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 isl_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_get_ctx(
527 __isl_keep isl_schedule *sched);
528 isl_ctx *isl_schedule_constraints_get_ctx(
529 __isl_keep isl_schedule_constraints *sc);
531 #include <isl/band.h>
532 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
534 #include <isl/ast_build.h>
535 isl_ctx *isl_ast_build_get_ctx(
536 __isl_keep isl_ast_build *build);
539 isl_ctx *isl_ast_expr_get_ctx(
540 __isl_keep isl_ast_expr *expr);
541 isl_ctx *isl_ast_node_get_ctx(
542 __isl_keep isl_ast_node *node);
546 An C<isl_val> represents an integer value, a rational value
547 or one of three special values, infinity, negative infinity and NaN.
548 Some predefined values can be created using the following functions.
551 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
552 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
553 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
554 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
555 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
556 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
558 Specific integer values can be created using the following functions.
561 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
563 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
565 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
566 size_t n, size_t size, const void *chunks);
568 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
569 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
570 The least significant digit is assumed to be stored first.
572 Value objects can be copied and freed using the following functions.
575 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
576 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
578 They can be inspected using the following functions.
581 long isl_val_get_num_si(__isl_keep isl_val *v);
582 long isl_val_get_den_si(__isl_keep isl_val *v);
583 double isl_val_get_d(__isl_keep isl_val *v);
584 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
586 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
587 size_t size, void *chunks);
589 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
590 of C<size> bytes needed to store the absolute value of the
592 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
593 which is assumed to have been preallocated by the caller.
594 The least significant digit is stored first.
595 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
596 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
597 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
599 An C<isl_val> can be modified using the following function.
602 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
605 The following unary properties are defined on C<isl_val>s.
608 int isl_val_sgn(__isl_keep isl_val *v);
609 int isl_val_is_zero(__isl_keep isl_val *v);
610 int isl_val_is_one(__isl_keep isl_val *v);
611 int isl_val_is_negone(__isl_keep isl_val *v);
612 int isl_val_is_nonneg(__isl_keep isl_val *v);
613 int isl_val_is_nonpos(__isl_keep isl_val *v);
614 int isl_val_is_pos(__isl_keep isl_val *v);
615 int isl_val_is_neg(__isl_keep isl_val *v);
616 int isl_val_is_int(__isl_keep isl_val *v);
617 int isl_val_is_rat(__isl_keep isl_val *v);
618 int isl_val_is_nan(__isl_keep isl_val *v);
619 int isl_val_is_infty(__isl_keep isl_val *v);
620 int isl_val_is_neginfty(__isl_keep isl_val *v);
622 Note that the sign of NaN is undefined.
624 The following binary properties are defined on pairs of C<isl_val>s.
627 int isl_val_lt(__isl_keep isl_val *v1,
628 __isl_keep isl_val *v2);
629 int isl_val_le(__isl_keep isl_val *v1,
630 __isl_keep isl_val *v2);
631 int isl_val_gt(__isl_keep isl_val *v1,
632 __isl_keep isl_val *v2);
633 int isl_val_ge(__isl_keep isl_val *v1,
634 __isl_keep isl_val *v2);
635 int isl_val_eq(__isl_keep isl_val *v1,
636 __isl_keep isl_val *v2);
637 int isl_val_ne(__isl_keep isl_val *v1,
638 __isl_keep isl_val *v2);
639 int isl_val_abs_eq(__isl_keep isl_val *v1,
640 __isl_keep isl_val *v2);
642 The function C<isl_val_abs_eq> checks whether its two arguments
643 are equal in absolute value.
645 For integer C<isl_val>s we additionally have the following binary property.
648 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
649 __isl_keep isl_val *v2);
651 An C<isl_val> can also be compared to an integer using the following
652 function. The result is undefined for NaN.
655 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
657 The following unary operations are available on C<isl_val>s.
660 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
661 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
662 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
663 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
664 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
665 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
666 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
668 The following binary operations are available on C<isl_val>s.
671 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
672 __isl_take isl_val *v2);
673 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
674 __isl_take isl_val *v2);
675 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
676 __isl_take isl_val *v2);
677 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
679 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
680 __isl_take isl_val *v2);
681 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
683 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
684 __isl_take isl_val *v2);
685 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
687 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
688 __isl_take isl_val *v2);
690 On integer values, we additionally have the following operations.
693 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
694 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
695 __isl_take isl_val *v2);
696 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
697 __isl_take isl_val *v2);
698 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
699 __isl_take isl_val *v2, __isl_give isl_val **x,
700 __isl_give isl_val **y);
702 The function C<isl_val_gcdext> returns the greatest common divisor g
703 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
704 that C<*x> * C<v1> + C<*y> * C<v2> = g.
706 =head3 GMP specific functions
708 These functions are only available if C<isl> has been compiled with C<GMP>
711 Specific integer and rational values can be created from C<GMP> values using
712 the following functions.
714 #include <isl/val_gmp.h>
715 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
717 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
718 const mpz_t n, const mpz_t d);
720 The numerator and denominator of a rational value can be extracted as
721 C<GMP> values using the following functions.
723 #include <isl/val_gmp.h>
724 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
725 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
727 =head2 Sets and Relations
729 C<isl> uses six types of objects for representing sets and relations,
730 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
731 C<isl_union_set> and C<isl_union_map>.
732 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
733 can be described as a conjunction of affine constraints, while
734 C<isl_set> and C<isl_map> represent unions of
735 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
736 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
737 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
738 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
739 where spaces are considered different if they have a different number
740 of dimensions and/or different names (see L<"Spaces">).
741 The difference between sets and relations (maps) is that sets have
742 one set of variables, while relations have two sets of variables,
743 input variables and output variables.
745 =head2 Error Handling
747 C<isl> supports different ways to react in case a runtime error is triggered.
748 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
749 with two maps that have incompatible spaces. There are three possible ways
750 to react on error: to warn, to continue or to abort.
752 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
753 the last error in the corresponding C<isl_ctx> and the function in which the
754 error was triggered returns C<NULL>. An error does not corrupt internal state,
755 such that isl can continue to be used. C<isl> also provides functions to
756 read the last error and to reset the memory that stores the last error. The
757 last error is only stored for information purposes. Its presence does not
758 change the behavior of C<isl>. Hence, resetting an error is not required to
759 continue to use isl, but only to observe new errors.
762 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
763 void isl_ctx_reset_error(isl_ctx *ctx);
765 Another option is to continue on error. This is similar to warn on error mode,
766 except that C<isl> does not print any warning. This allows a program to
767 implement its own error reporting.
769 The last option is to directly abort the execution of the program from within
770 the isl library. This makes it obviously impossible to recover from an error,
771 but it allows to directly spot the error location. By aborting on error,
772 debuggers break at the location the error occurred and can provide a stack
773 trace. Other tools that automatically provide stack traces on abort or that do
774 not want to continue execution after an error was triggered may also prefer to
777 The on error behavior of isl can be specified by calling
778 C<isl_options_set_on_error> or by setting the command line option
779 C<--isl-on-error>. Valid arguments for the function call are
780 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
781 choices for the command line option are C<warn>, C<continue> and C<abort>.
782 It is also possible to query the current error mode.
784 #include <isl/options.h>
785 int isl_options_set_on_error(isl_ctx *ctx, int val);
786 int isl_options_get_on_error(isl_ctx *ctx);
790 Identifiers are used to identify both individual dimensions
791 and tuples of dimensions. They consist of an optional name and an optional
792 user pointer. The name and the user pointer cannot both be C<NULL>, however.
793 Identifiers with the same name but different pointer values
794 are considered to be distinct.
795 Similarly, identifiers with different names but the same pointer value
796 are also considered to be distinct.
797 Equal identifiers are represented using the same object.
798 Pairs of identifiers can therefore be tested for equality using the
800 Identifiers can be constructed, copied, freed, inspected and printed
801 using the following functions.
804 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
805 __isl_keep const char *name, void *user);
806 __isl_give isl_id *isl_id_set_free_user(
807 __isl_take isl_id *id,
808 __isl_give void (*free_user)(void *user));
809 __isl_give isl_id *isl_id_copy(isl_id *id);
810 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
812 void *isl_id_get_user(__isl_keep isl_id *id);
813 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
815 __isl_give isl_printer *isl_printer_print_id(
816 __isl_take isl_printer *p, __isl_keep isl_id *id);
818 The callback set by C<isl_id_set_free_user> is called on the user
819 pointer when the last reference to the C<isl_id> is freed.
820 Note that C<isl_id_get_name> returns a pointer to some internal
821 data structure, so the result can only be used while the
822 corresponding C<isl_id> is alive.
826 Whenever a new set, relation or similar object is created from scratch,
827 the space in which it lives needs to be specified using an C<isl_space>.
828 Each space involves zero or more parameters and zero, one or two
829 tuples of set or input/output dimensions. The parameters and dimensions
830 are identified by an C<isl_dim_type> and a position.
831 The type C<isl_dim_param> refers to parameters,
832 the type C<isl_dim_set> refers to set dimensions (for spaces
833 with a single tuple of dimensions) and the types C<isl_dim_in>
834 and C<isl_dim_out> refer to input and output dimensions
835 (for spaces with two tuples of dimensions).
836 Local spaces (see L</"Local Spaces">) also contain dimensions
837 of type C<isl_dim_div>.
838 Note that parameters are only identified by their position within
839 a given object. Across different objects, parameters are (usually)
840 identified by their names or identifiers. Only unnamed parameters
841 are identified by their positions across objects. The use of unnamed
842 parameters is discouraged.
844 #include <isl/space.h>
845 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
846 unsigned nparam, unsigned n_in, unsigned n_out);
847 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
849 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
850 unsigned nparam, unsigned dim);
851 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
852 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
854 The space used for creating a parameter domain
855 needs to be created using C<isl_space_params_alloc>.
856 For other sets, the space
857 needs to be created using C<isl_space_set_alloc>, while
858 for a relation, the space
859 needs to be created using C<isl_space_alloc>.
861 To check whether a given space is that of a set or a map
862 or whether it is a parameter space, use these functions:
864 #include <isl/space.h>
865 int isl_space_is_params(__isl_keep isl_space *space);
866 int isl_space_is_set(__isl_keep isl_space *space);
867 int isl_space_is_map(__isl_keep isl_space *space);
869 Spaces can be compared using the following functions:
871 #include <isl/space.h>
872 int isl_space_is_equal(__isl_keep isl_space *space1,
873 __isl_keep isl_space *space2);
874 int isl_space_is_domain(__isl_keep isl_space *space1,
875 __isl_keep isl_space *space2);
876 int isl_space_is_range(__isl_keep isl_space *space1,
877 __isl_keep isl_space *space2);
878 int isl_space_tuple_is_equal(
879 __isl_keep isl_space *space1,
880 enum isl_dim_type type1,
881 __isl_keep isl_space *space2,
882 enum isl_dim_type type2);
884 C<isl_space_is_domain> checks whether the first argument is equal
885 to the domain of the second argument. This requires in particular that
886 the first argument is a set space and that the second argument
887 is a map space. C<isl_space_tuple_is_equal> checks whether the given
888 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
889 spaces are the same. That is, it checks if they have the same
890 identifier (if any), the same dimension and the same internal structure
893 It is often useful to create objects that live in the
894 same space as some other object. This can be accomplished
895 by creating the new objects
896 (see L</"Creating New Sets and Relations"> or
897 L</"Functions">) based on the space
898 of the original object.
901 __isl_give isl_space *isl_basic_set_get_space(
902 __isl_keep isl_basic_set *bset);
903 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
905 #include <isl/union_set.h>
906 __isl_give isl_space *isl_union_set_get_space(
907 __isl_keep isl_union_set *uset);
910 __isl_give isl_space *isl_basic_map_get_space(
911 __isl_keep isl_basic_map *bmap);
912 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
914 #include <isl/union_map.h>
915 __isl_give isl_space *isl_union_map_get_space(
916 __isl_keep isl_union_map *umap);
918 #include <isl/constraint.h>
919 __isl_give isl_space *isl_constraint_get_space(
920 __isl_keep isl_constraint *constraint);
922 #include <isl/polynomial.h>
923 __isl_give isl_space *isl_qpolynomial_get_domain_space(
924 __isl_keep isl_qpolynomial *qp);
925 __isl_give isl_space *isl_qpolynomial_get_space(
926 __isl_keep isl_qpolynomial *qp);
927 __isl_give isl_space *isl_qpolynomial_fold_get_space(
928 __isl_keep isl_qpolynomial_fold *fold);
929 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
930 __isl_keep isl_pw_qpolynomial *pwqp);
931 __isl_give isl_space *isl_pw_qpolynomial_get_space(
932 __isl_keep isl_pw_qpolynomial *pwqp);
933 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
934 __isl_keep isl_pw_qpolynomial_fold *pwf);
935 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
936 __isl_keep isl_pw_qpolynomial_fold *pwf);
937 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
938 __isl_keep isl_union_pw_qpolynomial *upwqp);
939 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
940 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
943 __isl_give isl_space *isl_multi_val_get_space(
944 __isl_keep isl_multi_val *mv);
947 __isl_give isl_space *isl_aff_get_domain_space(
948 __isl_keep isl_aff *aff);
949 __isl_give isl_space *isl_aff_get_space(
950 __isl_keep isl_aff *aff);
951 __isl_give isl_space *isl_pw_aff_get_domain_space(
952 __isl_keep isl_pw_aff *pwaff);
953 __isl_give isl_space *isl_pw_aff_get_space(
954 __isl_keep isl_pw_aff *pwaff);
955 __isl_give isl_space *isl_multi_aff_get_domain_space(
956 __isl_keep isl_multi_aff *maff);
957 __isl_give isl_space *isl_multi_aff_get_space(
958 __isl_keep isl_multi_aff *maff);
959 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
960 __isl_keep isl_pw_multi_aff *pma);
961 __isl_give isl_space *isl_pw_multi_aff_get_space(
962 __isl_keep isl_pw_multi_aff *pma);
963 __isl_give isl_space *isl_union_pw_aff_get_space(
964 __isl_keep isl_union_pw_aff *upa);
965 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
966 __isl_keep isl_union_pw_multi_aff *upma);
967 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
968 __isl_keep isl_multi_pw_aff *mpa);
969 __isl_give isl_space *isl_multi_pw_aff_get_space(
970 __isl_keep isl_multi_pw_aff *mpa);
971 __isl_give isl_space *
972 isl_multi_union_pw_aff_get_domain_space(
973 __isl_keep isl_multi_union_pw_aff *mupa);
974 __isl_give isl_space *
975 isl_multi_union_pw_aff_get_space(
976 __isl_keep isl_multi_union_pw_aff *mupa);
978 #include <isl/point.h>
979 __isl_give isl_space *isl_point_get_space(
980 __isl_keep isl_point *pnt);
982 The number of dimensions of a given type of space
983 may be read off from a space or an object that lives
984 in a space using the following functions.
985 In case of C<isl_space_dim>, type may be
986 C<isl_dim_param>, C<isl_dim_in> (only for relations),
987 C<isl_dim_out> (only for relations), C<isl_dim_set>
988 (only for sets) or C<isl_dim_all>.
990 #include <isl/space.h>
991 unsigned isl_space_dim(__isl_keep isl_space *space,
992 enum isl_dim_type type);
994 #include <isl/local_space.h>
995 int isl_local_space_dim(__isl_keep isl_local_space *ls,
996 enum isl_dim_type type);
999 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1000 enum isl_dim_type type);
1001 unsigned isl_set_dim(__isl_keep isl_set *set,
1002 enum isl_dim_type type);
1004 #include <isl/union_set.h>
1005 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
1006 enum isl_dim_type type);
1008 #include <isl/map.h>
1009 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1010 enum isl_dim_type type);
1011 unsigned isl_map_dim(__isl_keep isl_map *map,
1012 enum isl_dim_type type);
1014 #include <isl/union_map.h>
1015 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1016 enum isl_dim_type type);
1018 #include <isl/val.h>
1019 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1020 enum isl_dim_type type);
1022 #include <isl/aff.h>
1023 int isl_aff_dim(__isl_keep isl_aff *aff,
1024 enum isl_dim_type type);
1025 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1026 enum isl_dim_type type);
1027 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1028 enum isl_dim_type type);
1029 unsigned isl_pw_multi_aff_dim(
1030 __isl_keep isl_pw_multi_aff *pma,
1031 enum isl_dim_type type);
1032 unsigned isl_multi_pw_aff_dim(
1033 __isl_keep isl_multi_pw_aff *mpa,
1034 enum isl_dim_type type);
1035 unsigned isl_union_pw_aff_dim(
1036 __isl_keep isl_union_pw_aff *upa,
1037 enum isl_dim_type type);
1038 unsigned isl_union_pw_multi_aff_dim(
1039 __isl_keep isl_union_pw_multi_aff *upma,
1040 enum isl_dim_type type);
1041 unsigned isl_multi_union_pw_aff_dim(
1042 __isl_keep isl_multi_union_pw_aff *mupa,
1043 enum isl_dim_type type);
1045 #include <isl/polynomial.h>
1046 unsigned isl_union_pw_qpolynomial_dim(
1047 __isl_keep isl_union_pw_qpolynomial *upwqp,
1048 enum isl_dim_type type);
1049 unsigned isl_union_pw_qpolynomial_fold_dim(
1050 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1051 enum isl_dim_type type);
1053 Note that an C<isl_union_set>, an C<isl_union_map>,
1054 an C<isl_union_pw_multi_aff>,
1055 an C<isl_union_pw_qpolynomial> and
1056 an C<isl_union_pw_qpolynomial_fold>
1057 only have parameters.
1059 The identifiers or names of the individual dimensions of spaces
1060 may be set or read off using the following functions on spaces
1061 or objects that live in spaces.
1062 These functions are mostly useful to obtain the identifiers, positions
1063 or names of the parameters. Identifiers of individual dimensions are
1064 essentially only useful for printing. They are ignored by all other
1065 operations and may not be preserved across those operations.
1067 #include <isl/space.h>
1068 __isl_give isl_space *isl_space_set_dim_id(
1069 __isl_take isl_space *space,
1070 enum isl_dim_type type, unsigned pos,
1071 __isl_take isl_id *id);
1072 int isl_space_has_dim_id(__isl_keep isl_space *space,
1073 enum isl_dim_type type, unsigned pos);
1074 __isl_give isl_id *isl_space_get_dim_id(
1075 __isl_keep isl_space *space,
1076 enum isl_dim_type type, unsigned pos);
1077 __isl_give isl_space *isl_space_set_dim_name(
1078 __isl_take isl_space *space,
1079 enum isl_dim_type type, unsigned pos,
1080 __isl_keep const char *name);
1081 int isl_space_has_dim_name(__isl_keep isl_space *space,
1082 enum isl_dim_type type, unsigned pos);
1083 __isl_keep const char *isl_space_get_dim_name(
1084 __isl_keep isl_space *space,
1085 enum isl_dim_type type, unsigned pos);
1087 #include <isl/local_space.h>
1088 __isl_give isl_local_space *isl_local_space_set_dim_id(
1089 __isl_take isl_local_space *ls,
1090 enum isl_dim_type type, unsigned pos,
1091 __isl_take isl_id *id);
1092 int isl_local_space_has_dim_id(
1093 __isl_keep isl_local_space *ls,
1094 enum isl_dim_type type, unsigned pos);
1095 __isl_give isl_id *isl_local_space_get_dim_id(
1096 __isl_keep isl_local_space *ls,
1097 enum isl_dim_type type, unsigned pos);
1098 __isl_give isl_local_space *isl_local_space_set_dim_name(
1099 __isl_take isl_local_space *ls,
1100 enum isl_dim_type type, unsigned pos, const char *s);
1101 int isl_local_space_has_dim_name(
1102 __isl_keep isl_local_space *ls,
1103 enum isl_dim_type type, unsigned pos)
1104 const char *isl_local_space_get_dim_name(
1105 __isl_keep isl_local_space *ls,
1106 enum isl_dim_type type, unsigned pos);
1108 #include <isl/constraint.h>
1109 const char *isl_constraint_get_dim_name(
1110 __isl_keep isl_constraint *constraint,
1111 enum isl_dim_type type, unsigned pos);
1113 #include <isl/set.h>
1114 __isl_give isl_id *isl_basic_set_get_dim_id(
1115 __isl_keep isl_basic_set *bset,
1116 enum isl_dim_type type, unsigned pos);
1117 __isl_give isl_set *isl_set_set_dim_id(
1118 __isl_take isl_set *set, enum isl_dim_type type,
1119 unsigned pos, __isl_take isl_id *id);
1120 int isl_set_has_dim_id(__isl_keep isl_set *set,
1121 enum isl_dim_type type, unsigned pos);
1122 __isl_give isl_id *isl_set_get_dim_id(
1123 __isl_keep isl_set *set, enum isl_dim_type type,
1125 const char *isl_basic_set_get_dim_name(
1126 __isl_keep isl_basic_set *bset,
1127 enum isl_dim_type type, unsigned pos);
1128 int isl_set_has_dim_name(__isl_keep isl_set *set,
1129 enum isl_dim_type type, unsigned pos);
1130 const char *isl_set_get_dim_name(
1131 __isl_keep isl_set *set,
1132 enum isl_dim_type type, unsigned pos);
1134 #include <isl/map.h>
1135 __isl_give isl_map *isl_map_set_dim_id(
1136 __isl_take isl_map *map, enum isl_dim_type type,
1137 unsigned pos, __isl_take isl_id *id);
1138 int isl_basic_map_has_dim_id(
1139 __isl_keep isl_basic_map *bmap,
1140 enum isl_dim_type type, unsigned pos);
1141 int isl_map_has_dim_id(__isl_keep isl_map *map,
1142 enum isl_dim_type type, unsigned pos);
1143 __isl_give isl_id *isl_map_get_dim_id(
1144 __isl_keep isl_map *map, enum isl_dim_type type,
1146 __isl_give isl_id *isl_union_map_get_dim_id(
1147 __isl_keep isl_union_map *umap,
1148 enum isl_dim_type type, unsigned pos);
1149 const char *isl_basic_map_get_dim_name(
1150 __isl_keep isl_basic_map *bmap,
1151 enum isl_dim_type type, unsigned pos);
1152 int isl_map_has_dim_name(__isl_keep isl_map *map,
1153 enum isl_dim_type type, unsigned pos);
1154 const char *isl_map_get_dim_name(
1155 __isl_keep isl_map *map,
1156 enum isl_dim_type type, unsigned pos);
1158 #include <isl/val.h>
1159 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1160 __isl_take isl_multi_val *mv,
1161 enum isl_dim_type type, unsigned pos,
1162 __isl_take isl_id *id);
1163 __isl_give isl_id *isl_multi_val_get_dim_id(
1164 __isl_keep isl_multi_val *mv,
1165 enum isl_dim_type type, unsigned pos);
1166 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1167 __isl_take isl_multi_val *mv,
1168 enum isl_dim_type type, unsigned pos, const char *s);
1170 #include <isl/aff.h>
1171 __isl_give isl_aff *isl_aff_set_dim_id(
1172 __isl_take isl_aff *aff, enum isl_dim_type type,
1173 unsigned pos, __isl_take isl_id *id);
1174 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1175 __isl_take isl_multi_aff *maff,
1176 enum isl_dim_type type, unsigned pos,
1177 __isl_take isl_id *id);
1178 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1179 __isl_take isl_pw_aff *pma,
1180 enum isl_dim_type type, unsigned pos,
1181 __isl_take isl_id *id);
1182 __isl_give isl_multi_pw_aff *
1183 isl_multi_pw_aff_set_dim_id(
1184 __isl_take isl_multi_pw_aff *mpa,
1185 enum isl_dim_type type, unsigned pos,
1186 __isl_take isl_id *id);
1187 __isl_give isl_multi_union_pw_aff *
1188 isl_multi_union_pw_aff_set_dim_id(
1189 __isl_take isl_multi_union_pw_aff *mupa,
1190 enum isl_dim_type type, unsigned pos,
1191 __isl_take isl_id *id);
1192 __isl_give isl_id *isl_multi_aff_get_dim_id(
1193 __isl_keep isl_multi_aff *ma,
1194 enum isl_dim_type type, unsigned pos);
1195 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1196 enum isl_dim_type type, unsigned pos);
1197 __isl_give isl_id *isl_pw_aff_get_dim_id(
1198 __isl_keep isl_pw_aff *pa,
1199 enum isl_dim_type type, unsigned pos);
1200 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1201 __isl_keep isl_pw_multi_aff *pma,
1202 enum isl_dim_type type, unsigned pos);
1203 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1204 __isl_keep isl_multi_pw_aff *mpa,
1205 enum isl_dim_type type, unsigned pos);
1206 __isl_give isl_id *isl_multi_union_pw_aff_get_dim_id(
1207 __isl_keep isl_multi_union_pw_aff *mupa,
1208 enum isl_dim_type type, unsigned pos);
1209 __isl_give isl_aff *isl_aff_set_dim_name(
1210 __isl_take isl_aff *aff, enum isl_dim_type type,
1211 unsigned pos, const char *s);
1212 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1213 __isl_take isl_multi_aff *maff,
1214 enum isl_dim_type type, unsigned pos, const char *s);
1215 __isl_give isl_multi_pw_aff *
1216 isl_multi_pw_aff_set_dim_name(
1217 __isl_take isl_multi_pw_aff *mpa,
1218 enum isl_dim_type type, unsigned pos, const char *s);
1219 __isl_give isl_union_pw_aff *
1220 isl_union_pw_aff_set_dim_name(
1221 __isl_take isl_union_pw_aff *upa,
1222 enum isl_dim_type type, unsigned pos,
1224 __isl_give isl_union_pw_multi_aff *
1225 isl_union_pw_multi_aff_set_dim_name(
1226 __isl_take isl_union_pw_multi_aff *upma,
1227 enum isl_dim_type type, unsigned pos,
1229 __isl_give isl_multi_union_pw_aff *
1230 isl_multi_union_pw_aff_set_dim_name(
1231 __isl_take isl_multi_union_pw_aff *mupa,
1232 enum isl_dim_type type, unsigned pos,
1233 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1234 enum isl_dim_type type, unsigned pos);
1235 const char *isl_pw_aff_get_dim_name(
1236 __isl_keep isl_pw_aff *pa,
1237 enum isl_dim_type type, unsigned pos);
1238 const char *isl_pw_multi_aff_get_dim_name(
1239 __isl_keep isl_pw_multi_aff *pma,
1240 enum isl_dim_type type, unsigned pos);
1242 #include <isl/polynomial.h>
1243 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1244 __isl_take isl_qpolynomial *qp,
1245 enum isl_dim_type type, unsigned pos,
1247 __isl_give isl_pw_qpolynomial *
1248 isl_pw_qpolynomial_set_dim_name(
1249 __isl_take isl_pw_qpolynomial *pwqp,
1250 enum isl_dim_type type, unsigned pos,
1252 __isl_give isl_pw_qpolynomial_fold *
1253 isl_pw_qpolynomial_fold_set_dim_name(
1254 __isl_take isl_pw_qpolynomial_fold *pwf,
1255 enum isl_dim_type type, unsigned pos,
1257 __isl_give isl_union_pw_qpolynomial *
1258 isl_union_pw_qpolynomial_set_dim_name(
1259 __isl_take isl_union_pw_qpolynomial *upwqp,
1260 enum isl_dim_type type, unsigned pos,
1262 __isl_give isl_union_pw_qpolynomial_fold *
1263 isl_union_pw_qpolynomial_fold_set_dim_name(
1264 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1265 enum isl_dim_type type, unsigned pos,
1268 Note that C<isl_space_get_name> returns a pointer to some internal
1269 data structure, so the result can only be used while the
1270 corresponding C<isl_space> is alive.
1271 Also note that every function that operates on two sets or relations
1272 requires that both arguments have the same parameters. This also
1273 means that if one of the arguments has named parameters, then the
1274 other needs to have named parameters too and the names need to match.
1275 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1276 arguments may have different parameters (as long as they are named),
1277 in which case the result will have as parameters the union of the parameters of
1280 Given the identifier or name of a dimension (typically a parameter),
1281 its position can be obtained from the following functions.
1283 #include <isl/space.h>
1284 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1285 enum isl_dim_type type, __isl_keep isl_id *id);
1286 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1287 enum isl_dim_type type, const char *name);
1289 #include <isl/local_space.h>
1290 int isl_local_space_find_dim_by_name(
1291 __isl_keep isl_local_space *ls,
1292 enum isl_dim_type type, const char *name);
1294 #include <isl/val.h>
1295 int isl_multi_val_find_dim_by_id(
1296 __isl_keep isl_multi_val *mv,
1297 enum isl_dim_type type, __isl_keep isl_id *id);
1298 int isl_multi_val_find_dim_by_name(
1299 __isl_keep isl_multi_val *mv,
1300 enum isl_dim_type type, const char *name);
1302 #include <isl/set.h>
1303 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1304 enum isl_dim_type type, __isl_keep isl_id *id);
1305 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1306 enum isl_dim_type type, const char *name);
1308 #include <isl/map.h>
1309 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1310 enum isl_dim_type type, __isl_keep isl_id *id);
1311 int isl_basic_map_find_dim_by_name(
1312 __isl_keep isl_basic_map *bmap,
1313 enum isl_dim_type type, const char *name);
1314 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1315 enum isl_dim_type type, const char *name);
1316 int isl_union_map_find_dim_by_name(
1317 __isl_keep isl_union_map *umap,
1318 enum isl_dim_type type, const char *name);
1320 #include <isl/aff.h>
1321 int isl_multi_aff_find_dim_by_id(
1322 __isl_keep isl_multi_aff *ma,
1323 enum isl_dim_type type, __isl_keep isl_id *id);
1324 int isl_multi_pw_aff_find_dim_by_id(
1325 __isl_keep isl_multi_pw_aff *mpa,
1326 enum isl_dim_type type, __isl_keep isl_id *id);
1327 int isl_multi_union_pw_aff_find_dim_by_id(
1328 __isl_keep isl_union_multi_pw_aff *mupa,
1329 enum isl_dim_type type, __isl_keep isl_id *id);
1330 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1331 enum isl_dim_type type, const char *name);
1332 int isl_multi_aff_find_dim_by_name(
1333 __isl_keep isl_multi_aff *ma,
1334 enum isl_dim_type type, const char *name);
1335 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1336 enum isl_dim_type type, const char *name);
1337 int isl_multi_pw_aff_find_dim_by_name(
1338 __isl_keep isl_multi_pw_aff *mpa,
1339 enum isl_dim_type type, const char *name);
1340 int isl_pw_multi_aff_find_dim_by_name(
1341 __isl_keep isl_pw_multi_aff *pma,
1342 enum isl_dim_type type, const char *name);
1343 int isl_union_pw_aff_find_dim_by_name(
1344 __isl_keep isl_union_pw_aff *upa,
1345 enum isl_dim_type type, const char *name);
1346 int isl_union_pw_multi_aff_find_dim_by_name(
1347 __isl_keep isl_union_pw_multi_aff *upma,
1348 enum isl_dim_type type, const char *name);
1349 int isl_multi_union_pw_aff_find_dim_by_name(
1350 __isl_keep isl_multi_union_pw_aff *mupa,
1351 enum isl_dim_type type, const char *name);
1353 #include <isl/polynomial.h>
1354 int isl_pw_qpolynomial_find_dim_by_name(
1355 __isl_keep isl_pw_qpolynomial *pwqp,
1356 enum isl_dim_type type, const char *name);
1357 int isl_pw_qpolynomial_fold_find_dim_by_name(
1358 __isl_keep isl_pw_qpolynomial_fold *pwf,
1359 enum isl_dim_type type, const char *name);
1360 int isl_union_pw_qpolynomial_find_dim_by_name(
1361 __isl_keep isl_union_pw_qpolynomial *upwqp,
1362 enum isl_dim_type type, const char *name);
1363 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1364 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1365 enum isl_dim_type type, const char *name);
1367 The identifiers or names of entire spaces may be set or read off
1368 using the following functions.
1370 #include <isl/space.h>
1371 __isl_give isl_space *isl_space_set_tuple_id(
1372 __isl_take isl_space *space,
1373 enum isl_dim_type type, __isl_take isl_id *id);
1374 __isl_give isl_space *isl_space_reset_tuple_id(
1375 __isl_take isl_space *space, enum isl_dim_type type);
1376 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1377 enum isl_dim_type type);
1378 __isl_give isl_id *isl_space_get_tuple_id(
1379 __isl_keep isl_space *space, enum isl_dim_type type);
1380 __isl_give isl_space *isl_space_set_tuple_name(
1381 __isl_take isl_space *space,
1382 enum isl_dim_type type, const char *s);
1383 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1384 enum isl_dim_type type);
1385 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1386 enum isl_dim_type type);
1388 #include <isl/local_space.h>
1389 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1390 __isl_take isl_local_space *ls,
1391 enum isl_dim_type type, __isl_take isl_id *id);
1393 #include <isl/set.h>
1394 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1395 __isl_take isl_basic_set *bset,
1396 __isl_take isl_id *id);
1397 __isl_give isl_set *isl_set_set_tuple_id(
1398 __isl_take isl_set *set, __isl_take isl_id *id);
1399 __isl_give isl_set *isl_set_reset_tuple_id(
1400 __isl_take isl_set *set);
1401 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1402 __isl_give isl_id *isl_set_get_tuple_id(
1403 __isl_keep isl_set *set);
1404 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1405 __isl_take isl_basic_set *set, const char *s);
1406 __isl_give isl_set *isl_set_set_tuple_name(
1407 __isl_take isl_set *set, const char *s);
1408 const char *isl_basic_set_get_tuple_name(
1409 __isl_keep isl_basic_set *bset);
1410 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1411 const char *isl_set_get_tuple_name(
1412 __isl_keep isl_set *set);
1414 #include <isl/map.h>
1415 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1416 __isl_take isl_basic_map *bmap,
1417 enum isl_dim_type type, __isl_take isl_id *id);
1418 __isl_give isl_map *isl_map_set_tuple_id(
1419 __isl_take isl_map *map, enum isl_dim_type type,
1420 __isl_take isl_id *id);
1421 __isl_give isl_map *isl_map_reset_tuple_id(
1422 __isl_take isl_map *map, enum isl_dim_type type);
1423 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1424 enum isl_dim_type type);
1425 __isl_give isl_id *isl_map_get_tuple_id(
1426 __isl_keep isl_map *map, enum isl_dim_type type);
1427 __isl_give isl_map *isl_map_set_tuple_name(
1428 __isl_take isl_map *map,
1429 enum isl_dim_type type, const char *s);
1430 const char *isl_basic_map_get_tuple_name(
1431 __isl_keep isl_basic_map *bmap,
1432 enum isl_dim_type type);
1433 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1434 __isl_take isl_basic_map *bmap,
1435 enum isl_dim_type type, const char *s);
1436 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1437 enum isl_dim_type type);
1438 const char *isl_map_get_tuple_name(
1439 __isl_keep isl_map *map,
1440 enum isl_dim_type type);
1442 #include <isl/val.h>
1443 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1444 __isl_take isl_multi_val *mv,
1445 enum isl_dim_type type, __isl_take isl_id *id);
1446 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1447 __isl_take isl_multi_val *mv,
1448 enum isl_dim_type type);
1449 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1450 enum isl_dim_type type);
1451 __isl_give isl_id *isl_multi_val_get_tuple_id(
1452 __isl_keep isl_multi_val *mv,
1453 enum isl_dim_type type);
1454 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1455 __isl_take isl_multi_val *mv,
1456 enum isl_dim_type type, const char *s);
1457 const char *isl_multi_val_get_tuple_name(
1458 __isl_keep isl_multi_val *mv,
1459 enum isl_dim_type type);
1461 #include <isl/aff.h>
1462 __isl_give isl_aff *isl_aff_set_tuple_id(
1463 __isl_take isl_aff *aff,
1464 enum isl_dim_type type, __isl_take isl_id *id);
1465 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1466 __isl_take isl_multi_aff *maff,
1467 enum isl_dim_type type, __isl_take isl_id *id);
1468 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1469 __isl_take isl_pw_aff *pwaff,
1470 enum isl_dim_type type, __isl_take isl_id *id);
1471 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1472 __isl_take isl_pw_multi_aff *pma,
1473 enum isl_dim_type type, __isl_take isl_id *id);
1474 __isl_give isl_multi_union_pw_aff *
1475 isl_multi_union_pw_aff_set_tuple_id(
1476 __isl_take isl_multi_union_pw_aff *mupa,
1477 enum isl_dim_type type, __isl_take isl_id *id);
1478 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1479 __isl_take isl_multi_aff *ma,
1480 enum isl_dim_type type);
1481 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1482 __isl_take isl_pw_aff *pa,
1483 enum isl_dim_type type);
1484 __isl_give isl_multi_pw_aff *
1485 isl_multi_pw_aff_reset_tuple_id(
1486 __isl_take isl_multi_pw_aff *mpa,
1487 enum isl_dim_type type);
1488 __isl_give isl_pw_multi_aff *
1489 isl_pw_multi_aff_reset_tuple_id(
1490 __isl_take isl_pw_multi_aff *pma,
1491 enum isl_dim_type type);
1492 __isl_give isl_multi_union_pw_aff *
1493 isl_multi_union_pw_aff_reset_tuple_id(
1494 __isl_take isl_multi_union_pw_aff *mupa,
1495 enum isl_dim_type type);
1496 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1497 enum isl_dim_type type);
1498 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1499 __isl_keep isl_multi_aff *ma,
1500 enum isl_dim_type type);
1501 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1502 enum isl_dim_type type);
1503 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1504 __isl_keep isl_pw_aff *pa,
1505 enum isl_dim_type type);
1506 int isl_pw_multi_aff_has_tuple_id(
1507 __isl_keep isl_pw_multi_aff *pma,
1508 enum isl_dim_type type);
1509 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1510 __isl_keep isl_pw_multi_aff *pma,
1511 enum isl_dim_type type);
1512 int isl_multi_pw_aff_has_tuple_id(
1513 __isl_keep isl_multi_pw_aff *mpa,
1514 enum isl_dim_type type);
1515 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1516 __isl_keep isl_multi_pw_aff *mpa,
1517 enum isl_dim_type type);
1518 int isl_multi_union_pw_aff_has_tuple_id(
1519 __isl_keep isl_multi_union_pw_aff *mupa,
1520 enum isl_dim_type type);
1521 __isl_give isl_id *isl_multi_union_pw_aff_get_tuple_id(
1522 __isl_keep isl_multi_union_pw_aff *mupa,
1523 enum isl_dim_type type);
1524 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1525 __isl_take isl_multi_aff *maff,
1526 enum isl_dim_type type, const char *s);
1527 __isl_give isl_multi_pw_aff *
1528 isl_multi_pw_aff_set_tuple_name(
1529 __isl_take isl_multi_pw_aff *mpa,
1530 enum isl_dim_type type, const char *s);
1531 __isl_give isl_multi_union_pw_aff *
1532 isl_multi_union_pw_aff_set_tuple_name(
1533 __isl_take isl_multi_union_pw_aff *mupa,
1534 enum isl_dim_type type, const char *s);
1535 const char *isl_multi_aff_get_tuple_name(
1536 __isl_keep isl_multi_aff *multi,
1537 enum isl_dim_type type);
1538 int isl_pw_multi_aff_has_tuple_name(
1539 __isl_keep isl_pw_multi_aff *pma,
1540 enum isl_dim_type type);
1541 const char *isl_pw_multi_aff_get_tuple_name(
1542 __isl_keep isl_pw_multi_aff *pma,
1543 enum isl_dim_type type);
1544 const char *isl_multi_union_pw_aff_get_tuple_name(
1545 __isl_keep isl_multi_union_pw_aff *mupa,
1546 enum isl_dim_type type);
1548 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1549 or C<isl_dim_set>. As with C<isl_space_get_name>,
1550 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1552 Binary operations require the corresponding spaces of their arguments
1553 to have the same name.
1555 To keep the names of all parameters and tuples, but reset the user pointers
1556 of all the corresponding identifiers, use the following function.
