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);
991 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
992 enum isl_dim_type type);
993 unsigned isl_map_dim(__isl_keep isl_map *map,
994 enum isl_dim_type type);
996 #include <isl/union_map.h>
997 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
998 enum isl_dim_type type);
1000 #include <isl/val.h>
1001 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1002 enum isl_dim_type type);
1004 #include <isl/aff.h>
1005 int isl_aff_dim(__isl_keep isl_aff *aff,
1006 enum isl_dim_type type);
1007 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1008 enum isl_dim_type type);
1009 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1010 enum isl_dim_type type);
1011 unsigned isl_pw_multi_aff_dim(
1012 __isl_keep isl_pw_multi_aff *pma,
1013 enum isl_dim_type type);
1014 unsigned isl_multi_pw_aff_dim(
1015 __isl_keep isl_multi_pw_aff *mpa,
1016 enum isl_dim_type type);
1018 Note that an C<isl_union_map> only has parameters.
1020 The identifiers or names of the individual dimensions of spaces
1021 may be set or read off using the following functions on spaces
1022 or objects that live in spaces.
1023 These functions are mostly useful to obtain the identifiers, positions
1024 or names of the parameters. Identifiers of individual dimensions are
1025 essentially only useful for printing. They are ignored by all other
1026 operations and may not be preserved across those operations.
1028 #include <isl/space.h>
1029 __isl_give isl_space *isl_space_set_dim_id(
1030 __isl_take isl_space *space,
1031 enum isl_dim_type type, unsigned pos,
1032 __isl_take isl_id *id);
1033 int isl_space_has_dim_id(__isl_keep isl_space *space,
1034 enum isl_dim_type type, unsigned pos);
1035 __isl_give isl_id *isl_space_get_dim_id(
1036 __isl_keep isl_space *space,
1037 enum isl_dim_type type, unsigned pos);
1038 __isl_give isl_space *isl_space_set_dim_name(
1039 __isl_take isl_space *space,
1040 enum isl_dim_type type, unsigned pos,
1041 __isl_keep const char *name);
1042 int isl_space_has_dim_name(__isl_keep isl_space *space,
1043 enum isl_dim_type type, unsigned pos);
1044 __isl_keep const char *isl_space_get_dim_name(
1045 __isl_keep isl_space *space,
1046 enum isl_dim_type type, unsigned pos);
1048 #include <isl/local_space.h>
1049 __isl_give isl_local_space *isl_local_space_set_dim_id(
1050 __isl_take isl_local_space *ls,
1051 enum isl_dim_type type, unsigned pos,
1052 __isl_take isl_id *id);
1053 int isl_local_space_has_dim_id(
1054 __isl_keep isl_local_space *ls,
1055 enum isl_dim_type type, unsigned pos);
1056 __isl_give isl_id *isl_local_space_get_dim_id(
1057 __isl_keep isl_local_space *ls,
1058 enum isl_dim_type type, unsigned pos);
1059 __isl_give isl_local_space *isl_local_space_set_dim_name(
1060 __isl_take isl_local_space *ls,
1061 enum isl_dim_type type, unsigned pos, const char *s);
1062 int isl_local_space_has_dim_name(
1063 __isl_keep isl_local_space *ls,
1064 enum isl_dim_type type, unsigned pos)
1065 const char *isl_local_space_get_dim_name(
1066 __isl_keep isl_local_space *ls,
1067 enum isl_dim_type type, unsigned pos);
1069 #include <isl/constraint.h>
1070 const char *isl_constraint_get_dim_name(
1071 __isl_keep isl_constraint *constraint,
1072 enum isl_dim_type type, unsigned pos);
1074 #include <isl/set.h>
1075 __isl_give isl_id *isl_basic_set_get_dim_id(
1076 __isl_keep isl_basic_set *bset,
1077 enum isl_dim_type type, unsigned pos);
1078 __isl_give isl_set *isl_set_set_dim_id(
1079 __isl_take isl_set *set, enum isl_dim_type type,
1080 unsigned pos, __isl_take isl_id *id);
1081 int isl_set_has_dim_id(__isl_keep isl_set *set,
1082 enum isl_dim_type type, unsigned pos);
1083 __isl_give isl_id *isl_set_get_dim_id(
1084 __isl_keep isl_set *set, enum isl_dim_type type,
1086 const char *isl_basic_set_get_dim_name(
1087 __isl_keep isl_basic_set *bset,
1088 enum isl_dim_type type, unsigned pos);
1089 int isl_set_has_dim_name(__isl_keep isl_set *set,
1090 enum isl_dim_type type, unsigned pos);
1091 const char *isl_set_get_dim_name(
1092 __isl_keep isl_set *set,
1093 enum isl_dim_type type, unsigned pos);
1095 #include <isl/map.h>
1096 __isl_give isl_map *isl_map_set_dim_id(
1097 __isl_take isl_map *map, enum isl_dim_type type,
1098 unsigned pos, __isl_take isl_id *id);
1099 int isl_basic_map_has_dim_id(
1100 __isl_keep isl_basic_map *bmap,
1101 enum isl_dim_type type, unsigned pos);
1102 int isl_map_has_dim_id(__isl_keep isl_map *map,
1103 enum isl_dim_type type, unsigned pos);
1104 __isl_give isl_id *isl_map_get_dim_id(
1105 __isl_keep isl_map *map, enum isl_dim_type type,
1107 __isl_give isl_id *isl_union_map_get_dim_id(
1108 __isl_keep isl_union_map *umap,
1109 enum isl_dim_type type, unsigned pos);
1110 const char *isl_basic_map_get_dim_name(
1111 __isl_keep isl_basic_map *bmap,
1112 enum isl_dim_type type, unsigned pos);
1113 int isl_map_has_dim_name(__isl_keep isl_map *map,
1114 enum isl_dim_type type, unsigned pos);
1115 const char *isl_map_get_dim_name(
1116 __isl_keep isl_map *map,
1117 enum isl_dim_type type, unsigned pos);
1119 #include <isl/val.h>
1120 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1121 __isl_take isl_multi_val *mv,
1122 enum isl_dim_type type, unsigned pos,
1123 __isl_take isl_id *id);
1124 __isl_give isl_id *isl_multi_val_get_dim_id(
1125 __isl_keep isl_multi_val *mv,
1126 enum isl_dim_type type, unsigned pos);
1127 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1128 __isl_take isl_multi_val *mv,
1129 enum isl_dim_type type, unsigned pos, const char *s);
1131 #include <isl/aff.h>
1132 __isl_give isl_aff *isl_aff_set_dim_id(
1133 __isl_take isl_aff *aff, enum isl_dim_type type,
1134 unsigned pos, __isl_take isl_id *id);
1135 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1136 __isl_take isl_multi_aff *maff,
1137 enum isl_dim_type type, unsigned pos,
1138 __isl_take isl_id *id);
1139 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1140 __isl_take isl_pw_aff *pma,
1141 enum isl_dim_type type, unsigned pos,
1142 __isl_take isl_id *id);
1143 __isl_give isl_multi_pw_aff *
1144 isl_multi_pw_aff_set_dim_id(
1145 __isl_take isl_multi_pw_aff *mpa,
1146 enum isl_dim_type type, unsigned pos,
1147 __isl_take isl_id *id);
1148 __isl_give isl_id *isl_multi_aff_get_dim_id(
1149 __isl_keep isl_multi_aff *ma,
1150 enum isl_dim_type type, unsigned pos);
1151 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1152 enum isl_dim_type type, unsigned pos);
1153 __isl_give isl_id *isl_pw_aff_get_dim_id(
1154 __isl_keep isl_pw_aff *pa,
1155 enum isl_dim_type type, unsigned pos);
1156 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1157 __isl_keep isl_pw_multi_aff *pma,
1158 enum isl_dim_type type, unsigned pos);
1159 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1160 __isl_keep isl_multi_pw_aff *mpa,
1161 enum isl_dim_type type, unsigned pos);
1162 __isl_give isl_aff *isl_aff_set_dim_name(
1163 __isl_take isl_aff *aff, enum isl_dim_type type,
1164 unsigned pos, const char *s);
1165 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1166 __isl_take isl_multi_aff *maff,
1167 enum isl_dim_type type, unsigned pos, const char *s);
1168 __isl_give isl_multi_pw_aff *
1169 isl_multi_pw_aff_set_dim_name(
1170 __isl_take isl_multi_pw_aff *mpa,
1171 enum isl_dim_type type, unsigned pos, const char *s);
1172 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1173 enum isl_dim_type type, unsigned pos);
1174 const char *isl_pw_aff_get_dim_name(
1175 __isl_keep isl_pw_aff *pa,
1176 enum isl_dim_type type, unsigned pos);
1177 const char *isl_pw_multi_aff_get_dim_name(
1178 __isl_keep isl_pw_multi_aff *pma,
1179 enum isl_dim_type type, unsigned pos);
1181 #include <isl/polynomial.h>
1182 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1183 __isl_take isl_qpolynomial *qp,
1184 enum isl_dim_type type, unsigned pos,
1186 __isl_give isl_pw_qpolynomial *
1187 isl_pw_qpolynomial_set_dim_name(
1188 __isl_take isl_pw_qpolynomial *pwqp,
1189 enum isl_dim_type type, unsigned pos,
1191 __isl_give isl_pw_qpolynomial_fold *
1192 isl_pw_qpolynomial_fold_set_dim_name(
1193 __isl_take isl_pw_qpolynomial_fold *pwf,
1194 enum isl_dim_type type, unsigned pos,
1197 Note that C<isl_space_get_name> returns a pointer to some internal
1198 data structure, so the result can only be used while the
1199 corresponding C<isl_space> is alive.
1200 Also note that every function that operates on two sets or relations
1201 requires that both arguments have the same parameters. This also
1202 means that if one of the arguments has named parameters, then the
1203 other needs to have named parameters too and the names need to match.
1204 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1205 arguments may have different parameters (as long as they are named),
1206 in which case the result will have as parameters the union of the parameters of
1209 Given the identifier or name of a dimension (typically a parameter),
1210 its position can be obtained from the following functions.
1212 #include <isl/space.h>
1213 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1214 enum isl_dim_type type, __isl_keep isl_id *id);
1215 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1216 enum isl_dim_type type, const char *name);
1218 #include <isl/val.h>
1219 int isl_multi_val_find_dim_by_id(
1220 __isl_keep isl_multi_val *mv,
1221 enum isl_dim_type type, __isl_keep isl_id *id);
1223 #include <isl/set.h>
1224 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1225 enum isl_dim_type type, __isl_keep isl_id *id);
1226 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1227 enum isl_dim_type type, const char *name);
1229 #include <isl/map.h>
1230 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1231 enum isl_dim_type type, __isl_keep isl_id *id);
1232 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1233 enum isl_dim_type type, const char *name);
1235 #include <isl/aff.h>
1236 int isl_multi_aff_find_dim_by_id(
1237 __isl_keep isl_multi_aff *ma,
1238 enum isl_dim_type type, __isl_keep isl_id *id);
1239 int isl_multi_pw_aff_find_dim_by_id(
1240 __isl_keep isl_multi_pw_aff *mpa,
1241 enum isl_dim_type type, __isl_keep isl_id *id);
1243 The identifiers or names of entire spaces may be set or read off
1244 using the following functions.
1246 #include <isl/space.h>
1247 __isl_give isl_space *isl_space_set_tuple_id(
1248 __isl_take isl_space *space,
1249 enum isl_dim_type type, __isl_take isl_id *id);
1250 __isl_give isl_space *isl_space_reset_tuple_id(
1251 __isl_take isl_space *space, enum isl_dim_type type);
1252 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1253 enum isl_dim_type type);
1254 __isl_give isl_id *isl_space_get_tuple_id(
1255 __isl_keep isl_space *space, enum isl_dim_type type);
1256 __isl_give isl_space *isl_space_set_tuple_name(
1257 __isl_take isl_space *space,
1258 enum isl_dim_type type, const char *s);
1259 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1260 enum isl_dim_type type);
1261 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1262 enum isl_dim_type type);
1264 #include <isl/local_space.h>
1265 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1266 __isl_take isl_local_space *ls,
1267 enum isl_dim_type type, __isl_take isl_id *id);
1269 #include <isl/set.h>
1270 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1271 __isl_take isl_basic_set *bset,
1272 __isl_take isl_id *id);
1273 __isl_give isl_set *isl_set_set_tuple_id(
1274 __isl_take isl_set *set, __isl_take isl_id *id);
1275 __isl_give isl_set *isl_set_reset_tuple_id(
1276 __isl_take isl_set *set);
1277 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1278 __isl_give isl_id *isl_set_get_tuple_id(
1279 __isl_keep isl_set *set);
1280 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1281 __isl_take isl_basic_set *set, const char *s);
1282 __isl_give isl_set *isl_set_set_tuple_name(
1283 __isl_take isl_set *set, const char *s);
1284 const char *isl_basic_set_get_tuple_name(
1285 __isl_keep isl_basic_set *bset);
1286 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1287 const char *isl_set_get_tuple_name(
1288 __isl_keep isl_set *set);
1290 #include <isl/map.h>
1291 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1292 __isl_take isl_basic_map *bmap,
1293 enum isl_dim_type type, __isl_take isl_id *id);
1294 __isl_give isl_map *isl_map_set_tuple_id(
1295 __isl_take isl_map *map, enum isl_dim_type type,
1296 __isl_take isl_id *id);
1297 __isl_give isl_map *isl_map_reset_tuple_id(
1298 __isl_take isl_map *map, enum isl_dim_type type);
1299 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1300 enum isl_dim_type type);
1301 __isl_give isl_id *isl_map_get_tuple_id(
1302 __isl_keep isl_map *map, enum isl_dim_type type);
1303 __isl_give isl_map *isl_map_set_tuple_name(
1304 __isl_take isl_map *map,
1305 enum isl_dim_type type, const char *s);
1306 const char *isl_basic_map_get_tuple_name(
1307 __isl_keep isl_basic_map *bmap,
1308 enum isl_dim_type type);
1309 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1310 __isl_take isl_basic_map *bmap,
1311 enum isl_dim_type type, const char *s);
1312 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1313 enum isl_dim_type type);
1314 const char *isl_map_get_tuple_name(
1315 __isl_keep isl_map *map,
1316 enum isl_dim_type type);
1318 #include <isl/val.h>
1319 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1320 __isl_take isl_multi_val *mv,
1321 enum isl_dim_type type, __isl_take isl_id *id);
1322 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1323 __isl_take isl_multi_val *mv,
1324 enum isl_dim_type type);
1325 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1326 enum isl_dim_type type);
1327 __isl_give isl_id *isl_multi_val_get_tuple_id(
1328 __isl_keep isl_multi_val *mv,
1329 enum isl_dim_type type);
1330 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1331 __isl_take isl_multi_val *mv,
1332 enum isl_dim_type type, const char *s);
1333 const char *isl_multi_val_get_tuple_name(
1334 __isl_keep isl_multi_val *mv,
1335 enum isl_dim_type type);
1337 #include <isl/aff.h>
1338 __isl_give isl_aff *isl_aff_set_tuple_id(
1339 __isl_take isl_aff *aff,
1340 enum isl_dim_type type, __isl_take isl_id *id);
1341 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1342 __isl_take isl_multi_aff *maff,
1343 enum isl_dim_type type, __isl_take isl_id *id);
1344 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1345 __isl_take isl_pw_aff *pwaff,
1346 enum isl_dim_type type, __isl_take isl_id *id);
1347 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1348 __isl_take isl_pw_multi_aff *pma,
1349 enum isl_dim_type type, __isl_take isl_id *id);
1350 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1351 __isl_take isl_multi_aff *ma,
1352 enum isl_dim_type type);
1353 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1354 __isl_take isl_pw_aff *pa,
1355 enum isl_dim_type type);
1356 __isl_give isl_multi_pw_aff *
1357 isl_multi_pw_aff_reset_tuple_id(
1358 __isl_take isl_multi_pw_aff *mpa,
1359 enum isl_dim_type type);
1360 __isl_give isl_pw_multi_aff *
1361 isl_pw_multi_aff_reset_tuple_id(
1362 __isl_take isl_pw_multi_aff *pma,
1363 enum isl_dim_type type);
1364 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1365 enum isl_dim_type type);
1366 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1367 __isl_keep isl_multi_aff *ma,
1368 enum isl_dim_type type);
1369 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1370 enum isl_dim_type type);
1371 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1372 __isl_keep isl_pw_aff *pa,
1373 enum isl_dim_type type);
1374 int isl_pw_multi_aff_has_tuple_id(
1375 __isl_keep isl_pw_multi_aff *pma,
1376 enum isl_dim_type type);
1377 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1378 __isl_keep isl_pw_multi_aff *pma,
1379 enum isl_dim_type type);
1380 int isl_multi_pw_aff_has_tuple_id(
1381 __isl_keep isl_multi_pw_aff *mpa,
1382 enum isl_dim_type type);
1383 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1384 __isl_keep isl_multi_pw_aff *mpa,
1385 enum isl_dim_type type);
1386 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1387 __isl_take isl_multi_aff *maff,
1388 enum isl_dim_type type, const char *s);
1389 __isl_give isl_multi_pw_aff *
1390 isl_multi_pw_aff_set_tuple_name(
1391 __isl_take isl_multi_pw_aff *mpa,
1392 enum isl_dim_type type, const char *s);
1393 const char *isl_multi_aff_get_tuple_name(
1394 __isl_keep isl_multi_aff *multi,
1395 enum isl_dim_type type);
1396 int isl_pw_multi_aff_has_tuple_name(
1397 __isl_keep isl_pw_multi_aff *pma,
1398 enum isl_dim_type type);
1399 const char *isl_pw_multi_aff_get_tuple_name(
1400 __isl_keep isl_pw_multi_aff *pma,
1401 enum isl_dim_type type);
1403 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1404 or C<isl_dim_set>. As with C<isl_space_get_name>,
1405 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1407 Binary operations require the corresponding spaces of their arguments
1408 to have the same name.
1410 To keep the names of all parameters and tuples, but reset the user pointers
1411 of all the corresponding identifiers, use the following function.
1413 #include <isl/space.h>
1414 __isl_give isl_space *isl_space_reset_user(
1415 __isl_take isl_space *space);
1417 #include <isl/set.h>
1418 __isl_give isl_set *isl_set_reset_user(
1419 __isl_take isl_set *set);
1421 #include <isl/map.h>
1422 __isl_give isl_map *isl_map_reset_user(
1423 __isl_take isl_map *map);
1425 #include <isl/union_set.h>
1426 __isl_give isl_union_set *isl_union_set_reset_user(
1427 __isl_take isl_union_set *uset);
1429 #include <isl/union_map.h>
1430 __isl_give isl_union_map *isl_union_map_reset_user(
1431 __isl_take isl_union_map *umap);
1433 #include <isl/val.h>
1434 __isl_give isl_multi_val *isl_multi_val_reset_user(
1435 __isl_take isl_multi_val *mv);
1437 #include <isl/aff.h>
1438 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1439 __isl_take isl_multi_aff *ma);
1440 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1441 __isl_take isl_multi_pw_aff *mpa);
1443 Spaces can be nested. In particular, the domain of a set or
1444 the domain or range of a relation can be a nested relation.
1445 This process is also called I<wrapping>.
1446 The functions for detecting, constructing and deconstructing
1447 such nested spaces can be found in the wrapping properties
1448 of L</"Unary Properties">, the wrapping operations
1449 of L</"Unary Operations"> and the Cartesian product operations
1450 of L</"Basic Operations">.
1452 Spaces can be created from other spaces
1453 using the functions described in L</"Unary Operations">
1454 and L</"Binary Operations">.
1458 A local space is essentially a space with
1459 zero or more existentially quantified variables.
1460 The local space of various objects can be obtained
1461 using the following functions.
1463 #include <isl/constraint.h>
1464 __isl_give isl_local_space *isl_constraint_get_local_space(
1465 __isl_keep isl_constraint *constraint);
1467 #include <isl/set.h>
1468 __isl_give isl_local_space *isl_basic_set_get_local_space(
1469 __isl_keep isl_basic_set *bset);
1471 #include <isl/map.h>
1472 __isl_give isl_local_space *isl_basic_map_get_local_space(
1473 __isl_keep isl_basic_map *bmap);
1475 #include <isl/aff.h>
1476 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1477 __isl_keep isl_aff *aff);
1478 __isl_give isl_local_space *isl_aff_get_local_space(
1479 __isl_keep isl_aff *aff);
1481 A new local space can be created from a space using
1483 #include <isl/local_space.h>
1484 __isl_give isl_local_space *isl_local_space_from_space(
1485 __isl_take isl_space *space);
1487 They can be inspected, modified, copied and freed using the following functions.
1489 #include <isl/local_space.h>
1490 int isl_local_space_is_params(
1491 __isl_keep isl_local_space *ls);
1492 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1493 __isl_give isl_space *isl_local_space_get_space(
1494 __isl_keep isl_local_space *ls);
1495 __isl_give isl_aff *isl_local_space_get_div(
1496 __isl_keep isl_local_space *ls, int pos);
1497 __isl_give isl_local_space *isl_local_space_copy(
1498 __isl_keep isl_local_space *ls);
1499 __isl_null isl_local_space *isl_local_space_free(
1500 __isl_take isl_local_space *ls);
1502 Note that C<isl_local_space_get_div> can only be used on local spaces
1505 Two local spaces can be compared using
1507 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1508 __isl_keep isl_local_space *ls2);
1510 Local spaces can be created from other local spaces
1511 using the functions described in L</"Unary Operations">
1512 and L</"Binary Operations">.
1514 =head2 Creating New Sets and Relations
1516 C<isl> has functions for creating some standard sets and relations.
1520 =item * Empty sets and relations
1522 __isl_give isl_basic_set *isl_basic_set_empty(
1523 __isl_take isl_space *space);
1524 __isl_give isl_basic_map *isl_basic_map_empty(
1525 __isl_take isl_space *space);
1526 __isl_give isl_set *isl_set_empty(
1527 __isl_take isl_space *space);
1528 __isl_give isl_map *isl_map_empty(
1529 __isl_take isl_space *space);
1530 __isl_give isl_union_set *isl_union_set_empty(
1531 __isl_take isl_space *space);
1532 __isl_give isl_union_map *isl_union_map_empty(
1533 __isl_take isl_space *space);
1535 For C<isl_union_set>s and C<isl_union_map>s, the space
1536 is only used to specify the parameters.
1538 =item * Universe sets and relations
1540 __isl_give isl_basic_set *isl_basic_set_universe(
1541 __isl_take isl_space *space);
1542 __isl_give isl_basic_map *isl_basic_map_universe(
1543 __isl_take isl_space *space);
1544 __isl_give isl_set *isl_set_universe(
1545 __isl_take isl_space *space);
1546 __isl_give isl_map *isl_map_universe(
1547 __isl_take isl_space *space);
1548 __isl_give isl_union_set *isl_union_set_universe(
1549 __isl_take isl_union_set *uset);
1550 __isl_give isl_union_map *isl_union_map_universe(
1551 __isl_take isl_union_map *umap);
1553 The sets and relations constructed by the functions above
1554 contain all integer values, while those constructed by the
1555 functions below only contain non-negative values.
1557 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1558 __isl_take isl_space *space);
1559 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1560 __isl_take isl_space *space);
1561 __isl_give isl_set *isl_set_nat_universe(
1562 __isl_take isl_space *space);
1563 __isl_give isl_map *isl_map_nat_universe(
1564 __isl_take isl_space *space);
1566 =item * Identity relations
1568 __isl_give isl_basic_map *isl_basic_map_identity(
1569 __isl_take isl_space *space);
1570 __isl_give isl_map *isl_map_identity(
1571 __isl_take isl_space *space);
1573 The number of input and output dimensions in C<space> needs
1576 =item * Lexicographic order
1578 __isl_give isl_map *isl_map_lex_lt(
1579 __isl_take isl_space *set_space);
1580 __isl_give isl_map *isl_map_lex_le(
1581 __isl_take isl_space *set_space);
1582 __isl_give isl_map *isl_map_lex_gt(
1583 __isl_take isl_space *set_space);
1584 __isl_give isl_map *isl_map_lex_ge(
1585 __isl_take isl_space *set_space);
1586 __isl_give isl_map *isl_map_lex_lt_first(
1587 __isl_take isl_space *space, unsigned n);
1588 __isl_give isl_map *isl_map_lex_le_first(
1589 __isl_take isl_space *space, unsigned n);
1590 __isl_give isl_map *isl_map_lex_gt_first(
1591 __isl_take isl_space *space, unsigned n);
1592 __isl_give isl_map *isl_map_lex_ge_first(
1593 __isl_take isl_space *space, unsigned n);
1595 The first four functions take a space for a B<set>
1596 and return relations that express that the elements in the domain
1597 are lexicographically less
1598 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1599 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1600 than the elements in the range.
1601 The last four functions take a space for a map
1602 and return relations that express that the first C<n> dimensions
1603 in the domain are lexicographically less
1604 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1605 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1606 than the first C<n> dimensions in the range.
1610 A basic set or relation can be converted to a set or relation
1611 using the following functions.
1613 __isl_give isl_set *isl_set_from_basic_set(
1614 __isl_take isl_basic_set *bset);
1615 __isl_give isl_map *isl_map_from_basic_map(
1616 __isl_take isl_basic_map *bmap);
1618 Sets and relations can be converted to union sets and relations
1619 using the following functions.
1621 __isl_give isl_union_set *isl_union_set_from_basic_set(
1622 __isl_take isl_basic_set *bset);
1623 __isl_give isl_union_map *isl_union_map_from_basic_map(
1624 __isl_take isl_basic_map *bmap);
1625 __isl_give isl_union_set *isl_union_set_from_set(
1626 __isl_take isl_set *set);
1627 __isl_give isl_union_map *isl_union_map_from_map(
1628 __isl_take isl_map *map);
1630 The inverse conversions below can only be used if the input
1631 union set or relation is known to contain elements in exactly one
1634 __isl_give isl_set *isl_set_from_union_set(
1635 __isl_take isl_union_set *uset);
1636 __isl_give isl_map *isl_map_from_union_map(
1637 __isl_take isl_union_map *umap);
1639 Sets and relations can be copied and freed again using the following
1642 __isl_give isl_basic_set *isl_basic_set_copy(
1643 __isl_keep isl_basic_set *bset);
1644 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1645 __isl_give isl_union_set *isl_union_set_copy(
1646 __isl_keep isl_union_set *uset);
1647 __isl_give isl_basic_map *isl_basic_map_copy(
1648 __isl_keep isl_basic_map *bmap);
1649 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1650 __isl_give isl_union_map *isl_union_map_copy(
1651 __isl_keep isl_union_map *umap);
1652 __isl_null isl_basic_set *isl_basic_set_free(
1653 __isl_take isl_basic_set *bset);
1654 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1655 __isl_null isl_union_set *isl_union_set_free(
1656 __isl_take isl_union_set *uset);
1657 __isl_null isl_basic_map *isl_basic_map_free(
1658 __isl_take isl_basic_map *bmap);
1659 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1660 __isl_null isl_union_map *isl_union_map_free(
1661 __isl_take isl_union_map *umap);
1663 Other sets and relations can be constructed by starting
1664 from a universe set or relation, adding equality and/or
1665 inequality constraints and then projecting out the
1666 existentially quantified variables, if any.
1667 Constraints can be constructed, manipulated and
1668 added to (or removed from) (basic) sets and relations
1669 using the following functions.
1671 #include <isl/constraint.h>
1672 __isl_give isl_constraint *isl_equality_alloc(
1673 __isl_take isl_local_space *ls);
1674 __isl_give isl_constraint *isl_inequality_alloc(
1675 __isl_take isl_local_space *ls);
1676 __isl_give isl_constraint *isl_constraint_set_constant_si(
1677 __isl_take isl_constraint *constraint, int v);
1678 __isl_give isl_constraint *isl_constraint_set_constant_val(
1679 __isl_take isl_constraint *constraint,
1680 __isl_take isl_val *v);
1681 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1682 __isl_take isl_constraint *constraint,
1683 enum isl_dim_type type, int pos, int v);
1684 __isl_give isl_constraint *
1685 isl_constraint_set_coefficient_val(
1686 __isl_take isl_constraint *constraint,
1687 enum isl_dim_type type, int pos,
1688 __isl_take isl_val *v);
1689 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1690 __isl_take isl_basic_map *bmap,
1691 __isl_take isl_constraint *constraint);
1692 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1693 __isl_take isl_basic_set *bset,
1694 __isl_take isl_constraint *constraint);
1695 __isl_give isl_map *isl_map_add_constraint(
1696 __isl_take isl_map *map,
1697 __isl_take isl_constraint *constraint);
1698 __isl_give isl_set *isl_set_add_constraint(
1699 __isl_take isl_set *set,
1700 __isl_take isl_constraint *constraint);
1701 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1702 __isl_take isl_basic_set *bset,
1703 __isl_take isl_constraint *constraint);
1705 For example, to create a set containing the even integers
1706 between 10 and 42, you would use the following code.
1709 isl_local_space *ls;
1711 isl_basic_set *bset;
1713 space = isl_space_set_alloc(ctx, 0, 2);
1714 bset = isl_basic_set_universe(isl_space_copy(space));
1715 ls = isl_local_space_from_space(space);
1717 c = isl_equality_alloc(isl_local_space_copy(ls));
1718 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1719 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1720 bset = isl_basic_set_add_constraint(bset, c);
1722 c = isl_inequality_alloc(isl_local_space_copy(ls));
1723 c = isl_constraint_set_constant_si(c, -10);
1724 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1725 bset = isl_basic_set_add_constraint(bset, c);
1727 c = isl_inequality_alloc(ls);
1728 c = isl_constraint_set_constant_si(c, 42);
1729 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1730 bset = isl_basic_set_add_constraint(bset, c);
1732 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1736 isl_basic_set *bset;
1737 bset = isl_basic_set_read_from_str(ctx,
1738 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1740 A basic set or relation can also be constructed from two matrices
1741 describing the equalities and the inequalities.
1743 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1744 __isl_take isl_space *space,
1745 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1746 enum isl_dim_type c1,
1747 enum isl_dim_type c2, enum isl_dim_type c3,
1748 enum isl_dim_type c4);
1749 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1750 __isl_take isl_space *space,
1751 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1752 enum isl_dim_type c1,
1753 enum isl_dim_type c2, enum isl_dim_type c3,
1754 enum isl_dim_type c4, enum isl_dim_type c5);
1756 The C<isl_dim_type> arguments indicate the order in which
1757 different kinds of variables appear in the input matrices
1758 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1759 C<isl_dim_set> and C<isl_dim_div> for sets and
1760 of C<isl_dim_cst>, C<isl_dim_param>,
1761 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1763 A (basic or union) set or relation can also be constructed from a
1764 (union) (piecewise) (multiple) affine expression
1765 or a list of affine expressions
1766 (See L</"Functions">).
1768 __isl_give isl_basic_map *isl_basic_map_from_aff(
1769 __isl_take isl_aff *aff);
1770 __isl_give isl_map *isl_map_from_aff(
1771 __isl_take isl_aff *aff);
1772 __isl_give isl_set *isl_set_from_pw_aff(
1773 __isl_take isl_pw_aff *pwaff);
1774 __isl_give isl_map *isl_map_from_pw_aff(
1775 __isl_take isl_pw_aff *pwaff);
1776 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1777 __isl_take isl_space *domain_space,
1778 __isl_take isl_aff_list *list);
1779 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1780 __isl_take isl_multi_aff *maff)
1781 __isl_give isl_map *isl_map_from_multi_aff(
1782 __isl_take isl_multi_aff *maff)
1783 __isl_give isl_set *isl_set_from_pw_multi_aff(
1784 __isl_take isl_pw_multi_aff *pma);
1785 __isl_give isl_map *isl_map_from_pw_multi_aff(
1786 __isl_take isl_pw_multi_aff *pma);
1787 __isl_give isl_set *isl_set_from_multi_pw_aff(
1788 __isl_take isl_multi_pw_aff *mpa);
1789 __isl_give isl_map *isl_map_from_multi_pw_aff(
1790 __isl_take isl_multi_pw_aff *mpa);
1791 __isl_give isl_union_map *
1792 isl_union_map_from_union_pw_multi_aff(
1793 __isl_take isl_union_pw_multi_aff *upma);
1795 The C<domain_space> argument describes the domain of the resulting
1796 basic relation. It is required because the C<list> may consist
1797 of zero affine expressions.
1799 =head2 Inspecting Sets and Relations
1801 Usually, the user should not have to care about the actual constraints
1802 of the sets and maps, but should instead apply the abstract operations
1803 explained in the following sections.
1804 Occasionally, however, it may be required to inspect the individual
1805 coefficients of the constraints. This section explains how to do so.
