3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * Objects of type C<isl_union_pw_multi_aff> can no longer contain
216 two or more C<isl_pw_multi_aff> objects with the same domain space.
218 =item * The function C<isl_union_pw_multi_aff_add> now consistently
219 computes the sum on the shared definition domain.
220 The function C<isl_union_pw_multi_aff_union_add> has been added
221 to compute the sum on the union of definition domains.
222 The original behavior of C<isl_union_pw_multi_aff_add> was
223 confused and is no longer available.
229 C<isl> is released under the MIT license.
233 Permission is hereby granted, free of charge, to any person obtaining a copy of
234 this software and associated documentation files (the "Software"), to deal in
235 the Software without restriction, including without limitation the rights to
236 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
237 of the Software, and to permit persons to whom the Software is furnished to do
238 so, subject to the following conditions:
240 The above copyright notice and this permission notice shall be included in all
241 copies or substantial portions of the Software.
243 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
244 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
245 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
246 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
247 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
248 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
253 Note that by default C<isl> requires C<GMP>, which is released
254 under the GNU Lesser General Public License (LGPL). This means
255 that code linked against C<isl> is also linked against LGPL code.
257 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
258 library for exact integer arithmetic released under the MIT license.
262 The source of C<isl> can be obtained either as a tarball
263 or from the git repository. Both are available from
264 L<http://freshmeat.net/projects/isl/>.
265 The installation process depends on how you obtained
268 =head2 Installation from the git repository
272 =item 1 Clone or update the repository
274 The first time the source is obtained, you need to clone
277 git clone git://repo.or.cz/isl.git
279 To obtain updates, you need to pull in the latest changes
283 =item 2 Optionally get C<imath> submodule
285 To build C<isl> with C<imath>, you need to obtain the C<imath>
286 submodule by running in the git source tree of C<isl>
291 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
293 =item 2 Generate C<configure>
299 After performing the above steps, continue
300 with the L<Common installation instructions>.
302 =head2 Common installation instructions
306 =item 1 Obtain C<GMP>
308 By default, building C<isl> requires C<GMP>, including its headers files.
309 Your distribution may not provide these header files by default
310 and you may need to install a package called C<gmp-devel> or something
311 similar. Alternatively, C<GMP> can be built from
312 source, available from L<http://gmplib.org/>.
313 C<GMP> is not needed if you build C<isl> with C<imath>.
317 C<isl> uses the standard C<autoconf> C<configure> script.
322 optionally followed by some configure options.
323 A complete list of options can be obtained by running
327 Below we discuss some of the more common options.
333 Installation prefix for C<isl>
335 =item C<--with-int=[gmp|imath]>
337 Select the integer library to be used by C<isl>, the default is C<gmp>.
338 Note that C<isl> may run significantly slower if you use C<imath>.
340 =item C<--with-gmp-prefix>
342 Installation prefix for C<GMP> (architecture-independent files).
344 =item C<--with-gmp-exec-prefix>
346 Installation prefix for C<GMP> (architecture-dependent files).
354 =item 4 Install (optional)
360 =head1 Integer Set Library
362 =head2 Memory Management
364 Since a high-level operation on isl objects usually involves
365 several substeps and since the user is usually not interested in
366 the intermediate results, most functions that return a new object
367 will also release all the objects passed as arguments.
368 If the user still wants to use one or more of these arguments
369 after the function call, she should pass along a copy of the
370 object rather than the object itself.
371 The user is then responsible for making sure that the original
372 object gets used somewhere else or is explicitly freed.
374 The arguments and return values of all documented functions are
375 annotated to make clear which arguments are released and which
376 arguments are preserved. In particular, the following annotations
383 C<__isl_give> means that a new object is returned.
384 The user should make sure that the returned pointer is
385 used exactly once as a value for an C<__isl_take> argument.
386 In between, it can be used as a value for as many
387 C<__isl_keep> arguments as the user likes.
388 There is one exception, and that is the case where the
389 pointer returned is C<NULL>. Is this case, the user
390 is free to use it as an C<__isl_take> argument or not.
391 When applied to a C<char *>, the returned pointer needs to be
396 C<__isl_null> means that a C<NULL> value is returned.
400 C<__isl_take> means that the object the argument points to
401 is taken over by the function and may no longer be used
402 by the user as an argument to any other function.
403 The pointer value must be one returned by a function
404 returning an C<__isl_give> pointer.
405 If the user passes in a C<NULL> value, then this will
406 be treated as an error in the sense that the function will
407 not perform its usual operation. However, it will still
408 make sure that all the other C<__isl_take> arguments
413 C<__isl_keep> means that the function will only use the object
414 temporarily. After the function has finished, the user
415 can still use it as an argument to other functions.
416 A C<NULL> value will be treated in the same way as
417 a C<NULL> value for an C<__isl_take> argument.
418 This annotation may also be used on return values of
419 type C<const char *>, in which case the returned pointer should
420 not be freed by the user and is only valid until the object
421 from which it was derived is updated or freed.
425 =head2 Initialization
427 All manipulations of integer sets and relations occur within
428 the context of an C<isl_ctx>.
429 A given C<isl_ctx> can only be used within a single thread.
430 All arguments of a function are required to have been allocated
431 within the same context.
432 There are currently no functions available for moving an object
433 from one C<isl_ctx> to another C<isl_ctx>. This means that
434 there is currently no way of safely moving an object from one
435 thread to another, unless the whole C<isl_ctx> is moved.
437 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
438 freed using C<isl_ctx_free>.
439 All objects allocated within an C<isl_ctx> should be freed
440 before the C<isl_ctx> itself is freed.
442 isl_ctx *isl_ctx_alloc();
443 void isl_ctx_free(isl_ctx *ctx);
445 The user can impose a bound on the number of low-level I<operations>
446 that can be performed by an C<isl_ctx>. This bound can be set and
447 retrieved using the following functions. A bound of zero means that
448 no bound is imposed. The number of operations performed can be
449 reset using C<isl_ctx_reset_operations>. Note that the number
450 of low-level operations needed to perform a high-level computation
451 may differ significantly across different versions
452 of C<isl>, but it should be the same across different platforms
453 for the same version of C<isl>.
455 Warning: This feature is experimental. C<isl> has good support to abort and
456 bail out during the computation, but this feature may exercise error code paths
457 that are normally not used that much. Consequently, it is not unlikely that
458 hidden bugs will be exposed.
460 void isl_ctx_set_max_operations(isl_ctx *ctx,
461 unsigned long max_operations);
462 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
463 void isl_ctx_reset_operations(isl_ctx *ctx);
465 In order to be able to create an object in the same context
466 as another object, most object types (described later in
467 this document) provide a function to obtain the context
468 in which the object was created.
471 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
472 isl_ctx *isl_multi_val_get_ctx(
473 __isl_keep isl_multi_val *mv);
476 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
478 #include <isl/local_space.h>
479 isl_ctx *isl_local_space_get_ctx(
480 __isl_keep isl_local_space *ls);
483 isl_ctx *isl_set_list_get_ctx(
484 __isl_keep isl_set_list *list);
487 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
488 isl_ctx *isl_multi_aff_get_ctx(
489 __isl_keep isl_multi_aff *maff);
490 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
491 isl_ctx *isl_pw_multi_aff_get_ctx(
492 __isl_keep isl_pw_multi_aff *pma);
493 isl_ctx *isl_multi_pw_aff_get_ctx(
494 __isl_keep isl_multi_pw_aff *mpa);
495 isl_ctx *isl_union_pw_aff_get_ctx(
496 __isl_keep isl_union_pw_aff *upa);
497 isl_ctx *isl_union_pw_multi_aff_get_ctx(
498 __isl_keep isl_union_pw_multi_aff *upma);
500 #include <isl/id_to_ast_expr.h>
501 isl_ctx *isl_id_to_ast_expr_get_ctx(
502 __isl_keep id_to_ast_expr *id2expr);
504 #include <isl/point.h>
505 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
508 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
511 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
513 #include <isl/vertices.h>
514 isl_ctx *isl_vertices_get_ctx(
515 __isl_keep isl_vertices *vertices);
516 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
517 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
519 #include <isl/flow.h>
520 isl_ctx *isl_restriction_get_ctx(
521 __isl_keep isl_restriction *restr);
523 #include <isl/schedule.h>
524 isl_ctx *isl_schedule_constraints_get_ctx(
525 __isl_keep isl_schedule_constraints *sc);
527 #include <isl/band.h>
528 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
530 #include <isl/ast_build.h>
531 isl_ctx *isl_ast_build_get_ctx(
532 __isl_keep isl_ast_build *build);
535 isl_ctx *isl_ast_expr_get_ctx(
536 __isl_keep isl_ast_expr *expr);
537 isl_ctx *isl_ast_node_get_ctx(
538 __isl_keep isl_ast_node *node);
542 An C<isl_val> represents an integer value, a rational value
543 or one of three special values, infinity, negative infinity and NaN.
544 Some predefined values can be created using the following functions.
547 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
548 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
549 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
550 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
551 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
552 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
554 Specific integer values can be created using the following functions.
557 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
559 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
561 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
562 size_t n, size_t size, const void *chunks);
564 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
565 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
566 The least significant digit is assumed to be stored first.
568 Value objects can be copied and freed using the following functions.
571 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
572 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
574 They can be inspected using the following functions.
577 long isl_val_get_num_si(__isl_keep isl_val *v);
578 long isl_val_get_den_si(__isl_keep isl_val *v);
579 double isl_val_get_d(__isl_keep isl_val *v);
580 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
582 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
583 size_t size, void *chunks);
585 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
586 of C<size> bytes needed to store the absolute value of the
588 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
589 which is assumed to have been preallocated by the caller.
590 The least significant digit is stored first.
591 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
592 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
593 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
595 An C<isl_val> can be modified using the following function.
598 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
601 The following unary properties are defined on C<isl_val>s.
604 int isl_val_sgn(__isl_keep isl_val *v);
605 int isl_val_is_zero(__isl_keep isl_val *v);
606 int isl_val_is_one(__isl_keep isl_val *v);
607 int isl_val_is_negone(__isl_keep isl_val *v);
608 int isl_val_is_nonneg(__isl_keep isl_val *v);
609 int isl_val_is_nonpos(__isl_keep isl_val *v);
610 int isl_val_is_pos(__isl_keep isl_val *v);
611 int isl_val_is_neg(__isl_keep isl_val *v);
612 int isl_val_is_int(__isl_keep isl_val *v);
613 int isl_val_is_rat(__isl_keep isl_val *v);
614 int isl_val_is_nan(__isl_keep isl_val *v);
615 int isl_val_is_infty(__isl_keep isl_val *v);
616 int isl_val_is_neginfty(__isl_keep isl_val *v);
618 Note that the sign of NaN is undefined.
620 The following binary properties are defined on pairs of C<isl_val>s.
623 int isl_val_lt(__isl_keep isl_val *v1,
624 __isl_keep isl_val *v2);
625 int isl_val_le(__isl_keep isl_val *v1,
626 __isl_keep isl_val *v2);
627 int isl_val_gt(__isl_keep isl_val *v1,
628 __isl_keep isl_val *v2);
629 int isl_val_ge(__isl_keep isl_val *v1,
630 __isl_keep isl_val *v2);
631 int isl_val_eq(__isl_keep isl_val *v1,
632 __isl_keep isl_val *v2);
633 int isl_val_ne(__isl_keep isl_val *v1,
634 __isl_keep isl_val *v2);
635 int isl_val_abs_eq(__isl_keep isl_val *v1,
636 __isl_keep isl_val *v2);
638 The function C<isl_val_abs_eq> checks whether its two arguments
639 are equal in absolute value.
641 For integer C<isl_val>s we additionally have the following binary property.
644 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
645 __isl_keep isl_val *v2);
647 An C<isl_val> can also be compared to an integer using the following
648 function. The result is undefined for NaN.
651 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
653 The following unary operations are available on C<isl_val>s.
656 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
657 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
658 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
659 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
660 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
661 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
662 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
664 The following binary operations are available on C<isl_val>s.
667 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
668 __isl_take isl_val *v2);
669 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
670 __isl_take isl_val *v2);
671 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
672 __isl_take isl_val *v2);
673 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
675 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
676 __isl_take isl_val *v2);
677 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
679 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
680 __isl_take isl_val *v2);
681 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
683 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
684 __isl_take isl_val *v2);
686 On integer values, we additionally have the following operations.
689 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
690 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
691 __isl_take isl_val *v2);
692 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
693 __isl_take isl_val *v2);
694 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
695 __isl_take isl_val *v2, __isl_give isl_val **x,
696 __isl_give isl_val **y);
698 The function C<isl_val_gcdext> returns the greatest common divisor g
699 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
700 that C<*x> * C<v1> + C<*y> * C<v2> = g.
702 =head3 GMP specific functions
704 These functions are only available if C<isl> has been compiled with C<GMP>
707 Specific integer and rational values can be created from C<GMP> values using
708 the following functions.
710 #include <isl/val_gmp.h>
711 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
713 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
714 const mpz_t n, const mpz_t d);
716 The numerator and denominator of a rational value can be extracted as
717 C<GMP> values using the following functions.
719 #include <isl/val_gmp.h>
720 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
721 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
723 =head2 Sets and Relations
725 C<isl> uses six types of objects for representing sets and relations,
726 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
727 C<isl_union_set> and C<isl_union_map>.
728 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
729 can be described as a conjunction of affine constraints, while
730 C<isl_set> and C<isl_map> represent unions of
731 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
732 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
733 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
734 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
735 where spaces are considered different if they have a different number
736 of dimensions and/or different names (see L<"Spaces">).
737 The difference between sets and relations (maps) is that sets have
738 one set of variables, while relations have two sets of variables,
739 input variables and output variables.
741 =head2 Error Handling
743 C<isl> supports different ways to react in case a runtime error is triggered.
744 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
745 with two maps that have incompatible spaces. There are three possible ways
746 to react on error: to warn, to continue or to abort.
748 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
749 the last error in the corresponding C<isl_ctx> and the function in which the
750 error was triggered returns C<NULL>. An error does not corrupt internal state,
751 such that isl can continue to be used. C<isl> also provides functions to
752 read the last error and to reset the memory that stores the last error. The
753 last error is only stored for information purposes. Its presence does not
754 change the behavior of C<isl>. Hence, resetting an error is not required to
755 continue to use isl, but only to observe new errors.
758 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
759 void isl_ctx_reset_error(isl_ctx *ctx);
761 Another option is to continue on error. This is similar to warn on error mode,
762 except that C<isl> does not print any warning. This allows a program to
763 implement its own error reporting.
765 The last option is to directly abort the execution of the program from within
766 the isl library. This makes it obviously impossible to recover from an error,
767 but it allows to directly spot the error location. By aborting on error,
768 debuggers break at the location the error occurred and can provide a stack
769 trace. Other tools that automatically provide stack traces on abort or that do
770 not want to continue execution after an error was triggered may also prefer to
773 The on error behavior of isl can be specified by calling
774 C<isl_options_set_on_error> or by setting the command line option
775 C<--isl-on-error>. Valid arguments for the function call are
776 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
777 choices for the command line option are C<warn>, C<continue> and C<abort>.
778 It is also possible to query the current error mode.
780 #include <isl/options.h>
781 int isl_options_set_on_error(isl_ctx *ctx, int val);
782 int isl_options_get_on_error(isl_ctx *ctx);
786 Identifiers are used to identify both individual dimensions
787 and tuples of dimensions. They consist of an optional name and an optional
788 user pointer. The name and the user pointer cannot both be C<NULL>, however.
789 Identifiers with the same name but different pointer values
790 are considered to be distinct.
791 Similarly, identifiers with different names but the same pointer value
792 are also considered to be distinct.
793 Equal identifiers are represented using the same object.
794 Pairs of identifiers can therefore be tested for equality using the
796 Identifiers can be constructed, copied, freed, inspected and printed
797 using the following functions.
800 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
801 __isl_keep const char *name, void *user);
802 __isl_give isl_id *isl_id_set_free_user(
803 __isl_take isl_id *id,
804 __isl_give void (*free_user)(void *user));
805 __isl_give isl_id *isl_id_copy(isl_id *id);
806 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
808 void *isl_id_get_user(__isl_keep isl_id *id);
809 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
811 __isl_give isl_printer *isl_printer_print_id(
812 __isl_take isl_printer *p, __isl_keep isl_id *id);
814 The callback set by C<isl_id_set_free_user> is called on the user
815 pointer when the last reference to the C<isl_id> is freed.
816 Note that C<isl_id_get_name> returns a pointer to some internal
817 data structure, so the result can only be used while the
818 corresponding C<isl_id> is alive.
822 Whenever a new set, relation or similar object is created from scratch,
823 the space in which it lives needs to be specified using an C<isl_space>.
824 Each space involves zero or more parameters and zero, one or two
825 tuples of set or input/output dimensions. The parameters and dimensions
826 are identified by an C<isl_dim_type> and a position.
827 The type C<isl_dim_param> refers to parameters,
828 the type C<isl_dim_set> refers to set dimensions (for spaces
829 with a single tuple of dimensions) and the types C<isl_dim_in>
830 and C<isl_dim_out> refer to input and output dimensions
831 (for spaces with two tuples of dimensions).
832 Local spaces (see L</"Local Spaces">) also contain dimensions
833 of type C<isl_dim_div>.
834 Note that parameters are only identified by their position within
835 a given object. Across different objects, parameters are (usually)
836 identified by their names or identifiers. Only unnamed parameters
837 are identified by their positions across objects. The use of unnamed
838 parameters is discouraged.
840 #include <isl/space.h>
841 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
842 unsigned nparam, unsigned n_in, unsigned n_out);
843 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
845 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
846 unsigned nparam, unsigned dim);
847 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
848 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
850 The space used for creating a parameter domain
851 needs to be created using C<isl_space_params_alloc>.
852 For other sets, the space
853 needs to be created using C<isl_space_set_alloc>, while
854 for a relation, the space
855 needs to be created using C<isl_space_alloc>.
857 To check whether a given space is that of a set or a map
858 or whether it is a parameter space, use these functions:
860 #include <isl/space.h>
861 int isl_space_is_params(__isl_keep isl_space *space);
862 int isl_space_is_set(__isl_keep isl_space *space);
863 int isl_space_is_map(__isl_keep isl_space *space);
865 Spaces can be compared using the following functions:
867 #include <isl/space.h>
868 int isl_space_is_equal(__isl_keep isl_space *space1,
869 __isl_keep isl_space *space2);
870 int isl_space_is_domain(__isl_keep isl_space *space1,
871 __isl_keep isl_space *space2);
872 int isl_space_is_range(__isl_keep isl_space *space1,
873 __isl_keep isl_space *space2);
874 int isl_space_tuple_is_equal(
875 __isl_keep isl_space *space1,
876 enum isl_dim_type type1,
877 __isl_keep isl_space *space2,
878 enum isl_dim_type type2);
880 C<isl_space_is_domain> checks whether the first argument is equal
881 to the domain of the second argument. This requires in particular that
882 the first argument is a set space and that the second argument
883 is a map space. C<isl_space_tuple_is_equal> checks whether the given
884 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
885 spaces are the same. That is, it checks if they have the same
886 identifier (if any), the same dimension and the same internal structure
889 It is often useful to create objects that live in the
890 same space as some other object. This can be accomplished
891 by creating the new objects
892 (see L</"Creating New Sets and Relations"> or
893 L</"Functions">) based on the space
894 of the original object.
897 __isl_give isl_space *isl_basic_set_get_space(
898 __isl_keep isl_basic_set *bset);
899 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
901 #include <isl/union_set.h>
902 __isl_give isl_space *isl_union_set_get_space(
903 __isl_keep isl_union_set *uset);
906 __isl_give isl_space *isl_basic_map_get_space(
907 __isl_keep isl_basic_map *bmap);
908 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
910 #include <isl/union_map.h>
911 __isl_give isl_space *isl_union_map_get_space(
912 __isl_keep isl_union_map *umap);
914 #include <isl/constraint.h>
915 __isl_give isl_space *isl_constraint_get_space(
916 __isl_keep isl_constraint *constraint);
918 #include <isl/polynomial.h>
919 __isl_give isl_space *isl_qpolynomial_get_domain_space(
920 __isl_keep isl_qpolynomial *qp);
921 __isl_give isl_space *isl_qpolynomial_get_space(
922 __isl_keep isl_qpolynomial *qp);
923 __isl_give isl_space *isl_qpolynomial_fold_get_space(
924 __isl_keep isl_qpolynomial_fold *fold);
925 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
926 __isl_keep isl_pw_qpolynomial *pwqp);
927 __isl_give isl_space *isl_pw_qpolynomial_get_space(
928 __isl_keep isl_pw_qpolynomial *pwqp);
929 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
930 __isl_keep isl_pw_qpolynomial_fold *pwf);
931 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
932 __isl_keep isl_pw_qpolynomial_fold *pwf);
933 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
934 __isl_keep isl_union_pw_qpolynomial *upwqp);
935 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
936 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
939 __isl_give isl_space *isl_multi_val_get_space(
940 __isl_keep isl_multi_val *mv);
943 __isl_give isl_space *isl_aff_get_domain_space(
944 __isl_keep isl_aff *aff);
945 __isl_give isl_space *isl_aff_get_space(
946 __isl_keep isl_aff *aff);
947 __isl_give isl_space *isl_pw_aff_get_domain_space(
948 __isl_keep isl_pw_aff *pwaff);
949 __isl_give isl_space *isl_pw_aff_get_space(
950 __isl_keep isl_pw_aff *pwaff);
951 __isl_give isl_space *isl_multi_aff_get_domain_space(
952 __isl_keep isl_multi_aff *maff);
953 __isl_give isl_space *isl_multi_aff_get_space(
954 __isl_keep isl_multi_aff *maff);
955 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
956 __isl_keep isl_pw_multi_aff *pma);
957 __isl_give isl_space *isl_pw_multi_aff_get_space(
958 __isl_keep isl_pw_multi_aff *pma);
959 __isl_give isl_space *isl_union_pw_aff_get_space(
960 __isl_keep isl_union_pw_aff *upa);
961 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
962 __isl_keep isl_union_pw_multi_aff *upma);
963 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
964 __isl_keep isl_multi_pw_aff *mpa);
965 __isl_give isl_space *isl_multi_pw_aff_get_space(
966 __isl_keep isl_multi_pw_aff *mpa);
968 #include <isl/point.h>
969 __isl_give isl_space *isl_point_get_space(
970 __isl_keep isl_point *pnt);
972 The number of dimensions of a given type of space
973 may be read off from a space or an object that lives
974 in a space using the following functions.
975 In case of C<isl_space_dim>, type may be
976 C<isl_dim_param>, C<isl_dim_in> (only for relations),
977 C<isl_dim_out> (only for relations), C<isl_dim_set>
978 (only for sets) or C<isl_dim_all>.
980 #include <isl/space.h>
981 unsigned isl_space_dim(__isl_keep isl_space *space,
982 enum isl_dim_type type);
984 #include <isl/local_space.h>
985 int isl_local_space_dim(__isl_keep isl_local_space *ls,
986 enum isl_dim_type type);
989 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
990 enum isl_dim_type type);
991 unsigned isl_set_dim(__isl_keep isl_set *set,
992 enum isl_dim_type type);
994 #include <isl/union_set.h>
995 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
996 enum isl_dim_type type);
999 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1000 enum isl_dim_type type);
1001 unsigned isl_map_dim(__isl_keep isl_map *map,
1002 enum isl_dim_type type);
1004 #include <isl/union_map.h>
1005 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1006 enum isl_dim_type type);
1008 #include <isl/val.h>
1009 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1010 enum isl_dim_type type);
1012 #include <isl/aff.h>
1013 int isl_aff_dim(__isl_keep isl_aff *aff,
1014 enum isl_dim_type type);
1015 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1016 enum isl_dim_type type);
1017 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1018 enum isl_dim_type type);
1019 unsigned isl_pw_multi_aff_dim(
1020 __isl_keep isl_pw_multi_aff *pma,
1021 enum isl_dim_type type);
1022 unsigned isl_multi_pw_aff_dim(
1023 __isl_keep isl_multi_pw_aff *mpa,
1024 enum isl_dim_type type);
1025 unsigned isl_union_pw_aff_dim(
1026 __isl_keep isl_union_pw_aff *upa,
1027 enum isl_dim_type type);
1028 unsigned isl_union_pw_multi_aff_dim(
1029 __isl_keep isl_union_pw_multi_aff *upma,
1030 enum isl_dim_type type);
1032 #include <isl/polynomial.h>
1033 unsigned isl_union_pw_qpolynomial_dim(
1034 __isl_keep isl_union_pw_qpolynomial *upwqp,
1035 enum isl_dim_type type);
1036 unsigned isl_union_pw_qpolynomial_fold_dim(
1037 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1038 enum isl_dim_type type);
1040 Note that an C<isl_union_set>, an C<isl_union_map>,
1041 an C<isl_union_pw_multi_aff>,
1042 an C<isl_union_pw_qpolynomial> and
1043 an C<isl_union_pw_qpolynomial_fold>
1044 only have parameters.
1046 The identifiers or names of the individual dimensions of spaces
1047 may be set or read off using the following functions on spaces
1048 or objects that live in spaces.
1049 These functions are mostly useful to obtain the identifiers, positions
1050 or names of the parameters. Identifiers of individual dimensions are
1051 essentially only useful for printing. They are ignored by all other
1052 operations and may not be preserved across those operations.
