3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * Objects of type C<isl_union_pw_multi_aff> can no longer contain
216 two or more C<isl_pw_multi_aff> objects with the same domain space.
218 =item * The function C<isl_union_pw_multi_aff_add> now consistently
219 computes the sum on the shared definition domain.
220 The function C<isl_union_pw_multi_aff_union_add> has been added
221 to compute the sum on the union of definition domains.
222 The original behavior of C<isl_union_pw_multi_aff_add> was
223 confused and is no longer available.
229 C<isl> is released under the MIT license.
233 Permission is hereby granted, free of charge, to any person obtaining a copy of
234 this software and associated documentation files (the "Software"), to deal in
235 the Software without restriction, including without limitation the rights to
236 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
237 of the Software, and to permit persons to whom the Software is furnished to do
238 so, subject to the following conditions:
240 The above copyright notice and this permission notice shall be included in all
241 copies or substantial portions of the Software.
243 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
244 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
245 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
246 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
247 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
248 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
253 Note that by default C<isl> requires C<GMP>, which is released
254 under the GNU Lesser General Public License (LGPL). This means
255 that code linked against C<isl> is also linked against LGPL code.
257 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
258 library for exact integer arithmetic released under the MIT license.
262 The source of C<isl> can be obtained either as a tarball
263 or from the git repository. Both are available from
264 L<http://freshmeat.net/projects/isl/>.
265 The installation process depends on how you obtained
268 =head2 Installation from the git repository
272 =item 1 Clone or update the repository
274 The first time the source is obtained, you need to clone
277 git clone git://repo.or.cz/isl.git
279 To obtain updates, you need to pull in the latest changes
283 =item 2 Optionally get C<imath> submodule
285 To build C<isl> with C<imath>, you need to obtain the C<imath>
286 submodule by running in the git source tree of C<isl>
291 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
293 =item 2 Generate C<configure>
299 After performing the above steps, continue
300 with the L<Common installation instructions>.
302 =head2 Common installation instructions
306 =item 1 Obtain C<GMP>
308 By default, building C<isl> requires C<GMP>, including its headers files.
309 Your distribution may not provide these header files by default
310 and you may need to install a package called C<gmp-devel> or something
311 similar. Alternatively, C<GMP> can be built from
312 source, available from L<http://gmplib.org/>.
313 C<GMP> is not needed if you build C<isl> with C<imath>.
317 C<isl> uses the standard C<autoconf> C<configure> script.
322 optionally followed by some configure options.
323 A complete list of options can be obtained by running
327 Below we discuss some of the more common options.
333 Installation prefix for C<isl>
335 =item C<--with-int=[gmp|imath]>
337 Select the integer library to be used by C<isl>, the default is C<gmp>.
338 Note that C<isl> may run significantly slower if you use C<imath>.
340 =item C<--with-gmp-prefix>
342 Installation prefix for C<GMP> (architecture-independent files).
344 =item C<--with-gmp-exec-prefix>
346 Installation prefix for C<GMP> (architecture-dependent files).
354 =item 4 Install (optional)
360 =head1 Integer Set Library
362 =head2 Memory Management
364 Since a high-level operation on isl objects usually involves
365 several substeps and since the user is usually not interested in
366 the intermediate results, most functions that return a new object
367 will also release all the objects passed as arguments.
368 If the user still wants to use one or more of these arguments
369 after the function call, she should pass along a copy of the
370 object rather than the object itself.
371 The user is then responsible for making sure that the original
372 object gets used somewhere else or is explicitly freed.
374 The arguments and return values of all documented functions are
375 annotated to make clear which arguments are released and which
376 arguments are preserved. In particular, the following annotations
383 C<__isl_give> means that a new object is returned.
384 The user should make sure that the returned pointer is
385 used exactly once as a value for an C<__isl_take> argument.
386 In between, it can be used as a value for as many
387 C<__isl_keep> arguments as the user likes.
388 There is one exception, and that is the case where the
389 pointer returned is C<NULL>. Is this case, the user
390 is free to use it as an C<__isl_take> argument or not.
391 When applied to a C<char *>, the returned pointer needs to be
396 C<__isl_null> means that a C<NULL> value is returned.
400 C<__isl_take> means that the object the argument points to
401 is taken over by the function and may no longer be used
402 by the user as an argument to any other function.
403 The pointer value must be one returned by a function
404 returning an C<__isl_give> pointer.
405 If the user passes in a C<NULL> value, then this will
406 be treated as an error in the sense that the function will
407 not perform its usual operation. However, it will still
408 make sure that all the other C<__isl_take> arguments
413 C<__isl_keep> means that the function will only use the object
414 temporarily. After the function has finished, the user
415 can still use it as an argument to other functions.
416 A C<NULL> value will be treated in the same way as
417 a C<NULL> value for an C<__isl_take> argument.
418 This annotation may also be used on return values of
419 type C<const char *>, in which case the returned pointer should
420 not be freed by the user and is only valid until the object
421 from which it was derived is updated or freed.
425 =head2 Initialization
427 All manipulations of integer sets and relations occur within
428 the context of an C<isl_ctx>.
429 A given C<isl_ctx> can only be used within a single thread.
430 All arguments of a function are required to have been allocated
431 within the same context.
432 There are currently no functions available for moving an object
433 from one C<isl_ctx> to another C<isl_ctx>. This means that
434 there is currently no way of safely moving an object from one
435 thread to another, unless the whole C<isl_ctx> is moved.
437 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
438 freed using C<isl_ctx_free>.
439 All objects allocated within an C<isl_ctx> should be freed
440 before the C<isl_ctx> itself is freed.
442 isl_ctx *isl_ctx_alloc();
443 void isl_ctx_free(isl_ctx *ctx);
445 The user can impose a bound on the number of low-level I<operations>
446 that can be performed by an C<isl_ctx>. This bound can be set and
447 retrieved using the following functions. A bound of zero means that
448 no bound is imposed. The number of operations performed can be
449 reset using C<isl_ctx_reset_operations>. Note that the number
450 of low-level operations needed to perform a high-level computation
451 may differ significantly across different versions
452 of C<isl>, but it should be the same across different platforms
453 for the same version of C<isl>.
455 Warning: This feature is experimental. C<isl> has good support to abort and
456 bail out during the computation, but this feature may exercise error code paths
457 that are normally not used that much. Consequently, it is not unlikely that
458 hidden bugs will be exposed.
460 void isl_ctx_set_max_operations(isl_ctx *ctx,
461 unsigned long max_operations);
462 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
463 void isl_ctx_reset_operations(isl_ctx *ctx);
465 In order to be able to create an object in the same context
466 as another object, most object types (described later in
467 this document) provide a function to obtain the context
468 in which the object was created.
471 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
472 isl_ctx *isl_multi_val_get_ctx(
473 __isl_keep isl_multi_val *mv);
476 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
478 #include <isl/local_space.h>
479 isl_ctx *isl_local_space_get_ctx(
480 __isl_keep isl_local_space *ls);
483 isl_ctx *isl_set_list_get_ctx(
484 __isl_keep isl_set_list *list);
487 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
488 isl_ctx *isl_multi_aff_get_ctx(
489 __isl_keep isl_multi_aff *maff);
490 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
491 isl_ctx *isl_pw_multi_aff_get_ctx(
492 __isl_keep isl_pw_multi_aff *pma);
493 isl_ctx *isl_multi_pw_aff_get_ctx(
494 __isl_keep isl_multi_pw_aff *mpa);
495 isl_ctx *isl_union_pw_aff_get_ctx(
496 __isl_keep isl_union_pw_aff *upa);
497 isl_ctx *isl_union_pw_multi_aff_get_ctx(
498 __isl_keep isl_union_pw_multi_aff *upma);
499 isl_ctx *isl_multi_union_pw_aff_get_ctx(
500 __isl_keep isl_multi_union_pw_aff *mupa);
502 #include <isl/id_to_ast_expr.h>
503 isl_ctx *isl_id_to_ast_expr_get_ctx(
504 __isl_keep id_to_ast_expr *id2expr);
506 #include <isl/point.h>
507 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
510 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
513 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
515 #include <isl/vertices.h>
516 isl_ctx *isl_vertices_get_ctx(
517 __isl_keep isl_vertices *vertices);
518 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
519 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
521 #include <isl/flow.h>
522 isl_ctx *isl_restriction_get_ctx(
523 __isl_keep isl_restriction *restr);
525 #include <isl/schedule.h>
526 isl_ctx *isl_schedule_constraints_get_ctx(
527 __isl_keep isl_schedule_constraints *sc);
529 #include <isl/band.h>
530 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
532 #include <isl/ast_build.h>
533 isl_ctx *isl_ast_build_get_ctx(
534 __isl_keep isl_ast_build *build);
537 isl_ctx *isl_ast_expr_get_ctx(
538 __isl_keep isl_ast_expr *expr);
539 isl_ctx *isl_ast_node_get_ctx(
540 __isl_keep isl_ast_node *node);
544 An C<isl_val> represents an integer value, a rational value
545 or one of three special values, infinity, negative infinity and NaN.
546 Some predefined values can be created using the following functions.
549 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
550 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
551 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
552 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
553 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
554 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
556 Specific integer values can be created using the following functions.
559 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
561 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
563 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
564 size_t n, size_t size, const void *chunks);
566 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
567 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
568 The least significant digit is assumed to be stored first.
570 Value objects can be copied and freed using the following functions.
573 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
574 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
576 They can be inspected using the following functions.
579 long isl_val_get_num_si(__isl_keep isl_val *v);
580 long isl_val_get_den_si(__isl_keep isl_val *v);
581 double isl_val_get_d(__isl_keep isl_val *v);
582 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
584 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
585 size_t size, void *chunks);
587 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
588 of C<size> bytes needed to store the absolute value of the
590 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
591 which is assumed to have been preallocated by the caller.
592 The least significant digit is stored first.
593 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
594 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
595 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
597 An C<isl_val> can be modified using the following function.
600 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
603 The following unary properties are defined on C<isl_val>s.
606 int isl_val_sgn(__isl_keep isl_val *v);
607 int isl_val_is_zero(__isl_keep isl_val *v);
608 int isl_val_is_one(__isl_keep isl_val *v);
609 int isl_val_is_negone(__isl_keep isl_val *v);
610 int isl_val_is_nonneg(__isl_keep isl_val *v);
611 int isl_val_is_nonpos(__isl_keep isl_val *v);
612 int isl_val_is_pos(__isl_keep isl_val *v);
613 int isl_val_is_neg(__isl_keep isl_val *v);
614 int isl_val_is_int(__isl_keep isl_val *v);
615 int isl_val_is_rat(__isl_keep isl_val *v);
616 int isl_val_is_nan(__isl_keep isl_val *v);
617 int isl_val_is_infty(__isl_keep isl_val *v);
618 int isl_val_is_neginfty(__isl_keep isl_val *v);
620 Note that the sign of NaN is undefined.
622 The following binary properties are defined on pairs of C<isl_val>s.
625 int isl_val_lt(__isl_keep isl_val *v1,
626 __isl_keep isl_val *v2);
627 int isl_val_le(__isl_keep isl_val *v1,
628 __isl_keep isl_val *v2);
629 int isl_val_gt(__isl_keep isl_val *v1,
630 __isl_keep isl_val *v2);
631 int isl_val_ge(__isl_keep isl_val *v1,
632 __isl_keep isl_val *v2);
633 int isl_val_eq(__isl_keep isl_val *v1,
634 __isl_keep isl_val *v2);
635 int isl_val_ne(__isl_keep isl_val *v1,
636 __isl_keep isl_val *v2);
637 int isl_val_abs_eq(__isl_keep isl_val *v1,
638 __isl_keep isl_val *v2);
640 The function C<isl_val_abs_eq> checks whether its two arguments
641 are equal in absolute value.
643 For integer C<isl_val>s we additionally have the following binary property.
646 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
647 __isl_keep isl_val *v2);
649 An C<isl_val> can also be compared to an integer using the following
650 function. The result is undefined for NaN.
653 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
655 The following unary operations are available on C<isl_val>s.
658 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
659 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
660 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
661 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
662 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
663 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
664 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
666 The following binary operations are available on C<isl_val>s.
669 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
670 __isl_take isl_val *v2);
671 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
672 __isl_take isl_val *v2);
673 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
674 __isl_take isl_val *v2);
675 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
677 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
678 __isl_take isl_val *v2);
679 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
681 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
682 __isl_take isl_val *v2);
683 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
685 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
686 __isl_take isl_val *v2);
688 On integer values, we additionally have the following operations.
691 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
692 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
693 __isl_take isl_val *v2);
694 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
695 __isl_take isl_val *v2);
696 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
697 __isl_take isl_val *v2, __isl_give isl_val **x,
698 __isl_give isl_val **y);
700 The function C<isl_val_gcdext> returns the greatest common divisor g
701 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
702 that C<*x> * C<v1> + C<*y> * C<v2> = g.
704 =head3 GMP specific functions
706 These functions are only available if C<isl> has been compiled with C<GMP>
709 Specific integer and rational values can be created from C<GMP> values using
710 the following functions.
712 #include <isl/val_gmp.h>
713 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
715 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
716 const mpz_t n, const mpz_t d);
718 The numerator and denominator of a rational value can be extracted as
719 C<GMP> values using the following functions.
721 #include <isl/val_gmp.h>
722 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
723 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
725 =head2 Sets and Relations
727 C<isl> uses six types of objects for representing sets and relations,
728 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
729 C<isl_union_set> and C<isl_union_map>.
730 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
731 can be described as a conjunction of affine constraints, while
732 C<isl_set> and C<isl_map> represent unions of
733 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
734 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
735 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
736 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
737 where spaces are considered different if they have a different number
738 of dimensions and/or different names (see L<"Spaces">).
739 The difference between sets and relations (maps) is that sets have
740 one set of variables, while relations have two sets of variables,
741 input variables and output variables.
743 =head2 Error Handling
745 C<isl> supports different ways to react in case a runtime error is triggered.
746 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
747 with two maps that have incompatible spaces. There are three possible ways
748 to react on error: to warn, to continue or to abort.
750 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
751 the last error in the corresponding C<isl_ctx> and the function in which the
752 error was triggered returns C<NULL>. An error does not corrupt internal state,
753 such that isl can continue to be used. C<isl> also provides functions to
754 read the last error and to reset the memory that stores the last error. The
755 last error is only stored for information purposes. Its presence does not
756 change the behavior of C<isl>. Hence, resetting an error is not required to
757 continue to use isl, but only to observe new errors.
760 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
761 void isl_ctx_reset_error(isl_ctx *ctx);
763 Another option is to continue on error. This is similar to warn on error mode,
764 except that C<isl> does not print any warning. This allows a program to
765 implement its own error reporting.
767 The last option is to directly abort the execution of the program from within
768 the isl library. This makes it obviously impossible to recover from an error,
769 but it allows to directly spot the error location. By aborting on error,
770 debuggers break at the location the error occurred and can provide a stack
771 trace. Other tools that automatically provide stack traces on abort or that do
772 not want to continue execution after an error was triggered may also prefer to
775 The on error behavior of isl can be specified by calling
776 C<isl_options_set_on_error> or by setting the command line option
777 C<--isl-on-error>. Valid arguments for the function call are
778 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
779 choices for the command line option are C<warn>, C<continue> and C<abort>.
780 It is also possible to query the current error mode.
782 #include <isl/options.h>
783 int isl_options_set_on_error(isl_ctx *ctx, int val);
784 int isl_options_get_on_error(isl_ctx *ctx);
788 Identifiers are used to identify both individual dimensions
789 and tuples of dimensions. They consist of an optional name and an optional
790 user pointer. The name and the user pointer cannot both be C<NULL>, however.
791 Identifiers with the same name but different pointer values
792 are considered to be distinct.
793 Similarly, identifiers with different names but the same pointer value
794 are also considered to be distinct.
795 Equal identifiers are represented using the same object.
796 Pairs of identifiers can therefore be tested for equality using the
798 Identifiers can be constructed, copied, freed, inspected and printed
799 using the following functions.
802 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
803 __isl_keep const char *name, void *user);
804 __isl_give isl_id *isl_id_set_free_user(
805 __isl_take isl_id *id,
806 __isl_give void (*free_user)(void *user));
807 __isl_give isl_id *isl_id_copy(isl_id *id);
808 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
810 void *isl_id_get_user(__isl_keep isl_id *id);
811 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
813 __isl_give isl_printer *isl_printer_print_id(
814 __isl_take isl_printer *p, __isl_keep isl_id *id);
816 The callback set by C<isl_id_set_free_user> is called on the user
817 pointer when the last reference to the C<isl_id> is freed.
818 Note that C<isl_id_get_name> returns a pointer to some internal
819 data structure, so the result can only be used while the
820 corresponding C<isl_id> is alive.
824 Whenever a new set, relation or similar object is created from scratch,
825 the space in which it lives needs to be specified using an C<isl_space>.
826 Each space involves zero or more parameters and zero, one or two
827 tuples of set or input/output dimensions. The parameters and dimensions
828 are identified by an C<isl_dim_type> and a position.
829 The type C<isl_dim_param> refers to parameters,
830 the type C<isl_dim_set> refers to set dimensions (for spaces
831 with a single tuple of dimensions) and the types C<isl_dim_in>
832 and C<isl_dim_out> refer to input and output dimensions
833 (for spaces with two tuples of dimensions).
834 Local spaces (see L</"Local Spaces">) also contain dimensions
835 of type C<isl_dim_div>.
836 Note that parameters are only identified by their position within
837 a given object. Across different objects, parameters are (usually)
838 identified by their names or identifiers. Only unnamed parameters
839 are identified by their positions across objects. The use of unnamed
840 parameters is discouraged.
842 #include <isl/space.h>
843 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
844 unsigned nparam, unsigned n_in, unsigned n_out);
845 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
847 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
848 unsigned nparam, unsigned dim);
849 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
850 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
852 The space used for creating a parameter domain
853 needs to be created using C<isl_space_params_alloc>.
854 For other sets, the space
855 needs to be created using C<isl_space_set_alloc>, while
856 for a relation, the space
857 needs to be created using C<isl_space_alloc>.
859 To check whether a given space is that of a set or a map
860 or whether it is a parameter space, use these functions:
862 #include <isl/space.h>
863 int isl_space_is_params(__isl_keep isl_space *space);
864 int isl_space_is_set(__isl_keep isl_space *space);
865 int isl_space_is_map(__isl_keep isl_space *space);
867 Spaces can be compared using the following functions:
869 #include <isl/space.h>
870 int isl_space_is_equal(__isl_keep isl_space *space1,
871 __isl_keep isl_space *space2);
872 int isl_space_is_domain(__isl_keep isl_space *space1,
873 __isl_keep isl_space *space2);
874 int isl_space_is_range(__isl_keep isl_space *space1,
875 __isl_keep isl_space *space2);
876 int isl_space_tuple_is_equal(
877 __isl_keep isl_space *space1,
878 enum isl_dim_type type1,
879 __isl_keep isl_space *space2,
880 enum isl_dim_type type2);
882 C<isl_space_is_domain> checks whether the first argument is equal
883 to the domain of the second argument. This requires in particular that
884 the first argument is a set space and that the second argument
885 is a map space. C<isl_space_tuple_is_equal> checks whether the given
886 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
887 spaces are the same. That is, it checks if they have the same
888 identifier (if any), the same dimension and the same internal structure
891 It is often useful to create objects that live in the
892 same space as some other object. This can be accomplished
893 by creating the new objects
894 (see L</"Creating New Sets and Relations"> or
895 L</"Functions">) based on the space
896 of the original object.
899 __isl_give isl_space *isl_basic_set_get_space(
900 __isl_keep isl_basic_set *bset);
901 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
903 #include <isl/union_set.h>
904 __isl_give isl_space *isl_union_set_get_space(
905 __isl_keep isl_union_set *uset);
908 __isl_give isl_space *isl_basic_map_get_space(
909 __isl_keep isl_basic_map *bmap);
910 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
912 #include <isl/union_map.h>
913 __isl_give isl_space *isl_union_map_get_space(
914 __isl_keep isl_union_map *umap);
916 #include <isl/constraint.h>
917 __isl_give isl_space *isl_constraint_get_space(
918 __isl_keep isl_constraint *constraint);
920 #include <isl/polynomial.h>
921 __isl_give isl_space *isl_qpolynomial_get_domain_space(
922 __isl_keep isl_qpolynomial *qp);
923 __isl_give isl_space *isl_qpolynomial_get_space(
924 __isl_keep isl_qpolynomial *qp);
925 __isl_give isl_space *isl_qpolynomial_fold_get_space(
926 __isl_keep isl_qpolynomial_fold *fold);
927 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
928 __isl_keep isl_pw_qpolynomial *pwqp);
929 __isl_give isl_space *isl_pw_qpolynomial_get_space(
930 __isl_keep isl_pw_qpolynomial *pwqp);
931 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
932 __isl_keep isl_pw_qpolynomial_fold *pwf);
933 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
934 __isl_keep isl_pw_qpolynomial_fold *pwf);
935 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
936 __isl_keep isl_union_pw_qpolynomial *upwqp);
937 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
938 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
941 __isl_give isl_space *isl_multi_val_get_space(
942 __isl_keep isl_multi_val *mv);
945 __isl_give isl_space *isl_aff_get_domain_space(
946 __isl_keep isl_aff *aff);
947 __isl_give isl_space *isl_aff_get_space(
948 __isl_keep isl_aff *aff);
949 __isl_give isl_space *isl_pw_aff_get_domain_space(
950 __isl_keep isl_pw_aff *pwaff);
951 __isl_give isl_space *isl_pw_aff_get_space(
952 __isl_keep isl_pw_aff *pwaff);
953 __isl_give isl_space *isl_multi_aff_get_domain_space(
954 __isl_keep isl_multi_aff *maff);
955 __isl_give isl_space *isl_multi_aff_get_space(
956 __isl_keep isl_multi_aff *maff);
957 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
958 __isl_keep isl_pw_multi_aff *pma);
959 __isl_give isl_space *isl_pw_multi_aff_get_space(
960 __isl_keep isl_pw_multi_aff *pma);
961 __isl_give isl_space *isl_union_pw_aff_get_space(
962 __isl_keep isl_union_pw_aff *upa);
963 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
964 __isl_keep isl_union_pw_multi_aff *upma);
965 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
966 __isl_keep isl_multi_pw_aff *mpa);
967 __isl_give isl_space *isl_multi_pw_aff_get_space(
968 __isl_keep isl_multi_pw_aff *mpa);
969 __isl_give isl_space *
970 isl_multi_union_pw_aff_get_domain_space(
971 __isl_keep isl_multi_union_pw_aff *mupa);
972 __isl_give isl_space *
973 isl_multi_union_pw_aff_get_space(
974 __isl_keep isl_multi_union_pw_aff *mupa);
976 #include <isl/point.h>
977 __isl_give isl_space *isl_point_get_space(
978 __isl_keep isl_point *pnt);
980 The number of dimensions of a given type of space
981 may be read off from a space or an object that lives
982 in a space using the following functions.
983 In case of C<isl_space_dim>, type may be
984 C<isl_dim_param>, C<isl_dim_in> (only for relations),
985 C<isl_dim_out> (only for relations), C<isl_dim_set>
986 (only for sets) or C<isl_dim_all>.
988 #include <isl/space.h>
989 unsigned isl_space_dim(__isl_keep isl_space *space,
990 enum isl_dim_type type);
992 #include <isl/local_space.h>
993 int isl_local_space_dim(__isl_keep isl_local_space *ls,
994 enum isl_dim_type type);
997 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
998 enum isl_dim_type type);
999 unsigned isl_set_dim(__isl_keep isl_set *set,
1000 enum isl_dim_type type);
1002 #include <isl/union_set.h>
1003 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1004 enum isl_dim_type type);
1006 #include <isl/map.h>
1007 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1008 enum isl_dim_type type);
1009 unsigned isl_map_dim(__isl_keep isl_map *map,
1010 enum isl_dim_type type);
1012 #include <isl/union_map.h>
1013 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1014 enum isl_dim_type type);
1016 #include <isl/val.h>
1017 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1018 enum isl_dim_type type);
1020 #include <isl/aff.h>
1021 int isl_aff_dim(__isl_keep isl_aff *aff,
1022 enum isl_dim_type type);
1023 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1024 enum isl_dim_type type);
1025 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1026 enum isl_dim_type type);
1027 unsigned isl_pw_multi_aff_dim(
1028 __isl_keep isl_pw_multi_aff *pma,
1029 enum isl_dim_type type);
1030 unsigned isl_multi_pw_aff_dim(
1031 __isl_keep isl_multi_pw_aff *mpa,
1032 enum isl_dim_type type);
1033 unsigned isl_union_pw_aff_dim(
1034 __isl_keep isl_union_pw_aff *upa,
1035 enum isl_dim_type type);
1036 unsigned isl_union_pw_multi_aff_dim(
1037 __isl_keep isl_union_pw_multi_aff *upma,
1038 enum isl_dim_type type);
1039 unsigned isl_multi_union_pw_aff_dim(
1040 __isl_keep isl_multi_union_pw_aff *mupa,
1041 enum isl_dim_type type);
1043 #include <isl/polynomial.h>
1044 unsigned isl_union_pw_qpolynomial_dim(
1045 __isl_keep isl_union_pw_qpolynomial *upwqp,
1046 enum isl_dim_type type);
1047 unsigned isl_union_pw_qpolynomial_fold_dim(
1048 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1049 enum isl_dim_type type);
1051 Note that an C<isl_union_set>, an C<isl_union_map>,
1052 an C<isl_union_pw_multi_aff>,
1053 an C<isl_union_pw_qpolynomial> and
1054 an C<isl_union_pw_qpolynomial_fold>
1055 only have parameters.
1057 The identifiers or names of the individual dimensions of spaces
1058 may be set or read off using the following functions on spaces
1059 or objects that live in spaces.
1060 These functions are mostly useful to obtain the identifiers, positions
1061 or names of the parameters. Identifiers of individual dimensions are
1062 essentially only useful for printing. They are ignored by all other
1063 operations and may not be preserved across those operations.
1065 #include <isl/space.h>
1066 __isl_give isl_space *isl_space_set_dim_id(
1067 __isl_take isl_space *space,
1068 enum isl_dim_type type, unsigned pos,
1069 __isl_take isl_id *id);
1070 int isl_space_has_dim_id(__isl_keep isl_space *space,
1071 enum isl_dim_type type, unsigned pos);
1072 __isl_give isl_id *isl_space_get_dim_id(
1073 __isl_keep isl_space *space,
1074 enum isl_dim_type type, unsigned pos);
1075 __isl_give isl_space *isl_space_set_dim_name(
1076 __isl_take isl_space *space,
1077 enum isl_dim_type type, unsigned pos,
1078 __isl_keep const char *name);
1079 int isl_space_has_dim_name(__isl_keep isl_space *space,
1080 enum isl_dim_type type, unsigned pos);
1081 __isl_keep const char *isl_space_get_dim_name(
1082 __isl_keep isl_space *space,
1083 enum isl_dim_type type, unsigned pos);
1085 #include <isl/local_space.h>
1086 __isl_give isl_local_space *isl_local_space_set_dim_id(
1087 __isl_take isl_local_space *ls,
1088 enum isl_dim_type type, unsigned pos,
1089 __isl_take isl_id *id);
1090 int isl_local_space_has_dim_id(
1091 __isl_keep isl_local_space *ls,
1092 enum isl_dim_type type, unsigned pos);
1093 __isl_give isl_id *isl_local_space_get_dim_id(
1094 __isl_keep isl_local_space *ls,
1095 enum isl_dim_type type, unsigned pos);
1096 __isl_give isl_local_space *isl_local_space_set_dim_name(
1097 __isl_take isl_local_space *ls,
1098 enum isl_dim_type type, unsigned pos, const char *s);
1099 int isl_local_space_has_dim_name(
1100 __isl_keep isl_local_space *ls,
1101 enum isl_dim_type type, unsigned pos)
1102 const char *isl_local_space_get_dim_name(
1103 __isl_keep isl_local_space *ls,
1104 enum isl_dim_type type, unsigned pos);
1106 #include <isl/constraint.h>
1107 const char *isl_constraint_get_dim_name(
1108 __isl_keep isl_constraint *constraint,
1109 enum isl_dim_type type, unsigned pos);
1111 #include <isl/set.h>
1112 __isl_give isl_id *isl_basic_set_get_dim_id(
1113 __isl_keep isl_basic_set *bset,
1114 enum isl_dim_type type, unsigned pos);
1115 __isl_give isl_set *isl_set_set_dim_id(
1116 __isl_take isl_set *set, enum isl_dim_type type,
1117 unsigned pos, __isl_take isl_id *id);
1118 int isl_set_has_dim_id(__isl_keep isl_set *set,
1119 enum isl_dim_type type, unsigned pos);
1120 __isl_give isl_id *isl_set_get_dim_id(
1121 __isl_keep isl_set *set, enum isl_dim_type type,
1123 const char *isl_basic_set_get_dim_name(
1124 __isl_keep isl_basic_set *bset,
1125 enum isl_dim_type type, unsigned pos);
1126 int isl_set_has_dim_name(__isl_keep isl_set *set,
1127 enum isl_dim_type type, unsigned pos);
1128 const char *isl_set_get_dim_name(
1129 __isl_keep isl_set *set,
1130 enum isl_dim_type type, unsigned pos);
1132 #include <isl/map.h>
1133 __isl_give isl_map *isl_map_set_dim_id(
1134 __isl_take isl_map *map, enum isl_dim_type type,
1135 unsigned pos, __isl_take isl_id *id);
1136 int isl_basic_map_has_dim_id(
1137 __isl_keep isl_basic_map *bmap,
1138 enum isl_dim_type type, unsigned pos);
1139 int isl_map_has_dim_id(__isl_keep isl_map *map,
1140 enum isl_dim_type type, unsigned pos);
1141 __isl_give isl_id *isl_map_get_dim_id(
1142 __isl_keep isl_map *map, enum isl_dim_type type,
1144 __isl_give isl_id *isl_union_map_get_dim_id(
1145 __isl_keep isl_union_map *umap,
1146 enum isl_dim_type type, unsigned pos);
1147 const char *isl_basic_map_get_dim_name(
1148 __isl_keep isl_basic_map *bmap,
1149 enum isl_dim_type type, unsigned pos);
1150 int isl_map_has_dim_name(__isl_keep isl_map *map,
1151 enum isl_dim_type type, unsigned pos);
1152 const char *isl_map_get_dim_name(
1153 __isl_keep isl_map *map,
1154 enum isl_dim_type type, unsigned pos);
1156 #include <isl/val.h>
1157 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1158 __isl_take isl_multi_val *mv,
1159 enum isl_dim_type type, unsigned pos,
1160 __isl_take isl_id *id);
1161 __isl_give isl_id *isl_multi_val_get_dim_id(
1162 __isl_keep isl_multi_val *mv,
1163 enum isl_dim_type type, unsigned pos);
1164 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1165 __isl_take isl_multi_val *mv,
1166 enum isl_dim_type type, unsigned pos, const char *s);
1168 #include <isl/aff.h>
1169 __isl_give isl_aff *isl_aff_set_dim_id(
1170 __isl_take isl_aff *aff, enum isl_dim_type type,
1171 unsigned pos, __isl_take isl_id *id);
1172 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1173 __isl_take isl_multi_aff *maff,
1174 enum isl_dim_type type, unsigned pos,
1175 __isl_take isl_id *id);
1176 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1177 __isl_take isl_pw_aff *pma,
1178 enum isl_dim_type type, unsigned pos,
1179 __isl_take isl_id *id);
1180 __isl_give isl_multi_pw_aff *
1181 isl_multi_pw_aff_set_dim_id(
1182 __isl_take isl_multi_pw_aff *mpa,
1183 enum isl_dim_type type, unsigned pos,
1184 __isl_take isl_id *id);
1185 __isl_give isl_multi_union_pw_aff *
1186 isl_multi_union_pw_aff_set_dim_id(
1187 __isl_take isl_multi_union_pw_aff *mupa,
1188 enum isl_dim_type type, unsigned pos,
1189 __isl_take isl_id *id);
1190 __isl_give isl_id *isl_multi_aff_get_dim_id(
1191 __isl_keep isl_multi_aff *ma,
1192 enum isl_dim_type type, unsigned pos);
1193 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1194 enum isl_dim_type type, unsigned pos);
1195 __isl_give isl_id *isl_pw_aff_get_dim_id(
1196 __isl_keep isl_pw_aff *pa,
1197 enum isl_dim_type type, unsigned pos);
1198 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1199 __isl_keep isl_pw_multi_aff *pma,
1200 enum isl_dim_type type, unsigned pos);
1201 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1202 __isl_keep isl_multi_pw_aff *mpa,
1203 enum isl_dim_type type, unsigned pos);
1204 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1205 __isl_keep isl_multi_union_pw_aff *mupa,
1206 enum isl_dim_type type, unsigned pos);
1207 __isl_give isl_aff *isl_aff_set_dim_name(
1208 __isl_take isl_aff *aff, enum isl_dim_type type,
1209 unsigned pos, const char *s);
1210 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1211 __isl_take isl_multi_aff *maff,
1212 enum isl_dim_type type, unsigned pos, const char *s);
1213 __isl_give isl_multi_pw_aff *
1214 isl_multi_pw_aff_set_dim_name(
1215 __isl_take isl_multi_pw_aff *mpa,
1216 enum isl_dim_type type, unsigned pos, const char *s);
1217 __isl_give isl_union_pw_aff *
1218 isl_union_pw_aff_set_dim_name(
1219 __isl_take isl_union_pw_aff *upa,
1220 enum isl_dim_type type, unsigned pos,
1222 __isl_give isl_union_pw_multi_aff *
1223 isl_union_pw_multi_aff_set_dim_name(
1224 __isl_take isl_union_pw_multi_aff *upma,
1225 enum isl_dim_type type, unsigned pos,
1227 __isl_give isl_multi_union_pw_aff *
1228 isl_multi_union_pw_aff_set_dim_name(
1229 __isl_take isl_multi_union_pw_aff *mupa,
1230 enum isl_dim_type type, unsigned pos,
1231 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1232 enum isl_dim_type type, unsigned pos);
1233 const char *isl_pw_aff_get_dim_name(
1234 __isl_keep isl_pw_aff *pa,
1235 enum isl_dim_type type, unsigned pos);
1236 const char *isl_pw_multi_aff_get_dim_name(
1237 __isl_keep isl_pw_multi_aff *pma,
1238 enum isl_dim_type type, unsigned pos);
1240 #include <isl/polynomial.h>
1241 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1242 __isl_take isl_qpolynomial *qp,
1243 enum isl_dim_type type, unsigned pos,
1245 __isl_give isl_pw_qpolynomial *
1246 isl_pw_qpolynomial_set_dim_name(
1247 __isl_take isl_pw_qpolynomial *pwqp,
1248 enum isl_dim_type type, unsigned pos,
1250 __isl_give isl_pw_qpolynomial_fold *
1251 isl_pw_qpolynomial_fold_set_dim_name(
1252 __isl_take isl_pw_qpolynomial_fold *pwf,
1253 enum isl_dim_type type, unsigned pos,
1255 __isl_give isl_union_pw_qpolynomial *
1256 isl_union_pw_qpolynomial_set_dim_name(
1257 __isl_take isl_union_pw_qpolynomial *upwqp,
1258 enum isl_dim_type type, unsigned pos,
1260 __isl_give isl_union_pw_qpolynomial_fold *
1261 isl_union_pw_qpolynomial_fold_set_dim_name(
1262 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1263 enum isl_dim_type type, unsigned pos,
1266 Note that C<isl_space_get_name> returns a pointer to some internal
1267 data structure, so the result can only be used while the
1268 corresponding C<isl_space> is alive.
1269 Also note that every function that operates on two sets or relations
1270 requires that both arguments have the same parameters. This also
1271 means that if one of the arguments has named parameters, then the
1272 other needs to have named parameters too and the names need to match.
1273 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1274 arguments may have different parameters (as long as they are named),
1275 in which case the result will have as parameters the union of the parameters of
1278 Given the identifier or name of a dimension (typically a parameter),
1279 its position can be obtained from the following functions.
1281 #include <isl/space.h>
1282 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1283 enum isl_dim_type type, __isl_keep isl_id *id);
1284 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1285 enum isl_dim_type type, const char *name);
1287 #include <isl/local_space.h>
1288 int isl_local_space_find_dim_by_name(
1289 __isl_keep isl_local_space *ls,
1290 enum isl_dim_type type, const char *name);
1292 #include <isl/val.h>
1293 int isl_multi_val_find_dim_by_id(
1294 __isl_keep isl_multi_val *mv,
1295 enum isl_dim_type type, __isl_keep isl_id *id);
1296 int isl_multi_val_find_dim_by_name(
1297 __isl_keep isl_multi_val *mv,
1298 enum isl_dim_type type, const char *name);
1300 #include <isl/set.h>
1301 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1302 enum isl_dim_type type, __isl_keep isl_id *id);
1303 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1304 enum isl_dim_type type, const char *name);
1306 #include <isl/map.h>
1307 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1308 enum isl_dim_type type, __isl_keep isl_id *id);
1309 int isl_basic_map_find_dim_by_name(
1310 __isl_keep isl_basic_map *bmap,
1311 enum isl_dim_type type, const char *name);
1312 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1313 enum isl_dim_type type, const char *name);
1314 int isl_union_map_find_dim_by_name(
1315 __isl_keep isl_union_map *umap,
1316 enum isl_dim_type type, const char *name);
1318 #include <isl/aff.h>
1319 int isl_multi_aff_find_dim_by_id(
1320 __isl_keep isl_multi_aff *ma,
1321 enum isl_dim_type type, __isl_keep isl_id *id);
1322 int isl_multi_pw_aff_find_dim_by_id(
1323 __isl_keep isl_multi_pw_aff *mpa,
1324 enum isl_dim_type type, __isl_keep isl_id *id);
1325 int isl_multi_union_pw_aff_find_dim_by_id(
1326 __isl_keep isl_union_multi_pw_aff *mupa,
1327 enum isl_dim_type type, __isl_keep isl_id *id);
1328 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1329 enum isl_dim_type type, const char *name);
1330 int isl_multi_aff_find_dim_by_name(
1331 __isl_keep isl_multi_aff *ma,
1332 enum isl_dim_type type, const char *name);
1333 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1334 enum isl_dim_type type, const char *name);
1335 int isl_multi_pw_aff_find_dim_by_name(
1336 __isl_keep isl_multi_pw_aff *mpa,
1337 enum isl_dim_type type, const char *name);
1338 int isl_pw_multi_aff_find_dim_by_name(
1339 __isl_keep isl_pw_multi_aff *pma,
1340 enum isl_dim_type type, const char *name);
1341 int isl_union_pw_aff_find_dim_by_name(
1342 __isl_keep isl_union_pw_aff *upa,
1343 enum isl_dim_type type, const char *name);
1344 int isl_union_pw_multi_aff_find_dim_by_name(
1345 __isl_keep isl_union_pw_multi_aff *upma,
1346 enum isl_dim_type type, const char *name);
1347 int isl_multi_union_pw_aff_find_dim_by_name(
1348 __isl_keep isl_multi_union_pw_aff *mupa,
1349 enum isl_dim_type type, const char *name);
1351 #include <isl/polynomial.h>
1352 int isl_pw_qpolynomial_find_dim_by_name(
1353 __isl_keep isl_pw_qpolynomial *pwqp,
1354 enum isl_dim_type type, const char *name);
1355 int isl_pw_qpolynomial_fold_find_dim_by_name(
1356 __isl_keep isl_pw_qpolynomial_fold *pwf,
1357 enum isl_dim_type type, const char *name);
1358 int isl_union_pw_qpolynomial_find_dim_by_name(
1359 __isl_keep isl_union_pw_qpolynomial *upwqp,
1360 enum isl_dim_type type, const char *name);
1361 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1362 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1363 enum isl_dim_type type, const char *name);
1365 The identifiers or names of entire spaces may be set or read off
1366 using the following functions.