1806 In these cases, it may also be useful to have C<isl> compute
1807 an explicit representation of the existentially quantified variables.
1809 __isl_give isl_set *isl_set_compute_divs(
1810 __isl_take isl_set *set);
1811 __isl_give isl_map *isl_map_compute_divs(
1812 __isl_take isl_map *map);
1813 __isl_give isl_union_set *isl_union_set_compute_divs(
1814 __isl_take isl_union_set *uset);
1815 __isl_give isl_union_map *isl_union_map_compute_divs(
1816 __isl_take isl_union_map *umap);
1818 This explicit representation defines the existentially quantified
1819 variables as integer divisions of the other variables, possibly
1820 including earlier existentially quantified variables.
1821 An explicitly represented existentially quantified variable therefore
1822 has a unique value when the values of the other variables are known.
1823 If, furthermore, the same existentials, i.e., existentials
1824 with the same explicit representations, should appear in the
1825 same order in each of the disjuncts of a set or map, then the user should call
1826 either of the following functions.
1828 __isl_give isl_set *isl_set_align_divs(
1829 __isl_take isl_set *set);
1830 __isl_give isl_map *isl_map_align_divs(
1831 __isl_take isl_map *map);
1833 Alternatively, the existentially quantified variables can be removed
1834 using the following functions, which compute an overapproximation.
1836 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1837 __isl_take isl_basic_set *bset);
1838 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1839 __isl_take isl_basic_map *bmap);
1840 __isl_give isl_set *isl_set_remove_divs(
1841 __isl_take isl_set *set);
1842 __isl_give isl_map *isl_map_remove_divs(
1843 __isl_take isl_map *map);
1845 It is also possible to only remove those divs that are defined
1846 in terms of a given range of dimensions or only those for which
1847 no explicit representation is known.
1849 __isl_give isl_basic_set *
1850 isl_basic_set_remove_divs_involving_dims(
1851 __isl_take isl_basic_set *bset,
1852 enum isl_dim_type type,
1853 unsigned first, unsigned n);
1854 __isl_give isl_basic_map *
1855 isl_basic_map_remove_divs_involving_dims(
1856 __isl_take isl_basic_map *bmap,
1857 enum isl_dim_type type,
1858 unsigned first, unsigned n);
1859 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1860 __isl_take isl_set *set, enum isl_dim_type type,
1861 unsigned first, unsigned n);
1862 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1863 __isl_take isl_map *map, enum isl_dim_type type,
1864 unsigned first, unsigned n);
1866 __isl_give isl_basic_set *
1867 isl_basic_set_remove_unknown_divs(
1868 __isl_take isl_basic_set *bset);
1869 __isl_give isl_set *isl_set_remove_unknown_divs(
1870 __isl_take isl_set *set);
1871 __isl_give isl_map *isl_map_remove_unknown_divs(
1872 __isl_take isl_map *map);
1874 To iterate over all the sets or maps in a union set or map, use
1876 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1877 int (*fn)(__isl_take isl_set *set, void *user),
1879 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1880 int (*fn)(__isl_take isl_map *map, void *user),
1883 The number of sets or maps in a union set or map can be obtained
1886 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1887 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1889 To extract the set or map in a given space from a union, use
1891 __isl_give isl_set *isl_union_set_extract_set(
1892 __isl_keep isl_union_set *uset,
1893 __isl_take isl_space *space);
1894 __isl_give isl_map *isl_union_map_extract_map(
1895 __isl_keep isl_union_map *umap,
1896 __isl_take isl_space *space);
1898 To iterate over all the basic sets or maps in a set or map, use
1900 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1901 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1903 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1904 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1907 The callback function C<fn> should return 0 if successful and
1908 -1 if an error occurs. In the latter case, or if any other error
1909 occurs, the above functions will return -1.
1911 It should be noted that C<isl> does not guarantee that
1912 the basic sets or maps passed to C<fn> are disjoint.
1913 If this is required, then the user should call one of
1914 the following functions first.
1916 __isl_give isl_set *isl_set_make_disjoint(
1917 __isl_take isl_set *set);
1918 __isl_give isl_map *isl_map_make_disjoint(
1919 __isl_take isl_map *map);
1921 The number of basic sets in a set can be obtained
1922 or the number of basic maps in a map can be obtained
1925 #include <isl/set.h>
1926 int isl_set_n_basic_set(__isl_keep isl_set *set);
1928 #include <isl/map.h>
1929 int isl_map_n_basic_map(__isl_keep isl_map *map);
1931 To iterate over the constraints of a basic set or map, use
1933 #include <isl/constraint.h>
1935 int isl_basic_set_n_constraint(
1936 __isl_keep isl_basic_set *bset);
1937 int isl_basic_set_foreach_constraint(
1938 __isl_keep isl_basic_set *bset,
1939 int (*fn)(__isl_take isl_constraint *c, void *user),
1941 int isl_basic_map_n_constraint(
1942 __isl_keep isl_basic_map *bmap);
1943 int isl_basic_map_foreach_constraint(
1944 __isl_keep isl_basic_map *bmap,
1945 int (*fn)(__isl_take isl_constraint *c, void *user),
1947 __isl_null isl_constraint *isl_constraint_free(
1948 __isl_take isl_constraint *c);
1950 Again, the callback function C<fn> should return 0 if successful and
1951 -1 if an error occurs. In the latter case, or if any other error
1952 occurs, the above functions will return -1.
1953 The constraint C<c> represents either an equality or an inequality.
1954 Use the following function to find out whether a constraint
1955 represents an equality. If not, it represents an inequality.
1957 int isl_constraint_is_equality(
1958 __isl_keep isl_constraint *constraint);
1960 It is also possible to obtain a list of constraints from a basic
1963 #include <isl/constraint.h>
1964 __isl_give isl_constraint_list *
1965 isl_basic_map_get_constraint_list(
1966 __isl_keep isl_basic_map *bmap);
1967 __isl_give isl_constraint_list *
1968 isl_basic_set_get_constraint_list(
1969 __isl_keep isl_basic_set *bset);
1971 These functions require that all existentially quantified variables
1972 have an explicit representation.
1973 The returned list can be manipulated using the functions in L<"Lists">.
1975 The coefficients of the constraints can be inspected using
1976 the following functions.
1978 int isl_constraint_is_lower_bound(
1979 __isl_keep isl_constraint *constraint,
1980 enum isl_dim_type type, unsigned pos);
1981 int isl_constraint_is_upper_bound(
1982 __isl_keep isl_constraint *constraint,
1983 enum isl_dim_type type, unsigned pos);
1984 __isl_give isl_val *isl_constraint_get_constant_val(
1985 __isl_keep isl_constraint *constraint);
1986 __isl_give isl_val *isl_constraint_get_coefficient_val(
1987 __isl_keep isl_constraint *constraint,
1988 enum isl_dim_type type, int pos);
1990 The explicit representations of the existentially quantified
1991 variables can be inspected using the following function.
1992 Note that the user is only allowed to use this function
1993 if the inspected set or map is the result of a call
1994 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1995 The existentially quantified variable is equal to the floor
1996 of the returned affine expression. The affine expression
1997 itself can be inspected using the functions in
2000 __isl_give isl_aff *isl_constraint_get_div(
2001 __isl_keep isl_constraint *constraint, int pos);
2003 To obtain the constraints of a basic set or map in matrix
2004 form, use the following functions.
2006 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2007 __isl_keep isl_basic_set *bset,
2008 enum isl_dim_type c1, enum isl_dim_type c2,
2009 enum isl_dim_type c3, enum isl_dim_type c4);
2010 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2011 __isl_keep isl_basic_set *bset,
2012 enum isl_dim_type c1, enum isl_dim_type c2,
2013 enum isl_dim_type c3, enum isl_dim_type c4);
2014 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2015 __isl_keep isl_basic_map *bmap,
2016 enum isl_dim_type c1,
2017 enum isl_dim_type c2, enum isl_dim_type c3,
2018 enum isl_dim_type c4, enum isl_dim_type c5);
2019 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2020 __isl_keep isl_basic_map *bmap,
2021 enum isl_dim_type c1,
2022 enum isl_dim_type c2, enum isl_dim_type c3,
2023 enum isl_dim_type c4, enum isl_dim_type c5);
2025 The C<isl_dim_type> arguments dictate the order in which
2026 different kinds of variables appear in the resulting matrix.
2027 For set inputs, they should be a permutation of
2028 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2029 For map inputs, they should be a permutation of
2030 C<isl_dim_cst>, C<isl_dim_param>,
2031 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2035 Points are elements of a set. They can be used to construct
2036 simple sets (boxes) or they can be used to represent the
2037 individual elements of a set.
2038 The zero point (the origin) can be created using
2040 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2042 The coordinates of a point can be inspected, set and changed
2045 __isl_give isl_val *isl_point_get_coordinate_val(
2046 __isl_keep isl_point *pnt,
2047 enum isl_dim_type type, int pos);
2048 __isl_give isl_point *isl_point_set_coordinate_val(
2049 __isl_take isl_point *pnt,
2050 enum isl_dim_type type, int pos,
2051 __isl_take isl_val *v);
2053 __isl_give isl_point *isl_point_add_ui(
2054 __isl_take isl_point *pnt,
2055 enum isl_dim_type type, int pos, unsigned val);
2056 __isl_give isl_point *isl_point_sub_ui(
2057 __isl_take isl_point *pnt,
2058 enum isl_dim_type type, int pos, unsigned val);
2060 Points can be copied or freed using
2062 __isl_give isl_point *isl_point_copy(
2063 __isl_keep isl_point *pnt);
2064 void isl_point_free(__isl_take isl_point *pnt);
2066 A singleton set can be created from a point using
2068 __isl_give isl_basic_set *isl_basic_set_from_point(
2069 __isl_take isl_point *pnt);
2070 __isl_give isl_set *isl_set_from_point(
2071 __isl_take isl_point *pnt);
2073 and a box can be created from two opposite extremal points using
2075 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2076 __isl_take isl_point *pnt1,
2077 __isl_take isl_point *pnt2);
2078 __isl_give isl_set *isl_set_box_from_points(
2079 __isl_take isl_point *pnt1,
2080 __isl_take isl_point *pnt2);
2082 All elements of a B<bounded> (union) set can be enumerated using
2083 the following functions.
2085 int isl_set_foreach_point(__isl_keep isl_set *set,
2086 int (*fn)(__isl_take isl_point *pnt, void *user),
2088 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2089 int (*fn)(__isl_take isl_point *pnt, void *user),
2092 The function C<fn> is called for each integer point in
2093 C<set> with as second argument the last argument of
2094 the C<isl_set_foreach_point> call. The function C<fn>
2095 should return C<0> on success and C<-1> on failure.
2096 In the latter case, C<isl_set_foreach_point> will stop
2097 enumerating and return C<-1> as well.
2098 If the enumeration is performed successfully and to completion,
2099 then C<isl_set_foreach_point> returns C<0>.
2101 To obtain a single point of a (basic) set, use
2103 __isl_give isl_point *isl_basic_set_sample_point(
2104 __isl_take isl_basic_set *bset);
2105 __isl_give isl_point *isl_set_sample_point(
2106 __isl_take isl_set *set);
2108 If C<set> does not contain any (integer) points, then the
2109 resulting point will be ``void'', a property that can be
2112 int isl_point_is_void(__isl_keep isl_point *pnt);
2116 Besides sets and relation, C<isl> also supports various types of functions.
2117 Each of these types is derived from the value type (see L</"Values">)
2118 or from one of two primitive function types
2119 through the application of zero or more type constructors.
2120 We first describe the primitive type and then we describe
2121 the types derived from these primitive types.
2123 =head3 Primitive Functions
2125 C<isl> support two primitive function types, quasi-affine
2126 expressions and quasipolynomials.
2127 A quasi-affine expression is defined either over a parameter
2128 space or over a set and is composed of integer constants,
2129 parameters and set variables, addition, subtraction and
2130 integer division by an integer constant.
2131 For example, the quasi-affine expression
2133 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2135 maps C<x> to C<2*floor((4 n + x)/9>.
2136 A quasipolynomial is a polynomial expression in quasi-affine
2137 expression. That is, it additionally allows for multiplication.
2138 Note, though, that it is not allowed to construct an integer
2139 division of an expression involving multiplications.
2140 Here is an example of a quasipolynomial that is not
2141 quasi-affine expression
2143 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2145 Note that the external representations of quasi-affine expressions
2146 and quasipolynomials are different. Quasi-affine expressions
2147 use a notation with square brackets just like binary relations,
2148 while quasipolynomials do not. This might change at some point.
2150 If a primitive function is defined over a parameter space,
2151 then the space of the function itself is that of a set.
2152 If it is defined over a set, then the space of the function
2153 is that of a relation. In both cases, the set space (or
2154 the output space) is single-dimensional, anonymous and unstructured.
2155 To create functions with multiple dimensions or with other kinds
2156 of set or output spaces, use multiple expressions
2157 (see L</"Multiple Expressions">).
2161 =item * Quasi-affine Expressions
2163 Besides the expressions described above, a quasi-affine
2164 expression can also be set to NaN. Such expressions
2165 typically represent a failure to represent a result
2166 as a quasi-affine expression.
2168 The zero quasi affine expression or the quasi affine expression
2169 that is equal to a given value or
2170 a specified dimension on a given domain can be created using
2172 #include <isl/aff.h>
2173 __isl_give isl_aff *isl_aff_zero_on_domain(
2174 __isl_take isl_local_space *ls);
2175 __isl_give isl_aff *isl_aff_val_on_domain(
2176 __isl_take isl_local_space *ls,
2177 __isl_take isl_val *val);
2178 __isl_give isl_aff *isl_aff_var_on_domain(
2179 __isl_take isl_local_space *ls,
2180 enum isl_dim_type type, unsigned pos);
2181 __isl_give isl_aff *isl_aff_nan_on_domain(
2182 __isl_take isl_local_space *ls);
2184 Quasi affine expressions can be copied and freed using
2186 #include <isl/aff.h>
2187 __isl_give isl_aff *isl_aff_copy(
2188 __isl_keep isl_aff *aff);
2189 __isl_null isl_aff *isl_aff_free(
2190 __isl_take isl_aff *aff);
2192 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2193 using the following function. The constraint is required to have
2194 a non-zero coefficient for the specified dimension.
2196 #include <isl/constraint.h>
2197 __isl_give isl_aff *isl_constraint_get_bound(
2198 __isl_keep isl_constraint *constraint,
2199 enum isl_dim_type type, int pos);
2201 The entire affine expression of the constraint can also be extracted
2202 using the following function.
2204 #include <isl/constraint.h>
2205 __isl_give isl_aff *isl_constraint_get_aff(
2206 __isl_keep isl_constraint *constraint);
2208 Conversely, an equality constraint equating
2209 the affine expression to zero or an inequality constraint enforcing
2210 the affine expression to be non-negative, can be constructed using
2212 __isl_give isl_constraint *isl_equality_from_aff(
2213 __isl_take isl_aff *aff);
2214 __isl_give isl_constraint *isl_inequality_from_aff(
2215 __isl_take isl_aff *aff);
2217 The coefficients and the integer divisions of an affine expression
2218 can be inspected using the following functions.
2220 #include <isl/aff.h>
2221 __isl_give isl_val *isl_aff_get_constant_val(
2222 __isl_keep isl_aff *aff);
2223 __isl_give isl_val *isl_aff_get_coefficient_val(
2224 __isl_keep isl_aff *aff,
2225 enum isl_dim_type type, int pos);
2226 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2227 enum isl_dim_type type, int pos);
2228 __isl_give isl_val *isl_aff_get_denominator_val(
2229 __isl_keep isl_aff *aff);
2230 __isl_give isl_aff *isl_aff_get_div(
2231 __isl_keep isl_aff *aff, int pos);
2233 They can be modified using the following functions.
2235 #include <isl/aff.h>
2236 __isl_give isl_aff *isl_aff_set_constant_si(
2237 __isl_take isl_aff *aff, int v);
2238 __isl_give isl_aff *isl_aff_set_constant_val(
2239 __isl_take isl_aff *aff, __isl_take isl_val *v);
2240 __isl_give isl_aff *isl_aff_set_coefficient_si(
2241 __isl_take isl_aff *aff,
2242 enum isl_dim_type type, int pos, int v);
2243 __isl_give isl_aff *isl_aff_set_coefficient_val(
2244 __isl_take isl_aff *aff,
2245 enum isl_dim_type type, int pos,
2246 __isl_take isl_val *v);
2248 __isl_give isl_aff *isl_aff_add_constant_si(
2249 __isl_take isl_aff *aff, int v);
2250 __isl_give isl_aff *isl_aff_add_constant_val(
2251 __isl_take isl_aff *aff, __isl_take isl_val *v);
2252 __isl_give isl_aff *isl_aff_add_constant_num_si(
2253 __isl_take isl_aff *aff, int v);
2254 __isl_give isl_aff *isl_aff_add_coefficient_si(
2255 __isl_take isl_aff *aff,
2256 enum isl_dim_type type, int pos, int v);
2257 __isl_give isl_aff *isl_aff_add_coefficient_val(
2258 __isl_take isl_aff *aff,
2259 enum isl_dim_type type, int pos,
2260 __isl_take isl_val *v);
2262 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2263 set the I<numerator> of the constant or coefficient, while
2264 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2265 the constant or coefficient as a whole.
2266 The C<add_constant> and C<add_coefficient> functions add an integer
2267 or rational value to
2268 the possibly rational constant or coefficient.
2269 The C<add_constant_num> functions add an integer value to
2272 =item * Quasipolynomials
2274 Some simple quasipolynomials can be created using the following functions.
2276 #include <isl/polynomial.h>
2277 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2278 __isl_take isl_space *domain);
2279 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2280 __isl_take isl_space *domain);
2281 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2282 __isl_take isl_space *domain);
2283 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2284 __isl_take isl_space *domain);
2285 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2286 __isl_take isl_space *domain);
2287 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2288 __isl_take isl_space *domain,
2289 __isl_take isl_val *val);
2290 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2291 __isl_take isl_space *domain,
2292 enum isl_dim_type type, unsigned pos);
2293 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2294 __isl_take isl_aff *aff);
2296 Recall that the space in which a quasipolynomial lives is a map space
2297 with a one-dimensional range. The C<domain> argument in some of
2298 the functions above corresponds to the domain of this map space.
2300 Quasipolynomials can be copied and freed again using the following
2303 #include <isl/polynomial.h>
2304 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2305 __isl_keep isl_qpolynomial *qp);
2306 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2307 __isl_take isl_qpolynomial *qp);
2309 The constant term of a quasipolynomial can be extracted using
2311 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2312 __isl_keep isl_qpolynomial *qp);
2314 To iterate over all terms in a quasipolynomial,
2317 int isl_qpolynomial_foreach_term(
2318 __isl_keep isl_qpolynomial *qp,
2319 int (*fn)(__isl_take isl_term *term,
2320 void *user), void *user);
2322 The terms themselves can be inspected and freed using
2325 unsigned isl_term_dim(__isl_keep isl_term *term,
2326 enum isl_dim_type type);
2327 __isl_give isl_val *isl_term_get_coefficient_val(
2328 __isl_keep isl_term *term);
2329 int isl_term_get_exp(__isl_keep isl_term *term,
2330 enum isl_dim_type type, unsigned pos);
2331 __isl_give isl_aff *isl_term_get_div(
2332 __isl_keep isl_term *term, unsigned pos);
2333 void isl_term_free(__isl_take isl_term *term);
2335 Each term is a product of parameters, set variables and
2336 integer divisions. The function C<isl_term_get_exp>
2337 returns the exponent of a given dimensions in the given term.
2343 A reduction represents a maximum or a minimum of its
2345 The only reduction type defined by C<isl> is
2346 C<isl_qpolynomial_fold>.
2348 There are currently no functions to directly create such
2349 objects, but they do appear in the piecewise quasipolynomial
2350 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2352 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2354 Reductions can be copied and freed using
2355 the following functions.
2357 #include <isl/polynomial.h>
2358 __isl_give isl_qpolynomial_fold *
2359 isl_qpolynomial_fold_copy(
2360 __isl_keep isl_qpolynomial_fold *fold);
2361 void isl_qpolynomial_fold_free(
2362 __isl_take isl_qpolynomial_fold *fold);
2364 To iterate over all quasipolynomials in a reduction, use
2366 int isl_qpolynomial_fold_foreach_qpolynomial(
2367 __isl_keep isl_qpolynomial_fold *fold,
2368 int (*fn)(__isl_take isl_qpolynomial *qp,
2369 void *user), void *user);
2371 =head3 Multiple Expressions
2373 A multiple expression represents a sequence of zero or
2374 more base expressions, all defined on the same domain space.
2375 The domain space of the multiple expression is the same
2376 as that of the base expressions, but the range space
2377 can be any space. In case the base expressions have
2378 a set space, the corresponding multiple expression
2379 also has a set space.
2380 Objects of the value type do not have an associated space.
2381 The space of a multiple value is therefore always a set space.
2383 The multiple expression types defined by C<isl>
2384 are C<isl_multi_val>, C<isl_multi_aff> and C<isl_multi_pw_aff>.
2386 A multiple expression with the value zero for
2387 each output (or set) dimension can be created
2388 using the following functions.
2390 #include <isl/val.h>
2391 __isl_give isl_multi_val *isl_multi_val_zero(
2392 __isl_take isl_space *space);
2394 #include <isl/aff.h>
2395 __isl_give isl_multi_aff *isl_multi_aff_zero(
2396 __isl_take isl_space *space);
2397 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2398 __isl_take isl_space *space);
2400 An identity function can be created using the following
2401 functions. The space needs to be that of a relation
2402 with the same number of input and output dimensions.
2404 #include <isl/aff.h>
2405 __isl_give isl_multi_aff *isl_multi_aff_identity(
2406 __isl_take isl_space *space);
2407 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2408 __isl_take isl_space *space);
2410 A function that performs a projection on a universe
2411 relation or set can be created using the following functions.
2412 See also the corresponding
2413 projection operations in L</"Unary Operations">.
2415 #include <isl/aff.h>
2416 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2417 __isl_take isl_space *space);
2418 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2419 __isl_take isl_space *space);
2420 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2421 __isl_take isl_space *space,
2422 enum isl_dim_type type,
2423 unsigned first, unsigned n);
2425 A multiple expression can be created from a single
2426 base expression using the following functions.
2427 The space of the created multiple expression is the same
2428 as that of the base expression.
2430 #include <isl/aff.h>
2431 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2432 __isl_take isl_aff *aff);
2433 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2434 __isl_take isl_pw_aff *pa);
2436 A multiple expression can be created from a list
2437 of base expression in a specified space.
2438 The domain of this space needs to be the same
2439 as the domains of the base expressions in the list.
2440 If the base expressions have a set space (or no associated space),
2441 then this space also needs to be a set space.
2443 #include <isl/val.h>
2444 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2445 __isl_take isl_space *space,
2446 __isl_take isl_val_list *list);
2448 #include <isl/aff.h>
2449 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2450 __isl_take isl_space *space,
2451 __isl_take isl_aff_list *list);
2453 As a convenience, a multiple piecewise expression can
2454 also be created from a multiple expression.
2455 Each piecewise expression in the result has a single
2458 #include <isl/aff.h>
2459 __isl_give isl_multi_pw_aff *
2460 isl_multi_pw_aff_from_multi_aff(
2461 __isl_take isl_multi_aff *ma);
2463 Multiple expressions can be copied and freed using
2464 the following functions.
2466 #include <isl/val.h>
2467 __isl_give isl_multi_val *isl_multi_val_copy(
2468 __isl_keep isl_multi_val *mv);
2469 __isl_null isl_multi_val *isl_multi_val_free(
2470 __isl_take isl_multi_val *mv);
2472 #include <isl/aff.h>
2473 __isl_give isl_multi_aff *isl_multi_aff_copy(
2474 __isl_keep isl_multi_aff *maff);
2475 __isl_null isl_multi_aff *isl_multi_aff_free(
2476 __isl_take isl_multi_aff *maff);
2477 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2478 __isl_keep isl_multi_pw_aff *mpa);
2479 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2480 __isl_take isl_multi_pw_aff *mpa);
2482 The base expression at a given position of a multiple
2483 expression can be extracted using the following functions.
2485 #include <isl/val.h>
2486 __isl_give isl_val *isl_multi_val_get_val(
2487 __isl_keep isl_multi_val *mv, int pos);
2489 #include <isl/aff.h>
2490 __isl_give isl_aff *isl_multi_aff_get_aff(
2491 __isl_keep isl_multi_aff *multi, int pos);
2492 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2493 __isl_keep isl_multi_pw_aff *mpa, int pos);
2495 It can be replaced using the following functions.
2497 #include <isl/val.h>
2498 __isl_give isl_multi_val *isl_multi_val_set_val(
2499 __isl_take isl_multi_val *mv, int pos,
2500 __isl_take isl_val *val);
2502 #include <isl/aff.h>
2503 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2504 __isl_take isl_multi_aff *multi, int pos,
2505 __isl_take isl_aff *aff);
2507 =head3 Piecewise Expressions
2509 A piecewise expression is an expression that is described
2510 using zero or more base expression defined over the same
2511 number of cells in the domain space of the base expressions.
2512 All base expressions are defined over the same
2513 domain space and the cells are disjoint.
2514 The space of a piecewise expression is the same as
2515 that of the base expressions.
2516 If the union of the cells is a strict subset of the domain
2517 space, then the value of the piecewise expression outside
2518 this union is different for types derived from quasi-affine
2519 expressions and those derived from quasipolynomials.
2520 Piecewise expressions derived from quasi-affine expressions
2521 are considered to be undefined outside the union of their cells.
2522 Piecewise expressions derived from quasipolynomials
2523 are considered to be zero outside the union of their cells.
2525 Piecewise quasipolynomials are mainly used by the C<barvinok>
2526 library for representing the number of elements in a parametric set or map.
2527 For example, the piecewise quasipolynomial
2529 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2531 represents the number of points in the map
2533 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2535 The piecewise expression types defined by C<isl>
2536 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2537 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2539 A piecewise expression with no cells can be created using
2540 the following functions.
2542 #include <isl/aff.h>
2543 __isl_give isl_pw_aff *isl_pw_aff_empty(
2544 __isl_take isl_space *space);
2545 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2546 __isl_take isl_space *space);
2548 A piecewise expression with a single universe cell can be
2549 created using the following functions.
2551 #include <isl/aff.h>
2552 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2553 __isl_take isl_aff *aff);
2554 __isl_give isl_pw_multi_aff *
2555 isl_pw_multi_aff_from_multi_aff(
2556 __isl_take isl_multi_aff *ma);
2558 #include <isl/polynomial.h>
2559 __isl_give isl_pw_qpolynomial *
2560 isl_pw_qpolynomial_from_qpolynomial(
2561 __isl_take isl_qpolynomial *qp);
2563 A piecewise expression with a single specified cell can be
2564 created using the following functions.
2566 #include <isl/aff.h>
2567 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2568 __isl_take isl_set *set, __isl_take isl_aff *aff);
2569 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2570 __isl_take isl_set *set,
2571 __isl_take isl_multi_aff *maff);
2573 #include <isl/polynomial.h>
2574 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2575 __isl_take isl_set *set,
2576 __isl_take isl_qpolynomial *qp);
2578 The following convenience functions first create a base expression and
2579 then create a piecewise expression over a universe domain.
2581 #include <isl/aff.h>
2582 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2583 __isl_take isl_local_space *ls);
2584 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2585 __isl_take isl_local_space *ls,
2586 enum isl_dim_type type, unsigned pos);
2587 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2588 __isl_take isl_local_space *ls);
2589 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2590 __isl_take isl_space *space);
2591 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2592 __isl_take isl_space *space);
2593 __isl_give isl_pw_multi_aff *
2594 isl_pw_multi_aff_project_out_map(
2595 __isl_take isl_space *space,
2596 enum isl_dim_type type,
2597 unsigned first, unsigned n);
2599 #include <isl/polynomial.h>
2600 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2601 __isl_take isl_space *space);
2603 As a convenience, a piecewise multiple expression can
2604 also be created from a piecewise expression.
2605 Each multiple expression in the result is derived
2606 from the corresponding base expression.
2608 #include <isl/aff.h>
2609 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2610 __isl_take isl_pw_aff *pa);
2612 Similarly, a piecewise quasipolynomial can be
2613 created from a piecewise quasi-affine expression using
2614 the following function.
2616 #include <isl/polynomial.h>
2617 __isl_give isl_pw_qpolynomial *
2618 isl_pw_qpolynomial_from_pw_aff(
2619 __isl_take isl_pw_aff *pwaff);
2621 Piecewise expressions can be copied and freed using the following functions.
2623 #include <isl/aff.h>
2624 __isl_give isl_pw_aff *isl_pw_aff_copy(
2625 __isl_keep isl_pw_aff *pwaff);
2626 __isl_null isl_pw_aff *isl_pw_aff_free(
2627 __isl_take isl_pw_aff *pwaff);
2628 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2629 __isl_keep isl_pw_multi_aff *pma);
2630 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2631 __isl_take isl_pw_multi_aff *pma);
2633 #include <isl/polynomial.h>
2634 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2635 __isl_keep isl_pw_qpolynomial *pwqp);
2636 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2637 __isl_take isl_pw_qpolynomial *pwqp);
2638 __isl_give isl_pw_qpolynomial_fold *
2639 isl_pw_qpolynomial_fold_copy(
2640 __isl_keep isl_pw_qpolynomial_fold *pwf);
2641 __isl_null isl_pw_qpolynomial_fold *
2642 isl_pw_qpolynomial_fold_free(
2643 __isl_take isl_pw_qpolynomial_fold *pwf);
2645 To iterate over the different cells of a piecewise expression,
2646 use the following functions.
2648 #include <isl/aff.h>
2649 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2650 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2651 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2652 int (*fn)(__isl_take isl_set *set,
2653 __isl_take isl_aff *aff,
2654 void *user), void *user);
2655 int isl_pw_multi_aff_foreach_piece(
2656 __isl_keep isl_pw_multi_aff *pma,
2657 int (*fn)(__isl_take isl_set *set,
2658 __isl_take isl_multi_aff *maff,
2659 void *user), void *user);
2661 #include <isl/polynomial.h>
2662 int isl_pw_qpolynomial_foreach_piece(
2663 __isl_keep isl_pw_qpolynomial *pwqp,
2664 int (*fn)(__isl_take isl_set *set,
2665 __isl_take isl_qpolynomial *qp,
2666 void *user), void *user);
2667 int isl_pw_qpolynomial_foreach_lifted_piece(
2668 __isl_keep isl_pw_qpolynomial *pwqp,
2669 int (*fn)(__isl_take isl_set *set,
2670 __isl_take isl_qpolynomial *qp,
2671 void *user), void *user);
2672 int isl_pw_qpolynomial_fold_foreach_piece(
2673 __isl_keep isl_pw_qpolynomial_fold *pwf,
2674 int (*fn)(__isl_take isl_set *set,
2675 __isl_take isl_qpolynomial_fold *fold,
2676 void *user), void *user);
2677 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2678 __isl_keep isl_pw_qpolynomial_fold *pwf,
2679 int (*fn)(__isl_take isl_set *set,
2680 __isl_take isl_qpolynomial_fold *fold,
2681 void *user), void *user);
2683 As usual, the function C<fn> should return C<0> on success
2684 and C<-1> on failure. The difference between
2685 C<isl_pw_qpolynomial_foreach_piece> and
2686 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2687 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2688 compute unique representations for all existentially quantified
2689 variables and then turn these existentially quantified variables
2690 into extra set variables, adapting the associated quasipolynomial
2691 accordingly. This means that the C<set> passed to C<fn>
2692 will not have any existentially quantified variables, but that
2693 the dimensions of the sets may be different for different
2694 invocations of C<fn>.
2695 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2696 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2698 A piecewise expression consisting of the expressions at a given
2699 position of a piecewise multiple expression can be extracted
2700 using the following function.
2702 #include <isl/aff.h>
2703 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2704 __isl_keep isl_pw_multi_aff *pma, int pos);
2706 These expressions can be replaced using the following function.
2708 #include <isl/aff.h>
2709 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2710 __isl_take isl_pw_multi_aff *pma, unsigned pos,
2711 __isl_take isl_pw_aff *pa);
2713 Note that there is a difference between C<isl_multi_pw_aff> and
2714 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
2715 affine expressions, while the second is a piecewise sequence
2716 of affine expressions. In particular, each of the piecewise
2717 affine expressions in an C<isl_multi_pw_aff> may have a different
2718 domain, while all multiple expressions associated to a cell
2719 in an C<isl_pw_multi_aff> have the same domain.
2720 It is possible to convert between the two, but when converting
2721 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
2722 of the result is the intersection of the domains of the input.