1054 #include <isl/space.h>
1055 __isl_give isl_space *isl_space_set_dim_id(
1056 __isl_take isl_space *space,
1057 enum isl_dim_type type, unsigned pos,
1058 __isl_take isl_id *id);
1059 int isl_space_has_dim_id(__isl_keep isl_space *space,
1060 enum isl_dim_type type, unsigned pos);
1061 __isl_give isl_id *isl_space_get_dim_id(
1062 __isl_keep isl_space *space,
1063 enum isl_dim_type type, unsigned pos);
1064 __isl_give isl_space *isl_space_set_dim_name(
1065 __isl_take isl_space *space,
1066 enum isl_dim_type type, unsigned pos,
1067 __isl_keep const char *name);
1068 int isl_space_has_dim_name(__isl_keep isl_space *space,
1069 enum isl_dim_type type, unsigned pos);
1070 __isl_keep const char *isl_space_get_dim_name(
1071 __isl_keep isl_space *space,
1072 enum isl_dim_type type, unsigned pos);
1074 #include <isl/local_space.h>
1075 __isl_give isl_local_space *isl_local_space_set_dim_id(
1076 __isl_take isl_local_space *ls,
1077 enum isl_dim_type type, unsigned pos,
1078 __isl_take isl_id *id);
1079 int isl_local_space_has_dim_id(
1080 __isl_keep isl_local_space *ls,
1081 enum isl_dim_type type, unsigned pos);
1082 __isl_give isl_id *isl_local_space_get_dim_id(
1083 __isl_keep isl_local_space *ls,
1084 enum isl_dim_type type, unsigned pos);
1085 __isl_give isl_local_space *isl_local_space_set_dim_name(
1086 __isl_take isl_local_space *ls,
1087 enum isl_dim_type type, unsigned pos, const char *s);
1088 int isl_local_space_has_dim_name(
1089 __isl_keep isl_local_space *ls,
1090 enum isl_dim_type type, unsigned pos)
1091 const char *isl_local_space_get_dim_name(
1092 __isl_keep isl_local_space *ls,
1093 enum isl_dim_type type, unsigned pos);
1095 #include <isl/constraint.h>
1096 const char *isl_constraint_get_dim_name(
1097 __isl_keep isl_constraint *constraint,
1098 enum isl_dim_type type, unsigned pos);
1100 #include <isl/set.h>
1101 __isl_give isl_id *isl_basic_set_get_dim_id(
1102 __isl_keep isl_basic_set *bset,
1103 enum isl_dim_type type, unsigned pos);
1104 __isl_give isl_set *isl_set_set_dim_id(
1105 __isl_take isl_set *set, enum isl_dim_type type,
1106 unsigned pos, __isl_take isl_id *id);
1107 int isl_set_has_dim_id(__isl_keep isl_set *set,
1108 enum isl_dim_type type, unsigned pos);
1109 __isl_give isl_id *isl_set_get_dim_id(
1110 __isl_keep isl_set *set, enum isl_dim_type type,
1112 const char *isl_basic_set_get_dim_name(
1113 __isl_keep isl_basic_set *bset,
1114 enum isl_dim_type type, unsigned pos);
1115 int isl_set_has_dim_name(__isl_keep isl_set *set,
1116 enum isl_dim_type type, unsigned pos);
1117 const char *isl_set_get_dim_name(
1118 __isl_keep isl_set *set,
1119 enum isl_dim_type type, unsigned pos);
1121 #include <isl/map.h>
1122 __isl_give isl_map *isl_map_set_dim_id(
1123 __isl_take isl_map *map, enum isl_dim_type type,
1124 unsigned pos, __isl_take isl_id *id);
1125 int isl_basic_map_has_dim_id(
1126 __isl_keep isl_basic_map *bmap,
1127 enum isl_dim_type type, unsigned pos);
1128 int isl_map_has_dim_id(__isl_keep isl_map *map,
1129 enum isl_dim_type type, unsigned pos);
1130 __isl_give isl_id *isl_map_get_dim_id(
1131 __isl_keep isl_map *map, enum isl_dim_type type,
1133 __isl_give isl_id *isl_union_map_get_dim_id(
1134 __isl_keep isl_union_map *umap,
1135 enum isl_dim_type type, unsigned pos);
1136 const char *isl_basic_map_get_dim_name(
1137 __isl_keep isl_basic_map *bmap,
1138 enum isl_dim_type type, unsigned pos);
1139 int isl_map_has_dim_name(__isl_keep isl_map *map,
1140 enum isl_dim_type type, unsigned pos);
1141 const char *isl_map_get_dim_name(
1142 __isl_keep isl_map *map,
1143 enum isl_dim_type type, unsigned pos);
1145 #include <isl/val.h>
1146 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1147 __isl_take isl_multi_val *mv,
1148 enum isl_dim_type type, unsigned pos,
1149 __isl_take isl_id *id);
1150 __isl_give isl_id *isl_multi_val_get_dim_id(
1151 __isl_keep isl_multi_val *mv,
1152 enum isl_dim_type type, unsigned pos);
1153 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1154 __isl_take isl_multi_val *mv,
1155 enum isl_dim_type type, unsigned pos, const char *s);
1157 #include <isl/aff.h>
1158 __isl_give isl_aff *isl_aff_set_dim_id(
1159 __isl_take isl_aff *aff, enum isl_dim_type type,
1160 unsigned pos, __isl_take isl_id *id);
1161 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1162 __isl_take isl_multi_aff *maff,
1163 enum isl_dim_type type, unsigned pos,
1164 __isl_take isl_id *id);
1165 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1166 __isl_take isl_pw_aff *pma,
1167 enum isl_dim_type type, unsigned pos,
1168 __isl_take isl_id *id);
1169 __isl_give isl_multi_pw_aff *
1170 isl_multi_pw_aff_set_dim_id(
1171 __isl_take isl_multi_pw_aff *mpa,
1172 enum isl_dim_type type, unsigned pos,
1173 __isl_take isl_id *id);
1174 __isl_give isl_id *isl_multi_aff_get_dim_id(
1175 __isl_keep isl_multi_aff *ma,
1176 enum isl_dim_type type, unsigned pos);
1177 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1178 enum isl_dim_type type, unsigned pos);
1179 __isl_give isl_id *isl_pw_aff_get_dim_id(
1180 __isl_keep isl_pw_aff *pa,
1181 enum isl_dim_type type, unsigned pos);
1182 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1183 __isl_keep isl_pw_multi_aff *pma,
1184 enum isl_dim_type type, unsigned pos);
1185 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1186 __isl_keep isl_multi_pw_aff *mpa,
1187 enum isl_dim_type type, unsigned pos);
1188 __isl_give isl_aff *isl_aff_set_dim_name(
1189 __isl_take isl_aff *aff, enum isl_dim_type type,
1190 unsigned pos, const char *s);
1191 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1192 __isl_take isl_multi_aff *maff,
1193 enum isl_dim_type type, unsigned pos, const char *s);
1194 __isl_give isl_multi_pw_aff *
1195 isl_multi_pw_aff_set_dim_name(
1196 __isl_take isl_multi_pw_aff *mpa,
1197 enum isl_dim_type type, unsigned pos, const char *s);
1198 __isl_give isl_union_pw_aff *
1199 isl_union_pw_aff_set_dim_name(
1200 __isl_take isl_union_pw_aff *upa,
1201 enum isl_dim_type type, unsigned pos,
1203 __isl_give isl_union_pw_multi_aff *
1204 isl_union_pw_multi_aff_set_dim_name(
1205 __isl_take isl_union_pw_multi_aff *upma,
1206 enum isl_dim_type type, unsigned pos,
1208 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1209 enum isl_dim_type type, unsigned pos);
1210 const char *isl_pw_aff_get_dim_name(
1211 __isl_keep isl_pw_aff *pa,
1212 enum isl_dim_type type, unsigned pos);
1213 const char *isl_pw_multi_aff_get_dim_name(
1214 __isl_keep isl_pw_multi_aff *pma,
1215 enum isl_dim_type type, unsigned pos);
1217 #include <isl/polynomial.h>
1218 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1219 __isl_take isl_qpolynomial *qp,
1220 enum isl_dim_type type, unsigned pos,
1222 __isl_give isl_pw_qpolynomial *
1223 isl_pw_qpolynomial_set_dim_name(
1224 __isl_take isl_pw_qpolynomial *pwqp,
1225 enum isl_dim_type type, unsigned pos,
1227 __isl_give isl_pw_qpolynomial_fold *
1228 isl_pw_qpolynomial_fold_set_dim_name(
1229 __isl_take isl_pw_qpolynomial_fold *pwf,
1230 enum isl_dim_type type, unsigned pos,
1232 __isl_give isl_union_pw_qpolynomial *
1233 isl_union_pw_qpolynomial_set_dim_name(
1234 __isl_take isl_union_pw_qpolynomial *upwqp,
1235 enum isl_dim_type type, unsigned pos,
1237 __isl_give isl_union_pw_qpolynomial_fold *
1238 isl_union_pw_qpolynomial_fold_set_dim_name(
1239 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1240 enum isl_dim_type type, unsigned pos,
1243 Note that C<isl_space_get_name> returns a pointer to some internal
1244 data structure, so the result can only be used while the
1245 corresponding C<isl_space> is alive.
1246 Also note that every function that operates on two sets or relations
1247 requires that both arguments have the same parameters. This also
1248 means that if one of the arguments has named parameters, then the
1249 other needs to have named parameters too and the names need to match.
1250 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1251 arguments may have different parameters (as long as they are named),
1252 in which case the result will have as parameters the union of the parameters of
1255 Given the identifier or name of a dimension (typically a parameter),
1256 its position can be obtained from the following functions.
1258 #include <isl/space.h>
1259 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1260 enum isl_dim_type type, __isl_keep isl_id *id);
1261 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1262 enum isl_dim_type type, const char *name);
1264 #include <isl/local_space.h>
1265 int isl_local_space_find_dim_by_name(
1266 __isl_keep isl_local_space *ls,
1267 enum isl_dim_type type, const char *name);
1269 #include <isl/val.h>
1270 int isl_multi_val_find_dim_by_id(
1271 __isl_keep isl_multi_val *mv,
1272 enum isl_dim_type type, __isl_keep isl_id *id);
1273 int isl_multi_val_find_dim_by_name(
1274 __isl_keep isl_multi_val *mv,
1275 enum isl_dim_type type, const char *name);
1277 #include <isl/set.h>
1278 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1279 enum isl_dim_type type, __isl_keep isl_id *id);
1280 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1281 enum isl_dim_type type, const char *name);
1283 #include <isl/map.h>
1284 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1285 enum isl_dim_type type, __isl_keep isl_id *id);
1286 int isl_basic_map_find_dim_by_name(
1287 __isl_keep isl_basic_map *bmap,
1288 enum isl_dim_type type, const char *name);
1289 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1290 enum isl_dim_type type, const char *name);
1291 int isl_union_map_find_dim_by_name(
1292 __isl_keep isl_union_map *umap,
1293 enum isl_dim_type type, const char *name);
1295 #include <isl/aff.h>
1296 int isl_multi_aff_find_dim_by_id(
1297 __isl_keep isl_multi_aff *ma,
1298 enum isl_dim_type type, __isl_keep isl_id *id);
1299 int isl_multi_pw_aff_find_dim_by_id(
1300 __isl_keep isl_multi_pw_aff *mpa,
1301 enum isl_dim_type type, __isl_keep isl_id *id);
1302 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1303 enum isl_dim_type type, const char *name);
1304 int isl_multi_aff_find_dim_by_name(
1305 __isl_keep isl_multi_aff *ma,
1306 enum isl_dim_type type, const char *name);
1307 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1308 enum isl_dim_type type, const char *name);
1309 int isl_multi_pw_aff_find_dim_by_name(
1310 __isl_keep isl_multi_pw_aff *mpa,
1311 enum isl_dim_type type, const char *name);
1312 int isl_pw_multi_aff_find_dim_by_name(
1313 __isl_keep isl_pw_multi_aff *pma,
1314 enum isl_dim_type type, const char *name);
1315 int isl_union_pw_aff_find_dim_by_name(
1316 __isl_keep isl_union_pw_aff *upa,
1317 enum isl_dim_type type, const char *name);
1318 int isl_union_pw_multi_aff_find_dim_by_name(
1319 __isl_keep isl_union_pw_multi_aff *upma,
1320 enum isl_dim_type type, const char *name);
1322 #include <isl/polynomial.h>
1323 int isl_pw_qpolynomial_find_dim_by_name(
1324 __isl_keep isl_pw_qpolynomial *pwqp,
1325 enum isl_dim_type type, const char *name);
1326 int isl_pw_qpolynomial_fold_find_dim_by_name(
1327 __isl_keep isl_pw_qpolynomial_fold *pwf,
1328 enum isl_dim_type type, const char *name);
1329 int isl_union_pw_qpolynomial_find_dim_by_name(
1330 __isl_keep isl_union_pw_qpolynomial *upwqp,
1331 enum isl_dim_type type, const char *name);
1332 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1333 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1334 enum isl_dim_type type, const char *name);
1336 The identifiers or names of entire spaces may be set or read off
1337 using the following functions.
1339 #include <isl/space.h>
1340 __isl_give isl_space *isl_space_set_tuple_id(
1341 __isl_take isl_space *space,
1342 enum isl_dim_type type, __isl_take isl_id *id);
1343 __isl_give isl_space *isl_space_reset_tuple_id(
1344 __isl_take isl_space *space, enum isl_dim_type type);
1345 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1346 enum isl_dim_type type);
1347 __isl_give isl_id *isl_space_get_tuple_id(
1348 __isl_keep isl_space *space, enum isl_dim_type type);
1349 __isl_give isl_space *isl_space_set_tuple_name(
1350 __isl_take isl_space *space,
1351 enum isl_dim_type type, const char *s);
1352 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1353 enum isl_dim_type type);
1354 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1355 enum isl_dim_type type);
1357 #include <isl/local_space.h>
1358 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1359 __isl_take isl_local_space *ls,
1360 enum isl_dim_type type, __isl_take isl_id *id);
1362 #include <isl/set.h>
1363 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1364 __isl_take isl_basic_set *bset,
1365 __isl_take isl_id *id);
1366 __isl_give isl_set *isl_set_set_tuple_id(
1367 __isl_take isl_set *set, __isl_take isl_id *id);
1368 __isl_give isl_set *isl_set_reset_tuple_id(
1369 __isl_take isl_set *set);
1370 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1371 __isl_give isl_id *isl_set_get_tuple_id(
1372 __isl_keep isl_set *set);
1373 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1374 __isl_take isl_basic_set *set, const char *s);
1375 __isl_give isl_set *isl_set_set_tuple_name(
1376 __isl_take isl_set *set, const char *s);
1377 const char *isl_basic_set_get_tuple_name(
1378 __isl_keep isl_basic_set *bset);
1379 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1380 const char *isl_set_get_tuple_name(
1381 __isl_keep isl_set *set);
1383 #include <isl/map.h>
1384 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1385 __isl_take isl_basic_map *bmap,
1386 enum isl_dim_type type, __isl_take isl_id *id);
1387 __isl_give isl_map *isl_map_set_tuple_id(
1388 __isl_take isl_map *map, enum isl_dim_type type,
1389 __isl_take isl_id *id);
1390 __isl_give isl_map *isl_map_reset_tuple_id(
1391 __isl_take isl_map *map, enum isl_dim_type type);
1392 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1393 enum isl_dim_type type);
1394 __isl_give isl_id *isl_map_get_tuple_id(
1395 __isl_keep isl_map *map, enum isl_dim_type type);
1396 __isl_give isl_map *isl_map_set_tuple_name(
1397 __isl_take isl_map *map,
1398 enum isl_dim_type type, const char *s);
1399 const char *isl_basic_map_get_tuple_name(
1400 __isl_keep isl_basic_map *bmap,
1401 enum isl_dim_type type);
1402 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1403 __isl_take isl_basic_map *bmap,
1404 enum isl_dim_type type, const char *s);
1405 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1406 enum isl_dim_type type);
1407 const char *isl_map_get_tuple_name(
1408 __isl_keep isl_map *map,
1409 enum isl_dim_type type);
1411 #include <isl/val.h>
1412 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1413 __isl_take isl_multi_val *mv,
1414 enum isl_dim_type type, __isl_take isl_id *id);
1415 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1416 __isl_take isl_multi_val *mv,
1417 enum isl_dim_type type);
1418 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1419 enum isl_dim_type type);
1420 __isl_give isl_id *isl_multi_val_get_tuple_id(
1421 __isl_keep isl_multi_val *mv,
1422 enum isl_dim_type type);
1423 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1424 __isl_take isl_multi_val *mv,
1425 enum isl_dim_type type, const char *s);
1426 const char *isl_multi_val_get_tuple_name(
1427 __isl_keep isl_multi_val *mv,
1428 enum isl_dim_type type);
1430 #include <isl/aff.h>
1431 __isl_give isl_aff *isl_aff_set_tuple_id(
1432 __isl_take isl_aff *aff,
1433 enum isl_dim_type type, __isl_take isl_id *id);
1434 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1435 __isl_take isl_multi_aff *maff,
1436 enum isl_dim_type type, __isl_take isl_id *id);
1437 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1438 __isl_take isl_pw_aff *pwaff,
1439 enum isl_dim_type type, __isl_take isl_id *id);
1440 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1441 __isl_take isl_pw_multi_aff *pma,
1442 enum isl_dim_type type, __isl_take isl_id *id);
1443 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1444 __isl_take isl_multi_aff *ma,
1445 enum isl_dim_type type);
1446 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1447 __isl_take isl_pw_aff *pa,
1448 enum isl_dim_type type);
1449 __isl_give isl_multi_pw_aff *
1450 isl_multi_pw_aff_reset_tuple_id(
1451 __isl_take isl_multi_pw_aff *mpa,
1452 enum isl_dim_type type);
1453 __isl_give isl_pw_multi_aff *
1454 isl_pw_multi_aff_reset_tuple_id(
1455 __isl_take isl_pw_multi_aff *pma,
1456 enum isl_dim_type type);
1457 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1458 enum isl_dim_type type);
1459 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1460 __isl_keep isl_multi_aff *ma,
1461 enum isl_dim_type type);
1462 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1463 enum isl_dim_type type);
1464 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1465 __isl_keep isl_pw_aff *pa,
1466 enum isl_dim_type type);
1467 int isl_pw_multi_aff_has_tuple_id(
1468 __isl_keep isl_pw_multi_aff *pma,
1469 enum isl_dim_type type);
1470 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1471 __isl_keep isl_pw_multi_aff *pma,
1472 enum isl_dim_type type);
1473 int isl_multi_pw_aff_has_tuple_id(
1474 __isl_keep isl_multi_pw_aff *mpa,
1475 enum isl_dim_type type);
1476 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1477 __isl_keep isl_multi_pw_aff *mpa,
1478 enum isl_dim_type type);
1479 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1480 __isl_take isl_multi_aff *maff,
1481 enum isl_dim_type type, const char *s);
1482 __isl_give isl_multi_pw_aff *
1483 isl_multi_pw_aff_set_tuple_name(
1484 __isl_take isl_multi_pw_aff *mpa,
1485 enum isl_dim_type type, const char *s);
1486 const char *isl_multi_aff_get_tuple_name(
1487 __isl_keep isl_multi_aff *multi,
1488 enum isl_dim_type type);
1489 int isl_pw_multi_aff_has_tuple_name(
1490 __isl_keep isl_pw_multi_aff *pma,
1491 enum isl_dim_type type);
1492 const char *isl_pw_multi_aff_get_tuple_name(
1493 __isl_keep isl_pw_multi_aff *pma,
1494 enum isl_dim_type type);
1496 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1497 or C<isl_dim_set>. As with C<isl_space_get_name>,
1498 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1500 Binary operations require the corresponding spaces of their arguments
1501 to have the same name.
1503 To keep the names of all parameters and tuples, but reset the user pointers
1504 of all the corresponding identifiers, use the following function.
1506 #include <isl/space.h>
1507 __isl_give isl_space *isl_space_reset_user(
1508 __isl_take isl_space *space);
1510 #include <isl/set.h>
1511 __isl_give isl_set *isl_set_reset_user(
1512 __isl_take isl_set *set);
1514 #include <isl/map.h>
1515 __isl_give isl_map *isl_map_reset_user(
1516 __isl_take isl_map *map);
1518 #include <isl/union_set.h>
1519 __isl_give isl_union_set *isl_union_set_reset_user(
1520 __isl_take isl_union_set *uset);
1522 #include <isl/union_map.h>
1523 __isl_give isl_union_map *isl_union_map_reset_user(
1524 __isl_take isl_union_map *umap);
1526 #include <isl/val.h>
1527 __isl_give isl_multi_val *isl_multi_val_reset_user(
1528 __isl_take isl_multi_val *mv);
1530 #include <isl/aff.h>
1531 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1532 __isl_take isl_multi_aff *ma);
1533 __isl_give isl_pw_aff *isl_pw_aff_reset_user(
1534 __isl_take isl_pw_aff *pa);
1535 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1536 __isl_take isl_multi_pw_aff *mpa);
1537 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_reset_user(
1538 __isl_take isl_pw_multi_aff *pma);
1539 __isl_give isl_union_pw_aff *isl_union_pw_aff_reset_user(
1540 __isl_take isl_union_pw_aff *upa);
1541 __isl_give isl_union_pw_multi_aff *
1542 isl_union_pw_multi_aff_reset_user(
1543 __isl_take isl_union_pw_multi_aff *upma);
1545 #include <isl/polynomial.h>
1546 __isl_give isl_pw_qpolynomial *
1547 isl_pw_qpolynomial_reset_user(
1548 __isl_take isl_pw_qpolynomial *pwqp);
1549 __isl_give isl_union_pw_qpolynomial *
1550 isl_union_pw_qpolynomial_reset_user(
1551 __isl_take isl_union_pw_qpolynomial *upwqp);
1552 __isl_give isl_pw_qpolynomial_fold *
1553 isl_pw_qpolynomial_fold_reset_user(
1554 __isl_take isl_pw_qpolynomial_fold *pwf);
1555 __isl_give isl_union_pw_qpolynomial_fold *
1556 isl_union_pw_qpolynomial_fold_reset_user(
1557 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1559 Spaces can be nested. In particular, the domain of a set or
1560 the domain or range of a relation can be a nested relation.
1561 This process is also called I<wrapping>.
1562 The functions for detecting, constructing and deconstructing
1563 such nested spaces can be found in the wrapping properties
1564 of L</"Unary Properties">, the wrapping operations
1565 of L</"Unary Operations"> and the Cartesian product operations
1566 of L</"Basic Operations">.
1568 Spaces can be created from other spaces
1569 using the functions described in L</"Unary Operations">
1570 and L</"Binary Operations">.
1574 A local space is essentially a space with
1575 zero or more existentially quantified variables.
1576 The local space of various objects can be obtained
1577 using the following functions.
1579 #include <isl/constraint.h>
1580 __isl_give isl_local_space *isl_constraint_get_local_space(
1581 __isl_keep isl_constraint *constraint);
1583 #include <isl/set.h>
1584 __isl_give isl_local_space *isl_basic_set_get_local_space(
1585 __isl_keep isl_basic_set *bset);
1587 #include <isl/map.h>
1588 __isl_give isl_local_space *isl_basic_map_get_local_space(
1589 __isl_keep isl_basic_map *bmap);
1591 #include <isl/aff.h>
1592 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1593 __isl_keep isl_aff *aff);
1594 __isl_give isl_local_space *isl_aff_get_local_space(
1595 __isl_keep isl_aff *aff);
1597 A new local space can be created from a space using
1599 #include <isl/local_space.h>
1600 __isl_give isl_local_space *isl_local_space_from_space(
1601 __isl_take isl_space *space);
1603 They can be inspected, modified, copied and freed using the following functions.
1605 #include <isl/local_space.h>
1606 int isl_local_space_is_params(
1607 __isl_keep isl_local_space *ls);
1608 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1609 __isl_give isl_space *isl_local_space_get_space(
1610 __isl_keep isl_local_space *ls);
1611 __isl_give isl_aff *isl_local_space_get_div(
1612 __isl_keep isl_local_space *ls, int pos);
1613 __isl_give isl_local_space *isl_local_space_copy(
1614 __isl_keep isl_local_space *ls);
1615 __isl_null isl_local_space *isl_local_space_free(
1616 __isl_take isl_local_space *ls);
1618 Note that C<isl_local_space_get_div> can only be used on local spaces
1621 Two local spaces can be compared using
1623 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1624 __isl_keep isl_local_space *ls2);
1626 Local spaces can be created from other local spaces
1627 using the functions described in L</"Unary Operations">
1628 and L</"Binary Operations">.
1630 =head2 Creating New Sets and Relations
1632 C<isl> has functions for creating some standard sets and relations.
1636 =item * Empty sets and relations
1638 __isl_give isl_basic_set *isl_basic_set_empty(
1639 __isl_take isl_space *space);
1640 __isl_give isl_basic_map *isl_basic_map_empty(
1641 __isl_take isl_space *space);
1642 __isl_give isl_set *isl_set_empty(
1643 __isl_take isl_space *space);
1644 __isl_give isl_map *isl_map_empty(
1645 __isl_take isl_space *space);
1646 __isl_give isl_union_set *isl_union_set_empty(
1647 __isl_take isl_space *space);
1648 __isl_give isl_union_map *isl_union_map_empty(
1649 __isl_take isl_space *space);
1651 For C<isl_union_set>s and C<isl_union_map>s, the space
1652 is only used to specify the parameters.
1654 =item * Universe sets and relations
1656 __isl_give isl_basic_set *isl_basic_set_universe(
1657 __isl_take isl_space *space);
1658 __isl_give isl_basic_map *isl_basic_map_universe(
1659 __isl_take isl_space *space);
1660 __isl_give isl_set *isl_set_universe(
1661 __isl_take isl_space *space);
1662 __isl_give isl_map *isl_map_universe(
1663 __isl_take isl_space *space);
1664 __isl_give isl_union_set *isl_union_set_universe(
1665 __isl_take isl_union_set *uset);
1666 __isl_give isl_union_map *isl_union_map_universe(
1667 __isl_take isl_union_map *umap);
1669 The sets and relations constructed by the functions above
1670 contain all integer values, while those constructed by the
1671 functions below only contain non-negative values.
1673 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1674 __isl_take isl_space *space);
1675 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1676 __isl_take isl_space *space);
1677 __isl_give isl_set *isl_set_nat_universe(
1678 __isl_take isl_space *space);
1679 __isl_give isl_map *isl_map_nat_universe(
1680 __isl_take isl_space *space);
1682 =item * Identity relations
1684 __isl_give isl_basic_map *isl_basic_map_identity(
1685 __isl_take isl_space *space);
1686 __isl_give isl_map *isl_map_identity(
1687 __isl_take isl_space *space);
1689 The number of input and output dimensions in C<space> needs
1692 =item * Lexicographic order
1694 __isl_give isl_map *isl_map_lex_lt(
1695 __isl_take isl_space *set_space);
1696 __isl_give isl_map *isl_map_lex_le(
1697 __isl_take isl_space *set_space);
1698 __isl_give isl_map *isl_map_lex_gt(
1699 __isl_take isl_space *set_space);
1700 __isl_give isl_map *isl_map_lex_ge(
1701 __isl_take isl_space *set_space);
1702 __isl_give isl_map *isl_map_lex_lt_first(
1703 __isl_take isl_space *space, unsigned n);
1704 __isl_give isl_map *isl_map_lex_le_first(
1705 __isl_take isl_space *space, unsigned n);
1706 __isl_give isl_map *isl_map_lex_gt_first(
1707 __isl_take isl_space *space, unsigned n);
1708 __isl_give isl_map *isl_map_lex_ge_first(
1709 __isl_take isl_space *space, unsigned n);
1711 The first four functions take a space for a B<set>
1712 and return relations that express that the elements in the domain
1713 are lexicographically less
1714 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1715 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1716 than the elements in the range.