1368 #include <isl/space.h>
1369 __isl_give isl_space *isl_space_set_tuple_id(
1370 __isl_take isl_space *space,
1371 enum isl_dim_type type, __isl_take isl_id *id);
1372 __isl_give isl_space *isl_space_reset_tuple_id(
1373 __isl_take isl_space *space, enum isl_dim_type type);
1374 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1375 enum isl_dim_type type);
1376 __isl_give isl_id *isl_space_get_tuple_id(
1377 __isl_keep isl_space *space, enum isl_dim_type type);
1378 __isl_give isl_space *isl_space_set_tuple_name(
1379 __isl_take isl_space *space,
1380 enum isl_dim_type type, const char *s);
1381 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1382 enum isl_dim_type type);
1383 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1384 enum isl_dim_type type);
1386 #include <isl/local_space.h>
1387 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1388 __isl_take isl_local_space *ls,
1389 enum isl_dim_type type, __isl_take isl_id *id);
1391 #include <isl/set.h>
1392 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1393 __isl_take isl_basic_set *bset,
1394 __isl_take isl_id *id);
1395 __isl_give isl_set *isl_set_set_tuple_id(
1396 __isl_take isl_set *set, __isl_take isl_id *id);
1397 __isl_give isl_set *isl_set_reset_tuple_id(
1398 __isl_take isl_set *set);
1399 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1400 __isl_give isl_id *isl_set_get_tuple_id(
1401 __isl_keep isl_set *set);
1402 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1403 __isl_take isl_basic_set *set, const char *s);
1404 __isl_give isl_set *isl_set_set_tuple_name(
1405 __isl_take isl_set *set, const char *s);
1406 const char *isl_basic_set_get_tuple_name(
1407 __isl_keep isl_basic_set *bset);
1408 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1409 const char *isl_set_get_tuple_name(
1410 __isl_keep isl_set *set);
1412 #include <isl/map.h>
1413 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1414 __isl_take isl_basic_map *bmap,
1415 enum isl_dim_type type, __isl_take isl_id *id);
1416 __isl_give isl_map *isl_map_set_tuple_id(
1417 __isl_take isl_map *map, enum isl_dim_type type,
1418 __isl_take isl_id *id);
1419 __isl_give isl_map *isl_map_reset_tuple_id(
1420 __isl_take isl_map *map, enum isl_dim_type type);
1421 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1422 enum isl_dim_type type);
1423 __isl_give isl_id *isl_map_get_tuple_id(
1424 __isl_keep isl_map *map, enum isl_dim_type type);
1425 __isl_give isl_map *isl_map_set_tuple_name(
1426 __isl_take isl_map *map,
1427 enum isl_dim_type type, const char *s);
1428 const char *isl_basic_map_get_tuple_name(
1429 __isl_keep isl_basic_map *bmap,
1430 enum isl_dim_type type);
1431 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1432 __isl_take isl_basic_map *bmap,
1433 enum isl_dim_type type, const char *s);
1434 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1435 enum isl_dim_type type);
1436 const char *isl_map_get_tuple_name(
1437 __isl_keep isl_map *map,
1438 enum isl_dim_type type);
1440 #include <isl/val.h>
1441 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1442 __isl_take isl_multi_val *mv,
1443 enum isl_dim_type type, __isl_take isl_id *id);
1444 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1445 __isl_take isl_multi_val *mv,
1446 enum isl_dim_type type);
1447 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1448 enum isl_dim_type type);
1449 __isl_give isl_id *isl_multi_val_get_tuple_id(
1450 __isl_keep isl_multi_val *mv,
1451 enum isl_dim_type type);
1452 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1453 __isl_take isl_multi_val *mv,
1454 enum isl_dim_type type, const char *s);
1455 const char *isl_multi_val_get_tuple_name(
1456 __isl_keep isl_multi_val *mv,
1457 enum isl_dim_type type);
1459 #include <isl/aff.h>
1460 __isl_give isl_aff *isl_aff_set_tuple_id(
1461 __isl_take isl_aff *aff,
1462 enum isl_dim_type type, __isl_take isl_id *id);
1463 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1464 __isl_take isl_multi_aff *maff,
1465 enum isl_dim_type type, __isl_take isl_id *id);
1466 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1467 __isl_take isl_pw_aff *pwaff,
1468 enum isl_dim_type type, __isl_take isl_id *id);
1469 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1470 __isl_take isl_pw_multi_aff *pma,
1471 enum isl_dim_type type, __isl_take isl_id *id);
1472 __isl_give isl_multi_union_pw_aff *
1473 isl_multi_union_pw_aff_set_tuple_id(
1474 __isl_take isl_multi_union_pw_aff *mupa,
1475 enum isl_dim_type type, __isl_take isl_id *id);
1476 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1477 __isl_take isl_multi_aff *ma,
1478 enum isl_dim_type type);
1479 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1480 __isl_take isl_pw_aff *pa,
1481 enum isl_dim_type type);
1482 __isl_give isl_multi_pw_aff *
1483 isl_multi_pw_aff_reset_tuple_id(
1484 __isl_take isl_multi_pw_aff *mpa,
1485 enum isl_dim_type type);
1486 __isl_give isl_pw_multi_aff *
1487 isl_pw_multi_aff_reset_tuple_id(
1488 __isl_take isl_pw_multi_aff *pma,
1489 enum isl_dim_type type);
1490 __isl_give isl_multi_union_pw_aff *
1491 isl_multi_union_pw_aff_reset_tuple_id(
1492 __isl_take isl_multi_union_pw_aff *mupa,
1493 enum isl_dim_type type);
1494 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1495 enum isl_dim_type type);
1496 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1497 __isl_keep isl_multi_aff *ma,
1498 enum isl_dim_type type);
1499 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1500 enum isl_dim_type type);
1501 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1502 __isl_keep isl_pw_aff *pa,
1503 enum isl_dim_type type);
1504 int isl_pw_multi_aff_has_tuple_id(
1505 __isl_keep isl_pw_multi_aff *pma,
1506 enum isl_dim_type type);
1507 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1508 __isl_keep isl_pw_multi_aff *pma,
1509 enum isl_dim_type type);
1510 int isl_multi_pw_aff_has_tuple_id(
1511 __isl_keep isl_multi_pw_aff *mpa,
1512 enum isl_dim_type type);
1513 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1514 __isl_keep isl_multi_pw_aff *mpa,
1515 enum isl_dim_type type);
1516 int isl_multi_union_pw_aff_has_tuple_id(
1517 __isl_keep isl_multi_union_pw_aff *mupa,
1518 enum isl_dim_type type);
1519 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1520 __isl_keep isl_multi_union_pw_aff *mupa,
1521 enum isl_dim_type type);
1522 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1523 __isl_take isl_multi_aff *maff,
1524 enum isl_dim_type type, const char *s);
1525 __isl_give isl_multi_pw_aff *
1526 isl_multi_pw_aff_set_tuple_name(
1527 __isl_take isl_multi_pw_aff *mpa,
1528 enum isl_dim_type type, const char *s);
1529 __isl_give isl_multi_union_pw_aff *
1530 isl_multi_union_pw_aff_set_tuple_name(
1531 __isl_take isl_multi_union_pw_aff *mupa,
1532 enum isl_dim_type type, const char *s);
1533 const char *isl_multi_aff_get_tuple_name(
1534 __isl_keep isl_multi_aff *multi,
1535 enum isl_dim_type type);
1536 int isl_pw_multi_aff_has_tuple_name(
1537 __isl_keep isl_pw_multi_aff *pma,
1538 enum isl_dim_type type);
1539 const char *isl_pw_multi_aff_get_tuple_name(
1540 __isl_keep isl_pw_multi_aff *pma,
1541 enum isl_dim_type type);
1542 const char *isl_multi_union_pw_aff_get_tuple_name(
1543 __isl_keep isl_multi_union_pw_aff *mupa,
1544 enum isl_dim_type type);
1546 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1547 or C<isl_dim_set>. As with C<isl_space_get_name>,
1548 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1550 Binary operations require the corresponding spaces of their arguments
1551 to have the same name.
1553 To keep the names of all parameters and tuples, but reset the user pointers
1554 of all the corresponding identifiers, use the following function.
1556 #include <isl/space.h>
1557 __isl_give isl_space *isl_space_reset_user(
1558 __isl_take isl_space *space);
1560 #include <isl/set.h>
1561 __isl_give isl_set *isl_set_reset_user(
1562 __isl_take isl_set *set);
1564 #include <isl/map.h>
1565 __isl_give isl_map *isl_map_reset_user(
1566 __isl_take isl_map *map);
1568 #include <isl/union_set.h>
1569 __isl_give isl_union_set *isl_union_set_reset_user(
1570 __isl_take isl_union_set *uset);
1572 #include <isl/union_map.h>
1573 __isl_give isl_union_map *isl_union_map_reset_user(
1574 __isl_take isl_union_map *umap);
1576 #include <isl/val.h>
1577 __isl_give isl_multi_val *isl_multi_val_reset_user(
1578 __isl_take isl_multi_val *mv);
1580 #include <isl/aff.h>
1581 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1582 __isl_take isl_multi_aff *ma);
1583 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1584 __isl_take isl_pw_aff *pa);
1585 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1586 __isl_take isl_multi_pw_aff *mpa);
1587 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1588 __isl_take isl_pw_multi_aff *pma);
1589 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1590 __isl_take isl_union_pw_aff *upa);
1591 __isl_give isl_multi_union_pw_aff *
1592 isl_multi_union_pw_aff_reset_user(
1593 __isl_take isl_multi_union_pw_aff *mupa);
1594 __isl_give isl_union_pw_multi_aff *
1595 isl_union_pw_multi_aff_reset_user(
1596 __isl_take isl_union_pw_multi_aff *upma);
1598 #include <isl/polynomial.h>
1599 __isl_give isl_pw_qpolynomial *
1600 isl_pw_qpolynomial_reset_user(
1601 __isl_take isl_pw_qpolynomial *pwqp);
1602 __isl_give isl_union_pw_qpolynomial *
1603 isl_union_pw_qpolynomial_reset_user(
1604 __isl_take isl_union_pw_qpolynomial *upwqp);
1605 __isl_give isl_pw_qpolynomial_fold *
1606 isl_pw_qpolynomial_fold_reset_user(
1607 __isl_take isl_pw_qpolynomial_fold *pwf);
1608 __isl_give isl_union_pw_qpolynomial_fold *
1609 isl_union_pw_qpolynomial_fold_reset_user(
1610 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1612 Spaces can be nested. In particular, the domain of a set or
1613 the domain or range of a relation can be a nested relation.
1614 This process is also called I<wrapping>.
1615 The functions for detecting, constructing and deconstructing
1616 such nested spaces can be found in the wrapping properties
1617 of L</"Unary Properties">, the wrapping operations
1618 of L</"Unary Operations"> and the Cartesian product operations
1619 of L</"Basic Operations">.
1621 Spaces can be created from other spaces
1622 using the functions described in L</"Unary Operations">
1623 and L</"Binary Operations">.
1627 A local space is essentially a space with
1628 zero or more existentially quantified variables.
1629 The local space of various objects can be obtained
1630 using the following functions.
1632 #include <isl/constraint.h>
1633 __isl_give isl_local_space *isl_constraint_get_local_space(
1634 __isl_keep isl_constraint *constraint);
1636 #include <isl/set.h>
1637 __isl_give isl_local_space *isl_basic_set_get_local_space(
1638 __isl_keep isl_basic_set *bset);
1640 #include <isl/map.h>
1641 __isl_give isl_local_space *isl_basic_map_get_local_space(
1642 __isl_keep isl_basic_map *bmap);
1644 #include <isl/aff.h>
1645 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1646 __isl_keep isl_aff *aff);
1647 __isl_give isl_local_space *isl_aff_get_local_space(
1648 __isl_keep isl_aff *aff);
1650 A new local space can be created from a space using
1652 #include <isl/local_space.h>
1653 __isl_give isl_local_space *isl_local_space_from_space(
1654 __isl_take isl_space *space);
1656 They can be inspected, modified, copied and freed using the following functions.
1658 #include <isl/local_space.h>
1659 int isl_local_space_is_params(
1660 __isl_keep isl_local_space *ls);
1661 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1662 __isl_give isl_space *isl_local_space_get_space(
1663 __isl_keep isl_local_space *ls);
1664 __isl_give isl_aff *isl_local_space_get_div(
1665 __isl_keep isl_local_space *ls, int pos);
1666 __isl_give isl_local_space *isl_local_space_copy(
1667 __isl_keep isl_local_space *ls);
1668 __isl_null isl_local_space *isl_local_space_free(
1669 __isl_take isl_local_space *ls);
1671 Note that C<isl_local_space_get_div> can only be used on local spaces
1674 Two local spaces can be compared using
1676 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1677 __isl_keep isl_local_space *ls2);
1679 Local spaces can be created from other local spaces
1680 using the functions described in L</"Unary Operations">
1681 and L</"Binary Operations">.
1683 =head2 Creating New Sets and Relations
1685 C<isl> has functions for creating some standard sets and relations.
1689 =item * Empty sets and relations
1691 __isl_give isl_basic_set *isl_basic_set_empty(
1692 __isl_take isl_space *space);
1693 __isl_give isl_basic_map *isl_basic_map_empty(
1694 __isl_take isl_space *space);
1695 __isl_give isl_set *isl_set_empty(
1696 __isl_take isl_space *space);
1697 __isl_give isl_map *isl_map_empty(
1698 __isl_take isl_space *space);
1699 __isl_give isl_union_set *isl_union_set_empty(
1700 __isl_take isl_space *space);
1701 __isl_give isl_union_map *isl_union_map_empty(
1702 __isl_take isl_space *space);
1704 For C<isl_union_set>s and C<isl_union_map>s, the space
1705 is only used to specify the parameters.
1707 =item * Universe sets and relations
1709 __isl_give isl_basic_set *isl_basic_set_universe(
1710 __isl_take isl_space *space);
1711 __isl_give isl_basic_map *isl_basic_map_universe(
1712 __isl_take isl_space *space);
1713 __isl_give isl_set *isl_set_universe(
1714 __isl_take isl_space *space);
1715 __isl_give isl_map *isl_map_universe(
1716 __isl_take isl_space *space);
1717 __isl_give isl_union_set *isl_union_set_universe(
1718 __isl_take isl_union_set *uset);
1719 __isl_give isl_union_map *isl_union_map_universe(
1720 __isl_take isl_union_map *umap);
1722 The sets and relations constructed by the functions above
1723 contain all integer values, while those constructed by the
1724 functions below only contain non-negative values.
1726 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1727 __isl_take isl_space *space);
1728 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1729 __isl_take isl_space *space);
1730 __isl_give isl_set *isl_set_nat_universe(
1731 __isl_take isl_space *space);
1732 __isl_give isl_map *isl_map_nat_universe(
1733 __isl_take isl_space *space);
1735 =item * Identity relations
1737 __isl_give isl_basic_map *isl_basic_map_identity(
1738 __isl_take isl_space *space);
1739 __isl_give isl_map *isl_map_identity(
1740 __isl_take isl_space *space);
1742 The number of input and output dimensions in C<space> needs
1745 =item * Lexicographic order
1747 __isl_give isl_map *isl_map_lex_lt(
1748 __isl_take isl_space *set_space);
1749 __isl_give isl_map *isl_map_lex_le(
1750 __isl_take isl_space *set_space);
1751 __isl_give isl_map *isl_map_lex_gt(
1752 __isl_take isl_space *set_space);
1753 __isl_give isl_map *isl_map_lex_ge(
1754 __isl_take isl_space *set_space);
1755 __isl_give isl_map *isl_map_lex_lt_first(
1756 __isl_take isl_space *space, unsigned n);
1757 __isl_give isl_map *isl_map_lex_le_first(
1758 __isl_take isl_space *space, unsigned n);
1759 __isl_give isl_map *isl_map_lex_gt_first(
1760 __isl_take isl_space *space, unsigned n);
1761 __isl_give isl_map *isl_map_lex_ge_first(
1762 __isl_take isl_space *space, unsigned n);
1764 The first four functions take a space for a B<set>
1765 and return relations that express that the elements in the domain
1766 are lexicographically less
1767 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1768 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1769 than the elements in the range.
1770 The last four functions take a space for a map
1771 and return relations that express that the first C<n> dimensions
1772 in the domain are lexicographically less
1773 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1774 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1775 than the first C<n> dimensions in the range.
1779 A basic set or relation can be converted to a set or relation
1780 using the following functions.
1782 __isl_give isl_set *isl_set_from_basic_set(
1783 __isl_take isl_basic_set *bset);
1784 __isl_give isl_map *isl_map_from_basic_map(
1785 __isl_take isl_basic_map *bmap);
1787 Sets and relations can be converted to union sets and relations
1788 using the following functions.
1790 __isl_give isl_union_set *isl_union_set_from_basic_set(
1791 __isl_take isl_basic_set *bset);
1792 __isl_give isl_union_map *isl_union_map_from_basic_map(
1793 __isl_take isl_basic_map *bmap);
1794 __isl_give isl_union_set *isl_union_set_from_set(
1795 __isl_take isl_set *set);
1796 __isl_give isl_union_map *isl_union_map_from_map(
1797 __isl_take isl_map *map);
1799 The inverse conversions below can only be used if the input
1800 union set or relation is known to contain elements in exactly one
1803 __isl_give isl_set *isl_set_from_union_set(
1804 __isl_take isl_union_set *uset);
1805 __isl_give isl_map *isl_map_from_union_map(
1806 __isl_take isl_union_map *umap);
1808 Sets and relations can be copied and freed again using the following
1811 __isl_give isl_basic_set *isl_basic_set_copy(
1812 __isl_keep isl_basic_set *bset);
1813 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1814 __isl_give isl_union_set *isl_union_set_copy(
1815 __isl_keep isl_union_set *uset);
1816 __isl_give isl_basic_map *isl_basic_map_copy(
1817 __isl_keep isl_basic_map *bmap);
1818 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1819 __isl_give isl_union_map *isl_union_map_copy(
1820 __isl_keep isl_union_map *umap);
1821 __isl_null isl_basic_set *isl_basic_set_free(
1822 __isl_take isl_basic_set *bset);
1823 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1824 __isl_null isl_union_set *isl_union_set_free(
1825 __isl_take isl_union_set *uset);
1826 __isl_null isl_basic_map *isl_basic_map_free(
1827 __isl_take isl_basic_map *bmap);
1828 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1829 __isl_null isl_union_map *isl_union_map_free(
1830 __isl_take isl_union_map *umap);
1832 Other sets and relations can be constructed by starting
1833 from a universe set or relation, adding equality and/or
1834 inequality constraints and then projecting out the
1835 existentially quantified variables, if any.
1836 Constraints can be constructed, manipulated and
1837 added to (or removed from) (basic) sets and relations
1838 using the following functions.
1840 #include <isl/constraint.h>
1841 __isl_give isl_constraint *isl_equality_alloc(
1842 __isl_take isl_local_space *ls);
1843 __isl_give isl_constraint *isl_inequality_alloc(
1844 __isl_take isl_local_space *ls);
1845 __isl_give isl_constraint *isl_constraint_set_constant_si(
1846 __isl_take isl_constraint *constraint, int v);
1847 __isl_give isl_constraint *isl_constraint_set_constant_val(
1848 __isl_take isl_constraint *constraint,
1849 __isl_take isl_val *v);
1850 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1851 __isl_take isl_constraint *constraint,
1852 enum isl_dim_type type, int pos, int v);
1853 __isl_give isl_constraint *
1854 isl_constraint_set_coefficient_val(
1855 __isl_take isl_constraint *constraint,
1856 enum isl_dim_type type, int pos,
1857 __isl_take isl_val *v);
1858 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1859 __isl_take isl_basic_map *bmap,
1860 __isl_take isl_constraint *constraint);
1861 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1862 __isl_take isl_basic_set *bset,
1863 __isl_take isl_constraint *constraint);
1864 __isl_give isl_map *isl_map_add_constraint(
1865 __isl_take isl_map *map,
1866 __isl_take isl_constraint *constraint);
1867 __isl_give isl_set *isl_set_add_constraint(
1868 __isl_take isl_set *set,
1869 __isl_take isl_constraint *constraint);
1870 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1871 __isl_take isl_basic_set *bset,
1872 __isl_take isl_constraint *constraint);
1874 For example, to create a set containing the even integers
1875 between 10 and 42, you would use the following code.
1878 isl_local_space *ls;
1880 isl_basic_set *bset;
1882 space = isl_space_set_alloc(ctx, 0, 2);
1883 bset = isl_basic_set_universe(isl_space_copy(space));
1884 ls = isl_local_space_from_space(space);
1886 c = isl_equality_alloc(isl_local_space_copy(ls));
1887 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1888 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1889 bset = isl_basic_set_add_constraint(bset, c);
1891 c = isl_inequality_alloc(isl_local_space_copy(ls));
1892 c = isl_constraint_set_constant_si(c, -10);
1893 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1894 bset = isl_basic_set_add_constraint(bset, c);
1896 c = isl_inequality_alloc(ls);
1897 c = isl_constraint_set_constant_si(c, 42);
1898 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1899 bset = isl_basic_set_add_constraint(bset, c);
1901 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1905 isl_basic_set *bset;
1906 bset = isl_basic_set_read_from_str(ctx,
1907 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1909 A basic set or relation can also be constructed from two matrices
1910 describing the equalities and the inequalities.
1912 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1913 __isl_take isl_space *space,
1914 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1915 enum isl_dim_type c1,
1916 enum isl_dim_type c2, enum isl_dim_type c3,
1917 enum isl_dim_type c4);
1918 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1919 __isl_take isl_space *space,
1920 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1921 enum isl_dim_type c1,
1922 enum isl_dim_type c2, enum isl_dim_type c3,
1923 enum isl_dim_type c4, enum isl_dim_type c5);
1925 The C<isl_dim_type> arguments indicate the order in which
1926 different kinds of variables appear in the input matrices
1927 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1928 C<isl_dim_set> and C<isl_dim_div> for sets and
1929 of C<isl_dim_cst>, C<isl_dim_param>,
1930 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1932 A (basic or union) set or relation can also be constructed from a
1933 (union) (piecewise) (multiple) affine expression
1934 or a list of affine expressions
1935 (See L</"Functions">).
1937 __isl_give isl_basic_map *isl_basic_map_from_aff(
1938 __isl_take isl_aff *aff);
1939 __isl_give isl_map *isl_map_from_aff(
1940 __isl_take isl_aff *aff);
1941 __isl_give isl_set *isl_set_from_pw_aff(
1942 __isl_take isl_pw_aff *pwaff);
1943 __isl_give isl_map *isl_map_from_pw_aff(
1944 __isl_take isl_pw_aff *pwaff);
1945 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1946 __isl_take isl_space *domain_space,
1947 __isl_take isl_aff_list *list);
1948 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1949 __isl_take isl_multi_aff *maff)
1950 __isl_give isl_map *isl_map_from_multi_aff(
1951 __isl_take isl_multi_aff *maff)
1952 __isl_give isl_set *isl_set_from_pw_multi_aff(
1953 __isl_take isl_pw_multi_aff *pma);
1954 __isl_give isl_map *isl_map_from_pw_multi_aff(
1955 __isl_take isl_pw_multi_aff *pma);
1956 __isl_give isl_set *isl_set_from_multi_pw_aff(
1957 __isl_take isl_multi_pw_aff *mpa);
1958 __isl_give isl_map *isl_map_from_multi_pw_aff(
1959 __isl_take isl_multi_pw_aff *mpa);
1960 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
1961 __isl_take isl_union_pw_aff *upa);
1962 __isl_give isl_union_map *
1963 isl_union_map_from_union_pw_multi_aff(
1964 __isl_take isl_union_pw_multi_aff *upma);
1966 The C<domain_space> argument describes the domain of the resulting
1967 basic relation. It is required because the C<list> may consist
1968 of zero affine expressions.
1970 =head2 Inspecting Sets and Relations
1972 Usually, the user should not have to care about the actual constraints
1973 of the sets and maps, but should instead apply the abstract operations
1974 explained in the following sections.
1975 Occasionally, however, it may be required to inspect the individual
1976 coefficients of the constraints. This section explains how to do so.
1977 In these cases, it may also be useful to have C<isl> compute
1978 an explicit representation of the existentially quantified variables.
1980 __isl_give isl_set *isl_set_compute_divs(
1981 __isl_take isl_set *set);
1982 __isl_give isl_map *isl_map_compute_divs(
1983 __isl_take isl_map *map);
1984 __isl_give isl_union_set *isl_union_set_compute_divs(
1985 __isl_take isl_union_set *uset);
1986 __isl_give isl_union_map *isl_union_map_compute_divs(
1987 __isl_take isl_union_map *umap);
1989 This explicit representation defines the existentially quantified
1990 variables as integer divisions of the other variables, possibly
1991 including earlier existentially quantified variables.
1992 An explicitly represented existentially quantified variable therefore
1993 has a unique value when the values of the other variables are known.
1994 If, furthermore, the same existentials, i.e., existentials
1995 with the same explicit representations, should appear in the
1996 same order in each of the disjuncts of a set or map, then the user should call
1997 either of the following functions.
1999 __isl_give isl_set *isl_set_align_divs(
2000 __isl_take isl_set *set);
2001 __isl_give isl_map *isl_map_align_divs(
2002 __isl_take isl_map *map);
2004 Alternatively, the existentially quantified variables can be removed
2005 using the following functions, which compute an overapproximation.
2007 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2008 __isl_take isl_basic_set *bset);
2009 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2010 __isl_take isl_basic_map *bmap);
2011 __isl_give isl_set *isl_set_remove_divs(
2012 __isl_take isl_set *set);
2013 __isl_give isl_map *isl_map_remove_divs(
2014 __isl_take isl_map *map);
2016 It is also possible to only remove those divs that are defined
2017 in terms of a given range of dimensions or only those for which
2018 no explicit representation is known.
2020 __isl_give isl_basic_set *
2021 isl_basic_set_remove_divs_involving_dims(
2022 __isl_take isl_basic_set *bset,
2023 enum isl_dim_type type,
2024 unsigned first, unsigned n);
2025 __isl_give isl_basic_map *
2026 isl_basic_map_remove_divs_involving_dims(
2027 __isl_take isl_basic_map *bmap,
2028 enum isl_dim_type type,
2029 unsigned first, unsigned n);
2030 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2031 __isl_take isl_set *set, enum isl_dim_type type,
2032 unsigned first, unsigned n);
2033 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2034 __isl_take isl_map *map, enum isl_dim_type type,
2035 unsigned first, unsigned n);
2037 __isl_give isl_basic_set *
2038 isl_basic_set_remove_unknown_divs(
2039 __isl_take isl_basic_set *bset);
2040 __isl_give isl_set *isl_set_remove_unknown_divs(
2041 __isl_take isl_set *set);
2042 __isl_give isl_map *isl_map_remove_unknown_divs(
2043 __isl_take isl_map *map);
2045 To iterate over all the sets or maps in a union set or map, use
2047 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
2048 int (*fn)(__isl_take isl_set *set, void *user),
2050 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
2051 int (*fn)(__isl_take isl_map *map, void *user),
2054 The number of sets or maps in a union set or map can be obtained
2057 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2058 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2060 To extract the set or map in a given space from a union, use
2062 __isl_give isl_set *isl_union_set_extract_set(
2063 __isl_keep isl_union_set *uset,
2064 __isl_take isl_space *space);
2065 __isl_give isl_map *isl_union_map_extract_map(
2066 __isl_keep isl_union_map *umap,
2067 __isl_take isl_space *space);
2069 To iterate over all the basic sets or maps in a set or map, use
2071 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
2072 int (*fn)(__isl_take isl_basic_set *bset, void *user),
2074 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
2075 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
2078 The callback function C<fn> should return 0 if successful and
2079 -1 if an error occurs. In the latter case, or if any other error
2080 occurs, the above functions will return -1.
2082 It should be noted that C<isl> does not guarantee that
2083 the basic sets or maps passed to C<fn> are disjoint.
2084 If this is required, then the user should call one of
2085 the following functions first.
2087 __isl_give isl_set *isl_set_make_disjoint(
2088 __isl_take isl_set *set);
2089 __isl_give isl_map *isl_map_make_disjoint(
2090 __isl_take isl_map *map);
2092 The number of basic sets in a set can be obtained
2093 or the number of basic maps in a map can be obtained
2096 #include <isl/set.h>
2097 int isl_set_n_basic_set(__isl_keep isl_set *set);
2099 #include <isl/map.h>
2100 int isl_map_n_basic_map(__isl_keep isl_map *map);
2102 To iterate over the constraints of a basic set or map, use
2104 #include <isl/constraint.h>
2106 int isl_basic_set_n_constraint(
2107 __isl_keep isl_basic_set *bset);
2108 int isl_basic_set_foreach_constraint(
2109 __isl_keep isl_basic_set *bset,
2110 int (*fn)(__isl_take isl_constraint *c, void *user),
2112 int isl_basic_map_n_constraint(
2113 __isl_keep isl_basic_map *bmap);
2114 int isl_basic_map_foreach_constraint(
2115 __isl_keep isl_basic_map *bmap,
2116 int (*fn)(__isl_take isl_constraint *c, void *user),
2118 __isl_null isl_constraint *isl_constraint_free(
2119 __isl_take isl_constraint *c);
2121 Again, the callback function C<fn> should return 0 if successful and
2122 -1 if an error occurs. In the latter case, or if any other error
2123 occurs, the above functions will return -1.
2124 The constraint C<c> represents either an equality or an inequality.
2125 Use the following function to find out whether a constraint
2126 represents an equality. If not, it represents an inequality.
2128 int isl_constraint_is_equality(
2129 __isl_keep isl_constraint *constraint);
2131 It is also possible to obtain a list of constraints from a basic
2134 #include <isl/constraint.h>
2135 __isl_give isl_constraint_list *
2136 isl_basic_map_get_constraint_list(
2137 __isl_keep isl_basic_map *bmap);
2138 __isl_give isl_constraint_list *
2139 isl_basic_set_get_constraint_list(
2140 __isl_keep isl_basic_set *bset);
2142 These functions require that all existentially quantified variables
2143 have an explicit representation.
2144 The returned list can be manipulated using the functions in L<"Lists">.
2146 The coefficients of the constraints can be inspected using
2147 the following functions.
2149 int isl_constraint_is_lower_bound(
2150 __isl_keep isl_constraint *constraint,
2151 enum isl_dim_type type, unsigned pos);
2152 int isl_constraint_is_upper_bound(
2153 __isl_keep isl_constraint *constraint,
2154 enum isl_dim_type type, unsigned pos);
2155 __isl_give isl_val *isl_constraint_get_constant_val(
2156 __isl_keep isl_constraint *constraint);
2157 __isl_give isl_val *isl_constraint_get_coefficient_val(
2158 __isl_keep isl_constraint *constraint,
2159 enum isl_dim_type type, int pos);
2161 The explicit representations of the existentially quantified
2162 variables can be inspected using the following function.
2163 Note that the user is only allowed to use this function
2164 if the inspected set or map is the result of a call
2165 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2166 The existentially quantified variable is equal to the floor
2167 of the returned affine expression. The affine expression
2168 itself can be inspected using the functions in
2171 __isl_give isl_aff *isl_constraint_get_div(
2172 __isl_keep isl_constraint *constraint, int pos);
2174 To obtain the constraints of a basic set or map in matrix
2175 form, use the following functions.
2177 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2178 __isl_keep isl_basic_set *bset,
2179 enum isl_dim_type c1, enum isl_dim_type c2,
2180 enum isl_dim_type c3, enum isl_dim_type c4);
2181 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2182 __isl_keep isl_basic_set *bset,
2183 enum isl_dim_type c1, enum isl_dim_type c2,
2184 enum isl_dim_type c3, enum isl_dim_type c4);
2185 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2186 __isl_keep isl_basic_map *bmap,
2187 enum isl_dim_type c1,
2188 enum isl_dim_type c2, enum isl_dim_type c3,
2189 enum isl_dim_type c4, enum isl_dim_type c5);
2190 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2191 __isl_keep isl_basic_map *bmap,
2192 enum isl_dim_type c1,
2193 enum isl_dim_type c2, enum isl_dim_type c3,
2194 enum isl_dim_type c4, enum isl_dim_type c5);
2196 The C<isl_dim_type> arguments dictate the order in which
2197 different kinds of variables appear in the resulting matrix.
2198 For set inputs, they should be a permutation of
2199 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2200 For map inputs, they should be a permutation of
2201 C<isl_dim_cst>, C<isl_dim_param>,
2202 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2206 Points are elements of a set. They can be used to construct
2207 simple sets (boxes) or they can be used to represent the
2208 individual elements of a set.
2209 The zero point (the origin) can be created using
2211 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2213 The coordinates of a point can be inspected, set and changed
2216 __isl_give isl_val *isl_point_get_coordinate_val(
2217 __isl_keep isl_point *pnt,
2218 enum isl_dim_type type, int pos);
2219 __isl_give isl_point *isl_point_set_coordinate_val(
2220 __isl_take isl_point *pnt,
2221 enum isl_dim_type type, int pos,
2222 __isl_take isl_val *v);
2224 __isl_give isl_point *isl_point_add_ui(
2225 __isl_take isl_point *pnt,
2226 enum isl_dim_type type, int pos, unsigned val);
2227 __isl_give isl_point *isl_point_sub_ui(
2228 __isl_take isl_point *pnt,
2229 enum isl_dim_type type, int pos, unsigned val);
2231 Points can be copied or freed using
2233 __isl_give isl_point *isl_point_copy(
2234 __isl_keep isl_point *pnt);
2235 void isl_point_free(__isl_take isl_point *pnt);
2237 A singleton set can be created from a point using
2239 __isl_give isl_basic_set *isl_basic_set_from_point(
2240 __isl_take isl_point *pnt);
2241 __isl_give isl_set *isl_set_from_point(
2242 __isl_take isl_point *pnt);
2244 and a box can be created from two opposite extremal points using
2246 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2247 __isl_take isl_point *pnt1,
2248 __isl_take isl_point *pnt2);
2249 __isl_give isl_set *isl_set_box_from_points(
2250 __isl_take isl_point *pnt1,
2251 __isl_take isl_point *pnt2);
2253 All elements of a B<bounded> (union) set can be enumerated using
2254 the following functions.
2256 int isl_set_foreach_point(__isl_keep isl_set *set,
2257 int (*fn)(__isl_take isl_point *pnt, void *user),
2259 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2260 int (*fn)(__isl_take isl_point *pnt, void *user),
2263 The function C<fn> is called for each integer point in
2264 C<set> with as second argument the last argument of
2265 the C<isl_set_foreach_point> call. The function C<fn>
2266 should return C<0> on success and C<-1> on failure.
2267 In the latter case, C<isl_set_foreach_point> will stop
2268 enumerating and return C<-1> as well.
2269 If the enumeration is performed successfully and to completion,
2270 then C<isl_set_foreach_point> returns C<0>.
2272 To obtain a single point of a (basic) set, use
2274 __isl_give isl_point *isl_basic_set_sample_point(
2275 __isl_take isl_basic_set *bset);
2276 __isl_give isl_point *isl_set_sample_point(
2277 __isl_take isl_set *set);
2279 If C<set> does not contain any (integer) points, then the
2280 resulting point will be ``void'', a property that can be
2283 int isl_point_is_void(__isl_keep isl_point *pnt);
2287 Besides sets and relation, C<isl> also supports various types of functions.
2288 Each of these types is derived from the value type (see L</"Values">)
2289 or from one of two primitive function types
2290 through the application of zero or more type constructors.
2291 We first describe the primitive type and then we describe
2292 the types derived from these primitive types.
2294 =head3 Primitive Functions
2296 C<isl> support two primitive function types, quasi-affine
2297 expressions and quasipolynomials.
2298 A quasi-affine expression is defined either over a parameter
2299 space or over a set and is composed of integer constants,
2300 parameters and set variables, addition, subtraction and
2301 integer division by an integer constant.
2302 For example, the quasi-affine expression
2304 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2306 maps C<x> to C<2*floor((4 n + x)/9>.
2307 A quasipolynomial is a polynomial expression in quasi-affine
2308 expression. That is, it additionally allows for multiplication.
2309 Note, though, that it is not allowed to construct an integer
2310 division of an expression involving multiplications.
2311 Here is an example of a quasipolynomial that is not
2312 quasi-affine expression
2314 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2316 Note that the external representations of quasi-affine expressions
2317 and quasipolynomials are different. Quasi-affine expressions
2318 use a notation with square brackets just like binary relations,
2319 while quasipolynomials do not. This might change at some point.
2321 If a primitive function is defined over a parameter space,
2322 then the space of the function itself is that of a set.
2323 If it is defined over a set, then the space of the function
2324 is that of a relation. In both cases, the set space (or
2325 the output space) is single-dimensional, anonymous and unstructured.
2326 To create functions with multiple dimensions or with other kinds
2327 of set or output spaces, use multiple expressions
2328 (see L</"Multiple Expressions">).
2332 =item * Quasi-affine Expressions
2334 Besides the expressions described above, a quasi-affine
2335 expression can also be set to NaN. Such expressions
2336 typically represent a failure to represent a result
2337 as a quasi-affine expression.
2339 The zero quasi affine expression or the quasi affine expression
2340 that is equal to a given value or
2341 a specified dimension on a given domain can be created using
2343 #include <isl/aff.h>
2344 __isl_give isl_aff *isl_aff_zero_on_domain(
2345 __isl_take isl_local_space *ls);
2346 __isl_give isl_aff *isl_aff_val_on_domain(
2347 __isl_take isl_local_space *ls,
2348 __isl_take isl_val *val);
2349 __isl_give isl_aff *isl_aff_var_on_domain(
2350 __isl_take isl_local_space *ls,
2351 enum isl_dim_type type, unsigned pos);
2352 __isl_give isl_aff *isl_aff_nan_on_domain(
2353 __isl_take isl_local_space *ls);
2355 Quasi affine expressions can be copied and freed using
2357 #include <isl/aff.h>
2358 __isl_give isl_aff *isl_aff_copy(
2359 __isl_keep isl_aff *aff);
2360 __isl_null isl_aff *isl_aff_free(
2361 __isl_take isl_aff *aff);
2363 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2364 using the following function. The constraint is required to have
2365 a non-zero coefficient for the specified dimension.
2367 #include <isl/constraint.h>
2368 __isl_give isl_aff *isl_constraint_get_bound(
2369 __isl_keep isl_constraint *constraint,
2370 enum isl_dim_type type, int pos);
2372 The entire affine expression of the constraint can also be extracted
2373 using the following function.
2375 #include <isl/constraint.h>
2376 __isl_give isl_aff *isl_constraint_get_aff(
2377 __isl_keep isl_constraint *constraint);
2379 Conversely, an equality constraint equating
2380 the affine expression to zero or an inequality constraint enforcing
2381 the affine expression to be non-negative, can be constructed using
2383 __isl_give isl_constraint *isl_equality_from_aff(
2384 __isl_take isl_aff *aff);
2385 __isl_give isl_constraint *isl_inequality_from_aff(
2386 __isl_take isl_aff *aff);
2388 The coefficients and the integer divisions of an affine expression
2389 can be inspected using the following functions.