1558 #include <isl/space.h>
1559 __isl_give isl_space *isl_space_reset_user(
1560 __isl_take isl_space *space);
1562 #include <isl/set.h>
1563 __isl_give isl_set *isl_set_reset_user(
1564 __isl_take isl_set *set);
1566 #include <isl/map.h>
1567 __isl_give isl_map *isl_map_reset_user(
1568 __isl_take isl_map *map);
1570 #include <isl/union_set.h>
1571 __isl_give isl_union_set *isl_union_set_reset_user(
1572 __isl_take isl_union_set *uset);
1574 #include <isl/union_map.h>
1575 __isl_give isl_union_map *isl_union_map_reset_user(
1576 __isl_take isl_union_map *umap);
1578 #include <isl/val.h>
1579 __isl_give isl_multi_val *isl_multi_val_reset_user(
1580 __isl_take isl_multi_val *mv);
1582 #include <isl/aff.h>
1583 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1584 __isl_take isl_multi_aff *ma);
1585 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1586 __isl_take isl_pw_aff *pa);
1587 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1588 __isl_take isl_multi_pw_aff *mpa);
1589 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1590 __isl_take isl_pw_multi_aff *pma);
1591 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1592 __isl_take isl_union_pw_aff *upa);
1593 __isl_give isl_multi_union_pw_aff *
1594 isl_multi_union_pw_aff_reset_user(
1595 __isl_take isl_multi_union_pw_aff *mupa);
1596 __isl_give isl_union_pw_multi_aff *
1597 isl_union_pw_multi_aff_reset_user(
1598 __isl_take isl_union_pw_multi_aff *upma);
1600 #include <isl/polynomial.h>
1601 __isl_give isl_pw_qpolynomial *
1602 isl_pw_qpolynomial_reset_user(
1603 __isl_take isl_pw_qpolynomial *pwqp);
1604 __isl_give isl_union_pw_qpolynomial *
1605 isl_union_pw_qpolynomial_reset_user(
1606 __isl_take isl_union_pw_qpolynomial *upwqp);
1607 __isl_give isl_pw_qpolynomial_fold *
1608 isl_pw_qpolynomial_fold_reset_user(
1609 __isl_take isl_pw_qpolynomial_fold *pwf);
1610 __isl_give isl_union_pw_qpolynomial_fold *
1611 isl_union_pw_qpolynomial_fold_reset_user(
1612 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1614 Spaces can be nested. In particular, the domain of a set or
1615 the domain or range of a relation can be a nested relation.
1616 This process is also called I<wrapping>.
1617 The functions for detecting, constructing and deconstructing
1618 such nested spaces can be found in the wrapping properties
1619 of L</"Unary Properties">, the wrapping operations
1620 of L</"Unary Operations"> and the Cartesian product operations
1621 of L</"Basic Operations">.
1623 Spaces can be created from other spaces
1624 using the functions described in L</"Unary Operations">
1625 and L</"Binary Operations">.
1629 A local space is essentially a space with
1630 zero or more existentially quantified variables.
1631 The local space of various objects can be obtained
1632 using the following functions.
1634 #include <isl/constraint.h>
1635 __isl_give isl_local_space *isl_constraint_get_local_space(
1636 __isl_keep isl_constraint *constraint);
1638 #include <isl/set.h>
1639 __isl_give isl_local_space *isl_basic_set_get_local_space(
1640 __isl_keep isl_basic_set *bset);
1642 #include <isl/map.h>
1643 __isl_give isl_local_space *isl_basic_map_get_local_space(
1644 __isl_keep isl_basic_map *bmap);
1646 #include <isl/aff.h>
1647 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1648 __isl_keep isl_aff *aff);
1649 __isl_give isl_local_space *isl_aff_get_local_space(
1650 __isl_keep isl_aff *aff);
1652 A new local space can be created from a space using
1654 #include <isl/local_space.h>
1655 __isl_give isl_local_space *isl_local_space_from_space(
1656 __isl_take isl_space *space);
1658 They can be inspected, modified, copied and freed using the following functions.
1660 #include <isl/local_space.h>
1661 int isl_local_space_is_params(
1662 __isl_keep isl_local_space *ls);
1663 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1664 __isl_give isl_space *isl_local_space_get_space(
1665 __isl_keep isl_local_space *ls);
1666 __isl_give isl_aff *isl_local_space_get_div(
1667 __isl_keep isl_local_space *ls, int pos);
1668 __isl_give isl_local_space *isl_local_space_copy(
1669 __isl_keep isl_local_space *ls);
1670 __isl_null isl_local_space *isl_local_space_free(
1671 __isl_take isl_local_space *ls);
1673 Note that C<isl_local_space_get_div> can only be used on local spaces
1676 Two local spaces can be compared using
1678 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1679 __isl_keep isl_local_space *ls2);
1681 Local spaces can be created from other local spaces
1682 using the functions described in L</"Unary Operations">
1683 and L</"Binary Operations">.
1685 =head2 Creating New Sets and Relations
1687 C<isl> has functions for creating some standard sets and relations.
1691 =item * Empty sets and relations
1693 __isl_give isl_basic_set *isl_basic_set_empty(
1694 __isl_take isl_space *space);
1695 __isl_give isl_basic_map *isl_basic_map_empty(
1696 __isl_take isl_space *space);
1697 __isl_give isl_set *isl_set_empty(
1698 __isl_take isl_space *space);
1699 __isl_give isl_map *isl_map_empty(
1700 __isl_take isl_space *space);
1701 __isl_give isl_union_set *isl_union_set_empty(
1702 __isl_take isl_space *space);
1703 __isl_give isl_union_map *isl_union_map_empty(
1704 __isl_take isl_space *space);
1706 For C<isl_union_set>s and C<isl_union_map>s, the space
1707 is only used to specify the parameters.
1709 =item * Universe sets and relations
1711 __isl_give isl_basic_set *isl_basic_set_universe(
1712 __isl_take isl_space *space);
1713 __isl_give isl_basic_map *isl_basic_map_universe(
1714 __isl_take isl_space *space);
1715 __isl_give isl_set *isl_set_universe(
1716 __isl_take isl_space *space);
1717 __isl_give isl_map *isl_map_universe(
1718 __isl_take isl_space *space);
1719 __isl_give isl_union_set *isl_union_set_universe(
1720 __isl_take isl_union_set *uset);
1721 __isl_give isl_union_map *isl_union_map_universe(
1722 __isl_take isl_union_map *umap);
1724 The sets and relations constructed by the functions above
1725 contain all integer values, while those constructed by the
1726 functions below only contain non-negative values.
1728 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1729 __isl_take isl_space *space);
1730 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1731 __isl_take isl_space *space);
1732 __isl_give isl_set *isl_set_nat_universe(
1733 __isl_take isl_space *space);
1734 __isl_give isl_map *isl_map_nat_universe(
1735 __isl_take isl_space *space);
1737 =item * Identity relations
1739 __isl_give isl_basic_map *isl_basic_map_identity(
1740 __isl_take isl_space *space);
1741 __isl_give isl_map *isl_map_identity(
1742 __isl_take isl_space *space);
1744 The number of input and output dimensions in C<space> needs
1747 =item * Lexicographic order
1749 __isl_give isl_map *isl_map_lex_lt(
1750 __isl_take isl_space *set_space);
1751 __isl_give isl_map *isl_map_lex_le(
1752 __isl_take isl_space *set_space);
1753 __isl_give isl_map *isl_map_lex_gt(
1754 __isl_take isl_space *set_space);
1755 __isl_give isl_map *isl_map_lex_ge(
1756 __isl_take isl_space *set_space);
1757 __isl_give isl_map *isl_map_lex_lt_first(
1758 __isl_take isl_space *space, unsigned n);
1759 __isl_give isl_map *isl_map_lex_le_first(
1760 __isl_take isl_space *space, unsigned n);
1761 __isl_give isl_map *isl_map_lex_gt_first(
1762 __isl_take isl_space *space, unsigned n);
1763 __isl_give isl_map *isl_map_lex_ge_first(
1764 __isl_take isl_space *space, unsigned n);
1766 The first four functions take a space for a B<set>
1767 and return relations that express that the elements in the domain
1768 are lexicographically less
1769 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1770 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1771 than the elements in the range.
1772 The last four functions take a space for a map
1773 and return relations that express that the first C<n> dimensions
1774 in the domain are lexicographically less
1775 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1776 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1777 than the first C<n> dimensions in the range.
1781 A basic set or relation can be converted to a set or relation
1782 using the following functions.
1784 __isl_give isl_set *isl_set_from_basic_set(
1785 __isl_take isl_basic_set *bset);
1786 __isl_give isl_map *isl_map_from_basic_map(
1787 __isl_take isl_basic_map *bmap);
1789 Sets and relations can be converted to union sets and relations
1790 using the following functions.
1792 __isl_give isl_union_set *isl_union_set_from_basic_set(
1793 __isl_take isl_basic_set *bset);
1794 __isl_give isl_union_map *isl_union_map_from_basic_map(
1795 __isl_take isl_basic_map *bmap);
1796 __isl_give isl_union_set *isl_union_set_from_set(
1797 __isl_take isl_set *set);
1798 __isl_give isl_union_map *isl_union_map_from_map(
1799 __isl_take isl_map *map);
1801 The inverse conversions below can only be used if the input
1802 union set or relation is known to contain elements in exactly one
1805 __isl_give isl_set *isl_set_from_union_set(
1806 __isl_take isl_union_set *uset);
1807 __isl_give isl_map *isl_map_from_union_map(
1808 __isl_take isl_union_map *umap);
1810 Sets and relations can be copied and freed again using the following
1813 __isl_give isl_basic_set *isl_basic_set_copy(
1814 __isl_keep isl_basic_set *bset);
1815 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1816 __isl_give isl_union_set *isl_union_set_copy(
1817 __isl_keep isl_union_set *uset);
1818 __isl_give isl_basic_map *isl_basic_map_copy(
1819 __isl_keep isl_basic_map *bmap);
1820 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1821 __isl_give isl_union_map *isl_union_map_copy(
1822 __isl_keep isl_union_map *umap);
1823 __isl_null isl_basic_set *isl_basic_set_free(
1824 __isl_take isl_basic_set *bset);
1825 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1826 __isl_null isl_union_set *isl_union_set_free(
1827 __isl_take isl_union_set *uset);
1828 __isl_null isl_basic_map *isl_basic_map_free(
1829 __isl_take isl_basic_map *bmap);
1830 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1831 __isl_null isl_union_map *isl_union_map_free(
1832 __isl_take isl_union_map *umap);
1834 Other sets and relations can be constructed by starting
1835 from a universe set or relation, adding equality and/or
1836 inequality constraints and then projecting out the
1837 existentially quantified variables, if any.
1838 Constraints can be constructed, manipulated and
1839 added to (or removed from) (basic) sets and relations
1840 using the following functions.
1842 #include <isl/constraint.h>
1843 __isl_give isl_constraint *isl_equality_alloc(
1844 __isl_take isl_local_space *ls);
1845 __isl_give isl_constraint *isl_inequality_alloc(
1846 __isl_take isl_local_space *ls);
1847 __isl_give isl_constraint *isl_constraint_set_constant_si(
1848 __isl_take isl_constraint *constraint, int v);
1849 __isl_give isl_constraint *isl_constraint_set_constant_val(
1850 __isl_take isl_constraint *constraint,
1851 __isl_take isl_val *v);
1852 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1853 __isl_take isl_constraint *constraint,
1854 enum isl_dim_type type, int pos, int v);
1855 __isl_give isl_constraint *
1856 isl_constraint_set_coefficient_val(
1857 __isl_take isl_constraint *constraint,
1858 enum isl_dim_type type, int pos,
1859 __isl_take isl_val *v);
1860 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1861 __isl_take isl_basic_map *bmap,
1862 __isl_take isl_constraint *constraint);
1863 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1864 __isl_take isl_basic_set *bset,
1865 __isl_take isl_constraint *constraint);
1866 __isl_give isl_map *isl_map_add_constraint(
1867 __isl_take isl_map *map,
1868 __isl_take isl_constraint *constraint);
1869 __isl_give isl_set *isl_set_add_constraint(
1870 __isl_take isl_set *set,
1871 __isl_take isl_constraint *constraint);
1872 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1873 __isl_take isl_basic_set *bset,
1874 __isl_take isl_constraint *constraint);
1876 For example, to create a set containing the even integers
1877 between 10 and 42, you would use the following code.
1880 isl_local_space *ls;
1882 isl_basic_set *bset;
1884 space = isl_space_set_alloc(ctx, 0, 2);
1885 bset = isl_basic_set_universe(isl_space_copy(space));
1886 ls = isl_local_space_from_space(space);
1888 c = isl_equality_alloc(isl_local_space_copy(ls));
1889 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1890 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1891 bset = isl_basic_set_add_constraint(bset, c);
1893 c = isl_inequality_alloc(isl_local_space_copy(ls));
1894 c = isl_constraint_set_constant_si(c, -10);
1895 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1896 bset = isl_basic_set_add_constraint(bset, c);
1898 c = isl_inequality_alloc(ls);
1899 c = isl_constraint_set_constant_si(c, 42);
1900 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1901 bset = isl_basic_set_add_constraint(bset, c);
1903 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1907 isl_basic_set *bset;
1908 bset = isl_basic_set_read_from_str(ctx,
1909 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1911 A basic set or relation can also be constructed from two matrices
1912 describing the equalities and the inequalities.
1914 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1915 __isl_take isl_space *space,
1916 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1917 enum isl_dim_type c1,
1918 enum isl_dim_type c2, enum isl_dim_type c3,
1919 enum isl_dim_type c4);
1920 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1921 __isl_take isl_space *space,
1922 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1923 enum isl_dim_type c1,
1924 enum isl_dim_type c2, enum isl_dim_type c3,
1925 enum isl_dim_type c4, enum isl_dim_type c5);
1927 The C<isl_dim_type> arguments indicate the order in which
1928 different kinds of variables appear in the input matrices
1929 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1930 C<isl_dim_set> and C<isl_dim_div> for sets and
1931 of C<isl_dim_cst>, C<isl_dim_param>,
1932 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1934 A (basic or union) set or relation can also be constructed from a
1935 (union) (piecewise) (multiple) affine expression
1936 or a list of affine expressions
1937 (See L</"Functions">).
1939 __isl_give isl_basic_map *isl_basic_map_from_aff(
1940 __isl_take isl_aff *aff);
1941 __isl_give isl_map *isl_map_from_aff(
1942 __isl_take isl_aff *aff);
1943 __isl_give isl_set *isl_set_from_pw_aff(
1944 __isl_take isl_pw_aff *pwaff);
1945 __isl_give isl_map *isl_map_from_pw_aff(
1946 __isl_take isl_pw_aff *pwaff);
1947 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1948 __isl_take isl_space *domain_space,
1949 __isl_take isl_aff_list *list);
1950 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1951 __isl_take isl_multi_aff *maff)
1952 __isl_give isl_map *isl_map_from_multi_aff(
1953 __isl_take isl_multi_aff *maff)
1954 __isl_give isl_set *isl_set_from_pw_multi_aff(
1955 __isl_take isl_pw_multi_aff *pma);
1956 __isl_give isl_map *isl_map_from_pw_multi_aff(
1957 __isl_take isl_pw_multi_aff *pma);
1958 __isl_give isl_set *isl_set_from_multi_pw_aff(
1959 __isl_take isl_multi_pw_aff *mpa);
1960 __isl_give isl_map *isl_map_from_multi_pw_aff(
1961 __isl_take isl_multi_pw_aff *mpa);
1962 __isl_give isl_union_map *isl_union_map_from_union_pw_aff(
1963 __isl_take isl_union_pw_aff *upa);
1964 __isl_give isl_union_map *
1965 isl_union_map_from_union_pw_multi_aff(
1966 __isl_take isl_union_pw_multi_aff *upma);
1967 __isl_give isl_union_map *
1968 isl_union_map_from_multi_union_pw_aff(
1969 __isl_take isl_multi_union_pw_aff *mupa);
1971 The C<domain_space> argument describes the domain of the resulting
1972 basic relation. It is required because the C<list> may consist
1973 of zero affine expressions.
1974 The C<mupa> passed to C<isl_union_map_from_multi_union_pw_aff>
1975 is not allowed to be zero-dimensional. The domain of the result
1976 is the shared domain of the union piecewise affine elements.
1978 =head2 Inspecting Sets and Relations
1980 Usually, the user should not have to care about the actual constraints
1981 of the sets and maps, but should instead apply the abstract operations
1982 explained in the following sections.
1983 Occasionally, however, it may be required to inspect the individual
1984 coefficients of the constraints. This section explains how to do so.
1985 In these cases, it may also be useful to have C<isl> compute
1986 an explicit representation of the existentially quantified variables.
1988 __isl_give isl_set *isl_set_compute_divs(
1989 __isl_take isl_set *set);
1990 __isl_give isl_map *isl_map_compute_divs(
1991 __isl_take isl_map *map);
1992 __isl_give isl_union_set *isl_union_set_compute_divs(
1993 __isl_take isl_union_set *uset);
1994 __isl_give isl_union_map *isl_union_map_compute_divs(
1995 __isl_take isl_union_map *umap);
1997 This explicit representation defines the existentially quantified
1998 variables as integer divisions of the other variables, possibly
1999 including earlier existentially quantified variables.
2000 An explicitly represented existentially quantified variable therefore
2001 has a unique value when the values of the other variables are known.
2002 If, furthermore, the same existentials, i.e., existentials
2003 with the same explicit representations, should appear in the
2004 same order in each of the disjuncts of a set or map, then the user should call
2005 either of the following functions.
2007 __isl_give isl_set *isl_set_align_divs(
2008 __isl_take isl_set *set);
2009 __isl_give isl_map *isl_map_align_divs(
2010 __isl_take isl_map *map);
2012 Alternatively, the existentially quantified variables can be removed
2013 using the following functions, which compute an overapproximation.
2015 __isl_give isl_basic_set *isl_basic_set_remove_divs(
2016 __isl_take isl_basic_set *bset);
2017 __isl_give isl_basic_map *isl_basic_map_remove_divs(
2018 __isl_take isl_basic_map *bmap);
2019 __isl_give isl_set *isl_set_remove_divs(
2020 __isl_take isl_set *set);
2021 __isl_give isl_map *isl_map_remove_divs(
2022 __isl_take isl_map *map);
2024 It is also possible to only remove those divs that are defined
2025 in terms of a given range of dimensions or only those for which
2026 no explicit representation is known.
2028 __isl_give isl_basic_set *
2029 isl_basic_set_remove_divs_involving_dims(
2030 __isl_take isl_basic_set *bset,
2031 enum isl_dim_type type,
2032 unsigned first, unsigned n);
2033 __isl_give isl_basic_map *
2034 isl_basic_map_remove_divs_involving_dims(
2035 __isl_take isl_basic_map *bmap,
2036 enum isl_dim_type type,
2037 unsigned first, unsigned n);
2038 __isl_give isl_set *isl_set_remove_divs_involving_dims(
2039 __isl_take isl_set *set, enum isl_dim_type type,
2040 unsigned first, unsigned n);
2041 __isl_give isl_map *isl_map_remove_divs_involving_dims(
2042 __isl_take isl_map *map, enum isl_dim_type type,
2043 unsigned first, unsigned n);
2045 __isl_give isl_basic_set *
2046 isl_basic_set_remove_unknown_divs(
2047 __isl_take isl_basic_set *bset);
2048 __isl_give isl_set *isl_set_remove_unknown_divs(
2049 __isl_take isl_set *set);
2050 __isl_give isl_map *isl_map_remove_unknown_divs(
2051 __isl_take isl_map *map);
2053 To iterate over all the sets or maps in a union set or map, use
2055 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
2056 int (*fn)(__isl_take isl_set *set, void *user),
2058 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
2059 int (*fn)(__isl_take isl_map *map, void *user),
2062 The number of sets or maps in a union set or map can be obtained
2065 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2066 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2068 To extract the set or map in a given space from a union, use
2070 __isl_give isl_set *isl_union_set_extract_set(
2071 __isl_keep isl_union_set *uset,
2072 __isl_take isl_space *space);
2073 __isl_give isl_map *isl_union_map_extract_map(
2074 __isl_keep isl_union_map *umap,
2075 __isl_take isl_space *space);
2077 To iterate over all the basic sets or maps in a set or map, use
2079 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
2080 int (*fn)(__isl_take isl_basic_set *bset, void *user),
2082 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
2083 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
2086 The callback function C<fn> should return 0 if successful and
2087 -1 if an error occurs. In the latter case, or if any other error
2088 occurs, the above functions will return -1.
2090 It should be noted that C<isl> does not guarantee that
2091 the basic sets or maps passed to C<fn> are disjoint.
2092 If this is required, then the user should call one of
2093 the following functions first.
2095 __isl_give isl_set *isl_set_make_disjoint(
2096 __isl_take isl_set *set);
2097 __isl_give isl_map *isl_map_make_disjoint(
2098 __isl_take isl_map *map);
2100 The number of basic sets in a set can be obtained
2101 or the number of basic maps in a map can be obtained
2104 #include <isl/set.h>
2105 int isl_set_n_basic_set(__isl_keep isl_set *set);
2107 #include <isl/map.h>
2108 int isl_map_n_basic_map(__isl_keep isl_map *map);
2110 To iterate over the constraints of a basic set or map, use
2112 #include <isl/constraint.h>
2114 int isl_basic_set_n_constraint(
2115 __isl_keep isl_basic_set *bset);
2116 int isl_basic_set_foreach_constraint(
2117 __isl_keep isl_basic_set *bset,
2118 int (*fn)(__isl_take isl_constraint *c, void *user),
2120 int isl_basic_map_n_constraint(
2121 __isl_keep isl_basic_map *bmap);
2122 int isl_basic_map_foreach_constraint(
2123 __isl_keep isl_basic_map *bmap,
2124 int (*fn)(__isl_take isl_constraint *c, void *user),
2126 __isl_null isl_constraint *isl_constraint_free(
2127 __isl_take isl_constraint *c);
2129 Again, the callback function C<fn> should return 0 if successful and
2130 -1 if an error occurs. In the latter case, or if any other error
2131 occurs, the above functions will return -1.
2132 The constraint C<c> represents either an equality or an inequality.
2133 Use the following function to find out whether a constraint
2134 represents an equality. If not, it represents an inequality.
2136 int isl_constraint_is_equality(
2137 __isl_keep isl_constraint *constraint);
2139 It is also possible to obtain a list of constraints from a basic
2142 #include <isl/constraint.h>
2143 __isl_give isl_constraint_list *
2144 isl_basic_map_get_constraint_list(
2145 __isl_keep isl_basic_map *bmap);
2146 __isl_give isl_constraint_list *
2147 isl_basic_set_get_constraint_list(
2148 __isl_keep isl_basic_set *bset);
2150 These functions require that all existentially quantified variables
2151 have an explicit representation.
2152 The returned list can be manipulated using the functions in L<"Lists">.
2154 The coefficients of the constraints can be inspected using
2155 the following functions.
2157 int isl_constraint_is_lower_bound(
2158 __isl_keep isl_constraint *constraint,
2159 enum isl_dim_type type, unsigned pos);
2160 int isl_constraint_is_upper_bound(
2161 __isl_keep isl_constraint *constraint,
2162 enum isl_dim_type type, unsigned pos);
2163 __isl_give isl_val *isl_constraint_get_constant_val(
2164 __isl_keep isl_constraint *constraint);
2165 __isl_give isl_val *isl_constraint_get_coefficient_val(
2166 __isl_keep isl_constraint *constraint,
2167 enum isl_dim_type type, int pos);
2169 The explicit representations of the existentially quantified
2170 variables can be inspected using the following function.
2171 Note that the user is only allowed to use this function
2172 if the inspected set or map is the result of a call
2173 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2174 The existentially quantified variable is equal to the floor
2175 of the returned affine expression. The affine expression
2176 itself can be inspected using the functions in
2179 __isl_give isl_aff *isl_constraint_get_div(
2180 __isl_keep isl_constraint *constraint, int pos);
2182 To obtain the constraints of a basic set or map in matrix
2183 form, use the following functions.
2185 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2186 __isl_keep isl_basic_set *bset,
2187 enum isl_dim_type c1, enum isl_dim_type c2,
2188 enum isl_dim_type c3, enum isl_dim_type c4);
2189 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2190 __isl_keep isl_basic_set *bset,
2191 enum isl_dim_type c1, enum isl_dim_type c2,
2192 enum isl_dim_type c3, enum isl_dim_type c4);
2193 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2194 __isl_keep isl_basic_map *bmap,
2195 enum isl_dim_type c1,
2196 enum isl_dim_type c2, enum isl_dim_type c3,
2197 enum isl_dim_type c4, enum isl_dim_type c5);
2198 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2199 __isl_keep isl_basic_map *bmap,
2200 enum isl_dim_type c1,
2201 enum isl_dim_type c2, enum isl_dim_type c3,
2202 enum isl_dim_type c4, enum isl_dim_type c5);
2204 The C<isl_dim_type> arguments dictate the order in which
2205 different kinds of variables appear in the resulting matrix.
2206 For set inputs, they should be a permutation of
2207 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2208 For map inputs, they should be a permutation of
2209 C<isl_dim_cst>, C<isl_dim_param>,
2210 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2214 Points are elements of a set. They can be used to construct
2215 simple sets (boxes) or they can be used to represent the
2216 individual elements of a set.
2217 The zero point (the origin) can be created using
2219 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2221 The coordinates of a point can be inspected, set and changed
2224 __isl_give isl_val *isl_point_get_coordinate_val(
2225 __isl_keep isl_point *pnt,
2226 enum isl_dim_type type, int pos);
2227 __isl_give isl_point *isl_point_set_coordinate_val(
2228 __isl_take isl_point *pnt,
2229 enum isl_dim_type type, int pos,
2230 __isl_take isl_val *v);
2232 __isl_give isl_point *isl_point_add_ui(
2233 __isl_take isl_point *pnt,
2234 enum isl_dim_type type, int pos, unsigned val);
2235 __isl_give isl_point *isl_point_sub_ui(
2236 __isl_take isl_point *pnt,
2237 enum isl_dim_type type, int pos, unsigned val);
2239 Points can be copied or freed using
2241 __isl_give isl_point *isl_point_copy(
2242 __isl_keep isl_point *pnt);
2243 void isl_point_free(__isl_take isl_point *pnt);
2245 A singleton set can be created from a point using
2247 __isl_give isl_basic_set *isl_basic_set_from_point(
2248 __isl_take isl_point *pnt);
2249 __isl_give isl_set *isl_set_from_point(
2250 __isl_take isl_point *pnt);
2252 and a box can be created from two opposite extremal points using
2254 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2255 __isl_take isl_point *pnt1,
2256 __isl_take isl_point *pnt2);
2257 __isl_give isl_set *isl_set_box_from_points(
2258 __isl_take isl_point *pnt1,
2259 __isl_take isl_point *pnt2);
2261 All elements of a B<bounded> (union) set can be enumerated using
2262 the following functions.
2264 int isl_set_foreach_point(__isl_keep isl_set *set,
2265 int (*fn)(__isl_take isl_point *pnt, void *user),
2267 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2268 int (*fn)(__isl_take isl_point *pnt, void *user),
2271 The function C<fn> is called for each integer point in
2272 C<set> with as second argument the last argument of
2273 the C<isl_set_foreach_point> call. The function C<fn>
2274 should return C<0> on success and C<-1> on failure.
2275 In the latter case, C<isl_set_foreach_point> will stop
2276 enumerating and return C<-1> as well.
2277 If the enumeration is performed successfully and to completion,
2278 then C<isl_set_foreach_point> returns C<0>.
2280 To obtain a single point of a (basic) set, use
2282 __isl_give isl_point *isl_basic_set_sample_point(
2283 __isl_take isl_basic_set *bset);
2284 __isl_give isl_point *isl_set_sample_point(
2285 __isl_take isl_set *set);
2287 If C<set> does not contain any (integer) points, then the
2288 resulting point will be ``void'', a property that can be
2291 int isl_point_is_void(__isl_keep isl_point *pnt);
2295 Besides sets and relation, C<isl> also supports various types of functions.
2296 Each of these types is derived from the value type (see L</"Values">)
2297 or from one of two primitive function types
2298 through the application of zero or more type constructors.
2299 We first describe the primitive type and then we describe
2300 the types derived from these primitive types.
2302 =head3 Primitive Functions
2304 C<isl> support two primitive function types, quasi-affine
2305 expressions and quasipolynomials.
2306 A quasi-affine expression is defined either over a parameter
2307 space or over a set and is composed of integer constants,
2308 parameters and set variables, addition, subtraction and
2309 integer division by an integer constant.
2310 For example, the quasi-affine expression
2312 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2314 maps C<x> to C<2*floor((4 n + x)/9>.
2315 A quasipolynomial is a polynomial expression in quasi-affine
2316 expression. That is, it additionally allows for multiplication.
2317 Note, though, that it is not allowed to construct an integer
2318 division of an expression involving multiplications.
2319 Here is an example of a quasipolynomial that is not
2320 quasi-affine expression
2322 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2324 Note that the external representations of quasi-affine expressions
2325 and quasipolynomials are different. Quasi-affine expressions
2326 use a notation with square brackets just like binary relations,
2327 while quasipolynomials do not. This might change at some point.
2329 If a primitive function is defined over a parameter space,
2330 then the space of the function itself is that of a set.
2331 If it is defined over a set, then the space of the function
2332 is that of a relation. In both cases, the set space (or
2333 the output space) is single-dimensional, anonymous and unstructured.
2334 To create functions with multiple dimensions or with other kinds
2335 of set or output spaces, use multiple expressions
2336 (see L</"Multiple Expressions">).
2340 =item * Quasi-affine Expressions
2342 Besides the expressions described above, a quasi-affine
2343 expression can also be set to NaN. Such expressions
2344 typically represent a failure to represent a result
2345 as a quasi-affine expression.
2347 The zero quasi affine expression or the quasi affine expression
2348 that is equal to a given value or
2349 a specified dimension on a given domain can be created using
2351 #include <isl/aff.h>
2352 __isl_give isl_aff *isl_aff_zero_on_domain(
2353 __isl_take isl_local_space *ls);
2354 __isl_give isl_aff *isl_aff_val_on_domain(
2355 __isl_take isl_local_space *ls,
2356 __isl_take isl_val *val);
2357 __isl_give isl_aff *isl_aff_var_on_domain(
2358 __isl_take isl_local_space *ls,
2359 enum isl_dim_type type, unsigned pos);
2360 __isl_give isl_aff *isl_aff_nan_on_domain(
2361 __isl_take isl_local_space *ls);
2363 Quasi affine expressions can be copied and freed using
2365 #include <isl/aff.h>
2366 __isl_give isl_aff *isl_aff_copy(
2367 __isl_keep isl_aff *aff);
2368 __isl_null isl_aff *isl_aff_free(
2369 __isl_take isl_aff *aff);
2371 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2372 using the following function. The constraint is required to have
2373 a non-zero coefficient for the specified dimension.
2375 #include <isl/constraint.h>
2376 __isl_give isl_aff *isl_constraint_get_bound(
2377 __isl_keep isl_constraint *constraint,
2378 enum isl_dim_type type, int pos);
2380 The entire affine expression of the constraint can also be extracted
2381 using the following function.
2383 #include <isl/constraint.h>
2384 __isl_give isl_aff *isl_constraint_get_aff(
2385 __isl_keep isl_constraint *constraint);
2387 Conversely, an equality constraint equating
2388 the affine expression to zero or an inequality constraint enforcing
2389 the affine expression to be non-negative, can be constructed using
2391 __isl_give isl_constraint *isl_equality_from_aff(
2392 __isl_take isl_aff *aff);
2393 __isl_give isl_constraint *isl_inequality_from_aff(
2394 __isl_take isl_aff *aff);
2396 The coefficients and the integer divisions of an affine expression
2397 can be inspected using the following functions.
2399 #include <isl/aff.h>
2400 __isl_give isl_val *isl_aff_get_constant_val(
2401 __isl_keep isl_aff *aff);
2402 __isl_give isl_val *isl_aff_get_coefficient_val(
2403 __isl_keep isl_aff *aff,
2404 enum isl_dim_type type, int pos);
2405 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2406 enum isl_dim_type type, int pos);
2407 __isl_give isl_val *isl_aff_get_denominator_val(
2408 __isl_keep isl_aff *aff);
2409 __isl_give isl_aff *isl_aff_get_div(
2410 __isl_keep isl_aff *aff, int pos);
2412 They can be modified using the following functions.
2414 #include <isl/aff.h>
2415 __isl_give isl_aff *isl_aff_set_constant_si(
2416 __isl_take isl_aff *aff, int v);
2417 __isl_give isl_aff *isl_aff_set_constant_val(
2418 __isl_take isl_aff *aff, __isl_take isl_val *v);
2419 __isl_give isl_aff *isl_aff_set_coefficient_si(
2420 __isl_take isl_aff *aff,
2421 enum isl_dim_type type, int pos, int v);
2422 __isl_give isl_aff *isl_aff_set_coefficient_val(
2423 __isl_take isl_aff *aff,
2424 enum isl_dim_type type, int pos,
2425 __isl_take isl_val *v);
2427 __isl_give isl_aff *isl_aff_add_constant_si(
2428 __isl_take isl_aff *aff, int v);
2429 __isl_give isl_aff *isl_aff_add_constant_val(
2430 __isl_take isl_aff *aff, __isl_take isl_val *v);
2431 __isl_give isl_aff *isl_aff_add_constant_num_si(
2432 __isl_take isl_aff *aff, int v);
2433 __isl_give isl_aff *isl_aff_add_coefficient_si(
2434 __isl_take isl_aff *aff,
2435 enum isl_dim_type type, int pos, int v);
2436 __isl_give isl_aff *isl_aff_add_coefficient_val(
2437 __isl_take isl_aff *aff,
2438 enum isl_dim_type type, int pos,
2439 __isl_take isl_val *v);
2441 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2442 set the I<numerator> of the constant or coefficient, while
2443 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2444 the constant or coefficient as a whole.
2445 The C<add_constant> and C<add_coefficient> functions add an integer
2446 or rational value to
2447 the possibly rational constant or coefficient.
2448 The C<add_constant_num> functions add an integer value to
2451 =item * Quasipolynomials
2453 Some simple quasipolynomials can be created using the following functions.
2455 #include <isl/polynomial.h>
2456 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2457 __isl_take isl_space *domain);
2458 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2459 __isl_take isl_space *domain);
2460 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2461 __isl_take isl_space *domain);
2462 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2463 __isl_take isl_space *domain);
2464 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2465 __isl_take isl_space *domain);
2466 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2467 __isl_take isl_space *domain,
2468 __isl_take isl_val *val);
2469 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2470 __isl_take isl_space *domain,
2471 enum isl_dim_type type, unsigned pos);
2472 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2473 __isl_take isl_aff *aff);
2475 Recall that the space in which a quasipolynomial lives is a map space
2476 with a one-dimensional range. The C<domain> argument in some of
2477 the functions above corresponds to the domain of this map space.
2479 Quasipolynomials can be copied and freed again using the following
2482 #include <isl/polynomial.h>
2483 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2484 __isl_keep isl_qpolynomial *qp);
2485 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2486 __isl_take isl_qpolynomial *qp);
2488 The constant term of a quasipolynomial can be extracted using
2490 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2491 __isl_keep isl_qpolynomial *qp);
2493 To iterate over all terms in a quasipolynomial,
2496 int isl_qpolynomial_foreach_term(
2497 __isl_keep isl_qpolynomial *qp,
2498 int (*fn)(__isl_take isl_term *term,
2499 void *user), void *user);
2501 The terms themselves can be inspected and freed using
2504 unsigned isl_term_dim(__isl_keep isl_term *term,
2505 enum isl_dim_type type);
2506 __isl_give isl_val *isl_term_get_coefficient_val(
2507 __isl_keep isl_term *term);
2508 int isl_term_get_exp(__isl_keep isl_term *term,
2509 enum isl_dim_type type, unsigned pos);
2510 __isl_give isl_aff *isl_term_get_div(
2511 __isl_keep isl_term *term, unsigned pos);
2512 void isl_term_free(__isl_take isl_term *term);
2514 Each term is a product of parameters, set variables and
2515 integer divisions. The function C<isl_term_get_exp>
2516 returns the exponent of a given dimensions in the given term.
2522 A reduction represents a maximum or a minimum of its
2524 The only reduction type defined by C<isl> is
2525 C<isl_qpolynomial_fold>.
2527 There are currently no functions to directly create such
2528 objects, but they do appear in the piecewise quasipolynomial
2529 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2531 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2533 Reductions can be copied and freed using
2534 the following functions.
2536 #include <isl/polynomial.h>
2537 __isl_give isl_qpolynomial_fold *
2538 isl_qpolynomial_fold_copy(
2539 __isl_keep isl_qpolynomial_fold *fold);
2540 void isl_qpolynomial_fold_free(
2541 __isl_take isl_qpolynomial_fold *fold);
2543 To iterate over all quasipolynomials in a reduction, use
2545 int isl_qpolynomial_fold_foreach_qpolynomial(
2546 __isl_keep isl_qpolynomial_fold *fold,
2547 int (*fn)(__isl_take isl_qpolynomial *qp,
2548 void *user), void *user);
2550 =head3 Multiple Expressions
2552 A multiple expression represents a sequence of zero or
2553 more base expressions, all defined on the same domain space.
2554 The domain space of the multiple expression is the same
2555 as that of the base expressions, but the range space
2556 can be any space. In case the base expressions have
2557 a set space, the corresponding multiple expression
2558 also has a set space.
2559 Objects of the value type do not have an associated space.
2560 The space of a multiple value is therefore always a set space.
2561 Similarly, the space of a multiple union piecewise
2562 affine expression is always a set space.
2564 The multiple expression types defined by C<isl>
2565 are C<isl_multi_val>, C<isl_multi_aff>, C<isl_multi_pw_aff>,
2566 C<isl_multi_union_pw_aff>.
2568 A multiple expression with the value zero for
2569 each output (or set) dimension can be created
2570 using the following functions.
2572 #include <isl/val.h>
2573 __isl_give isl_multi_val *isl_multi_val_zero(
2574 __isl_take isl_space *space);
2576 #include <isl/aff.h>
2577 __isl_give isl_multi_aff *isl_multi_aff_zero(
2578 __isl_take isl_space *space);
2579 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2580 __isl_take isl_space *space);
2581 __isl_give isl_multi_union_pw_aff *
2582 isl_multi_union_pw_aff_zero(
2583 __isl_take isl_space *space);
2585 Since there is no canonical way of representing a zero
2586 value of type C<isl_union_pw_aff>, the space passed
2587 to C<isl_multi_union_pw_aff_zero> needs to be zero-dimensional.
2589 An identity function can be created using the following
2590 functions. The space needs to be that of a relation
2591 with the same number of input and output dimensions.
2593 #include <isl/aff.h>
2594 __isl_give isl_multi_aff *isl_multi_aff_identity(
2595 __isl_take isl_space *space);
2596 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2597 __isl_take isl_space *space);
2599 A function that performs a projection on a universe
2600 relation or set can be created using the following functions.
2601 See also the corresponding
2602 projection operations in L</"Unary Operations">.
2604 #include <isl/aff.h>
2605 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2606 __isl_take isl_space *space);
2607 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2608 __isl_take isl_space *space);
2609 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2610 __isl_take isl_space *space,
2611 enum isl_dim_type type,
2612 unsigned first, unsigned n);
2614 A multiple expression can be created from a single
2615 base expression using the following functions.
2616 The space of the created multiple expression is the same
2617 as that of the base expression, except for
2618 C<isl_multi_union_pw_aff_from_union_pw_aff> where the input
2619 lives in a parameter space and the output lives
2620 in a single-dimensional set space.
2622 #include <isl/aff.h>
2623 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2624 __isl_take isl_aff *aff);
2625 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2626 __isl_take isl_pw_aff *pa);
2627 __isl_give isl_multi_union_pw_aff *
2628 isl_multi_union_pw_aff_from_union_pw_aff(
2629 __isl_take isl_union_pw_aff *upa);
2631 A multiple expression can be created from a list
2632 of base expression in a specified space.
