 __isl_give isl_space *isl_aff_get_domain_space(
946 __isl_keep isl_aff *aff);
947 __isl_give isl_space *isl_aff_get_space(
948 __isl_keep isl_aff *aff);
949 __isl_give isl_space *isl_pw_aff_get_domain_space(
950 __isl_keep isl_pw_aff *pwaff);
951 __isl_give isl_space *isl_pw_aff_get_space(
952 __isl_keep isl_pw_aff *pwaff);
953 __isl_give isl_space *isl_multi_aff_get_domain_space(
954 __isl_keep isl_multi_aff *maff);
955 __isl_give isl_space *isl_multi_aff_get_space(
956 __isl_keep isl_multi_aff *maff);
957 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
958 __isl_keep isl_pw_multi_aff *pma);
959 __isl_give isl_space *isl_pw_multi_aff_get_space(
960 __isl_keep isl_pw_multi_aff *pma);
961 __isl_give isl_space *isl_union_pw_aff_get_space(
962 __isl_keep isl_union_pw_aff *upa);
963 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
964 __isl_keep isl_union_pw_multi_aff *upma);
965 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
966 __isl_keep isl_multi_pw_aff *mpa);
967 __isl_give isl_space *isl_multi_pw_aff_get_space(
968 __isl_keep isl_multi_pw_aff *mpa);
969 __isl_give isl_space *
970 isl_multi_union_pw_aff_get_domain_space(
971 __isl_keep isl_multi_union_pw_aff *mupa);
972 __isl_give isl_space *
973 isl_multi_union_pw_aff_get_space(
974 __isl_keep isl_multi_union_pw_aff *mupa);
976 #include <isl/point.h>
977 __isl_give isl_space *isl_point_get_space(
978 __isl_keep isl_point *pnt);
980 The number of dimensions of a given type of space
981 may be read off from a space or an object that lives
982 in a space using the following functions.
983 In case of C<isl_space_dim>, type may be
984 C<isl_dim_param>, C<isl_dim_in> (only for relations),
985 C<isl_dim_out> (only for relations), C<isl_dim_set>
986 (only for sets) or C<isl_dim_all>.
988 #include <isl/space.h>
989 unsigned isl_space_dim(__isl_keep isl_space *space,
990 enum isl_dim_type type);
992 #include <isl/local_space.h>
993 int isl_local_space_dim(__isl_keep isl_local_space *ls,
994 enum isl_dim_type type);
997 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
998 enum isl_dim_type type);
999 unsigned isl_set_dim(__isl_keep isl_set *set,
1000 enum isl_dim_type type);
1002 #include <isl/union_set.h>
1003 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1004 enum isl_dim_type type);
1006 #include <isl/map.h>
1007 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1008 enum isl_dim_type type);
1009 unsigned isl_map_dim(__isl_keep isl_map *map,
1010 enum isl_dim_type type);
1012 #include <isl/union_map.h>
1013 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1014 enum isl_dim_type type);
1016 #include <isl/val.h>
1017 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1018 enum isl_dim_type type);
1020 #include <isl/aff.h>
1021 int isl_aff_dim(__isl_keep isl_aff *aff,
1022 enum isl_dim_type type);
1023 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1024 enum isl_dim_type type);
1025 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1026 enum isl_dim_type type);
1027 unsigned isl_pw_multi_aff_dim(
1028 __isl_keep isl_pw_multi_aff *pma,
1029 enum isl_dim_type type);
1030 unsigned isl_multi_pw_aff_dim(
1031 __isl_keep isl_multi_pw_aff *mpa,
1032 enum isl_dim_type type);
1033 unsigned isl_union_pw_aff_dim(
1034 __isl_keep isl_union_pw_aff *upa,
1035 enum isl_dim_type type);
1036 unsigned isl_union_pw_multi_aff_dim(
1037 __isl_keep isl_union_pw_multi_aff *upma,
1038 enum isl_dim_type type);
1039 unsigned isl_multi_union_pw_aff_dim(
1040 __isl_keep isl_multi_union_pw_aff *mupa,
1041 enum isl_dim_type type);
1043 #include <isl/polynomial.h>
1044 unsigned isl_union_pw_qpolynomial_dim(
1045 __isl_keep isl_union_pw_qpolynomial *upwqp,
1046 enum isl_dim_type type);
1047 unsigned isl_union_pw_qpolynomial_fold_dim(
1048 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1049 enum isl_dim_type type);
1051 Note that an C<isl_union_set>, an C<isl_union_map>,
1052 an C<isl_union_pw_multi_aff>,
1053 an C<isl_union_pw_qpolynomial> and
1054 an C<isl_union_pw_qpolynomial_fold>
1055 only have parameters.
1057 The identifiers or names of the individual dimensions of spaces
1058 may be set or read off using the following functions on spaces
1059 or objects that live in spaces.
1060 These functions are mostly useful to obtain the identifiers, positions
1061 or names of the parameters. Identifiers of individual dimensions are
1062 essentially only useful for printing. They are ignored by all other
1063 operations and may not be preserved across those operations.
1065 #include <isl/space.h>
1066 __isl_give isl_space *isl_space_set_dim_id(
1067 __isl_take isl_space *space,
1068 enum isl_dim_type type, unsigned pos,
1069 __isl_take isl_id *id);
1070 int isl_space_has_dim_id(__isl_keep isl_space *space,
1071 enum isl_dim_type type, unsigned pos);
1072 __isl_give isl_id *isl_space_get_dim_id(
1073 __isl_keep isl_space *space,
1074 enum isl_dim_type type, unsigned pos);
1075 __isl_give isl_space *isl_space_set_dim_name(
1076 __isl_take isl_space *space,
1077 enum isl_dim_type type, unsigned pos,
1078 __isl_keep const char *name);
1079 int isl_space_has_dim_name(__isl_keep isl_space *space,
1080 enum isl_dim_type type, unsigned pos);
1081 __isl_keep const char *isl_space_get_dim_name(
1082 __isl_keep isl_space *space,
1083 enum isl_dim_type type, unsigned pos);
1085 #include <isl/local_space.h>
1086 __isl_give isl_local_space *isl_local_space_set_dim_id(
1087 __isl_take isl_local_space *ls,
1088 enum isl_dim_type type, unsigned pos,
1089 __isl_take isl_id *id);
1090 int isl_local_space_has_dim_id(
1091 __isl_keep isl_local_space *ls,
1092 enum isl_dim_type type, unsigned pos);
1093 __isl_give isl_id *isl_local_space_get_dim_id(
1094 __isl_keep isl_local_space *ls,
1095 enum isl_dim_type type, unsigned pos);
1096 __isl_give isl_local_space *isl_local_space_set_dim_name(
1097 __isl_take isl_local_space *ls,
1098 enum isl_dim_type type, unsigned pos, const char *s);
1099 int isl_local_space_has_dim_name(
1100 __isl_keep isl_local_space *ls,
1101 enum isl_dim_type type, unsigned pos)
1102 const char *isl_local_space_get_dim_name(
1103 __isl_keep isl_local_space *ls,
1104 enum isl_dim_type type, unsigned pos);
1106 #include <isl/constraint.h>
1107 const char *isl_constraint_get_dim_name(
1108 __isl_keep isl_constraint *constraint,
1109 enum isl_dim_type type, unsigned pos);
1111 #include <isl/set.h>
1112 __isl_give isl_id *isl_basic_set_get_dim_id(
1113 __isl_keep isl_basic_set *bset,
1114 enum isl_dim_type type, unsigned pos);
1115 __isl_give isl_set *isl_set_set_dim_id(
1116 __isl_take isl_set *set, enum isl_dim_type type,
1117 unsigned pos, __isl_take isl_id *id);
1118 int isl_set_has_dim_id(__isl_keep isl_set *set,
1119 enum isl_dim_type type, unsigned pos);
1120 __isl_give isl_id *isl_set_get_dim_id(
1121 __isl_keep isl_set *set, enum isl_dim_type type,
1123 const char *isl_basic_set_get_dim_name(
1124 __isl_keep isl_basic_set *bset,
1125 enum isl_dim_type type, unsigned pos);
1126 int isl_set_has_dim_name(__isl_keep isl_set *set,
1127 enum isl_dim_type type, unsigned pos);
1128 const char *isl_set_get_dim_name(
1129 __isl_keep isl_set *set,
1130 enum isl_dim_type type, unsigned pos);
1132 #include <isl/map.h>
1133 __isl_give isl_map *isl_map_set_dim_id(
1134 __isl_take isl_map *map, enum isl_dim_type type,
1135 unsigned pos, __isl_take isl_id *id);
1136 int isl_basic_map_has_dim_id(
1137 __isl_keep isl_basic_map *bmap,
1138 enum isl_dim_type type, unsigned pos);
1139 int isl_map_has_dim_id(__isl_keep isl_map *map,
1140 enum isl_dim_type type, unsigned pos);
1141 __isl_give isl_id *isl_map_get_dim_id(
1142 __isl_keep isl_map *map, enum isl_dim_type type,
1144 __isl_give isl_id *isl_union_map_get_dim_id(
1145 __isl_keep isl_union_map *umap,
1146 enum isl_dim_type type, unsigned pos);
1147 const char *isl_basic_map_get_dim_name(
1148 __isl_keep isl_basic_map *bmap,
1149 enum isl_dim_type type, unsigned pos);
1150 int isl_map_has_dim_name(__isl_keep isl_map *map,
1151 enum isl_dim_type type, unsigned pos);
1152 const char *isl_map_get_dim_name(
1153 __isl_keep isl_map *map,
1154 enum isl_dim_type type, unsigned pos);
1156 #include <isl/val.h>
1157 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1158 __isl_take isl_multi_val *mv,
1159 enum isl_dim_type type, unsigned pos,
1160 __isl_take isl_id *id);
1161 __isl_give isl_id *isl_multi_val_get_dim_id(
1162 __isl_keep isl_multi_val *mv,
1163 enum isl_dim_type type, unsigned pos);
1164 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1165 __isl_take isl_multi_val *mv,
1166 enum isl_dim_type type, unsigned pos, const char *s);
1168 #include <isl/aff.h>
1169 __isl_give isl_aff *isl_aff_set_dim_id(
1170 __isl_take isl_aff *aff, enum isl_dim_type type,
1171 unsigned pos, __isl_take isl_id *id);
1172 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1173 __isl_take isl_multi_aff *maff,
1174 enum isl_dim_type type, unsigned pos,
1175 __isl_take isl_id *id);
1176 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1177 __isl_take isl_pw_aff *pma,
1178 enum isl_dim_type type, unsigned pos,
1179 __isl_take isl_id *id);
1180 __isl_give isl_multi_pw_aff *
1181 isl_multi_pw_aff_set_dim_id(
1182 __isl_take isl_multi_pw_aff *mpa,
1183 enum isl_dim_type type, unsigned pos,
1184 __isl_take isl_id *id);
1185 __isl_give isl_multi_union_pw_aff *
1186 isl_multi_union_pw_aff_set_dim_id(
1187 __isl_take isl_multi_union_pw_aff *mupa,
1188 enum isl_dim_type type, unsigned pos,
1189 __isl_take isl_id *id);
1190 __isl_give isl_id *isl_multi_aff_get_dim_id(
1191 __isl_keep isl_multi_aff *ma,
1192 enum isl_dim_type type, unsigned pos);
1193 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1194 enum isl_dim_type type, unsigned pos);
1195 __isl_give isl_id *isl_pw_aff_get_dim_id(
1196 __isl_keep isl_pw_aff *pa,
1197 enum isl_dim_type type, unsigned pos);
1198 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1199 __isl_keep isl_pw_multi_aff *pma,
1200 enum isl_dim_type type, unsigned pos);
1201 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1202 __isl_keep isl_multi_pw_aff *mpa,
1203 enum isl_dim_type type, unsigned pos);
1204 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1205 __isl_keep isl_multi_union_pw_aff *mupa,
1206 enum isl_dim_type type, unsigned pos);
1207 __isl_give isl_aff *isl_aff_set_dim_name(
1208 __isl_take isl_aff *aff, enum isl_dim_type type,
1209 unsigned pos, const char *s);
1210 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1211 __isl_take isl_multi_aff *maff,
1212 enum isl_dim_type type, unsigned pos, const char *s);
1213 __isl_give isl_multi_pw_aff *
1214 isl_multi_pw_aff_set_dim_name(
1215 __isl_take isl_multi_pw_aff *mpa,
1216 enum isl_dim_type type, unsigned pos, const char *s);
1217 __isl_give isl_union_pw_aff *
1218 isl_union_pw_aff_set_dim_name(
1219 __isl_take isl_union_pw_aff *upa,
1220 enum isl_dim_type type, unsigned pos,
1222 __isl_give isl_union_pw_multi_aff *
1223 isl_union_pw_multi_aff_set_dim_name(
1224 __isl_take isl_union_pw_multi_aff *upma,
1225 enum isl_dim_type type, unsigned pos,
1227 __isl_give isl_multi_union_pw_aff *
1228 isl_multi_union_pw_aff_set_dim_name(
1229 __isl_take isl_multi_union_pw_aff *mupa,
1230 enum isl_dim_type type, unsigned pos,
1231 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1232 enum isl_dim_type type, unsigned pos);
1233 const char *isl_pw_aff_get_dim_name(
1234 __isl_keep isl_pw_aff *pa,
1235 enum isl_dim_type type, unsigned pos);
1236 const char *isl_pw_multi_aff_get_dim_name(
1237 __isl_keep isl_pw_multi_aff *pma,
1238 enum isl_dim_type type, unsigned pos);
1240 #include <isl/polynomial.h>
1241 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1242 __isl_take isl_qpolynomial *qp,
1243 enum isl_dim_type type, unsigned pos,
1245 __isl_give isl_pw_qpolynomial *
1246 isl_pw_qpolynomial_set_dim_name(
1247 __isl_take isl_pw_qpolynomial *pwqp,
1248 enum isl_dim_type type, unsigned pos,
1250 __isl_give isl_pw_qpolynomial_fold *
1251 isl_pw_qpolynomial_fold_set_dim_name(
1252 __isl_take isl_pw_qpolynomial_fold *pwf,
1253 enum isl_dim_type type, unsigned pos,
1255 __isl_give isl_union_pw_qpolynomial *
1256 isl_union_pw_qpolynomial_set_dim_name(
1257 __isl_take isl_union_pw_qpolynomial *upwqp,
1258 enum isl_dim_type type, unsigned pos,
1260 __isl_give isl_union_pw_qpolynomial_fold *
1261 isl_union_pw_qpolynomial_fold_set_dim_name(
1262 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1263 enum isl_dim_type type, unsigned pos,
1266 Note that C<isl_space_get_name> returns a pointer to some internal
1267 data structure, so the result can only be used while the
1268 corresponding C<isl_space> is alive.
1269 Also note that every function that operates on two sets or relations
1270 requires that both arguments have the same parameters. This also
1271 means that if one of the arguments has named parameters, then the
1272 other needs to have named parameters too and the names need to match.
1273 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1274 arguments may have different parameters (as long as they are named),
1275 in which case the result will have as parameters the union of the parameters of
1278 Given the identifier or name of a dimension (typically a parameter),
1279 its position can be obtained from the following functions.
1281 #include <isl/space.h>
1282 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1283 enum isl_dim_type type, __isl_keep isl_id *id);
1284 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1285 enum isl_dim_type type, const char *name);
1287 #include <isl/local_space.h>
1288 int isl_local_space_find_dim_by_name(
1289 __isl_keep isl_local_space *ls,
1290 enum isl_dim_type type, const char *name);
1292 #include <isl/val.h>
1293 int isl_multi_val_find_dim_by_id(
1294 __isl_keep isl_multi_val *mv,
1295 enum isl_dim_type type, __isl_keep isl_id *id);
1296 int isl_multi_val_find_dim_by_name(
1297 __isl_keep isl_multi_val *mv,
1298 enum isl_dim_type type, const char *name);
1300 #include <isl/set.h>
1301 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1302 enum isl_dim_type type, __isl_keep isl_id *id);
1303 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1304 enum isl_dim_type type, const char *name);
1306 #include <isl/map.h>
1307 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1308 enum isl_dim_type type, __isl_keep isl_id *id);
1309 int isl_basic_map_find_dim_by_name(
1310 __isl_keep isl_basic_map *bmap,
1311 enum isl_dim_type type, const char *name);
1312 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1313 enum isl_dim_type type, const char *name);
1314 int isl_union_map_find_dim_by_name(
1315 __isl_keep isl_union_map *umap,
1316 enum isl_dim_type type, const char *name);
1318 #include <isl/aff.h>
1319 int isl_multi_aff_find_dim_by_id(
1320 __isl_keep isl_multi_aff *ma,
1321 enum isl_dim_type type, __isl_keep isl_id *id);
1322 int isl_multi_pw_aff_find_dim_by_id(
1323 __isl_keep isl_multi_pw_aff *mpa,
1324 enum isl_dim_type type, __isl_keep isl_id *id);
1325 int isl_multi_union_pw_aff_find_dim_by_id(
1326 __isl_keep isl_union_multi_pw_aff *mupa,
1327 enum isl_dim_type type, __isl_keep isl_id *id);
1328 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1329 enum isl_dim_type type, const char *name);
1330 int isl_multi_aff_find_dim_by_name(
1331 __isl_keep isl_multi_aff *ma,
1332 enum isl_dim_type type, const char *name);
1333 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1334 enum isl_dim_type type, const char *name);
1335 int isl_multi_pw_aff_find_dim_by_name(
1336 __isl_keep isl_multi_pw_aff *mpa,
1337 enum isl_dim_type type, const char *name);
1338 int isl_pw_multi_aff_find_dim_by_name(
1339 __isl_keep isl_pw_multi_aff *pma,
1340 enum isl_dim_type type, const char *name);
1341 int isl_union_pw_aff_find_dim_by_name(
1342 __isl_keep isl_union_pw_aff *upa,
1343 enum isl_dim_type type, const char *name);
1344 int isl_union_pw_multi_aff_find_dim_by_name(
1345 __isl_keep isl_union_pw_multi_aff *upma,
1346 enum isl_dim_type type, const char *name);
1347 int isl_multi_union_pw_aff_find_dim_by_name(
1348 __isl_keep isl_multi_union_pw_aff *mupa,
1349 enum isl_dim_type type, const char *name);
1351 #include <isl/polynomial.h>
1352 int isl_pw_qpolynomial_find_dim_by_name(
1353 __isl_keep isl_pw_qpolynomial *pwqp,
1354 enum isl_dim_type type, const char *name);
1355 int isl_pw_qpolynomial_fold_find_dim_by_name(
1356 __isl_keep isl_pw_qpolynomial_fold *pwf,
1357 enum isl_dim_type type, const char *name);
1358 int isl_union_pw_qpolynomial_find_dim_by_name(
1359 __isl_keep isl_union_pw_qpolynomial *upwqp,
1360 enum isl_dim_type type, const char *name);
1361 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1362 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1363 enum isl_dim_type type, const char *name);
1365 The identifiers or names of entire spaces may be set or read off
1366 using the following functions.
1368 #include <isl/space.h>
1369 __isl_give isl_space *isl_space_set_tuple_id(
1370 __isl_take isl_space *space,
1371 enum isl_dim_type type, __isl_take isl_id *id);
1372 __isl_give isl_space *isl_space_reset_tuple_id(
1373 __isl_take isl_space *space, enum isl_dim_type type);
1374 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1375 enum isl_dim_type type);
1376 __isl_give isl_id *isl_space_get_tuple_id(
1377 __isl_keep isl_space *space, enum isl_dim_type type);
1378 __isl_give isl_space *isl_space_set_tuple_name(
1379 __isl_take isl_space *space,
1380 enum isl_dim_type type, const char *s);
1381 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1382 enum isl_dim_type type);
1383 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1384 enum isl_dim_type type);
1386 #include <isl/local_space.h>
1387 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1388 __isl_take isl_local_space *ls,
1389 enum isl_dim_type type, __isl_take isl_id *id);
1391 #include <isl/set.h>
1392 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1393 __isl_take isl_basic_set *bset,
1394 __isl_take isl_id *id);
1395 __isl_give isl_set *isl_set_set_tuple_id(
1396 __isl_take isl_set *set, __isl_take isl_id *id);
1397 __isl_give isl_set *isl_set_reset_tuple_id(
1398 __isl_take isl_set *set);
1399 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1400 __isl_give isl_id *isl_set_get_tuple_id(
1401 __isl_keep isl_set *set);
1402 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1403 __isl_take isl_basic_set *set, const char *s);
1404 __isl_give isl_set *isl_set_set_tuple_name(
1405 __isl_take isl_set *set, const char *s);
1406 const char *isl_basic_set_get_tuple_name(
1407 __isl_keep isl_basic_set *bset);
1408 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1409 const char *isl_set_get_tuple_name(
1410 __isl_keep isl_set *set);
1412 #include <isl/map.h>
1413 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1414 __isl_take isl_basic_map *bmap,
1415 enum isl_dim_type type, __isl_take isl_id *id);
1416 __isl_give isl_map *isl_map_set_tuple_id(
1417 __isl_take isl_map *map, enum isl_dim_type type,
1418 __isl_take isl_id *id);
1419 __isl_give isl_map *isl_map_reset_tuple_id(
1420 __isl_take isl_map *map, enum isl_dim_type type);
1421 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1422 enum isl_dim_type type);
1423 __isl_give isl_id *isl_map_get_tuple_id(
1424 __isl_keep isl_map *map, enum isl_dim_type type);
1425 __isl_give isl_map *isl_map_set_tuple_name(
1426 __isl_take isl_map *map,
1427 enum isl_dim_type type, const char *s);
1428 const char *isl_basic_map_get_tuple_name(
1429 __isl_keep isl_basic_map *bmap,
1430 enum isl_dim_type type);
1431 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1432 __isl_take isl_basic_map *bmap,
1433 enum isl_dim_type type, const char *s);
1434 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1435 enum isl_dim_type type);
1436 const char *isl_map_get_tuple_name(
1437 __isl_keep isl_map *map,
1438 enum isl_dim_type type);
1440 #include <isl/val.h>
1441 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1442 __isl_take isl_multi_val *mv,
1443 enum isl_dim_type type, __isl_take isl_id *id);
1444 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1445 __isl_take isl_multi_val *mv,
1446 enum isl_dim_type type);
1447 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1448 enum isl_dim_type type);
1449 __isl_give isl_id *isl_multi_val_get_tuple_id(
1450 __isl_keep isl_multi_val *mv,
1451 enum isl_dim_type type);
1452 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1453 __isl_take isl_multi_val *mv,
1454 enum isl_dim_type type, const char *s);
1455 const char *isl_multi_val_get_tuple_name(
1456 __isl_keep isl_multi_val *mv,
1457 enum isl_dim_type type);
1459 #include <isl/aff.h>
1460 __isl_give isl_aff *isl_aff_set_tuple_id(
1461 __isl_take isl_aff *aff,
1462 enum isl_dim_type type, __isl_take isl_id *id);
1463 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1464 __isl_take isl_multi_aff *maff,
1465 enum isl_dim_type type, __isl_take isl_id *id);
1466 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1467 __isl_take isl_pw_aff *pwaff,
1468 enum isl_dim_type type, __isl_take isl_id *id);
1469 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1470 __isl_take isl_pw_multi_aff *pma,
1471 enum isl_dim_type type, __isl_take isl_id *id);
1472 __isl_give isl_multi_union_pw_aff *
1473 isl_multi_union_pw_aff_set_tuple_id(
1474 __isl_take isl_multi_union_pw_aff *mupa,
1475 enum isl_dim_type type, __isl_take isl_id *id);
1476 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1477 __isl_take isl_multi_aff *ma,
1478 enum isl_dim_type type);
1479 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1480 __isl_take isl_pw_aff *pa,
1481 enum isl_dim_type type);
1482 __isl_give isl_multi_pw_aff *
1483 isl_multi_pw_aff_reset_tuple_id(
1484 __isl_take isl_multi_pw_aff *mpa,
1485 enum isl_dim_type type);
1486 __isl_give isl_pw_multi_aff *
1487 isl_pw_multi_aff_reset_tuple_id(
1488 __isl_take isl_pw_multi_aff *pma,
1489 enum isl_dim_type type);
1490 __isl_give isl_multi_union_pw_aff *
1491 isl_multi_union_pw_aff_reset_tuple_id(
1492 __isl_take isl_multi_union_pw_aff *mupa,
1493 enum isl_dim_type type);
1494 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1495 enum isl_dim_type type);
1496 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1497 __isl_keep isl_multi_aff *ma,
1498 enum isl_dim_type type);
1499 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1500 enum isl_dim_type type);
1501 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1502 __isl_keep isl_pw_aff *pa,
1503 enum isl_dim_type type);
1504 int isl_pw_multi_aff_has_tuple_id(
1505 __isl_keep isl_pw_multi_aff *pma,
1506 enum isl_dim_type type);
1507 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1508 __isl_keep isl_pw_multi_aff *pma,
1509 enum isl_dim_type type);
1510 int isl_multi_pw_aff_has_tuple_id(
1511 __isl_keep isl_multi_pw_aff *mpa,
1512 enum isl_dim_type type);
1513 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1514 __isl_keep isl_multi_pw_aff *mpa,
1515 enum isl_dim_type type);
1516 int isl_multi_union_pw_aff_has_tuple_id(
1517 __isl_keep isl_multi_union_pw_aff *mupa,
1518 enum isl_dim_type type);
1519 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1520 __isl_keep isl_multi_union_pw_aff *mupa,
1521 enum isl_dim_type type);
1522 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1523 __isl_take isl_multi_aff *maff,
1524 enum isl_dim_type type, const char *s);
1525 __isl_give isl_multi_pw_aff *
1526 isl_multi_pw_aff_set_tuple_name(
1527 __isl_take isl_multi_pw_aff *mpa,
1528 enum isl_dim_type type, const char *s);
1529 __isl_give isl_multi_union_pw_aff *
1530 isl_multi_union_pw_aff_set_tuple_name(
1531 __isl_take isl_multi_union_pw_aff *mupa,
1532 enum isl_dim_type type, const char *s);
1533 const char *isl_multi_aff_get_tuple_name(
1534 __isl_keep isl_multi_aff *multi,
1535 enum isl_dim_type type);
1536 int isl_pw_multi_aff_has_tuple_name(
1537 __isl_keep isl_pw_multi_aff *pma,
1538 enum isl_dim_type type);
1539 const char *isl_pw_multi_aff_get_tuple_name(
1540 __isl_keep isl_pw_multi_aff *pma,
1541 enum isl_dim_type type);
1542 const char *isl_multi_union_pw_aff_get_tuple_name(
1543 __isl_keep isl_multi_union_pw_aff *mupa,
1544 enum isl_dim_type type);
1546 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1547 or C<isl_dim_set>. As with C<isl_space_get_name>,
1548 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1550 Binary operations require the corresponding spaces of their arguments
1551 to have the same name.
1553 To keep the names of all parameters and tuples, but reset the user pointers
1554 of all the corresponding identifiers, use the following function.
1556 #include <isl/space.h>
1557 __isl_give isl_space *isl_space_reset_user(
1558 __isl_take isl_space *space);
1560 #include <isl/set.h>
1561 __isl_give isl_set *isl_set_reset_user(
1562 __isl_take isl_set *set);
1564 #include <isl/map.h>
1565 __isl_give isl_map *isl_map_reset_user(
1566 __isl_take isl_map *map);
1568 #include <isl/union_set.h>
1569 __isl_give isl_union_set *isl_union_set_reset_user(
1570 __isl_take isl_union_set *uset);
1572 #include <isl/union_map.h>
1573 __isl_give isl_union_map *isl_union_map_reset_user(
1574 __isl_take isl_union_map *umap);
1576 #include <isl/val.h>
1577 __isl_give isl_multi_val *isl_multi_val_reset_user(
1578 __isl_take isl_multi_val *mv);
1580 #include <isl/aff.h>
1581 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1582 __isl_take isl_multi_aff *ma);
1583 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1584 __isl_take isl_pw_aff *pa);
1585 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1586 __isl_take isl_multi_pw_aff *mpa);
1587 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1588 __isl_take isl_pw_multi_aff *pma);
1589 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1590 __isl_take isl_union_pw_aff *upa);
1591 __isl_give isl_multi_union_pw_aff *
1592 isl_multi_union_pw_aff_reset_user(
1593 __isl_take isl_multi_union_pw_aff *mupa);
1594 __isl_give isl_union_pw_multi_aff *
1595 isl_union_pw_multi_aff_reset_user(
1596 __isl_take isl_union_pw_multi_aff *upma);
1598 #include <isl/polynomial.h>
1599 __isl_give isl_pw_qpolynomial *
1600 isl_pw_qpolynomial_reset_user(
1601 __isl_take isl_pw_qpolynomial *pwqp);
1602 __isl_give isl_union_pw_qpolynomial *
1603 isl_union_pw_qpolynomial_reset_user(
1604 __isl_take isl_union_pw_qpolynomial *upwqp);
1605 __isl_give isl_pw_qpolynomial_fold *
1606 isl_pw_qpolynomial_fold_reset_user(
1607 __isl_take isl_pw_qpolynomial_fold *pwf);
1608 __isl_give isl_union_pw_qpolynomial_fold *
1609 isl_union_pw_qpolynomial_fold_reset_user(
1610 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1612 Spaces can be nested. In particular, the domain of a set or
1613 the domain or range of a relation can be a nested relation.
1614 This process is also called I<wrapping>.
1615 The functions for detecting, constructing and deconstructing
1616 such nested spaces can be found in the wrapping properties
1617 of L</"Unary Properties">, the wrapping operations
1618 of L</"Unary Operations"> and the Cartesian product operations
1619 of L</"Basic Operations">.
1621 Spaces can be created from other spaces
1622 using the functions described in L</"Unary Operations">
1623 and L</"Binary Operations">.
1627 A local space is essentially a space with
1628 zero or more existentially quantified variables.
1629 The local space of various objects can be obtained
1630 using the following functions.
1632 #include <isl/constraint.h>
1633 __isl_give isl_local_space *isl_constraint_get_local_space(
1634 __isl_keep isl_constraint *constraint);
1636 #include <isl/set.h>
1637 __isl_give isl_local_space *isl_basic_set_get_local_space(
1638 __isl_keep isl_basic_set *bset);
1640 #include <isl/map.h>
1641 __isl_give isl_local_space *isl_basic_map_get_local_space(
1642 __isl_keep isl_basic_map *bmap);
1644 #include <isl/aff.h>
1645 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1646 __isl_keep isl_aff *aff);
1647 __isl_give isl_local_space *isl_aff_get_local_space(
1648 __isl_keep isl_aff *aff);
1650 A new local space can be created from a space using
1652 #include <isl/local_space.h>
1653 __isl_give isl_local_space *isl_local_space_from_space(
1654 __isl_take isl_space *space);
1656 They can be inspected, modified, copied and freed using the following functions.
1658 #include <isl/local_space.h>
1659 int isl_local_space_is_params(
1660 __isl_keep isl_local_space *ls);
1661 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1662 __isl_give isl_space *isl_local_space_get_space(
1663 __isl_keep isl_local_space *ls);
1664 __isl_give isl_aff *isl_local_space_get_div(
1665 __isl_keep isl_local_space *ls, int pos);
1666 __isl_give isl_local_space *isl_local_space_copy(
1667 __isl_keep isl_local_space *ls);
1668 __isl_null isl_local_space *isl_local_space_free(
1669 __isl_take isl_local_space *ls);
1671 Note that C<isl_local_space_get_div> can only be used on local spaces
1674 Two local spaces can be compared using
1676 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1677 __isl_keep isl_local_space *ls2);
1679 Local spaces can be created from other local spaces
1680 using the functions described in L</"Unary Operations">
1681 and L</"Binary Operations">.
1683 =head2 Creating New Sets and Relations
1685 C<isl> has functions for creating some standard sets and relations.
1689 =item * Empty sets and relations
1691 __isl_give isl_basic_set *isl_basic_set_empty(
1692 __isl_take isl_space *space);
1693 __isl_give isl_basic_map *isl_basic_map_empty(
1694 __isl_take isl_space *space);
1695 __isl_give isl_set *isl_set_empty(
1696 __isl_take isl_space *space);
1697 __isl_give isl_map *isl_map_empty(
1698 __isl_take isl_space *space);
1699 __isl_give isl_union_set *isl_union_set_empty(
1700 __isl_take isl_space *space);
1701 __isl_give isl_union_map *isl_union_map_empty(
1702 __isl_take isl_space *space);
1704 For C<isl_union_set>s and C<isl_union_map>s, the space
1705 is only used to specify the parameters.
1707 =item * Universe sets and relations
1709 __isl_give isl_basic_set *isl_basic_set_universe(
1710 __isl_take isl_space *space);
1711 __isl_give isl_basic_map *isl_basic_map_universe(
1712 __isl_take isl_space *space);
1713 __isl_give isl_set *isl_set_universe(
1714 __isl_take isl_space *space);
1715 __isl_give isl_map *isl_map_universe(
1716 __isl_take isl_space *space);
1717 __isl_give isl_union_set *isl_union_set_universe(
1718 __isl_take isl_union_set *uset);
1719 __isl_give isl_union_map *isl_union_map_universe(
1720 __isl_take isl_union_map *umap);
1722 The sets and relations constructed by the functions above
1723 contain all integer values, while those constructed by the
1724 functions below only contain non-negative values.
1726 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1727 __isl_take isl_space *space);
1728 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1729 __isl_take isl_space *space);
1730 __isl_give isl_set *isl_set_nat_universe(
1731 __isl_take isl_space *space);
1732 __isl_give isl_map *isl_map_nat_universe(
1733 __isl_take isl_space *space);
1735 =item * Identity relations
1737 __isl_give isl_basic_map *isl_basic_map_identity(
1738 __isl_take isl_space *space);
1739 __isl_give isl_map *isl_map_identity(
1740 __isl_take isl_space *space);
1742 The number of input and output dimensions in C<space> needs
1745 =item * Lexicographic order
1747 __isl_give isl_map *isl_map_lex_lt(
1748 __isl_take isl_space *set_space);
1749 __isl_give isl_map *isl_map_lex_le(
1750 __isl_take isl_space *set_space);
1751 __isl_give isl_map *isl_map_lex_gt(
1752 __isl_take isl_space *set_space);
1753 __isl_give isl_map *isl_map_lex_ge(
1754 __isl_take isl_space *set_space);
1755 __isl_give isl_map *isl_map_lex_lt_first(
1756 __isl_take isl_space *space, unsigned n);
1757 __isl_give isl_map *isl_map_lex_le_first(
1758 __isl_take isl_space *space, unsigned n);
1759 __isl_give isl_map *isl_map_lex_gt_first(
1760 __isl_take isl_space *space, unsigned n);
1761 __isl_give isl_map *isl_map_lex_ge_first(
1762 __isl_take isl_space *space, unsigned n);
1764 The first four functions take a space for a B<set>
1765 and return relations that express that the elements in the domain
1766 are lexicographically less
1767 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1768 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1769 than the elements in the range.
1770 The last four functions take a space for a map
1771 and return relations that express that the first C<n> dimensions
1772 in the domain are lexicographically less
1773 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1774 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1775 than the first C<n> dimensions in the range.
1779 A basic set or relation can be converted to a set or relation
1780 using the following functions.
1782 __isl_give isl_set *isl_set_from_basic_set(
1783 __isl_take isl_basic_set *bset);
1784 __isl_give isl_map *isl_map_from_basic_map(
1785 __isl_take isl_basic_map *bmap);
1787 Sets and relations can be converted to union sets and relations
1788 using the following functions.
1790 __isl_give isl_union_set *isl_union_set_from_basic_set(
1791 __isl_take isl_basic_set *bset);
1792 __isl_give isl_union_map *isl_union_map_from_basic_map(
1793 __isl_take isl_basic_map *bmap);
1794 __isl_give isl_union_set *isl_union_set_from_set(
1795 __isl_take isl_set *set);
1796 __isl_give isl_union_map *isl_union_map_from_map(
1797 __isl_take isl_map *map);
1799 The inverse conversions below can only be used if the input
1800 union set or relation is known to contain elements in exactly one
1803 __isl_give isl_set *isl_set_from_union_set(
1804 __isl_take isl_union_set *uset);
1805 __isl_give isl_map *isl_map_from_union_map(
1806 __isl_take isl_union_map *umap);
1808 Sets and relations can be copied and freed again using the following
1811 __isl_give isl_basic_set *isl_basic_set_copy(
1812 __isl_keep isl_basic_set *bset);
1813 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1814 __isl_give isl_union_set *isl_union_set_copy(
1815 __isl_keep isl_union_set *uset);
1816 __isl_give isl_basic_map *isl_basic_map_copy(
1817 __isl_keep isl_basic_map *bmap);
1818 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1819 __isl_give isl_union_map *isl_union_map_copy(
1820 __isl_keep isl_union_map *umap);
1821 __isl_null isl_basic_set *isl_basic_set_free(
1822 __isl_take isl_basic_set *bset);
1823 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1824 __isl_null isl_union_set *isl_union_set_free(
1825 __isl_take isl_union_set *uset);
1826 __isl_null isl_basic_map *isl_basic_map_free(
1827 __isl_take isl_basic_map *bmap);
1828 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1829 __isl_null isl_union_map *isl_union_map_free(
1830 __isl_take isl_union_map *umap);
1832 Other sets and relations can be constructed by starting
1833 from a universe set or relation, adding equality and/or
1834 inequality constraints and then projecting out the
1835 existentially quantified variables, if any.