2723 The reverse conversion is exact.
2725 #include <isl/aff.h>
2726 __isl_give isl_pw_multi_aff *
2727 isl_pw_multi_aff_from_multi_pw_aff(
2728 __isl_take isl_multi_pw_aff *mpa);
2729 __isl_give isl_multi_pw_aff *
2730 isl_multi_pw_aff_from_pw_multi_aff(
2731 __isl_take isl_pw_multi_aff *pma);
2733 =head3 Union Expressions
2735 A union expression collects base expressions defined
2736 over different domains. The space of a union expression
2737 is that of the shared parameter space.
2739 The union expression types defined by C<isl>
2740 are C<isl_union_pw_multi_aff>, C<isl_union_pw_qpolynomial> and
2741 C<isl_union_pw_qpolynomial_fold>.
2743 An empty union expression can be created using the following functions.
2745 #include <isl/aff.h>
2746 __isl_give isl_union_pw_multi_aff *
2747 isl_union_pw_multi_aff_empty(
2748 __isl_take isl_space *space);
2750 #include <isl/polynomial.h>
2751 __isl_give isl_union_pw_qpolynomial *
2752 isl_union_pw_qpolynomial_zero(
2753 __isl_take isl_space *space);
2755 A union expression containing a single base expression
2756 can be created using the following functions.
2758 #include <isl/aff.h>
2759 __isl_give isl_union_pw_multi_aff *
2760 isl_union_pw_multi_aff_from_pw_multi_aff(
2761 __isl_take isl_pw_multi_aff *pma);
2763 #include <isl/polynomial.h>
2764 __isl_give isl_union_pw_qpolynomial *
2765 isl_union_pw_qpolynomial_from_pw_qpolynomial(
2766 __isl_take isl_pw_qpolynomial *pwqp);
2768 A base expression can be added to a union expression using
2769 the following functions.
2771 #include <isl/aff.h>
2772 __isl_give isl_union_pw_multi_aff *
2773 isl_union_pw_multi_aff_add_pw_multi_aff(
2774 __isl_take isl_union_pw_multi_aff *upma,
2775 __isl_take isl_pw_multi_aff *pma);
2777 #include <isl/polynomial.h>
2778 __isl_give isl_union_pw_qpolynomial *
2779 isl_union_pw_qpolynomial_add_pw_qpolynomial(
2780 __isl_take isl_union_pw_qpolynomial *upwqp,
2781 __isl_take isl_pw_qpolynomial *pwqp);
2783 Union expressions can be copied and freed using
2784 the following functions.
2786 #include <isl/aff.h>
2787 __isl_give isl_union_pw_multi_aff *
2788 isl_union_pw_multi_aff_copy(
2789 __isl_keep isl_union_pw_multi_aff *upma);
2790 __isl_null isl_union_pw_multi_aff *
2791 isl_union_pw_multi_aff_free(
2792 __isl_take isl_union_pw_multi_aff *upma);
2794 #include <isl/polynomial.h>
2795 __isl_give isl_union_pw_qpolynomial *
2796 isl_union_pw_qpolynomial_copy(
2797 __isl_keep isl_union_pw_qpolynomial *upwqp);
2798 __isl_null isl_union_pw_qpolynomial *
2799 isl_union_pw_qpolynomial_free(
2800 __isl_take isl_union_pw_qpolynomial *upwqp);
2801 __isl_give isl_union_pw_qpolynomial_fold *
2802 isl_union_pw_qpolynomial_fold_copy(
2803 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2804 __isl_null isl_union_pw_qpolynomial_fold *
2805 isl_union_pw_qpolynomial_fold_free(
2806 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2808 To iterate over the base expressions in a union expression,
2809 use the following functions.
2811 #include <isl/aff.h>
2812 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
2813 __isl_keep isl_union_pw_multi_aff *upma,
2814 int (*fn)(__isl_take isl_pw_multi_aff *pma,
2815 void *user), void *user);
2817 #include <isl/polynomial.h>
2818 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2819 __isl_keep isl_union_pw_qpolynomial *upwqp,
2820 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
2821 void *user), void *user);
2822 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2823 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2824 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2825 void *user), void *user);
2827 To extract the base expression in a given space from a union, use
2828 the following functions.
2830 #include <isl/aff.h>
2831 __isl_give isl_pw_multi_aff *
2832 isl_union_pw_multi_aff_extract_pw_multi_aff(
2833 __isl_keep isl_union_pw_multi_aff *upma,
2834 __isl_take isl_space *space);
2836 #include <isl/polynomial.h>
2837 __isl_give isl_pw_qpolynomial *
2838 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2839 __isl_keep isl_union_pw_qpolynomial *upwqp,
2840 __isl_take isl_space *space);
2842 =head2 Input and Output
2844 For set and relation,
2845 C<isl> supports its own input/output format, which is similar
2846 to the C<Omega> format, but also supports the C<PolyLib> format
2848 For other object types, typically only an C<isl> format is supported.
2850 =head3 C<isl> format
2852 The C<isl> format is similar to that of C<Omega>, but has a different
2853 syntax for describing the parameters and allows for the definition
2854 of an existentially quantified variable as the integer division
2855 of an affine expression.
2856 For example, the set of integers C<i> between C<0> and C<n>
2857 such that C<i % 10 <= 6> can be described as
2859 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
2862 A set or relation can have several disjuncts, separated
2863 by the keyword C<or>. Each disjunct is either a conjunction
2864 of constraints or a projection (C<exists>) of a conjunction
2865 of constraints. The constraints are separated by the keyword
2868 =head3 C<PolyLib> format
2870 If the represented set is a union, then the first line
2871 contains a single number representing the number of disjuncts.
2872 Otherwise, a line containing the number C<1> is optional.
2874 Each disjunct is represented by a matrix of constraints.
2875 The first line contains two numbers representing
2876 the number of rows and columns,
2877 where the number of rows is equal to the number of constraints
2878 and the number of columns is equal to two plus the number of variables.
2879 The following lines contain the actual rows of the constraint matrix.
2880 In each row, the first column indicates whether the constraint
2881 is an equality (C<0>) or inequality (C<1>). The final column
2882 corresponds to the constant term.
2884 If the set is parametric, then the coefficients of the parameters
2885 appear in the last columns before the constant column.
2886 The coefficients of any existentially quantified variables appear
2887 between those of the set variables and those of the parameters.
2889 =head3 Extended C<PolyLib> format
2891 The extended C<PolyLib> format is nearly identical to the
2892 C<PolyLib> format. The only difference is that the line
2893 containing the number of rows and columns of a constraint matrix
2894 also contains four additional numbers:
2895 the number of output dimensions, the number of input dimensions,
2896 the number of local dimensions (i.e., the number of existentially
2897 quantified variables) and the number of parameters.
2898 For sets, the number of ``output'' dimensions is equal
2899 to the number of set dimensions, while the number of ``input''
2904 Objects can be read from input using the following functions.
2906 #include <isl/val.h>
2907 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
2910 #include <isl/set.h>
2911 __isl_give isl_basic_set *isl_basic_set_read_from_file(
2912 isl_ctx *ctx, FILE *input);
2913 __isl_give isl_basic_set *isl_basic_set_read_from_str(
2914 isl_ctx *ctx, const char *str);
2915 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
2917 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
2920 #include <isl/map.h>
2921 __isl_give isl_basic_map *isl_basic_map_read_from_file(
2922 isl_ctx *ctx, FILE *input);
2923 __isl_give isl_basic_map *isl_basic_map_read_from_str(
2924 isl_ctx *ctx, const char *str);
2925 __isl_give isl_map *isl_map_read_from_file(
2926 isl_ctx *ctx, FILE *input);
2927 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
2930 #include <isl/union_set.h>
2931 __isl_give isl_union_set *isl_union_set_read_from_file(
2932 isl_ctx *ctx, FILE *input);
2933 __isl_give isl_union_set *isl_union_set_read_from_str(
2934 isl_ctx *ctx, const char *str);
2936 #include <isl/union_map.h>
2937 __isl_give isl_union_map *isl_union_map_read_from_file(
2938 isl_ctx *ctx, FILE *input);
2939 __isl_give isl_union_map *isl_union_map_read_from_str(
2940 isl_ctx *ctx, const char *str);
2942 #include <isl/aff.h>
2943 __isl_give isl_aff *isl_aff_read_from_str(
2944 isl_ctx *ctx, const char *str);
2945 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
2946 isl_ctx *ctx, const char *str);
2947 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
2948 isl_ctx *ctx, const char *str);
2949 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
2950 isl_ctx *ctx, const char *str);
2951 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
2952 isl_ctx *ctx, const char *str);
2953 __isl_give isl_union_pw_multi_aff *
2954 isl_union_pw_multi_aff_read_from_str(
2955 isl_ctx *ctx, const char *str);
2957 #include <isl/polynomial.h>
2958 __isl_give isl_union_pw_qpolynomial *
2959 isl_union_pw_qpolynomial_read_from_str(
2960 isl_ctx *ctx, const char *str);
2962 For sets and relations,
2963 the input format is autodetected and may be either the C<PolyLib> format
2964 or the C<isl> format.
2968 Before anything can be printed, an C<isl_printer> needs to
2971 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
2973 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
2974 __isl_null isl_printer *isl_printer_free(
2975 __isl_take isl_printer *printer);
2976 __isl_give char *isl_printer_get_str(
2977 __isl_keep isl_printer *printer);
2979 The printer can be inspected using the following functions.
2981 FILE *isl_printer_get_file(
2982 __isl_keep isl_printer *printer);
2983 int isl_printer_get_output_format(
2984 __isl_keep isl_printer *p);
2986 The behavior of the printer can be modified in various ways
2988 __isl_give isl_printer *isl_printer_set_output_format(
2989 __isl_take isl_printer *p, int output_format);
2990 __isl_give isl_printer *isl_printer_set_indent(
2991 __isl_take isl_printer *p, int indent);
2992 __isl_give isl_printer *isl_printer_set_indent_prefix(
2993 __isl_take isl_printer *p, const char *prefix);
2994 __isl_give isl_printer *isl_printer_indent(
2995 __isl_take isl_printer *p, int indent);
2996 __isl_give isl_printer *isl_printer_set_prefix(
2997 __isl_take isl_printer *p, const char *prefix);
2998 __isl_give isl_printer *isl_printer_set_suffix(
2999 __isl_take isl_printer *p, const char *suffix);
3001 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3002 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3003 and defaults to C<ISL_FORMAT_ISL>.
3004 Each line in the output is prefixed by C<indent_prefix>,
3005 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3006 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3007 In the C<PolyLib> format output,
3008 the coefficients of the existentially quantified variables
3009 appear between those of the set variables and those
3011 The function C<isl_printer_indent> increases the indentation
3012 by the specified amount (which may be negative).
3014 To actually print something, use
3016 #include <isl/printer.h>
3017 __isl_give isl_printer *isl_printer_print_double(
3018 __isl_take isl_printer *p, double d);
3020 #include <isl/val.h>
3021 __isl_give isl_printer *isl_printer_print_val(
3022 __isl_take isl_printer *p, __isl_keep isl_val *v);
3024 #include <isl/set.h>
3025 __isl_give isl_printer *isl_printer_print_basic_set(
3026 __isl_take isl_printer *printer,
3027 __isl_keep isl_basic_set *bset);
3028 __isl_give isl_printer *isl_printer_print_set(
3029 __isl_take isl_printer *printer,
3030 __isl_keep isl_set *set);
3032 #include <isl/map.h>
3033 __isl_give isl_printer *isl_printer_print_basic_map(
3034 __isl_take isl_printer *printer,
3035 __isl_keep isl_basic_map *bmap);
3036 __isl_give isl_printer *isl_printer_print_map(
3037 __isl_take isl_printer *printer,
3038 __isl_keep isl_map *map);
3040 #include <isl/union_set.h>
3041 __isl_give isl_printer *isl_printer_print_union_set(
3042 __isl_take isl_printer *p,
3043 __isl_keep isl_union_set *uset);
3045 #include <isl/union_map.h>
3046 __isl_give isl_printer *isl_printer_print_union_map(
3047 __isl_take isl_printer *p,
3048 __isl_keep isl_union_map *umap);
3050 #include <isl/val.h>
3051 __isl_give isl_printer *isl_printer_print_multi_val(
3052 __isl_take isl_printer *p,
3053 __isl_keep isl_multi_val *mv);
3055 #include <isl/aff.h>
3056 __isl_give isl_printer *isl_printer_print_aff(
3057 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3058 __isl_give isl_printer *isl_printer_print_multi_aff(
3059 __isl_take isl_printer *p,
3060 __isl_keep isl_multi_aff *maff);
3061 __isl_give isl_printer *isl_printer_print_pw_aff(
3062 __isl_take isl_printer *p,
3063 __isl_keep isl_pw_aff *pwaff);
3064 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3065 __isl_take isl_printer *p,
3066 __isl_keep isl_pw_multi_aff *pma);
3067 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3068 __isl_take isl_printer *p,
3069 __isl_keep isl_multi_pw_aff *mpa);
3070 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3071 __isl_take isl_printer *p,
3072 __isl_keep isl_union_pw_multi_aff *upma);
3074 #include <isl/polynomial.h>
3075 __isl_give isl_printer *isl_printer_print_qpolynomial(
3076 __isl_take isl_printer *p,
3077 __isl_keep isl_qpolynomial *qp);
3078 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3079 __isl_take isl_printer *p,
3080 __isl_keep isl_pw_qpolynomial *pwqp);
3081 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3082 __isl_take isl_printer *p,
3083 __isl_keep isl_union_pw_qpolynomial *upwqp);
3085 __isl_give isl_printer *
3086 isl_printer_print_pw_qpolynomial_fold(
3087 __isl_take isl_printer *p,
3088 __isl_keep isl_pw_qpolynomial_fold *pwf);
3089 __isl_give isl_printer *
3090 isl_printer_print_union_pw_qpolynomial_fold(
3091 __isl_take isl_printer *p,
3092 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3094 For C<isl_printer_print_qpolynomial>,
3095 C<isl_printer_print_pw_qpolynomial> and
3096 C<isl_printer_print_pw_qpolynomial_fold>,
3097 the output format of the printer
3098 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3099 For C<isl_printer_print_union_pw_qpolynomial> and
3100 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3102 In case of printing in C<ISL_FORMAT_C>, the user may want
3103 to set the names of all dimensions first.
3105 When called on a file printer, the following function flushes
3106 the file. When called on a string printer, the buffer is cleared.
3108 __isl_give isl_printer *isl_printer_flush(
3109 __isl_take isl_printer *p);
3111 Alternatively, a string representation can be obtained
3112 directly using the following functions, which always print
3115 #include <isl/space.h>
3116 __isl_give char *isl_space_to_str(
3117 __isl_keep isl_space *space);
3119 #include <isl/val.h>
3120 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3121 __isl_give char *isl_multi_val_to_str(
3122 __isl_keep isl_multi_val *mv);
3124 #include <isl/set.h>
3125 __isl_give char *isl_set_to_str(
3126 __isl_keep isl_set *set);
3128 #include <isl/union_set.h>
3129 __isl_give char *isl_union_set_to_str(
3130 __isl_keep isl_union_set *uset);
3132 #include <isl/map.h>
3133 __isl_give char *isl_map_to_str(
3134 __isl_keep isl_map *map);
3136 #include <isl/union_map.h>
3137 __isl_give char *isl_union_map_to_str(
3138 __isl_keep isl_union_map *umap);
3140 #include <isl/aff.h>
3141 __isl_give char *isl_multi_aff_to_str(
3142 __isl_keep isl_multi_aff *aff);
3143 __isl_give char *isl_union_pw_multi_aff_to_str(
3144 __isl_keep isl_union_pw_multi_aff *upma);
3148 =head3 Unary Properties
3154 The following functions test whether the given set or relation
3155 contains any integer points. The ``plain'' variants do not perform
3156 any computations, but simply check if the given set or relation
3157 is already known to be empty.
3159 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3160 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3161 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3162 int isl_set_is_empty(__isl_keep isl_set *set);
3163 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3164 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3165 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3166 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3167 int isl_map_is_empty(__isl_keep isl_map *map);
3168 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3170 =item * Universality
3172 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3173 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3174 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3176 =item * Single-valuedness
3178 #include <isl/set.h>
3179 int isl_set_is_singleton(__isl_keep isl_set *set);
3181 #include <isl/map.h>
3182 int isl_basic_map_is_single_valued(
3183 __isl_keep isl_basic_map *bmap);
3184 int isl_map_plain_is_single_valued(
3185 __isl_keep isl_map *map);
3186 int isl_map_is_single_valued(__isl_keep isl_map *map);
3188 #include <isl/union_map.h>
3189 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3193 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3194 int isl_map_is_injective(__isl_keep isl_map *map);
3195 int isl_union_map_plain_is_injective(
3196 __isl_keep isl_union_map *umap);
3197 int isl_union_map_is_injective(
3198 __isl_keep isl_union_map *umap);
3202 int isl_map_is_bijective(__isl_keep isl_map *map);
3203 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3207 __isl_give isl_val *
3208 isl_basic_map_plain_get_val_if_fixed(
3209 __isl_keep isl_basic_map *bmap,
3210 enum isl_dim_type type, unsigned pos);
3211 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3212 __isl_keep isl_set *set,
3213 enum isl_dim_type type, unsigned pos);
3214 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3215 __isl_keep isl_map *map,
3216 enum isl_dim_type type, unsigned pos);
3218 If the set or relation obviously lies on a hyperplane where the given dimension
3219 has a fixed value, then return that value.
3220 Otherwise return NaN.
3224 int isl_set_dim_residue_class_val(
3225 __isl_keep isl_set *set,
3226 int pos, __isl_give isl_val **modulo,
3227 __isl_give isl_val **residue);
3229 Check if the values of the given set dimension are equal to a fixed
3230 value modulo some integer value. If so, assign the modulo to C<*modulo>
3231 and the fixed value to C<*residue>. If the given dimension attains only
3232 a single value, then assign C<0> to C<*modulo> and the fixed value to
3234 If the dimension does not attain only a single value and if no modulo
3235 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3239 To check whether the description of a set, relation or function depends
3240 on one or more given dimensions,
3241 the following functions can be used.
3243 #include <isl/constraint.h>
3244 int isl_constraint_involves_dims(
3245 __isl_keep isl_constraint *constraint,
3246 enum isl_dim_type type, unsigned first, unsigned n);
3248 #include <isl/set.h>
3249 int isl_basic_set_involves_dims(
3250 __isl_keep isl_basic_set *bset,
3251 enum isl_dim_type type, unsigned first, unsigned n);
3252 int isl_set_involves_dims(__isl_keep isl_set *set,
3253 enum isl_dim_type type, unsigned first, unsigned n);
3255 #include <isl/map.h>
3256 int isl_basic_map_involves_dims(
3257 __isl_keep isl_basic_map *bmap,
3258 enum isl_dim_type type, unsigned first, unsigned n);
3259 int isl_map_involves_dims(__isl_keep isl_map *map,
3260 enum isl_dim_type type, unsigned first, unsigned n);
3262 #include <isl/aff.h>
3263 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3264 enum isl_dim_type type, unsigned first, unsigned n);
3265 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3266 enum isl_dim_type type, unsigned first, unsigned n);
3267 int isl_multi_aff_involves_dims(
3268 __isl_keep isl_multi_aff *ma,
3269 enum isl_dim_type type, unsigned first, unsigned n);
3270 int isl_multi_pw_aff_involves_dims(
3271 __isl_keep isl_multi_pw_aff *mpa,
3272 enum isl_dim_type type, unsigned first, unsigned n);
3274 Similarly, the following functions can be used to check whether
3275 a given dimension is involved in any lower or upper bound.
3277 #include <isl/set.h>
3278 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3279 enum isl_dim_type type, unsigned pos);
3280 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3281 enum isl_dim_type type, unsigned pos);
3283 Note that these functions return true even if there is a bound on
3284 the dimension on only some of the basic sets of C<set>.
3285 To check if they have a bound for all of the basic sets in C<set>,
3286 use the following functions instead.
3288 #include <isl/set.h>
3289 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3290 enum isl_dim_type type, unsigned pos);
3291 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3292 enum isl_dim_type type, unsigned pos);
3296 To check whether a set is a parameter domain, use this function:
3298 int isl_set_is_params(__isl_keep isl_set *set);
3299 int isl_union_set_is_params(
3300 __isl_keep isl_union_set *uset);
3304 The following functions check whether the space of the given
3305 (basic) set or relation range is a wrapped relation.
3307 #include <isl/space.h>
3308 int isl_space_is_wrapping(
3309 __isl_keep isl_space *space);
3310 int isl_space_domain_is_wrapping(
3311 __isl_keep isl_space *space);
3312 int isl_space_range_is_wrapping(
3313 __isl_keep isl_space *space);
3315 #include <isl/set.h>
3316 int isl_basic_set_is_wrapping(
3317 __isl_keep isl_basic_set *bset);
3318 int isl_set_is_wrapping(__isl_keep isl_set *set);
3320 #include <isl/map.h>
3321 int isl_map_domain_is_wrapping(
3322 __isl_keep isl_map *map);
3323 int isl_map_range_is_wrapping(
3324 __isl_keep isl_map *map);
3326 #include <isl/val.h>
3327 int isl_multi_val_range_is_wrapping(
3328 __isl_keep isl_multi_val *mv);
3330 #include <isl/aff.h>
3331 int isl_multi_aff_range_is_wrapping(
3332 __isl_keep isl_multi_aff *ma);
3333 int isl_multi_pw_aff_range_is_wrapping(
3334 __isl_keep isl_multi_pw_aff *mpa);
3336 The input to C<isl_space_is_wrapping> should
3337 be the space of a set, while that of
3338 C<isl_space_domain_is_wrapping> and
3339 C<isl_space_range_is_wrapping> should be the space of a relation.
3341 =item * Internal Product
3343 int isl_basic_map_can_zip(
3344 __isl_keep isl_basic_map *bmap);
3345 int isl_map_can_zip(__isl_keep isl_map *map);
3347 Check whether the product of domain and range of the given relation
3349 i.e., whether both domain and range are nested relations.
3353 int isl_basic_map_can_curry(
3354 __isl_keep isl_basic_map *bmap);
3355 int isl_map_can_curry(__isl_keep isl_map *map);
3357 Check whether the domain of the (basic) relation is a wrapped relation.
3359 int isl_basic_map_can_uncurry(
3360 __isl_keep isl_basic_map *bmap);
3361 int isl_map_can_uncurry(__isl_keep isl_map *map);
3363 Check whether the range of the (basic) relation is a wrapped relation.
3365 =item * Special Values
3367 #include <isl/aff.h>
3368 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3369 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3371 Check whether the given expression is a constant.
3373 #include <isl/aff.h>
3374 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3375 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3377 Check whether the given expression is equal to or involves NaN.
3379 #include <isl/aff.h>
3380 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3382 Check whether the affine expression is obviously zero.
3386 =head3 Binary Properties
3392 The following functions check whether two objects
3393 represent the same set, relation or function.
3394 The C<plain> variants only return true if the objects
3395 are obviously the same. That is, they may return false
3396 even if the objects are the same, but they will never
3397 return true if the objects are not the same.
3399 #include <isl/set.h>
3400 int isl_basic_set_plain_is_equal(
3401 __isl_keep isl_basic_set *bset1,
3402 __isl_keep isl_basic_set *bset2);
3403 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3404 __isl_keep isl_set *set2);
3405 int isl_set_is_equal(__isl_keep isl_set *set1,
3406 __isl_keep isl_set *set2);
3408 #include <isl/map.h>
3409 int isl_basic_map_is_equal(
3410 __isl_keep isl_basic_map *bmap1,
3411 __isl_keep isl_basic_map *bmap2);
3412 int isl_map_is_equal(__isl_keep isl_map *map1,
3413 __isl_keep isl_map *map2);
3414 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3415 __isl_keep isl_map *map2);
3417 #include <isl/union_set.h>
3418 int isl_union_set_is_equal(
3419 __isl_keep isl_union_set *uset1,
3420 __isl_keep isl_union_set *uset2);
3422 #include <isl/union_map.h>
3423 int isl_union_map_is_equal(
3424 __isl_keep isl_union_map *umap1,
3425 __isl_keep isl_union_map *umap2);
3427 #include <isl/aff.h>
3428 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3429 __isl_keep isl_aff *aff2);
3430 int isl_multi_aff_plain_is_equal(
3431 __isl_keep isl_multi_aff *maff1,
3432 __isl_keep isl_multi_aff *maff2);
3433 int isl_pw_aff_plain_is_equal(
3434 __isl_keep isl_pw_aff *pwaff1,
3435 __isl_keep isl_pw_aff *pwaff2);
3436 int isl_pw_multi_aff_plain_is_equal(
3437 __isl_keep isl_pw_multi_aff *pma1,
3438 __isl_keep isl_pw_multi_aff *pma2);
3439 int isl_multi_pw_aff_plain_is_equal(
3440 __isl_keep isl_multi_pw_aff *mpa1,
3441 __isl_keep isl_multi_pw_aff *mpa2);
3442 int isl_multi_pw_aff_is_equal(
3443 __isl_keep isl_multi_pw_aff *mpa1,
3444 __isl_keep isl_multi_pw_aff *mpa2);
3445 int isl_union_pw_multi_aff_plain_is_equal(
3446 __isl_keep isl_union_pw_multi_aff *upma1,
3447 __isl_keep isl_union_pw_multi_aff *upma2);
3449 #include <isl/polynomial.h>
3450 int isl_union_pw_qpolynomial_plain_is_equal(
3451 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3452 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3453 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3454 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3455 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3457 =item * Disjointness
3459 int isl_basic_set_is_disjoint(
3460 __isl_keep isl_basic_set *bset1,
3461 __isl_keep isl_basic_set *bset2);
3462 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3463 __isl_keep isl_set *set2);
3464 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3465 __isl_keep isl_set *set2);
3466 int isl_basic_map_is_disjoint(
3467 __isl_keep isl_basic_map *bmap1,
3468 __isl_keep isl_basic_map *bmap2);
3469 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3470 __isl_keep isl_map *map2);
3474 int isl_basic_set_is_subset(
3475 __isl_keep isl_basic_set *bset1,
3476 __isl_keep isl_basic_set *bset2);
3477 int isl_set_is_subset(__isl_keep isl_set *set1,
3478 __isl_keep isl_set *set2);
3479 int isl_set_is_strict_subset(
3480 __isl_keep isl_set *set1,
3481 __isl_keep isl_set *set2);
3482 int isl_union_set_is_subset(
3483 __isl_keep isl_union_set *uset1,
3484 __isl_keep isl_union_set *uset2);
3485 int isl_union_set_is_strict_subset(
3486 __isl_keep isl_union_set *uset1,
3487 __isl_keep isl_union_set *uset2);
3488 int isl_basic_map_is_subset(
3489 __isl_keep isl_basic_map *bmap1,
3490 __isl_keep isl_basic_map *bmap2);
3491 int isl_basic_map_is_strict_subset(
3492 __isl_keep isl_basic_map *bmap1,
3493 __isl_keep isl_basic_map *bmap2);
3494 int isl_map_is_subset(
3495 __isl_keep isl_map *map1,
3496 __isl_keep isl_map *map2);
3497 int isl_map_is_strict_subset(
3498 __isl_keep isl_map *map1,
3499 __isl_keep isl_map *map2);
3500 int isl_union_map_is_subset(
3501 __isl_keep isl_union_map *umap1,
3502 __isl_keep isl_union_map *umap2);
3503 int isl_union_map_is_strict_subset(
3504 __isl_keep isl_union_map *umap1,
3505 __isl_keep isl_union_map *umap2);
3507 Check whether the first argument is a (strict) subset of the
3512 Every comparison function returns a negative value if the first
3513 argument is considered smaller than the second, a positive value
3514 if the first argument is considered greater and zero if the two
3515 constraints are considered the same by the comparison criterion.
3517 #include <isl/constraint.h>
3518 int isl_constraint_plain_cmp(
3519 __isl_keep isl_constraint *c1,
3520 __isl_keep isl_constraint *c2);
3522 This function is useful for sorting C<isl_constraint>s.
3523 The order depends on the internal representation of the inputs.
3524 The order is fixed over different calls to the function (assuming
3525 the internal representation of the inputs has not changed), but may
3526 change over different versions of C<isl>.
3528 #include <isl/constraint.h>
3529 int isl_constraint_cmp_last_non_zero(
3530 __isl_keep isl_constraint *c1,
3531 __isl_keep isl_constraint *c2);
3533 This function can be used to sort constraints that live in the same
3534 local space. Constraints that involve ``earlier'' dimensions or
3535 that have a smaller coefficient for the shared latest dimension
3536 are considered smaller than other constraints.
3537 This function only defines a B<partial> order.
3539 #include <isl/set.h>
3540 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3541 __isl_keep isl_set *set2);
3543 This function is useful for sorting C<isl_set>s.
3544 The order depends on the internal representation of the inputs.
3545 The order is fixed over different calls to the function (assuming
3546 the internal representation of the inputs has not changed), but may
3547 change over different versions of C<isl>.
3549 #include <isl/aff.h>
3550 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3551 __isl_keep isl_pw_aff *pa2);
3553 The function C<isl_pw_aff_plain_cmp> can be used to sort
3554 C<isl_pw_aff>s. The order is not strictly defined.
3555 The current order sorts expressions that only involve
3556 earlier dimensions before those that involve later dimensions.
3560 =head2 Unary Operations
3566 __isl_give isl_set *isl_set_complement(
3567 __isl_take isl_set *set);
3568 __isl_give isl_map *isl_map_complement(
3569 __isl_take isl_map *map);
3573 #include <isl/space.h>
3574 __isl_give isl_space *isl_space_reverse(
3575 __isl_take isl_space *space);
3577 #include <isl/map.h>
3578 __isl_give isl_basic_map *isl_basic_map_reverse(
3579 __isl_take isl_basic_map *bmap);
3580 __isl_give isl_map *isl_map_reverse(
3581 __isl_take isl_map *map);
3583 #include <isl/union_map.h>
3584 __isl_give isl_union_map *isl_union_map_reverse(
3585 __isl_take isl_union_map *umap);
3589 #include <isl/space.h>
3590 __isl_give isl_space *isl_space_domain(
3591 __isl_take isl_space *space);
3592 __isl_give isl_space *isl_space_range(
3593 __isl_take isl_space *space);
3594 __isl_give isl_space *isl_space_params(
3595 __isl_take isl_space *space);
3597 #include <isl/local_space.h>
3598 __isl_give isl_local_space *isl_local_space_domain(
3599 __isl_take isl_local_space *ls);
3600 __isl_give isl_local_space *isl_local_space_range(
3601 __isl_take isl_local_space *ls);
3603 #include <isl/set.h>
3604 __isl_give isl_basic_set *isl_basic_set_project_out(
3605 __isl_take isl_basic_set *bset,
3606 enum isl_dim_type type, unsigned first, unsigned n);
3607 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3608 enum isl_dim_type type, unsigned first, unsigned n);
3609 __isl_give isl_basic_set *isl_basic_set_params(
3610 __isl_take isl_basic_set *bset);
3611 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
3613 #include <isl/map.h>
3614 __isl_give isl_basic_map *isl_basic_map_project_out(
3615 __isl_take isl_basic_map *bmap,
3616 enum isl_dim_type type, unsigned first, unsigned n);
3617 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3618 enum isl_dim_type type, unsigned first, unsigned n);
3619 __isl_give isl_basic_set *isl_basic_map_domain(
3620 __isl_take isl_basic_map *bmap);
3621 __isl_give isl_basic_set *isl_basic_map_range(
3622 __isl_take isl_basic_map *bmap);
3623 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
3624 __isl_give isl_set *isl_map_domain(
3625 __isl_take isl_map *bmap);
3626 __isl_give isl_set *isl_map_range(
3627 __isl_take isl_map *map);
3629 #include <isl/union_set.h>
3630 __isl_give isl_set *isl_union_set_params(
3631 __isl_take isl_union_set *uset);
3633 #include <isl/union_map.h>
3634 __isl_give isl_union_map *isl_union_map_project_out(
3635 __isl_take isl_union_map *umap,
3636 enum isl_dim_type type, unsigned first, unsigned n);
3637 __isl_give isl_set *isl_union_map_params(
3638 __isl_take isl_union_map *umap);
3639 __isl_give isl_union_set *isl_union_map_domain(
3640 __isl_take isl_union_map *umap);
3641 __isl_give isl_union_set *isl_union_map_range(
3642 __isl_take isl_union_map *umap);
3644 The function C<isl_union_map_project_out> can only project out
3647 #include <isl/aff.h>
3648 __isl_give isl_aff *isl_aff_project_domain_on_params(
3649 __isl_take isl_aff *aff);
3650 __isl_give isl_pw_multi_aff *
3651 isl_pw_multi_aff_project_domain_on_params(
3652 __isl_take isl_pw_multi_aff *pma);
3653 __isl_give isl_set *isl_pw_aff_domain(
3654 __isl_take isl_pw_aff *pwaff);
3655 __isl_give isl_set *isl_pw_multi_aff_domain(
3656 __isl_take isl_pw_multi_aff *pma);
3657 __isl_give isl_set *isl_multi_pw_aff_domain(
3658 __isl_take isl_multi_pw_aff *mpa);
3659 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3660 __isl_take isl_union_pw_multi_aff *upma);
3661 __isl_give isl_set *isl_pw_aff_params(
3662 __isl_take isl_pw_aff *pwa);
3664 #include <isl/polynomial.h>
3665 __isl_give isl_qpolynomial *
3666 isl_qpolynomial_project_domain_on_params(
3667 __isl_take isl_qpolynomial *qp);
3668 __isl_give isl_pw_qpolynomial *
3669 isl_pw_qpolynomial_project_domain_on_params(
3670 __isl_take isl_pw_qpolynomial *pwqp);
3671 __isl_give isl_pw_qpolynomial_fold *
3672 isl_pw_qpolynomial_fold_project_domain_on_params(
3673 __isl_take isl_pw_qpolynomial_fold *pwf);
3674 __isl_give isl_set *isl_pw_qpolynomial_domain(
3675 __isl_take isl_pw_qpolynomial *pwqp);
3676 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3677 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3678 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3679 __isl_take isl_union_pw_qpolynomial *upwqp);
3681 #include <isl/space.h>
3682 __isl_give isl_space *isl_space_domain_map(
3683 __isl_take isl_space *space);
3684 __isl_give isl_space *isl_space_range_map(
3685 __isl_take isl_space *space);
3687 #include <isl/map.h>
3688 __isl_give isl_basic_map *isl_basic_map_domain_map(
3689 __isl_take isl_basic_map *bmap);
3690 __isl_give isl_basic_map *isl_basic_map_range_map(
3691 __isl_take isl_basic_map *bmap);
3692 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
3693 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
3695 #include <isl/union_map.h>
3696 __isl_give isl_union_map *isl_union_map_domain_map(
3697 __isl_take isl_union_map *umap);
3698 __isl_give isl_union_map *isl_union_map_range_map(
3699 __isl_take isl_union_map *umap);
3701 The functions above construct a (basic, regular or union) relation
3702 that maps (a wrapped version of) the input relation to its domain or range.