2633 The domain of this space needs to be the same
2634 as the domains of the base expressions in the list.
2635 If the base expressions have a set space (or no associated space),
2636 then this space also needs to be a set space.
2638 #include <isl/val.h>
2639 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2640 __isl_take isl_space *space,
2641 __isl_take isl_val_list *list);
2643 #include <isl/aff.h>
2644 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2645 __isl_take isl_space *space,
2646 __isl_take isl_aff_list *list);
2647 __isl_give isl_multi_union_pw_aff *
2648 isl_multi_union_pw_aff_from_union_pw_aff_list(
2649 __isl_take isl_space *space,
2650 __isl_take isl_union_pw_aff_list *list);
2652 As a convenience, a multiple piecewise expression can
2653 also be created from a multiple expression.
2654 Each piecewise expression in the result has a single
2657 #include <isl/aff.h>
2658 __isl_give isl_multi_pw_aff *
2659 isl_multi_pw_aff_from_multi_aff(
2660 __isl_take isl_multi_aff *ma);
2662 Similarly, a multiple union expression can be
2663 created from a multiple expression.
2665 #include <isl/aff.h>
2666 __isl_give isl_multi_union_pw_aff *
2667 isl_multi_union_pw_aff_from_multi_aff(
2668 __isl_take isl_multi_aff *ma);
2669 __isl_give isl_multi_union_pw_aff *
2670 isl_multi_union_pw_aff_from_multi_pw_aff(
2671 __isl_take isl_multi_pw_aff *mpa);
2673 A multiple quasi-affine expression can be created from
2674 a multiple value with a given domain space using the following
2677 #include <isl/aff.h>
2678 __isl_give isl_multi_aff *
2679 isl_multi_aff_multi_val_on_space(
2680 __isl_take isl_space *space,
2681 __isl_take isl_multi_val *mv);
2684 a multiple union piecewise affine expression can be created from
2685 a multiple value with a given domain or
2686 a multiple affine expression with a given domain
2687 using the following functions.
2689 #include <isl/aff.h>
2690 __isl_give isl_multi_union_pw_aff *
2691 isl_multi_union_pw_aff_multi_val_on_domain(
2692 __isl_take isl_union_set *domain,
2693 __isl_take isl_multi_val *mv);
2694 __isl_give isl_multi_union_pw_aff *
2695 isl_multi_union_pw_aff_multi_aff_on_domain(
2696 __isl_take isl_union_set *domain,
2697 __isl_take isl_multi_aff *ma);
2699 Multiple expressions can be copied and freed using
2700 the following functions.
2702 #include <isl/val.h>
2703 __isl_give isl_multi_val *isl_multi_val_copy(
2704 __isl_keep isl_multi_val *mv);
2705 __isl_null isl_multi_val *isl_multi_val_free(
2706 __isl_take isl_multi_val *mv);
2708 #include <isl/aff.h>
2709 __isl_give isl_multi_aff *isl_multi_aff_copy(
2710 __isl_keep isl_multi_aff *maff);
2711 __isl_null isl_multi_aff *isl_multi_aff_free(
2712 __isl_take isl_multi_aff *maff);
2713 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2714 __isl_keep isl_multi_pw_aff *mpa);
2715 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2716 __isl_take isl_multi_pw_aff *mpa);
2717 __isl_give isl_multi_union_pw_aff *
2718 isl_multi_union_pw_aff_copy(
2719 __isl_keep isl_multi_union_pw_aff *mupa);
2720 __isl_null isl_multi_union_pw_aff *
2721 isl_multi_union_pw_aff_free(
2722 __isl_take isl_multi_union_pw_aff *mupa);
2724 The base expression at a given position of a multiple
2725 expression can be extracted using the following functions.
2727 #include <isl/val.h>
2728 __isl_give isl_val *isl_multi_val_get_val(
2729 __isl_keep isl_multi_val *mv, int pos);
2731 #include <isl/aff.h>
2732 __isl_give isl_aff *isl_multi_aff_get_aff(
2733 __isl_keep isl_multi_aff *multi, int pos);
2734 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2735 __isl_keep isl_multi_pw_aff *mpa, int pos);
2736 __isl_give isl_union_pw_aff *
2737 isl_multi_union_pw_aff_get_union_pw_aff(
2738 __isl_keep isl_multi_union_pw_aff *mupa, int pos);
2740 It can be replaced using the following functions.
2742 #include <isl/val.h>
2743 __isl_give isl_multi_val *isl_multi_val_set_val(
2744 __isl_take isl_multi_val *mv, int pos,
2745 __isl_take isl_val *val);
2747 #include <isl/aff.h>
2748 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2749 __isl_take isl_multi_aff *multi, int pos,
2750 __isl_take isl_aff *aff);
2751 __isl_give isl_multi_union_pw_aff *
2752 isl_multi_union_pw_aff_set_union_pw_aff(
2753 __isl_take isl_multi_union_pw_aff *mupa, int pos,
2754 __isl_take isl_union_pw_aff *upa);
2756 As a convenience, a sequence of base expressions that have
2757 their domains in a given space can be extracted from a sequence
2758 of union expressions using the following function.
2760 #include <isl/aff.h>
2761 __isl_give isl_multi_pw_aff *
2762 isl_multi_union_pw_aff_extract_multi_pw_aff(
2763 __isl_keep isl_multi_union_pw_aff *mupa,
2764 __isl_take isl_space *space);
2766 Note that there is a difference between C<isl_multi_union_pw_aff>
2767 and C<isl_union_pw_multi_aff> objects. The first is a sequence
2768 of unions of piecewise expressions, while the second is a union
2769 of piecewise sequences. In particular, multiple affine expressions
2770 in an C<isl_union_pw_multi_aff> may live in different spaces,
2771 while there is only a single multiple expression in
2772 an C<isl_multi_union_pw_aff>, which can therefore only live
2773 in a single space. This means that not every
2774 C<isl_union_pw_multi_aff> can be converted to
2775 an C<isl_multi_union_pw_aff>. Conversely, a zero-dimensional
2776 C<isl_multi_union_pw_aff> carries no information
2777 about any possible domain and therefore cannot be converted
2778 to an C<isl_union_pw_multi_aff>. Moreover, the elements
2779 of an C<isl_multi_union_pw_aff> may be defined over different domains,
2780 while each multiple expression inside an C<isl_union_pw_multi_aff>
2781 has a single domain. The conversion of an C<isl_union_pw_multi_aff>
2782 of dimension greater than one may therefore not be exact.
2783 The following functions can
2784 be used to perform these conversions when they are possible.
2786 #include <isl/aff.h>
2787 __isl_give isl_multi_union_pw_aff *
2788 isl_multi_union_pw_aff_from_union_pw_multi_aff(
2789 __isl_take isl_union_pw_multi_aff *upma);
2790 __isl_give isl_union_pw_multi_aff *
2791 isl_union_pw_multi_aff_from_multi_union_pw_aff(
2792 __isl_take isl_multi_union_pw_aff *mupa);
2794 =head3 Piecewise Expressions
2796 A piecewise expression is an expression that is described
2797 using zero or more base expression defined over the same
2798 number of cells in the domain space of the base expressions.
2799 All base expressions are defined over the same
2800 domain space and the cells are disjoint.
2801 The space of a piecewise expression is the same as
2802 that of the base expressions.
2803 If the union of the cells is a strict subset of the domain
2804 space, then the value of the piecewise expression outside
2805 this union is different for types derived from quasi-affine
2806 expressions and those derived from quasipolynomials.
2807 Piecewise expressions derived from quasi-affine expressions
2808 are considered to be undefined outside the union of their cells.
2809 Piecewise expressions derived from quasipolynomials
2810 are considered to be zero outside the union of their cells.
2812 Piecewise quasipolynomials are mainly used by the C<barvinok>
2813 library for representing the number of elements in a parametric set or map.
2814 For example, the piecewise quasipolynomial
2816 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2818 represents the number of points in the map
2820 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2822 The piecewise expression types defined by C<isl>
2823 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2824 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2826 A piecewise expression with no cells can be created using
2827 the following functions.
2829 #include <isl/aff.h>
2830 __isl_give isl_pw_aff *isl_pw_aff_empty(
2831 __isl_take isl_space *space);
2832 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2833 __isl_take isl_space *space);
2835 A piecewise expression with a single universe cell can be
2836 created using the following functions.
2838 #include <isl/aff.h>
2839 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2840 __isl_take isl_aff *aff);
2841 __isl_give isl_pw_multi_aff *
2842 isl_pw_multi_aff_from_multi_aff(
2843 __isl_take isl_multi_aff *ma);
2845 #include <isl/polynomial.h>
2846 __isl_give isl_pw_qpolynomial *
2847 isl_pw_qpolynomial_from_qpolynomial(
2848 __isl_take isl_qpolynomial *qp);
2850 A piecewise expression with a single specified cell can be
2851 created using the following functions.
2853 #include <isl/aff.h>
2854 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2855 __isl_take isl_set *set, __isl_take isl_aff *aff);
2856 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2857 __isl_take isl_set *set,
2858 __isl_take isl_multi_aff *maff);
2860 #include <isl/polynomial.h>
2861 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2862 __isl_take isl_set *set,
2863 __isl_take isl_qpolynomial *qp);
2865 The following convenience functions first create a base expression and
2866 then create a piecewise expression over a universe domain.
2868 #include <isl/aff.h>
2869 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2870 __isl_take isl_local_space *ls);
2871 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2872 __isl_take isl_local_space *ls,
2873 enum isl_dim_type type, unsigned pos);
2874 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2875 __isl_take isl_local_space *ls);
2876 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2877 __isl_take isl_space *space);
2878 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2879 __isl_take isl_space *space);
2880 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2881 __isl_take isl_space *space);
2882 __isl_give isl_pw_multi_aff *
2883 isl_pw_multi_aff_project_out_map(
2884 __isl_take isl_space *space,
2885 enum isl_dim_type type,
2886 unsigned first, unsigned n);
2888 #include <isl/polynomial.h>
2889 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2890 __isl_take isl_space *space);
2892 The following convenience functions first create a base expression and
2893 then create a piecewise expression over a given domain.
2895 #include <isl/aff.h>
2896 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2897 __isl_take isl_set *domain,
2898 __isl_take isl_val *v);
2899 __isl_give isl_pw_multi_aff *
2900 isl_pw_multi_aff_multi_val_on_domain(
2901 __isl_take isl_set *domain,
2902 __isl_take isl_multi_val *mv);
2904 As a convenience, a piecewise multiple expression can
2905 also be created from a piecewise expression.
2906 Each multiple expression in the result is derived
2907 from the corresponding base expression.
2909 #include <isl/aff.h>
2910 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2911 __isl_take isl_pw_aff *pa);
2913 Similarly, a piecewise quasipolynomial can be
2914 created from a piecewise quasi-affine expression using
2915 the following function.
2917 #include <isl/polynomial.h>
2918 __isl_give isl_pw_qpolynomial *
2919 isl_pw_qpolynomial_from_pw_aff(
2920 __isl_take isl_pw_aff *pwaff);
2922 Piecewise expressions can be copied and freed using the following functions.
2924 #include <isl/aff.h>
2925 __isl_give isl_pw_aff *isl_pw_aff_copy(
2926 __isl_keep isl_pw_aff *pwaff);
2927 __isl_null isl_pw_aff *isl_pw_aff_free(
2928 __isl_take isl_pw_aff *pwaff);
2929 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2930 __isl_keep isl_pw_multi_aff *pma);
2931 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2932 __isl_take isl_pw_multi_aff *pma);
2934 #include <isl/polynomial.h>
2935 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2936 __isl_keep isl_pw_qpolynomial *pwqp);
2937 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2938 __isl_take isl_pw_qpolynomial *pwqp);
2939 __isl_give isl_pw_qpolynomial_fold *
2940 isl_pw_qpolynomial_fold_copy(
2941 __isl_keep isl_pw_qpolynomial_fold *pwf);
2942 __isl_null isl_pw_qpolynomial_fold *
2943 isl_pw_qpolynomial_fold_free(
2944 __isl_take isl_pw_qpolynomial_fold *pwf);
2946 To iterate over the different cells of a piecewise expression,
2947 use the following functions.
2949 #include <isl/aff.h>
2950 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2951 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2952 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2953 int (*fn)(__isl_take isl_set *set,
2954 __isl_take isl_aff *aff,
2955 void *user), void *user);
2956 int isl_pw_multi_aff_foreach_piece(
2957 __isl_keep isl_pw_multi_aff *pma,
2958 int (*fn)(__isl_take isl_set *set,
2959 __isl_take isl_multi_aff *maff,
2960 void *user), void *user);
2962 #include <isl/polynomial.h>
2963 int isl_pw_qpolynomial_foreach_piece(
2964 __isl_keep isl_pw_qpolynomial *pwqp,
2965 int (*fn)(__isl_take isl_set *set,
2966 __isl_take isl_qpolynomial *qp,
2967 void *user), void *user);
2968 int isl_pw_qpolynomial_foreach_lifted_piece(
2969 __isl_keep isl_pw_qpolynomial *pwqp,
2970 int (*fn)(__isl_take isl_set *set,
2971 __isl_take isl_qpolynomial *qp,
2972 void *user), void *user);
2973 int isl_pw_qpolynomial_fold_foreach_piece(
2974 __isl_keep isl_pw_qpolynomial_fold *pwf,
2975 int (*fn)(__isl_take isl_set *set,
2976 __isl_take isl_qpolynomial_fold *fold,
2977 void *user), void *user);
2978 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2979 __isl_keep isl_pw_qpolynomial_fold *pwf,
2980 int (*fn)(__isl_take isl_set *set,
2981 __isl_take isl_qpolynomial_fold *fold,
2982 void *user), void *user);
2984 As usual, the function C<fn> should return C<0> on success
2985 and C<-1> on failure. The difference between
2986 C<isl_pw_qpolynomial_foreach_piece> and
2987 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2988 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2989 compute unique representations for all existentially quantified
2990 variables and then turn these existentially quantified variables
2991 into extra set variables, adapting the associated quasipolynomial
2992 accordingly. This means that the C<set> passed to C<fn>
2993 will not have any existentially quantified variables, but that
2994 the dimensions of the sets may be different for different
2995 invocations of C<fn>.
2996 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2997 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2999 A piecewise expression consisting of the expressions at a given
3000 position of a piecewise multiple expression can be extracted
3001 using the following function.
3003 #include <isl/aff.h>
3004 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3005 __isl_keep isl_pw_multi_aff *pma, int pos);
3007 These expressions can be replaced using the following function.
3009 #include <isl/aff.h>
3010 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3011 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3012 __isl_take isl_pw_aff *pa);
3014 Note that there is a difference between C<isl_multi_pw_aff> and
3015 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
3016 affine expressions, while the second is a piecewise sequence
3017 of affine expressions. In particular, each of the piecewise
3018 affine expressions in an C<isl_multi_pw_aff> may have a different
3019 domain, while all multiple expressions associated to a cell
3020 in an C<isl_pw_multi_aff> have the same domain.
3021 It is possible to convert between the two, but when converting
3022 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
3023 of the result is the intersection of the domains of the input.
3024 The reverse conversion is exact.
3026 #include <isl/aff.h>
3027 __isl_give isl_pw_multi_aff *
3028 isl_pw_multi_aff_from_multi_pw_aff(
3029 __isl_take isl_multi_pw_aff *mpa);
3030 __isl_give isl_multi_pw_aff *
3031 isl_multi_pw_aff_from_pw_multi_aff(
3032 __isl_take isl_pw_multi_aff *pma);
3034 =head3 Union Expressions
3036 A union expression collects base expressions defined
3037 over different domains. The space of a union expression
3038 is that of the shared parameter space.
3040 The union expression types defined by C<isl>
3041 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
3042 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
3044 An empty union expression can be created using the following functions.
3046 #include <isl/aff.h>
3047 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
3048 __isl_take isl_space *space);
3049 __isl_give isl_union_pw_multi_aff *
3050 isl_union_pw_multi_aff_empty(
3051 __isl_take isl_space *space);
3053 #include <isl/polynomial.h>
3054 __isl_give isl_union_pw_qpolynomial *
3055 isl_union_pw_qpolynomial_zero(
3056 __isl_take isl_space *space);
3058 A union expression containing a single base expression
3059 can be created using the following functions.
3061 #include <isl/aff.h>
3062 __isl_give isl_union_pw_aff *
3063 isl_union_pw_aff_from_pw_aff(
3064 __isl_take isl_pw_aff *pa);
3065 __isl_give isl_union_pw_multi_aff *
3066 isl_union_pw_multi_aff_from_aff(
3067 __isl_take isl_aff *aff);
3068 __isl_give isl_union_pw_multi_aff *
3069 isl_union_pw_multi_aff_from_pw_multi_aff(
3070 __isl_take isl_pw_multi_aff *pma);
3072 #include <isl/polynomial.h>
3073 __isl_give isl_union_pw_qpolynomial *
3074 isl_union_pw_qpolynomial_from_pw_qpolynomial(
3075 __isl_take isl_pw_qpolynomial *pwqp);
3077 The following functions create a base expression on each
3078 of the sets in the union set and collect the results.
3080 #include <isl/aff.h>
3081 __isl_give isl_union_pw_multi_aff *
3082 isl_union_pw_multi_aff_from_union_pw_aff(
3083 __isl_take isl_union_pw_aff *upa);
3084 __isl_give isl_union_pw_aff *
3085 isl_union_pw_multi_aff_get_union_pw_aff(
3086 __isl_keep isl_union_pw_multi_aff *upma, int pos);
3087 __isl_give isl_union_pw_aff *
3088 isl_union_pw_aff_val_on_domain(
3089 __isl_take isl_union_set *domain,
3090 __isl_take isl_val *v);
3091 __isl_give isl_union_pw_multi_aff *
3092 isl_union_pw_multi_aff_multi_val_on_domain(
3093 __isl_take isl_union_set *domain,
3094 __isl_take isl_multi_val *mv);
3096 An C<isl_union_pw_aff> that is equal to a (parametric) affine
3097 expression on a given domain can be created using the following
3100 #include <isl/aff.h>
3101 __isl_give isl_union_pw_aff *
3102 isl_union_pw_aff_aff_on_domain(
3103 __isl_take isl_union_set *domain,
3104 __isl_take isl_aff *aff);
3106 A base expression can be added to a union expression using
3107 the following functions.
3109 #include <isl/aff.h>
3110 __isl_give isl_union_pw_aff *
3111 isl_union_pw_aff_add_pw_aff(
3112 __isl_take isl_union_pw_aff *upa,
3113 __isl_take isl_pw_aff *pa);
3114 __isl_give isl_union_pw_multi_aff *
3115 isl_union_pw_multi_aff_add_pw_multi_aff(
3116 __isl_take isl_union_pw_multi_aff *upma,
3117 __isl_take isl_pw_multi_aff *pma);
3119 #include <isl/polynomial.h>
3120 __isl_give isl_union_pw_qpolynomial *
3121 isl_union_pw_qpolynomial_add_pw_qpolynomial(
3122 __isl_take isl_union_pw_qpolynomial *upwqp,
3123 __isl_take isl_pw_qpolynomial *pwqp);
3125 Union expressions can be copied and freed using
3126 the following functions.
3128 #include <isl/aff.h>
3129 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
3130 __isl_keep isl_union_pw_aff *upa);
3131 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
3132 __isl_take isl_union_pw_aff *upa);
3133 __isl_give isl_union_pw_multi_aff *
3134 isl_union_pw_multi_aff_copy(
3135 __isl_keep isl_union_pw_multi_aff *upma);
3136 __isl_null isl_union_pw_multi_aff *
3137 isl_union_pw_multi_aff_free(
3138 __isl_take isl_union_pw_multi_aff *upma);
3140 #include <isl/polynomial.h>
3141 __isl_give isl_union_pw_qpolynomial *
3142 isl_union_pw_qpolynomial_copy(
3143 __isl_keep isl_union_pw_qpolynomial *upwqp);
3144 __isl_null isl_union_pw_qpolynomial *
3145 isl_union_pw_qpolynomial_free(
3146 __isl_take isl_union_pw_qpolynomial *upwqp);
3147 __isl_give isl_union_pw_qpolynomial_fold *
3148 isl_union_pw_qpolynomial_fold_copy(
3149 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3150 __isl_null isl_union_pw_qpolynomial_fold *
3151 isl_union_pw_qpolynomial_fold_free(
3152 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3154 To iterate over the base expressions in a union expression,
3155 use the following functions.
3157 #include <isl/aff.h>
3158 int isl_union_pw_aff_n_pw_aff(
3159 __isl_keep isl_union_pw_aff *upa);
3160 int isl_union_pw_aff_foreach_pw_aff(
3161 __isl_keep isl_union_pw_aff *upa,
3162 int (*fn)(__isl_take isl_pw_aff *ma, void *user),
3164 int isl_union_pw_multi_aff_n_pw_multi_aff(
3165 __isl_keep isl_union_pw_multi_aff *upma);
3166 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3167 __isl_keep isl_union_pw_multi_aff *upma,
3168 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3169 void *user), void *user);
3171 #include <isl/polynomial.h>
3172 int isl_union_pw_qpolynomial_n_pw_qpolynomial(
3173 __isl_keep isl_union_pw_qpolynomial *upwqp);
3174 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3175 __isl_keep isl_union_pw_qpolynomial *upwqp,
3176 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3177 void *user), void *user);
3178 int isl_union_pw_qpolynomial_fold_n_pw_qpolynomial_fold(
3179 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3180 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3181 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3182 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3183 void *user), void *user);
3185 To extract the base expression in a given space from a union, use
3186 the following functions.
3188 #include <isl/aff.h>
3189 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3190 __isl_keep isl_union_pw_aff *upa,
3191 __isl_take isl_space *space);
3192 __isl_give isl_pw_multi_aff *
3193 isl_union_pw_multi_aff_extract_pw_multi_aff(
3194 __isl_keep isl_union_pw_multi_aff *upma,
3195 __isl_take isl_space *space);
3197 #include <isl/polynomial.h>
3198 __isl_give isl_pw_qpolynomial *
3199 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3200 __isl_keep isl_union_pw_qpolynomial *upwqp,
3201 __isl_take isl_space *space);
3203 =head2 Input and Output
3205 For set and relation,
3206 C<isl> supports its own input/output format, which is similar
3207 to the C<Omega> format, but also supports the C<PolyLib> format
3209 For other object types, typically only an C<isl> format is supported.
3211 =head3 C<isl> format
3213 The C<isl> format is similar to that of C<Omega>, but has a different
3214 syntax for describing the parameters and allows for the definition
3215 of an existentially quantified variable as the integer division
3216 of an affine expression.
3217 For example, the set of integers C<i> between C<0> and C<n>
3218 such that C<i % 10 <= 6> can be described as
3220 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3223 A set or relation can have several disjuncts, separated
3224 by the keyword C<or>. Each disjunct is either a conjunction
3225 of constraints or a projection (C<exists>) of a conjunction
3226 of constraints. The constraints are separated by the keyword
3229 =head3 C<PolyLib> format
3231 If the represented set is a union, then the first line
3232 contains a single number representing the number of disjuncts.
3233 Otherwise, a line containing the number C<1> is optional.
3235 Each disjunct is represented by a matrix of constraints.
3236 The first line contains two numbers representing
3237 the number of rows and columns,
3238 where the number of rows is equal to the number of constraints
3239 and the number of columns is equal to two plus the number of variables.
3240 The following lines contain the actual rows of the constraint matrix.
3241 In each row, the first column indicates whether the constraint
3242 is an equality (C<0>) or inequality (C<1>). The final column
3243 corresponds to the constant term.
3245 If the set is parametric, then the coefficients of the parameters
3246 appear in the last columns before the constant column.
3247 The coefficients of any existentially quantified variables appear
3248 between those of the set variables and those of the parameters.
3250 =head3 Extended C<PolyLib> format
3252 The extended C<PolyLib> format is nearly identical to the
3253 C<PolyLib> format. The only difference is that the line
3254 containing the number of rows and columns of a constraint matrix
3255 also contains four additional numbers:
3256 the number of output dimensions, the number of input dimensions,
3257 the number of local dimensions (i.e., the number of existentially
3258 quantified variables) and the number of parameters.
3259 For sets, the number of ``output'' dimensions is equal
3260 to the number of set dimensions, while the number of ``input''
3265 Objects can be read from input using the following functions.
3267 #include <isl/val.h>
3268 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3270 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3271 isl_ctx *ctx, const char *str);
3273 #include <isl/set.h>
3274 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3275 isl_ctx *ctx, FILE *input);
3276 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3277 isl_ctx *ctx, const char *str);
3278 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3280 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3283 #include <isl/map.h>
3284 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3285 isl_ctx *ctx, FILE *input);
3286 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3287 isl_ctx *ctx, const char *str);
3288 __isl_give isl_map *isl_map_read_from_file(
3289 isl_ctx *ctx, FILE *input);
3290 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3293 #include <isl/union_set.h>
3294 __isl_give isl_union_set *isl_union_set_read_from_file(
3295 isl_ctx *ctx, FILE *input);
3296 __isl_give isl_union_set *isl_union_set_read_from_str(
3297 isl_ctx *ctx, const char *str);
3299 #include <isl/union_map.h>
3300 __isl_give isl_union_map *isl_union_map_read_from_file(
3301 isl_ctx *ctx, FILE *input);
3302 __isl_give isl_union_map *isl_union_map_read_from_str(
3303 isl_ctx *ctx, const char *str);
3305 #include <isl/aff.h>
3306 __isl_give isl_aff *isl_aff_read_from_str(
3307 isl_ctx *ctx, const char *str);
3308 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3309 isl_ctx *ctx, const char *str);
3310 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3311 isl_ctx *ctx, const char *str);
3312 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3313 isl_ctx *ctx, const char *str);
3314 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3315 isl_ctx *ctx, const char *str);
3316 __isl_give isl_union_pw_multi_aff *
3317 isl_union_pw_multi_aff_read_from_str(
3318 isl_ctx *ctx, const char *str);
3319 __isl_give isl_multi_union_pw_aff *
3320 isl_multi_union_pw_aff_read_from_str(
3321 isl_ctx *ctx, const char *str);
3323 #include <isl/polynomial.h>
3324 __isl_give isl_union_pw_qpolynomial *
3325 isl_union_pw_qpolynomial_read_from_str(
3326 isl_ctx *ctx, const char *str);
3328 For sets and relations,
3329 the input format is autodetected and may be either the C<PolyLib> format
3330 or the C<isl> format.
3334 Before anything can be printed, an C<isl_printer> needs to
3337 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3339 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3340 __isl_null isl_printer *isl_printer_free(
3341 __isl_take isl_printer *printer);
3342 __isl_give char *isl_printer_get_str(
3343 __isl_keep isl_printer *printer);
3345 The printer can be inspected using the following functions.
3347 FILE *isl_printer_get_file(
3348 __isl_keep isl_printer *printer);
3349 int isl_printer_get_output_format(
3350 __isl_keep isl_printer *p);
3351 int isl_printer_get_yaml_style(__isl_keep isl_printer *p);
3353 The behavior of the printer can be modified in various ways
3355 __isl_give isl_printer *isl_printer_set_output_format(
3356 __isl_take isl_printer *p, int output_format);
3357 __isl_give isl_printer *isl_printer_set_indent(
3358 __isl_take isl_printer *p, int indent);
3359 __isl_give isl_printer *isl_printer_set_indent_prefix(
3360 __isl_take isl_printer *p, const char *prefix);
3361 __isl_give isl_printer *isl_printer_indent(
3362 __isl_take isl_printer *p, int indent);
3363 __isl_give isl_printer *isl_printer_set_prefix(
3364 __isl_take isl_printer *p, const char *prefix);
3365 __isl_give isl_printer *isl_printer_set_suffix(
3366 __isl_take isl_printer *p, const char *suffix);
3367 __isl_give isl_printer *isl_printer_set_yaml_style(
3368 __isl_take isl_printer *p, int yaml_style);
3370 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3371 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3372 and defaults to C<ISL_FORMAT_ISL>.
3373 Each line in the output is prefixed by C<indent_prefix>,
3374 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3375 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3376 In the C<PolyLib> format output,
3377 the coefficients of the existentially quantified variables
3378 appear between those of the set variables and those
3380 The function C<isl_printer_indent> increases the indentation
3381 by the specified amount (which may be negative).
3382 The YAML style may be either C<ISL_YAML_STYLE_BLOCK> or
3383 C<ISL_YAML_STYLE_FLOW> and when we are printing something
3386 To actually print something, use
3388 #include <isl/printer.h>
3389 __isl_give isl_printer *isl_printer_print_double(
3390 __isl_take isl_printer *p, double d);
3392 #include <isl/val.h>
3393 __isl_give isl_printer *isl_printer_print_val(
3394 __isl_take isl_printer *p, __isl_keep isl_val *v);
3396 #include <isl/set.h>
3397 __isl_give isl_printer *isl_printer_print_basic_set(
3398 __isl_take isl_printer *printer,
3399 __isl_keep isl_basic_set *bset);
3400 __isl_give isl_printer *isl_printer_print_set(
3401 __isl_take isl_printer *printer,
3402 __isl_keep isl_set *set);
3404 #include <isl/map.h>
3405 __isl_give isl_printer *isl_printer_print_basic_map(
3406 __isl_take isl_printer *printer,
3407 __isl_keep isl_basic_map *bmap);
3408 __isl_give isl_printer *isl_printer_print_map(
3409 __isl_take isl_printer *printer,
3410 __isl_keep isl_map *map);
3412 #include <isl/union_set.h>
3413 __isl_give isl_printer *isl_printer_print_union_set(
3414 __isl_take isl_printer *p,
3415 __isl_keep isl_union_set *uset);
3417 #include <isl/union_map.h>
3418 __isl_give isl_printer *isl_printer_print_union_map(
3419 __isl_take isl_printer *p,
3420 __isl_keep isl_union_map *umap);
3422 #include <isl/val.h>
3423 __isl_give isl_printer *isl_printer_print_multi_val(
3424 __isl_take isl_printer *p,
3425 __isl_keep isl_multi_val *mv);
3427 #include <isl/aff.h>
3428 __isl_give isl_printer *isl_printer_print_aff(
3429 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3430 __isl_give isl_printer *isl_printer_print_multi_aff(
3431 __isl_take isl_printer *p,
3432 __isl_keep isl_multi_aff *maff);
3433 __isl_give isl_printer *isl_printer_print_pw_aff(
3434 __isl_take isl_printer *p,
3435 __isl_keep isl_pw_aff *pwaff);
3436 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3437 __isl_take isl_printer *p,
3438 __isl_keep isl_pw_multi_aff *pma);
3439 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3440 __isl_take isl_printer *p,
3441 __isl_keep isl_multi_pw_aff *mpa);
3442 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3443 __isl_take isl_printer *p,
3444 __isl_keep isl_union_pw_aff *upa);
3445 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3446 __isl_take isl_printer *p,
3447 __isl_keep isl_union_pw_multi_aff *upma);
3448 __isl_give isl_printer *
3449 isl_printer_print_multi_union_pw_aff(
3450 __isl_take isl_printer *p,
3451 __isl_keep isl_multi_union_pw_aff *mupa);
3453 #include <isl/polynomial.h>
3454 __isl_give isl_printer *isl_printer_print_qpolynomial(
3455 __isl_take isl_printer *p,
3456 __isl_keep isl_qpolynomial *qp);
3457 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3458 __isl_take isl_printer *p,
3459 __isl_keep isl_pw_qpolynomial *pwqp);
3460 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3461 __isl_take isl_printer *p,
3462 __isl_keep isl_union_pw_qpolynomial *upwqp);
3464 __isl_give isl_printer *
3465 isl_printer_print_pw_qpolynomial_fold(
3466 __isl_take isl_printer *p,
3467 __isl_keep isl_pw_qpolynomial_fold *pwf);
3468 __isl_give isl_printer *
3469 isl_printer_print_union_pw_qpolynomial_fold(
3470 __isl_take isl_printer *p,
3471 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3473 For C<isl_printer_print_qpolynomial>,
3474 C<isl_printer_print_pw_qpolynomial> and
3475 C<isl_printer_print_pw_qpolynomial_fold>,
3476 the output format of the printer
3477 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3478 For C<isl_printer_print_union_pw_qpolynomial> and
3479 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3481 In case of printing in C<ISL_FORMAT_C>, the user may want
3482 to set the names of all dimensions first.
3484 C<isl> also provides limited support for printing YAML documents,
3485 just enough for the internal use for printing such documents.
3487 #include <isl/printer.h>
3488 __isl_give isl_printer *isl_printer_yaml_start_mapping(
3489 __isl_take isl_printer *p);
3490 __isl_give isl_printer *isl_printer_yaml_end_mapping(
3491 __isl_take isl_printer *p);
3492 __isl_give isl_printer *isl_printer_yaml_start_sequence(
3493 __isl_take isl_printer *p);
3494 __isl_give isl_printer *isl_printer_yaml_end_sequence(
3495 __isl_take isl_printer *p);
3496 __isl_give isl_printer *isl_printer_yaml_next(
3497 __isl_take isl_printer *p);
3499 A document is started by a call to either
3500 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3501 Anything printed to the printer after such a call belong to the
3502 first key of the mapping or the first element in the sequence.
3503 The function C<isl_printer_yaml_next> moves to the value if
3504 we are currently printing a mapping key, the next key if we
3505 are printing a value or the next element if we are printing
3506 an element in a sequence.
3507 Nested mappings and sequences are initiated by the same
3508 C<isl_printer_yaml_start_mapping> or C<isl_printer_yaml_start_sequence>.
3509 Each call to these functions needs to have a corresponding call to
3510 C<isl_printer_yaml_end_mapping> or C<isl_printer_yaml_end_sequence>.
3512 When called on a file printer, the following function flushes
3513 the file. When called on a string printer, the buffer is cleared.
3515 __isl_give isl_printer *isl_printer_flush(
3516 __isl_take isl_printer *p);
3518 Alternatively, a string representation can be obtained
3519 directly using the following functions, which always print
3522 #include <isl/space.h>
3523 __isl_give char *isl_space_to_str(
3524 __isl_keep isl_space *space);
3526 #include <isl/val.h>
3527 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3528 __isl_give char *isl_multi_val_to_str(
3529 __isl_keep isl_multi_val *mv);
3531 #include <isl/set.h>
3532 __isl_give char *isl_set_to_str(
3533 __isl_keep isl_set *set);
3535 #include <isl/union_set.h>
3536 __isl_give char *isl_union_set_to_str(
3537 __isl_keep isl_union_set *uset);
3539 #include <isl/map.h>
3540 __isl_give char *isl_map_to_str(
3541 __isl_keep isl_map *map);
3543 #include <isl/union_map.h>
3544 __isl_give char *isl_union_map_to_str(
3545 __isl_keep isl_union_map *umap);
3547 #include <isl/aff.h>
3548 __isl_give char *isl_multi_aff_to_str(
3549 __isl_keep isl_multi_aff *aff);
3550 __isl_give char *isl_union_pw_aff_to_str(
3551 __isl_keep isl_union_pw_aff *upa);
3552 __isl_give char *isl_union_pw_multi_aff_to_str(
3553 __isl_keep isl_union_pw_multi_aff *upma);
3554 __isl_give char *isl_multi_union_pw_aff_to_str(
3555 __isl_keep isl_multi_union_pw_aff *mupa);
3559 =head3 Unary Properties
3565 The following functions test whether the given set or relation
3566 contains any integer points. The ``plain'' variants do not perform
3567 any computations, but simply check if the given set or relation
3568 is already known to be empty.
3570 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3571 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3572 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3573 int isl_set_is_empty(__isl_keep isl_set *set);
3574 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3575 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3576 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3577 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3578 int isl_map_is_empty(__isl_keep isl_map *map);
3579 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3581 =item * Universality
3583 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3584 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3585 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3587 =item * Single-valuedness
3589 #include <isl/set.h>
3590 int isl_set_is_singleton(__isl_keep isl_set *set);
3592 #include <isl/map.h>
3593 int isl_basic_map_is_single_valued(
3594 __isl_keep isl_basic_map *bmap);
3595 int isl_map_plain_is_single_valued(
3596 __isl_keep isl_map *map);
3597 int isl_map_is_single_valued(__isl_keep isl_map *map);
3599 #include <isl/union_map.h>
3600 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3604 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3605 int isl_map_is_injective(__isl_keep isl_map *map);
3606 int isl_union_map_plain_is_injective(
3607 __isl_keep isl_union_map *umap);
3608 int isl_union_map_is_injective(
3609 __isl_keep isl_union_map *umap);
3613 int isl_map_is_bijective(__isl_keep isl_map *map);
3614 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3618 __isl_give isl_val *
3619 isl_basic_map_plain_get_val_if_fixed(
3620 __isl_keep isl_basic_map *bmap,
3621 enum isl_dim_type type, unsigned pos);
3622 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3623 __isl_keep isl_set *set,
3624 enum isl_dim_type type, unsigned pos);
3625 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3626 __isl_keep isl_map *map,
3627 enum isl_dim_type type, unsigned pos);
3629 If the set or relation obviously lies on a hyperplane where the given dimension
3630 has a fixed value, then return that value.
3631 Otherwise return NaN.
3635 int isl_set_dim_residue_class_val(
3636 __isl_keep isl_set *set,
3637 int pos, __isl_give isl_val **modulo,
3638 __isl_give isl_val **residue);
3640 Check if the values of the given set dimension are equal to a fixed
3641 value modulo some integer value. If so, assign the modulo to C<*modulo>
3642 and the fixed value to C<*residue>. If the given dimension attains only
3643 a single value, then assign C<0> to C<*modulo> and the fixed value to
3645 If the dimension does not attain only a single value and if no modulo
3646 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3650 To check whether the description of a set, relation or function depends
3651 on one or more given dimensions,
3652 the following functions can be used.
3654 #include <isl/constraint.h>
3655 int isl_constraint_involves_dims(
3656 __isl_keep isl_constraint *constraint,
3657 enum isl_dim_type type, unsigned first, unsigned n);
3659 #include <isl/set.h>
3660 int isl_basic_set_involves_dims(
3661 __isl_keep isl_basic_set *bset,
3662 enum isl_dim_type type, unsigned first, unsigned n);
3663 int isl_set_involves_dims(__isl_keep isl_set *set,
3664 enum isl_dim_type type, unsigned first, unsigned n);
3666 #include <isl/map.h>
3667 int isl_basic_map_involves_dims(
3668 __isl_keep isl_basic_map *bmap,
3669 enum isl_dim_type type, unsigned first, unsigned n);
3670 int isl_map_involves_dims(__isl_keep isl_map *map,
3671 enum isl_dim_type type, unsigned first, unsigned n);
3673 #include <isl/union_map.h>
3674 int isl_union_map_involves_dims(
3675 __isl_keep isl_union_map *umap,
3676 enum isl_dim_type type, unsigned first, unsigned n);
3678 #include <isl/aff.h>
3679 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3680 enum isl_dim_type type, unsigned first, unsigned n);
3681 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3682 enum isl_dim_type type, unsigned first, unsigned n);
3683 int isl_multi_aff_involves_dims(
3684 __isl_keep isl_multi_aff *ma,
3685 enum isl_dim_type type, unsigned first, unsigned n);
3686 int isl_multi_pw_aff_involves_dims(
3687 __isl_keep isl_multi_pw_aff *mpa,
3688 enum isl_dim_type type, unsigned first, unsigned n);
3690 Similarly, the following functions can be used to check whether
3691 a given dimension is involved in any lower or upper bound.
3693 #include <isl/set.h>
3694 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3695 enum isl_dim_type type, unsigned pos);
3696 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3697 enum isl_dim_type type, unsigned pos);
3699 Note that these functions return true even if there is a bound on
3700 the dimension on only some of the basic sets of C<set>.
3701 To check if they have a bound for all of the basic sets in C<set>,
3702 use the following functions instead.