1836 Constraints can be constructed, manipulated and
1837 added to (or removed from) (basic) sets and relations
1838 using the following functions.
1840 #include <isl/constraint.h>
1841 __isl_give isl_constraint *isl_equality_alloc(
1842 __isl_take isl_local_space *ls);
1843 __isl_give isl_constraint *isl_inequality_alloc(
1844 __isl_take isl_local_space *ls);
1845 __isl_give isl_constraint *isl_constraint_set_constant_si(
1846 __isl_take isl_constraint *constraint, int v);
1847 __isl_give isl_constraint *isl_constraint_set_constant_val(
1848 __isl_take isl_constraint *constraint,
1849 __isl_take isl_val *v);
1850 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1851 __isl_take isl_constraint *constraint,
1852 enum isl_dim_type type, int pos, int v);
1853 __isl_give isl_constraint *
1854 isl_constraint_set_coefficient_val(
1855 __isl_take isl_constraint *constraint,
1856 enum isl_dim_type type, int pos,
1857 __isl_take isl_val *v);
1858 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1859 __isl_take isl_basic_map *bmap,
1860 __isl_take isl_constraint *constraint);
1861 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1862 __isl_take isl_basic_set *bset,
1863 __isl_take isl_constraint *constraint);
1864 __isl_give isl_map *isl_map_add_constraint(
1865 __isl_take isl_map *map,
1866 __isl_take isl_constraint *constraint);
1867 __isl_give isl_set *isl_set_add_constraint(
1868 __isl_take isl_set *set,
1869 __isl_take isl_constraint *constraint);
1870 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1871 __isl_take isl_basic_set *bset,
1872 __isl_take isl_constraint *constraint);
1874 For example, to create a set containing the even integers
1875 between 10 and 42, you would use the following code.
1878 isl_local_space *ls;
1880 isl_basic_set *bset;
1882 space = isl_space_set_alloc(ctx, 0, 2);
1883 bset = isl_basic_set_universe(isl_space_copy(space));
1884 ls = isl_local_space_from_space(space);
1886 c = isl_equality_alloc(isl_local_space_copy(ls));
1887 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1888 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1889 bset = isl_basic_set_add_constraint(bset, c);
1891 c = isl_inequality_alloc(isl_local_space_copy(ls));
1892 c = isl_constraint_set_constant_si(c, -10);
1893 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1894 bset = isl_basic_set_add_constraint(bset, c);
1896 c = isl_inequality_alloc(ls);
1897 c = isl_constraint_set_constant_si(c, 42);
1898 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1899 bset = isl_basic_set_add_constraint(bset, c);
1901 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1905 isl_basic_set *bset;
1906 bset = isl_basic_set_read_from_str(ctx,
1907 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1909 A basic set or relation can also be constructed from two matrices
1910 describing the equalities and the inequalities.
1912 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1913 __isl_take isl_space *space,
1914 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1915 enum isl_dim_type c1,
1916 enum isl_dim_type c2, enum isl_dim_type c3,
1917 enum isl_dim_type c4);
1918 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1919 __isl_take isl_space *space,
1920 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1921 enum isl_dim_type c1,
1922 enum isl_dim_type c2, enum isl_dim_type c3,
1923 enum isl_dim_type c4, enum isl_dim_type c5);
1925 The C<isl_dim_type> arguments indicate the order in which
1926 different kinds of variables appear in the input matrices
1927 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1928 C<isl_dim_set> and C<isl_dim_div> for sets and
1929 of C<isl_dim_cst>, C<isl_dim_param>,
1930 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1932 A (basic or union) set or relation can also be constructed from a
1933 (union) (piecewise) (multiple) affine expression
1934 or a list of affine expressions
1935 (See L</"Functions">).
1937 __isl_give isl_basic_map *isl_basic_map_from_aff(
1938 __isl_take isl_aff *aff);
1939 __isl_give isl_map *isl_map_from_aff(
1940 __isl_take isl_aff *aff);
1941 __isl_give isl_set *isl_set_from_pw_aff(
1942 __isl_take isl_pw_aff *pwaff);
1943 __isl_give isl_map *isl_map_from_pw_aff(
1944 __isl_take isl_pw_aff *pwaff);
1945 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1946 __isl_take isl_space *domain_space,
1947 __isl_take isl_aff_list *list);
1948 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1949 __isl_take isl_multi_aff *maff)
1950 __isl_give isl_map *isl_map_from_multi_aff(
1951 __isl_take isl_multi_aff *maff)
1952 __isl_give isl_set *isl_set_from_pw_multi_aff(
1953 __isl_take isl_pw_multi_aff *pma);
1954 __isl_give isl_map *isl_map_from_pw_multi_aff(
1955 __isl_take isl_pw_multi_aff *pma);
1956 __isl_give isl_set *isl_set_from_multi_pw_aff(
1957 __isl_take isl_multi_pw_aff *mpa);
1958 __isl_give isl_map *isl_map_from_multi_pw_aff(
1959 __isl_take isl_multi_pw_aff *mpa);
1960 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
1961 __isl_take isl_union_pw_aff *upa);
1962 __isl_give isl_union_map *
1963 isl_union_map_from_union_pw_multi_aff(
1964 __isl_take isl_union_pw_multi_aff *upma);
1966 The C<domain_space> argument describes the domain of the resulting
1967 basic relation. It is required because the C<list> may consist
1968 of zero affine expressions.
1970 =head2 Inspecting Sets and Relations
1972 Usually, the user should not have to care about the actual constraints
1973 of the sets and maps, but should instead apply the abstract operations
1974 explained in the following sections.
1975 Occasionally, however, it may be required to inspect the individual
1976 coefficients of the constraints. This section explains how to do so.
1977 In these cases, it may also be useful to have C<isl> compute
1978 an explicit representation of the existentially quantified variables.
1980 __isl_give isl_set *isl_set_compute_divs(
1981 __isl_take isl_set *set);
1982 __isl_give isl_map *isl_map_compute_divs(
1983 __isl_take isl_map *map);
1984 __isl_give isl_union_set *isl_union_set_compute_divs(
1985 __isl_take isl_union_set *uset);
1986 __isl_give isl_union_map *isl_union_map_compute_divs(
1987 __isl_take isl_union_map *umap);
1989 This explicit representation defines the existentially quantified
1990 variables as integer divisions of the other variables, possibly
1991 including earlier existentially quantified variables.
1992 An explicitly represented existentially quantified variable therefore
1993 has a unique value when the values of the other variables are known.
1994 If, furthermore, the same existentials, i.e., existentials
1995 with the same explicit representations, should appear in the
1996 same order in each of the disjuncts of a set or map, then the user should call
1997 either of the following functions.
1999 __isl_give isl_set *isl_set_align_divs(
2000 __isl_take isl_set *set);
2001 __isl_give isl_map *isl_map_align_divs(
2002 __isl_take isl_map *map);
2004 Alternatively, the existentially quantified variables can be removed
2005 using the following functions, which compute an overapproximation.
2007 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2008 __isl_take isl_basic_set *bset);
2009 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2010 __isl_take isl_basic_map *bmap);
2011 __isl_give isl_set *isl_set_remove_divs(
2012 __isl_take isl_set *set);
2013 __isl_give isl_map *isl_map_remove_divs(
2014 __isl_take isl_map *map);
2016 It is also possible to only remove those divs that are defined
2017 in terms of a given range of dimensions or only those for which
2018 no explicit representation is known.
2020 __isl_give isl_basic_set *
2021 isl_basic_set_remove_divs_involving_dims(
2022 __isl_take isl_basic_set *bset,
2023 enum isl_dim_type type,
2024 unsigned first, unsigned n);
2025 __isl_give isl_basic_map *
2026 isl_basic_map_remove_divs_involving_dims(
2027 __isl_take isl_basic_map *bmap,
2028 enum isl_dim_type type,
2029 unsigned first, unsigned n);
2030 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2031 __isl_take isl_set *set, enum isl_dim_type type,
2032 unsigned first, unsigned n);
2033 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2034 __isl_take isl_map *map, enum isl_dim_type type,
2035 unsigned first, unsigned n);
2037 __isl_give isl_basic_set *
2038 isl_basic_set_remove_unknown_divs(
2039 __isl_take isl_basic_set *bset);
2040 __isl_give isl_set *isl_set_remove_unknown_divs(
2041 __isl_take isl_set *set);
2042 __isl_give isl_map *isl_map_remove_unknown_divs(
2043 __isl_take isl_map *map);
2045 To iterate over all the sets or maps in a union set or map, use
2047 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
2048 int (*fn)(__isl_take isl_set *set, void *user),
2050 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
2051 int (*fn)(__isl_take isl_map *map, void *user),
2054 The number of sets or maps in a union set or map can be obtained
2057 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2058 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2060 To extract the set or map in a given space from a union, use
2062 __isl_give isl_set *isl_union_set_extract_set(
2063 __isl_keep isl_union_set *uset,
2064 __isl_take isl_space *space);
2065 __isl_give isl_map *isl_union_map_extract_map(
2066 __isl_keep isl_union_map *umap,
2067 __isl_take isl_space *space);
2069 To iterate over all the basic sets or maps in a set or map, use
2071 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
2072 int (*fn)(__isl_take isl_basic_set *bset, void *user),
2074 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
2075 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
2078 The callback function C<fn> should return 0 if successful and
2079 -1 if an error occurs. In the latter case, or if any other error
2080 occurs, the above functions will return -1.
2082 It should be noted that C<isl> does not guarantee that
2083 the basic sets or maps passed to C<fn> are disjoint.
2084 If this is required, then the user should call one of
2085 the following functions first.
2087 __isl_give isl_set *isl_set_make_disjoint(
2088 __isl_take isl_set *set);
2089 __isl_give isl_map *isl_map_make_disjoint(
2090 __isl_take isl_map *map);
2092 The number of basic sets in a set can be obtained
2093 or the number of basic maps in a map can be obtained
2096 #include <isl/set.h>
2097 int isl_set_n_basic_set(__isl_keep isl_set *set);
2099 #include <isl/map.h>
2100 int isl_map_n_basic_map(__isl_keep isl_map *map);
2102 To iterate over the constraints of a basic set or map, use
2104 #include <isl/constraint.h>
2106 int isl_basic_set_n_constraint(
2107 __isl_keep isl_basic_set *bset);
2108 int isl_basic_set_foreach_constraint(
2109 __isl_keep isl_basic_set *bset,
2110 int (*fn)(__isl_take isl_constraint *c, void *user),
2112 int isl_basic_map_n_constraint(
2113 __isl_keep isl_basic_map *bmap);
2114 int isl_basic_map_foreach_constraint(
2115 __isl_keep isl_basic_map *bmap,
2116 int (*fn)(__isl_take isl_constraint *c, void *user),
2118 __isl_null isl_constraint *isl_constraint_free(
2119 __isl_take isl_constraint *c);
2121 Again, the callback function C<fn> should return 0 if successful and
2122 -1 if an error occurs. In the latter case, or if any other error
2123 occurs, the above functions will return -1.
2124 The constraint C<c> represents either an equality or an inequality.
2125 Use the following function to find out whether a constraint
2126 represents an equality. If not, it represents an inequality.
2128 int isl_constraint_is_equality(
2129 __isl_keep isl_constraint *constraint);
2131 It is also possible to obtain a list of constraints from a basic
2134 #include <isl/constraint.h>
2135 __isl_give isl_constraint_list *
2136 isl_basic_map_get_constraint_list(
2137 __isl_keep isl_basic_map *bmap);
2138 __isl_give isl_constraint_list *
2139 isl_basic_set_get_constraint_list(
2140 __isl_keep isl_basic_set *bset);
2142 These functions require that all existentially quantified variables
2143 have an explicit representation.
2144 The returned list can be manipulated using the functions in L<"Lists">.
2146 The coefficients of the constraints can be inspected using
2147 the following functions.
2149 int isl_constraint_is_lower_bound(
2150 __isl_keep isl_constraint *constraint,
2151 enum isl_dim_type type, unsigned pos);
2152 int isl_constraint_is_upper_bound(
2153 __isl_keep isl_constraint *constraint,
2154 enum isl_dim_type type, unsigned pos);
2155 __isl_give isl_val *isl_constraint_get_constant_val(
2156 __isl_keep isl_constraint *constraint);
2157 __isl_give isl_val *isl_constraint_get_coefficient_val(
2158 __isl_keep isl_constraint *constraint,
2159 enum isl_dim_type type, int pos);
2161 The explicit representations of the existentially quantified
2162 variables can be inspected using the following function.
2163 Note that the user is only allowed to use this function
2164 if the inspected set or map is the result of a call
2165 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2166 The existentially quantified variable is equal to the floor
2167 of the returned affine expression. The affine expression
2168 itself can be inspected using the functions in
2171 __isl_give isl_aff *isl_constraint_get_div(
2172 __isl_keep isl_constraint *constraint, int pos);
2174 To obtain the constraints of a basic set or map in matrix
2175 form, use the following functions.
2177 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2178 __isl_keep isl_basic_set *bset,
2179 enum isl_dim_type c1, enum isl_dim_type c2,
2180 enum isl_dim_type c3, enum isl_dim_type c4);
2181 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2182 __isl_keep isl_basic_set *bset,
2183 enum isl_dim_type c1, enum isl_dim_type c2,
2184 enum isl_dim_type c3, enum isl_dim_type c4);
2185 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2186 __isl_keep isl_basic_map *bmap,
2187 enum isl_dim_type c1,
2188 enum isl_dim_type c2, enum isl_dim_type c3,
2189 enum isl_dim_type c4, enum isl_dim_type c5);
2190 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2191 __isl_keep isl_basic_map *bmap,
2192 enum isl_dim_type c1,
2193 enum isl_dim_type c2, enum isl_dim_type c3,
2194 enum isl_dim_type c4, enum isl_dim_type c5);
2196 The C<isl_dim_type> arguments dictate the order in which
2197 different kinds of variables appear in the resulting matrix.
2198 For set inputs, they should be a permutation of
2199 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2200 For map inputs, they should be a permutation of
2201 C<isl_dim_cst>, C<isl_dim_param>,
2202 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2206 Points are elements of a set. They can be used to construct
2207 simple sets (boxes) or they can be used to represent the
2208 individual elements of a set.
2209 The zero point (the origin) can be created using
2211 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2213 The coordinates of a point can be inspected, set and changed
2216 __isl_give isl_val *isl_point_get_coordinate_val(
2217 __isl_keep isl_point *pnt,
2218 enum isl_dim_type type, int pos);
2219 __isl_give isl_point *isl_point_set_coordinate_val(
2220 __isl_take isl_point *pnt,
2221 enum isl_dim_type type, int pos,
2222 __isl_take isl_val *v);
2224 __isl_give isl_point *isl_point_add_ui(
2225 __isl_take isl_point *pnt,
2226 enum isl_dim_type type, int pos, unsigned val);
2227 __isl_give isl_point *isl_point_sub_ui(
2228 __isl_take isl_point *pnt,
2229 enum isl_dim_type type, int pos, unsigned val);
2231 Points can be copied or freed using
2233 __isl_give isl_point *isl_point_copy(
2234 __isl_keep isl_point *pnt);
2235 void isl_point_free(__isl_take isl_point *pnt);
2237 A singleton set can be created from a point using
2239 __isl_give isl_basic_set *isl_basic_set_from_point(
2240 __isl_take isl_point *pnt);
2241 __isl_give isl_set *isl_set_from_point(
2242 __isl_take isl_point *pnt);
2244 and a box can be created from two opposite extremal points using
2246 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2247 __isl_take isl_point *pnt1,
2248 __isl_take isl_point *pnt2);
2249 __isl_give isl_set *isl_set_box_from_points(
2250 __isl_take isl_point *pnt1,
2251 __isl_take isl_point *pnt2);
2253 All elements of a B<bounded> (union) set can be enumerated using
2254 the following functions.
2256 int isl_set_foreach_point(__isl_keep isl_set *set,
2257 int (*fn)(__isl_take isl_point *pnt, void *user),
2259 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2260 int (*fn)(__isl_take isl_point *pnt, void *user),
2263 The function C<fn> is called for each integer point in
2264 C<set> with as second argument the last argument of
2265 the C<isl_set_foreach_point> call. The function C<fn>
2266 should return C<0> on success and C<-1> on failure.
2267 In the latter case, C<isl_set_foreach_point> will stop
2268 enumerating and return C<-1> as well.
2269 If the enumeration is performed successfully and to completion,
2270 then C<isl_set_foreach_point> returns C<0>.
2272 To obtain a single point of a (basic) set, use
2274 __isl_give isl_point *isl_basic_set_sample_point(
2275 __isl_take isl_basic_set *bset);
2276 __isl_give isl_point *isl_set_sample_point(
2277 __isl_take isl_set *set);
2279 If C<set> does not contain any (integer) points, then the
2280 resulting point will be ``void'', a property that can be
2283 int isl_point_is_void(__isl_keep isl_point *pnt);
2287 Besides sets and relation, C<isl> also supports various types of functions.
2288 Each of these types is derived from the value type (see L</"Values">)
2289 or from one of two primitive function types
2290 through the application of zero or more type constructors.
2291 We first describe the primitive type and then we describe
2292 the types derived from these primitive types.
2294 =head3 Primitive Functions
2296 C<isl> support two primitive function types, quasi-affine
2297 expressions and quasipolynomials.
2298 A quasi-affine expression is defined either over a parameter
2299 space or over a set and is composed of integer constants,
2300 parameters and set variables, addition, subtraction and
2301 integer division by an integer constant.
2302 For example, the quasi-affine expression
2304 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2306 maps C<x> to C<2*floor((4 n + x)/9>.
2307 A quasipolynomial is a polynomial expression in quasi-affine
2308 expression. That is, it additionally allows for multiplication.
2309 Note, though, that it is not allowed to construct an integer
2310 division of an expression involving multiplications.
2311 Here is an example of a quasipolynomial that is not
2312 quasi-affine expression
2314 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2316 Note that the external representations of quasi-affine expressions
2317 and quasipolynomials are different. Quasi-affine expressions
2318 use a notation with square brackets just like binary relations,
2319 while quasipolynomials do not. This might change at some point.
2321 If a primitive function is defined over a parameter space,
2322 then the space of the function itself is that of a set.
2323 If it is defined over a set, then the space of the function
2324 is that of a relation. In both cases, the set space (or
2325 the output space) is single-dimensional, anonymous and unstructured.
2326 To create functions with multiple dimensions or with other kinds
2327 of set or output spaces, use multiple expressions
2328 (see L</"Multiple Expressions">).
2332 =item * Quasi-affine Expressions
2334 Besides the expressions described above, a quasi-affine
2335 expression can also be set to NaN. Such expressions
2336 typically represent a failure to represent a result
2337 as a quasi-affine expression.
2339 The zero quasi affine expression or the quasi affine expression
2340 that is equal to a given value or
2341 a specified dimension on a given domain can be created using
2343 #include <isl/aff.h>
2344 __isl_give isl_aff *isl_aff_zero_on_domain(
2345 __isl_take isl_local_space *ls);
2346 __isl_give isl_aff *isl_aff_val_on_domain(
2347 __isl_take isl_local_space *ls,
2348 __isl_take isl_val *val);
2349 __isl_give isl_aff *isl_aff_var_on_domain(
2350 __isl_take isl_local_space *ls,
2351 enum isl_dim_type type, unsigned pos);
2352 __isl_give isl_aff *isl_aff_nan_on_domain(
2353 __isl_take isl_local_space *ls);
2355 Quasi affine expressions can be copied and freed using
2357 #include <isl/aff.h>
2358 __isl_give isl_aff *isl_aff_copy(
2359 __isl_keep isl_aff *aff);
2360 __isl_null isl_aff *isl_aff_free(
2361 __isl_take isl_aff *aff);
2363 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2364 using the following function. The constraint is required to have
2365 a non-zero coefficient for the specified dimension.
2367 #include <isl/constraint.h>
2368 __isl_give isl_aff *isl_constraint_get_bound(
2369 __isl_keep isl_constraint *constraint,
2370 enum isl_dim_type type, int pos);
2372 The entire affine expression of the constraint can also be extracted
2373 using the following function.
2375 #include <isl/constraint.h>
2376 __isl_give isl_aff *isl_constraint_get_aff(
2377 __isl_keep isl_constraint *constraint);
2379 Conversely, an equality constraint equating
2380 the affine expression to zero or an inequality constraint enforcing
2381 the affine expression to be non-negative, can be constructed using
2383 __isl_give isl_constraint *isl_equality_from_aff(
2384 __isl_take isl_aff *aff);
2385 __isl_give isl_constraint *isl_inequality_from_aff(
2386 __isl_take isl_aff *aff);
2388 The coefficients and the integer divisions of an affine expression
2389 can be inspected using the following functions.
2391 #include <isl/aff.h>
2392 __isl_give isl_val *isl_aff_get_constant_val(
2393 __isl_keep isl_aff *aff);
2394 __isl_give isl_val *isl_aff_get_coefficient_val(
2395 __isl_keep isl_aff *aff,
2396 enum isl_dim_type type, int pos);
2397 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2398 enum isl_dim_type type, int pos);
2399 __isl_give isl_val *isl_aff_get_denominator_val(
2400 __isl_keep isl_aff *aff);
2401 __isl_give isl_aff *isl_aff_get_div(
2402 __isl_keep isl_aff *aff, int pos);
2404 They can be modified using the following functions.
2406 #include <isl/aff.h>
2407 __isl_give isl_aff *isl_aff_set_constant_si(
2408 __isl_take isl_aff *aff, int v);
2409 __isl_give isl_aff *isl_aff_set_constant_val(
2410 __isl_take isl_aff *aff, __isl_take isl_val *v);
2411 __isl_give isl_aff *isl_aff_set_coefficient_si(
2412 __isl_take isl_aff *aff,
2413 enum isl_dim_type type, int pos, int v);
2414 __isl_give isl_aff *isl_aff_set_coefficient_val(
2415 __isl_take isl_aff *aff,
2416 enum isl_dim_type type, int pos,
2417 __isl_take isl_val *v);
2419 __isl_give isl_aff *isl_aff_add_constant_si(
2420 __isl_take isl_aff *aff, int v);
2421 __isl_give isl_aff *isl_aff_add_constant_val(
2422 __isl_take isl_aff *aff, __isl_take isl_val *v);
2423 __isl_give isl_aff *isl_aff_add_constant_num_si(
2424 __isl_take isl_aff *aff, int v);
2425 __isl_give isl_aff *isl_aff_add_coefficient_si(
2426 __isl_take isl_aff *aff,
2427 enum isl_dim_type type, int pos, int v);
2428 __isl_give isl_aff *isl_aff_add_coefficient_val(
2429 __isl_take isl_aff *aff,
2430 enum isl_dim_type type, int pos,
2431 __isl_take isl_val *v);
2433 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2434 set the I<numerator> of the constant or coefficient, while
2435 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2436 the constant or coefficient as a whole.
2437 The C<add_constant> and C<add_coefficient> functions add an integer
2438 or rational value to
2439 the possibly rational constant or coefficient.
2440 The C<add_constant_num> functions add an integer value to
2443 =item * Quasipolynomials
2445 Some simple quasipolynomials can be created using the following functions.
2447 #include <isl/polynomial.h>
2448 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2449 __isl_take isl_space *domain);
2450 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2451 __isl_take isl_space *domain);
2452 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2453 __isl_take isl_space *domain);
2454 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2455 __isl_take isl_space *domain);
2456 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2457 __isl_take isl_space *domain);
2458 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2459 __isl_take isl_space *domain,
2460 __isl_take isl_val *val);
2461 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2462 __isl_take isl_space *domain,
2463 enum isl_dim_type type, unsigned pos);
2464 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2465 __isl_take isl_aff *aff);
2467 Recall that the space in which a quasipolynomial lives is a map space
2468 with a one-dimensional range. The C<domain> argument in some of
2469 the functions above corresponds to the domain of this map space.
2471 Quasipolynomials can be copied and freed again using the following
2474 #include <isl/polynomial.h>
2475 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2476 __isl_keep isl_qpolynomial *qp);
2477 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2478 __isl_take isl_qpolynomial *qp);
2480 The constant term of a quasipolynomial can be extracted using
2482 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2483 __isl_keep isl_qpolynomial *qp);
2485 To iterate over all terms in a quasipolynomial,
2488 int isl_qpolynomial_foreach_term(
2489 __isl_keep isl_qpolynomial *qp,
2490 int (*fn)(__isl_take isl_term *term,
2491 void *user), void *user);
2493 The terms themselves can be inspected and freed using
2496 unsigned isl_term_dim(__isl_keep isl_term *term,
2497 enum isl_dim_type type);
2498 __isl_give isl_val *isl_term_get_coefficient_val(
2499 __isl_keep isl_term *term);
2500 int isl_term_get_exp(__isl_keep isl_term *term,
2501 enum isl_dim_type type, unsigned pos);
2502 __isl_give isl_aff *isl_term_get_div(
2503 __isl_keep isl_term *term, unsigned pos);
2504 void isl_term_free(__isl_take isl_term *term);
2506 Each term is a product of parameters, set variables and
2507 integer divisions. The function C<isl_term_get_exp>
2508 returns the exponent of a given dimensions in the given term.
2514 A reduction represents a maximum or a minimum of its
2516 The only reduction type defined by C<isl> is
2517 C<isl_qpolynomial_fold>.
2519 There are currently no functions to directly create such
2520 objects, but they do appear in the piecewise quasipolynomial
2521 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2523 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2525 Reductions can be copied and freed using
2526 the following functions.
2528 #include <isl/polynomial.h>
2529 __isl_give isl_qpolynomial_fold *
2530 isl_qpolynomial_fold_copy(
2531 __isl_keep isl_qpolynomial_fold *fold);
2532 void isl_qpolynomial_fold_free(
2533 __isl_take isl_qpolynomial_fold *fold);
2535 To iterate over all quasipolynomials in a reduction, use
2537 int isl_qpolynomial_fold_foreach_qpolynomial(
2538 __isl_keep isl_qpolynomial_fold *fold,
2539 int (*fn)(__isl_take isl_qpolynomial *qp,
2540 void *user), void *user);
2542 =head3 Multiple Expressions
2544 A multiple expression represents a sequence of zero or
2545 more base expressions, all defined on the same domain space.
2546 The domain space of the multiple expression is the same
2547 as that of the base expressions, but the range space
2548 can be any space. In case the base expressions have
2549 a set space, the corresponding multiple expression
2550 also has a set space.
2551 Objects of the value type do not have an associated space.
2552 The space of a multiple value is therefore always a set space.
2553 Similarly, the space of a multiple union piecewise
2554 affine expression is always a set space.
2556 The multiple expression types defined by C<isl>
2557 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2558 C<isl_multi_union_pw_aff>.
2560 A multiple expression with the value zero for
2561 each output (or set) dimension can be created
2562 using the following functions.
2564 #include <isl/val.h>
2565 __isl_give isl_multi_val *isl_multi_val_zero(
2566 __isl_take isl_space *space);
2568 #include <isl/aff.h>
2569 __isl_give isl_multi_aff *isl_multi_aff_zero(
2570 __isl_take isl_space *space);
2571 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2572 __isl_take isl_space *space);
2573 __isl_give isl_multi_union_pw_aff *
2574 isl_multi_union_pw_aff_zero(
2575 __isl_take isl_space *space);
2577 Since there is no canonical way of representing a zero
2578 value of type C<isl_union_pw_aff>, the space passed
2579 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2581 An identity function can be created using the following
2582 functions. The space needs to be that of a relation
2583 with the same number of input and output dimensions.
2585 #include <isl/aff.h>
2586 __isl_give isl_multi_aff *isl_multi_aff_identity(
2587 __isl_take isl_space *space);
2588 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2589 __isl_take isl_space *space);
2591 A function that performs a projection on a universe
2592 relation or set can be created using the following functions.
2593 See also the corresponding
2594 projection operations in L</"Unary Operations">.
2596 #include <isl/aff.h>
2597 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2598 __isl_take isl_space *space);
2599 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2600 __isl_take isl_space *space);
2601 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2602 __isl_take isl_space *space,
2603 enum isl_dim_type type,
2604 unsigned first, unsigned n);
2606 A multiple expression can be created from a single
2607 base expression using the following functions.
2608 The space of the created multiple expression is the same
2609 as that of the base expression, except for
2610 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2611 lives in a parameter space and the output lives
2612 in a single-dimensional set space.
2614 #include <isl/aff.h>
2615 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2616 __isl_take isl_aff *aff);
2617 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2618 __isl_take isl_pw_aff *pa);
2619 __isl_give isl_multi_union_pw_aff *
2620 isl_multi_union_pw_aff_from_union_pw_aff(
2621 __isl_take isl_union_pw_aff *upa);
2623 A multiple expression can be created from a list
2624 of base expression in a specified space.
2625 The domain of this space needs to be the same
2626 as the domains of the base expressions in the list.
2627 If the base expressions have a set space (or no associated space),
2628 then this space also needs to be a set space.
2630 #include <isl/val.h>
2631 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2632 __isl_take isl_space *space,
2633 __isl_take isl_val_list *list);
2635 #include <isl/aff.h>
2636 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2637 __isl_take isl_space *space,
2638 __isl_take isl_aff_list *list);
2639 __isl_give isl_multi_union_pw_aff *
2640 isl_multi_union_pw_aff_from_union_pw_aff_list(
2641 __isl_take isl_space *space,
2642 __isl_take isl_union_pw_aff_list *list);
2644 As a convenience, a multiple piecewise expression can
2645 also be created from a multiple expression.
2646 Each piecewise expression in the result has a single
2649 #include <isl/aff.h>
2650 __isl_give isl_multi_pw_aff *
2651 isl_multi_pw_aff_from_multi_aff(
2652 __isl_take isl_multi_aff *ma);
2654 Similarly, a multiple union expression can be
2655 created from a multiple expression.
2657 #include <isl/aff.h>
2658 __isl_give isl_multi_union_pw_aff *
2659 isl_multi_union_pw_aff_from_multi_aff(
2660 __isl_take isl_multi_aff *ma);
2661 __isl_give isl_multi_union_pw_aff *
2662 isl_multi_union_pw_aff_from_multi_pw_aff(
2663 __isl_take isl_multi_pw_aff *mpa);
2665 A multiple quasi-affine expression can be created from
2666 a multiple value with a given domain space using the following
2669 #include <isl/aff.h>
2670 __isl_give isl_multi_aff *
2671 isl_multi_aff_multi_val_on_space(
2672 __isl_take isl_space *space,
2673 __isl_take isl_multi_val *mv);
2675 Multiple expressions can be copied and freed using
2676 the following functions.
2678 #include <isl/val.h>
2679 __isl_give isl_multi_val *isl_multi_val_copy(
2680 __isl_keep isl_multi_val *mv);
2681 __isl_null isl_multi_val *isl_multi_val_free(
2682 __isl_take isl_multi_val *mv);
2684 #include <isl/aff.h>
2685 __isl_give isl_multi_aff *isl_multi_aff_copy(
2686 __isl_keep isl_multi_aff *maff);
2687 __isl_null isl_multi_aff *isl_multi_aff_free(
2688 __isl_take isl_multi_aff *maff);
2689 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2690 __isl_keep isl_multi_pw_aff *mpa);
2691 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2692 __isl_take isl_multi_pw_aff *mpa);
2693 __isl_give isl_multi_union_pw_aff *
2694 isl_multi_union_pw_aff_copy(
2695 __isl_keep isl_multi_union_pw_aff *mupa);
2696 __isl_null isl_multi_union_pw_aff *
2697 isl_multi_union_pw_aff_free(
2698 __isl_take isl_multi_union_pw_aff *mupa);
2700 The base expression at a given position of a multiple
2701 expression can be extracted using the following functions.
2703 #include <isl/val.h>
2704 __isl_give isl_val *isl_multi_val_get_val(
2705 __isl_keep isl_multi_val *mv, int pos);
2707 #include <isl/aff.h>
2708 __isl_give isl_aff *isl_multi_aff_get_aff(
2709 __isl_keep isl_multi_aff *multi, int pos);
2710 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2711 __isl_keep isl_multi_pw_aff *mpa, int pos);
2712 __isl_give isl_union_pw_aff *
2713 isl_multi_union_pw_aff_get_union_pw_aff(
2714 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2716 It can be replaced using the following functions.
2718 #include <isl/val.h>
2719 __isl_give isl_multi_val *isl_multi_val_set_val(
2720 __isl_take isl_multi_val *mv, int pos,
2721 __isl_take isl_val *val);
2723 #include <isl/aff.h>
2724 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2725 __isl_take isl_multi_aff *multi, int pos,
2726 __isl_take isl_aff *aff);
2727 __isl_give isl_multi_union_pw_aff *
2728 isl_multi_union_pw_aff_set_union_pw_aff(
2729 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2730 __isl_take isl_union_pw_aff *upa);
2732 =head3 Piecewise Expressions
2734 A piecewise expression is an expression that is described
2735 using zero or more base expression defined over the same
2736 number of cells in the domain space of the base expressions.
2737 All base expressions are defined over the same
2738 domain space and the cells are disjoint.
2739 The space of a piecewise expression is the same as
2740 that of the base expressions.
2741 If the union of the cells is a strict subset of the domain
2742 space, then the value of the piecewise expression outside
2743 this union is different for types derived from quasi-affine
2744 expressions and those derived from quasipolynomials.
2745 Piecewise expressions derived from quasi-affine expressions
2746 are considered to be undefined outside the union of their cells.
2747 Piecewise expressions derived from quasipolynomials
2748 are considered to be zero outside the union of their cells.
2750 Piecewise quasipolynomials are mainly used by the C<barvinok>
2751 library for representing the number of elements in a parametric set or map.
2752 For example, the piecewise quasipolynomial
2754 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2756 represents the number of points in the map
2758 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2760 The piecewise expression types defined by C<isl>
2761 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2762 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2764 A piecewise expression with no cells can be created using
2765 the following functions.
2767 #include <isl/aff.h>
2768 __isl_give isl_pw_aff *isl_pw_aff_empty(
2769 __isl_take isl_space *space);
2770 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2771 __isl_take isl_space *space);
2773 A piecewise expression with a single universe cell can be
2774 created using the following functions.
2776 #include <isl/aff.h>
2777 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2778 __isl_take isl_aff *aff);
2779 __isl_give isl_pw_multi_aff *
2780 isl_pw_multi_aff_from_multi_aff(
2781 __isl_take isl_multi_aff *ma);
2783 #include <isl/polynomial.h>
2784 __isl_give isl_pw_qpolynomial *
2785 isl_pw_qpolynomial_from_qpolynomial(
2786 __isl_take isl_qpolynomial *qp);
2788 A piecewise expression with a single specified cell can be
2789 created using the following functions.
2791 #include <isl/aff.h>
2792 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2793 __isl_take isl_set *set, __isl_take isl_aff *aff);
2794 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2795 __isl_take isl_set *set,
2796 __isl_take isl_multi_aff *maff);
2798 #include <isl/polynomial.h>
2799 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2800 __isl_take isl_set *set,
2801 __isl_take isl_qpolynomial *qp);
2803 The following convenience functions first create a base expression and
2804 then create a piecewise expression over a universe domain.
2806 #include <isl/aff.h>
2807 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2808 __isl_take isl_local_space *ls);
2809 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2810 __isl_take isl_local_space *ls,
2811 enum isl_dim_type type, unsigned pos);
2812 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2813 __isl_take isl_local_space *ls);
2814 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2815 __isl_take isl_space *space);
2816 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2817 __isl_take isl_space *space);
2818 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2819 __isl_take isl_space *space);
2820 __isl_give isl_pw_multi_aff *
2821 isl_pw_multi_aff_project_out_map(
2822 __isl_take isl_space *space,
2823 enum isl_dim_type type,
2824 unsigned first, unsigned n);
2826 #include <isl/polynomial.h>
2827 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2828 __isl_take isl_space *space);
2830 The following convenience functions first create a base expression and
2831 then create a piecewise expression over a given domain.
2833 #include <isl/aff.h>
2834 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2835 __isl_take isl_set *domain,
2836 __isl_take isl_val *v);
2837 __isl_give isl_pw_multi_aff *
2838 isl_pw_multi_aff_multi_val_on_domain(
2839 __isl_take isl_set *domain,
2840 __isl_take isl_multi_val *mv);
2842 As a convenience, a piecewise multiple expression can
2843 also be created from a piecewise expression.