2391 #include <isl/aff.h>
2392 __isl_give isl_val *isl_aff_get_constant_val(
2393 __isl_keep isl_aff *aff);
2394 __isl_give isl_val *isl_aff_get_coefficient_val(
2395 __isl_keep isl_aff *aff,
2396 enum isl_dim_type type, int pos);
2397 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2398 enum isl_dim_type type, int pos);
2399 __isl_give isl_val *isl_aff_get_denominator_val(
2400 __isl_keep isl_aff *aff);
2401 __isl_give isl_aff *isl_aff_get_div(
2402 __isl_keep isl_aff *aff, int pos);
2404 They can be modified using the following functions.
2406 #include <isl/aff.h>
2407 __isl_give isl_aff *isl_aff_set_constant_si(
2408 __isl_take isl_aff *aff, int v);
2409 __isl_give isl_aff *isl_aff_set_constant_val(
2410 __isl_take isl_aff *aff, __isl_take isl_val *v);
2411 __isl_give isl_aff *isl_aff_set_coefficient_si(
2412 __isl_take isl_aff *aff,
2413 enum isl_dim_type type, int pos, int v);
2414 __isl_give isl_aff *isl_aff_set_coefficient_val(
2415 __isl_take isl_aff *aff,
2416 enum isl_dim_type type, int pos,
2417 __isl_take isl_val *v);
2419 __isl_give isl_aff *isl_aff_add_constant_si(
2420 __isl_take isl_aff *aff, int v);
2421 __isl_give isl_aff *isl_aff_add_constant_val(
2422 __isl_take isl_aff *aff, __isl_take isl_val *v);
2423 __isl_give isl_aff *isl_aff_add_constant_num_si(
2424 __isl_take isl_aff *aff, int v);
2425 __isl_give isl_aff *isl_aff_add_coefficient_si(
2426 __isl_take isl_aff *aff,
2427 enum isl_dim_type type, int pos, int v);
2428 __isl_give isl_aff *isl_aff_add_coefficient_val(
2429 __isl_take isl_aff *aff,
2430 enum isl_dim_type type, int pos,
2431 __isl_take isl_val *v);
2433 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2434 set the I<numerator> of the constant or coefficient, while
2435 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2436 the constant or coefficient as a whole.
2437 The C<add_constant> and C<add_coefficient> functions add an integer
2438 or rational value to
2439 the possibly rational constant or coefficient.
2440 The C<add_constant_num> functions add an integer value to
2443 =item * Quasipolynomials
2445 Some simple quasipolynomials can be created using the following functions.
2447 #include <isl/polynomial.h>
2448 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2449 __isl_take isl_space *domain);
2450 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2451 __isl_take isl_space *domain);
2452 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2453 __isl_take isl_space *domain);
2454 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2455 __isl_take isl_space *domain);
2456 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2457 __isl_take isl_space *domain);
2458 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2459 __isl_take isl_space *domain,
2460 __isl_take isl_val *val);
2461 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2462 __isl_take isl_space *domain,
2463 enum isl_dim_type type, unsigned pos);
2464 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2465 __isl_take isl_aff *aff);
2467 Recall that the space in which a quasipolynomial lives is a map space
2468 with a one-dimensional range. The C<domain> argument in some of
2469 the functions above corresponds to the domain of this map space.
2471 Quasipolynomials can be copied and freed again using the following
2474 #include <isl/polynomial.h>
2475 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2476 __isl_keep isl_qpolynomial *qp);
2477 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2478 __isl_take isl_qpolynomial *qp);
2480 The constant term of a quasipolynomial can be extracted using
2482 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2483 __isl_keep isl_qpolynomial *qp);
2485 To iterate over all terms in a quasipolynomial,
2488 int isl_qpolynomial_foreach_term(
2489 __isl_keep isl_qpolynomial *qp,
2490 int (*fn)(__isl_take isl_term *term,
2491 void *user), void *user);
2493 The terms themselves can be inspected and freed using
2496 unsigned isl_term_dim(__isl_keep isl_term *term,
2497 enum isl_dim_type type);
2498 __isl_give isl_val *isl_term_get_coefficient_val(
2499 __isl_keep isl_term *term);
2500 int isl_term_get_exp(__isl_keep isl_term *term,
2501 enum isl_dim_type type, unsigned pos);
2502 __isl_give isl_aff *isl_term_get_div(
2503 __isl_keep isl_term *term, unsigned pos);
2504 void isl_term_free(__isl_take isl_term *term);
2506 Each term is a product of parameters, set variables and
2507 integer divisions. The function C<isl_term_get_exp>
2508 returns the exponent of a given dimensions in the given term.
2514 A reduction represents a maximum or a minimum of its
2516 The only reduction type defined by C<isl> is
2517 C<isl_qpolynomial_fold>.
2519 There are currently no functions to directly create such
2520 objects, but they do appear in the piecewise quasipolynomial
2521 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2523 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2525 Reductions can be copied and freed using
2526 the following functions.
2528 #include <isl/polynomial.h>
2529 __isl_give isl_qpolynomial_fold *
2530 isl_qpolynomial_fold_copy(
2531 __isl_keep isl_qpolynomial_fold *fold);
2532 void isl_qpolynomial_fold_free(
2533 __isl_take isl_qpolynomial_fold *fold);
2535 To iterate over all quasipolynomials in a reduction, use
2537 int isl_qpolynomial_fold_foreach_qpolynomial(
2538 __isl_keep isl_qpolynomial_fold *fold,
2539 int (*fn)(__isl_take isl_qpolynomial *qp,
2540 void *user), void *user);
2542 =head3 Multiple Expressions
2544 A multiple expression represents a sequence of zero or
2545 more base expressions, all defined on the same domain space.
2546 The domain space of the multiple expression is the same
2547 as that of the base expressions, but the range space
2548 can be any space. In case the base expressions have
2549 a set space, the corresponding multiple expression
2550 also has a set space.
2551 Objects of the value type do not have an associated space.
2552 The space of a multiple value is therefore always a set space.
2553 Similarly, the space of a multiple union piecewise
2554 affine expression is always a set space.
2556 The multiple expression types defined by C<isl>
2557 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2558 C<isl_multi_union_pw_aff>.
2560 A multiple expression with the value zero for
2561 each output (or set) dimension can be created
2562 using the following functions.
2564 #include <isl/val.h>
2565 __isl_give isl_multi_val *isl_multi_val_zero(
2566 __isl_take isl_space *space);
2568 #include <isl/aff.h>
2569 __isl_give isl_multi_aff *isl_multi_aff_zero(
2570 __isl_take isl_space *space);
2571 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2572 __isl_take isl_space *space);
2573 __isl_give isl_multi_union_pw_aff *
2574 isl_multi_union_pw_aff_zero(
2575 __isl_take isl_space *space);
2577 Since there is no canonical way of representing a zero
2578 value of type C<isl_union_pw_aff>, the space passed
2579 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2581 An identity function can be created using the following
2582 functions. The space needs to be that of a relation
2583 with the same number of input and output dimensions.
2585 #include <isl/aff.h>
2586 __isl_give isl_multi_aff *isl_multi_aff_identity(
2587 __isl_take isl_space *space);
2588 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2589 __isl_take isl_space *space);
2591 A function that performs a projection on a universe
2592 relation or set can be created using the following functions.
2593 See also the corresponding
2594 projection operations in L</"Unary Operations">.
2596 #include <isl/aff.h>
2597 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2598 __isl_take isl_space *space);
2599 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2600 __isl_take isl_space *space);
2601 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2602 __isl_take isl_space *space,
2603 enum isl_dim_type type,
2604 unsigned first, unsigned n);
2606 A multiple expression can be created from a single
2607 base expression using the following functions.
2608 The space of the created multiple expression is the same
2609 as that of the base expression, except for
2610 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2611 lives in a parameter space and the output lives
2612 in a single-dimensional set space.
2614 #include <isl/aff.h>
2615 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2616 __isl_take isl_aff *aff);
2617 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2618 __isl_take isl_pw_aff *pa);
2619 __isl_give isl_multi_union_pw_aff *
2620 isl_multi_union_pw_aff_from_union_pw_aff(
2621 __isl_take isl_union_pw_aff *upa);
2623 A multiple expression can be created from a list
2624 of base expression in a specified space.
2625 The domain of this space needs to be the same
2626 as the domains of the base expressions in the list.
2627 If the base expressions have a set space (or no associated space),
2628 then this space also needs to be a set space.
2630 #include <isl/val.h>
2631 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2632 __isl_take isl_space *space,
2633 __isl_take isl_val_list *list);
2635 #include <isl/aff.h>
2636 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2637 __isl_take isl_space *space,
2638 __isl_take isl_aff_list *list);
2639 __isl_give isl_multi_union_pw_aff *
2640 isl_multi_union_pw_aff_from_union_pw_aff_list(
2641 __isl_take isl_space *space,
2642 __isl_take isl_union_pw_aff_list *list);
2644 As a convenience, a multiple piecewise expression can
2645 also be created from a multiple expression.
2646 Each piecewise expression in the result has a single
2649 #include <isl/aff.h>
2650 __isl_give isl_multi_pw_aff *
2651 isl_multi_pw_aff_from_multi_aff(
2652 __isl_take isl_multi_aff *ma);
2654 Similarly, a multiple union expression can be
2655 created from a multiple expression.
2657 #include <isl/aff.h>
2658 __isl_give isl_multi_union_pw_aff *
2659 isl_multi_union_pw_aff_from_multi_aff(
2660 __isl_take isl_multi_aff *ma);
2661 __isl_give isl_multi_union_pw_aff *
2662 isl_multi_union_pw_aff_from_multi_pw_aff(
2663 __isl_take isl_multi_pw_aff *mpa);
2665 A multiple quasi-affine expression can be created from
2666 a multiple value with a given domain space using the following
2669 #include <isl/aff.h>
2670 __isl_give isl_multi_aff *
2671 isl_multi_aff_multi_val_on_space(
2672 __isl_take isl_space *space,
2673 __isl_take isl_multi_val *mv);
2676 a multiple union piecewise affine expression can be created from
2677 a multiple value with a given domain using the following
2680 #include <isl/aff.h>
2681 __isl_give isl_multi_union_pw_aff *
2682 isl_multi_union_pw_aff_multi_val_on_domain(
2683 __isl_take isl_union_set *domain,
2684 __isl_take isl_multi_val *mv);
2686 Multiple expressions can be copied and freed using
2687 the following functions.
2689 #include <isl/val.h>
2690 __isl_give isl_multi_val *isl_multi_val_copy(
2691 __isl_keep isl_multi_val *mv);
2692 __isl_null isl_multi_val *isl_multi_val_free(
2693 __isl_take isl_multi_val *mv);
2695 #include <isl/aff.h>
2696 __isl_give isl_multi_aff *isl_multi_aff_copy(
2697 __isl_keep isl_multi_aff *maff);
2698 __isl_null isl_multi_aff *isl_multi_aff_free(
2699 __isl_take isl_multi_aff *maff);
2700 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2701 __isl_keep isl_multi_pw_aff *mpa);
2702 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2703 __isl_take isl_multi_pw_aff *mpa);
2704 __isl_give isl_multi_union_pw_aff *
2705 isl_multi_union_pw_aff_copy(
2706 __isl_keep isl_multi_union_pw_aff *mupa);
2707 __isl_null isl_multi_union_pw_aff *
2708 isl_multi_union_pw_aff_free(
2709 __isl_take isl_multi_union_pw_aff *mupa);
2711 The base expression at a given position of a multiple
2712 expression can be extracted using the following functions.
2714 #include <isl/val.h>
2715 __isl_give isl_val *isl_multi_val_get_val(
2716 __isl_keep isl_multi_val *mv, int pos);
2718 #include <isl/aff.h>
2719 __isl_give isl_aff *isl_multi_aff_get_aff(
2720 __isl_keep isl_multi_aff *multi, int pos);
2721 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2722 __isl_keep isl_multi_pw_aff *mpa, int pos);
2723 __isl_give isl_union_pw_aff *
2724 isl_multi_union_pw_aff_get_union_pw_aff(
2725 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2727 It can be replaced using the following functions.
2729 #include <isl/val.h>
2730 __isl_give isl_multi_val *isl_multi_val_set_val(
2731 __isl_take isl_multi_val *mv, int pos,
2732 __isl_take isl_val *val);
2734 #include <isl/aff.h>
2735 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2736 __isl_take isl_multi_aff *multi, int pos,
2737 __isl_take isl_aff *aff);
2738 __isl_give isl_multi_union_pw_aff *
2739 isl_multi_union_pw_aff_set_union_pw_aff(
2740 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2741 __isl_take isl_union_pw_aff *upa);
2743 Note that there is a difference between C<isl_multi_union_pw_aff>
2744 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2745 of unions of piecewise expressions, while the second is a union
2746 of piecewise sequences. In particular, multiple affine expressions
2747 in an C<isl_union_pw_multi_aff> may live in different spaces,
2748 while there is only a single multiple expression in
2749 an C<isl_multi_union_pw_aff>, which can therefore only live
2750 in a single space. This means that not every
2751 C<isl_union_pw_multi_aff> can be converted to
2752 an C<isl_multi_union_pw_aff>. The following function can
2753 be used to perform this conversion when it is possible.
2755 #include <isl/aff.h>
2756 __isl_give isl_multi_union_pw_aff *
2757 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2758 __isl_take isl_union_pw_multi_aff *upma);
2760 =head3 Piecewise Expressions
2762 A piecewise expression is an expression that is described
2763 using zero or more base expression defined over the same
2764 number of cells in the domain space of the base expressions.
2765 All base expressions are defined over the same
2766 domain space and the cells are disjoint.
2767 The space of a piecewise expression is the same as
2768 that of the base expressions.
2769 If the union of the cells is a strict subset of the domain
2770 space, then the value of the piecewise expression outside
2771 this union is different for types derived from quasi-affine
2772 expressions and those derived from quasipolynomials.
2773 Piecewise expressions derived from quasi-affine expressions
2774 are considered to be undefined outside the union of their cells.
2775 Piecewise expressions derived from quasipolynomials
2776 are considered to be zero outside the union of their cells.
2778 Piecewise quasipolynomials are mainly used by the C<barvinok>
2779 library for representing the number of elements in a parametric set or map.
2780 For example, the piecewise quasipolynomial
2782 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2784 represents the number of points in the map
2786 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2788 The piecewise expression types defined by C<isl>
2789 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2790 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2792 A piecewise expression with no cells can be created using
2793 the following functions.
2795 #include <isl/aff.h>
2796 __isl_give isl_pw_aff *isl_pw_aff_empty(
2797 __isl_take isl_space *space);
2798 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2799 __isl_take isl_space *space);
2801 A piecewise expression with a single universe cell can be
2802 created using the following functions.
2804 #include <isl/aff.h>
2805 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2806 __isl_take isl_aff *aff);
2807 __isl_give isl_pw_multi_aff *
2808 isl_pw_multi_aff_from_multi_aff(
2809 __isl_take isl_multi_aff *ma);
2811 #include <isl/polynomial.h>
2812 __isl_give isl_pw_qpolynomial *
2813 isl_pw_qpolynomial_from_qpolynomial(
2814 __isl_take isl_qpolynomial *qp);
2816 A piecewise expression with a single specified cell can be
2817 created using the following functions.
2819 #include <isl/aff.h>
2820 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2821 __isl_take isl_set *set, __isl_take isl_aff *aff);
2822 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2823 __isl_take isl_set *set,
2824 __isl_take isl_multi_aff *maff);
2826 #include <isl/polynomial.h>
2827 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2828 __isl_take isl_set *set,
2829 __isl_take isl_qpolynomial *qp);
2831 The following convenience functions first create a base expression and
2832 then create a piecewise expression over a universe domain.
2834 #include <isl/aff.h>
2835 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2836 __isl_take isl_local_space *ls);
2837 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2838 __isl_take isl_local_space *ls,
2839 enum isl_dim_type type, unsigned pos);
2840 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2841 __isl_take isl_local_space *ls);
2842 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2843 __isl_take isl_space *space);
2844 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2845 __isl_take isl_space *space);
2846 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2847 __isl_take isl_space *space);
2848 __isl_give isl_pw_multi_aff *
2849 isl_pw_multi_aff_project_out_map(
2850 __isl_take isl_space *space,
2851 enum isl_dim_type type,
2852 unsigned first, unsigned n);
2854 #include <isl/polynomial.h>
2855 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2856 __isl_take isl_space *space);
2858 The following convenience functions first create a base expression and
2859 then create a piecewise expression over a given domain.
2861 #include <isl/aff.h>
2862 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2863 __isl_take isl_set *domain,
2864 __isl_take isl_val *v);
2865 __isl_give isl_pw_multi_aff *
2866 isl_pw_multi_aff_multi_val_on_domain(
2867 __isl_take isl_set *domain,
2868 __isl_take isl_multi_val *mv);
2870 As a convenience, a piecewise multiple expression can
2871 also be created from a piecewise expression.
2872 Each multiple expression in the result is derived
2873 from the corresponding base expression.
2875 #include <isl/aff.h>
2876 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2877 __isl_take isl_pw_aff *pa);
2879 Similarly, a piecewise quasipolynomial can be
2880 created from a piecewise quasi-affine expression using
2881 the following function.
2883 #include <isl/polynomial.h>
2884 __isl_give isl_pw_qpolynomial *
2885 isl_pw_qpolynomial_from_pw_aff(
2886 __isl_take isl_pw_aff *pwaff);
2888 Piecewise expressions can be copied and freed using the following functions.
2890 #include <isl/aff.h>
2891 __isl_give isl_pw_aff *isl_pw_aff_copy(
2892 __isl_keep isl_pw_aff *pwaff);
2893 __isl_null isl_pw_aff *isl_pw_aff_free(
2894 __isl_take isl_pw_aff *pwaff);
2895 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2896 __isl_keep isl_pw_multi_aff *pma);
2897 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2898 __isl_take isl_pw_multi_aff *pma);
2900 #include <isl/polynomial.h>
2901 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2902 __isl_keep isl_pw_qpolynomial *pwqp);
2903 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2904 __isl_take isl_pw_qpolynomial *pwqp);
2905 __isl_give isl_pw_qpolynomial_fold *
2906 isl_pw_qpolynomial_fold_copy(
2907 __isl_keep isl_pw_qpolynomial_fold *pwf);
2908 __isl_null isl_pw_qpolynomial_fold *
2909 isl_pw_qpolynomial_fold_free(
2910 __isl_take isl_pw_qpolynomial_fold *pwf);
2912 To iterate over the different cells of a piecewise expression,
2913 use the following functions.
2915 #include <isl/aff.h>
2916 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2917 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2918 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2919 int (*fn)(__isl_take isl_set *set,
2920 __isl_take isl_aff *aff,
2921 void *user), void *user);
2922 int isl_pw_multi_aff_foreach_piece(
2923 __isl_keep isl_pw_multi_aff *pma,
2924 int (*fn)(__isl_take isl_set *set,
2925 __isl_take isl_multi_aff *maff,
2926 void *user), void *user);
2928 #include <isl/polynomial.h>
2929 int isl_pw_qpolynomial_foreach_piece(
2930 __isl_keep isl_pw_qpolynomial *pwqp,
2931 int (*fn)(__isl_take isl_set *set,
2932 __isl_take isl_qpolynomial *qp,
2933 void *user), void *user);
2934 int isl_pw_qpolynomial_foreach_lifted_piece(
2935 __isl_keep isl_pw_qpolynomial *pwqp,
2936 int (*fn)(__isl_take isl_set *set,
2937 __isl_take isl_qpolynomial *qp,
2938 void *user), void *user);
2939 int isl_pw_qpolynomial_fold_foreach_piece(
2940 __isl_keep isl_pw_qpolynomial_fold *pwf,
2941 int (*fn)(__isl_take isl_set *set,
2942 __isl_take isl_qpolynomial_fold *fold,
2943 void *user), void *user);
2944 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2945 __isl_keep isl_pw_qpolynomial_fold *pwf,
2946 int (*fn)(__isl_take isl_set *set,
2947 __isl_take isl_qpolynomial_fold *fold,
2948 void *user), void *user);
2950 As usual, the function C<fn> should return C<0> on success
2951 and C<-1> on failure. The difference between
2952 C<isl_pw_qpolynomial_foreach_piece> and
2953 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2954 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2955 compute unique representations for all existentially quantified
2956 variables and then turn these existentially quantified variables
2957 into extra set variables, adapting the associated quasipolynomial
2958 accordingly. This means that the C<set> passed to C<fn>
2959 will not have any existentially quantified variables, but that
2960 the dimensions of the sets may be different for different
2961 invocations of C<fn>.
2962 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2963 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2965 A piecewise expression consisting of the expressions at a given
2966 position of a piecewise multiple expression can be extracted
2967 using the following function.
2969 #include <isl/aff.h>
2970 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2971 __isl_keep isl_pw_multi_aff *pma, int pos);
2973 These expressions can be replaced using the following function.
2975 #include <isl/aff.h>
2976 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2977 __isl_take isl_pw_multi_aff *pma, unsigned pos,
2978 __isl_take isl_pw_aff *pa);
2980 Note that there is a difference between C<isl_multi_pw_aff> and
2981 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
2982 affine expressions, while the second is a piecewise sequence
2983 of affine expressions. In particular, each of the piecewise
2984 affine expressions in an C<isl_multi_pw_aff> may have a different
2985 domain, while all multiple expressions associated to a cell
2986 in an C<isl_pw_multi_aff> have the same domain.
2987 It is possible to convert between the two, but when converting
2988 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
2989 of the result is the intersection of the domains of the input.
2990 The reverse conversion is exact.
2992 #include <isl/aff.h>
2993 __isl_give isl_pw_multi_aff *
2994 isl_pw_multi_aff_from_multi_pw_aff(
2995 __isl_take isl_multi_pw_aff *mpa);
2996 __isl_give isl_multi_pw_aff *
2997 isl_multi_pw_aff_from_pw_multi_aff(
2998 __isl_take isl_pw_multi_aff *pma);
3000 =head3 Union Expressions
3002 A union expression collects base expressions defined
3003 over different domains. The space of a union expression
3004 is that of the shared parameter space.
3006 The union expression types defined by C<isl>
3007 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3008 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3010 An empty union expression can be created using the following functions.
3012 #include <isl/aff.h>
3013 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3014 __isl_take isl_space *space);
3015 __isl_give isl_union_pw_multi_aff *
3016 isl_union_pw_multi_aff_empty(
3017 __isl_take isl_space *space);
3019 #include <isl/polynomial.h>
3020 __isl_give isl_union_pw_qpolynomial *
3021 isl_union_pw_qpolynomial_zero(
3022 __isl_take isl_space *space);
3024 A union expression containing a single base expression
3025 can be created using the following functions.
3027 #include <isl/aff.h>
3028 __isl_give isl_union_pw_aff *
3029 isl_union_pw_aff_from_pw_aff(
3030 __isl_take isl_pw_aff *pa);
3031 __isl_give isl_union_pw_multi_aff *
3032 isl_union_pw_multi_aff_from_aff(
3033 __isl_take isl_aff *aff);
3034 __isl_give isl_union_pw_multi_aff *
3035 isl_union_pw_multi_aff_from_pw_multi_aff(
3036 __isl_take isl_pw_multi_aff *pma);
3038 #include <isl/polynomial.h>
3039 __isl_give isl_union_pw_qpolynomial *
3040 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3041 __isl_take isl_pw_qpolynomial *pwqp);
3043 The following functions create a base expression on each
3044 of the sets in the union set and collect the results.
3046 #include <isl/aff.h>
3047 __isl_give isl_union_pw_multi_aff *
3048 isl_union_pw_multi_aff_from_union_pw_aff(
3049 __isl_take isl_union_pw_aff *upa);
3050 __isl_give isl_union_pw_aff *
3051 isl_union_pw_multi_aff_get_union_pw_aff(
3052 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3053 __isl_give isl_union_pw_aff *
3054 isl_union_pw_aff_val_on_domain(
3055 __isl_take isl_union_set *domain,
3056 __isl_take isl_val *v);
3057 __isl_give isl_union_pw_multi_aff *
3058 isl_union_pw_multi_aff_multi_val_on_domain(
3059 __isl_take isl_union_set *domain,
3060 __isl_take isl_multi_val *mv);
3062 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3063 expression on a given domain can be created using the following
3066 #include <isl/aff.h>
3067 __isl_give isl_union_pw_aff *
3068 isl_union_pw_aff_aff_on_domain(
3069 __isl_take isl_union_set *domain,
3070 __isl_take isl_aff *aff);
3072 A base expression can be added to a union expression using
3073 the following functions.
3075 #include <isl/aff.h>
3076 __isl_give isl_union_pw_aff *
3077 isl_union_pw_aff_add_pw_aff(
3078 __isl_take isl_union_pw_aff *upa,
3079 __isl_take isl_pw_aff *pa);
3080 __isl_give isl_union_pw_multi_aff *
3081 isl_union_pw_multi_aff_add_pw_multi_aff(
3082 __isl_take isl_union_pw_multi_aff *upma,
3083 __isl_take isl_pw_multi_aff *pma);
3085 #include <isl/polynomial.h>
3086 __isl_give isl_union_pw_qpolynomial *
3087 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3088 __isl_take isl_union_pw_qpolynomial *upwqp,
3089 __isl_take isl_pw_qpolynomial *pwqp);
3091 Union expressions can be copied and freed using
3092 the following functions.
3094 #include <isl/aff.h>
3095 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3096 __isl_keep isl_union_pw_aff *upa);
3097 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3098 __isl_take isl_union_pw_aff *upa);
3099 __isl_give isl_union_pw_multi_aff *
3100 isl_union_pw_multi_aff_copy(
3101 __isl_keep isl_union_pw_multi_aff *upma);
3102 __isl_null isl_union_pw_multi_aff *
3103 isl_union_pw_multi_aff_free(
3104 __isl_take isl_union_pw_multi_aff *upma);
3106 #include <isl/polynomial.h>
3107 __isl_give isl_union_pw_qpolynomial *
3108 isl_union_pw_qpolynomial_copy(
3109 __isl_keep isl_union_pw_qpolynomial *upwqp);
3110 __isl_null isl_union_pw_qpolynomial *
3111 isl_union_pw_qpolynomial_free(
3112 __isl_take isl_union_pw_qpolynomial *upwqp);
3113 __isl_give isl_union_pw_qpolynomial_fold *
3114 isl_union_pw_qpolynomial_fold_copy(
3115 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3116 __isl_null isl_union_pw_qpolynomial_fold *
3117 isl_union_pw_qpolynomial_fold_free(
3118 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3120 To iterate over the base expressions in a union expression,
3121 use the following functions.
3123 #include <isl/aff.h>
3124 int isl_union_pw_aff_n_pw_multi_aff(
3125 __isl_keep isl_union_pw_aff *upa);
3126 int isl_union_pw_aff_foreach_pw_aff(
3127 __isl_keep isl_union_pw_aff *upa,
3128 int (*fn)(__isl_take isl_pw_aff *ma, void *user),
3130 int isl_union_pw_multi_aff_n_pw_multi_aff(
3131 __isl_keep isl_union_pw_multi_aff *upma);
3132 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3133 __isl_keep isl_union_pw_multi_aff *upma,
3134 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3135 void *user), void *user);
3137 #include <isl/polynomial.h>
3138 int isl_union_pw_qplynomial_n_pw_qpolynomial(
3139 __isl_keep isl_union_pw_qpolynomial *upwqp);
3140 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3141 __isl_keep isl_union_pw_qpolynomial *upwqp,
3142 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3143 void *user), void *user);
3144 int isl_union_pw_qplynomial_fold_n_pw_qpolynomial_fold(
3145 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3146 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3147 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3148 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3149 void *user), void *user);
3151 To extract the base expression in a given space from a union, use
3152 the following functions.
3154 #include <isl/aff.h>
3155 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3156 __isl_keep isl_union_pw_aff *upa,
3157 __isl_take isl_space *space);
3158 __isl_give isl_pw_multi_aff *
3159 isl_union_pw_multi_aff_extract_pw_multi_aff(
3160 __isl_keep isl_union_pw_multi_aff *upma,
3161 __isl_take isl_space *space);
3163 #include <isl/polynomial.h>
3164 __isl_give isl_pw_qpolynomial *
3165 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3166 __isl_keep isl_union_pw_qpolynomial *upwqp,
3167 __isl_take isl_space *space);
3169 =head2 Input and Output
3171 For set and relation,
3172 C<isl> supports its own input/output format, which is similar
3173 to the C<Omega> format, but also supports the C<PolyLib> format
3175 For other object types, typically only an C<isl> format is supported.
3177 =head3 C<isl> format
3179 The C<isl> format is similar to that of C<Omega>, but has a different
3180 syntax for describing the parameters and allows for the definition
3181 of an existentially quantified variable as the integer division
3182 of an affine expression.
3183 For example, the set of integers C<i> between C<0> and C<n>
3184 such that C<i % 10 <= 6> can be described as
3186 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3189 A set or relation can have several disjuncts, separated
3190 by the keyword C<or>. Each disjunct is either a conjunction
3191 of constraints or a projection (C<exists>) of a conjunction
3192 of constraints. The constraints are separated by the keyword
3195 =head3 C<PolyLib> format
3197 If the represented set is a union, then the first line
3198 contains a single number representing the number of disjuncts.
3199 Otherwise, a line containing the number C<1> is optional.
3201 Each disjunct is represented by a matrix of constraints.
3202 The first line contains two numbers representing
3203 the number of rows and columns,
3204 where the number of rows is equal to the number of constraints
3205 and the number of columns is equal to two plus the number of variables.
3206 The following lines contain the actual rows of the constraint matrix.
3207 In each row, the first column indicates whether the constraint
3208 is an equality (C<0>) or inequality (C<1>). The final column
3209 corresponds to the constant term.
3211 If the set is parametric, then the coefficients of the parameters
3212 appear in the last columns before the constant column.
3213 The coefficients of any existentially quantified variables appear
3214 between those of the set variables and those of the parameters.
3216 =head3 Extended C<PolyLib> format
3218 The extended C<PolyLib> format is nearly identical to the
3219 C<PolyLib> format. The only difference is that the line
3220 containing the number of rows and columns of a constraint matrix
3221 also contains four additional numbers:
3222 the number of output dimensions, the number of input dimensions,
3223 the number of local dimensions (i.e., the number of existentially
3224 quantified variables) and the number of parameters.
3225 For sets, the number of ``output'' dimensions is equal
3226 to the number of set dimensions, while the number of ``input''
3231 Objects can be read from input using the following functions.
3233 #include <isl/val.h>
3234 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3236 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3237 isl_ctx *ctx, const char *str);
3239 #include <isl/set.h>
3240 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3241 isl_ctx *ctx, FILE *input);
3242 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3243 isl_ctx *ctx, const char *str);
3244 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3246 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3249 #include <isl/map.h>
3250 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3251 isl_ctx *ctx, FILE *input);
3252 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3253 isl_ctx *ctx, const char *str);
3254 __isl_give isl_map *isl_map_read_from_file(
3255 isl_ctx *ctx, FILE *input);
3256 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3259 #include <isl/union_set.h>
3260 __isl_give isl_union_set *isl_union_set_read_from_file(
3261 isl_ctx *ctx, FILE *input);
3262 __isl_give isl_union_set *isl_union_set_read_from_str(
3263 isl_ctx *ctx, const char *str);
3265 #include <isl/union_map.h>
3266 __isl_give isl_union_map *isl_union_map_read_from_file(
3267 isl_ctx *ctx, FILE *input);
3268 __isl_give isl_union_map *isl_union_map_read_from_str(
3269 isl_ctx *ctx, const char *str);
3271 #include <isl/aff.h>
3272 __isl_give isl_aff *isl_aff_read_from_str(
3273 isl_ctx *ctx, const char *str);
3274 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3275 isl_ctx *ctx, const char *str);
3276 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3277 isl_ctx *ctx, const char *str);
3278 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3279 isl_ctx *ctx, const char *str);
3280 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3281 isl_ctx *ctx, const char *str);
3282 __isl_give isl_union_pw_multi_aff *
3283 isl_union_pw_multi_aff_read_from_str(
3284 isl_ctx *ctx, const char *str);
3286 #include <isl/polynomial.h>
3287 __isl_give isl_union_pw_qpolynomial *
3288 isl_union_pw_qpolynomial_read_from_str(
3289 isl_ctx *ctx, const char *str);
3291 For sets and relations,
3292 the input format is autodetected and may be either the C<PolyLib> format
3293 or the C<isl> format.
3297 Before anything can be printed, an C<isl_printer> needs to
3300 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3302 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3303 __isl_null isl_printer *isl_printer_free(
3304 __isl_take isl_printer *printer);
3305 __isl_give char *isl_printer_get_str(
3306 __isl_keep isl_printer *printer);
3308 The printer can be inspected using the following functions.
3310 FILE *isl_printer_get_file(
3311 __isl_keep isl_printer *printer);
3312 int isl_printer_get_output_format(
3313 __isl_keep isl_printer *p);
3315 The behavior of the printer can be modified in various ways
3317 __isl_give isl_printer *isl_printer_set_output_format(
3318 __isl_take isl_printer *p, int output_format);
3319 __isl_give isl_printer *isl_printer_set_indent(
3320 __isl_take isl_printer *p, int indent);
3321 __isl_give isl_printer *isl_printer_set_indent_prefix(
3322 __isl_take isl_printer *p, const char *prefix);
3323 __isl_give isl_printer *isl_printer_indent(
3324 __isl_take isl_printer *p, int indent);
3325 __isl_give isl_printer *isl_printer_set_prefix(
3326 __isl_take isl_printer *p, const char *prefix);
3327 __isl_give isl_printer *isl_printer_set_suffix(
3328 __isl_take isl_printer *p, const char *suffix);
3330 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3331 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3332 and defaults to C<ISL_FORMAT_ISL>.
3333 Each line in the output is prefixed by C<indent_prefix>,
3334 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3335 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3336 In the C<PolyLib> format output,
3337 the coefficients of the existentially quantified variables
3338 appear between those of the set variables and those
3340 The function C<isl_printer_indent> increases the indentation
3341 by the specified amount (which may be negative).
3343 To actually print something, use
3345 #include <isl/printer.h>
3346 __isl_give isl_printer *isl_printer_print_double(
3347 __isl_take isl_printer *p, double d);
3349 #include <isl/val.h>
3350 __isl_give isl_printer *isl_printer_print_val(
3351 __isl_take isl_printer *p, __isl_keep isl_val *v);
3353 #include <isl/set.h>
3354 __isl_give isl_printer *isl_printer_print_basic_set(
3355 __isl_take isl_printer *printer,
3356 __isl_keep isl_basic_set *bset);
3357 __isl_give isl_printer *isl_printer_print_set(
3358 __isl_take isl_printer *printer,
3359 __isl_keep isl_set *set);
3361 #include <isl/map.h>
3362 __isl_give isl_printer *isl_printer_print_basic_map(
3363 __isl_take isl_printer *printer,
3364 __isl_keep isl_basic_map *bmap);
3365 __isl_give isl_printer *isl_printer_print_map(
3366 __isl_take isl_printer *printer,
3367 __isl_keep isl_map *map);
3369 #include <isl/union_set.h>
3370 __isl_give isl_printer *isl_printer_print_union_set(
3371 __isl_take isl_printer *p,
3372 __isl_keep isl_union_set *uset);
3374 #include <isl/union_map.h>
3375 __isl_give isl_printer *isl_printer_print_union_map(
3376 __isl_take isl_printer *p,
3377 __isl_keep isl_union_map *umap);
3379 #include <isl/val.h>
3380 __isl_give isl_printer *isl_printer_print_multi_val(
3381 __isl_take isl_printer *p,
3382 __isl_keep isl_multi_val *mv);
3384 #include <isl/aff.h>
3385 __isl_give isl_printer *isl_printer_print_aff(
3386 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3387 __isl_give isl_printer *isl_printer_print_multi_aff(
3388 __isl_take isl_printer *p,
3389 __isl_keep isl_multi_aff *maff);
3390 __isl_give isl_printer *isl_printer_print_pw_aff(
3391 __isl_take isl_printer *p,
3392 __isl_keep isl_pw_aff *pwaff);
3393 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3394 __isl_take isl_printer *p,
3395 __isl_keep isl_pw_multi_aff *pma);
3396 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3397 __isl_take isl_printer *p,
3398 __isl_keep isl_multi_pw_aff *mpa);
3399 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3400 __isl_take isl_printer *p,
3401 __isl_keep isl_union_pw_aff *upa);
3402 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3403 __isl_take isl_printer *p,
3404 __isl_keep isl_union_pw_multi_aff *upma);
3405 __isl_give isl_printer *
3406 isl_printer_print_multi_union_pw_aff(
3407 __isl_take isl_printer *p,
3408 __isl_keep isl_multi_union_pw_aff *mupa);
3410 #include <isl/polynomial.h>
3411 __isl_give isl_printer *isl_printer_print_qpolynomial(
3412 __isl_take isl_printer *p,
3413 __isl_keep isl_qpolynomial *qp);
3414 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3415 __isl_take isl_printer *p,
3416 __isl_keep isl_pw_qpolynomial *pwqp);
3417 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3418 __isl_take isl_printer *p,
3419 __isl_keep isl_union_pw_qpolynomial *upwqp);
3421 __isl_give isl_printer *
3422 isl_printer_print_pw_qpolynomial_fold(
3423 __isl_take isl_printer *p,
3424 __isl_keep isl_pw_qpolynomial_fold *pwf);
3425 __isl_give isl_printer *
3426 isl_printer_print_union_pw_qpolynomial_fold(
3427 __isl_take isl_printer *p,
3428 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3430 For C<isl_printer_print_qpolynomial>,
3431 C<isl_printer_print_pw_qpolynomial> and
3432 C<isl_printer_print_pw_qpolynomial_fold>,
3433 the output format of the printer
3434 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3435 For C<isl_printer_print_union_pw_qpolynomial> and
3436 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3438 In case of printing in C<ISL_FORMAT_C>, the user may want
3439 to set the names of all dimensions first.
3441 When called on a file printer, the following function flushes
3442 the file. When called on a string printer, the buffer is cleared.
3444 __isl_give isl_printer *isl_printer_flush(
3445 __isl_take isl_printer *p);
3447 Alternatively, a string representation can be obtained
3448 directly using the following functions, which always print
3451 #include <isl/space.h>
3452 __isl_give char *isl_space_to_str(
3453 __isl_keep isl_space *space);
3455 #include <isl/val.h>
3456 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3457 __isl_give char *isl_multi_val_to_str(
3458 __isl_keep isl_multi_val *mv);
3460 #include <isl/set.h>
3461 __isl_give char *isl_set_to_str(
3462 __isl_keep isl_set *set);
3464 #include <isl/union_set.h>
3465 __isl_give char *isl_union_set_to_str(
3466 __isl_keep isl_union_set *uset);
3468 #include <isl/map.h>
3469 __isl_give char *isl_map_to_str(
3470 __isl_keep isl_map *map);
3472 #include <isl/union_map.h>
3473 __isl_give char *isl_union_map_to_str(
3474 __isl_keep isl_union_map *umap);
3476 #include <isl/aff.h>
3477 __isl_give char *isl_multi_aff_to_str(
3478 __isl_keep isl_multi_aff *aff);
3479 __isl_give char *isl_union_pw_aff_to_str(
3480 __isl_keep isl_union_pw_aff *upa);
3481 __isl_give char *isl_union_pw_multi_aff_to_str(
3482 __isl_keep isl_union_pw_multi_aff *upma);
3483 __isl_give char *isl_multi_union_pw_aff_to_str(
3484 __isl_keep isl_multi_union_pw_aff *mupa);
3488 =head3 Unary Properties
3494 The following functions test whether the given set or relation
3495 contains any integer points. The ``plain'' variants do not perform
3496 any computations, but simply check if the given set or relation
3497 is already known to be empty.