3704 #include <isl/set.h>
3705 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3706 enum isl_dim_type type, unsigned pos);
3707 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3708 enum isl_dim_type type, unsigned pos);
3712 To check whether a set is a parameter domain, use this function:
3714 int isl_set_is_params(__isl_keep isl_set *set);
3715 int isl_union_set_is_params(
3716 __isl_keep isl_union_set *uset);
3720 The following functions check whether the space of the given
3721 (basic) set or relation range is a wrapped relation.
3723 #include <isl/space.h>
3724 int isl_space_is_wrapping(
3725 __isl_keep isl_space *space);
3726 int isl_space_domain_is_wrapping(
3727 __isl_keep isl_space *space);
3728 int isl_space_range_is_wrapping(
3729 __isl_keep isl_space *space);
3731 #include <isl/set.h>
3732 int isl_basic_set_is_wrapping(
3733 __isl_keep isl_basic_set *bset);
3734 int isl_set_is_wrapping(__isl_keep isl_set *set);
3736 #include <isl/map.h>
3737 int isl_map_domain_is_wrapping(
3738 __isl_keep isl_map *map);
3739 int isl_map_range_is_wrapping(
3740 __isl_keep isl_map *map);
3742 #include <isl/val.h>
3743 int isl_multi_val_range_is_wrapping(
3744 __isl_keep isl_multi_val *mv);
3746 #include <isl/aff.h>
3747 int isl_multi_aff_range_is_wrapping(
3748 __isl_keep isl_multi_aff *ma);
3749 int isl_multi_pw_aff_range_is_wrapping(
3750 __isl_keep isl_multi_pw_aff *mpa);
3751 int isl_multi_union_pw_aff_range_is_wrapping(
3752 __isl_keep isl_multi_union_pw_aff *mupa);
3754 The input to C<isl_space_is_wrapping> should
3755 be the space of a set, while that of
3756 C<isl_space_domain_is_wrapping> and
3757 C<isl_space_range_is_wrapping> should be the space of a relation.
3759 =item * Internal Product
3761 int isl_basic_map_can_zip(
3762 __isl_keep isl_basic_map *bmap);
3763 int isl_map_can_zip(__isl_keep isl_map *map);
3765 Check whether the product of domain and range of the given relation
3767 i.e., whether both domain and range are nested relations.
3771 int isl_basic_map_can_curry(
3772 __isl_keep isl_basic_map *bmap);
3773 int isl_map_can_curry(__isl_keep isl_map *map);
3775 Check whether the domain of the (basic) relation is a wrapped relation.
3777 int isl_basic_map_can_uncurry(
3778 __isl_keep isl_basic_map *bmap);
3779 int isl_map_can_uncurry(__isl_keep isl_map *map);
3781 Check whether the range of the (basic) relation is a wrapped relation.
3783 =item * Special Values
3785 #include <isl/aff.h>
3786 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3787 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3789 Check whether the given expression is a constant.
3791 #include <isl/aff.h>
3792 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3793 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3795 Check whether the given expression is equal to or involves NaN.
3797 #include <isl/aff.h>
3798 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3800 Check whether the affine expression is obviously zero.
3804 =head3 Binary Properties
3810 The following functions check whether two objects
3811 represent the same set, relation or function.
3812 The C<plain> variants only return true if the objects
3813 are obviously the same. That is, they may return false
3814 even if the objects are the same, but they will never
3815 return true if the objects are not the same.
3817 #include <isl/set.h>
3818 int isl_basic_set_plain_is_equal(
3819 __isl_keep isl_basic_set *bset1,
3820 __isl_keep isl_basic_set *bset2);
3821 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3822 __isl_keep isl_set *set2);
3823 int isl_set_is_equal(__isl_keep isl_set *set1,
3824 __isl_keep isl_set *set2);
3826 #include <isl/map.h>
3827 int isl_basic_map_is_equal(
3828 __isl_keep isl_basic_map *bmap1,
3829 __isl_keep isl_basic_map *bmap2);
3830 int isl_map_is_equal(__isl_keep isl_map *map1,
3831 __isl_keep isl_map *map2);
3832 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3833 __isl_keep isl_map *map2);
3835 #include <isl/union_set.h>
3836 int isl_union_set_is_equal(
3837 __isl_keep isl_union_set *uset1,
3838 __isl_keep isl_union_set *uset2);
3840 #include <isl/union_map.h>
3841 int isl_union_map_is_equal(
3842 __isl_keep isl_union_map *umap1,
3843 __isl_keep isl_union_map *umap2);
3845 #include <isl/aff.h>
3846 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3847 __isl_keep isl_aff *aff2);
3848 int isl_multi_aff_plain_is_equal(
3849 __isl_keep isl_multi_aff *maff1,
3850 __isl_keep isl_multi_aff *maff2);
3851 int isl_pw_aff_plain_is_equal(
3852 __isl_keep isl_pw_aff *pwaff1,
3853 __isl_keep isl_pw_aff *pwaff2);
3854 int isl_pw_multi_aff_plain_is_equal(
3855 __isl_keep isl_pw_multi_aff *pma1,
3856 __isl_keep isl_pw_multi_aff *pma2);
3857 int isl_multi_pw_aff_plain_is_equal(
3858 __isl_keep isl_multi_pw_aff *mpa1,
3859 __isl_keep isl_multi_pw_aff *mpa2);
3860 int isl_multi_pw_aff_is_equal(
3861 __isl_keep isl_multi_pw_aff *mpa1,
3862 __isl_keep isl_multi_pw_aff *mpa2);
3863 int isl_union_pw_aff_plain_is_equal(
3864 __isl_keep isl_union_pw_aff *upa1,
3865 __isl_keep isl_union_pw_aff *upa2);
3866 int isl_union_pw_multi_aff_plain_is_equal(
3867 __isl_keep isl_union_pw_multi_aff *upma1,
3868 __isl_keep isl_union_pw_multi_aff *upma2);
3869 int isl_multi_union_pw_aff_plain_is_equal(
3870 __isl_keep isl_multi_union_pw_aff *mupa1,
3871 __isl_keep isl_multi_union_pw_aff *mupa2);
3873 #include <isl/polynomial.h>
3874 int isl_union_pw_qpolynomial_plain_is_equal(
3875 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3876 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3877 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3878 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3879 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3881 =item * Disjointness
3883 #include <isl/set.h>
3884 int isl_basic_set_is_disjoint(
3885 __isl_keep isl_basic_set *bset1,
3886 __isl_keep isl_basic_set *bset2);
3887 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3888 __isl_keep isl_set *set2);
3889 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3890 __isl_keep isl_set *set2);
3892 #include <isl/map.h>
3893 int isl_basic_map_is_disjoint(
3894 __isl_keep isl_basic_map *bmap1,
3895 __isl_keep isl_basic_map *bmap2);
3896 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3897 __isl_keep isl_map *map2);
3899 #include <isl/union_set.h>
3900 int isl_union_set_is_disjoint(
3901 __isl_keep isl_union_set *uset1,
3902 __isl_keep isl_union_set *uset2);
3904 #include <isl/union_map.h>
3905 int isl_union_map_is_disjoint(
3906 __isl_keep isl_union_map *umap1,
3907 __isl_keep isl_union_map *umap2);
3911 int isl_basic_set_is_subset(
3912 __isl_keep isl_basic_set *bset1,
3913 __isl_keep isl_basic_set *bset2);
3914 int isl_set_is_subset(__isl_keep isl_set *set1,
3915 __isl_keep isl_set *set2);
3916 int isl_set_is_strict_subset(
3917 __isl_keep isl_set *set1,
3918 __isl_keep isl_set *set2);
3919 int isl_union_set_is_subset(
3920 __isl_keep isl_union_set *uset1,
3921 __isl_keep isl_union_set *uset2);
3922 int isl_union_set_is_strict_subset(
3923 __isl_keep isl_union_set *uset1,
3924 __isl_keep isl_union_set *uset2);
3925 int isl_basic_map_is_subset(
3926 __isl_keep isl_basic_map *bmap1,
3927 __isl_keep isl_basic_map *bmap2);
3928 int isl_basic_map_is_strict_subset(
3929 __isl_keep isl_basic_map *bmap1,
3930 __isl_keep isl_basic_map *bmap2);
3931 int isl_map_is_subset(
3932 __isl_keep isl_map *map1,
3933 __isl_keep isl_map *map2);
3934 int isl_map_is_strict_subset(
3935 __isl_keep isl_map *map1,
3936 __isl_keep isl_map *map2);
3937 int isl_union_map_is_subset(
3938 __isl_keep isl_union_map *umap1,
3939 __isl_keep isl_union_map *umap2);
3940 int isl_union_map_is_strict_subset(
3941 __isl_keep isl_union_map *umap1,
3942 __isl_keep isl_union_map *umap2);
3944 Check whether the first argument is a (strict) subset of the
3949 Every comparison function returns a negative value if the first
3950 argument is considered smaller than the second, a positive value
3951 if the first argument is considered greater and zero if the two
3952 constraints are considered the same by the comparison criterion.
3954 #include <isl/constraint.h>
3955 int isl_constraint_plain_cmp(
3956 __isl_keep isl_constraint *c1,
3957 __isl_keep isl_constraint *c2);
3959 This function is useful for sorting C<isl_constraint>s.
3960 The order depends on the internal representation of the inputs.
3961 The order is fixed over different calls to the function (assuming
3962 the internal representation of the inputs has not changed), but may
3963 change over different versions of C<isl>.
3965 #include <isl/constraint.h>
3966 int isl_constraint_cmp_last_non_zero(
3967 __isl_keep isl_constraint *c1,
3968 __isl_keep isl_constraint *c2);
3970 This function can be used to sort constraints that live in the same
3971 local space. Constraints that involve ``earlier'' dimensions or
3972 that have a smaller coefficient for the shared latest dimension
3973 are considered smaller than other constraints.
3974 This function only defines a B<partial> order.
3976 #include <isl/set.h>
3977 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3978 __isl_keep isl_set *set2);
3980 This function is useful for sorting C<isl_set>s.
3981 The order depends on the internal representation of the inputs.
3982 The order is fixed over different calls to the function (assuming
3983 the internal representation of the inputs has not changed), but may
3984 change over different versions of C<isl>.
3986 #include <isl/aff.h>
3987 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3988 __isl_keep isl_pw_aff *pa2);
3990 The function C<isl_pw_aff_plain_cmp> can be used to sort
3991 C<isl_pw_aff>s. The order is not strictly defined.
3992 The current order sorts expressions that only involve
3993 earlier dimensions before those that involve later dimensions.
3997 =head2 Unary Operations
4003 __isl_give isl_set *isl_set_complement(
4004 __isl_take isl_set *set);
4005 __isl_give isl_map *isl_map_complement(
4006 __isl_take isl_map *map);
4010 #include <isl/space.h>
4011 __isl_give isl_space *isl_space_reverse(
4012 __isl_take isl_space *space);
4014 #include <isl/map.h>
4015 __isl_give isl_basic_map *isl_basic_map_reverse(
4016 __isl_take isl_basic_map *bmap);
4017 __isl_give isl_map *isl_map_reverse(
4018 __isl_take isl_map *map);
4020 #include <isl/union_map.h>
4021 __isl_give isl_union_map *isl_union_map_reverse(
4022 __isl_take isl_union_map *umap);
4026 #include <isl/space.h>
4027 __isl_give isl_space *isl_space_domain(
4028 __isl_take isl_space *space);
4029 __isl_give isl_space *isl_space_range(
4030 __isl_take isl_space *space);
4031 __isl_give isl_space *isl_space_params(
4032 __isl_take isl_space *space);
4034 #include <isl/local_space.h>
4035 __isl_give isl_local_space *isl_local_space_domain(
4036 __isl_take isl_local_space *ls);
4037 __isl_give isl_local_space *isl_local_space_range(
4038 __isl_take isl_local_space *ls);
4040 #include <isl/set.h>
4041 __isl_give isl_basic_set *isl_basic_set_project_out(
4042 __isl_take isl_basic_set *bset,
4043 enum isl_dim_type type, unsigned first, unsigned n);
4044 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
4045 enum isl_dim_type type, unsigned first, unsigned n);
4046 __isl_give isl_basic_set *isl_basic_set_params(
4047 __isl_take isl_basic_set *bset);
4048 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
4050 #include <isl/map.h>
4051 __isl_give isl_basic_map *isl_basic_map_project_out(
4052 __isl_take isl_basic_map *bmap,
4053 enum isl_dim_type type, unsigned first, unsigned n);
4054 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
4055 enum isl_dim_type type, unsigned first, unsigned n);
4056 __isl_give isl_basic_set *isl_basic_map_domain(
4057 __isl_take isl_basic_map *bmap);
4058 __isl_give isl_basic_set *isl_basic_map_range(
4059 __isl_take isl_basic_map *bmap);
4060 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
4061 __isl_give isl_set *isl_map_domain(
4062 __isl_take isl_map *bmap);
4063 __isl_give isl_set *isl_map_range(
4064 __isl_take isl_map *map);
4066 #include <isl/union_set.h>
4067 __isl_give isl_union_set *isl_union_set_project_out(
4068 __isl_take isl_union_set *uset,
4069 enum isl_dim_type type,
4070 unsigned first, unsigned n);
4071 __isl_give isl_set *isl_union_set_params(
4072 __isl_take isl_union_set *uset);
4074 The function C<isl_union_set_project_out> can only project out
4077 #include <isl/union_map.h>
4078 __isl_give isl_union_map *isl_union_map_project_out(
4079 __isl_take isl_union_map *umap,
4080 enum isl_dim_type type, unsigned first, unsigned n);
4081 __isl_give isl_set *isl_union_map_params(
4082 __isl_take isl_union_map *umap);
4083 __isl_give isl_union_set *isl_union_map_domain(
4084 __isl_take isl_union_map *umap);
4085 __isl_give isl_union_set *isl_union_map_range(
4086 __isl_take isl_union_map *umap);
4088 The function C<isl_union_map_project_out> can only project out
4091 #include <isl/aff.h>
4092 __isl_give isl_aff *isl_aff_project_domain_on_params(
4093 __isl_take isl_aff *aff);
4094 __isl_give isl_pw_multi_aff *
4095 isl_pw_multi_aff_project_domain_on_params(
4096 __isl_take isl_pw_multi_aff *pma);
4097 __isl_give isl_set *isl_pw_aff_domain(
4098 __isl_take isl_pw_aff *pwaff);
4099 __isl_give isl_set *isl_pw_multi_aff_domain(
4100 __isl_take isl_pw_multi_aff *pma);
4101 __isl_give isl_set *isl_multi_pw_aff_domain(
4102 __isl_take isl_multi_pw_aff *mpa);
4103 __isl_give isl_union_set *isl_union_pw_aff_domain(
4104 __isl_take isl_union_pw_aff *upa);
4105 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
4106 __isl_take isl_union_pw_multi_aff *upma);
4107 __isl_give isl_union_set *
4108 isl_multi_union_pw_aff_domain(
4109 __isl_take isl_multi_union_pw_aff *mupa);
4110 __isl_give isl_set *isl_pw_aff_params(
4111 __isl_take isl_pw_aff *pwa);
4113 The function C<isl_multi_union_pw_aff_domain> requires its
4114 input to have at least one set dimension.
4116 #include <isl/polynomial.h>
4117 __isl_give isl_qpolynomial *
4118 isl_qpolynomial_project_domain_on_params(
4119 __isl_take isl_qpolynomial *qp);
4120 __isl_give isl_pw_qpolynomial *
4121 isl_pw_qpolynomial_project_domain_on_params(
4122 __isl_take isl_pw_qpolynomial *pwqp);
4123 __isl_give isl_pw_qpolynomial_fold *
4124 isl_pw_qpolynomial_fold_project_domain_on_params(
4125 __isl_take isl_pw_qpolynomial_fold *pwf);
4126 __isl_give isl_set *isl_pw_qpolynomial_domain(
4127 __isl_take isl_pw_qpolynomial *pwqp);
4128 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4129 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4130 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4131 __isl_take isl_union_pw_qpolynomial *upwqp);
4133 #include <isl/space.h>
4134 __isl_give isl_space *isl_space_domain_map(
4135 __isl_take isl_space *space);
4136 __isl_give isl_space *isl_space_range_map(
4137 __isl_take isl_space *space);
4139 #include <isl/map.h>
4140 __isl_give isl_map *isl_set_wrapped_domain_map(
4141 __isl_take isl_set *set);
4142 __isl_give isl_basic_map *isl_basic_map_domain_map(
4143 __isl_take isl_basic_map *bmap);
4144 __isl_give isl_basic_map *isl_basic_map_range_map(
4145 __isl_take isl_basic_map *bmap);
4146 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
4147 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
4149 #include <isl/union_map.h>
4150 __isl_give isl_union_map *isl_union_map_domain_map(
4151 __isl_take isl_union_map *umap);
4152 __isl_give isl_union_pw_multi_aff *
4153 isl_union_map_domain_map_union_pw_multi_aff(
4154 __isl_take isl_union_map *umap);
4155 __isl_give isl_union_map *isl_union_map_range_map(
4156 __isl_take isl_union_map *umap);
4157 __isl_give isl_union_map *
4158 isl_union_set_wrapped_domain_map(
4159 __isl_take isl_union_set *uset);
4161 The functions above construct a (basic, regular or union) relation
4162 that maps (a wrapped version of) the input relation to its domain or range.
4163 C<isl_set_wrapped_domain_map> maps the input set to the domain
4164 of its wrapped relation.
4168 __isl_give isl_basic_set *isl_basic_set_eliminate(
4169 __isl_take isl_basic_set *bset,
4170 enum isl_dim_type type,
4171 unsigned first, unsigned n);
4172 __isl_give isl_set *isl_set_eliminate(
4173 __isl_take isl_set *set, enum isl_dim_type type,
4174 unsigned first, unsigned n);
4175 __isl_give isl_basic_map *isl_basic_map_eliminate(
4176 __isl_take isl_basic_map *bmap,
4177 enum isl_dim_type type,
4178 unsigned first, unsigned n);
4179 __isl_give isl_map *isl_map_eliminate(
4180 __isl_take isl_map *map, enum isl_dim_type type,
4181 unsigned first, unsigned n);
4183 Eliminate the coefficients for the given dimensions from the constraints,
4184 without removing the dimensions.
4186 =item * Constructing a set from a parameter domain
4188 A zero-dimensional space or (basic) set can be constructed
4189 on a given parameter domain using the following functions.
4191 #include <isl/space.h>
4192 __isl_give isl_space *isl_space_set_from_params(
4193 __isl_take isl_space *space);
4195 #include <isl/set.h>
4196 __isl_give isl_basic_set *isl_basic_set_from_params(
4197 __isl_take isl_basic_set *bset);
4198 __isl_give isl_set *isl_set_from_params(
4199 __isl_take isl_set *set);
4201 =item * Constructing a relation from a set
4203 Create a relation with the given set as domain or range.
4204 The range or domain of the created relation is a zero-dimensional
4205 flat anonymous space.
4207 #include <isl/space.h>
4208 __isl_give isl_space *isl_space_from_domain(
4209 __isl_take isl_space *space);
4210 __isl_give isl_space *isl_space_from_range(
4211 __isl_take isl_space *space);
4212 __isl_give isl_space *isl_space_map_from_set(
4213 __isl_take isl_space *space);
4214 __isl_give isl_space *isl_space_map_from_domain_and_range(
4215 __isl_take isl_space *domain,
4216 __isl_take isl_space *range);
4218 #include <isl/local_space.h>
4219 __isl_give isl_local_space *isl_local_space_from_domain(
4220 __isl_take isl_local_space *ls);
4222 #include <isl/map.h>
4223 __isl_give isl_map *isl_map_from_domain(
4224 __isl_take isl_set *set);
4225 __isl_give isl_map *isl_map_from_range(
4226 __isl_take isl_set *set);
4228 #include <isl/val.h>
4229 __isl_give isl_multi_val *isl_multi_val_from_range(
4230 __isl_take isl_multi_val *mv);
4232 #include <isl/aff.h>
4233 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4234 __isl_take isl_multi_aff *ma);
4235 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4236 __isl_take isl_pw_aff *pwa);
4237 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4238 __isl_take isl_multi_pw_aff *mpa);
4239 __isl_give isl_multi_union_pw_aff *
4240 isl_multi_union_pw_aff_from_range(
4241 __isl_take isl_multi_union_pw_aff *mupa);
4242 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4243 __isl_take isl_set *set);
4244 __isl_give isl_union_pw_multi_aff *
4245 isl_union_pw_multi_aff_from_domain(
4246 __isl_take isl_union_set *uset);
4250 #include <isl/set.h>
4251 __isl_give isl_basic_set *isl_basic_set_fix_si(
4252 __isl_take isl_basic_set *bset,
4253 enum isl_dim_type type, unsigned pos, int value);
4254 __isl_give isl_basic_set *isl_basic_set_fix_val(
4255 __isl_take isl_basic_set *bset,
4256 enum isl_dim_type type, unsigned pos,
4257 __isl_take isl_val *v);
4258 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4259 enum isl_dim_type type, unsigned pos, int value);
4260 __isl_give isl_set *isl_set_fix_val(
4261 __isl_take isl_set *set,
4262 enum isl_dim_type type, unsigned pos,
4263 __isl_take isl_val *v);
4265 #include <isl/map.h>
4266 __isl_give isl_basic_map *isl_basic_map_fix_si(
4267 __isl_take isl_basic_map *bmap,
4268 enum isl_dim_type type, unsigned pos, int value);
4269 __isl_give isl_basic_map *isl_basic_map_fix_val(
4270 __isl_take isl_basic_map *bmap,
4271 enum isl_dim_type type, unsigned pos,
4272 __isl_take isl_val *v);
4273 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4274 enum isl_dim_type type, unsigned pos, int value);
4275 __isl_give isl_map *isl_map_fix_val(
4276 __isl_take isl_map *map,
4277 enum isl_dim_type type, unsigned pos,
4278 __isl_take isl_val *v);
4280 #include <isl/aff.h>
4281 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4282 __isl_take isl_pw_multi_aff *pma,
4283 enum isl_dim_type type, unsigned pos, int value);
4285 #include <isl/polynomial.h>
4286 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4287 __isl_take isl_pw_qpolynomial *pwqp,
4288 enum isl_dim_type type, unsigned n,
4289 __isl_take isl_val *v);
4291 Intersect the set, relation or function domain
4292 with the hyperplane where the given
4293 dimension has the fixed given value.
4295 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4296 __isl_take isl_basic_map *bmap,
4297 enum isl_dim_type type, unsigned pos, int value);
4298 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4299 __isl_take isl_basic_map *bmap,
4300 enum isl_dim_type type, unsigned pos, int value);
4301 __isl_give isl_set *isl_set_lower_bound_si(
4302 __isl_take isl_set *set,
4303 enum isl_dim_type type, unsigned pos, int value);
4304 __isl_give isl_set *isl_set_lower_bound_val(
4305 __isl_take isl_set *set,
4306 enum isl_dim_type type, unsigned pos,
4307 __isl_take isl_val *value);
4308 __isl_give isl_map *isl_map_lower_bound_si(
4309 __isl_take isl_map *map,
4310 enum isl_dim_type type, unsigned pos, int value);
4311 __isl_give isl_set *isl_set_upper_bound_si(
4312 __isl_take isl_set *set,
4313 enum isl_dim_type type, unsigned pos, int value);
4314 __isl_give isl_set *isl_set_upper_bound_val(
4315 __isl_take isl_set *set,
4316 enum isl_dim_type type, unsigned pos,
4317 __isl_take isl_val *value);
4318 __isl_give isl_map *isl_map_upper_bound_si(
4319 __isl_take isl_map *map,
4320 enum isl_dim_type type, unsigned pos, int value);
4322 Intersect the set or relation with the half-space where the given
4323 dimension has a value bounded by the fixed given integer value.
4325 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4326 enum isl_dim_type type1, int pos1,
4327 enum isl_dim_type type2, int pos2);
4328 __isl_give isl_basic_map *isl_basic_map_equate(
4329 __isl_take isl_basic_map *bmap,
4330 enum isl_dim_type type1, int pos1,
4331 enum isl_dim_type type2, int pos2);
4332 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4333 enum isl_dim_type type1, int pos1,
4334 enum isl_dim_type type2, int pos2);
4336 Intersect the set or relation with the hyperplane where the given
4337 dimensions are equal to each other.
4339 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4340 enum isl_dim_type type1, int pos1,
4341 enum isl_dim_type type2, int pos2);
4343 Intersect the relation with the hyperplane where the given
4344 dimensions have opposite values.
4346 __isl_give isl_map *isl_map_order_le(
4347 __isl_take isl_map *map,
4348 enum isl_dim_type type1, int pos1,
4349 enum isl_dim_type type2, int pos2);
4350 __isl_give isl_basic_map *isl_basic_map_order_ge(
4351 __isl_take isl_basic_map *bmap,
4352 enum isl_dim_type type1, int pos1,
4353 enum isl_dim_type type2, int pos2);
4354 __isl_give isl_map *isl_map_order_ge(
4355 __isl_take isl_map *map,
4356 enum isl_dim_type type1, int pos1,
4357 enum isl_dim_type type2, int pos2);
4358 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4359 enum isl_dim_type type1, int pos1,
4360 enum isl_dim_type type2, int pos2);
4361 __isl_give isl_basic_map *isl_basic_map_order_gt(
4362 __isl_take isl_basic_map *bmap,
4363 enum isl_dim_type type1, int pos1,
4364 enum isl_dim_type type2, int pos2);
4365 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4366 enum isl_dim_type type1, int pos1,
4367 enum isl_dim_type type2, int pos2);
4369 Intersect the relation with the half-space where the given
4370 dimensions satisfy the given ordering.
4374 #include <isl/aff.h>
4375 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4376 __isl_take isl_aff *aff);
4377 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4378 __isl_take isl_aff *aff);
4379 __isl_give isl_set *isl_pw_aff_pos_set(
4380 __isl_take isl_pw_aff *pa);
4381 __isl_give isl_set *isl_pw_aff_nonneg_set(
4382 __isl_take isl_pw_aff *pwaff);
4383 __isl_give isl_set *isl_pw_aff_zero_set(
4384 __isl_take isl_pw_aff *pwaff);
4385 __isl_give isl_set *isl_pw_aff_non_zero_set(
4386 __isl_take isl_pw_aff *pwaff);
4387 __isl_give isl_union_set *
4388 isl_union_pw_aff_zero_union_set(
4389 __isl_take isl_union_pw_aff *upa);
4390 __isl_give isl_union_set *
4391 isl_multi_union_pw_aff_zero_union_set(
4392 __isl_take isl_multi_union_pw_aff *mupa);
4394 The function C<isl_aff_neg_basic_set> returns a basic set
4395 containing those elements in the domain space
4396 of C<aff> where C<aff> is negative.
4397 The function C<isl_pw_aff_nonneg_set> returns a set
4398 containing those elements in the domain
4399 of C<pwaff> where C<pwaff> is non-negative.
4400 The function C<isl_multi_union_pw_aff_zero_union_set>
4401 returns a union set containing those elements
4402 in the domains of its elements where they are all zero.
4406 __isl_give isl_map *isl_set_identity(
4407 __isl_take isl_set *set);
4408 __isl_give isl_union_map *isl_union_set_identity(
4409 __isl_take isl_union_set *uset);
4410 __isl_give isl_union_pw_multi_aff *
4411 isl_union_set_identity_union_pw_multi_aff(
4412 __isl_take isl_union_set *uset);
4414 Construct an identity relation on the given (union) set.
4416 =item * Function Extraction
4418 A piecewise quasi affine expression that is equal to 1 on a set
4419 and 0 outside the set can be created using the following function.
4421 #include <isl/aff.h>
4422 __isl_give isl_pw_aff *isl_set_indicator_function(
4423 __isl_take isl_set *set);
4425 A piecewise multiple quasi affine expression can be extracted
4426 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4427 and the C<isl_map> is single-valued.
4428 In case of a conversion from an C<isl_union_map>
4429 to an C<isl_union_pw_multi_aff>, these properties need to hold
4430 in each domain space.
4431 A conversion to a C<isl_multi_union_pw_aff> additionally
4432 requires that the input is non-empty and involves only a single
4435 #include <isl/aff.h>
4436 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4437 __isl_take isl_set *set);
4438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4439 __isl_take isl_map *map);
4441 __isl_give isl_union_pw_multi_aff *
4442 isl_union_pw_multi_aff_from_union_set(
4443 __isl_take isl_union_set *uset);
4444 __isl_give isl_union_pw_multi_aff *
4445 isl_union_pw_multi_aff_from_union_map(
4446 __isl_take isl_union_map *umap);
4448 __isl_give isl_multi_union_pw_aff *
4449 isl_multi_union_pw_aff_from_union_map(
4450 __isl_take isl_union_map *umap);
4454 __isl_give isl_basic_set *isl_basic_map_deltas(
4455 __isl_take isl_basic_map *bmap);
4456 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4457 __isl_give isl_union_set *isl_union_map_deltas(
4458 __isl_take isl_union_map *umap);
4460 These functions return a (basic) set containing the differences
4461 between image elements and corresponding domain elements in the input.
4463 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4464 __isl_take isl_basic_map *bmap);
4465 __isl_give isl_map *isl_map_deltas_map(
4466 __isl_take isl_map *map);
4467 __isl_give isl_union_map *isl_union_map_deltas_map(
4468 __isl_take isl_union_map *umap);
4470 The functions above construct a (basic, regular or union) relation
4471 that maps (a wrapped version of) the input relation to its delta set.
4475 Simplify the representation of a set, relation or functions by trying
4476 to combine pairs of basic sets or relations into a single
4477 basic set or relation.
4479 #include <isl/set.h>
4480 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4482 #include <isl/map.h>
4483 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4485 #include <isl/union_set.h>
4486 __isl_give isl_union_set *isl_union_set_coalesce(
4487 __isl_take isl_union_set *uset);
4489 #include <isl/union_map.h>
4490 __isl_give isl_union_map *isl_union_map_coalesce(
4491 __isl_take isl_union_map *umap);
4493 #include <isl/aff.h>
4494 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4495 __isl_take isl_pw_aff *pwqp);
4496 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4497 __isl_take isl_pw_multi_aff *pma);
4498 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4499 __isl_take isl_multi_pw_aff *mpa);
4500 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4501 __isl_take isl_union_pw_aff *upa);
4502 __isl_give isl_union_pw_multi_aff *
4503 isl_union_pw_multi_aff_coalesce(
4504 __isl_take isl_union_pw_multi_aff *upma);
4506 #include <isl/polynomial.h>
4507 __isl_give isl_pw_qpolynomial_fold *
4508 isl_pw_qpolynomial_fold_coalesce(
4509 __isl_take isl_pw_qpolynomial_fold *pwf);
4510 __isl_give isl_union_pw_qpolynomial *
4511 isl_union_pw_qpolynomial_coalesce(
4512 __isl_take isl_union_pw_qpolynomial *upwqp);
4513 __isl_give isl_union_pw_qpolynomial_fold *
4514 isl_union_pw_qpolynomial_fold_coalesce(
4515 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4517 One of the methods for combining pairs of basic sets or relations
4518 can result in coefficients that are much larger than those that appear
4519 in the constraints of the input. By default, the coefficients are
4520 not allowed to grow larger, but this can be changed by unsetting
4521 the following option.
4523 int isl_options_set_coalesce_bounded_wrapping(
4524 isl_ctx *ctx, int val);
4525 int isl_options_get_coalesce_bounded_wrapping(
4528 =item * Detecting equalities
4530 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4531 __isl_take isl_basic_set *bset);
4532 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4533 __isl_take isl_basic_map *bmap);
4534 __isl_give isl_set *isl_set_detect_equalities(
4535 __isl_take isl_set *set);
4536 __isl_give isl_map *isl_map_detect_equalities(
4537 __isl_take isl_map *map);
4538 __isl_give isl_union_set *isl_union_set_detect_equalities(
4539 __isl_take isl_union_set *uset);
4540 __isl_give isl_union_map *isl_union_map_detect_equalities(
4541 __isl_take isl_union_map *umap);
4543 Simplify the representation of a set or relation by detecting implicit
4546 =item * Removing redundant constraints
4548 #include <isl/set.h>
4549 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4550 __isl_take isl_basic_set *bset);
4551 __isl_give isl_set *isl_set_remove_redundancies(
4552 __isl_take isl_set *set);
4554 #include <isl/union_set.h>
4555 __isl_give isl_union_set *
4556 isl_union_set_remove_redundancies(
4557 __isl_take isl_union_set *uset);
4559 #include <isl/map.h>
4560 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4561 __isl_take isl_basic_map *bmap);
4562 __isl_give isl_map *isl_map_remove_redundancies(
4563 __isl_take isl_map *map);
4565 #include <isl/union_map.h>
4566 __isl_give isl_union_map *
4567 isl_union_map_remove_redundancies(
4568 __isl_take isl_union_map *umap);
4572 __isl_give isl_basic_set *isl_set_convex_hull(
4573 __isl_take isl_set *set);
4574 __isl_give isl_basic_map *isl_map_convex_hull(
4575 __isl_take isl_map *map);
4577 If the input set or relation has any existentially quantified
4578 variables, then the result of these operations is currently undefined.
4582 #include <isl/set.h>
4583 __isl_give isl_basic_set *
4584 isl_set_unshifted_simple_hull(
4585 __isl_take isl_set *set);
4586 __isl_give isl_basic_set *isl_set_simple_hull(
4587 __isl_take isl_set *set);
4588 __isl_give isl_basic_set *
4589 isl_set_unshifted_simple_hull_from_set_list(
4590 __isl_take isl_set *set,
4591 __isl_take isl_set_list *list);
4593 #include <isl/map.h>
4594 __isl_give isl_basic_map *
4595 isl_map_unshifted_simple_hull(
4596 __isl_take isl_map *map);
4597 __isl_give isl_basic_map *isl_map_simple_hull(
4598 __isl_take isl_map *map);
4599 __isl_give isl_basic_map *
4600 isl_map_unshifted_simple_hull_from_map_list(
4601 __isl_take isl_map *map,
4602 __isl_take isl_map_list *list);
4604 #include <isl/union_map.h>
4605 __isl_give isl_union_map *isl_union_map_simple_hull(
4606 __isl_take isl_union_map *umap);
4608 These functions compute a single basic set or relation
4609 that contains the whole input set or relation.
4610 In particular, the output is described by translates
4611 of the constraints describing the basic sets or relations in the input.
4612 In case of C<isl_set_unshifted_simple_hull>, only the original
4613 constraints are used, without any translation.
4614 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4615 C<isl_map_unshifted_simple_hull_from_map_list>, the
4616 constraints are taken from the elements of the second argument.
4620 (See \autoref{s:simple hull}.)
4626 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4627 __isl_take isl_basic_set *bset);
4628 __isl_give isl_basic_set *isl_set_affine_hull(
4629 __isl_take isl_set *set);
4630 __isl_give isl_union_set *isl_union_set_affine_hull(
4631 __isl_take isl_union_set *uset);
4632 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4633 __isl_take isl_basic_map *bmap);
4634 __isl_give isl_basic_map *isl_map_affine_hull(
4635 __isl_take isl_map *map);
4636 __isl_give isl_union_map *isl_union_map_affine_hull(
4637 __isl_take isl_union_map *umap);
4639 In case of union sets and relations, the affine hull is computed
4642 =item * Polyhedral hull
4644 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4645 __isl_take isl_set *set);
4646 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4647 __isl_take isl_map *map);
4648 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4649 __isl_take isl_union_set *uset);
4650 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4651 __isl_take isl_union_map *umap);
4653 These functions compute a single basic set or relation
4654 not involving any existentially quantified variables
4655 that contains the whole input set or relation.
4656 In case of union sets and relations, the polyhedral hull is computed
4659 =item * Other approximations
4661 #include <isl/set.h>
4662 __isl_give isl_basic_set *
4663 isl_basic_set_drop_constraints_involving_dims(
4664 __isl_take isl_basic_set *bset,
4665 enum isl_dim_type type,
4666 unsigned first, unsigned n);
4667 __isl_give isl_basic_set *
4668 isl_basic_set_drop_constraints_not_involving_dims(
4669 __isl_take isl_basic_set *bset,
4670 enum isl_dim_type type,
4671 unsigned first, unsigned n);
4672 __isl_give isl_set *
4673 isl_set_drop_constraints_involving_dims(
4674 __isl_take isl_set *set,
4675 enum isl_dim_type type,
4676 unsigned first, unsigned n);
4678 #include <isl/map.h>
4679 __isl_give isl_basic_map *
4680 isl_basic_map_drop_constraints_involving_dims(
4681 __isl_take isl_basic_map *bmap,
4682 enum isl_dim_type type,
4683 unsigned first, unsigned n);
4684 __isl_give isl_map *
4685 isl_map_drop_constraints_involving_dims(
4686 __isl_take isl_map *map,
4687 enum isl_dim_type type,
4688 unsigned first, unsigned n);
4690 These functions drop any constraints (not) involving the specified dimensions.
4691 Note that the result depends on the representation of the input.
4693 #include <isl/polynomial.h>
4694 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4695 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4696 __isl_give isl_union_pw_qpolynomial *
4697 isl_union_pw_qpolynomial_to_polynomial(
4698 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4700 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4701 the polynomial will be an overapproximation. If C<sign> is negative,
4702 it will be an underapproximation. If C<sign> is zero, the approximation
4703 will lie somewhere in between.
4707 __isl_give isl_basic_set *isl_basic_set_sample(
4708 __isl_take isl_basic_set *bset);
4709 __isl_give isl_basic_set *isl_set_sample(
4710 __isl_take isl_set *set);
4711 __isl_give isl_basic_map *isl_basic_map_sample(
4712 __isl_take isl_basic_map *bmap);
4713 __isl_give isl_basic_map *isl_map_sample(
4714 __isl_take isl_map *map);
4716 If the input (basic) set or relation is non-empty, then return
4717 a singleton subset of the input. Otherwise, return an empty set.
4719 =item * Optimization
4721 #include <isl/ilp.h>
4722 __isl_give isl_val *isl_basic_set_max_val(
4723 __isl_keep isl_basic_set *bset,
4724 __isl_keep isl_aff *obj);
4725 __isl_give isl_val *isl_set_min_val(
4726 __isl_keep isl_set *set,
4727 __isl_keep isl_aff *obj);
4728 __isl_give isl_val *isl_set_max_val(
4729 __isl_keep isl_set *set,
4730 __isl_keep isl_aff *obj);
4732 Compute the minimum or maximum of the integer affine expression C<obj>
4733 over the points in C<set>, returning the result in C<opt>.
4734 The result is C<NULL> in case of an error, the optimal value in case
4735 there is one, negative infinity or infinity if the problem is unbounded and
4736 NaN if the problem is empty.
4738 =item * Parametric optimization
4740 __isl_give isl_pw_aff *isl_set_dim_min(
4741 __isl_take isl_set *set, int pos);
4742 __isl_give isl_pw_aff *isl_set_dim_max(
4743 __isl_take isl_set *set, int pos);
4744 __isl_give isl_pw_aff *isl_map_dim_max(
4745 __isl_take isl_map *map, int pos);
4747 Compute the minimum or maximum of the given set or output dimension
4748 as a function of the parameters (and input dimensions), but independently
4749 of the other set or output dimensions.
4750 For lexicographic optimization, see L<"Lexicographic Optimization">.
4754 The following functions compute either the set of (rational) coefficient
4755 values of valid constraints for the given set or the set of (rational)
4756 values satisfying the constraints with coefficients from the given set.
4757 Internally, these two sets of functions perform essentially the
4758 same operations, except that the set of coefficients is assumed to
4759 be a cone, while the set of values may be any polyhedron.
4760 The current implementation is based on the Farkas lemma and
4761 Fourier-Motzkin elimination, but this may change or be made optional
4762 in future. In particular, future implementations may use different
4763 dualization algorithms or skip the elimination step.
