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_multi_aff_get_ctx(
496 __isl_keep isl_union_pw_multi_aff *upma);
498 #include <isl/id_to_ast_expr.h>
499 isl_ctx *isl_id_to_ast_expr_get_ctx(
500 __isl_keep id_to_ast_expr *id2expr);
502 #include <isl/point.h>
503 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
506 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
509 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
511 #include <isl/vertices.h>
512 isl_ctx *isl_vertices_get_ctx(
513 __isl_keep isl_vertices *vertices);
514 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
515 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
517 #include <isl/flow.h>
518 isl_ctx *isl_restriction_get_ctx(
519 __isl_keep isl_restriction *restr);
521 #include <isl/schedule.h>
522 isl_ctx *isl_schedule_constraints_get_ctx(
523 __isl_keep isl_schedule_constraints *sc);
525 #include <isl/band.h>
526 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
528 #include <isl/ast_build.h>
529 isl_ctx *isl_ast_build_get_ctx(
530 __isl_keep isl_ast_build *build);
533 isl_ctx *isl_ast_expr_get_ctx(
534 __isl_keep isl_ast_expr *expr);
535 isl_ctx *isl_ast_node_get_ctx(
536 __isl_keep isl_ast_node *node);
540 An C<isl_val> represents an integer value, a rational value
541 or one of three special values, infinity, negative infinity and NaN.
542 Some predefined values can be created using the following functions.
545 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
546 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
547 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
548 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
549 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
550 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
552 Specific integer values can be created using the following functions.
555 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
557 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
559 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
560 size_t n, size_t size, const void *chunks);
562 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
563 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
564 The least significant digit is assumed to be stored first.
566 Value objects can be copied and freed using the following functions.
569 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
570 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
572 They can be inspected using the following functions.
575 long isl_val_get_num_si(__isl_keep isl_val *v);
576 long isl_val_get_den_si(__isl_keep isl_val *v);
577 double isl_val_get_d(__isl_keep isl_val *v);
578 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
580 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
581 size_t size, void *chunks);
583 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
584 of C<size> bytes needed to store the absolute value of the
586 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
587 which is assumed to have been preallocated by the caller.
588 The least significant digit is stored first.
589 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
590 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
591 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
593 An C<isl_val> can be modified using the following function.
596 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
599 The following unary properties are defined on C<isl_val>s.
602 int isl_val_sgn(__isl_keep isl_val *v);
603 int isl_val_is_zero(__isl_keep isl_val *v);
604 int isl_val_is_one(__isl_keep isl_val *v);
605 int isl_val_is_negone(__isl_keep isl_val *v);
606 int isl_val_is_nonneg(__isl_keep isl_val *v);
607 int isl_val_is_nonpos(__isl_keep isl_val *v);
608 int isl_val_is_pos(__isl_keep isl_val *v);
609 int isl_val_is_neg(__isl_keep isl_val *v);
610 int isl_val_is_int(__isl_keep isl_val *v);
611 int isl_val_is_rat(__isl_keep isl_val *v);
612 int isl_val_is_nan(__isl_keep isl_val *v);
613 int isl_val_is_infty(__isl_keep isl_val *v);
614 int isl_val_is_neginfty(__isl_keep isl_val *v);
616 Note that the sign of NaN is undefined.
618 The following binary properties are defined on pairs of C<isl_val>s.
621 int isl_val_lt(__isl_keep isl_val *v1,
622 __isl_keep isl_val *v2);
623 int isl_val_le(__isl_keep isl_val *v1,
624 __isl_keep isl_val *v2);
625 int isl_val_gt(__isl_keep isl_val *v1,
626 __isl_keep isl_val *v2);
627 int isl_val_ge(__isl_keep isl_val *v1,
628 __isl_keep isl_val *v2);
629 int isl_val_eq(__isl_keep isl_val *v1,
630 __isl_keep isl_val *v2);
631 int isl_val_ne(__isl_keep isl_val *v1,
632 __isl_keep isl_val *v2);
633 int isl_val_abs_eq(__isl_keep isl_val *v1,
634 __isl_keep isl_val *v2);
636 The function C<isl_val_abs_eq> checks whether its two arguments
637 are equal in absolute value.
639 For integer C<isl_val>s we additionally have the following binary property.
642 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
643 __isl_keep isl_val *v2);
645 An C<isl_val> can also be compared to an integer using the following
646 function. The result is undefined for NaN.
649 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
651 The following unary operations are available on C<isl_val>s.
654 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
655 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
656 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
657 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
658 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
659 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
660 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
662 The following binary operations are available on C<isl_val>s.
665 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
666 __isl_take isl_val *v2);
667 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
668 __isl_take isl_val *v2);
669 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
670 __isl_take isl_val *v2);
671 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
673 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
674 __isl_take isl_val *v2);
675 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
677 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
678 __isl_take isl_val *v2);
679 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
681 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
682 __isl_take isl_val *v2);
684 On integer values, we additionally have the following operations.
687 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
688 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
689 __isl_take isl_val *v2);
690 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
691 __isl_take isl_val *v2);
692 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
693 __isl_take isl_val *v2, __isl_give isl_val **x,
694 __isl_give isl_val **y);
696 The function C<isl_val_gcdext> returns the greatest common divisor g
697 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
698 that C<*x> * C<v1> + C<*y> * C<v2> = g.
700 =head3 GMP specific functions
702 These functions are only available if C<isl> has been compiled with C<GMP>
705 Specific integer and rational values can be created from C<GMP> values using
706 the following functions.
708 #include <isl/val_gmp.h>
709 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
711 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
712 const mpz_t n, const mpz_t d);
714 The numerator and denominator of a rational value can be extracted as
715 C<GMP> values using the following functions.
717 #include <isl/val_gmp.h>
718 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
719 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
721 =head2 Sets and Relations
723 C<isl> uses six types of objects for representing sets and relations,
724 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
725 C<isl_union_set> and C<isl_union_map>.
726 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
727 can be described as a conjunction of affine constraints, while
728 C<isl_set> and C<isl_map> represent unions of
729 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
730 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
731 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
732 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
733 where spaces are considered different if they have a different number
734 of dimensions and/or different names (see L<"Spaces">).
735 The difference between sets and relations (maps) is that sets have
736 one set of variables, while relations have two sets of variables,
737 input variables and output variables.
739 =head2 Error Handling
741 C<isl> supports different ways to react in case a runtime error is triggered.
742 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
743 with two maps that have incompatible spaces. There are three possible ways
744 to react on error: to warn, to continue or to abort.
746 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
747 the last error in the corresponding C<isl_ctx> and the function in which the
748 error was triggered returns C<NULL>. An error does not corrupt internal state,
749 such that isl can continue to be used. C<isl> also provides functions to
750 read the last error and to reset the memory that stores the last error. The
751 last error is only stored for information purposes. Its presence does not
752 change the behavior of C<isl>. Hence, resetting an error is not required to
753 continue to use isl, but only to observe new errors.
756 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
757 void isl_ctx_reset_error(isl_ctx *ctx);
759 Another option is to continue on error. This is similar to warn on error mode,
760 except that C<isl> does not print any warning. This allows a program to
761 implement its own error reporting.
763 The last option is to directly abort the execution of the program from within
764 the isl library. This makes it obviously impossible to recover from an error,
765 but it allows to directly spot the error location. By aborting on error,
766 debuggers break at the location the error occurred and can provide a stack
767 trace. Other tools that automatically provide stack traces on abort or that do
768 not want to continue execution after an error was triggered may also prefer to
771 The on error behavior of isl can be specified by calling
772 C<isl_options_set_on_error> or by setting the command line option
773 C<--isl-on-error>. Valid arguments for the function call are
774 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
775 choices for the command line option are C<warn>, C<continue> and C<abort>.
776 It is also possible to query the current error mode.
778 #include <isl/options.h>
779 int isl_options_set_on_error(isl_ctx *ctx, int val);
780 int isl_options_get_on_error(isl_ctx *ctx);
784 Identifiers are used to identify both individual dimensions
785 and tuples of dimensions. They consist of an optional name and an optional
786 user pointer. The name and the user pointer cannot both be C<NULL>, however.
787 Identifiers with the same name but different pointer values
788 are considered to be distinct.
789 Similarly, identifiers with different names but the same pointer value
790 are also considered to be distinct.
791 Equal identifiers are represented using the same object.
792 Pairs of identifiers can therefore be tested for equality using the
794 Identifiers can be constructed, copied, freed, inspected and printed
795 using the following functions.
798 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
799 __isl_keep const char *name, void *user);
800 __isl_give isl_id *isl_id_set_free_user(
801 __isl_take isl_id *id,
802 __isl_give void (*free_user)(void *user));
803 __isl_give isl_id *isl_id_copy(isl_id *id);
804 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
806 void *isl_id_get_user(__isl_keep isl_id *id);
807 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
809 __isl_give isl_printer *isl_printer_print_id(
810 __isl_take isl_printer *p, __isl_keep isl_id *id);
812 The callback set by C<isl_id_set_free_user> is called on the user
813 pointer when the last reference to the C<isl_id> is freed.
814 Note that C<isl_id_get_name> returns a pointer to some internal
815 data structure, so the result can only be used while the
816 corresponding C<isl_id> is alive.
820 Whenever a new set, relation or similar object is created from scratch,
821 the space in which it lives needs to be specified using an C<isl_space>.
822 Each space involves zero or more parameters and zero, one or two
823 tuples of set or input/output dimensions. The parameters and dimensions
824 are identified by an C<isl_dim_type> and a position.
825 The type C<isl_dim_param> refers to parameters,
826 the type C<isl_dim_set> refers to set dimensions (for spaces
827 with a single tuple of dimensions) and the types C<isl_dim_in>
828 and C<isl_dim_out> refer to input and output dimensions
829 (for spaces with two tuples of dimensions).
830 Local spaces (see L</"Local Spaces">) also contain dimensions
831 of type C<isl_dim_div>.
832 Note that parameters are only identified by their position within
833 a given object. Across different objects, parameters are (usually)
834 identified by their names or identifiers. Only unnamed parameters
835 are identified by their positions across objects. The use of unnamed
836 parameters is discouraged.
838 #include <isl/space.h>
839 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
840 unsigned nparam, unsigned n_in, unsigned n_out);
841 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
843 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
844 unsigned nparam, unsigned dim);
845 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
846 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
848 The space used for creating a parameter domain
849 needs to be created using C<isl_space_params_alloc>.
850 For other sets, the space
851 needs to be created using C<isl_space_set_alloc>, while
852 for a relation, the space
853 needs to be created using C<isl_space_alloc>.
855 To check whether a given space is that of a set or a map
856 or whether it is a parameter space, use these functions:
858 #include <isl/space.h>
859 int isl_space_is_params(__isl_keep isl_space *space);
860 int isl_space_is_set(__isl_keep isl_space *space);
861 int isl_space_is_map(__isl_keep isl_space *space);
863 Spaces can be compared using the following functions:
865 #include <isl/space.h>
866 int isl_space_is_equal(__isl_keep isl_space *space1,
867 __isl_keep isl_space *space2);
868 int isl_space_is_domain(__isl_keep isl_space *space1,
869 __isl_keep isl_space *space2);
870 int isl_space_is_range(__isl_keep isl_space *space1,
871 __isl_keep isl_space *space2);
872 int isl_space_tuple_is_equal(
873 __isl_keep isl_space *space1,
874 enum isl_dim_type type1,
875 __isl_keep isl_space *space2,
876 enum isl_dim_type type2);
878 C<isl_space_is_domain> checks whether the first argument is equal
879 to the domain of the second argument. This requires in particular that
880 the first argument is a set space and that the second argument
881 is a map space. C<isl_space_tuple_is_equal> checks whether the given
882 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
883 spaces are the same. That is, it checks if they have the same
884 identifier (if any), the same dimension and the same internal structure
887 It is often useful to create objects that live in the
888 same space as some other object. This can be accomplished
889 by creating the new objects
890 (see L</"Creating New Sets and Relations"> or
891 L</"Functions">) based on the space
892 of the original object.
895 __isl_give isl_space *isl_basic_set_get_space(
896 __isl_keep isl_basic_set *bset);
897 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
899 #include <isl/union_set.h>
900 __isl_give isl_space *isl_union_set_get_space(
901 __isl_keep isl_union_set *uset);
904 __isl_give isl_space *isl_basic_map_get_space(
905 __isl_keep isl_basic_map *bmap);
906 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
908 #include <isl/union_map.h>
909 __isl_give isl_space *isl_union_map_get_space(
910 __isl_keep isl_union_map *umap);
912 #include <isl/constraint.h>
913 __isl_give isl_space *isl_constraint_get_space(
914 __isl_keep isl_constraint *constraint);
916 #include <isl/polynomial.h>
917 __isl_give isl_space *isl_qpolynomial_get_domain_space(
918 __isl_keep isl_qpolynomial *qp);
919 __isl_give isl_space *isl_qpolynomial_get_space(
920 __isl_keep isl_qpolynomial *qp);
921 __isl_give isl_space *isl_qpolynomial_fold_get_space(
922 __isl_keep isl_qpolynomial_fold *fold);
923 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
924 __isl_keep isl_pw_qpolynomial *pwqp);
925 __isl_give isl_space *isl_pw_qpolynomial_get_space(
926 __isl_keep isl_pw_qpolynomial *pwqp);
927 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
928 __isl_keep isl_pw_qpolynomial_fold *pwf);
929 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
930 __isl_keep isl_pw_qpolynomial_fold *pwf);
931 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
932 __isl_keep isl_union_pw_qpolynomial *upwqp);
933 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
934 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
937 __isl_give isl_space *isl_multi_val_get_space(
938 __isl_keep isl_multi_val *mv);
941 __isl_give isl_space *isl_aff_get_domain_space(
942 __isl_keep isl_aff *aff);
943 __isl_give isl_space *isl_aff_get_space(
944 __isl_keep isl_aff *aff);
945 __isl_give isl_space *isl_pw_aff_get_domain_space(
946 __isl_keep isl_pw_aff *pwaff);
947 __isl_give isl_space *isl_pw_aff_get_space(
948 __isl_keep isl_pw_aff *pwaff);
949 __isl_give isl_space *isl_multi_aff_get_domain_space(
950 __isl_keep isl_multi_aff *maff);
951 __isl_give isl_space *isl_multi_aff_get_space(
952 __isl_keep isl_multi_aff *maff);
953 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
954 __isl_keep isl_pw_multi_aff *pma);
955 __isl_give isl_space *isl_pw_multi_aff_get_space(
956 __isl_keep isl_pw_multi_aff *pma);
957 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
958 __isl_keep isl_union_pw_multi_aff *upma);
959 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
960 __isl_keep isl_multi_pw_aff *mpa);
961 __isl_give isl_space *isl_multi_pw_aff_get_space(
962 __isl_keep isl_multi_pw_aff *mpa);
964 #include <isl/point.h>
965 __isl_give isl_space *isl_point_get_space(
966 __isl_keep isl_point *pnt);
968 The number of dimensions of a given type of space
969 may be read off from a space or an object that lives
970 in a space using the following functions.
971 In case of C<isl_space_dim>, type may be
972 C<isl_dim_param>, C<isl_dim_in> (only for relations),
973 C<isl_dim_out> (only for relations), C<isl_dim_set>
974 (only for sets) or C<isl_dim_all>.
976 #include <isl/space.h>
977 unsigned isl_space_dim(__isl_keep isl_space *space,
978 enum isl_dim_type type);
980 #include <isl/local_space.h>
981 int isl_local_space_dim(__isl_keep isl_local_space *ls,
982 enum isl_dim_type type);
985 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
986 enum isl_dim_type type);
987 unsigned isl_set_dim(__isl_keep isl_set *set,
988 enum isl_dim_type type);
990 #include <isl/union_set.h>
991 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
992 enum isl_dim_type type);
995 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
996 enum isl_dim_type type);
997 unsigned isl_map_dim(__isl_keep isl_map *map,
998 enum isl_dim_type type);
1000 #include <isl/union_map.h>
1001 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1002 enum isl_dim_type type);
1004 #include <isl/val.h>
1005 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1006 enum isl_dim_type type);
1008 #include <isl/aff.h>
1009 int isl_aff_dim(__isl_keep isl_aff *aff,
1010 enum isl_dim_type type);
1011 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1012 enum isl_dim_type type);
1013 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1014 enum isl_dim_type type);
1015 unsigned isl_pw_multi_aff_dim(
1016 __isl_keep isl_pw_multi_aff *pma,
1017 enum isl_dim_type type);
1018 unsigned isl_multi_pw_aff_dim(
1019 __isl_keep isl_multi_pw_aff *mpa,
1020 enum isl_dim_type type);
1021 unsigned isl_union_pw_multi_aff_dim(
1022 __isl_keep isl_union_pw_multi_aff *upma,
1023 enum isl_dim_type type);
1025 #include <isl/polynomial.h>
1026 unsigned isl_union_pw_qpolynomial_dim(
1027 __isl_keep isl_union_pw_qpolynomial *upwqp,
1028 enum isl_dim_type type);
1029 unsigned isl_union_pw_qpolynomial_fold_dim(
1030 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1031 enum isl_dim_type type);
1033 Note that an C<isl_union_set>, an C<isl_union_map>,
1034 an C<isl_union_pw_multi_aff>,
1035 an C<isl_union_pw_qpolynomial> and
1036 an C<isl_union_pw_qpolynomial_fold>
1037 only have parameters.
1039 The identifiers or names of the individual dimensions of spaces
1040 may be set or read off using the following functions on spaces
1041 or objects that live in spaces.
1042 These functions are mostly useful to obtain the identifiers, positions
1043 or names of the parameters. Identifiers of individual dimensions are
1044 essentially only useful for printing. They are ignored by all other
1045 operations and may not be preserved across those operations.
1047 #include <isl/space.h>
1048 __isl_give isl_space *isl_space_set_dim_id(
1049 __isl_take isl_space *space,
1050 enum isl_dim_type type, unsigned pos,
1051 __isl_take isl_id *id);
1052 int isl_space_has_dim_id(__isl_keep isl_space *space,
1053 enum isl_dim_type type, unsigned pos);
1054 __isl_give isl_id *isl_space_get_dim_id(
1055 __isl_keep isl_space *space,
1056 enum isl_dim_type type, unsigned pos);
1057 __isl_give isl_space *isl_space_set_dim_name(
1058 __isl_take isl_space *space,
1059 enum isl_dim_type type, unsigned pos,
1060 __isl_keep const char *name);
1061 int isl_space_has_dim_name(__isl_keep isl_space *space,
1062 enum isl_dim_type type, unsigned pos);
1063 __isl_keep const char *isl_space_get_dim_name(
1064 __isl_keep isl_space *space,
1065 enum isl_dim_type type, unsigned pos);
1067 #include <isl/local_space.h>
1068 __isl_give isl_local_space *isl_local_space_set_dim_id(
1069 __isl_take isl_local_space *ls,
1070 enum isl_dim_type type, unsigned pos,
1071 __isl_take isl_id *id);
1072 int isl_local_space_has_dim_id(
1073 __isl_keep isl_local_space *ls,
1074 enum isl_dim_type type, unsigned pos);
1075 __isl_give isl_id *isl_local_space_get_dim_id(
1076 __isl_keep isl_local_space *ls,
1077 enum isl_dim_type type, unsigned pos);
1078 __isl_give isl_local_space *isl_local_space_set_dim_name(
1079 __isl_take isl_local_space *ls,
1080 enum isl_dim_type type, unsigned pos, const char *s);
1081 int isl_local_space_has_dim_name(
1082 __isl_keep isl_local_space *ls,
1083 enum isl_dim_type type, unsigned pos)
1084 const char *isl_local_space_get_dim_name(
1085 __isl_keep isl_local_space *ls,
1086 enum isl_dim_type type, unsigned pos);
1088 #include <isl/constraint.h>
1089 const char *isl_constraint_get_dim_name(
1090 __isl_keep isl_constraint *constraint,
1091 enum isl_dim_type type, unsigned pos);
1093 #include <isl/set.h>
1094 __isl_give isl_id *isl_basic_set_get_dim_id(
1095 __isl_keep isl_basic_set *bset,
1096 enum isl_dim_type type, unsigned pos);
1097 __isl_give isl_set *isl_set_set_dim_id(
1098 __isl_take isl_set *set, enum isl_dim_type type,
1099 unsigned pos, __isl_take isl_id *id);
1100 int isl_set_has_dim_id(__isl_keep isl_set *set,
1101 enum isl_dim_type type, unsigned pos);
1102 __isl_give isl_id *isl_set_get_dim_id(
1103 __isl_keep isl_set *set, enum isl_dim_type type,
1105 const char *isl_basic_set_get_dim_name(
1106 __isl_keep isl_basic_set *bset,
1107 enum isl_dim_type type, unsigned pos);
1108 int isl_set_has_dim_name(__isl_keep isl_set *set,
1109 enum isl_dim_type type, unsigned pos);
1110 const char *isl_set_get_dim_name(
1111 __isl_keep isl_set *set,
1112 enum isl_dim_type type, unsigned pos);
1114 #include <isl/map.h>
1115 __isl_give isl_map *isl_map_set_dim_id(
1116 __isl_take isl_map *map, enum isl_dim_type type,
1117 unsigned pos, __isl_take isl_id *id);
1118 int isl_basic_map_has_dim_id(
1119 __isl_keep isl_basic_map *bmap,
1120 enum isl_dim_type type, unsigned pos);
1121 int isl_map_has_dim_id(__isl_keep isl_map *map,
1122 enum isl_dim_type type, unsigned pos);
1123 __isl_give isl_id *isl_map_get_dim_id(
1124 __isl_keep isl_map *map, enum isl_dim_type type,
1126 __isl_give isl_id *isl_union_map_get_dim_id(
1127 __isl_keep isl_union_map *umap,
1128 enum isl_dim_type type, unsigned pos);
1129 const char *isl_basic_map_get_dim_name(
1130 __isl_keep isl_basic_map *bmap,
1131 enum isl_dim_type type, unsigned pos);
1132 int isl_map_has_dim_name(__isl_keep isl_map *map,
1133 enum isl_dim_type type, unsigned pos);
1134 const char *isl_map_get_dim_name(
1135 __isl_keep isl_map *map,
1136 enum isl_dim_type type, unsigned pos);
1138 #include <isl/val.h>
1139 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1140 __isl_take isl_multi_val *mv,
1141 enum isl_dim_type type, unsigned pos,
1142 __isl_take isl_id *id);
1143 __isl_give isl_id *isl_multi_val_get_dim_id(
1144 __isl_keep isl_multi_val *mv,
1145 enum isl_dim_type type, unsigned pos);
1146 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1147 __isl_take isl_multi_val *mv,
1148 enum isl_dim_type type, unsigned pos, const char *s);
1150 #include <isl/aff.h>
1151 __isl_give isl_aff *isl_aff_set_dim_id(
1152 __isl_take isl_aff *aff, enum isl_dim_type type,
1153 unsigned pos, __isl_take isl_id *id);
1154 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1155 __isl_take isl_multi_aff *maff,
1156 enum isl_dim_type type, unsigned pos,
1157 __isl_take isl_id *id);
1158 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1159 __isl_take isl_pw_aff *pma,
1160 enum isl_dim_type type, unsigned pos,
1161 __isl_take isl_id *id);
1162 __isl_give isl_multi_pw_aff *
1163 isl_multi_pw_aff_set_dim_id(
1164 __isl_take isl_multi_pw_aff *mpa,
1165 enum isl_dim_type type, unsigned pos,
1166 __isl_take isl_id *id);
1167 __isl_give isl_id *isl_multi_aff_get_dim_id(
1168 __isl_keep isl_multi_aff *ma,
1169 enum isl_dim_type type, unsigned pos);
1170 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1171 enum isl_dim_type type, unsigned pos);
1172 __isl_give isl_id *isl_pw_aff_get_dim_id(
1173 __isl_keep isl_pw_aff *pa,
1174 enum isl_dim_type type, unsigned pos);
1175 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1176 __isl_keep isl_pw_multi_aff *pma,
1177 enum isl_dim_type type, unsigned pos);
1178 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1179 __isl_keep isl_multi_pw_aff *mpa,
1180 enum isl_dim_type type, unsigned pos);
1181 __isl_give isl_aff *isl_aff_set_dim_name(
1182 __isl_take isl_aff *aff, enum isl_dim_type type,
1183 unsigned pos, const char *s);
1184 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1185 __isl_take isl_multi_aff *maff,
1186 enum isl_dim_type type, unsigned pos, const char *s);
1187 __isl_give isl_multi_pw_aff *
1188 isl_multi_pw_aff_set_dim_name(
1189 __isl_take isl_multi_pw_aff *mpa,
1190 enum isl_dim_type type, unsigned pos, const char *s);
1191 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1192 enum isl_dim_type type, unsigned pos);
1193 const char *isl_pw_aff_get_dim_name(
1194 __isl_keep isl_pw_aff *pa,
1195 enum isl_dim_type type, unsigned pos);
1196 const char *isl_pw_multi_aff_get_dim_name(
1197 __isl_keep isl_pw_multi_aff *pma,
1198 enum isl_dim_type type, unsigned pos);
1200 #include <isl/polynomial.h>
1201 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1202 __isl_take isl_qpolynomial *qp,
1203 enum isl_dim_type type, unsigned pos,
1205 __isl_give isl_pw_qpolynomial *
1206 isl_pw_qpolynomial_set_dim_name(
1207 __isl_take isl_pw_qpolynomial *pwqp,
1208 enum isl_dim_type type, unsigned pos,
1210 __isl_give isl_pw_qpolynomial_fold *
1211 isl_pw_qpolynomial_fold_set_dim_name(
1212 __isl_take isl_pw_qpolynomial_fold *pwf,
1213 enum isl_dim_type type, unsigned pos,
1216 Note that C<isl_space_get_name> returns a pointer to some internal
1217 data structure, so the result can only be used while the
1218 corresponding C<isl_space> is alive.
1219 Also note that every function that operates on two sets or relations
1220 requires that both arguments have the same parameters. This also
1221 means that if one of the arguments has named parameters, then the
1222 other needs to have named parameters too and the names need to match.
1223 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1224 arguments may have different parameters (as long as they are named),
1225 in which case the result will have as parameters the union of the parameters of
1228 Given the identifier or name of a dimension (typically a parameter),
1229 its position can be obtained from the following functions.
1231 #include <isl/space.h>
1232 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1233 enum isl_dim_type type, __isl_keep isl_id *id);
1234 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1235 enum isl_dim_type type, const char *name);
1237 #include <isl/local_space.h>
1238 int isl_local_space_find_dim_by_name(
1239 __isl_keep isl_local_space *ls,
1240 enum isl_dim_type type, const char *name);
1242 #include <isl/val.h>
1243 int isl_multi_val_find_dim_by_id(
1244 __isl_keep isl_multi_val *mv,
1245 enum isl_dim_type type, __isl_keep isl_id *id);
1246 int isl_multi_val_find_dim_by_name(
1247 __isl_keep isl_multi_val *mv,
1248 enum isl_dim_type type, const char *name);
1250 #include <isl/set.h>
1251 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1252 enum isl_dim_type type, __isl_keep isl_id *id);
1253 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1254 enum isl_dim_type type, const char *name);
1256 #include <isl/map.h>
1257 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1258 enum isl_dim_type type, __isl_keep isl_id *id);
1259 int isl_basic_map_find_dim_by_name(
1260 __isl_keep isl_basic_map *bmap,
1261 enum isl_dim_type type, const char *name);
1262 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1263 enum isl_dim_type type, const char *name);
1264 int isl_union_map_find_dim_by_name(
1265 __isl_keep isl_union_map *umap,
1266 enum isl_dim_type type, const char *name);
1268 #include <isl/aff.h>
1269 int isl_multi_aff_find_dim_by_id(
1270 __isl_keep isl_multi_aff *ma,
1271 enum isl_dim_type type, __isl_keep isl_id *id);
1272 int isl_multi_pw_aff_find_dim_by_id(
1273 __isl_keep isl_multi_pw_aff *mpa,
1274 enum isl_dim_type type, __isl_keep isl_id *id);
1275 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1276 enum isl_dim_type type, const char *name);
1277 int isl_multi_aff_find_dim_by_name(
1278 __isl_keep isl_multi_aff *ma,
1279 enum isl_dim_type type, const char *name);
1280 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1281 enum isl_dim_type type, const char *name);
1282 int isl_multi_pw_aff_find_dim_by_name(
1283 __isl_keep isl_multi_pw_aff *mpa,
1284 enum isl_dim_type type, const char *name);
1285 int isl_pw_multi_aff_find_dim_by_name(
1286 __isl_keep isl_pw_multi_aff *pma,
1287 enum isl_dim_type type, const char *name);
1288 int isl_union_pw_multi_aff_find_dim_by_name(
1289 __isl_keep isl_union_pw_multi_aff *upma,
1290 enum isl_dim_type type, const char *name);
1292 #include <isl/polynomial.h>
1293 int isl_pw_qpolynomial_find_dim_by_name(
1294 __isl_keep isl_pw_qpolynomial *pwqp,
1295 enum isl_dim_type type, const char *name);
1296 int isl_pw_qpolynomial_fold_find_dim_by_name(
1297 __isl_keep isl_pw_qpolynomial_fold *pwf,
1298 enum isl_dim_type type, const char *name);
1299 int isl_union_pw_qpolynomial_find_dim_by_name(
1300 __isl_keep isl_union_pw_qpolynomial *upwqp,
1301 enum isl_dim_type type, const char *name);
1302 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1303 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1304 enum isl_dim_type type, const char *name);
1306 The identifiers or names of entire spaces may be set or read off
1307 using the following functions.
1309 #include <isl/space.h>
1310 __isl_give isl_space *isl_space_set_tuple_id(
1311 __isl_take isl_space *space,
1312 enum isl_dim_type type, __isl_take isl_id *id);
1313 __isl_give isl_space *isl_space_reset_tuple_id(
1314 __isl_take isl_space *space, enum isl_dim_type type);
1315 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1316 enum isl_dim_type type);
1317 __isl_give isl_id *isl_space_get_tuple_id(
1318 __isl_keep isl_space *space, enum isl_dim_type type);
1319 __isl_give isl_space *isl_space_set_tuple_name(
1320 __isl_take isl_space *space,
1321 enum isl_dim_type type, const char *s);
1322 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1323 enum isl_dim_type type);
1324 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1325 enum isl_dim_type type);
1327 #include <isl/local_space.h>
1328 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1329 __isl_take isl_local_space *ls,
1330 enum isl_dim_type type, __isl_take isl_id *id);
1332 #include <isl/set.h>
1333 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1334 __isl_take isl_basic_set *bset,
1335 __isl_take isl_id *id);
1336 __isl_give isl_set *isl_set_set_tuple_id(
1337 __isl_take isl_set *set, __isl_take isl_id *id);
1338 __isl_give isl_set *isl_set_reset_tuple_id(
1339 __isl_take isl_set *set);
1340 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1341 __isl_give isl_id *isl_set_get_tuple_id(
1342 __isl_keep isl_set *set);
1343 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1344 __isl_take isl_basic_set *set, const char *s);
1345 __isl_give isl_set *isl_set_set_tuple_name(
1346 __isl_take isl_set *set, const char *s);
1347 const char *isl_basic_set_get_tuple_name(
1348 __isl_keep isl_basic_set *bset);
1349 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1350 const char *isl_set_get_tuple_name(
1351 __isl_keep isl_set *set);
1353 #include <isl/map.h>
1354 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1355 __isl_take isl_basic_map *bmap,
1356 enum isl_dim_type type, __isl_take isl_id *id);
1357 __isl_give isl_map *isl_map_set_tuple_id(
1358 __isl_take isl_map *map, enum isl_dim_type type,
1359 __isl_take isl_id *id);
1360 __isl_give isl_map *isl_map_reset_tuple_id(
1361 __isl_take isl_map *map, enum isl_dim_type type);
1362 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1363 enum isl_dim_type type);
1364 __isl_give isl_id *isl_map_get_tuple_id(
1365 __isl_keep isl_map *map, enum isl_dim_type type);
1366 __isl_give isl_map *isl_map_set_tuple_name(
1367 __isl_take isl_map *map,
1368 enum isl_dim_type type, const char *s);
1369 const char *isl_basic_map_get_tuple_name(
1370 __isl_keep isl_basic_map *bmap,
1371 enum isl_dim_type type);
1372 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1373 __isl_take isl_basic_map *bmap,
1374 enum isl_dim_type type, const char *s);
1375 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1376 enum isl_dim_type type);
1377 const char *isl_map_get_tuple_name(
1378 __isl_keep isl_map *map,
1379 enum isl_dim_type type);
1381 #include <isl/val.h>
1382 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1383 __isl_take isl_multi_val *mv,
1384 enum isl_dim_type type, __isl_take isl_id *id);
1385 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1386 __isl_take isl_multi_val *mv,
1387 enum isl_dim_type type);
1388 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1389 enum isl_dim_type type);
1390 __isl_give isl_id *isl_multi_val_get_tuple_id(
1391 __isl_keep isl_multi_val *mv,
1392 enum isl_dim_type type);
1393 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1394 __isl_take isl_multi_val *mv,
1395 enum isl_dim_type type, const char *s);
1396 const char *isl_multi_val_get_tuple_name(
1397 __isl_keep isl_multi_val *mv,
1398 enum isl_dim_type type);
1400 #include <isl/aff.h>
1401 __isl_give isl_aff *isl_aff_set_tuple_id(
1402 __isl_take isl_aff *aff,
1403 enum isl_dim_type type, __isl_take isl_id *id);
1404 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1405 __isl_take isl_multi_aff *maff,
1406 enum isl_dim_type type, __isl_take isl_id *id);
1407 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1408 __isl_take isl_pw_aff *pwaff,
1409 enum isl_dim_type type, __isl_take isl_id *id);
1410 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1411 __isl_take isl_pw_multi_aff *pma,
1412 enum isl_dim_type type, __isl_take isl_id *id);
1413 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1414 __isl_take isl_multi_aff *ma,
1415 enum isl_dim_type type);
1416 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1417 __isl_take isl_pw_aff *pa,
1418 enum isl_dim_type type);
1419 __isl_give isl_multi_pw_aff *
1420 isl_multi_pw_aff_reset_tuple_id(
1421 __isl_take isl_multi_pw_aff *mpa,
1422 enum isl_dim_type type);
1423 __isl_give isl_pw_multi_aff *
1424 isl_pw_multi_aff_reset_tuple_id(
1425 __isl_take isl_pw_multi_aff *pma,
1426 enum isl_dim_type type);
1427 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1428 enum isl_dim_type type);
1429 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1430 __isl_keep isl_multi_aff *ma,
1431 enum isl_dim_type type);
1432 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1433 enum isl_dim_type type);
1434 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1435 __isl_keep isl_pw_aff *pa,
1436 enum isl_dim_type type);
1437 int isl_pw_multi_aff_has_tuple_id(
1438 __isl_keep isl_pw_multi_aff *pma,
1439 enum isl_dim_type type);
1440 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1441 __isl_keep isl_pw_multi_aff *pma,
1442 enum isl_dim_type type);
1443 int isl_multi_pw_aff_has_tuple_id(
1444 __isl_keep isl_multi_pw_aff *mpa,
1445 enum isl_dim_type type);
1446 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1447 __isl_keep isl_multi_pw_aff *mpa,
1448 enum isl_dim_type type);
1449 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1450 __isl_take isl_multi_aff *maff,
1451 enum isl_dim_type type, const char *s);
1452 __isl_give isl_multi_pw_aff *
1453 isl_multi_pw_aff_set_tuple_name(
1454 __isl_take isl_multi_pw_aff *mpa,
1455 enum isl_dim_type type, const char *s);
1456 const char *isl_multi_aff_get_tuple_name(
1457 __isl_keep isl_multi_aff *multi,
1458 enum isl_dim_type type);
1459 int isl_pw_multi_aff_has_tuple_name(
1460 __isl_keep isl_pw_multi_aff *pma,
1461 enum isl_dim_type type);
1462 const char *isl_pw_multi_aff_get_tuple_name(
1463 __isl_keep isl_pw_multi_aff *pma,
1464 enum isl_dim_type type);
1466 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1467 or C<isl_dim_set>. As with C<isl_space_get_name>,
1468 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1470 Binary operations require the corresponding spaces of their arguments
1471 to have the same name.