3499 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3500 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3501 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3502 int isl_set_is_empty(__isl_keep isl_set *set);
3503 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3504 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3505 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3506 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3507 int isl_map_is_empty(__isl_keep isl_map *map);
3508 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3510 =item * Universality
3512 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3513 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3514 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3516 =item * Single-valuedness
3518 #include <isl/set.h>
3519 int isl_set_is_singleton(__isl_keep isl_set *set);
3521 #include <isl/map.h>
3522 int isl_basic_map_is_single_valued(
3523 __isl_keep isl_basic_map *bmap);
3524 int isl_map_plain_is_single_valued(
3525 __isl_keep isl_map *map);
3526 int isl_map_is_single_valued(__isl_keep isl_map *map);
3528 #include <isl/union_map.h>
3529 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3533 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3534 int isl_map_is_injective(__isl_keep isl_map *map);
3535 int isl_union_map_plain_is_injective(
3536 __isl_keep isl_union_map *umap);
3537 int isl_union_map_is_injective(
3538 __isl_keep isl_union_map *umap);
3542 int isl_map_is_bijective(__isl_keep isl_map *map);
3543 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3547 __isl_give isl_val *
3548 isl_basic_map_plain_get_val_if_fixed(
3549 __isl_keep isl_basic_map *bmap,
3550 enum isl_dim_type type, unsigned pos);
3551 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3552 __isl_keep isl_set *set,
3553 enum isl_dim_type type, unsigned pos);
3554 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3555 __isl_keep isl_map *map,
3556 enum isl_dim_type type, unsigned pos);
3558 If the set or relation obviously lies on a hyperplane where the given dimension
3559 has a fixed value, then return that value.
3560 Otherwise return NaN.
3564 int isl_set_dim_residue_class_val(
3565 __isl_keep isl_set *set,
3566 int pos, __isl_give isl_val **modulo,
3567 __isl_give isl_val **residue);
3569 Check if the values of the given set dimension are equal to a fixed
3570 value modulo some integer value. If so, assign the modulo to C<*modulo>
3571 and the fixed value to C<*residue>. If the given dimension attains only
3572 a single value, then assign C<0> to C<*modulo> and the fixed value to
3574 If the dimension does not attain only a single value and if no modulo
3575 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3579 To check whether the description of a set, relation or function depends
3580 on one or more given dimensions,
3581 the following functions can be used.
3583 #include <isl/constraint.h>
3584 int isl_constraint_involves_dims(
3585 __isl_keep isl_constraint *constraint,
3586 enum isl_dim_type type, unsigned first, unsigned n);
3588 #include <isl/set.h>
3589 int isl_basic_set_involves_dims(
3590 __isl_keep isl_basic_set *bset,
3591 enum isl_dim_type type, unsigned first, unsigned n);
3592 int isl_set_involves_dims(__isl_keep isl_set *set,
3593 enum isl_dim_type type, unsigned first, unsigned n);
3595 #include <isl/map.h>
3596 int isl_basic_map_involves_dims(
3597 __isl_keep isl_basic_map *bmap,
3598 enum isl_dim_type type, unsigned first, unsigned n);
3599 int isl_map_involves_dims(__isl_keep isl_map *map,
3600 enum isl_dim_type type, unsigned first, unsigned n);
3602 #include <isl/union_map.h>
3603 int isl_union_map_involves_dims(
3604 __isl_keep isl_union_map *umap,
3605 enum isl_dim_type type, unsigned first, unsigned n);
3607 #include <isl/aff.h>
3608 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3609 enum isl_dim_type type, unsigned first, unsigned n);
3610 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3611 enum isl_dim_type type, unsigned first, unsigned n);
3612 int isl_multi_aff_involves_dims(
3613 __isl_keep isl_multi_aff *ma,
3614 enum isl_dim_type type, unsigned first, unsigned n);
3615 int isl_multi_pw_aff_involves_dims(
3616 __isl_keep isl_multi_pw_aff *mpa,
3617 enum isl_dim_type type, unsigned first, unsigned n);
3619 Similarly, the following functions can be used to check whether
3620 a given dimension is involved in any lower or upper bound.
3622 #include <isl/set.h>
3623 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3624 enum isl_dim_type type, unsigned pos);
3625 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3626 enum isl_dim_type type, unsigned pos);
3628 Note that these functions return true even if there is a bound on
3629 the dimension on only some of the basic sets of C<set>.
3630 To check if they have a bound for all of the basic sets in C<set>,
3631 use the following functions instead.
3633 #include <isl/set.h>
3634 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3635 enum isl_dim_type type, unsigned pos);
3636 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3637 enum isl_dim_type type, unsigned pos);
3641 To check whether a set is a parameter domain, use this function:
3643 int isl_set_is_params(__isl_keep isl_set *set);
3644 int isl_union_set_is_params(
3645 __isl_keep isl_union_set *uset);
3649 The following functions check whether the space of the given
3650 (basic) set or relation range is a wrapped relation.
3652 #include <isl/space.h>
3653 int isl_space_is_wrapping(
3654 __isl_keep isl_space *space);
3655 int isl_space_domain_is_wrapping(
3656 __isl_keep isl_space *space);
3657 int isl_space_range_is_wrapping(
3658 __isl_keep isl_space *space);
3660 #include <isl/set.h>
3661 int isl_basic_set_is_wrapping(
3662 __isl_keep isl_basic_set *bset);
3663 int isl_set_is_wrapping(__isl_keep isl_set *set);
3665 #include <isl/map.h>
3666 int isl_map_domain_is_wrapping(
3667 __isl_keep isl_map *map);
3668 int isl_map_range_is_wrapping(
3669 __isl_keep isl_map *map);
3671 #include <isl/val.h>
3672 int isl_multi_val_range_is_wrapping(
3673 __isl_keep isl_multi_val *mv);
3675 #include <isl/aff.h>
3676 int isl_multi_aff_range_is_wrapping(
3677 __isl_keep isl_multi_aff *ma);
3678 int isl_multi_pw_aff_range_is_wrapping(
3679 __isl_keep isl_multi_pw_aff *mpa);
3680 int isl_multi_union_pw_aff_range_is_wrapping(
3681 __isl_keep isl_multi_union_pw_aff *mupa);
3683 The input to C<isl_space_is_wrapping> should
3684 be the space of a set, while that of
3685 C<isl_space_domain_is_wrapping> and
3686 C<isl_space_range_is_wrapping> should be the space of a relation.
3688 =item * Internal Product
3690 int isl_basic_map_can_zip(
3691 __isl_keep isl_basic_map *bmap);
3692 int isl_map_can_zip(__isl_keep isl_map *map);
3694 Check whether the product of domain and range of the given relation
3696 i.e., whether both domain and range are nested relations.
3700 int isl_basic_map_can_curry(
3701 __isl_keep isl_basic_map *bmap);
3702 int isl_map_can_curry(__isl_keep isl_map *map);
3704 Check whether the domain of the (basic) relation is a wrapped relation.
3706 int isl_basic_map_can_uncurry(
3707 __isl_keep isl_basic_map *bmap);
3708 int isl_map_can_uncurry(__isl_keep isl_map *map);
3710 Check whether the range of the (basic) relation is a wrapped relation.
3712 =item * Special Values
3714 #include <isl/aff.h>
3715 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3716 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3718 Check whether the given expression is a constant.
3720 #include <isl/aff.h>
3721 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3722 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3724 Check whether the given expression is equal to or involves NaN.
3726 #include <isl/aff.h>
3727 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3729 Check whether the affine expression is obviously zero.
3733 =head3 Binary Properties
3739 The following functions check whether two objects
3740 represent the same set, relation or function.
3741 The C<plain> variants only return true if the objects
3742 are obviously the same. That is, they may return false
3743 even if the objects are the same, but they will never
3744 return true if the objects are not the same.
3746 #include <isl/set.h>
3747 int isl_basic_set_plain_is_equal(
3748 __isl_keep isl_basic_set *bset1,
3749 __isl_keep isl_basic_set *bset2);
3750 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3751 __isl_keep isl_set *set2);
3752 int isl_set_is_equal(__isl_keep isl_set *set1,
3753 __isl_keep isl_set *set2);
3755 #include <isl/map.h>
3756 int isl_basic_map_is_equal(
3757 __isl_keep isl_basic_map *bmap1,
3758 __isl_keep isl_basic_map *bmap2);
3759 int isl_map_is_equal(__isl_keep isl_map *map1,
3760 __isl_keep isl_map *map2);
3761 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3762 __isl_keep isl_map *map2);
3764 #include <isl/union_set.h>
3765 int isl_union_set_is_equal(
3766 __isl_keep isl_union_set *uset1,
3767 __isl_keep isl_union_set *uset2);
3769 #include <isl/union_map.h>
3770 int isl_union_map_is_equal(
3771 __isl_keep isl_union_map *umap1,
3772 __isl_keep isl_union_map *umap2);
3774 #include <isl/aff.h>
3775 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3776 __isl_keep isl_aff *aff2);
3777 int isl_multi_aff_plain_is_equal(
3778 __isl_keep isl_multi_aff *maff1,
3779 __isl_keep isl_multi_aff *maff2);
3780 int isl_pw_aff_plain_is_equal(
3781 __isl_keep isl_pw_aff *pwaff1,
3782 __isl_keep isl_pw_aff *pwaff2);
3783 int isl_pw_multi_aff_plain_is_equal(
3784 __isl_keep isl_pw_multi_aff *pma1,
3785 __isl_keep isl_pw_multi_aff *pma2);
3786 int isl_multi_pw_aff_plain_is_equal(
3787 __isl_keep isl_multi_pw_aff *mpa1,
3788 __isl_keep isl_multi_pw_aff *mpa2);
3789 int isl_multi_pw_aff_is_equal(
3790 __isl_keep isl_multi_pw_aff *mpa1,
3791 __isl_keep isl_multi_pw_aff *mpa2);
3792 int isl_union_pw_aff_plain_is_equal(
3793 __isl_keep isl_union_pw_aff *upa1,
3794 __isl_keep isl_union_pw_aff *upa2);
3795 int isl_union_pw_multi_aff_plain_is_equal(
3796 __isl_keep isl_union_pw_multi_aff *upma1,
3797 __isl_keep isl_union_pw_multi_aff *upma2);
3798 int isl_multi_union_pw_aff_plain_is_equal(
3799 __isl_keep isl_multi_union_pw_aff *mupa1,
3800 __isl_keep isl_multi_union_pw_aff *mupa2);
3802 #include <isl/polynomial.h>
3803 int isl_union_pw_qpolynomial_plain_is_equal(
3804 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3805 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3806 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3807 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3808 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3810 =item * Disjointness
3812 #include <isl/set.h>
3813 int isl_basic_set_is_disjoint(
3814 __isl_keep isl_basic_set *bset1,
3815 __isl_keep isl_basic_set *bset2);
3816 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3817 __isl_keep isl_set *set2);
3818 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3819 __isl_keep isl_set *set2);
3821 #include <isl/map.h>
3822 int isl_basic_map_is_disjoint(
3823 __isl_keep isl_basic_map *bmap1,
3824 __isl_keep isl_basic_map *bmap2);
3825 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3826 __isl_keep isl_map *map2);
3828 #include <isl/union_set.h>
3829 int isl_union_set_is_disjoint(
3830 __isl_keep isl_union_set *uset1,
3831 __isl_keep isl_union_set *uset2);
3833 #include <isl/union_map.h>
3834 int isl_union_map_is_disjoint(
3835 __isl_keep isl_union_map *umap1,
3836 __isl_keep isl_union_map *umap2);
3840 int isl_basic_set_is_subset(
3841 __isl_keep isl_basic_set *bset1,
3842 __isl_keep isl_basic_set *bset2);
3843 int isl_set_is_subset(__isl_keep isl_set *set1,
3844 __isl_keep isl_set *set2);
3845 int isl_set_is_strict_subset(
3846 __isl_keep isl_set *set1,
3847 __isl_keep isl_set *set2);
3848 int isl_union_set_is_subset(
3849 __isl_keep isl_union_set *uset1,
3850 __isl_keep isl_union_set *uset2);
3851 int isl_union_set_is_strict_subset(
3852 __isl_keep isl_union_set *uset1,
3853 __isl_keep isl_union_set *uset2);
3854 int isl_basic_map_is_subset(
3855 __isl_keep isl_basic_map *bmap1,
3856 __isl_keep isl_basic_map *bmap2);
3857 int isl_basic_map_is_strict_subset(
3858 __isl_keep isl_basic_map *bmap1,
3859 __isl_keep isl_basic_map *bmap2);
3860 int isl_map_is_subset(
3861 __isl_keep isl_map *map1,
3862 __isl_keep isl_map *map2);
3863 int isl_map_is_strict_subset(
3864 __isl_keep isl_map *map1,
3865 __isl_keep isl_map *map2);
3866 int isl_union_map_is_subset(
3867 __isl_keep isl_union_map *umap1,
3868 __isl_keep isl_union_map *umap2);
3869 int isl_union_map_is_strict_subset(
3870 __isl_keep isl_union_map *umap1,
3871 __isl_keep isl_union_map *umap2);
3873 Check whether the first argument is a (strict) subset of the
3878 Every comparison function returns a negative value if the first
3879 argument is considered smaller than the second, a positive value
3880 if the first argument is considered greater and zero if the two
3881 constraints are considered the same by the comparison criterion.
3883 #include <isl/constraint.h>
3884 int isl_constraint_plain_cmp(
3885 __isl_keep isl_constraint *c1,
3886 __isl_keep isl_constraint *c2);
3888 This function is useful for sorting C<isl_constraint>s.
3889 The order depends on the internal representation of the inputs.
3890 The order is fixed over different calls to the function (assuming
3891 the internal representation of the inputs has not changed), but may
3892 change over different versions of C<isl>.
3894 #include <isl/constraint.h>
3895 int isl_constraint_cmp_last_non_zero(
3896 __isl_keep isl_constraint *c1,
3897 __isl_keep isl_constraint *c2);
3899 This function can be used to sort constraints that live in the same
3900 local space. Constraints that involve ``earlier'' dimensions or
3901 that have a smaller coefficient for the shared latest dimension
3902 are considered smaller than other constraints.
3903 This function only defines a B<partial> order.
3905 #include <isl/set.h>
3906 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3907 __isl_keep isl_set *set2);
3909 This function is useful for sorting C<isl_set>s.
3910 The order depends on the internal representation of the inputs.
3911 The order is fixed over different calls to the function (assuming
3912 the internal representation of the inputs has not changed), but may
3913 change over different versions of C<isl>.
3915 #include <isl/aff.h>
3916 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3917 __isl_keep isl_pw_aff *pa2);
3919 The function C<isl_pw_aff_plain_cmp> can be used to sort
3920 C<isl_pw_aff>s. The order is not strictly defined.
3921 The current order sorts expressions that only involve
3922 earlier dimensions before those that involve later dimensions.
3926 =head2 Unary Operations
3932 __isl_give isl_set *isl_set_complement(
3933 __isl_take isl_set *set);
3934 __isl_give isl_map *isl_map_complement(
3935 __isl_take isl_map *map);
3939 #include <isl/space.h>
3940 __isl_give isl_space *isl_space_reverse(
3941 __isl_take isl_space *space);
3943 #include <isl/map.h>
3944 __isl_give isl_basic_map *isl_basic_map_reverse(
3945 __isl_take isl_basic_map *bmap);
3946 __isl_give isl_map *isl_map_reverse(
3947 __isl_take isl_map *map);
3949 #include <isl/union_map.h>
3950 __isl_give isl_union_map *isl_union_map_reverse(
3951 __isl_take isl_union_map *umap);
3955 #include <isl/space.h>
3956 __isl_give isl_space *isl_space_domain(
3957 __isl_take isl_space *space);
3958 __isl_give isl_space *isl_space_range(
3959 __isl_take isl_space *space);
3960 __isl_give isl_space *isl_space_params(
3961 __isl_take isl_space *space);
3963 #include <isl/local_space.h>
3964 __isl_give isl_local_space *isl_local_space_domain(
3965 __isl_take isl_local_space *ls);
3966 __isl_give isl_local_space *isl_local_space_range(
3967 __isl_take isl_local_space *ls);
3969 #include <isl/set.h>
3970 __isl_give isl_basic_set *isl_basic_set_project_out(
3971 __isl_take isl_basic_set *bset,
3972 enum isl_dim_type type, unsigned first, unsigned n);
3973 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3974 enum isl_dim_type type, unsigned first, unsigned n);
3975 __isl_give isl_basic_set *isl_basic_set_params(
3976 __isl_take isl_basic_set *bset);
3977 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
3979 #include <isl/map.h>
3980 __isl_give isl_basic_map *isl_basic_map_project_out(
3981 __isl_take isl_basic_map *bmap,
3982 enum isl_dim_type type, unsigned first, unsigned n);
3983 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3984 enum isl_dim_type type, unsigned first, unsigned n);
3985 __isl_give isl_basic_set *isl_basic_map_domain(
3986 __isl_take isl_basic_map *bmap);
3987 __isl_give isl_basic_set *isl_basic_map_range(
3988 __isl_take isl_basic_map *bmap);
3989 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
3990 __isl_give isl_set *isl_map_domain(
3991 __isl_take isl_map *bmap);
3992 __isl_give isl_set *isl_map_range(
3993 __isl_take isl_map *map);
3995 #include <isl/union_set.h>
3996 __isl_give isl_union_set *isl_union_set_project_out(
3997 __isl_take isl_union_set *uset,
3998 enum isl_dim_type type,
3999 unsigned first, unsigned n);
4000 __isl_give isl_set *isl_union_set_params(
4001 __isl_take isl_union_set *uset);
4003 The function C<isl_union_set_project_out> can only project out
4006 #include <isl/union_map.h>
4007 __isl_give isl_union_map *isl_union_map_project_out(
4008 __isl_take isl_union_map *umap,
4009 enum isl_dim_type type, unsigned first, unsigned n);
4010 __isl_give isl_set *isl_union_map_params(
4011 __isl_take isl_union_map *umap);
4012 __isl_give isl_union_set *isl_union_map_domain(
4013 __isl_take isl_union_map *umap);
4014 __isl_give isl_union_set *isl_union_map_range(
4015 __isl_take isl_union_map *umap);
4017 The function C<isl_union_map_project_out> can only project out
4020 #include <isl/aff.h>
4021 __isl_give isl_aff *isl_aff_project_domain_on_params(
4022 __isl_take isl_aff *aff);
4023 __isl_give isl_pw_multi_aff *
4024 isl_pw_multi_aff_project_domain_on_params(
4025 __isl_take isl_pw_multi_aff *pma);
4026 __isl_give isl_set *isl_pw_aff_domain(
4027 __isl_take isl_pw_aff *pwaff);
4028 __isl_give isl_set *isl_pw_multi_aff_domain(
4029 __isl_take isl_pw_multi_aff *pma);
4030 __isl_give isl_set *isl_multi_pw_aff_domain(
4031 __isl_take isl_multi_pw_aff *mpa);
4032 __isl_give isl_union_set *isl_union_pw_aff_domain(
4033 __isl_take isl_union_pw_aff *upa);
4034 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4035 __isl_take isl_union_pw_multi_aff *upma);
4036 __isl_give isl_set *isl_pw_aff_params(
4037 __isl_take isl_pw_aff *pwa);
4039 #include <isl/polynomial.h>
4040 __isl_give isl_qpolynomial *
4041 isl_qpolynomial_project_domain_on_params(
4042 __isl_take isl_qpolynomial *qp);
4043 __isl_give isl_pw_qpolynomial *
4044 isl_pw_qpolynomial_project_domain_on_params(
4045 __isl_take isl_pw_qpolynomial *pwqp);
4046 __isl_give isl_pw_qpolynomial_fold *
4047 isl_pw_qpolynomial_fold_project_domain_on_params(
4048 __isl_take isl_pw_qpolynomial_fold *pwf);
4049 __isl_give isl_set *isl_pw_qpolynomial_domain(
4050 __isl_take isl_pw_qpolynomial *pwqp);
4051 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4052 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4053 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4054 __isl_take isl_union_pw_qpolynomial *upwqp);
4056 #include <isl/space.h>
4057 __isl_give isl_space *isl_space_domain_map(
4058 __isl_take isl_space *space);
4059 __isl_give isl_space *isl_space_range_map(
4060 __isl_take isl_space *space);
4062 #include <isl/map.h>
4063 __isl_give isl_map *isl_set_wrapped_domain_map(
4064 __isl_take isl_set *set);
4065 __isl_give isl_basic_map *isl_basic_map_domain_map(
4066 __isl_take isl_basic_map *bmap);
4067 __isl_give isl_basic_map *isl_basic_map_range_map(
4068 __isl_take isl_basic_map *bmap);
4069 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4070 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4072 #include <isl/union_map.h>
4073 __isl_give isl_union_map *isl_union_map_domain_map(
4074 __isl_take isl_union_map *umap);
4075 __isl_give isl_union_pw_multi_aff *
4076 isl_union_map_domain_map_union_pw_multi_aff(
4077 __isl_take isl_union_map *umap);
4078 __isl_give isl_union_map *isl_union_map_range_map(
4079 __isl_take isl_union_map *umap);
4080 __isl_give isl_union_map *
4081 isl_union_set_wrapped_domain_map(
4082 __isl_take isl_union_set *uset);
4084 The functions above construct a (basic, regular or union) relation
4085 that maps (a wrapped version of) the input relation to its domain or range.
4086 C<isl_set_wrapped_domain_map> maps the input set to the domain
4087 of its wrapped relation.
4091 __isl_give isl_basic_set *isl_basic_set_eliminate(
4092 __isl_take isl_basic_set *bset,
4093 enum isl_dim_type type,
4094 unsigned first, unsigned n);
4095 __isl_give isl_set *isl_set_eliminate(
4096 __isl_take isl_set *set, enum isl_dim_type type,
4097 unsigned first, unsigned n);
4098 __isl_give isl_basic_map *isl_basic_map_eliminate(
4099 __isl_take isl_basic_map *bmap,
4100 enum isl_dim_type type,
4101 unsigned first, unsigned n);
4102 __isl_give isl_map *isl_map_eliminate(
4103 __isl_take isl_map *map, enum isl_dim_type type,
4104 unsigned first, unsigned n);
4106 Eliminate the coefficients for the given dimensions from the constraints,
4107 without removing the dimensions.
4109 =item * Constructing a set from a parameter domain
4111 A zero-dimensional space or (basic) set can be constructed
4112 on a given parameter domain using the following functions.
4114 #include <isl/space.h>
4115 __isl_give isl_space *isl_space_set_from_params(
4116 __isl_take isl_space *space);
4118 #include <isl/set.h>
4119 __isl_give isl_basic_set *isl_basic_set_from_params(
4120 __isl_take isl_basic_set *bset);
4121 __isl_give isl_set *isl_set_from_params(
4122 __isl_take isl_set *set);
4124 =item * Constructing a relation from a set
4126 Create a relation with the given set as domain or range.
4127 The range or domain of the created relation is a zero-dimensional
4128 flat anonymous space.
4130 #include <isl/space.h>
4131 __isl_give isl_space *isl_space_from_domain(
4132 __isl_take isl_space *space);
4133 __isl_give isl_space *isl_space_from_range(
4134 __isl_take isl_space *space);
4135 __isl_give isl_space *isl_space_map_from_set(
4136 __isl_take isl_space *space);
4137 __isl_give isl_space *isl_space_map_from_domain_and_range(
4138 __isl_take isl_space *domain,
4139 __isl_take isl_space *range);
4141 #include <isl/local_space.h>
4142 __isl_give isl_local_space *isl_local_space_from_domain(
4143 __isl_take isl_local_space *ls);
4145 #include <isl/map.h>
4146 __isl_give isl_map *isl_map_from_domain(
4147 __isl_take isl_set *set);
4148 __isl_give isl_map *isl_map_from_range(
4149 __isl_take isl_set *set);
4151 #include <isl/val.h>
4152 __isl_give isl_multi_val *isl_multi_val_from_range(
4153 __isl_take isl_multi_val *mv);
4155 #include <isl/aff.h>
4156 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4157 __isl_take isl_multi_aff *ma);
4158 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4159 __isl_take isl_pw_aff *pwa);
4160 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4161 __isl_take isl_multi_pw_aff *mpa);
4162 __isl_give isl_multi_union_pw_aff *
4163 isl_multi_union_pw_aff_from_range(
4164 __isl_take isl_multi_union_pw_aff *mupa);
4165 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4166 __isl_take isl_set *set);
4167 __isl_give isl_union_pw_multi_aff *
4168 isl_union_pw_multi_aff_from_domain(
4169 __isl_take isl_union_set *uset);
4173 #include <isl/set.h>
4174 __isl_give isl_basic_set *isl_basic_set_fix_si(
4175 __isl_take isl_basic_set *bset,
4176 enum isl_dim_type type, unsigned pos, int value);
4177 __isl_give isl_basic_set *isl_basic_set_fix_val(
4178 __isl_take isl_basic_set *bset,
4179 enum isl_dim_type type, unsigned pos,
4180 __isl_take isl_val *v);
4181 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4182 enum isl_dim_type type, unsigned pos, int value);
4183 __isl_give isl_set *isl_set_fix_val(
4184 __isl_take isl_set *set,
4185 enum isl_dim_type type, unsigned pos,
4186 __isl_take isl_val *v);
4188 #include <isl/map.h>
4189 __isl_give isl_basic_map *isl_basic_map_fix_si(
4190 __isl_take isl_basic_map *bmap,
4191 enum isl_dim_type type, unsigned pos, int value);
4192 __isl_give isl_basic_map *isl_basic_map_fix_val(
4193 __isl_take isl_basic_map *bmap,
4194 enum isl_dim_type type, unsigned pos,
4195 __isl_take isl_val *v);
4196 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4197 enum isl_dim_type type, unsigned pos, int value);
4198 __isl_give isl_map *isl_map_fix_val(
4199 __isl_take isl_map *map,
4200 enum isl_dim_type type, unsigned pos,
4201 __isl_take isl_val *v);
4203 #include <isl/aff.h>
4204 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4205 __isl_take isl_pw_multi_aff *pma,
4206 enum isl_dim_type type, unsigned pos, int value);
4208 #include <isl/polynomial.h>
4209 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4210 __isl_take isl_pw_qpolynomial *pwqp,
4211 enum isl_dim_type type, unsigned n,
4212 __isl_take isl_val *v);
4214 Intersect the set, relation or function domain
4215 with the hyperplane where the given
4216 dimension has the fixed given value.
4218 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4219 __isl_take isl_basic_map *bmap,
4220 enum isl_dim_type type, unsigned pos, int value);
4221 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4222 __isl_take isl_basic_map *bmap,
4223 enum isl_dim_type type, unsigned pos, int value);
4224 __isl_give isl_set *isl_set_lower_bound_si(
4225 __isl_take isl_set *set,
4226 enum isl_dim_type type, unsigned pos, int value);
4227 __isl_give isl_set *isl_set_lower_bound_val(
4228 __isl_take isl_set *set,
4229 enum isl_dim_type type, unsigned pos,
4230 __isl_take isl_val *value);
4231 __isl_give isl_map *isl_map_lower_bound_si(
4232 __isl_take isl_map *map,
4233 enum isl_dim_type type, unsigned pos, int value);
4234 __isl_give isl_set *isl_set_upper_bound_si(
4235 __isl_take isl_set *set,
4236 enum isl_dim_type type, unsigned pos, int value);
4237 __isl_give isl_set *isl_set_upper_bound_val(
4238 __isl_take isl_set *set,
4239 enum isl_dim_type type, unsigned pos,
4240 __isl_take isl_val *value);
4241 __isl_give isl_map *isl_map_upper_bound_si(
4242 __isl_take isl_map *map,
4243 enum isl_dim_type type, unsigned pos, int value);
4245 Intersect the set or relation with the half-space where the given
4246 dimension has a value bounded by the fixed given integer value.
4248 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4249 enum isl_dim_type type1, int pos1,
4250 enum isl_dim_type type2, int pos2);
4251 __isl_give isl_basic_map *isl_basic_map_equate(
4252 __isl_take isl_basic_map *bmap,
4253 enum isl_dim_type type1, int pos1,
4254 enum isl_dim_type type2, int pos2);
4255 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4256 enum isl_dim_type type1, int pos1,
4257 enum isl_dim_type type2, int pos2);
4259 Intersect the set or relation with the hyperplane where the given
4260 dimensions are equal to each other.
4262 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4263 enum isl_dim_type type1, int pos1,
4264 enum isl_dim_type type2, int pos2);
4266 Intersect the relation with the hyperplane where the given
4267 dimensions have opposite values.
4269 __isl_give isl_map *isl_map_order_le(
4270 __isl_take isl_map *map,
4271 enum isl_dim_type type1, int pos1,
4272 enum isl_dim_type type2, int pos2);
4273 __isl_give isl_basic_map *isl_basic_map_order_ge(
4274 __isl_take isl_basic_map *bmap,
4275 enum isl_dim_type type1, int pos1,
4276 enum isl_dim_type type2, int pos2);
4277 __isl_give isl_map *isl_map_order_ge(
4278 __isl_take isl_map *map,
4279 enum isl_dim_type type1, int pos1,
4280 enum isl_dim_type type2, int pos2);
4281 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4282 enum isl_dim_type type1, int pos1,
4283 enum isl_dim_type type2, int pos2);
4284 __isl_give isl_basic_map *isl_basic_map_order_gt(
4285 __isl_take isl_basic_map *bmap,
4286 enum isl_dim_type type1, int pos1,
4287 enum isl_dim_type type2, int pos2);
4288 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4289 enum isl_dim_type type1, int pos1,
4290 enum isl_dim_type type2, int pos2);
4292 Intersect the relation with the half-space where the given
4293 dimensions satisfy the given ordering.
4297 #include <isl/aff.h>
4298 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4299 __isl_take isl_aff *aff);
4300 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4301 __isl_take isl_aff *aff);
4302 __isl_give isl_set *isl_pw_aff_pos_set(
4303 __isl_take isl_pw_aff *pa);
4304 __isl_give isl_set *isl_pw_aff_nonneg_set(
4305 __isl_take isl_pw_aff *pwaff);
4306 __isl_give isl_set *isl_pw_aff_zero_set(
4307 __isl_take isl_pw_aff *pwaff);
4308 __isl_give isl_set *isl_pw_aff_non_zero_set(
4309 __isl_take isl_pw_aff *pwaff);
4310 __isl_give isl_union_set *
4311 isl_union_pw_aff_zero_union_set(
4312 __isl_take isl_union_pw_aff *upa);
4314 The function C<isl_aff_neg_basic_set> returns a basic set
4315 containing those elements in the domain space
4316 of C<aff> where C<aff> is negative.
4317 The function C<isl_pw_aff_nonneg_set> returns a set
4318 containing those elements in the domain
4319 of C<pwaff> where C<pwaff> is non-negative.
4323 __isl_give isl_map *isl_set_identity(
4324 __isl_take isl_set *set);
4325 __isl_give isl_union_map *isl_union_set_identity(
4326 __isl_take isl_union_set *uset);
4327 __isl_give isl_union_pw_multi_aff *
4328 isl_union_set_identity_union_pw_multi_aff(
4329 __isl_take isl_union_set *uset);
4331 Construct an identity relation on the given (union) set.
4333 =item * Function Extraction
4335 A piecewise quasi affine expression that is equal to 1 on a set
4336 and 0 outside the set can be created using the following function.
4338 #include <isl/aff.h>
4339 __isl_give isl_pw_aff *isl_set_indicator_function(
4340 __isl_take isl_set *set);
4342 A piecewise multiple quasi affine expression can be extracted
4343 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4344 and the C<isl_map> is single-valued.
4345 In case of a conversion from an C<isl_union_map>
4346 to an C<isl_union_pw_multi_aff>, these properties need to hold
4347 in each domain space.
4348 A conversion to a C<isl_multi_union_pw_aff> additionally
4349 requires that the input is non-empty and involves only a single
4352 #include <isl/aff.h>
4353 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4354 __isl_take isl_set *set);
4355 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4356 __isl_take isl_map *map);
4358 __isl_give isl_union_pw_multi_aff *
4359 isl_union_pw_multi_aff_from_union_set(
4360 __isl_take isl_union_set *uset);
4361 __isl_give isl_union_pw_multi_aff *
4362 isl_union_pw_multi_aff_from_union_map(
4363 __isl_take isl_union_map *umap);
4365 __isl_give isl_multi_union_pw_aff *
4366 isl_multi_union_pw_aff_from_union_map(
4367 __isl_take isl_union_map *umap);
4371 __isl_give isl_basic_set *isl_basic_map_deltas(
4372 __isl_take isl_basic_map *bmap);
4373 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4374 __isl_give isl_union_set *isl_union_map_deltas(
4375 __isl_take isl_union_map *umap);
4377 These functions return a (basic) set containing the differences
4378 between image elements and corresponding domain elements in the input.
4380 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4381 __isl_take isl_basic_map *bmap);
4382 __isl_give isl_map *isl_map_deltas_map(
4383 __isl_take isl_map *map);
4384 __isl_give isl_union_map *isl_union_map_deltas_map(
4385 __isl_take isl_union_map *umap);
4387 The functions above construct a (basic, regular or union) relation
4388 that maps (a wrapped version of) the input relation to its delta set.
4392 Simplify the representation of a set, relation or functions by trying
4393 to combine pairs of basic sets or relations into a single
4394 basic set or relation.
4396 #include <isl/set.h>
4397 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4399 #include <isl/map.h>
4400 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4402 #include <isl/union_set.h>
4403 __isl_give isl_union_set *isl_union_set_coalesce(
4404 __isl_take isl_union_set *uset);
4406 #include <isl/union_map.h>
4407 __isl_give isl_union_map *isl_union_map_coalesce(
4408 __isl_take isl_union_map *umap);
4410 #include <isl/aff.h>
4411 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4412 __isl_take isl_pw_aff *pwqp);
4413 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4414 __isl_take isl_pw_multi_aff *pma);
4415 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4416 __isl_take isl_multi_pw_aff *mpa);
4417 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4418 __isl_take isl_union_pw_aff *upa);
4419 __isl_give isl_union_pw_multi_aff *
4420 isl_union_pw_multi_aff_coalesce(
4421 __isl_take isl_union_pw_multi_aff *upma);
4423 #include <isl/polynomial.h>
4424 __isl_give isl_pw_qpolynomial_fold *
4425 isl_pw_qpolynomial_fold_coalesce(
4426 __isl_take isl_pw_qpolynomial_fold *pwf);
4427 __isl_give isl_union_pw_qpolynomial *
4428 isl_union_pw_qpolynomial_coalesce(
4429 __isl_take isl_union_pw_qpolynomial *upwqp);
4430 __isl_give isl_union_pw_qpolynomial_fold *
4431 isl_union_pw_qpolynomial_fold_coalesce(
4432 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4434 One of the methods for combining pairs of basic sets or relations
4435 can result in coefficients that are much larger than those that appear
4436 in the constraints of the input. By default, the coefficients are
4437 not allowed to grow larger, but this can be changed by unsetting
4438 the following option.
4440 int isl_options_set_coalesce_bounded_wrapping(
4441 isl_ctx *ctx, int val);
4442 int isl_options_get_coalesce_bounded_wrapping(
4445 =item * Detecting equalities
4447 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4448 __isl_take isl_basic_set *bset);
4449 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4450 __isl_take isl_basic_map *bmap);
4451 __isl_give isl_set *isl_set_detect_equalities(
4452 __isl_take isl_set *set);
4453 __isl_give isl_map *isl_map_detect_equalities(
4454 __isl_take isl_map *map);
4455 __isl_give isl_union_set *isl_union_set_detect_equalities(
4456 __isl_take isl_union_set *uset);
4457 __isl_give isl_union_map *isl_union_map_detect_equalities(
4458 __isl_take isl_union_map *umap);
4460 Simplify the representation of a set or relation by detecting implicit
4463 =item * Removing redundant constraints
4465 #include <isl/set.h>
4466 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4467 __isl_take isl_basic_set *bset);
4468 __isl_give isl_set *isl_set_remove_redundancies(
4469 __isl_take isl_set *set);
4471 #include <isl/union_set.h>
4472 __isl_give isl_union_set *
4473 isl_union_set_remove_redundancies(
4474 __isl_take isl_union_set *uset);
4476 #include <isl/map.h>
4477 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4478 __isl_take isl_basic_map *bmap);
4479 __isl_give isl_map *isl_map_remove_redundancies(
4480 __isl_take isl_map *map);
4482 #include <isl/union_map.h>
4483 __isl_give isl_union_map *
4484 isl_union_map_remove_redundancies(
4485 __isl_take isl_union_map *umap);
4489 __isl_give isl_basic_set *isl_set_convex_hull(
4490 __isl_take isl_set *set);
4491 __isl_give isl_basic_map *isl_map_convex_hull(
4492 __isl_take isl_map *map);
4494 If the input set or relation has any existentially quantified
4495 variables, then the result of these operations is currently undefined.
4499 #include <isl/set.h>
4500 __isl_give isl_basic_set *
4501 isl_set_unshifted_simple_hull(
4502 __isl_take isl_set *set);
4503 __isl_give isl_basic_set *isl_set_simple_hull(
4504 __isl_take isl_set *set);
4505 __isl_give isl_basic_set *
4506 isl_set_unshifted_simple_hull_from_set_list(
4507 __isl_take isl_set *set,
4508 __isl_take isl_set_list *list);
4510 #include <isl/map.h>
4511 __isl_give isl_basic_map *
4512 isl_map_unshifted_simple_hull(
4513 __isl_take isl_map *map);
4514 __isl_give isl_basic_map *isl_map_simple_hull(
4515 __isl_take isl_map *map);
4516 __isl_give isl_basic_map *
4517 isl_map_unshifted_simple_hull_from_map_list(
4518 __isl_take isl_map *map,
4519 __isl_take isl_map_list *list);
4521 #include <isl/union_map.h>
4522 __isl_give isl_union_map *isl_union_map_simple_hull(
4523 __isl_take isl_union_map *umap);
4525 These functions compute a single basic set or relation
4526 that contains the whole input set or relation.
4527 In particular, the output is described by translates
4528 of the constraints describing the basic sets or relations in the input.
4529 In case of C<isl_set_unshifted_simple_hull>, only the original
4530 constraints are used, without any translation.
4531 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4532 C<isl_map_unshifted_simple_hull_from_map_list>, the
4533 constraints are taken from the elements of the second argument.
4537 (See \autoref{s:simple hull}.)
4543 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4544 __isl_take isl_basic_set *bset);
4545 __isl_give isl_basic_set *isl_set_affine_hull(
4546 __isl_take isl_set *set);
4547 __isl_give isl_union_set *isl_union_set_affine_hull(
4548 __isl_take isl_union_set *uset);
4549 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4550 __isl_take isl_basic_map *bmap);
4551 __isl_give isl_basic_map *isl_map_affine_hull(
4552 __isl_take isl_map *map);
4553 __isl_give isl_union_map *isl_union_map_affine_hull(
4554 __isl_take isl_union_map *umap);
4556 In case of union sets and relations, the affine hull is computed
4559 =item * Polyhedral hull
4561 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4562 __isl_take isl_set *set);
4563 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4564 __isl_take isl_map *map);
4565 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4566 __isl_take isl_union_set *uset);
4567 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4568 __isl_take isl_union_map *umap);
4570 These functions compute a single basic set or relation
4571 not involving any existentially quantified variables
4572 that contains the whole input set or relation.