4765 __isl_give isl_basic_set *isl_basic_set_coefficients(
4766 __isl_take isl_basic_set *bset);
4767 __isl_give isl_basic_set *isl_set_coefficients(
4768 __isl_take isl_set *set);
4769 __isl_give isl_union_set *isl_union_set_coefficients(
4770 __isl_take isl_union_set *bset);
4771 __isl_give isl_basic_set *isl_basic_set_solutions(
4772 __isl_take isl_basic_set *bset);
4773 __isl_give isl_basic_set *isl_set_solutions(
4774 __isl_take isl_set *set);
4775 __isl_give isl_union_set *isl_union_set_solutions(
4776 __isl_take isl_union_set *bset);
4780 __isl_give isl_map *isl_map_fixed_power_val(
4781 __isl_take isl_map *map,
4782 __isl_take isl_val *exp);
4783 __isl_give isl_union_map *
4784 isl_union_map_fixed_power_val(
4785 __isl_take isl_union_map *umap,
4786 __isl_take isl_val *exp);
4788 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4789 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4790 of C<map> is computed.
4792 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4794 __isl_give isl_union_map *isl_union_map_power(
4795 __isl_take isl_union_map *umap, int *exact);
4797 Compute a parametric representation for all positive powers I<k> of C<map>.
4798 The result maps I<k> to a nested relation corresponding to the
4799 I<k>th power of C<map>.
4800 The result may be an overapproximation. If the result is known to be exact,
4801 then C<*exact> is set to C<1>.
4803 =item * Transitive closure
4805 __isl_give isl_map *isl_map_transitive_closure(
4806 __isl_take isl_map *map, int *exact);
4807 __isl_give isl_union_map *isl_union_map_transitive_closure(
4808 __isl_take isl_union_map *umap, int *exact);
4810 Compute the transitive closure of C<map>.
4811 The result may be an overapproximation. If the result is known to be exact,
4812 then C<*exact> is set to C<1>.
4814 =item * Reaching path lengths
4816 __isl_give isl_map *isl_map_reaching_path_lengths(
4817 __isl_take isl_map *map, int *exact);
4819 Compute a relation that maps each element in the range of C<map>
4820 to the lengths of all paths composed of edges in C<map> that
4821 end up in the given element.
4822 The result may be an overapproximation. If the result is known to be exact,
4823 then C<*exact> is set to C<1>.
4824 To compute the I<maximal> path length, the resulting relation
4825 should be postprocessed by C<isl_map_lexmax>.
4826 In particular, if the input relation is a dependence relation
4827 (mapping sources to sinks), then the maximal path length corresponds
4828 to the free schedule.
4829 Note, however, that C<isl_map_lexmax> expects the maximum to be
4830 finite, so if the path lengths are unbounded (possibly due to
4831 the overapproximation), then you will get an error message.
4835 #include <isl/space.h>
4836 __isl_give isl_space *isl_space_wrap(
4837 __isl_take isl_space *space);
4838 __isl_give isl_space *isl_space_unwrap(
4839 __isl_take isl_space *space);
4841 #include <isl/local_space.h>
4842 __isl_give isl_local_space *isl_local_space_wrap(
4843 __isl_take isl_local_space *ls);
4845 #include <isl/set.h>
4846 __isl_give isl_basic_map *isl_basic_set_unwrap(
4847 __isl_take isl_basic_set *bset);
4848 __isl_give isl_map *isl_set_unwrap(
4849 __isl_take isl_set *set);
4851 #include <isl/map.h>
4852 __isl_give isl_basic_set *isl_basic_map_wrap(
4853 __isl_take isl_basic_map *bmap);
4854 __isl_give isl_set *isl_map_wrap(
4855 __isl_take isl_map *map);
4857 #include <isl/union_set.h>
4858 __isl_give isl_union_map *isl_union_set_unwrap(
4859 __isl_take isl_union_set *uset);
4861 #include <isl/union_map.h>
4862 __isl_give isl_union_set *isl_union_map_wrap(
4863 __isl_take isl_union_map *umap);
4865 The input to C<isl_space_unwrap> should
4866 be the space of a set, while that of
4867 C<isl_space_wrap> should be the space of a relation.
4868 Conversely, the output of C<isl_space_unwrap> is the space
4869 of a relation, while that of C<isl_space_wrap> is the space of a set.
4873 Remove any internal structure of domain (and range) of the given
4874 set or relation. If there is any such internal structure in the input,
4875 then the name of the space is also removed.
4877 #include <isl/local_space.h>
4878 __isl_give isl_local_space *
4879 isl_local_space_flatten_domain(
4880 __isl_take isl_local_space *ls);
4881 __isl_give isl_local_space *
4882 isl_local_space_flatten_range(
4883 __isl_take isl_local_space *ls);
4885 #include <isl/set.h>
4886 __isl_give isl_basic_set *isl_basic_set_flatten(
4887 __isl_take isl_basic_set *bset);
4888 __isl_give isl_set *isl_set_flatten(
4889 __isl_take isl_set *set);
4891 #include <isl/map.h>
4892 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4893 __isl_take isl_basic_map *bmap);
4894 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4895 __isl_take isl_basic_map *bmap);
4896 __isl_give isl_map *isl_map_flatten_range(
4897 __isl_take isl_map *map);
4898 __isl_give isl_map *isl_map_flatten_domain(
4899 __isl_take isl_map *map);
4900 __isl_give isl_basic_map *isl_basic_map_flatten(
4901 __isl_take isl_basic_map *bmap);
4902 __isl_give isl_map *isl_map_flatten(
4903 __isl_take isl_map *map);
4905 #include <isl/val.h>
4906 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4907 __isl_take isl_multi_val *mv);
4909 #include <isl/aff.h>
4910 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4911 __isl_take isl_multi_aff *ma);
4912 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4913 __isl_take isl_multi_aff *ma);
4914 __isl_give isl_multi_pw_aff *
4915 isl_multi_pw_aff_flatten_range(
4916 __isl_take isl_multi_pw_aff *mpa);
4917 __isl_give isl_multi_union_pw_aff *
4918 isl_multi_union_pw_aff_flatten_range(
4919 __isl_take isl_multi_union_pw_aff *mupa);
4921 #include <isl/map.h>
4922 __isl_give isl_map *isl_set_flatten_map(
4923 __isl_take isl_set *set);
4925 The function above constructs a relation
4926 that maps the input set to a flattened version of the set.
4930 Lift the input set to a space with extra dimensions corresponding
4931 to the existentially quantified variables in the input.
4932 In particular, the result lives in a wrapped map where the domain
4933 is the original space and the range corresponds to the original
4934 existentially quantified variables.
4936 #include <isl/set.h>
4937 __isl_give isl_basic_set *isl_basic_set_lift(
4938 __isl_take isl_basic_set *bset);
4939 __isl_give isl_set *isl_set_lift(
4940 __isl_take isl_set *set);
4941 __isl_give isl_union_set *isl_union_set_lift(
4942 __isl_take isl_union_set *uset);
4944 Given a local space that contains the existentially quantified
4945 variables of a set, a basic relation that, when applied to
4946 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4947 can be constructed using the following function.
4949 #include <isl/local_space.h>
4950 __isl_give isl_basic_map *isl_local_space_lifting(
4951 __isl_take isl_local_space *ls);
4953 #include <isl/aff.h>
4954 __isl_give isl_multi_aff *isl_multi_aff_lift(
4955 __isl_take isl_multi_aff *maff,
4956 __isl_give isl_local_space **ls);
4958 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4959 then it is assigned the local space that lies at the basis of
4960 the lifting applied.
4962 =item * Internal Product
4964 #include <isl/space.h>
4965 __isl_give isl_space *isl_space_zip(
4966 __isl_take isl_space *space);
4968 #include <isl/map.h>
4969 __isl_give isl_basic_map *isl_basic_map_zip(
4970 __isl_take isl_basic_map *bmap);
4971 __isl_give isl_map *isl_map_zip(
4972 __isl_take isl_map *map);
4974 #include <isl/union_map.h>
4975 __isl_give isl_union_map *isl_union_map_zip(
4976 __isl_take isl_union_map *umap);
4978 Given a relation with nested relations for domain and range,
4979 interchange the range of the domain with the domain of the range.
4983 #include <isl/space.h>
4984 __isl_give isl_space *isl_space_curry(
4985 __isl_take isl_space *space);
4986 __isl_give isl_space *isl_space_uncurry(
4987 __isl_take isl_space *space);
4989 #include <isl/map.h>
4990 __isl_give isl_basic_map *isl_basic_map_curry(
4991 __isl_take isl_basic_map *bmap);
4992 __isl_give isl_basic_map *isl_basic_map_uncurry(
4993 __isl_take isl_basic_map *bmap);
4994 __isl_give isl_map *isl_map_curry(
4995 __isl_take isl_map *map);
4996 __isl_give isl_map *isl_map_uncurry(
4997 __isl_take isl_map *map);
4999 #include <isl/union_map.h>
5000 __isl_give isl_union_map *isl_union_map_curry(
5001 __isl_take isl_union_map *umap);
5002 __isl_give isl_union_map *isl_union_map_uncurry(
5003 __isl_take isl_union_map *umap);
5005 Given a relation with a nested relation for domain,
5006 the C<curry> functions
5007 move the range of the nested relation out of the domain
5008 and use it as the domain of a nested relation in the range,
5009 with the original range as range of this nested relation.
5010 The C<uncurry> functions perform the inverse operation.
5012 =item * Aligning parameters
5014 Change the order of the parameters of the given set, relation
5016 such that the first parameters match those of C<model>.
5017 This may involve the introduction of extra parameters.
5018 All parameters need to be named.
5020 #include <isl/space.h>
5021 __isl_give isl_space *isl_space_align_params(
5022 __isl_take isl_space *space1,
5023 __isl_take isl_space *space2)
5025 #include <isl/set.h>
5026 __isl_give isl_basic_set *isl_basic_set_align_params(
5027 __isl_take isl_basic_set *bset,
5028 __isl_take isl_space *model);
5029 __isl_give isl_set *isl_set_align_params(
5030 __isl_take isl_set *set,
5031 __isl_take isl_space *model);
5033 #include <isl/map.h>
5034 __isl_give isl_basic_map *isl_basic_map_align_params(
5035 __isl_take isl_basic_map *bmap,
5036 __isl_take isl_space *model);
5037 __isl_give isl_map *isl_map_align_params(
5038 __isl_take isl_map *map,
5039 __isl_take isl_space *model);
5041 #include <isl/val.h>
5042 __isl_give isl_multi_val *isl_multi_val_align_params(
5043 __isl_take isl_multi_val *mv,
5044 __isl_take isl_space *model);
5046 #include <isl/aff.h>
5047 __isl_give isl_aff *isl_aff_align_params(
5048 __isl_take isl_aff *aff,
5049 __isl_take isl_space *model);
5050 __isl_give isl_multi_aff *isl_multi_aff_align_params(
5051 __isl_take isl_multi_aff *multi,
5052 __isl_take isl_space *model);
5053 __isl_give isl_pw_aff *isl_pw_aff_align_params(
5054 __isl_take isl_pw_aff *pwaff,
5055 __isl_take isl_space *model);
5056 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
5057 __isl_take isl_pw_multi_aff *pma,
5058 __isl_take isl_space *model);
5059 __isl_give isl_union_pw_aff *
5060 isl_union_pw_aff_align_params(
5061 __isl_take isl_union_pw_aff *upa,
5062 __isl_take isl_space *model);
5063 __isl_give isl_union_pw_multi_aff *
5064 isl_union_pw_multi_aff_align_params(
5065 __isl_take isl_union_pw_multi_aff *upma,
5066 __isl_take isl_space *model);
5067 __isl_give isl_multi_union_pw_aff *
5068 isl_multi_union_pw_aff_align_params(
5069 __isl_take isl_multi_union_pw_aff *mupa,
5070 __isl_take isl_space *model);
5072 #include <isl/polynomial.h>
5073 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
5074 __isl_take isl_qpolynomial *qp,
5075 __isl_take isl_space *model);
5077 =item * Unary Arithmethic Operations
5079 #include <isl/val.h>
5080 __isl_give isl_multi_val *isl_multi_val_neg(
5081 __isl_take isl_multi_val *mv);
5083 #include <isl/aff.h>
5084 __isl_give isl_aff *isl_aff_neg(
5085 __isl_take isl_aff *aff);
5086 __isl_give isl_multi_aff *isl_multi_aff_neg(
5087 __isl_take isl_multi_aff *ma);
5088 __isl_give isl_pw_aff *isl_pw_aff_neg(
5089 __isl_take isl_pw_aff *pwaff);
5090 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
5091 __isl_take isl_pw_multi_aff *pma);
5092 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
5093 __isl_take isl_multi_pw_aff *mpa);
5094 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
5095 __isl_take isl_union_pw_aff *upa);
5096 __isl_give isl_union_pw_multi_aff *
5097 isl_union_pw_multi_aff_neg(
5098 __isl_take isl_union_pw_multi_aff *upma);
5099 __isl_give isl_multi_union_pw_aff *
5100 isl_multi_union_pw_aff_neg(
5101 __isl_take isl_multi_union_pw_aff *mupa);
5102 __isl_give isl_aff *isl_aff_ceil(
5103 __isl_take isl_aff *aff);
5104 __isl_give isl_pw_aff *isl_pw_aff_ceil(
5105 __isl_take isl_pw_aff *pwaff);
5106 __isl_give isl_aff *isl_aff_floor(
5107 __isl_take isl_aff *aff);
5108 __isl_give isl_multi_aff *isl_multi_aff_floor(
5109 __isl_take isl_multi_aff *ma);
5110 __isl_give isl_pw_aff *isl_pw_aff_floor(
5111 __isl_take isl_pw_aff *pwaff);
5112 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
5113 __isl_take isl_union_pw_aff *upa);
5114 __isl_give isl_multi_union_pw_aff *
5115 isl_multi_union_pw_aff_floor(
5116 __isl_take isl_multi_union_pw_aff *mupa);
5118 #include <isl/aff.h>
5119 __isl_give isl_pw_aff *isl_pw_aff_list_min(
5120 __isl_take isl_pw_aff_list *list);
5121 __isl_give isl_pw_aff *isl_pw_aff_list_max(
5122 __isl_take isl_pw_aff_list *list);
5124 #include <isl/polynomial.h>
5125 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
5126 __isl_take isl_qpolynomial *qp);
5127 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
5128 __isl_take isl_pw_qpolynomial *pwqp);
5129 __isl_give isl_union_pw_qpolynomial *
5130 isl_union_pw_qpolynomial_neg(
5131 __isl_take isl_union_pw_qpolynomial *upwqp);
5132 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
5133 __isl_take isl_qpolynomial *qp,
5135 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
5136 __isl_take isl_pw_qpolynomial *pwqp,
5141 The following functions evaluate a function in a point.
5143 #include <isl/polynomial.h>
5144 __isl_give isl_val *isl_pw_qpolynomial_eval(
5145 __isl_take isl_pw_qpolynomial *pwqp,
5146 __isl_take isl_point *pnt);
5147 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
5148 __isl_take isl_pw_qpolynomial_fold *pwf,
5149 __isl_take isl_point *pnt);
5150 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
5151 __isl_take isl_union_pw_qpolynomial *upwqp,
5152 __isl_take isl_point *pnt);
5153 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
5154 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5155 __isl_take isl_point *pnt);
5157 =item * Dimension manipulation
5159 It is usually not advisable to directly change the (input or output)
5160 space of a set or a relation as this removes the name and the internal
5161 structure of the space. However, the functions below can be useful
5162 to add new parameters, assuming
5163 C<isl_set_align_params> and C<isl_map_align_params>
5166 #include <isl/space.h>
5167 __isl_give isl_space *isl_space_add_dims(
5168 __isl_take isl_space *space,
5169 enum isl_dim_type type, unsigned n);
5170 __isl_give isl_space *isl_space_insert_dims(
5171 __isl_take isl_space *space,
5172 enum isl_dim_type type, unsigned pos, unsigned n);
5173 __isl_give isl_space *isl_space_drop_dims(
5174 __isl_take isl_space *space,
5175 enum isl_dim_type type, unsigned first, unsigned n);
5176 __isl_give isl_space *isl_space_move_dims(
5177 __isl_take isl_space *space,
5178 enum isl_dim_type dst_type, unsigned dst_pos,
5179 enum isl_dim_type src_type, unsigned src_pos,
5182 #include <isl/local_space.h>
5183 __isl_give isl_local_space *isl_local_space_add_dims(
5184 __isl_take isl_local_space *ls,
5185 enum isl_dim_type type, unsigned n);
5186 __isl_give isl_local_space *isl_local_space_insert_dims(
5187 __isl_take isl_local_space *ls,
5188 enum isl_dim_type type, unsigned first, unsigned n);
5189 __isl_give isl_local_space *isl_local_space_drop_dims(
5190 __isl_take isl_local_space *ls,
5191 enum isl_dim_type type, unsigned first, unsigned n);
5193 #include <isl/set.h>
5194 __isl_give isl_basic_set *isl_basic_set_add_dims(
5195 __isl_take isl_basic_set *bset,
5196 enum isl_dim_type type, unsigned n);
5197 __isl_give isl_set *isl_set_add_dims(
5198 __isl_take isl_set *set,
5199 enum isl_dim_type type, unsigned n);
5200 __isl_give isl_basic_set *isl_basic_set_insert_dims(
5201 __isl_take isl_basic_set *bset,
5202 enum isl_dim_type type, unsigned pos,
5204 __isl_give isl_set *isl_set_insert_dims(
5205 __isl_take isl_set *set,
5206 enum isl_dim_type type, unsigned pos, unsigned n);
5207 __isl_give isl_basic_set *isl_basic_set_move_dims(
5208 __isl_take isl_basic_set *bset,
5209 enum isl_dim_type dst_type, unsigned dst_pos,
5210 enum isl_dim_type src_type, unsigned src_pos,
5212 __isl_give isl_set *isl_set_move_dims(
5213 __isl_take isl_set *set,
5214 enum isl_dim_type dst_type, unsigned dst_pos,
5215 enum isl_dim_type src_type, unsigned src_pos,
5218 #include <isl/map.h>
5219 __isl_give isl_map *isl_map_add_dims(
5220 __isl_take isl_map *map,
5221 enum isl_dim_type type, unsigned n);
5222 __isl_give isl_basic_map *isl_basic_map_insert_dims(
5223 __isl_take isl_basic_map *bmap,
5224 enum isl_dim_type type, unsigned pos,
5226 __isl_give isl_map *isl_map_insert_dims(
5227 __isl_take isl_map *map,
5228 enum isl_dim_type type, unsigned pos, unsigned n);
5229 __isl_give isl_basic_map *isl_basic_map_move_dims(
5230 __isl_take isl_basic_map *bmap,
5231 enum isl_dim_type dst_type, unsigned dst_pos,
5232 enum isl_dim_type src_type, unsigned src_pos,
5234 __isl_give isl_map *isl_map_move_dims(
5235 __isl_take isl_map *map,
5236 enum isl_dim_type dst_type, unsigned dst_pos,
5237 enum isl_dim_type src_type, unsigned src_pos,
5240 #include <isl/val.h>
5241 __isl_give isl_multi_val *isl_multi_val_insert_dims(
5242 __isl_take isl_multi_val *mv,
5243 enum isl_dim_type type, unsigned first, unsigned n);
5244 __isl_give isl_multi_val *isl_multi_val_add_dims(
5245 __isl_take isl_multi_val *mv,
5246 enum isl_dim_type type, unsigned n);
5247 __isl_give isl_multi_val *isl_multi_val_drop_dims(
5248 __isl_take isl_multi_val *mv,
5249 enum isl_dim_type type, unsigned first, unsigned n);
5251 #include <isl/aff.h>
5252 __isl_give isl_aff *isl_aff_insert_dims(
5253 __isl_take isl_aff *aff,
5254 enum isl_dim_type type, unsigned first, unsigned n);
5255 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5256 __isl_take isl_multi_aff *ma,
5257 enum isl_dim_type type, unsigned first, unsigned n);
5258 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5259 __isl_take isl_pw_aff *pwaff,
5260 enum isl_dim_type type, unsigned first, unsigned n);
5261 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5262 __isl_take isl_multi_pw_aff *mpa,
5263 enum isl_dim_type type, unsigned first, unsigned n);
5264 __isl_give isl_aff *isl_aff_add_dims(
5265 __isl_take isl_aff *aff,
5266 enum isl_dim_type type, unsigned n);
5267 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5268 __isl_take isl_multi_aff *ma,
5269 enum isl_dim_type type, unsigned n);
5270 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5271 __isl_take isl_pw_aff *pwaff,
5272 enum isl_dim_type type, unsigned n);
5273 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5274 __isl_take isl_multi_pw_aff *mpa,
5275 enum isl_dim_type type, unsigned n);
5276 __isl_give isl_aff *isl_aff_drop_dims(
5277 __isl_take isl_aff *aff,
5278 enum isl_dim_type type, unsigned first, unsigned n);
5279 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5280 __isl_take isl_multi_aff *maff,
5281 enum isl_dim_type type, unsigned first, unsigned n);
5282 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5283 __isl_take isl_pw_aff *pwaff,
5284 enum isl_dim_type type, unsigned first, unsigned n);
5285 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5286 __isl_take isl_pw_multi_aff *pma,
5287 enum isl_dim_type type, unsigned first, unsigned n);
5288 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5289 __isl_take isl_union_pw_aff *upa,
5290 enum isl_dim_type type, unsigned first, unsigned n);
5291 __isl_give isl_union_pw_multi_aff *
5292 isl_union_pw_multi_aff_drop_dims(
5293 __isl_take isl_union_pw_multi_aff *upma,
5294 enum isl_dim_type type,
5295 unsigned first, unsigned n);
5296 __isl_give isl_multi_union_pw_aff *
5297 isl_multi_union_pw_aff_drop_dims(
5298 __isl_take isl_multi_union_pw_aff *mupa,
5299 enum isl_dim_type type, unsigned first,
5301 __isl_give isl_aff *isl_aff_move_dims(
5302 __isl_take isl_aff *aff,
5303 enum isl_dim_type dst_type, unsigned dst_pos,
5304 enum isl_dim_type src_type, unsigned src_pos,
5306 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5307 __isl_take isl_multi_aff *ma,
5308 enum isl_dim_type dst_type, unsigned dst_pos,
5309 enum isl_dim_type src_type, unsigned src_pos,
5311 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5312 __isl_take isl_pw_aff *pa,
5313 enum isl_dim_type dst_type, unsigned dst_pos,
5314 enum isl_dim_type src_type, unsigned src_pos,
5316 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5317 __isl_take isl_multi_pw_aff *pma,
5318 enum isl_dim_type dst_type, unsigned dst_pos,
5319 enum isl_dim_type src_type, unsigned src_pos,
5322 #include <isl/polynomial.h>
5323 __isl_give isl_union_pw_qpolynomial *
5324 isl_union_pw_qpolynomial_drop_dims(
5325 __isl_take isl_union_pw_qpolynomial *upwqp,
5326 enum isl_dim_type type,
5327 unsigned first, unsigned n);
5328 __isl_give isl_union_pw_qpolynomial_fold *
5329 isl_union_pw_qpolynomial_fold_drop_dims(
5330 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5331 enum isl_dim_type type,
5332 unsigned first, unsigned n);
5334 The operations on union expressions can only manipulate parameters.
5338 =head2 Binary Operations
5340 The two arguments of a binary operation not only need to live
5341 in the same C<isl_ctx>, they currently also need to have
5342 the same (number of) parameters.
5344 =head3 Basic Operations
5348 =item * Intersection
5350 #include <isl/local_space.h>
5351 __isl_give isl_local_space *isl_local_space_intersect(
5352 __isl_take isl_local_space *ls1,
5353 __isl_take isl_local_space *ls2);
5355 #include <isl/set.h>
5356 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5357 __isl_take isl_basic_set *bset1,
5358 __isl_take isl_basic_set *bset2);
5359 __isl_give isl_basic_set *isl_basic_set_intersect(
5360 __isl_take isl_basic_set *bset1,
5361 __isl_take isl_basic_set *bset2);
5362 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5363 __isl_take struct isl_basic_set_list *list);
5364 __isl_give isl_set *isl_set_intersect_params(
5365 __isl_take isl_set *set,
5366 __isl_take isl_set *params);
5367 __isl_give isl_set *isl_set_intersect(
5368 __isl_take isl_set *set1,
5369 __isl_take isl_set *set2);
5371 #include <isl/map.h>
5372 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5373 __isl_take isl_basic_map *bmap,
5374 __isl_take isl_basic_set *bset);
5375 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5376 __isl_take isl_basic_map *bmap,
5377 __isl_take isl_basic_set *bset);
5378 __isl_give isl_basic_map *isl_basic_map_intersect(
5379 __isl_take isl_basic_map *bmap1,
5380 __isl_take isl_basic_map *bmap2);
5381 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5382 __isl_take isl_basic_map_list *list);
5383 __isl_give isl_map *isl_map_intersect_params(
5384 __isl_take isl_map *map,
5385 __isl_take isl_set *params);
5386 __isl_give isl_map *isl_map_intersect_domain(
5387 __isl_take isl_map *map,
5388 __isl_take isl_set *set);
5389 __isl_give isl_map *isl_map_intersect_range(
5390 __isl_take isl_map *map,
5391 __isl_take isl_set *set);
5392 __isl_give isl_map *isl_map_intersect(
5393 __isl_take isl_map *map1,
5394 __isl_take isl_map *map2);
5396 #include <isl/union_set.h>
5397 __isl_give isl_union_set *isl_union_set_intersect_params(
5398 __isl_take isl_union_set *uset,
5399 __isl_take isl_set *set);
5400 __isl_give isl_union_set *isl_union_set_intersect(
5401 __isl_take isl_union_set *uset1,
5402 __isl_take isl_union_set *uset2);
5404 #include <isl/union_map.h>
5405 __isl_give isl_union_map *isl_union_map_intersect_params(
5406 __isl_take isl_union_map *umap,
5407 __isl_take isl_set *set);
5408 __isl_give isl_union_map *isl_union_map_intersect_domain(
5409 __isl_take isl_union_map *umap,
5410 __isl_take isl_union_set *uset);
5411 __isl_give isl_union_map *isl_union_map_intersect_range(
5412 __isl_take isl_union_map *umap,
5413 __isl_take isl_union_set *uset);
5414 __isl_give isl_union_map *isl_union_map_intersect(
5415 __isl_take isl_union_map *umap1,
5416 __isl_take isl_union_map *umap2);
5418 #include <isl/aff.h>
5419 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5420 __isl_take isl_pw_aff *pa,
5421 __isl_take isl_set *set);
5422 __isl_give isl_multi_pw_aff *
5423 isl_multi_pw_aff_intersect_domain(
5424 __isl_take isl_multi_pw_aff *mpa,
5425 __isl_take isl_set *domain);
5426 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5427 __isl_take isl_pw_multi_aff *pma,
5428 __isl_take isl_set *set);
5429 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5430 __isl_take isl_union_pw_aff *upa,
5431 __isl_take isl_union_set *uset);
5432 __isl_give isl_union_pw_multi_aff *
5433 isl_union_pw_multi_aff_intersect_domain(
5434 __isl_take isl_union_pw_multi_aff *upma,
5435 __isl_take isl_union_set *uset);
5436 __isl_give isl_multi_union_pw_aff *
5437 isl_multi_union_pw_aff_intersect_domain(
5438 __isl_take isl_multi_union_pw_aff *mupa,
5439 __isl_take isl_union_set *uset);
5440 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5441 __isl_take isl_pw_aff *pa,
5442 __isl_take isl_set *set);
5443 __isl_give isl_multi_pw_aff *
5444 isl_multi_pw_aff_intersect_params(
5445 __isl_take isl_multi_pw_aff *mpa,
5446 __isl_take isl_set *set);
5447 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5448 __isl_take isl_pw_multi_aff *pma,
5449 __isl_take isl_set *set);
5450 __isl_give isl_union_pw_aff *
5451 isl_union_pw_aff_intersect_params(
5452 __isl_take isl_union_pw_aff *upa,
5453 __isl_give isl_union_pw_multi_aff *
5454 isl_union_pw_multi_aff_intersect_params(
5455 __isl_take isl_union_pw_multi_aff *upma,
5456 __isl_take isl_set *set);
5457 __isl_give isl_multi_union_pw_aff *
5458 isl_multi_union_pw_aff_intersect_params(
5459 __isl_take isl_multi_union_pw_aff *mupa,
5460 __isl_take isl_set *params);
5461 isl_multi_union_pw_aff_intersect_range(
5462 __isl_take isl_multi_union_pw_aff *mupa,
5463 __isl_take isl_set *set);
5465 #include <isl/polynomial.h>
5466 __isl_give isl_pw_qpolynomial *
5467 isl_pw_qpolynomial_intersect_domain(
5468 __isl_take isl_pw_qpolynomial *pwpq,
5469 __isl_take isl_set *set);
5470 __isl_give isl_union_pw_qpolynomial *
5471 isl_union_pw_qpolynomial_intersect_domain(
5472 __isl_take isl_union_pw_qpolynomial *upwpq,
5473 __isl_take isl_union_set *uset);
5474 __isl_give isl_union_pw_qpolynomial_fold *
5475 isl_union_pw_qpolynomial_fold_intersect_domain(
5476 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5477 __isl_take isl_union_set *uset);
5478 __isl_give isl_pw_qpolynomial *
5479 isl_pw_qpolynomial_intersect_params(
5480 __isl_take isl_pw_qpolynomial *pwpq,
5481 __isl_take isl_set *set);
5482 __isl_give isl_pw_qpolynomial_fold *
5483 isl_pw_qpolynomial_fold_intersect_params(
5484 __isl_take isl_pw_qpolynomial_fold *pwf,
5485 __isl_take isl_set *set);
5486 __isl_give isl_union_pw_qpolynomial *
5487 isl_union_pw_qpolynomial_intersect_params(
5488 __isl_take isl_union_pw_qpolynomial *upwpq,
5489 __isl_take isl_set *set);
5490 __isl_give isl_union_pw_qpolynomial_fold *
5491 isl_union_pw_qpolynomial_fold_intersect_params(
5492 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5493 __isl_take isl_set *set);
5495 The second argument to the C<_params> functions needs to be
5496 a parametric (basic) set. For the other functions, a parametric set
5497 for either argument is only allowed if the other argument is
5498 a parametric set as well.
5499 The list passed to C<isl_basic_set_list_intersect> needs to have
5500 at least one element and all elements need to live in the same space.
5501 The function C<isl_multi_union_pw_aff_intersect_range>
5502 restricts the input function to those shared domain elements
5503 that map to the specified range.
5507 #include <isl/set.h>
5508 __isl_give isl_set *isl_basic_set_union(
5509 __isl_take isl_basic_set *bset1,
5510 __isl_take isl_basic_set *bset2);
5511 __isl_give isl_set *isl_set_union(
5512 __isl_take isl_set *set1,
5513 __isl_take isl_set *set2);
5515 #include <isl/map.h>
5516 __isl_give isl_map *isl_basic_map_union(
5517 __isl_take isl_basic_map *bmap1,
5518 __isl_take isl_basic_map *bmap2);
5519 __isl_give isl_map *isl_map_union(
5520 __isl_take isl_map *map1,
5521 __isl_take isl_map *map2);
5523 #include <isl/union_set.h>
5524 __isl_give isl_union_set *isl_union_set_union(
5525 __isl_take isl_union_set *uset1,
5526 __isl_take isl_union_set *uset2);
5527 __isl_give isl_union_set *isl_union_set_list_union(
5528 __isl_take isl_union_set_list *list);
5530 #include <isl/union_map.h>
5531 __isl_give isl_union_map *isl_union_map_union(
5532 __isl_take isl_union_map *umap1,
5533 __isl_take isl_union_map *umap2);
5535 =item * Set difference
5537 #include <isl/set.h>
5538 __isl_give isl_set *isl_set_subtract(
5539 __isl_take isl_set *set1,
5540 __isl_take isl_set *set2);
5542 #include <isl/map.h>
5543 __isl_give isl_map *isl_map_subtract(
5544 __isl_take isl_map *map1,
5545 __isl_take isl_map *map2);
5546 __isl_give isl_map *isl_map_subtract_domain(
5547 __isl_take isl_map *map,
5548 __isl_take isl_set *dom);
5549 __isl_give isl_map *isl_map_subtract_range(
5550 __isl_take isl_map *map,
5551 __isl_take isl_set *dom);
5553 #include <isl/union_set.h>
5554 __isl_give isl_union_set *isl_union_set_subtract(
5555 __isl_take isl_union_set *uset1,
5556 __isl_take isl_union_set *uset2);
5558 #include <isl/union_map.h>
5559 __isl_give isl_union_map *isl_union_map_subtract(
5560 __isl_take isl_union_map *umap1,
5561 __isl_take isl_union_map *umap2);
5562 __isl_give isl_union_map *isl_union_map_subtract_domain(
5563 __isl_take isl_union_map *umap,
5564 __isl_take isl_union_set *dom);
5565 __isl_give isl_union_map *isl_union_map_subtract_range(
5566 __isl_take isl_union_map *umap,
5567 __isl_take isl_union_set *dom);
5569 #include <isl/aff.h>
5570 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5571 __isl_take isl_pw_aff *pa,
5572 __isl_take isl_set *set);
5573 __isl_give isl_pw_multi_aff *
5574 isl_pw_multi_aff_subtract_domain(
5575 __isl_take isl_pw_multi_aff *pma,
5576 __isl_take isl_set *set);
5577 __isl_give isl_union_pw_aff *
5578 isl_union_pw_aff_subtract_domain(
5579 __isl_take isl_union_pw_aff *upa,
5580 __isl_take isl_union_set *uset);
5581 __isl_give isl_union_pw_multi_aff *
5582 isl_union_pw_multi_aff_subtract_domain(
5583 __isl_take isl_union_pw_multi_aff *upma,
5584 __isl_take isl_set *set);
5586 #include <isl/polynomial.h>
5587 __isl_give isl_pw_qpolynomial *
5588 isl_pw_qpolynomial_subtract_domain(
5589 __isl_take isl_pw_qpolynomial *pwpq,
5590 __isl_take isl_set *set);
5591 __isl_give isl_pw_qpolynomial_fold *
5592 isl_pw_qpolynomial_fold_subtract_domain(
5593 __isl_take isl_pw_qpolynomial_fold *pwf,
5594 __isl_take isl_set *set);
5595 __isl_give isl_union_pw_qpolynomial *
5596 isl_union_pw_qpolynomial_subtract_domain(
5597 __isl_take isl_union_pw_qpolynomial *upwpq,
5598 __isl_take isl_union_set *uset);
5599 __isl_give isl_union_pw_qpolynomial_fold *
5600 isl_union_pw_qpolynomial_fold_subtract_domain(
5601 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5602 __isl_take isl_union_set *uset);
5606 #include <isl/space.h>
5607 __isl_give isl_space *isl_space_join(
5608 __isl_take isl_space *left,
5609 __isl_take isl_space *right);
5611 #include <isl/map.h>
5612 __isl_give isl_basic_set *isl_basic_set_apply(
5613 __isl_take isl_basic_set *bset,
5614 __isl_take isl_basic_map *bmap);
5615 __isl_give isl_set *isl_set_apply(
5616 __isl_take isl_set *set,
5617 __isl_take isl_map *map);
5618 __isl_give isl_union_set *isl_union_set_apply(
5619 __isl_take isl_union_set *uset,
5620 __isl_take isl_union_map *umap);
5621 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5622 __isl_take isl_basic_map *bmap1,
5623 __isl_take isl_basic_map *bmap2);
5624 __isl_give isl_basic_map *isl_basic_map_apply_range(
5625 __isl_take isl_basic_map *bmap1,
5626 __isl_take isl_basic_map *bmap2);
5627 __isl_give isl_map *isl_map_apply_domain(
5628 __isl_take isl_map *map1,
5629 __isl_take isl_map *map2);
5630 __isl_give isl_map *isl_map_apply_range(
5631 __isl_take isl_map *map1,
5632 __isl_take isl_map *map2);
5634 #include <isl/union_map.h>
5635 __isl_give isl_union_map *isl_union_map_apply_domain(
5636 __isl_take isl_union_map *umap1,
5637 __isl_take isl_union_map *umap2);
5638 __isl_give isl_union_map *isl_union_map_apply_range(
5639 __isl_take isl_union_map *umap1,
5640 __isl_take isl_union_map *umap2);
5642 #include <isl/aff.h>
5643 __isl_give isl_union_pw_aff *
5644 isl_multi_union_pw_aff_apply_aff(
5645 __isl_take isl_multi_union_pw_aff *mupa,
5646 __isl_take isl_aff *aff);
5647 __isl_give isl_union_pw_aff *
5648 isl_multi_union_pw_aff_apply_pw_aff(
5649 __isl_take isl_multi_union_pw_aff *mupa,
5650 __isl_take isl_pw_aff *pa);
5651 __isl_give isl_multi_union_pw_aff *
5652 isl_multi_union_pw_aff_apply_multi_aff(
5653 __isl_take isl_multi_union_pw_aff *mupa,
5654 __isl_take isl_multi_aff *ma);
5655 __isl_give isl_multi_union_pw_aff *
5656 isl_multi_union_pw_aff_apply_pw_multi_aff(
5657 __isl_take isl_multi_union_pw_aff *mupa,
5658 __isl_take isl_pw_multi_aff *pma);
5660 The result of C<isl_multi_union_pw_aff_apply_aff> is defined
5661 over the shared domain of the elements of the input. The dimension is
5662 required to be greater than zero.
5663 The C<isl_multi_union_pw_aff> argument of
5664 C<isl_multi_union_pw_aff_apply_multi_aff> is allowed to be zero-dimensional,
5665 but only if the range of the C<isl_multi_aff> argument
5666 is also zero-dimensional.
5667 Similarly for C<isl_multi_union_pw_aff_apply_pw_multi_aff>.
5669 #include <isl/polynomial.h>
5670 __isl_give isl_pw_qpolynomial_fold *
5671 isl_set_apply_pw_qpolynomial_fold(
5672 __isl_take isl_set *set,
5673 __isl_take isl_pw_qpolynomial_fold *pwf,
5675 __isl_give isl_pw_qpolynomial_fold *
5676 isl_map_apply_pw_qpolynomial_fold(
5677 __isl_take isl_map *map,
5678 __isl_take isl_pw_qpolynomial_fold *pwf,
5680 __isl_give isl_union_pw_qpolynomial_fold *
5681 isl_union_set_apply_union_pw_qpolynomial_fold(
5682 __isl_take isl_union_set *uset,
5683 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5685 __isl_give isl_union_pw_qpolynomial_fold *
5686 isl_union_map_apply_union_pw_qpolynomial_fold(
5687 __isl_take isl_union_map *umap,
5688 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5691 The functions taking a map
5692 compose the given map with the given piecewise quasipolynomial reduction.
5693 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5694 over all elements in the intersection of the range of the map
5695 and the domain of the piecewise quasipolynomial reduction
5696 as a function of an element in the domain of the map.
5697 The functions taking a set compute a bound over all elements in the
5698 intersection of the set and the domain of the
5699 piecewise quasipolynomial reduction.