1473 To keep the names of all parameters and tuples, but reset the user pointers
1474 of all the corresponding identifiers, use the following function.
1476 #include <isl/space.h>
1477 __isl_give isl_space *isl_space_reset_user(
1478 __isl_take isl_space *space);
1480 #include <isl/set.h>
1481 __isl_give isl_set *isl_set_reset_user(
1482 __isl_take isl_set *set);
1484 #include <isl/map.h>
1485 __isl_give isl_map *isl_map_reset_user(
1486 __isl_take isl_map *map);
1488 #include <isl/union_set.h>
1489 __isl_give isl_union_set *isl_union_set_reset_user(
1490 __isl_take isl_union_set *uset);
1492 #include <isl/union_map.h>
1493 __isl_give isl_union_map *isl_union_map_reset_user(
1494 __isl_take isl_union_map *umap);
1496 #include <isl/val.h>
1497 __isl_give isl_multi_val *isl_multi_val_reset_user(
1498 __isl_take isl_multi_val *mv);
1500 #include <isl/aff.h>
1501 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1502 __isl_take isl_multi_aff *ma);
1503 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1504 __isl_take isl_multi_pw_aff *mpa);
1506 Spaces can be nested. In particular, the domain of a set or
1507 the domain or range of a relation can be a nested relation.
1508 This process is also called I<wrapping>.
1509 The functions for detecting, constructing and deconstructing
1510 such nested spaces can be found in the wrapping properties
1511 of L</"Unary Properties">, the wrapping operations
1512 of L</"Unary Operations"> and the Cartesian product operations
1513 of L</"Basic Operations">.
1515 Spaces can be created from other spaces
1516 using the functions described in L</"Unary Operations">
1517 and L</"Binary Operations">.
1521 A local space is essentially a space with
1522 zero or more existentially quantified variables.
1523 The local space of various objects can be obtained
1524 using the following functions.
1526 #include <isl/constraint.h>
1527 __isl_give isl_local_space *isl_constraint_get_local_space(
1528 __isl_keep isl_constraint *constraint);
1530 #include <isl/set.h>
1531 __isl_give isl_local_space *isl_basic_set_get_local_space(
1532 __isl_keep isl_basic_set *bset);
1534 #include <isl/map.h>
1535 __isl_give isl_local_space *isl_basic_map_get_local_space(
1536 __isl_keep isl_basic_map *bmap);
1538 #include <isl/aff.h>
1539 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1540 __isl_keep isl_aff *aff);
1541 __isl_give isl_local_space *isl_aff_get_local_space(
1542 __isl_keep isl_aff *aff);
1544 A new local space can be created from a space using
1546 #include <isl/local_space.h>
1547 __isl_give isl_local_space *isl_local_space_from_space(
1548 __isl_take isl_space *space);
1550 They can be inspected, modified, copied and freed using the following functions.
1552 #include <isl/local_space.h>
1553 int isl_local_space_is_params(
1554 __isl_keep isl_local_space *ls);
1555 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1556 __isl_give isl_space *isl_local_space_get_space(
1557 __isl_keep isl_local_space *ls);
1558 __isl_give isl_aff *isl_local_space_get_div(
1559 __isl_keep isl_local_space *ls, int pos);
1560 __isl_give isl_local_space *isl_local_space_copy(
1561 __isl_keep isl_local_space *ls);
1562 __isl_null isl_local_space *isl_local_space_free(
1563 __isl_take isl_local_space *ls);
1565 Note that C<isl_local_space_get_div> can only be used on local spaces
1568 Two local spaces can be compared using
1570 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1571 __isl_keep isl_local_space *ls2);
1573 Local spaces can be created from other local spaces
1574 using the functions described in L</"Unary Operations">
1575 and L</"Binary Operations">.
1577 =head2 Creating New Sets and Relations
1579 C<isl> has functions for creating some standard sets and relations.
1583 =item * Empty sets and relations
1585 __isl_give isl_basic_set *isl_basic_set_empty(
1586 __isl_take isl_space *space);
1587 __isl_give isl_basic_map *isl_basic_map_empty(
1588 __isl_take isl_space *space);
1589 __isl_give isl_set *isl_set_empty(
1590 __isl_take isl_space *space);
1591 __isl_give isl_map *isl_map_empty(
1592 __isl_take isl_space *space);
1593 __isl_give isl_union_set *isl_union_set_empty(
1594 __isl_take isl_space *space);
1595 __isl_give isl_union_map *isl_union_map_empty(
1596 __isl_take isl_space *space);
1598 For C<isl_union_set>s and C<isl_union_map>s, the space
1599 is only used to specify the parameters.
1601 =item * Universe sets and relations
1603 __isl_give isl_basic_set *isl_basic_set_universe(
1604 __isl_take isl_space *space);
1605 __isl_give isl_basic_map *isl_basic_map_universe(
1606 __isl_take isl_space *space);
1607 __isl_give isl_set *isl_set_universe(
1608 __isl_take isl_space *space);
1609 __isl_give isl_map *isl_map_universe(
1610 __isl_take isl_space *space);
1611 __isl_give isl_union_set *isl_union_set_universe(
1612 __isl_take isl_union_set *uset);
1613 __isl_give isl_union_map *isl_union_map_universe(
1614 __isl_take isl_union_map *umap);
1616 The sets and relations constructed by the functions above
1617 contain all integer values, while those constructed by the
1618 functions below only contain non-negative values.
1620 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1621 __isl_take isl_space *space);
1622 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1623 __isl_take isl_space *space);
1624 __isl_give isl_set *isl_set_nat_universe(
1625 __isl_take isl_space *space);
1626 __isl_give isl_map *isl_map_nat_universe(
1627 __isl_take isl_space *space);
1629 =item * Identity relations
1631 __isl_give isl_basic_map *isl_basic_map_identity(
1632 __isl_take isl_space *space);
1633 __isl_give isl_map *isl_map_identity(
1634 __isl_take isl_space *space);
1636 The number of input and output dimensions in C<space> needs
1639 =item * Lexicographic order
1641 __isl_give isl_map *isl_map_lex_lt(
1642 __isl_take isl_space *set_space);
1643 __isl_give isl_map *isl_map_lex_le(
1644 __isl_take isl_space *set_space);
1645 __isl_give isl_map *isl_map_lex_gt(
1646 __isl_take isl_space *set_space);
1647 __isl_give isl_map *isl_map_lex_ge(
1648 __isl_take isl_space *set_space);
1649 __isl_give isl_map *isl_map_lex_lt_first(
1650 __isl_take isl_space *space, unsigned n);
1651 __isl_give isl_map *isl_map_lex_le_first(
1652 __isl_take isl_space *space, unsigned n);
1653 __isl_give isl_map *isl_map_lex_gt_first(
1654 __isl_take isl_space *space, unsigned n);
1655 __isl_give isl_map *isl_map_lex_ge_first(
1656 __isl_take isl_space *space, unsigned n);
1658 The first four functions take a space for a B<set>
1659 and return relations that express that the elements in the domain
1660 are lexicographically less
1661 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1662 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1663 than the elements in the range.
1664 The last four functions take a space for a map
1665 and return relations that express that the first C<n> dimensions
1666 in the domain are lexicographically less
1667 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1668 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1669 than the first C<n> dimensions in the range.
1673 A basic set or relation can be converted to a set or relation
1674 using the following functions.
1676 __isl_give isl_set *isl_set_from_basic_set(
1677 __isl_take isl_basic_set *bset);
1678 __isl_give isl_map *isl_map_from_basic_map(
1679 __isl_take isl_basic_map *bmap);
1681 Sets and relations can be converted to union sets and relations
1682 using the following functions.
1684 __isl_give isl_union_set *isl_union_set_from_basic_set(
1685 __isl_take isl_basic_set *bset);
1686 __isl_give isl_union_map *isl_union_map_from_basic_map(
1687 __isl_take isl_basic_map *bmap);
1688 __isl_give isl_union_set *isl_union_set_from_set(
1689 __isl_take isl_set *set);
1690 __isl_give isl_union_map *isl_union_map_from_map(
1691 __isl_take isl_map *map);
1693 The inverse conversions below can only be used if the input
1694 union set or relation is known to contain elements in exactly one
1697 __isl_give isl_set *isl_set_from_union_set(
1698 __isl_take isl_union_set *uset);
1699 __isl_give isl_map *isl_map_from_union_map(
1700 __isl_take isl_union_map *umap);
1702 Sets and relations can be copied and freed again using the following
1705 __isl_give isl_basic_set *isl_basic_set_copy(
1706 __isl_keep isl_basic_set *bset);
1707 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1708 __isl_give isl_union_set *isl_union_set_copy(
1709 __isl_keep isl_union_set *uset);
1710 __isl_give isl_basic_map *isl_basic_map_copy(
1711 __isl_keep isl_basic_map *bmap);
1712 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1713 __isl_give isl_union_map *isl_union_map_copy(
1714 __isl_keep isl_union_map *umap);
1715 __isl_null isl_basic_set *isl_basic_set_free(
1716 __isl_take isl_basic_set *bset);
1717 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1718 __isl_null isl_union_set *isl_union_set_free(
1719 __isl_take isl_union_set *uset);
1720 __isl_null isl_basic_map *isl_basic_map_free(
1721 __isl_take isl_basic_map *bmap);
1722 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1723 __isl_null isl_union_map *isl_union_map_free(
1724 __isl_take isl_union_map *umap);
1726 Other sets and relations can be constructed by starting
1727 from a universe set or relation, adding equality and/or
1728 inequality constraints and then projecting out the
1729 existentially quantified variables, if any.
1730 Constraints can be constructed, manipulated and
1731 added to (or removed from) (basic) sets and relations
1732 using the following functions.
1734 #include <isl/constraint.h>
1735 __isl_give isl_constraint *isl_equality_alloc(
1736 __isl_take isl_local_space *ls);
1737 __isl_give isl_constraint *isl_inequality_alloc(
1738 __isl_take isl_local_space *ls);
1739 __isl_give isl_constraint *isl_constraint_set_constant_si(
1740 __isl_take isl_constraint *constraint, int v);
1741 __isl_give isl_constraint *isl_constraint_set_constant_val(
1742 __isl_take isl_constraint *constraint,
1743 __isl_take isl_val *v);
1744 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1745 __isl_take isl_constraint *constraint,
1746 enum isl_dim_type type, int pos, int v);
1747 __isl_give isl_constraint *
1748 isl_constraint_set_coefficient_val(
1749 __isl_take isl_constraint *constraint,
1750 enum isl_dim_type type, int pos,
1751 __isl_take isl_val *v);
1752 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1753 __isl_take isl_basic_map *bmap,
1754 __isl_take isl_constraint *constraint);
1755 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1756 __isl_take isl_basic_set *bset,
1757 __isl_take isl_constraint *constraint);
1758 __isl_give isl_map *isl_map_add_constraint(
1759 __isl_take isl_map *map,
1760 __isl_take isl_constraint *constraint);
1761 __isl_give isl_set *isl_set_add_constraint(
1762 __isl_take isl_set *set,
1763 __isl_take isl_constraint *constraint);
1764 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1765 __isl_take isl_basic_set *bset,
1766 __isl_take isl_constraint *constraint);
1768 For example, to create a set containing the even integers
1769 between 10 and 42, you would use the following code.
1772 isl_local_space *ls;
1774 isl_basic_set *bset;
1776 space = isl_space_set_alloc(ctx, 0, 2);
1777 bset = isl_basic_set_universe(isl_space_copy(space));
1778 ls = isl_local_space_from_space(space);
1780 c = isl_equality_alloc(isl_local_space_copy(ls));
1781 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1782 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1783 bset = isl_basic_set_add_constraint(bset, c);
1785 c = isl_inequality_alloc(isl_local_space_copy(ls));
1786 c = isl_constraint_set_constant_si(c, -10);
1787 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1788 bset = isl_basic_set_add_constraint(bset, c);
1790 c = isl_inequality_alloc(ls);
1791 c = isl_constraint_set_constant_si(c, 42);
1792 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1793 bset = isl_basic_set_add_constraint(bset, c);
1795 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1799 isl_basic_set *bset;
1800 bset = isl_basic_set_read_from_str(ctx,
1801 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1803 A basic set or relation can also be constructed from two matrices
1804 describing the equalities and the inequalities.
1806 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1807 __isl_take isl_space *space,
1808 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1809 enum isl_dim_type c1,
1810 enum isl_dim_type c2, enum isl_dim_type c3,
1811 enum isl_dim_type c4);
1812 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1813 __isl_take isl_space *space,
1814 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1815 enum isl_dim_type c1,
1816 enum isl_dim_type c2, enum isl_dim_type c3,
1817 enum isl_dim_type c4, enum isl_dim_type c5);
1819 The C<isl_dim_type> arguments indicate the order in which
1820 different kinds of variables appear in the input matrices
1821 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1822 C<isl_dim_set> and C<isl_dim_div> for sets and
1823 of C<isl_dim_cst>, C<isl_dim_param>,
1824 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1826 A (basic or union) set or relation can also be constructed from a
1827 (union) (piecewise) (multiple) affine expression
1828 or a list of affine expressions
1829 (See L</"Functions">).
1831 __isl_give isl_basic_map *isl_basic_map_from_aff(
1832 __isl_take isl_aff *aff);
1833 __isl_give isl_map *isl_map_from_aff(
1834 __isl_take isl_aff *aff);
1835 __isl_give isl_set *isl_set_from_pw_aff(
1836 __isl_take isl_pw_aff *pwaff);
1837 __isl_give isl_map *isl_map_from_pw_aff(
1838 __isl_take isl_pw_aff *pwaff);
1839 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1840 __isl_take isl_space *domain_space,
1841 __isl_take isl_aff_list *list);
1842 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1843 __isl_take isl_multi_aff *maff)
1844 __isl_give isl_map *isl_map_from_multi_aff(
1845 __isl_take isl_multi_aff *maff)
1846 __isl_give isl_set *isl_set_from_pw_multi_aff(
1847 __isl_take isl_pw_multi_aff *pma);
1848 __isl_give isl_map *isl_map_from_pw_multi_aff(
1849 __isl_take isl_pw_multi_aff *pma);
1850 __isl_give isl_set *isl_set_from_multi_pw_aff(
1851 __isl_take isl_multi_pw_aff *mpa);
1852 __isl_give isl_map *isl_map_from_multi_pw_aff(
1853 __isl_take isl_multi_pw_aff *mpa);
1854 __isl_give isl_union_map *
1855 isl_union_map_from_union_pw_multi_aff(
1856 __isl_take isl_union_pw_multi_aff *upma);
1858 The C<domain_space> argument describes the domain of the resulting
1859 basic relation. It is required because the C<list> may consist
1860 of zero affine expressions.
1862 =head2 Inspecting Sets and Relations
1864 Usually, the user should not have to care about the actual constraints
1865 of the sets and maps, but should instead apply the abstract operations
1866 explained in the following sections.
1867 Occasionally, however, it may be required to inspect the individual
1868 coefficients of the constraints. This section explains how to do so.
1869 In these cases, it may also be useful to have C<isl> compute
1870 an explicit representation of the existentially quantified variables.
1872 __isl_give isl_set *isl_set_compute_divs(
1873 __isl_take isl_set *set);
1874 __isl_give isl_map *isl_map_compute_divs(
1875 __isl_take isl_map *map);
1876 __isl_give isl_union_set *isl_union_set_compute_divs(
1877 __isl_take isl_union_set *uset);
1878 __isl_give isl_union_map *isl_union_map_compute_divs(
1879 __isl_take isl_union_map *umap);
1881 This explicit representation defines the existentially quantified
1882 variables as integer divisions of the other variables, possibly
1883 including earlier existentially quantified variables.
1884 An explicitly represented existentially quantified variable therefore
1885 has a unique value when the values of the other variables are known.
1886 If, furthermore, the same existentials, i.e., existentials
1887 with the same explicit representations, should appear in the
1888 same order in each of the disjuncts of a set or map, then the user should call
1889 either of the following functions.
1891 __isl_give isl_set *isl_set_align_divs(
1892 __isl_take isl_set *set);
1893 __isl_give isl_map *isl_map_align_divs(
1894 __isl_take isl_map *map);
1896 Alternatively, the existentially quantified variables can be removed
1897 using the following functions, which compute an overapproximation.
1899 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1900 __isl_take isl_basic_set *bset);
1901 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1902 __isl_take isl_basic_map *bmap);
1903 __isl_give isl_set *isl_set_remove_divs(
1904 __isl_take isl_set *set);
1905 __isl_give isl_map *isl_map_remove_divs(
1906 __isl_take isl_map *map);
1908 It is also possible to only remove those divs that are defined
1909 in terms of a given range of dimensions or only those for which
1910 no explicit representation is known.
1912 __isl_give isl_basic_set *
1913 isl_basic_set_remove_divs_involving_dims(
1914 __isl_take isl_basic_set *bset,
1915 enum isl_dim_type type,
1916 unsigned first, unsigned n);
1917 __isl_give isl_basic_map *
1918 isl_basic_map_remove_divs_involving_dims(
1919 __isl_take isl_basic_map *bmap,
1920 enum isl_dim_type type,
1921 unsigned first, unsigned n);
1922 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1923 __isl_take isl_set *set, enum isl_dim_type type,
1924 unsigned first, unsigned n);
1925 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1926 __isl_take isl_map *map, enum isl_dim_type type,
1927 unsigned first, unsigned n);
1929 __isl_give isl_basic_set *
1930 isl_basic_set_remove_unknown_divs(
1931 __isl_take isl_basic_set *bset);
1932 __isl_give isl_set *isl_set_remove_unknown_divs(
1933 __isl_take isl_set *set);
1934 __isl_give isl_map *isl_map_remove_unknown_divs(
1935 __isl_take isl_map *map);
1937 To iterate over all the sets or maps in a union set or map, use
1939 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1940 int (*fn)(__isl_take isl_set *set, void *user),
1942 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1943 int (*fn)(__isl_take isl_map *map, void *user),
1946 The number of sets or maps in a union set or map can be obtained
1949 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1950 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1952 To extract the set or map in a given space from a union, use
1954 __isl_give isl_set *isl_union_set_extract_set(
1955 __isl_keep isl_union_set *uset,
1956 __isl_take isl_space *space);
1957 __isl_give isl_map *isl_union_map_extract_map(
1958 __isl_keep isl_union_map *umap,
1959 __isl_take isl_space *space);
1961 To iterate over all the basic sets or maps in a set or map, use
1963 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1964 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1966 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1967 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1970 The callback function C<fn> should return 0 if successful and
1971 -1 if an error occurs. In the latter case, or if any other error
1972 occurs, the above functions will return -1.
1974 It should be noted that C<isl> does not guarantee that
1975 the basic sets or maps passed to C<fn> are disjoint.
1976 If this is required, then the user should call one of
1977 the following functions first.
1979 __isl_give isl_set *isl_set_make_disjoint(
1980 __isl_take isl_set *set);
1981 __isl_give isl_map *isl_map_make_disjoint(
1982 __isl_take isl_map *map);
1984 The number of basic sets in a set can be obtained
1985 or the number of basic maps in a map can be obtained
1988 #include <isl/set.h>
1989 int isl_set_n_basic_set(__isl_keep isl_set *set);
1991 #include <isl/map.h>
1992 int isl_map_n_basic_map(__isl_keep isl_map *map);
1994 To iterate over the constraints of a basic set or map, use
1996 #include <isl/constraint.h>
1998 int isl_basic_set_n_constraint(
1999 __isl_keep isl_basic_set *bset);
2000 int isl_basic_set_foreach_constraint(
2001 __isl_keep isl_basic_set *bset,
2002 int (*fn)(__isl_take isl_constraint *c, void *user),
2004 int isl_basic_map_n_constraint(
2005 __isl_keep isl_basic_map *bmap);
2006 int isl_basic_map_foreach_constraint(
2007 __isl_keep isl_basic_map *bmap,
2008 int (*fn)(__isl_take isl_constraint *c, void *user),
2010 __isl_null isl_constraint *isl_constraint_free(
2011 __isl_take isl_constraint *c);
2013 Again, the callback function C<fn> should return 0 if successful and
2014 -1 if an error occurs. In the latter case, or if any other error
2015 occurs, the above functions will return -1.
2016 The constraint C<c> represents either an equality or an inequality.
2017 Use the following function to find out whether a constraint
2018 represents an equality. If not, it represents an inequality.
2020 int isl_constraint_is_equality(
2021 __isl_keep isl_constraint *constraint);
2023 It is also possible to obtain a list of constraints from a basic
2026 #include <isl/constraint.h>
2027 __isl_give isl_constraint_list *
2028 isl_basic_map_get_constraint_list(
2029 __isl_keep isl_basic_map *bmap);
2030 __isl_give isl_constraint_list *
2031 isl_basic_set_get_constraint_list(
2032 __isl_keep isl_basic_set *bset);
2034 These functions require that all existentially quantified variables
2035 have an explicit representation.
2036 The returned list can be manipulated using the functions in L<"Lists">.
2038 The coefficients of the constraints can be inspected using
2039 the following functions.
2041 int isl_constraint_is_lower_bound(
2042 __isl_keep isl_constraint *constraint,
2043 enum isl_dim_type type, unsigned pos);
2044 int isl_constraint_is_upper_bound(
2045 __isl_keep isl_constraint *constraint,
2046 enum isl_dim_type type, unsigned pos);
2047 __isl_give isl_val *isl_constraint_get_constant_val(
2048 __isl_keep isl_constraint *constraint);
2049 __isl_give isl_val *isl_constraint_get_coefficient_val(
2050 __isl_keep isl_constraint *constraint,
2051 enum isl_dim_type type, int pos);
2053 The explicit representations of the existentially quantified
2054 variables can be inspected using the following function.
2055 Note that the user is only allowed to use this function
2056 if the inspected set or map is the result of a call
2057 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2058 The existentially quantified variable is equal to the floor
2059 of the returned affine expression. The affine expression
2060 itself can be inspected using the functions in
2063 __isl_give isl_aff *isl_constraint_get_div(
2064 __isl_keep isl_constraint *constraint, int pos);
2066 To obtain the constraints of a basic set or map in matrix
2067 form, use the following functions.
2069 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2070 __isl_keep isl_basic_set *bset,
2071 enum isl_dim_type c1, enum isl_dim_type c2,
2072 enum isl_dim_type c3, enum isl_dim_type c4);
2073 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2074 __isl_keep isl_basic_set *bset,
2075 enum isl_dim_type c1, enum isl_dim_type c2,
2076 enum isl_dim_type c3, enum isl_dim_type c4);
2077 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2078 __isl_keep isl_basic_map *bmap,
2079 enum isl_dim_type c1,
2080 enum isl_dim_type c2, enum isl_dim_type c3,
2081 enum isl_dim_type c4, enum isl_dim_type c5);
2082 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2083 __isl_keep isl_basic_map *bmap,
2084 enum isl_dim_type c1,
2085 enum isl_dim_type c2, enum isl_dim_type c3,
2086 enum isl_dim_type c4, enum isl_dim_type c5);
2088 The C<isl_dim_type> arguments dictate the order in which
2089 different kinds of variables appear in the resulting matrix.
2090 For set inputs, they should be a permutation of
2091 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2092 For map inputs, they should be a permutation of
2093 C<isl_dim_cst>, C<isl_dim_param>,
2094 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2098 Points are elements of a set. They can be used to construct
2099 simple sets (boxes) or they can be used to represent the
2100 individual elements of a set.
2101 The zero point (the origin) can be created using
2103 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2105 The coordinates of a point can be inspected, set and changed
2108 __isl_give isl_val *isl_point_get_coordinate_val(
2109 __isl_keep isl_point *pnt,
2110 enum isl_dim_type type, int pos);
2111 __isl_give isl_point *isl_point_set_coordinate_val(
2112 __isl_take isl_point *pnt,
2113 enum isl_dim_type type, int pos,
2114 __isl_take isl_val *v);
2116 __isl_give isl_point *isl_point_add_ui(
2117 __isl_take isl_point *pnt,
2118 enum isl_dim_type type, int pos, unsigned val);
2119 __isl_give isl_point *isl_point_sub_ui(
2120 __isl_take isl_point *pnt,
2121 enum isl_dim_type type, int pos, unsigned val);
2123 Points can be copied or freed using
2125 __isl_give isl_point *isl_point_copy(
2126 __isl_keep isl_point *pnt);
2127 void isl_point_free(__isl_take isl_point *pnt);
2129 A singleton set can be created from a point using
2131 __isl_give isl_basic_set *isl_basic_set_from_point(
2132 __isl_take isl_point *pnt);
2133 __isl_give isl_set *isl_set_from_point(
2134 __isl_take isl_point *pnt);
2136 and a box can be created from two opposite extremal points using
2138 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2139 __isl_take isl_point *pnt1,
2140 __isl_take isl_point *pnt2);
2141 __isl_give isl_set *isl_set_box_from_points(
2142 __isl_take isl_point *pnt1,
2143 __isl_take isl_point *pnt2);
2145 All elements of a B<bounded> (union) set can be enumerated using
2146 the following functions.
2148 int isl_set_foreach_point(__isl_keep isl_set *set,
2149 int (*fn)(__isl_take isl_point *pnt, void *user),
2151 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2152 int (*fn)(__isl_take isl_point *pnt, void *user),
2155 The function C<fn> is called for each integer point in
2156 C<set> with as second argument the last argument of
2157 the C<isl_set_foreach_point> call. The function C<fn>
2158 should return C<0> on success and C<-1> on failure.
2159 In the latter case, C<isl_set_foreach_point> will stop
2160 enumerating and return C<-1> as well.
2161 If the enumeration is performed successfully and to completion,
2162 then C<isl_set_foreach_point> returns C<0>.
2164 To obtain a single point of a (basic) set, use
2166 __isl_give isl_point *isl_basic_set_sample_point(
2167 __isl_take isl_basic_set *bset);
2168 __isl_give isl_point *isl_set_sample_point(
2169 __isl_take isl_set *set);
2171 If C<set> does not contain any (integer) points, then the
2172 resulting point will be ``void'', a property that can be
2175 int isl_point_is_void(__isl_keep isl_point *pnt);
2179 Besides sets and relation, C<isl> also supports various types of functions.
2180 Each of these types is derived from the value type (see L</"Values">)
2181 or from one of two primitive function types
2182 through the application of zero or more type constructors.
2183 We first describe the primitive type and then we describe
2184 the types derived from these primitive types.
2186 =head3 Primitive Functions
2188 C<isl> support two primitive function types, quasi-affine
2189 expressions and quasipolynomials.
2190 A quasi-affine expression is defined either over a parameter
2191 space or over a set and is composed of integer constants,
2192 parameters and set variables, addition, subtraction and
2193 integer division by an integer constant.
2194 For example, the quasi-affine expression
2196 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2198 maps C<x> to C<2*floor((4 n + x)/9>.
2199 A quasipolynomial is a polynomial expression in quasi-affine
2200 expression. That is, it additionally allows for multiplication.
2201 Note, though, that it is not allowed to construct an integer
2202 division of an expression involving multiplications.
2203 Here is an example of a quasipolynomial that is not
2204 quasi-affine expression
2206 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2208 Note that the external representations of quasi-affine expressions
2209 and quasipolynomials are different. Quasi-affine expressions
2210 use a notation with square brackets just like binary relations,
2211 while quasipolynomials do not. This might change at some point.
2213 If a primitive function is defined over a parameter space,
2214 then the space of the function itself is that of a set.
2215 If it is defined over a set, then the space of the function
2216 is that of a relation. In both cases, the set space (or
2217 the output space) is single-dimensional, anonymous and unstructured.
2218 To create functions with multiple dimensions or with other kinds
2219 of set or output spaces, use multiple expressions
2220 (see L</"Multiple Expressions">).
2224 =item * Quasi-affine Expressions
2226 Besides the expressions described above, a quasi-affine
2227 expression can also be set to NaN. Such expressions
2228 typically represent a failure to represent a result
2229 as a quasi-affine expression.
2231 The zero quasi affine expression or the quasi affine expression
2232 that is equal to a given value or
2233 a specified dimension on a given domain can be created using
2235 #include <isl/aff.h>
2236 __isl_give isl_aff *isl_aff_zero_on_domain(
2237 __isl_take isl_local_space *ls);
2238 __isl_give isl_aff *isl_aff_val_on_domain(
2239 __isl_take isl_local_space *ls,
2240 __isl_take isl_val *val);
2241 __isl_give isl_aff *isl_aff_var_on_domain(
2242 __isl_take isl_local_space *ls,
2243 enum isl_dim_type type, unsigned pos);
2244 __isl_give isl_aff *isl_aff_nan_on_domain(
2245 __isl_take isl_local_space *ls);
2247 Quasi affine expressions can be copied and freed using
2249 #include <isl/aff.h>
2250 __isl_give isl_aff *isl_aff_copy(
2251 __isl_keep isl_aff *aff);
2252 __isl_null isl_aff *isl_aff_free(
2253 __isl_take isl_aff *aff);
2255 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2256 using the following function. The constraint is required to have
2257 a non-zero coefficient for the specified dimension.
2259 #include <isl/constraint.h>
2260 __isl_give isl_aff *isl_constraint_get_bound(
2261 __isl_keep isl_constraint *constraint,
2262 enum isl_dim_type type, int pos);
2264 The entire affine expression of the constraint can also be extracted
2265 using the following function.
2267 #include <isl/constraint.h>
2268 __isl_give isl_aff *isl_constraint_get_aff(
2269 __isl_keep isl_constraint *constraint);
2271 Conversely, an equality constraint equating
2272 the affine expression to zero or an inequality constraint enforcing
2273 the affine expression to be non-negative, can be constructed using
2275 __isl_give isl_constraint *isl_equality_from_aff(
2276 __isl_take isl_aff *aff);
2277 __isl_give isl_constraint *isl_inequality_from_aff(
2278 __isl_take isl_aff *aff);
2280 The coefficients and the integer divisions of an affine expression
2281 can be inspected using the following functions.
2283 #include <isl/aff.h>
2284 __isl_give isl_val *isl_aff_get_constant_val(
2285 __isl_keep isl_aff *aff);
2286 __isl_give isl_val *isl_aff_get_coefficient_val(
2287 __isl_keep isl_aff *aff,
2288 enum isl_dim_type type, int pos);
2289 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2290 enum isl_dim_type type, int pos);
2291 __isl_give isl_val *isl_aff_get_denominator_val(
2292 __isl_keep isl_aff *aff);
2293 __isl_give isl_aff *isl_aff_get_div(
2294 __isl_keep isl_aff *aff, int pos);
2296 They can be modified using the following functions.
2298 #include <isl/aff.h>
2299 __isl_give isl_aff *isl_aff_set_constant_si(
2300 __isl_take isl_aff *aff, int v);
2301 __isl_give isl_aff *isl_aff_set_constant_val(
2302 __isl_take isl_aff *aff, __isl_take isl_val *v);
2303 __isl_give isl_aff *isl_aff_set_coefficient_si(
2304 __isl_take isl_aff *aff,
2305 enum isl_dim_type type, int pos, int v);
2306 __isl_give isl_aff *isl_aff_set_coefficient_val(
2307 __isl_take isl_aff *aff,
2308 enum isl_dim_type type, int pos,
2309 __isl_take isl_val *v);
2311 __isl_give isl_aff *isl_aff_add_constant_si(
2312 __isl_take isl_aff *aff, int v);
2313 __isl_give isl_aff *isl_aff_add_constant_val(
2314 __isl_take isl_aff *aff, __isl_take isl_val *v);
2315 __isl_give isl_aff *isl_aff_add_constant_num_si(
2316 __isl_take isl_aff *aff, int v);
2317 __isl_give isl_aff *isl_aff_add_coefficient_si(
2318 __isl_take isl_aff *aff,
2319 enum isl_dim_type type, int pos, int v);
2320 __isl_give isl_aff *isl_aff_add_coefficient_val(
2321 __isl_take isl_aff *aff,
2322 enum isl_dim_type type, int pos,
2323 __isl_take isl_val *v);
2325 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2326 set the I<numerator> of the constant or coefficient, while
2327 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2328 the constant or coefficient as a whole.
2329 The C<add_constant> and C<add_coefficient> functions add an integer
2330 or rational value to
2331 the possibly rational constant or coefficient.
2332 The C<add_constant_num> functions add an integer value to
2335 =item * Quasipolynomials
2337 Some simple quasipolynomials can be created using the following functions.
2339 #include <isl/polynomial.h>
2340 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2341 __isl_take isl_space *domain);
2342 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2343 __isl_take isl_space *domain);
2344 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2345 __isl_take isl_space *domain);
2346 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2347 __isl_take isl_space *domain);
2348 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2349 __isl_take isl_space *domain);
2350 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2351 __isl_take isl_space *domain,
2352 __isl_take isl_val *val);
2353 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2354 __isl_take isl_space *domain,
2355 enum isl_dim_type type, unsigned pos);
2356 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2357 __isl_take isl_aff *aff);
2359 Recall that the space in which a quasipolynomial lives is a map space
2360 with a one-dimensional range. The C<domain> argument in some of
2361 the functions above corresponds to the domain of this map space.
2363 Quasipolynomials can be copied and freed again using the following
2366 #include <isl/polynomial.h>
2367 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2368 __isl_keep isl_qpolynomial *qp);
2369 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2370 __isl_take isl_qpolynomial *qp);
2372 The constant term of a quasipolynomial can be extracted using
2374 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2375 __isl_keep isl_qpolynomial *qp);
2377 To iterate over all terms in a quasipolynomial,
2380 int isl_qpolynomial_foreach_term(
2381 __isl_keep isl_qpolynomial *qp,
2382 int (*fn)(__isl_take isl_term *term,
2383 void *user), void *user);
2385 The terms themselves can be inspected and freed using
2388 unsigned isl_term_dim(__isl_keep isl_term *term,
2389 enum isl_dim_type type);
2390 __isl_give isl_val *isl_term_get_coefficient_val(
2391 __isl_keep isl_term *term);
2392 int isl_term_get_exp(__isl_keep isl_term *term,
2393 enum isl_dim_type type, unsigned pos);
2394 __isl_give isl_aff *isl_term_get_div(
2395 __isl_keep isl_term *term, unsigned pos);
2396 void isl_term_free(__isl_take isl_term *term);
2398 Each term is a product of parameters, set variables and
2399 integer divisions. The function C<isl_term_get_exp>
2400 returns the exponent of a given dimensions in the given term.
2406 A reduction represents a maximum or a minimum of its
2408 The only reduction type defined by C<isl> is
2409 C<isl_qpolynomial_fold>.
2411 There are currently no functions to directly create such
2412 objects, but they do appear in the piecewise quasipolynomial
2413 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2415 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2417 Reductions can be copied and freed using
2418 the following functions.
2420 #include <isl/polynomial.h>
2421 __isl_give isl_qpolynomial_fold *
2422 isl_qpolynomial_fold_copy(
2423 __isl_keep isl_qpolynomial_fold *fold);
2424 void isl_qpolynomial_fold_free(
2425 __isl_take isl_qpolynomial_fold *fold);
2427 To iterate over all quasipolynomials in a reduction, use
2429 int isl_qpolynomial_fold_foreach_qpolynomial(
2430 __isl_keep isl_qpolynomial_fold *fold,
2431 int (*fn)(__isl_take isl_qpolynomial *qp,
2432 void *user), void *user);
2434 =head3 Multiple Expressions
2436 A multiple expression represents a sequence of zero or
2437 more base expressions, all defined on the same domain space.
2438 The domain space of the multiple expression is the same
2439 as that of the base expressions, but the range space
2440 can be any space. In case the base expressions have
2441 a set space, the corresponding multiple expression
2442 also has a set space.