4573 In case of union sets and relations, the polyhedral hull is computed
4576 =item * Other approximations
4578 #include <isl/set.h>
4579 __isl_give isl_basic_set *
4580 isl_basic_set_drop_constraints_involving_dims(
4581 __isl_take isl_basic_set *bset,
4582 enum isl_dim_type type,
4583 unsigned first, unsigned n);
4584 __isl_give isl_basic_set *
4585 isl_basic_set_drop_constraints_not_involving_dims(
4586 __isl_take isl_basic_set *bset,
4587 enum isl_dim_type type,
4588 unsigned first, unsigned n);
4589 __isl_give isl_set *
4590 isl_set_drop_constraints_involving_dims(
4591 __isl_take isl_set *set,
4592 enum isl_dim_type type,
4593 unsigned first, unsigned n);
4595 #include <isl/map.h>
4596 __isl_give isl_basic_map *
4597 isl_basic_map_drop_constraints_involving_dims(
4598 __isl_take isl_basic_map *bmap,
4599 enum isl_dim_type type,
4600 unsigned first, unsigned n);
4601 __isl_give isl_map *
4602 isl_map_drop_constraints_involving_dims(
4603 __isl_take isl_map *map,
4604 enum isl_dim_type type,
4605 unsigned first, unsigned n);
4607 These functions drop any constraints (not) involving the specified dimensions.
4608 Note that the result depends on the representation of the input.
4610 #include <isl/polynomial.h>
4611 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4612 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4613 __isl_give isl_union_pw_qpolynomial *
4614 isl_union_pw_qpolynomial_to_polynomial(
4615 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4617 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4618 the polynomial will be an overapproximation. If C<sign> is negative,
4619 it will be an underapproximation. If C<sign> is zero, the approximation
4620 will lie somewhere in between.
4624 __isl_give isl_basic_set *isl_basic_set_sample(
4625 __isl_take isl_basic_set *bset);
4626 __isl_give isl_basic_set *isl_set_sample(
4627 __isl_take isl_set *set);
4628 __isl_give isl_basic_map *isl_basic_map_sample(
4629 __isl_take isl_basic_map *bmap);
4630 __isl_give isl_basic_map *isl_map_sample(
4631 __isl_take isl_map *map);
4633 If the input (basic) set or relation is non-empty, then return
4634 a singleton subset of the input. Otherwise, return an empty set.
4636 =item * Optimization
4638 #include <isl/ilp.h>
4639 __isl_give isl_val *isl_basic_set_max_val(
4640 __isl_keep isl_basic_set *bset,
4641 __isl_keep isl_aff *obj);
4642 __isl_give isl_val *isl_set_min_val(
4643 __isl_keep isl_set *set,
4644 __isl_keep isl_aff *obj);
4645 __isl_give isl_val *isl_set_max_val(
4646 __isl_keep isl_set *set,
4647 __isl_keep isl_aff *obj);
4649 Compute the minimum or maximum of the integer affine expression C<obj>
4650 over the points in C<set>, returning the result in C<opt>.
4651 The result is C<NULL> in case of an error, the optimal value in case
4652 there is one, negative infinity or infinity if the problem is unbounded and
4653 NaN if the problem is empty.
4655 =item * Parametric optimization
4657 __isl_give isl_pw_aff *isl_set_dim_min(
4658 __isl_take isl_set *set, int pos);
4659 __isl_give isl_pw_aff *isl_set_dim_max(
4660 __isl_take isl_set *set, int pos);
4661 __isl_give isl_pw_aff *isl_map_dim_max(
4662 __isl_take isl_map *map, int pos);
4664 Compute the minimum or maximum of the given set or output dimension
4665 as a function of the parameters (and input dimensions), but independently
4666 of the other set or output dimensions.
4667 For lexicographic optimization, see L<"Lexicographic Optimization">.
4671 The following functions compute either the set of (rational) coefficient
4672 values of valid constraints for the given set or the set of (rational)
4673 values satisfying the constraints with coefficients from the given set.
4674 Internally, these two sets of functions perform essentially the
4675 same operations, except that the set of coefficients is assumed to
4676 be a cone, while the set of values may be any polyhedron.
4677 The current implementation is based on the Farkas lemma and
4678 Fourier-Motzkin elimination, but this may change or be made optional
4679 in future. In particular, future implementations may use different
4680 dualization algorithms or skip the elimination step.
4682 __isl_give isl_basic_set *isl_basic_set_coefficients(
4683 __isl_take isl_basic_set *bset);
4684 __isl_give isl_basic_set *isl_set_coefficients(
4685 __isl_take isl_set *set);
4686 __isl_give isl_union_set *isl_union_set_coefficients(
4687 __isl_take isl_union_set *bset);
4688 __isl_give isl_basic_set *isl_basic_set_solutions(
4689 __isl_take isl_basic_set *bset);
4690 __isl_give isl_basic_set *isl_set_solutions(
4691 __isl_take isl_set *set);
4692 __isl_give isl_union_set *isl_union_set_solutions(
4693 __isl_take isl_union_set *bset);
4697 __isl_give isl_map *isl_map_fixed_power_val(
4698 __isl_take isl_map *map,
4699 __isl_take isl_val *exp);
4700 __isl_give isl_union_map *
4701 isl_union_map_fixed_power_val(
4702 __isl_take isl_union_map *umap,
4703 __isl_take isl_val *exp);
4705 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4706 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4707 of C<map> is computed.
4709 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4711 __isl_give isl_union_map *isl_union_map_power(
4712 __isl_take isl_union_map *umap, int *exact);
4714 Compute a parametric representation for all positive powers I<k> of C<map>.
4715 The result maps I<k> to a nested relation corresponding to the
4716 I<k>th power of C<map>.
4717 The result may be an overapproximation. If the result is known to be exact,
4718 then C<*exact> is set to C<1>.
4720 =item * Transitive closure
4722 __isl_give isl_map *isl_map_transitive_closure(
4723 __isl_take isl_map *map, int *exact);
4724 __isl_give isl_union_map *isl_union_map_transitive_closure(
4725 __isl_take isl_union_map *umap, int *exact);
4727 Compute the transitive closure of C<map>.
4728 The result may be an overapproximation. If the result is known to be exact,
4729 then C<*exact> is set to C<1>.
4731 =item * Reaching path lengths
4733 __isl_give isl_map *isl_map_reaching_path_lengths(
4734 __isl_take isl_map *map, int *exact);
4736 Compute a relation that maps each element in the range of C<map>
4737 to the lengths of all paths composed of edges in C<map> that
4738 end up in the given element.
4739 The result may be an overapproximation. If the result is known to be exact,
4740 then C<*exact> is set to C<1>.
4741 To compute the I<maximal> path length, the resulting relation
4742 should be postprocessed by C<isl_map_lexmax>.
4743 In particular, if the input relation is a dependence relation
4744 (mapping sources to sinks), then the maximal path length corresponds
4745 to the free schedule.
4746 Note, however, that C<isl_map_lexmax> expects the maximum to be
4747 finite, so if the path lengths are unbounded (possibly due to
4748 the overapproximation), then you will get an error message.
4752 #include <isl/space.h>
4753 __isl_give isl_space *isl_space_wrap(
4754 __isl_take isl_space *space);
4755 __isl_give isl_space *isl_space_unwrap(
4756 __isl_take isl_space *space);
4758 #include <isl/local_space.h>
4759 __isl_give isl_local_space *isl_local_space_wrap(
4760 __isl_take isl_local_space *ls);
4762 #include <isl/set.h>
4763 __isl_give isl_basic_map *isl_basic_set_unwrap(
4764 __isl_take isl_basic_set *bset);
4765 __isl_give isl_map *isl_set_unwrap(
4766 __isl_take isl_set *set);
4768 #include <isl/map.h>
4769 __isl_give isl_basic_set *isl_basic_map_wrap(
4770 __isl_take isl_basic_map *bmap);
4771 __isl_give isl_set *isl_map_wrap(
4772 __isl_take isl_map *map);
4774 #include <isl/union_set.h>
4775 __isl_give isl_union_map *isl_union_set_unwrap(
4776 __isl_take isl_union_set *uset);
4778 #include <isl/union_map.h>
4779 __isl_give isl_union_set *isl_union_map_wrap(
4780 __isl_take isl_union_map *umap);
4782 The input to C<isl_space_unwrap> should
4783 be the space of a set, while that of
4784 C<isl_space_wrap> should be the space of a relation.
4785 Conversely, the output of C<isl_space_unwrap> is the space
4786 of a relation, while that of C<isl_space_wrap> is the space of a set.
4790 Remove any internal structure of domain (and range) of the given
4791 set or relation. If there is any such internal structure in the input,
4792 then the name of the space is also removed.
4794 #include <isl/local_space.h>
4795 __isl_give isl_local_space *
4796 isl_local_space_flatten_domain(
4797 __isl_take isl_local_space *ls);
4798 __isl_give isl_local_space *
4799 isl_local_space_flatten_range(
4800 __isl_take isl_local_space *ls);
4802 #include <isl/set.h>
4803 __isl_give isl_basic_set *isl_basic_set_flatten(
4804 __isl_take isl_basic_set *bset);
4805 __isl_give isl_set *isl_set_flatten(
4806 __isl_take isl_set *set);
4808 #include <isl/map.h>
4809 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4810 __isl_take isl_basic_map *bmap);
4811 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4812 __isl_take isl_basic_map *bmap);
4813 __isl_give isl_map *isl_map_flatten_range(
4814 __isl_take isl_map *map);
4815 __isl_give isl_map *isl_map_flatten_domain(
4816 __isl_take isl_map *map);
4817 __isl_give isl_basic_map *isl_basic_map_flatten(
4818 __isl_take isl_basic_map *bmap);
4819 __isl_give isl_map *isl_map_flatten(
4820 __isl_take isl_map *map);
4822 #include <isl/val.h>
4823 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4824 __isl_take isl_multi_val *mv);
4826 #include <isl/aff.h>
4827 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4828 __isl_take isl_multi_aff *ma);
4829 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4830 __isl_take isl_multi_aff *ma);
4831 __isl_give isl_multi_pw_aff *
4832 isl_multi_pw_aff_flatten_range(
4833 __isl_take isl_multi_pw_aff *mpa);
4834 __isl_give isl_multi_union_pw_aff *
4835 isl_multi_union_pw_aff_flatten_range(
4836 __isl_take isl_multi_union_pw_aff *mupa);
4838 #include <isl/map.h>
4839 __isl_give isl_map *isl_set_flatten_map(
4840 __isl_take isl_set *set);
4842 The function above constructs a relation
4843 that maps the input set to a flattened version of the set.
4847 Lift the input set to a space with extra dimensions corresponding
4848 to the existentially quantified variables in the input.
4849 In particular, the result lives in a wrapped map where the domain
4850 is the original space and the range corresponds to the original
4851 existentially quantified variables.
4853 #include <isl/set.h>
4854 __isl_give isl_basic_set *isl_basic_set_lift(
4855 __isl_take isl_basic_set *bset);
4856 __isl_give isl_set *isl_set_lift(
4857 __isl_take isl_set *set);
4858 __isl_give isl_union_set *isl_union_set_lift(
4859 __isl_take isl_union_set *uset);
4861 Given a local space that contains the existentially quantified
4862 variables of a set, a basic relation that, when applied to
4863 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4864 can be constructed using the following function.
4866 #include <isl/local_space.h>
4867 __isl_give isl_basic_map *isl_local_space_lifting(
4868 __isl_take isl_local_space *ls);
4870 #include <isl/aff.h>
4871 __isl_give isl_multi_aff *isl_multi_aff_lift(
4872 __isl_take isl_multi_aff *maff,
4873 __isl_give isl_local_space **ls);
4875 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4876 then it is assigned the local space that lies at the basis of
4877 the lifting applied.
4879 =item * Internal Product
4881 #include <isl/space.h>
4882 __isl_give isl_space *isl_space_zip(
4883 __isl_take isl_space *space);
4885 #include <isl/map.h>
4886 __isl_give isl_basic_map *isl_basic_map_zip(
4887 __isl_take isl_basic_map *bmap);
4888 __isl_give isl_map *isl_map_zip(
4889 __isl_take isl_map *map);
4891 #include <isl/union_map.h>
4892 __isl_give isl_union_map *isl_union_map_zip(
4893 __isl_take isl_union_map *umap);
4895 Given a relation with nested relations for domain and range,
4896 interchange the range of the domain with the domain of the range.
4900 #include <isl/space.h>
4901 __isl_give isl_space *isl_space_curry(
4902 __isl_take isl_space *space);
4903 __isl_give isl_space *isl_space_uncurry(
4904 __isl_take isl_space *space);
4906 #include <isl/map.h>
4907 __isl_give isl_basic_map *isl_basic_map_curry(
4908 __isl_take isl_basic_map *bmap);
4909 __isl_give isl_basic_map *isl_basic_map_uncurry(
4910 __isl_take isl_basic_map *bmap);
4911 __isl_give isl_map *isl_map_curry(
4912 __isl_take isl_map *map);
4913 __isl_give isl_map *isl_map_uncurry(
4914 __isl_take isl_map *map);
4916 #include <isl/union_map.h>
4917 __isl_give isl_union_map *isl_union_map_curry(
4918 __isl_take isl_union_map *umap);
4919 __isl_give isl_union_map *isl_union_map_uncurry(
4920 __isl_take isl_union_map *umap);
4922 Given a relation with a nested relation for domain,
4923 the C<curry> functions
4924 move the range of the nested relation out of the domain
4925 and use it as the domain of a nested relation in the range,
4926 with the original range as range of this nested relation.
4927 The C<uncurry> functions perform the inverse operation.
4929 =item * Aligning parameters
4931 Change the order of the parameters of the given set, relation
4933 such that the first parameters match those of C<model>.
4934 This may involve the introduction of extra parameters.
4935 All parameters need to be named.
4937 #include <isl/space.h>
4938 __isl_give isl_space *isl_space_align_params(
4939 __isl_take isl_space *space1,
4940 __isl_take isl_space *space2)
4942 #include <isl/set.h>
4943 __isl_give isl_basic_set *isl_basic_set_align_params(
4944 __isl_take isl_basic_set *bset,
4945 __isl_take isl_space *model);
4946 __isl_give isl_set *isl_set_align_params(
4947 __isl_take isl_set *set,
4948 __isl_take isl_space *model);
4950 #include <isl/map.h>
4951 __isl_give isl_basic_map *isl_basic_map_align_params(
4952 __isl_take isl_basic_map *bmap,
4953 __isl_take isl_space *model);
4954 __isl_give isl_map *isl_map_align_params(
4955 __isl_take isl_map *map,
4956 __isl_take isl_space *model);
4958 #include <isl/val.h>
4959 __isl_give isl_multi_val *isl_multi_val_align_params(
4960 __isl_take isl_multi_val *mv,
4961 __isl_take isl_space *model);
4963 #include <isl/aff.h>
4964 __isl_give isl_aff *isl_aff_align_params(
4965 __isl_take isl_aff *aff,
4966 __isl_take isl_space *model);
4967 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4968 __isl_take isl_multi_aff *multi,
4969 __isl_take isl_space *model);
4970 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4971 __isl_take isl_pw_aff *pwaff,
4972 __isl_take isl_space *model);
4973 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4974 __isl_take isl_pw_multi_aff *pma,
4975 __isl_take isl_space *model);
4976 __isl_give isl_union_pw_aff *
4977 isl_union_pw_aff_align_params(
4978 __isl_take isl_union_pw_aff *upa,
4979 __isl_take isl_space *model);
4980 __isl_give isl_union_pw_multi_aff *
4981 isl_union_pw_multi_aff_align_params(
4982 __isl_take isl_union_pw_multi_aff *upma,
4983 __isl_take isl_space *model);
4984 __isl_give isl_multi_union_pw_aff *
4985 isl_multi_union_pw_aff_align_params(
4986 __isl_take isl_multi_union_pw_aff *mupa,
4987 __isl_take isl_space *model);
4989 #include <isl/polynomial.h>
4990 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4991 __isl_take isl_qpolynomial *qp,
4992 __isl_take isl_space *model);
4994 =item * Unary Arithmethic Operations
4996 #include <isl/val.h>
4997 __isl_give isl_multi_val *isl_multi_val_neg(
4998 __isl_take isl_multi_val *mv);
5000 #include <isl/aff.h>
5001 __isl_give isl_aff *isl_aff_neg(
5002 __isl_take isl_aff *aff);
5003 __isl_give isl_multi_aff *isl_multi_aff_neg(
5004 __isl_take isl_multi_aff *ma);
5005 __isl_give isl_pw_aff *isl_pw_aff_neg(
5006 __isl_take isl_pw_aff *pwaff);
5007 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5008 __isl_take isl_pw_multi_aff *pma);
5009 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5010 __isl_take isl_multi_pw_aff *mpa);
5011 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5012 __isl_take isl_union_pw_aff *upa);
5013 __isl_give isl_union_pw_multi_aff *
5014 isl_union_pw_multi_aff_neg(
5015 __isl_take isl_union_pw_multi_aff *upma);
5016 __isl_give isl_multi_union_pw_aff *
5017 isl_multi_union_pw_aff_neg(
5018 __isl_take isl_multi_union_pw_aff *mupa);
5019 __isl_give isl_aff *isl_aff_ceil(
5020 __isl_take isl_aff *aff);
5021 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5022 __isl_take isl_pw_aff *pwaff);
5023 __isl_give isl_aff *isl_aff_floor(
5024 __isl_take isl_aff *aff);
5025 __isl_give isl_multi_aff *isl_multi_aff_floor(
5026 __isl_take isl_multi_aff *ma);
5027 __isl_give isl_pw_aff *isl_pw_aff_floor(
5028 __isl_take isl_pw_aff *pwaff);
5029 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5030 __isl_take isl_union_pw_aff *upa);
5032 #include <isl/aff.h>
5033 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5034 __isl_take isl_pw_aff_list *list);
5035 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5036 __isl_take isl_pw_aff_list *list);
5038 #include <isl/polynomial.h>
5039 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5040 __isl_take isl_qpolynomial *qp);
5041 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5042 __isl_take isl_pw_qpolynomial *pwqp);
5043 __isl_give isl_union_pw_qpolynomial *
5044 isl_union_pw_qpolynomial_neg(
5045 __isl_take isl_union_pw_qpolynomial *upwqp);
5046 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5047 __isl_take isl_qpolynomial *qp,
5049 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5050 __isl_take isl_pw_qpolynomial *pwqp,
5055 The following functions evaluate a function in a point.
5057 #include <isl/polynomial.h>
5058 __isl_give isl_val *isl_pw_qpolynomial_eval(
5059 __isl_take isl_pw_qpolynomial *pwqp,
5060 __isl_take isl_point *pnt);
5061 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5062 __isl_take isl_pw_qpolynomial_fold *pwf,
5063 __isl_take isl_point *pnt);
5064 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5065 __isl_take isl_union_pw_qpolynomial *upwqp,
5066 __isl_take isl_point *pnt);
5067 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5068 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5069 __isl_take isl_point *pnt);
5071 =item * Dimension manipulation
5073 It is usually not advisable to directly change the (input or output)
5074 space of a set or a relation as this removes the name and the internal
5075 structure of the space. However, the functions below can be useful
5076 to add new parameters, assuming
5077 C<isl_set_align_params> and C<isl_map_align_params>
5080 #include <isl/space.h>
5081 __isl_give isl_space *isl_space_add_dims(
5082 __isl_take isl_space *space,
5083 enum isl_dim_type type, unsigned n);
5084 __isl_give isl_space *isl_space_insert_dims(
5085 __isl_take isl_space *space,
5086 enum isl_dim_type type, unsigned pos, unsigned n);
5087 __isl_give isl_space *isl_space_drop_dims(
5088 __isl_take isl_space *space,
5089 enum isl_dim_type type, unsigned first, unsigned n);
5090 __isl_give isl_space *isl_space_move_dims(
5091 __isl_take isl_space *space,
5092 enum isl_dim_type dst_type, unsigned dst_pos,
5093 enum isl_dim_type src_type, unsigned src_pos,
5096 #include <isl/local_space.h>
5097 __isl_give isl_local_space *isl_local_space_add_dims(
5098 __isl_take isl_local_space *ls,
5099 enum isl_dim_type type, unsigned n);
5100 __isl_give isl_local_space *isl_local_space_insert_dims(
5101 __isl_take isl_local_space *ls,
5102 enum isl_dim_type type, unsigned first, unsigned n);
5103 __isl_give isl_local_space *isl_local_space_drop_dims(
5104 __isl_take isl_local_space *ls,
5105 enum isl_dim_type type, unsigned first, unsigned n);
5107 #include <isl/set.h>
5108 __isl_give isl_basic_set *isl_basic_set_add_dims(
5109 __isl_take isl_basic_set *bset,
5110 enum isl_dim_type type, unsigned n);
5111 __isl_give isl_set *isl_set_add_dims(
5112 __isl_take isl_set *set,
5113 enum isl_dim_type type, unsigned n);
5114 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5115 __isl_take isl_basic_set *bset,
5116 enum isl_dim_type type, unsigned pos,
5118 __isl_give isl_set *isl_set_insert_dims(
5119 __isl_take isl_set *set,
5120 enum isl_dim_type type, unsigned pos, unsigned n);
5121 __isl_give isl_basic_set *isl_basic_set_move_dims(
5122 __isl_take isl_basic_set *bset,
5123 enum isl_dim_type dst_type, unsigned dst_pos,
5124 enum isl_dim_type src_type, unsigned src_pos,
5126 __isl_give isl_set *isl_set_move_dims(
5127 __isl_take isl_set *set,
5128 enum isl_dim_type dst_type, unsigned dst_pos,
5129 enum isl_dim_type src_type, unsigned src_pos,
5132 #include <isl/map.h>
5133 __isl_give isl_map *isl_map_add_dims(
5134 __isl_take isl_map *map,
5135 enum isl_dim_type type, unsigned n);
5136 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5137 __isl_take isl_basic_map *bmap,
5138 enum isl_dim_type type, unsigned pos,
5140 __isl_give isl_map *isl_map_insert_dims(
5141 __isl_take isl_map *map,
5142 enum isl_dim_type type, unsigned pos, unsigned n);
5143 __isl_give isl_basic_map *isl_basic_map_move_dims(
5144 __isl_take isl_basic_map *bmap,
5145 enum isl_dim_type dst_type, unsigned dst_pos,
5146 enum isl_dim_type src_type, unsigned src_pos,
5148 __isl_give isl_map *isl_map_move_dims(
5149 __isl_take isl_map *map,
5150 enum isl_dim_type dst_type, unsigned dst_pos,
5151 enum isl_dim_type src_type, unsigned src_pos,
5154 #include <isl/val.h>
5155 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5156 __isl_take isl_multi_val *mv,
5157 enum isl_dim_type type, unsigned first, unsigned n);
5158 __isl_give isl_multi_val *isl_multi_val_add_dims(
5159 __isl_take isl_multi_val *mv,
5160 enum isl_dim_type type, unsigned n);
5161 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5162 __isl_take isl_multi_val *mv,
5163 enum isl_dim_type type, unsigned first, unsigned n);
5165 #include <isl/aff.h>
5166 __isl_give isl_aff *isl_aff_insert_dims(
5167 __isl_take isl_aff *aff,
5168 enum isl_dim_type type, unsigned first, unsigned n);
5169 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5170 __isl_take isl_multi_aff *ma,
5171 enum isl_dim_type type, unsigned first, unsigned n);
5172 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5173 __isl_take isl_pw_aff *pwaff,
5174 enum isl_dim_type type, unsigned first, unsigned n);
5175 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5176 __isl_take isl_multi_pw_aff *mpa,
5177 enum isl_dim_type type, unsigned first, unsigned n);
5178 __isl_give isl_aff *isl_aff_add_dims(
5179 __isl_take isl_aff *aff,
5180 enum isl_dim_type type, unsigned n);
5181 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5182 __isl_take isl_multi_aff *ma,
5183 enum isl_dim_type type, unsigned n);
5184 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5185 __isl_take isl_pw_aff *pwaff,
5186 enum isl_dim_type type, unsigned n);
5187 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5188 __isl_take isl_multi_pw_aff *mpa,
5189 enum isl_dim_type type, unsigned n);
5190 __isl_give isl_aff *isl_aff_drop_dims(
5191 __isl_take isl_aff *aff,
5192 enum isl_dim_type type, unsigned first, unsigned n);
5193 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5194 __isl_take isl_multi_aff *maff,
5195 enum isl_dim_type type, unsigned first, unsigned n);
5196 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5197 __isl_take isl_pw_aff *pwaff,
5198 enum isl_dim_type type, unsigned first, unsigned n);
5199 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5200 __isl_take isl_pw_multi_aff *pma,
5201 enum isl_dim_type type, unsigned first, unsigned n);
5202 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5203 __isl_take isl_union_pw_aff *upa,
5204 enum isl_dim_type type, unsigned first, unsigned n);
5205 __isl_give isl_union_pw_multi_aff *
5206 isl_union_pw_multi_aff_drop_dims(
5207 __isl_take isl_union_pw_multi_aff *upma,
5208 enum isl_dim_type type,
5209 unsigned first, unsigned n);
5210 __isl_give isl_multi_union_pw_aff *
5211 isl_multi_union_pw_aff_drop_dims(
5212 __isl_take isl_multi_union_pw_aff *mupa,
5213 enum isl_dim_type type, unsigned first,
5215 __isl_give isl_aff *isl_aff_move_dims(
5216 __isl_take isl_aff *aff,
5217 enum isl_dim_type dst_type, unsigned dst_pos,
5218 enum isl_dim_type src_type, unsigned src_pos,
5220 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5221 __isl_take isl_multi_aff *ma,
5222 enum isl_dim_type dst_type, unsigned dst_pos,
5223 enum isl_dim_type src_type, unsigned src_pos,
5225 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5226 __isl_take isl_pw_aff *pa,
5227 enum isl_dim_type dst_type, unsigned dst_pos,
5228 enum isl_dim_type src_type, unsigned src_pos,
5230 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5231 __isl_take isl_multi_pw_aff *pma,
5232 enum isl_dim_type dst_type, unsigned dst_pos,
5233 enum isl_dim_type src_type, unsigned src_pos,
5236 #include <isl/polynomial.h>
5237 __isl_give isl_union_pw_qpolynomial *
5238 isl_union_pw_qpolynomial_drop_dims(
5239 __isl_take isl_union_pw_qpolynomial *upwqp,
5240 enum isl_dim_type type,
5241 unsigned first, unsigned n);
5242 __isl_give isl_union_pw_qpolynomial_fold *
5243 isl_union_pw_qpolynomial_fold_drop_dims(
5244 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5245 enum isl_dim_type type,
5246 unsigned first, unsigned n);
5248 The operations on union expressions can only manipulate parameters.
5252 =head2 Binary Operations
5254 The two arguments of a binary operation not only need to live
5255 in the same C<isl_ctx>, they currently also need to have
5256 the same (number of) parameters.
5258 =head3 Basic Operations
5262 =item * Intersection
5264 #include <isl/local_space.h>
5265 __isl_give isl_local_space *isl_local_space_intersect(
5266 __isl_take isl_local_space *ls1,
5267 __isl_take isl_local_space *ls2);
5269 #include <isl/set.h>
5270 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5271 __isl_take isl_basic_set *bset1,
5272 __isl_take isl_basic_set *bset2);
5273 __isl_give isl_basic_set *isl_basic_set_intersect(
5274 __isl_take isl_basic_set *bset1,
5275 __isl_take isl_basic_set *bset2);
5276 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5277 __isl_take struct isl_basic_set_list *list);
5278 __isl_give isl_set *isl_set_intersect_params(
5279 __isl_take isl_set *set,
5280 __isl_take isl_set *params);
5281 __isl_give isl_set *isl_set_intersect(
5282 __isl_take isl_set *set1,
5283 __isl_take isl_set *set2);
5285 #include <isl/map.h>
5286 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5287 __isl_take isl_basic_map *bmap,
5288 __isl_take isl_basic_set *bset);
5289 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5290 __isl_take isl_basic_map *bmap,
5291 __isl_take isl_basic_set *bset);
5292 __isl_give isl_basic_map *isl_basic_map_intersect(
5293 __isl_take isl_basic_map *bmap1,
5294 __isl_take isl_basic_map *bmap2);
5295 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5296 __isl_take isl_basic_map_list *list);
5297 __isl_give isl_map *isl_map_intersect_params(
5298 __isl_take isl_map *map,
5299 __isl_take isl_set *params);
5300 __isl_give isl_map *isl_map_intersect_domain(
5301 __isl_take isl_map *map,
5302 __isl_take isl_set *set);
5303 __isl_give isl_map *isl_map_intersect_range(
5304 __isl_take isl_map *map,
5305 __isl_take isl_set *set);
5306 __isl_give isl_map *isl_map_intersect(
5307 __isl_take isl_map *map1,
5308 __isl_take isl_map *map2);
5310 #include <isl/union_set.h>
5311 __isl_give isl_union_set *isl_union_set_intersect_params(
5312 __isl_take isl_union_set *uset,
5313 __isl_take isl_set *set);
5314 __isl_give isl_union_set *isl_union_set_intersect(
5315 __isl_take isl_union_set *uset1,
5316 __isl_take isl_union_set *uset2);
5318 #include <isl/union_map.h>
5319 __isl_give isl_union_map *isl_union_map_intersect_params(
5320 __isl_take isl_union_map *umap,
5321 __isl_take isl_set *set);
5322 __isl_give isl_union_map *isl_union_map_intersect_domain(
5323 __isl_take isl_union_map *umap,
5324 __isl_take isl_union_set *uset);
5325 __isl_give isl_union_map *isl_union_map_intersect_range(
5326 __isl_take isl_union_map *umap,
5327 __isl_take isl_union_set *uset);
5328 __isl_give isl_union_map *isl_union_map_intersect(
5329 __isl_take isl_union_map *umap1,
5330 __isl_take isl_union_map *umap2);
5332 #include <isl/aff.h>
5333 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5334 __isl_take isl_pw_aff *pa,
5335 __isl_take isl_set *set);
5336 __isl_give isl_multi_pw_aff *
5337 isl_multi_pw_aff_intersect_domain(
5338 __isl_take isl_multi_pw_aff *mpa,
5339 __isl_take isl_set *domain);
5340 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5341 __isl_take isl_pw_multi_aff *pma,
5342 __isl_take isl_set *set);
5343 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5344 __isl_take isl_union_pw_aff *upa,
5345 __isl_take isl_union_set *uset);
5346 __isl_give isl_union_pw_multi_aff *
5347 isl_union_pw_multi_aff_intersect_domain(
5348 __isl_take isl_union_pw_multi_aff *upma,
5349 __isl_take isl_union_set *uset);
5350 __isl_give isl_multi_union_pw_aff *
5351 isl_multi_union_pw_aff_intersect_domain(
5352 __isl_take isl_multi_union_pw_aff *mupa,
5353 __isl_take isl_union_set *uset);
5354 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5355 __isl_take isl_pw_aff *pa,
5356 __isl_take isl_set *set);
5357 __isl_give isl_multi_pw_aff *
5358 isl_multi_pw_aff_intersect_params(
5359 __isl_take isl_multi_pw_aff *mpa,
5360 __isl_take isl_set *set);
5361 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5362 __isl_take isl_pw_multi_aff *pma,
5363 __isl_take isl_set *set);
5364 __isl_give isl_union_pw_aff *
5365 isl_union_pw_aff_intersect_params(
5366 __isl_take isl_union_pw_aff *upa,
5367 __isl_give isl_union_pw_multi_aff *
5368 isl_union_pw_multi_aff_intersect_params(
5369 __isl_take isl_union_pw_multi_aff *upma,
5370 __isl_take isl_set *set);
5371 __isl_give isl_multi_union_pw_aff *
5372 isl_multi_union_pw_aff_intersect_params(
5373 __isl_take isl_multi_union_pw_aff *mupa,
5374 __isl_take isl_set *params);
5376 #include <isl/polynomial.h>
5377 __isl_give isl_pw_qpolynomial *
5378 isl_pw_qpolynomial_intersect_domain(
5379 __isl_take isl_pw_qpolynomial *pwpq,
5380 __isl_take isl_set *set);
5381 __isl_give isl_union_pw_qpolynomial *
5382 isl_union_pw_qpolynomial_intersect_domain(
5383 __isl_take isl_union_pw_qpolynomial *upwpq,
5384 __isl_take isl_union_set *uset);
5385 __isl_give isl_union_pw_qpolynomial_fold *
5386 isl_union_pw_qpolynomial_fold_intersect_domain(
5387 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5388 __isl_take isl_union_set *uset);
5389 __isl_give isl_pw_qpolynomial *
5390 isl_pw_qpolynomial_intersect_params(
5391 __isl_take isl_pw_qpolynomial *pwpq,
5392 __isl_take isl_set *set);
5393 __isl_give isl_pw_qpolynomial_fold *
5394 isl_pw_qpolynomial_fold_intersect_params(
5395 __isl_take isl_pw_qpolynomial_fold *pwf,
5396 __isl_take isl_set *set);
5397 __isl_give isl_union_pw_qpolynomial *
5398 isl_union_pw_qpolynomial_intersect_params(
5399 __isl_take isl_union_pw_qpolynomial *upwpq,
5400 __isl_take isl_set *set);
5401 __isl_give isl_union_pw_qpolynomial_fold *
5402 isl_union_pw_qpolynomial_fold_intersect_params(
5403 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5404 __isl_take isl_set *set);
5406 The second argument to the C<_params> functions needs to be
5407 a parametric (basic) set. For the other functions, a parametric set
5408 for either argument is only allowed if the other argument is
5409 a parametric set as well.
5410 The list passed to C<isl_basic_set_list_intersect> needs to have
5411 at least one element and all elements need to live in the same space.
5415 #include <isl/set.h>
5416 __isl_give isl_set *isl_basic_set_union(
5417 __isl_take isl_basic_set *bset1,
5418 __isl_take isl_basic_set *bset2);
5419 __isl_give isl_set *isl_set_union(
5420 __isl_take isl_set *set1,
5421 __isl_take isl_set *set2);
5423 #include <isl/map.h>
5424 __isl_give isl_map *isl_basic_map_union(
5425 __isl_take isl_basic_map *bmap1,
5426 __isl_take isl_basic_map *bmap2);
5427 __isl_give isl_map *isl_map_union(
5428 __isl_take isl_map *map1,
5429 __isl_take isl_map *map2);
5431 #include <isl/union_set.h>
5432 __isl_give isl_union_set *isl_union_set_union(
5433 __isl_take isl_union_set *uset1,
5434 __isl_take isl_union_set *uset2);
5435 __isl_give isl_union_set *isl_union_set_list_union(
5436 __isl_take isl_union_set_list *list);
5438 #include <isl/union_map.h>
5439 __isl_give isl_union_map *isl_union_map_union(
5440 __isl_take isl_union_map *umap1,
5441 __isl_take isl_union_map *umap2);
5443 =item * Set difference
5445 #include <isl/set.h>
5446 __isl_give isl_set *isl_set_subtract(
5447 __isl_take isl_set *set1,
5448 __isl_take isl_set *set2);
5450 #include <isl/map.h>
5451 __isl_give isl_map *isl_map_subtract(
5452 __isl_take isl_map *map1,
5453 __isl_take isl_map *map2);
5454 __isl_give isl_map *isl_map_subtract_domain(
5455 __isl_take isl_map *map,
5456 __isl_take isl_set *dom);
5457 __isl_give isl_map *isl_map_subtract_range(
5458 __isl_take isl_map *map,
5459 __isl_take isl_set *dom);
5461 #include <isl/union_set.h>
5462 __isl_give isl_union_set *isl_union_set_subtract(
5463 __isl_take isl_union_set *uset1,
5464 __isl_take isl_union_set *uset2);
5466 #include <isl/union_map.h>
5467 __isl_give isl_union_map *isl_union_map_subtract(
5468 __isl_take isl_union_map *umap1,
5469 __isl_take isl_union_map *umap2);
5470 __isl_give isl_union_map *isl_union_map_subtract_domain(
5471 __isl_take isl_union_map *umap,
5472 __isl_take isl_union_set *dom);
5473 __isl_give isl_union_map *isl_union_map_subtract_range(
5474 __isl_take isl_union_map *umap,
5475 __isl_take isl_union_set *dom);
5477 #include <isl/aff.h>
5478 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5479 __isl_take isl_pw_aff *pa,
5480 __isl_take isl_set *set);
5481 __isl_give isl_pw_multi_aff *
5482 isl_pw_multi_aff_subtract_domain(
5483 __isl_take isl_pw_multi_aff *pma,
5484 __isl_take isl_set *set);
5485 __isl_give isl_union_pw_aff *
5486 isl_union_pw_aff_subtract_domain(
5487 __isl_take isl_union_pw_aff *upa,
5488 __isl_take isl_union_set *uset);
5489 __isl_give isl_union_pw_multi_aff *
5490 isl_union_pw_multi_aff_subtract_domain(
5491 __isl_take isl_union_pw_multi_aff *upma,
5492 __isl_take isl_set *set);
5494 #include <isl/polynomial.h>
5495 __isl_give isl_pw_qpolynomial *
5496 isl_pw_qpolynomial_subtract_domain(
5497 __isl_take isl_pw_qpolynomial *pwpq,
5498 __isl_take isl_set *set);
5499 __isl_give isl_pw_qpolynomial_fold *
5500 isl_pw_qpolynomial_fold_subtract_domain(
5501 __isl_take isl_pw_qpolynomial_fold *pwf,
5502 __isl_take isl_set *set);
5503 __isl_give isl_union_pw_qpolynomial *
5504 isl_union_pw_qpolynomial_subtract_domain(
5505 __isl_take isl_union_pw_qpolynomial *upwpq,
5506 __isl_take isl_union_set *uset);
5507 __isl_give isl_union_pw_qpolynomial_fold *
5508 isl_union_pw_qpolynomial_fold_subtract_domain(
5509 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5510 __isl_take isl_union_set *uset);
5514 #include <isl/space.h>
5515 __isl_give isl_space *isl_space_join(
5516 __isl_take isl_space *left,
5517 __isl_take isl_space *right);
5519 #include <isl/map.h>
5520 __isl_give isl_basic_set *isl_basic_set_apply(
5521 __isl_take isl_basic_set *bset,
5522 __isl_take isl_basic_map *bmap);
5523 __isl_give isl_set *isl_set_apply(
5524 __isl_take isl_set *set,
5525 __isl_take isl_map *map);
5526 __isl_give isl_union_set *isl_union_set_apply(
5527 __isl_take isl_union_set *uset,
5528 __isl_take isl_union_map *umap);
5529 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5530 __isl_take isl_basic_map *bmap1,
5531 __isl_take isl_basic_map *bmap2);
5532 __isl_give isl_basic_map *isl_basic_map_apply_range(
5533 __isl_take isl_basic_map *bmap1,
5534 __isl_take isl_basic_map *bmap2);
5535 __isl_give isl_map *isl_map_apply_domain(
5536 __isl_take isl_map *map1,
5537 __isl_take isl_map *map2);
5538 __isl_give isl_map *isl_map_apply_range(
5539 __isl_take isl_map *map1,
5540 __isl_take isl_map *map2);
5542 #include <isl/union_map.h>
5543 __isl_give isl_union_map *isl_union_map_apply_domain(
5544 __isl_take isl_union_map *umap1,
5545 __isl_take isl_union_map *umap2);
5546 __isl_give isl_union_map *isl_union_map_apply_range(
5547 __isl_take isl_union_map *umap1,
5548 __isl_take isl_union_map *umap2);
5550 #include <isl/polynomial.h>
5551 __isl_give isl_pw_qpolynomial_fold *
5552 isl_set_apply_pw_qpolynomial_fold(
5553 __isl_take isl_set *set,
5554 __isl_take isl_pw_qpolynomial_fold *pwf,
5556 __isl_give isl_pw_qpolynomial_fold *
5557 isl_map_apply_pw_qpolynomial_fold(
5558 __isl_take isl_map *map,
5559 __isl_take isl_pw_qpolynomial_fold *pwf,
5561 __isl_give isl_union_pw_qpolynomial_fold *
5562 isl_union_set_apply_union_pw_qpolynomial_fold(
5563 __isl_take isl_union_set *uset,
5564 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5566 __isl_give isl_union_pw_qpolynomial_fold *
5567 isl_union_map_apply_union_pw_qpolynomial_fold(
5568 __isl_take isl_union_map *umap,
5569 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5572 The functions taking a map
5573 compose the given map with the given piecewise quasipolynomial reduction.