2844 Each multiple expression in the result is derived
2845 from the corresponding base expression.
2847 #include <isl/aff.h>
2848 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2849 __isl_take isl_pw_aff *pa);
2851 Similarly, a piecewise quasipolynomial can be
2852 created from a piecewise quasi-affine expression using
2853 the following function.
2855 #include <isl/polynomial.h>
2856 __isl_give isl_pw_qpolynomial *
2857 isl_pw_qpolynomial_from_pw_aff(
2858 __isl_take isl_pw_aff *pwaff);
2860 Piecewise expressions can be copied and freed using the following functions.
2862 #include <isl/aff.h>
2863 __isl_give isl_pw_aff *isl_pw_aff_copy(
2864 __isl_keep isl_pw_aff *pwaff);
2865 __isl_null isl_pw_aff *isl_pw_aff_free(
2866 __isl_take isl_pw_aff *pwaff);
2867 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2868 __isl_keep isl_pw_multi_aff *pma);
2869 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2870 __isl_take isl_pw_multi_aff *pma);
2872 #include <isl/polynomial.h>
2873 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2874 __isl_keep isl_pw_qpolynomial *pwqp);
2875 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2876 __isl_take isl_pw_qpolynomial *pwqp);
2877 __isl_give isl_pw_qpolynomial_fold *
2878 isl_pw_qpolynomial_fold_copy(
2879 __isl_keep isl_pw_qpolynomial_fold *pwf);
2880 __isl_null isl_pw_qpolynomial_fold *
2881 isl_pw_qpolynomial_fold_free(
2882 __isl_take isl_pw_qpolynomial_fold *pwf);
2884 To iterate over the different cells of a piecewise expression,
2885 use the following functions.
2887 #include <isl/aff.h>
2888 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2889 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2890 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2891 int (*fn)(__isl_take isl_set *set,
2892 __isl_take isl_aff *aff,
2893 void *user), void *user);
2894 int isl_pw_multi_aff_foreach_piece(
2895 __isl_keep isl_pw_multi_aff *pma,
2896 int (*fn)(__isl_take isl_set *set,
2897 __isl_take isl_multi_aff *maff,
2898 void *user), void *user);
2900 #include <isl/polynomial.h>
2901 int isl_pw_qpolynomial_foreach_piece(
2902 __isl_keep isl_pw_qpolynomial *pwqp,
2903 int (*fn)(__isl_take isl_set *set,
2904 __isl_take isl_qpolynomial *qp,
2905 void *user), void *user);
2906 int isl_pw_qpolynomial_foreach_lifted_piece(
2907 __isl_keep isl_pw_qpolynomial *pwqp,
2908 int (*fn)(__isl_take isl_set *set,
2909 __isl_take isl_qpolynomial *qp,
2910 void *user), void *user);
2911 int isl_pw_qpolynomial_fold_foreach_piece(
2912 __isl_keep isl_pw_qpolynomial_fold *pwf,
2913 int (*fn)(__isl_take isl_set *set,
2914 __isl_take isl_qpolynomial_fold *fold,
2915 void *user), void *user);
2916 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2917 __isl_keep isl_pw_qpolynomial_fold *pwf,
2918 int (*fn)(__isl_take isl_set *set,
2919 __isl_take isl_qpolynomial_fold *fold,
2920 void *user), void *user);
2922 As usual, the function C<fn> should return C<0> on success
2923 and C<-1> on failure. The difference between
2924 C<isl_pw_qpolynomial_foreach_piece> and
2925 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2926 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2927 compute unique representations for all existentially quantified
2928 variables and then turn these existentially quantified variables
2929 into extra set variables, adapting the associated quasipolynomial
2930 accordingly. This means that the C<set> passed to C<fn>
2931 will not have any existentially quantified variables, but that
2932 the dimensions of the sets may be different for different
2933 invocations of C<fn>.
2934 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2935 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2937 A piecewise expression consisting of the expressions at a given
2938 position of a piecewise multiple expression can be extracted
2939 using the following function.
2941 #include <isl/aff.h>
2942 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2943 __isl_keep isl_pw_multi_aff *pma, int pos);
2945 These expressions can be replaced using the following function.
2947 #include <isl/aff.h>
2948 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2949 __isl_take isl_pw_multi_aff *pma, unsigned pos,
2950 __isl_take isl_pw_aff *pa);
2952 Note that there is a difference between C<isl_multi_pw_aff> and
2953 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
2954 affine expressions, while the second is a piecewise sequence
2955 of affine expressions. In particular, each of the piecewise
2956 affine expressions in an C<isl_multi_pw_aff> may have a different
2957 domain, while all multiple expressions associated to a cell
2958 in an C<isl_pw_multi_aff> have the same domain.
2959 It is possible to convert between the two, but when converting
2960 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
2961 of the result is the intersection of the domains of the input.
2962 The reverse conversion is exact.
2964 #include <isl/aff.h>
2965 __isl_give isl_pw_multi_aff *
2966 isl_pw_multi_aff_from_multi_pw_aff(
2967 __isl_take isl_multi_pw_aff *mpa);
2968 __isl_give isl_multi_pw_aff *
2969 isl_multi_pw_aff_from_pw_multi_aff(
2970 __isl_take isl_pw_multi_aff *pma);
2972 =head3 Union Expressions
2974 A union expression collects base expressions defined
2975 over different domains. The space of a union expression
2976 is that of the shared parameter space.
2978 The union expression types defined by C<isl>
2979 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
2980 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
2982 An empty union expression can be created using the following functions.
2984 #include <isl/aff.h>
2985 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
2986 __isl_take isl_space *space);
2987 __isl_give isl_union_pw_multi_aff *
2988 isl_union_pw_multi_aff_empty(
2989 __isl_take isl_space *space);
2991 #include <isl/polynomial.h>
2992 __isl_give isl_union_pw_qpolynomial *
2993 isl_union_pw_qpolynomial_zero(
2994 __isl_take isl_space *space);
2996 A union expression containing a single base expression
2997 can be created using the following functions.
2999 #include <isl/aff.h>
3000 __isl_give isl_union_pw_aff *
3001 isl_union_pw_aff_from_pw_aff(
3002 __isl_take isl_pw_aff *pa);
3003 __isl_give isl_union_pw_multi_aff *
3004 isl_union_pw_multi_aff_from_aff(
3005 __isl_take isl_aff *aff);
3006 __isl_give isl_union_pw_multi_aff *
3007 isl_union_pw_multi_aff_from_pw_multi_aff(
3008 __isl_take isl_pw_multi_aff *pma);
3010 #include <isl/polynomial.h>
3011 __isl_give isl_union_pw_qpolynomial *
3012 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3013 __isl_take isl_pw_qpolynomial *pwqp);
3015 The following functions create a base expression on each
3016 of the sets in the union set and collect the results.
3018 #include <isl/aff.h>
3019 __isl_give isl_union_pw_multi_aff *
3020 isl_union_pw_multi_aff_from_union_pw_aff(
3021 __isl_take isl_union_pw_aff *upa);
3022 __isl_give isl_union_pw_aff *
3023 isl_union_pw_multi_aff_get_union_pw_aff(
3024 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3025 __isl_give isl_union_pw_aff *
3026 isl_union_pw_aff_val_on_domain(
3027 __isl_take isl_union_set *domain,
3028 __isl_take isl_val *v);
3029 __isl_give isl_union_pw_multi_aff *
3030 isl_union_pw_multi_aff_multi_val_on_domain(
3031 __isl_take isl_union_set *domain,
3032 __isl_take isl_multi_val *mv);
3034 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3035 expression on a given domain can be created using the following
3038 #include <isl/aff.h>
3039 __isl_give isl_union_pw_aff *
3040 isl_union_pw_aff_aff_on_domain(
3041 __isl_take isl_union_set *domain,
3042 __isl_take isl_aff *aff);
3044 A base expression can be added to a union expression using
3045 the following functions.
3047 #include <isl/aff.h>
3048 __isl_give isl_union_pw_aff *
3049 isl_union_pw_aff_add_pw_aff(
3050 __isl_take isl_union_pw_aff *upa,
3051 __isl_take isl_pw_aff *pa);
3052 __isl_give isl_union_pw_multi_aff *
3053 isl_union_pw_multi_aff_add_pw_multi_aff(
3054 __isl_take isl_union_pw_multi_aff *upma,
3055 __isl_take isl_pw_multi_aff *pma);
3057 #include <isl/polynomial.h>
3058 __isl_give isl_union_pw_qpolynomial *
3059 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3060 __isl_take isl_union_pw_qpolynomial *upwqp,
3061 __isl_take isl_pw_qpolynomial *pwqp);
3063 Union expressions can be copied and freed using
3064 the following functions.
3066 #include <isl/aff.h>
3067 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3068 __isl_keep isl_union_pw_aff *upa);
3069 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3070 __isl_take isl_union_pw_aff *upa);
3071 __isl_give isl_union_pw_multi_aff *
3072 isl_union_pw_multi_aff_copy(
3073 __isl_keep isl_union_pw_multi_aff *upma);
3074 __isl_null isl_union_pw_multi_aff *
3075 isl_union_pw_multi_aff_free(
3076 __isl_take isl_union_pw_multi_aff *upma);
3078 #include <isl/polynomial.h>
3079 __isl_give isl_union_pw_qpolynomial *
3080 isl_union_pw_qpolynomial_copy(
3081 __isl_keep isl_union_pw_qpolynomial *upwqp);
3082 __isl_null isl_union_pw_qpolynomial *
3083 isl_union_pw_qpolynomial_free(
3084 __isl_take isl_union_pw_qpolynomial *upwqp);
3085 __isl_give isl_union_pw_qpolynomial_fold *
3086 isl_union_pw_qpolynomial_fold_copy(
3087 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3088 __isl_null isl_union_pw_qpolynomial_fold *
3089 isl_union_pw_qpolynomial_fold_free(
3090 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3092 To iterate over the base expressions in a union expression,
3093 use the following functions.
3095 #include <isl/aff.h>
3096 int isl_union_pw_aff_n_pw_multi_aff(
3097 __isl_keep isl_union_pw_aff *upa);
3098 int isl_union_pw_aff_foreach_pw_aff(
3099 __isl_keep isl_union_pw_aff *upa,
3100 int (*fn)(__isl_take isl_pw_aff *ma, void *user),
3102 int isl_union_pw_multi_aff_n_pw_multi_aff(
3103 __isl_keep isl_union_pw_multi_aff *upma);
3104 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3105 __isl_keep isl_union_pw_multi_aff *upma,
3106 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3107 void *user), void *user);
3109 #include <isl/polynomial.h>
3110 int isl_union_pw_qplynomial_n_pw_qpolynomial(
3111 __isl_keep isl_union_pw_qpolynomial *upwqp);
3112 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3113 __isl_keep isl_union_pw_qpolynomial *upwqp,
3114 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3115 void *user), void *user);
3116 int isl_union_pw_qplynomial_fold_n_pw_qpolynomial_fold(
3117 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3118 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3119 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3120 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3121 void *user), void *user);
3123 To extract the base expression in a given space from a union, use
3124 the following functions.
3126 #include <isl/aff.h>
3127 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3128 __isl_keep isl_union_pw_aff *upa,
3129 __isl_take isl_space *space);
3130 __isl_give isl_pw_multi_aff *
3131 isl_union_pw_multi_aff_extract_pw_multi_aff(
3132 __isl_keep isl_union_pw_multi_aff *upma,
3133 __isl_take isl_space *space);
3135 #include <isl/polynomial.h>
3136 __isl_give isl_pw_qpolynomial *
3137 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3138 __isl_keep isl_union_pw_qpolynomial *upwqp,
3139 __isl_take isl_space *space);
3141 =head2 Input and Output
3143 For set and relation,
3144 C<isl> supports its own input/output format, which is similar
3145 to the C<Omega> format, but also supports the C<PolyLib> format
3147 For other object types, typically only an C<isl> format is supported.
3149 =head3 C<isl> format
3151 The C<isl> format is similar to that of C<Omega>, but has a different
3152 syntax for describing the parameters and allows for the definition
3153 of an existentially quantified variable as the integer division
3154 of an affine expression.
3155 For example, the set of integers C<i> between C<0> and C<n>
3156 such that C<i % 10 <= 6> can be described as
3158 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3161 A set or relation can have several disjuncts, separated
3162 by the keyword C<or>. Each disjunct is either a conjunction
3163 of constraints or a projection (C<exists>) of a conjunction
3164 of constraints. The constraints are separated by the keyword
3167 =head3 C<PolyLib> format
3169 If the represented set is a union, then the first line
3170 contains a single number representing the number of disjuncts.
3171 Otherwise, a line containing the number C<1> is optional.
3173 Each disjunct is represented by a matrix of constraints.
3174 The first line contains two numbers representing
3175 the number of rows and columns,
3176 where the number of rows is equal to the number of constraints
3177 and the number of columns is equal to two plus the number of variables.
3178 The following lines contain the actual rows of the constraint matrix.
3179 In each row, the first column indicates whether the constraint
3180 is an equality (C<0>) or inequality (C<1>). The final column
3181 corresponds to the constant term.
3183 If the set is parametric, then the coefficients of the parameters
3184 appear in the last columns before the constant column.
3185 The coefficients of any existentially quantified variables appear
3186 between those of the set variables and those of the parameters.
3188 =head3 Extended C<PolyLib> format
3190 The extended C<PolyLib> format is nearly identical to the
3191 C<PolyLib> format. The only difference is that the line
3192 containing the number of rows and columns of a constraint matrix
3193 also contains four additional numbers:
3194 the number of output dimensions, the number of input dimensions,
3195 the number of local dimensions (i.e., the number of existentially
3196 quantified variables) and the number of parameters.
3197 For sets, the number of ``output'' dimensions is equal
3198 to the number of set dimensions, while the number of ``input''
3203 Objects can be read from input using the following functions.
3205 #include <isl/val.h>
3206 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3208 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3209 isl_ctx *ctx, const char *str);
3211 #include <isl/set.h>
3212 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3213 isl_ctx *ctx, FILE *input);
3214 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3215 isl_ctx *ctx, const char *str);
3216 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3218 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3221 #include <isl/map.h>
3222 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3223 isl_ctx *ctx, FILE *input);
3224 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3225 isl_ctx *ctx, const char *str);
3226 __isl_give isl_map *isl_map_read_from_file(
3227 isl_ctx *ctx, FILE *input);
3228 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3231 #include <isl/union_set.h>
3232 __isl_give isl_union_set *isl_union_set_read_from_file(
3233 isl_ctx *ctx, FILE *input);
3234 __isl_give isl_union_set *isl_union_set_read_from_str(
3235 isl_ctx *ctx, const char *str);
3237 #include <isl/union_map.h>
3238 __isl_give isl_union_map *isl_union_map_read_from_file(
3239 isl_ctx *ctx, FILE *input);
3240 __isl_give isl_union_map *isl_union_map_read_from_str(
3241 isl_ctx *ctx, const char *str);
3243 #include <isl/aff.h>
3244 __isl_give isl_aff *isl_aff_read_from_str(
3245 isl_ctx *ctx, const char *str);
3246 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3247 isl_ctx *ctx, const char *str);
3248 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3249 isl_ctx *ctx, const char *str);
3250 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3251 isl_ctx *ctx, const char *str);
3252 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3253 isl_ctx *ctx, const char *str);
3254 __isl_give isl_union_pw_multi_aff *
3255 isl_union_pw_multi_aff_read_from_str(
3256 isl_ctx *ctx, const char *str);
3258 #include <isl/polynomial.h>
3259 __isl_give isl_union_pw_qpolynomial *
3260 isl_union_pw_qpolynomial_read_from_str(
3261 isl_ctx *ctx, const char *str);
3263 For sets and relations,
3264 the input format is autodetected and may be either the C<PolyLib> format
3265 or the C<isl> format.
3269 Before anything can be printed, an C<isl_printer> needs to
3272 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3274 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3275 __isl_null isl_printer *isl_printer_free(
3276 __isl_take isl_printer *printer);
3277 __isl_give char *isl_printer_get_str(
3278 __isl_keep isl_printer *printer);
3280 The printer can be inspected using the following functions.
3282 FILE *isl_printer_get_file(
3283 __isl_keep isl_printer *printer);
3284 int isl_printer_get_output_format(
3285 __isl_keep isl_printer *p);
3287 The behavior of the printer can be modified in various ways
3289 __isl_give isl_printer *isl_printer_set_output_format(
3290 __isl_take isl_printer *p, int output_format);
3291 __isl_give isl_printer *isl_printer_set_indent(
3292 __isl_take isl_printer *p, int indent);
3293 __isl_give isl_printer *isl_printer_set_indent_prefix(
3294 __isl_take isl_printer *p, const char *prefix);
3295 __isl_give isl_printer *isl_printer_indent(
3296 __isl_take isl_printer *p, int indent);
3297 __isl_give isl_printer *isl_printer_set_prefix(
3298 __isl_take isl_printer *p, const char *prefix);
3299 __isl_give isl_printer *isl_printer_set_suffix(
3300 __isl_take isl_printer *p, const char *suffix);
3302 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3303 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3304 and defaults to C<ISL_FORMAT_ISL>.
3305 Each line in the output is prefixed by C<indent_prefix>,
3306 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3307 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3308 In the C<PolyLib> format output,
3309 the coefficients of the existentially quantified variables
3310 appear between those of the set variables and those
3312 The function C<isl_printer_indent> increases the indentation
3313 by the specified amount (which may be negative).
3315 To actually print something, use
3317 #include <isl/printer.h>
3318 __isl_give isl_printer *isl_printer_print_double(
3319 __isl_take isl_printer *p, double d);
3321 #include <isl/val.h>
3322 __isl_give isl_printer *isl_printer_print_val(
3323 __isl_take isl_printer *p, __isl_keep isl_val *v);
3325 #include <isl/set.h>
3326 __isl_give isl_printer *isl_printer_print_basic_set(
3327 __isl_take isl_printer *printer,
3328 __isl_keep isl_basic_set *bset);
3329 __isl_give isl_printer *isl_printer_print_set(
3330 __isl_take isl_printer *printer,
3331 __isl_keep isl_set *set);
3333 #include <isl/map.h>
3334 __isl_give isl_printer *isl_printer_print_basic_map(
3335 __isl_take isl_printer *printer,
3336 __isl_keep isl_basic_map *bmap);
3337 __isl_give isl_printer *isl_printer_print_map(
3338 __isl_take isl_printer *printer,
3339 __isl_keep isl_map *map);
3341 #include <isl/union_set.h>
3342 __isl_give isl_printer *isl_printer_print_union_set(
3343 __isl_take isl_printer *p,
3344 __isl_keep isl_union_set *uset);
3346 #include <isl/union_map.h>
3347 __isl_give isl_printer *isl_printer_print_union_map(
3348 __isl_take isl_printer *p,
3349 __isl_keep isl_union_map *umap);
3351 #include <isl/val.h>
3352 __isl_give isl_printer *isl_printer_print_multi_val(
3353 __isl_take isl_printer *p,
3354 __isl_keep isl_multi_val *mv);
3356 #include <isl/aff.h>
3357 __isl_give isl_printer *isl_printer_print_aff(
3358 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3359 __isl_give isl_printer *isl_printer_print_multi_aff(
3360 __isl_take isl_printer *p,
3361 __isl_keep isl_multi_aff *maff);
3362 __isl_give isl_printer *isl_printer_print_pw_aff(
3363 __isl_take isl_printer *p,
3364 __isl_keep isl_pw_aff *pwaff);
3365 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3366 __isl_take isl_printer *p,
3367 __isl_keep isl_pw_multi_aff *pma);
3368 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3369 __isl_take isl_printer *p,
3370 __isl_keep isl_multi_pw_aff *mpa);
3371 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3372 __isl_take isl_printer *p,
3373 __isl_keep isl_union_pw_aff *upa);
3374 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3375 __isl_take isl_printer *p,
3376 __isl_keep isl_union_pw_multi_aff *upma);
3377 __isl_give isl_printer *
3378 isl_printer_print_multi_union_pw_aff(
3379 __isl_take isl_printer *p,
3380 __isl_keep isl_multi_union_pw_aff *mupa);
3382 #include <isl/polynomial.h>
3383 __isl_give isl_printer *isl_printer_print_qpolynomial(
3384 __isl_take isl_printer *p,
3385 __isl_keep isl_qpolynomial *qp);
3386 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3387 __isl_take isl_printer *p,
3388 __isl_keep isl_pw_qpolynomial *pwqp);
3389 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3390 __isl_take isl_printer *p,
3391 __isl_keep isl_union_pw_qpolynomial *upwqp);
3393 __isl_give isl_printer *
3394 isl_printer_print_pw_qpolynomial_fold(
3395 __isl_take isl_printer *p,
3396 __isl_keep isl_pw_qpolynomial_fold *pwf);
3397 __isl_give isl_printer *
3398 isl_printer_print_union_pw_qpolynomial_fold(
3399 __isl_take isl_printer *p,
3400 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3402 For C<isl_printer_print_qpolynomial>,
3403 C<isl_printer_print_pw_qpolynomial> and
3404 C<isl_printer_print_pw_qpolynomial_fold>,
3405 the output format of the printer
3406 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3407 For C<isl_printer_print_union_pw_qpolynomial> and
3408 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3410 In case of printing in C<ISL_FORMAT_C>, the user may want
3411 to set the names of all dimensions first.
3413 When called on a file printer, the following function flushes
3414 the file. When called on a string printer, the buffer is cleared.
3416 __isl_give isl_printer *isl_printer_flush(
3417 __isl_take isl_printer *p);
3419 Alternatively, a string representation can be obtained
3420 directly using the following functions, which always print
3423 #include <isl/space.h>
3424 __isl_give char *isl_space_to_str(
3425 __isl_keep isl_space *space);
3427 #include <isl/val.h>
3428 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3429 __isl_give char *isl_multi_val_to_str(
3430 __isl_keep isl_multi_val *mv);
3432 #include <isl/set.h>
3433 __isl_give char *isl_set_to_str(
3434 __isl_keep isl_set *set);
3436 #include <isl/union_set.h>
3437 __isl_give char *isl_union_set_to_str(
3438 __isl_keep isl_union_set *uset);
3440 #include <isl/map.h>
3441 __isl_give char *isl_map_to_str(
3442 __isl_keep isl_map *map);
3444 #include <isl/union_map.h>
3445 __isl_give char *isl_union_map_to_str(
3446 __isl_keep isl_union_map *umap);
3448 #include <isl/aff.h>
3449 __isl_give char *isl_multi_aff_to_str(
3450 __isl_keep isl_multi_aff *aff);
3451 __isl_give char *isl_union_pw_aff_to_str(
3452 __isl_keep isl_union_pw_aff *upa);
3453 __isl_give char *isl_union_pw_multi_aff_to_str(
3454 __isl_keep isl_union_pw_multi_aff *upma);
3455 __isl_give char *isl_multi_union_pw_aff_to_str(
3456 __isl_keep isl_multi_union_pw_aff *mupa);
3460 =head3 Unary Properties
3466 The following functions test whether the given set or relation
3467 contains any integer points. The ``plain'' variants do not perform
3468 any computations, but simply check if the given set or relation
3469 is already known to be empty.
3471 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3472 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3473 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3474 int isl_set_is_empty(__isl_keep isl_set *set);
3475 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3476 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3477 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3478 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3479 int isl_map_is_empty(__isl_keep isl_map *map);
3480 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3482 =item * Universality
3484 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3485 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3486 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3488 =item * Single-valuedness
3490 #include <isl/set.h>
3491 int isl_set_is_singleton(__isl_keep isl_set *set);
3493 #include <isl/map.h>
3494 int isl_basic_map_is_single_valued(
3495 __isl_keep isl_basic_map *bmap);
3496 int isl_map_plain_is_single_valued(
3497 __isl_keep isl_map *map);
3498 int isl_map_is_single_valued(__isl_keep isl_map *map);
3500 #include <isl/union_map.h>
3501 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3505 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3506 int isl_map_is_injective(__isl_keep isl_map *map);
3507 int isl_union_map_plain_is_injective(
3508 __isl_keep isl_union_map *umap);
3509 int isl_union_map_is_injective(
3510 __isl_keep isl_union_map *umap);
3514 int isl_map_is_bijective(__isl_keep isl_map *map);
3515 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3519 __isl_give isl_val *
3520 isl_basic_map_plain_get_val_if_fixed(
3521 __isl_keep isl_basic_map *bmap,
3522 enum isl_dim_type type, unsigned pos);
3523 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3524 __isl_keep isl_set *set,
3525 enum isl_dim_type type, unsigned pos);
3526 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3527 __isl_keep isl_map *map,
3528 enum isl_dim_type type, unsigned pos);
3530 If the set or relation obviously lies on a hyperplane where the given dimension
3531 has a fixed value, then return that value.
3532 Otherwise return NaN.
3536 int isl_set_dim_residue_class_val(
3537 __isl_keep isl_set *set,
3538 int pos, __isl_give isl_val **modulo,
3539 __isl_give isl_val **residue);
3541 Check if the values of the given set dimension are equal to a fixed
3542 value modulo some integer value. If so, assign the modulo to C<*modulo>
3543 and the fixed value to C<*residue>. If the given dimension attains only
3544 a single value, then assign C<0> to C<*modulo> and the fixed value to
3546 If the dimension does not attain only a single value and if no modulo
3547 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3551 To check whether the description of a set, relation or function depends
3552 on one or more given dimensions,
3553 the following functions can be used.
3555 #include <isl/constraint.h>
3556 int isl_constraint_involves_dims(
3557 __isl_keep isl_constraint *constraint,
3558 enum isl_dim_type type, unsigned first, unsigned n);
3560 #include <isl/set.h>
3561 int isl_basic_set_involves_dims(
3562 __isl_keep isl_basic_set *bset,
3563 enum isl_dim_type type, unsigned first, unsigned n);
3564 int isl_set_involves_dims(__isl_keep isl_set *set,
3565 enum isl_dim_type type, unsigned first, unsigned n);
3567 #include <isl/map.h>
3568 int isl_basic_map_involves_dims(
3569 __isl_keep isl_basic_map *bmap,
3570 enum isl_dim_type type, unsigned first, unsigned n);
3571 int isl_map_involves_dims(__isl_keep isl_map *map,
3572 enum isl_dim_type type, unsigned first, unsigned n);
3574 #include <isl/union_map.h>
3575 int isl_union_map_involves_dims(
3576 __isl_keep isl_union_map *umap,
3577 enum isl_dim_type type, unsigned first, unsigned n);
3579 #include <isl/aff.h>
3580 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3581 enum isl_dim_type type, unsigned first, unsigned n);
3582 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3583 enum isl_dim_type type, unsigned first, unsigned n);
3584 int isl_multi_aff_involves_dims(
3585 __isl_keep isl_multi_aff *ma,
3586 enum isl_dim_type type, unsigned first, unsigned n);
3587 int isl_multi_pw_aff_involves_dims(
3588 __isl_keep isl_multi_pw_aff *mpa,
3589 enum isl_dim_type type, unsigned first, unsigned n);
3591 Similarly, the following functions can be used to check whether
3592 a given dimension is involved in any lower or upper bound.
3594 #include <isl/set.h>
3595 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3596 enum isl_dim_type type, unsigned pos);
3597 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3598 enum isl_dim_type type, unsigned pos);
3600 Note that these functions return true even if there is a bound on
3601 the dimension on only some of the basic sets of C<set>.
3602 To check if they have a bound for all of the basic sets in C<set>,
3603 use the following functions instead.
3605 #include <isl/set.h>
3606 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3607 enum isl_dim_type type, unsigned pos);
3608 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3609 enum isl_dim_type type, unsigned pos);
3613 To check whether a set is a parameter domain, use this function:
3615 int isl_set_is_params(__isl_keep isl_set *set);
3616 int isl_union_set_is_params(
3617 __isl_keep isl_union_set *uset);
3621 The following functions check whether the space of the given
3622 (basic) set or relation range is a wrapped relation.
3624 #include <isl/space.h>
3625 int isl_space_is_wrapping(
3626 __isl_keep isl_space *space);
3627 int isl_space_domain_is_wrapping(
3628 __isl_keep isl_space *space);
3629 int isl_space_range_is_wrapping(
3630 __isl_keep isl_space *space);
3632 #include <isl/set.h>
3633 int isl_basic_set_is_wrapping(
3634 __isl_keep isl_basic_set *bset);
3635 int isl_set_is_wrapping(__isl_keep isl_set *set);
3637 #include <isl/map.h>
3638 int isl_map_domain_is_wrapping(
3639 __isl_keep isl_map *map);
3640 int isl_map_range_is_wrapping(
3641 __isl_keep isl_map *map);
3643 #include <isl/val.h>
3644 int isl_multi_val_range_is_wrapping(
3645 __isl_keep isl_multi_val *mv);
3647 #include <isl/aff.h>
3648 int isl_multi_aff_range_is_wrapping(
3649 __isl_keep isl_multi_aff *ma);
3650 int isl_multi_pw_aff_range_is_wrapping(
3651 __isl_keep isl_multi_pw_aff *mpa);
3652 int isl_multi_union_pw_aff_range_is_wrapping(
3653 __isl_keep isl_multi_union_pw_aff *mupa);
3655 The input to C<isl_space_is_wrapping> should
3656 be the space of a set, while that of
3657 C<isl_space_domain_is_wrapping> and
3658 C<isl_space_range_is_wrapping> should be the space of a relation.
3660 =item * Internal Product
3662 int isl_basic_map_can_zip(
3663 __isl_keep isl_basic_map *bmap);
3664 int isl_map_can_zip(__isl_keep isl_map *map);
3666 Check whether the product of domain and range of the given relation
3668 i.e., whether both domain and range are nested relations.
3672 int isl_basic_map_can_curry(
3673 __isl_keep isl_basic_map *bmap);
3674 int isl_map_can_curry(__isl_keep isl_map *map);
3676 Check whether the domain of the (basic) relation is a wrapped relation.
3678 int isl_basic_map_can_uncurry(
3679 __isl_keep isl_basic_map *bmap);
3680 int isl_map_can_uncurry(__isl_keep isl_map *map);
3682 Check whether the range of the (basic) relation is a wrapped relation.
3684 =item * Special Values
3686 #include <isl/aff.h>
3687 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3688 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3690 Check whether the given expression is a constant.
3692 #include <isl/aff.h>
3693 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3694 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3696 Check whether the given expression is equal to or involves NaN.
3698 #include <isl/aff.h>
3699 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3701 Check whether the affine expression is obviously zero.
3705 =head3 Binary Properties
3711 The following functions check whether two objects
3712 represent the same set, relation or function.
3713 The C<plain> variants only return true if the objects
3714 are obviously the same. That is, they may return false
3715 even if the objects are the same, but they will never
3716 return true if the objects are not the same.
3718 #include <isl/set.h>
3719 int isl_basic_set_plain_is_equal(
3720 __isl_keep isl_basic_set *bset1,
3721 __isl_keep isl_basic_set *bset2);
3722 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3723 __isl_keep isl_set *set2);
3724 int isl_set_is_equal(__isl_keep isl_set *set1,
3725 __isl_keep isl_set *set2);
3727 #include <isl/map.h>
3728 int isl_basic_map_is_equal(
3729 __isl_keep isl_basic_map *bmap1,
3730 __isl_keep isl_basic_map *bmap2);
3731 int isl_map_is_equal(__isl_keep isl_map *map1,
3732 __isl_keep isl_map *map2);
3733 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3734 __isl_keep isl_map *map2);
3736 #include <isl/union_set.h>
3737 int isl_union_set_is_equal(
3738 __isl_keep isl_union_set *uset1,
3739 __isl_keep isl_union_set *uset2);
3741 #include <isl/union_map.h>
3742 int isl_union_map_is_equal(
3743 __isl_keep isl_union_map *umap1,
3744 __isl_keep isl_union_map *umap2);
3746 #include <isl/aff.h>
3747 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3748 __isl_keep isl_aff *aff2);
3749 int isl_multi_aff_plain_is_equal(
3750 __isl_keep isl_multi_aff *maff1,
3751 __isl_keep isl_multi_aff *maff2);
3752 int isl_pw_aff_plain_is_equal(
3753 __isl_keep isl_pw_aff *pwaff1,
3754 __isl_keep isl_pw_aff *pwaff2);
3755 int isl_pw_multi_aff_plain_is_equal(
3756 __isl_keep isl_pw_multi_aff *pma1,
3757 __isl_keep isl_pw_multi_aff *pma2);
3758 int isl_multi_pw_aff_plain_is_equal(
3759 __isl_keep isl_multi_pw_aff *mpa1,
3760 __isl_keep isl_multi_pw_aff *mpa2);
3761 int isl_multi_pw_aff_is_equal(
3762 __isl_keep isl_multi_pw_aff *mpa1,
3763 __isl_keep isl_multi_pw_aff *mpa2);
3764 int isl_union_pw_aff_plain_is_equal(
3765 __isl_keep isl_union_pw_aff *upa1,
3766 __isl_keep isl_union_pw_aff *upa2);
3767 int isl_union_pw_multi_aff_plain_is_equal(
3768 __isl_keep isl_union_pw_multi_aff *upma1,
3769 __isl_keep isl_union_pw_multi_aff *upma2);
3770 int isl_multi_union_pw_aff_plain_is_equal(
3771 __isl_keep isl_multi_union_pw_aff *mupa1,
3772 __isl_keep isl_multi_union_pw_aff *mupa2);
3774 #include <isl/polynomial.h>
3775 int isl_union_pw_qpolynomial_plain_is_equal(
3776 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3777 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3778 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3779 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3780 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3782 =item * Disjointness
3784 #include <isl/set.h>
3785 int isl_basic_set_is_disjoint(
3786 __isl_keep isl_basic_set *bset1,
3787 __isl_keep isl_basic_set *bset2);
3788 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3789 __isl_keep isl_set *set2);
3790 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3791 __isl_keep isl_set *set2);
3793 #include <isl/map.h>
3794 int isl_basic_map_is_disjoint(
3795 __isl_keep isl_basic_map *bmap1,
3796 __isl_keep isl_basic_map *bmap2);
3797 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3798 __isl_keep isl_map *map2);
3800 #include <isl/union_set.h>
3801 int isl_union_set_is_disjoint(
3802 __isl_keep isl_union_set *uset1,
3803 __isl_keep isl_union_set *uset2);
3805 #include <isl/union_map.h>
3806 int isl_union_map_is_disjoint(
3807 __isl_keep isl_union_map *umap1,
3808 __isl_keep isl_union_map *umap2);
3812 int isl_basic_set_is_subset(
3813 __isl_keep isl_basic_set *bset1,
3814 __isl_keep isl_basic_set *bset2);
3815 int isl_set_is_subset(__isl_keep isl_set *set1,
3816 __isl_keep isl_set *set2);
3817 int isl_set_is_strict_subset(
3818 __isl_keep isl_set *set1,
3819 __isl_keep isl_set *set2);
3820 int isl_union_set_is_subset(
3821 __isl_keep isl_union_set *uset1,
3822 __isl_keep isl_union_set *uset2);
3823 int isl_union_set_is_strict_subset(
3824 __isl_keep isl_union_set *uset1,
3825 __isl_keep isl_union_set *uset2);
3826 int isl_basic_map_is_subset(
3827 __isl_keep isl_basic_map *bmap1,
3828 __isl_keep isl_basic_map *bmap2);
3829 int isl_basic_map_is_strict_subset(
3830 __isl_keep isl_basic_map *bmap1,
3831 __isl_keep isl_basic_map *bmap2);
3832 int isl_map_is_subset(
3833 __isl_keep isl_map *map1,
3834 __isl_keep isl_map *map2);
3835 int isl_map_is_strict_subset(
3836 __isl_keep isl_map *map1,
3837 __isl_keep isl_map *map2);
3838 int isl_union_map_is_subset(
3839 __isl_keep isl_union_map *umap1,
3840 __isl_keep isl_union_map *umap2);
3841 int isl_union_map_is_strict_subset(
3842 __isl_keep isl_union_map *umap1,
3843 __isl_keep isl_union_map *umap2);
3845 Check whether the first argument is a (strict) subset of the
3850 Every comparison function returns a negative value if the first
3851 argument is considered smaller than the second, a positive value
3852 if the first argument is considered greater and zero if the two
3853 constraints are considered the same by the comparison criterion.
3855 #include <isl/constraint.h>
3856 int isl_constraint_plain_cmp(
3857 __isl_keep isl_constraint *c1,
3858 __isl_keep isl_constraint *c2);
3860 This function is useful for sorting C<isl_constraint>s.
3861 The order depends on the internal representation of the inputs.
3862 The order is fixed over different calls to the function (assuming
3863 the internal representation of the inputs has not changed), but may
3864 change over different versions of C<isl>.