2443 Objects of the value type do not have an associated space.
2444 The space of a multiple value is therefore always a set space.
2446 The multiple expression types defined by C<isl>
2447 are C<isl_multi_val>, C<isl_multi_aff> and C<isl_multi_pw_aff>.
2449 A multiple expression with the value zero for
2450 each output (or set) dimension can be created
2451 using the following functions.
2453 #include <isl/val.h>
2454 __isl_give isl_multi_val *isl_multi_val_zero(
2455 __isl_take isl_space *space);
2457 #include <isl/aff.h>
2458 __isl_give isl_multi_aff *isl_multi_aff_zero(
2459 __isl_take isl_space *space);
2460 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2461 __isl_take isl_space *space);
2463 An identity function can be created using the following
2464 functions. The space needs to be that of a relation
2465 with the same number of input and output dimensions.
2467 #include <isl/aff.h>
2468 __isl_give isl_multi_aff *isl_multi_aff_identity(
2469 __isl_take isl_space *space);
2470 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2471 __isl_take isl_space *space);
2473 A function that performs a projection on a universe
2474 relation or set can be created using the following functions.
2475 See also the corresponding
2476 projection operations in L</"Unary Operations">.
2478 #include <isl/aff.h>
2479 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2480 __isl_take isl_space *space);
2481 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2482 __isl_take isl_space *space);
2483 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2484 __isl_take isl_space *space,
2485 enum isl_dim_type type,
2486 unsigned first, unsigned n);
2488 A multiple expression can be created from a single
2489 base expression using the following functions.
2490 The space of the created multiple expression is the same
2491 as that of the base expression.
2493 #include <isl/aff.h>
2494 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2495 __isl_take isl_aff *aff);
2496 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2497 __isl_take isl_pw_aff *pa);
2499 A multiple expression can be created from a list
2500 of base expression in a specified space.
2501 The domain of this space needs to be the same
2502 as the domains of the base expressions in the list.
2503 If the base expressions have a set space (or no associated space),
2504 then this space also needs to be a set space.
2506 #include <isl/val.h>
2507 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2508 __isl_take isl_space *space,
2509 __isl_take isl_val_list *list);
2511 #include <isl/aff.h>
2512 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2513 __isl_take isl_space *space,
2514 __isl_take isl_aff_list *list);
2516 As a convenience, a multiple piecewise expression can
2517 also be created from a multiple expression.
2518 Each piecewise expression in the result has a single
2521 #include <isl/aff.h>
2522 __isl_give isl_multi_pw_aff *
2523 isl_multi_pw_aff_from_multi_aff(
2524 __isl_take isl_multi_aff *ma);
2526 A multiple quasi-affine expression can be created from
2527 a multiple value with a given domain space using the following
2530 #include <isl/aff.h>
2531 __isl_give isl_multi_aff *
2532 isl_multi_aff_multi_val_on_space(
2533 __isl_take isl_space *space,
2534 __isl_take isl_multi_val *mv);
2536 Multiple expressions can be copied and freed using
2537 the following functions.
2539 #include <isl/val.h>
2540 __isl_give isl_multi_val *isl_multi_val_copy(
2541 __isl_keep isl_multi_val *mv);
2542 __isl_null isl_multi_val *isl_multi_val_free(
2543 __isl_take isl_multi_val *mv);
2545 #include <isl/aff.h>
2546 __isl_give isl_multi_aff *isl_multi_aff_copy(
2547 __isl_keep isl_multi_aff *maff);
2548 __isl_null isl_multi_aff *isl_multi_aff_free(
2549 __isl_take isl_multi_aff *maff);
2550 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2551 __isl_keep isl_multi_pw_aff *mpa);
2552 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2553 __isl_take isl_multi_pw_aff *mpa);
2555 The base expression at a given position of a multiple
2556 expression can be extracted using the following functions.
2558 #include <isl/val.h>
2559 __isl_give isl_val *isl_multi_val_get_val(
2560 __isl_keep isl_multi_val *mv, int pos);
2562 #include <isl/aff.h>
2563 __isl_give isl_aff *isl_multi_aff_get_aff(
2564 __isl_keep isl_multi_aff *multi, int pos);
2565 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2566 __isl_keep isl_multi_pw_aff *mpa, int pos);
2568 It can be replaced using the following functions.
2570 #include <isl/val.h>
2571 __isl_give isl_multi_val *isl_multi_val_set_val(
2572 __isl_take isl_multi_val *mv, int pos,
2573 __isl_take isl_val *val);
2575 #include <isl/aff.h>
2576 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2577 __isl_take isl_multi_aff *multi, int pos,
2578 __isl_take isl_aff *aff);
2580 =head3 Piecewise Expressions
2582 A piecewise expression is an expression that is described
2583 using zero or more base expression defined over the same
2584 number of cells in the domain space of the base expressions.
2585 All base expressions are defined over the same
2586 domain space and the cells are disjoint.
2587 The space of a piecewise expression is the same as
2588 that of the base expressions.
2589 If the union of the cells is a strict subset of the domain
2590 space, then the value of the piecewise expression outside
2591 this union is different for types derived from quasi-affine
2592 expressions and those derived from quasipolynomials.
2593 Piecewise expressions derived from quasi-affine expressions
2594 are considered to be undefined outside the union of their cells.
2595 Piecewise expressions derived from quasipolynomials
2596 are considered to be zero outside the union of their cells.
2598 Piecewise quasipolynomials are mainly used by the C<barvinok>
2599 library for representing the number of elements in a parametric set or map.
2600 For example, the piecewise quasipolynomial
2602 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2604 represents the number of points in the map
2606 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2608 The piecewise expression types defined by C<isl>
2609 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2610 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2612 A piecewise expression with no cells can be created using
2613 the following functions.
2615 #include <isl/aff.h>
2616 __isl_give isl_pw_aff *isl_pw_aff_empty(
2617 __isl_take isl_space *space);
2618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2619 __isl_take isl_space *space);
2621 A piecewise expression with a single universe cell can be
2622 created using the following functions.
2624 #include <isl/aff.h>
2625 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2626 __isl_take isl_aff *aff);
2627 __isl_give isl_pw_multi_aff *
2628 isl_pw_multi_aff_from_multi_aff(
2629 __isl_take isl_multi_aff *ma);
2631 #include <isl/polynomial.h>
2632 __isl_give isl_pw_qpolynomial *
2633 isl_pw_qpolynomial_from_qpolynomial(
2634 __isl_take isl_qpolynomial *qp);
2636 A piecewise expression with a single specified cell can be
2637 created using the following functions.
2639 #include <isl/aff.h>
2640 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2641 __isl_take isl_set *set, __isl_take isl_aff *aff);
2642 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2643 __isl_take isl_set *set,
2644 __isl_take isl_multi_aff *maff);
2646 #include <isl/polynomial.h>
2647 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2648 __isl_take isl_set *set,
2649 __isl_take isl_qpolynomial *qp);
2651 The following convenience functions first create a base expression and
2652 then create a piecewise expression over a universe domain.
2654 #include <isl/aff.h>
2655 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2656 __isl_take isl_local_space *ls);
2657 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2658 __isl_take isl_local_space *ls,
2659 enum isl_dim_type type, unsigned pos);
2660 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2661 __isl_take isl_local_space *ls);
2662 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2663 __isl_take isl_space *space);
2664 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2665 __isl_take isl_space *space);
2666 __isl_give isl_pw_multi_aff *
2667 isl_pw_multi_aff_project_out_map(
2668 __isl_take isl_space *space,
2669 enum isl_dim_type type,
2670 unsigned first, unsigned n);
2672 #include <isl/polynomial.h>
2673 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2674 __isl_take isl_space *space);
2676 The following convenience functions first create a base expression and
2677 then create a piecewise expression over a given domain.
2679 #include <isl/aff.h>
2680 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2681 __isl_take isl_set *domain,
2682 __isl_take isl_val *v);
2683 __isl_give isl_pw_multi_aff *
2684 isl_pw_multi_aff_multi_val_on_domain(
2685 __isl_take isl_set *domain,
2686 __isl_take isl_multi_val *mv);
2688 As a convenience, a piecewise multiple expression can
2689 also be created from a piecewise expression.
2690 Each multiple expression in the result is derived
2691 from the corresponding base expression.
2693 #include <isl/aff.h>
2694 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2695 __isl_take isl_pw_aff *pa);
2697 Similarly, a piecewise quasipolynomial can be
2698 created from a piecewise quasi-affine expression using
2699 the following function.
2701 #include <isl/polynomial.h>
2702 __isl_give isl_pw_qpolynomial *
2703 isl_pw_qpolynomial_from_pw_aff(
2704 __isl_take isl_pw_aff *pwaff);
2706 Piecewise expressions can be copied and freed using the following functions.
2708 #include <isl/aff.h>
2709 __isl_give isl_pw_aff *isl_pw_aff_copy(
2710 __isl_keep isl_pw_aff *pwaff);
2711 __isl_null isl_pw_aff *isl_pw_aff_free(
2712 __isl_take isl_pw_aff *pwaff);
2713 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2714 __isl_keep isl_pw_multi_aff *pma);
2715 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2716 __isl_take isl_pw_multi_aff *pma);
2718 #include <isl/polynomial.h>
2719 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2720 __isl_keep isl_pw_qpolynomial *pwqp);
2721 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2722 __isl_take isl_pw_qpolynomial *pwqp);
2723 __isl_give isl_pw_qpolynomial_fold *
2724 isl_pw_qpolynomial_fold_copy(
2725 __isl_keep isl_pw_qpolynomial_fold *pwf);
2726 __isl_null isl_pw_qpolynomial_fold *
2727 isl_pw_qpolynomial_fold_free(
2728 __isl_take isl_pw_qpolynomial_fold *pwf);
2730 To iterate over the different cells of a piecewise expression,
2731 use the following functions.
2733 #include <isl/aff.h>
2734 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2735 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2736 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2737 int (*fn)(__isl_take isl_set *set,
2738 __isl_take isl_aff *aff,
2739 void *user), void *user);
2740 int isl_pw_multi_aff_foreach_piece(
2741 __isl_keep isl_pw_multi_aff *pma,
2742 int (*fn)(__isl_take isl_set *set,
2743 __isl_take isl_multi_aff *maff,
2744 void *user), void *user);
2746 #include <isl/polynomial.h>
2747 int isl_pw_qpolynomial_foreach_piece(
2748 __isl_keep isl_pw_qpolynomial *pwqp,
2749 int (*fn)(__isl_take isl_set *set,
2750 __isl_take isl_qpolynomial *qp,
2751 void *user), void *user);
2752 int isl_pw_qpolynomial_foreach_lifted_piece(
2753 __isl_keep isl_pw_qpolynomial *pwqp,
2754 int (*fn)(__isl_take isl_set *set,
2755 __isl_take isl_qpolynomial *qp,
2756 void *user), void *user);
2757 int isl_pw_qpolynomial_fold_foreach_piece(
2758 __isl_keep isl_pw_qpolynomial_fold *pwf,
2759 int (*fn)(__isl_take isl_set *set,
2760 __isl_take isl_qpolynomial_fold *fold,
2761 void *user), void *user);
2762 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2763 __isl_keep isl_pw_qpolynomial_fold *pwf,
2764 int (*fn)(__isl_take isl_set *set,
2765 __isl_take isl_qpolynomial_fold *fold,
2766 void *user), void *user);
2768 As usual, the function C<fn> should return C<0> on success
2769 and C<-1> on failure. The difference between
2770 C<isl_pw_qpolynomial_foreach_piece> and
2771 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2772 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2773 compute unique representations for all existentially quantified
2774 variables and then turn these existentially quantified variables
2775 into extra set variables, adapting the associated quasipolynomial
2776 accordingly. This means that the C<set> passed to C<fn>
2777 will not have any existentially quantified variables, but that
2778 the dimensions of the sets may be different for different
2779 invocations of C<fn>.
2780 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2781 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2783 A piecewise expression consisting of the expressions at a given
2784 position of a piecewise multiple expression can be extracted
2785 using the following function.
2787 #include <isl/aff.h>
2788 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2789 __isl_keep isl_pw_multi_aff *pma, int pos);
2791 These expressions can be replaced using the following function.
2793 #include <isl/aff.h>
2794 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2795 __isl_take isl_pw_multi_aff *pma, unsigned pos,
2796 __isl_take isl_pw_aff *pa);
2798 Note that there is a difference between C<isl_multi_pw_aff> and
2799 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
2800 affine expressions, while the second is a piecewise sequence
2801 of affine expressions. In particular, each of the piecewise
2802 affine expressions in an C<isl_multi_pw_aff> may have a different
2803 domain, while all multiple expressions associated to a cell
2804 in an C<isl_pw_multi_aff> have the same domain.
2805 It is possible to convert between the two, but when converting
2806 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
2807 of the result is the intersection of the domains of the input.
2808 The reverse conversion is exact.
2810 #include <isl/aff.h>
2811 __isl_give isl_pw_multi_aff *
2812 isl_pw_multi_aff_from_multi_pw_aff(
2813 __isl_take isl_multi_pw_aff *mpa);
2814 __isl_give isl_multi_pw_aff *
2815 isl_multi_pw_aff_from_pw_multi_aff(
2816 __isl_take isl_pw_multi_aff *pma);
2818 =head3 Union Expressions
2820 A union expression collects base expressions defined
2821 over different domains. The space of a union expression
2822 is that of the shared parameter space.
2824 The union expression types defined by C<isl>
2825 are C<isl_union_pw_multi_aff>, C<isl_union_pw_qpolynomial> and
2826 C<isl_union_pw_qpolynomial_fold>.
2828 An empty union expression can be created using the following functions.
2830 #include <isl/aff.h>
2831 __isl_give isl_union_pw_multi_aff *
2832 isl_union_pw_multi_aff_empty(
2833 __isl_take isl_space *space);
2835 #include <isl/polynomial.h>
2836 __isl_give isl_union_pw_qpolynomial *
2837 isl_union_pw_qpolynomial_zero(
2838 __isl_take isl_space *space);
2840 A union expression containing a single base expression
2841 can be created using the following functions.
2843 #include <isl/aff.h>
2844 __isl_give isl_union_pw_multi_aff *
2845 isl_union_pw_multi_aff_from_pw_multi_aff(
2846 __isl_take isl_pw_multi_aff *pma);
2848 #include <isl/polynomial.h>
2849 __isl_give isl_union_pw_qpolynomial *
2850 isl_union_pw_qpolynomial_from_pw_qpolynomial(
2851 __isl_take isl_pw_qpolynomial *pwqp);
2853 The following function creates a base expression on each
2854 of the sets in the union set and collects the results.
2856 #include <isl/aff.h>
2857 __isl_give isl_union_pw_multi_aff *
2858 isl_union_pw_multi_aff_multi_val_on_domain(
2859 __isl_take isl_union_set *domain,
2860 __isl_take isl_multi_val *mv);
2862 A base expression can be added to a union expression using
2863 the following functions.
2865 #include <isl/aff.h>
2866 __isl_give isl_union_pw_multi_aff *
2867 isl_union_pw_multi_aff_add_pw_multi_aff(
2868 __isl_take isl_union_pw_multi_aff *upma,
2869 __isl_take isl_pw_multi_aff *pma);
2871 #include <isl/polynomial.h>
2872 __isl_give isl_union_pw_qpolynomial *
2873 isl_union_pw_qpolynomial_add_pw_qpolynomial(
2874 __isl_take isl_union_pw_qpolynomial *upwqp,
2875 __isl_take isl_pw_qpolynomial *pwqp);
2877 Union expressions can be copied and freed using
2878 the following functions.
2880 #include <isl/aff.h>
2881 __isl_give isl_union_pw_multi_aff *
2882 isl_union_pw_multi_aff_copy(
2883 __isl_keep isl_union_pw_multi_aff *upma);
2884 __isl_null isl_union_pw_multi_aff *
2885 isl_union_pw_multi_aff_free(
2886 __isl_take isl_union_pw_multi_aff *upma);
2888 #include <isl/polynomial.h>
2889 __isl_give isl_union_pw_qpolynomial *
2890 isl_union_pw_qpolynomial_copy(
2891 __isl_keep isl_union_pw_qpolynomial *upwqp);
2892 __isl_null isl_union_pw_qpolynomial *
2893 isl_union_pw_qpolynomial_free(
2894 __isl_take isl_union_pw_qpolynomial *upwqp);
2895 __isl_give isl_union_pw_qpolynomial_fold *
2896 isl_union_pw_qpolynomial_fold_copy(
2897 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2898 __isl_null isl_union_pw_qpolynomial_fold *
2899 isl_union_pw_qpolynomial_fold_free(
2900 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2902 To iterate over the base expressions in a union expression,
2903 use the following functions.
2905 #include <isl/aff.h>
2906 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
2907 __isl_keep isl_union_pw_multi_aff *upma,
2908 int (*fn)(__isl_take isl_pw_multi_aff *pma,
2909 void *user), void *user);
2911 #include <isl/polynomial.h>
2912 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2913 __isl_keep isl_union_pw_qpolynomial *upwqp,
2914 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
2915 void *user), void *user);
2916 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2917 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2918 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2919 void *user), void *user);
2921 To extract the base expression in a given space from a union, use
2922 the following functions.
2924 #include <isl/aff.h>
2925 __isl_give isl_pw_multi_aff *
2926 isl_union_pw_multi_aff_extract_pw_multi_aff(
2927 __isl_keep isl_union_pw_multi_aff *upma,
2928 __isl_take isl_space *space);
2930 #include <isl/polynomial.h>
2931 __isl_give isl_pw_qpolynomial *
2932 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2933 __isl_keep isl_union_pw_qpolynomial *upwqp,
2934 __isl_take isl_space *space);
2936 =head2 Input and Output
2938 For set and relation,
2939 C<isl> supports its own input/output format, which is similar
2940 to the C<Omega> format, but also supports the C<PolyLib> format
2942 For other object types, typically only an C<isl> format is supported.
2944 =head3 C<isl> format
2946 The C<isl> format is similar to that of C<Omega>, but has a different
2947 syntax for describing the parameters and allows for the definition
2948 of an existentially quantified variable as the integer division
2949 of an affine expression.
2950 For example, the set of integers C<i> between C<0> and C<n>
2951 such that C<i % 10 <= 6> can be described as
2953 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
2956 A set or relation can have several disjuncts, separated
2957 by the keyword C<or>. Each disjunct is either a conjunction
2958 of constraints or a projection (C<exists>) of a conjunction
2959 of constraints. The constraints are separated by the keyword
2962 =head3 C<PolyLib> format
2964 If the represented set is a union, then the first line
2965 contains a single number representing the number of disjuncts.
2966 Otherwise, a line containing the number C<1> is optional.
2968 Each disjunct is represented by a matrix of constraints.
2969 The first line contains two numbers representing
2970 the number of rows and columns,
2971 where the number of rows is equal to the number of constraints
2972 and the number of columns is equal to two plus the number of variables.
2973 The following lines contain the actual rows of the constraint matrix.
2974 In each row, the first column indicates whether the constraint
2975 is an equality (C<0>) or inequality (C<1>). The final column
2976 corresponds to the constant term.
2978 If the set is parametric, then the coefficients of the parameters
2979 appear in the last columns before the constant column.
2980 The coefficients of any existentially quantified variables appear
2981 between those of the set variables and those of the parameters.
2983 =head3 Extended C<PolyLib> format
2985 The extended C<PolyLib> format is nearly identical to the
2986 C<PolyLib> format. The only difference is that the line
2987 containing the number of rows and columns of a constraint matrix
2988 also contains four additional numbers:
2989 the number of output dimensions, the number of input dimensions,
2990 the number of local dimensions (i.e., the number of existentially
2991 quantified variables) and the number of parameters.
2992 For sets, the number of ``output'' dimensions is equal
2993 to the number of set dimensions, while the number of ``input''
2998 Objects can be read from input using the following functions.
3000 #include <isl/val.h>
3001 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3004 #include <isl/set.h>
3005 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3006 isl_ctx *ctx, FILE *input);
3007 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3008 isl_ctx *ctx, const char *str);
3009 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3011 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3014 #include <isl/map.h>
3015 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3016 isl_ctx *ctx, FILE *input);
3017 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3018 isl_ctx *ctx, const char *str);
3019 __isl_give isl_map *isl_map_read_from_file(
3020 isl_ctx *ctx, FILE *input);
3021 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3024 #include <isl/union_set.h>
3025 __isl_give isl_union_set *isl_union_set_read_from_file(
3026 isl_ctx *ctx, FILE *input);
3027 __isl_give isl_union_set *isl_union_set_read_from_str(
3028 isl_ctx *ctx, const char *str);
3030 #include <isl/union_map.h>
3031 __isl_give isl_union_map *isl_union_map_read_from_file(
3032 isl_ctx *ctx, FILE *input);
3033 __isl_give isl_union_map *isl_union_map_read_from_str(
3034 isl_ctx *ctx, const char *str);
3036 #include <isl/aff.h>
3037 __isl_give isl_aff *isl_aff_read_from_str(
3038 isl_ctx *ctx, const char *str);
3039 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3040 isl_ctx *ctx, const char *str);
3041 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3042 isl_ctx *ctx, const char *str);
3043 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3044 isl_ctx *ctx, const char *str);
3045 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3046 isl_ctx *ctx, const char *str);
3047 __isl_give isl_union_pw_multi_aff *
3048 isl_union_pw_multi_aff_read_from_str(
3049 isl_ctx *ctx, const char *str);
3051 #include <isl/polynomial.h>
3052 __isl_give isl_union_pw_qpolynomial *
3053 isl_union_pw_qpolynomial_read_from_str(
3054 isl_ctx *ctx, const char *str);
3056 For sets and relations,
3057 the input format is autodetected and may be either the C<PolyLib> format
3058 or the C<isl> format.
3062 Before anything can be printed, an C<isl_printer> needs to
3065 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3067 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3068 __isl_null isl_printer *isl_printer_free(
3069 __isl_take isl_printer *printer);
3070 __isl_give char *isl_printer_get_str(
3071 __isl_keep isl_printer *printer);
3073 The printer can be inspected using the following functions.
3075 FILE *isl_printer_get_file(
3076 __isl_keep isl_printer *printer);
3077 int isl_printer_get_output_format(
3078 __isl_keep isl_printer *p);
3080 The behavior of the printer can be modified in various ways
3082 __isl_give isl_printer *isl_printer_set_output_format(
3083 __isl_take isl_printer *p, int output_format);
3084 __isl_give isl_printer *isl_printer_set_indent(
3085 __isl_take isl_printer *p, int indent);
3086 __isl_give isl_printer *isl_printer_set_indent_prefix(
3087 __isl_take isl_printer *p, const char *prefix);
3088 __isl_give isl_printer *isl_printer_indent(
3089 __isl_take isl_printer *p, int indent);
3090 __isl_give isl_printer *isl_printer_set_prefix(
3091 __isl_take isl_printer *p, const char *prefix);
3092 __isl_give isl_printer *isl_printer_set_suffix(
3093 __isl_take isl_printer *p, const char *suffix);
3095 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3096 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3097 and defaults to C<ISL_FORMAT_ISL>.
3098 Each line in the output is prefixed by C<indent_prefix>,
3099 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3100 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3101 In the C<PolyLib> format output,
3102 the coefficients of the existentially quantified variables
3103 appear between those of the set variables and those
3105 The function C<isl_printer_indent> increases the indentation
3106 by the specified amount (which may be negative).
3108 To actually print something, use
3110 #include <isl/printer.h>
3111 __isl_give isl_printer *isl_printer_print_double(
3112 __isl_take isl_printer *p, double d);
3114 #include <isl/val.h>
3115 __isl_give isl_printer *isl_printer_print_val(
3116 __isl_take isl_printer *p, __isl_keep isl_val *v);
3118 #include <isl/set.h>
3119 __isl_give isl_printer *isl_printer_print_basic_set(
3120 __isl_take isl_printer *printer,
3121 __isl_keep isl_basic_set *bset);
3122 __isl_give isl_printer *isl_printer_print_set(
3123 __isl_take isl_printer *printer,
3124 __isl_keep isl_set *set);
3126 #include <isl/map.h>
3127 __isl_give isl_printer *isl_printer_print_basic_map(
3128 __isl_take isl_printer *printer,
3129 __isl_keep isl_basic_map *bmap);
3130 __isl_give isl_printer *isl_printer_print_map(
3131 __isl_take isl_printer *printer,
3132 __isl_keep isl_map *map);
3134 #include <isl/union_set.h>
3135 __isl_give isl_printer *isl_printer_print_union_set(
3136 __isl_take isl_printer *p,
3137 __isl_keep isl_union_set *uset);
3139 #include <isl/union_map.h>
3140 __isl_give isl_printer *isl_printer_print_union_map(
3141 __isl_take isl_printer *p,
3142 __isl_keep isl_union_map *umap);
3144 #include <isl/val.h>
3145 __isl_give isl_printer *isl_printer_print_multi_val(
3146 __isl_take isl_printer *p,
3147 __isl_keep isl_multi_val *mv);
3149 #include <isl/aff.h>
3150 __isl_give isl_printer *isl_printer_print_aff(
3151 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3152 __isl_give isl_printer *isl_printer_print_multi_aff(
3153 __isl_take isl_printer *p,
3154 __isl_keep isl_multi_aff *maff);
3155 __isl_give isl_printer *isl_printer_print_pw_aff(
3156 __isl_take isl_printer *p,
3157 __isl_keep isl_pw_aff *pwaff);
3158 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3159 __isl_take isl_printer *p,
3160 __isl_keep isl_pw_multi_aff *pma);
3161 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3162 __isl_take isl_printer *p,
3163 __isl_keep isl_multi_pw_aff *mpa);
3164 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3165 __isl_take isl_printer *p,
3166 __isl_keep isl_union_pw_multi_aff *upma);
3168 #include <isl/polynomial.h>
3169 __isl_give isl_printer *isl_printer_print_qpolynomial(
3170 __isl_take isl_printer *p,
3171 __isl_keep isl_qpolynomial *qp);
3172 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3173 __isl_take isl_printer *p,
3174 __isl_keep isl_pw_qpolynomial *pwqp);
3175 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3176 __isl_take isl_printer *p,
3177 __isl_keep isl_union_pw_qpolynomial *upwqp);
3179 __isl_give isl_printer *
3180 isl_printer_print_pw_qpolynomial_fold(
3181 __isl_take isl_printer *p,
3182 __isl_keep isl_pw_qpolynomial_fold *pwf);
3183 __isl_give isl_printer *
3184 isl_printer_print_union_pw_qpolynomial_fold(
3185 __isl_take isl_printer *p,
3186 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3188 For C<isl_printer_print_qpolynomial>,
3189 C<isl_printer_print_pw_qpolynomial> and
3190 C<isl_printer_print_pw_qpolynomial_fold>,
3191 the output format of the printer
3192 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3193 For C<isl_printer_print_union_pw_qpolynomial> and
3194 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3196 In case of printing in C<ISL_FORMAT_C>, the user may want
3197 to set the names of all dimensions first.
3199 When called on a file printer, the following function flushes
3200 the file. When called on a string printer, the buffer is cleared.
3202 __isl_give isl_printer *isl_printer_flush(
3203 __isl_take isl_printer *p);
3205 Alternatively, a string representation can be obtained
3206 directly using the following functions, which always print
3209 #include <isl/space.h>
3210 __isl_give char *isl_space_to_str(
3211 __isl_keep isl_space *space);
3213 #include <isl/val.h>
3214 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3215 __isl_give char *isl_multi_val_to_str(
3216 __isl_keep isl_multi_val *mv);
3218 #include <isl/set.h>
3219 __isl_give char *isl_set_to_str(
3220 __isl_keep isl_set *set);
3222 #include <isl/union_set.h>
3223 __isl_give char *isl_union_set_to_str(
3224 __isl_keep isl_union_set *uset);
3226 #include <isl/map.h>
3227 __isl_give char *isl_map_to_str(
3228 __isl_keep isl_map *map);
3230 #include <isl/union_map.h>
3231 __isl_give char *isl_union_map_to_str(
3232 __isl_keep isl_union_map *umap);
3234 #include <isl/aff.h>
3235 __isl_give char *isl_multi_aff_to_str(
3236 __isl_keep isl_multi_aff *aff);
3237 __isl_give char *isl_union_pw_multi_aff_to_str(
3238 __isl_keep isl_union_pw_multi_aff *upma);
3242 =head3 Unary Properties
3248 The following functions test whether the given set or relation
3249 contains any integer points. The ``plain'' variants do not perform
3250 any computations, but simply check if the given set or relation
3251 is already known to be empty.
3253 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3254 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3255 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3256 int isl_set_is_empty(__isl_keep isl_set *set);
3257 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3258 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3259 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3260 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3261 int isl_map_is_empty(__isl_keep isl_map *map);
3262 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3264 =item * Universality
3266 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3267 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3268 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3270 =item * Single-valuedness
3272 #include <isl/set.h>
3273 int isl_set_is_singleton(__isl_keep isl_set *set);
3275 #include <isl/map.h>
3276 int isl_basic_map_is_single_valued(
3277 __isl_keep isl_basic_map *bmap);
3278 int isl_map_plain_is_single_valued(
3279 __isl_keep isl_map *map);
3280 int isl_map_is_single_valued(__isl_keep isl_map *map);
3282 #include <isl/union_map.h>
3283 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3287 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3288 int isl_map_is_injective(__isl_keep isl_map *map);
3289 int isl_union_map_plain_is_injective(
3290 __isl_keep isl_union_map *umap);
3291 int isl_union_map_is_injective(
3292 __isl_keep isl_union_map *umap);
3296 int isl_map_is_bijective(__isl_keep isl_map *map);
3297 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3301 __isl_give isl_val *
3302 isl_basic_map_plain_get_val_if_fixed(
3303 __isl_keep isl_basic_map *bmap,
3304 enum isl_dim_type type, unsigned pos);
3305 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3306 __isl_keep isl_set *set,
3307 enum isl_dim_type type, unsigned pos);
3308 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3309 __isl_keep isl_map *map,
3310 enum isl_dim_type type, unsigned pos);
3312 If the set or relation obviously lies on a hyperplane where the given dimension
3313 has a fixed value, then return that value.
3314 Otherwise return NaN.
3318 int isl_set_dim_residue_class_val(
3319 __isl_keep isl_set *set,
3320 int pos, __isl_give isl_val **modulo,
3321 __isl_give isl_val **residue);
3323 Check if the values of the given set dimension are equal to a fixed
3324 value modulo some integer value. If so, assign the modulo to C<*modulo>
3325 and the fixed value to C<*residue>. If the given dimension attains only
3326 a single value, then assign C<0> to C<*modulo> and the fixed value to
3328 If the dimension does not attain only a single value and if no modulo
3329 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3333 To check whether the description of a set, relation or function depends
3334 on one or more given dimensions,
3335 the following functions can be used.
3337 #include <isl/constraint.h>
3338 int isl_constraint_involves_dims(
3339 __isl_keep isl_constraint *constraint,
3340 enum isl_dim_type type, unsigned first, unsigned n);
3342 #include <isl/set.h>
3343 int isl_basic_set_involves_dims(
3344 __isl_keep isl_basic_set *bset,
3345 enum isl_dim_type type, unsigned first, unsigned n);
3346 int isl_set_involves_dims(__isl_keep isl_set *set,
3347 enum isl_dim_type type, unsigned first, unsigned n);
3349 #include <isl/map.h>
3350 int isl_basic_map_involves_dims(
3351 __isl_keep isl_basic_map *bmap,
3352 enum isl_dim_type type, unsigned first, unsigned n);
3353 int isl_map_involves_dims(__isl_keep isl_map *map,
3354 enum isl_dim_type type, unsigned first, unsigned n);
3356 #include <isl/union_map.h>
3357 int isl_union_map_involves_dims(
3358 __isl_keep isl_union_map *umap,
3359 enum isl_dim_type type, unsigned first, unsigned n);
3361 #include <isl/aff.h>
3362 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3363 enum isl_dim_type type, unsigned first, unsigned n);
3364 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3365 enum isl_dim_type type, unsigned first, unsigned n);
3366 int isl_multi_aff_involves_dims(
3367 __isl_keep isl_multi_aff *ma,
3368 enum isl_dim_type type, unsigned first, unsigned n);
3369 int isl_multi_pw_aff_involves_dims(
3370 __isl_keep isl_multi_pw_aff *mpa,
3371 enum isl_dim_type type, unsigned first, unsigned n);
3373 Similarly, the following functions can be used to check whether
3374 a given dimension is involved in any lower or upper bound.
3376 #include <isl/set.h>
3377 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3378 enum isl_dim_type type, unsigned pos);
3379 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3380 enum isl_dim_type type, unsigned pos);
3382 Note that these functions return true even if there is a bound on
3383 the dimension on only some of the basic sets of C<set>.
3384 To check if they have a bound for all of the basic sets in C<set>,
3385 use the following functions instead.
3387 #include <isl/set.h>
3388 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3389 enum isl_dim_type type, unsigned pos);
3390 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3391 enum isl_dim_type type, unsigned pos);
3395 To check whether a set is a parameter domain, use this function:
3397 int isl_set_is_params(__isl_keep isl_set *set);
3398 int isl_union_set_is_params(
3399 __isl_keep isl_union_set *uset);
3403 The following functions check whether the space of the given
3404 (basic) set or relation range is a wrapped relation.
3406 #include <isl/space.h>
3407 int isl_space_is_wrapping(
3408 __isl_keep isl_space *space);
3409 int isl_space_domain_is_wrapping(
3410 __isl_keep isl_space *space);
3411 int isl_space_range_is_wrapping(
3412 __isl_keep isl_space *space);
3414 #include <isl/set.h>
3415 int isl_basic_set_is_wrapping(
3416 __isl_keep isl_basic_set *bset);
3417 int isl_set_is_wrapping(__isl_keep isl_set *set);
3419 #include <isl/map.h>
3420 int isl_map_domain_is_wrapping(
3421 __isl_keep isl_map *map);
3422 int isl_map_range_is_wrapping(
3423 __isl_keep isl_map *map);
3425 #include <isl/val.h>
3426 int isl_multi_val_range_is_wrapping(
3427 __isl_keep isl_multi_val *mv);
3429 #include <isl/aff.h>
3430 int isl_multi_aff_range_is_wrapping(
3431 __isl_keep isl_multi_aff *ma);
3432 int isl_multi_pw_aff_range_is_wrapping(
3433 __isl_keep isl_multi_pw_aff *mpa);
3435 The input to C<isl_space_is_wrapping> should
3436 be the space of a set, while that of
3437 C<isl_space_domain_is_wrapping> and
3438 C<isl_space_range_is_wrapping> should be the space of a relation.
3440 =item * Internal Product
3442 int isl_basic_map_can_zip(
3443 __isl_keep isl_basic_map *bmap);
3444 int isl_map_can_zip(__isl_keep isl_map *map);
3446 Check whether the product of domain and range of the given relation
3448 i.e., whether both domain and range are nested relations.
3452 int isl_basic_map_can_curry(
3453 __isl_keep isl_basic_map *bmap);
3454 int isl_map_can_curry(__isl_keep isl_map *map);
3456 Check whether the domain of the (basic) relation is a wrapped relation.
3458 int isl_basic_map_can_uncurry(
3459 __isl_keep isl_basic_map *bmap);
3460 int isl_map_can_uncurry(__isl_keep isl_map *map);
3462 Check whether the range of the (basic) relation is a wrapped relation.
3464 =item * Special Values
3466 #include <isl/aff.h>
3467 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3468 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3470 Check whether the given expression is a constant.
3472 #include <isl/aff.h>
3473 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3474 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3476 Check whether the given expression is equal to or involves NaN.
3478 #include <isl/aff.h>
3479 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3481 Check whether the affine expression is obviously zero.
3485 =head3 Binary Properties
3491 The following functions check whether two objects
3492 represent the same set, relation or function.
3493 The C<plain> variants only return true if the objects
3494 are obviously the same. That is, they may return false
3495 even if the objects are the same, but they will never
3496 return true if the objects are not the same.