1717 The last four functions take a space for a map
1718 and return relations that express that the first C<n> dimensions
1719 in the domain are lexicographically less
1720 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1721 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1722 than the first C<n> dimensions in the range.
1726 A basic set or relation can be converted to a set or relation
1727 using the following functions.
1729 __isl_give isl_set *isl_set_from_basic_set(
1730 __isl_take isl_basic_set *bset);
1731 __isl_give isl_map *isl_map_from_basic_map(
1732 __isl_take isl_basic_map *bmap);
1734 Sets and relations can be converted to union sets and relations
1735 using the following functions.
1737 __isl_give isl_union_set *isl_union_set_from_basic_set(
1738 __isl_take isl_basic_set *bset);
1739 __isl_give isl_union_map *isl_union_map_from_basic_map(
1740 __isl_take isl_basic_map *bmap);
1741 __isl_give isl_union_set *isl_union_set_from_set(
1742 __isl_take isl_set *set);
1743 __isl_give isl_union_map *isl_union_map_from_map(
1744 __isl_take isl_map *map);
1746 The inverse conversions below can only be used if the input
1747 union set or relation is known to contain elements in exactly one
1750 __isl_give isl_set *isl_set_from_union_set(
1751 __isl_take isl_union_set *uset);
1752 __isl_give isl_map *isl_map_from_union_map(
1753 __isl_take isl_union_map *umap);
1755 Sets and relations can be copied and freed again using the following
1758 __isl_give isl_basic_set *isl_basic_set_copy(
1759 __isl_keep isl_basic_set *bset);
1760 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1761 __isl_give isl_union_set *isl_union_set_copy(
1762 __isl_keep isl_union_set *uset);
1763 __isl_give isl_basic_map *isl_basic_map_copy(
1764 __isl_keep isl_basic_map *bmap);
1765 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1766 __isl_give isl_union_map *isl_union_map_copy(
1767 __isl_keep isl_union_map *umap);
1768 __isl_null isl_basic_set *isl_basic_set_free(
1769 __isl_take isl_basic_set *bset);
1770 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1771 __isl_null isl_union_set *isl_union_set_free(
1772 __isl_take isl_union_set *uset);
1773 __isl_null isl_basic_map *isl_basic_map_free(
1774 __isl_take isl_basic_map *bmap);
1775 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1776 __isl_null isl_union_map *isl_union_map_free(
1777 __isl_take isl_union_map *umap);
1779 Other sets and relations can be constructed by starting
1780 from a universe set or relation, adding equality and/or
1781 inequality constraints and then projecting out the
1782 existentially quantified variables, if any.
1783 Constraints can be constructed, manipulated and
1784 added to (or removed from) (basic) sets and relations
1785 using the following functions.
1787 #include <isl/constraint.h>
1788 __isl_give isl_constraint *isl_equality_alloc(
1789 __isl_take isl_local_space *ls);
1790 __isl_give isl_constraint *isl_inequality_alloc(
1791 __isl_take isl_local_space *ls);
1792 __isl_give isl_constraint *isl_constraint_set_constant_si(
1793 __isl_take isl_constraint *constraint, int v);
1794 __isl_give isl_constraint *isl_constraint_set_constant_val(
1795 __isl_take isl_constraint *constraint,
1796 __isl_take isl_val *v);
1797 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1798 __isl_take isl_constraint *constraint,
1799 enum isl_dim_type type, int pos, int v);
1800 __isl_give isl_constraint *
1801 isl_constraint_set_coefficient_val(
1802 __isl_take isl_constraint *constraint,
1803 enum isl_dim_type type, int pos,
1804 __isl_take isl_val *v);
1805 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1806 __isl_take isl_basic_map *bmap,
1807 __isl_take isl_constraint *constraint);
1808 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1809 __isl_take isl_basic_set *bset,
1810 __isl_take isl_constraint *constraint);
1811 __isl_give isl_map *isl_map_add_constraint(
1812 __isl_take isl_map *map,
1813 __isl_take isl_constraint *constraint);
1814 __isl_give isl_set *isl_set_add_constraint(
1815 __isl_take isl_set *set,
1816 __isl_take isl_constraint *constraint);
1817 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1818 __isl_take isl_basic_set *bset,
1819 __isl_take isl_constraint *constraint);
1821 For example, to create a set containing the even integers
1822 between 10 and 42, you would use the following code.
1825 isl_local_space *ls;
1827 isl_basic_set *bset;
1829 space = isl_space_set_alloc(ctx, 0, 2);
1830 bset = isl_basic_set_universe(isl_space_copy(space));
1831 ls = isl_local_space_from_space(space);
1833 c = isl_equality_alloc(isl_local_space_copy(ls));
1834 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1835 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1836 bset = isl_basic_set_add_constraint(bset, c);
1838 c = isl_inequality_alloc(isl_local_space_copy(ls));
1839 c = isl_constraint_set_constant_si(c, -10);
1840 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1841 bset = isl_basic_set_add_constraint(bset, c);
1843 c = isl_inequality_alloc(ls);
1844 c = isl_constraint_set_constant_si(c, 42);
1845 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1846 bset = isl_basic_set_add_constraint(bset, c);
1848 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1852 isl_basic_set *bset;
1853 bset = isl_basic_set_read_from_str(ctx,
1854 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1856 A basic set or relation can also be constructed from two matrices
1857 describing the equalities and the inequalities.
1859 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1860 __isl_take isl_space *space,
1861 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1862 enum isl_dim_type c1,
1863 enum isl_dim_type c2, enum isl_dim_type c3,
1864 enum isl_dim_type c4);
1865 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1866 __isl_take isl_space *space,
1867 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1868 enum isl_dim_type c1,
1869 enum isl_dim_type c2, enum isl_dim_type c3,
1870 enum isl_dim_type c4, enum isl_dim_type c5);
1872 The C<isl_dim_type> arguments indicate the order in which
1873 different kinds of variables appear in the input matrices
1874 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1875 C<isl_dim_set> and C<isl_dim_div> for sets and
1876 of C<isl_dim_cst>, C<isl_dim_param>,
1877 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1879 A (basic or union) set or relation can also be constructed from a
1880 (union) (piecewise) (multiple) affine expression
1881 or a list of affine expressions
1882 (See L</"Functions">).
1884 __isl_give isl_basic_map *isl_basic_map_from_aff(
1885 __isl_take isl_aff *aff);
1886 __isl_give isl_map *isl_map_from_aff(
1887 __isl_take isl_aff *aff);
1888 __isl_give isl_set *isl_set_from_pw_aff(
1889 __isl_take isl_pw_aff *pwaff);
1890 __isl_give isl_map *isl_map_from_pw_aff(
1891 __isl_take isl_pw_aff *pwaff);
1892 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1893 __isl_take isl_space *domain_space,
1894 __isl_take isl_aff_list *list);
1895 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1896 __isl_take isl_multi_aff *maff)
1897 __isl_give isl_map *isl_map_from_multi_aff(
1898 __isl_take isl_multi_aff *maff)
1899 __isl_give isl_set *isl_set_from_pw_multi_aff(
1900 __isl_take isl_pw_multi_aff *pma);
1901 __isl_give isl_map *isl_map_from_pw_multi_aff(
1902 __isl_take isl_pw_multi_aff *pma);
1903 __isl_give isl_set *isl_set_from_multi_pw_aff(
1904 __isl_take isl_multi_pw_aff *mpa);
1905 __isl_give isl_map *isl_map_from_multi_pw_aff(
1906 __isl_take isl_multi_pw_aff *mpa);
1907 __isl_give isl_union_map *
1908 isl_union_map_from_union_pw_multi_aff(
1909 __isl_take isl_union_pw_multi_aff *upma);
1911 The C<domain_space> argument describes the domain of the resulting
1912 basic relation. It is required because the C<list> may consist
1913 of zero affine expressions.
1915 =head2 Inspecting Sets and Relations
1917 Usually, the user should not have to care about the actual constraints
1918 of the sets and maps, but should instead apply the abstract operations
1919 explained in the following sections.
1920 Occasionally, however, it may be required to inspect the individual
1921 coefficients of the constraints. This section explains how to do so.
1922 In these cases, it may also be useful to have C<isl> compute
1923 an explicit representation of the existentially quantified variables.
1925 __isl_give isl_set *isl_set_compute_divs(
1926 __isl_take isl_set *set);
1927 __isl_give isl_map *isl_map_compute_divs(
1928 __isl_take isl_map *map);
1929 __isl_give isl_union_set *isl_union_set_compute_divs(
1930 __isl_take isl_union_set *uset);
1931 __isl_give isl_union_map *isl_union_map_compute_divs(
1932 __isl_take isl_union_map *umap);
1934 This explicit representation defines the existentially quantified
1935 variables as integer divisions of the other variables, possibly
1936 including earlier existentially quantified variables.
1937 An explicitly represented existentially quantified variable therefore
1938 has a unique value when the values of the other variables are known.
1939 If, furthermore, the same existentials, i.e., existentials
1940 with the same explicit representations, should appear in the
1941 same order in each of the disjuncts of a set or map, then the user should call
1942 either of the following functions.
1944 __isl_give isl_set *isl_set_align_divs(
1945 __isl_take isl_set *set);
1946 __isl_give isl_map *isl_map_align_divs(
1947 __isl_take isl_map *map);
1949 Alternatively, the existentially quantified variables can be removed
1950 using the following functions, which compute an overapproximation.
1952 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1953 __isl_take isl_basic_set *bset);
1954 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1955 __isl_take isl_basic_map *bmap);
1956 __isl_give isl_set *isl_set_remove_divs(
1957 __isl_take isl_set *set);
1958 __isl_give isl_map *isl_map_remove_divs(
1959 __isl_take isl_map *map);
1961 It is also possible to only remove those divs that are defined
1962 in terms of a given range of dimensions or only those for which
1963 no explicit representation is known.
1965 __isl_give isl_basic_set *
1966 isl_basic_set_remove_divs_involving_dims(
1967 __isl_take isl_basic_set *bset,
1968 enum isl_dim_type type,
1969 unsigned first, unsigned n);
1970 __isl_give isl_basic_map *
1971 isl_basic_map_remove_divs_involving_dims(
1972 __isl_take isl_basic_map *bmap,
1973 enum isl_dim_type type,
1974 unsigned first, unsigned n);
1975 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1976 __isl_take isl_set *set, enum isl_dim_type type,
1977 unsigned first, unsigned n);
1978 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1979 __isl_take isl_map *map, enum isl_dim_type type,
1980 unsigned first, unsigned n);
1982 __isl_give isl_basic_set *
1983 isl_basic_set_remove_unknown_divs(
1984 __isl_take isl_basic_set *bset);
1985 __isl_give isl_set *isl_set_remove_unknown_divs(
1986 __isl_take isl_set *set);
1987 __isl_give isl_map *isl_map_remove_unknown_divs(
1988 __isl_take isl_map *map);
1990 To iterate over all the sets or maps in a union set or map, use
1992 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1993 int (*fn)(__isl_take isl_set *set, void *user),
1995 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1996 int (*fn)(__isl_take isl_map *map, void *user),
1999 The number of sets or maps in a union set or map can be obtained
2002 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
2003 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
2005 To extract the set or map in a given space from a union, use
2007 __isl_give isl_set *isl_union_set_extract_set(
2008 __isl_keep isl_union_set *uset,
2009 __isl_take isl_space *space);
2010 __isl_give isl_map *isl_union_map_extract_map(
2011 __isl_keep isl_union_map *umap,
2012 __isl_take isl_space *space);
2014 To iterate over all the basic sets or maps in a set or map, use
2016 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
2017 int (*fn)(__isl_take isl_basic_set *bset, void *user),
2019 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
2020 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
2023 The callback function C<fn> should return 0 if successful and
2024 -1 if an error occurs. In the latter case, or if any other error
2025 occurs, the above functions will return -1.
2027 It should be noted that C<isl> does not guarantee that
2028 the basic sets or maps passed to C<fn> are disjoint.
2029 If this is required, then the user should call one of
2030 the following functions first.
2032 __isl_give isl_set *isl_set_make_disjoint(
2033 __isl_take isl_set *set);
2034 __isl_give isl_map *isl_map_make_disjoint(
2035 __isl_take isl_map *map);
2037 The number of basic sets in a set can be obtained
2038 or the number of basic maps in a map can be obtained
2041 #include <isl/set.h>
2042 int isl_set_n_basic_set(__isl_keep isl_set *set);
2044 #include <isl/map.h>
2045 int isl_map_n_basic_map(__isl_keep isl_map *map);
2047 To iterate over the constraints of a basic set or map, use
2049 #include <isl/constraint.h>
2051 int isl_basic_set_n_constraint(
2052 __isl_keep isl_basic_set *bset);
2053 int isl_basic_set_foreach_constraint(
2054 __isl_keep isl_basic_set *bset,
2055 int (*fn)(__isl_take isl_constraint *c, void *user),
2057 int isl_basic_map_n_constraint(
2058 __isl_keep isl_basic_map *bmap);
2059 int isl_basic_map_foreach_constraint(
2060 __isl_keep isl_basic_map *bmap,
2061 int (*fn)(__isl_take isl_constraint *c, void *user),
2063 __isl_null isl_constraint *isl_constraint_free(
2064 __isl_take isl_constraint *c);
2066 Again, the callback function C<fn> should return 0 if successful and
2067 -1 if an error occurs. In the latter case, or if any other error
2068 occurs, the above functions will return -1.
2069 The constraint C<c> represents either an equality or an inequality.
2070 Use the following function to find out whether a constraint
2071 represents an equality. If not, it represents an inequality.
2073 int isl_constraint_is_equality(
2074 __isl_keep isl_constraint *constraint);
2076 It is also possible to obtain a list of constraints from a basic
2079 #include <isl/constraint.h>
2080 __isl_give isl_constraint_list *
2081 isl_basic_map_get_constraint_list(
2082 __isl_keep isl_basic_map *bmap);
2083 __isl_give isl_constraint_list *
2084 isl_basic_set_get_constraint_list(
2085 __isl_keep isl_basic_set *bset);
2087 These functions require that all existentially quantified variables
2088 have an explicit representation.
2089 The returned list can be manipulated using the functions in L<"Lists">.
2091 The coefficients of the constraints can be inspected using
2092 the following functions.
2094 int isl_constraint_is_lower_bound(
2095 __isl_keep isl_constraint *constraint,
2096 enum isl_dim_type type, unsigned pos);
2097 int isl_constraint_is_upper_bound(
2098 __isl_keep isl_constraint *constraint,
2099 enum isl_dim_type type, unsigned pos);
2100 __isl_give isl_val *isl_constraint_get_constant_val(
2101 __isl_keep isl_constraint *constraint);
2102 __isl_give isl_val *isl_constraint_get_coefficient_val(
2103 __isl_keep isl_constraint *constraint,
2104 enum isl_dim_type type, int pos);
2106 The explicit representations of the existentially quantified
2107 variables can be inspected using the following function.
2108 Note that the user is only allowed to use this function
2109 if the inspected set or map is the result of a call
2110 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2111 The existentially quantified variable is equal to the floor
2112 of the returned affine expression. The affine expression
2113 itself can be inspected using the functions in
2116 __isl_give isl_aff *isl_constraint_get_div(
2117 __isl_keep isl_constraint *constraint, int pos);
2119 To obtain the constraints of a basic set or map in matrix
2120 form, use the following functions.
2122 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2123 __isl_keep isl_basic_set *bset,
2124 enum isl_dim_type c1, enum isl_dim_type c2,
2125 enum isl_dim_type c3, enum isl_dim_type c4);
2126 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2127 __isl_keep isl_basic_set *bset,
2128 enum isl_dim_type c1, enum isl_dim_type c2,
2129 enum isl_dim_type c3, enum isl_dim_type c4);
2130 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2131 __isl_keep isl_basic_map *bmap,
2132 enum isl_dim_type c1,
2133 enum isl_dim_type c2, enum isl_dim_type c3,
2134 enum isl_dim_type c4, enum isl_dim_type c5);
2135 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2136 __isl_keep isl_basic_map *bmap,
2137 enum isl_dim_type c1,
2138 enum isl_dim_type c2, enum isl_dim_type c3,
2139 enum isl_dim_type c4, enum isl_dim_type c5);
2141 The C<isl_dim_type> arguments dictate the order in which
2142 different kinds of variables appear in the resulting matrix.
2143 For set inputs, they should be a permutation of
2144 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2145 For map inputs, they should be a permutation of
2146 C<isl_dim_cst>, C<isl_dim_param>,
2147 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2151 Points are elements of a set. They can be used to construct
2152 simple sets (boxes) or they can be used to represent the
2153 individual elements of a set.
2154 The zero point (the origin) can be created using
2156 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2158 The coordinates of a point can be inspected, set and changed
2161 __isl_give isl_val *isl_point_get_coordinate_val(
2162 __isl_keep isl_point *pnt,
2163 enum isl_dim_type type, int pos);
2164 __isl_give isl_point *isl_point_set_coordinate_val(
2165 __isl_take isl_point *pnt,
2166 enum isl_dim_type type, int pos,
2167 __isl_take isl_val *v);
2169 __isl_give isl_point *isl_point_add_ui(
2170 __isl_take isl_point *pnt,
2171 enum isl_dim_type type, int pos, unsigned val);
2172 __isl_give isl_point *isl_point_sub_ui(
2173 __isl_take isl_point *pnt,
2174 enum isl_dim_type type, int pos, unsigned val);
2176 Points can be copied or freed using
2178 __isl_give isl_point *isl_point_copy(
2179 __isl_keep isl_point *pnt);
2180 void isl_point_free(__isl_take isl_point *pnt);
2182 A singleton set can be created from a point using
2184 __isl_give isl_basic_set *isl_basic_set_from_point(
2185 __isl_take isl_point *pnt);
2186 __isl_give isl_set *isl_set_from_point(
2187 __isl_take isl_point *pnt);
2189 and a box can be created from two opposite extremal points using
2191 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2192 __isl_take isl_point *pnt1,
2193 __isl_take isl_point *pnt2);
2194 __isl_give isl_set *isl_set_box_from_points(
2195 __isl_take isl_point *pnt1,
2196 __isl_take isl_point *pnt2);
2198 All elements of a B<bounded> (union) set can be enumerated using
2199 the following functions.
2201 int isl_set_foreach_point(__isl_keep isl_set *set,
2202 int (*fn)(__isl_take isl_point *pnt, void *user),
2204 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2205 int (*fn)(__isl_take isl_point *pnt, void *user),
2208 The function C<fn> is called for each integer point in
2209 C<set> with as second argument the last argument of
2210 the C<isl_set_foreach_point> call. The function C<fn>
2211 should return C<0> on success and C<-1> on failure.
2212 In the latter case, C<isl_set_foreach_point> will stop
2213 enumerating and return C<-1> as well.
2214 If the enumeration is performed successfully and to completion,
2215 then C<isl_set_foreach_point> returns C<0>.
2217 To obtain a single point of a (basic) set, use
2219 __isl_give isl_point *isl_basic_set_sample_point(
2220 __isl_take isl_basic_set *bset);
2221 __isl_give isl_point *isl_set_sample_point(
2222 __isl_take isl_set *set);
2224 If C<set> does not contain any (integer) points, then the
2225 resulting point will be ``void'', a property that can be
2228 int isl_point_is_void(__isl_keep isl_point *pnt);
2232 Besides sets and relation, C<isl> also supports various types of functions.
2233 Each of these types is derived from the value type (see L</"Values">)
2234 or from one of two primitive function types
2235 through the application of zero or more type constructors.
2236 We first describe the primitive type and then we describe
2237 the types derived from these primitive types.
2239 =head3 Primitive Functions
2241 C<isl> support two primitive function types, quasi-affine
2242 expressions and quasipolynomials.
2243 A quasi-affine expression is defined either over a parameter
2244 space or over a set and is composed of integer constants,
2245 parameters and set variables, addition, subtraction and
2246 integer division by an integer constant.
2247 For example, the quasi-affine expression
2249 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2251 maps C<x> to C<2*floor((4 n + x)/9>.
2252 A quasipolynomial is a polynomial expression in quasi-affine
2253 expression. That is, it additionally allows for multiplication.
2254 Note, though, that it is not allowed to construct an integer
2255 division of an expression involving multiplications.
2256 Here is an example of a quasipolynomial that is not
2257 quasi-affine expression
2259 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2261 Note that the external representations of quasi-affine expressions
2262 and quasipolynomials are different. Quasi-affine expressions
2263 use a notation with square brackets just like binary relations,
2264 while quasipolynomials do not. This might change at some point.
2266 If a primitive function is defined over a parameter space,
2267 then the space of the function itself is that of a set.
2268 If it is defined over a set, then the space of the function
2269 is that of a relation. In both cases, the set space (or
2270 the output space) is single-dimensional, anonymous and unstructured.
2271 To create functions with multiple dimensions or with other kinds
2272 of set or output spaces, use multiple expressions
2273 (see L</"Multiple Expressions">).
2277 =item * Quasi-affine Expressions
2279 Besides the expressions described above, a quasi-affine
2280 expression can also be set to NaN. Such expressions
2281 typically represent a failure to represent a result
2282 as a quasi-affine expression.
2284 The zero quasi affine expression or the quasi affine expression
2285 that is equal to a given value or
2286 a specified dimension on a given domain can be created using
2288 #include <isl/aff.h>
2289 __isl_give isl_aff *isl_aff_zero_on_domain(
2290 __isl_take isl_local_space *ls);
2291 __isl_give isl_aff *isl_aff_val_on_domain(
2292 __isl_take isl_local_space *ls,
2293 __isl_take isl_val *val);
2294 __isl_give isl_aff *isl_aff_var_on_domain(
2295 __isl_take isl_local_space *ls,
2296 enum isl_dim_type type, unsigned pos);
2297 __isl_give isl_aff *isl_aff_nan_on_domain(
2298 __isl_take isl_local_space *ls);
2300 Quasi affine expressions can be copied and freed using
2302 #include <isl/aff.h>
2303 __isl_give isl_aff *isl_aff_copy(
2304 __isl_keep isl_aff *aff);
2305 __isl_null isl_aff *isl_aff_free(
2306 __isl_take isl_aff *aff);
2308 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2309 using the following function. The constraint is required to have
2310 a non-zero coefficient for the specified dimension.
2312 #include <isl/constraint.h>
2313 __isl_give isl_aff *isl_constraint_get_bound(
2314 __isl_keep isl_constraint *constraint,
2315 enum isl_dim_type type, int pos);
2317 The entire affine expression of the constraint can also be extracted
2318 using the following function.
2320 #include <isl/constraint.h>
2321 __isl_give isl_aff *isl_constraint_get_aff(
2322 __isl_keep isl_constraint *constraint);
2324 Conversely, an equality constraint equating
2325 the affine expression to zero or an inequality constraint enforcing
2326 the affine expression to be non-negative, can be constructed using
2328 __isl_give isl_constraint *isl_equality_from_aff(
2329 __isl_take isl_aff *aff);
2330 __isl_give isl_constraint *isl_inequality_from_aff(
2331 __isl_take isl_aff *aff);
2333 The coefficients and the integer divisions of an affine expression
2334 can be inspected using the following functions.
2336 #include <isl/aff.h>
2337 __isl_give isl_val *isl_aff_get_constant_val(
2338 __isl_keep isl_aff *aff);
2339 __isl_give isl_val *isl_aff_get_coefficient_val(
2340 __isl_keep isl_aff *aff,
2341 enum isl_dim_type type, int pos);
2342 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2343 enum isl_dim_type type, int pos);
2344 __isl_give isl_val *isl_aff_get_denominator_val(
2345 __isl_keep isl_aff *aff);
2346 __isl_give isl_aff *isl_aff_get_div(
2347 __isl_keep isl_aff *aff, int pos);
2349 They can be modified using the following functions.
2351 #include <isl/aff.h>
2352 __isl_give isl_aff *isl_aff_set_constant_si(
2353 __isl_take isl_aff *aff, int v);
2354 __isl_give isl_aff *isl_aff_set_constant_val(
2355 __isl_take isl_aff *aff, __isl_take isl_val *v);
2356 __isl_give isl_aff *isl_aff_set_coefficient_si(
2357 __isl_take isl_aff *aff,
2358 enum isl_dim_type type, int pos, int v);
2359 __isl_give isl_aff *isl_aff_set_coefficient_val(
2360 __isl_take isl_aff *aff,
2361 enum isl_dim_type type, int pos,
2362 __isl_take isl_val *v);
2364 __isl_give isl_aff *isl_aff_add_constant_si(
2365 __isl_take isl_aff *aff, int v);
2366 __isl_give isl_aff *isl_aff_add_constant_val(
2367 __isl_take isl_aff *aff, __isl_take isl_val *v);
2368 __isl_give isl_aff *isl_aff_add_constant_num_si(
2369 __isl_take isl_aff *aff, int v);
2370 __isl_give isl_aff *isl_aff_add_coefficient_si(
2371 __isl_take isl_aff *aff,
2372 enum isl_dim_type type, int pos, int v);
2373 __isl_give isl_aff *isl_aff_add_coefficient_val(
2374 __isl_take isl_aff *aff,
2375 enum isl_dim_type type, int pos,
2376 __isl_take isl_val *v);
2378 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2379 set the I<numerator> of the constant or coefficient, while
2380 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2381 the constant or coefficient as a whole.
2382 The C<add_constant> and C<add_coefficient> functions add an integer
2383 or rational value to
2384 the possibly rational constant or coefficient.