5703 #include <isl/set.h>
5704 __isl_give isl_basic_set *
5705 isl_basic_set_preimage_multi_aff(
5706 __isl_take isl_basic_set *bset,
5707 __isl_take isl_multi_aff *ma);
5708 __isl_give isl_set *isl_set_preimage_multi_aff(
5709 __isl_take isl_set *set,
5710 __isl_take isl_multi_aff *ma);
5711 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5712 __isl_take isl_set *set,
5713 __isl_take isl_pw_multi_aff *pma);
5714 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5715 __isl_take isl_set *set,
5716 __isl_take isl_multi_pw_aff *mpa);
5718 #include <isl/union_set.h>
5719 __isl_give isl_union_set *
5720 isl_union_set_preimage_multi_aff(
5721 __isl_take isl_union_set *uset,
5722 __isl_take isl_multi_aff *ma);
5723 __isl_give isl_union_set *
5724 isl_union_set_preimage_pw_multi_aff(
5725 __isl_take isl_union_set *uset,
5726 __isl_take isl_pw_multi_aff *pma);
5727 __isl_give isl_union_set *
5728 isl_union_set_preimage_union_pw_multi_aff(
5729 __isl_take isl_union_set *uset,
5730 __isl_take isl_union_pw_multi_aff *upma);
5732 #include <isl/map.h>
5733 __isl_give isl_basic_map *
5734 isl_basic_map_preimage_domain_multi_aff(
5735 __isl_take isl_basic_map *bmap,
5736 __isl_take isl_multi_aff *ma);
5737 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5738 __isl_take isl_map *map,
5739 __isl_take isl_multi_aff *ma);
5740 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5741 __isl_take isl_map *map,
5742 __isl_take isl_multi_aff *ma);
5743 __isl_give isl_map *
5744 isl_map_preimage_domain_pw_multi_aff(
5745 __isl_take isl_map *map,
5746 __isl_take isl_pw_multi_aff *pma);
5747 __isl_give isl_map *
5748 isl_map_preimage_range_pw_multi_aff(
5749 __isl_take isl_map *map,
5750 __isl_take isl_pw_multi_aff *pma);
5751 __isl_give isl_map *
5752 isl_map_preimage_domain_multi_pw_aff(
5753 __isl_take isl_map *map,
5754 __isl_take isl_multi_pw_aff *mpa);
5755 __isl_give isl_basic_map *
5756 isl_basic_map_preimage_range_multi_aff(
5757 __isl_take isl_basic_map *bmap,
5758 __isl_take isl_multi_aff *ma);
5760 #include <isl/union_map.h>
5761 __isl_give isl_union_map *
5762 isl_union_map_preimage_domain_multi_aff(
5763 __isl_take isl_union_map *umap,
5764 __isl_take isl_multi_aff *ma);
5765 __isl_give isl_union_map *
5766 isl_union_map_preimage_range_multi_aff(
5767 __isl_take isl_union_map *umap,
5768 __isl_take isl_multi_aff *ma);
5769 __isl_give isl_union_map *
5770 isl_union_map_preimage_domain_pw_multi_aff(
5771 __isl_take isl_union_map *umap,
5772 __isl_take isl_pw_multi_aff *pma);
5773 __isl_give isl_union_map *
5774 isl_union_map_preimage_range_pw_multi_aff(
5775 __isl_take isl_union_map *umap,
5776 __isl_take isl_pw_multi_aff *pma);
5777 __isl_give isl_union_map *
5778 isl_union_map_preimage_domain_union_pw_multi_aff(
5779 __isl_take isl_union_map *umap,
5780 __isl_take isl_union_pw_multi_aff *upma);
5781 __isl_give isl_union_map *
5782 isl_union_map_preimage_range_union_pw_multi_aff(
5783 __isl_take isl_union_map *umap,
5784 __isl_take isl_union_pw_multi_aff *upma);
5786 These functions compute the preimage of the given set or map domain/range under
5787 the given function. In other words, the expression is plugged
5788 into the set description or into the domain/range of the map.
5792 #include <isl/aff.h>
5793 __isl_give isl_aff *isl_aff_pullback_aff(
5794 __isl_take isl_aff *aff1,
5795 __isl_take isl_aff *aff2);
5796 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5797 __isl_take isl_aff *aff,
5798 __isl_take isl_multi_aff *ma);
5799 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5800 __isl_take isl_pw_aff *pa,
5801 __isl_take isl_multi_aff *ma);
5802 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5803 __isl_take isl_pw_aff *pa,
5804 __isl_take isl_pw_multi_aff *pma);
5805 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5806 __isl_take isl_pw_aff *pa,
5807 __isl_take isl_multi_pw_aff *mpa);
5808 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5809 __isl_take isl_multi_aff *ma1,
5810 __isl_take isl_multi_aff *ma2);
5811 __isl_give isl_pw_multi_aff *
5812 isl_pw_multi_aff_pullback_multi_aff(
5813 __isl_take isl_pw_multi_aff *pma,
5814 __isl_take isl_multi_aff *ma);
5815 __isl_give isl_multi_pw_aff *
5816 isl_multi_pw_aff_pullback_multi_aff(
5817 __isl_take isl_multi_pw_aff *mpa,
5818 __isl_take isl_multi_aff *ma);
5819 __isl_give isl_pw_multi_aff *
5820 isl_pw_multi_aff_pullback_pw_multi_aff(
5821 __isl_take isl_pw_multi_aff *pma1,
5822 __isl_take isl_pw_multi_aff *pma2);
5823 __isl_give isl_multi_pw_aff *
5824 isl_multi_pw_aff_pullback_pw_multi_aff(
5825 __isl_take isl_multi_pw_aff *mpa,
5826 __isl_take isl_pw_multi_aff *pma);
5827 __isl_give isl_multi_pw_aff *
5828 isl_multi_pw_aff_pullback_multi_pw_aff(
5829 __isl_take isl_multi_pw_aff *mpa1,
5830 __isl_take isl_multi_pw_aff *mpa2);
5831 __isl_give isl_union_pw_aff *
5832 isl_union_pw_aff_pullback_union_pw_multi_aff(
5833 __isl_take isl_union_pw_aff *upa,
5834 __isl_take isl_union_pw_multi_aff *upma);
5835 __isl_give isl_union_pw_multi_aff *
5836 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5837 __isl_take isl_union_pw_multi_aff *upma1,
5838 __isl_take isl_union_pw_multi_aff *upma2);
5839 __isl_give isl_multi_union_pw_aff *
5840 isl_multi_union_pw_aff_pullback_union_pw_multi_aff(
5841 __isl_take isl_multi_union_pw_aff *mupa,
5842 __isl_take isl_union_pw_multi_aff *upma);
5844 These functions precompose the first expression by the second function.
5845 In other words, the second function is plugged
5846 into the first expression.
5850 #include <isl/aff.h>
5851 __isl_give isl_basic_set *isl_aff_le_basic_set(
5852 __isl_take isl_aff *aff1,
5853 __isl_take isl_aff *aff2);
5854 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5855 __isl_take isl_aff *aff1,
5856 __isl_take isl_aff *aff2);
5857 __isl_give isl_set *isl_pw_aff_eq_set(
5858 __isl_take isl_pw_aff *pwaff1,
5859 __isl_take isl_pw_aff *pwaff2);
5860 __isl_give isl_set *isl_pw_aff_ne_set(
5861 __isl_take isl_pw_aff *pwaff1,
5862 __isl_take isl_pw_aff *pwaff2);
5863 __isl_give isl_set *isl_pw_aff_le_set(
5864 __isl_take isl_pw_aff *pwaff1,
5865 __isl_take isl_pw_aff *pwaff2);
5866 __isl_give isl_set *isl_pw_aff_lt_set(
5867 __isl_take isl_pw_aff *pwaff1,
5868 __isl_take isl_pw_aff *pwaff2);
5869 __isl_give isl_set *isl_pw_aff_ge_set(
5870 __isl_take isl_pw_aff *pwaff1,
5871 __isl_take isl_pw_aff *pwaff2);
5872 __isl_give isl_set *isl_pw_aff_gt_set(
5873 __isl_take isl_pw_aff *pwaff1,
5874 __isl_take isl_pw_aff *pwaff2);
5876 __isl_give isl_set *isl_multi_aff_lex_le_set(
5877 __isl_take isl_multi_aff *ma1,
5878 __isl_take isl_multi_aff *ma2);
5879 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5880 __isl_take isl_multi_aff *ma1,
5881 __isl_take isl_multi_aff *ma2);
5883 __isl_give isl_set *isl_pw_aff_list_eq_set(
5884 __isl_take isl_pw_aff_list *list1,
5885 __isl_take isl_pw_aff_list *list2);
5886 __isl_give isl_set *isl_pw_aff_list_ne_set(
5887 __isl_take isl_pw_aff_list *list1,
5888 __isl_take isl_pw_aff_list *list2);
5889 __isl_give isl_set *isl_pw_aff_list_le_set(
5890 __isl_take isl_pw_aff_list *list1,
5891 __isl_take isl_pw_aff_list *list2);
5892 __isl_give isl_set *isl_pw_aff_list_lt_set(
5893 __isl_take isl_pw_aff_list *list1,
5894 __isl_take isl_pw_aff_list *list2);
5895 __isl_give isl_set *isl_pw_aff_list_ge_set(
5896 __isl_take isl_pw_aff_list *list1,
5897 __isl_take isl_pw_aff_list *list2);
5898 __isl_give isl_set *isl_pw_aff_list_gt_set(
5899 __isl_take isl_pw_aff_list *list1,
5900 __isl_take isl_pw_aff_list *list2);
5902 The function C<isl_aff_ge_basic_set> returns a basic set
5903 containing those elements in the shared space
5904 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5905 The function C<isl_pw_aff_ge_set> returns a set
5906 containing those elements in the shared domain
5907 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5908 greater than or equal to C<pwaff2>.
5909 The function C<isl_multi_aff_lex_le_set> returns a set
5910 containing those elements in the shared domain space
5911 where C<ma1> is lexicographically smaller than or
5913 The functions operating on C<isl_pw_aff_list> apply the corresponding
5914 C<isl_pw_aff> function to each pair of elements in the two lists.
5916 #include <isl/aff.h>
5917 __isl_give isl_map *isl_pw_aff_eq_map(
5918 __isl_take isl_pw_aff *pa1,
5919 __isl_take isl_pw_aff *pa2);
5920 __isl_give isl_map *isl_pw_aff_lt_map(
5921 __isl_take isl_pw_aff *pa1,
5922 __isl_take isl_pw_aff *pa2);
5923 __isl_give isl_map *isl_pw_aff_gt_map(
5924 __isl_take isl_pw_aff *pa1,
5925 __isl_take isl_pw_aff *pa2);
5927 __isl_give isl_map *isl_multi_pw_aff_eq_map(
5928 __isl_take isl_multi_pw_aff *mpa1,
5929 __isl_take isl_multi_pw_aff *mpa2);
5930 __isl_give isl_map *isl_multi_pw_aff_lex_lt_map(
5931 __isl_take isl_multi_pw_aff *mpa1,
5932 __isl_take isl_multi_pw_aff *mpa2);
5933 __isl_give isl_map *isl_multi_pw_aff_lex_gt_map(
5934 __isl_take isl_multi_pw_aff *mpa1,
5935 __isl_take isl_multi_pw_aff *mpa2);
5937 These functions return a map between domain elements of the arguments
5938 where the function values satisfy the given relation.
5940 #include <isl/union_map.h>
5941 __isl_give isl_union_map *
5942 isl_union_map_eq_at_multi_union_pw_aff(
5943 __isl_take isl_union_map *umap,
5944 __isl_take isl_multi_union_pw_aff *mupa);
5945 __isl_give isl_union_map *
5946 isl_union_map_lex_lt_at_multi_union_pw_aff(
5947 __isl_take isl_union_map *umap,
5948 __isl_take isl_multi_union_pw_aff *mupa);
5949 __isl_give isl_union_map *
5950 isl_union_map_lex_gt_at_multi_union_pw_aff(
5951 __isl_take isl_union_map *umap,
5952 __isl_take isl_multi_union_pw_aff *mupa);
5954 These functions select the subset of elements in the union map
5955 that have an equal or lexicographically smaller function value.
5957 =item * Cartesian Product
5959 #include <isl/space.h>
5960 __isl_give isl_space *isl_space_product(
5961 __isl_take isl_space *space1,
5962 __isl_take isl_space *space2);
5963 __isl_give isl_space *isl_space_domain_product(
5964 __isl_take isl_space *space1,
5965 __isl_take isl_space *space2);
5966 __isl_give isl_space *isl_space_range_product(
5967 __isl_take isl_space *space1,
5968 __isl_take isl_space *space2);
5971 C<isl_space_product>, C<isl_space_domain_product>
5972 and C<isl_space_range_product> take pairs or relation spaces and
5973 produce a single relations space, where either the domain, the range
5974 or both domain and range are wrapped spaces of relations between
5975 the domains and/or ranges of the input spaces.
5976 If the product is only constructed over the domain or the range
5977 then the ranges or the domains of the inputs should be the same.
5978 The function C<isl_space_product> also accepts a pair of set spaces,
5979 in which case it returns a wrapped space of a relation between the
5982 #include <isl/set.h>
5983 __isl_give isl_set *isl_set_product(
5984 __isl_take isl_set *set1,
5985 __isl_take isl_set *set2);
5987 #include <isl/map.h>
5988 __isl_give isl_basic_map *isl_basic_map_domain_product(
5989 __isl_take isl_basic_map *bmap1,
5990 __isl_take isl_basic_map *bmap2);
5991 __isl_give isl_basic_map *isl_basic_map_range_product(
5992 __isl_take isl_basic_map *bmap1,
5993 __isl_take isl_basic_map *bmap2);
5994 __isl_give isl_basic_map *isl_basic_map_product(
5995 __isl_take isl_basic_map *bmap1,
5996 __isl_take isl_basic_map *bmap2);
5997 __isl_give isl_map *isl_map_domain_product(
5998 __isl_take isl_map *map1,
5999 __isl_take isl_map *map2);
6000 __isl_give isl_map *isl_map_range_product(
6001 __isl_take isl_map *map1,
6002 __isl_take isl_map *map2);
6003 __isl_give isl_map *isl_map_product(
6004 __isl_take isl_map *map1,
6005 __isl_take isl_map *map2);
6007 #include <isl/union_set.h>
6008 __isl_give isl_union_set *isl_union_set_product(
6009 __isl_take isl_union_set *uset1,
6010 __isl_take isl_union_set *uset2);
6012 #include <isl/union_map.h>
6013 __isl_give isl_union_map *isl_union_map_domain_product(
6014 __isl_take isl_union_map *umap1,
6015 __isl_take isl_union_map *umap2);
6016 __isl_give isl_union_map *isl_union_map_range_product(
6017 __isl_take isl_union_map *umap1,
6018 __isl_take isl_union_map *umap2);
6019 __isl_give isl_union_map *isl_union_map_product(
6020 __isl_take isl_union_map *umap1,
6021 __isl_take isl_union_map *umap2);
6023 #include <isl/val.h>
6024 __isl_give isl_multi_val *isl_multi_val_range_product(
6025 __isl_take isl_multi_val *mv1,
6026 __isl_take isl_multi_val *mv2);
6027 __isl_give isl_multi_val *isl_multi_val_product(
6028 __isl_take isl_multi_val *mv1,
6029 __isl_take isl_multi_val *mv2);
6031 #include <isl/aff.h>
6032 __isl_give isl_multi_aff *isl_multi_aff_range_product(
6033 __isl_take isl_multi_aff *ma1,
6034 __isl_take isl_multi_aff *ma2);
6035 __isl_give isl_multi_aff *isl_multi_aff_product(
6036 __isl_take isl_multi_aff *ma1,
6037 __isl_take isl_multi_aff *ma2);
6038 __isl_give isl_multi_pw_aff *
6039 isl_multi_pw_aff_range_product(
6040 __isl_take isl_multi_pw_aff *mpa1,
6041 __isl_take isl_multi_pw_aff *mpa2);
6042 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
6043 __isl_take isl_multi_pw_aff *mpa1,
6044 __isl_take isl_multi_pw_aff *mpa2);
6045 __isl_give isl_pw_multi_aff *
6046 isl_pw_multi_aff_range_product(
6047 __isl_take isl_pw_multi_aff *pma1,
6048 __isl_take isl_pw_multi_aff *pma2);
6049 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
6050 __isl_take isl_pw_multi_aff *pma1,
6051 __isl_take isl_pw_multi_aff *pma2);
6052 __isl_give isl_multi_union_pw_aff *
6053 isl_multi_union_pw_aff_range_product(
6054 __isl_take isl_multi_union_pw_aff *mupa1,
6055 __isl_take isl_multi_union_pw_aff *mupa2);
6057 The above functions compute the cross product of the given
6058 sets, relations or functions. The domains and ranges of the results
6059 are wrapped maps between domains and ranges of the inputs.
6060 To obtain a ``flat'' product, use the following functions
6063 #include <isl/set.h>
6064 __isl_give isl_basic_set *isl_basic_set_flat_product(
6065 __isl_take isl_basic_set *bset1,
6066 __isl_take isl_basic_set *bset2);
6067 __isl_give isl_set *isl_set_flat_product(
6068 __isl_take isl_set *set1,
6069 __isl_take isl_set *set2);
6071 #include <isl/map.h>
6072 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
6073 __isl_take isl_basic_map *bmap1,
6074 __isl_take isl_basic_map *bmap2);
6075 __isl_give isl_map *isl_map_flat_domain_product(
6076 __isl_take isl_map *map1,
6077 __isl_take isl_map *map2);
6078 __isl_give isl_map *isl_map_flat_range_product(
6079 __isl_take isl_map *map1,
6080 __isl_take isl_map *map2);
6081 __isl_give isl_basic_map *isl_basic_map_flat_product(
6082 __isl_take isl_basic_map *bmap1,
6083 __isl_take isl_basic_map *bmap2);
6084 __isl_give isl_map *isl_map_flat_product(
6085 __isl_take isl_map *map1,
6086 __isl_take isl_map *map2);
6088 #include <isl/union_map.h>
6089 __isl_give isl_union_map *
6090 isl_union_map_flat_domain_product(
6091 __isl_take isl_union_map *umap1,
6092 __isl_take isl_union_map *umap2);
6093 __isl_give isl_union_map *
6094 isl_union_map_flat_range_product(
6095 __isl_take isl_union_map *umap1,
6096 __isl_take isl_union_map *umap2);
6098 #include <isl/val.h>
6099 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
6100 __isl_take isl_multi_val *mv1,
6101 __isl_take isl_multi_aff *mv2);
6103 #include <isl/aff.h>
6104 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
6105 __isl_take isl_multi_aff *ma1,
6106 __isl_take isl_multi_aff *ma2);
6107 __isl_give isl_pw_multi_aff *
6108 isl_pw_multi_aff_flat_range_product(
6109 __isl_take isl_pw_multi_aff *pma1,
6110 __isl_take isl_pw_multi_aff *pma2);
6111 __isl_give isl_multi_pw_aff *
6112 isl_multi_pw_aff_flat_range_product(
6113 __isl_take isl_multi_pw_aff *mpa1,
6114 __isl_take isl_multi_pw_aff *mpa2);
6115 __isl_give isl_union_pw_multi_aff *
6116 isl_union_pw_multi_aff_flat_range_product(
6117 __isl_take isl_union_pw_multi_aff *upma1,
6118 __isl_take isl_union_pw_multi_aff *upma2);
6119 __isl_give isl_multi_union_pw_aff *
6120 isl_multi_union_pw_aff_flat_range_product(
6121 __isl_take isl_multi_union_pw_aff *mupa1,
6122 __isl_take isl_multi_union_pw_aff *mupa2);
6124 #include <isl/space.h>
6125 __isl_give isl_space *isl_space_factor_domain(
6126 __isl_take isl_space *space);
6127 __isl_give isl_space *isl_space_factor_range(
6128 __isl_take isl_space *space);
6129 __isl_give isl_space *isl_space_domain_factor_domain(
6130 __isl_take isl_space *space);
6131 __isl_give isl_space *isl_space_domain_factor_range(
6132 __isl_take isl_space *space);
6133 __isl_give isl_space *isl_space_range_factor_domain(
6134 __isl_take isl_space *space);
6135 __isl_give isl_space *isl_space_range_factor_range(
6136 __isl_take isl_space *space);
6138 The functions C<isl_space_range_factor_domain> and
6139 C<isl_space_range_factor_range> extract the two arguments from
6140 the result of a call to C<isl_space_range_product>.
6142 The arguments of a call to C<isl_map_range_product> can be extracted
6143 from the result using the following functions.
6145 #include <isl/map.h>
6146 __isl_give isl_map *isl_map_factor_domain(
6147 __isl_take isl_map *map);
6148 __isl_give isl_map *isl_map_factor_range(
6149 __isl_take isl_map *map);
6150 __isl_give isl_map *isl_map_domain_factor_domain(
6151 __isl_take isl_map *map);
6152 __isl_give isl_map *isl_map_domain_factor_range(
6153 __isl_take isl_map *map);
6154 __isl_give isl_map *isl_map_range_factor_domain(
6155 __isl_take isl_map *map);
6156 __isl_give isl_map *isl_map_range_factor_range(
6157 __isl_take isl_map *map);
6159 #include <isl/union_map.h>
6160 __isl_give isl_union_map *isl_union_map_factor_domain(
6161 __isl_take isl_union_map *umap);
6162 __isl_give isl_union_map *isl_union_map_factor_range(
6163 __isl_take isl_union_map *umap);
6164 __isl_give isl_union_map *
6165 isl_union_map_domain_factor_domain(
6166 __isl_take isl_union_map *umap);
6167 __isl_give isl_union_map *
6168 isl_union_map_domain_factor_range(
6169 __isl_take isl_union_map *umap);
6170 __isl_give isl_union_map *
6171 isl_union_map_range_factor_range(
6172 __isl_take isl_union_map *umap);
6174 #include <isl/val.h>
6175 __isl_give isl_multi_val *
6176 isl_multi_val_range_factor_domain(
6177 __isl_take isl_multi_val *mv);
6178 __isl_give isl_multi_val *
6179 isl_multi_val_range_factor_range(
6180 __isl_take isl_multi_val *mv);
6182 #include <isl/aff.h>
6183 __isl_give isl_multi_aff *
6184 isl_multi_aff_range_factor_domain(
6185 __isl_take isl_multi_aff *ma);
6186 __isl_give isl_multi_aff *
6187 isl_multi_aff_range_factor_range(
6188 __isl_take isl_multi_aff *ma);
6189 __isl_give isl_multi_pw_aff *
6190 isl_multi_pw_aff_range_factor_domain(
6191 __isl_take isl_multi_pw_aff *mpa);
6192 __isl_give isl_multi_pw_aff *
6193 isl_multi_pw_aff_range_factor_range(
6194 __isl_take isl_multi_pw_aff *mpa);
6195 __isl_give isl_multi_union_pw_aff *
6196 isl_multi_union_pw_aff_range_factor_domain(
6197 __isl_take isl_multi_union_pw_aff *mupa);
6198 __isl_give isl_multi_union_pw_aff *
6199 isl_multi_union_pw_aff_range_factor_range(
6200 __isl_take isl_multi_union_pw_aff *mupa);
6202 The splice functions are a generalization of the flat product functions,
6203 where the second argument may be inserted at any position inside
6204 the first argument rather than being placed at the end.
6206 #include <isl/val.h>
6207 __isl_give isl_multi_val *isl_multi_val_range_splice(
6208 __isl_take isl_multi_val *mv1, unsigned pos,
6209 __isl_take isl_multi_val *mv2);
6211 #include <isl/aff.h>
6212 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
6213 __isl_take isl_multi_aff *ma1, unsigned pos,
6214 __isl_take isl_multi_aff *ma2);
6215 __isl_give isl_multi_aff *isl_multi_aff_splice(
6216 __isl_take isl_multi_aff *ma1,
6217 unsigned in_pos, unsigned out_pos,
6218 __isl_take isl_multi_aff *ma2);
6219 __isl_give isl_multi_pw_aff *
6220 isl_multi_pw_aff_range_splice(
6221 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
6222 __isl_take isl_multi_pw_aff *mpa2);
6223 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
6224 __isl_take isl_multi_pw_aff *mpa1,
6225 unsigned in_pos, unsigned out_pos,
6226 __isl_take isl_multi_pw_aff *mpa2);
6227 __isl_give isl_multi_union_pw_aff *
6228 isl_multi_union_pw_aff_range_splice(
6229 __isl_take isl_multi_union_pw_aff *mupa1,
6231 __isl_take isl_multi_union_pw_aff *mupa2);
6233 =item * Simplification
6235 When applied to a set or relation,
6236 the gist operation returns a set or relation that has the
6237 same intersection with the context as the input set or relation.
6238 Any implicit equality in the intersection is made explicit in the result,
6239 while all inequalities that are redundant with respect to the intersection
6241 In case of union sets and relations, the gist operation is performed
6244 When applied to a function,
6245 the gist operation applies the set gist operation to each of
6246 the cells in the domain of the input piecewise expression.
6247 The context is also exploited
6248 to simplify the expression associated to each cell.
6250 #include <isl/set.h>
6251 __isl_give isl_basic_set *isl_basic_set_gist(
6252 __isl_take isl_basic_set *bset,
6253 __isl_take isl_basic_set *context);
6254 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
6255 __isl_take isl_set *context);
6256 __isl_give isl_set *isl_set_gist_params(
6257 __isl_take isl_set *set,
6258 __isl_take isl_set *context);
6260 #include <isl/map.h>
6261 __isl_give isl_basic_map *isl_basic_map_gist(
6262 __isl_take isl_basic_map *bmap,
6263 __isl_take isl_basic_map *context);
6264 __isl_give isl_basic_map *isl_basic_map_gist_domain(
6265 __isl_take isl_basic_map *bmap,
6266 __isl_take isl_basic_set *context);
6267 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
6268 __isl_take isl_map *context);
6269 __isl_give isl_map *isl_map_gist_params(
6270 __isl_take isl_map *map,
6271 __isl_take isl_set *context);
6272 __isl_give isl_map *isl_map_gist_domain(
6273 __isl_take isl_map *map,
6274 __isl_take isl_set *context);
6275 __isl_give isl_map *isl_map_gist_range(
6276 __isl_take isl_map *map,
6277 __isl_take isl_set *context);
6279 #include <isl/union_set.h>
6280 __isl_give isl_union_set *isl_union_set_gist(
6281 __isl_take isl_union_set *uset,
6282 __isl_take isl_union_set *context);
6283 __isl_give isl_union_set *isl_union_set_gist_params(
6284 __isl_take isl_union_set *uset,
6285 __isl_take isl_set *set);
6287 #include <isl/union_map.h>
6288 __isl_give isl_union_map *isl_union_map_gist(
6289 __isl_take isl_union_map *umap,
6290 __isl_take isl_union_map *context);
6291 __isl_give isl_union_map *isl_union_map_gist_params(
6292 __isl_take isl_union_map *umap,
6293 __isl_take isl_set *set);
6294 __isl_give isl_union_map *isl_union_map_gist_domain(
6295 __isl_take isl_union_map *umap,
6296 __isl_take isl_union_set *uset);
6297 __isl_give isl_union_map *isl_union_map_gist_range(
6298 __isl_take isl_union_map *umap,
6299 __isl_take isl_union_set *uset);
6301 #include <isl/aff.h>
6302 __isl_give isl_aff *isl_aff_gist_params(
6303 __isl_take isl_aff *aff,
6304 __isl_take isl_set *context);
6305 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
6306 __isl_take isl_set *context);
6307 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
6308 __isl_take isl_multi_aff *maff,
6309 __isl_take isl_set *context);
6310 __isl_give isl_multi_aff *isl_multi_aff_gist(
6311 __isl_take isl_multi_aff *maff,
6312 __isl_take isl_set *context);
6313 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
6314 __isl_take isl_pw_aff *pwaff,
6315 __isl_take isl_set *context);
6316 __isl_give isl_pw_aff *isl_pw_aff_gist(
6317 __isl_take isl_pw_aff *pwaff,
6318 __isl_take isl_set *context);
6319 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
6320 __isl_take isl_pw_multi_aff *pma,
6321 __isl_take isl_set *set);
6322 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
6323 __isl_take isl_pw_multi_aff *pma,
6324 __isl_take isl_set *set);
6325 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
6326 __isl_take isl_multi_pw_aff *mpa,
6327 __isl_take isl_set *set);
6328 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
6329 __isl_take isl_multi_pw_aff *mpa,
6330 __isl_take isl_set *set);
6331 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
6332 __isl_take isl_union_pw_aff *upa,
6333 __isl_take isl_union_set *context);
6334 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
6335 __isl_take isl_union_pw_aff *upa,
6336 __isl_take isl_set *context);
6337 __isl_give isl_union_pw_multi_aff *
6338 isl_union_pw_multi_aff_gist_params(
6339 __isl_take isl_union_pw_multi_aff *upma,
6340 __isl_take isl_set *context);
6341 __isl_give isl_union_pw_multi_aff *
6342 isl_union_pw_multi_aff_gist(
6343 __isl_take isl_union_pw_multi_aff *upma,
6344 __isl_take isl_union_set *context);
6345 __isl_give isl_multi_union_pw_aff *
6346 isl_multi_union_pw_aff_gist_params(
6347 __isl_take isl_multi_union_pw_aff *aff,
6348 __isl_take isl_set *context);
6349 __isl_give isl_multi_union_pw_aff *
6350 isl_multi_union_pw_aff_gist(
6351 __isl_take isl_multi_union_pw_aff *aff,
6352 __isl_take isl_union_set *context);
6354 #include <isl/polynomial.h>
6355 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
6356 __isl_take isl_qpolynomial *qp,
6357 __isl_take isl_set *context);
6358 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
6359 __isl_take isl_qpolynomial *qp,
6360 __isl_take isl_set *context);
6361 __isl_give isl_qpolynomial_fold *
6362 isl_qpolynomial_fold_gist_params(
6363 __isl_take isl_qpolynomial_fold *fold,
6364 __isl_take isl_set *context);
6365 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
6366 __isl_take isl_qpolynomial_fold *fold,
6367 __isl_take isl_set *context);
6368 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
6369 __isl_take isl_pw_qpolynomial *pwqp,
6370 __isl_take isl_set *context);
6371 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
6372 __isl_take isl_pw_qpolynomial *pwqp,
6373 __isl_take isl_set *context);
6374 __isl_give isl_pw_qpolynomial_fold *
6375 isl_pw_qpolynomial_fold_gist(
6376 __isl_take isl_pw_qpolynomial_fold *pwf,
6377 __isl_take isl_set *context);
6378 __isl_give isl_pw_qpolynomial_fold *
6379 isl_pw_qpolynomial_fold_gist_params(
6380 __isl_take isl_pw_qpolynomial_fold *pwf,
6381 __isl_take isl_set *context);
6382 __isl_give isl_union_pw_qpolynomial *
6383 isl_union_pw_qpolynomial_gist_params(
6384 __isl_take isl_union_pw_qpolynomial *upwqp,
6385 __isl_take isl_set *context);
6386 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6387 __isl_take isl_union_pw_qpolynomial *upwqp,
6388 __isl_take isl_union_set *context);
6389 __isl_give isl_union_pw_qpolynomial_fold *
6390 isl_union_pw_qpolynomial_fold_gist(
6391 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6392 __isl_take isl_union_set *context);
6393 __isl_give isl_union_pw_qpolynomial_fold *
6394 isl_union_pw_qpolynomial_fold_gist_params(
6395 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6396 __isl_take isl_set *context);
6398 =item * Binary Arithmethic Operations
6400 #include <isl/val.h>
6401 __isl_give isl_multi_val *isl_multi_val_sub(
6402 __isl_take isl_multi_val *mv1,
6403 __isl_take isl_multi_val *mv2);
6405 #include <isl/aff.h>
6406 __isl_give isl_aff *isl_aff_add(
6407 __isl_take isl_aff *aff1,
6408 __isl_take isl_aff *aff2);
6409 __isl_give isl_multi_aff *isl_multi_aff_add(
6410 __isl_take isl_multi_aff *maff1,
6411 __isl_take isl_multi_aff *maff2);
6412 __isl_give isl_pw_aff *isl_pw_aff_add(
6413 __isl_take isl_pw_aff *pwaff1,
6414 __isl_take isl_pw_aff *pwaff2);
6415 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6416 __isl_take isl_pw_multi_aff *pma1,
6417 __isl_take isl_pw_multi_aff *pma2);
6418 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6419 __isl_take isl_union_pw_aff *upa1,
6420 __isl_take isl_union_pw_aff *upa2);
6421 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6422 __isl_take isl_union_pw_multi_aff *upma1,
6423 __isl_take isl_union_pw_multi_aff *upma2);
6424 __isl_give isl_pw_aff *isl_pw_aff_min(
6425 __isl_take isl_pw_aff *pwaff1,
6426 __isl_take isl_pw_aff *pwaff2);
6427 __isl_give isl_pw_aff *isl_pw_aff_max(
6428 __isl_take isl_pw_aff *pwaff1,
6429 __isl_take isl_pw_aff *pwaff2);
6430 __isl_give isl_aff *isl_aff_sub(
6431 __isl_take isl_aff *aff1,
6432 __isl_take isl_aff *aff2);
6433 __isl_give isl_multi_aff *isl_multi_aff_sub(
6434 __isl_take isl_multi_aff *ma1,
6435 __isl_take isl_multi_aff *ma2);
6436 __isl_give isl_pw_aff *isl_pw_aff_sub(
6437 __isl_take isl_pw_aff *pwaff1,
6438 __isl_take isl_pw_aff *pwaff2);
6439 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6440 __isl_take isl_multi_pw_aff *mpa1,
6441 __isl_take isl_multi_pw_aff *mpa2);
6442 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6443 __isl_take isl_pw_multi_aff *pma1,
6444 __isl_take isl_pw_multi_aff *pma2);
6445 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6446 __isl_take isl_union_pw_aff *upa1,
6447 __isl_take isl_union_pw_aff *upa2);
6448 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6449 __isl_take isl_union_pw_multi_aff *upma1,
6450 __isl_take isl_union_pw_multi_aff *upma2);
6451 __isl_give isl_multi_union_pw_aff *
6452 isl_multi_union_pw_aff_sub(
6453 __isl_take isl_multi_union_pw_aff *mupa1,
6454 __isl_take isl_multi_union_pw_aff *mupa2);
6456 C<isl_aff_sub> subtracts the second argument from the first.
6458 #include <isl/polynomial.h>
6459 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6460 __isl_take isl_qpolynomial *qp1,
6461 __isl_take isl_qpolynomial *qp2);
6462 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6463 __isl_take isl_pw_qpolynomial *pwqp1,
6464 __isl_take isl_pw_qpolynomial *pwqp2);
6465 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6466 __isl_take isl_pw_qpolynomial *pwqp1,
6467 __isl_take isl_pw_qpolynomial *pwqp2);
6468 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6469 __isl_take isl_pw_qpolynomial_fold *pwf1,
6470 __isl_take isl_pw_qpolynomial_fold *pwf2);
6471 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6472 __isl_take isl_union_pw_qpolynomial *upwqp1,
6473 __isl_take isl_union_pw_qpolynomial *upwqp2);
6474 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6475 __isl_take isl_qpolynomial *qp1,
6476 __isl_take isl_qpolynomial *qp2);
6477 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6478 __isl_take isl_pw_qpolynomial *pwqp1,
6479 __isl_take isl_pw_qpolynomial *pwqp2);
6480 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6481 __isl_take isl_union_pw_qpolynomial *upwqp1,
6482 __isl_take isl_union_pw_qpolynomial *upwqp2);
6483 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6484 __isl_take isl_pw_qpolynomial_fold *pwf1,
6485 __isl_take isl_pw_qpolynomial_fold *pwf2);
6486 __isl_give isl_union_pw_qpolynomial_fold *
6487 isl_union_pw_qpolynomial_fold_fold(
6488 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6489 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6491 #include <isl/aff.h>
6492 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6493 __isl_take isl_pw_aff *pwaff1,
6494 __isl_take isl_pw_aff *pwaff2);
6495 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6496 __isl_take isl_pw_multi_aff *pma1,
6497 __isl_take isl_pw_multi_aff *pma2);
6498 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6499 __isl_take isl_union_pw_aff *upa1,
6500 __isl_take isl_union_pw_aff *upa2);
6501 __isl_give isl_union_pw_multi_aff *
6502 isl_union_pw_multi_aff_union_add(
6503 __isl_take isl_union_pw_multi_aff *upma1,
6504 __isl_take isl_union_pw_multi_aff *upma2);
6505 __isl_give isl_multi_union_pw_aff *
6506 isl_multi_union_pw_aff_union_add(
6507 __isl_take isl_multi_union_pw_aff *mupa1,
6508 __isl_take isl_multi_union_pw_aff *mupa2);
6509 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6510 __isl_take isl_pw_aff *pwaff1,
6511 __isl_take isl_pw_aff *pwaff2);
6512 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6513 __isl_take isl_pw_aff *pwaff1,
6514 __isl_take isl_pw_aff *pwaff2);
6516 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6517 expression with a domain that is the union of those of C<pwaff1> and
6518 C<pwaff2> and such that on each cell, the quasi-affine expression is
6519 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6520 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6521 associated expression is the defined one.
6522 This in contrast to the C<isl_pw_aff_max> function, which is
6523 only defined on the shared definition domain of the arguments.