3706 __isl_give isl_basic_set *isl_basic_set_eliminate(
3707 __isl_take isl_basic_set *bset,
3708 enum isl_dim_type type,
3709 unsigned first, unsigned n);
3710 __isl_give isl_set *isl_set_eliminate(
3711 __isl_take isl_set *set, enum isl_dim_type type,
3712 unsigned first, unsigned n);
3713 __isl_give isl_basic_map *isl_basic_map_eliminate(
3714 __isl_take isl_basic_map *bmap,
3715 enum isl_dim_type type,
3716 unsigned first, unsigned n);
3717 __isl_give isl_map *isl_map_eliminate(
3718 __isl_take isl_map *map, enum isl_dim_type type,
3719 unsigned first, unsigned n);
3721 Eliminate the coefficients for the given dimensions from the constraints,
3722 without removing the dimensions.
3724 =item * Constructing a set from a parameter domain
3726 A zero-dimensional space or (basic) set can be constructed
3727 on a given parameter domain using the following functions.
3729 #include <isl/space.h>
3730 __isl_give isl_space *isl_space_set_from_params(
3731 __isl_take isl_space *space);
3733 #include <isl/set.h>
3734 __isl_give isl_basic_set *isl_basic_set_from_params(
3735 __isl_take isl_basic_set *bset);
3736 __isl_give isl_set *isl_set_from_params(
3737 __isl_take isl_set *set);
3739 =item * Constructing a relation from a set
3741 Create a relation with the given set as domain or range.
3742 The range or domain of the created relation is a zero-dimensional
3743 flat anonymous space.
3745 #include <isl/space.h>
3746 __isl_give isl_space *isl_space_from_domain(
3747 __isl_take isl_space *space);
3748 __isl_give isl_space *isl_space_from_range(
3749 __isl_take isl_space *space);
3750 __isl_give isl_space *isl_space_map_from_set(
3751 __isl_take isl_space *space);
3752 __isl_give isl_space *isl_space_map_from_domain_and_range(
3753 __isl_take isl_space *domain,
3754 __isl_take isl_space *range);
3756 #include <isl/local_space.h>
3757 __isl_give isl_local_space *isl_local_space_from_domain(
3758 __isl_take isl_local_space *ls);
3760 #include <isl/map.h>
3761 __isl_give isl_map *isl_map_from_domain(
3762 __isl_take isl_set *set);
3763 __isl_give isl_map *isl_map_from_range(
3764 __isl_take isl_set *set);
3766 #include <isl/val.h>
3767 __isl_give isl_multi_val *isl_multi_val_from_range(
3768 __isl_take isl_multi_val *mv);
3770 #include <isl/aff.h>
3771 __isl_give isl_multi_aff *isl_multi_aff_from_range(
3772 __isl_take isl_multi_aff *ma);
3773 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3774 __isl_take isl_pw_aff *pwa);
3775 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
3776 __isl_take isl_multi_pw_aff *mpa);
3777 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3778 __isl_take isl_set *set);
3779 __isl_give isl_union_pw_multi_aff *
3780 isl_union_pw_multi_aff_from_domain(
3781 __isl_take isl_union_set *uset);
3785 #include <isl/set.h>
3786 __isl_give isl_basic_set *isl_basic_set_fix_si(
3787 __isl_take isl_basic_set *bset,
3788 enum isl_dim_type type, unsigned pos, int value);
3789 __isl_give isl_basic_set *isl_basic_set_fix_val(
3790 __isl_take isl_basic_set *bset,
3791 enum isl_dim_type type, unsigned pos,
3792 __isl_take isl_val *v);
3793 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
3794 enum isl_dim_type type, unsigned pos, int value);
3795 __isl_give isl_set *isl_set_fix_val(
3796 __isl_take isl_set *set,
3797 enum isl_dim_type type, unsigned pos,
3798 __isl_take isl_val *v);
3800 #include <isl/map.h>
3801 __isl_give isl_basic_map *isl_basic_map_fix_si(
3802 __isl_take isl_basic_map *bmap,
3803 enum isl_dim_type type, unsigned pos, int value);
3804 __isl_give isl_basic_map *isl_basic_map_fix_val(
3805 __isl_take isl_basic_map *bmap,
3806 enum isl_dim_type type, unsigned pos,
3807 __isl_take isl_val *v);
3808 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
3809 enum isl_dim_type type, unsigned pos, int value);
3810 __isl_give isl_map *isl_map_fix_val(
3811 __isl_take isl_map *map,
3812 enum isl_dim_type type, unsigned pos,
3813 __isl_take isl_val *v);
3815 #include <isl/aff.h>
3816 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
3817 __isl_take isl_pw_multi_aff *pma,
3818 enum isl_dim_type type, unsigned pos, int value);
3820 #include <isl/polynomial.h>
3821 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
3822 __isl_take isl_pw_qpolynomial *pwqp,
3823 enum isl_dim_type type, unsigned n,
3824 __isl_take isl_val *v);
3826 Intersect the set, relation or function domain
3827 with the hyperplane where the given
3828 dimension has the fixed given value.
3830 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
3831 __isl_take isl_basic_map *bmap,
3832 enum isl_dim_type type, unsigned pos, int value);
3833 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
3834 __isl_take isl_basic_map *bmap,
3835 enum isl_dim_type type, unsigned pos, int value);
3836 __isl_give isl_set *isl_set_lower_bound_si(
3837 __isl_take isl_set *set,
3838 enum isl_dim_type type, unsigned pos, int value);
3839 __isl_give isl_set *isl_set_lower_bound_val(
3840 __isl_take isl_set *set,
3841 enum isl_dim_type type, unsigned pos,
3842 __isl_take isl_val *value);
3843 __isl_give isl_map *isl_map_lower_bound_si(
3844 __isl_take isl_map *map,
3845 enum isl_dim_type type, unsigned pos, int value);
3846 __isl_give isl_set *isl_set_upper_bound_si(
3847 __isl_take isl_set *set,
3848 enum isl_dim_type type, unsigned pos, int value);
3849 __isl_give isl_set *isl_set_upper_bound_val(
3850 __isl_take isl_set *set,
3851 enum isl_dim_type type, unsigned pos,
3852 __isl_take isl_val *value);
3853 __isl_give isl_map *isl_map_upper_bound_si(
3854 __isl_take isl_map *map,
3855 enum isl_dim_type type, unsigned pos, int value);
3857 Intersect the set or relation with the half-space where the given
3858 dimension has a value bounded by the fixed given integer value.
3860 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
3861 enum isl_dim_type type1, int pos1,
3862 enum isl_dim_type type2, int pos2);
3863 __isl_give isl_basic_map *isl_basic_map_equate(
3864 __isl_take isl_basic_map *bmap,
3865 enum isl_dim_type type1, int pos1,
3866 enum isl_dim_type type2, int pos2);
3867 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
3868 enum isl_dim_type type1, int pos1,
3869 enum isl_dim_type type2, int pos2);
3871 Intersect the set or relation with the hyperplane where the given
3872 dimensions are equal to each other.
3874 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
3875 enum isl_dim_type type1, int pos1,
3876 enum isl_dim_type type2, int pos2);
3878 Intersect the relation with the hyperplane where the given
3879 dimensions have opposite values.
3881 __isl_give isl_map *isl_map_order_le(
3882 __isl_take isl_map *map,
3883 enum isl_dim_type type1, int pos1,
3884 enum isl_dim_type type2, int pos2);
3885 __isl_give isl_basic_map *isl_basic_map_order_ge(
3886 __isl_take isl_basic_map *bmap,
3887 enum isl_dim_type type1, int pos1,
3888 enum isl_dim_type type2, int pos2);
3889 __isl_give isl_map *isl_map_order_ge(
3890 __isl_take isl_map *map,
3891 enum isl_dim_type type1, int pos1,
3892 enum isl_dim_type type2, int pos2);
3893 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
3894 enum isl_dim_type type1, int pos1,
3895 enum isl_dim_type type2, int pos2);
3896 __isl_give isl_basic_map *isl_basic_map_order_gt(
3897 __isl_take isl_basic_map *bmap,
3898 enum isl_dim_type type1, int pos1,
3899 enum isl_dim_type type2, int pos2);
3900 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
3901 enum isl_dim_type type1, int pos1,
3902 enum isl_dim_type type2, int pos2);
3904 Intersect the relation with the half-space where the given
3905 dimensions satisfy the given ordering.
3909 #include <isl/aff.h>
3910 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3911 __isl_take isl_aff *aff);
3912 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3913 __isl_take isl_aff *aff);
3914 __isl_give isl_set *isl_pw_aff_nonneg_set(
3915 __isl_take isl_pw_aff *pwaff);
3916 __isl_give isl_set *isl_pw_aff_zero_set(
3917 __isl_take isl_pw_aff *pwaff);
3918 __isl_give isl_set *isl_pw_aff_non_zero_set(
3919 __isl_take isl_pw_aff *pwaff);
3921 The function C<isl_aff_neg_basic_set> returns a basic set
3922 containing those elements in the domain space
3923 of C<aff> where C<aff> is negative.
3924 The function C<isl_pw_aff_nonneg_set> returns a set
3925 containing those elements in the domain
3926 of C<pwaff> where C<pwaff> is non-negative.
3930 __isl_give isl_map *isl_set_identity(
3931 __isl_take isl_set *set);
3932 __isl_give isl_union_map *isl_union_set_identity(
3933 __isl_take isl_union_set *uset);
3935 Construct an identity relation on the given (union) set.
3937 =item * Function Extraction
3939 A piecewise quasi affine expression that is equal to 1 on a set
3940 and 0 outside the set can be created using the following function.
3942 #include <isl/aff.h>
3943 __isl_give isl_pw_aff *isl_set_indicator_function(
3944 __isl_take isl_set *set);
3946 A piecewise multiple quasi affine expression can be extracted
3947 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3948 and the C<isl_map> is single-valued.
3949 In case of a conversion from an C<isl_union_map>
3950 to an C<isl_union_pw_multi_aff>, these properties need to hold
3951 in each domain space.
3953 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3954 __isl_take isl_set *set);
3955 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3956 __isl_take isl_map *map);
3958 __isl_give isl_union_pw_multi_aff *
3959 isl_union_pw_multi_aff_from_union_set(
3960 __isl_take isl_union_set *uset);
3961 __isl_give isl_union_pw_multi_aff *
3962 isl_union_pw_multi_aff_from_union_map(
3963 __isl_take isl_union_map *umap);
3967 __isl_give isl_basic_set *isl_basic_map_deltas(
3968 __isl_take isl_basic_map *bmap);
3969 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
3970 __isl_give isl_union_set *isl_union_map_deltas(
3971 __isl_take isl_union_map *umap);
3973 These functions return a (basic) set containing the differences
3974 between image elements and corresponding domain elements in the input.
3976 __isl_give isl_basic_map *isl_basic_map_deltas_map(
3977 __isl_take isl_basic_map *bmap);
3978 __isl_give isl_map *isl_map_deltas_map(
3979 __isl_take isl_map *map);
3980 __isl_give isl_union_map *isl_union_map_deltas_map(
3981 __isl_take isl_union_map *umap);
3983 The functions above construct a (basic, regular or union) relation
3984 that maps (a wrapped version of) the input relation to its delta set.
3988 Simplify the representation of a set, relation or functions by trying
3989 to combine pairs of basic sets or relations into a single
3990 basic set or relation.
3992 #include <isl/set.h>
3993 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
3995 #include <isl/map.h>
3996 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
3998 #include <isl/union_set.h>
3999 __isl_give isl_union_set *isl_union_set_coalesce(
4000 __isl_take isl_union_set *uset);
4002 #include <isl/union_map.h>
4003 __isl_give isl_union_map *isl_union_map_coalesce(
4004 __isl_take isl_union_map *umap);
4006 #include <isl/aff.h>
4007 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4008 __isl_take isl_pw_aff *pwqp);
4009 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4010 __isl_take isl_pw_multi_aff *pma);
4011 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4012 __isl_take isl_multi_pw_aff *mpa);
4013 __isl_give isl_union_pw_multi_aff *
4014 isl_union_pw_multi_aff_coalesce(
4015 __isl_take isl_union_pw_multi_aff *upma);
4017 #include <isl/polynomial.h>
4018 __isl_give isl_pw_qpolynomial_fold *
4019 isl_pw_qpolynomial_fold_coalesce(
4020 __isl_take isl_pw_qpolynomial_fold *pwf);
4021 __isl_give isl_union_pw_qpolynomial *
4022 isl_union_pw_qpolynomial_coalesce(
4023 __isl_take isl_union_pw_qpolynomial *upwqp);
4024 __isl_give isl_union_pw_qpolynomial_fold *
4025 isl_union_pw_qpolynomial_fold_coalesce(
4026 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4028 One of the methods for combining pairs of basic sets or relations
4029 can result in coefficients that are much larger than those that appear
4030 in the constraints of the input. By default, the coefficients are
4031 not allowed to grow larger, but this can be changed by unsetting
4032 the following option.
4034 int isl_options_set_coalesce_bounded_wrapping(
4035 isl_ctx *ctx, int val);
4036 int isl_options_get_coalesce_bounded_wrapping(
4039 =item * Detecting equalities
4041 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4042 __isl_take isl_basic_set *bset);
4043 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4044 __isl_take isl_basic_map *bmap);
4045 __isl_give isl_set *isl_set_detect_equalities(
4046 __isl_take isl_set *set);
4047 __isl_give isl_map *isl_map_detect_equalities(
4048 __isl_take isl_map *map);
4049 __isl_give isl_union_set *isl_union_set_detect_equalities(
4050 __isl_take isl_union_set *uset);
4051 __isl_give isl_union_map *isl_union_map_detect_equalities(
4052 __isl_take isl_union_map *umap);
4054 Simplify the representation of a set or relation by detecting implicit
4057 =item * Removing redundant constraints
4059 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4060 __isl_take isl_basic_set *bset);
4061 __isl_give isl_set *isl_set_remove_redundancies(
4062 __isl_take isl_set *set);
4063 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4064 __isl_take isl_basic_map *bmap);
4065 __isl_give isl_map *isl_map_remove_redundancies(
4066 __isl_take isl_map *map);
4070 __isl_give isl_basic_set *isl_set_convex_hull(
4071 __isl_take isl_set *set);
4072 __isl_give isl_basic_map *isl_map_convex_hull(
4073 __isl_take isl_map *map);
4075 If the input set or relation has any existentially quantified
4076 variables, then the result of these operations is currently undefined.
4080 #include <isl/set.h>
4081 __isl_give isl_basic_set *
4082 isl_set_unshifted_simple_hull(
4083 __isl_take isl_set *set);
4084 __isl_give isl_basic_set *isl_set_simple_hull(
4085 __isl_take isl_set *set);
4086 __isl_give isl_basic_set *
4087 isl_set_unshifted_simple_hull_from_set_list(
4088 __isl_take isl_set *set,
4089 __isl_take isl_set_list *list);
4091 #include <isl/map.h>
4092 __isl_give isl_basic_map *
4093 isl_map_unshifted_simple_hull(
4094 __isl_take isl_map *map);
4095 __isl_give isl_basic_map *isl_map_simple_hull(
4096 __isl_take isl_map *map);
4098 #include <isl/union_map.h>
4099 __isl_give isl_union_map *isl_union_map_simple_hull(
4100 __isl_take isl_union_map *umap);
4102 These functions compute a single basic set or relation
4103 that contains the whole input set or relation.
4104 In particular, the output is described by translates
4105 of the constraints describing the basic sets or relations in the input.
4106 In case of C<isl_set_unshifted_simple_hull>, only the original
4107 constraints are used, without any translation.
4108 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
4109 constraints are taken from the elements of the second argument.
4113 (See \autoref{s:simple hull}.)
4119 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4120 __isl_take isl_basic_set *bset);
4121 __isl_give isl_basic_set *isl_set_affine_hull(
4122 __isl_take isl_set *set);
4123 __isl_give isl_union_set *isl_union_set_affine_hull(
4124 __isl_take isl_union_set *uset);
4125 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4126 __isl_take isl_basic_map *bmap);
4127 __isl_give isl_basic_map *isl_map_affine_hull(
4128 __isl_take isl_map *map);
4129 __isl_give isl_union_map *isl_union_map_affine_hull(
4130 __isl_take isl_union_map *umap);
4132 In case of union sets and relations, the affine hull is computed
4135 =item * Polyhedral hull
4137 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4138 __isl_take isl_set *set);
4139 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4140 __isl_take isl_map *map);
4141 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4142 __isl_take isl_union_set *uset);
4143 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4144 __isl_take isl_union_map *umap);
4146 These functions compute a single basic set or relation
4147 not involving any existentially quantified variables
4148 that contains the whole input set or relation.
4149 In case of union sets and relations, the polyhedral hull is computed
4152 =item * Other approximations
4154 #include <isl/set.h>
4155 __isl_give isl_basic_set *
4156 isl_basic_set_drop_constraints_involving_dims(
4157 __isl_take isl_basic_set *bset,
4158 enum isl_dim_type type,
4159 unsigned first, unsigned n);
4160 __isl_give isl_basic_set *
4161 isl_basic_set_drop_constraints_not_involving_dims(
4162 __isl_take isl_basic_set *bset,
4163 enum isl_dim_type type,
4164 unsigned first, unsigned n);
4165 __isl_give isl_set *
4166 isl_set_drop_constraints_involving_dims(
4167 __isl_take isl_set *set,
4168 enum isl_dim_type type,
4169 unsigned first, unsigned n);
4171 #include <isl/map.h>
4172 __isl_give isl_basic_map *
4173 isl_basic_map_drop_constraints_involving_dims(
4174 __isl_take isl_basic_map *bmap,
4175 enum isl_dim_type type,
4176 unsigned first, unsigned n);
4177 __isl_give isl_map *
4178 isl_map_drop_constraints_involving_dims(
4179 __isl_take isl_map *map,
4180 enum isl_dim_type type,
4181 unsigned first, unsigned n);
4183 These functions drop any constraints (not) involving the specified dimensions.
4184 Note that the result depends on the representation of the input.
4186 #include <isl/polynomial.h>
4187 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4188 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4189 __isl_give isl_union_pw_qpolynomial *
4190 isl_union_pw_qpolynomial_to_polynomial(
4191 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4193 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4194 the polynomial will be an overapproximation. If C<sign> is negative,
4195 it will be an underapproximation. If C<sign> is zero, the approximation
4196 will lie somewhere in between.
4200 __isl_give isl_basic_set *isl_basic_set_sample(
4201 __isl_take isl_basic_set *bset);
4202 __isl_give isl_basic_set *isl_set_sample(
4203 __isl_take isl_set *set);
4204 __isl_give isl_basic_map *isl_basic_map_sample(
4205 __isl_take isl_basic_map *bmap);
4206 __isl_give isl_basic_map *isl_map_sample(
4207 __isl_take isl_map *map);
4209 If the input (basic) set or relation is non-empty, then return
4210 a singleton subset of the input. Otherwise, return an empty set.
4212 =item * Optimization
4214 #include <isl/ilp.h>
4215 __isl_give isl_val *isl_basic_set_max_val(
4216 __isl_keep isl_basic_set *bset,
4217 __isl_keep isl_aff *obj);
4218 __isl_give isl_val *isl_set_min_val(
4219 __isl_keep isl_set *set,
4220 __isl_keep isl_aff *obj);
4221 __isl_give isl_val *isl_set_max_val(
4222 __isl_keep isl_set *set,
4223 __isl_keep isl_aff *obj);
4225 Compute the minimum or maximum of the integer affine expression C<obj>
4226 over the points in C<set>, returning the result in C<opt>.
4227 The result is C<NULL> in case of an error, the optimal value in case
4228 there is one, negative infinity or infinity if the problem is unbounded and
4229 NaN if the problem is empty.
4231 =item * Parametric optimization
4233 __isl_give isl_pw_aff *isl_set_dim_min(
4234 __isl_take isl_set *set, int pos);
4235 __isl_give isl_pw_aff *isl_set_dim_max(
4236 __isl_take isl_set *set, int pos);
4237 __isl_give isl_pw_aff *isl_map_dim_max(
4238 __isl_take isl_map *map, int pos);
4240 Compute the minimum or maximum of the given set or output dimension
4241 as a function of the parameters (and input dimensions), but independently
4242 of the other set or output dimensions.
4243 For lexicographic optimization, see L<"Lexicographic Optimization">.
4247 The following functions compute either the set of (rational) coefficient
4248 values of valid constraints for the given set or the set of (rational)
4249 values satisfying the constraints with coefficients from the given set.
4250 Internally, these two sets of functions perform essentially the
4251 same operations, except that the set of coefficients is assumed to
4252 be a cone, while the set of values may be any polyhedron.
4253 The current implementation is based on the Farkas lemma and
4254 Fourier-Motzkin elimination, but this may change or be made optional
4255 in future. In particular, future implementations may use different
4256 dualization algorithms or skip the elimination step.
4258 __isl_give isl_basic_set *isl_basic_set_coefficients(
4259 __isl_take isl_basic_set *bset);
4260 __isl_give isl_basic_set *isl_set_coefficients(
4261 __isl_take isl_set *set);
4262 __isl_give isl_union_set *isl_union_set_coefficients(
4263 __isl_take isl_union_set *bset);
4264 __isl_give isl_basic_set *isl_basic_set_solutions(
4265 __isl_take isl_basic_set *bset);
4266 __isl_give isl_basic_set *isl_set_solutions(
4267 __isl_take isl_set *set);
4268 __isl_give isl_union_set *isl_union_set_solutions(
4269 __isl_take isl_union_set *bset);
4273 __isl_give isl_map *isl_map_fixed_power_val(
4274 __isl_take isl_map *map,
4275 __isl_take isl_val *exp);
4276 __isl_give isl_union_map *
4277 isl_union_map_fixed_power_val(
4278 __isl_take isl_union_map *umap,
4279 __isl_take isl_val *exp);
4281 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4282 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4283 of C<map> is computed.
4285 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4287 __isl_give isl_union_map *isl_union_map_power(
4288 __isl_take isl_union_map *umap, int *exact);
4290 Compute a parametric representation for all positive powers I<k> of C<map>.
4291 The result maps I<k> to a nested relation corresponding to the
4292 I<k>th power of C<map>.
4293 The result may be an overapproximation. If the result is known to be exact,
4294 then C<*exact> is set to C<1>.
4296 =item * Transitive closure
4298 __isl_give isl_map *isl_map_transitive_closure(
4299 __isl_take isl_map *map, int *exact);
4300 __isl_give isl_union_map *isl_union_map_transitive_closure(
4301 __isl_take isl_union_map *umap, int *exact);
4303 Compute the transitive closure of C<map>.
4304 The result may be an overapproximation. If the result is known to be exact,
4305 then C<*exact> is set to C<1>.
4307 =item * Reaching path lengths
4309 __isl_give isl_map *isl_map_reaching_path_lengths(
4310 __isl_take isl_map *map, int *exact);
4312 Compute a relation that maps each element in the range of C<map>
4313 to the lengths of all paths composed of edges in C<map> that
4314 end up in the given element.
4315 The result may be an overapproximation. If the result is known to be exact,
4316 then C<*exact> is set to C<1>.
4317 To compute the I<maximal> path length, the resulting relation
4318 should be postprocessed by C<isl_map_lexmax>.
4319 In particular, if the input relation is a dependence relation
4320 (mapping sources to sinks), then the maximal path length corresponds
4321 to the free schedule.
4322 Note, however, that C<isl_map_lexmax> expects the maximum to be
4323 finite, so if the path lengths are unbounded (possibly due to
4324 the overapproximation), then you will get an error message.
4328 #include <isl/space.h>
4329 __isl_give isl_space *isl_space_wrap(
4330 __isl_take isl_space *space);
4331 __isl_give isl_space *isl_space_unwrap(
4332 __isl_take isl_space *space);
4334 #include <isl/set.h>
4335 __isl_give isl_basic_map *isl_basic_set_unwrap(
4336 __isl_take isl_basic_set *bset);
4337 __isl_give isl_map *isl_set_unwrap(
4338 __isl_take isl_set *set);
4340 #include <isl/map.h>
4341 __isl_give isl_basic_set *isl_basic_map_wrap(
4342 __isl_take isl_basic_map *bmap);
4343 __isl_give isl_set *isl_map_wrap(
4344 __isl_take isl_map *map);
4346 #include <isl/union_set.h>
4347 __isl_give isl_union_map *isl_union_set_unwrap(
4348 __isl_take isl_union_set *uset);
4350 #include <isl/union_map.h>
4351 __isl_give isl_union_set *isl_union_map_wrap(
4352 __isl_take isl_union_map *umap);
4354 The input to C<isl_space_unwrap> should
4355 be the space of a set, while that of
4356 C<isl_space_wrap> should be the space of a relation.
4357 Conversely, the output of C<isl_space_unwrap> is the space
4358 of a relation, while that of C<isl_space_wrap> is the space of a set.
4362 Remove any internal structure of domain (and range) of the given
4363 set or relation. If there is any such internal structure in the input,
4364 then the name of the space is also removed.
4366 #include <isl/local_space.h>
4367 __isl_give isl_local_space *
4368 isl_local_space_flatten_domain(
4369 __isl_take isl_local_space *ls);
4370 __isl_give isl_local_space *
4371 isl_local_space_flatten_range(
4372 __isl_take isl_local_space *ls);
4374 #include <isl/set.h>
4375 __isl_give isl_basic_set *isl_basic_set_flatten(
4376 __isl_take isl_basic_set *bset);
4377 __isl_give isl_set *isl_set_flatten(
4378 __isl_take isl_set *set);
4380 #include <isl/map.h>
4381 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4382 __isl_take isl_basic_map *bmap);
4383 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4384 __isl_take isl_basic_map *bmap);
4385 __isl_give isl_map *isl_map_flatten_range(
4386 __isl_take isl_map *map);
4387 __isl_give isl_map *isl_map_flatten_domain(
4388 __isl_take isl_map *map);
4389 __isl_give isl_basic_map *isl_basic_map_flatten(
4390 __isl_take isl_basic_map *bmap);
4391 __isl_give isl_map *isl_map_flatten(
4392 __isl_take isl_map *map);
4394 #include <isl/val.h>
4395 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4396 __isl_take isl_multi_val *mv);
4398 #include <isl/aff.h>
4399 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4400 __isl_take isl_multi_aff *ma);
4401 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4402 __isl_take isl_multi_aff *ma);
4403 __isl_give isl_multi_pw_aff *
4404 isl_multi_pw_aff_flatten_range(
4405 __isl_take isl_multi_pw_aff *mpa);
4407 #include <isl/map.h>
4408 __isl_give isl_map *isl_set_flatten_map(
4409 __isl_take isl_set *set);
4411 The function above constructs a relation
4412 that maps the input set to a flattened version of the set.
4416 Lift the input set to a space with extra dimensions corresponding
4417 to the existentially quantified variables in the input.
4418 In particular, the result lives in a wrapped map where the domain
4419 is the original space and the range corresponds to the original
4420 existentially quantified variables.
4422 #include <isl/set.h>
4423 __isl_give isl_basic_set *isl_basic_set_lift(
4424 __isl_take isl_basic_set *bset);
4425 __isl_give isl_set *isl_set_lift(
4426 __isl_take isl_set *set);
4427 __isl_give isl_union_set *isl_union_set_lift(
4428 __isl_take isl_union_set *uset);
4430 Given a local space that contains the existentially quantified
4431 variables of a set, a basic relation that, when applied to
4432 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4433 can be constructed using the following function.
4435 #include <isl/local_space.h>
4436 __isl_give isl_basic_map *isl_local_space_lifting(
4437 __isl_take isl_local_space *ls);
4439 #include <isl/aff.h>
4440 __isl_give isl_multi_aff *isl_multi_aff_lift(
4441 __isl_take isl_multi_aff *maff,
4442 __isl_give isl_local_space **ls);
4444 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4445 then it is assigned the local space that lies at the basis of
4446 the lifting applied.
4448 =item * Internal Product
4450 #include <isl/space.h>
4451 __isl_give isl_space *isl_space_zip(
4452 __isl_take isl_space *space);
4454 #include <isl/map.h>
4455 __isl_give isl_basic_map *isl_basic_map_zip(
4456 __isl_take isl_basic_map *bmap);
4457 __isl_give isl_map *isl_map_zip(
4458 __isl_take isl_map *map);
4460 #include <isl/union_map.h>
4461 __isl_give isl_union_map *isl_union_map_zip(
4462 __isl_take isl_union_map *umap);
4464 Given a relation with nested relations for domain and range,
4465 interchange the range of the domain with the domain of the range.
4469 #include <isl/space.h>
4470 __isl_give isl_space *isl_space_curry(
4471 __isl_take isl_space *space);
4472 __isl_give isl_space *isl_space_uncurry(
4473 __isl_take isl_space *space);
4475 #include <isl/map.h>
4476 __isl_give isl_basic_map *isl_basic_map_curry(
4477 __isl_take isl_basic_map *bmap);
4478 __isl_give isl_basic_map *isl_basic_map_uncurry(
4479 __isl_take isl_basic_map *bmap);
4480 __isl_give isl_map *isl_map_curry(
4481 __isl_take isl_map *map);
4482 __isl_give isl_map *isl_map_uncurry(
4483 __isl_take isl_map *map);
4485 #include <isl/union_map.h>
4486 __isl_give isl_union_map *isl_union_map_curry(
4487 __isl_take isl_union_map *umap);
4488 __isl_give isl_union_map *isl_union_map_uncurry(
4489 __isl_take isl_union_map *umap);
4491 Given a relation with a nested relation for domain,
4492 the C<curry> functions
4493 move the range of the nested relation out of the domain
4494 and use it as the domain of a nested relation in the range,
4495 with the original range as range of this nested relation.
4496 The C<uncurry> functions perform the inverse operation.
4498 =item * Aligning parameters
4500 Change the order of the parameters of the given set, relation
4502 such that the first parameters match those of C<model>.