5574 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5575 over all elements in the intersection of the range of the map
5576 and the domain of the piecewise quasipolynomial reduction
5577 as a function of an element in the domain of the map.
5578 The functions taking a set compute a bound over all elements in the
5579 intersection of the set and the domain of the
5580 piecewise quasipolynomial reduction.
5584 #include <isl/set.h>
5585 __isl_give isl_basic_set *
5586 isl_basic_set_preimage_multi_aff(
5587 __isl_take isl_basic_set *bset,
5588 __isl_take isl_multi_aff *ma);
5589 __isl_give isl_set *isl_set_preimage_multi_aff(
5590 __isl_take isl_set *set,
5591 __isl_take isl_multi_aff *ma);
5592 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5593 __isl_take isl_set *set,
5594 __isl_take isl_pw_multi_aff *pma);
5595 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5596 __isl_take isl_set *set,
5597 __isl_take isl_multi_pw_aff *mpa);
5599 #include <isl/union_set.h>
5600 __isl_give isl_union_set *
5601 isl_union_set_preimage_multi_aff(
5602 __isl_take isl_union_set *uset,
5603 __isl_take isl_multi_aff *ma);
5604 __isl_give isl_union_set *
5605 isl_union_set_preimage_pw_multi_aff(
5606 __isl_take isl_union_set *uset,
5607 __isl_take isl_pw_multi_aff *pma);
5608 __isl_give isl_union_set *
5609 isl_union_set_preimage_union_pw_multi_aff(
5610 __isl_take isl_union_set *uset,
5611 __isl_take isl_union_pw_multi_aff *upma);
5613 #include <isl/map.h>
5614 __isl_give isl_basic_map *
5615 isl_basic_map_preimage_domain_multi_aff(
5616 __isl_take isl_basic_map *bmap,
5617 __isl_take isl_multi_aff *ma);
5618 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5619 __isl_take isl_map *map,
5620 __isl_take isl_multi_aff *ma);
5621 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5622 __isl_take isl_map *map,
5623 __isl_take isl_multi_aff *ma);
5624 __isl_give isl_map *
5625 isl_map_preimage_domain_pw_multi_aff(
5626 __isl_take isl_map *map,
5627 __isl_take isl_pw_multi_aff *pma);
5628 __isl_give isl_map *
5629 isl_map_preimage_range_pw_multi_aff(
5630 __isl_take isl_map *map,
5631 __isl_take isl_pw_multi_aff *pma);
5632 __isl_give isl_map *
5633 isl_map_preimage_domain_multi_pw_aff(
5634 __isl_take isl_map *map,
5635 __isl_take isl_multi_pw_aff *mpa);
5636 __isl_give isl_basic_map *
5637 isl_basic_map_preimage_range_multi_aff(
5638 __isl_take isl_basic_map *bmap,
5639 __isl_take isl_multi_aff *ma);
5641 #include <isl/union_map.h>
5642 __isl_give isl_union_map *
5643 isl_union_map_preimage_domain_multi_aff(
5644 __isl_take isl_union_map *umap,
5645 __isl_take isl_multi_aff *ma);
5646 __isl_give isl_union_map *
5647 isl_union_map_preimage_range_multi_aff(
5648 __isl_take isl_union_map *umap,
5649 __isl_take isl_multi_aff *ma);
5650 __isl_give isl_union_map *
5651 isl_union_map_preimage_domain_pw_multi_aff(
5652 __isl_take isl_union_map *umap,
5653 __isl_take isl_pw_multi_aff *pma);
5654 __isl_give isl_union_map *
5655 isl_union_map_preimage_range_pw_multi_aff(
5656 __isl_take isl_union_map *umap,
5657 __isl_take isl_pw_multi_aff *pma);
5658 __isl_give isl_union_map *
5659 isl_union_map_preimage_domain_union_pw_multi_aff(
5660 __isl_take isl_union_map *umap,
5661 __isl_take isl_union_pw_multi_aff *upma);
5662 __isl_give isl_union_map *
5663 isl_union_map_preimage_range_union_pw_multi_aff(
5664 __isl_take isl_union_map *umap,
5665 __isl_take isl_union_pw_multi_aff *upma);
5667 These functions compute the preimage of the given set or map domain/range under
5668 the given function. In other words, the expression is plugged
5669 into the set description or into the domain/range of the map.
5673 #include <isl/aff.h>
5674 __isl_give isl_aff *isl_aff_pullback_aff(
5675 __isl_take isl_aff *aff1,
5676 __isl_take isl_aff *aff2);
5677 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5678 __isl_take isl_aff *aff,
5679 __isl_take isl_multi_aff *ma);
5680 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5681 __isl_take isl_pw_aff *pa,
5682 __isl_take isl_multi_aff *ma);
5683 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5684 __isl_take isl_pw_aff *pa,
5685 __isl_take isl_pw_multi_aff *pma);
5686 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5687 __isl_take isl_pw_aff *pa,
5688 __isl_take isl_multi_pw_aff *mpa);
5689 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5690 __isl_take isl_multi_aff *ma1,
5691 __isl_take isl_multi_aff *ma2);
5692 __isl_give isl_pw_multi_aff *
5693 isl_pw_multi_aff_pullback_multi_aff(
5694 __isl_take isl_pw_multi_aff *pma,
5695 __isl_take isl_multi_aff *ma);
5696 __isl_give isl_multi_pw_aff *
5697 isl_multi_pw_aff_pullback_multi_aff(
5698 __isl_take isl_multi_pw_aff *mpa,
5699 __isl_take isl_multi_aff *ma);
5700 __isl_give isl_pw_multi_aff *
5701 isl_pw_multi_aff_pullback_pw_multi_aff(
5702 __isl_take isl_pw_multi_aff *pma1,
5703 __isl_take isl_pw_multi_aff *pma2);
5704 __isl_give isl_multi_pw_aff *
5705 isl_multi_pw_aff_pullback_pw_multi_aff(
5706 __isl_take isl_multi_pw_aff *mpa,
5707 __isl_take isl_pw_multi_aff *pma);
5708 __isl_give isl_multi_pw_aff *
5709 isl_multi_pw_aff_pullback_multi_pw_aff(
5710 __isl_take isl_multi_pw_aff *mpa1,
5711 __isl_take isl_multi_pw_aff *mpa2);
5712 __isl_give isl_union_pw_aff *
5713 isl_union_pw_aff_pullback_union_pw_multi_aff(
5714 __isl_take isl_union_pw_aff *upa,
5715 __isl_take isl_union_pw_multi_aff *upma);
5716 __isl_give isl_union_pw_multi_aff *
5717 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5718 __isl_take isl_union_pw_multi_aff *upma1,
5719 __isl_take isl_union_pw_multi_aff *upma2);
5721 These functions precompose the first expression by the second function.
5722 In other words, the second function is plugged
5723 into the first expression.
5727 #include <isl/aff.h>
5728 __isl_give isl_basic_set *isl_aff_le_basic_set(
5729 __isl_take isl_aff *aff1,
5730 __isl_take isl_aff *aff2);
5731 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5732 __isl_take isl_aff *aff1,
5733 __isl_take isl_aff *aff2);
5734 __isl_give isl_set *isl_pw_aff_eq_set(
5735 __isl_take isl_pw_aff *pwaff1,
5736 __isl_take isl_pw_aff *pwaff2);
5737 __isl_give isl_set *isl_pw_aff_ne_set(
5738 __isl_take isl_pw_aff *pwaff1,
5739 __isl_take isl_pw_aff *pwaff2);
5740 __isl_give isl_set *isl_pw_aff_le_set(
5741 __isl_take isl_pw_aff *pwaff1,
5742 __isl_take isl_pw_aff *pwaff2);
5743 __isl_give isl_set *isl_pw_aff_lt_set(
5744 __isl_take isl_pw_aff *pwaff1,
5745 __isl_take isl_pw_aff *pwaff2);
5746 __isl_give isl_set *isl_pw_aff_ge_set(
5747 __isl_take isl_pw_aff *pwaff1,
5748 __isl_take isl_pw_aff *pwaff2);
5749 __isl_give isl_set *isl_pw_aff_gt_set(
5750 __isl_take isl_pw_aff *pwaff1,
5751 __isl_take isl_pw_aff *pwaff2);
5753 __isl_give isl_set *isl_multi_aff_lex_le_set(
5754 __isl_take isl_multi_aff *ma1,
5755 __isl_take isl_multi_aff *ma2);
5756 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5757 __isl_take isl_multi_aff *ma1,
5758 __isl_take isl_multi_aff *ma2);
5760 __isl_give isl_set *isl_pw_aff_list_eq_set(
5761 __isl_take isl_pw_aff_list *list1,
5762 __isl_take isl_pw_aff_list *list2);
5763 __isl_give isl_set *isl_pw_aff_list_ne_set(
5764 __isl_take isl_pw_aff_list *list1,
5765 __isl_take isl_pw_aff_list *list2);
5766 __isl_give isl_set *isl_pw_aff_list_le_set(
5767 __isl_take isl_pw_aff_list *list1,
5768 __isl_take isl_pw_aff_list *list2);
5769 __isl_give isl_set *isl_pw_aff_list_lt_set(
5770 __isl_take isl_pw_aff_list *list1,
5771 __isl_take isl_pw_aff_list *list2);
5772 __isl_give isl_set *isl_pw_aff_list_ge_set(
5773 __isl_take isl_pw_aff_list *list1,
5774 __isl_take isl_pw_aff_list *list2);
5775 __isl_give isl_set *isl_pw_aff_list_gt_set(
5776 __isl_take isl_pw_aff_list *list1,
5777 __isl_take isl_pw_aff_list *list2);
5779 The function C<isl_aff_ge_basic_set> returns a basic set
5780 containing those elements in the shared space
5781 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5782 The function C<isl_pw_aff_ge_set> returns a set
5783 containing those elements in the shared domain
5784 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5785 greater than or equal to C<pwaff2>.
5786 The function C<isl_multi_aff_lex_le_set> returns a set
5787 containing those elements in the shared domain space
5788 where C<ma1> is lexicographically smaller than or
5790 The functions operating on C<isl_pw_aff_list> apply the corresponding
5791 C<isl_pw_aff> function to each pair of elements in the two lists.
5793 =item * Cartesian Product
5795 #include <isl/space.h>
5796 __isl_give isl_space *isl_space_product(
5797 __isl_take isl_space *space1,
5798 __isl_take isl_space *space2);
5799 __isl_give isl_space *isl_space_domain_product(
5800 __isl_take isl_space *space1,
5801 __isl_take isl_space *space2);
5802 __isl_give isl_space *isl_space_range_product(
5803 __isl_take isl_space *space1,
5804 __isl_take isl_space *space2);
5807 C<isl_space_product>, C<isl_space_domain_product>
5808 and C<isl_space_range_product> take pairs or relation spaces and
5809 produce a single relations space, where either the domain, the range
5810 or both domain and range are wrapped spaces of relations between
5811 the domains and/or ranges of the input spaces.
5812 If the product is only constructed over the domain or the range
5813 then the ranges or the domains of the inputs should be the same.
5814 The function C<isl_space_product> also accepts a pair of set spaces,
5815 in which case it returns a wrapped space of a relation between the
5818 #include <isl/set.h>
5819 __isl_give isl_set *isl_set_product(
5820 __isl_take isl_set *set1,
5821 __isl_take isl_set *set2);
5823 #include <isl/map.h>
5824 __isl_give isl_basic_map *isl_basic_map_domain_product(
5825 __isl_take isl_basic_map *bmap1,
5826 __isl_take isl_basic_map *bmap2);
5827 __isl_give isl_basic_map *isl_basic_map_range_product(
5828 __isl_take isl_basic_map *bmap1,
5829 __isl_take isl_basic_map *bmap2);
5830 __isl_give isl_basic_map *isl_basic_map_product(
5831 __isl_take isl_basic_map *bmap1,
5832 __isl_take isl_basic_map *bmap2);
5833 __isl_give isl_map *isl_map_domain_product(
5834 __isl_take isl_map *map1,
5835 __isl_take isl_map *map2);
5836 __isl_give isl_map *isl_map_range_product(
5837 __isl_take isl_map *map1,
5838 __isl_take isl_map *map2);
5839 __isl_give isl_map *isl_map_product(
5840 __isl_take isl_map *map1,
5841 __isl_take isl_map *map2);
5843 #include <isl/union_set.h>
5844 __isl_give isl_union_set *isl_union_set_product(
5845 __isl_take isl_union_set *uset1,
5846 __isl_take isl_union_set *uset2);
5848 #include <isl/union_map.h>
5849 __isl_give isl_union_map *isl_union_map_domain_product(
5850 __isl_take isl_union_map *umap1,
5851 __isl_take isl_union_map *umap2);
5852 __isl_give isl_union_map *isl_union_map_range_product(
5853 __isl_take isl_union_map *umap1,
5854 __isl_take isl_union_map *umap2);
5855 __isl_give isl_union_map *isl_union_map_product(
5856 __isl_take isl_union_map *umap1,
5857 __isl_take isl_union_map *umap2);
5859 #include <isl/val.h>
5860 __isl_give isl_multi_val *isl_multi_val_range_product(
5861 __isl_take isl_multi_val *mv1,
5862 __isl_take isl_multi_val *mv2);
5863 __isl_give isl_multi_val *isl_multi_val_product(
5864 __isl_take isl_multi_val *mv1,
5865 __isl_take isl_multi_val *mv2);
5867 #include <isl/aff.h>
5868 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5869 __isl_take isl_multi_aff *ma1,
5870 __isl_take isl_multi_aff *ma2);
5871 __isl_give isl_multi_aff *isl_multi_aff_product(
5872 __isl_take isl_multi_aff *ma1,
5873 __isl_take isl_multi_aff *ma2);
5874 __isl_give isl_multi_pw_aff *
5875 isl_multi_pw_aff_range_product(
5876 __isl_take isl_multi_pw_aff *mpa1,
5877 __isl_take isl_multi_pw_aff *mpa2);
5878 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5879 __isl_take isl_multi_pw_aff *mpa1,
5880 __isl_take isl_multi_pw_aff *mpa2);
5881 __isl_give isl_pw_multi_aff *
5882 isl_pw_multi_aff_range_product(
5883 __isl_take isl_pw_multi_aff *pma1,
5884 __isl_take isl_pw_multi_aff *pma2);
5885 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5886 __isl_take isl_pw_multi_aff *pma1,
5887 __isl_take isl_pw_multi_aff *pma2);
5888 __isl_give isl_multi_union_pw_aff *
5889 isl_multi_union_pw_aff_range_product(
5890 __isl_take isl_multi_union_pw_aff *mupa1,
5891 __isl_take isl_multi_union_pw_aff *mupa2);
5893 The above functions compute the cross product of the given
5894 sets, relations or functions. The domains and ranges of the results
5895 are wrapped maps between domains and ranges of the inputs.
5896 To obtain a ``flat'' product, use the following functions
5899 #include <isl/set.h>
5900 __isl_give isl_basic_set *isl_basic_set_flat_product(
5901 __isl_take isl_basic_set *bset1,
5902 __isl_take isl_basic_set *bset2);
5903 __isl_give isl_set *isl_set_flat_product(
5904 __isl_take isl_set *set1,
5905 __isl_take isl_set *set2);
5907 #include <isl/map.h>
5908 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5909 __isl_take isl_basic_map *bmap1,
5910 __isl_take isl_basic_map *bmap2);
5911 __isl_give isl_map *isl_map_flat_domain_product(
5912 __isl_take isl_map *map1,
5913 __isl_take isl_map *map2);
5914 __isl_give isl_map *isl_map_flat_range_product(
5915 __isl_take isl_map *map1,
5916 __isl_take isl_map *map2);
5917 __isl_give isl_basic_map *isl_basic_map_flat_product(
5918 __isl_take isl_basic_map *bmap1,
5919 __isl_take isl_basic_map *bmap2);
5920 __isl_give isl_map *isl_map_flat_product(
5921 __isl_take isl_map *map1,
5922 __isl_take isl_map *map2);
5924 #include <isl/union_map.h>
5925 __isl_give isl_union_map *
5926 isl_union_map_flat_domain_product(
5927 __isl_take isl_union_map *umap1,
5928 __isl_take isl_union_map *umap2);
5929 __isl_give isl_union_map *
5930 isl_union_map_flat_range_product(
5931 __isl_take isl_union_map *umap1,
5932 __isl_take isl_union_map *umap2);
5934 #include <isl/val.h>
5935 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
5936 __isl_take isl_multi_val *mv1,
5937 __isl_take isl_multi_aff *mv2);
5939 #include <isl/aff.h>
5940 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
5941 __isl_take isl_multi_aff *ma1,
5942 __isl_take isl_multi_aff *ma2);
5943 __isl_give isl_pw_multi_aff *
5944 isl_pw_multi_aff_flat_range_product(
5945 __isl_take isl_pw_multi_aff *pma1,
5946 __isl_take isl_pw_multi_aff *pma2);
5947 __isl_give isl_multi_pw_aff *
5948 isl_multi_pw_aff_flat_range_product(
5949 __isl_take isl_multi_pw_aff *mpa1,
5950 __isl_take isl_multi_pw_aff *mpa2);
5951 __isl_give isl_union_pw_multi_aff *
5952 isl_union_pw_multi_aff_flat_range_product(
5953 __isl_take isl_union_pw_multi_aff *upma1,
5954 __isl_take isl_union_pw_multi_aff *upma2);
5955 __isl_give isl_multi_union_pw_aff *
5956 isl_multi_union_pw_aff_flat_range_product(
5957 __isl_take isl_multi_union_pw_aff *mupa1,
5958 __isl_take isl_multi_union_pw_aff *mupa2);
5960 #include <isl/space.h>
5961 __isl_give isl_space *isl_space_factor_domain(
5962 __isl_take isl_space *space);
5963 __isl_give isl_space *isl_space_factor_range(
5964 __isl_take isl_space *space);
5965 __isl_give isl_space *isl_space_domain_factor_domain(
5966 __isl_take isl_space *space);
5967 __isl_give isl_space *isl_space_domain_factor_range(
5968 __isl_take isl_space *space);
5969 __isl_give isl_space *isl_space_range_factor_domain(
5970 __isl_take isl_space *space);
5971 __isl_give isl_space *isl_space_range_factor_range(
5972 __isl_take isl_space *space);
5974 The functions C<isl_space_range_factor_domain> and
5975 C<isl_space_range_factor_range> extract the two arguments from
5976 the result of a call to C<isl_space_range_product>.
5978 The arguments of a call to C<isl_map_range_product> can be extracted
5979 from the result using the following functions.
5981 #include <isl/map.h>
5982 __isl_give isl_map *isl_map_factor_domain(
5983 __isl_take isl_map *map);
5984 __isl_give isl_map *isl_map_factor_range(
5985 __isl_take isl_map *map);
5986 __isl_give isl_map *isl_map_domain_factor_domain(
5987 __isl_take isl_map *map);
5988 __isl_give isl_map *isl_map_domain_factor_range(
5989 __isl_take isl_map *map);
5990 __isl_give isl_map *isl_map_range_factor_domain(
5991 __isl_take isl_map *map);
5992 __isl_give isl_map *isl_map_range_factor_range(
5993 __isl_take isl_map *map);
5995 #include <isl/union_map.h>
5996 __isl_give isl_union_map *isl_union_map_factor_domain(
5997 __isl_take isl_union_map *umap);
5998 __isl_give isl_union_map *isl_union_map_factor_range(
5999 __isl_take isl_union_map *umap);
6000 __isl_give isl_union_map *
6001 isl_union_map_domain_factor_domain(
6002 __isl_take isl_union_map *umap);
6003 __isl_give isl_union_map *
6004 isl_union_map_domain_factor_range(
6005 __isl_take isl_union_map *umap);
6006 __isl_give isl_union_map *
6007 isl_union_map_range_factor_range(
6008 __isl_take isl_union_map *umap);
6010 #include <isl/val.h>
6011 __isl_give isl_multi_val *
6012 isl_multi_val_range_factor_domain(
6013 __isl_take isl_multi_val *mv);
6014 __isl_give isl_multi_val *
6015 isl_multi_val_range_factor_range(
6016 __isl_take isl_multi_val *mv);
6018 #include <isl/aff.h>
6019 __isl_give isl_multi_aff *
6020 isl_multi_aff_range_factor_domain(
6021 __isl_take isl_multi_aff *ma);
6022 __isl_give isl_multi_aff *
6023 isl_multi_aff_range_factor_range(
6024 __isl_take isl_multi_aff *ma);
6025 __isl_give isl_multi_pw_aff *
6026 isl_multi_pw_aff_range_factor_domain(
6027 __isl_take isl_multi_pw_aff *mpa);
6028 __isl_give isl_multi_pw_aff *
6029 isl_multi_pw_aff_range_factor_range(
6030 __isl_take isl_multi_pw_aff *mpa);
6031 __isl_give isl_multi_union_pw_aff *
6032 isl_multi_union_pw_aff_range_factor_domain(
6033 __isl_take isl_multi_union_pw_aff *mupa);
6034 __isl_give isl_multi_union_pw_aff *
6035 isl_multi_union_pw_aff_range_factor_range(
6036 __isl_take isl_multi_union_pw_aff *mupa);
6038 The splice functions are a generalization of the flat product functions,
6039 where the second argument may be inserted at any position inside
6040 the first argument rather than being placed at the end.
6042 #include <isl/val.h>
6043 __isl_give isl_multi_val *isl_multi_val_range_splice(
6044 __isl_take isl_multi_val *mv1, unsigned pos,
6045 __isl_take isl_multi_val *mv2);
6047 #include <isl/aff.h>
6048 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6049 __isl_take isl_multi_aff *ma1, unsigned pos,
6050 __isl_take isl_multi_aff *ma2);
6051 __isl_give isl_multi_aff *isl_multi_aff_splice(
6052 __isl_take isl_multi_aff *ma1,
6053 unsigned in_pos, unsigned out_pos,
6054 __isl_take isl_multi_aff *ma2);
6055 __isl_give isl_multi_pw_aff *
6056 isl_multi_pw_aff_range_splice(
6057 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6058 __isl_take isl_multi_pw_aff *mpa2);
6059 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6060 __isl_take isl_multi_pw_aff *mpa1,
6061 unsigned in_pos, unsigned out_pos,
6062 __isl_take isl_multi_pw_aff *mpa2);
6063 __isl_give isl_multi_union_pw_aff *
6064 isl_multi_union_pw_aff_range_splice(
6065 __isl_take isl_multi_union_pw_aff *mupa1,
6067 __isl_take isl_multi_union_pw_aff *mupa2);
6069 =item * Simplification
6071 When applied to a set or relation,
6072 the gist operation returns a set or relation that has the
6073 same intersection with the context as the input set or relation.
6074 Any implicit equality in the intersection is made explicit in the result,
6075 while all inequalities that are redundant with respect to the intersection
6077 In case of union sets and relations, the gist operation is performed
6080 When applied to a function,
6081 the gist operation applies the set gist operation to each of
6082 the cells in the domain of the input piecewise expression.
6083 The context is also exploited
6084 to simplify the expression associated to each cell.
6086 #include <isl/set.h>
6087 __isl_give isl_basic_set *isl_basic_set_gist(
6088 __isl_take isl_basic_set *bset,
6089 __isl_take isl_basic_set *context);
6090 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6091 __isl_take isl_set *context);
6092 __isl_give isl_set *isl_set_gist_params(
6093 __isl_take isl_set *set,
6094 __isl_take isl_set *context);
6096 #include <isl/map.h>
6097 __isl_give isl_basic_map *isl_basic_map_gist(
6098 __isl_take isl_basic_map *bmap,
6099 __isl_take isl_basic_map *context);
6100 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6101 __isl_take isl_basic_map *bmap,
6102 __isl_take isl_basic_set *context);
6103 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6104 __isl_take isl_map *context);
6105 __isl_give isl_map *isl_map_gist_params(
6106 __isl_take isl_map *map,
6107 __isl_take isl_set *context);
6108 __isl_give isl_map *isl_map_gist_domain(
6109 __isl_take isl_map *map,
6110 __isl_take isl_set *context);
6111 __isl_give isl_map *isl_map_gist_range(
6112 __isl_take isl_map *map,
6113 __isl_take isl_set *context);
6115 #include <isl/union_set.h>
6116 __isl_give isl_union_set *isl_union_set_gist(
6117 __isl_take isl_union_set *uset,
6118 __isl_take isl_union_set *context);
6119 __isl_give isl_union_set *isl_union_set_gist_params(
6120 __isl_take isl_union_set *uset,
6121 __isl_take isl_set *set);
6123 #include <isl/union_map.h>
6124 __isl_give isl_union_map *isl_union_map_gist(
6125 __isl_take isl_union_map *umap,
6126 __isl_take isl_union_map *context);
6127 __isl_give isl_union_map *isl_union_map_gist_params(
6128 __isl_take isl_union_map *umap,
6129 __isl_take isl_set *set);
6130 __isl_give isl_union_map *isl_union_map_gist_domain(
6131 __isl_take isl_union_map *umap,
6132 __isl_take isl_union_set *uset);
6133 __isl_give isl_union_map *isl_union_map_gist_range(
6134 __isl_take isl_union_map *umap,
6135 __isl_take isl_union_set *uset);
6137 #include <isl/aff.h>
6138 __isl_give isl_aff *isl_aff_gist_params(
6139 __isl_take isl_aff *aff,
6140 __isl_take isl_set *context);
6141 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6142 __isl_take isl_set *context);
6143 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6144 __isl_take isl_multi_aff *maff,
6145 __isl_take isl_set *context);
6146 __isl_give isl_multi_aff *isl_multi_aff_gist(
6147 __isl_take isl_multi_aff *maff,
6148 __isl_take isl_set *context);
6149 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6150 __isl_take isl_pw_aff *pwaff,
6151 __isl_take isl_set *context);
6152 __isl_give isl_pw_aff *isl_pw_aff_gist(
6153 __isl_take isl_pw_aff *pwaff,
6154 __isl_take isl_set *context);
6155 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6156 __isl_take isl_pw_multi_aff *pma,
6157 __isl_take isl_set *set);
6158 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6159 __isl_take isl_pw_multi_aff *pma,
6160 __isl_take isl_set *set);
6161 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6162 __isl_take isl_multi_pw_aff *mpa,
6163 __isl_take isl_set *set);
6164 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6165 __isl_take isl_multi_pw_aff *mpa,
6166 __isl_take isl_set *set);
6167 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6168 __isl_take isl_union_pw_aff *upa,
6169 __isl_take isl_union_set *context);
6170 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6171 __isl_take isl_union_pw_aff *upa,
6172 __isl_take isl_set *context);
6173 __isl_give isl_union_pw_multi_aff *
6174 isl_union_pw_multi_aff_gist_params(
6175 __isl_take isl_union_pw_multi_aff *upma,
6176 __isl_take isl_set *context);
6177 __isl_give isl_union_pw_multi_aff *
6178 isl_union_pw_multi_aff_gist(
6179 __isl_take isl_union_pw_multi_aff *upma,
6180 __isl_take isl_union_set *context);
6181 __isl_give isl_multi_union_pw_aff *
6182 isl_multi_union_pw_aff_gist_params(
6183 __isl_take isl_multi_union_pw_aff *aff,
6184 __isl_take isl_set *context);
6185 __isl_give isl_multi_union_pw_aff *
6186 isl_multi_union_pw_aff_gist(
6187 __isl_take isl_multi_union_pw_aff *aff,
6188 __isl_take isl_union_set *context);
6190 #include <isl/polynomial.h>
6191 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6192 __isl_take isl_qpolynomial *qp,
6193 __isl_take isl_set *context);
6194 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6195 __isl_take isl_qpolynomial *qp,
6196 __isl_take isl_set *context);
6197 __isl_give isl_qpolynomial_fold *
6198 isl_qpolynomial_fold_gist_params(
6199 __isl_take isl_qpolynomial_fold *fold,
6200 __isl_take isl_set *context);
6201 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6202 __isl_take isl_qpolynomial_fold *fold,
6203 __isl_take isl_set *context);
6204 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6205 __isl_take isl_pw_qpolynomial *pwqp,
6206 __isl_take isl_set *context);
6207 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6208 __isl_take isl_pw_qpolynomial *pwqp,
6209 __isl_take isl_set *context);
6210 __isl_give isl_pw_qpolynomial_fold *
6211 isl_pw_qpolynomial_fold_gist(
6212 __isl_take isl_pw_qpolynomial_fold *pwf,
6213 __isl_take isl_set *context);
6214 __isl_give isl_pw_qpolynomial_fold *
6215 isl_pw_qpolynomial_fold_gist_params(
6216 __isl_take isl_pw_qpolynomial_fold *pwf,
6217 __isl_take isl_set *context);
6218 __isl_give isl_union_pw_qpolynomial *
6219 isl_union_pw_qpolynomial_gist_params(
6220 __isl_take isl_union_pw_qpolynomial *upwqp,
6221 __isl_take isl_set *context);
6222 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6223 __isl_take isl_union_pw_qpolynomial *upwqp,
6224 __isl_take isl_union_set *context);
6225 __isl_give isl_union_pw_qpolynomial_fold *
6226 isl_union_pw_qpolynomial_fold_gist(
6227 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6228 __isl_take isl_union_set *context);
6229 __isl_give isl_union_pw_qpolynomial_fold *
6230 isl_union_pw_qpolynomial_fold_gist_params(
6231 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6232 __isl_take isl_set *context);
6234 =item * Binary Arithmethic Operations
6236 #include <isl/val.h>
6237 __isl_give isl_multi_val *isl_multi_val_sub(
6238 __isl_take isl_multi_val *mv1,
6239 __isl_take isl_multi_val *mv2);
6241 #include <isl/aff.h>
6242 __isl_give isl_aff *isl_aff_add(
6243 __isl_take isl_aff *aff1,
6244 __isl_take isl_aff *aff2);
6245 __isl_give isl_multi_aff *isl_multi_aff_add(
6246 __isl_take isl_multi_aff *maff1,
6247 __isl_take isl_multi_aff *maff2);
6248 __isl_give isl_pw_aff *isl_pw_aff_add(
6249 __isl_take isl_pw_aff *pwaff1,
6250 __isl_take isl_pw_aff *pwaff2);
6251 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6252 __isl_take isl_pw_multi_aff *pma1,
6253 __isl_take isl_pw_multi_aff *pma2);
6254 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6255 __isl_take isl_union_pw_aff *upa1,
6256 __isl_take isl_union_pw_aff *upa2);
6257 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6258 __isl_take isl_union_pw_multi_aff *upma1,
6259 __isl_take isl_union_pw_multi_aff *upma2);
6260 __isl_give isl_pw_aff *isl_pw_aff_min(
6261 __isl_take isl_pw_aff *pwaff1,
6262 __isl_take isl_pw_aff *pwaff2);
6263 __isl_give isl_pw_aff *isl_pw_aff_max(
6264 __isl_take isl_pw_aff *pwaff1,
6265 __isl_take isl_pw_aff *pwaff2);
6266 __isl_give isl_aff *isl_aff_sub(
6267 __isl_take isl_aff *aff1,
6268 __isl_take isl_aff *aff2);
6269 __isl_give isl_multi_aff *isl_multi_aff_sub(
6270 __isl_take isl_multi_aff *ma1,
6271 __isl_take isl_multi_aff *ma2);
6272 __isl_give isl_pw_aff *isl_pw_aff_sub(
6273 __isl_take isl_pw_aff *pwaff1,
6274 __isl_take isl_pw_aff *pwaff2);
6275 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6276 __isl_take isl_multi_pw_aff *mpa1,
6277 __isl_take isl_multi_pw_aff *mpa2);
6278 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6279 __isl_take isl_pw_multi_aff *pma1,
6280 __isl_take isl_pw_multi_aff *pma2);
6281 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6282 __isl_take isl_union_pw_aff *upa1,
6283 __isl_take isl_union_pw_aff *upa2);
6284 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6285 __isl_take isl_union_pw_multi_aff *upma1,
6286 __isl_take isl_union_pw_multi_aff *upma2);
6287 __isl_give isl_multi_union_pw_aff *
6288 isl_multi_union_pw_aff_sub(
6289 __isl_take isl_multi_union_pw_aff *mupa1,
6290 __isl_take isl_multi_union_pw_aff *mupa2);
6292 C<isl_aff_sub> subtracts the second argument from the first.
6294 #include <isl/polynomial.h>
6295 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6296 __isl_take isl_qpolynomial *qp1,
6297 __isl_take isl_qpolynomial *qp2);
6298 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6299 __isl_take isl_pw_qpolynomial *pwqp1,
6300 __isl_take isl_pw_qpolynomial *pwqp2);
6301 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6302 __isl_take isl_pw_qpolynomial *pwqp1,
6303 __isl_take isl_pw_qpolynomial *pwqp2);
6304 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6305 __isl_take isl_pw_qpolynomial_fold *pwf1,
6306 __isl_take isl_pw_qpolynomial_fold *pwf2);
6307 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6308 __isl_take isl_union_pw_qpolynomial *upwqp1,
6309 __isl_take isl_union_pw_qpolynomial *upwqp2);
6310 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6311 __isl_take isl_qpolynomial *qp1,
6312 __isl_take isl_qpolynomial *qp2);
6313 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6314 __isl_take isl_pw_qpolynomial *pwqp1,
6315 __isl_take isl_pw_qpolynomial *pwqp2);
6316 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6317 __isl_take isl_union_pw_qpolynomial *upwqp1,
6318 __isl_take isl_union_pw_qpolynomial *upwqp2);
6319 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6320 __isl_take isl_pw_qpolynomial_fold *pwf1,
6321 __isl_take isl_pw_qpolynomial_fold *pwf2);
6322 __isl_give isl_union_pw_qpolynomial_fold *
6323 isl_union_pw_qpolynomial_fold_fold(
6324 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6325 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6327 #include <isl/aff.h>
6328 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6329 __isl_take isl_pw_aff *pwaff1,
6330 __isl_take isl_pw_aff *pwaff2);
6331 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6332 __isl_take isl_pw_multi_aff *pma1,
6333 __isl_take isl_pw_multi_aff *pma2);
6334 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6335 __isl_take isl_union_pw_aff *upa1,
6336 __isl_take isl_union_pw_aff *upa2);
6337 __isl_give isl_union_pw_multi_aff *
6338 isl_union_pw_multi_aff_union_add(
6339 __isl_take isl_union_pw_multi_aff *upma1,
6340 __isl_take isl_union_pw_multi_aff *upma2);
6341 __isl_give isl_multi_union_pw_aff *
6342 isl_multi_union_pw_aff_union_add(
6343 __isl_take isl_multi_union_pw_aff *mupa1,
6344 __isl_take isl_multi_union_pw_aff *mupa2);
6345 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6346 __isl_take isl_pw_aff *pwaff1,
6347 __isl_take isl_pw_aff *pwaff2);
6348 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6349 __isl_take isl_pw_aff *pwaff1,
6350 __isl_take isl_pw_aff *pwaff2);
6352 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6353 expression with a domain that is the union of those of C<pwaff1> and
6354 C<pwaff2> and such that on each cell, the quasi-affine expression is
6355 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6356 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6357 associated expression is the defined one.
6358 This in contrast to the C<isl_pw_aff_max> function, which is
6359 only defined on the shared definition domain of the arguments.