3866 #include <isl/constraint.h>
3867 int isl_constraint_cmp_last_non_zero(
3868 __isl_keep isl_constraint *c1,
3869 __isl_keep isl_constraint *c2);
3871 This function can be used to sort constraints that live in the same
3872 local space. Constraints that involve ``earlier'' dimensions or
3873 that have a smaller coefficient for the shared latest dimension
3874 are considered smaller than other constraints.
3875 This function only defines a B<partial> order.
3877 #include <isl/set.h>
3878 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3879 __isl_keep isl_set *set2);
3881 This function is useful for sorting C<isl_set>s.
3882 The order depends on the internal representation of the inputs.
3883 The order is fixed over different calls to the function (assuming
3884 the internal representation of the inputs has not changed), but may
3885 change over different versions of C<isl>.
3887 #include <isl/aff.h>
3888 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3889 __isl_keep isl_pw_aff *pa2);
3891 The function C<isl_pw_aff_plain_cmp> can be used to sort
3892 C<isl_pw_aff>s. The order is not strictly defined.
3893 The current order sorts expressions that only involve
3894 earlier dimensions before those that involve later dimensions.
3898 =head2 Unary Operations
3904 __isl_give isl_set *isl_set_complement(
3905 __isl_take isl_set *set);
3906 __isl_give isl_map *isl_map_complement(
3907 __isl_take isl_map *map);
3911 #include <isl/space.h>
3912 __isl_give isl_space *isl_space_reverse(
3913 __isl_take isl_space *space);
3915 #include <isl/map.h>
3916 __isl_give isl_basic_map *isl_basic_map_reverse(
3917 __isl_take isl_basic_map *bmap);
3918 __isl_give isl_map *isl_map_reverse(
3919 __isl_take isl_map *map);
3921 #include <isl/union_map.h>
3922 __isl_give isl_union_map *isl_union_map_reverse(
3923 __isl_take isl_union_map *umap);
3927 #include <isl/space.h>
3928 __isl_give isl_space *isl_space_domain(
3929 __isl_take isl_space *space);
3930 __isl_give isl_space *isl_space_range(
3931 __isl_take isl_space *space);
3932 __isl_give isl_space *isl_space_params(
3933 __isl_take isl_space *space);
3935 #include <isl/local_space.h>
3936 __isl_give isl_local_space *isl_local_space_domain(
3937 __isl_take isl_local_space *ls);
3938 __isl_give isl_local_space *isl_local_space_range(
3939 __isl_take isl_local_space *ls);
3941 #include <isl/set.h>
3942 __isl_give isl_basic_set *isl_basic_set_project_out(
3943 __isl_take isl_basic_set *bset,
3944 enum isl_dim_type type, unsigned first, unsigned n);
3945 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3946 enum isl_dim_type type, unsigned first, unsigned n);
3947 __isl_give isl_basic_set *isl_basic_set_params(
3948 __isl_take isl_basic_set *bset);
3949 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
3951 #include <isl/map.h>
3952 __isl_give isl_basic_map *isl_basic_map_project_out(
3953 __isl_take isl_basic_map *bmap,
3954 enum isl_dim_type type, unsigned first, unsigned n);
3955 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3956 enum isl_dim_type type, unsigned first, unsigned n);
3957 __isl_give isl_basic_set *isl_basic_map_domain(
3958 __isl_take isl_basic_map *bmap);
3959 __isl_give isl_basic_set *isl_basic_map_range(
3960 __isl_take isl_basic_map *bmap);
3961 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
3962 __isl_give isl_set *isl_map_domain(
3963 __isl_take isl_map *bmap);
3964 __isl_give isl_set *isl_map_range(
3965 __isl_take isl_map *map);
3967 #include <isl/union_set.h>
3968 __isl_give isl_union_set *isl_union_set_project_out(
3969 __isl_take isl_union_set *uset,
3970 enum isl_dim_type type,
3971 unsigned first, unsigned n);
3972 __isl_give isl_set *isl_union_set_params(
3973 __isl_take isl_union_set *uset);
3975 The function C<isl_union_set_project_out> can only project out
3978 #include <isl/union_map.h>
3979 __isl_give isl_union_map *isl_union_map_project_out(
3980 __isl_take isl_union_map *umap,
3981 enum isl_dim_type type, unsigned first, unsigned n);
3982 __isl_give isl_set *isl_union_map_params(
3983 __isl_take isl_union_map *umap);
3984 __isl_give isl_union_set *isl_union_map_domain(
3985 __isl_take isl_union_map *umap);
3986 __isl_give isl_union_set *isl_union_map_range(
3987 __isl_take isl_union_map *umap);
3989 The function C<isl_union_map_project_out> can only project out
3992 #include <isl/aff.h>
3993 __isl_give isl_aff *isl_aff_project_domain_on_params(
3994 __isl_take isl_aff *aff);
3995 __isl_give isl_pw_multi_aff *
3996 isl_pw_multi_aff_project_domain_on_params(
3997 __isl_take isl_pw_multi_aff *pma);
3998 __isl_give isl_set *isl_pw_aff_domain(
3999 __isl_take isl_pw_aff *pwaff);
4000 __isl_give isl_set *isl_pw_multi_aff_domain(
4001 __isl_take isl_pw_multi_aff *pma);
4002 __isl_give isl_set *isl_multi_pw_aff_domain(
4003 __isl_take isl_multi_pw_aff *mpa);
4004 __isl_give isl_union_set *isl_union_pw_aff_domain(
4005 __isl_take isl_union_pw_aff *upa);
4006 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4007 __isl_take isl_union_pw_multi_aff *upma);
4008 __isl_give isl_set *isl_pw_aff_params(
4009 __isl_take isl_pw_aff *pwa);
4011 #include <isl/polynomial.h>
4012 __isl_give isl_qpolynomial *
4013 isl_qpolynomial_project_domain_on_params(
4014 __isl_take isl_qpolynomial *qp);
4015 __isl_give isl_pw_qpolynomial *
4016 isl_pw_qpolynomial_project_domain_on_params(
4017 __isl_take isl_pw_qpolynomial *pwqp);
4018 __isl_give isl_pw_qpolynomial_fold *
4019 isl_pw_qpolynomial_fold_project_domain_on_params(
4020 __isl_take isl_pw_qpolynomial_fold *pwf);
4021 __isl_give isl_set *isl_pw_qpolynomial_domain(
4022 __isl_take isl_pw_qpolynomial *pwqp);
4023 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4024 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4025 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4026 __isl_take isl_union_pw_qpolynomial *upwqp);
4028 #include <isl/space.h>
4029 __isl_give isl_space *isl_space_domain_map(
4030 __isl_take isl_space *space);
4031 __isl_give isl_space *isl_space_range_map(
4032 __isl_take isl_space *space);
4034 #include <isl/map.h>
4035 __isl_give isl_map *isl_set_wrapped_domain_map(
4036 __isl_take isl_set *set);
4037 __isl_give isl_basic_map *isl_basic_map_domain_map(
4038 __isl_take isl_basic_map *bmap);
4039 __isl_give isl_basic_map *isl_basic_map_range_map(
4040 __isl_take isl_basic_map *bmap);
4041 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4042 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4044 #include <isl/union_map.h>
4045 __isl_give isl_union_map *isl_union_map_domain_map(
4046 __isl_take isl_union_map *umap);
4047 __isl_give isl_union_pw_multi_aff *
4048 isl_union_map_domain_map_union_pw_multi_aff(
4049 __isl_take isl_union_map *umap);
4050 __isl_give isl_union_map *isl_union_map_range_map(
4051 __isl_take isl_union_map *umap);
4052 __isl_give isl_union_map *
4053 isl_union_set_wrapped_domain_map(
4054 __isl_take isl_union_set *uset);
4056 The functions above construct a (basic, regular or union) relation
4057 that maps (a wrapped version of) the input relation to its domain or range.
4058 C<isl_set_wrapped_domain_map> maps the input set to the domain
4059 of its wrapped relation.
4063 __isl_give isl_basic_set *isl_basic_set_eliminate(
4064 __isl_take isl_basic_set *bset,
4065 enum isl_dim_type type,
4066 unsigned first, unsigned n);
4067 __isl_give isl_set *isl_set_eliminate(
4068 __isl_take isl_set *set, enum isl_dim_type type,
4069 unsigned first, unsigned n);
4070 __isl_give isl_basic_map *isl_basic_map_eliminate(
4071 __isl_take isl_basic_map *bmap,
4072 enum isl_dim_type type,
4073 unsigned first, unsigned n);
4074 __isl_give isl_map *isl_map_eliminate(
4075 __isl_take isl_map *map, enum isl_dim_type type,
4076 unsigned first, unsigned n);
4078 Eliminate the coefficients for the given dimensions from the constraints,
4079 without removing the dimensions.
4081 =item * Constructing a set from a parameter domain
4083 A zero-dimensional space or (basic) set can be constructed
4084 on a given parameter domain using the following functions.
4086 #include <isl/space.h>
4087 __isl_give isl_space *isl_space_set_from_params(
4088 __isl_take isl_space *space);
4090 #include <isl/set.h>
4091 __isl_give isl_basic_set *isl_basic_set_from_params(
4092 __isl_take isl_basic_set *bset);
4093 __isl_give isl_set *isl_set_from_params(
4094 __isl_take isl_set *set);
4096 =item * Constructing a relation from a set
4098 Create a relation with the given set as domain or range.
4099 The range or domain of the created relation is a zero-dimensional
4100 flat anonymous space.
4102 #include <isl/space.h>
4103 __isl_give isl_space *isl_space_from_domain(
4104 __isl_take isl_space *space);
4105 __isl_give isl_space *isl_space_from_range(
4106 __isl_take isl_space *space);
4107 __isl_give isl_space *isl_space_map_from_set(
4108 __isl_take isl_space *space);
4109 __isl_give isl_space *isl_space_map_from_domain_and_range(
4110 __isl_take isl_space *domain,
4111 __isl_take isl_space *range);
4113 #include <isl/local_space.h>
4114 __isl_give isl_local_space *isl_local_space_from_domain(
4115 __isl_take isl_local_space *ls);
4117 #include <isl/map.h>
4118 __isl_give isl_map *isl_map_from_domain(
4119 __isl_take isl_set *set);
4120 __isl_give isl_map *isl_map_from_range(
4121 __isl_take isl_set *set);
4123 #include <isl/val.h>
4124 __isl_give isl_multi_val *isl_multi_val_from_range(
4125 __isl_take isl_multi_val *mv);
4127 #include <isl/aff.h>
4128 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4129 __isl_take isl_multi_aff *ma);
4130 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4131 __isl_take isl_pw_aff *pwa);
4132 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4133 __isl_take isl_multi_pw_aff *mpa);
4134 __isl_give isl_multi_union_pw_aff *
4135 isl_multi_union_pw_aff_from_range(
4136 __isl_take isl_multi_union_pw_aff *mupa);
4137 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4138 __isl_take isl_set *set);
4139 __isl_give isl_union_pw_multi_aff *
4140 isl_union_pw_multi_aff_from_domain(
4141 __isl_take isl_union_set *uset);
4145 #include <isl/set.h>
4146 __isl_give isl_basic_set *isl_basic_set_fix_si(
4147 __isl_take isl_basic_set *bset,
4148 enum isl_dim_type type, unsigned pos, int value);
4149 __isl_give isl_basic_set *isl_basic_set_fix_val(
4150 __isl_take isl_basic_set *bset,
4151 enum isl_dim_type type, unsigned pos,
4152 __isl_take isl_val *v);
4153 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4154 enum isl_dim_type type, unsigned pos, int value);
4155 __isl_give isl_set *isl_set_fix_val(
4156 __isl_take isl_set *set,
4157 enum isl_dim_type type, unsigned pos,
4158 __isl_take isl_val *v);
4160 #include <isl/map.h>
4161 __isl_give isl_basic_map *isl_basic_map_fix_si(
4162 __isl_take isl_basic_map *bmap,
4163 enum isl_dim_type type, unsigned pos, int value);
4164 __isl_give isl_basic_map *isl_basic_map_fix_val(
4165 __isl_take isl_basic_map *bmap,
4166 enum isl_dim_type type, unsigned pos,
4167 __isl_take isl_val *v);
4168 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4169 enum isl_dim_type type, unsigned pos, int value);
4170 __isl_give isl_map *isl_map_fix_val(
4171 __isl_take isl_map *map,
4172 enum isl_dim_type type, unsigned pos,
4173 __isl_take isl_val *v);
4175 #include <isl/aff.h>
4176 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4177 __isl_take isl_pw_multi_aff *pma,
4178 enum isl_dim_type type, unsigned pos, int value);
4180 #include <isl/polynomial.h>
4181 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4182 __isl_take isl_pw_qpolynomial *pwqp,
4183 enum isl_dim_type type, unsigned n,
4184 __isl_take isl_val *v);
4186 Intersect the set, relation or function domain
4187 with the hyperplane where the given
4188 dimension has the fixed given value.
4190 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4191 __isl_take isl_basic_map *bmap,
4192 enum isl_dim_type type, unsigned pos, int value);
4193 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4194 __isl_take isl_basic_map *bmap,
4195 enum isl_dim_type type, unsigned pos, int value);
4196 __isl_give isl_set *isl_set_lower_bound_si(
4197 __isl_take isl_set *set,
4198 enum isl_dim_type type, unsigned pos, int value);
4199 __isl_give isl_set *isl_set_lower_bound_val(
4200 __isl_take isl_set *set,
4201 enum isl_dim_type type, unsigned pos,
4202 __isl_take isl_val *value);
4203 __isl_give isl_map *isl_map_lower_bound_si(
4204 __isl_take isl_map *map,
4205 enum isl_dim_type type, unsigned pos, int value);
4206 __isl_give isl_set *isl_set_upper_bound_si(
4207 __isl_take isl_set *set,
4208 enum isl_dim_type type, unsigned pos, int value);
4209 __isl_give isl_set *isl_set_upper_bound_val(
4210 __isl_take isl_set *set,
4211 enum isl_dim_type type, unsigned pos,
4212 __isl_take isl_val *value);
4213 __isl_give isl_map *isl_map_upper_bound_si(
4214 __isl_take isl_map *map,
4215 enum isl_dim_type type, unsigned pos, int value);
4217 Intersect the set or relation with the half-space where the given
4218 dimension has a value bounded by the fixed given integer value.
4220 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4221 enum isl_dim_type type1, int pos1,
4222 enum isl_dim_type type2, int pos2);
4223 __isl_give isl_basic_map *isl_basic_map_equate(
4224 __isl_take isl_basic_map *bmap,
4225 enum isl_dim_type type1, int pos1,
4226 enum isl_dim_type type2, int pos2);
4227 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4228 enum isl_dim_type type1, int pos1,
4229 enum isl_dim_type type2, int pos2);
4231 Intersect the set or relation with the hyperplane where the given
4232 dimensions are equal to each other.
4234 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4235 enum isl_dim_type type1, int pos1,
4236 enum isl_dim_type type2, int pos2);
4238 Intersect the relation with the hyperplane where the given
4239 dimensions have opposite values.
4241 __isl_give isl_map *isl_map_order_le(
4242 __isl_take isl_map *map,
4243 enum isl_dim_type type1, int pos1,
4244 enum isl_dim_type type2, int pos2);
4245 __isl_give isl_basic_map *isl_basic_map_order_ge(
4246 __isl_take isl_basic_map *bmap,
4247 enum isl_dim_type type1, int pos1,
4248 enum isl_dim_type type2, int pos2);
4249 __isl_give isl_map *isl_map_order_ge(
4250 __isl_take isl_map *map,
4251 enum isl_dim_type type1, int pos1,
4252 enum isl_dim_type type2, int pos2);
4253 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4254 enum isl_dim_type type1, int pos1,
4255 enum isl_dim_type type2, int pos2);
4256 __isl_give isl_basic_map *isl_basic_map_order_gt(
4257 __isl_take isl_basic_map *bmap,
4258 enum isl_dim_type type1, int pos1,
4259 enum isl_dim_type type2, int pos2);
4260 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4261 enum isl_dim_type type1, int pos1,
4262 enum isl_dim_type type2, int pos2);
4264 Intersect the relation with the half-space where the given
4265 dimensions satisfy the given ordering.
4269 #include <isl/aff.h>
4270 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4271 __isl_take isl_aff *aff);
4272 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4273 __isl_take isl_aff *aff);
4274 __isl_give isl_set *isl_pw_aff_pos_set(
4275 __isl_take isl_pw_aff *pa);
4276 __isl_give isl_set *isl_pw_aff_nonneg_set(
4277 __isl_take isl_pw_aff *pwaff);
4278 __isl_give isl_set *isl_pw_aff_zero_set(
4279 __isl_take isl_pw_aff *pwaff);
4280 __isl_give isl_set *isl_pw_aff_non_zero_set(
4281 __isl_take isl_pw_aff *pwaff);
4282 __isl_give isl_union_set *
4283 isl_union_pw_aff_zero_union_set(
4284 __isl_take isl_union_pw_aff *upa);
4286 The function C<isl_aff_neg_basic_set> returns a basic set
4287 containing those elements in the domain space
4288 of C<aff> where C<aff> is negative.
4289 The function C<isl_pw_aff_nonneg_set> returns a set
4290 containing those elements in the domain
4291 of C<pwaff> where C<pwaff> is non-negative.
4295 __isl_give isl_map *isl_set_identity(
4296 __isl_take isl_set *set);
4297 __isl_give isl_union_map *isl_union_set_identity(
4298 __isl_take isl_union_set *uset);
4299 __isl_give isl_union_pw_multi_aff *
4300 isl_union_set_identity_union_pw_multi_aff(
4301 __isl_take isl_union_set *uset);
4303 Construct an identity relation on the given (union) set.
4305 =item * Function Extraction
4307 A piecewise quasi affine expression that is equal to 1 on a set
4308 and 0 outside the set can be created using the following function.
4310 #include <isl/aff.h>
4311 __isl_give isl_pw_aff *isl_set_indicator_function(
4312 __isl_take isl_set *set);
4314 A piecewise multiple quasi affine expression can be extracted
4315 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4316 and the C<isl_map> is single-valued.
4317 In case of a conversion from an C<isl_union_map>
4318 to an C<isl_union_pw_multi_aff>, these properties need to hold
4319 in each domain space.
4321 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4322 __isl_take isl_set *set);
4323 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4324 __isl_take isl_map *map);
4326 __isl_give isl_union_pw_multi_aff *
4327 isl_union_pw_multi_aff_from_union_set(
4328 __isl_take isl_union_set *uset);
4329 __isl_give isl_union_pw_multi_aff *
4330 isl_union_pw_multi_aff_from_union_map(
4331 __isl_take isl_union_map *umap);
4335 __isl_give isl_basic_set *isl_basic_map_deltas(
4336 __isl_take isl_basic_map *bmap);
4337 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4338 __isl_give isl_union_set *isl_union_map_deltas(
4339 __isl_take isl_union_map *umap);
4341 These functions return a (basic) set containing the differences
4342 between image elements and corresponding domain elements in the input.
4344 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4345 __isl_take isl_basic_map *bmap);
4346 __isl_give isl_map *isl_map_deltas_map(
4347 __isl_take isl_map *map);
4348 __isl_give isl_union_map *isl_union_map_deltas_map(
4349 __isl_take isl_union_map *umap);
4351 The functions above construct a (basic, regular or union) relation
4352 that maps (a wrapped version of) the input relation to its delta set.
4356 Simplify the representation of a set, relation or functions by trying
4357 to combine pairs of basic sets or relations into a single
4358 basic set or relation.
4360 #include <isl/set.h>
4361 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4363 #include <isl/map.h>
4364 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4366 #include <isl/union_set.h>
4367 __isl_give isl_union_set *isl_union_set_coalesce(
4368 __isl_take isl_union_set *uset);
4370 #include <isl/union_map.h>
4371 __isl_give isl_union_map *isl_union_map_coalesce(
4372 __isl_take isl_union_map *umap);
4374 #include <isl/aff.h>
4375 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4376 __isl_take isl_pw_aff *pwqp);
4377 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4378 __isl_take isl_pw_multi_aff *pma);
4379 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4380 __isl_take isl_multi_pw_aff *mpa);
4381 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4382 __isl_take isl_union_pw_aff *upa);
4383 __isl_give isl_union_pw_multi_aff *
4384 isl_union_pw_multi_aff_coalesce(
4385 __isl_take isl_union_pw_multi_aff *upma);
4387 #include <isl/polynomial.h>
4388 __isl_give isl_pw_qpolynomial_fold *
4389 isl_pw_qpolynomial_fold_coalesce(
4390 __isl_take isl_pw_qpolynomial_fold *pwf);
4391 __isl_give isl_union_pw_qpolynomial *
4392 isl_union_pw_qpolynomial_coalesce(
4393 __isl_take isl_union_pw_qpolynomial *upwqp);
4394 __isl_give isl_union_pw_qpolynomial_fold *
4395 isl_union_pw_qpolynomial_fold_coalesce(
4396 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4398 One of the methods for combining pairs of basic sets or relations
4399 can result in coefficients that are much larger than those that appear
4400 in the constraints of the input. By default, the coefficients are
4401 not allowed to grow larger, but this can be changed by unsetting
4402 the following option.
4404 int isl_options_set_coalesce_bounded_wrapping(
4405 isl_ctx *ctx, int val);
4406 int isl_options_get_coalesce_bounded_wrapping(
4409 =item * Detecting equalities
4411 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4412 __isl_take isl_basic_set *bset);
4413 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4414 __isl_take isl_basic_map *bmap);
4415 __isl_give isl_set *isl_set_detect_equalities(
4416 __isl_take isl_set *set);
4417 __isl_give isl_map *isl_map_detect_equalities(
4418 __isl_take isl_map *map);
4419 __isl_give isl_union_set *isl_union_set_detect_equalities(
4420 __isl_take isl_union_set *uset);
4421 __isl_give isl_union_map *isl_union_map_detect_equalities(
4422 __isl_take isl_union_map *umap);
4424 Simplify the representation of a set or relation by detecting implicit
4427 =item * Removing redundant constraints
4429 #include <isl/set.h>
4430 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4431 __isl_take isl_basic_set *bset);
4432 __isl_give isl_set *isl_set_remove_redundancies(
4433 __isl_take isl_set *set);
4435 #include <isl/union_set.h>
4436 __isl_give isl_union_set *
4437 isl_union_set_remove_redundancies(
4438 __isl_take isl_union_set *uset);
4440 #include <isl/map.h>
4441 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4442 __isl_take isl_basic_map *bmap);
4443 __isl_give isl_map *isl_map_remove_redundancies(
4444 __isl_take isl_map *map);
4446 #include <isl/union_map.h>
4447 __isl_give isl_union_map *
4448 isl_union_map_remove_redundancies(
4449 __isl_take isl_union_map *umap);
4453 __isl_give isl_basic_set *isl_set_convex_hull(
4454 __isl_take isl_set *set);
4455 __isl_give isl_basic_map *isl_map_convex_hull(
4456 __isl_take isl_map *map);
4458 If the input set or relation has any existentially quantified
4459 variables, then the result of these operations is currently undefined.
4463 #include <isl/set.h>
4464 __isl_give isl_basic_set *
4465 isl_set_unshifted_simple_hull(
4466 __isl_take isl_set *set);
4467 __isl_give isl_basic_set *isl_set_simple_hull(
4468 __isl_take isl_set *set);
4469 __isl_give isl_basic_set *
4470 isl_set_unshifted_simple_hull_from_set_list(
4471 __isl_take isl_set *set,
4472 __isl_take isl_set_list *list);
4474 #include <isl/map.h>
4475 __isl_give isl_basic_map *
4476 isl_map_unshifted_simple_hull(
4477 __isl_take isl_map *map);
4478 __isl_give isl_basic_map *isl_map_simple_hull(
4479 __isl_take isl_map *map);
4480 __isl_give isl_basic_map *
4481 isl_map_unshifted_simple_hull_from_map_list(
4482 __isl_take isl_map *map,
4483 __isl_take isl_map_list *list);
4485 #include <isl/union_map.h>
4486 __isl_give isl_union_map *isl_union_map_simple_hull(
4487 __isl_take isl_union_map *umap);
4489 These functions compute a single basic set or relation
4490 that contains the whole input set or relation.
4491 In particular, the output is described by translates
4492 of the constraints describing the basic sets or relations in the input.
4493 In case of C<isl_set_unshifted_simple_hull>, only the original
4494 constraints are used, without any translation.
4495 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4496 C<isl_map_unshifted_simple_hull_from_map_list>, the
4497 constraints are taken from the elements of the second argument.
4501 (See \autoref{s:simple hull}.)
4507 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4508 __isl_take isl_basic_set *bset);
4509 __isl_give isl_basic_set *isl_set_affine_hull(
4510 __isl_take isl_set *set);
4511 __isl_give isl_union_set *isl_union_set_affine_hull(
4512 __isl_take isl_union_set *uset);
4513 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4514 __isl_take isl_basic_map *bmap);
4515 __isl_give isl_basic_map *isl_map_affine_hull(
4516 __isl_take isl_map *map);
4517 __isl_give isl_union_map *isl_union_map_affine_hull(
4518 __isl_take isl_union_map *umap);
4520 In case of union sets and relations, the affine hull is computed
4523 =item * Polyhedral hull
4525 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4526 __isl_take isl_set *set);
4527 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4528 __isl_take isl_map *map);
4529 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4530 __isl_take isl_union_set *uset);
4531 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4532 __isl_take isl_union_map *umap);
4534 These functions compute a single basic set or relation
4535 not involving any existentially quantified variables
4536 that contains the whole input set or relation.
4537 In case of union sets and relations, the polyhedral hull is computed
4540 =item * Other approximations
4542 #include <isl/set.h>
4543 __isl_give isl_basic_set *
4544 isl_basic_set_drop_constraints_involving_dims(
4545 __isl_take isl_basic_set *bset,
4546 enum isl_dim_type type,
4547 unsigned first, unsigned n);
4548 __isl_give isl_basic_set *
4549 isl_basic_set_drop_constraints_not_involving_dims(
4550 __isl_take isl_basic_set *bset,
4551 enum isl_dim_type type,
4552 unsigned first, unsigned n);
4553 __isl_give isl_set *
4554 isl_set_drop_constraints_involving_dims(
4555 __isl_take isl_set *set,
4556 enum isl_dim_type type,
4557 unsigned first, unsigned n);
4559 #include <isl/map.h>
4560 __isl_give isl_basic_map *
4561 isl_basic_map_drop_constraints_involving_dims(
4562 __isl_take isl_basic_map *bmap,
4563 enum isl_dim_type type,
4564 unsigned first, unsigned n);
4565 __isl_give isl_map *
4566 isl_map_drop_constraints_involving_dims(
4567 __isl_take isl_map *map,
4568 enum isl_dim_type type,
4569 unsigned first, unsigned n);
4571 These functions drop any constraints (not) involving the specified dimensions.
4572 Note that the result depends on the representation of the input.
4574 #include <isl/polynomial.h>
4575 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4576 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4577 __isl_give isl_union_pw_qpolynomial *
4578 isl_union_pw_qpolynomial_to_polynomial(
4579 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4581 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4582 the polynomial will be an overapproximation. If C<sign> is negative,
4583 it will be an underapproximation. If C<sign> is zero, the approximation
4584 will lie somewhere in between.
4588 __isl_give isl_basic_set *isl_basic_set_sample(
4589 __isl_take isl_basic_set *bset);
4590 __isl_give isl_basic_set *isl_set_sample(
4591 __isl_take isl_set *set);
4592 __isl_give isl_basic_map *isl_basic_map_sample(
4593 __isl_take isl_basic_map *bmap);
4594 __isl_give isl_basic_map *isl_map_sample(
4595 __isl_take isl_map *map);
4597 If the input (basic) set or relation is non-empty, then return
4598 a singleton subset of the input. Otherwise, return an empty set.
4600 =item * Optimization
4602 #include <isl/ilp.h>
4603 __isl_give isl_val *isl_basic_set_max_val(
4604 __isl_keep isl_basic_set *bset,
4605 __isl_keep isl_aff *obj);
4606 __isl_give isl_val *isl_set_min_val(
4607 __isl_keep isl_set *set,
4608 __isl_keep isl_aff *obj);
4609 __isl_give isl_val *isl_set_max_val(
4610 __isl_keep isl_set *set,
4611 __isl_keep isl_aff *obj);
4613 Compute the minimum or maximum of the integer affine expression C<obj>
4614 over the points in C<set>, returning the result in C<opt>.
4615 The result is C<NULL> in case of an error, the optimal value in case
4616 there is one, negative infinity or infinity if the problem is unbounded and
4617 NaN if the problem is empty.
4619 =item * Parametric optimization
4621 __isl_give isl_pw_aff *isl_set_dim_min(
4622 __isl_take isl_set *set, int pos);
4623 __isl_give isl_pw_aff *isl_set_dim_max(
4624 __isl_take isl_set *set, int pos);
4625 __isl_give isl_pw_aff *isl_map_dim_max(
4626 __isl_take isl_map *map, int pos);
4628 Compute the minimum or maximum of the given set or output dimension
4629 as a function of the parameters (and input dimensions), but independently
4630 of the other set or output dimensions.
4631 For lexicographic optimization, see L<"Lexicographic Optimization">.
4635 The following functions compute either the set of (rational) coefficient
4636 values of valid constraints for the given set or the set of (rational)
4637 values satisfying the constraints with coefficients from the given set.
4638 Internally, these two sets of functions perform essentially the
4639 same operations, except that the set of coefficients is assumed to
4640 be a cone, while the set of values may be any polyhedron.
4641 The current implementation is based on the Farkas lemma and
4642 Fourier-Motzkin elimination, but this may change or be made optional
4643 in future. In particular, future implementations may use different
4644 dualization algorithms or skip the elimination step.
4646 __isl_give isl_basic_set *isl_basic_set_coefficients(
4647 __isl_take isl_basic_set *bset);
4648 __isl_give isl_basic_set *isl_set_coefficients(
4649 __isl_take isl_set *set);
4650 __isl_give isl_union_set *isl_union_set_coefficients(
4651 __isl_take isl_union_set *bset);
4652 __isl_give isl_basic_set *isl_basic_set_solutions(
4653 __isl_take isl_basic_set *bset);
4654 __isl_give isl_basic_set *isl_set_solutions(
4655 __isl_take isl_set *set);
4656 __isl_give isl_union_set *isl_union_set_solutions(
4657 __isl_take isl_union_set *bset);
4661 __isl_give isl_map *isl_map_fixed_power_val(
4662 __isl_take isl_map *map,
4663 __isl_take isl_val *exp);
4664 __isl_give isl_union_map *
4665 isl_union_map_fixed_power_val(
4666 __isl_take isl_union_map *umap,
4667 __isl_take isl_val *exp);
4669 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4670 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4671 of C<map> is computed.
4673 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4675 __isl_give isl_union_map *isl_union_map_power(
4676 __isl_take isl_union_map *umap, int *exact);
4678 Compute a parametric representation for all positive powers I<k> of C<map>.
4679 The result maps I<k> to a nested relation corresponding to the
4680 I<k>th power of C<map>.
4681 The result may be an overapproximation. If the result is known to be exact,
4682 then C<*exact> is set to C<1>.
4684 =item * Transitive closure
4686 __isl_give isl_map *isl_map_transitive_closure(
4687 __isl_take isl_map *map, int *exact);
4688 __isl_give isl_union_map *isl_union_map_transitive_closure(
4689 __isl_take isl_union_map *umap, int *exact);
4691 Compute the transitive closure of C<map>.
4692 The result may be an overapproximation. If the result is known to be exact,
4693 then C<*exact> is set to C<1>.
4695 =item * Reaching path lengths
4697 __isl_give isl_map *isl_map_reaching_path_lengths(
4698 __isl_take isl_map *map, int *exact);
4700 Compute a relation that maps each element in the range of C<map>
4701 to the lengths of all paths composed of edges in C<map> that
4702 end up in the given element.
4703 The result may be an overapproximation. If the result is known to be exact,
4704 then C<*exact> is set to C<1>.
4705 To compute the I<maximal> path length, the resulting relation
4706 should be postprocessed by C<isl_map_lexmax>.
4707 In particular, if the input relation is a dependence relation
4708 (mapping sources to sinks), then the maximal path length corresponds
4709 to the free schedule.
4710 Note, however, that C<isl_map_lexmax> expects the maximum to be
4711 finite, so if the path lengths are unbounded (possibly due to
4712 the overapproximation), then you will get an error message.
4716 #include <isl/space.h>
4717 __isl_give isl_space *isl_space_wrap(
4718 __isl_take isl_space *space);
4719 __isl_give isl_space *isl_space_unwrap(
4720 __isl_take isl_space *space);
4722 #include <isl/local_space.h>
4723 __isl_give isl_local_space *isl_local_space_wrap(
4724 __isl_take isl_local_space *ls);
4726 #include <isl/set.h>
4727 __isl_give isl_basic_map *isl_basic_set_unwrap(
4728 __isl_take isl_basic_set *bset);
4729 __isl_give isl_map *isl_set_unwrap(
4730 __isl_take isl_set *set);
4732 #include <isl/map.h>
4733 __isl_give isl_basic_set *isl_basic_map_wrap(
4734 __isl_take isl_basic_map *bmap);
4735 __isl_give isl_set *isl_map_wrap(
4736 __isl_take isl_map *map);
4738 #include <isl/union_set.h>
4739 __isl_give isl_union_map *isl_union_set_unwrap(
4740 __isl_take isl_union_set *uset);
4742 #include <isl/union_map.h>
4743 __isl_give isl_union_set *isl_union_map_wrap(
4744 __isl_take isl_union_map *umap);
4746 The input to C<isl_space_unwrap> should
4747 be the space of a set, while that of
4748 C<isl_space_wrap> should be the space of a relation.
4749 Conversely, the output of C<isl_space_unwrap> is the space
4750 of a relation, while that of C<isl_space_wrap> is the space of a set.
4754 Remove any internal structure of domain (and range) of the given
4755 set or relation. If there is any such internal structure in the input,
4756 then the name of the space is also removed.
4758 #include <isl/local_space.h>
4759 __isl_give isl_local_space *
4760 isl_local_space_flatten_domain(
4761 __isl_take isl_local_space *ls);
4762 __isl_give isl_local_space *
4763 isl_local_space_flatten_range(
4764 __isl_take isl_local_space *ls);
4766 #include <isl/set.h>
4767 __isl_give isl_basic_set *isl_basic_set_flatten(
4768 __isl_take isl_basic_set *bset);
4769 __isl_give isl_set *isl_set_flatten(
4770 __isl_take isl_set *set);
4772 #include <isl/map.h>
4773 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4774 __isl_take isl_basic_map *bmap);
4775 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4776 __isl_take isl_basic_map *bmap);
4777 __isl_give isl_map *isl_map_flatten_range(
4778 __isl_take isl_map *map);
4779 __isl_give isl_map *isl_map_flatten_domain(
4780 __isl_take isl_map *map);
4781 __isl_give isl_basic_map *isl_basic_map_flatten(
4782 __isl_take isl_basic_map *bmap);
4783 __isl_give isl_map *isl_map_flatten(
4784 __isl_take isl_map *map);
4786 #include <isl/val.h>
4787 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4788 __isl_take isl_multi_val *mv);
4790 #include <isl/aff.h>
4791 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4792 __isl_take isl_multi_aff *ma);
4793 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4794 __isl_take isl_multi_aff *ma);
4795 __isl_give isl_multi_pw_aff *
4796 isl_multi_pw_aff_flatten_range(
4797 __isl_take isl_multi_pw_aff *mpa);
4798 __isl_give isl_multi_union_pw_aff *
4799 isl_multi_union_pw_aff_flatten_range(
4800 __isl_take isl_multi_union_pw_aff *mupa);
4802 #include <isl/map.h>
4803 __isl_give isl_map *isl_set_flatten_map(
4804 __isl_take isl_set *set);
4806 The function above constructs a relation
4807 that maps the input set to a flattened version of the set.
4811 Lift the input set to a space with extra dimensions corresponding
4812 to the existentially quantified variables in the input.
4813 In particular, the result lives in a wrapped map where the domain
4814 is the original space and the range corresponds to the original
4815 existentially quantified variables.
4817 #include <isl/set.h>
4818 __isl_give isl_basic_set *isl_basic_set_lift(
4819 __isl_take isl_basic_set *bset);
4820 __isl_give isl_set *isl_set_lift(
4821 __isl_take isl_set *set);
4822 __isl_give isl_union_set *isl_union_set_lift(
4823 __isl_take isl_union_set *uset);
4825 Given a local space that contains the existentially quantified
4826 variables of a set, a basic relation that, when applied to
4827 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4828 can be constructed using the following function.
4830 #include <isl/local_space.h>
4831 __isl_give isl_basic_map *isl_local_space_lifting(
4832 __isl_take isl_local_space *ls);
4834 #include <isl/aff.h>
4835 __isl_give isl_multi_aff *isl_multi_aff_lift(
4836 __isl_take isl_multi_aff *maff,
4837 __isl_give isl_local_space **ls);
4839 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4840 then it is assigned the local space that lies at the basis of
4841 the lifting applied.