2385 The C<add_constant_num> functions add an integer value to
2388 =item * Quasipolynomials
2390 Some simple quasipolynomials can be created using the following functions.
2392 #include <isl/polynomial.h>
2393 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2394 __isl_take isl_space *domain);
2395 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2396 __isl_take isl_space *domain);
2397 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2398 __isl_take isl_space *domain);
2399 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2400 __isl_take isl_space *domain);
2401 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2402 __isl_take isl_space *domain);
2403 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2404 __isl_take isl_space *domain,
2405 __isl_take isl_val *val);
2406 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2407 __isl_take isl_space *domain,
2408 enum isl_dim_type type, unsigned pos);
2409 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2410 __isl_take isl_aff *aff);
2412 Recall that the space in which a quasipolynomial lives is a map space
2413 with a one-dimensional range. The C<domain> argument in some of
2414 the functions above corresponds to the domain of this map space.
2416 Quasipolynomials can be copied and freed again using the following
2419 #include <isl/polynomial.h>
2420 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2421 __isl_keep isl_qpolynomial *qp);
2422 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2423 __isl_take isl_qpolynomial *qp);
2425 The constant term of a quasipolynomial can be extracted using
2427 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2428 __isl_keep isl_qpolynomial *qp);
2430 To iterate over all terms in a quasipolynomial,
2433 int isl_qpolynomial_foreach_term(
2434 __isl_keep isl_qpolynomial *qp,
2435 int (*fn)(__isl_take isl_term *term,
2436 void *user), void *user);
2438 The terms themselves can be inspected and freed using
2441 unsigned isl_term_dim(__isl_keep isl_term *term,
2442 enum isl_dim_type type);
2443 __isl_give isl_val *isl_term_get_coefficient_val(
2444 __isl_keep isl_term *term);
2445 int isl_term_get_exp(__isl_keep isl_term *term,
2446 enum isl_dim_type type, unsigned pos);
2447 __isl_give isl_aff *isl_term_get_div(
2448 __isl_keep isl_term *term, unsigned pos);
2449 void isl_term_free(__isl_take isl_term *term);
2451 Each term is a product of parameters, set variables and
2452 integer divisions. The function C<isl_term_get_exp>
2453 returns the exponent of a given dimensions in the given term.
2459 A reduction represents a maximum or a minimum of its
2461 The only reduction type defined by C<isl> is
2462 C<isl_qpolynomial_fold>.
2464 There are currently no functions to directly create such
2465 objects, but they do appear in the piecewise quasipolynomial
2466 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2468 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2470 Reductions can be copied and freed using
2471 the following functions.
2473 #include <isl/polynomial.h>
2474 __isl_give isl_qpolynomial_fold *
2475 isl_qpolynomial_fold_copy(
2476 __isl_keep isl_qpolynomial_fold *fold);
2477 void isl_qpolynomial_fold_free(
2478 __isl_take isl_qpolynomial_fold *fold);
2480 To iterate over all quasipolynomials in a reduction, use
2482 int isl_qpolynomial_fold_foreach_qpolynomial(
2483 __isl_keep isl_qpolynomial_fold *fold,
2484 int (*fn)(__isl_take isl_qpolynomial *qp,
2485 void *user), void *user);
2487 =head3 Multiple Expressions
2489 A multiple expression represents a sequence of zero or
2490 more base expressions, all defined on the same domain space.
2491 The domain space of the multiple expression is the same
2492 as that of the base expressions, but the range space
2493 can be any space. In case the base expressions have
2494 a set space, the corresponding multiple expression
2495 also has a set space.
2496 Objects of the value type do not have an associated space.
2497 The space of a multiple value is therefore always a set space.
2499 The multiple expression types defined by C<isl>
2500 are C<isl_multi_val>, C<isl_multi_aff> and C<isl_multi_pw_aff>.
2502 A multiple expression with the value zero for
2503 each output (or set) dimension can be created
2504 using the following functions.
2506 #include <isl/val.h>
2507 __isl_give isl_multi_val *isl_multi_val_zero(
2508 __isl_take isl_space *space);
2510 #include <isl/aff.h>
2511 __isl_give isl_multi_aff *isl_multi_aff_zero(
2512 __isl_take isl_space *space);
2513 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2514 __isl_take isl_space *space);
2516 An identity function can be created using the following
2517 functions. The space needs to be that of a relation
2518 with the same number of input and output dimensions.
2520 #include <isl/aff.h>
2521 __isl_give isl_multi_aff *isl_multi_aff_identity(
2522 __isl_take isl_space *space);
2523 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2524 __isl_take isl_space *space);
2526 A function that performs a projection on a universe
2527 relation or set can be created using the following functions.
2528 See also the corresponding
2529 projection operations in L</"Unary Operations">.
2531 #include <isl/aff.h>
2532 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2533 __isl_take isl_space *space);
2534 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2535 __isl_take isl_space *space);
2536 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2537 __isl_take isl_space *space,
2538 enum isl_dim_type type,
2539 unsigned first, unsigned n);
2541 A multiple expression can be created from a single
2542 base expression using the following functions.
2543 The space of the created multiple expression is the same
2544 as that of the base expression.
2546 #include <isl/aff.h>
2547 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2548 __isl_take isl_aff *aff);
2549 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2550 __isl_take isl_pw_aff *pa);
2552 A multiple expression can be created from a list
2553 of base expression in a specified space.
2554 The domain of this space needs to be the same
2555 as the domains of the base expressions in the list.
2556 If the base expressions have a set space (or no associated space),
2557 then this space also needs to be a set space.
2559 #include <isl/val.h>
2560 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2561 __isl_take isl_space *space,
2562 __isl_take isl_val_list *list);
2564 #include <isl/aff.h>
2565 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2566 __isl_take isl_space *space,
2567 __isl_take isl_aff_list *list);
2569 As a convenience, a multiple piecewise expression can
2570 also be created from a multiple expression.
2571 Each piecewise expression in the result has a single
2574 #include <isl/aff.h>
2575 __isl_give isl_multi_pw_aff *
2576 isl_multi_pw_aff_from_multi_aff(
2577 __isl_take isl_multi_aff *ma);
2579 A multiple quasi-affine expression can be created from
2580 a multiple value with a given domain space using the following
2583 #include <isl/aff.h>
2584 __isl_give isl_multi_aff *
2585 isl_multi_aff_multi_val_on_space(
2586 __isl_take isl_space *space,
2587 __isl_take isl_multi_val *mv);
2589 Multiple expressions can be copied and freed using
2590 the following functions.
2592 #include <isl/val.h>
2593 __isl_give isl_multi_val *isl_multi_val_copy(
2594 __isl_keep isl_multi_val *mv);
2595 __isl_null isl_multi_val *isl_multi_val_free(
2596 __isl_take isl_multi_val *mv);
2598 #include <isl/aff.h>
2599 __isl_give isl_multi_aff *isl_multi_aff_copy(
2600 __isl_keep isl_multi_aff *maff);
2601 __isl_null isl_multi_aff *isl_multi_aff_free(
2602 __isl_take isl_multi_aff *maff);
2603 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2604 __isl_keep isl_multi_pw_aff *mpa);
2605 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2606 __isl_take isl_multi_pw_aff *mpa);
2608 The base expression at a given position of a multiple
2609 expression can be extracted using the following functions.
2611 #include <isl/val.h>
2612 __isl_give isl_val *isl_multi_val_get_val(
2613 __isl_keep isl_multi_val *mv, int pos);
2615 #include <isl/aff.h>
2616 __isl_give isl_aff *isl_multi_aff_get_aff(
2617 __isl_keep isl_multi_aff *multi, int pos);
2618 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2619 __isl_keep isl_multi_pw_aff *mpa, int pos);
2621 It can be replaced using the following functions.
2623 #include <isl/val.h>
2624 __isl_give isl_multi_val *isl_multi_val_set_val(
2625 __isl_take isl_multi_val *mv, int pos,
2626 __isl_take isl_val *val);
2628 #include <isl/aff.h>
2629 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2630 __isl_take isl_multi_aff *multi, int pos,
2631 __isl_take isl_aff *aff);
2633 =head3 Piecewise Expressions
2635 A piecewise expression is an expression that is described
2636 using zero or more base expression defined over the same
2637 number of cells in the domain space of the base expressions.
2638 All base expressions are defined over the same
2639 domain space and the cells are disjoint.
2640 The space of a piecewise expression is the same as
2641 that of the base expressions.
2642 If the union of the cells is a strict subset of the domain
2643 space, then the value of the piecewise expression outside
2644 this union is different for types derived from quasi-affine
2645 expressions and those derived from quasipolynomials.
2646 Piecewise expressions derived from quasi-affine expressions
2647 are considered to be undefined outside the union of their cells.
2648 Piecewise expressions derived from quasipolynomials
2649 are considered to be zero outside the union of their cells.
2651 Piecewise quasipolynomials are mainly used by the C<barvinok>
2652 library for representing the number of elements in a parametric set or map.
2653 For example, the piecewise quasipolynomial
2655 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2657 represents the number of points in the map
2659 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2661 The piecewise expression types defined by C<isl>
2662 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2663 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2665 A piecewise expression with no cells can be created using
2666 the following functions.
2668 #include <isl/aff.h>
2669 __isl_give isl_pw_aff *isl_pw_aff_empty(
2670 __isl_take isl_space *space);
2671 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2672 __isl_take isl_space *space);
2674 A piecewise expression with a single universe cell can be
2675 created using the following functions.
2677 #include <isl/aff.h>
2678 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2679 __isl_take isl_aff *aff);
2680 __isl_give isl_pw_multi_aff *
2681 isl_pw_multi_aff_from_multi_aff(
2682 __isl_take isl_multi_aff *ma);
2684 #include <isl/polynomial.h>
2685 __isl_give isl_pw_qpolynomial *
2686 isl_pw_qpolynomial_from_qpolynomial(
2687 __isl_take isl_qpolynomial *qp);
2689 A piecewise expression with a single specified cell can be
2690 created using the following functions.
2692 #include <isl/aff.h>
2693 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2694 __isl_take isl_set *set, __isl_take isl_aff *aff);
2695 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2696 __isl_take isl_set *set,
2697 __isl_take isl_multi_aff *maff);
2699 #include <isl/polynomial.h>
2700 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2701 __isl_take isl_set *set,
2702 __isl_take isl_qpolynomial *qp);
2704 The following convenience functions first create a base expression and
2705 then create a piecewise expression over a universe domain.
2707 #include <isl/aff.h>
2708 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2709 __isl_take isl_local_space *ls);
2710 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2711 __isl_take isl_local_space *ls,
2712 enum isl_dim_type type, unsigned pos);
2713 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2714 __isl_take isl_local_space *ls);
2715 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2716 __isl_take isl_space *space);
2717 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2718 __isl_take isl_space *space);
2719 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_range_map(
2720 __isl_take isl_space *space);
2721 __isl_give isl_pw_multi_aff *
2722 isl_pw_multi_aff_project_out_map(
2723 __isl_take isl_space *space,
2724 enum isl_dim_type type,
2725 unsigned first, unsigned n);
2727 #include <isl/polynomial.h>
2728 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2729 __isl_take isl_space *space);
2731 The following convenience functions first create a base expression and
2732 then create a piecewise expression over a given domain.
2734 #include <isl/aff.h>
2735 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2736 __isl_take isl_set *domain,
2737 __isl_take isl_val *v);
2738 __isl_give isl_pw_multi_aff *
2739 isl_pw_multi_aff_multi_val_on_domain(
2740 __isl_take isl_set *domain,
2741 __isl_take isl_multi_val *mv);
2743 As a convenience, a piecewise multiple expression can
2744 also be created from a piecewise expression.
2745 Each multiple expression in the result is derived
2746 from the corresponding base expression.
2748 #include <isl/aff.h>
2749 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2750 __isl_take isl_pw_aff *pa);
2752 Similarly, a piecewise quasipolynomial can be
2753 created from a piecewise quasi-affine expression using
2754 the following function.
2756 #include <isl/polynomial.h>
2757 __isl_give isl_pw_qpolynomial *
2758 isl_pw_qpolynomial_from_pw_aff(
2759 __isl_take isl_pw_aff *pwaff);
2761 Piecewise expressions can be copied and freed using the following functions.
2763 #include <isl/aff.h>
2764 __isl_give isl_pw_aff *isl_pw_aff_copy(
2765 __isl_keep isl_pw_aff *pwaff);
2766 __isl_null isl_pw_aff *isl_pw_aff_free(
2767 __isl_take isl_pw_aff *pwaff);
2768 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2769 __isl_keep isl_pw_multi_aff *pma);
2770 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2771 __isl_take isl_pw_multi_aff *pma);
2773 #include <isl/polynomial.h>
2774 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2775 __isl_keep isl_pw_qpolynomial *pwqp);
2776 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2777 __isl_take isl_pw_qpolynomial *pwqp);
2778 __isl_give isl_pw_qpolynomial_fold *
2779 isl_pw_qpolynomial_fold_copy(
2780 __isl_keep isl_pw_qpolynomial_fold *pwf);
2781 __isl_null isl_pw_qpolynomial_fold *
2782 isl_pw_qpolynomial_fold_free(
2783 __isl_take isl_pw_qpolynomial_fold *pwf);
2785 To iterate over the different cells of a piecewise expression,
2786 use the following functions.
2788 #include <isl/aff.h>
2789 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2790 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2791 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2792 int (*fn)(__isl_take isl_set *set,
2793 __isl_take isl_aff *aff,
2794 void *user), void *user);
2795 int isl_pw_multi_aff_foreach_piece(
2796 __isl_keep isl_pw_multi_aff *pma,
2797 int (*fn)(__isl_take isl_set *set,
2798 __isl_take isl_multi_aff *maff,
2799 void *user), void *user);
2801 #include <isl/polynomial.h>
2802 int isl_pw_qpolynomial_foreach_piece(
2803 __isl_keep isl_pw_qpolynomial *pwqp,
2804 int (*fn)(__isl_take isl_set *set,
2805 __isl_take isl_qpolynomial *qp,
2806 void *user), void *user);
2807 int isl_pw_qpolynomial_foreach_lifted_piece(
2808 __isl_keep isl_pw_qpolynomial *pwqp,
2809 int (*fn)(__isl_take isl_set *set,
2810 __isl_take isl_qpolynomial *qp,
2811 void *user), void *user);
2812 int isl_pw_qpolynomial_fold_foreach_piece(
2813 __isl_keep isl_pw_qpolynomial_fold *pwf,
2814 int (*fn)(__isl_take isl_set *set,
2815 __isl_take isl_qpolynomial_fold *fold,
2816 void *user), void *user);
2817 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2818 __isl_keep isl_pw_qpolynomial_fold *pwf,
2819 int (*fn)(__isl_take isl_set *set,
2820 __isl_take isl_qpolynomial_fold *fold,
2821 void *user), void *user);
2823 As usual, the function C<fn> should return C<0> on success
2824 and C<-1> on failure. The difference between
2825 C<isl_pw_qpolynomial_foreach_piece> and
2826 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2827 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2828 compute unique representations for all existentially quantified
2829 variables and then turn these existentially quantified variables
2830 into extra set variables, adapting the associated quasipolynomial
2831 accordingly. This means that the C<set> passed to C<fn>
2832 will not have any existentially quantified variables, but that
2833 the dimensions of the sets may be different for different
2834 invocations of C<fn>.
2835 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2836 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2838 A piecewise expression consisting of the expressions at a given
2839 position of a piecewise multiple expression can be extracted
2840 using the following function.
2842 #include <isl/aff.h>
2843 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2844 __isl_keep isl_pw_multi_aff *pma, int pos);
2846 These expressions can be replaced using the following function.
2848 #include <isl/aff.h>
2849 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2850 __isl_take isl_pw_multi_aff *pma, unsigned pos,
2851 __isl_take isl_pw_aff *pa);
2853 Note that there is a difference between C<isl_multi_pw_aff> and
2854 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
2855 affine expressions, while the second is a piecewise sequence
2856 of affine expressions. In particular, each of the piecewise
2857 affine expressions in an C<isl_multi_pw_aff> may have a different
2858 domain, while all multiple expressions associated to a cell
2859 in an C<isl_pw_multi_aff> have the same domain.
2860 It is possible to convert between the two, but when converting
2861 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
2862 of the result is the intersection of the domains of the input.
2863 The reverse conversion is exact.
2865 #include <isl/aff.h>
2866 __isl_give isl_pw_multi_aff *
2867 isl_pw_multi_aff_from_multi_pw_aff(
2868 __isl_take isl_multi_pw_aff *mpa);
2869 __isl_give isl_multi_pw_aff *
2870 isl_multi_pw_aff_from_pw_multi_aff(
2871 __isl_take isl_pw_multi_aff *pma);
2873 =head3 Union Expressions
2875 A union expression collects base expressions defined
2876 over different domains. The space of a union expression
2877 is that of the shared parameter space.
2879 The union expression types defined by C<isl>
2880 are C<isl_union_pw_aff>, C<isl_union_pw_multi_aff>,
2881 C<isl_union_pw_qpolynomial> and C<isl_union_pw_qpolynomial_fold>.
2883 An empty union expression can be created using the following functions.
2885 #include <isl/aff.h>
2886 __isl_give isl_union_pw_aff *isl_union_pw_aff_empty(
2887 __isl_take isl_space *space);
2888 __isl_give isl_union_pw_multi_aff *
2889 isl_union_pw_multi_aff_empty(
2890 __isl_take isl_space *space);
2892 #include <isl/polynomial.h>
2893 __isl_give isl_union_pw_qpolynomial *
2894 isl_union_pw_qpolynomial_zero(
2895 __isl_take isl_space *space);
2897 A union expression containing a single base expression
2898 can be created using the following functions.
2900 #include <isl/aff.h>
2901 __isl_give isl_union_pw_aff *
2902 isl_union_pw_aff_from_pw_aff(
2903 __isl_take isl_pw_aff *pa);
2904 __isl_give isl_union_pw_multi_aff *
2905 isl_union_pw_multi_aff_from_aff(
2906 __isl_take isl_aff *aff);
2907 __isl_give isl_union_pw_multi_aff *
2908 isl_union_pw_multi_aff_from_pw_multi_aff(
2909 __isl_take isl_pw_multi_aff *pma);
2911 #include <isl/polynomial.h>
2912 __isl_give isl_union_pw_qpolynomial *
2913 isl_union_pw_qpolynomial_from_pw_qpolynomial(
2914 __isl_take isl_pw_qpolynomial *pwqp);
2916 The following functions create a base expression on each
2917 of the sets in the union set and collect the results.
2919 #include <isl/aff.h>
2920 __isl_give isl_union_pw_aff *
2921 isl_union_pw_multi_aff_get_union_pw_aff(
2922 __isl_keep isl_union_pw_multi_aff *upma, int pos);
2923 __isl_give isl_union_pw_aff *
2924 isl_union_pw_aff_val_on_domain(
2925 __isl_take isl_union_set *domain,
2926 __isl_take isl_val *v);
2927 __isl_give isl_union_pw_multi_aff *
2928 isl_union_pw_multi_aff_multi_val_on_domain(
2929 __isl_take isl_union_set *domain,
2930 __isl_take isl_multi_val *mv);
2932 An C<isl_union_pw_aff> that is equal to a (parametric) affine
2933 expression on a given domain can be created using the following
2936 #include <isl/aff.h>
2937 __isl_give isl_union_pw_aff *
2938 isl_union_pw_aff_aff_on_domain(
2939 __isl_take isl_union_set *domain,
2940 __isl_take isl_aff *aff);
2942 A base expression can be added to a union expression using
2943 the following functions.
2945 #include <isl/aff.h>
2946 __isl_give isl_union_pw_aff *
2947 isl_union_pw_aff_add_pw_aff(
2948 __isl_take isl_union_pw_aff *upa,
2949 __isl_take isl_pw_aff *pa);
2950 __isl_give isl_union_pw_multi_aff *
2951 isl_union_pw_multi_aff_add_pw_multi_aff(
2952 __isl_take isl_union_pw_multi_aff *upma,
2953 __isl_take isl_pw_multi_aff *pma);
2955 #include <isl/polynomial.h>
2956 __isl_give isl_union_pw_qpolynomial *
2957 isl_union_pw_qpolynomial_add_pw_qpolynomial(
2958 __isl_take isl_union_pw_qpolynomial *upwqp,
2959 __isl_take isl_pw_qpolynomial *pwqp);
2961 Union expressions can be copied and freed using
2962 the following functions.
2964 #include <isl/aff.h>
2965 __isl_give isl_union_pw_aff *isl_union_pw_aff_copy(
2966 __isl_keep isl_union_pw_aff *upa);
2967 __isl_null isl_union_pw_aff *isl_union_pw_aff_free(
2968 __isl_take isl_union_pw_aff *upa);
2969 __isl_give isl_union_pw_multi_aff *
2970 isl_union_pw_multi_aff_copy(
2971 __isl_keep isl_union_pw_multi_aff *upma);
2972 __isl_null isl_union_pw_multi_aff *
2973 isl_union_pw_multi_aff_free(
2974 __isl_take isl_union_pw_multi_aff *upma);
2976 #include <isl/polynomial.h>
2977 __isl_give isl_union_pw_qpolynomial *
2978 isl_union_pw_qpolynomial_copy(
2979 __isl_keep isl_union_pw_qpolynomial *upwqp);
2980 __isl_null isl_union_pw_qpolynomial *
2981 isl_union_pw_qpolynomial_free(
2982 __isl_take isl_union_pw_qpolynomial *upwqp);
2983 __isl_give isl_union_pw_qpolynomial_fold *
2984 isl_union_pw_qpolynomial_fold_copy(
2985 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2986 __isl_null isl_union_pw_qpolynomial_fold *
2987 isl_union_pw_qpolynomial_fold_free(
2988 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2990 To iterate over the base expressions in a union expression,
2991 use the following functions.
2993 #include <isl/aff.h>
2994 int isl_union_pw_aff_n_pw_multi_aff(
2995 __isl_keep isl_union_pw_aff *upa);
2996 int isl_union_pw_aff_foreach_pw_aff(
2997 __isl_keep isl_union_pw_aff *upa,
2998 int (*fn)(__isl_take isl_pw_aff *ma, void *user),
3000 int isl_union_pw_multi_aff_n_pw_multi_aff(
3001 __isl_keep isl_union_pw_multi_aff *upma);
3002 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3003 __isl_keep isl_union_pw_multi_aff *upma,
3004 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3005 void *user), void *user);
3007 #include <isl/polynomial.h>
3008 int isl_union_pw_qplynomial_n_pw_qpolynomial(
3009 __isl_keep isl_union_pw_qpolynomial *upwqp);
3010 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3011 __isl_keep isl_union_pw_qpolynomial *upwqp,
3012 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
3013 void *user), void *user);
3014 int isl_union_pw_qplynomial_fold_n_pw_qpolynomial_fold(
3015 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3016 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
3017 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
3018 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
3019 void *user), void *user);
3021 To extract the base expression in a given space from a union, use
3022 the following functions.
3024 #include <isl/aff.h>
3025 __isl_give isl_pw_aff *isl_union_pw_aff_extract_pw_aff(
3026 __isl_keep isl_union_pw_aff *upa,
3027 __isl_take isl_space *space);
3028 __isl_give isl_pw_multi_aff *
3029 isl_union_pw_multi_aff_extract_pw_multi_aff(
3030 __isl_keep isl_union_pw_multi_aff *upma,
3031 __isl_take isl_space *space);
3033 #include <isl/polynomial.h>
3034 __isl_give isl_pw_qpolynomial *
3035 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3036 __isl_keep isl_union_pw_qpolynomial *upwqp,
3037 __isl_take isl_space *space);
3039 =head2 Input and Output
3041 For set and relation,
3042 C<isl> supports its own input/output format, which is similar
3043 to the C<Omega> format, but also supports the C<PolyLib> format
3045 For other object types, typically only an C<isl> format is supported.
3047 =head3 C<isl> format
3049 The C<isl> format is similar to that of C<Omega>, but has a different
3050 syntax for describing the parameters and allows for the definition
3051 of an existentially quantified variable as the integer division
3052 of an affine expression.
3053 For example, the set of integers C<i> between C<0> and C<n>
3054 such that C<i % 10 <= 6> can be described as
3056 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
3059 A set or relation can have several disjuncts, separated
3060 by the keyword C<or>. Each disjunct is either a conjunction
3061 of constraints or a projection (C<exists>) of a conjunction
3062 of constraints. The constraints are separated by the keyword
3065 =head3 C<PolyLib> format
3067 If the represented set is a union, then the first line
3068 contains a single number representing the number of disjuncts.
3069 Otherwise, a line containing the number C<1> is optional.
3071 Each disjunct is represented by a matrix of constraints.
3072 The first line contains two numbers representing
3073 the number of rows and columns,
3074 where the number of rows is equal to the number of constraints
3075 and the number of columns is equal to two plus the number of variables.
3076 The following lines contain the actual rows of the constraint matrix.
3077 In each row, the first column indicates whether the constraint
3078 is an equality (C<0>) or inequality (C<1>). The final column
3079 corresponds to the constant term.
3081 If the set is parametric, then the coefficients of the parameters
3082 appear in the last columns before the constant column.
3083 The coefficients of any existentially quantified variables appear
3084 between those of the set variables and those of the parameters.
3086 =head3 Extended C<PolyLib> format
3088 The extended C<PolyLib> format is nearly identical to the
3089 C<PolyLib> format. The only difference is that the line
3090 containing the number of rows and columns of a constraint matrix
3091 also contains four additional numbers:
3092 the number of output dimensions, the number of input dimensions,
3093 the number of local dimensions (i.e., the number of existentially
3094 quantified variables) and the number of parameters.