3498 #include <isl/set.h>
3499 int isl_basic_set_plain_is_equal(
3500 __isl_keep isl_basic_set *bset1,
3501 __isl_keep isl_basic_set *bset2);
3502 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3503 __isl_keep isl_set *set2);
3504 int isl_set_is_equal(__isl_keep isl_set *set1,
3505 __isl_keep isl_set *set2);
3507 #include <isl/map.h>
3508 int isl_basic_map_is_equal(
3509 __isl_keep isl_basic_map *bmap1,
3510 __isl_keep isl_basic_map *bmap2);
3511 int isl_map_is_equal(__isl_keep isl_map *map1,
3512 __isl_keep isl_map *map2);
3513 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3514 __isl_keep isl_map *map2);
3516 #include <isl/union_set.h>
3517 int isl_union_set_is_equal(
3518 __isl_keep isl_union_set *uset1,
3519 __isl_keep isl_union_set *uset2);
3521 #include <isl/union_map.h>
3522 int isl_union_map_is_equal(
3523 __isl_keep isl_union_map *umap1,
3524 __isl_keep isl_union_map *umap2);
3526 #include <isl/aff.h>
3527 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3528 __isl_keep isl_aff *aff2);
3529 int isl_multi_aff_plain_is_equal(
3530 __isl_keep isl_multi_aff *maff1,
3531 __isl_keep isl_multi_aff *maff2);
3532 int isl_pw_aff_plain_is_equal(
3533 __isl_keep isl_pw_aff *pwaff1,
3534 __isl_keep isl_pw_aff *pwaff2);
3535 int isl_pw_multi_aff_plain_is_equal(
3536 __isl_keep isl_pw_multi_aff *pma1,
3537 __isl_keep isl_pw_multi_aff *pma2);
3538 int isl_multi_pw_aff_plain_is_equal(
3539 __isl_keep isl_multi_pw_aff *mpa1,
3540 __isl_keep isl_multi_pw_aff *mpa2);
3541 int isl_multi_pw_aff_is_equal(
3542 __isl_keep isl_multi_pw_aff *mpa1,
3543 __isl_keep isl_multi_pw_aff *mpa2);
3544 int isl_union_pw_multi_aff_plain_is_equal(
3545 __isl_keep isl_union_pw_multi_aff *upma1,
3546 __isl_keep isl_union_pw_multi_aff *upma2);
3548 #include <isl/polynomial.h>
3549 int isl_union_pw_qpolynomial_plain_is_equal(
3550 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3551 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3552 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3553 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3554 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3556 =item * Disjointness
3558 #include <isl/set.h>
3559 int isl_basic_set_is_disjoint(
3560 __isl_keep isl_basic_set *bset1,
3561 __isl_keep isl_basic_set *bset2);
3562 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3563 __isl_keep isl_set *set2);
3564 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3565 __isl_keep isl_set *set2);
3567 #include <isl/map.h>
3568 int isl_basic_map_is_disjoint(
3569 __isl_keep isl_basic_map *bmap1,
3570 __isl_keep isl_basic_map *bmap2);
3571 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3572 __isl_keep isl_map *map2);
3574 #include <isl/union_set.h>
3575 int isl_union_set_is_disjoint(
3576 __isl_keep isl_union_set *uset1,
3577 __isl_keep isl_union_set *uset2);
3579 #include <isl/union_map.h>
3580 int isl_union_map_is_disjoint(
3581 __isl_keep isl_union_map *umap1,
3582 __isl_keep isl_union_map *umap2);
3586 int isl_basic_set_is_subset(
3587 __isl_keep isl_basic_set *bset1,
3588 __isl_keep isl_basic_set *bset2);
3589 int isl_set_is_subset(__isl_keep isl_set *set1,
3590 __isl_keep isl_set *set2);
3591 int isl_set_is_strict_subset(
3592 __isl_keep isl_set *set1,
3593 __isl_keep isl_set *set2);
3594 int isl_union_set_is_subset(
3595 __isl_keep isl_union_set *uset1,
3596 __isl_keep isl_union_set *uset2);
3597 int isl_union_set_is_strict_subset(
3598 __isl_keep isl_union_set *uset1,
3599 __isl_keep isl_union_set *uset2);
3600 int isl_basic_map_is_subset(
3601 __isl_keep isl_basic_map *bmap1,
3602 __isl_keep isl_basic_map *bmap2);
3603 int isl_basic_map_is_strict_subset(
3604 __isl_keep isl_basic_map *bmap1,
3605 __isl_keep isl_basic_map *bmap2);
3606 int isl_map_is_subset(
3607 __isl_keep isl_map *map1,
3608 __isl_keep isl_map *map2);
3609 int isl_map_is_strict_subset(
3610 __isl_keep isl_map *map1,
3611 __isl_keep isl_map *map2);
3612 int isl_union_map_is_subset(
3613 __isl_keep isl_union_map *umap1,
3614 __isl_keep isl_union_map *umap2);
3615 int isl_union_map_is_strict_subset(
3616 __isl_keep isl_union_map *umap1,
3617 __isl_keep isl_union_map *umap2);
3619 Check whether the first argument is a (strict) subset of the
3624 Every comparison function returns a negative value if the first
3625 argument is considered smaller than the second, a positive value
3626 if the first argument is considered greater and zero if the two
3627 constraints are considered the same by the comparison criterion.
3629 #include <isl/constraint.h>
3630 int isl_constraint_plain_cmp(
3631 __isl_keep isl_constraint *c1,
3632 __isl_keep isl_constraint *c2);
3634 This function is useful for sorting C<isl_constraint>s.
3635 The order depends on the internal representation of the inputs.
3636 The order is fixed over different calls to the function (assuming
3637 the internal representation of the inputs has not changed), but may
3638 change over different versions of C<isl>.
3640 #include <isl/constraint.h>
3641 int isl_constraint_cmp_last_non_zero(
3642 __isl_keep isl_constraint *c1,
3643 __isl_keep isl_constraint *c2);
3645 This function can be used to sort constraints that live in the same
3646 local space. Constraints that involve ``earlier'' dimensions or
3647 that have a smaller coefficient for the shared latest dimension
3648 are considered smaller than other constraints.
3649 This function only defines a B<partial> order.
3651 #include <isl/set.h>
3652 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3653 __isl_keep isl_set *set2);
3655 This function is useful for sorting C<isl_set>s.
3656 The order depends on the internal representation of the inputs.
3657 The order is fixed over different calls to the function (assuming
3658 the internal representation of the inputs has not changed), but may
3659 change over different versions of C<isl>.
3661 #include <isl/aff.h>
3662 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3663 __isl_keep isl_pw_aff *pa2);
3665 The function C<isl_pw_aff_plain_cmp> can be used to sort
3666 C<isl_pw_aff>s. The order is not strictly defined.
3667 The current order sorts expressions that only involve
3668 earlier dimensions before those that involve later dimensions.
3672 =head2 Unary Operations
3678 __isl_give isl_set *isl_set_complement(
3679 __isl_take isl_set *set);
3680 __isl_give isl_map *isl_map_complement(
3681 __isl_take isl_map *map);
3685 #include <isl/space.h>
3686 __isl_give isl_space *isl_space_reverse(
3687 __isl_take isl_space *space);
3689 #include <isl/map.h>
3690 __isl_give isl_basic_map *isl_basic_map_reverse(
3691 __isl_take isl_basic_map *bmap);
3692 __isl_give isl_map *isl_map_reverse(
3693 __isl_take isl_map *map);
3695 #include <isl/union_map.h>
3696 __isl_give isl_union_map *isl_union_map_reverse(
3697 __isl_take isl_union_map *umap);
3701 #include <isl/space.h>
3702 __isl_give isl_space *isl_space_domain(
3703 __isl_take isl_space *space);
3704 __isl_give isl_space *isl_space_range(
3705 __isl_take isl_space *space);
3706 __isl_give isl_space *isl_space_params(
3707 __isl_take isl_space *space);
3709 #include <isl/local_space.h>
3710 __isl_give isl_local_space *isl_local_space_domain(
3711 __isl_take isl_local_space *ls);
3712 __isl_give isl_local_space *isl_local_space_range(
3713 __isl_take isl_local_space *ls);
3715 #include <isl/set.h>
3716 __isl_give isl_basic_set *isl_basic_set_project_out(
3717 __isl_take isl_basic_set *bset,
3718 enum isl_dim_type type, unsigned first, unsigned n);
3719 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3720 enum isl_dim_type type, unsigned first, unsigned n);
3721 __isl_give isl_basic_set *isl_basic_set_params(
3722 __isl_take isl_basic_set *bset);
3723 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
3725 #include <isl/map.h>
3726 __isl_give isl_basic_map *isl_basic_map_project_out(
3727 __isl_take isl_basic_map *bmap,
3728 enum isl_dim_type type, unsigned first, unsigned n);
3729 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3730 enum isl_dim_type type, unsigned first, unsigned n);
3731 __isl_give isl_basic_set *isl_basic_map_domain(
3732 __isl_take isl_basic_map *bmap);
3733 __isl_give isl_basic_set *isl_basic_map_range(
3734 __isl_take isl_basic_map *bmap);
3735 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
3736 __isl_give isl_set *isl_map_domain(
3737 __isl_take isl_map *bmap);
3738 __isl_give isl_set *isl_map_range(
3739 __isl_take isl_map *map);
3741 #include <isl/union_set.h>
3742 __isl_give isl_union_set *isl_union_set_project_out(
3743 __isl_take isl_union_set *uset,
3744 enum isl_dim_type type,
3745 unsigned first, unsigned n);
3746 __isl_give isl_set *isl_union_set_params(
3747 __isl_take isl_union_set *uset);
3749 The function C<isl_union_set_project_out> can only project out
3752 #include <isl/union_map.h>
3753 __isl_give isl_union_map *isl_union_map_project_out(
3754 __isl_take isl_union_map *umap,
3755 enum isl_dim_type type, unsigned first, unsigned n);
3756 __isl_give isl_set *isl_union_map_params(
3757 __isl_take isl_union_map *umap);
3758 __isl_give isl_union_set *isl_union_map_domain(
3759 __isl_take isl_union_map *umap);
3760 __isl_give isl_union_set *isl_union_map_range(
3761 __isl_take isl_union_map *umap);
3763 The function C<isl_union_map_project_out> can only project out
3766 #include <isl/aff.h>
3767 __isl_give isl_aff *isl_aff_project_domain_on_params(
3768 __isl_take isl_aff *aff);
3769 __isl_give isl_pw_multi_aff *
3770 isl_pw_multi_aff_project_domain_on_params(
3771 __isl_take isl_pw_multi_aff *pma);
3772 __isl_give isl_set *isl_pw_aff_domain(
3773 __isl_take isl_pw_aff *pwaff);
3774 __isl_give isl_set *isl_pw_multi_aff_domain(
3775 __isl_take isl_pw_multi_aff *pma);
3776 __isl_give isl_set *isl_multi_pw_aff_domain(
3777 __isl_take isl_multi_pw_aff *mpa);
3778 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3779 __isl_take isl_union_pw_multi_aff *upma);
3780 __isl_give isl_set *isl_pw_aff_params(
3781 __isl_take isl_pw_aff *pwa);
3783 #include <isl/polynomial.h>
3784 __isl_give isl_qpolynomial *
3785 isl_qpolynomial_project_domain_on_params(
3786 __isl_take isl_qpolynomial *qp);
3787 __isl_give isl_pw_qpolynomial *
3788 isl_pw_qpolynomial_project_domain_on_params(
3789 __isl_take isl_pw_qpolynomial *pwqp);
3790 __isl_give isl_pw_qpolynomial_fold *
3791 isl_pw_qpolynomial_fold_project_domain_on_params(
3792 __isl_take isl_pw_qpolynomial_fold *pwf);
3793 __isl_give isl_set *isl_pw_qpolynomial_domain(
3794 __isl_take isl_pw_qpolynomial *pwqp);
3795 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3796 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3797 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3798 __isl_take isl_union_pw_qpolynomial *upwqp);
3800 #include <isl/space.h>
3801 __isl_give isl_space *isl_space_domain_map(
3802 __isl_take isl_space *space);
3803 __isl_give isl_space *isl_space_range_map(
3804 __isl_take isl_space *space);
3806 #include <isl/map.h>
3807 __isl_give isl_map *isl_set_wrapped_domain_map(
3808 __isl_take isl_set *set);
3809 __isl_give isl_basic_map *isl_basic_map_domain_map(
3810 __isl_take isl_basic_map *bmap);
3811 __isl_give isl_basic_map *isl_basic_map_range_map(
3812 __isl_take isl_basic_map *bmap);
3813 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
3814 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
3816 #include <isl/union_map.h>
3817 __isl_give isl_union_map *isl_union_map_domain_map(
3818 __isl_take isl_union_map *umap);
3819 __isl_give isl_union_map *isl_union_map_range_map(
3820 __isl_take isl_union_map *umap);
3821 __isl_give isl_union_map *
3822 isl_union_set_wrapped_domain_map(
3823 __isl_take isl_union_set *uset);
3825 The functions above construct a (basic, regular or union) relation
3826 that maps (a wrapped version of) the input relation to its domain or range.
3827 C<isl_set_wrapped_domain_map> maps the input set to the domain
3828 of its wrapped relation.
3832 __isl_give isl_basic_set *isl_basic_set_eliminate(
3833 __isl_take isl_basic_set *bset,
3834 enum isl_dim_type type,
3835 unsigned first, unsigned n);
3836 __isl_give isl_set *isl_set_eliminate(
3837 __isl_take isl_set *set, enum isl_dim_type type,
3838 unsigned first, unsigned n);
3839 __isl_give isl_basic_map *isl_basic_map_eliminate(
3840 __isl_take isl_basic_map *bmap,
3841 enum isl_dim_type type,
3842 unsigned first, unsigned n);
3843 __isl_give isl_map *isl_map_eliminate(
3844 __isl_take isl_map *map, enum isl_dim_type type,
3845 unsigned first, unsigned n);
3847 Eliminate the coefficients for the given dimensions from the constraints,
3848 without removing the dimensions.
3850 =item * Constructing a set from a parameter domain
3852 A zero-dimensional space or (basic) set can be constructed
3853 on a given parameter domain using the following functions.
3855 #include <isl/space.h>
3856 __isl_give isl_space *isl_space_set_from_params(
3857 __isl_take isl_space *space);
3859 #include <isl/set.h>
3860 __isl_give isl_basic_set *isl_basic_set_from_params(
3861 __isl_take isl_basic_set *bset);
3862 __isl_give isl_set *isl_set_from_params(
3863 __isl_take isl_set *set);
3865 =item * Constructing a relation from a set
3867 Create a relation with the given set as domain or range.
3868 The range or domain of the created relation is a zero-dimensional
3869 flat anonymous space.
3871 #include <isl/space.h>
3872 __isl_give isl_space *isl_space_from_domain(
3873 __isl_take isl_space *space);
3874 __isl_give isl_space *isl_space_from_range(
3875 __isl_take isl_space *space);
3876 __isl_give isl_space *isl_space_map_from_set(
3877 __isl_take isl_space *space);
3878 __isl_give isl_space *isl_space_map_from_domain_and_range(
3879 __isl_take isl_space *domain,
3880 __isl_take isl_space *range);
3882 #include <isl/local_space.h>
3883 __isl_give isl_local_space *isl_local_space_from_domain(
3884 __isl_take isl_local_space *ls);
3886 #include <isl/map.h>
3887 __isl_give isl_map *isl_map_from_domain(
3888 __isl_take isl_set *set);
3889 __isl_give isl_map *isl_map_from_range(
3890 __isl_take isl_set *set);
3892 #include <isl/val.h>
3893 __isl_give isl_multi_val *isl_multi_val_from_range(
3894 __isl_take isl_multi_val *mv);
3896 #include <isl/aff.h>
3897 __isl_give isl_multi_aff *isl_multi_aff_from_range(
3898 __isl_take isl_multi_aff *ma);
3899 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3900 __isl_take isl_pw_aff *pwa);
3901 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
3902 __isl_take isl_multi_pw_aff *mpa);
3903 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3904 __isl_take isl_set *set);
3905 __isl_give isl_union_pw_multi_aff *
3906 isl_union_pw_multi_aff_from_domain(
3907 __isl_take isl_union_set *uset);
3911 #include <isl/set.h>
3912 __isl_give isl_basic_set *isl_basic_set_fix_si(
3913 __isl_take isl_basic_set *bset,
3914 enum isl_dim_type type, unsigned pos, int value);
3915 __isl_give isl_basic_set *isl_basic_set_fix_val(
3916 __isl_take isl_basic_set *bset,
3917 enum isl_dim_type type, unsigned pos,
3918 __isl_take isl_val *v);
3919 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
3920 enum isl_dim_type type, unsigned pos, int value);
3921 __isl_give isl_set *isl_set_fix_val(
3922 __isl_take isl_set *set,
3923 enum isl_dim_type type, unsigned pos,
3924 __isl_take isl_val *v);
3926 #include <isl/map.h>
3927 __isl_give isl_basic_map *isl_basic_map_fix_si(
3928 __isl_take isl_basic_map *bmap,
3929 enum isl_dim_type type, unsigned pos, int value);
3930 __isl_give isl_basic_map *isl_basic_map_fix_val(
3931 __isl_take isl_basic_map *bmap,
3932 enum isl_dim_type type, unsigned pos,
3933 __isl_take isl_val *v);
3934 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
3935 enum isl_dim_type type, unsigned pos, int value);
3936 __isl_give isl_map *isl_map_fix_val(
3937 __isl_take isl_map *map,
3938 enum isl_dim_type type, unsigned pos,
3939 __isl_take isl_val *v);
3941 #include <isl/aff.h>
3942 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
3943 __isl_take isl_pw_multi_aff *pma,
3944 enum isl_dim_type type, unsigned pos, int value);
3946 #include <isl/polynomial.h>
3947 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
3948 __isl_take isl_pw_qpolynomial *pwqp,
3949 enum isl_dim_type type, unsigned n,
3950 __isl_take isl_val *v);
3952 Intersect the set, relation or function domain
3953 with the hyperplane where the given
3954 dimension has the fixed given value.
3956 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
3957 __isl_take isl_basic_map *bmap,
3958 enum isl_dim_type type, unsigned pos, int value);
3959 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
3960 __isl_take isl_basic_map *bmap,
3961 enum isl_dim_type type, unsigned pos, int value);
3962 __isl_give isl_set *isl_set_lower_bound_si(
3963 __isl_take isl_set *set,
3964 enum isl_dim_type type, unsigned pos, int value);
3965 __isl_give isl_set *isl_set_lower_bound_val(
3966 __isl_take isl_set *set,
3967 enum isl_dim_type type, unsigned pos,
3968 __isl_take isl_val *value);
3969 __isl_give isl_map *isl_map_lower_bound_si(
3970 __isl_take isl_map *map,
3971 enum isl_dim_type type, unsigned pos, int value);
3972 __isl_give isl_set *isl_set_upper_bound_si(
3973 __isl_take isl_set *set,
3974 enum isl_dim_type type, unsigned pos, int value);
3975 __isl_give isl_set *isl_set_upper_bound_val(
3976 __isl_take isl_set *set,
3977 enum isl_dim_type type, unsigned pos,
3978 __isl_take isl_val *value);
3979 __isl_give isl_map *isl_map_upper_bound_si(
3980 __isl_take isl_map *map,
3981 enum isl_dim_type type, unsigned pos, int value);
3983 Intersect the set or relation with the half-space where the given
3984 dimension has a value bounded by the fixed given integer value.
3986 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
3987 enum isl_dim_type type1, int pos1,
3988 enum isl_dim_type type2, int pos2);
3989 __isl_give isl_basic_map *isl_basic_map_equate(
3990 __isl_take isl_basic_map *bmap,
3991 enum isl_dim_type type1, int pos1,
3992 enum isl_dim_type type2, int pos2);
3993 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
3994 enum isl_dim_type type1, int pos1,
3995 enum isl_dim_type type2, int pos2);
3997 Intersect the set or relation with the hyperplane where the given
3998 dimensions are equal to each other.
4000 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4001 enum isl_dim_type type1, int pos1,
4002 enum isl_dim_type type2, int pos2);
4004 Intersect the relation with the hyperplane where the given
4005 dimensions have opposite values.
4007 __isl_give isl_map *isl_map_order_le(
4008 __isl_take isl_map *map,
4009 enum isl_dim_type type1, int pos1,
4010 enum isl_dim_type type2, int pos2);
4011 __isl_give isl_basic_map *isl_basic_map_order_ge(
4012 __isl_take isl_basic_map *bmap,
4013 enum isl_dim_type type1, int pos1,
4014 enum isl_dim_type type2, int pos2);
4015 __isl_give isl_map *isl_map_order_ge(
4016 __isl_take isl_map *map,
4017 enum isl_dim_type type1, int pos1,
4018 enum isl_dim_type type2, int pos2);
4019 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4020 enum isl_dim_type type1, int pos1,
4021 enum isl_dim_type type2, int pos2);
4022 __isl_give isl_basic_map *isl_basic_map_order_gt(
4023 __isl_take isl_basic_map *bmap,
4024 enum isl_dim_type type1, int pos1,
4025 enum isl_dim_type type2, int pos2);
4026 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4027 enum isl_dim_type type1, int pos1,
4028 enum isl_dim_type type2, int pos2);
4030 Intersect the relation with the half-space where the given
4031 dimensions satisfy the given ordering.
4035 #include <isl/aff.h>
4036 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4037 __isl_take isl_aff *aff);
4038 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4039 __isl_take isl_aff *aff);
4040 __isl_give isl_set *isl_pw_aff_nonneg_set(
4041 __isl_take isl_pw_aff *pwaff);
4042 __isl_give isl_set *isl_pw_aff_zero_set(
4043 __isl_take isl_pw_aff *pwaff);
4044 __isl_give isl_set *isl_pw_aff_non_zero_set(
4045 __isl_take isl_pw_aff *pwaff);
4047 The function C<isl_aff_neg_basic_set> returns a basic set
4048 containing those elements in the domain space
4049 of C<aff> where C<aff> is negative.
4050 The function C<isl_pw_aff_nonneg_set> returns a set
4051 containing those elements in the domain
4052 of C<pwaff> where C<pwaff> is non-negative.
4056 __isl_give isl_map *isl_set_identity(
4057 __isl_take isl_set *set);
4058 __isl_give isl_union_map *isl_union_set_identity(
4059 __isl_take isl_union_set *uset);
4060 __isl_give isl_union_pw_multi_aff *
4061 isl_union_set_identity_union_pw_multi_aff(
4062 __isl_take isl_union_set *uset);
4064 Construct an identity relation on the given (union) set.
4066 =item * Function Extraction
4068 A piecewise quasi affine expression that is equal to 1 on a set
4069 and 0 outside the set can be created using the following function.
4071 #include <isl/aff.h>
4072 __isl_give isl_pw_aff *isl_set_indicator_function(
4073 __isl_take isl_set *set);
4075 A piecewise multiple quasi affine expression can be extracted
4076 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4077 and the C<isl_map> is single-valued.
4078 In case of a conversion from an C<isl_union_map>
4079 to an C<isl_union_pw_multi_aff>, these properties need to hold
4080 in each domain space.
4082 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4083 __isl_take isl_set *set);
4084 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4085 __isl_take isl_map *map);
4087 __isl_give isl_union_pw_multi_aff *
4088 isl_union_pw_multi_aff_from_union_set(
4089 __isl_take isl_union_set *uset);
4090 __isl_give isl_union_pw_multi_aff *
4091 isl_union_pw_multi_aff_from_union_map(
4092 __isl_take isl_union_map *umap);
4096 __isl_give isl_basic_set *isl_basic_map_deltas(
4097 __isl_take isl_basic_map *bmap);
4098 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4099 __isl_give isl_union_set *isl_union_map_deltas(
4100 __isl_take isl_union_map *umap);
4102 These functions return a (basic) set containing the differences
4103 between image elements and corresponding domain elements in the input.
4105 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4106 __isl_take isl_basic_map *bmap);
4107 __isl_give isl_map *isl_map_deltas_map(
4108 __isl_take isl_map *map);
4109 __isl_give isl_union_map *isl_union_map_deltas_map(
4110 __isl_take isl_union_map *umap);
4112 The functions above construct a (basic, regular or union) relation
4113 that maps (a wrapped version of) the input relation to its delta set.
4117 Simplify the representation of a set, relation or functions by trying
4118 to combine pairs of basic sets or relations into a single
4119 basic set or relation.
4121 #include <isl/set.h>
4122 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4124 #include <isl/map.h>
4125 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4127 #include <isl/union_set.h>
4128 __isl_give isl_union_set *isl_union_set_coalesce(
4129 __isl_take isl_union_set *uset);
4131 #include <isl/union_map.h>
4132 __isl_give isl_union_map *isl_union_map_coalesce(
4133 __isl_take isl_union_map *umap);
4135 #include <isl/aff.h>
4136 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4137 __isl_take isl_pw_aff *pwqp);
4138 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4139 __isl_take isl_pw_multi_aff *pma);
4140 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4141 __isl_take isl_multi_pw_aff *mpa);
4142 __isl_give isl_union_pw_multi_aff *
4143 isl_union_pw_multi_aff_coalesce(
4144 __isl_take isl_union_pw_multi_aff *upma);
4146 #include <isl/polynomial.h>
4147 __isl_give isl_pw_qpolynomial_fold *
4148 isl_pw_qpolynomial_fold_coalesce(
4149 __isl_take isl_pw_qpolynomial_fold *pwf);
4150 __isl_give isl_union_pw_qpolynomial *
4151 isl_union_pw_qpolynomial_coalesce(
4152 __isl_take isl_union_pw_qpolynomial *upwqp);
4153 __isl_give isl_union_pw_qpolynomial_fold *
4154 isl_union_pw_qpolynomial_fold_coalesce(
4155 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4157 One of the methods for combining pairs of basic sets or relations
4158 can result in coefficients that are much larger than those that appear
4159 in the constraints of the input. By default, the coefficients are
4160 not allowed to grow larger, but this can be changed by unsetting
4161 the following option.
4163 int isl_options_set_coalesce_bounded_wrapping(
4164 isl_ctx *ctx, int val);
4165 int isl_options_get_coalesce_bounded_wrapping(
4168 =item * Detecting equalities
4170 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4171 __isl_take isl_basic_set *bset);
4172 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4173 __isl_take isl_basic_map *bmap);
4174 __isl_give isl_set *isl_set_detect_equalities(
4175 __isl_take isl_set *set);
4176 __isl_give isl_map *isl_map_detect_equalities(
4177 __isl_take isl_map *map);
4178 __isl_give isl_union_set *isl_union_set_detect_equalities(
4179 __isl_take isl_union_set *uset);
4180 __isl_give isl_union_map *isl_union_map_detect_equalities(
4181 __isl_take isl_union_map *umap);
4183 Simplify the representation of a set or relation by detecting implicit
4186 =item * Removing redundant constraints
4188 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4189 __isl_take isl_basic_set *bset);
4190 __isl_give isl_set *isl_set_remove_redundancies(
4191 __isl_take isl_set *set);
4192 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4193 __isl_take isl_basic_map *bmap);
4194 __isl_give isl_map *isl_map_remove_redundancies(
4195 __isl_take isl_map *map);
4199 __isl_give isl_basic_set *isl_set_convex_hull(
4200 __isl_take isl_set *set);
4201 __isl_give isl_basic_map *isl_map_convex_hull(
4202 __isl_take isl_map *map);
4204 If the input set or relation has any existentially quantified
4205 variables, then the result of these operations is currently undefined.
4209 #include <isl/set.h>
4210 __isl_give isl_basic_set *
4211 isl_set_unshifted_simple_hull(
4212 __isl_take isl_set *set);
4213 __isl_give isl_basic_set *isl_set_simple_hull(
4214 __isl_take isl_set *set);
4215 __isl_give isl_basic_set *
4216 isl_set_unshifted_simple_hull_from_set_list(
4217 __isl_take isl_set *set,
4218 __isl_take isl_set_list *list);
4220 #include <isl/map.h>
4221 __isl_give isl_basic_map *
4222 isl_map_unshifted_simple_hull(
4223 __isl_take isl_map *map);
4224 __isl_give isl_basic_map *isl_map_simple_hull(
4225 __isl_take isl_map *map);
4227 #include <isl/union_map.h>
4228 __isl_give isl_union_map *isl_union_map_simple_hull(
4229 __isl_take isl_union_map *umap);
4231 These functions compute a single basic set or relation
4232 that contains the whole input set or relation.
4233 In particular, the output is described by translates
4234 of the constraints describing the basic sets or relations in the input.
4235 In case of C<isl_set_unshifted_simple_hull>, only the original
4236 constraints are used, without any translation.
4237 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
4238 constraints are taken from the elements of the second argument.
4242 (See \autoref{s:simple hull}.)
4248 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4249 __isl_take isl_basic_set *bset);
4250 __isl_give isl_basic_set *isl_set_affine_hull(
4251 __isl_take isl_set *set);
4252 __isl_give isl_union_set *isl_union_set_affine_hull(
4253 __isl_take isl_union_set *uset);
4254 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4255 __isl_take isl_basic_map *bmap);
4256 __isl_give isl_basic_map *isl_map_affine_hull(
4257 __isl_take isl_map *map);
4258 __isl_give isl_union_map *isl_union_map_affine_hull(
4259 __isl_take isl_union_map *umap);
4261 In case of union sets and relations, the affine hull is computed
4264 =item * Polyhedral hull
4266 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4267 __isl_take isl_set *set);
4268 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4269 __isl_take isl_map *map);
4270 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4271 __isl_take isl_union_set *uset);
4272 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4273 __isl_take isl_union_map *umap);
4275 These functions compute a single basic set or relation
4276 not involving any existentially quantified variables
4277 that contains the whole input set or relation.
4278 In case of union sets and relations, the polyhedral hull is computed
4281 =item * Other approximations
4283 #include <isl/set.h>
4284 __isl_give isl_basic_set *
4285 isl_basic_set_drop_constraints_involving_dims(
4286 __isl_take isl_basic_set *bset,
4287 enum isl_dim_type type,
4288 unsigned first, unsigned n);
4289 __isl_give isl_basic_set *
4290 isl_basic_set_drop_constraints_not_involving_dims(
4291 __isl_take isl_basic_set *bset,
4292 enum isl_dim_type type,
4293 unsigned first, unsigned n);
4294 __isl_give isl_set *
4295 isl_set_drop_constraints_involving_dims(
4296 __isl_take isl_set *set,
4297 enum isl_dim_type type,
4298 unsigned first, unsigned n);
4300 #include <isl/map.h>
4301 __isl_give isl_basic_map *
4302 isl_basic_map_drop_constraints_involving_dims(
4303 __isl_take isl_basic_map *bmap,
4304 enum isl_dim_type type,
4305 unsigned first, unsigned n);
4306 __isl_give isl_map *
4307 isl_map_drop_constraints_involving_dims(
4308 __isl_take isl_map *map,
4309 enum isl_dim_type type,
4310 unsigned first, unsigned n);
4312 These functions drop any constraints (not) involving the specified dimensions.
4313 Note that the result depends on the representation of the input.
4315 #include <isl/polynomial.h>
4316 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4317 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4318 __isl_give isl_union_pw_qpolynomial *
4319 isl_union_pw_qpolynomial_to_polynomial(
4320 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4322 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4323 the polynomial will be an overapproximation. If C<sign> is negative,
4324 it will be an underapproximation. If C<sign> is zero, the approximation
4325 will lie somewhere in between.
4329 __isl_give isl_basic_set *isl_basic_set_sample(
4330 __isl_take isl_basic_set *bset);
4331 __isl_give isl_basic_set *isl_set_sample(
4332 __isl_take isl_set *set);
4333 __isl_give isl_basic_map *isl_basic_map_sample(
4334 __isl_take isl_basic_map *bmap);
4335 __isl_give isl_basic_map *isl_map_sample(
4336 __isl_take isl_map *map);
4338 If the input (basic) set or relation is non-empty, then return
4339 a singleton subset of the input. Otherwise, return an empty set.
4341 =item * Optimization
4343 #include <isl/ilp.h>
4344 __isl_give isl_val *isl_basic_set_max_val(
4345 __isl_keep isl_basic_set *bset,
4346 __isl_keep isl_aff *obj);
4347 __isl_give isl_val *isl_set_min_val(
4348 __isl_keep isl_set *set,
4349 __isl_keep isl_aff *obj);
4350 __isl_give isl_val *isl_set_max_val(
4351 __isl_keep isl_set *set,
4352 __isl_keep isl_aff *obj);
4354 Compute the minimum or maximum of the integer affine expression C<obj>
4355 over the points in C<set>, returning the result in C<opt>.
4356 The result is C<NULL> in case of an error, the optimal value in case
4357 there is one, negative infinity or infinity if the problem is unbounded and
4358 NaN if the problem is empty.
4360 =item * Parametric optimization
4362 __isl_give isl_pw_aff *isl_set_dim_min(
4363 __isl_take isl_set *set, int pos);
4364 __isl_give isl_pw_aff *isl_set_dim_max(
4365 __isl_take isl_set *set, int pos);
4366 __isl_give isl_pw_aff *isl_map_dim_max(
4367 __isl_take isl_map *map, int pos);
4369 Compute the minimum or maximum of the given set or output dimension
4370 as a function of the parameters (and input dimensions), but independently
4371 of the other set or output dimensions.
4372 For lexicographic optimization, see L<"Lexicographic Optimization">.
4376 The following functions compute either the set of (rational) coefficient
4377 values of valid constraints for the given set or the set of (rational)
4378 values satisfying the constraints with coefficients from the given set.
4379 Internally, these two sets of functions perform essentially the
4380 same operations, except that the set of coefficients is assumed to
4381 be a cone, while the set of values may be any polyhedron.
4382 The current implementation is based on the Farkas lemma and
4383 Fourier-Motzkin elimination, but this may change or be made optional
4384 in future. In particular, future implementations may use different
4385 dualization algorithms or skip the elimination step.
4387 __isl_give isl_basic_set *isl_basic_set_coefficients(
4388 __isl_take isl_basic_set *bset);
4389 __isl_give isl_basic_set *isl_set_coefficients(
4390 __isl_take isl_set *set);
4391 __isl_give isl_union_set *isl_union_set_coefficients(
4392 __isl_take isl_union_set *bset);
4393 __isl_give isl_basic_set *isl_basic_set_solutions(
4394 __isl_take isl_basic_set *bset);
4395 __isl_give isl_basic_set *isl_set_solutions(
4396 __isl_take isl_set *set);
4397 __isl_give isl_union_set *isl_union_set_solutions(
4398 __isl_take isl_union_set *bset);
4402 __isl_give isl_map *isl_map_fixed_power_val(
4403 __isl_take isl_map *map,
4404 __isl_take isl_val *exp);
4405 __isl_give isl_union_map *
4406 isl_union_map_fixed_power_val(
4407 __isl_take isl_union_map *umap,
4408 __isl_take isl_val *exp);
4410 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4411 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4412 of C<map> is computed.
4414 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4416 __isl_give isl_union_map *isl_union_map_power(
4417 __isl_take isl_union_map *umap, int *exact);
4419 Compute a parametric representation for all positive powers I<k> of C<map>.
4420 The result maps I<k> to a nested relation corresponding to the
4421 I<k>th power of C<map>.
4422 The result may be an overapproximation. If the result is known to be exact,
4423 then C<*exact> is set to C<1>.
4425 =item * Transitive closure
4427 __isl_give isl_map *isl_map_transitive_closure(
4428 __isl_take isl_map *map, int *exact);
4429 __isl_give isl_union_map *isl_union_map_transitive_closure(
4430 __isl_take isl_union_map *umap, int *exact);
4432 Compute the transitive closure of C<map>.
4433 The result may be an overapproximation. If the result is known to be exact,
4434 then C<*exact> is set to C<1>.
4436 =item * Reaching path lengths
4438 __isl_give isl_map *isl_map_reaching_path_lengths(
4439 __isl_take isl_map *map, int *exact);
4441 Compute a relation that maps each element in the range of C<map>
4442 to the lengths of all paths composed of edges in C<map> that
4443 end up in the given element.