4843 =item * Internal Product
4845 #include <isl/space.h>
4846 __isl_give isl_space *isl_space_zip(
4847 __isl_take isl_space *space);
4849 #include <isl/map.h>
4850 __isl_give isl_basic_map *isl_basic_map_zip(
4851 __isl_take isl_basic_map *bmap);
4852 __isl_give isl_map *isl_map_zip(
4853 __isl_take isl_map *map);
4855 #include <isl/union_map.h>
4856 __isl_give isl_union_map *isl_union_map_zip(
4857 __isl_take isl_union_map *umap);
4859 Given a relation with nested relations for domain and range,
4860 interchange the range of the domain with the domain of the range.
4864 #include <isl/space.h>
4865 __isl_give isl_space *isl_space_curry(
4866 __isl_take isl_space *space);
4867 __isl_give isl_space *isl_space_uncurry(
4868 __isl_take isl_space *space);
4870 #include <isl/map.h>
4871 __isl_give isl_basic_map *isl_basic_map_curry(
4872 __isl_take isl_basic_map *bmap);
4873 __isl_give isl_basic_map *isl_basic_map_uncurry(
4874 __isl_take isl_basic_map *bmap);
4875 __isl_give isl_map *isl_map_curry(
4876 __isl_take isl_map *map);
4877 __isl_give isl_map *isl_map_uncurry(
4878 __isl_take isl_map *map);
4880 #include <isl/union_map.h>
4881 __isl_give isl_union_map *isl_union_map_curry(
4882 __isl_take isl_union_map *umap);
4883 __isl_give isl_union_map *isl_union_map_uncurry(
4884 __isl_take isl_union_map *umap);
4886 Given a relation with a nested relation for domain,
4887 the C<curry> functions
4888 move the range of the nested relation out of the domain
4889 and use it as the domain of a nested relation in the range,
4890 with the original range as range of this nested relation.
4891 The C<uncurry> functions perform the inverse operation.
4893 =item * Aligning parameters
4895 Change the order of the parameters of the given set, relation
4897 such that the first parameters match those of C<model>.
4898 This may involve the introduction of extra parameters.
4899 All parameters need to be named.
4901 #include <isl/space.h>
4902 __isl_give isl_space *isl_space_align_params(
4903 __isl_take isl_space *space1,
4904 __isl_take isl_space *space2)
4906 #include <isl/set.h>
4907 __isl_give isl_basic_set *isl_basic_set_align_params(
4908 __isl_take isl_basic_set *bset,
4909 __isl_take isl_space *model);
4910 __isl_give isl_set *isl_set_align_params(
4911 __isl_take isl_set *set,
4912 __isl_take isl_space *model);
4914 #include <isl/map.h>
4915 __isl_give isl_basic_map *isl_basic_map_align_params(
4916 __isl_take isl_basic_map *bmap,
4917 __isl_take isl_space *model);
4918 __isl_give isl_map *isl_map_align_params(
4919 __isl_take isl_map *map,
4920 __isl_take isl_space *model);
4922 #include <isl/val.h>
4923 __isl_give isl_multi_val *isl_multi_val_align_params(
4924 __isl_take isl_multi_val *mv,
4925 __isl_take isl_space *model);
4927 #include <isl/aff.h>
4928 __isl_give isl_aff *isl_aff_align_params(
4929 __isl_take isl_aff *aff,
4930 __isl_take isl_space *model);
4931 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4932 __isl_take isl_multi_aff *multi,
4933 __isl_take isl_space *model);
4934 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4935 __isl_take isl_pw_aff *pwaff,
4936 __isl_take isl_space *model);
4937 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4938 __isl_take isl_pw_multi_aff *pma,
4939 __isl_take isl_space *model);
4940 __isl_give isl_union_pw_aff *
4941 isl_union_pw_aff_align_params(
4942 __isl_take isl_union_pw_aff *upa,
4943 __isl_take isl_space *model);
4944 __isl_give isl_union_pw_multi_aff *
4945 isl_union_pw_multi_aff_align_params(
4946 __isl_take isl_union_pw_multi_aff *upma,
4947 __isl_take isl_space *model);
4948 __isl_give isl_multi_union_pw_aff *
4949 isl_multi_union_pw_aff_align_params(
4950 __isl_take isl_multi_union_pw_aff *mupa,
4951 __isl_take isl_space *model);
4953 #include <isl/polynomial.h>
4954 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4955 __isl_take isl_qpolynomial *qp,
4956 __isl_take isl_space *model);
4958 =item * Unary Arithmethic Operations
4960 #include <isl/val.h>
4961 __isl_give isl_multi_val *isl_multi_val_neg(
4962 __isl_take isl_multi_val *mv);
4964 #include <isl/aff.h>
4965 __isl_give isl_aff *isl_aff_neg(
4966 __isl_take isl_aff *aff);
4967 __isl_give isl_multi_aff *isl_multi_aff_neg(
4968 __isl_take isl_multi_aff *ma);
4969 __isl_give isl_pw_aff *isl_pw_aff_neg(
4970 __isl_take isl_pw_aff *pwaff);
4971 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
4972 __isl_take isl_pw_multi_aff *pma);
4973 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
4974 __isl_take isl_multi_pw_aff *mpa);
4975 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
4976 __isl_take isl_union_pw_aff *upa);
4977 __isl_give isl_union_pw_multi_aff *
4978 isl_union_pw_multi_aff_neg(
4979 __isl_take isl_union_pw_multi_aff *upma);
4980 __isl_give isl_multi_union_pw_aff *
4981 isl_multi_union_pw_aff_neg(
4982 __isl_take isl_multi_union_pw_aff *mupa);
4983 __isl_give isl_aff *isl_aff_ceil(
4984 __isl_take isl_aff *aff);
4985 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4986 __isl_take isl_pw_aff *pwaff);
4987 __isl_give isl_aff *isl_aff_floor(
4988 __isl_take isl_aff *aff);
4989 __isl_give isl_multi_aff *isl_multi_aff_floor(
4990 __isl_take isl_multi_aff *ma);
4991 __isl_give isl_pw_aff *isl_pw_aff_floor(
4992 __isl_take isl_pw_aff *pwaff);
4993 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
4994 __isl_take isl_union_pw_aff *upa);
4996 #include <isl/aff.h>
4997 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4998 __isl_take isl_pw_aff_list *list);
4999 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5000 __isl_take isl_pw_aff_list *list);
5002 #include <isl/polynomial.h>
5003 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5004 __isl_take isl_qpolynomial *qp);
5005 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5006 __isl_take isl_pw_qpolynomial *pwqp);
5007 __isl_give isl_union_pw_qpolynomial *
5008 isl_union_pw_qpolynomial_neg(
5009 __isl_take isl_union_pw_qpolynomial *upwqp);
5010 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5011 __isl_take isl_qpolynomial *qp,
5013 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5014 __isl_take isl_pw_qpolynomial *pwqp,
5019 The following functions evaluate a function in a point.
5021 #include <isl/polynomial.h>
5022 __isl_give isl_val *isl_pw_qpolynomial_eval(
5023 __isl_take isl_pw_qpolynomial *pwqp,
5024 __isl_take isl_point *pnt);
5025 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5026 __isl_take isl_pw_qpolynomial_fold *pwf,
5027 __isl_take isl_point *pnt);
5028 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5029 __isl_take isl_union_pw_qpolynomial *upwqp,
5030 __isl_take isl_point *pnt);
5031 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5032 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5033 __isl_take isl_point *pnt);
5035 =item * Dimension manipulation
5037 It is usually not advisable to directly change the (input or output)
5038 space of a set or a relation as this removes the name and the internal
5039 structure of the space. However, the functions below can be useful
5040 to add new parameters, assuming
5041 C<isl_set_align_params> and C<isl_map_align_params>
5044 #include <isl/space.h>
5045 __isl_give isl_space *isl_space_add_dims(
5046 __isl_take isl_space *space,
5047 enum isl_dim_type type, unsigned n);
5048 __isl_give isl_space *isl_space_insert_dims(
5049 __isl_take isl_space *space,
5050 enum isl_dim_type type, unsigned pos, unsigned n);
5051 __isl_give isl_space *isl_space_drop_dims(
5052 __isl_take isl_space *space,
5053 enum isl_dim_type type, unsigned first, unsigned n);
5054 __isl_give isl_space *isl_space_move_dims(
5055 __isl_take isl_space *space,
5056 enum isl_dim_type dst_type, unsigned dst_pos,
5057 enum isl_dim_type src_type, unsigned src_pos,
5060 #include <isl/local_space.h>
5061 __isl_give isl_local_space *isl_local_space_add_dims(
5062 __isl_take isl_local_space *ls,
5063 enum isl_dim_type type, unsigned n);
5064 __isl_give isl_local_space *isl_local_space_insert_dims(
5065 __isl_take isl_local_space *ls,
5066 enum isl_dim_type type, unsigned first, unsigned n);
5067 __isl_give isl_local_space *isl_local_space_drop_dims(
5068 __isl_take isl_local_space *ls,
5069 enum isl_dim_type type, unsigned first, unsigned n);
5071 #include <isl/set.h>
5072 __isl_give isl_basic_set *isl_basic_set_add_dims(
5073 __isl_take isl_basic_set *bset,
5074 enum isl_dim_type type, unsigned n);
5075 __isl_give isl_set *isl_set_add_dims(
5076 __isl_take isl_set *set,
5077 enum isl_dim_type type, unsigned n);
5078 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5079 __isl_take isl_basic_set *bset,
5080 enum isl_dim_type type, unsigned pos,
5082 __isl_give isl_set *isl_set_insert_dims(
5083 __isl_take isl_set *set,
5084 enum isl_dim_type type, unsigned pos, unsigned n);
5085 __isl_give isl_basic_set *isl_basic_set_move_dims(
5086 __isl_take isl_basic_set *bset,
5087 enum isl_dim_type dst_type, unsigned dst_pos,
5088 enum isl_dim_type src_type, unsigned src_pos,
5090 __isl_give isl_set *isl_set_move_dims(
5091 __isl_take isl_set *set,
5092 enum isl_dim_type dst_type, unsigned dst_pos,
5093 enum isl_dim_type src_type, unsigned src_pos,
5096 #include <isl/map.h>
5097 __isl_give isl_map *isl_map_add_dims(
5098 __isl_take isl_map *map,
5099 enum isl_dim_type type, unsigned n);
5100 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5101 __isl_take isl_basic_map *bmap,
5102 enum isl_dim_type type, unsigned pos,
5104 __isl_give isl_map *isl_map_insert_dims(
5105 __isl_take isl_map *map,
5106 enum isl_dim_type type, unsigned pos, unsigned n);
5107 __isl_give isl_basic_map *isl_basic_map_move_dims(
5108 __isl_take isl_basic_map *bmap,
5109 enum isl_dim_type dst_type, unsigned dst_pos,
5110 enum isl_dim_type src_type, unsigned src_pos,
5112 __isl_give isl_map *isl_map_move_dims(
5113 __isl_take isl_map *map,
5114 enum isl_dim_type dst_type, unsigned dst_pos,
5115 enum isl_dim_type src_type, unsigned src_pos,
5118 #include <isl/val.h>
5119 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5120 __isl_take isl_multi_val *mv,
5121 enum isl_dim_type type, unsigned first, unsigned n);
5122 __isl_give isl_multi_val *isl_multi_val_add_dims(
5123 __isl_take isl_multi_val *mv,
5124 enum isl_dim_type type, unsigned n);
5125 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5126 __isl_take isl_multi_val *mv,
5127 enum isl_dim_type type, unsigned first, unsigned n);
5129 #include <isl/aff.h>
5130 __isl_give isl_aff *isl_aff_insert_dims(
5131 __isl_take isl_aff *aff,
5132 enum isl_dim_type type, unsigned first, unsigned n);
5133 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5134 __isl_take isl_multi_aff *ma,
5135 enum isl_dim_type type, unsigned first, unsigned n);
5136 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5137 __isl_take isl_pw_aff *pwaff,
5138 enum isl_dim_type type, unsigned first, unsigned n);
5139 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5140 __isl_take isl_multi_pw_aff *mpa,
5141 enum isl_dim_type type, unsigned first, unsigned n);
5142 __isl_give isl_aff *isl_aff_add_dims(
5143 __isl_take isl_aff *aff,
5144 enum isl_dim_type type, unsigned n);
5145 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5146 __isl_take isl_multi_aff *ma,
5147 enum isl_dim_type type, unsigned n);
5148 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5149 __isl_take isl_pw_aff *pwaff,
5150 enum isl_dim_type type, unsigned n);
5151 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5152 __isl_take isl_multi_pw_aff *mpa,
5153 enum isl_dim_type type, unsigned n);
5154 __isl_give isl_aff *isl_aff_drop_dims(
5155 __isl_take isl_aff *aff,
5156 enum isl_dim_type type, unsigned first, unsigned n);
5157 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5158 __isl_take isl_multi_aff *maff,
5159 enum isl_dim_type type, unsigned first, unsigned n);
5160 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5161 __isl_take isl_pw_aff *pwaff,
5162 enum isl_dim_type type, unsigned first, unsigned n);
5163 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5164 __isl_take isl_pw_multi_aff *pma,
5165 enum isl_dim_type type, unsigned first, unsigned n);
5166 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5167 __isl_take isl_union_pw_aff *upa,
5168 enum isl_dim_type type, unsigned first, unsigned n);
5169 __isl_give isl_union_pw_multi_aff *
5170 isl_union_pw_multi_aff_drop_dims(
5171 __isl_take isl_union_pw_multi_aff *upma,
5172 enum isl_dim_type type,
5173 unsigned first, unsigned n);
5174 __isl_give isl_multi_union_pw_aff *
5175 isl_multi_union_pw_aff_drop_dims(
5176 __isl_take isl_multi_union_pw_aff *mupa,
5177 enum isl_dim_type type, unsigned first,
5179 __isl_give isl_aff *isl_aff_move_dims(
5180 __isl_take isl_aff *aff,
5181 enum isl_dim_type dst_type, unsigned dst_pos,
5182 enum isl_dim_type src_type, unsigned src_pos,
5184 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5185 __isl_take isl_multi_aff *ma,
5186 enum isl_dim_type dst_type, unsigned dst_pos,
5187 enum isl_dim_type src_type, unsigned src_pos,
5189 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5190 __isl_take isl_pw_aff *pa,
5191 enum isl_dim_type dst_type, unsigned dst_pos,
5192 enum isl_dim_type src_type, unsigned src_pos,
5194 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5195 __isl_take isl_multi_pw_aff *pma,
5196 enum isl_dim_type dst_type, unsigned dst_pos,
5197 enum isl_dim_type src_type, unsigned src_pos,
5200 #include <isl/polynomial.h>
5201 __isl_give isl_union_pw_qpolynomial *
5202 isl_union_pw_qpolynomial_drop_dims(
5203 __isl_take isl_union_pw_qpolynomial *upwqp,
5204 enum isl_dim_type type,
5205 unsigned first, unsigned n);
5206 __isl_give isl_union_pw_qpolynomial_fold *
5207 isl_union_pw_qpolynomial_fold_drop_dims(
5208 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5209 enum isl_dim_type type,
5210 unsigned first, unsigned n);
5212 The operations on union expressions can only manipulate parameters.
5216 =head2 Binary Operations
5218 The two arguments of a binary operation not only need to live
5219 in the same C<isl_ctx>, they currently also need to have
5220 the same (number of) parameters.
5222 =head3 Basic Operations
5226 =item * Intersection
5228 #include <isl/local_space.h>
5229 __isl_give isl_local_space *isl_local_space_intersect(
5230 __isl_take isl_local_space *ls1,
5231 __isl_take isl_local_space *ls2);
5233 #include <isl/set.h>
5234 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5235 __isl_take isl_basic_set *bset1,
5236 __isl_take isl_basic_set *bset2);
5237 __isl_give isl_basic_set *isl_basic_set_intersect(
5238 __isl_take isl_basic_set *bset1,
5239 __isl_take isl_basic_set *bset2);
5240 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5241 __isl_take struct isl_basic_set_list *list);
5242 __isl_give isl_set *isl_set_intersect_params(
5243 __isl_take isl_set *set,
5244 __isl_take isl_set *params);
5245 __isl_give isl_set *isl_set_intersect(
5246 __isl_take isl_set *set1,
5247 __isl_take isl_set *set2);
5249 #include <isl/map.h>
5250 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5251 __isl_take isl_basic_map *bmap,
5252 __isl_take isl_basic_set *bset);
5253 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5254 __isl_take isl_basic_map *bmap,
5255 __isl_take isl_basic_set *bset);
5256 __isl_give isl_basic_map *isl_basic_map_intersect(
5257 __isl_take isl_basic_map *bmap1,
5258 __isl_take isl_basic_map *bmap2);
5259 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5260 __isl_take isl_basic_map_list *list);
5261 __isl_give isl_map *isl_map_intersect_params(
5262 __isl_take isl_map *map,
5263 __isl_take isl_set *params);
5264 __isl_give isl_map *isl_map_intersect_domain(
5265 __isl_take isl_map *map,
5266 __isl_take isl_set *set);
5267 __isl_give isl_map *isl_map_intersect_range(
5268 __isl_take isl_map *map,
5269 __isl_take isl_set *set);
5270 __isl_give isl_map *isl_map_intersect(
5271 __isl_take isl_map *map1,
5272 __isl_take isl_map *map2);
5274 #include <isl/union_set.h>
5275 __isl_give isl_union_set *isl_union_set_intersect_params(
5276 __isl_take isl_union_set *uset,
5277 __isl_take isl_set *set);
5278 __isl_give isl_union_set *isl_union_set_intersect(
5279 __isl_take isl_union_set *uset1,
5280 __isl_take isl_union_set *uset2);
5282 #include <isl/union_map.h>
5283 __isl_give isl_union_map *isl_union_map_intersect_params(
5284 __isl_take isl_union_map *umap,
5285 __isl_take isl_set *set);
5286 __isl_give isl_union_map *isl_union_map_intersect_domain(
5287 __isl_take isl_union_map *umap,
5288 __isl_take isl_union_set *uset);
5289 __isl_give isl_union_map *isl_union_map_intersect_range(
5290 __isl_take isl_union_map *umap,
5291 __isl_take isl_union_set *uset);
5292 __isl_give isl_union_map *isl_union_map_intersect(
5293 __isl_take isl_union_map *umap1,
5294 __isl_take isl_union_map *umap2);
5296 #include <isl/aff.h>
5297 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5298 __isl_take isl_pw_aff *pa,
5299 __isl_take isl_set *set);
5300 __isl_give isl_multi_pw_aff *
5301 isl_multi_pw_aff_intersect_domain(
5302 __isl_take isl_multi_pw_aff *mpa,
5303 __isl_take isl_set *domain);
5304 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5305 __isl_take isl_pw_multi_aff *pma,
5306 __isl_take isl_set *set);
5307 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5308 __isl_take isl_union_pw_aff *upa,
5309 __isl_take isl_union_set *uset);
5310 __isl_give isl_union_pw_multi_aff *
5311 isl_union_pw_multi_aff_intersect_domain(
5312 __isl_take isl_union_pw_multi_aff *upma,
5313 __isl_take isl_union_set *uset);
5314 __isl_give isl_multi_union_pw_aff *
5315 isl_multi_union_pw_aff_intersect_domain(
5316 __isl_take isl_multi_union_pw_aff *mupa,
5317 __isl_take isl_union_set *uset);
5318 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5319 __isl_take isl_pw_aff *pa,
5320 __isl_take isl_set *set);
5321 __isl_give isl_multi_pw_aff *
5322 isl_multi_pw_aff_intersect_params(
5323 __isl_take isl_multi_pw_aff *mpa,
5324 __isl_take isl_set *set);
5325 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5326 __isl_take isl_pw_multi_aff *pma,
5327 __isl_take isl_set *set);
5328 __isl_give isl_union_pw_aff *
5329 isl_union_pw_aff_intersect_params(
5330 __isl_take isl_union_pw_aff *upa,
5331 __isl_give isl_union_pw_multi_aff *
5332 isl_union_pw_multi_aff_intersect_params(
5333 __isl_take isl_union_pw_multi_aff *upma,
5334 __isl_take isl_set *set);
5335 __isl_give isl_multi_union_pw_aff *
5336 isl_multi_union_pw_aff_intersect_params(
5337 __isl_take isl_multi_union_pw_aff *mupa,
5338 __isl_take isl_set *params);
5340 #include <isl/polynomial.h>
5341 __isl_give isl_pw_qpolynomial *
5342 isl_pw_qpolynomial_intersect_domain(
5343 __isl_take isl_pw_qpolynomial *pwpq,
5344 __isl_take isl_set *set);
5345 __isl_give isl_union_pw_qpolynomial *
5346 isl_union_pw_qpolynomial_intersect_domain(
5347 __isl_take isl_union_pw_qpolynomial *upwpq,
5348 __isl_take isl_union_set *uset);
5349 __isl_give isl_union_pw_qpolynomial_fold *
5350 isl_union_pw_qpolynomial_fold_intersect_domain(
5351 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5352 __isl_take isl_union_set *uset);
5353 __isl_give isl_pw_qpolynomial *
5354 isl_pw_qpolynomial_intersect_params(
5355 __isl_take isl_pw_qpolynomial *pwpq,
5356 __isl_take isl_set *set);
5357 __isl_give isl_pw_qpolynomial_fold *
5358 isl_pw_qpolynomial_fold_intersect_params(
5359 __isl_take isl_pw_qpolynomial_fold *pwf,
5360 __isl_take isl_set *set);
5361 __isl_give isl_union_pw_qpolynomial *
5362 isl_union_pw_qpolynomial_intersect_params(
5363 __isl_take isl_union_pw_qpolynomial *upwpq,
5364 __isl_take isl_set *set);
5365 __isl_give isl_union_pw_qpolynomial_fold *
5366 isl_union_pw_qpolynomial_fold_intersect_params(
5367 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5368 __isl_take isl_set *set);
5370 The second argument to the C<_params> functions needs to be
5371 a parametric (basic) set. For the other functions, a parametric set
5372 for either argument is only allowed if the other argument is
5373 a parametric set as well.
5374 The list passed to C<isl_basic_set_list_intersect> needs to have
5375 at least one element and all elements need to live in the same space.
5379 #include <isl/set.h>
5380 __isl_give isl_set *isl_basic_set_union(
5381 __isl_take isl_basic_set *bset1,
5382 __isl_take isl_basic_set *bset2);
5383 __isl_give isl_set *isl_set_union(
5384 __isl_take isl_set *set1,
5385 __isl_take isl_set *set2);
5387 #include <isl/map.h>
5388 __isl_give isl_map *isl_basic_map_union(
5389 __isl_take isl_basic_map *bmap1,
5390 __isl_take isl_basic_map *bmap2);
5391 __isl_give isl_map *isl_map_union(
5392 __isl_take isl_map *map1,
5393 __isl_take isl_map *map2);
5395 #include <isl/union_set.h>
5396 __isl_give isl_union_set *isl_union_set_union(
5397 __isl_take isl_union_set *uset1,
5398 __isl_take isl_union_set *uset2);
5399 __isl_give isl_union_set *isl_union_set_list_union(
5400 __isl_take isl_union_set_list *list);
5402 #include <isl/union_map.h>
5403 __isl_give isl_union_map *isl_union_map_union(
5404 __isl_take isl_union_map *umap1,
5405 __isl_take isl_union_map *umap2);
5407 =item * Set difference
5409 #include <isl/set.h>
5410 __isl_give isl_set *isl_set_subtract(
5411 __isl_take isl_set *set1,
5412 __isl_take isl_set *set2);
5414 #include <isl/map.h>
5415 __isl_give isl_map *isl_map_subtract(
5416 __isl_take isl_map *map1,
5417 __isl_take isl_map *map2);
5418 __isl_give isl_map *isl_map_subtract_domain(
5419 __isl_take isl_map *map,
5420 __isl_take isl_set *dom);
5421 __isl_give isl_map *isl_map_subtract_range(
5422 __isl_take isl_map *map,
5423 __isl_take isl_set *dom);
5425 #include <isl/union_set.h>
5426 __isl_give isl_union_set *isl_union_set_subtract(
5427 __isl_take isl_union_set *uset1,
5428 __isl_take isl_union_set *uset2);
5430 #include <isl/union_map.h>
5431 __isl_give isl_union_map *isl_union_map_subtract(
5432 __isl_take isl_union_map *umap1,
5433 __isl_take isl_union_map *umap2);
5434 __isl_give isl_union_map *isl_union_map_subtract_domain(
5435 __isl_take isl_union_map *umap,
5436 __isl_take isl_union_set *dom);
5437 __isl_give isl_union_map *isl_union_map_subtract_range(
5438 __isl_take isl_union_map *umap,
5439 __isl_take isl_union_set *dom);
5441 #include <isl/aff.h>
5442 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5443 __isl_take isl_pw_aff *pa,
5444 __isl_take isl_set *set);
5445 __isl_give isl_pw_multi_aff *
5446 isl_pw_multi_aff_subtract_domain(
5447 __isl_take isl_pw_multi_aff *pma,
5448 __isl_take isl_set *set);
5449 __isl_give isl_union_pw_aff *
5450 isl_union_pw_aff_subtract_domain(
5451 __isl_take isl_union_pw_aff *upa,
5452 __isl_take isl_union_set *uset);
5453 __isl_give isl_union_pw_multi_aff *
5454 isl_union_pw_multi_aff_subtract_domain(
5455 __isl_take isl_union_pw_multi_aff *upma,
5456 __isl_take isl_set *set);
5458 #include <isl/polynomial.h>
5459 __isl_give isl_pw_qpolynomial *
5460 isl_pw_qpolynomial_subtract_domain(
5461 __isl_take isl_pw_qpolynomial *pwpq,
5462 __isl_take isl_set *set);
5463 __isl_give isl_pw_qpolynomial_fold *
5464 isl_pw_qpolynomial_fold_subtract_domain(
5465 __isl_take isl_pw_qpolynomial_fold *pwf,
5466 __isl_take isl_set *set);
5467 __isl_give isl_union_pw_qpolynomial *
5468 isl_union_pw_qpolynomial_subtract_domain(
5469 __isl_take isl_union_pw_qpolynomial *upwpq,
5470 __isl_take isl_union_set *uset);
5471 __isl_give isl_union_pw_qpolynomial_fold *
5472 isl_union_pw_qpolynomial_fold_subtract_domain(
5473 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5474 __isl_take isl_union_set *uset);
5478 #include <isl/space.h>
5479 __isl_give isl_space *isl_space_join(
5480 __isl_take isl_space *left,
5481 __isl_take isl_space *right);
5483 #include <isl/map.h>
5484 __isl_give isl_basic_set *isl_basic_set_apply(
5485 __isl_take isl_basic_set *bset,
5486 __isl_take isl_basic_map *bmap);
5487 __isl_give isl_set *isl_set_apply(
5488 __isl_take isl_set *set,
5489 __isl_take isl_map *map);
5490 __isl_give isl_union_set *isl_union_set_apply(
5491 __isl_take isl_union_set *uset,
5492 __isl_take isl_union_map *umap);
5493 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5494 __isl_take isl_basic_map *bmap1,
5495 __isl_take isl_basic_map *bmap2);
5496 __isl_give isl_basic_map *isl_basic_map_apply_range(
5497 __isl_take isl_basic_map *bmap1,
5498 __isl_take isl_basic_map *bmap2);
5499 __isl_give isl_map *isl_map_apply_domain(
5500 __isl_take isl_map *map1,
5501 __isl_take isl_map *map2);
5502 __isl_give isl_map *isl_map_apply_range(
5503 __isl_take isl_map *map1,
5504 __isl_take isl_map *map2);
5506 #include <isl/union_map.h>
5507 __isl_give isl_union_map *isl_union_map_apply_domain(
5508 __isl_take isl_union_map *umap1,
5509 __isl_take isl_union_map *umap2);
5510 __isl_give isl_union_map *isl_union_map_apply_range(
5511 __isl_take isl_union_map *umap1,
5512 __isl_take isl_union_map *umap2);
5514 #include <isl/polynomial.h>
5515 __isl_give isl_pw_qpolynomial_fold *
5516 isl_set_apply_pw_qpolynomial_fold(
5517 __isl_take isl_set *set,
5518 __isl_take isl_pw_qpolynomial_fold *pwf,
5520 __isl_give isl_pw_qpolynomial_fold *
5521 isl_map_apply_pw_qpolynomial_fold(
5522 __isl_take isl_map *map,
5523 __isl_take isl_pw_qpolynomial_fold *pwf,
5525 __isl_give isl_union_pw_qpolynomial_fold *
5526 isl_union_set_apply_union_pw_qpolynomial_fold(
5527 __isl_take isl_union_set *uset,
5528 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5530 __isl_give isl_union_pw_qpolynomial_fold *
5531 isl_union_map_apply_union_pw_qpolynomial_fold(
5532 __isl_take isl_union_map *umap,
5533 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5536 The functions taking a map
5537 compose the given map with the given piecewise quasipolynomial reduction.
5538 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5539 over all elements in the intersection of the range of the map
5540 and the domain of the piecewise quasipolynomial reduction
5541 as a function of an element in the domain of the map.
5542 The functions taking a set compute a bound over all elements in the
5543 intersection of the set and the domain of the
5544 piecewise quasipolynomial reduction.
5548 #include <isl/set.h>
5549 __isl_give isl_basic_set *
5550 isl_basic_set_preimage_multi_aff(
5551 __isl_take isl_basic_set *bset,
5552 __isl_take isl_multi_aff *ma);
5553 __isl_give isl_set *isl_set_preimage_multi_aff(
5554 __isl_take isl_set *set,
5555 __isl_take isl_multi_aff *ma);
5556 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5557 __isl_take isl_set *set,
5558 __isl_take isl_pw_multi_aff *pma);
5559 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5560 __isl_take isl_set *set,
5561 __isl_take isl_multi_pw_aff *mpa);
5563 #include <isl/union_set.h>
5564 __isl_give isl_union_set *
5565 isl_union_set_preimage_multi_aff(
5566 __isl_take isl_union_set *uset,
5567 __isl_take isl_multi_aff *ma);
5568 __isl_give isl_union_set *
5569 isl_union_set_preimage_pw_multi_aff(
5570 __isl_take isl_union_set *uset,
5571 __isl_take isl_pw_multi_aff *pma);
5572 __isl_give isl_union_set *
5573 isl_union_set_preimage_union_pw_multi_aff(
5574 __isl_take isl_union_set *uset,
5575 __isl_take isl_union_pw_multi_aff *upma);
5577 #include <isl/map.h>
5578 __isl_give isl_basic_map *
5579 isl_basic_map_preimage_domain_multi_aff(
5580 __isl_take isl_basic_map *bmap,
5581 __isl_take isl_multi_aff *ma);
5582 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5583 __isl_take isl_map *map,
5584 __isl_take isl_multi_aff *ma);
5585 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5586 __isl_take isl_map *map,
5587 __isl_take isl_multi_aff *ma);
5588 __isl_give isl_map *
5589 isl_map_preimage_domain_pw_multi_aff(
5590 __isl_take isl_map *map,
5591 __isl_take isl_pw_multi_aff *pma);
5592 __isl_give isl_map *
5593 isl_map_preimage_range_pw_multi_aff(
5594 __isl_take isl_map *map,
5595 __isl_take isl_pw_multi_aff *pma);
5596 __isl_give isl_map *
5597 isl_map_preimage_domain_multi_pw_aff(
5598 __isl_take isl_map *map,
5599 __isl_take isl_multi_pw_aff *mpa);
5600 __isl_give isl_basic_map *
5601 isl_basic_map_preimage_range_multi_aff(
5602 __isl_take isl_basic_map *bmap,
5603 __isl_take isl_multi_aff *ma);
5605 #include <isl/union_map.h>
5606 __isl_give isl_union_map *
5607 isl_union_map_preimage_domain_multi_aff(
5608 __isl_take isl_union_map *umap,
5609 __isl_take isl_multi_aff *ma);
5610 __isl_give isl_union_map *
5611 isl_union_map_preimage_range_multi_aff(
5612 __isl_take isl_union_map *umap,
5613 __isl_take isl_multi_aff *ma);
5614 __isl_give isl_union_map *
5615 isl_union_map_preimage_domain_pw_multi_aff(
5616 __isl_take isl_union_map *umap,
5617 __isl_take isl_pw_multi_aff *pma);
5618 __isl_give isl_union_map *
5619 isl_union_map_preimage_range_pw_multi_aff(
5620 __isl_take isl_union_map *umap,
5621 __isl_take isl_pw_multi_aff *pma);
5622 __isl_give isl_union_map *
5623 isl_union_map_preimage_domain_union_pw_multi_aff(
5624 __isl_take isl_union_map *umap,
5625 __isl_take isl_union_pw_multi_aff *upma);
5626 __isl_give isl_union_map *
5627 isl_union_map_preimage_range_union_pw_multi_aff(
5628 __isl_take isl_union_map *umap,
5629 __isl_take isl_union_pw_multi_aff *upma);
5631 These functions compute the preimage of the given set or map domain/range under
5632 the given function. In other words, the expression is plugged
5633 into the set description or into the domain/range of the map.
5637 #include <isl/aff.h>
5638 __isl_give isl_aff *isl_aff_pullback_aff(
5639 __isl_take isl_aff *aff1,
5640 __isl_take isl_aff *aff2);
5641 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5642 __isl_take isl_aff *aff,
5643 __isl_take isl_multi_aff *ma);
5644 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5645 __isl_take isl_pw_aff *pa,
5646 __isl_take isl_multi_aff *ma);
5647 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5648 __isl_take isl_pw_aff *pa,
5649 __isl_take isl_pw_multi_aff *pma);
5650 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5651 __isl_take isl_pw_aff *pa,
5652 __isl_take isl_multi_pw_aff *mpa);
5653 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5654 __isl_take isl_multi_aff *ma1,
5655 __isl_take isl_multi_aff *ma2);
5656 __isl_give isl_pw_multi_aff *
5657 isl_pw_multi_aff_pullback_multi_aff(
5658 __isl_take isl_pw_multi_aff *pma,
5659 __isl_take isl_multi_aff *ma);
5660 __isl_give isl_multi_pw_aff *
5661 isl_multi_pw_aff_pullback_multi_aff(
5662 __isl_take isl_multi_pw_aff *mpa,
5663 __isl_take isl_multi_aff *ma);
5664 __isl_give isl_pw_multi_aff *
5665 isl_pw_multi_aff_pullback_pw_multi_aff(
5666 __isl_take isl_pw_multi_aff *pma1,
5667 __isl_take isl_pw_multi_aff *pma2);
5668 __isl_give isl_multi_pw_aff *
5669 isl_multi_pw_aff_pullback_pw_multi_aff(
5670 __isl_take isl_multi_pw_aff *mpa,
5671 __isl_take isl_pw_multi_aff *pma);
5672 __isl_give isl_multi_pw_aff *
5673 isl_multi_pw_aff_pullback_multi_pw_aff(
5674 __isl_take isl_multi_pw_aff *mpa1,
5675 __isl_take isl_multi_pw_aff *mpa2);
5676 __isl_give isl_union_pw_aff *
5677 isl_union_pw_aff_pullback_union_pw_multi_aff(
5678 __isl_take isl_union_pw_aff *upa,
5679 __isl_take isl_union_pw_multi_aff *upma);
5680 __isl_give isl_union_pw_multi_aff *
5681 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5682 __isl_take isl_union_pw_multi_aff *upma1,
5683 __isl_take isl_union_pw_multi_aff *upma2);
5685 These functions precompose the first expression by the second function.
5686 In other words, the second function is plugged
5687 into the first expression.