3095 For sets, the number of ``output'' dimensions is equal
3096 to the number of set dimensions, while the number of ``input''
3101 Objects can be read from input using the following functions.
3103 #include <isl/val.h>
3104 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3106 __isl_give isl_multi_val *isl_multi_val_read_from_str(
3107 isl_ctx *ctx, const char *str);
3109 #include <isl/set.h>
3110 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3111 isl_ctx *ctx, FILE *input);
3112 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3113 isl_ctx *ctx, const char *str);
3114 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3116 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3119 #include <isl/map.h>
3120 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3121 isl_ctx *ctx, FILE *input);
3122 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3123 isl_ctx *ctx, const char *str);
3124 __isl_give isl_map *isl_map_read_from_file(
3125 isl_ctx *ctx, FILE *input);
3126 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3129 #include <isl/union_set.h>
3130 __isl_give isl_union_set *isl_union_set_read_from_file(
3131 isl_ctx *ctx, FILE *input);
3132 __isl_give isl_union_set *isl_union_set_read_from_str(
3133 isl_ctx *ctx, const char *str);
3135 #include <isl/union_map.h>
3136 __isl_give isl_union_map *isl_union_map_read_from_file(
3137 isl_ctx *ctx, FILE *input);
3138 __isl_give isl_union_map *isl_union_map_read_from_str(
3139 isl_ctx *ctx, const char *str);
3141 #include <isl/aff.h>
3142 __isl_give isl_aff *isl_aff_read_from_str(
3143 isl_ctx *ctx, const char *str);
3144 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3145 isl_ctx *ctx, const char *str);
3146 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3147 isl_ctx *ctx, const char *str);
3148 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3149 isl_ctx *ctx, const char *str);
3150 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3151 isl_ctx *ctx, const char *str);
3152 __isl_give isl_union_pw_multi_aff *
3153 isl_union_pw_multi_aff_read_from_str(
3154 isl_ctx *ctx, const char *str);
3156 #include <isl/polynomial.h>
3157 __isl_give isl_union_pw_qpolynomial *
3158 isl_union_pw_qpolynomial_read_from_str(
3159 isl_ctx *ctx, const char *str);
3161 For sets and relations,
3162 the input format is autodetected and may be either the C<PolyLib> format
3163 or the C<isl> format.
3167 Before anything can be printed, an C<isl_printer> needs to
3170 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3172 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3173 __isl_null isl_printer *isl_printer_free(
3174 __isl_take isl_printer *printer);
3175 __isl_give char *isl_printer_get_str(
3176 __isl_keep isl_printer *printer);
3178 The printer can be inspected using the following functions.
3180 FILE *isl_printer_get_file(
3181 __isl_keep isl_printer *printer);
3182 int isl_printer_get_output_format(
3183 __isl_keep isl_printer *p);
3185 The behavior of the printer can be modified in various ways
3187 __isl_give isl_printer *isl_printer_set_output_format(
3188 __isl_take isl_printer *p, int output_format);
3189 __isl_give isl_printer *isl_printer_set_indent(
3190 __isl_take isl_printer *p, int indent);
3191 __isl_give isl_printer *isl_printer_set_indent_prefix(
3192 __isl_take isl_printer *p, const char *prefix);
3193 __isl_give isl_printer *isl_printer_indent(
3194 __isl_take isl_printer *p, int indent);
3195 __isl_give isl_printer *isl_printer_set_prefix(
3196 __isl_take isl_printer *p, const char *prefix);
3197 __isl_give isl_printer *isl_printer_set_suffix(
3198 __isl_take isl_printer *p, const char *suffix);
3200 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3201 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3202 and defaults to C<ISL_FORMAT_ISL>.
3203 Each line in the output is prefixed by C<indent_prefix>,
3204 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3205 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3206 In the C<PolyLib> format output,
3207 the coefficients of the existentially quantified variables
3208 appear between those of the set variables and those
3210 The function C<isl_printer_indent> increases the indentation
3211 by the specified amount (which may be negative).
3213 To actually print something, use
3215 #include <isl/printer.h>
3216 __isl_give isl_printer *isl_printer_print_double(
3217 __isl_take isl_printer *p, double d);
3219 #include <isl/val.h>
3220 __isl_give isl_printer *isl_printer_print_val(
3221 __isl_take isl_printer *p, __isl_keep isl_val *v);
3223 #include <isl/set.h>
3224 __isl_give isl_printer *isl_printer_print_basic_set(
3225 __isl_take isl_printer *printer,
3226 __isl_keep isl_basic_set *bset);
3227 __isl_give isl_printer *isl_printer_print_set(
3228 __isl_take isl_printer *printer,
3229 __isl_keep isl_set *set);
3231 #include <isl/map.h>
3232 __isl_give isl_printer *isl_printer_print_basic_map(
3233 __isl_take isl_printer *printer,
3234 __isl_keep isl_basic_map *bmap);
3235 __isl_give isl_printer *isl_printer_print_map(
3236 __isl_take isl_printer *printer,
3237 __isl_keep isl_map *map);
3239 #include <isl/union_set.h>
3240 __isl_give isl_printer *isl_printer_print_union_set(
3241 __isl_take isl_printer *p,
3242 __isl_keep isl_union_set *uset);
3244 #include <isl/union_map.h>
3245 __isl_give isl_printer *isl_printer_print_union_map(
3246 __isl_take isl_printer *p,
3247 __isl_keep isl_union_map *umap);
3249 #include <isl/val.h>
3250 __isl_give isl_printer *isl_printer_print_multi_val(
3251 __isl_take isl_printer *p,
3252 __isl_keep isl_multi_val *mv);
3254 #include <isl/aff.h>
3255 __isl_give isl_printer *isl_printer_print_aff(
3256 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3257 __isl_give isl_printer *isl_printer_print_multi_aff(
3258 __isl_take isl_printer *p,
3259 __isl_keep isl_multi_aff *maff);
3260 __isl_give isl_printer *isl_printer_print_pw_aff(
3261 __isl_take isl_printer *p,
3262 __isl_keep isl_pw_aff *pwaff);
3263 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3264 __isl_take isl_printer *p,
3265 __isl_keep isl_pw_multi_aff *pma);
3266 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3267 __isl_take isl_printer *p,
3268 __isl_keep isl_multi_pw_aff *mpa);
3269 __isl_give isl_printer *isl_printer_print_union_pw_aff(
3270 __isl_take isl_printer *p,
3271 __isl_keep isl_union_pw_aff *upa);
3272 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3273 __isl_take isl_printer *p,
3274 __isl_keep isl_union_pw_multi_aff *upma);
3276 #include <isl/polynomial.h>
3277 __isl_give isl_printer *isl_printer_print_qpolynomial(
3278 __isl_take isl_printer *p,
3279 __isl_keep isl_qpolynomial *qp);
3280 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3281 __isl_take isl_printer *p,
3282 __isl_keep isl_pw_qpolynomial *pwqp);
3283 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3284 __isl_take isl_printer *p,
3285 __isl_keep isl_union_pw_qpolynomial *upwqp);
3287 __isl_give isl_printer *
3288 isl_printer_print_pw_qpolynomial_fold(
3289 __isl_take isl_printer *p,
3290 __isl_keep isl_pw_qpolynomial_fold *pwf);
3291 __isl_give isl_printer *
3292 isl_printer_print_union_pw_qpolynomial_fold(
3293 __isl_take isl_printer *p,
3294 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3296 For C<isl_printer_print_qpolynomial>,
3297 C<isl_printer_print_pw_qpolynomial> and
3298 C<isl_printer_print_pw_qpolynomial_fold>,
3299 the output format of the printer
3300 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3301 For C<isl_printer_print_union_pw_qpolynomial> and
3302 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3304 In case of printing in C<ISL_FORMAT_C>, the user may want
3305 to set the names of all dimensions first.
3307 When called on a file printer, the following function flushes
3308 the file. When called on a string printer, the buffer is cleared.
3310 __isl_give isl_printer *isl_printer_flush(
3311 __isl_take isl_printer *p);
3313 Alternatively, a string representation can be obtained
3314 directly using the following functions, which always print
3317 #include <isl/space.h>
3318 __isl_give char *isl_space_to_str(
3319 __isl_keep isl_space *space);
3321 #include <isl/val.h>
3322 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3323 __isl_give char *isl_multi_val_to_str(
3324 __isl_keep isl_multi_val *mv);
3326 #include <isl/set.h>
3327 __isl_give char *isl_set_to_str(
3328 __isl_keep isl_set *set);
3330 #include <isl/union_set.h>
3331 __isl_give char *isl_union_set_to_str(
3332 __isl_keep isl_union_set *uset);
3334 #include <isl/map.h>
3335 __isl_give char *isl_map_to_str(
3336 __isl_keep isl_map *map);
3338 #include <isl/union_map.h>
3339 __isl_give char *isl_union_map_to_str(
3340 __isl_keep isl_union_map *umap);
3342 #include <isl/aff.h>
3343 __isl_give char *isl_multi_aff_to_str(
3344 __isl_keep isl_multi_aff *aff);
3345 __isl_give char *isl_union_pw_aff_to_str(
3346 __isl_keep isl_union_pw_aff *upa);
3347 __isl_give char *isl_union_pw_multi_aff_to_str(
3348 __isl_keep isl_union_pw_multi_aff *upma);
3352 =head3 Unary Properties
3358 The following functions test whether the given set or relation
3359 contains any integer points. The ``plain'' variants do not perform
3360 any computations, but simply check if the given set or relation
3361 is already known to be empty.
3363 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3364 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3365 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3366 int isl_set_is_empty(__isl_keep isl_set *set);
3367 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3368 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3369 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3370 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3371 int isl_map_is_empty(__isl_keep isl_map *map);
3372 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3374 =item * Universality
3376 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3377 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3378 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3380 =item * Single-valuedness
3382 #include <isl/set.h>
3383 int isl_set_is_singleton(__isl_keep isl_set *set);
3385 #include <isl/map.h>
3386 int isl_basic_map_is_single_valued(
3387 __isl_keep isl_basic_map *bmap);
3388 int isl_map_plain_is_single_valued(
3389 __isl_keep isl_map *map);
3390 int isl_map_is_single_valued(__isl_keep isl_map *map);
3392 #include <isl/union_map.h>
3393 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3397 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3398 int isl_map_is_injective(__isl_keep isl_map *map);
3399 int isl_union_map_plain_is_injective(
3400 __isl_keep isl_union_map *umap);
3401 int isl_union_map_is_injective(
3402 __isl_keep isl_union_map *umap);
3406 int isl_map_is_bijective(__isl_keep isl_map *map);
3407 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3411 __isl_give isl_val *
3412 isl_basic_map_plain_get_val_if_fixed(
3413 __isl_keep isl_basic_map *bmap,
3414 enum isl_dim_type type, unsigned pos);
3415 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3416 __isl_keep isl_set *set,
3417 enum isl_dim_type type, unsigned pos);
3418 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3419 __isl_keep isl_map *map,
3420 enum isl_dim_type type, unsigned pos);
3422 If the set or relation obviously lies on a hyperplane where the given dimension
3423 has a fixed value, then return that value.
3424 Otherwise return NaN.
3428 int isl_set_dim_residue_class_val(
3429 __isl_keep isl_set *set,
3430 int pos, __isl_give isl_val **modulo,
3431 __isl_give isl_val **residue);
3433 Check if the values of the given set dimension are equal to a fixed
3434 value modulo some integer value. If so, assign the modulo to C<*modulo>
3435 and the fixed value to C<*residue>. If the given dimension attains only
3436 a single value, then assign C<0> to C<*modulo> and the fixed value to
3438 If the dimension does not attain only a single value and if no modulo
3439 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3443 To check whether the description of a set, relation or function depends
3444 on one or more given dimensions,
3445 the following functions can be used.
3447 #include <isl/constraint.h>
3448 int isl_constraint_involves_dims(
3449 __isl_keep isl_constraint *constraint,
3450 enum isl_dim_type type, unsigned first, unsigned n);
3452 #include <isl/set.h>
3453 int isl_basic_set_involves_dims(
3454 __isl_keep isl_basic_set *bset,
3455 enum isl_dim_type type, unsigned first, unsigned n);
3456 int isl_set_involves_dims(__isl_keep isl_set *set,
3457 enum isl_dim_type type, unsigned first, unsigned n);
3459 #include <isl/map.h>
3460 int isl_basic_map_involves_dims(
3461 __isl_keep isl_basic_map *bmap,
3462 enum isl_dim_type type, unsigned first, unsigned n);
3463 int isl_map_involves_dims(__isl_keep isl_map *map,
3464 enum isl_dim_type type, unsigned first, unsigned n);
3466 #include <isl/union_map.h>
3467 int isl_union_map_involves_dims(
3468 __isl_keep isl_union_map *umap,
3469 enum isl_dim_type type, unsigned first, unsigned n);
3471 #include <isl/aff.h>
3472 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3473 enum isl_dim_type type, unsigned first, unsigned n);
3474 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3475 enum isl_dim_type type, unsigned first, unsigned n);
3476 int isl_multi_aff_involves_dims(
3477 __isl_keep isl_multi_aff *ma,
3478 enum isl_dim_type type, unsigned first, unsigned n);
3479 int isl_multi_pw_aff_involves_dims(
3480 __isl_keep isl_multi_pw_aff *mpa,
3481 enum isl_dim_type type, unsigned first, unsigned n);
3483 Similarly, the following functions can be used to check whether
3484 a given dimension is involved in any lower or upper bound.
3486 #include <isl/set.h>
3487 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3488 enum isl_dim_type type, unsigned pos);
3489 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3490 enum isl_dim_type type, unsigned pos);
3492 Note that these functions return true even if there is a bound on
3493 the dimension on only some of the basic sets of C<set>.
3494 To check if they have a bound for all of the basic sets in C<set>,
3495 use the following functions instead.
3497 #include <isl/set.h>
3498 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3499 enum isl_dim_type type, unsigned pos);
3500 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3501 enum isl_dim_type type, unsigned pos);
3505 To check whether a set is a parameter domain, use this function:
3507 int isl_set_is_params(__isl_keep isl_set *set);
3508 int isl_union_set_is_params(
3509 __isl_keep isl_union_set *uset);
3513 The following functions check whether the space of the given
3514 (basic) set or relation range is a wrapped relation.
3516 #include <isl/space.h>
3517 int isl_space_is_wrapping(
3518 __isl_keep isl_space *space);
3519 int isl_space_domain_is_wrapping(
3520 __isl_keep isl_space *space);
3521 int isl_space_range_is_wrapping(
3522 __isl_keep isl_space *space);
3524 #include <isl/set.h>
3525 int isl_basic_set_is_wrapping(
3526 __isl_keep isl_basic_set *bset);
3527 int isl_set_is_wrapping(__isl_keep isl_set *set);
3529 #include <isl/map.h>
3530 int isl_map_domain_is_wrapping(
3531 __isl_keep isl_map *map);
3532 int isl_map_range_is_wrapping(
3533 __isl_keep isl_map *map);
3535 #include <isl/val.h>
3536 int isl_multi_val_range_is_wrapping(
3537 __isl_keep isl_multi_val *mv);
3539 #include <isl/aff.h>
3540 int isl_multi_aff_range_is_wrapping(
3541 __isl_keep isl_multi_aff *ma);
3542 int isl_multi_pw_aff_range_is_wrapping(
3543 __isl_keep isl_multi_pw_aff *mpa);
3545 The input to C<isl_space_is_wrapping> should
3546 be the space of a set, while that of
3547 C<isl_space_domain_is_wrapping> and
3548 C<isl_space_range_is_wrapping> should be the space of a relation.
3550 =item * Internal Product
3552 int isl_basic_map_can_zip(
3553 __isl_keep isl_basic_map *bmap);
3554 int isl_map_can_zip(__isl_keep isl_map *map);
3556 Check whether the product of domain and range of the given relation
3558 i.e., whether both domain and range are nested relations.
3562 int isl_basic_map_can_curry(
3563 __isl_keep isl_basic_map *bmap);
3564 int isl_map_can_curry(__isl_keep isl_map *map);
3566 Check whether the domain of the (basic) relation is a wrapped relation.
3568 int isl_basic_map_can_uncurry(
3569 __isl_keep isl_basic_map *bmap);
3570 int isl_map_can_uncurry(__isl_keep isl_map *map);
3572 Check whether the range of the (basic) relation is a wrapped relation.
3574 =item * Special Values
3576 #include <isl/aff.h>
3577 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3578 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3580 Check whether the given expression is a constant.
3582 #include <isl/aff.h>
3583 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3584 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3586 Check whether the given expression is equal to or involves NaN.
3588 #include <isl/aff.h>
3589 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3591 Check whether the affine expression is obviously zero.
3595 =head3 Binary Properties
3601 The following functions check whether two objects
3602 represent the same set, relation or function.
3603 The C<plain> variants only return true if the objects
3604 are obviously the same. That is, they may return false
3605 even if the objects are the same, but they will never
3606 return true if the objects are not the same.
3608 #include <isl/set.h>
3609 int isl_basic_set_plain_is_equal(
3610 __isl_keep isl_basic_set *bset1,
3611 __isl_keep isl_basic_set *bset2);
3612 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3613 __isl_keep isl_set *set2);
3614 int isl_set_is_equal(__isl_keep isl_set *set1,
3615 __isl_keep isl_set *set2);
3617 #include <isl/map.h>
3618 int isl_basic_map_is_equal(
3619 __isl_keep isl_basic_map *bmap1,
3620 __isl_keep isl_basic_map *bmap2);
3621 int isl_map_is_equal(__isl_keep isl_map *map1,
3622 __isl_keep isl_map *map2);
3623 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3624 __isl_keep isl_map *map2);
3626 #include <isl/union_set.h>
3627 int isl_union_set_is_equal(
3628 __isl_keep isl_union_set *uset1,
3629 __isl_keep isl_union_set *uset2);
3631 #include <isl/union_map.h>
3632 int isl_union_map_is_equal(
3633 __isl_keep isl_union_map *umap1,
3634 __isl_keep isl_union_map *umap2);
3636 #include <isl/aff.h>
3637 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3638 __isl_keep isl_aff *aff2);
3639 int isl_multi_aff_plain_is_equal(
3640 __isl_keep isl_multi_aff *maff1,
3641 __isl_keep isl_multi_aff *maff2);
3642 int isl_pw_aff_plain_is_equal(
3643 __isl_keep isl_pw_aff *pwaff1,
3644 __isl_keep isl_pw_aff *pwaff2);
3645 int isl_pw_multi_aff_plain_is_equal(
3646 __isl_keep isl_pw_multi_aff *pma1,
3647 __isl_keep isl_pw_multi_aff *pma2);
3648 int isl_multi_pw_aff_plain_is_equal(
3649 __isl_keep isl_multi_pw_aff *mpa1,
3650 __isl_keep isl_multi_pw_aff *mpa2);
3651 int isl_multi_pw_aff_is_equal(
3652 __isl_keep isl_multi_pw_aff *mpa1,
3653 __isl_keep isl_multi_pw_aff *mpa2);
3654 int isl_union_pw_aff_plain_is_equal(
3655 __isl_keep isl_union_pw_aff *upa1,
3656 __isl_keep isl_union_pw_aff *upa2);
3657 int isl_union_pw_multi_aff_plain_is_equal(
3658 __isl_keep isl_union_pw_multi_aff *upma1,
3659 __isl_keep isl_union_pw_multi_aff *upma2);
3661 #include <isl/polynomial.h>
3662 int isl_union_pw_qpolynomial_plain_is_equal(
3663 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3664 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3665 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3666 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3667 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3669 =item * Disjointness
3671 #include <isl/set.h>
3672 int isl_basic_set_is_disjoint(
3673 __isl_keep isl_basic_set *bset1,
3674 __isl_keep isl_basic_set *bset2);
3675 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3676 __isl_keep isl_set *set2);
3677 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3678 __isl_keep isl_set *set2);
3680 #include <isl/map.h>
3681 int isl_basic_map_is_disjoint(
3682 __isl_keep isl_basic_map *bmap1,
3683 __isl_keep isl_basic_map *bmap2);
3684 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3685 __isl_keep isl_map *map2);
3687 #include <isl/union_set.h>
3688 int isl_union_set_is_disjoint(
3689 __isl_keep isl_union_set *uset1,
3690 __isl_keep isl_union_set *uset2);
3692 #include <isl/union_map.h>
3693 int isl_union_map_is_disjoint(
3694 __isl_keep isl_union_map *umap1,
3695 __isl_keep isl_union_map *umap2);
3699 int isl_basic_set_is_subset(
3700 __isl_keep isl_basic_set *bset1,
3701 __isl_keep isl_basic_set *bset2);
3702 int isl_set_is_subset(__isl_keep isl_set *set1,
3703 __isl_keep isl_set *set2);
3704 int isl_set_is_strict_subset(
3705 __isl_keep isl_set *set1,
3706 __isl_keep isl_set *set2);
3707 int isl_union_set_is_subset(
3708 __isl_keep isl_union_set *uset1,
3709 __isl_keep isl_union_set *uset2);
3710 int isl_union_set_is_strict_subset(
3711 __isl_keep isl_union_set *uset1,
3712 __isl_keep isl_union_set *uset2);
3713 int isl_basic_map_is_subset(
3714 __isl_keep isl_basic_map *bmap1,
3715 __isl_keep isl_basic_map *bmap2);
3716 int isl_basic_map_is_strict_subset(
3717 __isl_keep isl_basic_map *bmap1,
3718 __isl_keep isl_basic_map *bmap2);
3719 int isl_map_is_subset(
3720 __isl_keep isl_map *map1,
3721 __isl_keep isl_map *map2);
3722 int isl_map_is_strict_subset(
3723 __isl_keep isl_map *map1,
3724 __isl_keep isl_map *map2);
3725 int isl_union_map_is_subset(
3726 __isl_keep isl_union_map *umap1,
3727 __isl_keep isl_union_map *umap2);
3728 int isl_union_map_is_strict_subset(
3729 __isl_keep isl_union_map *umap1,
3730 __isl_keep isl_union_map *umap2);
3732 Check whether the first argument is a (strict) subset of the
3737 Every comparison function returns a negative value if the first
3738 argument is considered smaller than the second, a positive value
3739 if the first argument is considered greater and zero if the two
3740 constraints are considered the same by the comparison criterion.
3742 #include <isl/constraint.h>
3743 int isl_constraint_plain_cmp(
3744 __isl_keep isl_constraint *c1,
3745 __isl_keep isl_constraint *c2);
3747 This function is useful for sorting C<isl_constraint>s.
3748 The order depends on the internal representation of the inputs.
3749 The order is fixed over different calls to the function (assuming
3750 the internal representation of the inputs has not changed), but may
3751 change over different versions of C<isl>.
3753 #include <isl/constraint.h>
3754 int isl_constraint_cmp_last_non_zero(
3755 __isl_keep isl_constraint *c1,
3756 __isl_keep isl_constraint *c2);
3758 This function can be used to sort constraints that live in the same
3759 local space. Constraints that involve ``earlier'' dimensions or
3760 that have a smaller coefficient for the shared latest dimension
3761 are considered smaller than other constraints.
3762 This function only defines a B<partial> order.
3764 #include <isl/set.h>
3765 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3766 __isl_keep isl_set *set2);
3768 This function is useful for sorting C<isl_set>s.
3769 The order depends on the internal representation of the inputs.
3770 The order is fixed over different calls to the function (assuming
3771 the internal representation of the inputs has not changed), but may
3772 change over different versions of C<isl>.
3774 #include <isl/aff.h>
3775 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3776 __isl_keep isl_pw_aff *pa2);
3778 The function C<isl_pw_aff_plain_cmp> can be used to sort
3779 C<isl_pw_aff>s. The order is not strictly defined.
3780 The current order sorts expressions that only involve
3781 earlier dimensions before those that involve later dimensions.
3785 =head2 Unary Operations
3791 __isl_give isl_set *isl_set_complement(
3792 __isl_take isl_set *set);
3793 __isl_give isl_map *isl_map_complement(
3794 __isl_take isl_map *map);
3798 #include <isl/space.h>
3799 __isl_give isl_space *isl_space_reverse(
3800 __isl_take isl_space *space);
3802 #include <isl/map.h>
3803 __isl_give isl_basic_map *isl_basic_map_reverse(
3804 __isl_take isl_basic_map *bmap);
3805 __isl_give isl_map *isl_map_reverse(
3806 __isl_take isl_map *map);
3808 #include <isl/union_map.h>
3809 __isl_give isl_union_map *isl_union_map_reverse(
3810 __isl_take isl_union_map *umap);
3814 #include <isl/space.h>
3815 __isl_give isl_space *isl_space_domain(
3816 __isl_take isl_space *space);
3817 __isl_give isl_space *isl_space_range(
3818 __isl_take isl_space *space);
3819 __isl_give isl_space *isl_space_params(
3820 __isl_take isl_space *space);
3822 #include <isl/local_space.h>
3823 __isl_give isl_local_space *isl_local_space_domain(
3824 __isl_take isl_local_space *ls);
3825 __isl_give isl_local_space *isl_local_space_range(
3826 __isl_take isl_local_space *ls);
3828 #include <isl/set.h>
3829 __isl_give isl_basic_set *isl_basic_set_project_out(
3830 __isl_take isl_basic_set *bset,
3831 enum isl_dim_type type, unsigned first, unsigned n);
3832 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3833 enum isl_dim_type type, unsigned first, unsigned n);
3834 __isl_give isl_basic_set *isl_basic_set_params(
3835 __isl_take isl_basic_set *bset);
3836 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
3838 #include <isl/map.h>
3839 __isl_give isl_basic_map *isl_basic_map_project_out(
3840 __isl_take isl_basic_map *bmap,
3841 enum isl_dim_type type, unsigned first, unsigned n);
3842 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3843 enum isl_dim_type type, unsigned first, unsigned n);
3844 __isl_give isl_basic_set *isl_basic_map_domain(
3845 __isl_take isl_basic_map *bmap);
3846 __isl_give isl_basic_set *isl_basic_map_range(
3847 __isl_take isl_basic_map *bmap);
3848 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
3849 __isl_give isl_set *isl_map_domain(
3850 __isl_take isl_map *bmap);
3851 __isl_give isl_set *isl_map_range(
3852 __isl_take isl_map *map);
3854 #include <isl/union_set.h>
3855 __isl_give isl_union_set *isl_union_set_project_out(
3856 __isl_take isl_union_set *uset,
3857 enum isl_dim_type type,
3858 unsigned first, unsigned n);
3859 __isl_give isl_set *isl_union_set_params(
3860 __isl_take isl_union_set *uset);
3862 The function C<isl_union_set_project_out> can only project out
3865 #include <isl/union_map.h>
3866 __isl_give isl_union_map *isl_union_map_project_out(
3867 __isl_take isl_union_map *umap,
3868 enum isl_dim_type type, unsigned first, unsigned n);
3869 __isl_give isl_set *isl_union_map_params(
3870 __isl_take isl_union_map *umap);
3871 __isl_give isl_union_set *isl_union_map_domain(
3872 __isl_take isl_union_map *umap);
3873 __isl_give isl_union_set *isl_union_map_range(
3874 __isl_take isl_union_map *umap);
3876 The function C<isl_union_map_project_out> can only project out
3879 #include <isl/aff.h>
3880 __isl_give isl_aff *isl_aff_project_domain_on_params(
3881 __isl_take isl_aff *aff);
3882 __isl_give isl_pw_multi_aff *
3883 isl_pw_multi_aff_project_domain_on_params(
3884 __isl_take isl_pw_multi_aff *pma);
3885 __isl_give isl_set *isl_pw_aff_domain(
3886 __isl_take isl_pw_aff *pwaff);
3887 __isl_give isl_set *isl_pw_multi_aff_domain(
3888 __isl_take isl_pw_multi_aff *pma);
3889 __isl_give isl_set *isl_multi_pw_aff_domain(
3890 __isl_take isl_multi_pw_aff *mpa);
3891 __isl_give isl_union_set *isl_union_pw_aff_domain(
3892 __isl_take isl_union_pw_aff *upa);
3893 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3894 __isl_take isl_union_pw_multi_aff *upma);
3895 __isl_give isl_set *isl_pw_aff_params(
3896 __isl_take isl_pw_aff *pwa);
3898 #include <isl/polynomial.h>
3899 __isl_give isl_qpolynomial *
3900 isl_qpolynomial_project_domain_on_params(
3901 __isl_take isl_qpolynomial *qp);
3902 __isl_give isl_pw_qpolynomial *
3903 isl_pw_qpolynomial_project_domain_on_params(
3904 __isl_take isl_pw_qpolynomial *pwqp);
3905 __isl_give isl_pw_qpolynomial_fold *
3906 isl_pw_qpolynomial_fold_project_domain_on_params(
3907 __isl_take isl_pw_qpolynomial_fold *pwf);
3908 __isl_give isl_set *isl_pw_qpolynomial_domain(
3909 __isl_take isl_pw_qpolynomial *pwqp);
3910 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3911 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3912 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3913 __isl_take isl_union_pw_qpolynomial *upwqp);
3915 #include <isl/space.h>
3916 __isl_give isl_space *isl_space_domain_map(
3917 __isl_take isl_space *space);
3918 __isl_give isl_space *isl_space_range_map(
3919 __isl_take isl_space *space);
3921 #include <isl/map.h>
3922 __isl_give isl_map *isl_set_wrapped_domain_map(
3923 __isl_take isl_set *set);
3924 __isl_give isl_basic_map *isl_basic_map_domain_map(
3925 __isl_take isl_basic_map *bmap);
3926 __isl_give isl_basic_map *isl_basic_map_range_map(
3927 __isl_take isl_basic_map *bmap);
3928 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
3929 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
3931 #include <isl/union_map.h>
3932 __isl_give isl_union_map *isl_union_map_domain_map(
3933 __isl_take isl_union_map *umap);
3934 __isl_give isl_union_pw_multi_aff *
3935 isl_union_map_domain_map_union_pw_multi_aff(
3936 __isl_take isl_union_map *umap);
3937 __isl_give isl_union_map *isl_union_map_range_map(
3938 __isl_take isl_union_map *umap);
3939 __isl_give isl_union_map *
3940 isl_union_set_wrapped_domain_map(
3941 __isl_take isl_union_set *uset);
3943 The functions above construct a (basic, regular or union) relation
3944 that maps (a wrapped version of) the input relation to its domain or range.