4444 The result may be an overapproximation. If the result is known to be exact,
4445 then C<*exact> is set to C<1>.
4446 To compute the I<maximal> path length, the resulting relation
4447 should be postprocessed by C<isl_map_lexmax>.
4448 In particular, if the input relation is a dependence relation
4449 (mapping sources to sinks), then the maximal path length corresponds
4450 to the free schedule.
4451 Note, however, that C<isl_map_lexmax> expects the maximum to be
4452 finite, so if the path lengths are unbounded (possibly due to
4453 the overapproximation), then you will get an error message.
4457 #include <isl/space.h>
4458 __isl_give isl_space *isl_space_wrap(
4459 __isl_take isl_space *space);
4460 __isl_give isl_space *isl_space_unwrap(
4461 __isl_take isl_space *space);
4463 #include <isl/set.h>
4464 __isl_give isl_basic_map *isl_basic_set_unwrap(
4465 __isl_take isl_basic_set *bset);
4466 __isl_give isl_map *isl_set_unwrap(
4467 __isl_take isl_set *set);
4469 #include <isl/map.h>
4470 __isl_give isl_basic_set *isl_basic_map_wrap(
4471 __isl_take isl_basic_map *bmap);
4472 __isl_give isl_set *isl_map_wrap(
4473 __isl_take isl_map *map);
4475 #include <isl/union_set.h>
4476 __isl_give isl_union_map *isl_union_set_unwrap(
4477 __isl_take isl_union_set *uset);
4479 #include <isl/union_map.h>
4480 __isl_give isl_union_set *isl_union_map_wrap(
4481 __isl_take isl_union_map *umap);
4483 The input to C<isl_space_unwrap> should
4484 be the space of a set, while that of
4485 C<isl_space_wrap> should be the space of a relation.
4486 Conversely, the output of C<isl_space_unwrap> is the space
4487 of a relation, while that of C<isl_space_wrap> is the space of a set.
4491 Remove any internal structure of domain (and range) of the given
4492 set or relation. If there is any such internal structure in the input,
4493 then the name of the space is also removed.
4495 #include <isl/local_space.h>
4496 __isl_give isl_local_space *
4497 isl_local_space_flatten_domain(
4498 __isl_take isl_local_space *ls);
4499 __isl_give isl_local_space *
4500 isl_local_space_flatten_range(
4501 __isl_take isl_local_space *ls);
4503 #include <isl/set.h>
4504 __isl_give isl_basic_set *isl_basic_set_flatten(
4505 __isl_take isl_basic_set *bset);
4506 __isl_give isl_set *isl_set_flatten(
4507 __isl_take isl_set *set);
4509 #include <isl/map.h>
4510 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4511 __isl_take isl_basic_map *bmap);
4512 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4513 __isl_take isl_basic_map *bmap);
4514 __isl_give isl_map *isl_map_flatten_range(
4515 __isl_take isl_map *map);
4516 __isl_give isl_map *isl_map_flatten_domain(
4517 __isl_take isl_map *map);
4518 __isl_give isl_basic_map *isl_basic_map_flatten(
4519 __isl_take isl_basic_map *bmap);
4520 __isl_give isl_map *isl_map_flatten(
4521 __isl_take isl_map *map);
4523 #include <isl/val.h>
4524 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4525 __isl_take isl_multi_val *mv);
4527 #include <isl/aff.h>
4528 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4529 __isl_take isl_multi_aff *ma);
4530 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4531 __isl_take isl_multi_aff *ma);
4532 __isl_give isl_multi_pw_aff *
4533 isl_multi_pw_aff_flatten_range(
4534 __isl_take isl_multi_pw_aff *mpa);
4536 #include <isl/map.h>
4537 __isl_give isl_map *isl_set_flatten_map(
4538 __isl_take isl_set *set);
4540 The function above constructs a relation
4541 that maps the input set to a flattened version of the set.
4545 Lift the input set to a space with extra dimensions corresponding
4546 to the existentially quantified variables in the input.
4547 In particular, the result lives in a wrapped map where the domain
4548 is the original space and the range corresponds to the original
4549 existentially quantified variables.
4551 #include <isl/set.h>
4552 __isl_give isl_basic_set *isl_basic_set_lift(
4553 __isl_take isl_basic_set *bset);
4554 __isl_give isl_set *isl_set_lift(
4555 __isl_take isl_set *set);
4556 __isl_give isl_union_set *isl_union_set_lift(
4557 __isl_take isl_union_set *uset);
4559 Given a local space that contains the existentially quantified
4560 variables of a set, a basic relation that, when applied to
4561 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4562 can be constructed using the following function.
4564 #include <isl/local_space.h>
4565 __isl_give isl_basic_map *isl_local_space_lifting(
4566 __isl_take isl_local_space *ls);
4568 #include <isl/aff.h>
4569 __isl_give isl_multi_aff *isl_multi_aff_lift(
4570 __isl_take isl_multi_aff *maff,
4571 __isl_give isl_local_space **ls);
4573 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4574 then it is assigned the local space that lies at the basis of
4575 the lifting applied.
4577 =item * Internal Product
4579 #include <isl/space.h>
4580 __isl_give isl_space *isl_space_zip(
4581 __isl_take isl_space *space);
4583 #include <isl/map.h>
4584 __isl_give isl_basic_map *isl_basic_map_zip(
4585 __isl_take isl_basic_map *bmap);
4586 __isl_give isl_map *isl_map_zip(
4587 __isl_take isl_map *map);
4589 #include <isl/union_map.h>
4590 __isl_give isl_union_map *isl_union_map_zip(
4591 __isl_take isl_union_map *umap);
4593 Given a relation with nested relations for domain and range,
4594 interchange the range of the domain with the domain of the range.
4598 #include <isl/space.h>
4599 __isl_give isl_space *isl_space_curry(
4600 __isl_take isl_space *space);
4601 __isl_give isl_space *isl_space_uncurry(
4602 __isl_take isl_space *space);
4604 #include <isl/map.h>
4605 __isl_give isl_basic_map *isl_basic_map_curry(
4606 __isl_take isl_basic_map *bmap);
4607 __isl_give isl_basic_map *isl_basic_map_uncurry(
4608 __isl_take isl_basic_map *bmap);
4609 __isl_give isl_map *isl_map_curry(
4610 __isl_take isl_map *map);
4611 __isl_give isl_map *isl_map_uncurry(
4612 __isl_take isl_map *map);
4614 #include <isl/union_map.h>
4615 __isl_give isl_union_map *isl_union_map_curry(
4616 __isl_take isl_union_map *umap);
4617 __isl_give isl_union_map *isl_union_map_uncurry(
4618 __isl_take isl_union_map *umap);
4620 Given a relation with a nested relation for domain,
4621 the C<curry> functions
4622 move the range of the nested relation out of the domain
4623 and use it as the domain of a nested relation in the range,
4624 with the original range as range of this nested relation.
4625 The C<uncurry> functions perform the inverse operation.
4627 =item * Aligning parameters
4629 Change the order of the parameters of the given set, relation
4631 such that the first parameters match those of C<model>.
4632 This may involve the introduction of extra parameters.
4633 All parameters need to be named.
4635 #include <isl/space.h>
4636 __isl_give isl_space *isl_space_align_params(
4637 __isl_take isl_space *space1,
4638 __isl_take isl_space *space2)
4640 #include <isl/set.h>
4641 __isl_give isl_basic_set *isl_basic_set_align_params(
4642 __isl_take isl_basic_set *bset,
4643 __isl_take isl_space *model);
4644 __isl_give isl_set *isl_set_align_params(
4645 __isl_take isl_set *set,
4646 __isl_take isl_space *model);
4648 #include <isl/map.h>
4649 __isl_give isl_basic_map *isl_basic_map_align_params(
4650 __isl_take isl_basic_map *bmap,
4651 __isl_take isl_space *model);
4652 __isl_give isl_map *isl_map_align_params(
4653 __isl_take isl_map *map,
4654 __isl_take isl_space *model);
4656 #include <isl/val.h>
4657 __isl_give isl_multi_val *isl_multi_val_align_params(
4658 __isl_take isl_multi_val *mv,
4659 __isl_take isl_space *model);
4661 #include <isl/aff.h>
4662 __isl_give isl_aff *isl_aff_align_params(
4663 __isl_take isl_aff *aff,
4664 __isl_take isl_space *model);
4665 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4666 __isl_take isl_multi_aff *multi,
4667 __isl_take isl_space *model);
4668 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4669 __isl_take isl_pw_aff *pwaff,
4670 __isl_take isl_space *model);
4671 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4672 __isl_take isl_pw_multi_aff *pma,
4673 __isl_take isl_space *model);
4674 __isl_give isl_union_pw_multi_aff *
4675 isl_union_pw_multi_aff_align_params(
4676 __isl_take isl_union_pw_multi_aff *upma,
4677 __isl_take isl_space *model);
4679 #include <isl/polynomial.h>
4680 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4681 __isl_take isl_qpolynomial *qp,
4682 __isl_take isl_space *model);
4684 =item * Unary Arithmethic Operations
4686 #include <isl/aff.h>
4687 __isl_give isl_aff *isl_aff_neg(
4688 __isl_take isl_aff *aff);
4689 __isl_give isl_pw_aff *isl_pw_aff_neg(
4690 __isl_take isl_pw_aff *pwaff);
4691 __isl_give isl_aff *isl_aff_ceil(
4692 __isl_take isl_aff *aff);
4693 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4694 __isl_take isl_pw_aff *pwaff);
4695 __isl_give isl_aff *isl_aff_floor(
4696 __isl_take isl_aff *aff);
4697 __isl_give isl_multi_aff *isl_multi_aff_floor(
4698 __isl_take isl_multi_aff *ma);
4699 __isl_give isl_pw_aff *isl_pw_aff_floor(
4700 __isl_take isl_pw_aff *pwaff);
4702 #include <isl/aff.h>
4703 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4704 __isl_take isl_pw_aff_list *list);
4705 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4706 __isl_take isl_pw_aff_list *list);
4708 #include <isl/polynomial.h>
4709 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4710 __isl_take isl_qpolynomial *qp);
4711 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4712 __isl_take isl_pw_qpolynomial *pwqp);
4713 __isl_give isl_union_pw_qpolynomial *
4714 isl_union_pw_qpolynomial_neg(
4715 __isl_take isl_union_pw_qpolynomial *upwqp);
4716 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4717 __isl_take isl_qpolynomial *qp,
4719 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4720 __isl_take isl_pw_qpolynomial *pwqp,
4725 The following functions evaluate a function in a point.
4727 #include <isl/polynomial.h>
4728 __isl_give isl_val *isl_pw_qpolynomial_eval(
4729 __isl_take isl_pw_qpolynomial *pwqp,
4730 __isl_take isl_point *pnt);
4731 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
4732 __isl_take isl_pw_qpolynomial_fold *pwf,
4733 __isl_take isl_point *pnt);
4734 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4735 __isl_take isl_union_pw_qpolynomial *upwqp,
4736 __isl_take isl_point *pnt);
4737 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
4738 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4739 __isl_take isl_point *pnt);
4741 =item * Dimension manipulation
4743 It is usually not advisable to directly change the (input or output)
4744 space of a set or a relation as this removes the name and the internal
4745 structure of the space. However, the functions below can be useful
4746 to add new parameters, assuming
4747 C<isl_set_align_params> and C<isl_map_align_params>
4750 #include <isl/space.h>
4751 __isl_give isl_space *isl_space_add_dims(
4752 __isl_take isl_space *space,
4753 enum isl_dim_type type, unsigned n);
4754 __isl_give isl_space *isl_space_insert_dims(
4755 __isl_take isl_space *space,
4756 enum isl_dim_type type, unsigned pos, unsigned n);
4757 __isl_give isl_space *isl_space_drop_dims(
4758 __isl_take isl_space *space,
4759 enum isl_dim_type type, unsigned first, unsigned n);
4760 __isl_give isl_space *isl_space_move_dims(
4761 __isl_take isl_space *space,
4762 enum isl_dim_type dst_type, unsigned dst_pos,
4763 enum isl_dim_type src_type, unsigned src_pos,
4766 #include <isl/local_space.h>
4767 __isl_give isl_local_space *isl_local_space_add_dims(
4768 __isl_take isl_local_space *ls,
4769 enum isl_dim_type type, unsigned n);
4770 __isl_give isl_local_space *isl_local_space_insert_dims(
4771 __isl_take isl_local_space *ls,
4772 enum isl_dim_type type, unsigned first, unsigned n);
4773 __isl_give isl_local_space *isl_local_space_drop_dims(
4774 __isl_take isl_local_space *ls,
4775 enum isl_dim_type type, unsigned first, unsigned n);
4777 #include <isl/set.h>
4778 __isl_give isl_basic_set *isl_basic_set_add_dims(
4779 __isl_take isl_basic_set *bset,
4780 enum isl_dim_type type, unsigned n);
4781 __isl_give isl_set *isl_set_add_dims(
4782 __isl_take isl_set *set,
4783 enum isl_dim_type type, unsigned n);
4784 __isl_give isl_basic_set *isl_basic_set_insert_dims(
4785 __isl_take isl_basic_set *bset,
4786 enum isl_dim_type type, unsigned pos,
4788 __isl_give isl_set *isl_set_insert_dims(
4789 __isl_take isl_set *set,
4790 enum isl_dim_type type, unsigned pos, unsigned n);
4791 __isl_give isl_basic_set *isl_basic_set_move_dims(
4792 __isl_take isl_basic_set *bset,
4793 enum isl_dim_type dst_type, unsigned dst_pos,
4794 enum isl_dim_type src_type, unsigned src_pos,
4796 __isl_give isl_set *isl_set_move_dims(
4797 __isl_take isl_set *set,
4798 enum isl_dim_type dst_type, unsigned dst_pos,
4799 enum isl_dim_type src_type, unsigned src_pos,
4802 #include <isl/map.h>
4803 __isl_give isl_map *isl_map_add_dims(
4804 __isl_take isl_map *map,
4805 enum isl_dim_type type, unsigned n);
4806 __isl_give isl_basic_map *isl_basic_map_insert_dims(
4807 __isl_take isl_basic_map *bmap,
4808 enum isl_dim_type type, unsigned pos,
4810 __isl_give isl_map *isl_map_insert_dims(
4811 __isl_take isl_map *map,
4812 enum isl_dim_type type, unsigned pos, unsigned n);
4813 __isl_give isl_basic_map *isl_basic_map_move_dims(
4814 __isl_take isl_basic_map *bmap,
4815 enum isl_dim_type dst_type, unsigned dst_pos,
4816 enum isl_dim_type src_type, unsigned src_pos,
4818 __isl_give isl_map *isl_map_move_dims(
4819 __isl_take isl_map *map,
4820 enum isl_dim_type dst_type, unsigned dst_pos,
4821 enum isl_dim_type src_type, unsigned src_pos,
4824 #include <isl/val.h>
4825 __isl_give isl_multi_val *isl_multi_val_insert_dims(
4826 __isl_take isl_multi_val *mv,
4827 enum isl_dim_type type, unsigned first, unsigned n);
4828 __isl_give isl_multi_val *isl_multi_val_add_dims(
4829 __isl_take isl_multi_val *mv,
4830 enum isl_dim_type type, unsigned n);
4831 __isl_give isl_multi_val *isl_multi_val_drop_dims(
4832 __isl_take isl_multi_val *mv,
4833 enum isl_dim_type type, unsigned first, unsigned n);
4835 #include <isl/aff.h>
4836 __isl_give isl_aff *isl_aff_insert_dims(
4837 __isl_take isl_aff *aff,
4838 enum isl_dim_type type, unsigned first, unsigned n);
4839 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4840 __isl_take isl_multi_aff *ma,
4841 enum isl_dim_type type, unsigned first, unsigned n);
4842 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4843 __isl_take isl_pw_aff *pwaff,
4844 enum isl_dim_type type, unsigned first, unsigned n);
4845 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4846 __isl_take isl_multi_pw_aff *mpa,
4847 enum isl_dim_type type, unsigned first, unsigned n);
4848 __isl_give isl_aff *isl_aff_add_dims(
4849 __isl_take isl_aff *aff,
4850 enum isl_dim_type type, unsigned n);
4851 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4852 __isl_take isl_multi_aff *ma,
4853 enum isl_dim_type type, unsigned n);
4854 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4855 __isl_take isl_pw_aff *pwaff,
4856 enum isl_dim_type type, unsigned n);
4857 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4858 __isl_take isl_multi_pw_aff *mpa,
4859 enum isl_dim_type type, unsigned n);
4860 __isl_give isl_aff *isl_aff_drop_dims(
4861 __isl_take isl_aff *aff,
4862 enum isl_dim_type type, unsigned first, unsigned n);
4863 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4864 __isl_take isl_multi_aff *maff,
4865 enum isl_dim_type type, unsigned first, unsigned n);
4866 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4867 __isl_take isl_pw_aff *pwaff,
4868 enum isl_dim_type type, unsigned first, unsigned n);
4869 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4870 __isl_take isl_pw_multi_aff *pma,
4871 enum isl_dim_type type, unsigned first, unsigned n);
4872 __isl_give isl_aff *isl_aff_move_dims(
4873 __isl_take isl_aff *aff,
4874 enum isl_dim_type dst_type, unsigned dst_pos,
4875 enum isl_dim_type src_type, unsigned src_pos,
4877 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
4878 __isl_take isl_multi_aff *ma,
4879 enum isl_dim_type dst_type, unsigned dst_pos,
4880 enum isl_dim_type src_type, unsigned src_pos,
4882 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4883 __isl_take isl_pw_aff *pa,
4884 enum isl_dim_type dst_type, unsigned dst_pos,
4885 enum isl_dim_type src_type, unsigned src_pos,
4887 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4888 __isl_take isl_multi_pw_aff *pma,
4889 enum isl_dim_type dst_type, unsigned dst_pos,
4890 enum isl_dim_type src_type, unsigned src_pos,
4895 =head2 Binary Operations
4897 The two arguments of a binary operation not only need to live
4898 in the same C<isl_ctx>, they currently also need to have
4899 the same (number of) parameters.
4901 =head3 Basic Operations
4905 =item * Intersection
4907 #include <isl/local_space.h>
4908 __isl_give isl_local_space *isl_local_space_intersect(
4909 __isl_take isl_local_space *ls1,
4910 __isl_take isl_local_space *ls2);
4912 #include <isl/set.h>
4913 __isl_give isl_basic_set *isl_basic_set_intersect_params(
4914 __isl_take isl_basic_set *bset1,
4915 __isl_take isl_basic_set *bset2);
4916 __isl_give isl_basic_set *isl_basic_set_intersect(
4917 __isl_take isl_basic_set *bset1,
4918 __isl_take isl_basic_set *bset2);
4919 __isl_give isl_basic_set *isl_basic_set_list_intersect(
4920 __isl_take struct isl_basic_set_list *list);
4921 __isl_give isl_set *isl_set_intersect_params(
4922 __isl_take isl_set *set,
4923 __isl_take isl_set *params);
4924 __isl_give isl_set *isl_set_intersect(
4925 __isl_take isl_set *set1,
4926 __isl_take isl_set *set2);
4928 #include <isl/map.h>
4929 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
4930 __isl_take isl_basic_map *bmap,
4931 __isl_take isl_basic_set *bset);
4932 __isl_give isl_basic_map *isl_basic_map_intersect_range(
4933 __isl_take isl_basic_map *bmap,
4934 __isl_take isl_basic_set *bset);
4935 __isl_give isl_basic_map *isl_basic_map_intersect(
4936 __isl_take isl_basic_map *bmap1,
4937 __isl_take isl_basic_map *bmap2);
4938 __isl_give isl_basic_map *isl_basic_map_list_intersect(
4939 __isl_take isl_basic_map_list *list);
4940 __isl_give isl_map *isl_map_intersect_params(
4941 __isl_take isl_map *map,
4942 __isl_take isl_set *params);
4943 __isl_give isl_map *isl_map_intersect_domain(
4944 __isl_take isl_map *map,
4945 __isl_take isl_set *set);
4946 __isl_give isl_map *isl_map_intersect_range(
4947 __isl_take isl_map *map,
4948 __isl_take isl_set *set);
4949 __isl_give isl_map *isl_map_intersect(
4950 __isl_take isl_map *map1,
4951 __isl_take isl_map *map2);
4953 #include <isl/union_set.h>
4954 __isl_give isl_union_set *isl_union_set_intersect_params(
4955 __isl_take isl_union_set *uset,
4956 __isl_take isl_set *set);
4957 __isl_give isl_union_set *isl_union_set_intersect(
4958 __isl_take isl_union_set *uset1,
4959 __isl_take isl_union_set *uset2);
4961 #include <isl/union_map.h>
4962 __isl_give isl_union_map *isl_union_map_intersect_params(
4963 __isl_take isl_union_map *umap,
4964 __isl_take isl_set *set);
4965 __isl_give isl_union_map *isl_union_map_intersect_domain(
4966 __isl_take isl_union_map *umap,
4967 __isl_take isl_union_set *uset);
4968 __isl_give isl_union_map *isl_union_map_intersect_range(
4969 __isl_take isl_union_map *umap,
4970 __isl_take isl_union_set *uset);
4971 __isl_give isl_union_map *isl_union_map_intersect(
4972 __isl_take isl_union_map *umap1,
4973 __isl_take isl_union_map *umap2);
4975 #include <isl/aff.h>
4976 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4977 __isl_take isl_pw_aff *pa,
4978 __isl_take isl_set *set);
4979 __isl_give isl_multi_pw_aff *
4980 isl_multi_pw_aff_intersect_domain(
4981 __isl_take isl_multi_pw_aff *mpa,
4982 __isl_take isl_set *domain);
4983 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4984 __isl_take isl_pw_multi_aff *pma,
4985 __isl_take isl_set *set);
4986 __isl_give isl_union_pw_multi_aff *
4987 isl_union_pw_multi_aff_intersect_domain(
4988 __isl_take isl_union_pw_multi_aff *upma,
4989 __isl_take isl_union_set *uset);
4990 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4991 __isl_take isl_pw_aff *pa,
4992 __isl_take isl_set *set);
4993 __isl_give isl_multi_pw_aff *
4994 isl_multi_pw_aff_intersect_params(
4995 __isl_take isl_multi_pw_aff *mpa,
4996 __isl_take isl_set *set);
4997 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4998 __isl_take isl_pw_multi_aff *pma,
4999 __isl_take isl_set *set);
5000 __isl_give isl_union_pw_multi_aff *
5001 isl_union_pw_multi_aff_intersect_params(
5002 __isl_take isl_union_pw_multi_aff *upma,
5003 __isl_take isl_set *set);
5005 #include <isl/polynomial.h>
5006 __isl_give isl_pw_qpolynomial *
5007 isl_pw_qpolynomial_intersect_domain(
5008 __isl_take isl_pw_qpolynomial *pwpq,
5009 __isl_take isl_set *set);
5010 __isl_give isl_union_pw_qpolynomial *
5011 isl_union_pw_qpolynomial_intersect_domain(
5012 __isl_take isl_union_pw_qpolynomial *upwpq,
5013 __isl_take isl_union_set *uset);
5014 __isl_give isl_union_pw_qpolynomial_fold *
5015 isl_union_pw_qpolynomial_fold_intersect_domain(
5016 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5017 __isl_take isl_union_set *uset);
5018 __isl_give isl_pw_qpolynomial *
5019 isl_pw_qpolynomial_intersect_params(
5020 __isl_take isl_pw_qpolynomial *pwpq,
5021 __isl_take isl_set *set);
5022 __isl_give isl_pw_qpolynomial_fold *
5023 isl_pw_qpolynomial_fold_intersect_params(
5024 __isl_take isl_pw_qpolynomial_fold *pwf,
5025 __isl_take isl_set *set);
5026 __isl_give isl_union_pw_qpolynomial *
5027 isl_union_pw_qpolynomial_intersect_params(
5028 __isl_take isl_union_pw_qpolynomial *upwpq,
5029 __isl_take isl_set *set);
5030 __isl_give isl_union_pw_qpolynomial_fold *
5031 isl_union_pw_qpolynomial_fold_intersect_params(
5032 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5033 __isl_take isl_set *set);
5035 The second argument to the C<_params> functions needs to be
5036 a parametric (basic) set. For the other functions, a parametric set
5037 for either argument is only allowed if the other argument is
5038 a parametric set as well.
5039 The list passed to C<isl_basic_set_list_intersect> needs to have
5040 at least one element and all elements need to live in the same space.
5044 #include <isl/set.h>
5045 __isl_give isl_set *isl_basic_set_union(
5046 __isl_take isl_basic_set *bset1,
5047 __isl_take isl_basic_set *bset2);
5048 __isl_give isl_set *isl_set_union(
5049 __isl_take isl_set *set1,
5050 __isl_take isl_set *set2);
5052 #include <isl/map.h>
5053 __isl_give isl_map *isl_basic_map_union(
5054 __isl_take isl_basic_map *bmap1,
5055 __isl_take isl_basic_map *bmap2);
5056 __isl_give isl_map *isl_map_union(
5057 __isl_take isl_map *map1,
5058 __isl_take isl_map *map2);
5060 #include <isl/union_set.h>
5061 __isl_give isl_union_set *isl_union_set_union(
5062 __isl_take isl_union_set *uset1,
5063 __isl_take isl_union_set *uset2);
5064 __isl_give isl_union_set *isl_union_set_list_union(
5065 __isl_take isl_union_set_list *list);
5067 #include <isl/union_map.h>
5068 __isl_give isl_union_map *isl_union_map_union(
5069 __isl_take isl_union_map *umap1,
5070 __isl_take isl_union_map *umap2);
5072 =item * Set difference
5074 #include <isl/set.h>
5075 __isl_give isl_set *isl_set_subtract(
5076 __isl_take isl_set *set1,
5077 __isl_take isl_set *set2);
5079 #include <isl/map.h>
5080 __isl_give isl_map *isl_map_subtract(
5081 __isl_take isl_map *map1,
5082 __isl_take isl_map *map2);
5083 __isl_give isl_map *isl_map_subtract_domain(
5084 __isl_take isl_map *map,
5085 __isl_take isl_set *dom);
5086 __isl_give isl_map *isl_map_subtract_range(
5087 __isl_take isl_map *map,
5088 __isl_take isl_set *dom);
5090 #include <isl/union_set.h>
5091 __isl_give isl_union_set *isl_union_set_subtract(
5092 __isl_take isl_union_set *uset1,
5093 __isl_take isl_union_set *uset2);
5095 #include <isl/union_map.h>
5096 __isl_give isl_union_map *isl_union_map_subtract(
5097 __isl_take isl_union_map *umap1,
5098 __isl_take isl_union_map *umap2);
5099 __isl_give isl_union_map *isl_union_map_subtract_domain(
5100 __isl_take isl_union_map *umap,
5101 __isl_take isl_union_set *dom);
5102 __isl_give isl_union_map *isl_union_map_subtract_range(
5103 __isl_take isl_union_map *umap,
5104 __isl_take isl_union_set *dom);
5106 #include <isl/aff.h>
5107 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5108 __isl_take isl_pw_aff *pa,
5109 __isl_take isl_set *set);
5110 __isl_give isl_pw_multi_aff *
5111 isl_pw_multi_aff_subtract_domain(
5112 __isl_take isl_pw_multi_aff *pma,
5113 __isl_take isl_set *set);
5114 __isl_give isl_union_pw_multi_aff *
5115 isl_union_pw_multi_aff_subtract_domain(
5116 __isl_take isl_union_pw_multi_aff *upma,
5117 __isl_take isl_union_set *uset);
5119 #include <isl/polynomial.h>
5120 __isl_give isl_pw_qpolynomial *
5121 isl_pw_qpolynomial_subtract_domain(
5122 __isl_take isl_pw_qpolynomial *pwpq,
5123 __isl_take isl_set *set);
5124 __isl_give isl_pw_qpolynomial_fold *
5125 isl_pw_qpolynomial_fold_subtract_domain(
5126 __isl_take isl_pw_qpolynomial_fold *pwf,
5127 __isl_take isl_set *set);
5128 __isl_give isl_union_pw_qpolynomial *
5129 isl_union_pw_qpolynomial_subtract_domain(
5130 __isl_take isl_union_pw_qpolynomial *upwpq,
5131 __isl_take isl_union_set *uset);
5132 __isl_give isl_union_pw_qpolynomial_fold *
5133 isl_union_pw_qpolynomial_fold_subtract_domain(
5134 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5135 __isl_take isl_union_set *uset);
5139 #include <isl/space.h>
5140 __isl_give isl_space *isl_space_join(
5141 __isl_take isl_space *left,
5142 __isl_take isl_space *right);
5144 #include <isl/map.h>
5145 __isl_give isl_basic_set *isl_basic_set_apply(
5146 __isl_take isl_basic_set *bset,
5147 __isl_take isl_basic_map *bmap);
5148 __isl_give isl_set *isl_set_apply(
5149 __isl_take isl_set *set,
5150 __isl_take isl_map *map);
5151 __isl_give isl_union_set *isl_union_set_apply(
5152 __isl_take isl_union_set *uset,
5153 __isl_take isl_union_map *umap);
5154 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5155 __isl_take isl_basic_map *bmap1,
5156 __isl_take isl_basic_map *bmap2);
5157 __isl_give isl_basic_map *isl_basic_map_apply_range(
5158 __isl_take isl_basic_map *bmap1,
5159 __isl_take isl_basic_map *bmap2);
5160 __isl_give isl_map *isl_map_apply_domain(
5161 __isl_take isl_map *map1,
5162 __isl_take isl_map *map2);
5163 __isl_give isl_map *isl_map_apply_range(
5164 __isl_take isl_map *map1,
5165 __isl_take isl_map *map2);
5167 #include <isl/union_map.h>
5168 __isl_give isl_union_map *isl_union_map_apply_domain(
5169 __isl_take isl_union_map *umap1,
5170 __isl_take isl_union_map *umap2);
5171 __isl_give isl_union_map *isl_union_map_apply_range(
5172 __isl_take isl_union_map *umap1,
5173 __isl_take isl_union_map *umap2);
5175 #include <isl/polynomial.h>
5176 __isl_give isl_pw_qpolynomial_fold *
5177 isl_set_apply_pw_qpolynomial_fold(
5178 __isl_take isl_set *set,
5179 __isl_take isl_pw_qpolynomial_fold *pwf,
5181 __isl_give isl_pw_qpolynomial_fold *
5182 isl_map_apply_pw_qpolynomial_fold(
5183 __isl_take isl_map *map,
5184 __isl_take isl_pw_qpolynomial_fold *pwf,
5186 __isl_give isl_union_pw_qpolynomial_fold *
5187 isl_union_set_apply_union_pw_qpolynomial_fold(
5188 __isl_take isl_union_set *uset,
5189 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5191 __isl_give isl_union_pw_qpolynomial_fold *
5192 isl_union_map_apply_union_pw_qpolynomial_fold(
5193 __isl_take isl_union_map *umap,
5194 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5197 The functions taking a map
5198 compose the given map with the given piecewise quasipolynomial reduction.
5199 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5200 over all elements in the intersection of the range of the map
5201 and the domain of the piecewise quasipolynomial reduction
5202 as a function of an element in the domain of the map.
5203 The functions taking a set compute a bound over all elements in the
5204 intersection of the set and the domain of the
5205 piecewise quasipolynomial reduction.
5209 #include <isl/set.h>
5210 __isl_give isl_basic_set *
5211 isl_basic_set_preimage_multi_aff(
5212 __isl_take isl_basic_set *bset,
5213 __isl_take isl_multi_aff *ma);
5214 __isl_give isl_set *isl_set_preimage_multi_aff(
5215 __isl_take isl_set *set,
5216 __isl_take isl_multi_aff *ma);
5217 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5218 __isl_take isl_set *set,
5219 __isl_take isl_pw_multi_aff *pma);
5220 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5221 __isl_take isl_set *set,
5222 __isl_take isl_multi_pw_aff *mpa);
5224 #include <isl/union_set.h>
5225 __isl_give isl_union_set *
5226 isl_union_set_preimage_multi_aff(
5227 __isl_take isl_union_set *uset,
5228 __isl_take isl_multi_aff *ma);
5229 __isl_give isl_union_set *
5230 isl_union_set_preimage_pw_multi_aff(
5231 __isl_take isl_union_set *uset,
5232 __isl_take isl_pw_multi_aff *pma);
5233 __isl_give isl_union_set *
5234 isl_union_set_preimage_union_pw_multi_aff(
5235 __isl_take isl_union_set *uset,
5236 __isl_take isl_union_pw_multi_aff *upma);
5238 #include <isl/map.h>
5239 __isl_give isl_basic_map *
5240 isl_basic_map_preimage_domain_multi_aff(
5241 __isl_take isl_basic_map *bmap,
5242 __isl_take isl_multi_aff *ma);
5243 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5244 __isl_take isl_map *map,
5245 __isl_take isl_multi_aff *ma);
5246 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5247 __isl_take isl_map *map,
5248 __isl_take isl_multi_aff *ma);
5249 __isl_give isl_map *
5250 isl_map_preimage_domain_pw_multi_aff(
5251 __isl_take isl_map *map,
5252 __isl_take isl_pw_multi_aff *pma);
5253 __isl_give isl_map *
5254 isl_map_preimage_range_pw_multi_aff(
5255 __isl_take isl_map *map,
5256 __isl_take isl_pw_multi_aff *pma);
5257 __isl_give isl_map *
5258 isl_map_preimage_domain_multi_pw_aff(
5259 __isl_take isl_map *map,
5260 __isl_take isl_multi_pw_aff *mpa);
5261 __isl_give isl_basic_map *
5262 isl_basic_map_preimage_range_multi_aff(
5263 __isl_take isl_basic_map *bmap,
5264 __isl_take isl_multi_aff *ma);
5266 #include <isl/union_map.h>
5267 __isl_give isl_union_map *
5268 isl_union_map_preimage_domain_multi_aff(
5269 __isl_take isl_union_map *umap,
5270 __isl_take isl_multi_aff *ma);
5271 __isl_give isl_union_map *
5272 isl_union_map_preimage_range_multi_aff(
5273 __isl_take isl_union_map *umap,
5274 __isl_take isl_multi_aff *ma);
5275 __isl_give isl_union_map *
5276 isl_union_map_preimage_domain_pw_multi_aff(
5277 __isl_take isl_union_map *umap,
5278 __isl_take isl_pw_multi_aff *pma);
5279 __isl_give isl_union_map *
5280 isl_union_map_preimage_range_pw_multi_aff(
5281 __isl_take isl_union_map *umap,
5282 __isl_take isl_pw_multi_aff *pma);
5283 __isl_give isl_union_map *
5284 isl_union_map_preimage_domain_union_pw_multi_aff(
5285 __isl_take isl_union_map *umap,
5286 __isl_take isl_union_pw_multi_aff *upma);
5287 __isl_give isl_union_map *
5288 isl_union_map_preimage_range_union_pw_multi_aff(
5289 __isl_take isl_union_map *umap,
5290 __isl_take isl_union_pw_multi_aff *upma);
5292 These functions compute the preimage of the given set or map domain/range under
5293 the given function. In other words, the expression is plugged
5294 into the set description or into the domain/range of the map.