5691 #include <isl/aff.h>
5692 __isl_give isl_basic_set *isl_aff_le_basic_set(
5693 __isl_take isl_aff *aff1,
5694 __isl_take isl_aff *aff2);
5695 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5696 __isl_take isl_aff *aff1,
5697 __isl_take isl_aff *aff2);
5698 __isl_give isl_set *isl_pw_aff_eq_set(
5699 __isl_take isl_pw_aff *pwaff1,
5700 __isl_take isl_pw_aff *pwaff2);
5701 __isl_give isl_set *isl_pw_aff_ne_set(
5702 __isl_take isl_pw_aff *pwaff1,
5703 __isl_take isl_pw_aff *pwaff2);
5704 __isl_give isl_set *isl_pw_aff_le_set(
5705 __isl_take isl_pw_aff *pwaff1,
5706 __isl_take isl_pw_aff *pwaff2);
5707 __isl_give isl_set *isl_pw_aff_lt_set(
5708 __isl_take isl_pw_aff *pwaff1,
5709 __isl_take isl_pw_aff *pwaff2);
5710 __isl_give isl_set *isl_pw_aff_ge_set(
5711 __isl_take isl_pw_aff *pwaff1,
5712 __isl_take isl_pw_aff *pwaff2);
5713 __isl_give isl_set *isl_pw_aff_gt_set(
5714 __isl_take isl_pw_aff *pwaff1,
5715 __isl_take isl_pw_aff *pwaff2);
5717 __isl_give isl_set *isl_multi_aff_lex_le_set(
5718 __isl_take isl_multi_aff *ma1,
5719 __isl_take isl_multi_aff *ma2);
5720 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5721 __isl_take isl_multi_aff *ma1,
5722 __isl_take isl_multi_aff *ma2);
5724 __isl_give isl_set *isl_pw_aff_list_eq_set(
5725 __isl_take isl_pw_aff_list *list1,
5726 __isl_take isl_pw_aff_list *list2);
5727 __isl_give isl_set *isl_pw_aff_list_ne_set(
5728 __isl_take isl_pw_aff_list *list1,
5729 __isl_take isl_pw_aff_list *list2);
5730 __isl_give isl_set *isl_pw_aff_list_le_set(
5731 __isl_take isl_pw_aff_list *list1,
5732 __isl_take isl_pw_aff_list *list2);
5733 __isl_give isl_set *isl_pw_aff_list_lt_set(
5734 __isl_take isl_pw_aff_list *list1,
5735 __isl_take isl_pw_aff_list *list2);
5736 __isl_give isl_set *isl_pw_aff_list_ge_set(
5737 __isl_take isl_pw_aff_list *list1,
5738 __isl_take isl_pw_aff_list *list2);
5739 __isl_give isl_set *isl_pw_aff_list_gt_set(
5740 __isl_take isl_pw_aff_list *list1,
5741 __isl_take isl_pw_aff_list *list2);
5743 The function C<isl_aff_ge_basic_set> returns a basic set
5744 containing those elements in the shared space
5745 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5746 The function C<isl_pw_aff_ge_set> returns a set
5747 containing those elements in the shared domain
5748 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5749 greater than or equal to C<pwaff2>.
5750 The function C<isl_multi_aff_lex_le_set> returns a set
5751 containing those elements in the shared domain space
5752 where C<ma1> is lexicographically smaller than or
5754 The functions operating on C<isl_pw_aff_list> apply the corresponding
5755 C<isl_pw_aff> function to each pair of elements in the two lists.
5757 =item * Cartesian Product
5759 #include <isl/space.h>
5760 __isl_give isl_space *isl_space_product(
5761 __isl_take isl_space *space1,
5762 __isl_take isl_space *space2);
5763 __isl_give isl_space *isl_space_domain_product(
5764 __isl_take isl_space *space1,
5765 __isl_take isl_space *space2);
5766 __isl_give isl_space *isl_space_range_product(
5767 __isl_take isl_space *space1,
5768 __isl_take isl_space *space2);
5771 C<isl_space_product>, C<isl_space_domain_product>
5772 and C<isl_space_range_product> take pairs or relation spaces and
5773 produce a single relations space, where either the domain, the range
5774 or both domain and range are wrapped spaces of relations between
5775 the domains and/or ranges of the input spaces.
5776 If the product is only constructed over the domain or the range
5777 then the ranges or the domains of the inputs should be the same.
5778 The function C<isl_space_product> also accepts a pair of set spaces,
5779 in which case it returns a wrapped space of a relation between the
5782 #include <isl/set.h>
5783 __isl_give isl_set *isl_set_product(
5784 __isl_take isl_set *set1,
5785 __isl_take isl_set *set2);
5787 #include <isl/map.h>
5788 __isl_give isl_basic_map *isl_basic_map_domain_product(
5789 __isl_take isl_basic_map *bmap1,
5790 __isl_take isl_basic_map *bmap2);
5791 __isl_give isl_basic_map *isl_basic_map_range_product(
5792 __isl_take isl_basic_map *bmap1,
5793 __isl_take isl_basic_map *bmap2);
5794 __isl_give isl_basic_map *isl_basic_map_product(
5795 __isl_take isl_basic_map *bmap1,
5796 __isl_take isl_basic_map *bmap2);
5797 __isl_give isl_map *isl_map_domain_product(
5798 __isl_take isl_map *map1,
5799 __isl_take isl_map *map2);
5800 __isl_give isl_map *isl_map_range_product(
5801 __isl_take isl_map *map1,
5802 __isl_take isl_map *map2);
5803 __isl_give isl_map *isl_map_product(
5804 __isl_take isl_map *map1,
5805 __isl_take isl_map *map2);
5807 #include <isl/union_set.h>
5808 __isl_give isl_union_set *isl_union_set_product(
5809 __isl_take isl_union_set *uset1,
5810 __isl_take isl_union_set *uset2);
5812 #include <isl/union_map.h>
5813 __isl_give isl_union_map *isl_union_map_domain_product(
5814 __isl_take isl_union_map *umap1,
5815 __isl_take isl_union_map *umap2);
5816 __isl_give isl_union_map *isl_union_map_range_product(
5817 __isl_take isl_union_map *umap1,
5818 __isl_take isl_union_map *umap2);
5819 __isl_give isl_union_map *isl_union_map_product(
5820 __isl_take isl_union_map *umap1,
5821 __isl_take isl_union_map *umap2);
5823 #include <isl/val.h>
5824 __isl_give isl_multi_val *isl_multi_val_range_product(
5825 __isl_take isl_multi_val *mv1,
5826 __isl_take isl_multi_val *mv2);
5827 __isl_give isl_multi_val *isl_multi_val_product(
5828 __isl_take isl_multi_val *mv1,
5829 __isl_take isl_multi_val *mv2);
5831 #include <isl/aff.h>
5832 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5833 __isl_take isl_multi_aff *ma1,
5834 __isl_take isl_multi_aff *ma2);
5835 __isl_give isl_multi_aff *isl_multi_aff_product(
5836 __isl_take isl_multi_aff *ma1,
5837 __isl_take isl_multi_aff *ma2);
5838 __isl_give isl_multi_pw_aff *
5839 isl_multi_pw_aff_range_product(
5840 __isl_take isl_multi_pw_aff *mpa1,
5841 __isl_take isl_multi_pw_aff *mpa2);
5842 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5843 __isl_take isl_multi_pw_aff *mpa1,
5844 __isl_take isl_multi_pw_aff *mpa2);
5845 __isl_give isl_pw_multi_aff *
5846 isl_pw_multi_aff_range_product(
5847 __isl_take isl_pw_multi_aff *pma1,
5848 __isl_take isl_pw_multi_aff *pma2);
5849 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5850 __isl_take isl_pw_multi_aff *pma1,
5851 __isl_take isl_pw_multi_aff *pma2);
5852 __isl_give isl_multi_union_pw_aff *
5853 isl_multi_union_pw_aff_range_product(
5854 __isl_take isl_multi_union_pw_aff *mupa1,
5855 __isl_take isl_multi_union_pw_aff *mupa2);
5857 The above functions compute the cross product of the given
5858 sets, relations or functions. The domains and ranges of the results
5859 are wrapped maps between domains and ranges of the inputs.
5860 To obtain a ``flat'' product, use the following functions
5863 #include <isl/set.h>
5864 __isl_give isl_basic_set *isl_basic_set_flat_product(
5865 __isl_take isl_basic_set *bset1,
5866 __isl_take isl_basic_set *bset2);
5867 __isl_give isl_set *isl_set_flat_product(
5868 __isl_take isl_set *set1,
5869 __isl_take isl_set *set2);
5871 #include <isl/map.h>
5872 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5873 __isl_take isl_basic_map *bmap1,
5874 __isl_take isl_basic_map *bmap2);
5875 __isl_give isl_map *isl_map_flat_domain_product(
5876 __isl_take isl_map *map1,
5877 __isl_take isl_map *map2);
5878 __isl_give isl_map *isl_map_flat_range_product(
5879 __isl_take isl_map *map1,
5880 __isl_take isl_map *map2);
5881 __isl_give isl_basic_map *isl_basic_map_flat_product(
5882 __isl_take isl_basic_map *bmap1,
5883 __isl_take isl_basic_map *bmap2);
5884 __isl_give isl_map *isl_map_flat_product(
5885 __isl_take isl_map *map1,
5886 __isl_take isl_map *map2);
5888 #include <isl/union_map.h>
5889 __isl_give isl_union_map *
5890 isl_union_map_flat_domain_product(
5891 __isl_take isl_union_map *umap1,
5892 __isl_take isl_union_map *umap2);
5893 __isl_give isl_union_map *
5894 isl_union_map_flat_range_product(
5895 __isl_take isl_union_map *umap1,
5896 __isl_take isl_union_map *umap2);
5898 #include <isl/val.h>
5899 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
5900 __isl_take isl_multi_val *mv1,
5901 __isl_take isl_multi_aff *mv2);
5903 #include <isl/aff.h>
5904 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
5905 __isl_take isl_multi_aff *ma1,
5906 __isl_take isl_multi_aff *ma2);
5907 __isl_give isl_pw_multi_aff *
5908 isl_pw_multi_aff_flat_range_product(
5909 __isl_take isl_pw_multi_aff *pma1,
5910 __isl_take isl_pw_multi_aff *pma2);
5911 __isl_give isl_multi_pw_aff *
5912 isl_multi_pw_aff_flat_range_product(
5913 __isl_take isl_multi_pw_aff *mpa1,
5914 __isl_take isl_multi_pw_aff *mpa2);
5915 __isl_give isl_union_pw_multi_aff *
5916 isl_union_pw_multi_aff_flat_range_product(
5917 __isl_take isl_union_pw_multi_aff *upma1,
5918 __isl_take isl_union_pw_multi_aff *upma2);
5919 __isl_give isl_multi_union_pw_aff *
5920 isl_multi_union_pw_aff_flat_range_product(
5921 __isl_take isl_multi_union_pw_aff *mupa1,
5922 __isl_take isl_multi_union_pw_aff *mupa2);
5924 #include <isl/space.h>
5925 __isl_give isl_space *isl_space_factor_domain(
5926 __isl_take isl_space *space);
5927 __isl_give isl_space *isl_space_factor_range(
5928 __isl_take isl_space *space);
5929 __isl_give isl_space *isl_space_domain_factor_domain(
5930 __isl_take isl_space *space);
5931 __isl_give isl_space *isl_space_domain_factor_range(
5932 __isl_take isl_space *space);
5933 __isl_give isl_space *isl_space_range_factor_domain(
5934 __isl_take isl_space *space);
5935 __isl_give isl_space *isl_space_range_factor_range(
5936 __isl_take isl_space *space);
5938 The functions C<isl_space_range_factor_domain> and
5939 C<isl_space_range_factor_range> extract the two arguments from
5940 the result of a call to C<isl_space_range_product>.
5942 The arguments of a call to C<isl_map_range_product> can be extracted
5943 from the result using the following functions.
5945 #include <isl/map.h>
5946 __isl_give isl_map *isl_map_factor_domain(
5947 __isl_take isl_map *map);
5948 __isl_give isl_map *isl_map_factor_range(
5949 __isl_take isl_map *map);
5950 __isl_give isl_map *isl_map_domain_factor_domain(
5951 __isl_take isl_map *map);
5952 __isl_give isl_map *isl_map_domain_factor_range(
5953 __isl_take isl_map *map);
5954 __isl_give isl_map *isl_map_range_factor_domain(
5955 __isl_take isl_map *map);
5956 __isl_give isl_map *isl_map_range_factor_range(
5957 __isl_take isl_map *map);
5959 #include <isl/union_map.h>
5960 __isl_give isl_union_map *isl_union_map_factor_domain(
5961 __isl_take isl_union_map *umap);
5962 __isl_give isl_union_map *isl_union_map_factor_range(
5963 __isl_take isl_union_map *umap);
5964 __isl_give isl_union_map *
5965 isl_union_map_domain_factor_domain(
5966 __isl_take isl_union_map *umap);
5967 __isl_give isl_union_map *
5968 isl_union_map_domain_factor_range(
5969 __isl_take isl_union_map *umap);
5970 __isl_give isl_union_map *
5971 isl_union_map_range_factor_range(
5972 __isl_take isl_union_map *umap);
5974 #include <isl/val.h>
5975 __isl_give isl_multi_val *
5976 isl_multi_val_range_factor_domain(
5977 __isl_take isl_multi_val *mv);
5978 __isl_give isl_multi_val *
5979 isl_multi_val_range_factor_range(
5980 __isl_take isl_multi_val *mv);
5982 #include <isl/aff.h>
5983 __isl_give isl_multi_aff *
5984 isl_multi_aff_range_factor_domain(
5985 __isl_take isl_multi_aff *ma);
5986 __isl_give isl_multi_aff *
5987 isl_multi_aff_range_factor_range(
5988 __isl_take isl_multi_aff *ma);
5989 __isl_give isl_multi_pw_aff *
5990 isl_multi_pw_aff_range_factor_domain(
5991 __isl_take isl_multi_pw_aff *mpa);
5992 __isl_give isl_multi_pw_aff *
5993 isl_multi_pw_aff_range_factor_range(
5994 __isl_take isl_multi_pw_aff *mpa);
5995 __isl_give isl_multi_union_pw_aff *
5996 isl_multi_union_pw_aff_range_factor_domain(
5997 __isl_take isl_multi_union_pw_aff *mupa);
5998 __isl_give isl_multi_union_pw_aff *
5999 isl_multi_union_pw_aff_range_factor_range(
6000 __isl_take isl_multi_union_pw_aff *mupa);
6002 The splice functions are a generalization of the flat product functions,
6003 where the second argument may be inserted at any position inside
6004 the first argument rather than being placed at the end.
6006 #include <isl/val.h>
6007 __isl_give isl_multi_val *isl_multi_val_range_splice(
6008 __isl_take isl_multi_val *mv1, unsigned pos,
6009 __isl_take isl_multi_val *mv2);
6011 #include <isl/aff.h>
6012 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6013 __isl_take isl_multi_aff *ma1, unsigned pos,
6014 __isl_take isl_multi_aff *ma2);
6015 __isl_give isl_multi_aff *isl_multi_aff_splice(
6016 __isl_take isl_multi_aff *ma1,
6017 unsigned in_pos, unsigned out_pos,
6018 __isl_take isl_multi_aff *ma2);
6019 __isl_give isl_multi_pw_aff *
6020 isl_multi_pw_aff_range_splice(
6021 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6022 __isl_take isl_multi_pw_aff *mpa2);
6023 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6024 __isl_take isl_multi_pw_aff *mpa1,
6025 unsigned in_pos, unsigned out_pos,
6026 __isl_take isl_multi_pw_aff *mpa2);
6027 __isl_give isl_multi_union_pw_aff *
6028 isl_multi_union_pw_aff_range_splice(
6029 __isl_take isl_multi_union_pw_aff *mupa1,
6031 __isl_take isl_multi_union_pw_aff *mupa2);
6033 =item * Simplification
6035 When applied to a set or relation,
6036 the gist operation returns a set or relation that has the
6037 same intersection with the context as the input set or relation.
6038 Any implicit equality in the intersection is made explicit in the result,
6039 while all inequalities that are redundant with respect to the intersection
6041 In case of union sets and relations, the gist operation is performed
6044 When applied to a function,
6045 the gist operation applies the set gist operation to each of
6046 the cells in the domain of the input piecewise expression.
6047 The context is also exploited
6048 to simplify the expression associated to each cell.
6050 #include <isl/set.h>
6051 __isl_give isl_basic_set *isl_basic_set_gist(
6052 __isl_take isl_basic_set *bset,
6053 __isl_take isl_basic_set *context);
6054 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6055 __isl_take isl_set *context);
6056 __isl_give isl_set *isl_set_gist_params(
6057 __isl_take isl_set *set,
6058 __isl_take isl_set *context);
6060 #include <isl/map.h>
6061 __isl_give isl_basic_map *isl_basic_map_gist(
6062 __isl_take isl_basic_map *bmap,
6063 __isl_take isl_basic_map *context);
6064 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6065 __isl_take isl_basic_map *bmap,
6066 __isl_take isl_basic_set *context);
6067 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6068 __isl_take isl_map *context);
6069 __isl_give isl_map *isl_map_gist_params(
6070 __isl_take isl_map *map,
6071 __isl_take isl_set *context);
6072 __isl_give isl_map *isl_map_gist_domain(
6073 __isl_take isl_map *map,
6074 __isl_take isl_set *context);
6075 __isl_give isl_map *isl_map_gist_range(
6076 __isl_take isl_map *map,
6077 __isl_take isl_set *context);
6079 #include <isl/union_set.h>
6080 __isl_give isl_union_set *isl_union_set_gist(
6081 __isl_take isl_union_set *uset,
6082 __isl_take isl_union_set *context);
6083 __isl_give isl_union_set *isl_union_set_gist_params(
6084 __isl_take isl_union_set *uset,
6085 __isl_take isl_set *set);
6087 #include <isl/union_map.h>
6088 __isl_give isl_union_map *isl_union_map_gist(
6089 __isl_take isl_union_map *umap,
6090 __isl_take isl_union_map *context);
6091 __isl_give isl_union_map *isl_union_map_gist_params(
6092 __isl_take isl_union_map *umap,
6093 __isl_take isl_set *set);
6094 __isl_give isl_union_map *isl_union_map_gist_domain(
6095 __isl_take isl_union_map *umap,
6096 __isl_take isl_union_set *uset);
6097 __isl_give isl_union_map *isl_union_map_gist_range(
6098 __isl_take isl_union_map *umap,
6099 __isl_take isl_union_set *uset);
6101 #include <isl/aff.h>
6102 __isl_give isl_aff *isl_aff_gist_params(
6103 __isl_take isl_aff *aff,
6104 __isl_take isl_set *context);
6105 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6106 __isl_take isl_set *context);
6107 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6108 __isl_take isl_multi_aff *maff,
6109 __isl_take isl_set *context);
6110 __isl_give isl_multi_aff *isl_multi_aff_gist(
6111 __isl_take isl_multi_aff *maff,
6112 __isl_take isl_set *context);
6113 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6114 __isl_take isl_pw_aff *pwaff,
6115 __isl_take isl_set *context);
6116 __isl_give isl_pw_aff *isl_pw_aff_gist(
6117 __isl_take isl_pw_aff *pwaff,
6118 __isl_take isl_set *context);
6119 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6120 __isl_take isl_pw_multi_aff *pma,
6121 __isl_take isl_set *set);
6122 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6123 __isl_take isl_pw_multi_aff *pma,
6124 __isl_take isl_set *set);
6125 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6126 __isl_take isl_multi_pw_aff *mpa,
6127 __isl_take isl_set *set);
6128 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6129 __isl_take isl_multi_pw_aff *mpa,
6130 __isl_take isl_set *set);
6131 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6132 __isl_take isl_union_pw_aff *upa,
6133 __isl_take isl_union_set *context);
6134 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6135 __isl_take isl_union_pw_aff *upa,
6136 __isl_take isl_set *context);
6137 __isl_give isl_union_pw_multi_aff *
6138 isl_union_pw_multi_aff_gist_params(
6139 __isl_take isl_union_pw_multi_aff *upma,
6140 __isl_take isl_set *context);
6141 __isl_give isl_union_pw_multi_aff *
6142 isl_union_pw_multi_aff_gist(
6143 __isl_take isl_union_pw_multi_aff *upma,
6144 __isl_take isl_union_set *context);
6145 __isl_give isl_multi_union_pw_aff *
6146 isl_multi_union_pw_aff_gist_params(
6147 __isl_take isl_multi_union_pw_aff *aff,
6148 __isl_take isl_set *context);
6149 __isl_give isl_multi_union_pw_aff *
6150 isl_multi_union_pw_aff_gist(
6151 __isl_take isl_multi_union_pw_aff *aff,
6152 __isl_take isl_union_set *context);
6154 #include <isl/polynomial.h>
6155 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6156 __isl_take isl_qpolynomial *qp,
6157 __isl_take isl_set *context);
6158 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6159 __isl_take isl_qpolynomial *qp,
6160 __isl_take isl_set *context);
6161 __isl_give isl_qpolynomial_fold *
6162 isl_qpolynomial_fold_gist_params(
6163 __isl_take isl_qpolynomial_fold *fold,
6164 __isl_take isl_set *context);
6165 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6166 __isl_take isl_qpolynomial_fold *fold,
6167 __isl_take isl_set *context);
6168 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6169 __isl_take isl_pw_qpolynomial *pwqp,
6170 __isl_take isl_set *context);
6171 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6172 __isl_take isl_pw_qpolynomial *pwqp,
6173 __isl_take isl_set *context);
6174 __isl_give isl_pw_qpolynomial_fold *
6175 isl_pw_qpolynomial_fold_gist(
6176 __isl_take isl_pw_qpolynomial_fold *pwf,
6177 __isl_take isl_set *context);
6178 __isl_give isl_pw_qpolynomial_fold *
6179 isl_pw_qpolynomial_fold_gist_params(
6180 __isl_take isl_pw_qpolynomial_fold *pwf,
6181 __isl_take isl_set *context);
6182 __isl_give isl_union_pw_qpolynomial *
6183 isl_union_pw_qpolynomial_gist_params(
6184 __isl_take isl_union_pw_qpolynomial *upwqp,
6185 __isl_take isl_set *context);
6186 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6187 __isl_take isl_union_pw_qpolynomial *upwqp,
6188 __isl_take isl_union_set *context);
6189 __isl_give isl_union_pw_qpolynomial_fold *
6190 isl_union_pw_qpolynomial_fold_gist(
6191 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6192 __isl_take isl_union_set *context);
6193 __isl_give isl_union_pw_qpolynomial_fold *
6194 isl_union_pw_qpolynomial_fold_gist_params(
6195 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6196 __isl_take isl_set *context);
6198 =item * Binary Arithmethic Operations
6200 #include <isl/val.h>
6201 __isl_give isl_multi_val *isl_multi_val_sub(
6202 __isl_take isl_multi_val *mv1,
6203 __isl_take isl_multi_val *mv2);
6205 #include <isl/aff.h>
6206 __isl_give isl_aff *isl_aff_add(
6207 __isl_take isl_aff *aff1,
6208 __isl_take isl_aff *aff2);
6209 __isl_give isl_multi_aff *isl_multi_aff_add(
6210 __isl_take isl_multi_aff *maff1,
6211 __isl_take isl_multi_aff *maff2);
6212 __isl_give isl_pw_aff *isl_pw_aff_add(
6213 __isl_take isl_pw_aff *pwaff1,
6214 __isl_take isl_pw_aff *pwaff2);
6215 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6216 __isl_take isl_pw_multi_aff *pma1,
6217 __isl_take isl_pw_multi_aff *pma2);
6218 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6219 __isl_take isl_union_pw_aff *upa1,
6220 __isl_take isl_union_pw_aff *upa2);
6221 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6222 __isl_take isl_union_pw_multi_aff *upma1,
6223 __isl_take isl_union_pw_multi_aff *upma2);
6224 __isl_give isl_pw_aff *isl_pw_aff_min(
6225 __isl_take isl_pw_aff *pwaff1,
6226 __isl_take isl_pw_aff *pwaff2);
6227 __isl_give isl_pw_aff *isl_pw_aff_max(
6228 __isl_take isl_pw_aff *pwaff1,
6229 __isl_take isl_pw_aff *pwaff2);
6230 __isl_give isl_aff *isl_aff_sub(
6231 __isl_take isl_aff *aff1,
6232 __isl_take isl_aff *aff2);
6233 __isl_give isl_multi_aff *isl_multi_aff_sub(
6234 __isl_take isl_multi_aff *ma1,
6235 __isl_take isl_multi_aff *ma2);
6236 __isl_give isl_pw_aff *isl_pw_aff_sub(
6237 __isl_take isl_pw_aff *pwaff1,
6238 __isl_take isl_pw_aff *pwaff2);
6239 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6240 __isl_take isl_multi_pw_aff *mpa1,
6241 __isl_take isl_multi_pw_aff *mpa2);
6242 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6243 __isl_take isl_pw_multi_aff *pma1,
6244 __isl_take isl_pw_multi_aff *pma2);
6245 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6246 __isl_take isl_union_pw_aff *upa1,
6247 __isl_take isl_union_pw_aff *upa2);
6248 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6249 __isl_take isl_union_pw_multi_aff *upma1,
6250 __isl_take isl_union_pw_multi_aff *upma2);
6251 __isl_give isl_multi_union_pw_aff *
6252 isl_multi_union_pw_aff_sub(
6253 __isl_take isl_multi_union_pw_aff *mupa1,
6254 __isl_take isl_multi_union_pw_aff *mupa2);
6256 C<isl_aff_sub> subtracts the second argument from the first.
6258 #include <isl/polynomial.h>
6259 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6260 __isl_take isl_qpolynomial *qp1,
6261 __isl_take isl_qpolynomial *qp2);
6262 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6263 __isl_take isl_pw_qpolynomial *pwqp1,
6264 __isl_take isl_pw_qpolynomial *pwqp2);
6265 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6266 __isl_take isl_pw_qpolynomial *pwqp1,
6267 __isl_take isl_pw_qpolynomial *pwqp2);
6268 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6269 __isl_take isl_pw_qpolynomial_fold *pwf1,
6270 __isl_take isl_pw_qpolynomial_fold *pwf2);
6271 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6272 __isl_take isl_union_pw_qpolynomial *upwqp1,
6273 __isl_take isl_union_pw_qpolynomial *upwqp2);
6274 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6275 __isl_take isl_qpolynomial *qp1,
6276 __isl_take isl_qpolynomial *qp2);
6277 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6278 __isl_take isl_pw_qpolynomial *pwqp1,
6279 __isl_take isl_pw_qpolynomial *pwqp2);
6280 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6281 __isl_take isl_union_pw_qpolynomial *upwqp1,
6282 __isl_take isl_union_pw_qpolynomial *upwqp2);
6283 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6284 __isl_take isl_pw_qpolynomial_fold *pwf1,
6285 __isl_take isl_pw_qpolynomial_fold *pwf2);
6286 __isl_give isl_union_pw_qpolynomial_fold *
6287 isl_union_pw_qpolynomial_fold_fold(
6288 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6289 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6291 #include <isl/aff.h>
6292 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6293 __isl_take isl_pw_aff *pwaff1,
6294 __isl_take isl_pw_aff *pwaff2);
6295 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6296 __isl_take isl_pw_multi_aff *pma1,
6297 __isl_take isl_pw_multi_aff *pma2);
6298 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6299 __isl_take isl_union_pw_aff *upa1,
6300 __isl_take isl_union_pw_aff *upa2);
6301 __isl_give isl_union_pw_multi_aff *
6302 isl_union_pw_multi_aff_union_add(
6303 __isl_take isl_union_pw_multi_aff *upma1,
6304 __isl_take isl_union_pw_multi_aff *upma2);
6305 __isl_give isl_multi_union_pw_aff *
6306 isl_multi_union_pw_aff_union_add(
6307 __isl_take isl_multi_union_pw_aff *mupa1,
6308 __isl_take isl_multi_union_pw_aff *mupa2);
6309 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6310 __isl_take isl_pw_aff *pwaff1,
6311 __isl_take isl_pw_aff *pwaff2);
6312 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6313 __isl_take isl_pw_aff *pwaff1,
6314 __isl_take isl_pw_aff *pwaff2);
6316 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6317 expression with a domain that is the union of those of C<pwaff1> and
6318 C<pwaff2> and such that on each cell, the quasi-affine expression is
6319 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6320 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6321 associated expression is the defined one.
6322 This in contrast to the C<isl_pw_aff_max> function, which is
6323 only defined on the shared definition domain of the arguments.
6325 #include <isl/val.h>
6326 __isl_give isl_multi_val *isl_multi_val_add_val(
6327 __isl_take isl_multi_val *mv,
6328 __isl_take isl_val *v);
6329 __isl_give isl_multi_val *isl_multi_val_mod_val(
6330 __isl_take isl_multi_val *mv,
6331 __isl_take isl_val *v);
6332 __isl_give isl_multi_val *isl_multi_val_scale_val(
6333 __isl_take isl_multi_val *mv,
6334 __isl_take isl_val *v);
6335 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6336 __isl_take isl_multi_val *mv,
6337 __isl_take isl_val *v);
6339 #include <isl/aff.h>
6340 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6341 __isl_take isl_val *mod);
6342 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6343 __isl_take isl_pw_aff *pa,
6344 __isl_take isl_val *mod);
6345 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6346 __isl_take isl_union_pw_aff *upa,
6347 __isl_take isl_val *f);
6348 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6349 __isl_take isl_val *v);
6350 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6351 __isl_take isl_multi_aff *ma,
6352 __isl_take isl_val *v);
6353 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6354 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6355 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6356 __isl_take isl_multi_pw_aff *mpa,
6357 __isl_take isl_val *v);
6358 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6359 __isl_take isl_pw_multi_aff *pma,
6360 __isl_take isl_val *v);
6361 __isl_give isl_union_pw_multi_aff *
6362 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6363 __isl_take isl_union_pw_aff *upa,
6364 __isl_take isl_val *f);
6365 isl_union_pw_multi_aff_scale_val(
6366 __isl_take isl_union_pw_multi_aff *upma,
6367 __isl_take isl_val *val);
6368 __isl_give isl_multi_union_pw_aff *
6369 isl_multi_union_pw_aff_scale_val(
6370 __isl_take isl_multi_union_pw_aff *mupa,
6371 __isl_take isl_val *v);
6372 __isl_give isl_aff *isl_aff_scale_down_ui(
6373 __isl_take isl_aff *aff, unsigned f);
6374 __isl_give isl_aff *isl_aff_scale_down_val(
6375 __isl_take isl_aff *aff, __isl_take isl_val *v);
6376 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6377 __isl_take isl_multi_aff *ma,
6378 __isl_take isl_val *v);
6379 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6380 __isl_take isl_pw_aff *pa,
6381 __isl_take isl_val *f);
6382 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6383 __isl_take isl_multi_pw_aff *mpa,
6384 __isl_take isl_val *v);
6385 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6386 __isl_take isl_pw_multi_aff *pma,
6387 __isl_take isl_val *v);
6388 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6389 __isl_take isl_union_pw_aff *upa,
6390 __isl_take isl_val *v);
6391 __isl_give isl_union_pw_multi_aff *
6392 isl_union_pw_multi_aff_scale_down_val(
6393 __isl_take isl_union_pw_multi_aff *upma,
6394 __isl_take isl_val *val);
6395 __isl_give isl_multi_union_pw_aff *
6396 isl_multi_union_pw_aff_scale_down_val(
6397 __isl_take isl_multi_union_pw_aff *mupa,
6398 __isl_take isl_val *v);
6400 #include <isl/polynomial.h>
6401 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6402 __isl_take isl_qpolynomial *qp,
6403 __isl_take isl_val *v);
6404 __isl_give isl_qpolynomial_fold *
6405 isl_qpolynomial_fold_scale_val(
6406 __isl_take isl_qpolynomial_fold *fold,
6407 __isl_take isl_val *v);
6408 __isl_give isl_pw_qpolynomial *
6409 isl_pw_qpolynomial_scale_val(
6410 __isl_take isl_pw_qpolynomial *pwqp,
6411 __isl_take isl_val *v);
6412 __isl_give isl_pw_qpolynomial_fold *
6413 isl_pw_qpolynomial_fold_scale_val(
6414 __isl_take isl_pw_qpolynomial_fold *pwf,
6415 __isl_take isl_val *v);
6416 __isl_give isl_union_pw_qpolynomial *
6417 isl_union_pw_qpolynomial_scale_val(
6418 __isl_take isl_union_pw_qpolynomial *upwqp,
6419 __isl_take isl_val *v);
6420 __isl_give isl_union_pw_qpolynomial_fold *
6421 isl_union_pw_qpolynomial_fold_scale_val(
6422 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6423 __isl_take isl_val *v);
6424 __isl_give isl_qpolynomial *
6425 isl_qpolynomial_scale_down_val(
6426 __isl_take isl_qpolynomial *qp,
6427 __isl_take isl_val *v);
6428 __isl_give isl_qpolynomial_fold *
6429 isl_qpolynomial_fold_scale_down_val(
6430 __isl_take isl_qpolynomial_fold *fold,
6431 __isl_take isl_val *v);
6432 __isl_give isl_pw_qpolynomial *
6433 isl_pw_qpolynomial_scale_down_val(
6434 __isl_take isl_pw_qpolynomial *pwqp,
6435 __isl_take isl_val *v);
6436 __isl_give isl_pw_qpolynomial_fold *
6437 isl_pw_qpolynomial_fold_scale_down_val(
6438 __isl_take isl_pw_qpolynomial_fold *pwf,
6439 __isl_take isl_val *v);
6440 __isl_give isl_union_pw_qpolynomial *
6441 isl_union_pw_qpolynomial_scale_down_val(
6442 __isl_take isl_union_pw_qpolynomial *upwqp,
6443 __isl_take isl_val *v);
6444 __isl_give isl_union_pw_qpolynomial_fold *
6445 isl_union_pw_qpolynomial_fold_scale_down_val(
6446 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6447 __isl_take isl_val *v);
6449 #include <isl/val.h>
6450 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6451 __isl_take isl_multi_val *mv1,
6452 __isl_take isl_multi_val *mv2);
6453 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6454 __isl_take isl_multi_val *mv1,
6455 __isl_take isl_multi_val *mv2);
6456 __isl_give isl_multi_val *
6457 isl_multi_val_scale_down_multi_val(
6458 __isl_take isl_multi_val *mv1,
6459 __isl_take isl_multi_val *mv2);
6461 #include <isl/aff.h>
6462 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6463 __isl_take isl_multi_aff *ma,
6464 __isl_take isl_multi_val *mv);
6465 __isl_give isl_multi_union_pw_aff *
6466 isl_multi_union_pw_aff_mod_multi_val(
6467 __isl_take isl_multi_union_pw_aff *upma,
6468 __isl_take isl_multi_val *mv);
6469 __isl_give isl_multi_pw_aff *
6470 isl_multi_pw_aff_mod_multi_val(
6471 __isl_take isl_multi_pw_aff *mpa,
6472 __isl_take isl_multi_val *mv);
6473 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6474 __isl_take isl_multi_aff *ma,
6475 __isl_take isl_multi_val *mv);
6476 __isl_give isl_pw_multi_aff *
6477 isl_pw_multi_aff_scale_multi_val(
6478 __isl_take isl_pw_multi_aff *pma,
6479 __isl_take isl_multi_val *mv);
6480 __isl_give isl_multi_pw_aff *
6481 isl_multi_pw_aff_scale_multi_val(
6482 __isl_take isl_multi_pw_aff *mpa,
6483 __isl_take isl_multi_val *mv);
6484 __isl_give isl_multi_union_pw_aff *
6485 isl_multi_union_pw_aff_scale_multi_val(
6486 __isl_take isl_multi_union_pw_aff *mupa,
6487 __isl_take isl_multi_val *mv);
6488 __isl_give isl_union_pw_multi_aff *
6489 isl_union_pw_multi_aff_scale_multi_val(
6490 __isl_take isl_union_pw_multi_aff *upma,
6491 __isl_take isl_multi_val *mv);
6492 __isl_give isl_multi_aff *
6493 isl_multi_aff_scale_down_multi_val(
6494 __isl_take isl_multi_aff *ma,
6495 __isl_take isl_multi_val *mv);
6496 __isl_give isl_multi_pw_aff *
6497 isl_multi_pw_aff_scale_down_multi_val(
6498 __isl_take isl_multi_pw_aff *mpa,
6499 __isl_take isl_multi_val *mv);
6500 __isl_give isl_multi_union_pw_aff *
6501 isl_multi_union_pw_aff_scale_down_multi_val(
6502 __isl_take isl_multi_union_pw_aff *mupa,
6503 __isl_take isl_multi_val *mv);
6505 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6506 by the corresponding elements of C<mv>.
6508 #include <isl/aff.h>
6509 __isl_give isl_aff *isl_aff_mul(
6510 __isl_take isl_aff *aff1,
6511 __isl_take isl_aff *aff2);
6512 __isl_give isl_aff *isl_aff_div(
6513 __isl_take isl_aff *aff1,
6514 __isl_take isl_aff *aff2);
6515 __isl_give isl_pw_aff *isl_pw_aff_mul(
6516 __isl_take isl_pw_aff *pwaff1,
6517 __isl_take isl_pw_aff *pwaff2);
6518 __isl_give isl_pw_aff *isl_pw_aff_div(
6519 __isl_take isl_pw_aff *pa1,
6520 __isl_take isl_pw_aff *pa2);
6521 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6522 __isl_take isl_pw_aff *pa1,
6523 __isl_take isl_pw_aff *pa2);
6524 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6525 __isl_take isl_pw_aff *pa1,
6526 __isl_take isl_pw_aff *pa2);
6528 When multiplying two affine expressions, at least one of the two needs
6529 to be a constant. Similarly, when dividing an affine expression by another,
6530 the second expression needs to be a constant.