3945 C<isl_set_wrapped_domain_map> maps the input set to the domain
3946 of its wrapped relation.
3950 __isl_give isl_basic_set *isl_basic_set_eliminate(
3951 __isl_take isl_basic_set *bset,
3952 enum isl_dim_type type,
3953 unsigned first, unsigned n);
3954 __isl_give isl_set *isl_set_eliminate(
3955 __isl_take isl_set *set, enum isl_dim_type type,
3956 unsigned first, unsigned n);
3957 __isl_give isl_basic_map *isl_basic_map_eliminate(
3958 __isl_take isl_basic_map *bmap,
3959 enum isl_dim_type type,
3960 unsigned first, unsigned n);
3961 __isl_give isl_map *isl_map_eliminate(
3962 __isl_take isl_map *map, enum isl_dim_type type,
3963 unsigned first, unsigned n);
3965 Eliminate the coefficients for the given dimensions from the constraints,
3966 without removing the dimensions.
3968 =item * Constructing a set from a parameter domain
3970 A zero-dimensional space or (basic) set can be constructed
3971 on a given parameter domain using the following functions.
3973 #include <isl/space.h>
3974 __isl_give isl_space *isl_space_set_from_params(
3975 __isl_take isl_space *space);
3977 #include <isl/set.h>
3978 __isl_give isl_basic_set *isl_basic_set_from_params(
3979 __isl_take isl_basic_set *bset);
3980 __isl_give isl_set *isl_set_from_params(
3981 __isl_take isl_set *set);
3983 =item * Constructing a relation from a set
3985 Create a relation with the given set as domain or range.
3986 The range or domain of the created relation is a zero-dimensional
3987 flat anonymous space.
3989 #include <isl/space.h>
3990 __isl_give isl_space *isl_space_from_domain(
3991 __isl_take isl_space *space);
3992 __isl_give isl_space *isl_space_from_range(
3993 __isl_take isl_space *space);
3994 __isl_give isl_space *isl_space_map_from_set(
3995 __isl_take isl_space *space);
3996 __isl_give isl_space *isl_space_map_from_domain_and_range(
3997 __isl_take isl_space *domain,
3998 __isl_take isl_space *range);
4000 #include <isl/local_space.h>
4001 __isl_give isl_local_space *isl_local_space_from_domain(
4002 __isl_take isl_local_space *ls);
4004 #include <isl/map.h>
4005 __isl_give isl_map *isl_map_from_domain(
4006 __isl_take isl_set *set);
4007 __isl_give isl_map *isl_map_from_range(
4008 __isl_take isl_set *set);
4010 #include <isl/val.h>
4011 __isl_give isl_multi_val *isl_multi_val_from_range(
4012 __isl_take isl_multi_val *mv);
4014 #include <isl/aff.h>
4015 __isl_give isl_multi_aff *isl_multi_aff_from_range(
4016 __isl_take isl_multi_aff *ma);
4017 __isl_give isl_pw_aff *isl_pw_aff_from_range(
4018 __isl_take isl_pw_aff *pwa);
4019 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
4020 __isl_take isl_multi_pw_aff *mpa);
4021 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
4022 __isl_take isl_set *set);
4023 __isl_give isl_union_pw_multi_aff *
4024 isl_union_pw_multi_aff_from_domain(
4025 __isl_take isl_union_set *uset);
4029 #include <isl/set.h>
4030 __isl_give isl_basic_set *isl_basic_set_fix_si(
4031 __isl_take isl_basic_set *bset,
4032 enum isl_dim_type type, unsigned pos, int value);
4033 __isl_give isl_basic_set *isl_basic_set_fix_val(
4034 __isl_take isl_basic_set *bset,
4035 enum isl_dim_type type, unsigned pos,
4036 __isl_take isl_val *v);
4037 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
4038 enum isl_dim_type type, unsigned pos, int value);
4039 __isl_give isl_set *isl_set_fix_val(
4040 __isl_take isl_set *set,
4041 enum isl_dim_type type, unsigned pos,
4042 __isl_take isl_val *v);
4044 #include <isl/map.h>
4045 __isl_give isl_basic_map *isl_basic_map_fix_si(
4046 __isl_take isl_basic_map *bmap,
4047 enum isl_dim_type type, unsigned pos, int value);
4048 __isl_give isl_basic_map *isl_basic_map_fix_val(
4049 __isl_take isl_basic_map *bmap,
4050 enum isl_dim_type type, unsigned pos,
4051 __isl_take isl_val *v);
4052 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
4053 enum isl_dim_type type, unsigned pos, int value);
4054 __isl_give isl_map *isl_map_fix_val(
4055 __isl_take isl_map *map,
4056 enum isl_dim_type type, unsigned pos,
4057 __isl_take isl_val *v);
4059 #include <isl/aff.h>
4060 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
4061 __isl_take isl_pw_multi_aff *pma,
4062 enum isl_dim_type type, unsigned pos, int value);
4064 #include <isl/polynomial.h>
4065 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
4066 __isl_take isl_pw_qpolynomial *pwqp,
4067 enum isl_dim_type type, unsigned n,
4068 __isl_take isl_val *v);
4070 Intersect the set, relation or function domain
4071 with the hyperplane where the given
4072 dimension has the fixed given value.
4074 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
4075 __isl_take isl_basic_map *bmap,
4076 enum isl_dim_type type, unsigned pos, int value);
4077 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
4078 __isl_take isl_basic_map *bmap,
4079 enum isl_dim_type type, unsigned pos, int value);
4080 __isl_give isl_set *isl_set_lower_bound_si(
4081 __isl_take isl_set *set,
4082 enum isl_dim_type type, unsigned pos, int value);
4083 __isl_give isl_set *isl_set_lower_bound_val(
4084 __isl_take isl_set *set,
4085 enum isl_dim_type type, unsigned pos,
4086 __isl_take isl_val *value);
4087 __isl_give isl_map *isl_map_lower_bound_si(
4088 __isl_take isl_map *map,
4089 enum isl_dim_type type, unsigned pos, int value);
4090 __isl_give isl_set *isl_set_upper_bound_si(
4091 __isl_take isl_set *set,
4092 enum isl_dim_type type, unsigned pos, int value);
4093 __isl_give isl_set *isl_set_upper_bound_val(
4094 __isl_take isl_set *set,
4095 enum isl_dim_type type, unsigned pos,
4096 __isl_take isl_val *value);
4097 __isl_give isl_map *isl_map_upper_bound_si(
4098 __isl_take isl_map *map,
4099 enum isl_dim_type type, unsigned pos, int value);
4101 Intersect the set or relation with the half-space where the given
4102 dimension has a value bounded by the fixed given integer value.
4104 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
4105 enum isl_dim_type type1, int pos1,
4106 enum isl_dim_type type2, int pos2);
4107 __isl_give isl_basic_map *isl_basic_map_equate(
4108 __isl_take isl_basic_map *bmap,
4109 enum isl_dim_type type1, int pos1,
4110 enum isl_dim_type type2, int pos2);
4111 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
4112 enum isl_dim_type type1, int pos1,
4113 enum isl_dim_type type2, int pos2);
4115 Intersect the set or relation with the hyperplane where the given
4116 dimensions are equal to each other.
4118 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
4119 enum isl_dim_type type1, int pos1,
4120 enum isl_dim_type type2, int pos2);
4122 Intersect the relation with the hyperplane where the given
4123 dimensions have opposite values.
4125 __isl_give isl_map *isl_map_order_le(
4126 __isl_take isl_map *map,
4127 enum isl_dim_type type1, int pos1,
4128 enum isl_dim_type type2, int pos2);
4129 __isl_give isl_basic_map *isl_basic_map_order_ge(
4130 __isl_take isl_basic_map *bmap,
4131 enum isl_dim_type type1, int pos1,
4132 enum isl_dim_type type2, int pos2);
4133 __isl_give isl_map *isl_map_order_ge(
4134 __isl_take isl_map *map,
4135 enum isl_dim_type type1, int pos1,
4136 enum isl_dim_type type2, int pos2);
4137 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4138 enum isl_dim_type type1, int pos1,
4139 enum isl_dim_type type2, int pos2);
4140 __isl_give isl_basic_map *isl_basic_map_order_gt(
4141 __isl_take isl_basic_map *bmap,
4142 enum isl_dim_type type1, int pos1,
4143 enum isl_dim_type type2, int pos2);
4144 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4145 enum isl_dim_type type1, int pos1,
4146 enum isl_dim_type type2, int pos2);
4148 Intersect the relation with the half-space where the given
4149 dimensions satisfy the given ordering.
4153 #include <isl/aff.h>
4154 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4155 __isl_take isl_aff *aff);
4156 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4157 __isl_take isl_aff *aff);
4158 __isl_give isl_set *isl_pw_aff_pos_set(
4159 __isl_take isl_pw_aff *pa);
4160 __isl_give isl_set *isl_pw_aff_nonneg_set(
4161 __isl_take isl_pw_aff *pwaff);
4162 __isl_give isl_set *isl_pw_aff_zero_set(
4163 __isl_take isl_pw_aff *pwaff);
4164 __isl_give isl_set *isl_pw_aff_non_zero_set(
4165 __isl_take isl_pw_aff *pwaff);
4167 The function C<isl_aff_neg_basic_set> returns a basic set
4168 containing those elements in the domain space
4169 of C<aff> where C<aff> is negative.
4170 The function C<isl_pw_aff_nonneg_set> returns a set
4171 containing those elements in the domain
4172 of C<pwaff> where C<pwaff> is non-negative.
4176 __isl_give isl_map *isl_set_identity(
4177 __isl_take isl_set *set);
4178 __isl_give isl_union_map *isl_union_set_identity(
4179 __isl_take isl_union_set *uset);
4180 __isl_give isl_union_pw_multi_aff *
4181 isl_union_set_identity_union_pw_multi_aff(
4182 __isl_take isl_union_set *uset);
4184 Construct an identity relation on the given (union) set.
4186 =item * Function Extraction
4188 A piecewise quasi affine expression that is equal to 1 on a set
4189 and 0 outside the set can be created using the following function.
4191 #include <isl/aff.h>
4192 __isl_give isl_pw_aff *isl_set_indicator_function(
4193 __isl_take isl_set *set);
4195 A piecewise multiple quasi affine expression can be extracted
4196 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4197 and the C<isl_map> is single-valued.
4198 In case of a conversion from an C<isl_union_map>
4199 to an C<isl_union_pw_multi_aff>, these properties need to hold
4200 in each domain space.
4202 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4203 __isl_take isl_set *set);
4204 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4205 __isl_take isl_map *map);
4207 __isl_give isl_union_pw_multi_aff *
4208 isl_union_pw_multi_aff_from_union_set(
4209 __isl_take isl_union_set *uset);
4210 __isl_give isl_union_pw_multi_aff *
4211 isl_union_pw_multi_aff_from_union_map(
4212 __isl_take isl_union_map *umap);
4216 __isl_give isl_basic_set *isl_basic_map_deltas(
4217 __isl_take isl_basic_map *bmap);
4218 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4219 __isl_give isl_union_set *isl_union_map_deltas(
4220 __isl_take isl_union_map *umap);
4222 These functions return a (basic) set containing the differences
4223 between image elements and corresponding domain elements in the input.
4225 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4226 __isl_take isl_basic_map *bmap);
4227 __isl_give isl_map *isl_map_deltas_map(
4228 __isl_take isl_map *map);
4229 __isl_give isl_union_map *isl_union_map_deltas_map(
4230 __isl_take isl_union_map *umap);
4232 The functions above construct a (basic, regular or union) relation
4233 that maps (a wrapped version of) the input relation to its delta set.
4237 Simplify the representation of a set, relation or functions by trying
4238 to combine pairs of basic sets or relations into a single
4239 basic set or relation.
4241 #include <isl/set.h>
4242 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4244 #include <isl/map.h>
4245 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4247 #include <isl/union_set.h>
4248 __isl_give isl_union_set *isl_union_set_coalesce(
4249 __isl_take isl_union_set *uset);
4251 #include <isl/union_map.h>
4252 __isl_give isl_union_map *isl_union_map_coalesce(
4253 __isl_take isl_union_map *umap);
4255 #include <isl/aff.h>
4256 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4257 __isl_take isl_pw_aff *pwqp);
4258 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4259 __isl_take isl_pw_multi_aff *pma);
4260 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4261 __isl_take isl_multi_pw_aff *mpa);
4262 __isl_give isl_union_pw_aff *isl_union_pw_aff_coalesce(
4263 __isl_take isl_union_pw_aff *upa);
4264 __isl_give isl_union_pw_multi_aff *
4265 isl_union_pw_multi_aff_coalesce(
4266 __isl_take isl_union_pw_multi_aff *upma);
4268 #include <isl/polynomial.h>
4269 __isl_give isl_pw_qpolynomial_fold *
4270 isl_pw_qpolynomial_fold_coalesce(
4271 __isl_take isl_pw_qpolynomial_fold *pwf);
4272 __isl_give isl_union_pw_qpolynomial *
4273 isl_union_pw_qpolynomial_coalesce(
4274 __isl_take isl_union_pw_qpolynomial *upwqp);
4275 __isl_give isl_union_pw_qpolynomial_fold *
4276 isl_union_pw_qpolynomial_fold_coalesce(
4277 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4279 One of the methods for combining pairs of basic sets or relations
4280 can result in coefficients that are much larger than those that appear
4281 in the constraints of the input. By default, the coefficients are
4282 not allowed to grow larger, but this can be changed by unsetting
4283 the following option.
4285 int isl_options_set_coalesce_bounded_wrapping(
4286 isl_ctx *ctx, int val);
4287 int isl_options_get_coalesce_bounded_wrapping(
4290 =item * Detecting equalities
4292 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4293 __isl_take isl_basic_set *bset);
4294 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4295 __isl_take isl_basic_map *bmap);
4296 __isl_give isl_set *isl_set_detect_equalities(
4297 __isl_take isl_set *set);
4298 __isl_give isl_map *isl_map_detect_equalities(
4299 __isl_take isl_map *map);
4300 __isl_give isl_union_set *isl_union_set_detect_equalities(
4301 __isl_take isl_union_set *uset);
4302 __isl_give isl_union_map *isl_union_map_detect_equalities(
4303 __isl_take isl_union_map *umap);
4305 Simplify the representation of a set or relation by detecting implicit
4308 =item * Removing redundant constraints
4310 #include <isl/set.h>
4311 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4312 __isl_take isl_basic_set *bset);
4313 __isl_give isl_set *isl_set_remove_redundancies(
4314 __isl_take isl_set *set);
4316 #include <isl/union_set.h>
4317 __isl_give isl_union_set *
4318 isl_union_set_remove_redundancies(
4319 __isl_take isl_union_set *uset);
4321 #include <isl/map.h>
4322 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4323 __isl_take isl_basic_map *bmap);
4324 __isl_give isl_map *isl_map_remove_redundancies(
4325 __isl_take isl_map *map);
4327 #include <isl/union_map.h>
4328 __isl_give isl_union_map *
4329 isl_union_map_remove_redundancies(
4330 __isl_take isl_union_map *umap);
4334 __isl_give isl_basic_set *isl_set_convex_hull(
4335 __isl_take isl_set *set);
4336 __isl_give isl_basic_map *isl_map_convex_hull(
4337 __isl_take isl_map *map);
4339 If the input set or relation has any existentially quantified
4340 variables, then the result of these operations is currently undefined.
4344 #include <isl/set.h>
4345 __isl_give isl_basic_set *
4346 isl_set_unshifted_simple_hull(
4347 __isl_take isl_set *set);
4348 __isl_give isl_basic_set *isl_set_simple_hull(
4349 __isl_take isl_set *set);
4350 __isl_give isl_basic_set *
4351 isl_set_unshifted_simple_hull_from_set_list(
4352 __isl_take isl_set *set,
4353 __isl_take isl_set_list *list);
4355 #include <isl/map.h>
4356 __isl_give isl_basic_map *
4357 isl_map_unshifted_simple_hull(
4358 __isl_take isl_map *map);
4359 __isl_give isl_basic_map *isl_map_simple_hull(
4360 __isl_take isl_map *map);
4361 __isl_give isl_basic_map *
4362 isl_map_unshifted_simple_hull_from_map_list(
4363 __isl_take isl_map *map,
4364 __isl_take isl_map_list *list);
4366 #include <isl/union_map.h>
4367 __isl_give isl_union_map *isl_union_map_simple_hull(
4368 __isl_take isl_union_map *umap);
4370 These functions compute a single basic set or relation
4371 that contains the whole input set or relation.
4372 In particular, the output is described by translates
4373 of the constraints describing the basic sets or relations in the input.
4374 In case of C<isl_set_unshifted_simple_hull>, only the original
4375 constraints are used, without any translation.
4376 In case of C<isl_set_unshifted_simple_hull_from_set_list> and
4377 C<isl_map_unshifted_simple_hull_from_map_list>, the
4378 constraints are taken from the elements of the second argument.
4382 (See \autoref{s:simple hull}.)
4388 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4389 __isl_take isl_basic_set *bset);
4390 __isl_give isl_basic_set *isl_set_affine_hull(
4391 __isl_take isl_set *set);
4392 __isl_give isl_union_set *isl_union_set_affine_hull(
4393 __isl_take isl_union_set *uset);
4394 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4395 __isl_take isl_basic_map *bmap);
4396 __isl_give isl_basic_map *isl_map_affine_hull(
4397 __isl_take isl_map *map);
4398 __isl_give isl_union_map *isl_union_map_affine_hull(
4399 __isl_take isl_union_map *umap);
4401 In case of union sets and relations, the affine hull is computed
4404 =item * Polyhedral hull
4406 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4407 __isl_take isl_set *set);
4408 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4409 __isl_take isl_map *map);
4410 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4411 __isl_take isl_union_set *uset);
4412 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4413 __isl_take isl_union_map *umap);
4415 These functions compute a single basic set or relation
4416 not involving any existentially quantified variables
4417 that contains the whole input set or relation.
4418 In case of union sets and relations, the polyhedral hull is computed
4421 =item * Other approximations
4423 #include <isl/set.h>
4424 __isl_give isl_basic_set *
4425 isl_basic_set_drop_constraints_involving_dims(
4426 __isl_take isl_basic_set *bset,
4427 enum isl_dim_type type,
4428 unsigned first, unsigned n);
4429 __isl_give isl_basic_set *
4430 isl_basic_set_drop_constraints_not_involving_dims(
4431 __isl_take isl_basic_set *bset,
4432 enum isl_dim_type type,
4433 unsigned first, unsigned n);
4434 __isl_give isl_set *
4435 isl_set_drop_constraints_involving_dims(
4436 __isl_take isl_set *set,
4437 enum isl_dim_type type,
4438 unsigned first, unsigned n);
4440 #include <isl/map.h>
4441 __isl_give isl_basic_map *
4442 isl_basic_map_drop_constraints_involving_dims(
4443 __isl_take isl_basic_map *bmap,
4444 enum isl_dim_type type,
4445 unsigned first, unsigned n);
4446 __isl_give isl_map *
4447 isl_map_drop_constraints_involving_dims(
4448 __isl_take isl_map *map,
4449 enum isl_dim_type type,
4450 unsigned first, unsigned n);
4452 These functions drop any constraints (not) involving the specified dimensions.
4453 Note that the result depends on the representation of the input.
4455 #include <isl/polynomial.h>
4456 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4457 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4458 __isl_give isl_union_pw_qpolynomial *
4459 isl_union_pw_qpolynomial_to_polynomial(
4460 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4462 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4463 the polynomial will be an overapproximation. If C<sign> is negative,
4464 it will be an underapproximation. If C<sign> is zero, the approximation
4465 will lie somewhere in between.
4469 __isl_give isl_basic_set *isl_basic_set_sample(
4470 __isl_take isl_basic_set *bset);
4471 __isl_give isl_basic_set *isl_set_sample(
4472 __isl_take isl_set *set);
4473 __isl_give isl_basic_map *isl_basic_map_sample(
4474 __isl_take isl_basic_map *bmap);
4475 __isl_give isl_basic_map *isl_map_sample(
4476 __isl_take isl_map *map);
4478 If the input (basic) set or relation is non-empty, then return
4479 a singleton subset of the input. Otherwise, return an empty set.
4481 =item * Optimization
4483 #include <isl/ilp.h>
4484 __isl_give isl_val *isl_basic_set_max_val(
4485 __isl_keep isl_basic_set *bset,
4486 __isl_keep isl_aff *obj);
4487 __isl_give isl_val *isl_set_min_val(
4488 __isl_keep isl_set *set,
4489 __isl_keep isl_aff *obj);
4490 __isl_give isl_val *isl_set_max_val(
4491 __isl_keep isl_set *set,
4492 __isl_keep isl_aff *obj);
4494 Compute the minimum or maximum of the integer affine expression C<obj>
4495 over the points in C<set>, returning the result in C<opt>.
4496 The result is C<NULL> in case of an error, the optimal value in case
4497 there is one, negative infinity or infinity if the problem is unbounded and
4498 NaN if the problem is empty.
4500 =item * Parametric optimization
4502 __isl_give isl_pw_aff *isl_set_dim_min(
4503 __isl_take isl_set *set, int pos);
4504 __isl_give isl_pw_aff *isl_set_dim_max(
4505 __isl_take isl_set *set, int pos);
4506 __isl_give isl_pw_aff *isl_map_dim_max(
4507 __isl_take isl_map *map, int pos);
4509 Compute the minimum or maximum of the given set or output dimension
4510 as a function of the parameters (and input dimensions), but independently
4511 of the other set or output dimensions.
4512 For lexicographic optimization, see L<"Lexicographic Optimization">.
4516 The following functions compute either the set of (rational) coefficient
4517 values of valid constraints for the given set or the set of (rational)
4518 values satisfying the constraints with coefficients from the given set.
4519 Internally, these two sets of functions perform essentially the
4520 same operations, except that the set of coefficients is assumed to
4521 be a cone, while the set of values may be any polyhedron.
4522 The current implementation is based on the Farkas lemma and
4523 Fourier-Motzkin elimination, but this may change or be made optional
4524 in future. In particular, future implementations may use different
4525 dualization algorithms or skip the elimination step.
4527 __isl_give isl_basic_set *isl_basic_set_coefficients(
4528 __isl_take isl_basic_set *bset);
4529 __isl_give isl_basic_set *isl_set_coefficients(
4530 __isl_take isl_set *set);
4531 __isl_give isl_union_set *isl_union_set_coefficients(
4532 __isl_take isl_union_set *bset);
4533 __isl_give isl_basic_set *isl_basic_set_solutions(
4534 __isl_take isl_basic_set *bset);
4535 __isl_give isl_basic_set *isl_set_solutions(
4536 __isl_take isl_set *set);
4537 __isl_give isl_union_set *isl_union_set_solutions(
4538 __isl_take isl_union_set *bset);
4542 __isl_give isl_map *isl_map_fixed_power_val(
4543 __isl_take isl_map *map,
4544 __isl_take isl_val *exp);
4545 __isl_give isl_union_map *
4546 isl_union_map_fixed_power_val(
4547 __isl_take isl_union_map *umap,
4548 __isl_take isl_val *exp);
4550 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4551 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4552 of C<map> is computed.
4554 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4556 __isl_give isl_union_map *isl_union_map_power(
4557 __isl_take isl_union_map *umap, int *exact);
4559 Compute a parametric representation for all positive powers I<k> of C<map>.
4560 The result maps I<k> to a nested relation corresponding to the
4561 I<k>th power of C<map>.
4562 The result may be an overapproximation. If the result is known to be exact,
4563 then C<*exact> is set to C<1>.