5298 #include <isl/aff.h>
5299 __isl_give isl_aff *isl_aff_pullback_aff(
5300 __isl_take isl_aff *aff1,
5301 __isl_take isl_aff *aff2);
5302 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5303 __isl_take isl_aff *aff,
5304 __isl_take isl_multi_aff *ma);
5305 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5306 __isl_take isl_pw_aff *pa,
5307 __isl_take isl_multi_aff *ma);
5308 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5309 __isl_take isl_pw_aff *pa,
5310 __isl_take isl_pw_multi_aff *pma);
5311 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5312 __isl_take isl_pw_aff *pa,
5313 __isl_take isl_multi_pw_aff *mpa);
5314 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5315 __isl_take isl_multi_aff *ma1,
5316 __isl_take isl_multi_aff *ma2);
5317 __isl_give isl_pw_multi_aff *
5318 isl_pw_multi_aff_pullback_multi_aff(
5319 __isl_take isl_pw_multi_aff *pma,
5320 __isl_take isl_multi_aff *ma);
5321 __isl_give isl_multi_pw_aff *
5322 isl_multi_pw_aff_pullback_multi_aff(
5323 __isl_take isl_multi_pw_aff *mpa,
5324 __isl_take isl_multi_aff *ma);
5325 __isl_give isl_pw_multi_aff *
5326 isl_pw_multi_aff_pullback_pw_multi_aff(
5327 __isl_take isl_pw_multi_aff *pma1,
5328 __isl_take isl_pw_multi_aff *pma2);
5329 __isl_give isl_multi_pw_aff *
5330 isl_multi_pw_aff_pullback_pw_multi_aff(
5331 __isl_take isl_multi_pw_aff *mpa,
5332 __isl_take isl_pw_multi_aff *pma);
5333 __isl_give isl_multi_pw_aff *
5334 isl_multi_pw_aff_pullback_multi_pw_aff(
5335 __isl_take isl_multi_pw_aff *mpa1,
5336 __isl_take isl_multi_pw_aff *mpa2);
5338 These functions precompose the first expression by the second function.
5339 In other words, the second function is plugged
5340 into the first expression.
5344 #include <isl/aff.h>
5345 __isl_give isl_basic_set *isl_aff_le_basic_set(
5346 __isl_take isl_aff *aff1,
5347 __isl_take isl_aff *aff2);
5348 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5349 __isl_take isl_aff *aff1,
5350 __isl_take isl_aff *aff2);
5351 __isl_give isl_set *isl_pw_aff_eq_set(
5352 __isl_take isl_pw_aff *pwaff1,
5353 __isl_take isl_pw_aff *pwaff2);
5354 __isl_give isl_set *isl_pw_aff_ne_set(
5355 __isl_take isl_pw_aff *pwaff1,
5356 __isl_take isl_pw_aff *pwaff2);
5357 __isl_give isl_set *isl_pw_aff_le_set(
5358 __isl_take isl_pw_aff *pwaff1,
5359 __isl_take isl_pw_aff *pwaff2);
5360 __isl_give isl_set *isl_pw_aff_lt_set(
5361 __isl_take isl_pw_aff *pwaff1,
5362 __isl_take isl_pw_aff *pwaff2);
5363 __isl_give isl_set *isl_pw_aff_ge_set(
5364 __isl_take isl_pw_aff *pwaff1,
5365 __isl_take isl_pw_aff *pwaff2);
5366 __isl_give isl_set *isl_pw_aff_gt_set(
5367 __isl_take isl_pw_aff *pwaff1,
5368 __isl_take isl_pw_aff *pwaff2);
5370 __isl_give isl_set *isl_multi_aff_lex_le_set(
5371 __isl_take isl_multi_aff *ma1,
5372 __isl_take isl_multi_aff *ma2);
5373 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5374 __isl_take isl_multi_aff *ma1,
5375 __isl_take isl_multi_aff *ma2);
5377 __isl_give isl_set *isl_pw_aff_list_eq_set(
5378 __isl_take isl_pw_aff_list *list1,
5379 __isl_take isl_pw_aff_list *list2);
5380 __isl_give isl_set *isl_pw_aff_list_ne_set(
5381 __isl_take isl_pw_aff_list *list1,
5382 __isl_take isl_pw_aff_list *list2);
5383 __isl_give isl_set *isl_pw_aff_list_le_set(
5384 __isl_take isl_pw_aff_list *list1,
5385 __isl_take isl_pw_aff_list *list2);
5386 __isl_give isl_set *isl_pw_aff_list_lt_set(
5387 __isl_take isl_pw_aff_list *list1,
5388 __isl_take isl_pw_aff_list *list2);
5389 __isl_give isl_set *isl_pw_aff_list_ge_set(
5390 __isl_take isl_pw_aff_list *list1,
5391 __isl_take isl_pw_aff_list *list2);
5392 __isl_give isl_set *isl_pw_aff_list_gt_set(
5393 __isl_take isl_pw_aff_list *list1,
5394 __isl_take isl_pw_aff_list *list2);
5396 The function C<isl_aff_ge_basic_set> returns a basic set
5397 containing those elements in the shared space
5398 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5399 The function C<isl_pw_aff_ge_set> returns a set
5400 containing those elements in the shared domain
5401 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5402 greater than or equal to C<pwaff2>.
5403 The function C<isl_multi_aff_lex_le_set> returns a set
5404 containing those elements in the shared domain space
5405 where C<ma1> is lexicographically smaller than or
5407 The functions operating on C<isl_pw_aff_list> apply the corresponding
5408 C<isl_pw_aff> function to each pair of elements in the two lists.
5410 =item * Cartesian Product
5412 #include <isl/space.h>
5413 __isl_give isl_space *isl_space_product(
5414 __isl_take isl_space *space1,
5415 __isl_take isl_space *space2);
5416 __isl_give isl_space *isl_space_domain_product(
5417 __isl_take isl_space *space1,
5418 __isl_take isl_space *space2);
5419 __isl_give isl_space *isl_space_range_product(
5420 __isl_take isl_space *space1,
5421 __isl_take isl_space *space2);
5424 C<isl_space_product>, C<isl_space_domain_product>
5425 and C<isl_space_range_product> take pairs or relation spaces and
5426 produce a single relations space, where either the domain, the range
5427 or both domain and range are wrapped spaces of relations between
5428 the domains and/or ranges of the input spaces.
5429 If the product is only constructed over the domain or the range
5430 then the ranges or the domains of the inputs should be the same.
5431 The function C<isl_space_product> also accepts a pair of set spaces,
5432 in which case it returns a wrapped space of a relation between the
5435 #include <isl/set.h>
5436 __isl_give isl_set *isl_set_product(
5437 __isl_take isl_set *set1,
5438 __isl_take isl_set *set2);
5440 #include <isl/map.h>
5441 __isl_give isl_basic_map *isl_basic_map_domain_product(
5442 __isl_take isl_basic_map *bmap1,
5443 __isl_take isl_basic_map *bmap2);
5444 __isl_give isl_basic_map *isl_basic_map_range_product(
5445 __isl_take isl_basic_map *bmap1,
5446 __isl_take isl_basic_map *bmap2);
5447 __isl_give isl_basic_map *isl_basic_map_product(
5448 __isl_take isl_basic_map *bmap1,
5449 __isl_take isl_basic_map *bmap2);
5450 __isl_give isl_map *isl_map_domain_product(
5451 __isl_take isl_map *map1,
5452 __isl_take isl_map *map2);
5453 __isl_give isl_map *isl_map_range_product(
5454 __isl_take isl_map *map1,
5455 __isl_take isl_map *map2);
5456 __isl_give isl_map *isl_map_product(
5457 __isl_take isl_map *map1,
5458 __isl_take isl_map *map2);
5460 #include <isl/union_set.h>
5461 __isl_give isl_union_set *isl_union_set_product(
5462 __isl_take isl_union_set *uset1,
5463 __isl_take isl_union_set *uset2);
5465 #include <isl/union_map.h>
5466 __isl_give isl_union_map *isl_union_map_domain_product(
5467 __isl_take isl_union_map *umap1,
5468 __isl_take isl_union_map *umap2);
5469 __isl_give isl_union_map *isl_union_map_range_product(
5470 __isl_take isl_union_map *umap1,
5471 __isl_take isl_union_map *umap2);
5472 __isl_give isl_union_map *isl_union_map_product(
5473 __isl_take isl_union_map *umap1,
5474 __isl_take isl_union_map *umap2);
5476 #include <isl/val.h>
5477 __isl_give isl_multi_val *isl_multi_val_range_product(
5478 __isl_take isl_multi_val *mv1,
5479 __isl_take isl_multi_val *mv2);
5480 __isl_give isl_multi_val *isl_multi_val_product(
5481 __isl_take isl_multi_val *mv1,
5482 __isl_take isl_multi_val *mv2);
5484 #include <isl/aff.h>
5485 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5486 __isl_take isl_multi_aff *ma1,
5487 __isl_take isl_multi_aff *ma2);
5488 __isl_give isl_multi_aff *isl_multi_aff_product(
5489 __isl_take isl_multi_aff *ma1,
5490 __isl_take isl_multi_aff *ma2);
5491 __isl_give isl_multi_pw_aff *
5492 isl_multi_pw_aff_range_product(
5493 __isl_take isl_multi_pw_aff *mpa1,
5494 __isl_take isl_multi_pw_aff *mpa2);
5495 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5496 __isl_take isl_multi_pw_aff *mpa1,
5497 __isl_take isl_multi_pw_aff *mpa2);
5498 __isl_give isl_pw_multi_aff *
5499 isl_pw_multi_aff_range_product(
5500 __isl_take isl_pw_multi_aff *pma1,
5501 __isl_take isl_pw_multi_aff *pma2);
5502 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5503 __isl_take isl_pw_multi_aff *pma1,
5504 __isl_take isl_pw_multi_aff *pma2);
5506 The above functions compute the cross product of the given
5507 sets, relations or functions. The domains and ranges of the results
5508 are wrapped maps between domains and ranges of the inputs.
5509 To obtain a ``flat'' product, use the following functions
5512 #include <isl/set.h>
5513 __isl_give isl_basic_set *isl_basic_set_flat_product(
5514 __isl_take isl_basic_set *bset1,
5515 __isl_take isl_basic_set *bset2);
5516 __isl_give isl_set *isl_set_flat_product(
5517 __isl_take isl_set *set1,
5518 __isl_take isl_set *set2);
5520 #include <isl/map.h>
5521 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5522 __isl_take isl_basic_map *bmap1,
5523 __isl_take isl_basic_map *bmap2);
5524 __isl_give isl_map *isl_map_flat_domain_product(
5525 __isl_take isl_map *map1,
5526 __isl_take isl_map *map2);
5527 __isl_give isl_map *isl_map_flat_range_product(
5528 __isl_take isl_map *map1,
5529 __isl_take isl_map *map2);
5530 __isl_give isl_basic_map *isl_basic_map_flat_product(
5531 __isl_take isl_basic_map *bmap1,
5532 __isl_take isl_basic_map *bmap2);
5533 __isl_give isl_map *isl_map_flat_product(
5534 __isl_take isl_map *map1,
5535 __isl_take isl_map *map2);
5537 #include <isl/union_map.h>
5538 __isl_give isl_union_map *
5539 isl_union_map_flat_domain_product(
5540 __isl_take isl_union_map *umap1,
5541 __isl_take isl_union_map *umap2);
5542 __isl_give isl_union_map *
5543 isl_union_map_flat_range_product(
5544 __isl_take isl_union_map *umap1,
5545 __isl_take isl_union_map *umap2);
5547 #include <isl/val.h>
5548 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
5549 __isl_take isl_multi_val *mv1,
5550 __isl_take isl_multi_aff *mv2);
5552 #include <isl/aff.h>
5553 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
5554 __isl_take isl_multi_aff *ma1,
5555 __isl_take isl_multi_aff *ma2);
5556 __isl_give isl_pw_multi_aff *
5557 isl_pw_multi_aff_flat_range_product(
5558 __isl_take isl_pw_multi_aff *pma1,
5559 __isl_take isl_pw_multi_aff *pma2);
5560 __isl_give isl_multi_pw_aff *
5561 isl_multi_pw_aff_flat_range_product(
5562 __isl_take isl_multi_pw_aff *mpa1,
5563 __isl_take isl_multi_pw_aff *mpa2);
5564 __isl_give isl_union_pw_multi_aff *
5565 isl_union_pw_multi_aff_flat_range_product(
5566 __isl_take isl_union_pw_multi_aff *upma1,
5567 __isl_take isl_union_pw_multi_aff *upma2);
5569 #include <isl/space.h>
5570 __isl_give isl_space *isl_space_factor_domain(
5571 __isl_take isl_space *space);
5572 __isl_give isl_space *isl_space_factor_range(
5573 __isl_take isl_space *space);
5574 __isl_give isl_space *isl_space_domain_factor_domain(
5575 __isl_take isl_space *space);
5576 __isl_give isl_space *isl_space_domain_factor_range(
5577 __isl_take isl_space *space);
5578 __isl_give isl_space *isl_space_range_factor_domain(
5579 __isl_take isl_space *space);
5580 __isl_give isl_space *isl_space_range_factor_range(
5581 __isl_take isl_space *space);
5583 The functions C<isl_space_range_factor_domain> and
5584 C<isl_space_range_factor_range> extract the two arguments from
5585 the result of a call to C<isl_space_range_product>.
5587 The arguments of a call to C<isl_map_range_product> can be extracted
5588 from the result using the following functions.
5590 #include <isl/map.h>
5591 __isl_give isl_map *isl_map_factor_domain(
5592 __isl_take isl_map *map);
5593 __isl_give isl_map *isl_map_factor_range(
5594 __isl_take isl_map *map);
5595 __isl_give isl_map *isl_map_domain_factor_domain(
5596 __isl_take isl_map *map);
5597 __isl_give isl_map *isl_map_domain_factor_range(
5598 __isl_take isl_map *map);
5599 __isl_give isl_map *isl_map_range_factor_domain(
5600 __isl_take isl_map *map);
5601 __isl_give isl_map *isl_map_range_factor_range(
5602 __isl_take isl_map *map);
5604 #include <isl/union_map.h>
5605 __isl_give isl_union_map *isl_union_map_factor_domain(
5606 __isl_take isl_union_map *umap);
5607 __isl_give isl_union_map *isl_union_map_factor_range(
5608 __isl_take isl_union_map *umap);
5609 __isl_give isl_union_map *
5610 isl_union_map_domain_factor_domain(
5611 __isl_take isl_union_map *umap);
5612 __isl_give isl_union_map *
5613 isl_union_map_domain_factor_range(
5614 __isl_take isl_union_map *umap);
5615 __isl_give isl_union_map *
5616 isl_union_map_range_factor_range(
5617 __isl_take isl_union_map *umap);
5619 #include <isl/val.h>
5620 __isl_give isl_multi_val *
5621 isl_multi_val_range_factor_domain(
5622 __isl_take isl_multi_val *mv);
5623 __isl_give isl_multi_val *
5624 isl_multi_val_range_factor_range(
5625 __isl_take isl_multi_val *mv);
5627 #include <isl/aff.h>
5628 __isl_give isl_multi_aff *
5629 isl_multi_aff_range_factor_domain(
5630 __isl_take isl_multi_aff *ma);
5631 __isl_give isl_multi_aff *
5632 isl_multi_aff_range_factor_range(
5633 __isl_take isl_multi_aff *ma);
5634 __isl_give isl_multi_pw_aff *
5635 isl_multi_pw_aff_range_factor_domain(
5636 __isl_take isl_multi_pw_aff *mpa);
5637 __isl_give isl_multi_pw_aff *
5638 isl_multi_pw_aff_range_factor_range(
5639 __isl_take isl_multi_pw_aff *mpa);
5641 The splice functions are a generalization of the flat product functions,
5642 where the second argument may be inserted at any position inside
5643 the first argument rather than being placed at the end.
5645 #include <isl/val.h>
5646 __isl_give isl_multi_val *isl_multi_val_range_splice(
5647 __isl_take isl_multi_val *mv1, unsigned pos,
5648 __isl_take isl_multi_val *mv2);
5650 #include <isl/aff.h>
5651 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
5652 __isl_take isl_multi_aff *ma1, unsigned pos,
5653 __isl_take isl_multi_aff *ma2);
5654 __isl_give isl_multi_aff *isl_multi_aff_splice(
5655 __isl_take isl_multi_aff *ma1,
5656 unsigned in_pos, unsigned out_pos,
5657 __isl_take isl_multi_aff *ma2);
5658 __isl_give isl_multi_pw_aff *
5659 isl_multi_pw_aff_range_splice(
5660 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
5661 __isl_take isl_multi_pw_aff *mpa2);
5662 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
5663 __isl_take isl_multi_pw_aff *mpa1,
5664 unsigned in_pos, unsigned out_pos,
5665 __isl_take isl_multi_pw_aff *mpa2);
5667 =item * Simplification
5669 When applied to a set or relation,
5670 the gist operation returns a set or relation that has the
5671 same intersection with the context as the input set or relation.
5672 Any implicit equality in the intersection is made explicit in the result,
5673 while all inequalities that are redundant with respect to the intersection
5675 In case of union sets and relations, the gist operation is performed
5678 When applied to a function,
5679 the gist operation applies the set gist operation to each of
5680 the cells in the domain of the input piecewise expression.
5681 The context is also exploited
5682 to simplify the expression associated to each cell.
5684 #include <isl/set.h>
5685 __isl_give isl_basic_set *isl_basic_set_gist(
5686 __isl_take isl_basic_set *bset,
5687 __isl_take isl_basic_set *context);
5688 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
5689 __isl_take isl_set *context);
5690 __isl_give isl_set *isl_set_gist_params(
5691 __isl_take isl_set *set,
5692 __isl_take isl_set *context);
5694 #include <isl/map.h>
5695 __isl_give isl_basic_map *isl_basic_map_gist(
5696 __isl_take isl_basic_map *bmap,
5697 __isl_take isl_basic_map *context);
5698 __isl_give isl_basic_map *isl_basic_map_gist_domain(
5699 __isl_take isl_basic_map *bmap,
5700 __isl_take isl_basic_set *context);
5701 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
5702 __isl_take isl_map *context);
5703 __isl_give isl_map *isl_map_gist_params(
5704 __isl_take isl_map *map,
5705 __isl_take isl_set *context);
5706 __isl_give isl_map *isl_map_gist_domain(
5707 __isl_take isl_map *map,
5708 __isl_take isl_set *context);
5709 __isl_give isl_map *isl_map_gist_range(
5710 __isl_take isl_map *map,
5711 __isl_take isl_set *context);
5713 #include <isl/union_set.h>
5714 __isl_give isl_union_set *isl_union_set_gist(
5715 __isl_take isl_union_set *uset,
5716 __isl_take isl_union_set *context);
5717 __isl_give isl_union_set *isl_union_set_gist_params(
5718 __isl_take isl_union_set *uset,
5719 __isl_take isl_set *set);
5721 #include <isl/union_map.h>
5722 __isl_give isl_union_map *isl_union_map_gist(
5723 __isl_take isl_union_map *umap,
5724 __isl_take isl_union_map *context);
5725 __isl_give isl_union_map *isl_union_map_gist_params(
5726 __isl_take isl_union_map *umap,
5727 __isl_take isl_set *set);
5728 __isl_give isl_union_map *isl_union_map_gist_domain(
5729 __isl_take isl_union_map *umap,
5730 __isl_take isl_union_set *uset);
5731 __isl_give isl_union_map *isl_union_map_gist_range(
5732 __isl_take isl_union_map *umap,
5733 __isl_take isl_union_set *uset);
5735 #include <isl/aff.h>
5736 __isl_give isl_aff *isl_aff_gist_params(
5737 __isl_take isl_aff *aff,
5738 __isl_take isl_set *context);
5739 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
5740 __isl_take isl_set *context);
5741 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
5742 __isl_take isl_multi_aff *maff,
5743 __isl_take isl_set *context);
5744 __isl_give isl_multi_aff *isl_multi_aff_gist(
5745 __isl_take isl_multi_aff *maff,
5746 __isl_take isl_set *context);
5747 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
5748 __isl_take isl_pw_aff *pwaff,
5749 __isl_take isl_set *context);
5750 __isl_give isl_pw_aff *isl_pw_aff_gist(
5751 __isl_take isl_pw_aff *pwaff,
5752 __isl_take isl_set *context);
5753 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
5754 __isl_take isl_pw_multi_aff *pma,
5755 __isl_take isl_set *set);
5756 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
5757 __isl_take isl_pw_multi_aff *pma,
5758 __isl_take isl_set *set);
5759 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
5760 __isl_take isl_multi_pw_aff *mpa,
5761 __isl_take isl_set *set);
5762 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
5763 __isl_take isl_multi_pw_aff *mpa,
5764 __isl_take isl_set *set);
5765 __isl_give isl_union_pw_multi_aff *
5766 isl_union_pw_multi_aff_gist_params(
5767 __isl_take isl_union_pw_multi_aff *upma,
5768 __isl_take isl_set *context);
5769 __isl_give isl_union_pw_multi_aff *
5770 isl_union_pw_multi_aff_gist(
5771 __isl_take isl_union_pw_multi_aff *upma,
5772 __isl_take isl_union_set *context);
5774 #include <isl/polynomial.h>
5775 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5776 __isl_take isl_qpolynomial *qp,
5777 __isl_take isl_set *context);
5778 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5779 __isl_take isl_qpolynomial *qp,
5780 __isl_take isl_set *context);
5781 __isl_give isl_qpolynomial_fold *
5782 isl_qpolynomial_fold_gist_params(
5783 __isl_take isl_qpolynomial_fold *fold,
5784 __isl_take isl_set *context);
5785 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5786 __isl_take isl_qpolynomial_fold *fold,
5787 __isl_take isl_set *context);
5788 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5789 __isl_take isl_pw_qpolynomial *pwqp,
5790 __isl_take isl_set *context);
5791 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5792 __isl_take isl_pw_qpolynomial *pwqp,
5793 __isl_take isl_set *context);
5794 __isl_give isl_pw_qpolynomial_fold *
5795 isl_pw_qpolynomial_fold_gist(
5796 __isl_take isl_pw_qpolynomial_fold *pwf,
5797 __isl_take isl_set *context);
5798 __isl_give isl_pw_qpolynomial_fold *
5799 isl_pw_qpolynomial_fold_gist_params(
5800 __isl_take isl_pw_qpolynomial_fold *pwf,
5801 __isl_take isl_set *context);
5802 __isl_give isl_union_pw_qpolynomial *
5803 isl_union_pw_qpolynomial_gist_params(
5804 __isl_take isl_union_pw_qpolynomial *upwqp,
5805 __isl_take isl_set *context);
5806 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5807 __isl_take isl_union_pw_qpolynomial *upwqp,
5808 __isl_take isl_union_set *context);
5809 __isl_give isl_union_pw_qpolynomial_fold *
5810 isl_union_pw_qpolynomial_fold_gist(
5811 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5812 __isl_take isl_union_set *context);
5813 __isl_give isl_union_pw_qpolynomial_fold *
5814 isl_union_pw_qpolynomial_fold_gist_params(
5815 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5816 __isl_take isl_set *context);
5818 =item * Binary Arithmethic Operations
5820 #include <isl/aff.h>
5821 __isl_give isl_aff *isl_aff_add(
5822 __isl_take isl_aff *aff1,
5823 __isl_take isl_aff *aff2);
5824 __isl_give isl_multi_aff *isl_multi_aff_add(
5825 __isl_take isl_multi_aff *maff1,
5826 __isl_take isl_multi_aff *maff2);
5827 __isl_give isl_pw_aff *isl_pw_aff_add(
5828 __isl_take isl_pw_aff *pwaff1,
5829 __isl_take isl_pw_aff *pwaff2);
5830 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
5831 __isl_take isl_pw_multi_aff *pma1,
5832 __isl_take isl_pw_multi_aff *pma2);
5833 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
5834 __isl_take isl_union_pw_multi_aff *upma1,
5835 __isl_take isl_union_pw_multi_aff *upma2);
5836 __isl_give isl_pw_aff *isl_pw_aff_min(
5837 __isl_take isl_pw_aff *pwaff1,
5838 __isl_take isl_pw_aff *pwaff2);
5839 __isl_give isl_pw_aff *isl_pw_aff_max(
5840 __isl_take isl_pw_aff *pwaff1,
5841 __isl_take isl_pw_aff *pwaff2);
5842 __isl_give isl_aff *isl_aff_sub(
5843 __isl_take isl_aff *aff1,
5844 __isl_take isl_aff *aff2);
5845 __isl_give isl_multi_aff *isl_multi_aff_sub(
5846 __isl_take isl_multi_aff *ma1,
5847 __isl_take isl_multi_aff *ma2);
5848 __isl_give isl_pw_aff *isl_pw_aff_sub(
5849 __isl_take isl_pw_aff *pwaff1,
5850 __isl_take isl_pw_aff *pwaff2);
5851 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
5852 __isl_take isl_pw_multi_aff *pma1,
5853 __isl_take isl_pw_multi_aff *pma2);
5854 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
5855 __isl_take isl_union_pw_multi_aff *upma1,
5856 __isl_take isl_union_pw_multi_aff *upma2);
5858 C<isl_aff_sub> subtracts the second argument from the first.
5860 #include <isl/polynomial.h>
5861 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5862 __isl_take isl_qpolynomial *qp1,
5863 __isl_take isl_qpolynomial *qp2);
5864 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5865 __isl_take isl_pw_qpolynomial *pwqp1,
5866 __isl_take isl_pw_qpolynomial *pwqp2);
5867 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5868 __isl_take isl_pw_qpolynomial *pwqp1,
5869 __isl_take isl_pw_qpolynomial *pwqp2);
5870 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5871 __isl_take isl_pw_qpolynomial_fold *pwf1,
5872 __isl_take isl_pw_qpolynomial_fold *pwf2);
5873 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5874 __isl_take isl_union_pw_qpolynomial *upwqp1,
5875 __isl_take isl_union_pw_qpolynomial *upwqp2);
5876 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5877 __isl_take isl_qpolynomial *qp1,
5878 __isl_take isl_qpolynomial *qp2);
5879 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5880 __isl_take isl_pw_qpolynomial *pwqp1,
5881 __isl_take isl_pw_qpolynomial *pwqp2);
5882 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5883 __isl_take isl_union_pw_qpolynomial *upwqp1,
5884 __isl_take isl_union_pw_qpolynomial *upwqp2);
5885 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5886 __isl_take isl_pw_qpolynomial_fold *pwf1,
5887 __isl_take isl_pw_qpolynomial_fold *pwf2);
5888 __isl_give isl_union_pw_qpolynomial_fold *
5889 isl_union_pw_qpolynomial_fold_fold(
5890 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5891 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5893 #include <isl/aff.h>
5894 __isl_give isl_pw_aff *isl_pw_aff_union_add(
5895 __isl_take isl_pw_aff *pwaff1,
5896 __isl_take isl_pw_aff *pwaff2);
5897 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
5898 __isl_take isl_pw_multi_aff *pma1,
5899 __isl_take isl_pw_multi_aff *pma2);
5900 __isl_give isl_union_pw_multi_aff *
5901 isl_union_pw_multi_aff_union_add(
5902 __isl_take isl_union_pw_multi_aff *upma1,
5903 __isl_take isl_union_pw_multi_aff *upma2);
5904 __isl_give isl_pw_aff *isl_pw_aff_union_min(
5905 __isl_take isl_pw_aff *pwaff1,
5906 __isl_take isl_pw_aff *pwaff2);
5907 __isl_give isl_pw_aff *isl_pw_aff_union_max(
5908 __isl_take isl_pw_aff *pwaff1,
5909 __isl_take isl_pw_aff *pwaff2);
5911 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
5912 expression with a domain that is the union of those of C<pwaff1> and
5913 C<pwaff2> and such that on each cell, the quasi-affine expression is
5914 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
5915 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
5916 associated expression is the defined one.
5917 This in contrast to the C<isl_pw_aff_max> function, which is
5918 only defined on the shared definition domain of the arguments.
5920 #include <isl/val.h>
5921 __isl_give isl_multi_val *isl_multi_val_add_val(
5922 __isl_take isl_multi_val *mv,
5923 __isl_take isl_val *v);
5924 __isl_give isl_multi_val *isl_multi_val_mod_val(
5925 __isl_take isl_multi_val *mv,
5926 __isl_take isl_val *v);
5927 __isl_give isl_multi_val *isl_multi_val_scale_val(
5928 __isl_take isl_multi_val *mv,
5929 __isl_take isl_val *v);
5930 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
5931 __isl_take isl_multi_val *mv,
5932 __isl_take isl_val *v);
5934 #include <isl/aff.h>
5935 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
5936 __isl_take isl_val *mod);
5937 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
5938 __isl_take isl_pw_aff *pa,
5939 __isl_take isl_val *mod);
5940 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
5941 __isl_take isl_val *v);
5942 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
5943 __isl_take isl_multi_aff *ma,
5944 __isl_take isl_val *v);
5945 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
5946 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
5947 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
5948 __isl_take isl_multi_pw_aff *mpa,
5949 __isl_take isl_val *v);
5950 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
5951 __isl_take isl_pw_multi_aff *pma,
5952 __isl_take isl_val *v);
5953 __isl_give isl_union_pw_multi_aff *
5954 isl_union_pw_multi_aff_scale_val(
5955 __isl_take isl_union_pw_multi_aff *upma,
5956 __isl_take isl_val *val);
5957 __isl_give isl_aff *isl_aff_scale_down_ui(
5958 __isl_take isl_aff *aff, unsigned f);
5959 __isl_give isl_aff *isl_aff_scale_down_val(
5960 __isl_take isl_aff *aff, __isl_take isl_val *v);
5961 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
5962 __isl_take isl_multi_aff *ma,
5963 __isl_take isl_val *v);
5964 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
5965 __isl_take isl_pw_aff *pa,
5966 __isl_take isl_val *f);
5967 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
5968 __isl_take isl_multi_pw_aff *mpa,
5969 __isl_take isl_val *v);
5970 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
5971 __isl_take isl_pw_multi_aff *pma,
5972 __isl_take isl_val *v);
5973 __isl_give isl_union_pw_multi_aff *
5974 isl_union_pw_multi_aff_scale_down_val(
5975 __isl_take isl_union_pw_multi_aff *upma,
5976 __isl_take isl_val *val);
5978 #include <isl/polynomial.h>
5979 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5980 __isl_take isl_qpolynomial *qp,
5981 __isl_take isl_val *v);
5982 __isl_give isl_qpolynomial_fold *
5983 isl_qpolynomial_fold_scale_val(
5984 __isl_take isl_qpolynomial_fold *fold,
5985 __isl_take isl_val *v);
5986 __isl_give isl_pw_qpolynomial *
5987 isl_pw_qpolynomial_scale_val(
5988 __isl_take isl_pw_qpolynomial *pwqp,
5989 __isl_take isl_val *v);
5990 __isl_give isl_pw_qpolynomial_fold *
5991 isl_pw_qpolynomial_fold_scale_val(
5992 __isl_take isl_pw_qpolynomial_fold *pwf,
5993 __isl_take isl_val *v);
5994 __isl_give isl_union_pw_qpolynomial *
5995 isl_union_pw_qpolynomial_scale_val(
5996 __isl_take isl_union_pw_qpolynomial *upwqp,
5997 __isl_take isl_val *v);
5998 __isl_give isl_union_pw_qpolynomial_fold *
5999 isl_union_pw_qpolynomial_fold_scale_val(
6000 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6001 __isl_take isl_val *v);
6002 __isl_give isl_qpolynomial *
6003 isl_qpolynomial_scale_down_val(
6004 __isl_take isl_qpolynomial *qp,
6005 __isl_take isl_val *v);
6006 __isl_give isl_qpolynomial_fold *
6007 isl_qpolynomial_fold_scale_down_val(
6008 __isl_take isl_qpolynomial_fold *fold,
6009 __isl_take isl_val *v);
6010 __isl_give isl_pw_qpolynomial *
6011 isl_pw_qpolynomial_scale_down_val(
6012 __isl_take isl_pw_qpolynomial *pwqp,
6013 __isl_take isl_val *v);
6014 __isl_give isl_pw_qpolynomial_fold *
6015 isl_pw_qpolynomial_fold_scale_down_val(
6016 __isl_take isl_pw_qpolynomial_fold *pwf,
6017 __isl_take isl_val *v);
6018 __isl_give isl_union_pw_qpolynomial *
6019 isl_union_pw_qpolynomial_scale_down_val(
6020 __isl_take isl_union_pw_qpolynomial *upwqp,
6021 __isl_take isl_val *v);
6022 __isl_give isl_union_pw_qpolynomial_fold *
6023 isl_union_pw_qpolynomial_fold_scale_down_val(
6024 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6025 __isl_take isl_val *v);
6027 #include <isl/val.h>
6028 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6029 __isl_take isl_multi_val *mv1,
6030 __isl_take isl_multi_val *mv2);
6031 __isl_give isl_multi_val *
6032 isl_multi_val_scale_down_multi_val(
6033 __isl_take isl_multi_val *mv1,
6034 __isl_take isl_multi_val *mv2);
6036 #include <isl/aff.h>
6037 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6038 __isl_take isl_multi_aff *ma,
6039 __isl_take isl_multi_val *mv);
6040 __isl_give isl_pw_multi_aff *
6041 isl_pw_multi_aff_scale_multi_val(
6042 __isl_take isl_pw_multi_aff *pma,
6043 __isl_take isl_multi_val *mv);
6044 __isl_give isl_multi_pw_aff *
6045 isl_multi_pw_aff_scale_multi_val(
6046 __isl_take isl_multi_pw_aff *mpa,
6047 __isl_take isl_multi_val *mv);
6048 __isl_give isl_union_pw_multi_aff *
6049 isl_union_pw_multi_aff_scale_multi_val(
6050 __isl_take isl_union_pw_multi_aff *upma,
6051 __isl_take isl_multi_val *mv);
6052 __isl_give isl_multi_aff *
6053 isl_multi_aff_scale_down_multi_val(
6054 __isl_take isl_multi_aff *ma,
6055 __isl_take isl_multi_val *mv);
6056 __isl_give isl_multi_pw_aff *
6057 isl_multi_pw_aff_scale_down_multi_val(
6058 __isl_take isl_multi_pw_aff *mpa,
6059 __isl_take isl_multi_val *mv);
6061 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6062 by the corresponding elements of C<mv>.
6064 #include <isl/aff.h>
6065 __isl_give isl_aff *isl_aff_mul(
6066 __isl_take isl_aff *aff1,
6067 __isl_take isl_aff *aff2);
6068 __isl_give isl_aff *isl_aff_div(
6069 __isl_take isl_aff *aff1,
6070 __isl_take isl_aff *aff2);
6071 __isl_give isl_pw_aff *isl_pw_aff_mul(
6072 __isl_take isl_pw_aff *pwaff1,
6073 __isl_take isl_pw_aff *pwaff2);
6074 __isl_give isl_pw_aff *isl_pw_aff_div(
6075 __isl_take isl_pw_aff *pa1,
6076 __isl_take isl_pw_aff *pa2);
6077 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6078 __isl_take isl_pw_aff *pa1,
6079 __isl_take isl_pw_aff *pa2);
6080 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6081 __isl_take isl_pw_aff *pa1,
6082 __isl_take isl_pw_aff *pa2);
6084 When multiplying two affine expressions, at least one of the two needs
6085 to be a constant. Similarly, when dividing an affine expression by another,
6086 the second expression needs to be a constant.
6087 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6088 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6091 #include <isl/polynomial.h>
6092 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6093 __isl_take isl_qpolynomial *qp1,
6094 __isl_take isl_qpolynomial *qp2);
6095 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6096 __isl_take isl_pw_qpolynomial *pwqp1,
6097 __isl_take isl_pw_qpolynomial *pwqp2);
6098 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6099 __isl_take isl_union_pw_qpolynomial *upwqp1,
6100 __isl_take isl_union_pw_qpolynomial *upwqp2);
6104 =head3 Lexicographic Optimization
6106 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6107 the following functions
6108 compute a set that contains the lexicographic minimum or maximum
6109 of the elements in C<set> (or C<bset>) for those values of the parameters
6110 that satisfy C<dom>.
6111 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6112 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6114 In other words, the union of the parameter values
6115 for which the result is non-empty and of C<*empty>
6118 #include <isl/set.h>
6119 __isl_give isl_set *isl_basic_set_partial_lexmin(
6120 __isl_take isl_basic_set *bset,
6121 __isl_take isl_basic_set *dom,
6122 __isl_give isl_set **empty);
6123 __isl_give isl_set *isl_basic_set_partial_lexmax(
6124 __isl_take isl_basic_set *bset,
6125 __isl_take isl_basic_set *dom,
6126 __isl_give isl_set **empty);
6127 __isl_give isl_set *isl_set_partial_lexmin(
6128 __isl_take isl_set *set, __isl_take isl_set *dom,
6129 __isl_give isl_set **empty);
6130 __isl_give isl_set *isl_set_partial_lexmax(
6131 __isl_take isl_set *set, __isl_take isl_set *dom,
6132 __isl_give isl_set **empty);
6134 Given a (basic) set C<set> (or C<bset>), the following functions simply
6135 return a set containing the lexicographic minimum or maximum
6136 of the elements in C<set> (or C<bset>).