6525 #include <isl/val.h>
6526 __isl_give isl_multi_val *isl_multi_val_add_val(
6527 __isl_take isl_multi_val *mv,
6528 __isl_take isl_val *v);
6529 __isl_give isl_multi_val *isl_multi_val_mod_val(
6530 __isl_take isl_multi_val *mv,
6531 __isl_take isl_val *v);
6532 __isl_give isl_multi_val *isl_multi_val_scale_val(
6533 __isl_take isl_multi_val *mv,
6534 __isl_take isl_val *v);
6535 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6536 __isl_take isl_multi_val *mv,
6537 __isl_take isl_val *v);
6539 #include <isl/aff.h>
6540 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6541 __isl_take isl_val *mod);
6542 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6543 __isl_take isl_pw_aff *pa,
6544 __isl_take isl_val *mod);
6545 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6546 __isl_take isl_union_pw_aff *upa,
6547 __isl_take isl_val *f);
6548 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6549 __isl_take isl_val *v);
6550 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6551 __isl_take isl_multi_aff *ma,
6552 __isl_take isl_val *v);
6553 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6554 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6555 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6556 __isl_take isl_multi_pw_aff *mpa,
6557 __isl_take isl_val *v);
6558 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6559 __isl_take isl_pw_multi_aff *pma,
6560 __isl_take isl_val *v);
6561 __isl_give isl_union_pw_multi_aff *
6562 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6563 __isl_take isl_union_pw_aff *upa,
6564 __isl_take isl_val *f);
6565 isl_union_pw_multi_aff_scale_val(
6566 __isl_take isl_union_pw_multi_aff *upma,
6567 __isl_take isl_val *val);
6568 __isl_give isl_multi_union_pw_aff *
6569 isl_multi_union_pw_aff_scale_val(
6570 __isl_take isl_multi_union_pw_aff *mupa,
6571 __isl_take isl_val *v);
6572 __isl_give isl_aff *isl_aff_scale_down_ui(
6573 __isl_take isl_aff *aff, unsigned f);
6574 __isl_give isl_aff *isl_aff_scale_down_val(
6575 __isl_take isl_aff *aff, __isl_take isl_val *v);
6576 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6577 __isl_take isl_multi_aff *ma,
6578 __isl_take isl_val *v);
6579 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6580 __isl_take isl_pw_aff *pa,
6581 __isl_take isl_val *f);
6582 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6583 __isl_take isl_multi_pw_aff *mpa,
6584 __isl_take isl_val *v);
6585 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6586 __isl_take isl_pw_multi_aff *pma,
6587 __isl_take isl_val *v);
6588 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6589 __isl_take isl_union_pw_aff *upa,
6590 __isl_take isl_val *v);
6591 __isl_give isl_union_pw_multi_aff *
6592 isl_union_pw_multi_aff_scale_down_val(
6593 __isl_take isl_union_pw_multi_aff *upma,
6594 __isl_take isl_val *val);
6595 __isl_give isl_multi_union_pw_aff *
6596 isl_multi_union_pw_aff_scale_down_val(
6597 __isl_take isl_multi_union_pw_aff *mupa,
6598 __isl_take isl_val *v);
6600 #include <isl/polynomial.h>
6601 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6602 __isl_take isl_qpolynomial *qp,
6603 __isl_take isl_val *v);
6604 __isl_give isl_qpolynomial_fold *
6605 isl_qpolynomial_fold_scale_val(
6606 __isl_take isl_qpolynomial_fold *fold,
6607 __isl_take isl_val *v);
6608 __isl_give isl_pw_qpolynomial *
6609 isl_pw_qpolynomial_scale_val(
6610 __isl_take isl_pw_qpolynomial *pwqp,
6611 __isl_take isl_val *v);
6612 __isl_give isl_pw_qpolynomial_fold *
6613 isl_pw_qpolynomial_fold_scale_val(
6614 __isl_take isl_pw_qpolynomial_fold *pwf,
6615 __isl_take isl_val *v);
6616 __isl_give isl_union_pw_qpolynomial *
6617 isl_union_pw_qpolynomial_scale_val(
6618 __isl_take isl_union_pw_qpolynomial *upwqp,
6619 __isl_take isl_val *v);
6620 __isl_give isl_union_pw_qpolynomial_fold *
6621 isl_union_pw_qpolynomial_fold_scale_val(
6622 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6623 __isl_take isl_val *v);
6624 __isl_give isl_qpolynomial *
6625 isl_qpolynomial_scale_down_val(
6626 __isl_take isl_qpolynomial *qp,
6627 __isl_take isl_val *v);
6628 __isl_give isl_qpolynomial_fold *
6629 isl_qpolynomial_fold_scale_down_val(
6630 __isl_take isl_qpolynomial_fold *fold,
6631 __isl_take isl_val *v);
6632 __isl_give isl_pw_qpolynomial *
6633 isl_pw_qpolynomial_scale_down_val(
6634 __isl_take isl_pw_qpolynomial *pwqp,
6635 __isl_take isl_val *v);
6636 __isl_give isl_pw_qpolynomial_fold *
6637 isl_pw_qpolynomial_fold_scale_down_val(
6638 __isl_take isl_pw_qpolynomial_fold *pwf,
6639 __isl_take isl_val *v);
6640 __isl_give isl_union_pw_qpolynomial *
6641 isl_union_pw_qpolynomial_scale_down_val(
6642 __isl_take isl_union_pw_qpolynomial *upwqp,
6643 __isl_take isl_val *v);
6644 __isl_give isl_union_pw_qpolynomial_fold *
6645 isl_union_pw_qpolynomial_fold_scale_down_val(
6646 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6647 __isl_take isl_val *v);
6649 #include <isl/val.h>
6650 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6651 __isl_take isl_multi_val *mv1,
6652 __isl_take isl_multi_val *mv2);
6653 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6654 __isl_take isl_multi_val *mv1,
6655 __isl_take isl_multi_val *mv2);
6656 __isl_give isl_multi_val *
6657 isl_multi_val_scale_down_multi_val(
6658 __isl_take isl_multi_val *mv1,
6659 __isl_take isl_multi_val *mv2);
6661 #include <isl/aff.h>
6662 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6663 __isl_take isl_multi_aff *ma,
6664 __isl_take isl_multi_val *mv);
6665 __isl_give isl_multi_union_pw_aff *
6666 isl_multi_union_pw_aff_mod_multi_val(
6667 __isl_take isl_multi_union_pw_aff *upma,
6668 __isl_take isl_multi_val *mv);
6669 __isl_give isl_multi_pw_aff *
6670 isl_multi_pw_aff_mod_multi_val(
6671 __isl_take isl_multi_pw_aff *mpa,
6672 __isl_take isl_multi_val *mv);
6673 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6674 __isl_take isl_multi_aff *ma,
6675 __isl_take isl_multi_val *mv);
6676 __isl_give isl_pw_multi_aff *
6677 isl_pw_multi_aff_scale_multi_val(
6678 __isl_take isl_pw_multi_aff *pma,
6679 __isl_take isl_multi_val *mv);
6680 __isl_give isl_multi_pw_aff *
6681 isl_multi_pw_aff_scale_multi_val(
6682 __isl_take isl_multi_pw_aff *mpa,
6683 __isl_take isl_multi_val *mv);
6684 __isl_give isl_multi_union_pw_aff *
6685 isl_multi_union_pw_aff_scale_multi_val(
6686 __isl_take isl_multi_union_pw_aff *mupa,
6687 __isl_take isl_multi_val *mv);
6688 __isl_give isl_union_pw_multi_aff *
6689 isl_union_pw_multi_aff_scale_multi_val(
6690 __isl_take isl_union_pw_multi_aff *upma,
6691 __isl_take isl_multi_val *mv);
6692 __isl_give isl_multi_aff *
6693 isl_multi_aff_scale_down_multi_val(
6694 __isl_take isl_multi_aff *ma,
6695 __isl_take isl_multi_val *mv);
6696 __isl_give isl_multi_pw_aff *
6697 isl_multi_pw_aff_scale_down_multi_val(
6698 __isl_take isl_multi_pw_aff *mpa,
6699 __isl_take isl_multi_val *mv);
6700 __isl_give isl_multi_union_pw_aff *
6701 isl_multi_union_pw_aff_scale_down_multi_val(
6702 __isl_take isl_multi_union_pw_aff *mupa,
6703 __isl_take isl_multi_val *mv);
6705 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6706 by the corresponding elements of C<mv>.
6708 #include <isl/aff.h>
6709 __isl_give isl_aff *isl_aff_mul(
6710 __isl_take isl_aff *aff1,
6711 __isl_take isl_aff *aff2);
6712 __isl_give isl_aff *isl_aff_div(
6713 __isl_take isl_aff *aff1,
6714 __isl_take isl_aff *aff2);
6715 __isl_give isl_pw_aff *isl_pw_aff_mul(
6716 __isl_take isl_pw_aff *pwaff1,
6717 __isl_take isl_pw_aff *pwaff2);
6718 __isl_give isl_pw_aff *isl_pw_aff_div(
6719 __isl_take isl_pw_aff *pa1,
6720 __isl_take isl_pw_aff *pa2);
6721 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6722 __isl_take isl_pw_aff *pa1,
6723 __isl_take isl_pw_aff *pa2);
6724 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6725 __isl_take isl_pw_aff *pa1,
6726 __isl_take isl_pw_aff *pa2);
6728 When multiplying two affine expressions, at least one of the two needs
6729 to be a constant. Similarly, when dividing an affine expression by another,
6730 the second expression needs to be a constant.
6731 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6732 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6735 #include <isl/polynomial.h>
6736 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6737 __isl_take isl_qpolynomial *qp1,
6738 __isl_take isl_qpolynomial *qp2);
6739 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6740 __isl_take isl_pw_qpolynomial *pwqp1,
6741 __isl_take isl_pw_qpolynomial *pwqp2);
6742 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6743 __isl_take isl_union_pw_qpolynomial *upwqp1,
6744 __isl_take isl_union_pw_qpolynomial *upwqp2);
6748 =head3 Lexicographic Optimization
6750 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6751 the following functions
6752 compute a set that contains the lexicographic minimum or maximum
6753 of the elements in C<set> (or C<bset>) for those values of the parameters
6754 that satisfy C<dom>.
6755 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6756 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6758 In other words, the union of the parameter values
6759 for which the result is non-empty and of C<*empty>
6762 #include <isl/set.h>
6763 __isl_give isl_set *isl_basic_set_partial_lexmin(
6764 __isl_take isl_basic_set *bset,
6765 __isl_take isl_basic_set *dom,
6766 __isl_give isl_set **empty);
6767 __isl_give isl_set *isl_basic_set_partial_lexmax(
6768 __isl_take isl_basic_set *bset,
6769 __isl_take isl_basic_set *dom,
6770 __isl_give isl_set **empty);
6771 __isl_give isl_set *isl_set_partial_lexmin(
6772 __isl_take isl_set *set, __isl_take isl_set *dom,
6773 __isl_give isl_set **empty);
6774 __isl_give isl_set *isl_set_partial_lexmax(
6775 __isl_take isl_set *set, __isl_take isl_set *dom,
6776 __isl_give isl_set **empty);
6778 Given a (basic) set C<set> (or C<bset>), the following functions simply
6779 return a set containing the lexicographic minimum or maximum
6780 of the elements in C<set> (or C<bset>).
6781 In case of union sets, the optimum is computed per space.
6783 #include <isl/set.h>
6784 __isl_give isl_set *isl_basic_set_lexmin(
6785 __isl_take isl_basic_set *bset);
6786 __isl_give isl_set *isl_basic_set_lexmax(
6787 __isl_take isl_basic_set *bset);
6788 __isl_give isl_set *isl_set_lexmin(
6789 __isl_take isl_set *set);
6790 __isl_give isl_set *isl_set_lexmax(
6791 __isl_take isl_set *set);
6792 __isl_give isl_union_set *isl_union_set_lexmin(
6793 __isl_take isl_union_set *uset);
6794 __isl_give isl_union_set *isl_union_set_lexmax(
6795 __isl_take isl_union_set *uset);
6797 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6798 the following functions
6799 compute a relation that maps each element of C<dom>
6800 to the single lexicographic minimum or maximum
6801 of the elements that are associated to that same
6802 element in C<map> (or C<bmap>).
6803 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6804 that contains the elements in C<dom> that do not map
6805 to any elements in C<map> (or C<bmap>).
6806 In other words, the union of the domain of the result and of C<*empty>
6809 #include <isl/map.h>
6810 __isl_give isl_map *isl_basic_map_partial_lexmax(
6811 __isl_take isl_basic_map *bmap,
6812 __isl_take isl_basic_set *dom,
6813 __isl_give isl_set **empty);
6814 __isl_give isl_map *isl_basic_map_partial_lexmin(
6815 __isl_take isl_basic_map *bmap,
6816 __isl_take isl_basic_set *dom,
6817 __isl_give isl_set **empty);
6818 __isl_give isl_map *isl_map_partial_lexmax(
6819 __isl_take isl_map *map, __isl_take isl_set *dom,
6820 __isl_give isl_set **empty);
6821 __isl_give isl_map *isl_map_partial_lexmin(
6822 __isl_take isl_map *map, __isl_take isl_set *dom,
6823 __isl_give isl_set **empty);
6825 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6826 return a map mapping each element in the domain of
6827 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6828 of all elements associated to that element.
6829 In case of union relations, the optimum is computed per space.
6831 #include <isl/map.h>
6832 __isl_give isl_map *isl_basic_map_lexmin(
6833 __isl_take isl_basic_map *bmap);
6834 __isl_give isl_map *isl_basic_map_lexmax(
6835 __isl_take isl_basic_map *bmap);
6836 __isl_give isl_map *isl_map_lexmin(
6837 __isl_take isl_map *map);
6838 __isl_give isl_map *isl_map_lexmax(
6839 __isl_take isl_map *map);
6840 __isl_give isl_union_map *isl_union_map_lexmin(
6841 __isl_take isl_union_map *umap);
6842 __isl_give isl_union_map *isl_union_map_lexmax(
6843 __isl_take isl_union_map *umap);
6845 The following functions return their result in the form of
6846 a piecewise multi-affine expression,
6847 but are otherwise equivalent to the corresponding functions
6848 returning a basic set or relation.
6850 #include <isl/set.h>
6851 __isl_give isl_pw_multi_aff *
6852 isl_basic_set_partial_lexmin_pw_multi_aff(
6853 __isl_take isl_basic_set *bset,
6854 __isl_take isl_basic_set *dom,
6855 __isl_give isl_set **empty);
6856 __isl_give isl_pw_multi_aff *
6857 isl_basic_set_partial_lexmax_pw_multi_aff(
6858 __isl_take isl_basic_set *bset,
6859 __isl_take isl_basic_set *dom,
6860 __isl_give isl_set **empty);
6861 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6862 __isl_take isl_set *set);
6863 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6864 __isl_take isl_set *set);
6866 #include <isl/map.h>
6867 __isl_give isl_pw_multi_aff *
6868 isl_basic_map_lexmin_pw_multi_aff(
6869 __isl_take isl_basic_map *bmap);
6870 __isl_give isl_pw_multi_aff *
6871 isl_basic_map_partial_lexmin_pw_multi_aff(
6872 __isl_take isl_basic_map *bmap,
6873 __isl_take isl_basic_set *dom,
6874 __isl_give isl_set **empty);
6875 __isl_give isl_pw_multi_aff *
6876 isl_basic_map_partial_lexmax_pw_multi_aff(
6877 __isl_take isl_basic_map *bmap,
6878 __isl_take isl_basic_set *dom,
6879 __isl_give isl_set **empty);
6880 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6881 __isl_take isl_map *map);
6882 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6883 __isl_take isl_map *map);
6885 The following functions return the lexicographic minimum or maximum
6886 on the shared domain of the inputs and the single defined function
6887 on those parts of the domain where only a single function is defined.
6889 #include <isl/aff.h>
6890 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6891 __isl_take isl_pw_multi_aff *pma1,
6892 __isl_take isl_pw_multi_aff *pma2);
6893 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6894 __isl_take isl_pw_multi_aff *pma1,
6895 __isl_take isl_pw_multi_aff *pma2);
6897 =head2 Ternary Operations
6899 #include <isl/aff.h>
6900 __isl_give isl_pw_aff *isl_pw_aff_cond(
6901 __isl_take isl_pw_aff *cond,
6902 __isl_take isl_pw_aff *pwaff_true,
6903 __isl_take isl_pw_aff *pwaff_false);
6905 The function C<isl_pw_aff_cond> performs a conditional operator
6906 and returns an expression that is equal to C<pwaff_true>
6907 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6908 where C<cond> is zero.
6912 Lists are defined over several element types, including
6913 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
6914 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6915 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6916 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6917 Here we take lists of C<isl_set>s as an example.
6918 Lists can be created, copied, modified and freed using the following functions.
6920 #include <isl/set.h>
6921 __isl_give isl_set_list *isl_set_list_from_set(
6922 __isl_take isl_set *el);
6923 __isl_give isl_set_list *isl_set_list_alloc(
6924 isl_ctx *ctx, int n);
6925 __isl_give isl_set_list *isl_set_list_copy(
6926 __isl_keep isl_set_list *list);
6927 __isl_give isl_set_list *isl_set_list_insert(
6928 __isl_take isl_set_list *list, unsigned pos,
6929 __isl_take isl_set *el);
6930 __isl_give isl_set_list *isl_set_list_add(
6931 __isl_take isl_set_list *list,
6932 __isl_take isl_set *el);
6933 __isl_give isl_set_list *isl_set_list_drop(
6934 __isl_take isl_set_list *list,
6935 unsigned first, unsigned n);
6936 __isl_give isl_set_list *isl_set_list_set_set(
6937 __isl_take isl_set_list *list, int index,
6938 __isl_take isl_set *set);
6939 __isl_give isl_set_list *isl_set_list_concat(
6940 __isl_take isl_set_list *list1,
6941 __isl_take isl_set_list *list2);
6942 __isl_give isl_set_list *isl_set_list_sort(
6943 __isl_take isl_set_list *list,
6944 int (*cmp)(__isl_keep isl_set *a,
6945 __isl_keep isl_set *b, void *user),
6947 __isl_null isl_set_list *isl_set_list_free(
6948 __isl_take isl_set_list *list);
6950 C<isl_set_list_alloc> creates an empty list with an initial capacity
6951 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
6952 add elements to a list, increasing its capacity as needed.
6953 C<isl_set_list_from_set> creates a list with a single element.
6955 Lists can be inspected using the following functions.
6957 #include <isl/set.h>
6958 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6959 __isl_give isl_set *isl_set_list_get_set(
6960 __isl_keep isl_set_list *list, int index);
6961 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6962 int (*fn)(__isl_take isl_set *el, void *user),
6964 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6965 int (*follows)(__isl_keep isl_set *a,
6966 __isl_keep isl_set *b, void *user),
6968 int (*fn)(__isl_take isl_set *el, void *user),
6971 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6972 strongly connected components of the graph with as vertices the elements
6973 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6974 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6975 should return C<-1> on error.
6977 Lists can be printed using
6979 #include <isl/set.h>
6980 __isl_give isl_printer *isl_printer_print_set_list(
6981 __isl_take isl_printer *p,
6982 __isl_keep isl_set_list *list);
6984 =head2 Associative arrays
6986 Associative arrays map isl objects of a specific type to isl objects
6987 of some (other) specific type. They are defined for several pairs
6988 of types, including (C<isl_map>, C<isl_basic_set>),
6989 (C<isl_id>, C<isl_ast_expr>) and.
6990 (C<isl_id>, C<isl_pw_aff>).
6991 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6994 Associative arrays can be created, copied and freed using
6995 the following functions.
6997 #include <isl/id_to_ast_expr.h>
6998 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_alloc(
6999 isl_ctx *ctx, int min_size);
7000 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_copy(
7001 __isl_keep isl_id_to_ast_expr *id2expr);
7002 __isl_null isl_id_to_ast_expr *isl_id_to_ast_expr_free(
7003 __isl_take isl_id_to_ast_expr *id2expr);
7005 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
7006 to specify the expected size of the associative array.
7007 The associative array will be grown automatically as needed.
7009 Associative arrays can be inspected using the following functions.
7011 #include <isl/id_to_ast_expr.h>
7012 int isl_id_to_ast_expr_has(
7013 __isl_keep isl_id_to_ast_expr *id2expr,
7014 __isl_keep isl_id *key);
7015 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
7016 __isl_keep isl_id_to_ast_expr *id2expr,
7017 __isl_take isl_id *key);
7018 int isl_id_to_ast_expr_foreach(
7019 __isl_keep isl_id_to_ast_expr *id2expr,
7020 int (*fn)(__isl_take isl_id *key,
7021 __isl_take isl_ast_expr *val, void *user),
7024 They can be modified using the following function.
7026 #include <isl/id_to_ast_expr.h>
7027 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_set(
7028 __isl_take isl_id_to_ast_expr *id2expr,
7029 __isl_take isl_id *key,
7030 __isl_take isl_ast_expr *val);
7031 __isl_give isl_id_to_ast_expr *isl_id_to_ast_expr_drop(
7032 __isl_take isl_id_to_ast_expr *id2expr,
7033 __isl_take isl_id *key);
7035 Associative arrays can be printed using the following function.
7037 #include <isl/id_to_ast_expr.h>
7038 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
7039 __isl_take isl_printer *p,
7040 __isl_keep isl_id_to_ast_expr *id2expr);
7044 Vectors can be created, copied and freed using the following functions.
7046 #include <isl/vec.h>
7047 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
7049 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
7050 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
7052 Note that the elements of a newly created vector may have arbitrary values.
7053 The elements can be changed and inspected using the following functions.
7055 int isl_vec_size(__isl_keep isl_vec *vec);
7056 __isl_give isl_val *isl_vec_get_element_val(
7057 __isl_keep isl_vec *vec, int pos);
7058 __isl_give isl_vec *isl_vec_set_element_si(
7059 __isl_take isl_vec *vec, int pos, int v);
7060 __isl_give isl_vec *isl_vec_set_element_val(
7061 __isl_take isl_vec *vec, int pos,
7062 __isl_take isl_val *v);
7063 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
7065 __isl_give isl_vec *isl_vec_set_val(
7066 __isl_take isl_vec *vec, __isl_take isl_val *v);
7067 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
7068 __isl_keep isl_vec *vec2, int pos);
7070 C<isl_vec_get_element> will return a negative value if anything went wrong.
7071 In that case, the value of C<*v> is undefined.
7073 The following function can be used to concatenate two vectors.
7075 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
7076 __isl_take isl_vec *vec2);
7080 Matrices can be created, copied and freed using the following functions.
7082 #include <isl/mat.h>
7083 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
7084 unsigned n_row, unsigned n_col);
7085 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
7086 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
7088 Note that the elements of a newly created matrix may have arbitrary values.
7089 The elements can be changed and inspected using the following functions.
7091 int isl_mat_rows(__isl_keep isl_mat *mat);
7092 int isl_mat_cols(__isl_keep isl_mat *mat);
7093 __isl_give isl_val *isl_mat_get_element_val(
7094 __isl_keep isl_mat *mat, int row, int col);
7095 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
7096 int row, int col, int v);
7097 __isl_give isl_mat *isl_mat_set_element_val(
7098 __isl_take isl_mat *mat, int row, int col,
7099 __isl_take isl_val *v);
7101 C<isl_mat_get_element> will return a negative value if anything went wrong.
7102 In that case, the value of C<*v> is undefined.
7104 The following function can be used to compute the (right) inverse
7105 of a matrix, i.e., a matrix such that the product of the original
7106 and the inverse (in that order) is a multiple of the identity matrix.
7107 The input matrix is assumed to be of full row-rank.
7109 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
7111 The following function can be used to compute the (right) kernel
7112 (or null space) of a matrix, i.e., a matrix such that the product of
7113 the original and the kernel (in that order) is the zero matrix.
7115 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
7117 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
7119 The following functions determine
7120 an upper or lower bound on a quasipolynomial over its domain.
7122 __isl_give isl_pw_qpolynomial_fold *
7123 isl_pw_qpolynomial_bound(
7124 __isl_take isl_pw_qpolynomial *pwqp,
7125 enum isl_fold type, int *tight);
7127 __isl_give isl_union_pw_qpolynomial_fold *
7128 isl_union_pw_qpolynomial_bound(
7129 __isl_take isl_union_pw_qpolynomial *upwqp,
7130 enum isl_fold type, int *tight);
7132 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
7133 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
7134 is the returned bound is known be tight, i.e., for each value
7135 of the parameters there is at least
7136 one element in the domain that reaches the bound.
7137 If the domain of C<pwqp> is not wrapping, then the bound is computed
7138 over all elements in that domain and the result has a purely parametric
7139 domain. If the domain of C<pwqp> is wrapping, then the bound is
7140 computed over the range of the wrapped relation. The domain of the
7141 wrapped relation becomes the domain of the result.
7143 =head2 Parametric Vertex Enumeration
7145 The parametric vertex enumeration described in this section
7146 is mainly intended to be used internally and by the C<barvinok>
7149 #include <isl/vertices.h>
7150 __isl_give isl_vertices *isl_basic_set_compute_vertices(
7151 __isl_keep isl_basic_set *bset);
7153 The function C<isl_basic_set_compute_vertices> performs the
7154 actual computation of the parametric vertices and the chamber
7155 decomposition and store the result in an C<isl_vertices> object.
7156 This information can be queried by either iterating over all
7157 the vertices or iterating over all the chambers or cells
7158 and then iterating over all vertices that are active on the chamber.
7160 int isl_vertices_foreach_vertex(
7161 __isl_keep isl_vertices *vertices,
7162 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7165 int isl_vertices_foreach_cell(
7166 __isl_keep isl_vertices *vertices,
7167 int (*fn)(__isl_take isl_cell *cell, void *user),
7169 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
7170 int (*fn)(__isl_take isl_vertex *vertex, void *user),
7173 Other operations that can be performed on an C<isl_vertices> object are
7176 int isl_vertices_get_n_vertices(
7177 __isl_keep isl_vertices *vertices);
7178 void isl_vertices_free(__isl_take isl_vertices *vertices);
7180 Vertices can be inspected and destroyed using the following functions.
7182 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
7183 __isl_give isl_basic_set *isl_vertex_get_domain(
7184 __isl_keep isl_vertex *vertex);
7185 __isl_give isl_multi_aff *isl_vertex_get_expr(
7186 __isl_keep isl_vertex *vertex);
7187 void isl_vertex_free(__isl_take isl_vertex *vertex);
7189 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
7190 describing the vertex in terms of the parameters,
7191 while C<isl_vertex_get_domain> returns the activity domain
7194 Chambers can be inspected and destroyed using the following functions.
7196 __isl_give isl_basic_set *isl_cell_get_domain(
7197 __isl_keep isl_cell *cell);
7198 void isl_cell_free(__isl_take isl_cell *cell);
7200 =head1 Polyhedral Compilation Library
7202 This section collects functionality in C<isl> that has been specifically
7203 designed for use during polyhedral compilation.
7205 =head2 Dependence Analysis
7207 C<isl> contains specialized functionality for performing
7208 array dataflow analysis. That is, given a I<sink> access relation
7209 and a collection of possible I<source> access relations,
7210 C<isl> can compute relations that describe
7211 for each iteration of the sink access, which iteration
7212 of which of the source access relations was the last
7213 to access the same data element before the given iteration
7215 The resulting dependence relations map source iterations
7216 to the corresponding sink iterations.
7217 To compute standard flow dependences, the sink should be
7218 a read, while the sources should be writes.
7219 If any of the source accesses are marked as being I<may>
7220 accesses, then there will be a dependence from the last
7221 I<must> access B<and> from any I<may> access that follows
7222 this last I<must> access.
7223 In particular, if I<all> sources are I<may> accesses,
7224 then memory based dependence analysis is performed.
7225 If, on the other hand, all sources are I<must> accesses,
7226 then value based dependence analysis is performed.
7228 #include <isl/flow.h>
7230 typedef int (*isl_access_level_before)(void *first, void *second);
7232 __isl_give isl_access_info *isl_access_info_alloc(
7233 __isl_take isl_map *sink,
7234 void *sink_user, isl_access_level_before fn,
7236 __isl_give isl_access_info *isl_access_info_add_source(
7237 __isl_take isl_access_info *acc,
7238 __isl_take isl_map *source, int must,
7240 __isl_null isl_access_info *isl_access_info_free(
7241 __isl_take isl_access_info *acc);
7243 __isl_give isl_flow *isl_access_info_compute_flow(
7244 __isl_take isl_access_info *acc);
7246 int isl_flow_foreach(__isl_keep isl_flow *deps,
7247 int (*fn)(__isl_take isl_map *dep, int must,
7248 void *dep_user, void *user),
7250 __isl_give isl_map *isl_flow_get_no_source(
7251 __isl_keep isl_flow *deps, int must);
7252 void isl_flow_free(__isl_take isl_flow *deps);
7254 The function C<isl_access_info_compute_flow> performs the actual
7255 dependence analysis. The other functions are used to construct
7256 the input for this function or to read off the output.
7258 The input is collected in an C<isl_access_info>, which can
7259 be created through a call to C<isl_access_info_alloc>.
7260 The arguments to this functions are the sink access relation
7261 C<sink>, a token C<sink_user> used to identify the sink
7262 access to the user, a callback function for specifying the
7263 relative order of source and sink accesses, and the number
7264 of source access relations that will be added.
7265 The callback function has type C<int (*)(void *first, void *second)>.
7266 The function is called with two user supplied tokens identifying
7267 either a source or the sink and it should return the shared nesting
7268 level and the relative order of the two accesses.
7269 In particular, let I<n> be the number of loops shared by
7270 the two accesses. If C<first> precedes C<second> textually,
7271 then the function should return I<2 * n + 1>; otherwise,
7272 it should return I<2 * n>.
7273 The sources can be added to the C<isl_access_info> by performing
7274 (at most) C<max_source> calls to C<isl_access_info_add_source>.
7275 C<must> indicates whether the source is a I<must> access
7276 or a I<may> access. Note that a multi-valued access relation
7277 should only be marked I<must> if every iteration in the domain
7278 of the relation accesses I<all> elements in its image.
7279 The C<source_user> token is again used to identify
7280 the source access. The range of the source access relation
7281 C<source> should have the same dimension as the range
7282 of the sink access relation.
7283 The C<isl_access_info_free> function should usually not be
7284 called explicitly, because it is called implicitly by
7285 C<isl_access_info_compute_flow>.
7287 The result of the dependence analysis is collected in an
7288 C<isl_flow>. There may be elements of
7289 the sink access for which no preceding source access could be
7290 found or for which all preceding sources are I<may> accesses.
7291 The relations containing these elements can be obtained through
7292 calls to C<isl_flow_get_no_source>, the first with C<must> set
7293 and the second with C<must> unset.
7294 In the case of standard flow dependence analysis,
7295 with the sink a read and the sources I<must> writes,
7296 the first relation corresponds to the reads from uninitialized
7297 array elements and the second relation is empty.
7298 The actual flow dependences can be extracted using
7299 C<isl_flow_foreach>. This function will call the user-specified
7300 callback function C<fn> for each B<non-empty> dependence between
7301 a source and the sink. The callback function is called
7302 with four arguments, the actual flow dependence relation
7303 mapping source iterations to sink iterations, a boolean that
7304 indicates whether it is a I<must> or I<may> dependence, a token
7305 identifying the source and an additional C<void *> with value
7306 equal to the third argument of the C<isl_flow_foreach> call.
7307 A dependence is marked I<must> if it originates from a I<must>
7308 source and if it is not followed by any I<may> sources.
7310 After finishing with an C<isl_flow>, the user should call
7311 C<isl_flow_free> to free all associated memory.
7313 A higher-level interface to dependence analysis is provided
7314 by the following function.
7316 #include <isl/flow.h>
7318 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
7319 __isl_take isl_union_map *must_source,
7320 __isl_take isl_union_map *may_source,
7321 __isl_take isl_union_map *schedule,
7322 __isl_give isl_union_map **must_dep,
7323 __isl_give isl_union_map **may_dep,
7324 __isl_give isl_union_map **must_no_source,
7325 __isl_give isl_union_map **may_no_source);
7327 The arrays are identified by the tuple names of the ranges
7328 of the accesses. The iteration domains by the tuple names
7329 of the domains of the accesses and of the schedule.
7330 The relative order of the iteration domains is given by the
7331 schedule. The relations returned through C<must_no_source>
7332 and C<may_no_source> are subsets of C<sink>.
7333 Any of C<must_dep>, C<may_dep>, C<must_no_source>
7334 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
7335 any of the other arguments is treated as an error.
7337 =head3 Interaction with Dependence Analysis
7339 During the dependence analysis, we frequently need to perform
7340 the following operation. Given a relation between sink iterations
7341 and potential source iterations from a particular source domain,
7342 what is the last potential source iteration corresponding to each
7343 sink iteration. It can sometimes be convenient to adjust
7344 the set of potential source iterations before or after each such operation.
7345 The prototypical example is fuzzy array dataflow analysis,
7346 where we need to analyze if, based on data-dependent constraints,
7347 the sink iteration can ever be executed without one or more of
7348 the corresponding potential source iterations being executed.
7349 If so, we can introduce extra parameters and select an unknown
7350 but fixed source iteration from the potential source iterations.
7351 To be able to perform such manipulations, C<isl> provides the following
7354 #include <isl/flow.h>
7356 typedef __isl_give isl_restriction *(*isl_access_restrict)(
7357 __isl_keep isl_map *source_map,
7358 __isl_keep isl_set *sink, void *source_user,
7360 __isl_give isl_access_info *isl_access_info_set_restrict(
7361 __isl_take isl_access_info *acc,
7362 isl_access_restrict fn, void *user);
7364 The function C<isl_access_info_set_restrict> should be called
7365 before calling C<isl_access_info_compute_flow> and registers a callback function
7366 that will be called any time C<isl> is about to compute the last
7367 potential source. The first argument is the (reverse) proto-dependence,
7368 mapping sink iterations to potential source iterations.
7369 The second argument represents the sink iterations for which
7370 we want to compute the last source iteration.
7371 The third argument is the token corresponding to the source
7372 and the final argument is the token passed to C<isl_access_info_set_restrict>.
7373 The callback is expected to return a restriction on either the input or
7374 the output of the operation computing the last potential source.
7375 If the input needs to be restricted then restrictions are needed
7376 for both the source and the sink iterations. The sink iterations
7377 and the potential source iterations will be intersected with these sets.
7378 If the output needs to be restricted then only a restriction on the source
7379 iterations is required.
7380 If any error occurs, the callback should return C<NULL>.
7381 An C<isl_restriction> object can be created, freed and inspected
7382 using the following functions.
7384 #include <isl/flow.h>
7386 __isl_give isl_restriction *isl_restriction_input(
7387 __isl_take isl_set *source_restr,
7388 __isl_take isl_set *sink_restr);
7389 __isl_give isl_restriction *isl_restriction_output(
7390 __isl_take isl_set *source_restr);
7391 __isl_give isl_restriction *isl_restriction_none(
7392 __isl_take isl_map *source_map);
7393 __isl_give isl_restriction *isl_restriction_empty(
7394 __isl_take isl_map *source_map);
7395 __isl_null isl_restriction *isl_restriction_free(
7396 __isl_take isl_restriction *restr);
7398 C<isl_restriction_none> and C<isl_restriction_empty> are special
7399 cases of C<isl_restriction_input>. C<isl_restriction_none>
7400 is essentially equivalent to
7402 isl_restriction_input(isl_set_universe(
7403 isl_space_range(isl_map_get_space(source_map))),
7405 isl_space_domain(isl_map_get_space(source_map))));
7407 whereas C<isl_restriction_empty> is essentially equivalent to
7409 isl_restriction_input(isl_set_empty(
7410 isl_space_range(isl_map_get_space(source_map))),
7412 isl_space_domain(isl_map_get_space(source_map))));
7416 B<The functionality described in this section is fairly new
7417 and may be subject to change.>
7419 #include <isl/schedule.h>
7420 __isl_give isl_schedule *
7421 isl_schedule_constraints_compute_schedule(
7422 __isl_take isl_schedule_constraints *sc);
7423 __isl_give isl_schedule *isl_schedule_copy(
7424 __isl_keep isl_schedule *sched);
7425 __isl_null isl_schedule *isl_schedule_free(
7426 __isl_take isl_schedule *sched);
7428 The function C<isl_schedule_constraints_compute_schedule> can be
7429 used to compute a schedule that satisfies the given schedule constraints.
7430 These schedule constraints include the iteration domain for which
7431 a schedule should be computed and dependences between pairs of
7432 iterations. In particular, these dependences include
7433 I<validity> dependences and I<proximity> dependences.
7434 By default, the algorithm used to construct the schedule is similar
7435 to that of C<Pluto>.
7436 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
7438 The generated schedule respects all validity dependences.
7439 That is, all dependence distances over these dependences in the
7440 scheduled space are lexicographically positive.
7441 The default algorithm tries to ensure that the dependence distances
7442 over coincidence constraints are zero and to minimize the
7443 dependence distances over proximity dependences.
7444 Moreover, it tries to obtain sequences (bands) of schedule dimensions
7445 for groups of domains where the dependence distances over validity
7446 dependences have only non-negative values.
7447 When using Feautrier's algorithm, the coincidence and proximity constraints
7448 are only taken into account during the extension to a
7449 full-dimensional schedule.
7451 An C<isl_schedule_constraints> object can be constructed
7452 and manipulated using the following functions.
7454 #include <isl/schedule.h>
7455 __isl_give isl_schedule_constraints *
7456 isl_schedule_constraints_copy(
7457 __isl_keep isl_schedule_constraints *sc);
7458 __isl_give isl_schedule_constraints *
7459 isl_schedule_constraints_on_domain(
7460 __isl_take isl_union_set *domain);
7461 __isl_give isl_schedule_constraints *
7462 isl_schedule_constraints_set_validity(
7463 __isl_take isl_schedule_constraints *sc,
7464 __isl_take isl_union_map *validity);
7465 __isl_give isl_schedule_constraints *
7466 isl_schedule_constraints_set_coincidence(
7467 __isl_take isl_schedule_constraints *sc,
7468 __isl_take isl_union_map *coincidence);
7469 __isl_give isl_schedule_constraints *
7470 isl_schedule_constraints_set_proximity(
7471 __isl_take isl_schedule_constraints *sc,
7472 __isl_take isl_union_map *proximity);
7473 __isl_give isl_schedule_constraints *
7474 isl_schedule_constraints_set_conditional_validity(
7475 __isl_take isl_schedule_constraints *sc,
7476 __isl_take isl_union_map *condition,
7477 __isl_take isl_union_map *validity);
7478 __isl_null isl_schedule_constraints *
7479 isl_schedule_constraints_free(
7480 __isl_take isl_schedule_constraints *sc);
7482 The initial C<isl_schedule_constraints> object created by
7483 C<isl_schedule_constraints_on_domain> does not impose any constraints.
7484 That is, it has an empty set of dependences.
7485 The function C<isl_schedule_constraints_set_validity> replaces the
7486 validity dependences, mapping domain elements I<i> to domain
7487 elements that should be scheduled after I<i>.
7488 The function C<isl_schedule_constraints_set_coincidence> replaces the
7489 coincidence dependences, mapping domain elements I<i> to domain
7490 elements that should be scheduled together with I<I>, if possible.
7491 The function C<isl_schedule_constraints_set_proximity> replaces the
7492 proximity dependences, mapping domain elements I<i> to domain
7493 elements that should be scheduled either before I<I>
7494 or as early as possible after I<i>.
7496 The function C<isl_schedule_constraints_set_conditional_validity>
7497 replaces the conditional validity constraints.
7498 A conditional validity constraint is only imposed when any of the corresponding
7499 conditions is satisfied, i.e., when any of them is non-zero.
7500 That is, the scheduler ensures that within each band if the dependence
7501 distances over the condition constraints are not all zero
7502 then all corresponding conditional validity constraints are respected.
7503 A conditional validity constraint corresponds to a condition
7504 if the two are adjacent, i.e., if the domain of one relation intersect
7505 the range of the other relation.
7506 The typical use case of conditional validity constraints is
7507 to allow order constraints between live ranges to be violated
7508 as long as the live ranges themselves are local to the band.
7509 To allow more fine-grained control over which conditions correspond
7510 to which conditional validity constraints, the domains and ranges
7511 of these relations may include I<tags>. That is, the domains and
7512 ranges of those relation may themselves be wrapped relations
7513 where the iteration domain appears in the domain of those wrapped relations
7514 and the range of the wrapped relations can be arbitrarily chosen
7515 by the user. Conditions and conditional validity constraints are only
7516 considered adjacent to each other if the entire wrapped relation matches.
7517 In particular, a relation with a tag will never be considered adjacent
7518 to a relation without a tag.
7520 The following function computes a schedule directly from
7521 an iteration domain and validity and proximity dependences
7522 and is implemented in terms of the functions described above.
7523 The use of C<isl_union_set_compute_schedule> is discouraged.
7525 #include <isl/schedule.h>
7526 __isl_give isl_schedule *isl_union_set_compute_schedule(
7527 __isl_take isl_union_set *domain,
7528 __isl_take isl_union_map *validity,
7529 __isl_take isl_union_map *proximity);
7531 A mapping from the domains to the scheduled space can be obtained
7532 from an C<isl_schedule> using the following function.
7534 __isl_give isl_union_map *isl_schedule_get_map(
7535 __isl_keep isl_schedule *sched);
7537 A representation of the schedule can be printed using
7539 __isl_give isl_printer *isl_printer_print_schedule(
7540 __isl_take isl_printer *p,
7541 __isl_keep isl_schedule *schedule);
7543 A representation of the schedule as a forest of bands can be obtained
7544 using the following function.
7546 __isl_give isl_band_list *isl_schedule_get_band_forest(
7547 __isl_keep isl_schedule *schedule);
7549 The individual bands can be visited in depth-first post-order
7550 using the following function.
7552 #include <isl/schedule.h>
7553 int isl_schedule_foreach_band(
7554 __isl_keep isl_schedule *sched,
7555 int (*fn)(__isl_keep isl_band *band, void *user),
7558 The list can be manipulated as explained in L<"Lists">.
7559 The bands inside the list can be copied and freed using the following
7562 #include <isl/band.h>
7563 __isl_give isl_band *isl_band_copy(
7564 __isl_keep isl_band *band);
7565 __isl_null isl_band *isl_band_free(
7566 __isl_take isl_band *band);
7568 Each band contains zero or more scheduling dimensions.
7569 These are referred to as the members of the band.
7570 The section of the schedule that corresponds to the band is
7571 referred to as the partial schedule of the band.
7572 For those nodes that participate in a band, the outer scheduling
7573 dimensions form the prefix schedule, while the inner scheduling
7574 dimensions form the suffix schedule.
7575 That is, if we take a cut of the band forest, then the union of
7576 the concatenations of the prefix, partial and suffix schedules of
7577 each band in the cut is equal to the entire schedule (modulo
7578 some possible padding at the end with zero scheduling dimensions).
7579 The properties of a band can be inspected using the following functions.
7581 #include <isl/band.h>
7582 int isl_band_has_children(__isl_keep isl_band *band);
7583 __isl_give isl_band_list *isl_band_get_children(
7584 __isl_keep isl_band *band);
7586 __isl_give isl_union_map *isl_band_get_prefix_schedule(
7587 __isl_keep isl_band *band);
7588 __isl_give isl_union_map *isl_band_get_partial_schedule(
7589 __isl_keep isl_band *band);
7590 __isl_give isl_union_map *isl_band_get_suffix_schedule(
7591 __isl_keep isl_band *band);
7593 int isl_band_n_member(__isl_keep isl_band *band);
7594 int isl_band_member_is_coincident(
7595 __isl_keep isl_band *band, int pos);
7597 int isl_band_list_foreach_band(
7598 __isl_keep isl_band_list *list,
7599 int (*fn)(__isl_keep isl_band *band, void *user),
7602 Note that a scheduling dimension is considered to be ``coincident''
7603 if it satisfies the coincidence constraints within its band.