4503 This may involve the introduction of extra parameters.
4504 All parameters need to be named.
4506 #include <isl/space.h>
4507 __isl_give isl_space *isl_space_align_params(
4508 __isl_take isl_space *space1,
4509 __isl_take isl_space *space2)
4511 #include <isl/set.h>
4512 __isl_give isl_basic_set *isl_basic_set_align_params(
4513 __isl_take isl_basic_set *bset,
4514 __isl_take isl_space *model);
4515 __isl_give isl_set *isl_set_align_params(
4516 __isl_take isl_set *set,
4517 __isl_take isl_space *model);
4519 #include <isl/map.h>
4520 __isl_give isl_basic_map *isl_basic_map_align_params(
4521 __isl_take isl_basic_map *bmap,
4522 __isl_take isl_space *model);
4523 __isl_give isl_map *isl_map_align_params(
4524 __isl_take isl_map *map,
4525 __isl_take isl_space *model);
4527 #include <isl/val.h>
4528 __isl_give isl_multi_val *isl_multi_val_align_params(
4529 __isl_take isl_multi_val *mv,
4530 __isl_take isl_space *model);
4532 #include <isl/aff.h>
4533 __isl_give isl_aff *isl_aff_align_params(
4534 __isl_take isl_aff *aff,
4535 __isl_take isl_space *model);
4536 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4537 __isl_take isl_multi_aff *multi,
4538 __isl_take isl_space *model);
4539 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4540 __isl_take isl_pw_aff *pwaff,
4541 __isl_take isl_space *model);
4542 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4543 __isl_take isl_pw_multi_aff *pma,
4544 __isl_take isl_space *model);
4545 __isl_give isl_union_pw_multi_aff *
4546 isl_union_pw_multi_aff_align_params(
4547 __isl_take isl_union_pw_multi_aff *upma,
4548 __isl_take isl_space *model);
4550 #include <isl/polynomial.h>
4551 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4552 __isl_take isl_qpolynomial *qp,
4553 __isl_take isl_space *model);
4555 =item * Unary Arithmethic Operations
4557 #include <isl/aff.h>
4558 __isl_give isl_aff *isl_aff_neg(
4559 __isl_take isl_aff *aff);
4560 __isl_give isl_pw_aff *isl_pw_aff_neg(
4561 __isl_take isl_pw_aff *pwaff);
4562 __isl_give isl_aff *isl_aff_ceil(
4563 __isl_take isl_aff *aff);
4564 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4565 __isl_take isl_pw_aff *pwaff);
4566 __isl_give isl_aff *isl_aff_floor(
4567 __isl_take isl_aff *aff);
4568 __isl_give isl_multi_aff *isl_multi_aff_floor(
4569 __isl_take isl_multi_aff *ma);
4570 __isl_give isl_pw_aff *isl_pw_aff_floor(
4571 __isl_take isl_pw_aff *pwaff);
4573 #include <isl/aff.h>
4574 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4575 __isl_take isl_pw_aff_list *list);
4576 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4577 __isl_take isl_pw_aff_list *list);
4579 #include <isl/polynomial.h>
4580 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4581 __isl_take isl_qpolynomial *qp);
4582 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4583 __isl_take isl_pw_qpolynomial *pwqp);
4584 __isl_give isl_union_pw_qpolynomial *
4585 isl_union_pw_qpolynomial_neg(
4586 __isl_take isl_union_pw_qpolynomial *upwqp);
4587 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4588 __isl_take isl_qpolynomial *qp,
4590 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4591 __isl_take isl_pw_qpolynomial *pwqp,
4596 The following functions evaluate a function in a point.
4598 #include <isl/polynomial.h>
4599 __isl_give isl_val *isl_pw_qpolynomial_eval(
4600 __isl_take isl_pw_qpolynomial *pwqp,
4601 __isl_take isl_point *pnt);
4602 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
4603 __isl_take isl_pw_qpolynomial_fold *pwf,
4604 __isl_take isl_point *pnt);
4605 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4606 __isl_take isl_union_pw_qpolynomial *upwqp,
4607 __isl_take isl_point *pnt);
4608 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
4609 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4610 __isl_take isl_point *pnt);
4612 =item * Dimension manipulation
4614 It is usually not advisable to directly change the (input or output)
4615 space of a set or a relation as this removes the name and the internal
4616 structure of the space. However, the functions below can be useful
4617 to add new parameters, assuming
4618 C<isl_set_align_params> and C<isl_map_align_params>
4621 #include <isl/space.h>
4622 __isl_give isl_space *isl_space_add_dims(
4623 __isl_take isl_space *space,
4624 enum isl_dim_type type, unsigned n);
4625 __isl_give isl_space *isl_space_insert_dims(
4626 __isl_take isl_space *space,
4627 enum isl_dim_type type, unsigned pos, unsigned n);
4628 __isl_give isl_space *isl_space_drop_dims(
4629 __isl_take isl_space *space,
4630 enum isl_dim_type type, unsigned first, unsigned n);
4631 __isl_give isl_space *isl_space_move_dims(
4632 __isl_take isl_space *space,
4633 enum isl_dim_type dst_type, unsigned dst_pos,
4634 enum isl_dim_type src_type, unsigned src_pos,
4637 #include <isl/local_space.h>
4638 __isl_give isl_local_space *isl_local_space_add_dims(
4639 __isl_take isl_local_space *ls,
4640 enum isl_dim_type type, unsigned n);
4641 __isl_give isl_local_space *isl_local_space_insert_dims(
4642 __isl_take isl_local_space *ls,
4643 enum isl_dim_type type, unsigned first, unsigned n);
4644 __isl_give isl_local_space *isl_local_space_drop_dims(
4645 __isl_take isl_local_space *ls,
4646 enum isl_dim_type type, unsigned first, unsigned n);
4648 #include <isl/set.h>
4649 __isl_give isl_basic_set *isl_basic_set_add_dims(
4650 __isl_take isl_basic_set *bset,
4651 enum isl_dim_type type, unsigned n);
4652 __isl_give isl_set *isl_set_add_dims(
4653 __isl_take isl_set *set,
4654 enum isl_dim_type type, unsigned n);
4655 __isl_give isl_basic_set *isl_basic_set_insert_dims(
4656 __isl_take isl_basic_set *bset,
4657 enum isl_dim_type type, unsigned pos,
4659 __isl_give isl_set *isl_set_insert_dims(
4660 __isl_take isl_set *set,
4661 enum isl_dim_type type, unsigned pos, unsigned n);
4662 __isl_give isl_basic_set *isl_basic_set_move_dims(
4663 __isl_take isl_basic_set *bset,
4664 enum isl_dim_type dst_type, unsigned dst_pos,
4665 enum isl_dim_type src_type, unsigned src_pos,
4667 __isl_give isl_set *isl_set_move_dims(
4668 __isl_take isl_set *set,
4669 enum isl_dim_type dst_type, unsigned dst_pos,
4670 enum isl_dim_type src_type, unsigned src_pos,
4673 #include <isl/map.h>
4674 __isl_give isl_map *isl_map_add_dims(
4675 __isl_take isl_map *map,
4676 enum isl_dim_type type, unsigned n);
4677 __isl_give isl_basic_map *isl_basic_map_insert_dims(
4678 __isl_take isl_basic_map *bmap,
4679 enum isl_dim_type type, unsigned pos,
4681 __isl_give isl_map *isl_map_insert_dims(
4682 __isl_take isl_map *map,
4683 enum isl_dim_type type, unsigned pos, unsigned n);
4684 __isl_give isl_basic_map *isl_basic_map_move_dims(
4685 __isl_take isl_basic_map *bmap,
4686 enum isl_dim_type dst_type, unsigned dst_pos,
4687 enum isl_dim_type src_type, unsigned src_pos,
4689 __isl_give isl_map *isl_map_move_dims(
4690 __isl_take isl_map *map,
4691 enum isl_dim_type dst_type, unsigned dst_pos,
4692 enum isl_dim_type src_type, unsigned src_pos,
4695 #include <isl/val.h>
4696 __isl_give isl_multi_val *isl_multi_val_insert_dims(
4697 __isl_take isl_multi_val *mv,
4698 enum isl_dim_type type, unsigned first, unsigned n);
4699 __isl_give isl_multi_val *isl_multi_val_add_dims(
4700 __isl_take isl_multi_val *mv,
4701 enum isl_dim_type type, unsigned n);
4702 __isl_give isl_multi_val *isl_multi_val_drop_dims(
4703 __isl_take isl_multi_val *mv,
4704 enum isl_dim_type type, unsigned first, unsigned n);
4706 #include <isl/aff.h>
4707 __isl_give isl_aff *isl_aff_insert_dims(
4708 __isl_take isl_aff *aff,
4709 enum isl_dim_type type, unsigned first, unsigned n);
4710 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4711 __isl_take isl_multi_aff *ma,
4712 enum isl_dim_type type, unsigned first, unsigned n);
4713 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4714 __isl_take isl_pw_aff *pwaff,
4715 enum isl_dim_type type, unsigned first, unsigned n);
4716 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4717 __isl_take isl_multi_pw_aff *mpa,
4718 enum isl_dim_type type, unsigned first, unsigned n);
4719 __isl_give isl_aff *isl_aff_add_dims(
4720 __isl_take isl_aff *aff,
4721 enum isl_dim_type type, unsigned n);
4722 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4723 __isl_take isl_multi_aff *ma,
4724 enum isl_dim_type type, unsigned n);
4725 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4726 __isl_take isl_pw_aff *pwaff,
4727 enum isl_dim_type type, unsigned n);
4728 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4729 __isl_take isl_multi_pw_aff *mpa,
4730 enum isl_dim_type type, unsigned n);
4731 __isl_give isl_aff *isl_aff_drop_dims(
4732 __isl_take isl_aff *aff,
4733 enum isl_dim_type type, unsigned first, unsigned n);
4734 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4735 __isl_take isl_multi_aff *maff,
4736 enum isl_dim_type type, unsigned first, unsigned n);
4737 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4738 __isl_take isl_pw_aff *pwaff,
4739 enum isl_dim_type type, unsigned first, unsigned n);
4740 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4741 __isl_take isl_pw_multi_aff *pma,
4742 enum isl_dim_type type, unsigned first, unsigned n);
4743 __isl_give isl_aff *isl_aff_move_dims(
4744 __isl_take isl_aff *aff,
4745 enum isl_dim_type dst_type, unsigned dst_pos,
4746 enum isl_dim_type src_type, unsigned src_pos,
4748 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
4749 __isl_take isl_multi_aff *ma,
4750 enum isl_dim_type dst_type, unsigned dst_pos,
4751 enum isl_dim_type src_type, unsigned src_pos,
4753 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4754 __isl_take isl_pw_aff *pa,
4755 enum isl_dim_type dst_type, unsigned dst_pos,
4756 enum isl_dim_type src_type, unsigned src_pos,
4758 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4759 __isl_take isl_multi_pw_aff *pma,
4760 enum isl_dim_type dst_type, unsigned dst_pos,
4761 enum isl_dim_type src_type, unsigned src_pos,
4766 =head2 Binary Operations
4768 The two arguments of a binary operation not only need to live
4769 in the same C<isl_ctx>, they currently also need to have
4770 the same (number of) parameters.
4772 =head3 Basic Operations
4776 =item * Intersection
4778 #include <isl/local_space.h>
4779 __isl_give isl_local_space *isl_local_space_intersect(
4780 __isl_take isl_local_space *ls1,
4781 __isl_take isl_local_space *ls2);
4783 #include <isl/set.h>
4784 __isl_give isl_basic_set *isl_basic_set_intersect_params(
4785 __isl_take isl_basic_set *bset1,
4786 __isl_take isl_basic_set *bset2);
4787 __isl_give isl_basic_set *isl_basic_set_intersect(
4788 __isl_take isl_basic_set *bset1,
4789 __isl_take isl_basic_set *bset2);
4790 __isl_give isl_basic_set *isl_basic_set_list_intersect(
4791 __isl_take struct isl_basic_set_list *list);
4792 __isl_give isl_set *isl_set_intersect_params(
4793 __isl_take isl_set *set,
4794 __isl_take isl_set *params);
4795 __isl_give isl_set *isl_set_intersect(
4796 __isl_take isl_set *set1,
4797 __isl_take isl_set *set2);
4799 #include <isl/map.h>
4800 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
4801 __isl_take isl_basic_map *bmap,
4802 __isl_take isl_basic_set *bset);
4803 __isl_give isl_basic_map *isl_basic_map_intersect_range(
4804 __isl_take isl_basic_map *bmap,
4805 __isl_take isl_basic_set *bset);
4806 __isl_give isl_basic_map *isl_basic_map_intersect(
4807 __isl_take isl_basic_map *bmap1,
4808 __isl_take isl_basic_map *bmap2);
4809 __isl_give isl_map *isl_map_intersect_params(
4810 __isl_take isl_map *map,
4811 __isl_take isl_set *params);
4812 __isl_give isl_map *isl_map_intersect_domain(
4813 __isl_take isl_map *map,
4814 __isl_take isl_set *set);
4815 __isl_give isl_map *isl_map_intersect_range(
4816 __isl_take isl_map *map,
4817 __isl_take isl_set *set);
4818 __isl_give isl_map *isl_map_intersect(
4819 __isl_take isl_map *map1,
4820 __isl_take isl_map *map2);
4822 #include <isl/union_set.h>
4823 __isl_give isl_union_set *isl_union_set_intersect_params(
4824 __isl_take isl_union_set *uset,
4825 __isl_take isl_set *set);
4826 __isl_give isl_union_set *isl_union_set_intersect(
4827 __isl_take isl_union_set *uset1,
4828 __isl_take isl_union_set *uset2);
4830 #include <isl/union_map.h>
4831 __isl_give isl_union_map *isl_union_map_intersect_params(
4832 __isl_take isl_union_map *umap,
4833 __isl_take isl_set *set);
4834 __isl_give isl_union_map *isl_union_map_intersect_domain(
4835 __isl_take isl_union_map *umap,
4836 __isl_take isl_union_set *uset);
4837 __isl_give isl_union_map *isl_union_map_intersect_range(
4838 __isl_take isl_union_map *umap,
4839 __isl_take isl_union_set *uset);
4840 __isl_give isl_union_map *isl_union_map_intersect(
4841 __isl_take isl_union_map *umap1,
4842 __isl_take isl_union_map *umap2);
4844 #include <isl/aff.h>
4845 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4846 __isl_take isl_pw_aff *pa,
4847 __isl_take isl_set *set);
4848 __isl_give isl_multi_pw_aff *
4849 isl_multi_pw_aff_intersect_domain(
4850 __isl_take isl_multi_pw_aff *mpa,
4851 __isl_take isl_set *domain);
4852 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4853 __isl_take isl_pw_multi_aff *pma,
4854 __isl_take isl_set *set);
4855 __isl_give isl_union_pw_multi_aff *
4856 isl_union_pw_multi_aff_intersect_domain(
4857 __isl_take isl_union_pw_multi_aff *upma,
4858 __isl_take isl_union_set *uset);
4859 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4860 __isl_take isl_pw_aff *pa,
4861 __isl_take isl_set *set);
4862 __isl_give isl_multi_pw_aff *
4863 isl_multi_pw_aff_intersect_params(
4864 __isl_take isl_multi_pw_aff *mpa,
4865 __isl_take isl_set *set);
4866 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4867 __isl_take isl_pw_multi_aff *pma,
4868 __isl_take isl_set *set);
4869 __isl_give isl_union_pw_multi_aff *
4870 isl_union_pw_multi_aff_intersect_params(
4871 __isl_take isl_union_pw_multi_aff *upma,
4872 __isl_take isl_set *set);
4874 #include <isl/polynomial.h>
4875 __isl_give isl_pw_qpolynomial *
4876 isl_pw_qpolynomial_intersect_domain(
4877 __isl_take isl_pw_qpolynomial *pwpq,
4878 __isl_take isl_set *set);
4879 __isl_give isl_union_pw_qpolynomial *
4880 isl_union_pw_qpolynomial_intersect_domain(
4881 __isl_take isl_union_pw_qpolynomial *upwpq,
4882 __isl_take isl_union_set *uset);
4883 __isl_give isl_union_pw_qpolynomial_fold *
4884 isl_union_pw_qpolynomial_fold_intersect_domain(
4885 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4886 __isl_take isl_union_set *uset);
4887 __isl_give isl_pw_qpolynomial *
4888 isl_pw_qpolynomial_intersect_params(
4889 __isl_take isl_pw_qpolynomial *pwpq,
4890 __isl_take isl_set *set);
4891 __isl_give isl_pw_qpolynomial_fold *
4892 isl_pw_qpolynomial_fold_intersect_params(
4893 __isl_take isl_pw_qpolynomial_fold *pwf,
4894 __isl_take isl_set *set);
4895 __isl_give isl_union_pw_qpolynomial *
4896 isl_union_pw_qpolynomial_intersect_params(
4897 __isl_take isl_union_pw_qpolynomial *upwpq,
4898 __isl_take isl_set *set);
4899 __isl_give isl_union_pw_qpolynomial_fold *
4900 isl_union_pw_qpolynomial_fold_intersect_params(
4901 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4902 __isl_take isl_set *set);
4904 The second argument to the C<_params> functions needs to be
4905 a parametric (basic) set. For the other functions, a parametric set
4906 for either argument is only allowed if the other argument is
4907 a parametric set as well.
4908 The list passed to C<isl_basic_set_list_intersect> needs to have
4909 at least one element and all elements need to live in the same space.
4913 __isl_give isl_set *isl_basic_set_union(
4914 __isl_take isl_basic_set *bset1,
4915 __isl_take isl_basic_set *bset2);
4916 __isl_give isl_map *isl_basic_map_union(
4917 __isl_take isl_basic_map *bmap1,
4918 __isl_take isl_basic_map *bmap2);
4919 __isl_give isl_set *isl_set_union(
4920 __isl_take isl_set *set1,
4921 __isl_take isl_set *set2);
4922 __isl_give isl_map *isl_map_union(
4923 __isl_take isl_map *map1,
4924 __isl_take isl_map *map2);
4925 __isl_give isl_union_set *isl_union_set_union(
4926 __isl_take isl_union_set *uset1,
4927 __isl_take isl_union_set *uset2);
4928 __isl_give isl_union_map *isl_union_map_union(
4929 __isl_take isl_union_map *umap1,
4930 __isl_take isl_union_map *umap2);
4932 =item * Set difference
4934 __isl_give isl_set *isl_set_subtract(
4935 __isl_take isl_set *set1,
4936 __isl_take isl_set *set2);
4937 __isl_give isl_map *isl_map_subtract(
4938 __isl_take isl_map *map1,
4939 __isl_take isl_map *map2);
4940 __isl_give isl_map *isl_map_subtract_domain(
4941 __isl_take isl_map *map,
4942 __isl_take isl_set *dom);
4943 __isl_give isl_map *isl_map_subtract_range(
4944 __isl_take isl_map *map,
4945 __isl_take isl_set *dom);
4946 __isl_give isl_union_set *isl_union_set_subtract(
4947 __isl_take isl_union_set *uset1,
4948 __isl_take isl_union_set *uset2);
4949 __isl_give isl_union_map *isl_union_map_subtract(
4950 __isl_take isl_union_map *umap1,
4951 __isl_take isl_union_map *umap2);
4952 __isl_give isl_union_map *isl_union_map_subtract_domain(
4953 __isl_take isl_union_map *umap,
4954 __isl_take isl_union_set *dom);
4955 __isl_give isl_union_map *isl_union_map_subtract_range(
4956 __isl_take isl_union_map *umap,
4957 __isl_take isl_union_set *dom);
4961 #include <isl/space.h>
4962 __isl_give isl_space *isl_space_join(
4963 __isl_take isl_space *left,
4964 __isl_take isl_space *right);
4966 #include <isl/map.h>
4967 __isl_give isl_basic_set *isl_basic_set_apply(
4968 __isl_take isl_basic_set *bset,
4969 __isl_take isl_basic_map *bmap);
4970 __isl_give isl_set *isl_set_apply(
4971 __isl_take isl_set *set,
4972 __isl_take isl_map *map);
4973 __isl_give isl_union_set *isl_union_set_apply(
4974 __isl_take isl_union_set *uset,
4975 __isl_take isl_union_map *umap);
4976 __isl_give isl_basic_map *isl_basic_map_apply_domain(
4977 __isl_take isl_basic_map *bmap1,
4978 __isl_take isl_basic_map *bmap2);
4979 __isl_give isl_basic_map *isl_basic_map_apply_range(
4980 __isl_take isl_basic_map *bmap1,
4981 __isl_take isl_basic_map *bmap2);
4982 __isl_give isl_map *isl_map_apply_domain(
4983 __isl_take isl_map *map1,
4984 __isl_take isl_map *map2);
4985 __isl_give isl_map *isl_map_apply_range(
4986 __isl_take isl_map *map1,
4987 __isl_take isl_map *map2);
4989 #include <isl/union_map.h>
4990 __isl_give isl_union_map *isl_union_map_apply_domain(
4991 __isl_take isl_union_map *umap1,
4992 __isl_take isl_union_map *umap2);
4993 __isl_give isl_union_map *isl_union_map_apply_range(
4994 __isl_take isl_union_map *umap1,
4995 __isl_take isl_union_map *umap2);
4997 #include <isl/polynomial.h>
4998 __isl_give isl_pw_qpolynomial_fold *
4999 isl_set_apply_pw_qpolynomial_fold(
5000 __isl_take isl_set *set,
5001 __isl_take isl_pw_qpolynomial_fold *pwf,
5003 __isl_give isl_pw_qpolynomial_fold *
5004 isl_map_apply_pw_qpolynomial_fold(
5005 __isl_take isl_map *map,
5006 __isl_take isl_pw_qpolynomial_fold *pwf,
5008 __isl_give isl_union_pw_qpolynomial_fold *
5009 isl_union_set_apply_union_pw_qpolynomial_fold(
5010 __isl_take isl_union_set *uset,
5011 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5013 __isl_give isl_union_pw_qpolynomial_fold *
5014 isl_union_map_apply_union_pw_qpolynomial_fold(
5015 __isl_take isl_union_map *umap,
5016 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5019 The functions taking a map
5020 compose the given map with the given piecewise quasipolynomial reduction.
5021 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5022 over all elements in the intersection of the range of the map
5023 and the domain of the piecewise quasipolynomial reduction
5024 as a function of an element in the domain of the map.
5025 The functions taking a set compute a bound over all elements in the
5026 intersection of the set and the domain of the
5027 piecewise quasipolynomial reduction.
5031 #include <isl/set.h>
5032 __isl_give isl_basic_set *
5033 isl_basic_set_preimage_multi_aff(
5034 __isl_take isl_basic_set *bset,
5035 __isl_take isl_multi_aff *ma);
5036 __isl_give isl_set *isl_set_preimage_multi_aff(
5037 __isl_take isl_set *set,
5038 __isl_take isl_multi_aff *ma);
5039 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5040 __isl_take isl_set *set,
5041 __isl_take isl_pw_multi_aff *pma);
5042 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5043 __isl_take isl_set *set,
5044 __isl_take isl_multi_pw_aff *mpa);
5046 #include <isl/union_set.h>
5047 __isl_give isl_union_set *
5048 isl_union_set_preimage_multi_aff(
5049 __isl_take isl_union_set *uset,
5050 __isl_take isl_multi_aff *ma);
5051 __isl_give isl_union_set *
5052 isl_union_set_preimage_pw_multi_aff(
5053 __isl_take isl_union_set *uset,
5054 __isl_take isl_pw_multi_aff *pma);
5055 __isl_give isl_union_set *
5056 isl_union_set_preimage_union_pw_multi_aff(
5057 __isl_take isl_union_set *uset,
5058 __isl_take isl_union_pw_multi_aff *upma);
5060 #include <isl/map.h>
5061 __isl_give isl_basic_map *
5062 isl_basic_map_preimage_domain_multi_aff(
5063 __isl_take isl_basic_map *bmap,
5064 __isl_take isl_multi_aff *ma);
5065 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5066 __isl_take isl_map *map,
5067 __isl_take isl_multi_aff *ma);
5068 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5069 __isl_take isl_map *map,
5070 __isl_take isl_multi_aff *ma);
5071 __isl_give isl_map *
5072 isl_map_preimage_domain_pw_multi_aff(
5073 __isl_take isl_map *map,
5074 __isl_take isl_pw_multi_aff *pma);
5075 __isl_give isl_map *
5076 isl_map_preimage_range_pw_multi_aff(
5077 __isl_take isl_map *map,
5078 __isl_take isl_pw_multi_aff *pma);
5079 __isl_give isl_map *
5080 isl_map_preimage_domain_multi_pw_aff(
5081 __isl_take isl_map *map,
5082 __isl_take isl_multi_pw_aff *mpa);
5083 __isl_give isl_basic_map *
5084 isl_basic_map_preimage_range_multi_aff(
5085 __isl_take isl_basic_map *bmap,
5086 __isl_take isl_multi_aff *ma);
5088 #include <isl/union_map.h>
5089 __isl_give isl_union_map *
5090 isl_union_map_preimage_domain_multi_aff(
5091 __isl_take isl_union_map *umap,
5092 __isl_take isl_multi_aff *ma);
5093 __isl_give isl_union_map *
5094 isl_union_map_preimage_range_multi_aff(
5095 __isl_take isl_union_map *umap,
5096 __isl_take isl_multi_aff *ma);
5097 __isl_give isl_union_map *
5098 isl_union_map_preimage_domain_pw_multi_aff(
5099 __isl_take isl_union_map *umap,
5100 __isl_take isl_pw_multi_aff *pma);
5101 __isl_give isl_union_map *
5102 isl_union_map_preimage_range_pw_multi_aff(
5103 __isl_take isl_union_map *umap,
5104 __isl_take isl_pw_multi_aff *pma);
5105 __isl_give isl_union_map *
5106 isl_union_map_preimage_domain_union_pw_multi_aff(
5107 __isl_take isl_union_map *umap,
5108 __isl_take isl_union_pw_multi_aff *upma);
5109 __isl_give isl_union_map *
5110 isl_union_map_preimage_range_union_pw_multi_aff(
5111 __isl_take isl_union_map *umap,
5112 __isl_take isl_union_pw_multi_aff *upma);
5114 These functions compute the preimage of the given set or map domain/range under
5115 the given function. In other words, the expression is plugged
5116 into the set description or into the domain/range of the map.
5120 #include <isl/aff.h>
5121 __isl_give isl_aff *isl_aff_pullback_aff(
5122 __isl_take isl_aff *aff1,
5123 __isl_take isl_aff *aff2);
5124 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5125 __isl_take isl_aff *aff,
5126 __isl_take isl_multi_aff *ma);
5127 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5128 __isl_take isl_pw_aff *pa,
5129 __isl_take isl_multi_aff *ma);
5130 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5131 __isl_take isl_pw_aff *pa,
5132 __isl_take isl_pw_multi_aff *pma);
5133 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5134 __isl_take isl_pw_aff *pa,
5135 __isl_take isl_multi_pw_aff *mpa);
5136 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5137 __isl_take isl_multi_aff *ma1,
5138 __isl_take isl_multi_aff *ma2);
5139 __isl_give isl_pw_multi_aff *
5140 isl_pw_multi_aff_pullback_multi_aff(
5141 __isl_take isl_pw_multi_aff *pma,
5142 __isl_take isl_multi_aff *ma);
5143 __isl_give isl_multi_pw_aff *
5144 isl_multi_pw_aff_pullback_multi_aff(
5145 __isl_take isl_multi_pw_aff *mpa,
5146 __isl_take isl_multi_aff *ma);
5147 __isl_give isl_pw_multi_aff *
5148 isl_pw_multi_aff_pullback_pw_multi_aff(
5149 __isl_take isl_pw_multi_aff *pma1,
5150 __isl_take isl_pw_multi_aff *pma2);
5151 __isl_give isl_multi_pw_aff *
5152 isl_multi_pw_aff_pullback_pw_multi_aff(
5153 __isl_take isl_multi_pw_aff *mpa,
5154 __isl_take isl_pw_multi_aff *pma);
5155 __isl_give isl_multi_pw_aff *
5156 isl_multi_pw_aff_pullback_multi_pw_aff(
5157 __isl_take isl_multi_pw_aff *mpa1,
5158 __isl_take isl_multi_pw_aff *mpa2);
5160 These functions precompose the first expression by the second function.
5161 In other words, the second function is plugged
5162 into the first expression.
5166 #include <isl/aff.h>
5167 __isl_give isl_basic_set *isl_aff_le_basic_set(
5168 __isl_take isl_aff *aff1,
5169 __isl_take isl_aff *aff2);
5170 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5171 __isl_take isl_aff *aff1,
5172 __isl_take isl_aff *aff2);
5173 __isl_give isl_set *isl_pw_aff_eq_set(
5174 __isl_take isl_pw_aff *pwaff1,
5175 __isl_take isl_pw_aff *pwaff2);
5176 __isl_give isl_set *isl_pw_aff_ne_set(
5177 __isl_take isl_pw_aff *pwaff1,
5178 __isl_take isl_pw_aff *pwaff2);
5179 __isl_give isl_set *isl_pw_aff_le_set(
5180 __isl_take isl_pw_aff *pwaff1,
5181 __isl_take isl_pw_aff *pwaff2);
5182 __isl_give isl_set *isl_pw_aff_lt_set(
5183 __isl_take isl_pw_aff *pwaff1,
5184 __isl_take isl_pw_aff *pwaff2);
5185 __isl_give isl_set *isl_pw_aff_ge_set(
5186 __isl_take isl_pw_aff *pwaff1,
5187 __isl_take isl_pw_aff *pwaff2);
5188 __isl_give isl_set *isl_pw_aff_gt_set(
5189 __isl_take isl_pw_aff *pwaff1,
5190 __isl_take isl_pw_aff *pwaff2);
5192 __isl_give isl_set *isl_multi_aff_lex_le_set(
5193 __isl_take isl_multi_aff *ma1,
5194 __isl_take isl_multi_aff *ma2);
5195 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5196 __isl_take isl_multi_aff *ma1,
5197 __isl_take isl_multi_aff *ma2);
5199 __isl_give isl_set *isl_pw_aff_list_eq_set(
5200 __isl_take isl_pw_aff_list *list1,
5201 __isl_take isl_pw_aff_list *list2);
5202 __isl_give isl_set *isl_pw_aff_list_ne_set(
5203 __isl_take isl_pw_aff_list *list1,
5204 __isl_take isl_pw_aff_list *list2);
5205 __isl_give isl_set *isl_pw_aff_list_le_set(
5206 __isl_take isl_pw_aff_list *list1,
5207 __isl_take isl_pw_aff_list *list2);
5208 __isl_give isl_set *isl_pw_aff_list_lt_set(
5209 __isl_take isl_pw_aff_list *list1,
5210 __isl_take isl_pw_aff_list *list2);
5211 __isl_give isl_set *isl_pw_aff_list_ge_set(
5212 __isl_take isl_pw_aff_list *list1,
5213 __isl_take isl_pw_aff_list *list2);
5214 __isl_give isl_set *isl_pw_aff_list_gt_set(
5215 __isl_take isl_pw_aff_list *list1,
5216 __isl_take isl_pw_aff_list *list2);
5218 The function C<isl_aff_ge_basic_set> returns a basic set
5219 containing those elements in the shared space
5220 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5221 The function C<isl_pw_aff_ge_set> returns a set
5222 containing those elements in the shared domain
5223 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5224 greater than or equal to C<pwaff2>.
5225 The function C<isl_multi_aff_lex_le_set> returns a set
5226 containing those elements in the shared domain space
5227 where C<ma1> is lexicographically smaller than or
5229 The functions operating on C<isl_pw_aff_list> apply the corresponding
5230 C<isl_pw_aff> function to each pair of elements in the two lists.
5232 =item * Cartesian Product
5234 #include <isl/space.h>
5235 __isl_give isl_space *isl_space_product(
5236 __isl_take isl_space *space1,
5237 __isl_take isl_space *space2);
5238 __isl_give isl_space *isl_space_domain_product(
5239 __isl_take isl_space *space1,
5240 __isl_take isl_space *space2);
5241 __isl_give isl_space *isl_space_range_product(
5242 __isl_take isl_space *space1,
5243 __isl_take isl_space *space2);
5246 C<isl_space_product>, C<isl_space_domain_product>
5247 and C<isl_space_range_product> take pairs or relation spaces and
5248 produce a single relations space, where either the domain, the range
5249 or both domain and range are wrapped spaces of relations between
5250 the domains and/or ranges of the input spaces.
5251 If the product is only constructed over the domain or the range
5252 then the ranges or the domains of the inputs should be the same.