6137 In case of union sets, the optimum is computed per space.
6139 #include <isl/set.h>
6140 __isl_give isl_set *isl_basic_set_lexmin(
6141 __isl_take isl_basic_set *bset);
6142 __isl_give isl_set *isl_basic_set_lexmax(
6143 __isl_take isl_basic_set *bset);
6144 __isl_give isl_set *isl_set_lexmin(
6145 __isl_take isl_set *set);
6146 __isl_give isl_set *isl_set_lexmax(
6147 __isl_take isl_set *set);
6148 __isl_give isl_union_set *isl_union_set_lexmin(
6149 __isl_take isl_union_set *uset);
6150 __isl_give isl_union_set *isl_union_set_lexmax(
6151 __isl_take isl_union_set *uset);
6153 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6154 the following functions
6155 compute a relation that maps each element of C<dom>
6156 to the single lexicographic minimum or maximum
6157 of the elements that are associated to that same
6158 element in C<map> (or C<bmap>).
6159 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6160 that contains the elements in C<dom> that do not map
6161 to any elements in C<map> (or C<bmap>).
6162 In other words, the union of the domain of the result and of C<*empty>
6165 #include <isl/map.h>
6166 __isl_give isl_map *isl_basic_map_partial_lexmax(
6167 __isl_take isl_basic_map *bmap,
6168 __isl_take isl_basic_set *dom,
6169 __isl_give isl_set **empty);
6170 __isl_give isl_map *isl_basic_map_partial_lexmin(
6171 __isl_take isl_basic_map *bmap,
6172 __isl_take isl_basic_set *dom,
6173 __isl_give isl_set **empty);
6174 __isl_give isl_map *isl_map_partial_lexmax(
6175 __isl_take isl_map *map, __isl_take isl_set *dom,
6176 __isl_give isl_set **empty);
6177 __isl_give isl_map *isl_map_partial_lexmin(
6178 __isl_take isl_map *map, __isl_take isl_set *dom,
6179 __isl_give isl_set **empty);
6181 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6182 return a map mapping each element in the domain of
6183 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6184 of all elements associated to that element.
6185 In case of union relations, the optimum is computed per space.
6187 #include <isl/map.h>
6188 __isl_give isl_map *isl_basic_map_lexmin(
6189 __isl_take isl_basic_map *bmap);
6190 __isl_give isl_map *isl_basic_map_lexmax(
6191 __isl_take isl_basic_map *bmap);
6192 __isl_give isl_map *isl_map_lexmin(
6193 __isl_take isl_map *map);
6194 __isl_give isl_map *isl_map_lexmax(
6195 __isl_take isl_map *map);
6196 __isl_give isl_union_map *isl_union_map_lexmin(
6197 __isl_take isl_union_map *umap);
6198 __isl_give isl_union_map *isl_union_map_lexmax(
6199 __isl_take isl_union_map *umap);
6201 The following functions return their result in the form of
6202 a piecewise multi-affine expression,
6203 but are otherwise equivalent to the corresponding functions
6204 returning a basic set or relation.
6206 #include <isl/set.h>
6207 __isl_give isl_pw_multi_aff *
6208 isl_basic_set_partial_lexmin_pw_multi_aff(
6209 __isl_take isl_basic_set *bset,
6210 __isl_take isl_basic_set *dom,
6211 __isl_give isl_set **empty);
6212 __isl_give isl_pw_multi_aff *
6213 isl_basic_set_partial_lexmax_pw_multi_aff(
6214 __isl_take isl_basic_set *bset,
6215 __isl_take isl_basic_set *dom,
6216 __isl_give isl_set **empty);
6217 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6218 __isl_take isl_set *set);
6219 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6220 __isl_take isl_set *set);
6222 #include <isl/map.h>
6223 __isl_give isl_pw_multi_aff *
6224 isl_basic_map_lexmin_pw_multi_aff(
6225 __isl_take isl_basic_map *bmap);
6226 __isl_give isl_pw_multi_aff *
6227 isl_basic_map_partial_lexmin_pw_multi_aff(
6228 __isl_take isl_basic_map *bmap,
6229 __isl_take isl_basic_set *dom,
6230 __isl_give isl_set **empty);
6231 __isl_give isl_pw_multi_aff *
6232 isl_basic_map_partial_lexmax_pw_multi_aff(
6233 __isl_take isl_basic_map *bmap,
6234 __isl_take isl_basic_set *dom,
6235 __isl_give isl_set **empty);
6236 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6237 __isl_take isl_map *map);
6238 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6239 __isl_take isl_map *map);
6241 The following functions return the lexicographic minimum or maximum
6242 on the shared domain of the inputs and the single defined function
6243 on those parts of the domain where only a single function is defined.
6245 #include <isl/aff.h>
6246 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6247 __isl_take isl_pw_multi_aff *pma1,
6248 __isl_take isl_pw_multi_aff *pma2);
6249 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6250 __isl_take isl_pw_multi_aff *pma1,
6251 __isl_take isl_pw_multi_aff *pma2);
6253 =head2 Ternary Operations
6255 #include <isl/aff.h>
6256 __isl_give isl_pw_aff *isl_pw_aff_cond(
6257 __isl_take isl_pw_aff *cond,
6258 __isl_take isl_pw_aff *pwaff_true,
6259 __isl_take isl_pw_aff *pwaff_false);
6261 The function C<isl_pw_aff_cond> performs a conditional operator
6262 and returns an expression that is equal to C<pwaff_true>
6263 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6264 where C<cond> is zero.
6268 Lists are defined over several element types, including
6269 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>,
6270 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6271 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6272 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6273 Here we take lists of C<isl_set>s as an example.
6274 Lists can be created, copied, modified and freed using the following functions.
6276 #include <isl/set.h>
6277 __isl_give isl_set_list *isl_set_list_from_set(
6278 __isl_take isl_set *el);
6279 __isl_give isl_set_list *isl_set_list_alloc(
6280 isl_ctx *ctx, int n);
6281 __isl_give isl_set_list *isl_set_list_copy(
6282 __isl_keep isl_set_list *list);
6283 __isl_give isl_set_list *isl_set_list_insert(
6284 __isl_take isl_set_list *list, unsigned pos,
6285 __isl_take isl_set *el);
6286 __isl_give isl_set_list *isl_set_list_add(
6287 __isl_take isl_set_list *list,
6288 __isl_take isl_set *el);
6289 __isl_give isl_set_list *isl_set_list_drop(
6290 __isl_take isl_set_list *list,
6291 unsigned first, unsigned n);
6292 __isl_give isl_set_list *isl_set_list_set_set(
6293 __isl_take isl_set_list *list, int index,
6294 __isl_take isl_set *set);
6295 __isl_give isl_set_list *isl_set_list_concat(
6296 __isl_take isl_set_list *list1,
6297 __isl_take isl_set_list *list2);
6298 __isl_give isl_set_list *isl_set_list_sort(
6299 __isl_take isl_set_list *list,
6300 int (*cmp)(__isl_keep isl_set *a,
6301 __isl_keep isl_set *b, void *user),
6303 __isl_null isl_set_list *isl_set_list_free(
6304 __isl_take isl_set_list *list);
6306 C<isl_set_list_alloc> creates an empty list with a capacity for
6307 C<n> elements. C<isl_set_list_from_set> creates a list with a single
6310 Lists can be inspected using the following functions.
6312 #include <isl/set.h>
6313 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6314 __isl_give isl_set *isl_set_list_get_set(
6315 __isl_keep isl_set_list *list, int index);
6316 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6317 int (*fn)(__isl_take isl_set *el, void *user),
6319 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6320 int (*follows)(__isl_keep isl_set *a,
6321 __isl_keep isl_set *b, void *user),
6323 int (*fn)(__isl_take isl_set *el, void *user),
6326 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6327 strongly connected components of the graph with as vertices the elements
6328 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6329 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6330 should return C<-1> on error.
6332 Lists can be printed using
6334 #include <isl/set.h>
6335 __isl_give isl_printer *isl_printer_print_set_list(
6336 __isl_take isl_printer *p,
6337 __isl_keep isl_set_list *list);
6339 =head2 Associative arrays
6341 Associative arrays map isl objects of a specific type to isl objects
6342 of some (other) specific type. They are defined for several pairs
6343 of types, including (C<isl_map>, C<isl_basic_set>),
6344 (C<isl_id>, C<isl_ast_expr>) and.
6345 (C<isl_id>, C<isl_pw_aff>).
6346 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6349 Associative arrays can be created, copied and freed using
6350 the following functions.
6352 #include <isl/id_to_ast_expr.h>
6353 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6354 isl_ctx *ctx, int min_size);
6355 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6356 __isl_keep id_to_ast_expr *id2expr);
6357 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6358 __isl_take id_to_ast_expr *id2expr);
6360 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6361 to specify the expected size of the associative array.
6362 The associative array will be grown automatically as needed.
6364 Associative arrays can be inspected using the following functions.
6366 #include <isl/id_to_ast_expr.h>
6367 int isl_id_to_ast_expr_has(
6368 __isl_keep id_to_ast_expr *id2expr,
6369 __isl_keep isl_id *key);
6370 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6371 __isl_keep id_to_ast_expr *id2expr,
6372 __isl_take isl_id *key);
6373 int isl_id_to_ast_expr_foreach(
6374 __isl_keep id_to_ast_expr *id2expr,
6375 int (*fn)(__isl_take isl_id *key,
6376 __isl_take isl_ast_expr *val, void *user),
6379 They can be modified using the following function.
6381 #include <isl/id_to_ast_expr.h>
6382 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6383 __isl_take id_to_ast_expr *id2expr,
6384 __isl_take isl_id *key,
6385 __isl_take isl_ast_expr *val);
6386 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6387 __isl_take id_to_ast_expr *id2expr,
6388 __isl_take isl_id *key);
6390 Associative arrays can be printed using the following function.
6392 #include <isl/id_to_ast_expr.h>
6393 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6394 __isl_take isl_printer *p,
6395 __isl_keep id_to_ast_expr *id2expr);
6399 Vectors can be created, copied and freed using the following functions.
6401 #include <isl/vec.h>
6402 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6404 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6405 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6407 Note that the elements of a newly created vector may have arbitrary values.
6408 The elements can be changed and inspected using the following functions.
6410 int isl_vec_size(__isl_keep isl_vec *vec);
6411 __isl_give isl_val *isl_vec_get_element_val(
6412 __isl_keep isl_vec *vec, int pos);
6413 __isl_give isl_vec *isl_vec_set_element_si(
6414 __isl_take isl_vec *vec, int pos, int v);
6415 __isl_give isl_vec *isl_vec_set_element_val(
6416 __isl_take isl_vec *vec, int pos,
6417 __isl_take isl_val *v);
6418 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6420 __isl_give isl_vec *isl_vec_set_val(
6421 __isl_take isl_vec *vec, __isl_take isl_val *v);
6422 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6423 __isl_keep isl_vec *vec2, int pos);
6425 C<isl_vec_get_element> will return a negative value if anything went wrong.
6426 In that case, the value of C<*v> is undefined.
6428 The following function can be used to concatenate two vectors.
6430 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6431 __isl_take isl_vec *vec2);
6435 Matrices can be created, copied and freed using the following functions.
6437 #include <isl/mat.h>
6438 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6439 unsigned n_row, unsigned n_col);
6440 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6441 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6443 Note that the elements of a newly created matrix may have arbitrary values.
6444 The elements can be changed and inspected using the following functions.
6446 int isl_mat_rows(__isl_keep isl_mat *mat);
6447 int isl_mat_cols(__isl_keep isl_mat *mat);
6448 __isl_give isl_val *isl_mat_get_element_val(
6449 __isl_keep isl_mat *mat, int row, int col);
6450 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
6451 int row, int col, int v);
6452 __isl_give isl_mat *isl_mat_set_element_val(
6453 __isl_take isl_mat *mat, int row, int col,
6454 __isl_take isl_val *v);
6456 C<isl_mat_get_element> will return a negative value if anything went wrong.
6457 In that case, the value of C<*v> is undefined.
6459 The following function can be used to compute the (right) inverse
6460 of a matrix, i.e., a matrix such that the product of the original
6461 and the inverse (in that order) is a multiple of the identity matrix.
6462 The input matrix is assumed to be of full row-rank.
6464 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
6466 The following function can be used to compute the (right) kernel
6467 (or null space) of a matrix, i.e., a matrix such that the product of
6468 the original and the kernel (in that order) is the zero matrix.
6470 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
6472 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
6474 The following functions determine
6475 an upper or lower bound on a quasipolynomial over its domain.
6477 __isl_give isl_pw_qpolynomial_fold *
6478 isl_pw_qpolynomial_bound(
6479 __isl_take isl_pw_qpolynomial *pwqp,
6480 enum isl_fold type, int *tight);
6482 __isl_give isl_union_pw_qpolynomial_fold *
6483 isl_union_pw_qpolynomial_bound(
6484 __isl_take isl_union_pw_qpolynomial *upwqp,
6485 enum isl_fold type, int *tight);
6487 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
6488 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
6489 is the returned bound is known be tight, i.e., for each value
6490 of the parameters there is at least
6491 one element in the domain that reaches the bound.
6492 If the domain of C<pwqp> is not wrapping, then the bound is computed
6493 over all elements in that domain and the result has a purely parametric
6494 domain. If the domain of C<pwqp> is wrapping, then the bound is
6495 computed over the range of the wrapped relation. The domain of the
6496 wrapped relation becomes the domain of the result.
6498 =head2 Parametric Vertex Enumeration
6500 The parametric vertex enumeration described in this section
6501 is mainly intended to be used internally and by the C<barvinok>
6504 #include <isl/vertices.h>
6505 __isl_give isl_vertices *isl_basic_set_compute_vertices(
6506 __isl_keep isl_basic_set *bset);
6508 The function C<isl_basic_set_compute_vertices> performs the
6509 actual computation of the parametric vertices and the chamber
6510 decomposition and store the result in an C<isl_vertices> object.
6511 This information can be queried by either iterating over all
6512 the vertices or iterating over all the chambers or cells
6513 and then iterating over all vertices that are active on the chamber.
6515 int isl_vertices_foreach_vertex(
6516 __isl_keep isl_vertices *vertices,
6517 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6520 int isl_vertices_foreach_cell(
6521 __isl_keep isl_vertices *vertices,
6522 int (*fn)(__isl_take isl_cell *cell, void *user),
6524 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
6525 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6528 Other operations that can be performed on an C<isl_vertices> object are
6531 int isl_vertices_get_n_vertices(
6532 __isl_keep isl_vertices *vertices);
6533 void isl_vertices_free(__isl_take isl_vertices *vertices);
6535 Vertices can be inspected and destroyed using the following functions.
6537 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
6538 __isl_give isl_basic_set *isl_vertex_get_domain(
6539 __isl_keep isl_vertex *vertex);
6540 __isl_give isl_multi_aff *isl_vertex_get_expr(
6541 __isl_keep isl_vertex *vertex);
6542 void isl_vertex_free(__isl_take isl_vertex *vertex);
6544 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
6545 describing the vertex in terms of the parameters,
6546 while C<isl_vertex_get_domain> returns the activity domain
6549 Chambers can be inspected and destroyed using the following functions.
6551 __isl_give isl_basic_set *isl_cell_get_domain(
6552 __isl_keep isl_cell *cell);
6553 void isl_cell_free(__isl_take isl_cell *cell);
6555 =head1 Polyhedral Compilation Library
6557 This section collects functionality in C<isl> that has been specifically
6558 designed for use during polyhedral compilation.
6560 =head2 Dependence Analysis
6562 C<isl> contains specialized functionality for performing
6563 array dataflow analysis. That is, given a I<sink> access relation
6564 and a collection of possible I<source> access relations,
6565 C<isl> can compute relations that describe
6566 for each iteration of the sink access, which iteration
6567 of which of the source access relations was the last
6568 to access the same data element before the given iteration
6570 The resulting dependence relations map source iterations
6571 to the corresponding sink iterations.
6572 To compute standard flow dependences, the sink should be
6573 a read, while the sources should be writes.
6574 If any of the source accesses are marked as being I<may>
6575 accesses, then there will be a dependence from the last
6576 I<must> access B<and> from any I<may> access that follows
6577 this last I<must> access.
6578 In particular, if I<all> sources are I<may> accesses,
6579 then memory based dependence analysis is performed.
6580 If, on the other hand, all sources are I<must> accesses,
6581 then value based dependence analysis is performed.
6583 #include <isl/flow.h>
6585 typedef int (*isl_access_level_before)(void *first, void *second);
6587 __isl_give isl_access_info *isl_access_info_alloc(
6588 __isl_take isl_map *sink,
6589 void *sink_user, isl_access_level_before fn,
6591 __isl_give isl_access_info *isl_access_info_add_source(
6592 __isl_take isl_access_info *acc,
6593 __isl_take isl_map *source, int must,
6595 __isl_null isl_access_info *isl_access_info_free(
6596 __isl_take isl_access_info *acc);
6598 __isl_give isl_flow *isl_access_info_compute_flow(
6599 __isl_take isl_access_info *acc);
6601 int isl_flow_foreach(__isl_keep isl_flow *deps,
6602 int (*fn)(__isl_take isl_map *dep, int must,
6603 void *dep_user, void *user),
6605 __isl_give isl_map *isl_flow_get_no_source(
6606 __isl_keep isl_flow *deps, int must);
6607 void isl_flow_free(__isl_take isl_flow *deps);
6609 The function C<isl_access_info_compute_flow> performs the actual
6610 dependence analysis. The other functions are used to construct
6611 the input for this function or to read off the output.
6613 The input is collected in an C<isl_access_info>, which can
6614 be created through a call to C<isl_access_info_alloc>.
6615 The arguments to this functions are the sink access relation
6616 C<sink>, a token C<sink_user> used to identify the sink
6617 access to the user, a callback function for specifying the
6618 relative order of source and sink accesses, and the number
6619 of source access relations that will be added.
6620 The callback function has type C<int (*)(void *first, void *second)>.
6621 The function is called with two user supplied tokens identifying
6622 either a source or the sink and it should return the shared nesting
6623 level and the relative order of the two accesses.
6624 In particular, let I<n> be the number of loops shared by
6625 the two accesses. If C<first> precedes C<second> textually,
6626 then the function should return I<2 * n + 1>; otherwise,
6627 it should return I<2 * n>.
6628 The sources can be added to the C<isl_access_info> by performing
6629 (at most) C<max_source> calls to C<isl_access_info_add_source>.
6630 C<must> indicates whether the source is a I<must> access
6631 or a I<may> access. Note that a multi-valued access relation
6632 should only be marked I<must> if every iteration in the domain
6633 of the relation accesses I<all> elements in its image.
6634 The C<source_user> token is again used to identify
6635 the source access. The range of the source access relation
6636 C<source> should have the same dimension as the range
6637 of the sink access relation.
6638 The C<isl_access_info_free> function should usually not be
6639 called explicitly, because it is called implicitly by
6640 C<isl_access_info_compute_flow>.
6642 The result of the dependence analysis is collected in an
6643 C<isl_flow>. There may be elements of
6644 the sink access for which no preceding source access could be
6645 found or for which all preceding sources are I<may> accesses.
6646 The relations containing these elements can be obtained through
6647 calls to C<isl_flow_get_no_source>, the first with C<must> set
6648 and the second with C<must> unset.
6649 In the case of standard flow dependence analysis,
6650 with the sink a read and the sources I<must> writes,
6651 the first relation corresponds to the reads from uninitialized
6652 array elements and the second relation is empty.
6653 The actual flow dependences can be extracted using
6654 C<isl_flow_foreach>. This function will call the user-specified
6655 callback function C<fn> for each B<non-empty> dependence between
6656 a source and the sink. The callback function is called
6657 with four arguments, the actual flow dependence relation
6658 mapping source iterations to sink iterations, a boolean that
6659 indicates whether it is a I<must> or I<may> dependence, a token
6660 identifying the source and an additional C<void *> with value
6661 equal to the third argument of the C<isl_flow_foreach> call.
6662 A dependence is marked I<must> if it originates from a I<must>
6663 source and if it is not followed by any I<may> sources.
6665 After finishing with an C<isl_flow>, the user should call
6666 C<isl_flow_free> to free all associated memory.
6668 A higher-level interface to dependence analysis is provided
6669 by the following function.
6671 #include <isl/flow.h>
6673 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
6674 __isl_take isl_union_map *must_source,
6675 __isl_take isl_union_map *may_source,
6676 __isl_take isl_union_map *schedule,
6677 __isl_give isl_union_map **must_dep,
6678 __isl_give isl_union_map **may_dep,
6679 __isl_give isl_union_map **must_no_source,
6680 __isl_give isl_union_map **may_no_source);
6682 The arrays are identified by the tuple names of the ranges
6683 of the accesses. The iteration domains by the tuple names
6684 of the domains of the accesses and of the schedule.
6685 The relative order of the iteration domains is given by the
6686 schedule. The relations returned through C<must_no_source>
6687 and C<may_no_source> are subsets of C<sink>.
6688 Any of C<must_dep>, C<may_dep>, C<must_no_source>
6689 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
6690 any of the other arguments is treated as an error.
6692 =head3 Interaction with Dependence Analysis
6694 During the dependence analysis, we frequently need to perform
6695 the following operation. Given a relation between sink iterations
6696 and potential source iterations from a particular source domain,
6697 what is the last potential source iteration corresponding to each
6698 sink iteration. It can sometimes be convenient to adjust
6699 the set of potential source iterations before or after each such operation.
6700 The prototypical example is fuzzy array dataflow analysis,
6701 where we need to analyze if, based on data-dependent constraints,
6702 the sink iteration can ever be executed without one or more of
6703 the corresponding potential source iterations being executed.
6704 If so, we can introduce extra parameters and select an unknown
6705 but fixed source iteration from the potential source iterations.
6706 To be able to perform such manipulations, C<isl> provides the following
6709 #include <isl/flow.h>
6711 typedef __isl_give isl_restriction *(*isl_access_restrict)(
6712 __isl_keep isl_map *source_map,
6713 __isl_keep isl_set *sink, void *source_user,
6715 __isl_give isl_access_info *isl_access_info_set_restrict(
6716 __isl_take isl_access_info *acc,
6717 isl_access_restrict fn, void *user);
6719 The function C<isl_access_info_set_restrict> should be called
6720 before calling C<isl_access_info_compute_flow> and registers a callback function
6721 that will be called any time C<isl> is about to compute the last
6722 potential source. The first argument is the (reverse) proto-dependence,
6723 mapping sink iterations to potential source iterations.
6724 The second argument represents the sink iterations for which
6725 we want to compute the last source iteration.
6726 The third argument is the token corresponding to the source
6727 and the final argument is the token passed to C<isl_access_info_set_restrict>.
6728 The callback is expected to return a restriction on either the input or
6729 the output of the operation computing the last potential source.
6730 If the input needs to be restricted then restrictions are needed
6731 for both the source and the sink iterations. The sink iterations
6732 and the potential source iterations will be intersected with these sets.
6733 If the output needs to be restricted then only a restriction on the source
6734 iterations is required.
6735 If any error occurs, the callback should return C<NULL>.
6736 An C<isl_restriction> object can be created, freed and inspected
6737 using the following functions.
6739 #include <isl/flow.h>
6741 __isl_give isl_restriction *isl_restriction_input(
6742 __isl_take isl_set *source_restr,
6743 __isl_take isl_set *sink_restr);
6744 __isl_give isl_restriction *isl_restriction_output(
6745 __isl_take isl_set *source_restr);
6746 __isl_give isl_restriction *isl_restriction_none(
6747 __isl_take isl_map *source_map);
6748 __isl_give isl_restriction *isl_restriction_empty(
6749 __isl_take isl_map *source_map);
6750 __isl_null isl_restriction *isl_restriction_free(
6751 __isl_take isl_restriction *restr);
6753 C<isl_restriction_none> and C<isl_restriction_empty> are special
6754 cases of C<isl_restriction_input>. C<isl_restriction_none>
6755 is essentially equivalent to
6757 isl_restriction_input(isl_set_universe(
6758 isl_space_range(isl_map_get_space(source_map))),
6760 isl_space_domain(isl_map_get_space(source_map))));
6762 whereas C<isl_restriction_empty> is essentially equivalent to
6764 isl_restriction_input(isl_set_empty(
6765 isl_space_range(isl_map_get_space(source_map))),
6767 isl_space_domain(isl_map_get_space(source_map))));
6771 B<The functionality described in this section is fairly new
6772 and may be subject to change.>
6774 #include <isl/schedule.h>
6775 __isl_give isl_schedule *
6776 isl_schedule_constraints_compute_schedule(
6777 __isl_take isl_schedule_constraints *sc);
6778 __isl_null isl_schedule *isl_schedule_free(
6779 __isl_take isl_schedule *sched);
6781 The function C<isl_schedule_constraints_compute_schedule> can be
6782 used to compute a schedule that satisfies the given schedule constraints.
6783 These schedule constraints include the iteration domain for which
6784 a schedule should be computed and dependences between pairs of
6785 iterations. In particular, these dependences include
6786 I<validity> dependences and I<proximity> dependences.
6787 By default, the algorithm used to construct the schedule is similar
6788 to that of C<Pluto>.
6789 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6791 The generated schedule respects all validity dependences.
6792 That is, all dependence distances over these dependences in the
6793 scheduled space are lexicographically positive.
6794 The default algorithm tries to ensure that the dependence distances
6795 over coincidence constraints are zero and to minimize the
6796 dependence distances over proximity dependences.
6797 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6798 for groups of domains where the dependence distances over validity
6799 dependences have only non-negative values.
6800 When using Feautrier's algorithm, the coincidence and proximity constraints
6801 are only taken into account during the extension to a
6802 full-dimensional schedule.
6804 An C<isl_schedule_constraints> object can be constructed
6805 and manipulated using the following functions.
6807 #include <isl/schedule.h>
6808 __isl_give isl_schedule_constraints *
6809 isl_schedule_constraints_copy(
6810 __isl_keep isl_schedule_constraints *sc);
6811 __isl_give isl_schedule_constraints *
6812 isl_schedule_constraints_on_domain(
6813 __isl_take isl_union_set *domain);
6814 __isl_give isl_schedule_constraints *
6815 isl_schedule_constraints_set_validity(
6816 __isl_take isl_schedule_constraints *sc,
6817 __isl_take isl_union_map *validity);
6818 __isl_give isl_schedule_constraints *
6819 isl_schedule_constraints_set_coincidence(
6820 __isl_take isl_schedule_constraints *sc,
6821 __isl_take isl_union_map *coincidence);
6822 __isl_give isl_schedule_constraints *
6823 isl_schedule_constraints_set_proximity(
6824 __isl_take isl_schedule_constraints *sc,
6825 __isl_take isl_union_map *proximity);
6826 __isl_give isl_schedule_constraints *
6827 isl_schedule_constraints_set_conditional_validity(
6828 __isl_take isl_schedule_constraints *sc,
6829 __isl_take isl_union_map *condition,
6830 __isl_take isl_union_map *validity);
6831 __isl_null isl_schedule_constraints *
6832 isl_schedule_constraints_free(
6833 __isl_take isl_schedule_constraints *sc);
6835 The initial C<isl_schedule_constraints> object created by
6836 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6837 That is, it has an empty set of dependences.
6838 The function C<isl_schedule_constraints_set_validity> replaces the
6839 validity dependences, mapping domain elements I<i> to domain
6840 elements that should be scheduled after I<i>.
6841 The function C<isl_schedule_constraints_set_coincidence> replaces the
6842 coincidence dependences, mapping domain elements I<i> to domain
6843 elements that should be scheduled together with I<I>, if possible.
6844 The function C<isl_schedule_constraints_set_proximity> replaces the
6845 proximity dependences, mapping domain elements I<i> to domain
6846 elements that should be scheduled either before I<I>
6847 or as early as possible after I<i>.
6849 The function C<isl_schedule_constraints_set_conditional_validity>
6850 replaces the conditional validity constraints.
6851 A conditional validity constraint is only imposed when any of the corresponding
6852 conditions is satisfied, i.e., when any of them is non-zero.
6853 That is, the scheduler ensures that within each band if the dependence
6854 distances over the condition constraints are not all zero
6855 then all corresponding conditional validity constraints are respected.
6856 A conditional validity constraint corresponds to a condition
6857 if the two are adjacent, i.e., if the domain of one relation intersect
6858 the range of the other relation.
6859 The typical use case of conditional validity constraints is
6860 to allow order constraints between live ranges to be violated
6861 as long as the live ranges themselves are local to the band.
6862 To allow more fine-grained control over which conditions correspond
6863 to which conditional validity constraints, the domains and ranges
6864 of these relations may include I<tags>. That is, the domains and
6865 ranges of those relation may themselves be wrapped relations
6866 where the iteration domain appears in the domain of those wrapped relations
6867 and the range of the wrapped relations can be arbitrarily chosen
6868 by the user. Conditions and conditional validity constraints are only
6869 considered adjacent to each other if the entire wrapped relation matches.
6870 In particular, a relation with a tag will never be considered adjacent
6871 to a relation without a tag.
6873 The following function computes a schedule directly from
6874 an iteration domain and validity and proximity dependences
6875 and is implemented in terms of the functions described above.
6876 The use of C<isl_union_set_compute_schedule> is discouraged.
6878 #include <isl/schedule.h>
6879 __isl_give isl_schedule *isl_union_set_compute_schedule(
6880 __isl_take isl_union_set *domain,
6881 __isl_take isl_union_map *validity,
6882 __isl_take isl_union_map *proximity);
6884 A mapping from the domains to the scheduled space can be obtained
6885 from an C<isl_schedule> using the following function.
6887 __isl_give isl_union_map *isl_schedule_get_map(
6888 __isl_keep isl_schedule *sched);
6890 A representation of the schedule can be printed using
6892 __isl_give isl_printer *isl_printer_print_schedule(
6893 __isl_take isl_printer *p,
6894 __isl_keep isl_schedule *schedule);
6896 A representation of the schedule as a forest of bands can be obtained
6897 using the following function.
6899 __isl_give isl_band_list *isl_schedule_get_band_forest(
6900 __isl_keep isl_schedule *schedule);
6902 The individual bands can be visited in depth-first post-order
6903 using the following function.
6905 #include <isl/schedule.h>
6906 int isl_schedule_foreach_band(
6907 __isl_keep isl_schedule *sched,
6908 int (*fn)(__isl_keep isl_band *band, void *user),
6911 The list can be manipulated as explained in L<"Lists">.
6912 The bands inside the list can be copied and freed using the following
6915 #include <isl/band.h>
6916 __isl_give isl_band *isl_band_copy(
6917 __isl_keep isl_band *band);
6918 __isl_null isl_band *isl_band_free(
6919 __isl_take isl_band *band);
6921 Each band contains zero or more scheduling dimensions.
6922 These are referred to as the members of the band.
6923 The section of the schedule that corresponds to the band is
6924 referred to as the partial schedule of the band.
6925 For those nodes that participate in a band, the outer scheduling
6926 dimensions form the prefix schedule, while the inner scheduling
6927 dimensions form the suffix schedule.
6928 That is, if we take a cut of the band forest, then the union of
6929 the concatenations of the prefix, partial and suffix schedules of
6930 each band in the cut is equal to the entire schedule (modulo
6931 some possible padding at the end with zero scheduling dimensions).
6932 The properties of a band can be inspected using the following functions.
6934 #include <isl/band.h>
6935 int isl_band_has_children(__isl_keep isl_band *band);
6936 __isl_give isl_band_list *isl_band_get_children(
6937 __isl_keep isl_band *band);
6939 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6940 __isl_keep isl_band *band);
6941 __isl_give isl_union_map *isl_band_get_partial_schedule(
6942 __isl_keep isl_band *band);
6943 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6944 __isl_keep isl_band *band);
6946 int isl_band_n_member(__isl_keep isl_band *band);
6947 int isl_band_member_is_coincident(
6948 __isl_keep isl_band *band, int pos);
6950 int isl_band_list_foreach_band(
6951 __isl_keep isl_band_list *list,
6952 int (*fn)(__isl_keep isl_band *band, void *user),
6955 Note that a scheduling dimension is considered to be ``coincident''
6956 if it satisfies the coincidence constraints within its band.
6957 That is, if the dependence distances of the coincidence
6958 constraints are all zero in that direction (for fixed
6959 iterations of outer bands).
6960 Like C<isl_schedule_foreach_band>,
6961 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6962 in depth-first post-order.
6964 A band can be tiled using the following function.
6966 #include <isl/band.h>
6967 int isl_band_tile(__isl_keep isl_band *band,
6968 __isl_take isl_vec *sizes);
6970 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6972 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6973 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6975 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6977 The C<isl_band_tile> function tiles the band using the given tile sizes
6978 inside its schedule.
6979 A new child band is created to represent the point loops and it is
6980 inserted between the modified band and its children.
6981 The C<tile_scale_tile_loops> option specifies whether the tile
6982 loops iterators should be scaled by the tile sizes.
6983 If the C<tile_shift_point_loops> option is set, then the point loops
6984 are shifted to start at zero.
6986 A band can be split into two nested bands using the following function.
6988 int isl_band_split(__isl_keep isl_band *band, int pos);
6990 The resulting outer band contains the first C<pos> dimensions of C<band>
6991 while the inner band contains the remaining dimensions.
6993 A representation of the band can be printed using
6995 #include <isl/band.h>
6996 __isl_give isl_printer *isl_printer_print_band(
6997 __isl_take isl_printer *p,
6998 __isl_keep isl_band *band);
7002 #include <isl/schedule.h>
7003 int isl_options_set_schedule_max_coefficient(
7004 isl_ctx *ctx, int val);
7005 int isl_options_get_schedule_max_coefficient(
7007 int isl_options_set_schedule_max_constant_term(
7008 isl_ctx *ctx, int val);
7009 int isl_options_get_schedule_max_constant_term(
7011 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
7012 int isl_options_get_schedule_fuse(isl_ctx *ctx);
7013 int isl_options_set_schedule_maximize_band_depth(
7014 isl_ctx *ctx, int val);
7015 int isl_options_get_schedule_maximize_band_depth(
7017 int isl_options_set_schedule_outer_coincidence(
7018 isl_ctx *ctx, int val);
7019 int isl_options_get_schedule_outer_coincidence(
7021 int isl_options_set_schedule_split_scaled(
7022 isl_ctx *ctx, int val);
7023 int isl_options_get_schedule_split_scaled(
7025 int isl_options_set_schedule_algorithm(
7026 isl_ctx *ctx, int val);
7027 int isl_options_get_schedule_algorithm(
7029 int isl_options_set_schedule_separate_components(
7030 isl_ctx *ctx, int val);
7031 int isl_options_get_schedule_separate_components(
7036 =item * schedule_max_coefficient
7038 This option enforces that the coefficients for variable and parameter
7039 dimensions in the calculated schedule are not larger than the specified value.
7040 This option can significantly increase the speed of the scheduling calculation
7041 and may also prevent fusing of unrelated dimensions. A value of -1 means that
7042 this option does not introduce bounds on the variable or parameter
7045 =item * schedule_max_constant_term
7047 This option enforces that the constant coefficients in the calculated schedule
7048 are not larger than the maximal constant term. This option can significantly
7049 increase the speed of the scheduling calculation and may also prevent fusing of
7050 unrelated dimensions. A value of -1 means that this option does not introduce
7051 bounds on the constant coefficients.
7053 =item * schedule_fuse
7055 This option controls the level of fusion.
7056 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
7057 resulting schedule will be distributed as much as possible.
7058 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
7059 try to fuse loops in the resulting schedule.