6531 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6532 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6535 #include <isl/polynomial.h>
6536 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6537 __isl_take isl_qpolynomial *qp1,
6538 __isl_take isl_qpolynomial *qp2);
6539 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6540 __isl_take isl_pw_qpolynomial *pwqp1,
6541 __isl_take isl_pw_qpolynomial *pwqp2);
6542 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6543 __isl_take isl_union_pw_qpolynomial *upwqp1,
6544 __isl_take isl_union_pw_qpolynomial *upwqp2);
6548 =head3 Lexicographic Optimization
6550 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6551 the following functions
6552 compute a set that contains the lexicographic minimum or maximum
6553 of the elements in C<set> (or C<bset>) for those values of the parameters
6554 that satisfy C<dom>.
6555 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6556 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6558 In other words, the union of the parameter values
6559 for which the result is non-empty and of C<*empty>
6562 #include <isl/set.h>
6563 __isl_give isl_set *isl_basic_set_partial_lexmin(
6564 __isl_take isl_basic_set *bset,
6565 __isl_take isl_basic_set *dom,
6566 __isl_give isl_set **empty);
6567 __isl_give isl_set *isl_basic_set_partial_lexmax(
6568 __isl_take isl_basic_set *bset,
6569 __isl_take isl_basic_set *dom,
6570 __isl_give isl_set **empty);
6571 __isl_give isl_set *isl_set_partial_lexmin(
6572 __isl_take isl_set *set, __isl_take isl_set *dom,
6573 __isl_give isl_set **empty);
6574 __isl_give isl_set *isl_set_partial_lexmax(
6575 __isl_take isl_set *set, __isl_take isl_set *dom,
6576 __isl_give isl_set **empty);
6578 Given a (basic) set C<set> (or C<bset>), the following functions simply
6579 return a set containing the lexicographic minimum or maximum
6580 of the elements in C<set> (or C<bset>).
6581 In case of union sets, the optimum is computed per space.
6583 #include <isl/set.h>
6584 __isl_give isl_set *isl_basic_set_lexmin(
6585 __isl_take isl_basic_set *bset);
6586 __isl_give isl_set *isl_basic_set_lexmax(
6587 __isl_take isl_basic_set *bset);
6588 __isl_give isl_set *isl_set_lexmin(
6589 __isl_take isl_set *set);
6590 __isl_give isl_set *isl_set_lexmax(
6591 __isl_take isl_set *set);
6592 __isl_give isl_union_set *isl_union_set_lexmin(
6593 __isl_take isl_union_set *uset);
6594 __isl_give isl_union_set *isl_union_set_lexmax(
6595 __isl_take isl_union_set *uset);
6597 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6598 the following functions
6599 compute a relation that maps each element of C<dom>
6600 to the single lexicographic minimum or maximum
6601 of the elements that are associated to that same
6602 element in C<map> (or C<bmap>).
6603 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6604 that contains the elements in C<dom> that do not map
6605 to any elements in C<map> (or C<bmap>).
6606 In other words, the union of the domain of the result and of C<*empty>
6609 #include <isl/map.h>
6610 __isl_give isl_map *isl_basic_map_partial_lexmax(
6611 __isl_take isl_basic_map *bmap,
6612 __isl_take isl_basic_set *dom,
6613 __isl_give isl_set **empty);
6614 __isl_give isl_map *isl_basic_map_partial_lexmin(
6615 __isl_take isl_basic_map *bmap,
6616 __isl_take isl_basic_set *dom,
6617 __isl_give isl_set **empty);
6618 __isl_give isl_map *isl_map_partial_lexmax(
6619 __isl_take isl_map *map, __isl_take isl_set *dom,
6620 __isl_give isl_set **empty);
6621 __isl_give isl_map *isl_map_partial_lexmin(
6622 __isl_take isl_map *map, __isl_take isl_set *dom,
6623 __isl_give isl_set **empty);
6625 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6626 return a map mapping each element in the domain of
6627 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6628 of all elements associated to that element.
6629 In case of union relations, the optimum is computed per space.
6631 #include <isl/map.h>
6632 __isl_give isl_map *isl_basic_map_lexmin(
6633 __isl_take isl_basic_map *bmap);
6634 __isl_give isl_map *isl_basic_map_lexmax(
6635 __isl_take isl_basic_map *bmap);
6636 __isl_give isl_map *isl_map_lexmin(
6637 __isl_take isl_map *map);
6638 __isl_give isl_map *isl_map_lexmax(
6639 __isl_take isl_map *map);
6640 __isl_give isl_union_map *isl_union_map_lexmin(
6641 __isl_take isl_union_map *umap);
6642 __isl_give isl_union_map *isl_union_map_lexmax(
6643 __isl_take isl_union_map *umap);
6645 The following functions return their result in the form of
6646 a piecewise multi-affine expression,
6647 but are otherwise equivalent to the corresponding functions
6648 returning a basic set or relation.
6650 #include <isl/set.h>
6651 __isl_give isl_pw_multi_aff *
6652 isl_basic_set_partial_lexmin_pw_multi_aff(
6653 __isl_take isl_basic_set *bset,
6654 __isl_take isl_basic_set *dom,
6655 __isl_give isl_set **empty);
6656 __isl_give isl_pw_multi_aff *
6657 isl_basic_set_partial_lexmax_pw_multi_aff(
6658 __isl_take isl_basic_set *bset,
6659 __isl_take isl_basic_set *dom,
6660 __isl_give isl_set **empty);
6661 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6662 __isl_take isl_set *set);
6663 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6664 __isl_take isl_set *set);
6666 #include <isl/map.h>
6667 __isl_give isl_pw_multi_aff *
6668 isl_basic_map_lexmin_pw_multi_aff(
6669 __isl_take isl_basic_map *bmap);
6670 __isl_give isl_pw_multi_aff *
6671 isl_basic_map_partial_lexmin_pw_multi_aff(
6672 __isl_take isl_basic_map *bmap,
6673 __isl_take isl_basic_set *dom,
6674 __isl_give isl_set **empty);
6675 __isl_give isl_pw_multi_aff *
6676 isl_basic_map_partial_lexmax_pw_multi_aff(
6677 __isl_take isl_basic_map *bmap,
6678 __isl_take isl_basic_set *dom,
6679 __isl_give isl_set **empty);
6680 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6681 __isl_take isl_map *map);
6682 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6683 __isl_take isl_map *map);
6685 The following functions return the lexicographic minimum or maximum
6686 on the shared domain of the inputs and the single defined function
6687 on those parts of the domain where only a single function is defined.
6689 #include <isl/aff.h>
6690 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6691 __isl_take isl_pw_multi_aff *pma1,
6692 __isl_take isl_pw_multi_aff *pma2);
6693 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6694 __isl_take isl_pw_multi_aff *pma1,
6695 __isl_take isl_pw_multi_aff *pma2);
6697 =head2 Ternary Operations
6699 #include <isl/aff.h>
6700 __isl_give isl_pw_aff *isl_pw_aff_cond(
6701 __isl_take isl_pw_aff *cond,
6702 __isl_take isl_pw_aff *pwaff_true,
6703 __isl_take isl_pw_aff *pwaff_false);
6705 The function C<isl_pw_aff_cond> performs a conditional operator
6706 and returns an expression that is equal to C<pwaff_true>
6707 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6708 where C<cond> is zero.
6712 Lists are defined over several element types, including
6713 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
6714 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6715 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6716 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6717 Here we take lists of C<isl_set>s as an example.
6718 Lists can be created, copied, modified and freed using the following functions.
6720 #include <isl/set.h>
6721 __isl_give isl_set_list *isl_set_list_from_set(
6722 __isl_take isl_set *el);
6723 __isl_give isl_set_list *isl_set_list_alloc(
6724 isl_ctx *ctx, int n);
6725 __isl_give isl_set_list *isl_set_list_copy(
6726 __isl_keep isl_set_list *list);
6727 __isl_give isl_set_list *isl_set_list_insert(
6728 __isl_take isl_set_list *list, unsigned pos,
6729 __isl_take isl_set *el);
6730 __isl_give isl_set_list *isl_set_list_add(
6731 __isl_take isl_set_list *list,
6732 __isl_take isl_set *el);
6733 __isl_give isl_set_list *isl_set_list_drop(
6734 __isl_take isl_set_list *list,
6735 unsigned first, unsigned n);
6736 __isl_give isl_set_list *isl_set_list_set_set(
6737 __isl_take isl_set_list *list, int index,
6738 __isl_take isl_set *set);
6739 __isl_give isl_set_list *isl_set_list_concat(
6740 __isl_take isl_set_list *list1,
6741 __isl_take isl_set_list *list2);
6742 __isl_give isl_set_list *isl_set_list_sort(
6743 __isl_take isl_set_list *list,
6744 int (*cmp)(__isl_keep isl_set *a,
6745 __isl_keep isl_set *b, void *user),
6747 __isl_null isl_set_list *isl_set_list_free(
6748 __isl_take isl_set_list *list);
6750 C<isl_set_list_alloc> creates an empty list with an initial capacity
6751 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
6752 add elements to a list, increasing its capacity as needed.
6753 C<isl_set_list_from_set> creates a list with a single element.
6755 Lists can be inspected using the following functions.
6757 #include <isl/set.h>
6758 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6759 __isl_give isl_set *isl_set_list_get_set(
6760 __isl_keep isl_set_list *list, int index);
6761 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6762 int (*fn)(__isl_take isl_set *el, void *user),
6764 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6765 int (*follows)(__isl_keep isl_set *a,
6766 __isl_keep isl_set *b, void *user),
6768 int (*fn)(__isl_take isl_set *el, void *user),
6771 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6772 strongly connected components of the graph with as vertices the elements
6773 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6774 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6775 should return C<-1> on error.
6777 Lists can be printed using
6779 #include <isl/set.h>
6780 __isl_give isl_printer *isl_printer_print_set_list(
6781 __isl_take isl_printer *p,
6782 __isl_keep isl_set_list *list);
6784 =head2 Associative arrays
6786 Associative arrays map isl objects of a specific type to isl objects
6787 of some (other) specific type. They are defined for several pairs
6788 of types, including (C<isl_map>, C<isl_basic_set>),
6789 (C<isl_id>, C<isl_ast_expr>) and.
6790 (C<isl_id>, C<isl_pw_aff>).
6791 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6794 Associative arrays can be created, copied and freed using
6795 the following functions.
6797 #include <isl/id_to_ast_expr.h>
6798 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6799 isl_ctx *ctx, int min_size);
6800 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6801 __isl_keep id_to_ast_expr *id2expr);
6802 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6803 __isl_take id_to_ast_expr *id2expr);
6805 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6806 to specify the expected size of the associative array.
6807 The associative array will be grown automatically as needed.
6809 Associative arrays can be inspected using the following functions.
6811 #include <isl/id_to_ast_expr.h>
6812 int isl_id_to_ast_expr_has(
6813 __isl_keep id_to_ast_expr *id2expr,
6814 __isl_keep isl_id *key);
6815 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6816 __isl_keep id_to_ast_expr *id2expr,
6817 __isl_take isl_id *key);
6818 int isl_id_to_ast_expr_foreach(
6819 __isl_keep id_to_ast_expr *id2expr,
6820 int (*fn)(__isl_take isl_id *key,
6821 __isl_take isl_ast_expr *val, void *user),
6824 They can be modified using the following function.
6826 #include <isl/id_to_ast_expr.h>
6827 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6828 __isl_take id_to_ast_expr *id2expr,
6829 __isl_take isl_id *key,
6830 __isl_take isl_ast_expr *val);
6831 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6832 __isl_take id_to_ast_expr *id2expr,
6833 __isl_take isl_id *key);
6835 Associative arrays can be printed using the following function.
6837 #include <isl/id_to_ast_expr.h>
6838 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6839 __isl_take isl_printer *p,
6840 __isl_keep id_to_ast_expr *id2expr);
6844 Vectors can be created, copied and freed using the following functions.
6846 #include <isl/vec.h>
6847 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6849 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6850 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6852 Note that the elements of a newly created vector may have arbitrary values.
6853 The elements can be changed and inspected using the following functions.
6855 int isl_vec_size(__isl_keep isl_vec *vec);
6856 __isl_give isl_val *isl_vec_get_element_val(
6857 __isl_keep isl_vec *vec, int pos);
6858 __isl_give isl_vec *isl_vec_set_element_si(
6859 __isl_take isl_vec *vec, int pos, int v);
6860 __isl_give isl_vec *isl_vec_set_element_val(
6861 __isl_take isl_vec *vec, int pos,
6862 __isl_take isl_val *v);
6863 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6865 __isl_give isl_vec *isl_vec_set_val(
6866 __isl_take isl_vec *vec, __isl_take isl_val *v);
6867 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6868 __isl_keep isl_vec *vec2, int pos);
6870 C<isl_vec_get_element> will return a negative value if anything went wrong.
6871 In that case, the value of C<*v> is undefined.
6873 The following function can be used to concatenate two vectors.
6875 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6876 __isl_take isl_vec *vec2);
6880 Matrices can be created, copied and freed using the following functions.
6882 #include <isl/mat.h>
6883 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6884 unsigned n_row, unsigned n_col);
6885 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6886 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6888 Note that the elements of a newly created matrix may have arbitrary values.
6889 The elements can be changed and inspected using the following functions.
6891 int isl_mat_rows(__isl_keep isl_mat *mat);
6892 int isl_mat_cols(__isl_keep isl_mat *mat);
6893 __isl_give isl_val *isl_mat_get_element_val(
6894 __isl_keep isl_mat *mat, int row, int col);
6895 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
6896 int row, int col, int v);
6897 __isl_give isl_mat *isl_mat_set_element_val(
6898 __isl_take isl_mat *mat, int row, int col,
6899 __isl_take isl_val *v);
6901 C<isl_mat_get_element> will return a negative value if anything went wrong.
6902 In that case, the value of C<*v> is undefined.
6904 The following function can be used to compute the (right) inverse
6905 of a matrix, i.e., a matrix such that the product of the original
6906 and the inverse (in that order) is a multiple of the identity matrix.
6907 The input matrix is assumed to be of full row-rank.
6909 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
6911 The following function can be used to compute the (right) kernel
6912 (or null space) of a matrix, i.e., a matrix such that the product of
6913 the original and the kernel (in that order) is the zero matrix.
6915 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
6917 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
6919 The following functions determine
6920 an upper or lower bound on a quasipolynomial over its domain.
6922 __isl_give isl_pw_qpolynomial_fold *
6923 isl_pw_qpolynomial_bound(
6924 __isl_take isl_pw_qpolynomial *pwqp,
6925 enum isl_fold type, int *tight);
6927 __isl_give isl_union_pw_qpolynomial_fold *
6928 isl_union_pw_qpolynomial_bound(
6929 __isl_take isl_union_pw_qpolynomial *upwqp,
6930 enum isl_fold type, int *tight);
6932 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
6933 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
6934 is the returned bound is known be tight, i.e., for each value
6935 of the parameters there is at least
6936 one element in the domain that reaches the bound.
6937 If the domain of C<pwqp> is not wrapping, then the bound is computed
6938 over all elements in that domain and the result has a purely parametric
6939 domain. If the domain of C<pwqp> is wrapping, then the bound is
6940 computed over the range of the wrapped relation. The domain of the
6941 wrapped relation becomes the domain of the result.
6943 =head2 Parametric Vertex Enumeration
6945 The parametric vertex enumeration described in this section
6946 is mainly intended to be used internally and by the C<barvinok>
6949 #include <isl/vertices.h>
6950 __isl_give isl_vertices *isl_basic_set_compute_vertices(
6951 __isl_keep isl_basic_set *bset);
6953 The function C<isl_basic_set_compute_vertices> performs the
6954 actual computation of the parametric vertices and the chamber
6955 decomposition and store the result in an C<isl_vertices> object.
6956 This information can be queried by either iterating over all
6957 the vertices or iterating over all the chambers or cells
6958 and then iterating over all vertices that are active on the chamber.
6960 int isl_vertices_foreach_vertex(
6961 __isl_keep isl_vertices *vertices,
6962 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6965 int isl_vertices_foreach_cell(
6966 __isl_keep isl_vertices *vertices,
6967 int (*fn)(__isl_take isl_cell *cell, void *user),
6969 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
6970 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6973 Other operations that can be performed on an C<isl_vertices> object are
6976 int isl_vertices_get_n_vertices(
6977 __isl_keep isl_vertices *vertices);
6978 void isl_vertices_free(__isl_take isl_vertices *vertices);
6980 Vertices can be inspected and destroyed using the following functions.
6982 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
6983 __isl_give isl_basic_set *isl_vertex_get_domain(
6984 __isl_keep isl_vertex *vertex);
6985 __isl_give isl_multi_aff *isl_vertex_get_expr(
6986 __isl_keep isl_vertex *vertex);
6987 void isl_vertex_free(__isl_take isl_vertex *vertex);
6989 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
6990 describing the vertex in terms of the parameters,
6991 while C<isl_vertex_get_domain> returns the activity domain
6994 Chambers can be inspected and destroyed using the following functions.
6996 __isl_give isl_basic_set *isl_cell_get_domain(
6997 __isl_keep isl_cell *cell);
6998 void isl_cell_free(__isl_take isl_cell *cell);
7000 =head1 Polyhedral Compilation Library
7002 This section collects functionality in C<isl> that has been specifically
7003 designed for use during polyhedral compilation.
7005 =head2 Dependence Analysis
7007 C<isl> contains specialized functionality for performing
7008 array dataflow analysis. That is, given a I<sink> access relation
7009 and a collection of possible I<source> access relations,
7010 C<isl> can compute relations that describe
7011 for each iteration of the sink access, which iteration
7012 of which of the source access relations was the last
7013 to access the same data element before the given iteration
7015 The resulting dependence relations map source iterations
7016 to the corresponding sink iterations.
7017 To compute standard flow dependences, the sink should be
7018 a read, while the sources should be writes.
7019 If any of the source accesses are marked as being I<may>
7020 accesses, then there will be a dependence from the last
7021 I<must> access B<and> from any I<may> access that follows
7022 this last I<must> access.
7023 In particular, if I<all> sources are I<may> accesses,
7024 then memory based dependence analysis is performed.
7025 If, on the other hand, all sources are I<must> accesses,
7026 then value based dependence analysis is performed.
7028 #include <isl/flow.h>
7030 typedef int (*isl_access_level_before)(void *first, void *second);
7032 __isl_give isl_access_info *isl_access_info_alloc(
7033 __isl_take isl_map *sink,
7034 void *sink_user, isl_access_level_before fn,
7036 __isl_give isl_access_info *isl_access_info_add_source(
7037 __isl_take isl_access_info *acc,
7038 __isl_take isl_map *source, int must,
7040 __isl_null isl_access_info *isl_access_info_free(
7041 __isl_take isl_access_info *acc);
7043 __isl_give isl_flow *isl_access_info_compute_flow(
7044 __isl_take isl_access_info *acc);
7046 int isl_flow_foreach(__isl_keep isl_flow *deps,
7047 int (*fn)(__isl_take isl_map *dep, int must,
7048 void *dep_user, void *user),
7050 __isl_give isl_map *isl_flow_get_no_source(
7051 __isl_keep isl_flow *deps, int must);
7052 void isl_flow_free(__isl_take isl_flow *deps);
7054 The function C<isl_access_info_compute_flow> performs the actual
7055 dependence analysis. The other functions are used to construct
7056 the input for this function or to read off the output.
7058 The input is collected in an C<isl_access_info>, which can
7059 be created through a call to C<isl_access_info_alloc>.
7060 The arguments to this functions are the sink access relation
7061 C<sink>, a token C<sink_user> used to identify the sink
7062 access to the user, a callback function for specifying the
7063 relative order of source and sink accesses, and the number
7064 of source access relations that will be added.
7065 The callback function has type C<int (*)(void *first, void *second)>.
7066 The function is called with two user supplied tokens identifying
7067 either a source or the sink and it should return the shared nesting
7068 level and the relative order of the two accesses.
7069 In particular, let I<n> be the number of loops shared by
7070 the two accesses. If C<first> precedes C<second> textually,
7071 then the function should return I<2 * n + 1>; otherwise,
7072 it should return I<2 * n>.
7073 The sources can be added to the C<isl_access_info> by performing
7074 (at most) C<max_source> calls to C<isl_access_info_add_source>.
7075 C<must> indicates whether the source is a I<must> access
7076 or a I<may> access. Note that a multi-valued access relation
7077 should only be marked I<must> if every iteration in the domain
7078 of the relation accesses I<all> elements in its image.
7079 The C<source_user> token is again used to identify
7080 the source access. The range of the source access relation
7081 C<source> should have the same dimension as the range
7082 of the sink access relation.
7083 The C<isl_access_info_free> function should usually not be
7084 called explicitly, because it is called implicitly by
7085 C<isl_access_info_compute_flow>.
7087 The result of the dependence analysis is collected in an
7088 C<isl_flow>. There may be elements of
7089 the sink access for which no preceding source access could be
7090 found or for which all preceding sources are I<may> accesses.
7091 The relations containing these elements can be obtained through
7092 calls to C<isl_flow_get_no_source>, the first with C<must> set
7093 and the second with C<must> unset.
7094 In the case of standard flow dependence analysis,
7095 with the sink a read and the sources I<must> writes,
7096 the first relation corresponds to the reads from uninitialized
7097 array elements and the second relation is empty.
7098 The actual flow dependences can be extracted using
7099 C<isl_flow_foreach>. This function will call the user-specified
7100 callback function C<fn> for each B<non-empty> dependence between
7101 a source and the sink. The callback function is called
7102 with four arguments, the actual flow dependence relation
7103 mapping source iterations to sink iterations, a boolean that
7104 indicates whether it is a I<must> or I<may> dependence, a token
7105 identifying the source and an additional C<void *> with value
7106 equal to the third argument of the C<isl_flow_foreach> call.
7107 A dependence is marked I<must> if it originates from a I<must>
7108 source and if it is not followed by any I<may> sources.
7110 After finishing with an C<isl_flow>, the user should call
7111 C<isl_flow_free> to free all associated memory.
7113 A higher-level interface to dependence analysis is provided
7114 by the following function.
7116 #include <isl/flow.h>
7118 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
7119 __isl_take isl_union_map *must_source,
7120 __isl_take isl_union_map *may_source,
7121 __isl_take isl_union_map *schedule,
7122 __isl_give isl_union_map **must_dep,
7123 __isl_give isl_union_map **may_dep,
7124 __isl_give isl_union_map **must_no_source,
7125 __isl_give isl_union_map **may_no_source);
7127 The arrays are identified by the tuple names of the ranges
7128 of the accesses. The iteration domains by the tuple names
7129 of the domains of the accesses and of the schedule.
7130 The relative order of the iteration domains is given by the
7131 schedule. The relations returned through C<must_no_source>
7132 and C<may_no_source> are subsets of C<sink>.
7133 Any of C<must_dep>, C<may_dep>, C<must_no_source>
7134 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
7135 any of the other arguments is treated as an error.
7137 =head3 Interaction with Dependence Analysis
7139 During the dependence analysis, we frequently need to perform
7140 the following operation. Given a relation between sink iterations
7141 and potential source iterations from a particular source domain,
7142 what is the last potential source iteration corresponding to each
7143 sink iteration. It can sometimes be convenient to adjust
7144 the set of potential source iterations before or after each such operation.
7145 The prototypical example is fuzzy array dataflow analysis,
7146 where we need to analyze if, based on data-dependent constraints,
7147 the sink iteration can ever be executed without one or more of
7148 the corresponding potential source iterations being executed.
7149 If so, we can introduce extra parameters and select an unknown
7150 but fixed source iteration from the potential source iterations.
7151 To be able to perform such manipulations, C<isl> provides the following
7154 #include <isl/flow.h>
7156 typedef __isl_give isl_restriction *(*isl_access_restrict)(
7157 __isl_keep isl_map *source_map,
7158 __isl_keep isl_set *sink, void *source_user,
7160 __isl_give isl_access_info *isl_access_info_set_restrict(
7161 __isl_take isl_access_info *acc,
7162 isl_access_restrict fn, void *user);
7164 The function C<isl_access_info_set_restrict> should be called
7165 before calling C<isl_access_info_compute_flow> and registers a callback function
7166 that will be called any time C<isl> is about to compute the last
7167 potential source. The first argument is the (reverse) proto-dependence,
7168 mapping sink iterations to potential source iterations.
7169 The second argument represents the sink iterations for which
7170 we want to compute the last source iteration.
7171 The third argument is the token corresponding to the source
7172 and the final argument is the token passed to C<isl_access_info_set_restrict>.
7173 The callback is expected to return a restriction on either the input or
7174 the output of the operation computing the last potential source.
7175 If the input needs to be restricted then restrictions are needed
7176 for both the source and the sink iterations. The sink iterations
7177 and the potential source iterations will be intersected with these sets.
7178 If the output needs to be restricted then only a restriction on the source
7179 iterations is required.
7180 If any error occurs, the callback should return C<NULL>.
7181 An C<isl_restriction> object can be created, freed and inspected
7182 using the following functions.
7184 #include <isl/flow.h>
7186 __isl_give isl_restriction *isl_restriction_input(
7187 __isl_take isl_set *source_restr,
7188 __isl_take isl_set *sink_restr);
7189 __isl_give isl_restriction *isl_restriction_output(
7190 __isl_take isl_set *source_restr);
7191 __isl_give isl_restriction *isl_restriction_none(
7192 __isl_take isl_map *source_map);
7193 __isl_give isl_restriction *isl_restriction_empty(
7194 __isl_take isl_map *source_map);
7195 __isl_null isl_restriction *isl_restriction_free(
7196 __isl_take isl_restriction *restr);
7198 C<isl_restriction_none> and C<isl_restriction_empty> are special
7199 cases of C<isl_restriction_input>. C<isl_restriction_none>
7200 is essentially equivalent to
7202 isl_restriction_input(isl_set_universe(
7203 isl_space_range(isl_map_get_space(source_map))),
7205 isl_space_domain(isl_map_get_space(source_map))));
7207 whereas C<isl_restriction_empty> is essentially equivalent to
7209 isl_restriction_input(isl_set_empty(
7210 isl_space_range(isl_map_get_space(source_map))),
7212 isl_space_domain(isl_map_get_space(source_map))));
7216 B<The functionality described in this section is fairly new
7217 and may be subject to change.>
7219 #include <isl/schedule.h>
7220 __isl_give isl_schedule *
7221 isl_schedule_constraints_compute_schedule(
7222 __isl_take isl_schedule_constraints *sc);
7223 __isl_null isl_schedule *isl_schedule_free(
7224 __isl_take isl_schedule *sched);
7226 The function C<isl_schedule_constraints_compute_schedule> can be
7227 used to compute a schedule that satisfies the given schedule constraints.
7228 These schedule constraints include the iteration domain for which
7229 a schedule should be computed and dependences between pairs of
7230 iterations. In particular, these dependences include
7231 I<validity> dependences and I<proximity> dependences.
7232 By default, the algorithm used to construct the schedule is similar
7233 to that of C<Pluto>.
7234 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
7236 The generated schedule respects all validity dependences.
7237 That is, all dependence distances over these dependences in the
7238 scheduled space are lexicographically positive.
7239 The default algorithm tries to ensure that the dependence distances
7240 over coincidence constraints are zero and to minimize the
7241 dependence distances over proximity dependences.
7242 Moreover, it tries to obtain sequences (bands) of schedule dimensions
7243 for groups of domains where the dependence distances over validity
7244 dependences have only non-negative values.
7245 When using Feautrier's algorithm, the coincidence and proximity constraints
7246 are only taken into account during the extension to a
7247 full-dimensional schedule.
7249 An C<isl_schedule_constraints> object can be constructed
7250 and manipulated using the following functions.
7252 #include <isl/schedule.h>
7253 __isl_give isl_schedule_constraints *
7254 isl_schedule_constraints_copy(
7255 __isl_keep isl_schedule_constraints *sc);
7256 __isl_give isl_schedule_constraints *
7257 isl_schedule_constraints_on_domain(
7258 __isl_take isl_union_set *domain);
7259 __isl_give isl_schedule_constraints *
7260 isl_schedule_constraints_set_validity(
7261 __isl_take isl_schedule_constraints *sc,
7262 __isl_take isl_union_map *validity);
7263 __isl_give isl_schedule_constraints *
7264 isl_schedule_constraints_set_coincidence(
7265 __isl_take isl_schedule_constraints *sc,
7266 __isl_take isl_union_map *coincidence);
7267 __isl_give isl_schedule_constraints *
7268 isl_schedule_constraints_set_proximity(
7269 __isl_take isl_schedule_constraints *sc,
7270 __isl_take isl_union_map *proximity);
7271 __isl_give isl_schedule_constraints *
7272 isl_schedule_constraints_set_conditional_validity(
7273 __isl_take isl_schedule_constraints *sc,
7274 __isl_take isl_union_map *condition,
7275 __isl_take isl_union_map *validity);
7276 __isl_null isl_schedule_constraints *
7277 isl_schedule_constraints_free(
7278 __isl_take isl_schedule_constraints *sc);
7280 The initial C<isl_schedule_constraints> object created by
7281 C<isl_schedule_constraints_on_domain> does not impose any constraints.
7282 That is, it has an empty set of dependences.
7283 The function C<isl_schedule_constraints_set_validity> replaces the
7284 validity dependences, mapping domain elements I<i> to domain
7285 elements that should be scheduled after I<i>.
7286 The function C<isl_schedule_constraints_set_coincidence> replaces the
7287 coincidence dependences, mapping domain elements I<i> to domain
7288 elements that should be scheduled together with I<I>, if possible.
7289 The function C<isl_schedule_constraints_set_proximity> replaces the
7290 proximity dependences, mapping domain elements I<i> to domain
7291 elements that should be scheduled either before I<I>
7292 or as early as possible after I<i>.
7294 The function C<isl_schedule_constraints_set_conditional_validity>
7295 replaces the conditional validity constraints.
7296 A conditional validity constraint is only imposed when any of the corresponding
7297 conditions is satisfied, i.e., when any of them is non-zero.
7298 That is, the scheduler ensures that within each band if the dependence
7299 distances over the condition constraints are not all zero
7300 then all corresponding conditional validity constraints are respected.
7301 A conditional validity constraint corresponds to a condition
7302 if the two are adjacent, i.e., if the domain of one relation intersect
7303 the range of the other relation.
7304 The typical use case of conditional validity constraints is
7305 to allow order constraints between live ranges to be violated
7306 as long as the live ranges themselves are local to the band.
7307 To allow more fine-grained control over which conditions correspond
7308 to which conditional validity constraints, the domains and ranges
7309 of these relations may include I<tags>. That is, the domains and
7310 ranges of those relation may themselves be wrapped relations
7311 where the iteration domain appears in the domain of those wrapped relations
7312 and the range of the wrapped relations can be arbitrarily chosen
7313 by the user. Conditions and conditional validity constraints are only
7314 considered adjacent to each other if the entire wrapped relation matches.
7315 In particular, a relation with a tag will never be considered adjacent
7316 to a relation without a tag.
7318 The following function computes a schedule directly from
7319 an iteration domain and validity and proximity dependences
7320 and is implemented in terms of the functions described above.
7321 The use of C<isl_union_set_compute_schedule> is discouraged.
7323 #include <isl/schedule.h>
7324 __isl_give isl_schedule *isl_union_set_compute_schedule(
7325 __isl_take isl_union_set *domain,
7326 __isl_take isl_union_map *validity,
7327 __isl_take isl_union_map *proximity);
7329 A mapping from the domains to the scheduled space can be obtained
7330 from an C<isl_schedule> using the following function.
7332 __isl_give isl_union_map *isl_schedule_get_map(
7333 __isl_keep isl_schedule *sched);
7335 A representation of the schedule can be printed using
7337 __isl_give isl_printer *isl_printer_print_schedule(
7338 __isl_take isl_printer *p,
7339 __isl_keep isl_schedule *schedule);
7341 A representation of the schedule as a forest of bands can be obtained
7342 using the following function.
7344 __isl_give isl_band_list *isl_schedule_get_band_forest(
7345 __isl_keep isl_schedule *schedule);
7347 The individual bands can be visited in depth-first post-order
7348 using the following function.
7350 #include <isl/schedule.h>
7351 int isl_schedule_foreach_band(
7352 __isl_keep isl_schedule *sched,
7353 int (*fn)(__isl_keep isl_band *band, void *user),
7356 The list can be manipulated as explained in L<"Lists">.
7357 The bands inside the list can be copied and freed using the following
7360 #include <isl/band.h>
7361 __isl_give isl_band *isl_band_copy(
7362 __isl_keep isl_band *band);
7363 __isl_null isl_band *isl_band_free(
7364 __isl_take isl_band *band);
7366 Each band contains zero or more scheduling dimensions.
7367 These are referred to as the members of the band.
7368 The section of the schedule that corresponds to the band is
7369 referred to as the partial schedule of the band.
7370 For those nodes that participate in a band, the outer scheduling
7371 dimensions form the prefix schedule, while the inner scheduling
7372 dimensions form the suffix schedule.
7373 That is, if we take a cut of the band forest, then the union of
7374 the concatenations of the prefix, partial and suffix schedules of
7375 each band in the cut is equal to the entire schedule (modulo
7376 some possible padding at the end with zero scheduling dimensions).
7377 The properties of a band can be inspected using the following functions.
7379 #include <isl/band.h>
7380 int isl_band_has_children(__isl_keep isl_band *band);
7381 __isl_give isl_band_list *isl_band_get_children(
7382 __isl_keep isl_band *band);
7384 __isl_give isl_union_map *isl_band_get_prefix_schedule(
7385 __isl_keep isl_band *band);
7386 __isl_give isl_union_map *isl_band_get_partial_schedule(
7387 __isl_keep isl_band *band);
7388 __isl_give isl_union_map *isl_band_get_suffix_schedule(
7389 __isl_keep isl_band *band);
7391 int isl_band_n_member(__isl_keep isl_band *band);
7392 int isl_band_member_is_coincident(
7393 __isl_keep isl_band *band, int pos);
7395 int isl_band_list_foreach_band(
7396 __isl_keep isl_band_list *list,
7397 int (*fn)(__isl_keep isl_band *band, void *user),
7400 Note that a scheduling dimension is considered to be ``coincident''
7401 if it satisfies the coincidence constraints within its band.
7402 That is, if the dependence distances of the coincidence
7403 constraints are all zero in that direction (for fixed
7404 iterations of outer bands).
7405 Like C<isl_schedule_foreach_band>,
7406 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
7407 in depth-first post-order.
7409 A band can be tiled using the following function.
7411 #include <isl/band.h>
7412 int isl_band_tile(__isl_keep isl_band *band,
7413 __isl_take isl_vec *sizes);
7415 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
7417 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
7418 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
7420 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
7422 The C<isl_band_tile> function tiles the band using the given tile sizes
7423 inside its schedule.
7424 A new child band is created to represent the point loops and it is
7425 inserted between the modified band and its children.
7426 The C<tile_scale_tile_loops> option specifies whether the tile
7427 loops iterators should be scaled by the tile sizes.
7428 If the C<tile_shift_point_loops> option is set, then the point loops
7429 are shifted to start at zero.
7431 A band can be split into two nested bands using the following function.
7433 int isl_band_split(__isl_keep isl_band *band, int pos);
7435 The resulting outer band contains the first C<pos> dimensions of C<band>
7436 while the inner band contains the remaining dimensions.
7438 A representation of the band can be printed using
7440 #include <isl/band.h>
7441 __isl_give isl_printer *isl_printer_print_band(
7442 __isl_take isl_printer *p,
7443 __isl_keep isl_band *band);
7447 #include <isl/schedule.h>
7448 int isl_options_set_schedule_max_coefficient(
7449 isl_ctx *ctx, int val);
7450 int isl_options_get_schedule_max_coefficient(
7452 int isl_options_set_schedule_max_constant_term(
7453 isl_ctx *ctx, int val);
7454 int isl_options_get_schedule_max_constant_term(
7456 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
7457 int isl_options_get_schedule_fuse(isl_ctx *ctx);
7458 int isl_options_set_schedule_maximize_band_depth(
7459 isl_ctx *ctx, int val);
7460 int isl_options_get_schedule_maximize_band_depth(
7462 int isl_options_set_schedule_outer_coincidence(
7463 isl_ctx *ctx, int val);
7464 int isl_options_get_schedule_outer_coincidence(
7466 int isl_options_set_schedule_split_scaled(
7467 isl_ctx *ctx, int val);
7468 int isl_options_get_schedule_split_scaled(
7470 int isl_options_set_schedule_algorithm(
7471 isl_ctx *ctx, int val);
7472 int isl_options_get_schedule_algorithm(
7474 int isl_options_set_schedule_separate_components(
7475 isl_ctx *ctx, int val);
7476 int isl_options_get_schedule_separate_components(
7481 =item * schedule_max_coefficient
7483 This option enforces that the coefficients for variable and parameter
7484 dimensions in the calculated schedule are not larger than the specified value.