5253 The function C<isl_space_product> also accepts a pair of set spaces,
5254 in which case it returns a wrapped space of a relation between the
5257 #include <isl/set.h>
5258 __isl_give isl_set *isl_set_product(
5259 __isl_take isl_set *set1,
5260 __isl_take isl_set *set2);
5262 #include <isl/map.h>
5263 __isl_give isl_basic_map *isl_basic_map_domain_product(
5264 __isl_take isl_basic_map *bmap1,
5265 __isl_take isl_basic_map *bmap2);
5266 __isl_give isl_basic_map *isl_basic_map_range_product(
5267 __isl_take isl_basic_map *bmap1,
5268 __isl_take isl_basic_map *bmap2);
5269 __isl_give isl_basic_map *isl_basic_map_product(
5270 __isl_take isl_basic_map *bmap1,
5271 __isl_take isl_basic_map *bmap2);
5272 __isl_give isl_map *isl_map_domain_product(
5273 __isl_take isl_map *map1,
5274 __isl_take isl_map *map2);
5275 __isl_give isl_map *isl_map_range_product(
5276 __isl_take isl_map *map1,
5277 __isl_take isl_map *map2);
5278 __isl_give isl_map *isl_map_product(
5279 __isl_take isl_map *map1,
5280 __isl_take isl_map *map2);
5282 #include <isl/union_set.h>
5283 __isl_give isl_union_set *isl_union_set_product(
5284 __isl_take isl_union_set *uset1,
5285 __isl_take isl_union_set *uset2);
5287 #include <isl/union_map.h>
5288 __isl_give isl_union_map *isl_union_map_domain_product(
5289 __isl_take isl_union_map *umap1,
5290 __isl_take isl_union_map *umap2);
5291 __isl_give isl_union_map *isl_union_map_range_product(
5292 __isl_take isl_union_map *umap1,
5293 __isl_take isl_union_map *umap2);
5294 __isl_give isl_union_map *isl_union_map_product(
5295 __isl_take isl_union_map *umap1,
5296 __isl_take isl_union_map *umap2);
5298 #include <isl/val.h>
5299 __isl_give isl_multi_val *isl_multi_val_range_product(
5300 __isl_take isl_multi_val *mv1,
5301 __isl_take isl_multi_val *mv2);
5302 __isl_give isl_multi_val *isl_multi_val_product(
5303 __isl_take isl_multi_val *mv1,
5304 __isl_take isl_multi_val *mv2);
5306 #include <isl/aff.h>
5307 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5308 __isl_take isl_multi_aff *ma1,
5309 __isl_take isl_multi_aff *ma2);
5310 __isl_give isl_multi_aff *isl_multi_aff_product(
5311 __isl_take isl_multi_aff *ma1,
5312 __isl_take isl_multi_aff *ma2);
5313 __isl_give isl_multi_pw_aff *
5314 isl_multi_pw_aff_range_product(
5315 __isl_take isl_multi_pw_aff *mpa1,
5316 __isl_take isl_multi_pw_aff *mpa2);
5317 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5318 __isl_take isl_multi_pw_aff *mpa1,
5319 __isl_take isl_multi_pw_aff *mpa2);
5320 __isl_give isl_pw_multi_aff *
5321 isl_pw_multi_aff_range_product(
5322 __isl_take isl_pw_multi_aff *pma1,
5323 __isl_take isl_pw_multi_aff *pma2);
5324 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5325 __isl_take isl_pw_multi_aff *pma1,
5326 __isl_take isl_pw_multi_aff *pma2);
5328 The above functions compute the cross product of the given
5329 sets, relations or functions. The domains and ranges of the results
5330 are wrapped maps between domains and ranges of the inputs.
5331 To obtain a ``flat'' product, use the following functions
5334 #include <isl/set.h>
5335 __isl_give isl_basic_set *isl_basic_set_flat_product(
5336 __isl_take isl_basic_set *bset1,
5337 __isl_take isl_basic_set *bset2);
5338 __isl_give isl_set *isl_set_flat_product(
5339 __isl_take isl_set *set1,
5340 __isl_take isl_set *set2);
5342 #include <isl/map.h>
5343 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5344 __isl_take isl_basic_map *bmap1,
5345 __isl_take isl_basic_map *bmap2);
5346 __isl_give isl_map *isl_map_flat_domain_product(
5347 __isl_take isl_map *map1,
5348 __isl_take isl_map *map2);
5349 __isl_give isl_map *isl_map_flat_range_product(
5350 __isl_take isl_map *map1,
5351 __isl_take isl_map *map2);
5352 __isl_give isl_basic_map *isl_basic_map_flat_product(
5353 __isl_take isl_basic_map *bmap1,
5354 __isl_take isl_basic_map *bmap2);
5355 __isl_give isl_map *isl_map_flat_product(
5356 __isl_take isl_map *map1,
5357 __isl_take isl_map *map2);
5359 #include <isl/union_map.h>
5360 __isl_give isl_union_map *
5361 isl_union_map_flat_range_product(
5362 __isl_take isl_union_map *umap1,
5363 __isl_take isl_union_map *umap2);
5365 #include <isl/val.h>
5366 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
5367 __isl_take isl_multi_val *mv1,
5368 __isl_take isl_multi_aff *mv2);
5370 #include <isl/aff.h>
5371 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
5372 __isl_take isl_multi_aff *ma1,
5373 __isl_take isl_multi_aff *ma2);
5374 __isl_give isl_pw_multi_aff *
5375 isl_pw_multi_aff_flat_range_product(
5376 __isl_take isl_pw_multi_aff *pma1,
5377 __isl_take isl_pw_multi_aff *pma2);
5378 __isl_give isl_multi_pw_aff *
5379 isl_multi_pw_aff_flat_range_product(
5380 __isl_take isl_multi_pw_aff *mpa1,
5381 __isl_take isl_multi_pw_aff *mpa2);
5382 __isl_give isl_union_pw_multi_aff *
5383 isl_union_pw_multi_aff_flat_range_product(
5384 __isl_take isl_union_pw_multi_aff *upma1,
5385 __isl_take isl_union_pw_multi_aff *upma2);
5387 #include <isl/space.h>
5388 __isl_give isl_space *isl_space_domain_factor_domain(
5389 __isl_take isl_space *space);
5390 __isl_give isl_space *isl_space_range_factor_domain(
5391 __isl_take isl_space *space);
5392 __isl_give isl_space *isl_space_range_factor_range(
5393 __isl_take isl_space *space);
5395 The functions C<isl_space_range_factor_domain> and
5396 C<isl_space_range_factor_range> extract the two arguments from
5397 the result of a call to C<isl_space_range_product>.
5399 The arguments of a call to C<isl_map_range_product> can be extracted
5400 from the result using the following two functions.
5402 #include <isl/map.h>
5403 __isl_give isl_map *isl_map_range_factor_domain(
5404 __isl_take isl_map *map);
5405 __isl_give isl_map *isl_map_range_factor_range(
5406 __isl_take isl_map *map);
5408 #include <isl/val.h>
5409 __isl_give isl_multi_val *
5410 isl_multi_val_range_factor_domain(
5411 __isl_take isl_multi_val *mv);
5412 __isl_give isl_multi_val *
5413 isl_multi_val_range_factor_range(
5414 __isl_take isl_multi_val *mv);
5416 #include <isl/aff.h>
5417 __isl_give isl_multi_aff *
5418 isl_multi_aff_range_factor_domain(
5419 __isl_take isl_multi_aff *ma);
5420 __isl_give isl_multi_aff *
5421 isl_multi_aff_range_factor_range(
5422 __isl_take isl_multi_aff *ma);
5423 __isl_give isl_multi_pw_aff *
5424 isl_multi_pw_aff_range_factor_domain(
5425 __isl_take isl_multi_pw_aff *mpa);
5426 __isl_give isl_multi_pw_aff *
5427 isl_multi_pw_aff_range_factor_range(
5428 __isl_take isl_multi_pw_aff *mpa);
5430 The splice functions are a generalization of the flat product functions,
5431 where the second argument may be inserted at any position inside
5432 the first argument rather than being placed at the end.
5434 #include <isl/val.h>
5435 __isl_give isl_multi_val *isl_multi_val_range_splice(
5436 __isl_take isl_multi_val *mv1, unsigned pos,
5437 __isl_take isl_multi_val *mv2);
5439 #include <isl/aff.h>
5440 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
5441 __isl_take isl_multi_aff *ma1, unsigned pos,
5442 __isl_take isl_multi_aff *ma2);
5443 __isl_give isl_multi_aff *isl_multi_aff_splice(
5444 __isl_take isl_multi_aff *ma1,
5445 unsigned in_pos, unsigned out_pos,
5446 __isl_take isl_multi_aff *ma2);
5447 __isl_give isl_multi_pw_aff *
5448 isl_multi_pw_aff_range_splice(
5449 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
5450 __isl_take isl_multi_pw_aff *mpa2);
5451 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
5452 __isl_take isl_multi_pw_aff *mpa1,
5453 unsigned in_pos, unsigned out_pos,
5454 __isl_take isl_multi_pw_aff *mpa2);
5456 =item * Simplification
5458 When applied to a set or relation,
5459 the gist operation returns a set or relation that has the
5460 same intersection with the context as the input set or relation.
5461 Any implicit equality in the intersection is made explicit in the result,
5462 while all inequalities that are redundant with respect to the intersection
5464 In case of union sets and relations, the gist operation is performed
5467 When applied to a function,
5468 the gist operation applies the set gist operation to each of
5469 the cells in the domain of the input piecewise expression.
5470 The context is also exploited
5471 to simplify the expression associated to each cell.
5473 #include <isl/set.h>
5474 __isl_give isl_basic_set *isl_basic_set_gist(
5475 __isl_take isl_basic_set *bset,
5476 __isl_take isl_basic_set *context);
5477 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
5478 __isl_take isl_set *context);
5479 __isl_give isl_set *isl_set_gist_params(
5480 __isl_take isl_set *set,
5481 __isl_take isl_set *context);
5483 #include <isl/map.h>
5484 __isl_give isl_basic_map *isl_basic_map_gist(
5485 __isl_take isl_basic_map *bmap,
5486 __isl_take isl_basic_map *context);
5487 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
5488 __isl_take isl_map *context);
5489 __isl_give isl_map *isl_map_gist_params(
5490 __isl_take isl_map *map,
5491 __isl_take isl_set *context);
5492 __isl_give isl_map *isl_map_gist_domain(
5493 __isl_take isl_map *map,
5494 __isl_take isl_set *context);
5495 __isl_give isl_map *isl_map_gist_range(
5496 __isl_take isl_map *map,
5497 __isl_take isl_set *context);
5499 #include <isl/union_set.h>
5500 __isl_give isl_union_set *isl_union_set_gist(
5501 __isl_take isl_union_set *uset,
5502 __isl_take isl_union_set *context);
5503 __isl_give isl_union_set *isl_union_set_gist_params(
5504 __isl_take isl_union_set *uset,
5505 __isl_take isl_set *set);
5507 #include <isl/union_map.h>
5508 __isl_give isl_union_map *isl_union_map_gist(
5509 __isl_take isl_union_map *umap,
5510 __isl_take isl_union_map *context);
5511 __isl_give isl_union_map *isl_union_map_gist_params(
5512 __isl_take isl_union_map *umap,
5513 __isl_take isl_set *set);
5514 __isl_give isl_union_map *isl_union_map_gist_domain(
5515 __isl_take isl_union_map *umap,
5516 __isl_take isl_union_set *uset);
5517 __isl_give isl_union_map *isl_union_map_gist_range(
5518 __isl_take isl_union_map *umap,
5519 __isl_take isl_union_set *uset);
5521 #include <isl/aff.h>
5522 __isl_give isl_aff *isl_aff_gist_params(
5523 __isl_take isl_aff *aff,
5524 __isl_take isl_set *context);
5525 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
5526 __isl_take isl_set *context);
5527 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
5528 __isl_take isl_multi_aff *maff,
5529 __isl_take isl_set *context);
5530 __isl_give isl_multi_aff *isl_multi_aff_gist(
5531 __isl_take isl_multi_aff *maff,
5532 __isl_take isl_set *context);
5533 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
5534 __isl_take isl_pw_aff *pwaff,
5535 __isl_take isl_set *context);
5536 __isl_give isl_pw_aff *isl_pw_aff_gist(
5537 __isl_take isl_pw_aff *pwaff,
5538 __isl_take isl_set *context);
5539 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
5540 __isl_take isl_pw_multi_aff *pma,
5541 __isl_take isl_set *set);
5542 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
5543 __isl_take isl_pw_multi_aff *pma,
5544 __isl_take isl_set *set);
5545 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
5546 __isl_take isl_multi_pw_aff *mpa,
5547 __isl_take isl_set *set);
5548 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
5549 __isl_take isl_multi_pw_aff *mpa,
5550 __isl_take isl_set *set);
5551 __isl_give isl_union_pw_multi_aff *
5552 isl_union_pw_multi_aff_gist_params(
5553 __isl_take isl_union_pw_multi_aff *upma,
5554 __isl_take isl_set *context);
5555 __isl_give isl_union_pw_multi_aff *
5556 isl_union_pw_multi_aff_gist(
5557 __isl_take isl_union_pw_multi_aff *upma,
5558 __isl_take isl_union_set *context);
5560 #include <isl/polynomial.h>
5561 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5562 __isl_take isl_qpolynomial *qp,
5563 __isl_take isl_set *context);
5564 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5565 __isl_take isl_qpolynomial *qp,
5566 __isl_take isl_set *context);
5567 __isl_give isl_qpolynomial_fold *
5568 isl_qpolynomial_fold_gist_params(
5569 __isl_take isl_qpolynomial_fold *fold,
5570 __isl_take isl_set *context);
5571 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5572 __isl_take isl_qpolynomial_fold *fold,
5573 __isl_take isl_set *context);
5574 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5575 __isl_take isl_pw_qpolynomial *pwqp,
5576 __isl_take isl_set *context);
5577 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5578 __isl_take isl_pw_qpolynomial *pwqp,
5579 __isl_take isl_set *context);
5580 __isl_give isl_pw_qpolynomial_fold *
5581 isl_pw_qpolynomial_fold_gist(
5582 __isl_take isl_pw_qpolynomial_fold *pwf,
5583 __isl_take isl_set *context);
5584 __isl_give isl_pw_qpolynomial_fold *
5585 isl_pw_qpolynomial_fold_gist_params(
5586 __isl_take isl_pw_qpolynomial_fold *pwf,
5587 __isl_take isl_set *context);
5588 __isl_give isl_union_pw_qpolynomial *
5589 isl_union_pw_qpolynomial_gist_params(
5590 __isl_take isl_union_pw_qpolynomial *upwqp,
5591 __isl_take isl_set *context);
5592 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5593 __isl_take isl_union_pw_qpolynomial *upwqp,
5594 __isl_take isl_union_set *context);
5595 __isl_give isl_union_pw_qpolynomial_fold *
5596 isl_union_pw_qpolynomial_fold_gist(
5597 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5598 __isl_take isl_union_set *context);
5599 __isl_give isl_union_pw_qpolynomial_fold *
5600 isl_union_pw_qpolynomial_fold_gist_params(
5601 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5602 __isl_take isl_set *context);
5604 =item * Binary Arithmethic Operations
5606 #include <isl/aff.h>
5607 __isl_give isl_aff *isl_aff_add(
5608 __isl_take isl_aff *aff1,
5609 __isl_take isl_aff *aff2);
5610 __isl_give isl_multi_aff *isl_multi_aff_add(
5611 __isl_take isl_multi_aff *maff1,
5612 __isl_take isl_multi_aff *maff2);
5613 __isl_give isl_pw_aff *isl_pw_aff_add(
5614 __isl_take isl_pw_aff *pwaff1,
5615 __isl_take isl_pw_aff *pwaff2);
5616 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
5617 __isl_take isl_pw_multi_aff *pma1,
5618 __isl_take isl_pw_multi_aff *pma2);
5619 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
5620 __isl_take isl_union_pw_multi_aff *upma1,
5621 __isl_take isl_union_pw_multi_aff *upma2);
5622 __isl_give isl_pw_aff *isl_pw_aff_min(
5623 __isl_take isl_pw_aff *pwaff1,
5624 __isl_take isl_pw_aff *pwaff2);
5625 __isl_give isl_pw_aff *isl_pw_aff_max(
5626 __isl_take isl_pw_aff *pwaff1,
5627 __isl_take isl_pw_aff *pwaff2);
5628 __isl_give isl_aff *isl_aff_sub(
5629 __isl_take isl_aff *aff1,
5630 __isl_take isl_aff *aff2);
5631 __isl_give isl_multi_aff *isl_multi_aff_sub(
5632 __isl_take isl_multi_aff *ma1,
5633 __isl_take isl_multi_aff *ma2);
5634 __isl_give isl_pw_aff *isl_pw_aff_sub(
5635 __isl_take isl_pw_aff *pwaff1,
5636 __isl_take isl_pw_aff *pwaff2);
5637 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
5638 __isl_take isl_pw_multi_aff *pma1,
5639 __isl_take isl_pw_multi_aff *pma2);
5640 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
5641 __isl_take isl_union_pw_multi_aff *upma1,
5642 __isl_take isl_union_pw_multi_aff *upma2);
5644 C<isl_aff_sub> subtracts the second argument from the first.
5646 #include <isl/polynomial.h>
5647 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5648 __isl_take isl_qpolynomial *qp1,
5649 __isl_take isl_qpolynomial *qp2);
5650 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5651 __isl_take isl_pw_qpolynomial *pwqp1,
5652 __isl_take isl_pw_qpolynomial *pwqp2);
5653 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5654 __isl_take isl_pw_qpolynomial *pwqp1,
5655 __isl_take isl_pw_qpolynomial *pwqp2);
5656 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5657 __isl_take isl_pw_qpolynomial_fold *pwf1,
5658 __isl_take isl_pw_qpolynomial_fold *pwf2);
5659 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5660 __isl_take isl_union_pw_qpolynomial *upwqp1,
5661 __isl_take isl_union_pw_qpolynomial *upwqp2);
5662 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5663 __isl_take isl_qpolynomial *qp1,
5664 __isl_take isl_qpolynomial *qp2);
5665 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5666 __isl_take isl_pw_qpolynomial *pwqp1,
5667 __isl_take isl_pw_qpolynomial *pwqp2);
5668 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5669 __isl_take isl_union_pw_qpolynomial *upwqp1,
5670 __isl_take isl_union_pw_qpolynomial *upwqp2);
5671 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5672 __isl_take isl_pw_qpolynomial_fold *pwf1,
5673 __isl_take isl_pw_qpolynomial_fold *pwf2);
5674 __isl_give isl_union_pw_qpolynomial_fold *
5675 isl_union_pw_qpolynomial_fold_fold(
5676 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5677 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5679 #include <isl/aff.h>
5680 __isl_give isl_pw_aff *isl_pw_aff_union_add(
5681 __isl_take isl_pw_aff *pwaff1,
5682 __isl_take isl_pw_aff *pwaff2);
5683 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
5684 __isl_take isl_pw_multi_aff *pma1,
5685 __isl_take isl_pw_multi_aff *pma2);
5686 __isl_give isl_union_pw_multi_aff *
5687 isl_union_pw_multi_aff_union_add(
5688 __isl_take isl_union_pw_multi_aff *upma1,
5689 __isl_take isl_union_pw_multi_aff *upma2);
5690 __isl_give isl_pw_aff *isl_pw_aff_union_min(
5691 __isl_take isl_pw_aff *pwaff1,
5692 __isl_take isl_pw_aff *pwaff2);
5693 __isl_give isl_pw_aff *isl_pw_aff_union_max(
5694 __isl_take isl_pw_aff *pwaff1,
5695 __isl_take isl_pw_aff *pwaff2);
5697 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
5698 expression with a domain that is the union of those of C<pwaff1> and
5699 C<pwaff2> and such that on each cell, the quasi-affine expression is
5700 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
5701 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
5702 associated expression is the defined one.
5703 This in contrast to the C<isl_pw_aff_max> function, which is
5704 only defined on the shared definition domain of the arguments.
5706 #include <isl/val.h>
5707 __isl_give isl_multi_val *isl_multi_val_add_val(
5708 __isl_take isl_multi_val *mv,
5709 __isl_take isl_val *v);
5710 __isl_give isl_multi_val *isl_multi_val_mod_val(
5711 __isl_take isl_multi_val *mv,
5712 __isl_take isl_val *v);
5713 __isl_give isl_multi_val *isl_multi_val_scale_val(
5714 __isl_take isl_multi_val *mv,
5715 __isl_take isl_val *v);
5717 #include <isl/aff.h>
5718 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
5719 __isl_take isl_val *mod);
5720 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
5721 __isl_take isl_pw_aff *pa,
5722 __isl_take isl_val *mod);
5723 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
5724 __isl_take isl_val *v);
5725 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
5726 __isl_take isl_multi_aff *ma,
5727 __isl_take isl_val *v);
5728 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
5729 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
5730 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
5731 __isl_take isl_multi_pw_aff *mpa,
5732 __isl_take isl_val *v);
5733 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
5734 __isl_take isl_pw_multi_aff *pma,
5735 __isl_take isl_val *v);
5736 __isl_give isl_union_pw_multi_aff *
5737 isl_union_pw_multi_aff_scale_val(
5738 __isl_take isl_union_pw_multi_aff *upma,
5739 __isl_take isl_val *val);
5740 __isl_give isl_aff *isl_aff_scale_down_ui(
5741 __isl_take isl_aff *aff, unsigned f);
5742 __isl_give isl_aff *isl_aff_scale_down_val(
5743 __isl_take isl_aff *aff, __isl_take isl_val *v);
5744 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
5745 __isl_take isl_pw_aff *pa,
5746 __isl_take isl_val *f);
5748 #include <isl/polynomial.h>
5749 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5750 __isl_take isl_qpolynomial *qp,
5751 __isl_take isl_val *v);
5752 __isl_give isl_qpolynomial_fold *
5753 isl_qpolynomial_fold_scale_val(
5754 __isl_take isl_qpolynomial_fold *fold,
5755 __isl_take isl_val *v);
5756 __isl_give isl_pw_qpolynomial *
5757 isl_pw_qpolynomial_scale_val(
5758 __isl_take isl_pw_qpolynomial *pwqp,
5759 __isl_take isl_val *v);
5760 __isl_give isl_pw_qpolynomial_fold *
5761 isl_pw_qpolynomial_fold_scale_val(
5762 __isl_take isl_pw_qpolynomial_fold *pwf,
5763 __isl_take isl_val *v);
5764 __isl_give isl_union_pw_qpolynomial *
5765 isl_union_pw_qpolynomial_scale_val(
5766 __isl_take isl_union_pw_qpolynomial *upwqp,
5767 __isl_take isl_val *v);
5768 __isl_give isl_union_pw_qpolynomial_fold *
5769 isl_union_pw_qpolynomial_fold_scale_val(
5770 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5771 __isl_take isl_val *v);
5773 #include <isl/val.h>
5774 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
5775 __isl_take isl_multi_val *mv1,
5776 __isl_take isl_multi_val *mv2);
5777 __isl_give isl_multi_val *
5778 isl_multi_val_scale_down_multi_val(
5779 __isl_take isl_multi_val *mv1,
5780 __isl_take isl_multi_val *mv2);
5782 #include <isl/aff.h>
5783 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
5784 __isl_take isl_multi_aff *ma,
5785 __isl_take isl_multi_val *mv);
5786 __isl_give isl_pw_multi_aff *
5787 isl_pw_multi_aff_scale_multi_val(
5788 __isl_take isl_pw_multi_aff *pma,
5789 __isl_take isl_multi_val *mv);
5790 __isl_give isl_multi_pw_aff *
5791 isl_multi_pw_aff_scale_multi_val(
5792 __isl_take isl_multi_pw_aff *mpa,
5793 __isl_take isl_multi_val *mv);
5794 __isl_give isl_union_pw_multi_aff *
5795 isl_union_pw_multi_aff_scale_multi_val(
5796 __isl_take isl_union_pw_multi_aff *upma,
5797 __isl_take isl_multi_val *mv);
5798 __isl_give isl_multi_aff *
5799 isl_multi_aff_scale_down_multi_val(
5800 __isl_take isl_multi_aff *ma,
5801 __isl_take isl_multi_val *mv);
5802 __isl_give isl_multi_pw_aff *
5803 isl_multi_pw_aff_scale_down_multi_val(
5804 __isl_take isl_multi_pw_aff *mpa,
5805 __isl_take isl_multi_val *mv);
5807 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
5808 by the corresponding elements of C<mv>.
5810 #include <isl/aff.h>
5811 __isl_give isl_aff *isl_aff_mul(
5812 __isl_take isl_aff *aff1,
5813 __isl_take isl_aff *aff2);
5814 __isl_give isl_aff *isl_aff_div(
5815 __isl_take isl_aff *aff1,
5816 __isl_take isl_aff *aff2);
5817 __isl_give isl_pw_aff *isl_pw_aff_mul(
5818 __isl_take isl_pw_aff *pwaff1,
5819 __isl_take isl_pw_aff *pwaff2);
5820 __isl_give isl_pw_aff *isl_pw_aff_div(
5821 __isl_take isl_pw_aff *pa1,
5822 __isl_take isl_pw_aff *pa2);
5823 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
5824 __isl_take isl_pw_aff *pa1,
5825 __isl_take isl_pw_aff *pa2);
5826 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
5827 __isl_take isl_pw_aff *pa1,
5828 __isl_take isl_pw_aff *pa2);
5830 When multiplying two affine expressions, at least one of the two needs
5831 to be a constant. Similarly, when dividing an affine expression by another,
5832 the second expression needs to be a constant.
5833 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
5834 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
5837 #include <isl/polynomial.h>
5838 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5839 __isl_take isl_qpolynomial *qp1,
5840 __isl_take isl_qpolynomial *qp2);
5841 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5842 __isl_take isl_pw_qpolynomial *pwqp1,
5843 __isl_take isl_pw_qpolynomial *pwqp2);
5844 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5845 __isl_take isl_union_pw_qpolynomial *upwqp1,
5846 __isl_take isl_union_pw_qpolynomial *upwqp2);
5850 =head3 Lexicographic Optimization
5852 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
5853 the following functions
5854 compute a set that contains the lexicographic minimum or maximum
5855 of the elements in C<set> (or C<bset>) for those values of the parameters
5856 that satisfy C<dom>.
5857 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
5858 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
5860 In other words, the union of the parameter values
5861 for which the result is non-empty and of C<*empty>
5864 #include <isl/set.h>
5865 __isl_give isl_set *isl_basic_set_partial_lexmin(
5866 __isl_take isl_basic_set *bset,
5867 __isl_take isl_basic_set *dom,
5868 __isl_give isl_set **empty);
5869 __isl_give isl_set *isl_basic_set_partial_lexmax(
5870 __isl_take isl_basic_set *bset,
5871 __isl_take isl_basic_set *dom,
5872 __isl_give isl_set **empty);
5873 __isl_give isl_set *isl_set_partial_lexmin(
5874 __isl_take isl_set *set, __isl_take isl_set *dom,
5875 __isl_give isl_set **empty);
5876 __isl_give isl_set *isl_set_partial_lexmax(
5877 __isl_take isl_set *set, __isl_take isl_set *dom,
5878 __isl_give isl_set **empty);
5880 Given a (basic) set C<set> (or C<bset>), the following functions simply
5881 return a set containing the lexicographic minimum or maximum
5882 of the elements in C<set> (or C<bset>).
5883 In case of union sets, the optimum is computed per space.
5885 #include <isl/set.h>
5886 __isl_give isl_set *isl_basic_set_lexmin(
5887 __isl_take isl_basic_set *bset);
5888 __isl_give isl_set *isl_basic_set_lexmax(
5889 __isl_take isl_basic_set *bset);
5890 __isl_give isl_set *isl_set_lexmin(
5891 __isl_take isl_set *set);
5892 __isl_give isl_set *isl_set_lexmax(
5893 __isl_take isl_set *set);
5894 __isl_give isl_union_set *isl_union_set_lexmin(
5895 __isl_take isl_union_set *uset);
5896 __isl_give isl_union_set *isl_union_set_lexmax(
5897 __isl_take isl_union_set *uset);
5899 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
5900 the following functions
5901 compute a relation that maps each element of C<dom>
5902 to the single lexicographic minimum or maximum
5903 of the elements that are associated to that same
5904 element in C<map> (or C<bmap>).
5905 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
5906 that contains the elements in C<dom> that do not map
5907 to any elements in C<map> (or C<bmap>).
5908 In other words, the union of the domain of the result and of C<*empty>
5911 #include <isl/map.h>
5912 __isl_give isl_map *isl_basic_map_partial_lexmax(
5913 __isl_take isl_basic_map *bmap,
5914 __isl_take isl_basic_set *dom,
5915 __isl_give isl_set **empty);
5916 __isl_give isl_map *isl_basic_map_partial_lexmin(
5917 __isl_take isl_basic_map *bmap,
5918 __isl_take isl_basic_set *dom,
5919 __isl_give isl_set **empty);
5920 __isl_give isl_map *isl_map_partial_lexmax(
5921 __isl_take isl_map *map, __isl_take isl_set *dom,
5922 __isl_give isl_set **empty);
5923 __isl_give isl_map *isl_map_partial_lexmin(
5924 __isl_take isl_map *map, __isl_take isl_set *dom,
5925 __isl_give isl_set **empty);
5927 Given a (basic) map C<map> (or C<bmap>), the following functions simply
5928 return a map mapping each element in the domain of
5929 C<map> (or C<bmap>) to the lexicographic minimum or maximum
5930 of all elements associated to that element.
5931 In case of union relations, the optimum is computed per space.
5933 #include <isl/map.h>
5934 __isl_give isl_map *isl_basic_map_lexmin(
5935 __isl_take isl_basic_map *bmap);
5936 __isl_give isl_map *isl_basic_map_lexmax(
5937 __isl_take isl_basic_map *bmap);
5938 __isl_give isl_map *isl_map_lexmin(
5939 __isl_take isl_map *map);
5940 __isl_give isl_map *isl_map_lexmax(
5941 __isl_take isl_map *map);
5942 __isl_give isl_union_map *isl_union_map_lexmin(
5943 __isl_take isl_union_map *umap);
5944 __isl_give isl_union_map *isl_union_map_lexmax(
5945 __isl_take isl_union_map *umap);
5947 The following functions return their result in the form of
5948 a piecewise multi-affine expression,
5949 but are otherwise equivalent to the corresponding functions
5950 returning a basic set or relation.
5952 #include <isl/set.h>
5953 __isl_give isl_pw_multi_aff *
5954 isl_basic_set_partial_lexmin_pw_multi_aff(
5955 __isl_take isl_basic_set *bset,
5956 __isl_take isl_basic_set *dom,
5957 __isl_give isl_set **empty);
5958 __isl_give isl_pw_multi_aff *
5959 isl_basic_set_partial_lexmax_pw_multi_aff(
5960 __isl_take isl_basic_set *bset,
5961 __isl_take isl_basic_set *dom,
5962 __isl_give isl_set **empty);
5963 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
5964 __isl_take isl_set *set);
5965 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
5966 __isl_take isl_set *set);
5968 #include <isl/map.h>
5969 __isl_give isl_pw_multi_aff *
5970 isl_basic_map_lexmin_pw_multi_aff(
5971 __isl_take isl_basic_map *bmap);
5972 __isl_give isl_pw_multi_aff *
5973 isl_basic_map_partial_lexmin_pw_multi_aff(
5974 __isl_take isl_basic_map *bmap,
5975 __isl_take isl_basic_set *dom,
5976 __isl_give isl_set **empty);
5977 __isl_give isl_pw_multi_aff *
5978 isl_basic_map_partial_lexmax_pw_multi_aff(
5979 __isl_take isl_basic_map *bmap,
5980 __isl_take isl_basic_set *dom,
5981 __isl_give isl_set **empty);
5982 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
5983 __isl_take isl_map *map);
5984 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
5985 __isl_take isl_map *map);
5987 The following functions return the lexicographic minimum or maximum
5988 on the shared domain of the inputs and the single defined function
5989 on those parts of the domain where only a single function is defined.
5991 #include <isl/aff.h>
5992 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
5993 __isl_take isl_pw_multi_aff *pma1,
5994 __isl_take isl_pw_multi_aff *pma2);
5995 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
5996 __isl_take isl_pw_multi_aff *pma1,
5997 __isl_take isl_pw_multi_aff *pma2);
5999 =head2 Ternary Operations
6001 #include <isl/aff.h>
6002 __isl_give isl_pw_aff *isl_pw_aff_cond(
6003 __isl_take isl_pw_aff *cond,
6004 __isl_take isl_pw_aff *pwaff_true,
6005 __isl_take isl_pw_aff *pwaff_false);
6007 The function C<isl_pw_aff_cond> performs a conditional operator
6008 and returns an expression that is equal to C<pwaff_true>
6009 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6010 where C<cond> is zero.