7061 =item * schedule_maximize_band_depth
7063 If this option is set, we do not split bands at the point
7064 where we detect splitting is necessary. Instead, we
7065 backtrack and split bands as early as possible. This
7066 reduces the number of splits and maximizes the width of
7067 the bands. Wider bands give more possibilities for tiling.
7068 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
7069 then bands will be split as early as possible, even if there is no need.
7070 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
7072 =item * schedule_outer_coincidence
7074 If this option is set, then we try to construct schedules
7075 where the outermost scheduling dimension in each band
7076 satisfies the coincidence constraints.
7078 =item * schedule_split_scaled
7080 If this option is set, then we try to construct schedules in which the
7081 constant term is split off from the linear part if the linear parts of
7082 the scheduling rows for all nodes in the graphs have a common non-trivial
7084 The constant term is then placed in a separate band and the linear
7087 =item * schedule_algorithm
7089 Selects the scheduling algorithm to be used.
7090 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
7091 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
7093 =item * schedule_separate_components
7095 If at any point the dependence graph contains any (weakly connected) components,
7096 then these components are scheduled separately.
7097 If this option is not set, then some iterations of the domains
7098 in these components may be scheduled together.
7099 If this option is set, then the components are given consecutive
7104 =head2 AST Generation
7106 This section describes the C<isl> functionality for generating
7107 ASTs that visit all the elements
7108 in a domain in an order specified by a schedule.
7109 In particular, given a C<isl_union_map>, an AST is generated
7110 that visits all the elements in the domain of the C<isl_union_map>
7111 according to the lexicographic order of the corresponding image
7112 element(s). If the range of the C<isl_union_map> consists of
7113 elements in more than one space, then each of these spaces is handled
7114 separately in an arbitrary order.
7115 It should be noted that the image elements only specify the I<order>
7116 in which the corresponding domain elements should be visited.
7117 No direct relation between the image elements and the loop iterators
7118 in the generated AST should be assumed.
7120 Each AST is generated within a build. The initial build
7121 simply specifies the constraints on the parameters (if any)
7122 and can be created, inspected, copied and freed using the following functions.
7124 #include <isl/ast_build.h>
7125 __isl_give isl_ast_build *isl_ast_build_from_context(
7126 __isl_take isl_set *set);
7127 __isl_give isl_ast_build *isl_ast_build_copy(
7128 __isl_keep isl_ast_build *build);
7129 __isl_null isl_ast_build *isl_ast_build_free(
7130 __isl_take isl_ast_build *build);
7132 The C<set> argument is usually a parameter set with zero or more parameters.
7133 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
7134 and L</"Fine-grained Control over AST Generation">.
7135 Finally, the AST itself can be constructed using the following
7138 #include <isl/ast_build.h>
7139 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
7140 __isl_keep isl_ast_build *build,
7141 __isl_take isl_union_map *schedule);
7143 =head3 Inspecting the AST
7145 The basic properties of an AST node can be obtained as follows.
7147 #include <isl/ast.h>
7148 enum isl_ast_node_type isl_ast_node_get_type(
7149 __isl_keep isl_ast_node *node);
7151 The type of an AST node is one of
7152 C<isl_ast_node_for>,
7154 C<isl_ast_node_block> or
7155 C<isl_ast_node_user>.
7156 An C<isl_ast_node_for> represents a for node.
7157 An C<isl_ast_node_if> represents an if node.
7158 An C<isl_ast_node_block> represents a compound node.
7159 An C<isl_ast_node_user> represents an expression statement.
7160 An expression statement typically corresponds to a domain element, i.e.,
7161 one of the elements that is visited by the AST.
7163 Each type of node has its own additional properties.
7165 #include <isl/ast.h>
7166 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7167 __isl_keep isl_ast_node *node);
7168 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7169 __isl_keep isl_ast_node *node);
7170 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7171 __isl_keep isl_ast_node *node);
7172 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7173 __isl_keep isl_ast_node *node);
7174 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7175 __isl_keep isl_ast_node *node);
7176 int isl_ast_node_for_is_degenerate(
7177 __isl_keep isl_ast_node *node);
7179 An C<isl_ast_for> is considered degenerate if it is known to execute
7182 #include <isl/ast.h>
7183 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7184 __isl_keep isl_ast_node *node);
7185 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7186 __isl_keep isl_ast_node *node);
7187 int isl_ast_node_if_has_else(
7188 __isl_keep isl_ast_node *node);
7189 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7190 __isl_keep isl_ast_node *node);
7192 __isl_give isl_ast_node_list *
7193 isl_ast_node_block_get_children(
7194 __isl_keep isl_ast_node *node);
7196 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7197 __isl_keep isl_ast_node *node);
7199 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7200 the following functions.
7202 #include <isl/ast.h>
7203 enum isl_ast_expr_type isl_ast_expr_get_type(
7204 __isl_keep isl_ast_expr *expr);
7206 The type of an AST expression is one of
7208 C<isl_ast_expr_id> or
7209 C<isl_ast_expr_int>.
7210 An C<isl_ast_expr_op> represents the result of an operation.
7211 An C<isl_ast_expr_id> represents an identifier.
7212 An C<isl_ast_expr_int> represents an integer value.
7214 Each type of expression has its own additional properties.
7216 #include <isl/ast.h>
7217 enum isl_ast_op_type isl_ast_expr_get_op_type(
7218 __isl_keep isl_ast_expr *expr);
7219 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7220 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7221 __isl_keep isl_ast_expr *expr, int pos);
7222 int isl_ast_node_foreach_ast_op_type(
7223 __isl_keep isl_ast_node *node,
7224 int (*fn)(enum isl_ast_op_type type, void *user),
7227 C<isl_ast_expr_get_op_type> returns the type of the operation
7228 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7229 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7231 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7232 C<isl_ast_op_type> that appears in C<node>.
7233 The operation type is one of the following.
7237 =item C<isl_ast_op_and>
7239 Logical I<and> of two arguments.
7240 Both arguments can be evaluated.
7242 =item C<isl_ast_op_and_then>
7244 Logical I<and> of two arguments.
7245 The second argument can only be evaluated if the first evaluates to true.
7247 =item C<isl_ast_op_or>
7249 Logical I<or> of two arguments.
7250 Both arguments can be evaluated.
7252 =item C<isl_ast_op_or_else>
7254 Logical I<or> of two arguments.
7255 The second argument can only be evaluated if the first evaluates to false.
7257 =item C<isl_ast_op_max>
7259 Maximum of two or more arguments.
7261 =item C<isl_ast_op_min>
7263 Minimum of two or more arguments.
7265 =item C<isl_ast_op_minus>
7269 =item C<isl_ast_op_add>
7271 Sum of two arguments.
7273 =item C<isl_ast_op_sub>
7275 Difference of two arguments.
7277 =item C<isl_ast_op_mul>
7279 Product of two arguments.
7281 =item C<isl_ast_op_div>
7283 Exact division. That is, the result is known to be an integer.
7285 =item C<isl_ast_op_fdiv_q>
7287 Result of integer division, rounded towards negative
7290 =item C<isl_ast_op_pdiv_q>
7292 Result of integer division, where dividend is known to be non-negative.
7294 =item C<isl_ast_op_pdiv_r>
7296 Remainder of integer division, where dividend is known to be non-negative.
7298 =item C<isl_ast_op_zdiv_r>
7300 Equal to zero iff the remainder on integer division is zero.
7302 =item C<isl_ast_op_cond>
7304 Conditional operator defined on three arguments.
7305 If the first argument evaluates to true, then the result
7306 is equal to the second argument. Otherwise, the result
7307 is equal to the third argument.
7308 The second and third argument may only be evaluated if
7309 the first argument evaluates to true and false, respectively.
7310 Corresponds to C<a ? b : c> in C.
7312 =item C<isl_ast_op_select>
7314 Conditional operator defined on three arguments.
7315 If the first argument evaluates to true, then the result
7316 is equal to the second argument. Otherwise, the result
7317 is equal to the third argument.
7318 The second and third argument may be evaluated independently
7319 of the value of the first argument.
7320 Corresponds to C<a * b + (1 - a) * c> in C.
7322 =item C<isl_ast_op_eq>
7326 =item C<isl_ast_op_le>
7328 Less than or equal relation.
7330 =item C<isl_ast_op_lt>
7334 =item C<isl_ast_op_ge>
7336 Greater than or equal relation.
7338 =item C<isl_ast_op_gt>
7340 Greater than relation.
7342 =item C<isl_ast_op_call>
7345 The number of arguments of the C<isl_ast_expr> is one more than
7346 the number of arguments in the function call, the first argument
7347 representing the function being called.
7349 =item C<isl_ast_op_access>
7352 The number of arguments of the C<isl_ast_expr> is one more than
7353 the number of index expressions in the array access, the first argument
7354 representing the array being accessed.
7356 =item C<isl_ast_op_member>
7359 This operation has two arguments, a structure and the name of
7360 the member of the structure being accessed.
7364 #include <isl/ast.h>
7365 __isl_give isl_id *isl_ast_expr_get_id(
7366 __isl_keep isl_ast_expr *expr);
7368 Return the identifier represented by the AST expression.
7370 #include <isl/ast.h>
7371 __isl_give isl_val *isl_ast_expr_get_val(
7372 __isl_keep isl_ast_expr *expr);
7374 Return the integer represented by the AST expression.
7376 =head3 Properties of ASTs
7378 #include <isl/ast.h>
7379 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7380 __isl_keep isl_ast_expr *expr2);
7382 Check if two C<isl_ast_expr>s are equal to each other.
7384 =head3 Manipulating and printing the AST
7386 AST nodes can be copied and freed using the following functions.
7388 #include <isl/ast.h>
7389 __isl_give isl_ast_node *isl_ast_node_copy(
7390 __isl_keep isl_ast_node *node);
7391 __isl_null isl_ast_node *isl_ast_node_free(
7392 __isl_take isl_ast_node *node);
7394 AST expressions can be copied and freed using the following functions.
7396 #include <isl/ast.h>
7397 __isl_give isl_ast_expr *isl_ast_expr_copy(
7398 __isl_keep isl_ast_expr *expr);
7399 __isl_null isl_ast_expr *isl_ast_expr_free(
7400 __isl_take isl_ast_expr *expr);
7402 New AST expressions can be created either directly or within
7403 the context of an C<isl_ast_build>.
7405 #include <isl/ast.h>
7406 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7407 __isl_take isl_val *v);
7408 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7409 __isl_take isl_id *id);
7410 __isl_give isl_ast_expr *isl_ast_expr_neg(
7411 __isl_take isl_ast_expr *expr);
7412 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7413 __isl_take isl_ast_expr *expr);
7414 __isl_give isl_ast_expr *isl_ast_expr_add(
7415 __isl_take isl_ast_expr *expr1,
7416 __isl_take isl_ast_expr *expr2);
7417 __isl_give isl_ast_expr *isl_ast_expr_sub(
7418 __isl_take isl_ast_expr *expr1,
7419 __isl_take isl_ast_expr *expr2);
7420 __isl_give isl_ast_expr *isl_ast_expr_mul(
7421 __isl_take isl_ast_expr *expr1,
7422 __isl_take isl_ast_expr *expr2);
7423 __isl_give isl_ast_expr *isl_ast_expr_div(
7424 __isl_take isl_ast_expr *expr1,
7425 __isl_take isl_ast_expr *expr2);
7426 __isl_give isl_ast_expr *isl_ast_expr_and(
7427 __isl_take isl_ast_expr *expr1,
7428 __isl_take isl_ast_expr *expr2)
7429 __isl_give isl_ast_expr *isl_ast_expr_or(
7430 __isl_take isl_ast_expr *expr1,
7431 __isl_take isl_ast_expr *expr2)
7432 __isl_give isl_ast_expr *isl_ast_expr_eq(
7433 __isl_take isl_ast_expr *expr1,
7434 __isl_take isl_ast_expr *expr2);
7435 __isl_give isl_ast_expr *isl_ast_expr_le(
7436 __isl_take isl_ast_expr *expr1,
7437 __isl_take isl_ast_expr *expr2);
7438 __isl_give isl_ast_expr *isl_ast_expr_lt(
7439 __isl_take isl_ast_expr *expr1,
7440 __isl_take isl_ast_expr *expr2);
7441 __isl_give isl_ast_expr *isl_ast_expr_ge(
7442 __isl_take isl_ast_expr *expr1,
7443 __isl_take isl_ast_expr *expr2);
7444 __isl_give isl_ast_expr *isl_ast_expr_gt(
7445 __isl_take isl_ast_expr *expr1,
7446 __isl_take isl_ast_expr *expr2);
7447 __isl_give isl_ast_expr *isl_ast_expr_access(
7448 __isl_take isl_ast_expr *array,
7449 __isl_take isl_ast_expr_list *indices);
7451 The function C<isl_ast_expr_address_of> can be applied to an
7452 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
7453 to represent the address of the C<isl_ast_expr_access>.
7455 #include <isl/ast_build.h>
7456 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
7457 __isl_keep isl_ast_build *build,
7458 __isl_take isl_pw_aff *pa);
7459 __isl_give isl_ast_expr *
7460 isl_ast_build_access_from_pw_multi_aff(
7461 __isl_keep isl_ast_build *build,
7462 __isl_take isl_pw_multi_aff *pma);
7463 __isl_give isl_ast_expr *
7464 isl_ast_build_access_from_multi_pw_aff(
7465 __isl_keep isl_ast_build *build,
7466 __isl_take isl_multi_pw_aff *mpa);
7467 __isl_give isl_ast_expr *
7468 isl_ast_build_call_from_pw_multi_aff(
7469 __isl_keep isl_ast_build *build,
7470 __isl_take isl_pw_multi_aff *pma);
7471 __isl_give isl_ast_expr *
7472 isl_ast_build_call_from_multi_pw_aff(
7473 __isl_keep isl_ast_build *build,
7474 __isl_take isl_multi_pw_aff *mpa);
7476 The domains of C<pa>, C<mpa> and C<pma> should correspond
7477 to the schedule space of C<build>.
7478 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
7479 the function being called.
7480 If the accessed space is a nested relation, then it is taken
7481 to represent an access of the member specified by the range
7482 of this nested relation of the structure specified by the domain
7483 of the nested relation.
7485 The following functions can be used to modify an C<isl_ast_expr>.
7487 #include <isl/ast.h>
7488 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
7489 __isl_take isl_ast_expr *expr, int pos,
7490 __isl_take isl_ast_expr *arg);
7492 Replace the argument of C<expr> at position C<pos> by C<arg>.
7494 #include <isl/ast.h>
7495 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
7496 __isl_take isl_ast_expr *expr,
7497 __isl_take isl_id_to_ast_expr *id2expr);
7499 The function C<isl_ast_expr_substitute_ids> replaces the
7500 subexpressions of C<expr> of type C<isl_ast_expr_id>
7501 by the corresponding expression in C<id2expr>, if there is any.
7504 User specified data can be attached to an C<isl_ast_node> and obtained
7505 from the same C<isl_ast_node> using the following functions.
7507 #include <isl/ast.h>
7508 __isl_give isl_ast_node *isl_ast_node_set_annotation(
7509 __isl_take isl_ast_node *node,
7510 __isl_take isl_id *annotation);
7511 __isl_give isl_id *isl_ast_node_get_annotation(
7512 __isl_keep isl_ast_node *node);
7514 Basic printing can be performed using the following functions.
7516 #include <isl/ast.h>
7517 __isl_give isl_printer *isl_printer_print_ast_expr(
7518 __isl_take isl_printer *p,
7519 __isl_keep isl_ast_expr *expr);
7520 __isl_give isl_printer *isl_printer_print_ast_node(
7521 __isl_take isl_printer *p,
7522 __isl_keep isl_ast_node *node);
7523 __isl_give char *isl_ast_expr_to_str(
7524 __isl_keep isl_ast_expr *expr);
7526 More advanced printing can be performed using the following functions.
7528 #include <isl/ast.h>
7529 __isl_give isl_printer *isl_ast_op_type_print_macro(
7530 enum isl_ast_op_type type,
7531 __isl_take isl_printer *p);
7532 __isl_give isl_printer *isl_ast_node_print_macros(
7533 __isl_keep isl_ast_node *node,
7534 __isl_take isl_printer *p);
7535 __isl_give isl_printer *isl_ast_node_print(
7536 __isl_keep isl_ast_node *node,
7537 __isl_take isl_printer *p,
7538 __isl_take isl_ast_print_options *options);
7539 __isl_give isl_printer *isl_ast_node_for_print(
7540 __isl_keep isl_ast_node *node,
7541 __isl_take isl_printer *p,
7542 __isl_take isl_ast_print_options *options);
7543 __isl_give isl_printer *isl_ast_node_if_print(
7544 __isl_keep isl_ast_node *node,
7545 __isl_take isl_printer *p,
7546 __isl_take isl_ast_print_options *options);
7548 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
7549 C<isl> may print out an AST that makes use of macros such
7550 as C<floord>, C<min> and C<max>.
7551 C<isl_ast_op_type_print_macro> prints out the macro
7552 corresponding to a specific C<isl_ast_op_type>.
7553 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
7554 for expressions where these macros would be used and prints
7555 out the required macro definitions.
7556 Essentially, C<isl_ast_node_print_macros> calls
7557 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
7558 as function argument.
7559 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
7560 C<isl_ast_node_if_print> print an C<isl_ast_node>
7561 in C<ISL_FORMAT_C>, but allow for some extra control
7562 through an C<isl_ast_print_options> object.
7563 This object can be created using the following functions.
7565 #include <isl/ast.h>
7566 __isl_give isl_ast_print_options *
7567 isl_ast_print_options_alloc(isl_ctx *ctx);
7568 __isl_give isl_ast_print_options *
7569 isl_ast_print_options_copy(
7570 __isl_keep isl_ast_print_options *options);
7571 __isl_null isl_ast_print_options *
7572 isl_ast_print_options_free(
7573 __isl_take isl_ast_print_options *options);
7575 __isl_give isl_ast_print_options *
7576 isl_ast_print_options_set_print_user(
7577 __isl_take isl_ast_print_options *options,
7578 __isl_give isl_printer *(*print_user)(
7579 __isl_take isl_printer *p,
7580 __isl_take isl_ast_print_options *options,
7581 __isl_keep isl_ast_node *node, void *user),
7583 __isl_give isl_ast_print_options *
7584 isl_ast_print_options_set_print_for(
7585 __isl_take isl_ast_print_options *options,
7586 __isl_give isl_printer *(*print_for)(
7587 __isl_take isl_printer *p,
7588 __isl_take isl_ast_print_options *options,
7589 __isl_keep isl_ast_node *node, void *user),
7592 The callback set by C<isl_ast_print_options_set_print_user>
7593 is called whenever a node of type C<isl_ast_node_user> needs to
7595 The callback set by C<isl_ast_print_options_set_print_for>
7596 is called whenever a node of type C<isl_ast_node_for> needs to
7598 Note that C<isl_ast_node_for_print> will I<not> call the
7599 callback set by C<isl_ast_print_options_set_print_for> on the node
7600 on which C<isl_ast_node_for_print> is called, but only on nested
7601 nodes of type C<isl_ast_node_for>. It is therefore safe to
7602 call C<isl_ast_node_for_print> from within the callback set by
7603 C<isl_ast_print_options_set_print_for>.
7605 The following option determines the type to be used for iterators
7606 while printing the AST.
7608 int isl_options_set_ast_iterator_type(
7609 isl_ctx *ctx, const char *val);
7610 const char *isl_options_get_ast_iterator_type(
7613 The AST printer only prints body nodes as blocks if these
7614 blocks cannot be safely omitted.
7615 For example, a C<for> node with one body node will not be
7616 surrounded with braces in C<ISL_FORMAT_C>.
7617 A block will always be printed by setting the following option.
7619 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
7621 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
7625 #include <isl/ast_build.h>
7626 int isl_options_set_ast_build_atomic_upper_bound(
7627 isl_ctx *ctx, int val);
7628 int isl_options_get_ast_build_atomic_upper_bound(
7630 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
7632 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
7633 int isl_options_set_ast_build_exploit_nested_bounds(
7634 isl_ctx *ctx, int val);
7635 int isl_options_get_ast_build_exploit_nested_bounds(
7637 int isl_options_set_ast_build_group_coscheduled(
7638 isl_ctx *ctx, int val);
7639 int isl_options_get_ast_build_group_coscheduled(
7641 int isl_options_set_ast_build_scale_strides(
7642 isl_ctx *ctx, int val);
7643 int isl_options_get_ast_build_scale_strides(
7645 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
7647 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
7648 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
7650 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
7654 =item * ast_build_atomic_upper_bound
7656 Generate loop upper bounds that consist of the current loop iterator,
7657 an operator and an expression not involving the iterator.
7658 If this option is not set, then the current loop iterator may appear
7659 several times in the upper bound.
7660 For example, when this option is turned off, AST generation
7663 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
7667 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
7670 When the option is turned on, the following AST is generated
7672 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
7675 =item * ast_build_prefer_pdiv
7677 If this option is turned off, then the AST generation will
7678 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
7679 operators, but no C<isl_ast_op_pdiv_q> or
7680 C<isl_ast_op_pdiv_r> operators.
7681 If this options is turned on, then C<isl> will try to convert
7682 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
7683 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
7685 =item * ast_build_exploit_nested_bounds
7687 Simplify conditions based on bounds of nested for loops.
7688 In particular, remove conditions that are implied by the fact
7689 that one or more nested loops have at least one iteration,
7690 meaning that the upper bound is at least as large as the lower bound.
7691 For example, when this option is turned off, AST generation
7694 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
7700 for (int c0 = 0; c0 <= N; c0 += 1)
7701 for (int c1 = 0; c1 <= M; c1 += 1)
7704 When the option is turned on, the following AST is generated
7706 for (int c0 = 0; c0 <= N; c0 += 1)
7707 for (int c1 = 0; c1 <= M; c1 += 1)
7710 =item * ast_build_group_coscheduled
7712 If two domain elements are assigned the same schedule point, then
7713 they may be executed in any order and they may even appear in different
7714 loops. If this options is set, then the AST generator will make
7715 sure that coscheduled domain elements do not appear in separate parts
7716 of the AST. This is useful in case of nested AST generation
7717 if the outer AST generation is given only part of a schedule
7718 and the inner AST generation should handle the domains that are
7719 coscheduled by this initial part of the schedule together.
7720 For example if an AST is generated for a schedule
7722 { A[i] -> [0]; B[i] -> [0] }
7724 then the C<isl_ast_build_set_create_leaf> callback described
7725 below may get called twice, once for each domain.
7726 Setting this option ensures that the callback is only called once
7727 on both domains together.
7729 =item * ast_build_separation_bounds
7731 This option specifies which bounds to use during separation.
7732 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
7733 then all (possibly implicit) bounds on the current dimension will
7734 be used during separation.
7735 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
7736 then only those bounds that are explicitly available will
7737 be used during separation.
7739 =item * ast_build_scale_strides
7741 This option specifies whether the AST generator is allowed
7742 to scale down iterators of strided loops.
7744 =item * ast_build_allow_else
7746 This option specifies whether the AST generator is allowed
7747 to construct if statements with else branches.
7749 =item * ast_build_allow_or
7751 This option specifies whether the AST generator is allowed
7752 to construct if conditions with disjunctions.
7756 =head3 Fine-grained Control over AST Generation
7758 Besides specifying the constraints on the parameters,
7759 an C<isl_ast_build> object can be used to control
7760 various aspects of the AST generation process.
7761 The most prominent way of control is through ``options'',
7762 which can be set using the following function.
7764 #include <isl/ast_build.h>
7765 __isl_give isl_ast_build *
7766 isl_ast_build_set_options(
7767 __isl_take isl_ast_build *control,
7768 __isl_take isl_union_map *options);
7770 The options are encoded in an C<isl_union_map>.
7771 The domain of this union relation refers to the schedule domain,
7772 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
7773 In the case of nested AST generation (see L</"Nested AST Generation">),
7774 the domain of C<options> should refer to the extra piece of the schedule.
7775 That is, it should be equal to the range of the wrapped relation in the
7776 range of the schedule.
7777 The range of the options can consist of elements in one or more spaces,
7778 the names of which determine the effect of the option.
7779 The values of the range typically also refer to the schedule dimension
7780 to which the option applies. In case of nested AST generation
7781 (see L</"Nested AST Generation">), these values refer to the position
7782 of the schedule dimension within the innermost AST generation.
7783 The constraints on the domain elements of
7784 the option should only refer to this dimension and earlier dimensions.
7785 We consider the following spaces.
7789 =item C<separation_class>
7791 This space is a wrapped relation between two one dimensional spaces.
7792 The input space represents the schedule dimension to which the option
7793 applies and the output space represents the separation class.
7794 While constructing a loop corresponding to the specified schedule
7795 dimension(s), the AST generator will try to generate separate loops
7796 for domain elements that are assigned different classes.
7797 If only some of the elements are assigned a class, then those elements
7798 that are not assigned any class will be treated as belonging to a class
7799 that is separate from the explicitly assigned classes.
7800 The typical use case for this option is to separate full tiles from
7802 The other options, described below, are applied after the separation
7805 As an example, consider the separation into full and partial tiles
7806 of a tiling of a triangular domain.
7807 Take, for example, the domain
7809 { A[i,j] : 0 <= i,j and i + j <= 100 }
7811 and a tiling into tiles of 10 by 10. The input to the AST generator
7812 is then the schedule
7814 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7817 Without any options, the following AST is generated
7819 for (int c0 = 0; c0 <= 10; c0 += 1)
7820 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7821 for (int c2 = 10 * c0;
7822 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7824 for (int c3 = 10 * c1;
7825 c3 <= min(10 * c1 + 9, -c2 + 100);
7829 Separation into full and partial tiles can be obtained by assigning
7830 a class, say C<0>, to the full tiles. The full tiles are represented by those
7831 values of the first and second schedule dimensions for which there are
7832 values of the third and fourth dimensions to cover an entire tile.
7833 That is, we need to specify the following option
7835 { [a,b,c,d] -> separation_class[[0]->[0]] :
7836 exists b': 0 <= 10a,10b' and
7837 10a+9+10b'+9 <= 100;
7838 [a,b,c,d] -> separation_class[[1]->[0]] :
7839 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7843 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7844 a >= 0 and b >= 0 and b <= 8 - a;
7845 [a, b, c, d] -> separation_class[[0] -> [0]] :
7848 With this option, the generated AST is as follows
7851 for (int c0 = 0; c0 <= 8; c0 += 1) {
7852 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7853 for (int c2 = 10 * c0;
7854 c2 <= 10 * c0 + 9; c2 += 1)
7855 for (int c3 = 10 * c1;
7856 c3 <= 10 * c1 + 9; c3 += 1)
7858 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7859 for (int c2 = 10 * c0;
7860 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7862 for (int c3 = 10 * c1;
7863 c3 <= min(-c2 + 100, 10 * c1 + 9);
7867 for (int c0 = 9; c0 <= 10; c0 += 1)
7868 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7869 for (int c2 = 10 * c0;
7870 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7872 for (int c3 = 10 * c1;
7873 c3 <= min(10 * c1 + 9, -c2 + 100);
7880 This is a single-dimensional space representing the schedule dimension(s)
7881 to which ``separation'' should be applied. Separation tries to split
7882 a loop into several pieces if this can avoid the generation of guards
7884 See also the C<atomic> option.
7888 This is a single-dimensional space representing the schedule dimension(s)
7889 for which the domains should be considered ``atomic''. That is, the
7890 AST generator will make sure that any given domain space will only appear
7891 in a single loop at the specified level.
7893 Consider the following schedule
7895 { a[i] -> [i] : 0 <= i < 10;
7896 b[i] -> [i+1] : 0 <= i < 10 }
7898 If the following option is specified
7900 { [i] -> separate[x] }
7902 then the following AST will be generated
7906 for (int c0 = 1; c0 <= 9; c0 += 1) {
7913 If, on the other hand, the following option is specified
7915 { [i] -> atomic[x] }
7917 then the following AST will be generated
7919 for (int c0 = 0; c0 <= 10; c0 += 1) {
7926 If neither C<atomic> nor C<separate> is specified, then the AST generator
7927 may produce either of these two results or some intermediate form.
7931 This is a single-dimensional space representing the schedule dimension(s)
7932 that should be I<completely> unrolled.
7933 To obtain a partial unrolling, the user should apply an additional
7934 strip-mining to the schedule and fully unroll the inner loop.
7938 Additional control is available through the following functions.
7940 #include <isl/ast_build.h>
7941 __isl_give isl_ast_build *
7942 isl_ast_build_set_iterators(
7943 __isl_take isl_ast_build *control,
7944 __isl_take isl_id_list *iterators);
7946 The function C<isl_ast_build_set_iterators> allows the user to
7947 specify a list of iterator C<isl_id>s to be used as iterators.
7948 If the input schedule is injective, then
7949 the number of elements in this list should be as large as the dimension
7950 of the schedule space, but no direct correspondence should be assumed
7951 between dimensions and elements.
7952 If the input schedule is not injective, then an additional number
7953 of C<isl_id>s equal to the largest dimension of the input domains
7955 If the number of provided C<isl_id>s is insufficient, then additional
7956 names are automatically generated.
7958 #include <isl/ast_build.h>
7959 __isl_give isl_ast_build *
7960 isl_ast_build_set_create_leaf(
7961 __isl_take isl_ast_build *control,
7962 __isl_give isl_ast_node *(*fn)(
7963 __isl_take isl_ast_build *build,
7964 void *user), void *user);
7967 C<isl_ast_build_set_create_leaf> function allows for the
7968 specification of a callback that should be called whenever the AST
7969 generator arrives at an element of the schedule domain.
7970 The callback should return an AST node that should be inserted
7971 at the corresponding position of the AST. The default action (when
7972 the callback is not set) is to continue generating parts of the AST to scan
7973 all the domain elements associated to the schedule domain element
7974 and to insert user nodes, ``calling'' the domain element, for each of them.
7975 The C<build> argument contains the current state of the C<isl_ast_build>.
7976 To ease nested AST generation (see L</"Nested AST Generation">),
7977 all control information that is
7978 specific to the current AST generation such as the options and
7979 the callbacks has been removed from this C<isl_ast_build>.
7980 The callback would typically return the result of a nested
7982 user defined node created using the following function.
7984 #include <isl/ast.h>
7985 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7986 __isl_take isl_ast_expr *expr);
7988 #include <isl/ast_build.h>
7989 __isl_give isl_ast_build *
7990 isl_ast_build_set_at_each_domain(
7991 __isl_take isl_ast_build *build,
7992 __isl_give isl_ast_node *(*fn)(
7993 __isl_take isl_ast_node *node,
7994 __isl_keep isl_ast_build *build,
7995 void *user), void *user);
7996 __isl_give isl_ast_build *
7997 isl_ast_build_set_before_each_for(
7998 __isl_take isl_ast_build *build,
7999 __isl_give isl_id *(*fn)(
8000 __isl_keep isl_ast_build *build,
8001 void *user), void *user);
8002 __isl_give isl_ast_build *
8003 isl_ast_build_set_after_each_for(
8004 __isl_take isl_ast_build *build,
8005 __isl_give isl_ast_node *(*fn)(
8006 __isl_take isl_ast_node *node,
8007 __isl_keep isl_ast_build *build,
8008 void *user), void *user);
8010 The callback set by C<isl_ast_build_set_at_each_domain> will
8011 be called for each domain AST node.
8012 The callbacks set by C<isl_ast_build_set_before_each_for>
8013 and C<isl_ast_build_set_after_each_for> will be called
8014 for each for AST node. The first will be called in depth-first
8015 pre-order, while the second will be called in depth-first post-order.
8016 Since C<isl_ast_build_set_before_each_for> is called before the for
8017 node is actually constructed, it is only passed an C<isl_ast_build>.
8018 The returned C<isl_id> will be added as an annotation (using
8019 C<isl_ast_node_set_annotation>) to the constructed for node.
8020 In particular, if the user has also specified an C<after_each_for>
8021 callback, then the annotation can be retrieved from the node passed to
8022 that callback using C<isl_ast_node_get_annotation>.
8023 All callbacks should C<NULL> on failure.
8024 The given C<isl_ast_build> can be used to create new
8025 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
8026 or C<isl_ast_build_call_from_pw_multi_aff>.
8028 =head3 Nested AST Generation
8030 C<isl> allows the user to create an AST within the context
8031 of another AST. These nested ASTs are created using the
8032 same C<isl_ast_build_ast_from_schedule> function that is used to create the
8033 outer AST. The C<build> argument should be an C<isl_ast_build>
8034 passed to a callback set by
8035 C<isl_ast_build_set_create_leaf>.
8036 The space of the range of the C<schedule> argument should refer
8037 to this build. In particular, the space should be a wrapped
8038 relation and the domain of this wrapped relation should be the
8039 same as that of the range of the schedule returned by
8040 C<isl_ast_build_get_schedule> below.
8041 In practice, the new schedule is typically
8042 created by calling C<isl_union_map_range_product> on the old schedule
8043 and some extra piece of the schedule.
8044 The space of the schedule domain is also available from
8045 the C<isl_ast_build>.
8047 #include <isl/ast_build.h>
8048 __isl_give isl_union_map *isl_ast_build_get_schedule(
8049 __isl_keep isl_ast_build *build);
8050 __isl_give isl_space *isl_ast_build_get_schedule_space(
8051 __isl_keep isl_ast_build *build);
8052 __isl_give isl_ast_build *isl_ast_build_restrict(
8053 __isl_take isl_ast_build *build,
8054 __isl_take isl_set *set);
8056 The C<isl_ast_build_get_schedule> function returns a (partial)
8057 schedule for the domains elements for which part of the AST still needs to
8058 be generated in the current build.
8059 In particular, the domain elements are mapped to those iterations of the loops
8060 enclosing the current point of the AST generation inside which
8061 the domain elements are executed.
8062 No direct correspondence between
8063 the input schedule and this schedule should be assumed.
8064 The space obtained from C<isl_ast_build_get_schedule_space> can be used
8065 to create a set for C<isl_ast_build_restrict> to intersect
8066 with the current build. In particular, the set passed to
8067 C<isl_ast_build_restrict> can have additional parameters.
8068 The ids of the set dimensions in the space returned by
8069 C<isl_ast_build_get_schedule_space> correspond to the
8070 iterators of the already generated loops.
8071 The user should not rely on the ids of the output dimensions
8072 of the relations in the union relation returned by
8073 C<isl_ast_build_get_schedule> having any particular value.
8077 Although C<isl> is mainly meant to be used as a library,
8078 it also contains some basic applications that use some
8079 of the functionality of C<isl>.
8080 The input may be specified in either the L<isl format>
8081 or the L<PolyLib format>.
8083 =head2 C<isl_polyhedron_sample>
8085 C<isl_polyhedron_sample> takes a polyhedron as input and prints
8086 an integer element of the polyhedron, if there is any.
8087 The first column in the output is the denominator and is always
8088 equal to 1. If the polyhedron contains no integer points,
8089 then a vector of length zero is printed.
8093 C<isl_pip> takes the same input as the C<example> program
8094 from the C<piplib> distribution, i.e., a set of constraints
8095 on the parameters, a line containing only -1 and finally a set
8096 of constraints on a parametric polyhedron.
8097 The coefficients of the parameters appear in the last columns
8098 (but before the final constant column).
8099 The output is the lexicographic minimum of the parametric polyhedron.
8100 As C<isl> currently does not have its own output format, the output
8101 is just a dump of the internal state.
8103 =head2 C<isl_polyhedron_minimize>
8105 C<isl_polyhedron_minimize> computes the minimum of some linear
8106 or affine objective function over the integer points in a polyhedron.
8107 If an affine objective function
8108 is given, then the constant should appear in the last column.
8110 =head2 C<isl_polytope_scan>
8112 Given a polytope, C<isl_polytope_scan> prints
8113 all integer points in the polytope.
8115 =head2 C<isl_codegen>
8117 Given a schedule, a context set and an options relation,
8118 C<isl_codegen> prints out an AST that scans the domain elements
8119 of the schedule in the order of their image(s) taking into account
8120 the constraints in the context set.