7485 This option can significantly increase the speed of the scheduling calculation
7486 and may also prevent fusing of unrelated dimensions. A value of -1 means that
7487 this option does not introduce bounds on the variable or parameter
7490 =item * schedule_max_constant_term
7492 This option enforces that the constant coefficients in the calculated schedule
7493 are not larger than the maximal constant term. This option can significantly
7494 increase the speed of the scheduling calculation and may also prevent fusing of
7495 unrelated dimensions. A value of -1 means that this option does not introduce
7496 bounds on the constant coefficients.
7498 =item * schedule_fuse
7500 This option controls the level of fusion.
7501 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
7502 resulting schedule will be distributed as much as possible.
7503 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
7504 try to fuse loops in the resulting schedule.
7506 =item * schedule_maximize_band_depth
7508 If this option is set, we do not split bands at the point
7509 where we detect splitting is necessary. Instead, we
7510 backtrack and split bands as early as possible. This
7511 reduces the number of splits and maximizes the width of
7512 the bands. Wider bands give more possibilities for tiling.
7513 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
7514 then bands will be split as early as possible, even if there is no need.
7515 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
7517 =item * schedule_outer_coincidence
7519 If this option is set, then we try to construct schedules
7520 where the outermost scheduling dimension in each band
7521 satisfies the coincidence constraints.
7523 =item * schedule_split_scaled
7525 If this option is set, then we try to construct schedules in which the
7526 constant term is split off from the linear part if the linear parts of
7527 the scheduling rows for all nodes in the graphs have a common non-trivial
7529 The constant term is then placed in a separate band and the linear
7532 =item * schedule_algorithm
7534 Selects the scheduling algorithm to be used.
7535 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
7536 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
7538 =item * schedule_separate_components
7540 If at any point the dependence graph contains any (weakly connected) components,
7541 then these components are scheduled separately.
7542 If this option is not set, then some iterations of the domains
7543 in these components may be scheduled together.
7544 If this option is set, then the components are given consecutive
7549 =head2 AST Generation
7551 This section describes the C<isl> functionality for generating
7552 ASTs that visit all the elements
7553 in a domain in an order specified by a schedule.
7554 In particular, given a C<isl_union_map>, an AST is generated
7555 that visits all the elements in the domain of the C<isl_union_map>
7556 according to the lexicographic order of the corresponding image
7557 element(s). If the range of the C<isl_union_map> consists of
7558 elements in more than one space, then each of these spaces is handled
7559 separately in an arbitrary order.
7560 It should be noted that the image elements only specify the I<order>
7561 in which the corresponding domain elements should be visited.
7562 No direct relation between the image elements and the loop iterators
7563 in the generated AST should be assumed.
7565 Each AST is generated within a build. The initial build
7566 simply specifies the constraints on the parameters (if any)
7567 and can be created, inspected, copied and freed using the following functions.
7569 #include <isl/ast_build.h>
7570 __isl_give isl_ast_build *isl_ast_build_from_context(
7571 __isl_take isl_set *set);
7572 __isl_give isl_ast_build *isl_ast_build_copy(
7573 __isl_keep isl_ast_build *build);
7574 __isl_null isl_ast_build *isl_ast_build_free(
7575 __isl_take isl_ast_build *build);
7577 The C<set> argument is usually a parameter set with zero or more parameters.
7578 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
7579 and L</"Fine-grained Control over AST Generation">.
7580 Finally, the AST itself can be constructed using the following
7583 #include <isl/ast_build.h>
7584 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
7585 __isl_keep isl_ast_build *build,
7586 __isl_take isl_union_map *schedule);
7588 =head3 Inspecting the AST
7590 The basic properties of an AST node can be obtained as follows.
7592 #include <isl/ast.h>
7593 enum isl_ast_node_type isl_ast_node_get_type(
7594 __isl_keep isl_ast_node *node);
7596 The type of an AST node is one of
7597 C<isl_ast_node_for>,
7599 C<isl_ast_node_block> or
7600 C<isl_ast_node_user>.
7601 An C<isl_ast_node_for> represents a for node.
7602 An C<isl_ast_node_if> represents an if node.
7603 An C<isl_ast_node_block> represents a compound node.
7604 An C<isl_ast_node_user> represents an expression statement.
7605 An expression statement typically corresponds to a domain element, i.e.,
7606 one of the elements that is visited by the AST.
7608 Each type of node has its own additional properties.
7610 #include <isl/ast.h>
7611 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7612 __isl_keep isl_ast_node *node);
7613 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7614 __isl_keep isl_ast_node *node);
7615 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7616 __isl_keep isl_ast_node *node);
7617 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7618 __isl_keep isl_ast_node *node);
7619 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7620 __isl_keep isl_ast_node *node);
7621 int isl_ast_node_for_is_degenerate(
7622 __isl_keep isl_ast_node *node);
7624 An C<isl_ast_for> is considered degenerate if it is known to execute
7627 #include <isl/ast.h>
7628 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7629 __isl_keep isl_ast_node *node);
7630 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7631 __isl_keep isl_ast_node *node);
7632 int isl_ast_node_if_has_else(
7633 __isl_keep isl_ast_node *node);
7634 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7635 __isl_keep isl_ast_node *node);
7637 __isl_give isl_ast_node_list *
7638 isl_ast_node_block_get_children(
7639 __isl_keep isl_ast_node *node);
7641 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7642 __isl_keep isl_ast_node *node);
7644 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7645 the following functions.
7647 #include <isl/ast.h>
7648 enum isl_ast_expr_type isl_ast_expr_get_type(
7649 __isl_keep isl_ast_expr *expr);
7651 The type of an AST expression is one of
7653 C<isl_ast_expr_id> or
7654 C<isl_ast_expr_int>.
7655 An C<isl_ast_expr_op> represents the result of an operation.
7656 An C<isl_ast_expr_id> represents an identifier.
7657 An C<isl_ast_expr_int> represents an integer value.
7659 Each type of expression has its own additional properties.
7661 #include <isl/ast.h>
7662 enum isl_ast_op_type isl_ast_expr_get_op_type(
7663 __isl_keep isl_ast_expr *expr);
7664 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7665 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7666 __isl_keep isl_ast_expr *expr, int pos);
7667 int isl_ast_node_foreach_ast_op_type(
7668 __isl_keep isl_ast_node *node,
7669 int (*fn)(enum isl_ast_op_type type, void *user),
7672 C<isl_ast_expr_get_op_type> returns the type of the operation
7673 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7674 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7676 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7677 C<isl_ast_op_type> that appears in C<node>.
7678 The operation type is one of the following.
7682 =item C<isl_ast_op_and>
7684 Logical I<and> of two arguments.
7685 Both arguments can be evaluated.
7687 =item C<isl_ast_op_and_then>
7689 Logical I<and> of two arguments.
7690 The second argument can only be evaluated if the first evaluates to true.
7692 =item C<isl_ast_op_or>
7694 Logical I<or> of two arguments.
7695 Both arguments can be evaluated.
7697 =item C<isl_ast_op_or_else>
7699 Logical I<or> of two arguments.
7700 The second argument can only be evaluated if the first evaluates to false.
7702 =item C<isl_ast_op_max>
7704 Maximum of two or more arguments.
7706 =item C<isl_ast_op_min>
7708 Minimum of two or more arguments.
7710 =item C<isl_ast_op_minus>
7714 =item C<isl_ast_op_add>
7716 Sum of two arguments.
7718 =item C<isl_ast_op_sub>
7720 Difference of two arguments.
7722 =item C<isl_ast_op_mul>
7724 Product of two arguments.
7726 =item C<isl_ast_op_div>
7728 Exact division. That is, the result is known to be an integer.
7730 =item C<isl_ast_op_fdiv_q>
7732 Result of integer division, rounded towards negative
7735 =item C<isl_ast_op_pdiv_q>
7737 Result of integer division, where dividend is known to be non-negative.
7739 =item C<isl_ast_op_pdiv_r>
7741 Remainder of integer division, where dividend is known to be non-negative.
7743 =item C<isl_ast_op_zdiv_r>
7745 Equal to zero iff the remainder on integer division is zero.
7747 =item C<isl_ast_op_cond>
7749 Conditional operator defined on three arguments.
7750 If the first argument evaluates to true, then the result
7751 is equal to the second argument. Otherwise, the result
7752 is equal to the third argument.
7753 The second and third argument may only be evaluated if
7754 the first argument evaluates to true and false, respectively.
7755 Corresponds to C<a ? b : c> in C.
7757 =item C<isl_ast_op_select>
7759 Conditional operator defined on three arguments.
7760 If the first argument evaluates to true, then the result
7761 is equal to the second argument. Otherwise, the result
7762 is equal to the third argument.
7763 The second and third argument may be evaluated independently
7764 of the value of the first argument.
7765 Corresponds to C<a * b + (1 - a) * c> in C.
7767 =item C<isl_ast_op_eq>
7771 =item C<isl_ast_op_le>
7773 Less than or equal relation.
7775 =item C<isl_ast_op_lt>
7779 =item C<isl_ast_op_ge>
7781 Greater than or equal relation.
7783 =item C<isl_ast_op_gt>
7785 Greater than relation.
7787 =item C<isl_ast_op_call>
7790 The number of arguments of the C<isl_ast_expr> is one more than
7791 the number of arguments in the function call, the first argument
7792 representing the function being called.
7794 =item C<isl_ast_op_access>
7797 The number of arguments of the C<isl_ast_expr> is one more than
7798 the number of index expressions in the array access, the first argument
7799 representing the array being accessed.
7801 =item C<isl_ast_op_member>
7804 This operation has two arguments, a structure and the name of
7805 the member of the structure being accessed.
7809 #include <isl/ast.h>
7810 __isl_give isl_id *isl_ast_expr_get_id(
7811 __isl_keep isl_ast_expr *expr);
7813 Return the identifier represented by the AST expression.
7815 #include <isl/ast.h>
7816 __isl_give isl_val *isl_ast_expr_get_val(
7817 __isl_keep isl_ast_expr *expr);
7819 Return the integer represented by the AST expression.
7821 =head3 Properties of ASTs
7823 #include <isl/ast.h>
7824 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7825 __isl_keep isl_ast_expr *expr2);
7827 Check if two C<isl_ast_expr>s are equal to each other.
7829 =head3 Manipulating and printing the AST
7831 AST nodes can be copied and freed using the following functions.
7833 #include <isl/ast.h>
7834 __isl_give isl_ast_node *isl_ast_node_copy(
7835 __isl_keep isl_ast_node *node);
7836 __isl_null isl_ast_node *isl_ast_node_free(
7837 __isl_take isl_ast_node *node);
7839 AST expressions can be copied and freed using the following functions.
7841 #include <isl/ast.h>
7842 __isl_give isl_ast_expr *isl_ast_expr_copy(
7843 __isl_keep isl_ast_expr *expr);
7844 __isl_null isl_ast_expr *isl_ast_expr_free(
7845 __isl_take isl_ast_expr *expr);
7847 New AST expressions can be created either directly or within
7848 the context of an C<isl_ast_build>.
7850 #include <isl/ast.h>
7851 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7852 __isl_take isl_val *v);
7853 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7854 __isl_take isl_id *id);
7855 __isl_give isl_ast_expr *isl_ast_expr_neg(
7856 __isl_take isl_ast_expr *expr);
7857 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7858 __isl_take isl_ast_expr *expr);
7859 __isl_give isl_ast_expr *isl_ast_expr_add(
7860 __isl_take isl_ast_expr *expr1,
7861 __isl_take isl_ast_expr *expr2);
7862 __isl_give isl_ast_expr *isl_ast_expr_sub(
7863 __isl_take isl_ast_expr *expr1,
7864 __isl_take isl_ast_expr *expr2);
7865 __isl_give isl_ast_expr *isl_ast_expr_mul(
7866 __isl_take isl_ast_expr *expr1,
7867 __isl_take isl_ast_expr *expr2);
7868 __isl_give isl_ast_expr *isl_ast_expr_div(
7869 __isl_take isl_ast_expr *expr1,
7870 __isl_take isl_ast_expr *expr2);
7871 __isl_give isl_ast_expr *isl_ast_expr_and(
7872 __isl_take isl_ast_expr *expr1,
7873 __isl_take isl_ast_expr *expr2)
7874 __isl_give isl_ast_expr *isl_ast_expr_or(
7875 __isl_take isl_ast_expr *expr1,
7876 __isl_take isl_ast_expr *expr2)
7877 __isl_give isl_ast_expr *isl_ast_expr_eq(
7878 __isl_take isl_ast_expr *expr1,
7879 __isl_take isl_ast_expr *expr2);
7880 __isl_give isl_ast_expr *isl_ast_expr_le(
7881 __isl_take isl_ast_expr *expr1,
7882 __isl_take isl_ast_expr *expr2);
7883 __isl_give isl_ast_expr *isl_ast_expr_lt(
7884 __isl_take isl_ast_expr *expr1,
7885 __isl_take isl_ast_expr *expr2);
7886 __isl_give isl_ast_expr *isl_ast_expr_ge(
7887 __isl_take isl_ast_expr *expr1,
7888 __isl_take isl_ast_expr *expr2);
7889 __isl_give isl_ast_expr *isl_ast_expr_gt(
7890 __isl_take isl_ast_expr *expr1,
7891 __isl_take isl_ast_expr *expr2);
7892 __isl_give isl_ast_expr *isl_ast_expr_access(
7893 __isl_take isl_ast_expr *array,
7894 __isl_take isl_ast_expr_list *indices);
7896 The function C<isl_ast_expr_address_of> can be applied to an
7897 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
7898 to represent the address of the C<isl_ast_expr_access>.
7900 #include <isl/ast_build.h>
7901 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
7902 __isl_keep isl_ast_build *build,
7903 __isl_take isl_pw_aff *pa);
7904 __isl_give isl_ast_expr *
7905 isl_ast_build_access_from_pw_multi_aff(
7906 __isl_keep isl_ast_build *build,
7907 __isl_take isl_pw_multi_aff *pma);
7908 __isl_give isl_ast_expr *
7909 isl_ast_build_access_from_multi_pw_aff(
7910 __isl_keep isl_ast_build *build,
7911 __isl_take isl_multi_pw_aff *mpa);
7912 __isl_give isl_ast_expr *
7913 isl_ast_build_call_from_pw_multi_aff(
7914 __isl_keep isl_ast_build *build,
7915 __isl_take isl_pw_multi_aff *pma);
7916 __isl_give isl_ast_expr *
7917 isl_ast_build_call_from_multi_pw_aff(
7918 __isl_keep isl_ast_build *build,
7919 __isl_take isl_multi_pw_aff *mpa);
7921 The domains of C<pa>, C<mpa> and C<pma> should correspond
7922 to the schedule space of C<build>.
7923 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
7924 the function being called.
7925 If the accessed space is a nested relation, then it is taken
7926 to represent an access of the member specified by the range
7927 of this nested relation of the structure specified by the domain
7928 of the nested relation.
7930 The following functions can be used to modify an C<isl_ast_expr>.
7932 #include <isl/ast.h>
7933 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
7934 __isl_take isl_ast_expr *expr, int pos,
7935 __isl_take isl_ast_expr *arg);
7937 Replace the argument of C<expr> at position C<pos> by C<arg>.
7939 #include <isl/ast.h>
7940 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
7941 __isl_take isl_ast_expr *expr,
7942 __isl_take isl_id_to_ast_expr *id2expr);
7944 The function C<isl_ast_expr_substitute_ids> replaces the
7945 subexpressions of C<expr> of type C<isl_ast_expr_id>
7946 by the corresponding expression in C<id2expr>, if there is any.
7949 User specified data can be attached to an C<isl_ast_node> and obtained
7950 from the same C<isl_ast_node> using the following functions.
7952 #include <isl/ast.h>
7953 __isl_give isl_ast_node *isl_ast_node_set_annotation(
7954 __isl_take isl_ast_node *node,
7955 __isl_take isl_id *annotation);
7956 __isl_give isl_id *isl_ast_node_get_annotation(
7957 __isl_keep isl_ast_node *node);
7959 Basic printing can be performed using the following functions.
7961 #include <isl/ast.h>
7962 __isl_give isl_printer *isl_printer_print_ast_expr(
7963 __isl_take isl_printer *p,
7964 __isl_keep isl_ast_expr *expr);
7965 __isl_give isl_printer *isl_printer_print_ast_node(
7966 __isl_take isl_printer *p,
7967 __isl_keep isl_ast_node *node);
7968 __isl_give char *isl_ast_expr_to_str(
7969 __isl_keep isl_ast_expr *expr);
7971 More advanced printing can be performed using the following functions.
7973 #include <isl/ast.h>
7974 __isl_give isl_printer *isl_ast_op_type_print_macro(
7975 enum isl_ast_op_type type,
7976 __isl_take isl_printer *p);
7977 __isl_give isl_printer *isl_ast_node_print_macros(
7978 __isl_keep isl_ast_node *node,
7979 __isl_take isl_printer *p);
7980 __isl_give isl_printer *isl_ast_node_print(
7981 __isl_keep isl_ast_node *node,
7982 __isl_take isl_printer *p,
7983 __isl_take isl_ast_print_options *options);
7984 __isl_give isl_printer *isl_ast_node_for_print(
7985 __isl_keep isl_ast_node *node,
7986 __isl_take isl_printer *p,
7987 __isl_take isl_ast_print_options *options);
7988 __isl_give isl_printer *isl_ast_node_if_print(
7989 __isl_keep isl_ast_node *node,
7990 __isl_take isl_printer *p,
7991 __isl_take isl_ast_print_options *options);
7993 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
7994 C<isl> may print out an AST that makes use of macros such
7995 as C<floord>, C<min> and C<max>.
7996 C<isl_ast_op_type_print_macro> prints out the macro
7997 corresponding to a specific C<isl_ast_op_type>.
7998 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
7999 for expressions where these macros would be used and prints
8000 out the required macro definitions.
8001 Essentially, C<isl_ast_node_print_macros> calls
8002 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
8003 as function argument.
8004 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
8005 C<isl_ast_node_if_print> print an C<isl_ast_node>
8006 in C<ISL_FORMAT_C>, but allow for some extra control
8007 through an C<isl_ast_print_options> object.
8008 This object can be created using the following functions.
8010 #include <isl/ast.h>
8011 __isl_give isl_ast_print_options *
8012 isl_ast_print_options_alloc(isl_ctx *ctx);
8013 __isl_give isl_ast_print_options *
8014 isl_ast_print_options_copy(
8015 __isl_keep isl_ast_print_options *options);
8016 __isl_null isl_ast_print_options *
8017 isl_ast_print_options_free(
8018 __isl_take isl_ast_print_options *options);
8020 __isl_give isl_ast_print_options *
8021 isl_ast_print_options_set_print_user(
8022 __isl_take isl_ast_print_options *options,
8023 __isl_give isl_printer *(*print_user)(
8024 __isl_take isl_printer *p,
8025 __isl_take isl_ast_print_options *options,
8026 __isl_keep isl_ast_node *node, void *user),
8028 __isl_give isl_ast_print_options *
8029 isl_ast_print_options_set_print_for(
8030 __isl_take isl_ast_print_options *options,
8031 __isl_give isl_printer *(*print_for)(
8032 __isl_take isl_printer *p,
8033 __isl_take isl_ast_print_options *options,
8034 __isl_keep isl_ast_node *node, void *user),
8037 The callback set by C<isl_ast_print_options_set_print_user>
8038 is called whenever a node of type C<isl_ast_node_user> needs to
8040 The callback set by C<isl_ast_print_options_set_print_for>
8041 is called whenever a node of type C<isl_ast_node_for> needs to
8043 Note that C<isl_ast_node_for_print> will I<not> call the
8044 callback set by C<isl_ast_print_options_set_print_for> on the node
8045 on which C<isl_ast_node_for_print> is called, but only on nested
8046 nodes of type C<isl_ast_node_for>. It is therefore safe to
8047 call C<isl_ast_node_for_print> from within the callback set by
8048 C<isl_ast_print_options_set_print_for>.
8050 The following option determines the type to be used for iterators
8051 while printing the AST.
8053 int isl_options_set_ast_iterator_type(
8054 isl_ctx *ctx, const char *val);
8055 const char *isl_options_get_ast_iterator_type(
8058 The AST printer only prints body nodes as blocks if these
8059 blocks cannot be safely omitted.
8060 For example, a C<for> node with one body node will not be
8061 surrounded with braces in C<ISL_FORMAT_C>.
8062 A block will always be printed by setting the following option.
8064 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
8066 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
8070 #include <isl/ast_build.h>
8071 int isl_options_set_ast_build_atomic_upper_bound(
8072 isl_ctx *ctx, int val);
8073 int isl_options_get_ast_build_atomic_upper_bound(
8075 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
8077 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
8078 int isl_options_set_ast_build_exploit_nested_bounds(
8079 isl_ctx *ctx, int val);
8080 int isl_options_get_ast_build_exploit_nested_bounds(
8082 int isl_options_set_ast_build_group_coscheduled(
8083 isl_ctx *ctx, int val);
8084 int isl_options_get_ast_build_group_coscheduled(
8086 int isl_options_set_ast_build_scale_strides(
8087 isl_ctx *ctx, int val);
8088 int isl_options_get_ast_build_scale_strides(
8090 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
8092 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
8093 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
8095 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
8099 =item * ast_build_atomic_upper_bound
8101 Generate loop upper bounds that consist of the current loop iterator,
8102 an operator and an expression not involving the iterator.
8103 If this option is not set, then the current loop iterator may appear
8104 several times in the upper bound.
8105 For example, when this option is turned off, AST generation
8108 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
8112 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
8115 When the option is turned on, the following AST is generated
8117 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
8120 =item * ast_build_prefer_pdiv
8122 If this option is turned off, then the AST generation will
8123 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
8124 operators, but no C<isl_ast_op_pdiv_q> or
8125 C<isl_ast_op_pdiv_r> operators.
8126 If this options is turned on, then C<isl> will try to convert
8127 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
8128 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
8130 =item * ast_build_exploit_nested_bounds
8132 Simplify conditions based on bounds of nested for loops.
8133 In particular, remove conditions that are implied by the fact
8134 that one or more nested loops have at least one iteration,
8135 meaning that the upper bound is at least as large as the lower bound.
8136 For example, when this option is turned off, AST generation
8139 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
8145 for (int c0 = 0; c0 <= N; c0 += 1)
8146 for (int c1 = 0; c1 <= M; c1 += 1)
8149 When the option is turned on, the following AST is generated
8151 for (int c0 = 0; c0 <= N; c0 += 1)
8152 for (int c1 = 0; c1 <= M; c1 += 1)
8155 =item * ast_build_group_coscheduled
8157 If two domain elements are assigned the same schedule point, then
8158 they may be executed in any order and they may even appear in different
8159 loops. If this options is set, then the AST generator will make
8160 sure that coscheduled domain elements do not appear in separate parts
8161 of the AST. This is useful in case of nested AST generation
8162 if the outer AST generation is given only part of a schedule
8163 and the inner AST generation should handle the domains that are
8164 coscheduled by this initial part of the schedule together.
8165 For example if an AST is generated for a schedule
8167 { A[i] -> [0]; B[i] -> [0] }
8169 then the C<isl_ast_build_set_create_leaf> callback described
8170 below may get called twice, once for each domain.
8171 Setting this option ensures that the callback is only called once
8172 on both domains together.
8174 =item * ast_build_separation_bounds
8176 This option specifies which bounds to use during separation.
8177 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
8178 then all (possibly implicit) bounds on the current dimension will
8179 be used during separation.
8180 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
8181 then only those bounds that are explicitly available will
8182 be used during separation.
8184 =item * ast_build_scale_strides
8186 This option specifies whether the AST generator is allowed
8187 to scale down iterators of strided loops.
8189 =item * ast_build_allow_else
8191 This option specifies whether the AST generator is allowed
8192 to construct if statements with else branches.
8194 =item * ast_build_allow_or
8196 This option specifies whether the AST generator is allowed
8197 to construct if conditions with disjunctions.
8201 =head3 Fine-grained Control over AST Generation
8203 Besides specifying the constraints on the parameters,
8204 an C<isl_ast_build> object can be used to control
8205 various aspects of the AST generation process.
8206 The most prominent way of control is through ``options'',
8207 which can be set using the following function.
8209 #include <isl/ast_build.h>
8210 __isl_give isl_ast_build *
8211 isl_ast_build_set_options(
8212 __isl_take isl_ast_build *control,
8213 __isl_take isl_union_map *options);
8215 The options are encoded in an C<isl_union_map>.
8216 The domain of this union relation refers to the schedule domain,
8217 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
8218 In the case of nested AST generation (see L</"Nested AST Generation">),
8219 the domain of C<options> should refer to the extra piece of the schedule.
8220 That is, it should be equal to the range of the wrapped relation in the
8221 range of the schedule.
8222 The range of the options can consist of elements in one or more spaces,
8223 the names of which determine the effect of the option.
8224 The values of the range typically also refer to the schedule dimension
8225 to which the option applies. In case of nested AST generation
8226 (see L</"Nested AST Generation">), these values refer to the position
8227 of the schedule dimension within the innermost AST generation.
8228 The constraints on the domain elements of
8229 the option should only refer to this dimension and earlier dimensions.
8230 We consider the following spaces.
8234 =item C<separation_class>
8236 This space is a wrapped relation between two one dimensional spaces.
8237 The input space represents the schedule dimension to which the option
8238 applies and the output space represents the separation class.
8239 While constructing a loop corresponding to the specified schedule
8240 dimension(s), the AST generator will try to generate separate loops
8241 for domain elements that are assigned different classes.
8242 If only some of the elements are assigned a class, then those elements
8243 that are not assigned any class will be treated as belonging to a class
8244 that is separate from the explicitly assigned classes.
8245 The typical use case for this option is to separate full tiles from
8247 The other options, described below, are applied after the separation
8250 As an example, consider the separation into full and partial tiles
8251 of a tiling of a triangular domain.
8252 Take, for example, the domain
8254 { A[i,j] : 0 <= i,j and i + j <= 100 }
8256 and a tiling into tiles of 10 by 10. The input to the AST generator
8257 is then the schedule
8259 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
8262 Without any options, the following AST is generated
8264 for (int c0 = 0; c0 <= 10; c0 += 1)
8265 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8266 for (int c2 = 10 * c0;
8267 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8269 for (int c3 = 10 * c1;
8270 c3 <= min(10 * c1 + 9, -c2 + 100);
8274 Separation into full and partial tiles can be obtained by assigning
8275 a class, say C<0>, to the full tiles. The full tiles are represented by those
8276 values of the first and second schedule dimensions for which there are
8277 values of the third and fourth dimensions to cover an entire tile.
8278 That is, we need to specify the following option
8280 { [a,b,c,d] -> separation_class[[0]->[0]] :
8281 exists b': 0 <= 10a,10b' and
8282 10a+9+10b'+9 <= 100;
8283 [a,b,c,d] -> separation_class[[1]->[0]] :
8284 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
8288 { [a, b, c, d] -> separation_class[[1] -> [0]] :
8289 a >= 0 and b >= 0 and b <= 8 - a;
8290 [a, b, c, d] -> separation_class[[0] -> [0]] :
8293 With this option, the generated AST is as follows
8296 for (int c0 = 0; c0 <= 8; c0 += 1) {
8297 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
8298 for (int c2 = 10 * c0;
8299 c2 <= 10 * c0 + 9; c2 += 1)
8300 for (int c3 = 10 * c1;
8301 c3 <= 10 * c1 + 9; c3 += 1)
8303 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
8304 for (int c2 = 10 * c0;
8305 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8307 for (int c3 = 10 * c1;
8308 c3 <= min(-c2 + 100, 10 * c1 + 9);
8312 for (int c0 = 9; c0 <= 10; c0 += 1)
8313 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8314 for (int c2 = 10 * c0;
8315 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8317 for (int c3 = 10 * c1;
8318 c3 <= min(10 * c1 + 9, -c2 + 100);
8325 This is a single-dimensional space representing the schedule dimension(s)
8326 to which ``separation'' should be applied. Separation tries to split
8327 a loop into several pieces if this can avoid the generation of guards
8329 See also the C<atomic> option.
8333 This is a single-dimensional space representing the schedule dimension(s)
8334 for which the domains should be considered ``atomic''. That is, the
8335 AST generator will make sure that any given domain space will only appear
8336 in a single loop at the specified level.
8338 Consider the following schedule
8340 { a[i] -> [i] : 0 <= i < 10;
8341 b[i] -> [i+1] : 0 <= i < 10 }
8343 If the following option is specified
8345 { [i] -> separate[x] }
8347 then the following AST will be generated
8351 for (int c0 = 1; c0 <= 9; c0 += 1) {
8358 If, on the other hand, the following option is specified
8360 { [i] -> atomic[x] }
8362 then the following AST will be generated
8364 for (int c0 = 0; c0 <= 10; c0 += 1) {
8371 If neither C<atomic> nor C<separate> is specified, then the AST generator
8372 may produce either of these two results or some intermediate form.
8376 This is a single-dimensional space representing the schedule dimension(s)
8377 that should be I<completely> unrolled.
8378 To obtain a partial unrolling, the user should apply an additional
8379 strip-mining to the schedule and fully unroll the inner loop.
8383 Additional control is available through the following functions.
8385 #include <isl/ast_build.h>
8386 __isl_give isl_ast_build *
8387 isl_ast_build_set_iterators(
8388 __isl_take isl_ast_build *control,
8389 __isl_take isl_id_list *iterators);
8391 The function C<isl_ast_build_set_iterators> allows the user to
8392 specify a list of iterator C<isl_id>s to be used as iterators.
8393 If the input schedule is injective, then
8394 the number of elements in this list should be as large as the dimension
8395 of the schedule space, but no direct correspondence should be assumed
8396 between dimensions and elements.
8397 If the input schedule is not injective, then an additional number
8398 of C<isl_id>s equal to the largest dimension of the input domains
8400 If the number of provided C<isl_id>s is insufficient, then additional
8401 names are automatically generated.
8403 #include <isl/ast_build.h>
8404 __isl_give isl_ast_build *
8405 isl_ast_build_set_create_leaf(
8406 __isl_take isl_ast_build *control,
8407 __isl_give isl_ast_node *(*fn)(
8408 __isl_take isl_ast_build *build,
8409 void *user), void *user);
8412 C<isl_ast_build_set_create_leaf> function allows for the
8413 specification of a callback that should be called whenever the AST
8414 generator arrives at an element of the schedule domain.
8415 The callback should return an AST node that should be inserted
8416 at the corresponding position of the AST. The default action (when
8417 the callback is not set) is to continue generating parts of the AST to scan
8418 all the domain elements associated to the schedule domain element
8419 and to insert user nodes, ``calling'' the domain element, for each of them.
8420 The C<build> argument contains the current state of the C<isl_ast_build>.
8421 To ease nested AST generation (see L</"Nested AST Generation">),
8422 all control information that is
8423 specific to the current AST generation such as the options and
8424 the callbacks has been removed from this C<isl_ast_build>.
8425 The callback would typically return the result of a nested
8427 user defined node created using the following function.
8429 #include <isl/ast.h>
8430 __isl_give isl_ast_node *isl_ast_node_alloc_user(
8431 __isl_take isl_ast_expr *expr);
8433 #include <isl/ast_build.h>
8434 __isl_give isl_ast_build *
8435 isl_ast_build_set_at_each_domain(
8436 __isl_take isl_ast_build *build,
8437 __isl_give isl_ast_node *(*fn)(
8438 __isl_take isl_ast_node *node,
8439 __isl_keep isl_ast_build *build,
8440 void *user), void *user);
8441 __isl_give isl_ast_build *
8442 isl_ast_build_set_before_each_for(
8443 __isl_take isl_ast_build *build,
8444 __isl_give isl_id *(*fn)(
8445 __isl_keep isl_ast_build *build,
8446 void *user), void *user);
8447 __isl_give isl_ast_build *
8448 isl_ast_build_set_after_each_for(
8449 __isl_take isl_ast_build *build,
8450 __isl_give isl_ast_node *(*fn)(
8451 __isl_take isl_ast_node *node,
8452 __isl_keep isl_ast_build *build,
8453 void *user), void *user);
8455 The callback set by C<isl_ast_build_set_at_each_domain> will
8456 be called for each domain AST node.
8457 The callbacks set by C<isl_ast_build_set_before_each_for>
8458 and C<isl_ast_build_set_after_each_for> will be called
8459 for each for AST node. The first will be called in depth-first
8460 pre-order, while the second will be called in depth-first post-order.
8461 Since C<isl_ast_build_set_before_each_for> is called before the for
8462 node is actually constructed, it is only passed an C<isl_ast_build>.
8463 The returned C<isl_id> will be added as an annotation (using
8464 C<isl_ast_node_set_annotation>) to the constructed for node.
8465 In particular, if the user has also specified an C<after_each_for>
8466 callback, then the annotation can be retrieved from the node passed to
8467 that callback using C<isl_ast_node_get_annotation>.
8468 All callbacks should C<NULL> on failure.
8469 The given C<isl_ast_build> can be used to create new
8470 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
8471 or C<isl_ast_build_call_from_pw_multi_aff>.
8473 =head3 Nested AST Generation
8475 C<isl> allows the user to create an AST within the context
8476 of another AST. These nested ASTs are created using the
8477 same C<isl_ast_build_ast_from_schedule> function that is used to create the
8478 outer AST. The C<build> argument should be an C<isl_ast_build>
8479 passed to a callback set by
8480 C<isl_ast_build_set_create_leaf>.
8481 The space of the range of the C<schedule> argument should refer
8482 to this build. In particular, the space should be a wrapped
8483 relation and the domain of this wrapped relation should be the
8484 same as that of the range of the schedule returned by
8485 C<isl_ast_build_get_schedule> below.
8486 In practice, the new schedule is typically
8487 created by calling C<isl_union_map_range_product> on the old schedule
8488 and some extra piece of the schedule.
8489 The space of the schedule domain is also available from
8490 the C<isl_ast_build>.
8492 #include <isl/ast_build.h>
8493 __isl_give isl_union_map *isl_ast_build_get_schedule(
8494 __isl_keep isl_ast_build *build);
8495 __isl_give isl_space *isl_ast_build_get_schedule_space(
8496 __isl_keep isl_ast_build *build);
8497 __isl_give isl_ast_build *isl_ast_build_restrict(
8498 __isl_take isl_ast_build *build,
8499 __isl_take isl_set *set);
8501 The C<isl_ast_build_get_schedule> function returns a (partial)
8502 schedule for the domains elements for which part of the AST still needs to
8503 be generated in the current build.
8504 In particular, the domain elements are mapped to those iterations of the loops
8505 enclosing the current point of the AST generation inside which
8506 the domain elements are executed.
8507 No direct correspondence between
8508 the input schedule and this schedule should be assumed.
8509 The space obtained from C<isl_ast_build_get_schedule_space> can be used
8510 to create a set for C<isl_ast_build_restrict> to intersect
8511 with the current build. In particular, the set passed to
8512 C<isl_ast_build_restrict> can have additional parameters.
8513 The ids of the set dimensions in the space returned by
8514 C<isl_ast_build_get_schedule_space> correspond to the
8515 iterators of the already generated loops.
8516 The user should not rely on the ids of the output dimensions
8517 of the relations in the union relation returned by
8518 C<isl_ast_build_get_schedule> having any particular value.
8522 Although C<isl> is mainly meant to be used as a library,
8523 it also contains some basic applications that use some
8524 of the functionality of C<isl>.
8525 The input may be specified in either the L<isl format>
8526 or the L<PolyLib format>.
8528 =head2 C<isl_polyhedron_sample>
8530 C<isl_polyhedron_sample> takes a polyhedron as input and prints
8531 an integer element of the polyhedron, if there is any.
8532 The first column in the output is the denominator and is always
8533 equal to 1. If the polyhedron contains no integer points,
8534 then a vector of length zero is printed.
8538 C<isl_pip> takes the same input as the C<example> program
8539 from the C<piplib> distribution, i.e., a set of constraints
8540 on the parameters, a line containing only -1 and finally a set
8541 of constraints on a parametric polyhedron.
8542 The coefficients of the parameters appear in the last columns
8543 (but before the final constant column).
8544 The output is the lexicographic minimum of the parametric polyhedron.
8545 As C<isl> currently does not have its own output format, the output
8546 is just a dump of the internal state.
8548 =head2 C<isl_polyhedron_minimize>
8550 C<isl_polyhedron_minimize> computes the minimum of some linear
8551 or affine objective function over the integer points in a polyhedron.
8552 If an affine objective function
8553 is given, then the constant should appear in the last column.
8555 =head2 C<isl_polytope_scan>
8557 Given a polytope, C<isl_polytope_scan> prints
8558 all integer points in the polytope.
8560 =head2 C<isl_codegen>
8562 Given a schedule, a context set and an options relation,
8563 C<isl_codegen> prints out an AST that scans the domain elements
8564 of the schedule in the order of their image(s) taking into account
8565 the constraints in the context set.