6014 Lists are defined over several element types, including
6015 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
6016 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
6017 Here we take lists of C<isl_set>s as an example.
6018 Lists can be created, copied, modified and freed using the following functions.
6020 #include <isl/set.h>
6021 __isl_give isl_set_list *isl_set_list_from_set(
6022 __isl_take isl_set *el);
6023 __isl_give isl_set_list *isl_set_list_alloc(
6024 isl_ctx *ctx, int n);
6025 __isl_give isl_set_list *isl_set_list_copy(
6026 __isl_keep isl_set_list *list);
6027 __isl_give isl_set_list *isl_set_list_insert(
6028 __isl_take isl_set_list *list, unsigned pos,
6029 __isl_take isl_set *el);
6030 __isl_give isl_set_list *isl_set_list_add(
6031 __isl_take isl_set_list *list,
6032 __isl_take isl_set *el);
6033 __isl_give isl_set_list *isl_set_list_drop(
6034 __isl_take isl_set_list *list,
6035 unsigned first, unsigned n);
6036 __isl_give isl_set_list *isl_set_list_set_set(
6037 __isl_take isl_set_list *list, int index,
6038 __isl_take isl_set *set);
6039 __isl_give isl_set_list *isl_set_list_concat(
6040 __isl_take isl_set_list *list1,
6041 __isl_take isl_set_list *list2);
6042 __isl_give isl_set_list *isl_set_list_sort(
6043 __isl_take isl_set_list *list,
6044 int (*cmp)(__isl_keep isl_set *a,
6045 __isl_keep isl_set *b, void *user),
6047 __isl_null isl_set_list *isl_set_list_free(
6048 __isl_take isl_set_list *list);
6050 C<isl_set_list_alloc> creates an empty list with a capacity for
6051 C<n> elements. C<isl_set_list_from_set> creates a list with a single
6054 Lists can be inspected using the following functions.
6056 #include <isl/set.h>
6057 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6058 __isl_give isl_set *isl_set_list_get_set(
6059 __isl_keep isl_set_list *list, int index);
6060 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6061 int (*fn)(__isl_take isl_set *el, void *user),
6063 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6064 int (*follows)(__isl_keep isl_set *a,
6065 __isl_keep isl_set *b, void *user),
6067 int (*fn)(__isl_take isl_set *el, void *user),
6070 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6071 strongly connected components of the graph with as vertices the elements
6072 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6073 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6074 should return C<-1> on error.
6076 Lists can be printed using
6078 #include <isl/set.h>
6079 __isl_give isl_printer *isl_printer_print_set_list(
6080 __isl_take isl_printer *p,
6081 __isl_keep isl_set_list *list);
6083 =head2 Associative arrays
6085 Associative arrays map isl objects of a specific type to isl objects
6086 of some (other) specific type. They are defined for several pairs
6087 of types, including (C<isl_map>, C<isl_basic_set>),
6088 (C<isl_id>, C<isl_ast_expr>) and.
6089 (C<isl_id>, C<isl_pw_aff>).
6090 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6093 Associative arrays can be created, copied and freed using
6094 the following functions.
6096 #include <isl/id_to_ast_expr.h>
6097 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6098 isl_ctx *ctx, int min_size);
6099 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6100 __isl_keep id_to_ast_expr *id2expr);
6101 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6102 __isl_take id_to_ast_expr *id2expr);
6104 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6105 to specify the expected size of the associative array.
6106 The associative array will be grown automatically as needed.
6108 Associative arrays can be inspected using the following functions.
6110 #include <isl/id_to_ast_expr.h>
6111 int isl_id_to_ast_expr_has(
6112 __isl_keep id_to_ast_expr *id2expr,
6113 __isl_keep isl_id *key);
6114 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6115 __isl_keep id_to_ast_expr *id2expr,
6116 __isl_take isl_id *key);
6117 int isl_id_to_ast_expr_foreach(
6118 __isl_keep id_to_ast_expr *id2expr,
6119 int (*fn)(__isl_take isl_id *key,
6120 __isl_take isl_ast_expr *val, void *user),
6123 They can be modified using the following function.
6125 #include <isl/id_to_ast_expr.h>
6126 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6127 __isl_take id_to_ast_expr *id2expr,
6128 __isl_take isl_id *key,
6129 __isl_take isl_ast_expr *val);
6130 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6131 __isl_take id_to_ast_expr *id2expr,
6132 __isl_take isl_id *key);
6134 Associative arrays can be printed using the following function.
6136 #include <isl/id_to_ast_expr.h>
6137 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6138 __isl_take isl_printer *p,
6139 __isl_keep id_to_ast_expr *id2expr);
6143 Vectors can be created, copied and freed using the following functions.
6145 #include <isl/vec.h>
6146 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6148 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6149 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6151 Note that the elements of a newly created vector may have arbitrary values.
6152 The elements can be changed and inspected using the following functions.
6154 int isl_vec_size(__isl_keep isl_vec *vec);
6155 __isl_give isl_val *isl_vec_get_element_val(
6156 __isl_keep isl_vec *vec, int pos);
6157 __isl_give isl_vec *isl_vec_set_element_si(
6158 __isl_take isl_vec *vec, int pos, int v);
6159 __isl_give isl_vec *isl_vec_set_element_val(
6160 __isl_take isl_vec *vec, int pos,
6161 __isl_take isl_val *v);
6162 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6164 __isl_give isl_vec *isl_vec_set_val(
6165 __isl_take isl_vec *vec, __isl_take isl_val *v);
6166 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6167 __isl_keep isl_vec *vec2, int pos);
6169 C<isl_vec_get_element> will return a negative value if anything went wrong.
6170 In that case, the value of C<*v> is undefined.
6172 The following function can be used to concatenate two vectors.
6174 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6175 __isl_take isl_vec *vec2);
6179 Matrices can be created, copied and freed using the following functions.
6181 #include <isl/mat.h>
6182 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6183 unsigned n_row, unsigned n_col);
6184 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6185 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6187 Note that the elements of a newly created matrix may have arbitrary values.
6188 The elements can be changed and inspected using the following functions.
6190 int isl_mat_rows(__isl_keep isl_mat *mat);
6191 int isl_mat_cols(__isl_keep isl_mat *mat);
6192 __isl_give isl_val *isl_mat_get_element_val(
6193 __isl_keep isl_mat *mat, int row, int col);
6194 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
6195 int row, int col, int v);
6196 __isl_give isl_mat *isl_mat_set_element_val(
6197 __isl_take isl_mat *mat, int row, int col,
6198 __isl_take isl_val *v);
6200 C<isl_mat_get_element> will return a negative value if anything went wrong.
6201 In that case, the value of C<*v> is undefined.
6203 The following function can be used to compute the (right) inverse
6204 of a matrix, i.e., a matrix such that the product of the original
6205 and the inverse (in that order) is a multiple of the identity matrix.
6206 The input matrix is assumed to be of full row-rank.
6208 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
6210 The following function can be used to compute the (right) kernel
6211 (or null space) of a matrix, i.e., a matrix such that the product of
6212 the original and the kernel (in that order) is the zero matrix.
6214 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
6216 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
6218 The following functions determine
6219 an upper or lower bound on a quasipolynomial over its domain.
6221 __isl_give isl_pw_qpolynomial_fold *
6222 isl_pw_qpolynomial_bound(
6223 __isl_take isl_pw_qpolynomial *pwqp,
6224 enum isl_fold type, int *tight);
6226 __isl_give isl_union_pw_qpolynomial_fold *
6227 isl_union_pw_qpolynomial_bound(
6228 __isl_take isl_union_pw_qpolynomial *upwqp,
6229 enum isl_fold type, int *tight);
6231 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
6232 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
6233 is the returned bound is known be tight, i.e., for each value
6234 of the parameters there is at least
6235 one element in the domain that reaches the bound.
6236 If the domain of C<pwqp> is not wrapping, then the bound is computed
6237 over all elements in that domain and the result has a purely parametric
6238 domain. If the domain of C<pwqp> is wrapping, then the bound is
6239 computed over the range of the wrapped relation. The domain of the
6240 wrapped relation becomes the domain of the result.
6242 =head2 Parametric Vertex Enumeration
6244 The parametric vertex enumeration described in this section
6245 is mainly intended to be used internally and by the C<barvinok>
6248 #include <isl/vertices.h>
6249 __isl_give isl_vertices *isl_basic_set_compute_vertices(
6250 __isl_keep isl_basic_set *bset);
6252 The function C<isl_basic_set_compute_vertices> performs the
6253 actual computation of the parametric vertices and the chamber
6254 decomposition and store the result in an C<isl_vertices> object.
6255 This information can be queried by either iterating over all
6256 the vertices or iterating over all the chambers or cells
6257 and then iterating over all vertices that are active on the chamber.
6259 int isl_vertices_foreach_vertex(
6260 __isl_keep isl_vertices *vertices,
6261 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6264 int isl_vertices_foreach_cell(
6265 __isl_keep isl_vertices *vertices,
6266 int (*fn)(__isl_take isl_cell *cell, void *user),
6268 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
6269 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6272 Other operations that can be performed on an C<isl_vertices> object are
6275 int isl_vertices_get_n_vertices(
6276 __isl_keep isl_vertices *vertices);
6277 void isl_vertices_free(__isl_take isl_vertices *vertices);
6279 Vertices can be inspected and destroyed using the following functions.
6281 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
6282 __isl_give isl_basic_set *isl_vertex_get_domain(
6283 __isl_keep isl_vertex *vertex);
6284 __isl_give isl_multi_aff *isl_vertex_get_expr(
6285 __isl_keep isl_vertex *vertex);
6286 void isl_vertex_free(__isl_take isl_vertex *vertex);
6288 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
6289 describing the vertex in terms of the parameters,
6290 while C<isl_vertex_get_domain> returns the activity domain
6293 Chambers can be inspected and destroyed using the following functions.
6295 __isl_give isl_basic_set *isl_cell_get_domain(
6296 __isl_keep isl_cell *cell);
6297 void isl_cell_free(__isl_take isl_cell *cell);
6299 =head1 Polyhedral Compilation Library
6301 This section collects functionality in C<isl> that has been specifically
6302 designed for use during polyhedral compilation.
6304 =head2 Dependence Analysis
6306 C<isl> contains specialized functionality for performing
6307 array dataflow analysis. That is, given a I<sink> access relation
6308 and a collection of possible I<source> access relations,
6309 C<isl> can compute relations that describe
6310 for each iteration of the sink access, which iteration
6311 of which of the source access relations was the last
6312 to access the same data element before the given iteration
6314 The resulting dependence relations map source iterations
6315 to the corresponding sink iterations.
6316 To compute standard flow dependences, the sink should be
6317 a read, while the sources should be writes.
6318 If any of the source accesses are marked as being I<may>
6319 accesses, then there will be a dependence from the last
6320 I<must> access B<and> from any I<may> access that follows
6321 this last I<must> access.
6322 In particular, if I<all> sources are I<may> accesses,
6323 then memory based dependence analysis is performed.
6324 If, on the other hand, all sources are I<must> accesses,
6325 then value based dependence analysis is performed.
6327 #include <isl/flow.h>
6329 typedef int (*isl_access_level_before)(void *first, void *second);
6331 __isl_give isl_access_info *isl_access_info_alloc(
6332 __isl_take isl_map *sink,
6333 void *sink_user, isl_access_level_before fn,
6335 __isl_give isl_access_info *isl_access_info_add_source(
6336 __isl_take isl_access_info *acc,
6337 __isl_take isl_map *source, int must,
6339 __isl_null isl_access_info *isl_access_info_free(
6340 __isl_take isl_access_info *acc);
6342 __isl_give isl_flow *isl_access_info_compute_flow(
6343 __isl_take isl_access_info *acc);
6345 int isl_flow_foreach(__isl_keep isl_flow *deps,
6346 int (*fn)(__isl_take isl_map *dep, int must,
6347 void *dep_user, void *user),
6349 __isl_give isl_map *isl_flow_get_no_source(
6350 __isl_keep isl_flow *deps, int must);
6351 void isl_flow_free(__isl_take isl_flow *deps);
6353 The function C<isl_access_info_compute_flow> performs the actual
6354 dependence analysis. The other functions are used to construct
6355 the input for this function or to read off the output.
6357 The input is collected in an C<isl_access_info>, which can
6358 be created through a call to C<isl_access_info_alloc>.
6359 The arguments to this functions are the sink access relation
6360 C<sink>, a token C<sink_user> used to identify the sink
6361 access to the user, a callback function for specifying the
6362 relative order of source and sink accesses, and the number
6363 of source access relations that will be added.
6364 The callback function has type C<int (*)(void *first, void *second)>.
6365 The function is called with two user supplied tokens identifying
6366 either a source or the sink and it should return the shared nesting
6367 level and the relative order of the two accesses.
6368 In particular, let I<n> be the number of loops shared by
6369 the two accesses. If C<first> precedes C<second> textually,
6370 then the function should return I<2 * n + 1>; otherwise,
6371 it should return I<2 * n>.
6372 The sources can be added to the C<isl_access_info> by performing
6373 (at most) C<max_source> calls to C<isl_access_info_add_source>.
6374 C<must> indicates whether the source is a I<must> access
6375 or a I<may> access. Note that a multi-valued access relation
6376 should only be marked I<must> if every iteration in the domain
6377 of the relation accesses I<all> elements in its image.
6378 The C<source_user> token is again used to identify
6379 the source access. The range of the source access relation
6380 C<source> should have the same dimension as the range
6381 of the sink access relation.
6382 The C<isl_access_info_free> function should usually not be
6383 called explicitly, because it is called implicitly by
6384 C<isl_access_info_compute_flow>.
6386 The result of the dependence analysis is collected in an
6387 C<isl_flow>. There may be elements of
6388 the sink access for which no preceding source access could be
6389 found or for which all preceding sources are I<may> accesses.
6390 The relations containing these elements can be obtained through
6391 calls to C<isl_flow_get_no_source>, the first with C<must> set
6392 and the second with C<must> unset.
6393 In the case of standard flow dependence analysis,
6394 with the sink a read and the sources I<must> writes,
6395 the first relation corresponds to the reads from uninitialized
6396 array elements and the second relation is empty.
6397 The actual flow dependences can be extracted using
6398 C<isl_flow_foreach>. This function will call the user-specified
6399 callback function C<fn> for each B<non-empty> dependence between
6400 a source and the sink. The callback function is called
6401 with four arguments, the actual flow dependence relation
6402 mapping source iterations to sink iterations, a boolean that
6403 indicates whether it is a I<must> or I<may> dependence, a token
6404 identifying the source and an additional C<void *> with value
6405 equal to the third argument of the C<isl_flow_foreach> call.
6406 A dependence is marked I<must> if it originates from a I<must>
6407 source and if it is not followed by any I<may> sources.
6409 After finishing with an C<isl_flow>, the user should call
6410 C<isl_flow_free> to free all associated memory.
6412 A higher-level interface to dependence analysis is provided
6413 by the following function.
6415 #include <isl/flow.h>
6417 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
6418 __isl_take isl_union_map *must_source,
6419 __isl_take isl_union_map *may_source,
6420 __isl_take isl_union_map *schedule,
6421 __isl_give isl_union_map **must_dep,
6422 __isl_give isl_union_map **may_dep,
6423 __isl_give isl_union_map **must_no_source,
6424 __isl_give isl_union_map **may_no_source);
6426 The arrays are identified by the tuple names of the ranges
6427 of the accesses. The iteration domains by the tuple names
6428 of the domains of the accesses and of the schedule.
6429 The relative order of the iteration domains is given by the
6430 schedule. The relations returned through C<must_no_source>
6431 and C<may_no_source> are subsets of C<sink>.
6432 Any of C<must_dep>, C<may_dep>, C<must_no_source>
6433 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
6434 any of the other arguments is treated as an error.
6436 =head3 Interaction with Dependence Analysis
6438 During the dependence analysis, we frequently need to perform
6439 the following operation. Given a relation between sink iterations
6440 and potential source iterations from a particular source domain,
6441 what is the last potential source iteration corresponding to each
6442 sink iteration. It can sometimes be convenient to adjust
6443 the set of potential source iterations before or after each such operation.
6444 The prototypical example is fuzzy array dataflow analysis,
6445 where we need to analyze if, based on data-dependent constraints,
6446 the sink iteration can ever be executed without one or more of
6447 the corresponding potential source iterations being executed.
6448 If so, we can introduce extra parameters and select an unknown
6449 but fixed source iteration from the potential source iterations.
6450 To be able to perform such manipulations, C<isl> provides the following
6453 #include <isl/flow.h>
6455 typedef __isl_give isl_restriction *(*isl_access_restrict)(
6456 __isl_keep isl_map *source_map,
6457 __isl_keep isl_set *sink, void *source_user,
6459 __isl_give isl_access_info *isl_access_info_set_restrict(
6460 __isl_take isl_access_info *acc,
6461 isl_access_restrict fn, void *user);
6463 The function C<isl_access_info_set_restrict> should be called
6464 before calling C<isl_access_info_compute_flow> and registers a callback function
6465 that will be called any time C<isl> is about to compute the last
6466 potential source. The first argument is the (reverse) proto-dependence,
6467 mapping sink iterations to potential source iterations.
6468 The second argument represents the sink iterations for which
6469 we want to compute the last source iteration.
6470 The third argument is the token corresponding to the source
6471 and the final argument is the token passed to C<isl_access_info_set_restrict>.
6472 The callback is expected to return a restriction on either the input or
6473 the output of the operation computing the last potential source.
6474 If the input needs to be restricted then restrictions are needed
6475 for both the source and the sink iterations. The sink iterations
6476 and the potential source iterations will be intersected with these sets.
6477 If the output needs to be restricted then only a restriction on the source
6478 iterations is required.
6479 If any error occurs, the callback should return C<NULL>.
6480 An C<isl_restriction> object can be created, freed and inspected
6481 using the following functions.
6483 #include <isl/flow.h>
6485 __isl_give isl_restriction *isl_restriction_input(
6486 __isl_take isl_set *source_restr,
6487 __isl_take isl_set *sink_restr);
6488 __isl_give isl_restriction *isl_restriction_output(
6489 __isl_take isl_set *source_restr);
6490 __isl_give isl_restriction *isl_restriction_none(
6491 __isl_take isl_map *source_map);
6492 __isl_give isl_restriction *isl_restriction_empty(
6493 __isl_take isl_map *source_map);
6494 __isl_null isl_restriction *isl_restriction_free(
6495 __isl_take isl_restriction *restr);
6497 C<isl_restriction_none> and C<isl_restriction_empty> are special
6498 cases of C<isl_restriction_input>. C<isl_restriction_none>
6499 is essentially equivalent to
6501 isl_restriction_input(isl_set_universe(
6502 isl_space_range(isl_map_get_space(source_map))),
6504 isl_space_domain(isl_map_get_space(source_map))));
6506 whereas C<isl_restriction_empty> is essentially equivalent to
6508 isl_restriction_input(isl_set_empty(
6509 isl_space_range(isl_map_get_space(source_map))),
6511 isl_space_domain(isl_map_get_space(source_map))));
6515 B<The functionality described in this section is fairly new
6516 and may be subject to change.>
6518 #include <isl/schedule.h>
6519 __isl_give isl_schedule *
6520 isl_schedule_constraints_compute_schedule(
6521 __isl_take isl_schedule_constraints *sc);
6522 __isl_null isl_schedule *isl_schedule_free(
6523 __isl_take isl_schedule *sched);
6525 The function C<isl_schedule_constraints_compute_schedule> can be
6526 used to compute a schedule that satisfies the given schedule constraints.
6527 These schedule constraints include the iteration domain for which
6528 a schedule should be computed and dependences between pairs of
6529 iterations. In particular, these dependences include
6530 I<validity> dependences and I<proximity> dependences.
6531 By default, the algorithm used to construct the schedule is similar
6532 to that of C<Pluto>.
6533 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6535 The generated schedule respects all validity dependences.
6536 That is, all dependence distances over these dependences in the
6537 scheduled space are lexicographically positive.
6538 The default algorithm tries to ensure that the dependence distances
6539 over coincidence constraints are zero and to minimize the
6540 dependence distances over proximity dependences.
6541 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6542 for groups of domains where the dependence distances over validity
6543 dependences have only non-negative values.
6544 When using Feautrier's algorithm, the coincidence and proximity constraints
6545 are only taken into account during the extension to a
6546 full-dimensional schedule.
6548 An C<isl_schedule_constraints> object can be constructed
6549 and manipulated using the following functions.
6551 #include <isl/schedule.h>
6552 __isl_give isl_schedule_constraints *
6553 isl_schedule_constraints_copy(
6554 __isl_keep isl_schedule_constraints *sc);
6555 __isl_give isl_schedule_constraints *
6556 isl_schedule_constraints_on_domain(
6557 __isl_take isl_union_set *domain);
6558 __isl_give isl_schedule_constraints *
6559 isl_schedule_constraints_set_validity(
6560 __isl_take isl_schedule_constraints *sc,
6561 __isl_take isl_union_map *validity);
6562 __isl_give isl_schedule_constraints *
6563 isl_schedule_constraints_set_coincidence(
6564 __isl_take isl_schedule_constraints *sc,
6565 __isl_take isl_union_map *coincidence);
6566 __isl_give isl_schedule_constraints *
6567 isl_schedule_constraints_set_proximity(
6568 __isl_take isl_schedule_constraints *sc,
6569 __isl_take isl_union_map *proximity);
6570 __isl_give isl_schedule_constraints *
6571 isl_schedule_constraints_set_conditional_validity(
6572 __isl_take isl_schedule_constraints *sc,
6573 __isl_take isl_union_map *condition,
6574 __isl_take isl_union_map *validity);
6575 __isl_null isl_schedule_constraints *
6576 isl_schedule_constraints_free(
6577 __isl_take isl_schedule_constraints *sc);
6579 The initial C<isl_schedule_constraints> object created by
6580 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6581 That is, it has an empty set of dependences.
6582 The function C<isl_schedule_constraints_set_validity> replaces the
6583 validity dependences, mapping domain elements I<i> to domain
6584 elements that should be scheduled after I<i>.
6585 The function C<isl_schedule_constraints_set_coincidence> replaces the
6586 coincidence dependences, mapping domain elements I<i> to domain
6587 elements that should be scheduled together with I<I>, if possible.
6588 The function C<isl_schedule_constraints_set_proximity> replaces the
6589 proximity dependences, mapping domain elements I<i> to domain
6590 elements that should be scheduled either before I<I>
6591 or as early as possible after I<i>.
6593 The function C<isl_schedule_constraints_set_conditional_validity>
6594 replaces the conditional validity constraints.
6595 A conditional validity constraint is only imposed when any of the corresponding
6596 conditions is satisfied, i.e., when any of them is non-zero.
6597 That is, the scheduler ensures that within each band if the dependence
6598 distances over the condition constraints are not all zero
6599 then all corresponding conditional validity constraints are respected.
6600 A conditional validity constraint corresponds to a condition
6601 if the two are adjacent, i.e., if the domain of one relation intersect
6602 the range of the other relation.
6603 The typical use case of conditional validity constraints is
6604 to allow order constraints between live ranges to be violated
6605 as long as the live ranges themselves are local to the band.
6606 To allow more fine-grained control over which conditions correspond
6607 to which conditional validity constraints, the domains and ranges
6608 of these relations may include I<tags>. That is, the domains and
6609 ranges of those relation may themselves be wrapped relations
6610 where the iteration domain appears in the domain of those wrapped relations
6611 and the range of the wrapped relations can be arbitrarily chosen
6612 by the user. Conditions and conditional validity constraints are only
6613 considered adjacent to each other if the entire wrapped relation matches.
6614 In particular, a relation with a tag will never be considered adjacent
6615 to a relation without a tag.
6617 The following function computes a schedule directly from
6618 an iteration domain and validity and proximity dependences
6619 and is implemented in terms of the functions described above.
6620 The use of C<isl_union_set_compute_schedule> is discouraged.
6622 #include <isl/schedule.h>
6623 __isl_give isl_schedule *isl_union_set_compute_schedule(
6624 __isl_take isl_union_set *domain,
6625 __isl_take isl_union_map *validity,
6626 __isl_take isl_union_map *proximity);
6628 A mapping from the domains to the scheduled space can be obtained
6629 from an C<isl_schedule> using the following function.
6631 __isl_give isl_union_map *isl_schedule_get_map(
6632 __isl_keep isl_schedule *sched);
6634 A representation of the schedule can be printed using
6636 __isl_give isl_printer *isl_printer_print_schedule(
6637 __isl_take isl_printer *p,
6638 __isl_keep isl_schedule *schedule);
6640 A representation of the schedule as a forest of bands can be obtained
6641 using the following function.
6643 __isl_give isl_band_list *isl_schedule_get_band_forest(
6644 __isl_keep isl_schedule *schedule);
6646 The individual bands can be visited in depth-first post-order
6647 using the following function.
6649 #include <isl/schedule.h>
6650 int isl_schedule_foreach_band(
6651 __isl_keep isl_schedule *sched,
6652 int (*fn)(__isl_keep isl_band *band, void *user),
6655 The list can be manipulated as explained in L<"Lists">.
6656 The bands inside the list can be copied and freed using the following
6659 #include <isl/band.h>
6660 __isl_give isl_band *isl_band_copy(
6661 __isl_keep isl_band *band);
6662 __isl_null isl_band *isl_band_free(
6663 __isl_take isl_band *band);
6665 Each band contains zero or more scheduling dimensions.
6666 These are referred to as the members of the band.
6667 The section of the schedule that corresponds to the band is
6668 referred to as the partial schedule of the band.
6669 For those nodes that participate in a band, the outer scheduling
6670 dimensions form the prefix schedule, while the inner scheduling
6671 dimensions form the suffix schedule.
6672 That is, if we take a cut of the band forest, then the union of
6673 the concatenations of the prefix, partial and suffix schedules of
6674 each band in the cut is equal to the entire schedule (modulo
6675 some possible padding at the end with zero scheduling dimensions).
6676 The properties of a band can be inspected using the following functions.
6678 #include <isl/band.h>
6679 int isl_band_has_children(__isl_keep isl_band *band);
6680 __isl_give isl_band_list *isl_band_get_children(
6681 __isl_keep isl_band *band);
6683 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6684 __isl_keep isl_band *band);
6685 __isl_give isl_union_map *isl_band_get_partial_schedule(
6686 __isl_keep isl_band *band);
6687 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6688 __isl_keep isl_band *band);
6690 int isl_band_n_member(__isl_keep isl_band *band);
6691 int isl_band_member_is_coincident(
6692 __isl_keep isl_band *band, int pos);
6694 int isl_band_list_foreach_band(
6695 __isl_keep isl_band_list *list,
6696 int (*fn)(__isl_keep isl_band *band, void *user),
6699 Note that a scheduling dimension is considered to be ``coincident''
6700 if it satisfies the coincidence constraints within its band.
6701 That is, if the dependence distances of the coincidence
6702 constraints are all zero in that direction (for fixed
6703 iterations of outer bands).
6704 Like C<isl_schedule_foreach_band>,
6705 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6706 in depth-first post-order.
6708 A band can be tiled using the following function.
6710 #include <isl/band.h>
6711 int isl_band_tile(__isl_keep isl_band *band,
6712 __isl_take isl_vec *sizes);
6714 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6716 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6717 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6719 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6721 The C<isl_band_tile> function tiles the band using the given tile sizes
6722 inside its schedule.
6723 A new child band is created to represent the point loops and it is
6724 inserted between the modified band and its children.
6725 The C<tile_scale_tile_loops> option specifies whether the tile
6726 loops iterators should be scaled by the tile sizes.
6727 If the C<tile_shift_point_loops> option is set, then the point loops
6728 are shifted to start at zero.
6730 A band can be split into two nested bands using the following function.
6732 int isl_band_split(__isl_keep isl_band *band, int pos);
6734 The resulting outer band contains the first C<pos> dimensions of C<band>
6735 while the inner band contains the remaining dimensions.
6737 A representation of the band can be printed using
6739 #include <isl/band.h>
6740 __isl_give isl_printer *isl_printer_print_band(
6741 __isl_take isl_printer *p,
6742 __isl_keep isl_band *band);
6746 #include <isl/schedule.h>
6747 int isl_options_set_schedule_max_coefficient(
6748 isl_ctx *ctx, int val);
6749 int isl_options_get_schedule_max_coefficient(
6751 int isl_options_set_schedule_max_constant_term(
6752 isl_ctx *ctx, int val);
6753 int isl_options_get_schedule_max_constant_term(
6755 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6756 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6757 int isl_options_set_schedule_maximize_band_depth(
6758 isl_ctx *ctx, int val);
6759 int isl_options_get_schedule_maximize_band_depth(
6761 int isl_options_set_schedule_outer_coincidence(
6762 isl_ctx *ctx, int val);
6763 int isl_options_get_schedule_outer_coincidence(
6765 int isl_options_set_schedule_split_scaled(
6766 isl_ctx *ctx, int val);
6767 int isl_options_get_schedule_split_scaled(
6769 int isl_options_set_schedule_algorithm(
6770 isl_ctx *ctx, int val);
6771 int isl_options_get_schedule_algorithm(
6773 int isl_options_set_schedule_separate_components(
6774 isl_ctx *ctx, int val);
6775 int isl_options_get_schedule_separate_components(
6780 =item * schedule_max_coefficient
6782 This option enforces that the coefficients for variable and parameter
6783 dimensions in the calculated schedule are not larger than the specified value.
6784 This option can significantly increase the speed of the scheduling calculation
6785 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6786 this option does not introduce bounds on the variable or parameter
6789 =item * schedule_max_constant_term
6791 This option enforces that the constant coefficients in the calculated schedule
6792 are not larger than the maximal constant term. This option can significantly
6793 increase the speed of the scheduling calculation and may also prevent fusing of
6794 unrelated dimensions. A value of -1 means that this option does not introduce
6795 bounds on the constant coefficients.
6797 =item * schedule_fuse
6799 This option controls the level of fusion.
6800 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6801 resulting schedule will be distributed as much as possible.
6802 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6803 try to fuse loops in the resulting schedule.
6805 =item * schedule_maximize_band_depth
6807 If this option is set, we do not split bands at the point
6808 where we detect splitting is necessary. Instead, we
6809 backtrack and split bands as early as possible. This
6810 reduces the number of splits and maximizes the width of
6811 the bands. Wider bands give more possibilities for tiling.
6812 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6813 then bands will be split as early as possible, even if there is no need.
6814 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6816 =item * schedule_outer_coincidence
6818 If this option is set, then we try to construct schedules
6819 where the outermost scheduling dimension in each band
6820 satisfies the coincidence constraints.
6822 =item * schedule_split_scaled
6824 If this option is set, then we try to construct schedules in which the
6825 constant term is split off from the linear part if the linear parts of
6826 the scheduling rows for all nodes in the graphs have a common non-trivial
6828 The constant term is then placed in a separate band and the linear
6831 =item * schedule_algorithm
6833 Selects the scheduling algorithm to be used.
6834 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6835 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6837 =item * schedule_separate_components
6839 If at any point the dependence graph contains any (weakly connected) components,
6840 then these components are scheduled separately.
6841 If this option is not set, then some iterations of the domains
6842 in these components may be scheduled together.
6843 If this option is set, then the components are given consecutive
6848 =head2 AST Generation
6850 This section describes the C<isl> functionality for generating
6851 ASTs that visit all the elements
6852 in a domain in an order specified by a schedule.
6853 In particular, given a C<isl_union_map>, an AST is generated
6854 that visits all the elements in the domain of the C<isl_union_map>
6855 according to the lexicographic order of the corresponding image
6856 element(s). If the range of the C<isl_union_map> consists of
6857 elements in more than one space, then each of these spaces is handled
6858 separately in an arbitrary order.
6859 It should be noted that the image elements only specify the I<order>
6860 in which the corresponding domain elements should be visited.
6861 No direct relation between the image elements and the loop iterators
6862 in the generated AST should be assumed.
6864 Each AST is generated within a build. The initial build
6865 simply specifies the constraints on the parameters (if any)
6866 and can be created, inspected, copied and freed using the following functions.
6868 #include <isl/ast_build.h>
6869 __isl_give isl_ast_build *isl_ast_build_from_context(
6870 __isl_take isl_set *set);
6871 __isl_give isl_ast_build *isl_ast_build_copy(
6872 __isl_keep isl_ast_build *build);
6873 __isl_null isl_ast_build *isl_ast_build_free(
6874 __isl_take isl_ast_build *build);
6876 The C<set> argument is usually a parameter set with zero or more parameters.
6877 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6878 and L</"Fine-grained Control over AST Generation">.
6879 Finally, the AST itself can be constructed using the following
6882 #include <isl/ast_build.h>
6883 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6884 __isl_keep isl_ast_build *build,
6885 __isl_take isl_union_map *schedule);
6887 =head3 Inspecting the AST
6889 The basic properties of an AST node can be obtained as follows.
6891 #include <isl/ast.h>
6892 enum isl_ast_node_type isl_ast_node_get_type(
6893 __isl_keep isl_ast_node *node);
6895 The type of an AST node is one of
6896 C<isl_ast_node_for>,
6898 C<isl_ast_node_block> or
6899 C<isl_ast_node_user>.
6900 An C<isl_ast_node_for> represents a for node.
6901 An C<isl_ast_node_if> represents an if node.
6902 An C<isl_ast_node_block> represents a compound node.
6903 An C<isl_ast_node_user> represents an expression statement.
6904 An expression statement typically corresponds to a domain element, i.e.,
6905 one of the elements that is visited by the AST.