4565 =item * Transitive closure
4567 __isl_give isl_map *isl_map_transitive_closure(
4568 __isl_take isl_map *map, int *exact);
4569 __isl_give isl_union_map *isl_union_map_transitive_closure(
4570 __isl_take isl_union_map *umap, int *exact);
4572 Compute the transitive closure of C<map>.
4573 The result may be an overapproximation. If the result is known to be exact,
4574 then C<*exact> is set to C<1>.
4576 =item * Reaching path lengths
4578 __isl_give isl_map *isl_map_reaching_path_lengths(
4579 __isl_take isl_map *map, int *exact);
4581 Compute a relation that maps each element in the range of C<map>
4582 to the lengths of all paths composed of edges in C<map> that
4583 end up in the given element.
4584 The result may be an overapproximation. If the result is known to be exact,
4585 then C<*exact> is set to C<1>.
4586 To compute the I<maximal> path length, the resulting relation
4587 should be postprocessed by C<isl_map_lexmax>.
4588 In particular, if the input relation is a dependence relation
4589 (mapping sources to sinks), then the maximal path length corresponds
4590 to the free schedule.
4591 Note, however, that C<isl_map_lexmax> expects the maximum to be
4592 finite, so if the path lengths are unbounded (possibly due to
4593 the overapproximation), then you will get an error message.
4597 #include <isl/space.h>
4598 __isl_give isl_space *isl_space_wrap(
4599 __isl_take isl_space *space);
4600 __isl_give isl_space *isl_space_unwrap(
4601 __isl_take isl_space *space);
4603 #include <isl/local_space.h>
4604 __isl_give isl_local_space *isl_local_space_wrap(
4605 __isl_take isl_local_space *ls);
4607 #include <isl/set.h>
4608 __isl_give isl_basic_map *isl_basic_set_unwrap(
4609 __isl_take isl_basic_set *bset);
4610 __isl_give isl_map *isl_set_unwrap(
4611 __isl_take isl_set *set);
4613 #include <isl/map.h>
4614 __isl_give isl_basic_set *isl_basic_map_wrap(
4615 __isl_take isl_basic_map *bmap);
4616 __isl_give isl_set *isl_map_wrap(
4617 __isl_take isl_map *map);
4619 #include <isl/union_set.h>
4620 __isl_give isl_union_map *isl_union_set_unwrap(
4621 __isl_take isl_union_set *uset);
4623 #include <isl/union_map.h>
4624 __isl_give isl_union_set *isl_union_map_wrap(
4625 __isl_take isl_union_map *umap);
4627 The input to C<isl_space_unwrap> should
4628 be the space of a set, while that of
4629 C<isl_space_wrap> should be the space of a relation.
4630 Conversely, the output of C<isl_space_unwrap> is the space
4631 of a relation, while that of C<isl_space_wrap> is the space of a set.
4635 Remove any internal structure of domain (and range) of the given
4636 set or relation. If there is any such internal structure in the input,
4637 then the name of the space is also removed.
4639 #include <isl/local_space.h>
4640 __isl_give isl_local_space *
4641 isl_local_space_flatten_domain(
4642 __isl_take isl_local_space *ls);
4643 __isl_give isl_local_space *
4644 isl_local_space_flatten_range(
4645 __isl_take isl_local_space *ls);
4647 #include <isl/set.h>
4648 __isl_give isl_basic_set *isl_basic_set_flatten(
4649 __isl_take isl_basic_set *bset);
4650 __isl_give isl_set *isl_set_flatten(
4651 __isl_take isl_set *set);
4653 #include <isl/map.h>
4654 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4655 __isl_take isl_basic_map *bmap);
4656 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4657 __isl_take isl_basic_map *bmap);
4658 __isl_give isl_map *isl_map_flatten_range(
4659 __isl_take isl_map *map);
4660 __isl_give isl_map *isl_map_flatten_domain(
4661 __isl_take isl_map *map);
4662 __isl_give isl_basic_map *isl_basic_map_flatten(
4663 __isl_take isl_basic_map *bmap);
4664 __isl_give isl_map *isl_map_flatten(
4665 __isl_take isl_map *map);
4667 #include <isl/val.h>
4668 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4669 __isl_take isl_multi_val *mv);
4671 #include <isl/aff.h>
4672 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4673 __isl_take isl_multi_aff *ma);
4674 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4675 __isl_take isl_multi_aff *ma);
4676 __isl_give isl_multi_pw_aff *
4677 isl_multi_pw_aff_flatten_range(
4678 __isl_take isl_multi_pw_aff *mpa);
4680 #include <isl/map.h>
4681 __isl_give isl_map *isl_set_flatten_map(
4682 __isl_take isl_set *set);
4684 The function above constructs a relation
4685 that maps the input set to a flattened version of the set.
4689 Lift the input set to a space with extra dimensions corresponding
4690 to the existentially quantified variables in the input.
4691 In particular, the result lives in a wrapped map where the domain
4692 is the original space and the range corresponds to the original
4693 existentially quantified variables.
4695 #include <isl/set.h>
4696 __isl_give isl_basic_set *isl_basic_set_lift(
4697 __isl_take isl_basic_set *bset);
4698 __isl_give isl_set *isl_set_lift(
4699 __isl_take isl_set *set);
4700 __isl_give isl_union_set *isl_union_set_lift(
4701 __isl_take isl_union_set *uset);
4703 Given a local space that contains the existentially quantified
4704 variables of a set, a basic relation that, when applied to
4705 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4706 can be constructed using the following function.
4708 #include <isl/local_space.h>
4709 __isl_give isl_basic_map *isl_local_space_lifting(
4710 __isl_take isl_local_space *ls);
4712 #include <isl/aff.h>
4713 __isl_give isl_multi_aff *isl_multi_aff_lift(
4714 __isl_take isl_multi_aff *maff,
4715 __isl_give isl_local_space **ls);
4717 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4718 then it is assigned the local space that lies at the basis of
4719 the lifting applied.
4721 =item * Internal Product
4723 #include <isl/space.h>
4724 __isl_give isl_space *isl_space_zip(
4725 __isl_take isl_space *space);
4727 #include <isl/map.h>
4728 __isl_give isl_basic_map *isl_basic_map_zip(
4729 __isl_take isl_basic_map *bmap);
4730 __isl_give isl_map *isl_map_zip(
4731 __isl_take isl_map *map);
4733 #include <isl/union_map.h>
4734 __isl_give isl_union_map *isl_union_map_zip(
4735 __isl_take isl_union_map *umap);
4737 Given a relation with nested relations for domain and range,
4738 interchange the range of the domain with the domain of the range.
4742 #include <isl/space.h>
4743 __isl_give isl_space *isl_space_curry(
4744 __isl_take isl_space *space);
4745 __isl_give isl_space *isl_space_uncurry(
4746 __isl_take isl_space *space);
4748 #include <isl/map.h>
4749 __isl_give isl_basic_map *isl_basic_map_curry(
4750 __isl_take isl_basic_map *bmap);
4751 __isl_give isl_basic_map *isl_basic_map_uncurry(
4752 __isl_take isl_basic_map *bmap);
4753 __isl_give isl_map *isl_map_curry(
4754 __isl_take isl_map *map);
4755 __isl_give isl_map *isl_map_uncurry(
4756 __isl_take isl_map *map);
4758 #include <isl/union_map.h>
4759 __isl_give isl_union_map *isl_union_map_curry(
4760 __isl_take isl_union_map *umap);
4761 __isl_give isl_union_map *isl_union_map_uncurry(
4762 __isl_take isl_union_map *umap);
4764 Given a relation with a nested relation for domain,
4765 the C<curry> functions
4766 move the range of the nested relation out of the domain
4767 and use it as the domain of a nested relation in the range,
4768 with the original range as range of this nested relation.
4769 The C<uncurry> functions perform the inverse operation.
4771 =item * Aligning parameters
4773 Change the order of the parameters of the given set, relation
4775 such that the first parameters match those of C<model>.
4776 This may involve the introduction of extra parameters.
4777 All parameters need to be named.
4779 #include <isl/space.h>
4780 __isl_give isl_space *isl_space_align_params(
4781 __isl_take isl_space *space1,
4782 __isl_take isl_space *space2)
4784 #include <isl/set.h>
4785 __isl_give isl_basic_set *isl_basic_set_align_params(
4786 __isl_take isl_basic_set *bset,
4787 __isl_take isl_space *model);
4788 __isl_give isl_set *isl_set_align_params(
4789 __isl_take isl_set *set,
4790 __isl_take isl_space *model);
4792 #include <isl/map.h>
4793 __isl_give isl_basic_map *isl_basic_map_align_params(
4794 __isl_take isl_basic_map *bmap,
4795 __isl_take isl_space *model);
4796 __isl_give isl_map *isl_map_align_params(
4797 __isl_take isl_map *map,
4798 __isl_take isl_space *model);
4800 #include <isl/val.h>
4801 __isl_give isl_multi_val *isl_multi_val_align_params(
4802 __isl_take isl_multi_val *mv,
4803 __isl_take isl_space *model);
4805 #include <isl/aff.h>
4806 __isl_give isl_aff *isl_aff_align_params(
4807 __isl_take isl_aff *aff,
4808 __isl_take isl_space *model);
4809 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4810 __isl_take isl_multi_aff *multi,
4811 __isl_take isl_space *model);
4812 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4813 __isl_take isl_pw_aff *pwaff,
4814 __isl_take isl_space *model);
4815 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4816 __isl_take isl_pw_multi_aff *pma,
4817 __isl_take isl_space *model);
4818 __isl_give isl_union_pw_aff *
4819 isl_union_pw_aff_align_params(
4820 __isl_take isl_union_pw_aff *upa,
4821 __isl_take isl_space *model);
4822 __isl_give isl_union_pw_multi_aff *
4823 isl_union_pw_multi_aff_align_params(
4824 __isl_take isl_union_pw_multi_aff *upma,
4825 __isl_take isl_space *model);
4827 #include <isl/polynomial.h>
4828 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4829 __isl_take isl_qpolynomial *qp,
4830 __isl_take isl_space *model);
4832 =item * Unary Arithmethic Operations
4834 #include <isl/val.h>
4835 __isl_give isl_multi_val *isl_multi_val_neg(
4836 __isl_take isl_multi_val *mv);
4838 #include <isl/aff.h>
4839 __isl_give isl_aff *isl_aff_neg(
4840 __isl_take isl_aff *aff);
4841 __isl_give isl_multi_aff *isl_multi_aff_neg(
4842 __isl_take isl_multi_aff *ma);
4843 __isl_give isl_pw_aff *isl_pw_aff_neg(
4844 __isl_take isl_pw_aff *pwaff);
4845 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_neg(
4846 __isl_take isl_pw_multi_aff *pma);
4847 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_neg(
4848 __isl_take isl_multi_pw_aff *mpa);
4849 __isl_give isl_union_pw_aff *isl_union_pw_aff_neg(
4850 __isl_take isl_union_pw_aff *upa);
4851 __isl_give isl_union_pw_multi_aff *
4852 isl_union_pw_multi_aff_neg(
4853 __isl_take isl_union_pw_multi_aff *upma);
4854 __isl_give isl_aff *isl_aff_ceil(
4855 __isl_take isl_aff *aff);
4856 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4857 __isl_take isl_pw_aff *pwaff);
4858 __isl_give isl_aff *isl_aff_floor(
4859 __isl_take isl_aff *aff);
4860 __isl_give isl_multi_aff *isl_multi_aff_floor(
4861 __isl_take isl_multi_aff *ma);
4862 __isl_give isl_pw_aff *isl_pw_aff_floor(
4863 __isl_take isl_pw_aff *pwaff);
4864 __isl_give isl_union_pw_aff *isl_union_pw_aff_floor(
4865 __isl_take isl_union_pw_aff *upa);
4867 #include <isl/aff.h>
4868 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4869 __isl_take isl_pw_aff_list *list);
4870 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4871 __isl_take isl_pw_aff_list *list);
4873 #include <isl/polynomial.h>
4874 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4875 __isl_take isl_qpolynomial *qp);
4876 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4877 __isl_take isl_pw_qpolynomial *pwqp);
4878 __isl_give isl_union_pw_qpolynomial *
4879 isl_union_pw_qpolynomial_neg(
4880 __isl_take isl_union_pw_qpolynomial *upwqp);
4881 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4882 __isl_take isl_qpolynomial *qp,
4884 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4885 __isl_take isl_pw_qpolynomial *pwqp,
4890 The following functions evaluate a function in a point.
4892 #include <isl/polynomial.h>
4893 __isl_give isl_val *isl_pw_qpolynomial_eval(
4894 __isl_take isl_pw_qpolynomial *pwqp,
4895 __isl_take isl_point *pnt);
4896 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
4897 __isl_take isl_pw_qpolynomial_fold *pwf,
4898 __isl_take isl_point *pnt);
4899 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4900 __isl_take isl_union_pw_qpolynomial *upwqp,
4901 __isl_take isl_point *pnt);
4902 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
4903 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4904 __isl_take isl_point *pnt);
4906 =item * Dimension manipulation
4908 It is usually not advisable to directly change the (input or output)
4909 space of a set or a relation as this removes the name and the internal
4910 structure of the space. However, the functions below can be useful
4911 to add new parameters, assuming
4912 C<isl_set_align_params> and C<isl_map_align_params>
4915 #include <isl/space.h>
4916 __isl_give isl_space *isl_space_add_dims(
4917 __isl_take isl_space *space,
4918 enum isl_dim_type type, unsigned n);
4919 __isl_give isl_space *isl_space_insert_dims(
4920 __isl_take isl_space *space,
4921 enum isl_dim_type type, unsigned pos, unsigned n);
4922 __isl_give isl_space *isl_space_drop_dims(
4923 __isl_take isl_space *space,
4924 enum isl_dim_type type, unsigned first, unsigned n);
4925 __isl_give isl_space *isl_space_move_dims(
4926 __isl_take isl_space *space,
4927 enum isl_dim_type dst_type, unsigned dst_pos,
4928 enum isl_dim_type src_type, unsigned src_pos,
4931 #include <isl/local_space.h>
4932 __isl_give isl_local_space *isl_local_space_add_dims(
4933 __isl_take isl_local_space *ls,
4934 enum isl_dim_type type, unsigned n);
4935 __isl_give isl_local_space *isl_local_space_insert_dims(
4936 __isl_take isl_local_space *ls,
4937 enum isl_dim_type type, unsigned first, unsigned n);
4938 __isl_give isl_local_space *isl_local_space_drop_dims(
4939 __isl_take isl_local_space *ls,
4940 enum isl_dim_type type, unsigned first, unsigned n);
4942 #include <isl/set.h>
4943 __isl_give isl_basic_set *isl_basic_set_add_dims(
4944 __isl_take isl_basic_set *bset,
4945 enum isl_dim_type type, unsigned n);
4946 __isl_give isl_set *isl_set_add_dims(
4947 __isl_take isl_set *set,
4948 enum isl_dim_type type, unsigned n);
4949 __isl_give isl_basic_set *isl_basic_set_insert_dims(
4950 __isl_take isl_basic_set *bset,
4951 enum isl_dim_type type, unsigned pos,
4953 __isl_give isl_set *isl_set_insert_dims(
4954 __isl_take isl_set *set,
4955 enum isl_dim_type type, unsigned pos, unsigned n);
4956 __isl_give isl_basic_set *isl_basic_set_move_dims(
4957 __isl_take isl_basic_set *bset,
4958 enum isl_dim_type dst_type, unsigned dst_pos,
4959 enum isl_dim_type src_type, unsigned src_pos,
4961 __isl_give isl_set *isl_set_move_dims(
4962 __isl_take isl_set *set,
4963 enum isl_dim_type dst_type, unsigned dst_pos,
4964 enum isl_dim_type src_type, unsigned src_pos,
4967 #include <isl/map.h>
4968 __isl_give isl_map *isl_map_add_dims(
4969 __isl_take isl_map *map,
4970 enum isl_dim_type type, unsigned n);
4971 __isl_give isl_basic_map *isl_basic_map_insert_dims(
4972 __isl_take isl_basic_map *bmap,
4973 enum isl_dim_type type, unsigned pos,
4975 __isl_give isl_map *isl_map_insert_dims(
4976 __isl_take isl_map *map,
4977 enum isl_dim_type type, unsigned pos, unsigned n);
4978 __isl_give isl_basic_map *isl_basic_map_move_dims(
4979 __isl_take isl_basic_map *bmap,
4980 enum isl_dim_type dst_type, unsigned dst_pos,
4981 enum isl_dim_type src_type, unsigned src_pos,
4983 __isl_give isl_map *isl_map_move_dims(
4984 __isl_take isl_map *map,
4985 enum isl_dim_type dst_type, unsigned dst_pos,
4986 enum isl_dim_type src_type, unsigned src_pos,
4989 #include <isl/val.h>
4990 __isl_give isl_multi_val *isl_multi_val_insert_dims(
4991 __isl_take isl_multi_val *mv,
4992 enum isl_dim_type type, unsigned first, unsigned n);
4993 __isl_give isl_multi_val *isl_multi_val_add_dims(
4994 __isl_take isl_multi_val *mv,
4995 enum isl_dim_type type, unsigned n);
4996 __isl_give isl_multi_val *isl_multi_val_drop_dims(
4997 __isl_take isl_multi_val *mv,
4998 enum isl_dim_type type, unsigned first, unsigned n);
5000 #include <isl/aff.h>
5001 __isl_give isl_aff *isl_aff_insert_dims(
5002 __isl_take isl_aff *aff,
5003 enum isl_dim_type type, unsigned first, unsigned n);
5004 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
5005 __isl_take isl_multi_aff *ma,
5006 enum isl_dim_type type, unsigned first, unsigned n);
5007 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
5008 __isl_take isl_pw_aff *pwaff,
5009 enum isl_dim_type type, unsigned first, unsigned n);
5010 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
5011 __isl_take isl_multi_pw_aff *mpa,
5012 enum isl_dim_type type, unsigned first, unsigned n);
5013 __isl_give isl_aff *isl_aff_add_dims(
5014 __isl_take isl_aff *aff,
5015 enum isl_dim_type type, unsigned n);
5016 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
5017 __isl_take isl_multi_aff *ma,
5018 enum isl_dim_type type, unsigned n);
5019 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
5020 __isl_take isl_pw_aff *pwaff,
5021 enum isl_dim_type type, unsigned n);
5022 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
5023 __isl_take isl_multi_pw_aff *mpa,
5024 enum isl_dim_type type, unsigned n);
5025 __isl_give isl_aff *isl_aff_drop_dims(
5026 __isl_take isl_aff *aff,
5027 enum isl_dim_type type, unsigned first, unsigned n);
5028 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
5029 __isl_take isl_multi_aff *maff,
5030 enum isl_dim_type type, unsigned first, unsigned n);
5031 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
5032 __isl_take isl_pw_aff *pwaff,
5033 enum isl_dim_type type, unsigned first, unsigned n);
5034 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
5035 __isl_take isl_pw_multi_aff *pma,
5036 enum isl_dim_type type, unsigned first, unsigned n);
5037 __isl_give isl_union_pw_aff *isl_union_pw_aff_drop_dims(
5038 __isl_take isl_union_pw_aff *upa,
5039 enum isl_dim_type type, unsigned first, unsigned n);
5040 __isl_give isl_union_pw_multi_aff *
5041 isl_union_pw_multi_aff_drop_dims(
5042 __isl_take isl_union_pw_multi_aff *upma,
5043 enum isl_dim_type type,
5044 unsigned first, unsigned n);
5045 __isl_give isl_aff *isl_aff_move_dims(
5046 __isl_take isl_aff *aff,
5047 enum isl_dim_type dst_type, unsigned dst_pos,
5048 enum isl_dim_type src_type, unsigned src_pos,
5050 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
5051 __isl_take isl_multi_aff *ma,
5052 enum isl_dim_type dst_type, unsigned dst_pos,
5053 enum isl_dim_type src_type, unsigned src_pos,
5055 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
5056 __isl_take isl_pw_aff *pa,
5057 enum isl_dim_type dst_type, unsigned dst_pos,
5058 enum isl_dim_type src_type, unsigned src_pos,
5060 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
5061 __isl_take isl_multi_pw_aff *pma,
5062 enum isl_dim_type dst_type, unsigned dst_pos,
5063 enum isl_dim_type src_type, unsigned src_pos,
5066 #include <isl/polynomial.h>
5067 __isl_give isl_union_pw_qpolynomial *
5068 isl_union_pw_qpolynomial_drop_dims(
5069 __isl_take isl_union_pw_qpolynomial *upwqp,
5070 enum isl_dim_type type,
5071 unsigned first, unsigned n);
5072 __isl_give isl_union_pw_qpolynomial_fold *
5073 isl_union_pw_qpolynomial_fold_drop_dims(
5074 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5075 enum isl_dim_type type,
5076 unsigned first, unsigned n);
5078 The operations on union expressions can only manipulate parameters.
5082 =head2 Binary Operations
5084 The two arguments of a binary operation not only need to live
5085 in the same C<isl_ctx>, they currently also need to have
5086 the same (number of) parameters.
5088 =head3 Basic Operations
5092 =item * Intersection
5094 #include <isl/local_space.h>
5095 __isl_give isl_local_space *isl_local_space_intersect(
5096 __isl_take isl_local_space *ls1,
5097 __isl_take isl_local_space *ls2);
5099 #include <isl/set.h>
5100 __isl_give isl_basic_set *isl_basic_set_intersect_params(
5101 __isl_take isl_basic_set *bset1,
5102 __isl_take isl_basic_set *bset2);
5103 __isl_give isl_basic_set *isl_basic_set_intersect(
5104 __isl_take isl_basic_set *bset1,
5105 __isl_take isl_basic_set *bset2);
5106 __isl_give isl_basic_set *isl_basic_set_list_intersect(
5107 __isl_take struct isl_basic_set_list *list);
5108 __isl_give isl_set *isl_set_intersect_params(
5109 __isl_take isl_set *set,
5110 __isl_take isl_set *params);
5111 __isl_give isl_set *isl_set_intersect(
5112 __isl_take isl_set *set1,
5113 __isl_take isl_set *set2);
5115 #include <isl/map.h>
5116 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
5117 __isl_take isl_basic_map *bmap,
5118 __isl_take isl_basic_set *bset);
5119 __isl_give isl_basic_map *isl_basic_map_intersect_range(
5120 __isl_take isl_basic_map *bmap,
5121 __isl_take isl_basic_set *bset);
5122 __isl_give isl_basic_map *isl_basic_map_intersect(
5123 __isl_take isl_basic_map *bmap1,
5124 __isl_take isl_basic_map *bmap2);
5125 __isl_give isl_basic_map *isl_basic_map_list_intersect(
5126 __isl_take isl_basic_map_list *list);
5127 __isl_give isl_map *isl_map_intersect_params(
5128 __isl_take isl_map *map,
5129 __isl_take isl_set *params);
5130 __isl_give isl_map *isl_map_intersect_domain(
5131 __isl_take isl_map *map,
5132 __isl_take isl_set *set);
5133 __isl_give isl_map *isl_map_intersect_range(
5134 __isl_take isl_map *map,
5135 __isl_take isl_set *set);
5136 __isl_give isl_map *isl_map_intersect(
5137 __isl_take isl_map *map1,
5138 __isl_take isl_map *map2);
5140 #include <isl/union_set.h>
5141 __isl_give isl_union_set *isl_union_set_intersect_params(
5142 __isl_take isl_union_set *uset,
5143 __isl_take isl_set *set);
5144 __isl_give isl_union_set *isl_union_set_intersect(
5145 __isl_take isl_union_set *uset1,
5146 __isl_take isl_union_set *uset2);
5148 #include <isl/union_map.h>
5149 __isl_give isl_union_map *isl_union_map_intersect_params(
5150 __isl_take isl_union_map *umap,
5151 __isl_take isl_set *set);
5152 __isl_give isl_union_map *isl_union_map_intersect_domain(
5153 __isl_take isl_union_map *umap,
5154 __isl_take isl_union_set *uset);
5155 __isl_give isl_union_map *isl_union_map_intersect_range(
5156 __isl_take isl_union_map *umap,
5157 __isl_take isl_union_set *uset);
5158 __isl_give isl_union_map *isl_union_map_intersect(
5159 __isl_take isl_union_map *umap1,
5160 __isl_take isl_union_map *umap2);
5162 #include <isl/aff.h>
5163 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
5164 __isl_take isl_pw_aff *pa,
5165 __isl_take isl_set *set);
5166 __isl_give isl_multi_pw_aff *
5167 isl_multi_pw_aff_intersect_domain(
5168 __isl_take isl_multi_pw_aff *mpa,
5169 __isl_take isl_set *domain);
5170 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
5171 __isl_take isl_pw_multi_aff *pma,
5172 __isl_take isl_set *set);
5173 __isl_give isl_union_pw_aff *isl_union_pw_aff_intersect_domain(
5174 __isl_take isl_union_pw_aff *upa,
5175 __isl_take isl_union_set *uset);
5176 __isl_give isl_union_pw_multi_aff *
5177 isl_union_pw_multi_aff_intersect_domain(
5178 __isl_take isl_union_pw_multi_aff *upma,
5179 __isl_take isl_union_set *uset);
5180 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
5181 __isl_take isl_pw_aff *pa,
5182 __isl_take isl_set *set);
5183 __isl_give isl_multi_pw_aff *
5184 isl_multi_pw_aff_intersect_params(
5185 __isl_take isl_multi_pw_aff *mpa,
5186 __isl_take isl_set *set);
5187 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
5188 __isl_take isl_pw_multi_aff *pma,
5189 __isl_take isl_set *set);
5190 __isl_give isl_union_pw_aff *
5191 isl_union_pw_aff_intersect_params(
5192 __isl_take isl_union_pw_aff *upa,
5193 __isl_give isl_union_pw_multi_aff *
5194 isl_union_pw_multi_aff_intersect_params(
5195 __isl_take isl_union_pw_multi_aff *upma,
5196 __isl_take isl_set *set);
5198 #include <isl/polynomial.h>
5199 __isl_give isl_pw_qpolynomial *
5200 isl_pw_qpolynomial_intersect_domain(
5201 __isl_take isl_pw_qpolynomial *pwpq,
5202 __isl_take isl_set *set);
5203 __isl_give isl_union_pw_qpolynomial *
5204 isl_union_pw_qpolynomial_intersect_domain(
5205 __isl_take isl_union_pw_qpolynomial *upwpq,
5206 __isl_take isl_union_set *uset);
5207 __isl_give isl_union_pw_qpolynomial_fold *
5208 isl_union_pw_qpolynomial_fold_intersect_domain(
5209 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5210 __isl_take isl_union_set *uset);
5211 __isl_give isl_pw_qpolynomial *
5212 isl_pw_qpolynomial_intersect_params(
5213 __isl_take isl_pw_qpolynomial *pwpq,
5214 __isl_take isl_set *set);
5215 __isl_give isl_pw_qpolynomial_fold *
5216 isl_pw_qpolynomial_fold_intersect_params(
5217 __isl_take isl_pw_qpolynomial_fold *pwf,
5218 __isl_take isl_set *set);
5219 __isl_give isl_union_pw_qpolynomial *
5220 isl_union_pw_qpolynomial_intersect_params(
5221 __isl_take isl_union_pw_qpolynomial *upwpq,
5222 __isl_take isl_set *set);
5223 __isl_give isl_union_pw_qpolynomial_fold *
5224 isl_union_pw_qpolynomial_fold_intersect_params(
5225 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5226 __isl_take isl_set *set);
5228 The second argument to the C<_params> functions needs to be
5229 a parametric (basic) set. For the other functions, a parametric set
5230 for either argument is only allowed if the other argument is
5231 a parametric set as well.