7604 That is, if the dependence distances of the coincidence
7605 constraints are all zero in that direction (for fixed
7606 iterations of outer bands).
7607 Like C<isl_schedule_foreach_band>,
7608 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
7609 in depth-first post-order.
7611 A band can be tiled using the following function.
7613 #include <isl/band.h>
7614 int isl_band_tile(__isl_keep isl_band *band,
7615 __isl_take isl_vec *sizes);
7617 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
7619 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
7620 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
7622 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
7624 The C<isl_band_tile> function tiles the band using the given tile sizes
7625 inside its schedule.
7626 A new child band is created to represent the point loops and it is
7627 inserted between the modified band and its children.
7628 The C<tile_scale_tile_loops> option specifies whether the tile
7629 loops iterators should be scaled by the tile sizes.
7630 If the C<tile_shift_point_loops> option is set, then the point loops
7631 are shifted to start at zero.
7633 A band can be split into two nested bands using the following function.
7635 int isl_band_split(__isl_keep isl_band *band, int pos);
7637 The resulting outer band contains the first C<pos> dimensions of C<band>
7638 while the inner band contains the remaining dimensions.
7640 A representation of the band can be printed using
7642 #include <isl/band.h>
7643 __isl_give isl_printer *isl_printer_print_band(
7644 __isl_take isl_printer *p,
7645 __isl_keep isl_band *band);
7649 #include <isl/schedule.h>
7650 int isl_options_set_schedule_max_coefficient(
7651 isl_ctx *ctx, int val);
7652 int isl_options_get_schedule_max_coefficient(
7654 int isl_options_set_schedule_max_constant_term(
7655 isl_ctx *ctx, int val);
7656 int isl_options_get_schedule_max_constant_term(
7658 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
7659 int isl_options_get_schedule_fuse(isl_ctx *ctx);
7660 int isl_options_set_schedule_maximize_band_depth(
7661 isl_ctx *ctx, int val);
7662 int isl_options_get_schedule_maximize_band_depth(
7664 int isl_options_set_schedule_outer_coincidence(
7665 isl_ctx *ctx, int val);
7666 int isl_options_get_schedule_outer_coincidence(
7668 int isl_options_set_schedule_split_scaled(
7669 isl_ctx *ctx, int val);
7670 int isl_options_get_schedule_split_scaled(
7672 int isl_options_set_schedule_algorithm(
7673 isl_ctx *ctx, int val);
7674 int isl_options_get_schedule_algorithm(
7676 int isl_options_set_schedule_separate_components(
7677 isl_ctx *ctx, int val);
7678 int isl_options_get_schedule_separate_components(
7683 =item * schedule_max_coefficient
7685 This option enforces that the coefficients for variable and parameter
7686 dimensions in the calculated schedule are not larger than the specified value.
7687 This option can significantly increase the speed of the scheduling calculation
7688 and may also prevent fusing of unrelated dimensions. A value of -1 means that
7689 this option does not introduce bounds on the variable or parameter
7692 =item * schedule_max_constant_term
7694 This option enforces that the constant coefficients in the calculated schedule
7695 are not larger than the maximal constant term. This option can significantly
7696 increase the speed of the scheduling calculation and may also prevent fusing of
7697 unrelated dimensions. A value of -1 means that this option does not introduce
7698 bounds on the constant coefficients.
7700 =item * schedule_fuse
7702 This option controls the level of fusion.
7703 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
7704 resulting schedule will be distributed as much as possible.
7705 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
7706 try to fuse loops in the resulting schedule.
7708 =item * schedule_maximize_band_depth
7710 If this option is set, we do not split bands at the point
7711 where we detect splitting is necessary. Instead, we
7712 backtrack and split bands as early as possible. This
7713 reduces the number of splits and maximizes the width of
7714 the bands. Wider bands give more possibilities for tiling.
7715 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
7716 then bands will be split as early as possible, even if there is no need.
7717 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
7719 =item * schedule_outer_coincidence
7721 If this option is set, then we try to construct schedules
7722 where the outermost scheduling dimension in each band
7723 satisfies the coincidence constraints.
7725 =item * schedule_split_scaled
7727 If this option is set, then we try to construct schedules in which the
7728 constant term is split off from the linear part if the linear parts of
7729 the scheduling rows for all nodes in the graphs have a common non-trivial
7731 The constant term is then placed in a separate band and the linear
7734 =item * schedule_algorithm
7736 Selects the scheduling algorithm to be used.
7737 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
7738 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
7740 =item * schedule_separate_components
7742 If at any point the dependence graph contains any (weakly connected) components,
7743 then these components are scheduled separately.
7744 If this option is not set, then some iterations of the domains
7745 in these components may be scheduled together.
7746 If this option is set, then the components are given consecutive
7751 =head2 AST Generation
7753 This section describes the C<isl> functionality for generating
7754 ASTs that visit all the elements
7755 in a domain in an order specified by a schedule.
7756 In particular, given a C<isl_union_map>, an AST is generated
7757 that visits all the elements in the domain of the C<isl_union_map>
7758 according to the lexicographic order of the corresponding image
7759 element(s). If the range of the C<isl_union_map> consists of
7760 elements in more than one space, then each of these spaces is handled
7761 separately in an arbitrary order.
7762 It should be noted that the image elements only specify the I<order>
7763 in which the corresponding domain elements should be visited.
7764 No direct relation between the image elements and the loop iterators
7765 in the generated AST should be assumed.
7767 Each AST is generated within a build. The initial build
7768 simply specifies the constraints on the parameters (if any)
7769 and can be created, inspected, copied and freed using the following functions.
7771 #include <isl/ast_build.h>
7772 __isl_give isl_ast_build *isl_ast_build_from_context(
7773 __isl_take isl_set *set);
7774 __isl_give isl_ast_build *isl_ast_build_copy(
7775 __isl_keep isl_ast_build *build);
7776 __isl_null isl_ast_build *isl_ast_build_free(
7777 __isl_take isl_ast_build *build);
7779 The C<set> argument is usually a parameter set with zero or more parameters.
7780 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
7781 and L</"Fine-grained Control over AST Generation">.
7782 Finally, the AST itself can be constructed using the following
7785 #include <isl/ast_build.h>
7786 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
7787 __isl_keep isl_ast_build *build,
7788 __isl_take isl_union_map *schedule);
7790 =head3 Inspecting the AST
7792 The basic properties of an AST node can be obtained as follows.
7794 #include <isl/ast.h>
7795 enum isl_ast_node_type isl_ast_node_get_type(
7796 __isl_keep isl_ast_node *node);
7798 The type of an AST node is one of
7799 C<isl_ast_node_for>,
7801 C<isl_ast_node_block> or
7802 C<isl_ast_node_user>.
7803 An C<isl_ast_node_for> represents a for node.
7804 An C<isl_ast_node_if> represents an if node.
7805 An C<isl_ast_node_block> represents a compound node.
7806 An C<isl_ast_node_user> represents an expression statement.
7807 An expression statement typically corresponds to a domain element, i.e.,
7808 one of the elements that is visited by the AST.
7810 Each type of node has its own additional properties.
7812 #include <isl/ast.h>
7813 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7814 __isl_keep isl_ast_node *node);
7815 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7816 __isl_keep isl_ast_node *node);
7817 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7818 __isl_keep isl_ast_node *node);
7819 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7820 __isl_keep isl_ast_node *node);
7821 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7822 __isl_keep isl_ast_node *node);
7823 int isl_ast_node_for_is_degenerate(
7824 __isl_keep isl_ast_node *node);
7826 An C<isl_ast_for> is considered degenerate if it is known to execute
7829 #include <isl/ast.h>
7830 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7831 __isl_keep isl_ast_node *node);
7832 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7833 __isl_keep isl_ast_node *node);
7834 int isl_ast_node_if_has_else(
7835 __isl_keep isl_ast_node *node);
7836 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7837 __isl_keep isl_ast_node *node);
7839 __isl_give isl_ast_node_list *
7840 isl_ast_node_block_get_children(
7841 __isl_keep isl_ast_node *node);
7843 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7844 __isl_keep isl_ast_node *node);
7846 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7847 the following functions.
7849 #include <isl/ast.h>
7850 enum isl_ast_expr_type isl_ast_expr_get_type(
7851 __isl_keep isl_ast_expr *expr);
7853 The type of an AST expression is one of
7855 C<isl_ast_expr_id> or
7856 C<isl_ast_expr_int>.
7857 An C<isl_ast_expr_op> represents the result of an operation.
7858 An C<isl_ast_expr_id> represents an identifier.
7859 An C<isl_ast_expr_int> represents an integer value.
7861 Each type of expression has its own additional properties.
7863 #include <isl/ast.h>
7864 enum isl_ast_op_type isl_ast_expr_get_op_type(
7865 __isl_keep isl_ast_expr *expr);
7866 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7867 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7868 __isl_keep isl_ast_expr *expr, int pos);
7869 int isl_ast_node_foreach_ast_op_type(
7870 __isl_keep isl_ast_node *node,
7871 int (*fn)(enum isl_ast_op_type type, void *user),
7874 C<isl_ast_expr_get_op_type> returns the type of the operation
7875 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7876 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7878 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7879 C<isl_ast_op_type> that appears in C<node>.
7880 The operation type is one of the following.
7884 =item C<isl_ast_op_and>
7886 Logical I<and> of two arguments.
7887 Both arguments can be evaluated.
7889 =item C<isl_ast_op_and_then>
7891 Logical I<and> of two arguments.
7892 The second argument can only be evaluated if the first evaluates to true.
7894 =item C<isl_ast_op_or>
7896 Logical I<or> of two arguments.
7897 Both arguments can be evaluated.
7899 =item C<isl_ast_op_or_else>
7901 Logical I<or> of two arguments.
7902 The second argument can only be evaluated if the first evaluates to false.
7904 =item C<isl_ast_op_max>
7906 Maximum of two or more arguments.
7908 =item C<isl_ast_op_min>
7910 Minimum of two or more arguments.
7912 =item C<isl_ast_op_minus>
7916 =item C<isl_ast_op_add>
7918 Sum of two arguments.
7920 =item C<isl_ast_op_sub>
7922 Difference of two arguments.
7924 =item C<isl_ast_op_mul>
7926 Product of two arguments.
7928 =item C<isl_ast_op_div>
7930 Exact division. That is, the result is known to be an integer.
7932 =item C<isl_ast_op_fdiv_q>
7934 Result of integer division, rounded towards negative
7937 =item C<isl_ast_op_pdiv_q>
7939 Result of integer division, where dividend is known to be non-negative.
7941 =item C<isl_ast_op_pdiv_r>
7943 Remainder of integer division, where dividend is known to be non-negative.
7945 =item C<isl_ast_op_zdiv_r>
7947 Equal to zero iff the remainder on integer division is zero.
7949 =item C<isl_ast_op_cond>
7951 Conditional operator defined on three arguments.
7952 If the first argument evaluates to true, then the result
7953 is equal to the second argument. Otherwise, the result
7954 is equal to the third argument.
7955 The second and third argument may only be evaluated if
7956 the first argument evaluates to true and false, respectively.
7957 Corresponds to C<a ? b : c> in C.
7959 =item C<isl_ast_op_select>
7961 Conditional operator defined on three arguments.
7962 If the first argument evaluates to true, then the result
7963 is equal to the second argument. Otherwise, the result
7964 is equal to the third argument.
7965 The second and third argument may be evaluated independently
7966 of the value of the first argument.
7967 Corresponds to C<a * b + (1 - a) * c> in C.
7969 =item C<isl_ast_op_eq>
7973 =item C<isl_ast_op_le>
7975 Less than or equal relation.
7977 =item C<isl_ast_op_lt>
7981 =item C<isl_ast_op_ge>
7983 Greater than or equal relation.
7985 =item C<isl_ast_op_gt>
7987 Greater than relation.
7989 =item C<isl_ast_op_call>
7992 The number of arguments of the C<isl_ast_expr> is one more than
7993 the number of arguments in the function call, the first argument
7994 representing the function being called.
7996 =item C<isl_ast_op_access>
7999 The number of arguments of the C<isl_ast_expr> is one more than
8000 the number of index expressions in the array access, the first argument
8001 representing the array being accessed.
8003 =item C<isl_ast_op_member>
8006 This operation has two arguments, a structure and the name of
8007 the member of the structure being accessed.
8011 #include <isl/ast.h>
8012 __isl_give isl_id *isl_ast_expr_get_id(
8013 __isl_keep isl_ast_expr *expr);
8015 Return the identifier represented by the AST expression.
8017 #include <isl/ast.h>
8018 __isl_give isl_val *isl_ast_expr_get_val(
8019 __isl_keep isl_ast_expr *expr);
8021 Return the integer represented by the AST expression.
8023 =head3 Properties of ASTs
8025 #include <isl/ast.h>
8026 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
8027 __isl_keep isl_ast_expr *expr2);
8029 Check if two C<isl_ast_expr>s are equal to each other.
8031 =head3 Manipulating and printing the AST
8033 AST nodes can be copied and freed using the following functions.
8035 #include <isl/ast.h>
8036 __isl_give isl_ast_node *isl_ast_node_copy(
8037 __isl_keep isl_ast_node *node);
8038 __isl_null isl_ast_node *isl_ast_node_free(
8039 __isl_take isl_ast_node *node);
8041 AST expressions can be copied and freed using the following functions.
8043 #include <isl/ast.h>
8044 __isl_give isl_ast_expr *isl_ast_expr_copy(
8045 __isl_keep isl_ast_expr *expr);
8046 __isl_null isl_ast_expr *isl_ast_expr_free(
8047 __isl_take isl_ast_expr *expr);
8049 New AST expressions can be created either directly or within
8050 the context of an C<isl_ast_build>.
8052 #include <isl/ast.h>
8053 __isl_give isl_ast_expr *isl_ast_expr_from_val(
8054 __isl_take isl_val *v);
8055 __isl_give isl_ast_expr *isl_ast_expr_from_id(
8056 __isl_take isl_id *id);
8057 __isl_give isl_ast_expr *isl_ast_expr_neg(
8058 __isl_take isl_ast_expr *expr);
8059 __isl_give isl_ast_expr *isl_ast_expr_address_of(
8060 __isl_take isl_ast_expr *expr);
8061 __isl_give isl_ast_expr *isl_ast_expr_add(
8062 __isl_take isl_ast_expr *expr1,
8063 __isl_take isl_ast_expr *expr2);
8064 __isl_give isl_ast_expr *isl_ast_expr_sub(
8065 __isl_take isl_ast_expr *expr1,
8066 __isl_take isl_ast_expr *expr2);
8067 __isl_give isl_ast_expr *isl_ast_expr_mul(
8068 __isl_take isl_ast_expr *expr1,
8069 __isl_take isl_ast_expr *expr2);
8070 __isl_give isl_ast_expr *isl_ast_expr_div(
8071 __isl_take isl_ast_expr *expr1,
8072 __isl_take isl_ast_expr *expr2);
8073 __isl_give isl_ast_expr *isl_ast_expr_and(
8074 __isl_take isl_ast_expr *expr1,
8075 __isl_take isl_ast_expr *expr2)
8076 __isl_give isl_ast_expr *isl_ast_expr_or(
8077 __isl_take isl_ast_expr *expr1,
8078 __isl_take isl_ast_expr *expr2)
8079 __isl_give isl_ast_expr *isl_ast_expr_eq(
8080 __isl_take isl_ast_expr *expr1,
8081 __isl_take isl_ast_expr *expr2);
8082 __isl_give isl_ast_expr *isl_ast_expr_le(
8083 __isl_take isl_ast_expr *expr1,
8084 __isl_take isl_ast_expr *expr2);
8085 __isl_give isl_ast_expr *isl_ast_expr_lt(
8086 __isl_take isl_ast_expr *expr1,
8087 __isl_take isl_ast_expr *expr2);
8088 __isl_give isl_ast_expr *isl_ast_expr_ge(
8089 __isl_take isl_ast_expr *expr1,
8090 __isl_take isl_ast_expr *expr2);
8091 __isl_give isl_ast_expr *isl_ast_expr_gt(
8092 __isl_take isl_ast_expr *expr1,
8093 __isl_take isl_ast_expr *expr2);
8094 __isl_give isl_ast_expr *isl_ast_expr_access(
8095 __isl_take isl_ast_expr *array,
8096 __isl_take isl_ast_expr_list *indices);
8098 The function C<isl_ast_expr_address_of> can be applied to an
8099 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
8100 to represent the address of the C<isl_ast_expr_access>.
8102 #include <isl/ast_build.h>
8103 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
8104 __isl_keep isl_ast_build *build,
8105 __isl_take isl_pw_aff *pa);
8106 __isl_give isl_ast_expr *
8107 isl_ast_build_access_from_pw_multi_aff(
8108 __isl_keep isl_ast_build *build,
8109 __isl_take isl_pw_multi_aff *pma);
8110 __isl_give isl_ast_expr *
8111 isl_ast_build_access_from_multi_pw_aff(
8112 __isl_keep isl_ast_build *build,
8113 __isl_take isl_multi_pw_aff *mpa);
8114 __isl_give isl_ast_expr *
8115 isl_ast_build_call_from_pw_multi_aff(
8116 __isl_keep isl_ast_build *build,
8117 __isl_take isl_pw_multi_aff *pma);
8118 __isl_give isl_ast_expr *
8119 isl_ast_build_call_from_multi_pw_aff(
8120 __isl_keep isl_ast_build *build,
8121 __isl_take isl_multi_pw_aff *mpa);
8123 The domains of C<pa>, C<mpa> and C<pma> should correspond
8124 to the schedule space of C<build>.
8125 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
8126 the function being called.
8127 If the accessed space is a nested relation, then it is taken
8128 to represent an access of the member specified by the range
8129 of this nested relation of the structure specified by the domain
8130 of the nested relation.
8132 The following functions can be used to modify an C<isl_ast_expr>.
8134 #include <isl/ast.h>
8135 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
8136 __isl_take isl_ast_expr *expr, int pos,
8137 __isl_take isl_ast_expr *arg);
8139 Replace the argument of C<expr> at position C<pos> by C<arg>.
8141 #include <isl/ast.h>
8142 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
8143 __isl_take isl_ast_expr *expr,
8144 __isl_take isl_id_to_ast_expr *id2expr);
8146 The function C<isl_ast_expr_substitute_ids> replaces the
8147 subexpressions of C<expr> of type C<isl_ast_expr_id>
8148 by the corresponding expression in C<id2expr>, if there is any.
8151 User specified data can be attached to an C<isl_ast_node> and obtained
8152 from the same C<isl_ast_node> using the following functions.
8154 #include <isl/ast.h>
8155 __isl_give isl_ast_node *isl_ast_node_set_annotation(
8156 __isl_take isl_ast_node *node,
8157 __isl_take isl_id *annotation);
8158 __isl_give isl_id *isl_ast_node_get_annotation(
8159 __isl_keep isl_ast_node *node);
8161 Basic printing can be performed using the following functions.
8163 #include <isl/ast.h>
8164 __isl_give isl_printer *isl_printer_print_ast_expr(
8165 __isl_take isl_printer *p,
8166 __isl_keep isl_ast_expr *expr);
8167 __isl_give isl_printer *isl_printer_print_ast_node(
8168 __isl_take isl_printer *p,
8169 __isl_keep isl_ast_node *node);
8170 __isl_give char *isl_ast_expr_to_str(
8171 __isl_keep isl_ast_expr *expr);
8173 More advanced printing can be performed using the following functions.
8175 #include <isl/ast.h>
8176 __isl_give isl_printer *isl_ast_op_type_print_macro(
8177 enum isl_ast_op_type type,
8178 __isl_take isl_printer *p);
8179 __isl_give isl_printer *isl_ast_node_print_macros(
8180 __isl_keep isl_ast_node *node,
8181 __isl_take isl_printer *p);
8182 __isl_give isl_printer *isl_ast_node_print(
8183 __isl_keep isl_ast_node *node,
8184 __isl_take isl_printer *p,
8185 __isl_take isl_ast_print_options *options);
8186 __isl_give isl_printer *isl_ast_node_for_print(
8187 __isl_keep isl_ast_node *node,
8188 __isl_take isl_printer *p,
8189 __isl_take isl_ast_print_options *options);
8190 __isl_give isl_printer *isl_ast_node_if_print(
8191 __isl_keep isl_ast_node *node,
8192 __isl_take isl_printer *p,
8193 __isl_take isl_ast_print_options *options);
8195 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
8196 C<isl> may print out an AST that makes use of macros such
8197 as C<floord>, C<min> and C<max>.
8198 C<isl_ast_op_type_print_macro> prints out the macro
8199 corresponding to a specific C<isl_ast_op_type>.
8200 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
8201 for expressions where these macros would be used and prints
8202 out the required macro definitions.
8203 Essentially, C<isl_ast_node_print_macros> calls
8204 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
8205 as function argument.
8206 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
8207 C<isl_ast_node_if_print> print an C<isl_ast_node>
8208 in C<ISL_FORMAT_C>, but allow for some extra control
8209 through an C<isl_ast_print_options> object.
8210 This object can be created using the following functions.
8212 #include <isl/ast.h>
8213 __isl_give isl_ast_print_options *
8214 isl_ast_print_options_alloc(isl_ctx *ctx);
8215 __isl_give isl_ast_print_options *
8216 isl_ast_print_options_copy(
8217 __isl_keep isl_ast_print_options *options);
8218 __isl_null isl_ast_print_options *
8219 isl_ast_print_options_free(
8220 __isl_take isl_ast_print_options *options);
8222 __isl_give isl_ast_print_options *
8223 isl_ast_print_options_set_print_user(
8224 __isl_take isl_ast_print_options *options,
8225 __isl_give isl_printer *(*print_user)(
8226 __isl_take isl_printer *p,
8227 __isl_take isl_ast_print_options *options,
8228 __isl_keep isl_ast_node *node, void *user),
8230 __isl_give isl_ast_print_options *
8231 isl_ast_print_options_set_print_for(
8232 __isl_take isl_ast_print_options *options,
8233 __isl_give isl_printer *(*print_for)(
8234 __isl_take isl_printer *p,
8235 __isl_take isl_ast_print_options *options,
8236 __isl_keep isl_ast_node *node, void *user),
8239 The callback set by C<isl_ast_print_options_set_print_user>
8240 is called whenever a node of type C<isl_ast_node_user> needs to
8242 The callback set by C<isl_ast_print_options_set_print_for>
8243 is called whenever a node of type C<isl_ast_node_for> needs to
8245 Note that C<isl_ast_node_for_print> will I<not> call the
8246 callback set by C<isl_ast_print_options_set_print_for> on the node
8247 on which C<isl_ast_node_for_print> is called, but only on nested
8248 nodes of type C<isl_ast_node_for>. It is therefore safe to
8249 call C<isl_ast_node_for_print> from within the callback set by
8250 C<isl_ast_print_options_set_print_for>.
8252 The following option determines the type to be used for iterators
8253 while printing the AST.
8255 int isl_options_set_ast_iterator_type(
8256 isl_ctx *ctx, const char *val);
8257 const char *isl_options_get_ast_iterator_type(
8260 The AST printer only prints body nodes as blocks if these
8261 blocks cannot be safely omitted.
8262 For example, a C<for> node with one body node will not be
8263 surrounded with braces in C<ISL_FORMAT_C>.
8264 A block will always be printed by setting the following option.
8266 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
8268 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
8272 #include <isl/ast_build.h>
8273 int isl_options_set_ast_build_atomic_upper_bound(
8274 isl_ctx *ctx, int val);
8275 int isl_options_get_ast_build_atomic_upper_bound(
8277 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
8279 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
8280 int isl_options_set_ast_build_exploit_nested_bounds(
8281 isl_ctx *ctx, int val);
8282 int isl_options_get_ast_build_exploit_nested_bounds(
8284 int isl_options_set_ast_build_group_coscheduled(
8285 isl_ctx *ctx, int val);
8286 int isl_options_get_ast_build_group_coscheduled(
8288 int isl_options_set_ast_build_scale_strides(
8289 isl_ctx *ctx, int val);
8290 int isl_options_get_ast_build_scale_strides(
8292 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
8294 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
8295 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
8297 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
8301 =item * ast_build_atomic_upper_bound
8303 Generate loop upper bounds that consist of the current loop iterator,
8304 an operator and an expression not involving the iterator.
8305 If this option is not set, then the current loop iterator may appear
8306 several times in the upper bound.
8307 For example, when this option is turned off, AST generation
8310 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
8314 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
8317 When the option is turned on, the following AST is generated
8319 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
8322 =item * ast_build_prefer_pdiv
8324 If this option is turned off, then the AST generation will
8325 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
8326 operators, but no C<isl_ast_op_pdiv_q> or
8327 C<isl_ast_op_pdiv_r> operators.
8328 If this options is turned on, then C<isl> will try to convert
8329 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
8330 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
8332 =item * ast_build_exploit_nested_bounds
8334 Simplify conditions based on bounds of nested for loops.
8335 In particular, remove conditions that are implied by the fact
8336 that one or more nested loops have at least one iteration,
8337 meaning that the upper bound is at least as large as the lower bound.
8338 For example, when this option is turned off, AST generation
8341 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
8347 for (int c0 = 0; c0 <= N; c0 += 1)
8348 for (int c1 = 0; c1 <= M; c1 += 1)
8351 When the option is turned on, the following AST is generated
8353 for (int c0 = 0; c0 <= N; c0 += 1)
8354 for (int c1 = 0; c1 <= M; c1 += 1)
8357 =item * ast_build_group_coscheduled
8359 If two domain elements are assigned the same schedule point, then
8360 they may be executed in any order and they may even appear in different
8361 loops. If this options is set, then the AST generator will make
8362 sure that coscheduled domain elements do not appear in separate parts
8363 of the AST. This is useful in case of nested AST generation
8364 if the outer AST generation is given only part of a schedule
8365 and the inner AST generation should handle the domains that are
8366 coscheduled by this initial part of the schedule together.
8367 For example if an AST is generated for a schedule
8369 { A[i] -> [0]; B[i] -> [0] }
8371 then the C<isl_ast_build_set_create_leaf> callback described
8372 below may get called twice, once for each domain.
8373 Setting this option ensures that the callback is only called once
8374 on both domains together.
8376 =item * ast_build_separation_bounds
8378 This option specifies which bounds to use during separation.
8379 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
8380 then all (possibly implicit) bounds on the current dimension will
8381 be used during separation.
8382 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
8383 then only those bounds that are explicitly available will
8384 be used during separation.
8386 =item * ast_build_scale_strides
8388 This option specifies whether the AST generator is allowed
8389 to scale down iterators of strided loops.
8391 =item * ast_build_allow_else
8393 This option specifies whether the AST generator is allowed
8394 to construct if statements with else branches.
8396 =item * ast_build_allow_or
8398 This option specifies whether the AST generator is allowed
8399 to construct if conditions with disjunctions.
8403 =head3 Fine-grained Control over AST Generation
8405 Besides specifying the constraints on the parameters,
8406 an C<isl_ast_build> object can be used to control
8407 various aspects of the AST generation process.
8408 The most prominent way of control is through ``options'',
8409 which can be set using the following function.
8411 #include <isl/ast_build.h>
8412 __isl_give isl_ast_build *
8413 isl_ast_build_set_options(
8414 __isl_take isl_ast_build *control,
8415 __isl_take isl_union_map *options);
8417 The options are encoded in an C<isl_union_map>.
8418 The domain of this union relation refers to the schedule domain,
8419 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
8420 In the case of nested AST generation (see L</"Nested AST Generation">),
8421 the domain of C<options> should refer to the extra piece of the schedule.
8422 That is, it should be equal to the range of the wrapped relation in the
8423 range of the schedule.
8424 The range of the options can consist of elements in one or more spaces,
8425 the names of which determine the effect of the option.
8426 The values of the range typically also refer to the schedule dimension
8427 to which the option applies. In case of nested AST generation
8428 (see L</"Nested AST Generation">), these values refer to the position
8429 of the schedule dimension within the innermost AST generation.
8430 The constraints on the domain elements of
8431 the option should only refer to this dimension and earlier dimensions.
8432 We consider the following spaces.
8436 =item C<separation_class>
8438 This space is a wrapped relation between two one dimensional spaces.
8439 The input space represents the schedule dimension to which the option
8440 applies and the output space represents the separation class.
8441 While constructing a loop corresponding to the specified schedule
8442 dimension(s), the AST generator will try to generate separate loops
8443 for domain elements that are assigned different classes.
8444 If only some of the elements are assigned a class, then those elements
8445 that are not assigned any class will be treated as belonging to a class
8446 that is separate from the explicitly assigned classes.
8447 The typical use case for this option is to separate full tiles from
8449 The other options, described below, are applied after the separation
8452 As an example, consider the separation into full and partial tiles
8453 of a tiling of a triangular domain.
8454 Take, for example, the domain
8456 { A[i,j] : 0 <= i,j and i + j <= 100 }
8458 and a tiling into tiles of 10 by 10. The input to the AST generator
8459 is then the schedule
8461 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
8464 Without any options, the following AST is generated
8466 for (int c0 = 0; c0 <= 10; c0 += 1)
8467 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8468 for (int c2 = 10 * c0;
8469 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8471 for (int c3 = 10 * c1;
8472 c3 <= min(10 * c1 + 9, -c2 + 100);
8476 Separation into full and partial tiles can be obtained by assigning
8477 a class, say C<0>, to the full tiles. The full tiles are represented by those
8478 values of the first and second schedule dimensions for which there are
8479 values of the third and fourth dimensions to cover an entire tile.
8480 That is, we need to specify the following option
8482 { [a,b,c,d] -> separation_class[[0]->[0]] :
8483 exists b': 0 <= 10a,10b' and
8484 10a+9+10b'+9 <= 100;
8485 [a,b,c,d] -> separation_class[[1]->[0]] :
8486 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
8490 { [a, b, c, d] -> separation_class[[1] -> [0]] :
8491 a >= 0 and b >= 0 and b <= 8 - a;
8492 [a, b, c, d] -> separation_class[[0] -> [0]] :
8495 With this option, the generated AST is as follows
8498 for (int c0 = 0; c0 <= 8; c0 += 1) {
8499 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
8500 for (int c2 = 10 * c0;
8501 c2 <= 10 * c0 + 9; c2 += 1)
8502 for (int c3 = 10 * c1;
8503 c3 <= 10 * c1 + 9; c3 += 1)
8505 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
8506 for (int c2 = 10 * c0;
8507 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8509 for (int c3 = 10 * c1;
8510 c3 <= min(-c2 + 100, 10 * c1 + 9);
8514 for (int c0 = 9; c0 <= 10; c0 += 1)
8515 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8516 for (int c2 = 10 * c0;
8517 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8519 for (int c3 = 10 * c1;
8520 c3 <= min(10 * c1 + 9, -c2 + 100);
8527 This is a single-dimensional space representing the schedule dimension(s)
8528 to which ``separation'' should be applied. Separation tries to split
8529 a loop into several pieces if this can avoid the generation of guards
8531 See also the C<atomic> option.
8535 This is a single-dimensional space representing the schedule dimension(s)
8536 for which the domains should be considered ``atomic''. That is, the
8537 AST generator will make sure that any given domain space will only appear
8538 in a single loop at the specified level.
8540 Consider the following schedule
8542 { a[i] -> [i] : 0 <= i < 10;
8543 b[i] -> [i+1] : 0 <= i < 10 }
8545 If the following option is specified
8547 { [i] -> separate[x] }
8549 then the following AST will be generated
8553 for (int c0 = 1; c0 <= 9; c0 += 1) {
8560 If, on the other hand, the following option is specified
8562 { [i] -> atomic[x] }
8564 then the following AST will be generated
8566 for (int c0 = 0; c0 <= 10; c0 += 1) {
8573 If neither C<atomic> nor C<separate> is specified, then the AST generator
8574 may produce either of these two results or some intermediate form.
8578 This is a single-dimensional space representing the schedule dimension(s)
8579 that should be I<completely> unrolled.
8580 To obtain a partial unrolling, the user should apply an additional
8581 strip-mining to the schedule and fully unroll the inner loop.
8585 Additional control is available through the following functions.
8587 #include <isl/ast_build.h>
8588 __isl_give isl_ast_build *
8589 isl_ast_build_set_iterators(
8590 __isl_take isl_ast_build *control,
8591 __isl_take isl_id_list *iterators);
8593 The function C<isl_ast_build_set_iterators> allows the user to
8594 specify a list of iterator C<isl_id>s to be used as iterators.
8595 If the input schedule is injective, then
8596 the number of elements in this list should be as large as the dimension
8597 of the schedule space, but no direct correspondence should be assumed
8598 between dimensions and elements.
8599 If the input schedule is not injective, then an additional number
8600 of C<isl_id>s equal to the largest dimension of the input domains
8602 If the number of provided C<isl_id>s is insufficient, then additional
8603 names are automatically generated.
8605 #include <isl/ast_build.h>
8606 __isl_give isl_ast_build *
8607 isl_ast_build_set_create_leaf(
8608 __isl_take isl_ast_build *control,
8609 __isl_give isl_ast_node *(*fn)(
8610 __isl_take isl_ast_build *build,
8611 void *user), void *user);
8614 C<isl_ast_build_set_create_leaf> function allows for the
8615 specification of a callback that should be called whenever the AST
8616 generator arrives at an element of the schedule domain.
8617 The callback should return an AST node that should be inserted
8618 at the corresponding position of the AST. The default action (when
8619 the callback is not set) is to continue generating parts of the AST to scan
8620 all the domain elements associated to the schedule domain element
8621 and to insert user nodes, ``calling'' the domain element, for each of them.
8622 The C<build> argument contains the current state of the C<isl_ast_build>.
8623 To ease nested AST generation (see L</"Nested AST Generation">),
8624 all control information that is
8625 specific to the current AST generation such as the options and
8626 the callbacks has been removed from this C<isl_ast_build>.
8627 The callback would typically return the result of a nested
8629 user defined node created using the following function.
8631 #include <isl/ast.h>
8632 __isl_give isl_ast_node *isl_ast_node_alloc_user(
8633 __isl_take isl_ast_expr *expr);
8635 #include <isl/ast_build.h>
8636 __isl_give isl_ast_build *
8637 isl_ast_build_set_at_each_domain(
8638 __isl_take isl_ast_build *build,
8639 __isl_give isl_ast_node *(*fn)(
8640 __isl_take isl_ast_node *node,
8641 __isl_keep isl_ast_build *build,
8642 void *user), void *user);
8643 __isl_give isl_ast_build *
8644 isl_ast_build_set_before_each_for(
8645 __isl_take isl_ast_build *build,
8646 __isl_give isl_id *(*fn)(
8647 __isl_keep isl_ast_build *build,
8648 void *user), void *user);
8649 __isl_give isl_ast_build *
8650 isl_ast_build_set_after_each_for(
8651 __isl_take isl_ast_build *build,
8652 __isl_give isl_ast_node *(*fn)(
8653 __isl_take isl_ast_node *node,
8654 __isl_keep isl_ast_build *build,
8655 void *user), void *user);
8657 The callback set by C<isl_ast_build_set_at_each_domain> will
8658 be called for each domain AST node.
8659 The callbacks set by C<isl_ast_build_set_before_each_for>
8660 and C<isl_ast_build_set_after_each_for> will be called
8661 for each for AST node. The first will be called in depth-first
8662 pre-order, while the second will be called in depth-first post-order.
8663 Since C<isl_ast_build_set_before_each_for> is called before the for
8664 node is actually constructed, it is only passed an C<isl_ast_build>.
8665 The returned C<isl_id> will be added as an annotation (using
8666 C<isl_ast_node_set_annotation>) to the constructed for node.
8667 In particular, if the user has also specified an C<after_each_for>
8668 callback, then the annotation can be retrieved from the node passed to
8669 that callback using C<isl_ast_node_get_annotation>.
8670 All callbacks should C<NULL> on failure.
8671 The given C<isl_ast_build> can be used to create new
8672 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
8673 or C<isl_ast_build_call_from_pw_multi_aff>.
8675 =head3 Nested AST Generation
8677 C<isl> allows the user to create an AST within the context
8678 of another AST. These nested ASTs are created using the
8679 same C<isl_ast_build_ast_from_schedule> function that is used to create the
8680 outer AST. The C<build> argument should be an C<isl_ast_build>
8681 passed to a callback set by
8682 C<isl_ast_build_set_create_leaf>.
8683 The space of the range of the C<schedule> argument should refer
8684 to this build. In particular, the space should be a wrapped
8685 relation and the domain of this wrapped relation should be the
8686 same as that of the range of the schedule returned by
8687 C<isl_ast_build_get_schedule> below.
8688 In practice, the new schedule is typically
8689 created by calling C<isl_union_map_range_product> on the old schedule
8690 and some extra piece of the schedule.
8691 The space of the schedule domain is also available from
8692 the C<isl_ast_build>.
8694 #include <isl/ast_build.h>
8695 __isl_give isl_union_map *isl_ast_build_get_schedule(
8696 __isl_keep isl_ast_build *build);
8697 __isl_give isl_space *isl_ast_build_get_schedule_space(
8698 __isl_keep isl_ast_build *build);
8699 __isl_give isl_ast_build *isl_ast_build_restrict(
8700 __isl_take isl_ast_build *build,
8701 __isl_take isl_set *set);
8703 The C<isl_ast_build_get_schedule> function returns a (partial)
8704 schedule for the domains elements for which part of the AST still needs to
8705 be generated in the current build.
8706 In particular, the domain elements are mapped to those iterations of the loops
8707 enclosing the current point of the AST generation inside which
8708 the domain elements are executed.
8709 No direct correspondence between
8710 the input schedule and this schedule should be assumed.
8711 The space obtained from C<isl_ast_build_get_schedule_space> can be used
8712 to create a set for C<isl_ast_build_restrict> to intersect
8713 with the current build. In particular, the set passed to
8714 C<isl_ast_build_restrict> can have additional parameters.
8715 The ids of the set dimensions in the space returned by
8716 C<isl_ast_build_get_schedule_space> correspond to the
8717 iterators of the already generated loops.
8718 The user should not rely on the ids of the output dimensions
8719 of the relations in the union relation returned by
8720 C<isl_ast_build_get_schedule> having any particular value.
8724 Although C<isl> is mainly meant to be used as a library,
8725 it also contains some basic applications that use some
8726 of the functionality of C<isl>.
8727 The input may be specified in either the L<isl format>
8728 or the L<PolyLib format>.
8730 =head2 C<isl_polyhedron_sample>
8732 C<isl_polyhedron_sample> takes a polyhedron as input and prints
8733 an integer element of the polyhedron, if there is any.
8734 The first column in the output is the denominator and is always
8735 equal to 1. If the polyhedron contains no integer points,
8736 then a vector of length zero is printed.
8740 C<isl_pip> takes the same input as the C<example> program
8741 from the C<piplib> distribution, i.e., a set of constraints
8742 on the parameters, a line containing only -1 and finally a set
8743 of constraints on a parametric polyhedron.
8744 The coefficients of the parameters appear in the last columns
8745 (but before the final constant column).
8746 The output is the lexicographic minimum of the parametric polyhedron.
8747 As C<isl> currently does not have its own output format, the output
8748 is just a dump of the internal state.
8750 =head2 C<isl_polyhedron_minimize>
8752 C<isl_polyhedron_minimize> computes the minimum of some linear
8753 or affine objective function over the integer points in a polyhedron.
8754 If an affine objective function
8755 is given, then the constant should appear in the last column.
8757 =head2 C<isl_polytope_scan>
8759 Given a polytope, C<isl_polytope_scan> prints
8760 all integer points in the polytope.
8762 =head2 C<isl_codegen>
8764 Given a schedule, a context set and an options relation,
8765 C<isl_codegen> prints out an AST that scans the domain elements
8766 of the schedule in the order of their image(s) taking into account
8767 the constraints in the context set.