6361 #include <isl/val.h>
6362 __isl_give isl_multi_val *isl_multi_val_add_val(
6363 __isl_take isl_multi_val *mv,
6364 __isl_take isl_val *v);
6365 __isl_give isl_multi_val *isl_multi_val_mod_val(
6366 __isl_take isl_multi_val *mv,
6367 __isl_take isl_val *v);
6368 __isl_give isl_multi_val *isl_multi_val_scale_val(
6369 __isl_take isl_multi_val *mv,
6370 __isl_take isl_val *v);
6371 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6372 __isl_take isl_multi_val *mv,
6373 __isl_take isl_val *v);
6375 #include <isl/aff.h>
6376 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6377 __isl_take isl_val *mod);
6378 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6379 __isl_take isl_pw_aff *pa,
6380 __isl_take isl_val *mod);
6381 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6382 __isl_take isl_union_pw_aff *upa,
6383 __isl_take isl_val *f);
6384 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6385 __isl_take isl_val *v);
6386 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6387 __isl_take isl_multi_aff *ma,
6388 __isl_take isl_val *v);
6389 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6390 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6391 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6392 __isl_take isl_multi_pw_aff *mpa,
6393 __isl_take isl_val *v);
6394 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6395 __isl_take isl_pw_multi_aff *pma,
6396 __isl_take isl_val *v);
6397 __isl_give isl_union_pw_multi_aff *
6398 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6399 __isl_take isl_union_pw_aff *upa,
6400 __isl_take isl_val *f);
6401 isl_union_pw_multi_aff_scale_val(
6402 __isl_take isl_union_pw_multi_aff *upma,
6403 __isl_take isl_val *val);
6404 __isl_give isl_multi_union_pw_aff *
6405 isl_multi_union_pw_aff_scale_val(
6406 __isl_take isl_multi_union_pw_aff *mupa,
6407 __isl_take isl_val *v);
6408 __isl_give isl_aff *isl_aff_scale_down_ui(
6409 __isl_take isl_aff *aff, unsigned f);
6410 __isl_give isl_aff *isl_aff_scale_down_val(
6411 __isl_take isl_aff *aff, __isl_take isl_val *v);
6412 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6413 __isl_take isl_multi_aff *ma,
6414 __isl_take isl_val *v);
6415 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6416 __isl_take isl_pw_aff *pa,
6417 __isl_take isl_val *f);
6418 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6419 __isl_take isl_multi_pw_aff *mpa,
6420 __isl_take isl_val *v);
6421 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6422 __isl_take isl_pw_multi_aff *pma,
6423 __isl_take isl_val *v);
6424 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6425 __isl_take isl_union_pw_aff *upa,
6426 __isl_take isl_val *v);
6427 __isl_give isl_union_pw_multi_aff *
6428 isl_union_pw_multi_aff_scale_down_val(
6429 __isl_take isl_union_pw_multi_aff *upma,
6430 __isl_take isl_val *val);
6431 __isl_give isl_multi_union_pw_aff *
6432 isl_multi_union_pw_aff_scale_down_val(
6433 __isl_take isl_multi_union_pw_aff *mupa,
6434 __isl_take isl_val *v);
6436 #include <isl/polynomial.h>
6437 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6438 __isl_take isl_qpolynomial *qp,
6439 __isl_take isl_val *v);
6440 __isl_give isl_qpolynomial_fold *
6441 isl_qpolynomial_fold_scale_val(
6442 __isl_take isl_qpolynomial_fold *fold,
6443 __isl_take isl_val *v);
6444 __isl_give isl_pw_qpolynomial *
6445 isl_pw_qpolynomial_scale_val(
6446 __isl_take isl_pw_qpolynomial *pwqp,
6447 __isl_take isl_val *v);
6448 __isl_give isl_pw_qpolynomial_fold *
6449 isl_pw_qpolynomial_fold_scale_val(
6450 __isl_take isl_pw_qpolynomial_fold *pwf,
6451 __isl_take isl_val *v);
6452 __isl_give isl_union_pw_qpolynomial *
6453 isl_union_pw_qpolynomial_scale_val(
6454 __isl_take isl_union_pw_qpolynomial *upwqp,
6455 __isl_take isl_val *v);
6456 __isl_give isl_union_pw_qpolynomial_fold *
6457 isl_union_pw_qpolynomial_fold_scale_val(
6458 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6459 __isl_take isl_val *v);
6460 __isl_give isl_qpolynomial *
6461 isl_qpolynomial_scale_down_val(
6462 __isl_take isl_qpolynomial *qp,
6463 __isl_take isl_val *v);
6464 __isl_give isl_qpolynomial_fold *
6465 isl_qpolynomial_fold_scale_down_val(
6466 __isl_take isl_qpolynomial_fold *fold,
6467 __isl_take isl_val *v);
6468 __isl_give isl_pw_qpolynomial *
6469 isl_pw_qpolynomial_scale_down_val(
6470 __isl_take isl_pw_qpolynomial *pwqp,
6471 __isl_take isl_val *v);
6472 __isl_give isl_pw_qpolynomial_fold *
6473 isl_pw_qpolynomial_fold_scale_down_val(
6474 __isl_take isl_pw_qpolynomial_fold *pwf,
6475 __isl_take isl_val *v);
6476 __isl_give isl_union_pw_qpolynomial *
6477 isl_union_pw_qpolynomial_scale_down_val(
6478 __isl_take isl_union_pw_qpolynomial *upwqp,
6479 __isl_take isl_val *v);
6480 __isl_give isl_union_pw_qpolynomial_fold *
6481 isl_union_pw_qpolynomial_fold_scale_down_val(
6482 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6483 __isl_take isl_val *v);
6485 #include <isl/val.h>
6486 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6487 __isl_take isl_multi_val *mv1,
6488 __isl_take isl_multi_val *mv2);
6489 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6490 __isl_take isl_multi_val *mv1,
6491 __isl_take isl_multi_val *mv2);
6492 __isl_give isl_multi_val *
6493 isl_multi_val_scale_down_multi_val(
6494 __isl_take isl_multi_val *mv1,
6495 __isl_take isl_multi_val *mv2);
6497 #include <isl/aff.h>
6498 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6499 __isl_take isl_multi_aff *ma,
6500 __isl_take isl_multi_val *mv);
6501 __isl_give isl_multi_union_pw_aff *
6502 isl_multi_union_pw_aff_mod_multi_val(
6503 __isl_take isl_multi_union_pw_aff *upma,
6504 __isl_take isl_multi_val *mv);
6505 __isl_give isl_multi_pw_aff *
6506 isl_multi_pw_aff_mod_multi_val(
6507 __isl_take isl_multi_pw_aff *mpa,
6508 __isl_take isl_multi_val *mv);
6509 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6510 __isl_take isl_multi_aff *ma,
6511 __isl_take isl_multi_val *mv);
6512 __isl_give isl_pw_multi_aff *
6513 isl_pw_multi_aff_scale_multi_val(
6514 __isl_take isl_pw_multi_aff *pma,
6515 __isl_take isl_multi_val *mv);
6516 __isl_give isl_multi_pw_aff *
6517 isl_multi_pw_aff_scale_multi_val(
6518 __isl_take isl_multi_pw_aff *mpa,
6519 __isl_take isl_multi_val *mv);
6520 __isl_give isl_multi_union_pw_aff *
6521 isl_multi_union_pw_aff_scale_multi_val(
6522 __isl_take isl_multi_union_pw_aff *mupa,
6523 __isl_take isl_multi_val *mv);
6524 __isl_give isl_union_pw_multi_aff *
6525 isl_union_pw_multi_aff_scale_multi_val(
6526 __isl_take isl_union_pw_multi_aff *upma,
6527 __isl_take isl_multi_val *mv);
6528 __isl_give isl_multi_aff *
6529 isl_multi_aff_scale_down_multi_val(
6530 __isl_take isl_multi_aff *ma,
6531 __isl_take isl_multi_val *mv);
6532 __isl_give isl_multi_pw_aff *
6533 isl_multi_pw_aff_scale_down_multi_val(
6534 __isl_take isl_multi_pw_aff *mpa,
6535 __isl_take isl_multi_val *mv);
6536 __isl_give isl_multi_union_pw_aff *
6537 isl_multi_union_pw_aff_scale_down_multi_val(
6538 __isl_take isl_multi_union_pw_aff *mupa,
6539 __isl_take isl_multi_val *mv);
6541 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6542 by the corresponding elements of C<mv>.
6544 #include <isl/aff.h>
6545 __isl_give isl_aff *isl_aff_mul(
6546 __isl_take isl_aff *aff1,
6547 __isl_take isl_aff *aff2);
6548 __isl_give isl_aff *isl_aff_div(
6549 __isl_take isl_aff *aff1,
6550 __isl_take isl_aff *aff2);
6551 __isl_give isl_pw_aff *isl_pw_aff_mul(
6552 __isl_take isl_pw_aff *pwaff1,
6553 __isl_take isl_pw_aff *pwaff2);
6554 __isl_give isl_pw_aff *isl_pw_aff_div(
6555 __isl_take isl_pw_aff *pa1,
6556 __isl_take isl_pw_aff *pa2);
6557 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6558 __isl_take isl_pw_aff *pa1,
6559 __isl_take isl_pw_aff *pa2);
6560 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6561 __isl_take isl_pw_aff *pa1,
6562 __isl_take isl_pw_aff *pa2);
6564 When multiplying two affine expressions, at least one of the two needs
6565 to be a constant. Similarly, when dividing an affine expression by another,
6566 the second expression needs to be a constant.
6567 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6568 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6571 #include <isl/polynomial.h>
6572 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6573 __isl_take isl_qpolynomial *qp1,
6574 __isl_take isl_qpolynomial *qp2);
6575 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6576 __isl_take isl_pw_qpolynomial *pwqp1,
6577 __isl_take isl_pw_qpolynomial *pwqp2);
6578 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6579 __isl_take isl_union_pw_qpolynomial *upwqp1,
6580 __isl_take isl_union_pw_qpolynomial *upwqp2);
6584 =head3 Lexicographic Optimization
6586 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6587 the following functions
6588 compute a set that contains the lexicographic minimum or maximum
6589 of the elements in C<set> (or C<bset>) for those values of the parameters
6590 that satisfy C<dom>.
6591 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6592 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6594 In other words, the union of the parameter values
6595 for which the result is non-empty and of C<*empty>
6598 #include <isl/set.h>
6599 __isl_give isl_set *isl_basic_set_partial_lexmin(
6600 __isl_take isl_basic_set *bset,
6601 __isl_take isl_basic_set *dom,
6602 __isl_give isl_set **empty);
6603 __isl_give isl_set *isl_basic_set_partial_lexmax(
6604 __isl_take isl_basic_set *bset,
6605 __isl_take isl_basic_set *dom,
6606 __isl_give isl_set **empty);
6607 __isl_give isl_set *isl_set_partial_lexmin(
6608 __isl_take isl_set *set, __isl_take isl_set *dom,
6609 __isl_give isl_set **empty);
6610 __isl_give isl_set *isl_set_partial_lexmax(
6611 __isl_take isl_set *set, __isl_take isl_set *dom,
6612 __isl_give isl_set **empty);
6614 Given a (basic) set C<set> (or C<bset>), the following functions simply
6615 return a set containing the lexicographic minimum or maximum
6616 of the elements in C<set> (or C<bset>).
6617 In case of union sets, the optimum is computed per space.
6619 #include <isl/set.h>
6620 __isl_give isl_set *isl_basic_set_lexmin(
6621 __isl_take isl_basic_set *bset);
6622 __isl_give isl_set *isl_basic_set_lexmax(
6623 __isl_take isl_basic_set *bset);
6624 __isl_give isl_set *isl_set_lexmin(
6625 __isl_take isl_set *set);
6626 __isl_give isl_set *isl_set_lexmax(
6627 __isl_take isl_set *set);
6628 __isl_give isl_union_set *isl_union_set_lexmin(
6629 __isl_take isl_union_set *uset);
6630 __isl_give isl_union_set *isl_union_set_lexmax(
6631 __isl_take isl_union_set *uset);
6633 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6634 the following functions
6635 compute a relation that maps each element of C<dom>
6636 to the single lexicographic minimum or maximum
6637 of the elements that are associated to that same
6638 element in C<map> (or C<bmap>).
6639 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6640 that contains the elements in C<dom> that do not map
6641 to any elements in C<map> (or C<bmap>).
6642 In other words, the union of the domain of the result and of C<*empty>
6645 #include <isl/map.h>
6646 __isl_give isl_map *isl_basic_map_partial_lexmax(
6647 __isl_take isl_basic_map *bmap,
6648 __isl_take isl_basic_set *dom,
6649 __isl_give isl_set **empty);
6650 __isl_give isl_map *isl_basic_map_partial_lexmin(
6651 __isl_take isl_basic_map *bmap,
6652 __isl_take isl_basic_set *dom,
6653 __isl_give isl_set **empty);
6654 __isl_give isl_map *isl_map_partial_lexmax(
6655 __isl_take isl_map *map, __isl_take isl_set *dom,
6656 __isl_give isl_set **empty);
6657 __isl_give isl_map *isl_map_partial_lexmin(
6658 __isl_take isl_map *map, __isl_take isl_set *dom,
6659 __isl_give isl_set **empty);
6661 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6662 return a map mapping each element in the domain of
6663 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6664 of all elements associated to that element.
6665 In case of union relations, the optimum is computed per space.
6667 #include <isl/map.h>
6668 __isl_give isl_map *isl_basic_map_lexmin(
6669 __isl_take isl_basic_map *bmap);
6670 __isl_give isl_map *isl_basic_map_lexmax(
6671 __isl_take isl_basic_map *bmap);
6672 __isl_give isl_map *isl_map_lexmin(
6673 __isl_take isl_map *map);
6674 __isl_give isl_map *isl_map_lexmax(
6675 __isl_take isl_map *map);
6676 __isl_give isl_union_map *isl_union_map_lexmin(
6677 __isl_take isl_union_map *umap);
6678 __isl_give isl_union_map *isl_union_map_lexmax(
6679 __isl_take isl_union_map *umap);
6681 The following functions return their result in the form of
6682 a piecewise multi-affine expression,
6683 but are otherwise equivalent to the corresponding functions
6684 returning a basic set or relation.
6686 #include <isl/set.h>
6687 __isl_give isl_pw_multi_aff *
6688 isl_basic_set_partial_lexmin_pw_multi_aff(
6689 __isl_take isl_basic_set *bset,
6690 __isl_take isl_basic_set *dom,
6691 __isl_give isl_set **empty);
6692 __isl_give isl_pw_multi_aff *
6693 isl_basic_set_partial_lexmax_pw_multi_aff(
6694 __isl_take isl_basic_set *bset,
6695 __isl_take isl_basic_set *dom,
6696 __isl_give isl_set **empty);
6697 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6698 __isl_take isl_set *set);
6699 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6700 __isl_take isl_set *set);
6702 #include <isl/map.h>
6703 __isl_give isl_pw_multi_aff *
6704 isl_basic_map_lexmin_pw_multi_aff(
6705 __isl_take isl_basic_map *bmap);
6706 __isl_give isl_pw_multi_aff *
6707 isl_basic_map_partial_lexmin_pw_multi_aff(
6708 __isl_take isl_basic_map *bmap,
6709 __isl_take isl_basic_set *dom,
6710 __isl_give isl_set **empty);
6711 __isl_give isl_pw_multi_aff *
6712 isl_basic_map_partial_lexmax_pw_multi_aff(
6713 __isl_take isl_basic_map *bmap,
6714 __isl_take isl_basic_set *dom,
6715 __isl_give isl_set **empty);
6716 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6717 __isl_take isl_map *map);
6718 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6719 __isl_take isl_map *map);
6721 The following functions return the lexicographic minimum or maximum
6722 on the shared domain of the inputs and the single defined function
6723 on those parts of the domain where only a single function is defined.
6725 #include <isl/aff.h>
6726 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6727 __isl_take isl_pw_multi_aff *pma1,
6728 __isl_take isl_pw_multi_aff *pma2);
6729 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6730 __isl_take isl_pw_multi_aff *pma1,
6731 __isl_take isl_pw_multi_aff *pma2);
6733 =head2 Ternary Operations
6735 #include <isl/aff.h>
6736 __isl_give isl_pw_aff *isl_pw_aff_cond(
6737 __isl_take isl_pw_aff *cond,
6738 __isl_take isl_pw_aff *pwaff_true,
6739 __isl_take isl_pw_aff *pwaff_false);
6741 The function C<isl_pw_aff_cond> performs a conditional operator
6742 and returns an expression that is equal to C<pwaff_true>
6743 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6744 where C<cond> is zero.
6748 Lists are defined over several element types, including
6749 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
6750 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6751 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6752 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6753 Here we take lists of C<isl_set>s as an example.
6754 Lists can be created, copied, modified and freed using the following functions.
6756 #include <isl/set.h>
6757 __isl_give isl_set_list *isl_set_list_from_set(
6758 __isl_take isl_set *el);
6759 __isl_give isl_set_list *isl_set_list_alloc(
6760 isl_ctx *ctx, int n);
6761 __isl_give isl_set_list *isl_set_list_copy(
6762 __isl_keep isl_set_list *list);
6763 __isl_give isl_set_list *isl_set_list_insert(
6764 __isl_take isl_set_list *list, unsigned pos,
6765 __isl_take isl_set *el);
6766 __isl_give isl_set_list *isl_set_list_add(
6767 __isl_take isl_set_list *list,
6768 __isl_take isl_set *el);
6769 __isl_give isl_set_list *isl_set_list_drop(
6770 __isl_take isl_set_list *list,
6771 unsigned first, unsigned n);
6772 __isl_give isl_set_list *isl_set_list_set_set(
6773 __isl_take isl_set_list *list, int index,
6774 __isl_take isl_set *set);
6775 __isl_give isl_set_list *isl_set_list_concat(
6776 __isl_take isl_set_list *list1,
6777 __isl_take isl_set_list *list2);
6778 __isl_give isl_set_list *isl_set_list_sort(
6779 __isl_take isl_set_list *list,
6780 int (*cmp)(__isl_keep isl_set *a,
6781 __isl_keep isl_set *b, void *user),
6783 __isl_null isl_set_list *isl_set_list_free(
6784 __isl_take isl_set_list *list);
6786 C<isl_set_list_alloc> creates an empty list with an initial capacity
6787 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
6788 add elements to a list, increasing its capacity as needed.
6789 C<isl_set_list_from_set> creates a list with a single element.
6791 Lists can be inspected using the following functions.
6793 #include <isl/set.h>
6794 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6795 __isl_give isl_set *isl_set_list_get_set(
6796 __isl_keep isl_set_list *list, int index);
6797 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6798 int (*fn)(__isl_take isl_set *el, void *user),
6800 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6801 int (*follows)(__isl_keep isl_set *a,
6802 __isl_keep isl_set *b, void *user),
6804 int (*fn)(__isl_take isl_set *el, void *user),
6807 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6808 strongly connected components of the graph with as vertices the elements
6809 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6810 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6811 should return C<-1> on error.
6813 Lists can be printed using
6815 #include <isl/set.h>
6816 __isl_give isl_printer *isl_printer_print_set_list(
6817 __isl_take isl_printer *p,
6818 __isl_keep isl_set_list *list);
6820 =head2 Associative arrays
6822 Associative arrays map isl objects of a specific type to isl objects
6823 of some (other) specific type. They are defined for several pairs
6824 of types, including (C<isl_map>, C<isl_basic_set>),
6825 (C<isl_id>, C<isl_ast_expr>) and.
6826 (C<isl_id>, C<isl_pw_aff>).
6827 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6830 Associative arrays can be created, copied and freed using
6831 the following functions.
6833 #include <isl/id_to_ast_expr.h>
6834 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6835 isl_ctx *ctx, int min_size);
6836 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6837 __isl_keep id_to_ast_expr *id2expr);
6838 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6839 __isl_take id_to_ast_expr *id2expr);
6841 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6842 to specify the expected size of the associative array.
6843 The associative array will be grown automatically as needed.
6845 Associative arrays can be inspected using the following functions.
6847 #include <isl/id_to_ast_expr.h>
6848 int isl_id_to_ast_expr_has(
6849 __isl_keep id_to_ast_expr *id2expr,
6850 __isl_keep isl_id *key);
6851 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6852 __isl_keep id_to_ast_expr *id2expr,
6853 __isl_take isl_id *key);
6854 int isl_id_to_ast_expr_foreach(
6855 __isl_keep id_to_ast_expr *id2expr,
6856 int (*fn)(__isl_take isl_id *key,
6857 __isl_take isl_ast_expr *val, void *user),
6860 They can be modified using the following function.
6862 #include <isl/id_to_ast_expr.h>
6863 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6864 __isl_take id_to_ast_expr *id2expr,
6865 __isl_take isl_id *key,
6866 __isl_take isl_ast_expr *val);
6867 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6868 __isl_take id_to_ast_expr *id2expr,
6869 __isl_take isl_id *key);
6871 Associative arrays can be printed using the following function.
6873 #include <isl/id_to_ast_expr.h>
6874 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6875 __isl_take isl_printer *p,
6876 __isl_keep id_to_ast_expr *id2expr);
6880 Vectors can be created, copied and freed using the following functions.
6882 #include <isl/vec.h>
6883 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6885 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6886 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6888 Note that the elements of a newly created vector may have arbitrary values.
6889 The elements can be changed and inspected using the following functions.
6891 int isl_vec_size(__isl_keep isl_vec *vec);
6892 __isl_give isl_val *isl_vec_get_element_val(
6893 __isl_keep isl_vec *vec, int pos);
6894 __isl_give isl_vec *isl_vec_set_element_si(
6895 __isl_take isl_vec *vec, int pos, int v);
6896 __isl_give isl_vec *isl_vec_set_element_val(
6897 __isl_take isl_vec *vec, int pos,
6898 __isl_take isl_val *v);
6899 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6901 __isl_give isl_vec *isl_vec_set_val(
6902 __isl_take isl_vec *vec, __isl_take isl_val *v);
6903 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6904 __isl_keep isl_vec *vec2, int pos);
6906 C<isl_vec_get_element> will return a negative value if anything went wrong.
6907 In that case, the value of C<*v> is undefined.
6909 The following function can be used to concatenate two vectors.
6911 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6912 __isl_take isl_vec *vec2);
6916 Matrices can be created, copied and freed using the following functions.
6918 #include <isl/mat.h>
6919 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6920 unsigned n_row, unsigned n_col);
6921 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6922 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6924 Note that the elements of a newly created matrix may have arbitrary values.
6925 The elements can be changed and inspected using the following functions.
6927 int isl_mat_rows(__isl_keep isl_mat *mat);
6928 int isl_mat_cols(__isl_keep isl_mat *mat);
6929 __isl_give isl_val *isl_mat_get_element_val(
6930 __isl_keep isl_mat *mat, int row, int col);
6931 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
6932 int row, int col, int v);
6933 __isl_give isl_mat *isl_mat_set_element_val(
6934 __isl_take isl_mat *mat, int row, int col,
6935 __isl_take isl_val *v);
6937 C<isl_mat_get_element> will return a negative value if anything went wrong.
6938 In that case, the value of C<*v> is undefined.
6940 The following function can be used to compute the (right) inverse
6941 of a matrix, i.e., a matrix such that the product of the original
6942 and the inverse (in that order) is a multiple of the identity matrix.
6943 The input matrix is assumed to be of full row-rank.
6945 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
6947 The following function can be used to compute the (right) kernel
6948 (or null space) of a matrix, i.e., a matrix such that the product of
6949 the original and the kernel (in that order) is the zero matrix.
6951 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
6953 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
6955 The following functions determine
6956 an upper or lower bound on a quasipolynomial over its domain.
6958 __isl_give isl_pw_qpolynomial_fold *
6959 isl_pw_qpolynomial_bound(
6960 __isl_take isl_pw_qpolynomial *pwqp,
6961 enum isl_fold type, int *tight);
6963 __isl_give isl_union_pw_qpolynomial_fold *
6964 isl_union_pw_qpolynomial_bound(
6965 __isl_take isl_union_pw_qpolynomial *upwqp,
6966 enum isl_fold type, int *tight);
6968 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
6969 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
6970 is the returned bound is known be tight, i.e., for each value
6971 of the parameters there is at least
6972 one element in the domain that reaches the bound.
6973 If the domain of C<pwqp> is not wrapping, then the bound is computed
6974 over all elements in that domain and the result has a purely parametric
6975 domain. If the domain of C<pwqp> is wrapping, then the bound is
6976 computed over the range of the wrapped relation. The domain of the
6977 wrapped relation becomes the domain of the result.
6979 =head2 Parametric Vertex Enumeration
6981 The parametric vertex enumeration described in this section
6982 is mainly intended to be used internally and by the C<barvinok>
6985 #include <isl/vertices.h>
6986 __isl_give isl_vertices *isl_basic_set_compute_vertices(
6987 __isl_keep isl_basic_set *bset);
6989 The function C<isl_basic_set_compute_vertices> performs the
6990 actual computation of the parametric vertices and the chamber
6991 decomposition and store the result in an C<isl_vertices> object.
6992 This information can be queried by either iterating over all
6993 the vertices or iterating over all the chambers or cells
6994 and then iterating over all vertices that are active on the chamber.
6996 int isl_vertices_foreach_vertex(
6997 __isl_keep isl_vertices *vertices,
6998 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7001 int isl_vertices_foreach_cell(
7002 __isl_keep isl_vertices *vertices,
7003 int (*fn)(__isl_take isl_cell *cell, void *user),
7005 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7006 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7009 Other operations that can be performed on an C<isl_vertices> object are
7012 int isl_vertices_get_n_vertices(
7013 __isl_keep isl_vertices *vertices);
7014 void isl_vertices_free(__isl_take isl_vertices *vertices);
7016 Vertices can be inspected and destroyed using the following functions.
7018 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7019 __isl_give isl_basic_set *isl_vertex_get_domain(
7020 __isl_keep isl_vertex *vertex);
7021 __isl_give isl_multi_aff *isl_vertex_get_expr(
7022 __isl_keep isl_vertex *vertex);
7023 void isl_vertex_free(__isl_take isl_vertex *vertex);
7025 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7026 describing the vertex in terms of the parameters,
7027 while C<isl_vertex_get_domain> returns the activity domain
7030 Chambers can be inspected and destroyed using the following functions.
7032 __isl_give isl_basic_set *isl_cell_get_domain(
7033 __isl_keep isl_cell *cell);
7034 void isl_cell_free(__isl_take isl_cell *cell);
7036 =head1 Polyhedral Compilation Library
7038 This section collects functionality in C<isl> that has been specifically
7039 designed for use during polyhedral compilation.
7041 =head2 Dependence Analysis
7043 C<isl> contains specialized functionality for performing
7044 array dataflow analysis. That is, given a I<sink> access relation
7045 and a collection of possible I<source> access relations,
7046 C<isl> can compute relations that describe
7047 for each iteration of the sink access, which iteration
7048 of which of the source access relations was the last
7049 to access the same data element before the given iteration
7051 The resulting dependence relations map source iterations
7052 to the corresponding sink iterations.
7053 To compute standard flow dependences, the sink should be
7054 a read, while the sources should be writes.
7055 If any of the source accesses are marked as being I<may>
7056 accesses, then there will be a dependence from the last
7057 I<must> access B<and> from any I<may> access that follows
7058 this last I<must> access.
7059 In particular, if I<all> sources are I<may> accesses,
7060 then memory based dependence analysis is performed.
7061 If, on the other hand, all sources are I<must> accesses,
7062 then value based dependence analysis is performed.
7064 #include <isl/flow.h>
7066 typedef int (*isl_access_level_before)(void *first, void *second);
7068 __isl_give isl_access_info *isl_access_info_alloc(
7069 __isl_take isl_map *sink,
7070 void *sink_user, isl_access_level_before fn,
7072 __isl_give isl_access_info *isl_access_info_add_source(
7073 __isl_take isl_access_info *acc,
7074 __isl_take isl_map *source, int must,
7076 __isl_null isl_access_info *isl_access_info_free(
7077 __isl_take isl_access_info *acc);
7079 __isl_give isl_flow *isl_access_info_compute_flow(
7080 __isl_take isl_access_info *acc);
7082 int isl_flow_foreach(__isl_keep isl_flow *deps,
7083 int (*fn)(__isl_take isl_map *dep, int must,
7084 void *dep_user, void *user),
7086 __isl_give isl_map *isl_flow_get_no_source(
7087 __isl_keep isl_flow *deps, int must);
7088 void isl_flow_free(__isl_take isl_flow *deps);
7090 The function C<isl_access_info_compute_flow> performs the actual
7091 dependence analysis. The other functions are used to construct
7092 the input for this function or to read off the output.
7094 The input is collected in an C<isl_access_info>, which can
7095 be created through a call to C<isl_access_info_alloc>.
7096 The arguments to this functions are the sink access relation
7097 C<sink>, a token C<sink_user> used to identify the sink
7098 access to the user, a callback function for specifying the
7099 relative order of source and sink accesses, and the number
7100 of source access relations that will be added.
7101 The callback function has type C<int (*)(void *first, void *second)>.
7102 The function is called with two user supplied tokens identifying
7103 either a source or the sink and it should return the shared nesting
7104 level and the relative order of the two accesses.
7105 In particular, let I<n> be the number of loops shared by
7106 the two accesses. If C<first> precedes C<second> textually,
7107 then the function should return I<2 * n + 1>; otherwise,
7108 it should return I<2 * n>.
7109 The sources can be added to the C<isl_access_info> by performing
7110 (at most) C<max_source> calls to C<isl_access_info_add_source>.
7111 C<must> indicates whether the source is a I<must> access
7112 or a I<may> access. Note that a multi-valued access relation
7113 should only be marked I<must> if every iteration in the domain
7114 of the relation accesses I<all> elements in its image.
7115 The C<source_user> token is again used to identify
7116 the source access. The range of the source access relation
7117 C<source> should have the same dimension as the range
7118 of the sink access relation.
7119 The C<isl_access_info_free> function should usually not be
7120 called explicitly, because it is called implicitly by
7121 C<isl_access_info_compute_flow>.
7123 The result of the dependence analysis is collected in an
7124 C<isl_flow>. There may be elements of
7125 the sink access for which no preceding source access could be
7126 found or for which all preceding sources are I<may> accesses.
7127 The relations containing these elements can be obtained through
7128 calls to C<isl_flow_get_no_source>, the first with C<must> set
7129 and the second with C<must> unset.
7130 In the case of standard flow dependence analysis,
7131 with the sink a read and the sources I<must> writes,
7132 the first relation corresponds to the reads from uninitialized
7133 array elements and the second relation is empty.
7134 The actual flow dependences can be extracted using
7135 C<isl_flow_foreach>. This function will call the user-specified
7136 callback function C<fn> for each B<non-empty> dependence between
7137 a source and the sink. The callback function is called
7138 with four arguments, the actual flow dependence relation
7139 mapping source iterations to sink iterations, a boolean that
7140 indicates whether it is a I<must> or I<may> dependence, a token
7141 identifying the source and an additional C<void *> with value
7142 equal to the third argument of the C<isl_flow_foreach> call.
7143 A dependence is marked I<must> if it originates from a I<must>
7144 source and if it is not followed by any I<may> sources.
7146 After finishing with an C<isl_flow>, the user should call
7147 C<isl_flow_free> to free all associated memory.
7149 A higher-level interface to dependence analysis is provided
7150 by the following function.
7152 #include <isl/flow.h>
7154 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
7155 __isl_take isl_union_map *must_source,
7156 __isl_take isl_union_map *may_source,
7157 __isl_take isl_union_map *schedule,
7158 __isl_give isl_union_map **must_dep,
7159 __isl_give isl_union_map **may_dep,
7160 __isl_give isl_union_map **must_no_source,
7161 __isl_give isl_union_map **may_no_source);
7163 The arrays are identified by the tuple names of the ranges
7164 of the accesses. The iteration domains by the tuple names
7165 of the domains of the accesses and of the schedule.
7166 The relative order of the iteration domains is given by the
7167 schedule. The relations returned through C<must_no_source>
7168 and C<may_no_source> are subsets of C<sink>.
7169 Any of C<must_dep>, C<may_dep>, C<must_no_source>
7170 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
7171 any of the other arguments is treated as an error.
7173 =head3 Interaction with Dependence Analysis
7175 During the dependence analysis, we frequently need to perform
7176 the following operation. Given a relation between sink iterations
7177 and potential source iterations from a particular source domain,
7178 what is the last potential source iteration corresponding to each
7179 sink iteration. It can sometimes be convenient to adjust
7180 the set of potential source iterations before or after each such operation.
7181 The prototypical example is fuzzy array dataflow analysis,
7182 where we need to analyze if, based on data-dependent constraints,
7183 the sink iteration can ever be executed without one or more of
7184 the corresponding potential source iterations being executed.
7185 If so, we can introduce extra parameters and select an unknown
7186 but fixed source iteration from the potential source iterations.
7187 To be able to perform such manipulations, C<isl> provides the following
7190 #include <isl/flow.h>
7192 typedef __isl_give isl_restriction *(*isl_access_restrict)(
7193 __isl_keep isl_map *source_map,
7194 __isl_keep isl_set *sink, void *source_user,
7196 __isl_give isl_access_info *isl_access_info_set_restrict(
7197 __isl_take isl_access_info *acc,
7198 isl_access_restrict fn, void *user);
7200 The function C<isl_access_info_set_restrict> should be called
7201 before calling C<isl_access_info_compute_flow> and registers a callback function
7202 that will be called any time C<isl> is about to compute the last
7203 potential source. The first argument is the (reverse) proto-dependence,
7204 mapping sink iterations to potential source iterations.
7205 The second argument represents the sink iterations for which
7206 we want to compute the last source iteration.
7207 The third argument is the token corresponding to the source
7208 and the final argument is the token passed to C<isl_access_info_set_restrict>.
7209 The callback is expected to return a restriction on either the input or
7210 the output of the operation computing the last potential source.
7211 If the input needs to be restricted then restrictions are needed
7212 for both the source and the sink iterations. The sink iterations
7213 and the potential source iterations will be intersected with these sets.
7214 If the output needs to be restricted then only a restriction on the source
7215 iterations is required.
7216 If any error occurs, the callback should return C<NULL>.
7217 An C<isl_restriction> object can be created, freed and inspected
7218 using the following functions.
7220 #include <isl/flow.h>
7222 __isl_give isl_restriction *isl_restriction_input(
7223 __isl_take isl_set *source_restr,
7224 __isl_take isl_set *sink_restr);
7225 __isl_give isl_restriction *isl_restriction_output(
7226 __isl_take isl_set *source_restr);
7227 __isl_give isl_restriction *isl_restriction_none(
7228 __isl_take isl_map *source_map);
7229 __isl_give isl_restriction *isl_restriction_empty(
7230 __isl_take isl_map *source_map);
7231 __isl_null isl_restriction *isl_restriction_free(
7232 __isl_take isl_restriction *restr);
7234 C<isl_restriction_none> and C<isl_restriction_empty> are special
7235 cases of C<isl_restriction_input>. C<isl_restriction_none>
7236 is essentially equivalent to
7238 isl_restriction_input(isl_set_universe(
7239 isl_space_range(isl_map_get_space(source_map))),
7241 isl_space_domain(isl_map_get_space(source_map))));
7243 whereas C<isl_restriction_empty> is essentially equivalent to
7245 isl_restriction_input(isl_set_empty(
7246 isl_space_range(isl_map_get_space(source_map))),
7248 isl_space_domain(isl_map_get_space(source_map))));
7252 B<The functionality described in this section is fairly new
7253 and may be subject to change.>
7255 #include <isl/schedule.h>
7256 __isl_give isl_schedule *
7257 isl_schedule_constraints_compute_schedule(
7258 __isl_take isl_schedule_constraints *sc);
7259 __isl_null isl_schedule *isl_schedule_free(
7260 __isl_take isl_schedule *sched);
7262 The function C<isl_schedule_constraints_compute_schedule> can be
7263 used to compute a schedule that satisfies the given schedule constraints.
7264 These schedule constraints include the iteration domain for which
7265 a schedule should be computed and dependences between pairs of
7266 iterations. In particular, these dependences include
7267 I<validity> dependences and I<proximity> dependences.
7268 By default, the algorithm used to construct the schedule is similar
7269 to that of C<Pluto>.
7270 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
7272 The generated schedule respects all validity dependences.
7273 That is, all dependence distances over these dependences in the
7274 scheduled space are lexicographically positive.
7275 The default algorithm tries to ensure that the dependence distances
7276 over coincidence constraints are zero and to minimize the
7277 dependence distances over proximity dependences.
7278 Moreover, it tries to obtain sequences (bands) of schedule dimensions
7279 for groups of domains where the dependence distances over validity
7280 dependences have only non-negative values.
7281 When using Feautrier's algorithm, the coincidence and proximity constraints
7282 are only taken into account during the extension to a
7283 full-dimensional schedule.
7285 An C<isl_schedule_constraints> object can be constructed
7286 and manipulated using the following functions.
7288 #include <isl/schedule.h>
7289 __isl_give isl_schedule_constraints *
7290 isl_schedule_constraints_copy(
7291 __isl_keep isl_schedule_constraints *sc);
7292 __isl_give isl_schedule_constraints *
7293 isl_schedule_constraints_on_domain(
7294 __isl_take isl_union_set *domain);
7295 __isl_give isl_schedule_constraints *
7296 isl_schedule_constraints_set_validity(
7297 __isl_take isl_schedule_constraints *sc,
7298 __isl_take isl_union_map *validity);
7299 __isl_give isl_schedule_constraints *
7300 isl_schedule_constraints_set_coincidence(
7301 __isl_take isl_schedule_constraints *sc,
7302 __isl_take isl_union_map *coincidence);
7303 __isl_give isl_schedule_constraints *
7304 isl_schedule_constraints_set_proximity(
7305 __isl_take isl_schedule_constraints *sc,
7306 __isl_take isl_union_map *proximity);
7307 __isl_give isl_schedule_constraints *
7308 isl_schedule_constraints_set_conditional_validity(
7309 __isl_take isl_schedule_constraints *sc,
7310 __isl_take isl_union_map *condition,
7311 __isl_take isl_union_map *validity);
7312 __isl_null isl_schedule_constraints *
7313 isl_schedule_constraints_free(
7314 __isl_take isl_schedule_constraints *sc);
7316 The initial C<isl_schedule_constraints> object created by
7317 C<isl_schedule_constraints_on_domain> does not impose any constraints.
7318 That is, it has an empty set of dependences.
7319 The function C<isl_schedule_constraints_set_validity> replaces the
7320 validity dependences, mapping domain elements I<i> to domain
7321 elements that should be scheduled after I<i>.
7322 The function C<isl_schedule_constraints_set_coincidence> replaces the
7323 coincidence dependences, mapping domain elements I<i> to domain
7324 elements that should be scheduled together with I<I>, if possible.
7325 The function C<isl_schedule_constraints_set_proximity> replaces the
7326 proximity dependences, mapping domain elements I<i> to domain
7327 elements that should be scheduled either before I<I>
7328 or as early as possible after I<i>.
7330 The function C<isl_schedule_constraints_set_conditional_validity>
7331 replaces the conditional validity constraints.
7332 A conditional validity constraint is only imposed when any of the corresponding
7333 conditions is satisfied, i.e., when any of them is non-zero.
7334 That is, the scheduler ensures that within each band if the dependence
7335 distances over the condition constraints are not all zero
7336 then all corresponding conditional validity constraints are respected.
7337 A conditional validity constraint corresponds to a condition
7338 if the two are adjacent, i.e., if the domain of one relation intersect
7339 the range of the other relation.
7340 The typical use case of conditional validity constraints is
7341 to allow order constraints between live ranges to be violated
7342 as long as the live ranges themselves are local to the band.
7343 To allow more fine-grained control over which conditions correspond
7344 to which conditional validity constraints, the domains and ranges
7345 of these relations may include I<tags>. That is, the domains and
7346 ranges of those relation may themselves be wrapped relations
7347 where the iteration domain appears in the domain of those wrapped relations
7348 and the range of the wrapped relations can be arbitrarily chosen
7349 by the user. Conditions and conditional validity constraints are only
7350 considered adjacent to each other if the entire wrapped relation matches.
7351 In particular, a relation with a tag will never be considered adjacent
7352 to a relation without a tag.
7354 The following function computes a schedule directly from
7355 an iteration domain and validity and proximity dependences
7356 and is implemented in terms of the functions described above.
7357 The use of C<isl_union_set_compute_schedule> is discouraged.
7359 #include <isl/schedule.h>
7360 __isl_give isl_schedule *isl_union_set_compute_schedule(
7361 __isl_take isl_union_set *domain,
7362 __isl_take isl_union_map *validity,
7363 __isl_take isl_union_map *proximity);
7365 A mapping from the domains to the scheduled space can be obtained
7366 from an C<isl_schedule> using the following function.
7368 __isl_give isl_union_map *isl_schedule_get_map(
7369 __isl_keep isl_schedule *sched);
7371 A representation of the schedule can be printed using
7373 __isl_give isl_printer *isl_printer_print_schedule(
7374 __isl_take isl_printer *p,
7375 __isl_keep isl_schedule *schedule);
7377 A representation of the schedule as a forest of bands can be obtained
7378 using the following function.
7380 __isl_give isl_band_list *isl_schedule_get_band_forest(
7381 __isl_keep isl_schedule *schedule);
7383 The individual bands can be visited in depth-first post-order
7384 using the following function.
7386 #include <isl/schedule.h>
7387 int isl_schedule_foreach_band(
7388 __isl_keep isl_schedule *sched,
7389 int (*fn)(__isl_keep isl_band *band, void *user),
7392 The list can be manipulated as explained in L<"Lists">.
7393 The bands inside the list can be copied and freed using the following
7396 #include <isl/band.h>
7397 __isl_give isl_band *isl_band_copy(
7398 __isl_keep isl_band *band);
7399 __isl_null isl_band *isl_band_free(
7400 __isl_take isl_band *band);
7402 Each band contains zero or more scheduling dimensions.
7403 These are referred to as the members of the band.
7404 The section of the schedule that corresponds to the band is
7405 referred to as the partial schedule of the band.
7406 For those nodes that participate in a band, the outer scheduling
7407 dimensions form the prefix schedule, while the inner scheduling
7408 dimensions form the suffix schedule.
7409 That is, if we take a cut of the band forest, then the union of
7410 the concatenations of the prefix, partial and suffix schedules of
7411 each band in the cut is equal to the entire schedule (modulo
7412 some possible padding at the end with zero scheduling dimensions).
7413 The properties of a band can be inspected using the following functions.
7415 #include <isl/band.h>
7416 int isl_band_has_children(__isl_keep isl_band *band);
7417 __isl_give isl_band_list *isl_band_get_children(
7418 __isl_keep isl_band *band);
7420 __isl_give isl_union_map *isl_band_get_prefix_schedule(
7421 __isl_keep isl_band *band);
7422 __isl_give isl_union_map *isl_band_get_partial_schedule(
7423 __isl_keep isl_band *band);
7424 __isl_give isl_union_map *isl_band_get_suffix_schedule(
7425 __isl_keep isl_band *band);
7427 int isl_band_n_member(__isl_keep isl_band *band);
7428 int isl_band_member_is_coincident(
7429 __isl_keep isl_band *band, int pos);
7431 int isl_band_list_foreach_band(
7432 __isl_keep isl_band_list *list,
7433 int (*fn)(__isl_keep isl_band *band, void *user),
7436 Note that a scheduling dimension is considered to be ``coincident''
7437 if it satisfies the coincidence constraints within its band.