6907 Each type of node has its own additional properties.
6909 #include <isl/ast.h>
6910 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6911 __isl_keep isl_ast_node *node);
6912 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6913 __isl_keep isl_ast_node *node);
6914 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6915 __isl_keep isl_ast_node *node);
6916 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6917 __isl_keep isl_ast_node *node);
6918 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6919 __isl_keep isl_ast_node *node);
6920 int isl_ast_node_for_is_degenerate(
6921 __isl_keep isl_ast_node *node);
6923 An C<isl_ast_for> is considered degenerate if it is known to execute
6926 #include <isl/ast.h>
6927 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6928 __isl_keep isl_ast_node *node);
6929 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6930 __isl_keep isl_ast_node *node);
6931 int isl_ast_node_if_has_else(
6932 __isl_keep isl_ast_node *node);
6933 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6934 __isl_keep isl_ast_node *node);
6936 __isl_give isl_ast_node_list *
6937 isl_ast_node_block_get_children(
6938 __isl_keep isl_ast_node *node);
6940 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6941 __isl_keep isl_ast_node *node);
6943 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6944 the following functions.
6946 #include <isl/ast.h>
6947 enum isl_ast_expr_type isl_ast_expr_get_type(
6948 __isl_keep isl_ast_expr *expr);
6950 The type of an AST expression is one of
6952 C<isl_ast_expr_id> or
6953 C<isl_ast_expr_int>.
6954 An C<isl_ast_expr_op> represents the result of an operation.
6955 An C<isl_ast_expr_id> represents an identifier.
6956 An C<isl_ast_expr_int> represents an integer value.
6958 Each type of expression has its own additional properties.
6960 #include <isl/ast.h>
6961 enum isl_ast_op_type isl_ast_expr_get_op_type(
6962 __isl_keep isl_ast_expr *expr);
6963 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6964 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6965 __isl_keep isl_ast_expr *expr, int pos);
6966 int isl_ast_node_foreach_ast_op_type(
6967 __isl_keep isl_ast_node *node,
6968 int (*fn)(enum isl_ast_op_type type, void *user),
6971 C<isl_ast_expr_get_op_type> returns the type of the operation
6972 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6973 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6975 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6976 C<isl_ast_op_type> that appears in C<node>.
6977 The operation type is one of the following.
6981 =item C<isl_ast_op_and>
6983 Logical I<and> of two arguments.
6984 Both arguments can be evaluated.
6986 =item C<isl_ast_op_and_then>
6988 Logical I<and> of two arguments.
6989 The second argument can only be evaluated if the first evaluates to true.
6991 =item C<isl_ast_op_or>
6993 Logical I<or> of two arguments.
6994 Both arguments can be evaluated.
6996 =item C<isl_ast_op_or_else>
6998 Logical I<or> of two arguments.
6999 The second argument can only be evaluated if the first evaluates to false.
7001 =item C<isl_ast_op_max>
7003 Maximum of two or more arguments.
7005 =item C<isl_ast_op_min>
7007 Minimum of two or more arguments.
7009 =item C<isl_ast_op_minus>
7013 =item C<isl_ast_op_add>
7015 Sum of two arguments.
7017 =item C<isl_ast_op_sub>
7019 Difference of two arguments.
7021 =item C<isl_ast_op_mul>
7023 Product of two arguments.
7025 =item C<isl_ast_op_div>
7027 Exact division. That is, the result is known to be an integer.
7029 =item C<isl_ast_op_fdiv_q>
7031 Result of integer division, rounded towards negative
7034 =item C<isl_ast_op_pdiv_q>
7036 Result of integer division, where dividend is known to be non-negative.
7038 =item C<isl_ast_op_pdiv_r>
7040 Remainder of integer division, where dividend is known to be non-negative.
7042 =item C<isl_ast_op_zdiv_r>
7044 Equal to zero iff the remainder on integer division is zero.
7046 =item C<isl_ast_op_cond>
7048 Conditional operator defined on three arguments.
7049 If the first argument evaluates to true, then the result
7050 is equal to the second argument. Otherwise, the result
7051 is equal to the third argument.
7052 The second and third argument may only be evaluated if
7053 the first argument evaluates to true and false, respectively.
7054 Corresponds to C<a ? b : c> in C.
7056 =item C<isl_ast_op_select>
7058 Conditional operator defined on three arguments.
7059 If the first argument evaluates to true, then the result
7060 is equal to the second argument. Otherwise, the result
7061 is equal to the third argument.
7062 The second and third argument may be evaluated independently
7063 of the value of the first argument.
7064 Corresponds to C<a * b + (1 - a) * c> in C.
7066 =item C<isl_ast_op_eq>
7070 =item C<isl_ast_op_le>
7072 Less than or equal relation.
7074 =item C<isl_ast_op_lt>
7078 =item C<isl_ast_op_ge>
7080 Greater than or equal relation.
7082 =item C<isl_ast_op_gt>
7084 Greater than relation.
7086 =item C<isl_ast_op_call>
7089 The number of arguments of the C<isl_ast_expr> is one more than
7090 the number of arguments in the function call, the first argument
7091 representing the function being called.
7093 =item C<isl_ast_op_access>
7096 The number of arguments of the C<isl_ast_expr> is one more than
7097 the number of index expressions in the array access, the first argument
7098 representing the array being accessed.
7100 =item C<isl_ast_op_member>
7103 This operation has two arguments, a structure and the name of
7104 the member of the structure being accessed.
7108 #include <isl/ast.h>
7109 __isl_give isl_id *isl_ast_expr_get_id(
7110 __isl_keep isl_ast_expr *expr);
7112 Return the identifier represented by the AST expression.
7114 #include <isl/ast.h>
7115 __isl_give isl_val *isl_ast_expr_get_val(
7116 __isl_keep isl_ast_expr *expr);
7118 Return the integer represented by the AST expression.
7120 =head3 Properties of ASTs
7122 #include <isl/ast.h>
7123 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7124 __isl_keep isl_ast_expr *expr2);
7126 Check if two C<isl_ast_expr>s are equal to each other.
7128 =head3 Manipulating and printing the AST
7130 AST nodes can be copied and freed using the following functions.
7132 #include <isl/ast.h>
7133 __isl_give isl_ast_node *isl_ast_node_copy(
7134 __isl_keep isl_ast_node *node);
7135 __isl_null isl_ast_node *isl_ast_node_free(
7136 __isl_take isl_ast_node *node);
7138 AST expressions can be copied and freed using the following functions.
7140 #include <isl/ast.h>
7141 __isl_give isl_ast_expr *isl_ast_expr_copy(
7142 __isl_keep isl_ast_expr *expr);
7143 __isl_null isl_ast_expr *isl_ast_expr_free(
7144 __isl_take isl_ast_expr *expr);
7146 New AST expressions can be created either directly or within
7147 the context of an C<isl_ast_build>.
7149 #include <isl/ast.h>
7150 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7151 __isl_take isl_val *v);
7152 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7153 __isl_take isl_id *id);
7154 __isl_give isl_ast_expr *isl_ast_expr_neg(
7155 __isl_take isl_ast_expr *expr);
7156 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7157 __isl_take isl_ast_expr *expr);
7158 __isl_give isl_ast_expr *isl_ast_expr_add(
7159 __isl_take isl_ast_expr *expr1,
7160 __isl_take isl_ast_expr *expr2);
7161 __isl_give isl_ast_expr *isl_ast_expr_sub(
7162 __isl_take isl_ast_expr *expr1,
7163 __isl_take isl_ast_expr *expr2);
7164 __isl_give isl_ast_expr *isl_ast_expr_mul(
7165 __isl_take isl_ast_expr *expr1,
7166 __isl_take isl_ast_expr *expr2);
7167 __isl_give isl_ast_expr *isl_ast_expr_div(
7168 __isl_take isl_ast_expr *expr1,
7169 __isl_take isl_ast_expr *expr2);
7170 __isl_give isl_ast_expr *isl_ast_expr_and(
7171 __isl_take isl_ast_expr *expr1,
7172 __isl_take isl_ast_expr *expr2)
7173 __isl_give isl_ast_expr *isl_ast_expr_or(
7174 __isl_take isl_ast_expr *expr1,
7175 __isl_take isl_ast_expr *expr2)
7176 __isl_give isl_ast_expr *isl_ast_expr_eq(
7177 __isl_take isl_ast_expr *expr1,
7178 __isl_take isl_ast_expr *expr2);
7179 __isl_give isl_ast_expr *isl_ast_expr_le(
7180 __isl_take isl_ast_expr *expr1,
7181 __isl_take isl_ast_expr *expr2);
7182 __isl_give isl_ast_expr *isl_ast_expr_lt(
7183 __isl_take isl_ast_expr *expr1,
7184 __isl_take isl_ast_expr *expr2);
7185 __isl_give isl_ast_expr *isl_ast_expr_ge(
7186 __isl_take isl_ast_expr *expr1,
7187 __isl_take isl_ast_expr *expr2);
7188 __isl_give isl_ast_expr *isl_ast_expr_gt(
7189 __isl_take isl_ast_expr *expr1,
7190 __isl_take isl_ast_expr *expr2);
7191 __isl_give isl_ast_expr *isl_ast_expr_access(
7192 __isl_take isl_ast_expr *array,
7193 __isl_take isl_ast_expr_list *indices);
7195 The function C<isl_ast_expr_address_of> can be applied to an
7196 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
7197 to represent the address of the C<isl_ast_expr_access>.
7199 #include <isl/ast_build.h>
7200 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
7201 __isl_keep isl_ast_build *build,
7202 __isl_take isl_pw_aff *pa);
7203 __isl_give isl_ast_expr *
7204 isl_ast_build_access_from_pw_multi_aff(
7205 __isl_keep isl_ast_build *build,
7206 __isl_take isl_pw_multi_aff *pma);
7207 __isl_give isl_ast_expr *
7208 isl_ast_build_access_from_multi_pw_aff(
7209 __isl_keep isl_ast_build *build,
7210 __isl_take isl_multi_pw_aff *mpa);
7211 __isl_give isl_ast_expr *
7212 isl_ast_build_call_from_pw_multi_aff(
7213 __isl_keep isl_ast_build *build,
7214 __isl_take isl_pw_multi_aff *pma);
7215 __isl_give isl_ast_expr *
7216 isl_ast_build_call_from_multi_pw_aff(
7217 __isl_keep isl_ast_build *build,
7218 __isl_take isl_multi_pw_aff *mpa);
7220 The domains of C<pa>, C<mpa> and C<pma> should correspond
7221 to the schedule space of C<build>.
7222 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
7223 the function being called.
7224 If the accessed space is a nested relation, then it is taken
7225 to represent an access of the member specified by the range
7226 of this nested relation of the structure specified by the domain
7227 of the nested relation.
7229 The following functions can be used to modify an C<isl_ast_expr>.
7231 #include <isl/ast.h>
7232 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
7233 __isl_take isl_ast_expr *expr, int pos,
7234 __isl_take isl_ast_expr *arg);
7236 Replace the argument of C<expr> at position C<pos> by C<arg>.
7238 #include <isl/ast.h>
7239 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
7240 __isl_take isl_ast_expr *expr,
7241 __isl_take isl_id_to_ast_expr *id2expr);
7243 The function C<isl_ast_expr_substitute_ids> replaces the
7244 subexpressions of C<expr> of type C<isl_ast_expr_id>
7245 by the corresponding expression in C<id2expr>, if there is any.
7248 User specified data can be attached to an C<isl_ast_node> and obtained
7249 from the same C<isl_ast_node> using the following functions.
7251 #include <isl/ast.h>
7252 __isl_give isl_ast_node *isl_ast_node_set_annotation(
7253 __isl_take isl_ast_node *node,
7254 __isl_take isl_id *annotation);
7255 __isl_give isl_id *isl_ast_node_get_annotation(
7256 __isl_keep isl_ast_node *node);
7258 Basic printing can be performed using the following functions.
7260 #include <isl/ast.h>
7261 __isl_give isl_printer *isl_printer_print_ast_expr(
7262 __isl_take isl_printer *p,
7263 __isl_keep isl_ast_expr *expr);
7264 __isl_give isl_printer *isl_printer_print_ast_node(
7265 __isl_take isl_printer *p,
7266 __isl_keep isl_ast_node *node);
7267 __isl_give char *isl_ast_expr_to_str(
7268 __isl_keep isl_ast_expr *expr);
7270 More advanced printing can be performed using the following functions.
7272 #include <isl/ast.h>
7273 __isl_give isl_printer *isl_ast_op_type_print_macro(
7274 enum isl_ast_op_type type,
7275 __isl_take isl_printer *p);
7276 __isl_give isl_printer *isl_ast_node_print_macros(
7277 __isl_keep isl_ast_node *node,
7278 __isl_take isl_printer *p);
7279 __isl_give isl_printer *isl_ast_node_print(
7280 __isl_keep isl_ast_node *node,
7281 __isl_take isl_printer *p,
7282 __isl_take isl_ast_print_options *options);
7283 __isl_give isl_printer *isl_ast_node_for_print(
7284 __isl_keep isl_ast_node *node,
7285 __isl_take isl_printer *p,
7286 __isl_take isl_ast_print_options *options);
7287 __isl_give isl_printer *isl_ast_node_if_print(
7288 __isl_keep isl_ast_node *node,
7289 __isl_take isl_printer *p,
7290 __isl_take isl_ast_print_options *options);
7292 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
7293 C<isl> may print out an AST that makes use of macros such
7294 as C<floord>, C<min> and C<max>.
7295 C<isl_ast_op_type_print_macro> prints out the macro
7296 corresponding to a specific C<isl_ast_op_type>.
7297 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
7298 for expressions where these macros would be used and prints
7299 out the required macro definitions.
7300 Essentially, C<isl_ast_node_print_macros> calls
7301 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
7302 as function argument.
7303 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
7304 C<isl_ast_node_if_print> print an C<isl_ast_node>
7305 in C<ISL_FORMAT_C>, but allow for some extra control
7306 through an C<isl_ast_print_options> object.
7307 This object can be created using the following functions.
7309 #include <isl/ast.h>
7310 __isl_give isl_ast_print_options *
7311 isl_ast_print_options_alloc(isl_ctx *ctx);
7312 __isl_give isl_ast_print_options *
7313 isl_ast_print_options_copy(
7314 __isl_keep isl_ast_print_options *options);
7315 __isl_null isl_ast_print_options *
7316 isl_ast_print_options_free(
7317 __isl_take isl_ast_print_options *options);
7319 __isl_give isl_ast_print_options *
7320 isl_ast_print_options_set_print_user(
7321 __isl_take isl_ast_print_options *options,
7322 __isl_give isl_printer *(*print_user)(
7323 __isl_take isl_printer *p,
7324 __isl_take isl_ast_print_options *options,
7325 __isl_keep isl_ast_node *node, void *user),
7327 __isl_give isl_ast_print_options *
7328 isl_ast_print_options_set_print_for(
7329 __isl_take isl_ast_print_options *options,
7330 __isl_give isl_printer *(*print_for)(
7331 __isl_take isl_printer *p,
7332 __isl_take isl_ast_print_options *options,
7333 __isl_keep isl_ast_node *node, void *user),
7336 The callback set by C<isl_ast_print_options_set_print_user>
7337 is called whenever a node of type C<isl_ast_node_user> needs to
7339 The callback set by C<isl_ast_print_options_set_print_for>
7340 is called whenever a node of type C<isl_ast_node_for> needs to
7342 Note that C<isl_ast_node_for_print> will I<not> call the
7343 callback set by C<isl_ast_print_options_set_print_for> on the node
7344 on which C<isl_ast_node_for_print> is called, but only on nested
7345 nodes of type C<isl_ast_node_for>. It is therefore safe to
7346 call C<isl_ast_node_for_print> from within the callback set by
7347 C<isl_ast_print_options_set_print_for>.
7349 The following option determines the type to be used for iterators
7350 while printing the AST.
7352 int isl_options_set_ast_iterator_type(
7353 isl_ctx *ctx, const char *val);
7354 const char *isl_options_get_ast_iterator_type(
7357 The AST printer only prints body nodes as blocks if these
7358 blocks cannot be safely omitted.
7359 For example, a C<for> node with one body node will not be
7360 surrounded with braces in C<ISL_FORMAT_C>.
7361 A block will always be printed by setting the following option.
7363 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
7365 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
7369 #include <isl/ast_build.h>
7370 int isl_options_set_ast_build_atomic_upper_bound(
7371 isl_ctx *ctx, int val);
7372 int isl_options_get_ast_build_atomic_upper_bound(
7374 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
7376 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
7377 int isl_options_set_ast_build_exploit_nested_bounds(
7378 isl_ctx *ctx, int val);
7379 int isl_options_get_ast_build_exploit_nested_bounds(
7381 int isl_options_set_ast_build_group_coscheduled(
7382 isl_ctx *ctx, int val);
7383 int isl_options_get_ast_build_group_coscheduled(
7385 int isl_options_set_ast_build_scale_strides(
7386 isl_ctx *ctx, int val);
7387 int isl_options_get_ast_build_scale_strides(
7389 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
7391 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
7392 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
7394 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
7398 =item * ast_build_atomic_upper_bound
7400 Generate loop upper bounds that consist of the current loop iterator,
7401 an operator and an expression not involving the iterator.
7402 If this option is not set, then the current loop iterator may appear
7403 several times in the upper bound.
7404 For example, when this option is turned off, AST generation
7407 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
7411 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
7414 When the option is turned on, the following AST is generated
7416 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
7419 =item * ast_build_prefer_pdiv
7421 If this option is turned off, then the AST generation will
7422 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
7423 operators, but no C<isl_ast_op_pdiv_q> or
7424 C<isl_ast_op_pdiv_r> operators.
7425 If this options is turned on, then C<isl> will try to convert
7426 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
7427 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
7429 =item * ast_build_exploit_nested_bounds
7431 Simplify conditions based on bounds of nested for loops.
7432 In particular, remove conditions that are implied by the fact
7433 that one or more nested loops have at least one iteration,
7434 meaning that the upper bound is at least as large as the lower bound.
7435 For example, when this option is turned off, AST generation
7438 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
7444 for (int c0 = 0; c0 <= N; c0 += 1)
7445 for (int c1 = 0; c1 <= M; c1 += 1)
7448 When the option is turned on, the following AST is generated
7450 for (int c0 = 0; c0 <= N; c0 += 1)
7451 for (int c1 = 0; c1 <= M; c1 += 1)
7454 =item * ast_build_group_coscheduled
7456 If two domain elements are assigned the same schedule point, then
7457 they may be executed in any order and they may even appear in different
7458 loops. If this options is set, then the AST generator will make
7459 sure that coscheduled domain elements do not appear in separate parts
7460 of the AST. This is useful in case of nested AST generation
7461 if the outer AST generation is given only part of a schedule
7462 and the inner AST generation should handle the domains that are
7463 coscheduled by this initial part of the schedule together.
7464 For example if an AST is generated for a schedule
7466 { A[i] -> [0]; B[i] -> [0] }
7468 then the C<isl_ast_build_set_create_leaf> callback described
7469 below may get called twice, once for each domain.
7470 Setting this option ensures that the callback is only called once
7471 on both domains together.
7473 =item * ast_build_separation_bounds
7475 This option specifies which bounds to use during separation.
7476 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
7477 then all (possibly implicit) bounds on the current dimension will
7478 be used during separation.
7479 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
7480 then only those bounds that are explicitly available will
7481 be used during separation.
7483 =item * ast_build_scale_strides
7485 This option specifies whether the AST generator is allowed
7486 to scale down iterators of strided loops.
7488 =item * ast_build_allow_else
7490 This option specifies whether the AST generator is allowed
7491 to construct if statements with else branches.
7493 =item * ast_build_allow_or
7495 This option specifies whether the AST generator is allowed
7496 to construct if conditions with disjunctions.
7500 =head3 Fine-grained Control over AST Generation
7502 Besides specifying the constraints on the parameters,
7503 an C<isl_ast_build> object can be used to control
7504 various aspects of the AST generation process.
7505 The most prominent way of control is through ``options'',
7506 which can be set using the following function.
7508 #include <isl/ast_build.h>
7509 __isl_give isl_ast_build *
7510 isl_ast_build_set_options(
7511 __isl_take isl_ast_build *control,
7512 __isl_take isl_union_map *options);
7514 The options are encoded in an C<isl_union_map>.
7515 The domain of this union relation refers to the schedule domain,
7516 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
7517 In the case of nested AST generation (see L</"Nested AST Generation">),
7518 the domain of C<options> should refer to the extra piece of the schedule.
7519 That is, it should be equal to the range of the wrapped relation in the
7520 range of the schedule.
7521 The range of the options can consist of elements in one or more spaces,
7522 the names of which determine the effect of the option.
7523 The values of the range typically also refer to the schedule dimension
7524 to which the option applies. In case of nested AST generation
7525 (see L</"Nested AST Generation">), these values refer to the position
7526 of the schedule dimension within the innermost AST generation.
7527 The constraints on the domain elements of
7528 the option should only refer to this dimension and earlier dimensions.
7529 We consider the following spaces.
7533 =item C<separation_class>
7535 This space is a wrapped relation between two one dimensional spaces.
7536 The input space represents the schedule dimension to which the option
7537 applies and the output space represents the separation class.
7538 While constructing a loop corresponding to the specified schedule
7539 dimension(s), the AST generator will try to generate separate loops
7540 for domain elements that are assigned different classes.
7541 If only some of the elements are assigned a class, then those elements
7542 that are not assigned any class will be treated as belonging to a class
7543 that is separate from the explicitly assigned classes.
7544 The typical use case for this option is to separate full tiles from
7546 The other options, described below, are applied after the separation
7549 As an example, consider the separation into full and partial tiles
7550 of a tiling of a triangular domain.
7551 Take, for example, the domain
7553 { A[i,j] : 0 <= i,j and i + j <= 100 }
7555 and a tiling into tiles of 10 by 10. The input to the AST generator
7556 is then the schedule
7558 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7561 Without any options, the following AST is generated
7563 for (int c0 = 0; c0 <= 10; c0 += 1)
7564 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7565 for (int c2 = 10 * c0;
7566 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7568 for (int c3 = 10 * c1;
7569 c3 <= min(10 * c1 + 9, -c2 + 100);
7573 Separation into full and partial tiles can be obtained by assigning
7574 a class, say C<0>, to the full tiles. The full tiles are represented by those
7575 values of the first and second schedule dimensions for which there are
7576 values of the third and fourth dimensions to cover an entire tile.
7577 That is, we need to specify the following option
7579 { [a,b,c,d] -> separation_class[[0]->[0]] :
7580 exists b': 0 <= 10a,10b' and
7581 10a+9+10b'+9 <= 100;
7582 [a,b,c,d] -> separation_class[[1]->[0]] :
7583 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7587 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7588 a >= 0 and b >= 0 and b <= 8 - a;
7589 [a, b, c, d] -> separation_class[[0] -> [0]] :
7592 With this option, the generated AST is as follows
7595 for (int c0 = 0; c0 <= 8; c0 += 1) {
7596 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7597 for (int c2 = 10 * c0;
7598 c2 <= 10 * c0 + 9; c2 += 1)
7599 for (int c3 = 10 * c1;
7600 c3 <= 10 * c1 + 9; c3 += 1)
7602 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7603 for (int c2 = 10 * c0;
7604 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7606 for (int c3 = 10 * c1;
7607 c3 <= min(-c2 + 100, 10 * c1 + 9);
7611 for (int c0 = 9; c0 <= 10; c0 += 1)
7612 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7613 for (int c2 = 10 * c0;
7614 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7616 for (int c3 = 10 * c1;
7617 c3 <= min(10 * c1 + 9, -c2 + 100);
7624 This is a single-dimensional space representing the schedule dimension(s)
7625 to which ``separation'' should be applied. Separation tries to split
7626 a loop into several pieces if this can avoid the generation of guards
7628 See also the C<atomic> option.
7632 This is a single-dimensional space representing the schedule dimension(s)
7633 for which the domains should be considered ``atomic''. That is, the
7634 AST generator will make sure that any given domain space will only appear
7635 in a single loop at the specified level.
7637 Consider the following schedule
7639 { a[i] -> [i] : 0 <= i < 10;
7640 b[i] -> [i+1] : 0 <= i < 10 }
7642 If the following option is specified
7644 { [i] -> separate[x] }
7646 then the following AST will be generated
7650 for (int c0 = 1; c0 <= 9; c0 += 1) {
7657 If, on the other hand, the following option is specified
7659 { [i] -> atomic[x] }
7661 then the following AST will be generated
7663 for (int c0 = 0; c0 <= 10; c0 += 1) {
7670 If neither C<atomic> nor C<separate> is specified, then the AST generator
7671 may produce either of these two results or some intermediate form.
7675 This is a single-dimensional space representing the schedule dimension(s)
7676 that should be I<completely> unrolled.
7677 To obtain a partial unrolling, the user should apply an additional
7678 strip-mining to the schedule and fully unroll the inner loop.
7682 Additional control is available through the following functions.
7684 #include <isl/ast_build.h>
7685 __isl_give isl_ast_build *
7686 isl_ast_build_set_iterators(
7687 __isl_take isl_ast_build *control,
7688 __isl_take isl_id_list *iterators);
7690 The function C<isl_ast_build_set_iterators> allows the user to
7691 specify a list of iterator C<isl_id>s to be used as iterators.
7692 If the input schedule is injective, then
7693 the number of elements in this list should be as large as the dimension
7694 of the schedule space, but no direct correspondence should be assumed
7695 between dimensions and elements.
7696 If the input schedule is not injective, then an additional number
7697 of C<isl_id>s equal to the largest dimension of the input domains
7699 If the number of provided C<isl_id>s is insufficient, then additional
7700 names are automatically generated.
7702 #include <isl/ast_build.h>
7703 __isl_give isl_ast_build *
7704 isl_ast_build_set_create_leaf(
7705 __isl_take isl_ast_build *control,
7706 __isl_give isl_ast_node *(*fn)(
7707 __isl_take isl_ast_build *build,
7708 void *user), void *user);
7711 C<isl_ast_build_set_create_leaf> function allows for the
7712 specification of a callback that should be called whenever the AST
7713 generator arrives at an element of the schedule domain.
7714 The callback should return an AST node that should be inserted
7715 at the corresponding position of the AST. The default action (when
7716 the callback is not set) is to continue generating parts of the AST to scan
7717 all the domain elements associated to the schedule domain element
7718 and to insert user nodes, ``calling'' the domain element, for each of them.
7719 The C<build> argument contains the current state of the C<isl_ast_build>.
7720 To ease nested AST generation (see L</"Nested AST Generation">),
7721 all control information that is
7722 specific to the current AST generation such as the options and
7723 the callbacks has been removed from this C<isl_ast_build>.
7724 The callback would typically return the result of a nested
7726 user defined node created using the following function.
7728 #include <isl/ast.h>
7729 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7730 __isl_take isl_ast_expr *expr);
7732 #include <isl/ast_build.h>
7733 __isl_give isl_ast_build *
7734 isl_ast_build_set_at_each_domain(
7735 __isl_take isl_ast_build *build,
7736 __isl_give isl_ast_node *(*fn)(
7737 __isl_take isl_ast_node *node,
7738 __isl_keep isl_ast_build *build,
7739 void *user), void *user);
7740 __isl_give isl_ast_build *
7741 isl_ast_build_set_before_each_for(
7742 __isl_take isl_ast_build *build,
7743 __isl_give isl_id *(*fn)(
7744 __isl_keep isl_ast_build *build,
7745 void *user), void *user);
7746 __isl_give isl_ast_build *
7747 isl_ast_build_set_after_each_for(
7748 __isl_take isl_ast_build *build,
7749 __isl_give isl_ast_node *(*fn)(
7750 __isl_take isl_ast_node *node,
7751 __isl_keep isl_ast_build *build,
7752 void *user), void *user);
7754 The callback set by C<isl_ast_build_set_at_each_domain> will
7755 be called for each domain AST node.
7756 The callbacks set by C<isl_ast_build_set_before_each_for>
7757 and C<isl_ast_build_set_after_each_for> will be called
7758 for each for AST node. The first will be called in depth-first
7759 pre-order, while the second will be called in depth-first post-order.
7760 Since C<isl_ast_build_set_before_each_for> is called before the for
7761 node is actually constructed, it is only passed an C<isl_ast_build>.
7762 The returned C<isl_id> will be added as an annotation (using
7763 C<isl_ast_node_set_annotation>) to the constructed for node.
7764 In particular, if the user has also specified an C<after_each_for>
7765 callback, then the annotation can be retrieved from the node passed to
7766 that callback using C<isl_ast_node_get_annotation>.
7767 All callbacks should C<NULL> on failure.
7768 The given C<isl_ast_build> can be used to create new
7769 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7770 or C<isl_ast_build_call_from_pw_multi_aff>.
7772 =head3 Nested AST Generation
7774 C<isl> allows the user to create an AST within the context
7775 of another AST. These nested ASTs are created using the
7776 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7777 outer AST. The C<build> argument should be an C<isl_ast_build>
7778 passed to a callback set by
7779 C<isl_ast_build_set_create_leaf>.
7780 The space of the range of the C<schedule> argument should refer
7781 to this build. In particular, the space should be a wrapped
7782 relation and the domain of this wrapped relation should be the
7783 same as that of the range of the schedule returned by
7784 C<isl_ast_build_get_schedule> below.
7785 In practice, the new schedule is typically
7786 created by calling C<isl_union_map_range_product> on the old schedule
7787 and some extra piece of the schedule.
7788 The space of the schedule domain is also available from
7789 the C<isl_ast_build>.
7791 #include <isl/ast_build.h>
7792 __isl_give isl_union_map *isl_ast_build_get_schedule(
7793 __isl_keep isl_ast_build *build);
7794 __isl_give isl_space *isl_ast_build_get_schedule_space(
7795 __isl_keep isl_ast_build *build);
7796 __isl_give isl_ast_build *isl_ast_build_restrict(
7797 __isl_take isl_ast_build *build,
7798 __isl_take isl_set *set);
7800 The C<isl_ast_build_get_schedule> function returns a (partial)
7801 schedule for the domains elements for which part of the AST still needs to
7802 be generated in the current build.
7803 In particular, the domain elements are mapped to those iterations of the loops
7804 enclosing the current point of the AST generation inside which
7805 the domain elements are executed.
7806 No direct correspondence between
7807 the input schedule and this schedule should be assumed.
7808 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7809 to create a set for C<isl_ast_build_restrict> to intersect
7810 with the current build. In particular, the set passed to
7811 C<isl_ast_build_restrict> can have additional parameters.
7812 The ids of the set dimensions in the space returned by
7813 C<isl_ast_build_get_schedule_space> correspond to the
7814 iterators of the already generated loops.
7815 The user should not rely on the ids of the output dimensions
7816 of the relations in the union relation returned by
7817 C<isl_ast_build_get_schedule> having any particular value.
7821 Although C<isl> is mainly meant to be used as a library,
7822 it also contains some basic applications that use some
7823 of the functionality of C<isl>.
7824 The input may be specified in either the L<isl format>
7825 or the L<PolyLib format>.
7827 =head2 C<isl_polyhedron_sample>
7829 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7830 an integer element of the polyhedron, if there is any.
7831 The first column in the output is the denominator and is always
7832 equal to 1. If the polyhedron contains no integer points,
7833 then a vector of length zero is printed.
7837 C<isl_pip> takes the same input as the C<example> program
7838 from the C<piplib> distribution, i.e., a set of constraints
7839 on the parameters, a line containing only -1 and finally a set
7840 of constraints on a parametric polyhedron.
7841 The coefficients of the parameters appear in the last columns
7842 (but before the final constant column).
7843 The output is the lexicographic minimum of the parametric polyhedron.
7844 As C<isl> currently does not have its own output format, the output
7845 is just a dump of the internal state.
7847 =head2 C<isl_polyhedron_minimize>
7849 C<isl_polyhedron_minimize> computes the minimum of some linear
7850 or affine objective function over the integer points in a polyhedron.
7851 If an affine objective function
7852 is given, then the constant should appear in the last column.
7854 =head2 C<isl_polytope_scan>
7856 Given a polytope, C<isl_polytope_scan> prints
7857 all integer points in the polytope.
7859 =head2 C<isl_codegen>
7861 Given a schedule, a context set and an options relation,
7862 C<isl_codegen> prints out an AST that scans the domain elements
7863 of the schedule in the order of their image(s) taking into account
7864 the constraints in the context set.