7438 That is, if the dependence distances of the coincidence
7439 constraints are all zero in that direction (for fixed
7440 iterations of outer bands).
7441 Like C<isl_schedule_foreach_band>,
7442 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
7443 in depth-first post-order.
7445 A band can be tiled using the following function.
7447 #include <isl/band.h>
7448 int isl_band_tile(__isl_keep isl_band *band,
7449 __isl_take isl_vec *sizes);
7451 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
7453 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
7454 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
7456 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
7458 The C<isl_band_tile> function tiles the band using the given tile sizes
7459 inside its schedule.
7460 A new child band is created to represent the point loops and it is
7461 inserted between the modified band and its children.
7462 The C<tile_scale_tile_loops> option specifies whether the tile
7463 loops iterators should be scaled by the tile sizes.
7464 If the C<tile_shift_point_loops> option is set, then the point loops
7465 are shifted to start at zero.
7467 A band can be split into two nested bands using the following function.
7469 int isl_band_split(__isl_keep isl_band *band, int pos);
7471 The resulting outer band contains the first C<pos> dimensions of C<band>
7472 while the inner band contains the remaining dimensions.
7474 A representation of the band can be printed using
7476 #include <isl/band.h>
7477 __isl_give isl_printer *isl_printer_print_band(
7478 __isl_take isl_printer *p,
7479 __isl_keep isl_band *band);
7483 #include <isl/schedule.h>
7484 int isl_options_set_schedule_max_coefficient(
7485 isl_ctx *ctx, int val);
7486 int isl_options_get_schedule_max_coefficient(
7488 int isl_options_set_schedule_max_constant_term(
7489 isl_ctx *ctx, int val);
7490 int isl_options_get_schedule_max_constant_term(
7492 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
7493 int isl_options_get_schedule_fuse(isl_ctx *ctx);
7494 int isl_options_set_schedule_maximize_band_depth(
7495 isl_ctx *ctx, int val);
7496 int isl_options_get_schedule_maximize_band_depth(
7498 int isl_options_set_schedule_outer_coincidence(
7499 isl_ctx *ctx, int val);
7500 int isl_options_get_schedule_outer_coincidence(
7502 int isl_options_set_schedule_split_scaled(
7503 isl_ctx *ctx, int val);
7504 int isl_options_get_schedule_split_scaled(
7506 int isl_options_set_schedule_algorithm(
7507 isl_ctx *ctx, int val);
7508 int isl_options_get_schedule_algorithm(
7510 int isl_options_set_schedule_separate_components(
7511 isl_ctx *ctx, int val);
7512 int isl_options_get_schedule_separate_components(
7517 =item * schedule_max_coefficient
7519 This option enforces that the coefficients for variable and parameter
7520 dimensions in the calculated schedule are not larger than the specified value.
7521 This option can significantly increase the speed of the scheduling calculation
7522 and may also prevent fusing of unrelated dimensions. A value of -1 means that
7523 this option does not introduce bounds on the variable or parameter
7526 =item * schedule_max_constant_term
7528 This option enforces that the constant coefficients in the calculated schedule
7529 are not larger than the maximal constant term. This option can significantly
7530 increase the speed of the scheduling calculation and may also prevent fusing of
7531 unrelated dimensions. A value of -1 means that this option does not introduce
7532 bounds on the constant coefficients.
7534 =item * schedule_fuse
7536 This option controls the level of fusion.
7537 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
7538 resulting schedule will be distributed as much as possible.
7539 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
7540 try to fuse loops in the resulting schedule.
7542 =item * schedule_maximize_band_depth
7544 If this option is set, we do not split bands at the point
7545 where we detect splitting is necessary. Instead, we
7546 backtrack and split bands as early as possible. This
7547 reduces the number of splits and maximizes the width of
7548 the bands. Wider bands give more possibilities for tiling.
7549 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
7550 then bands will be split as early as possible, even if there is no need.
7551 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
7553 =item * schedule_outer_coincidence
7555 If this option is set, then we try to construct schedules
7556 where the outermost scheduling dimension in each band
7557 satisfies the coincidence constraints.
7559 =item * schedule_split_scaled
7561 If this option is set, then we try to construct schedules in which the
7562 constant term is split off from the linear part if the linear parts of
7563 the scheduling rows for all nodes in the graphs have a common non-trivial
7565 The constant term is then placed in a separate band and the linear
7568 =item * schedule_algorithm
7570 Selects the scheduling algorithm to be used.
7571 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
7572 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
7574 =item * schedule_separate_components
7576 If at any point the dependence graph contains any (weakly connected) components,
7577 then these components are scheduled separately.
7578 If this option is not set, then some iterations of the domains
7579 in these components may be scheduled together.
7580 If this option is set, then the components are given consecutive
7585 =head2 AST Generation
7587 This section describes the C<isl> functionality for generating
7588 ASTs that visit all the elements
7589 in a domain in an order specified by a schedule.
7590 In particular, given a C<isl_union_map>, an AST is generated
7591 that visits all the elements in the domain of the C<isl_union_map>
7592 according to the lexicographic order of the corresponding image
7593 element(s). If the range of the C<isl_union_map> consists of
7594 elements in more than one space, then each of these spaces is handled
7595 separately in an arbitrary order.
7596 It should be noted that the image elements only specify the I<order>
7597 in which the corresponding domain elements should be visited.
7598 No direct relation between the image elements and the loop iterators
7599 in the generated AST should be assumed.
7601 Each AST is generated within a build. The initial build
7602 simply specifies the constraints on the parameters (if any)
7603 and can be created, inspected, copied and freed using the following functions.
7605 #include <isl/ast_build.h>
7606 __isl_give isl_ast_build *isl_ast_build_from_context(
7607 __isl_take isl_set *set);
7608 __isl_give isl_ast_build *isl_ast_build_copy(
7609 __isl_keep isl_ast_build *build);
7610 __isl_null isl_ast_build *isl_ast_build_free(
7611 __isl_take isl_ast_build *build);
7613 The C<set> argument is usually a parameter set with zero or more parameters.
7614 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
7615 and L</"Fine-grained Control over AST Generation">.
7616 Finally, the AST itself can be constructed using the following
7619 #include <isl/ast_build.h>
7620 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
7621 __isl_keep isl_ast_build *build,
7622 __isl_take isl_union_map *schedule);
7624 =head3 Inspecting the AST
7626 The basic properties of an AST node can be obtained as follows.
7628 #include <isl/ast.h>
7629 enum isl_ast_node_type isl_ast_node_get_type(
7630 __isl_keep isl_ast_node *node);
7632 The type of an AST node is one of
7633 C<isl_ast_node_for>,
7635 C<isl_ast_node_block> or
7636 C<isl_ast_node_user>.
7637 An C<isl_ast_node_for> represents a for node.
7638 An C<isl_ast_node_if> represents an if node.
7639 An C<isl_ast_node_block> represents a compound node.
7640 An C<isl_ast_node_user> represents an expression statement.
7641 An expression statement typically corresponds to a domain element, i.e.,
7642 one of the elements that is visited by the AST.
7644 Each type of node has its own additional properties.
7646 #include <isl/ast.h>
7647 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7648 __isl_keep isl_ast_node *node);
7649 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7650 __isl_keep isl_ast_node *node);
7651 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7652 __isl_keep isl_ast_node *node);
7653 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7654 __isl_keep isl_ast_node *node);
7655 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7656 __isl_keep isl_ast_node *node);
7657 int isl_ast_node_for_is_degenerate(
7658 __isl_keep isl_ast_node *node);
7660 An C<isl_ast_for> is considered degenerate if it is known to execute
7663 #include <isl/ast.h>
7664 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7665 __isl_keep isl_ast_node *node);
7666 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7667 __isl_keep isl_ast_node *node);
7668 int isl_ast_node_if_has_else(
7669 __isl_keep isl_ast_node *node);
7670 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7671 __isl_keep isl_ast_node *node);
7673 __isl_give isl_ast_node_list *
7674 isl_ast_node_block_get_children(
7675 __isl_keep isl_ast_node *node);
7677 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7678 __isl_keep isl_ast_node *node);
7680 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7681 the following functions.
7683 #include <isl/ast.h>
7684 enum isl_ast_expr_type isl_ast_expr_get_type(
7685 __isl_keep isl_ast_expr *expr);
7687 The type of an AST expression is one of
7689 C<isl_ast_expr_id> or
7690 C<isl_ast_expr_int>.
7691 An C<isl_ast_expr_op> represents the result of an operation.
7692 An C<isl_ast_expr_id> represents an identifier.
7693 An C<isl_ast_expr_int> represents an integer value.
7695 Each type of expression has its own additional properties.
7697 #include <isl/ast.h>
7698 enum isl_ast_op_type isl_ast_expr_get_op_type(
7699 __isl_keep isl_ast_expr *expr);
7700 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7701 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7702 __isl_keep isl_ast_expr *expr, int pos);
7703 int isl_ast_node_foreach_ast_op_type(
7704 __isl_keep isl_ast_node *node,
7705 int (*fn)(enum isl_ast_op_type type, void *user),
7708 C<isl_ast_expr_get_op_type> returns the type of the operation
7709 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7710 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7712 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7713 C<isl_ast_op_type> that appears in C<node>.
7714 The operation type is one of the following.
7718 =item C<isl_ast_op_and>
7720 Logical I<and> of two arguments.
7721 Both arguments can be evaluated.
7723 =item C<isl_ast_op_and_then>
7725 Logical I<and> of two arguments.
7726 The second argument can only be evaluated if the first evaluates to true.
7728 =item C<isl_ast_op_or>
7730 Logical I<or> of two arguments.
7731 Both arguments can be evaluated.
7733 =item C<isl_ast_op_or_else>
7735 Logical I<or> of two arguments.
7736 The second argument can only be evaluated if the first evaluates to false.
7738 =item C<isl_ast_op_max>
7740 Maximum of two or more arguments.
7742 =item C<isl_ast_op_min>
7744 Minimum of two or more arguments.
7746 =item C<isl_ast_op_minus>
7750 =item C<isl_ast_op_add>
7752 Sum of two arguments.
7754 =item C<isl_ast_op_sub>
7756 Difference of two arguments.
7758 =item C<isl_ast_op_mul>
7760 Product of two arguments.
7762 =item C<isl_ast_op_div>
7764 Exact division. That is, the result is known to be an integer.
7766 =item C<isl_ast_op_fdiv_q>
7768 Result of integer division, rounded towards negative
7771 =item C<isl_ast_op_pdiv_q>
7773 Result of integer division, where dividend is known to be non-negative.
7775 =item C<isl_ast_op_pdiv_r>
7777 Remainder of integer division, where dividend is known to be non-negative.
7779 =item C<isl_ast_op_zdiv_r>
7781 Equal to zero iff the remainder on integer division is zero.
7783 =item C<isl_ast_op_cond>
7785 Conditional operator defined on three arguments.
7786 If the first argument evaluates to true, then the result
7787 is equal to the second argument. Otherwise, the result
7788 is equal to the third argument.
7789 The second and third argument may only be evaluated if
7790 the first argument evaluates to true and false, respectively.
7791 Corresponds to C<a ? b : c> in C.
7793 =item C<isl_ast_op_select>
7795 Conditional operator defined on three arguments.
7796 If the first argument evaluates to true, then the result
7797 is equal to the second argument. Otherwise, the result
7798 is equal to the third argument.
7799 The second and third argument may be evaluated independently
7800 of the value of the first argument.
7801 Corresponds to C<a * b + (1 - a) * c> in C.
7803 =item C<isl_ast_op_eq>
7807 =item C<isl_ast_op_le>
7809 Less than or equal relation.
7811 =item C<isl_ast_op_lt>
7815 =item C<isl_ast_op_ge>
7817 Greater than or equal relation.
7819 =item C<isl_ast_op_gt>
7821 Greater than relation.
7823 =item C<isl_ast_op_call>
7826 The number of arguments of the C<isl_ast_expr> is one more than
7827 the number of arguments in the function call, the first argument
7828 representing the function being called.
7830 =item C<isl_ast_op_access>
7833 The number of arguments of the C<isl_ast_expr> is one more than
7834 the number of index expressions in the array access, the first argument
7835 representing the array being accessed.
7837 =item C<isl_ast_op_member>
7840 This operation has two arguments, a structure and the name of
7841 the member of the structure being accessed.
7845 #include <isl/ast.h>
7846 __isl_give isl_id *isl_ast_expr_get_id(
7847 __isl_keep isl_ast_expr *expr);
7849 Return the identifier represented by the AST expression.
7851 #include <isl/ast.h>
7852 __isl_give isl_val *isl_ast_expr_get_val(
7853 __isl_keep isl_ast_expr *expr);
7855 Return the integer represented by the AST expression.
7857 =head3 Properties of ASTs
7859 #include <isl/ast.h>
7860 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7861 __isl_keep isl_ast_expr *expr2);
7863 Check if two C<isl_ast_expr>s are equal to each other.
7865 =head3 Manipulating and printing the AST
7867 AST nodes can be copied and freed using the following functions.
7869 #include <isl/ast.h>
7870 __isl_give isl_ast_node *isl_ast_node_copy(
7871 __isl_keep isl_ast_node *node);
7872 __isl_null isl_ast_node *isl_ast_node_free(
7873 __isl_take isl_ast_node *node);
7875 AST expressions can be copied and freed using the following functions.
7877 #include <isl/ast.h>
7878 __isl_give isl_ast_expr *isl_ast_expr_copy(
7879 __isl_keep isl_ast_expr *expr);
7880 __isl_null isl_ast_expr *isl_ast_expr_free(
7881 __isl_take isl_ast_expr *expr);
7883 New AST expressions can be created either directly or within
7884 the context of an C<isl_ast_build>.
7886 #include <isl/ast.h>
7887 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7888 __isl_take isl_val *v);
7889 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7890 __isl_take isl_id *id);
7891 __isl_give isl_ast_expr *isl_ast_expr_neg(
7892 __isl_take isl_ast_expr *expr);
7893 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7894 __isl_take isl_ast_expr *expr);
7895 __isl_give isl_ast_expr *isl_ast_expr_add(
7896 __isl_take isl_ast_expr *expr1,
7897 __isl_take isl_ast_expr *expr2);
7898 __isl_give isl_ast_expr *isl_ast_expr_sub(
7899 __isl_take isl_ast_expr *expr1,
7900 __isl_take isl_ast_expr *expr2);
7901 __isl_give isl_ast_expr *isl_ast_expr_mul(
7902 __isl_take isl_ast_expr *expr1,
7903 __isl_take isl_ast_expr *expr2);
7904 __isl_give isl_ast_expr *isl_ast_expr_div(
7905 __isl_take isl_ast_expr *expr1,
7906 __isl_take isl_ast_expr *expr2);
7907 __isl_give isl_ast_expr *isl_ast_expr_and(
7908 __isl_take isl_ast_expr *expr1,
7909 __isl_take isl_ast_expr *expr2)
7910 __isl_give isl_ast_expr *isl_ast_expr_or(
7911 __isl_take isl_ast_expr *expr1,
7912 __isl_take isl_ast_expr *expr2)
7913 __isl_give isl_ast_expr *isl_ast_expr_eq(
7914 __isl_take isl_ast_expr *expr1,
7915 __isl_take isl_ast_expr *expr2);
7916 __isl_give isl_ast_expr *isl_ast_expr_le(
7917 __isl_take isl_ast_expr *expr1,
7918 __isl_take isl_ast_expr *expr2);
7919 __isl_give isl_ast_expr *isl_ast_expr_lt(
7920 __isl_take isl_ast_expr *expr1,
7921 __isl_take isl_ast_expr *expr2);
7922 __isl_give isl_ast_expr *isl_ast_expr_ge(
7923 __isl_take isl_ast_expr *expr1,
7924 __isl_take isl_ast_expr *expr2);
7925 __isl_give isl_ast_expr *isl_ast_expr_gt(
7926 __isl_take isl_ast_expr *expr1,
7927 __isl_take isl_ast_expr *expr2);
7928 __isl_give isl_ast_expr *isl_ast_expr_access(
7929 __isl_take isl_ast_expr *array,
7930 __isl_take isl_ast_expr_list *indices);
7932 The function C<isl_ast_expr_address_of> can be applied to an
7933 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
7934 to represent the address of the C<isl_ast_expr_access>.
7936 #include <isl/ast_build.h>
7937 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
7938 __isl_keep isl_ast_build *build,
7939 __isl_take isl_pw_aff *pa);
7940 __isl_give isl_ast_expr *
7941 isl_ast_build_access_from_pw_multi_aff(
7942 __isl_keep isl_ast_build *build,
7943 __isl_take isl_pw_multi_aff *pma);
7944 __isl_give isl_ast_expr *
7945 isl_ast_build_access_from_multi_pw_aff(
7946 __isl_keep isl_ast_build *build,
7947 __isl_take isl_multi_pw_aff *mpa);
7948 __isl_give isl_ast_expr *
7949 isl_ast_build_call_from_pw_multi_aff(
7950 __isl_keep isl_ast_build *build,
7951 __isl_take isl_pw_multi_aff *pma);
7952 __isl_give isl_ast_expr *
7953 isl_ast_build_call_from_multi_pw_aff(
7954 __isl_keep isl_ast_build *build,
7955 __isl_take isl_multi_pw_aff *mpa);
7957 The domains of C<pa>, C<mpa> and C<pma> should correspond
7958 to the schedule space of C<build>.
7959 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
7960 the function being called.
7961 If the accessed space is a nested relation, then it is taken
7962 to represent an access of the member specified by the range
7963 of this nested relation of the structure specified by the domain
7964 of the nested relation.
7966 The following functions can be used to modify an C<isl_ast_expr>.
7968 #include <isl/ast.h>
7969 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
7970 __isl_take isl_ast_expr *expr, int pos,
7971 __isl_take isl_ast_expr *arg);
7973 Replace the argument of C<expr> at position C<pos> by C<arg>.
7975 #include <isl/ast.h>
7976 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
7977 __isl_take isl_ast_expr *expr,
7978 __isl_take isl_id_to_ast_expr *id2expr);
7980 The function C<isl_ast_expr_substitute_ids> replaces the
7981 subexpressions of C<expr> of type C<isl_ast_expr_id>
7982 by the corresponding expression in C<id2expr>, if there is any.
7985 User specified data can be attached to an C<isl_ast_node> and obtained
7986 from the same C<isl_ast_node> using the following functions.
7988 #include <isl/ast.h>
7989 __isl_give isl_ast_node *isl_ast_node_set_annotation(
7990 __isl_take isl_ast_node *node,
7991 __isl_take isl_id *annotation);
7992 __isl_give isl_id *isl_ast_node_get_annotation(
7993 __isl_keep isl_ast_node *node);
7995 Basic printing can be performed using the following functions.
7997 #include <isl/ast.h>
7998 __isl_give isl_printer *isl_printer_print_ast_expr(
7999 __isl_take isl_printer *p,
8000 __isl_keep isl_ast_expr *expr);
8001 __isl_give isl_printer *isl_printer_print_ast_node(
8002 __isl_take isl_printer *p,
8003 __isl_keep isl_ast_node *node);
8004 __isl_give char *isl_ast_expr_to_str(
8005 __isl_keep isl_ast_expr *expr);
8007 More advanced printing can be performed using the following functions.
8009 #include <isl/ast.h>
8010 __isl_give isl_printer *isl_ast_op_type_print_macro(
8011 enum isl_ast_op_type type,
8012 __isl_take isl_printer *p);
8013 __isl_give isl_printer *isl_ast_node_print_macros(
8014 __isl_keep isl_ast_node *node,
8015 __isl_take isl_printer *p);
8016 __isl_give isl_printer *isl_ast_node_print(
8017 __isl_keep isl_ast_node *node,
8018 __isl_take isl_printer *p,
8019 __isl_take isl_ast_print_options *options);
8020 __isl_give isl_printer *isl_ast_node_for_print(
8021 __isl_keep isl_ast_node *node,
8022 __isl_take isl_printer *p,
8023 __isl_take isl_ast_print_options *options);
8024 __isl_give isl_printer *isl_ast_node_if_print(
8025 __isl_keep isl_ast_node *node,
8026 __isl_take isl_printer *p,
8027 __isl_take isl_ast_print_options *options);
8029 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
8030 C<isl> may print out an AST that makes use of macros such
8031 as C<floord>, C<min> and C<max>.
8032 C<isl_ast_op_type_print_macro> prints out the macro
8033 corresponding to a specific C<isl_ast_op_type>.
8034 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
8035 for expressions where these macros would be used and prints
8036 out the required macro definitions.
8037 Essentially, C<isl_ast_node_print_macros> calls
8038 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
8039 as function argument.
8040 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
8041 C<isl_ast_node_if_print> print an C<isl_ast_node>
8042 in C<ISL_FORMAT_C>, but allow for some extra control
8043 through an C<isl_ast_print_options> object.
8044 This object can be created using the following functions.
8046 #include <isl/ast.h>
8047 __isl_give isl_ast_print_options *
8048 isl_ast_print_options_alloc(isl_ctx *ctx);
8049 __isl_give isl_ast_print_options *
8050 isl_ast_print_options_copy(
8051 __isl_keep isl_ast_print_options *options);
8052 __isl_null isl_ast_print_options *
8053 isl_ast_print_options_free(
8054 __isl_take isl_ast_print_options *options);
8056 __isl_give isl_ast_print_options *
8057 isl_ast_print_options_set_print_user(
8058 __isl_take isl_ast_print_options *options,
8059 __isl_give isl_printer *(*print_user)(
8060 __isl_take isl_printer *p,
8061 __isl_take isl_ast_print_options *options,
8062 __isl_keep isl_ast_node *node, void *user),
8064 __isl_give isl_ast_print_options *
8065 isl_ast_print_options_set_print_for(
8066 __isl_take isl_ast_print_options *options,
8067 __isl_give isl_printer *(*print_for)(
8068 __isl_take isl_printer *p,
8069 __isl_take isl_ast_print_options *options,
8070 __isl_keep isl_ast_node *node, void *user),
8073 The callback set by C<isl_ast_print_options_set_print_user>
8074 is called whenever a node of type C<isl_ast_node_user> needs to
8076 The callback set by C<isl_ast_print_options_set_print_for>
8077 is called whenever a node of type C<isl_ast_node_for> needs to
8079 Note that C<isl_ast_node_for_print> will I<not> call the
8080 callback set by C<isl_ast_print_options_set_print_for> on the node
8081 on which C<isl_ast_node_for_print> is called, but only on nested
8082 nodes of type C<isl_ast_node_for>. It is therefore safe to
8083 call C<isl_ast_node_for_print> from within the callback set by
8084 C<isl_ast_print_options_set_print_for>.
8086 The following option determines the type to be used for iterators
8087 while printing the AST.
8089 int isl_options_set_ast_iterator_type(
8090 isl_ctx *ctx, const char *val);
8091 const char *isl_options_get_ast_iterator_type(
8094 The AST printer only prints body nodes as blocks if these
8095 blocks cannot be safely omitted.
8096 For example, a C<for> node with one body node will not be
8097 surrounded with braces in C<ISL_FORMAT_C>.
8098 A block will always be printed by setting the following option.
8100 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
8102 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
8106 #include <isl/ast_build.h>
8107 int isl_options_set_ast_build_atomic_upper_bound(
8108 isl_ctx *ctx, int val);
8109 int isl_options_get_ast_build_atomic_upper_bound(
8111 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
8113 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
8114 int isl_options_set_ast_build_exploit_nested_bounds(
8115 isl_ctx *ctx, int val);
8116 int isl_options_get_ast_build_exploit_nested_bounds(
8118 int isl_options_set_ast_build_group_coscheduled(
8119 isl_ctx *ctx, int val);
8120 int isl_options_get_ast_build_group_coscheduled(
8122 int isl_options_set_ast_build_scale_strides(
8123 isl_ctx *ctx, int val);
8124 int isl_options_get_ast_build_scale_strides(
8126 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
8128 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
8129 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
8131 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
8135 =item * ast_build_atomic_upper_bound
8137 Generate loop upper bounds that consist of the current loop iterator,
8138 an operator and an expression not involving the iterator.
8139 If this option is not set, then the current loop iterator may appear
8140 several times in the upper bound.
8141 For example, when this option is turned off, AST generation
8144 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
8148 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
8151 When the option is turned on, the following AST is generated
8153 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
8156 =item * ast_build_prefer_pdiv
8158 If this option is turned off, then the AST generation will
8159 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
8160 operators, but no C<isl_ast_op_pdiv_q> or
8161 C<isl_ast_op_pdiv_r> operators.
8162 If this options is turned on, then C<isl> will try to convert
8163 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
8164 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
8166 =item * ast_build_exploit_nested_bounds
8168 Simplify conditions based on bounds of nested for loops.
8169 In particular, remove conditions that are implied by the fact
8170 that one or more nested loops have at least one iteration,
8171 meaning that the upper bound is at least as large as the lower bound.
8172 For example, when this option is turned off, AST generation
8175 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
8181 for (int c0 = 0; c0 <= N; c0 += 1)
8182 for (int c1 = 0; c1 <= M; c1 += 1)
8185 When the option is turned on, the following AST is generated
8187 for (int c0 = 0; c0 <= N; c0 += 1)
8188 for (int c1 = 0; c1 <= M; c1 += 1)
8191 =item * ast_build_group_coscheduled
8193 If two domain elements are assigned the same schedule point, then
8194 they may be executed in any order and they may even appear in different
8195 loops. If this options is set, then the AST generator will make
8196 sure that coscheduled domain elements do not appear in separate parts
8197 of the AST. This is useful in case of nested AST generation
8198 if the outer AST generation is given only part of a schedule
8199 and the inner AST generation should handle the domains that are
8200 coscheduled by this initial part of the schedule together.
8201 For example if an AST is generated for a schedule
8203 { A[i] -> [0]; B[i] -> [0] }
8205 then the C<isl_ast_build_set_create_leaf> callback described
8206 below may get called twice, once for each domain.
8207 Setting this option ensures that the callback is only called once
8208 on both domains together.
8210 =item * ast_build_separation_bounds
8212 This option specifies which bounds to use during separation.
8213 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
8214 then all (possibly implicit) bounds on the current dimension will
8215 be used during separation.
8216 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
8217 then only those bounds that are explicitly available will
8218 be used during separation.
8220 =item * ast_build_scale_strides
8222 This option specifies whether the AST generator is allowed
8223 to scale down iterators of strided loops.
8225 =item * ast_build_allow_else
8227 This option specifies whether the AST generator is allowed
8228 to construct if statements with else branches.
8230 =item * ast_build_allow_or
8232 This option specifies whether the AST generator is allowed
8233 to construct if conditions with disjunctions.
8237 =head3 Fine-grained Control over AST Generation
8239 Besides specifying the constraints on the parameters,
8240 an C<isl_ast_build> object can be used to control
8241 various aspects of the AST generation process.
8242 The most prominent way of control is through ``options'',
8243 which can be set using the following function.
8245 #include <isl/ast_build.h>
8246 __isl_give isl_ast_build *
8247 isl_ast_build_set_options(
8248 __isl_take isl_ast_build *control,
8249 __isl_take isl_union_map *options);
8251 The options are encoded in an C<isl_union_map>.
8252 The domain of this union relation refers to the schedule domain,
8253 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
8254 In the case of nested AST generation (see L</"Nested AST Generation">),
8255 the domain of C<options> should refer to the extra piece of the schedule.
8256 That is, it should be equal to the range of the wrapped relation in the
8257 range of the schedule.
8258 The range of the options can consist of elements in one or more spaces,
8259 the names of which determine the effect of the option.
8260 The values of the range typically also refer to the schedule dimension
8261 to which the option applies. In case of nested AST generation
8262 (see L</"Nested AST Generation">), these values refer to the position
8263 of the schedule dimension within the innermost AST generation.
8264 The constraints on the domain elements of
8265 the option should only refer to this dimension and earlier dimensions.
8266 We consider the following spaces.
8270 =item C<separation_class>
8272 This space is a wrapped relation between two one dimensional spaces.
8273 The input space represents the schedule dimension to which the option
8274 applies and the output space represents the separation class.
8275 While constructing a loop corresponding to the specified schedule
8276 dimension(s), the AST generator will try to generate separate loops
8277 for domain elements that are assigned different classes.
8278 If only some of the elements are assigned a class, then those elements
8279 that are not assigned any class will be treated as belonging to a class
8280 that is separate from the explicitly assigned classes.
8281 The typical use case for this option is to separate full tiles from
8283 The other options, described below, are applied after the separation
8286 As an example, consider the separation into full and partial tiles
8287 of a tiling of a triangular domain.
8288 Take, for example, the domain
8290 { A[i,j] : 0 <= i,j and i + j <= 100 }
8292 and a tiling into tiles of 10 by 10. The input to the AST generator
8293 is then the schedule
8295 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
8298 Without any options, the following AST is generated
8300 for (int c0 = 0; c0 <= 10; c0 += 1)
8301 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8302 for (int c2 = 10 * c0;
8303 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8305 for (int c3 = 10 * c1;
8306 c3 <= min(10 * c1 + 9, -c2 + 100);
8310 Separation into full and partial tiles can be obtained by assigning
8311 a class, say C<0>, to the full tiles. The full tiles are represented by those
8312 values of the first and second schedule dimensions for which there are
8313 values of the third and fourth dimensions to cover an entire tile.
8314 That is, we need to specify the following option
8316 { [a,b,c,d] -> separation_class[[0]->[0]] :
8317 exists b': 0 <= 10a,10b' and
8318 10a+9+10b'+9 <= 100;
8319 [a,b,c,d] -> separation_class[[1]->[0]] :
8320 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
8324 { [a, b, c, d] -> separation_class[[1] -> [0]] :
8325 a >= 0 and b >= 0 and b <= 8 - a;
8326 [a, b, c, d] -> separation_class[[0] -> [0]] :
8329 With this option, the generated AST is as follows
8332 for (int c0 = 0; c0 <= 8; c0 += 1) {
8333 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
8334 for (int c2 = 10 * c0;
8335 c2 <= 10 * c0 + 9; c2 += 1)
8336 for (int c3 = 10 * c1;
8337 c3 <= 10 * c1 + 9; c3 += 1)
8339 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
8340 for (int c2 = 10 * c0;
8341 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8343 for (int c3 = 10 * c1;
8344 c3 <= min(-c2 + 100, 10 * c1 + 9);
8348 for (int c0 = 9; c0 <= 10; c0 += 1)
8349 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8350 for (int c2 = 10 * c0;
8351 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8353 for (int c3 = 10 * c1;
8354 c3 <= min(10 * c1 + 9, -c2 + 100);
8361 This is a single-dimensional space representing the schedule dimension(s)
8362 to which ``separation'' should be applied. Separation tries to split
8363 a loop into several pieces if this can avoid the generation of guards
8365 See also the C<atomic> option.
8369 This is a single-dimensional space representing the schedule dimension(s)
8370 for which the domains should be considered ``atomic''. That is, the
8371 AST generator will make sure that any given domain space will only appear
8372 in a single loop at the specified level.
8374 Consider the following schedule
8376 { a[i] -> [i] : 0 <= i < 10;
8377 b[i] -> [i+1] : 0 <= i < 10 }
8379 If the following option is specified
8381 { [i] -> separate[x] }
8383 then the following AST will be generated
8387 for (int c0 = 1; c0 <= 9; c0 += 1) {
8394 If, on the other hand, the following option is specified
8396 { [i] -> atomic[x] }
8398 then the following AST will be generated
8400 for (int c0 = 0; c0 <= 10; c0 += 1) {
8407 If neither C<atomic> nor C<separate> is specified, then the AST generator
8408 may produce either of these two results or some intermediate form.
8412 This is a single-dimensional space representing the schedule dimension(s)
8413 that should be I<completely> unrolled.
8414 To obtain a partial unrolling, the user should apply an additional
8415 strip-mining to the schedule and fully unroll the inner loop.
8419 Additional control is available through the following functions.
8421 #include <isl/ast_build.h>
8422 __isl_give isl_ast_build *
8423 isl_ast_build_set_iterators(
8424 __isl_take isl_ast_build *control,
8425 __isl_take isl_id_list *iterators);
8427 The function C<isl_ast_build_set_iterators> allows the user to
8428 specify a list of iterator C<isl_id>s to be used as iterators.
8429 If the input schedule is injective, then
8430 the number of elements in this list should be as large as the dimension
8431 of the schedule space, but no direct correspondence should be assumed
8432 between dimensions and elements.
8433 If the input schedule is not injective, then an additional number
8434 of C<isl_id>s equal to the largest dimension of the input domains
8436 If the number of provided C<isl_id>s is insufficient, then additional
8437 names are automatically generated.
8439 #include <isl/ast_build.h>
8440 __isl_give isl_ast_build *
8441 isl_ast_build_set_create_leaf(
8442 __isl_take isl_ast_build *control,
8443 __isl_give isl_ast_node *(*fn)(
8444 __isl_take isl_ast_build *build,
8445 void *user), void *user);
8448 C<isl_ast_build_set_create_leaf> function allows for the
8449 specification of a callback that should be called whenever the AST
8450 generator arrives at an element of the schedule domain.
8451 The callback should return an AST node that should be inserted
8452 at the corresponding position of the AST. The default action (when
8453 the callback is not set) is to continue generating parts of the AST to scan
8454 all the domain elements associated to the schedule domain element
8455 and to insert user nodes, ``calling'' the domain element, for each of them.
8456 The C<build> argument contains the current state of the C<isl_ast_build>.
8457 To ease nested AST generation (see L</"Nested AST Generation">),
8458 all control information that is
8459 specific to the current AST generation such as the options and
8460 the callbacks has been removed from this C<isl_ast_build>.
8461 The callback would typically return the result of a nested
8463 user defined node created using the following function.
8465 #include <isl/ast.h>
8466 __isl_give isl_ast_node *isl_ast_node_alloc_user(
8467 __isl_take isl_ast_expr *expr);
8469 #include <isl/ast_build.h>
8470 __isl_give isl_ast_build *
8471 isl_ast_build_set_at_each_domain(
8472 __isl_take isl_ast_build *build,
8473 __isl_give isl_ast_node *(*fn)(
8474 __isl_take isl_ast_node *node,
8475 __isl_keep isl_ast_build *build,
8476 void *user), void *user);
8477 __isl_give isl_ast_build *
8478 isl_ast_build_set_before_each_for(
8479 __isl_take isl_ast_build *build,
8480 __isl_give isl_id *(*fn)(
8481 __isl_keep isl_ast_build *build,
8482 void *user), void *user);
8483 __isl_give isl_ast_build *
8484 isl_ast_build_set_after_each_for(
8485 __isl_take isl_ast_build *build,
8486 __isl_give isl_ast_node *(*fn)(
8487 __isl_take isl_ast_node *node,
8488 __isl_keep isl_ast_build *build,
8489 void *user), void *user);
8491 The callback set by C<isl_ast_build_set_at_each_domain> will
8492 be called for each domain AST node.
8493 The callbacks set by C<isl_ast_build_set_before_each_for>
8494 and C<isl_ast_build_set_after_each_for> will be called
8495 for each for AST node. The first will be called in depth-first
8496 pre-order, while the second will be called in depth-first post-order.
8497 Since C<isl_ast_build_set_before_each_for> is called before the for
8498 node is actually constructed, it is only passed an C<isl_ast_build>.
8499 The returned C<isl_id> will be added as an annotation (using
8500 C<isl_ast_node_set_annotation>) to the constructed for node.
8501 In particular, if the user has also specified an C<after_each_for>
8502 callback, then the annotation can be retrieved from the node passed to
8503 that callback using C<isl_ast_node_get_annotation>.
8504 All callbacks should C<NULL> on failure.
8505 The given C<isl_ast_build> can be used to create new
8506 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
8507 or C<isl_ast_build_call_from_pw_multi_aff>.
8509 =head3 Nested AST Generation
8511 C<isl> allows the user to create an AST within the context
8512 of another AST. These nested ASTs are created using the
8513 same C<isl_ast_build_ast_from_schedule> function that is used to create the
8514 outer AST. The C<build> argument should be an C<isl_ast_build>
8515 passed to a callback set by
8516 C<isl_ast_build_set_create_leaf>.
8517 The space of the range of the C<schedule> argument should refer
8518 to this build. In particular, the space should be a wrapped
8519 relation and the domain of this wrapped relation should be the
8520 same as that of the range of the schedule returned by
8521 C<isl_ast_build_get_schedule> below.
8522 In practice, the new schedule is typically
8523 created by calling C<isl_union_map_range_product> on the old schedule
8524 and some extra piece of the schedule.
8525 The space of the schedule domain is also available from
8526 the C<isl_ast_build>.
8528 #include <isl/ast_build.h>
8529 __isl_give isl_union_map *isl_ast_build_get_schedule(
8530 __isl_keep isl_ast_build *build);
8531 __isl_give isl_space *isl_ast_build_get_schedule_space(
8532 __isl_keep isl_ast_build *build);
8533 __isl_give isl_ast_build *isl_ast_build_restrict(
8534 __isl_take isl_ast_build *build,
8535 __isl_take isl_set *set);
8537 The C<isl_ast_build_get_schedule> function returns a (partial)
8538 schedule for the domains elements for which part of the AST still needs to
8539 be generated in the current build.
8540 In particular, the domain elements are mapped to those iterations of the loops
8541 enclosing the current point of the AST generation inside which
8542 the domain elements are executed.
8543 No direct correspondence between
8544 the input schedule and this schedule should be assumed.
8545 The space obtained from C<isl_ast_build_get_schedule_space> can be used
8546 to create a set for C<isl_ast_build_restrict> to intersect
8547 with the current build. In particular, the set passed to
8548 C<isl_ast_build_restrict> can have additional parameters.
8549 The ids of the set dimensions in the space returned by
8550 C<isl_ast_build_get_schedule_space> correspond to the
8551 iterators of the already generated loops.
8552 The user should not rely on the ids of the output dimensions
8553 of the relations in the union relation returned by
8554 C<isl_ast_build_get_schedule> having any particular value.
8558 Although C<isl> is mainly meant to be used as a library,
8559 it also contains some basic applications that use some
8560 of the functionality of C<isl>.
8561 The input may be specified in either the L<isl format>
8562 or the L<PolyLib format>.
8564 =head2 C<isl_polyhedron_sample>
8566 C<isl_polyhedron_sample> takes a polyhedron as input and prints
8567 an integer element of the polyhedron, if there is any.
8568 The first column in the output is the denominator and is always
8569 equal to 1. If the polyhedron contains no integer points,
8570 then a vector of length zero is printed.
8574 C<isl_pip> takes the same input as the C<example> program
8575 from the C<piplib> distribution, i.e., a set of constraints
8576 on the parameters, a line containing only -1 and finally a set
8577 of constraints on a parametric polyhedron.
8578 The coefficients of the parameters appear in the last columns
8579 (but before the final constant column).
8580 The output is the lexicographic minimum of the parametric polyhedron.
8581 As C<isl> currently does not have its own output format, the output
8582 is just a dump of the internal state.
8584 =head2 C<isl_polyhedron_minimize>
8586 C<isl_polyhedron_minimize> computes the minimum of some linear
8587 or affine objective function over the integer points in a polyhedron.
8588 If an affine objective function
8589 is given, then the constant should appear in the last column.
8591 =head2 C<isl_polytope_scan>
8593 Given a polytope, C<isl_polytope_scan> prints
8594 all integer points in the polytope.
8596 =head2 C<isl_codegen>
8598 Given a schedule, a context set and an options relation,
8599 C<isl_codegen> prints out an AST that scans the domain elements
8600 of the schedule in the order of their image(s) taking into account
8601 the constraints in the context set.