5232 The list passed to C<isl_basic_set_list_intersect> needs to have
5233 at least one element and all elements need to live in the same space.
5237 #include <isl/set.h>
5238 __isl_give isl_set *isl_basic_set_union(
5239 __isl_take isl_basic_set *bset1,
5240 __isl_take isl_basic_set *bset2);
5241 __isl_give isl_set *isl_set_union(
5242 __isl_take isl_set *set1,
5243 __isl_take isl_set *set2);
5245 #include <isl/map.h>
5246 __isl_give isl_map *isl_basic_map_union(
5247 __isl_take isl_basic_map *bmap1,
5248 __isl_take isl_basic_map *bmap2);
5249 __isl_give isl_map *isl_map_union(
5250 __isl_take isl_map *map1,
5251 __isl_take isl_map *map2);
5253 #include <isl/union_set.h>
5254 __isl_give isl_union_set *isl_union_set_union(
5255 __isl_take isl_union_set *uset1,
5256 __isl_take isl_union_set *uset2);
5257 __isl_give isl_union_set *isl_union_set_list_union(
5258 __isl_take isl_union_set_list *list);
5260 #include <isl/union_map.h>
5261 __isl_give isl_union_map *isl_union_map_union(
5262 __isl_take isl_union_map *umap1,
5263 __isl_take isl_union_map *umap2);
5265 =item * Set difference
5267 #include <isl/set.h>
5268 __isl_give isl_set *isl_set_subtract(
5269 __isl_take isl_set *set1,
5270 __isl_take isl_set *set2);
5272 #include <isl/map.h>
5273 __isl_give isl_map *isl_map_subtract(
5274 __isl_take isl_map *map1,
5275 __isl_take isl_map *map2);
5276 __isl_give isl_map *isl_map_subtract_domain(
5277 __isl_take isl_map *map,
5278 __isl_take isl_set *dom);
5279 __isl_give isl_map *isl_map_subtract_range(
5280 __isl_take isl_map *map,
5281 __isl_take isl_set *dom);
5283 #include <isl/union_set.h>
5284 __isl_give isl_union_set *isl_union_set_subtract(
5285 __isl_take isl_union_set *uset1,
5286 __isl_take isl_union_set *uset2);
5288 #include <isl/union_map.h>
5289 __isl_give isl_union_map *isl_union_map_subtract(
5290 __isl_take isl_union_map *umap1,
5291 __isl_take isl_union_map *umap2);
5292 __isl_give isl_union_map *isl_union_map_subtract_domain(
5293 __isl_take isl_union_map *umap,
5294 __isl_take isl_union_set *dom);
5295 __isl_give isl_union_map *isl_union_map_subtract_range(
5296 __isl_take isl_union_map *umap,
5297 __isl_take isl_union_set *dom);
5299 #include <isl/aff.h>
5300 __isl_give isl_pw_aff *isl_pw_aff_subtract_domain(
5301 __isl_take isl_pw_aff *pa,
5302 __isl_take isl_set *set);
5303 __isl_give isl_pw_multi_aff *
5304 isl_pw_multi_aff_subtract_domain(
5305 __isl_take isl_pw_multi_aff *pma,
5306 __isl_take isl_set *set);
5307 __isl_give isl_union_pw_aff *
5308 isl_union_pw_aff_subtract_domain(
5309 __isl_take isl_union_pw_aff *upa,
5310 __isl_take isl_union_set *uset);
5311 __isl_give isl_union_pw_multi_aff *
5312 isl_union_pw_multi_aff_subtract_domain(
5313 __isl_take isl_union_pw_multi_aff *upma,
5314 __isl_take isl_set *set);
5316 #include <isl/polynomial.h>
5317 __isl_give isl_pw_qpolynomial *
5318 isl_pw_qpolynomial_subtract_domain(
5319 __isl_take isl_pw_qpolynomial *pwpq,
5320 __isl_take isl_set *set);
5321 __isl_give isl_pw_qpolynomial_fold *
5322 isl_pw_qpolynomial_fold_subtract_domain(
5323 __isl_take isl_pw_qpolynomial_fold *pwf,
5324 __isl_take isl_set *set);
5325 __isl_give isl_union_pw_qpolynomial *
5326 isl_union_pw_qpolynomial_subtract_domain(
5327 __isl_take isl_union_pw_qpolynomial *upwpq,
5328 __isl_take isl_union_set *uset);
5329 __isl_give isl_union_pw_qpolynomial_fold *
5330 isl_union_pw_qpolynomial_fold_subtract_domain(
5331 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5332 __isl_take isl_union_set *uset);
5336 #include <isl/space.h>
5337 __isl_give isl_space *isl_space_join(
5338 __isl_take isl_space *left,
5339 __isl_take isl_space *right);
5341 #include <isl/map.h>
5342 __isl_give isl_basic_set *isl_basic_set_apply(
5343 __isl_take isl_basic_set *bset,
5344 __isl_take isl_basic_map *bmap);
5345 __isl_give isl_set *isl_set_apply(
5346 __isl_take isl_set *set,
5347 __isl_take isl_map *map);
5348 __isl_give isl_union_set *isl_union_set_apply(
5349 __isl_take isl_union_set *uset,
5350 __isl_take isl_union_map *umap);
5351 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5352 __isl_take isl_basic_map *bmap1,
5353 __isl_take isl_basic_map *bmap2);
5354 __isl_give isl_basic_map *isl_basic_map_apply_range(
5355 __isl_take isl_basic_map *bmap1,
5356 __isl_take isl_basic_map *bmap2);
5357 __isl_give isl_map *isl_map_apply_domain(
5358 __isl_take isl_map *map1,
5359 __isl_take isl_map *map2);
5360 __isl_give isl_map *isl_map_apply_range(
5361 __isl_take isl_map *map1,
5362 __isl_take isl_map *map2);
5364 #include <isl/union_map.h>
5365 __isl_give isl_union_map *isl_union_map_apply_domain(
5366 __isl_take isl_union_map *umap1,
5367 __isl_take isl_union_map *umap2);
5368 __isl_give isl_union_map *isl_union_map_apply_range(
5369 __isl_take isl_union_map *umap1,
5370 __isl_take isl_union_map *umap2);
5372 #include <isl/polynomial.h>
5373 __isl_give isl_pw_qpolynomial_fold *
5374 isl_set_apply_pw_qpolynomial_fold(
5375 __isl_take isl_set *set,
5376 __isl_take isl_pw_qpolynomial_fold *pwf,
5378 __isl_give isl_pw_qpolynomial_fold *
5379 isl_map_apply_pw_qpolynomial_fold(
5380 __isl_take isl_map *map,
5381 __isl_take isl_pw_qpolynomial_fold *pwf,
5383 __isl_give isl_union_pw_qpolynomial_fold *
5384 isl_union_set_apply_union_pw_qpolynomial_fold(
5385 __isl_take isl_union_set *uset,
5386 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5388 __isl_give isl_union_pw_qpolynomial_fold *
5389 isl_union_map_apply_union_pw_qpolynomial_fold(
5390 __isl_take isl_union_map *umap,
5391 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5394 The functions taking a map
5395 compose the given map with the given piecewise quasipolynomial reduction.
5396 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5397 over all elements in the intersection of the range of the map
5398 and the domain of the piecewise quasipolynomial reduction
5399 as a function of an element in the domain of the map.
5400 The functions taking a set compute a bound over all elements in the
5401 intersection of the set and the domain of the
5402 piecewise quasipolynomial reduction.
5406 #include <isl/set.h>
5407 __isl_give isl_basic_set *
5408 isl_basic_set_preimage_multi_aff(
5409 __isl_take isl_basic_set *bset,
5410 __isl_take isl_multi_aff *ma);
5411 __isl_give isl_set *isl_set_preimage_multi_aff(
5412 __isl_take isl_set *set,
5413 __isl_take isl_multi_aff *ma);
5414 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5415 __isl_take isl_set *set,
5416 __isl_take isl_pw_multi_aff *pma);
5417 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5418 __isl_take isl_set *set,
5419 __isl_take isl_multi_pw_aff *mpa);
5421 #include <isl/union_set.h>
5422 __isl_give isl_union_set *
5423 isl_union_set_preimage_multi_aff(
5424 __isl_take isl_union_set *uset,
5425 __isl_take isl_multi_aff *ma);
5426 __isl_give isl_union_set *
5427 isl_union_set_preimage_pw_multi_aff(
5428 __isl_take isl_union_set *uset,
5429 __isl_take isl_pw_multi_aff *pma);
5430 __isl_give isl_union_set *
5431 isl_union_set_preimage_union_pw_multi_aff(
5432 __isl_take isl_union_set *uset,
5433 __isl_take isl_union_pw_multi_aff *upma);
5435 #include <isl/map.h>
5436 __isl_give isl_basic_map *
5437 isl_basic_map_preimage_domain_multi_aff(
5438 __isl_take isl_basic_map *bmap,
5439 __isl_take isl_multi_aff *ma);
5440 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5441 __isl_take isl_map *map,
5442 __isl_take isl_multi_aff *ma);
5443 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5444 __isl_take isl_map *map,
5445 __isl_take isl_multi_aff *ma);
5446 __isl_give isl_map *
5447 isl_map_preimage_domain_pw_multi_aff(
5448 __isl_take isl_map *map,
5449 __isl_take isl_pw_multi_aff *pma);
5450 __isl_give isl_map *
5451 isl_map_preimage_range_pw_multi_aff(
5452 __isl_take isl_map *map,
5453 __isl_take isl_pw_multi_aff *pma);
5454 __isl_give isl_map *
5455 isl_map_preimage_domain_multi_pw_aff(
5456 __isl_take isl_map *map,
5457 __isl_take isl_multi_pw_aff *mpa);
5458 __isl_give isl_basic_map *
5459 isl_basic_map_preimage_range_multi_aff(
5460 __isl_take isl_basic_map *bmap,
5461 __isl_take isl_multi_aff *ma);
5463 #include <isl/union_map.h>
5464 __isl_give isl_union_map *
5465 isl_union_map_preimage_domain_multi_aff(
5466 __isl_take isl_union_map *umap,
5467 __isl_take isl_multi_aff *ma);
5468 __isl_give isl_union_map *
5469 isl_union_map_preimage_range_multi_aff(
5470 __isl_take isl_union_map *umap,
5471 __isl_take isl_multi_aff *ma);
5472 __isl_give isl_union_map *
5473 isl_union_map_preimage_domain_pw_multi_aff(
5474 __isl_take isl_union_map *umap,
5475 __isl_take isl_pw_multi_aff *pma);
5476 __isl_give isl_union_map *
5477 isl_union_map_preimage_range_pw_multi_aff(
5478 __isl_take isl_union_map *umap,
5479 __isl_take isl_pw_multi_aff *pma);
5480 __isl_give isl_union_map *
5481 isl_union_map_preimage_domain_union_pw_multi_aff(
5482 __isl_take isl_union_map *umap,
5483 __isl_take isl_union_pw_multi_aff *upma);
5484 __isl_give isl_union_map *
5485 isl_union_map_preimage_range_union_pw_multi_aff(
5486 __isl_take isl_union_map *umap,
5487 __isl_take isl_union_pw_multi_aff *upma);
5489 These functions compute the preimage of the given set or map domain/range under
5490 the given function. In other words, the expression is plugged
5491 into the set description or into the domain/range of the map.
5495 #include <isl/aff.h>
5496 __isl_give isl_aff *isl_aff_pullback_aff(
5497 __isl_take isl_aff *aff1,
5498 __isl_take isl_aff *aff2);
5499 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5500 __isl_take isl_aff *aff,
5501 __isl_take isl_multi_aff *ma);
5502 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5503 __isl_take isl_pw_aff *pa,
5504 __isl_take isl_multi_aff *ma);
5505 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5506 __isl_take isl_pw_aff *pa,
5507 __isl_take isl_pw_multi_aff *pma);
5508 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5509 __isl_take isl_pw_aff *pa,
5510 __isl_take isl_multi_pw_aff *mpa);
5511 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5512 __isl_take isl_multi_aff *ma1,
5513 __isl_take isl_multi_aff *ma2);
5514 __isl_give isl_pw_multi_aff *
5515 isl_pw_multi_aff_pullback_multi_aff(
5516 __isl_take isl_pw_multi_aff *pma,
5517 __isl_take isl_multi_aff *ma);
5518 __isl_give isl_multi_pw_aff *
5519 isl_multi_pw_aff_pullback_multi_aff(
5520 __isl_take isl_multi_pw_aff *mpa,
5521 __isl_take isl_multi_aff *ma);
5522 __isl_give isl_pw_multi_aff *
5523 isl_pw_multi_aff_pullback_pw_multi_aff(
5524 __isl_take isl_pw_multi_aff *pma1,
5525 __isl_take isl_pw_multi_aff *pma2);
5526 __isl_give isl_multi_pw_aff *
5527 isl_multi_pw_aff_pullback_pw_multi_aff(
5528 __isl_take isl_multi_pw_aff *mpa,
5529 __isl_take isl_pw_multi_aff *pma);
5530 __isl_give isl_multi_pw_aff *
5531 isl_multi_pw_aff_pullback_multi_pw_aff(
5532 __isl_take isl_multi_pw_aff *mpa1,
5533 __isl_take isl_multi_pw_aff *mpa2);
5534 __isl_give isl_union_pw_multi_aff *
5535 isl_union_pw_multi_aff_pullback_union_pw_multi_aff(
5536 __isl_take isl_union_pw_multi_aff *upma1,
5537 __isl_take isl_union_pw_multi_aff *upma2);
5539 These functions precompose the first expression by the second function.
5540 In other words, the second function is plugged
5541 into the first expression.
5545 #include <isl/aff.h>
5546 __isl_give isl_basic_set *isl_aff_le_basic_set(
5547 __isl_take isl_aff *aff1,
5548 __isl_take isl_aff *aff2);
5549 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5550 __isl_take isl_aff *aff1,
5551 __isl_take isl_aff *aff2);
5552 __isl_give isl_set *isl_pw_aff_eq_set(
5553 __isl_take isl_pw_aff *pwaff1,
5554 __isl_take isl_pw_aff *pwaff2);
5555 __isl_give isl_set *isl_pw_aff_ne_set(
5556 __isl_take isl_pw_aff *pwaff1,
5557 __isl_take isl_pw_aff *pwaff2);
5558 __isl_give isl_set *isl_pw_aff_le_set(
5559 __isl_take isl_pw_aff *pwaff1,
5560 __isl_take isl_pw_aff *pwaff2);
5561 __isl_give isl_set *isl_pw_aff_lt_set(
5562 __isl_take isl_pw_aff *pwaff1,
5563 __isl_take isl_pw_aff *pwaff2);
5564 __isl_give isl_set *isl_pw_aff_ge_set(
5565 __isl_take isl_pw_aff *pwaff1,
5566 __isl_take isl_pw_aff *pwaff2);
5567 __isl_give isl_set *isl_pw_aff_gt_set(
5568 __isl_take isl_pw_aff *pwaff1,
5569 __isl_take isl_pw_aff *pwaff2);
5571 __isl_give isl_set *isl_multi_aff_lex_le_set(
5572 __isl_take isl_multi_aff *ma1,
5573 __isl_take isl_multi_aff *ma2);
5574 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5575 __isl_take isl_multi_aff *ma1,
5576 __isl_take isl_multi_aff *ma2);
5578 __isl_give isl_set *isl_pw_aff_list_eq_set(
5579 __isl_take isl_pw_aff_list *list1,
5580 __isl_take isl_pw_aff_list *list2);
5581 __isl_give isl_set *isl_pw_aff_list_ne_set(
5582 __isl_take isl_pw_aff_list *list1,
5583 __isl_take isl_pw_aff_list *list2);
5584 __isl_give isl_set *isl_pw_aff_list_le_set(
5585 __isl_take isl_pw_aff_list *list1,
5586 __isl_take isl_pw_aff_list *list2);
5587 __isl_give isl_set *isl_pw_aff_list_lt_set(
5588 __isl_take isl_pw_aff_list *list1,
5589 __isl_take isl_pw_aff_list *list2);
5590 __isl_give isl_set *isl_pw_aff_list_ge_set(
5591 __isl_take isl_pw_aff_list *list1,
5592 __isl_take isl_pw_aff_list *list2);
5593 __isl_give isl_set *isl_pw_aff_list_gt_set(
5594 __isl_take isl_pw_aff_list *list1,
5595 __isl_take isl_pw_aff_list *list2);
5597 The function C<isl_aff_ge_basic_set> returns a basic set
5598 containing those elements in the shared space
5599 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5600 The function C<isl_pw_aff_ge_set> returns a set
5601 containing those elements in the shared domain
5602 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5603 greater than or equal to C<pwaff2>.
5604 The function C<isl_multi_aff_lex_le_set> returns a set
5605 containing those elements in the shared domain space
5606 where C<ma1> is lexicographically smaller than or
5608 The functions operating on C<isl_pw_aff_list> apply the corresponding
5609 C<isl_pw_aff> function to each pair of elements in the two lists.
5611 =item * Cartesian Product
5613 #include <isl/space.h>
5614 __isl_give isl_space *isl_space_product(
5615 __isl_take isl_space *space1,
5616 __isl_take isl_space *space2);
5617 __isl_give isl_space *isl_space_domain_product(
5618 __isl_take isl_space *space1,
5619 __isl_take isl_space *space2);
5620 __isl_give isl_space *isl_space_range_product(
5621 __isl_take isl_space *space1,
5622 __isl_take isl_space *space2);
5625 C<isl_space_product>, C<isl_space_domain_product>
5626 and C<isl_space_range_product> take pairs or relation spaces and
5627 produce a single relations space, where either the domain, the range
5628 or both domain and range are wrapped spaces of relations between
5629 the domains and/or ranges of the input spaces.
5630 If the product is only constructed over the domain or the range
5631 then the ranges or the domains of the inputs should be the same.
5632 The function C<isl_space_product> also accepts a pair of set spaces,
5633 in which case it returns a wrapped space of a relation between the
5636 #include <isl/set.h>
5637 __isl_give isl_set *isl_set_product(
5638 __isl_take isl_set *set1,
5639 __isl_take isl_set *set2);
5641 #include <isl/map.h>
5642 __isl_give isl_basic_map *isl_basic_map_domain_product(
5643 __isl_take isl_basic_map *bmap1,
5644 __isl_take isl_basic_map *bmap2);
5645 __isl_give isl_basic_map *isl_basic_map_range_product(
5646 __isl_take isl_basic_map *bmap1,
5647 __isl_take isl_basic_map *bmap2);
5648 __isl_give isl_basic_map *isl_basic_map_product(
5649 __isl_take isl_basic_map *bmap1,
5650 __isl_take isl_basic_map *bmap2);
5651 __isl_give isl_map *isl_map_domain_product(
5652 __isl_take isl_map *map1,
5653 __isl_take isl_map *map2);
5654 __isl_give isl_map *isl_map_range_product(
5655 __isl_take isl_map *map1,
5656 __isl_take isl_map *map2);
5657 __isl_give isl_map *isl_map_product(
5658 __isl_take isl_map *map1,
5659 __isl_take isl_map *map2);
5661 #include <isl/union_set.h>
5662 __isl_give isl_union_set *isl_union_set_product(
5663 __isl_take isl_union_set *uset1,
5664 __isl_take isl_union_set *uset2);
5666 #include <isl/union_map.h>
5667 __isl_give isl_union_map *isl_union_map_domain_product(
5668 __isl_take isl_union_map *umap1,
5669 __isl_take isl_union_map *umap2);
5670 __isl_give isl_union_map *isl_union_map_range_product(
5671 __isl_take isl_union_map *umap1,
5672 __isl_take isl_union_map *umap2);
5673 __isl_give isl_union_map *isl_union_map_product(
5674 __isl_take isl_union_map *umap1,
5675 __isl_take isl_union_map *umap2);
5677 #include <isl/val.h>
5678 __isl_give isl_multi_val *isl_multi_val_range_product(
5679 __isl_take isl_multi_val *mv1,
5680 __isl_take isl_multi_val *mv2);
5681 __isl_give isl_multi_val *isl_multi_val_product(
5682 __isl_take isl_multi_val *mv1,
5683 __isl_take isl_multi_val *mv2);
5685 #include <isl/aff.h>
5686 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5687 __isl_take isl_multi_aff *ma1,
5688 __isl_take isl_multi_aff *ma2);
5689 __isl_give isl_multi_aff *isl_multi_aff_product(
5690 __isl_take isl_multi_aff *ma1,
5691 __isl_take isl_multi_aff *ma2);
5692 __isl_give isl_multi_pw_aff *
5693 isl_multi_pw_aff_range_product(
5694 __isl_take isl_multi_pw_aff *mpa1,
5695 __isl_take isl_multi_pw_aff *mpa2);
5696 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5697 __isl_take isl_multi_pw_aff *mpa1,
5698 __isl_take isl_multi_pw_aff *mpa2);
5699 __isl_give isl_pw_multi_aff *
5700 isl_pw_multi_aff_range_product(
5701 __isl_take isl_pw_multi_aff *pma1,
5702 __isl_take isl_pw_multi_aff *pma2);
5703 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5704 __isl_take isl_pw_multi_aff *pma1,
5705 __isl_take isl_pw_multi_aff *pma2);
5707 The above functions compute the cross product of the given
5708 sets, relations or functions. The domains and ranges of the results
5709 are wrapped maps between domains and ranges of the inputs.
5710 To obtain a ``flat'' product, use the following functions
5713 #include <isl/set.h>
5714 __isl_give isl_basic_set *isl_basic_set_flat_product(
5715 __isl_take isl_basic_set *bset1,
5716 __isl_take isl_basic_set *bset2);
5717 __isl_give isl_set *isl_set_flat_product(
5718 __isl_take isl_set *set1,
5719 __isl_take isl_set *set2);
5721 #include <isl/map.h>
5722 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5723 __isl_take isl_basic_map *bmap1,
5724 __isl_take isl_basic_map *bmap2);
5725 __isl_give isl_map *isl_map_flat_domain_product(
5726 __isl_take isl_map *map1,
5727 __isl_take isl_map *map2);
5728 __isl_give isl_map *isl_map_flat_range_product(
5729 __isl_take isl_map *map1,
5730 __isl_take isl_map *map2);
5731 __isl_give isl_basic_map *isl_basic_map_flat_product(
5732 __isl_take isl_basic_map *bmap1,
5733 __isl_take isl_basic_map *bmap2);
5734 __isl_give isl_map *isl_map_flat_product(
5735 __isl_take isl_map *map1,
5736 __isl_take isl_map *map2);
5738 #include <isl/union_map.h>
5739 __isl_give isl_union_map *
5740 isl_union_map_flat_domain_product(
5741 __isl_take isl_union_map *umap1,
5742 __isl_take isl_union_map *umap2);
5743 __isl_give isl_union_map *
5744 isl_union_map_flat_range_product(
5745 __isl_take isl_union_map *umap1,
5746 __isl_take isl_union_map *umap2);
5748 #include <isl/val.h>
5749 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
5750 __isl_take isl_multi_val *mv1,
5751 __isl_take isl_multi_aff *mv2);
5753 #include <isl/aff.h>
5754 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
5755 __isl_take isl_multi_aff *ma1,
5756 __isl_take isl_multi_aff *ma2);
5757 __isl_give isl_pw_multi_aff *
5758 isl_pw_multi_aff_flat_range_product(
5759 __isl_take isl_pw_multi_aff *pma1,
5760 __isl_take isl_pw_multi_aff *pma2);
5761 __isl_give isl_multi_pw_aff *
5762 isl_multi_pw_aff_flat_range_product(
5763 __isl_take isl_multi_pw_aff *mpa1,
5764 __isl_take isl_multi_pw_aff *mpa2);
5765 __isl_give isl_union_pw_multi_aff *
5766 isl_union_pw_multi_aff_flat_range_product(
5767 __isl_take isl_union_pw_multi_aff *upma1,
5768 __isl_take isl_union_pw_multi_aff *upma2);
5770 #include <isl/space.h>
5771 __isl_give isl_space *isl_space_factor_domain(
5772 __isl_take isl_space *space);
5773 __isl_give isl_space *isl_space_factor_range(
5774 __isl_take isl_space *space);
5775 __isl_give isl_space *isl_space_domain_factor_domain(
5776 __isl_take isl_space *space);
5777 __isl_give isl_space *isl_space_domain_factor_range(
5778 __isl_take isl_space *space);
5779 __isl_give isl_space *isl_space_range_factor_domain(
5780 __isl_take isl_space *space);
5781 __isl_give isl_space *isl_space_range_factor_range(
5782 __isl_take isl_space *space);
5784 The functions C<isl_space_range_factor_domain> and
5785 C<isl_space_range_factor_range> extract the two arguments from
5786 the result of a call to C<isl_space_range_product>.
5788 The arguments of a call to C<isl_map_range_product> can be extracted
5789 from the result using the following functions.
5791 #include <isl/map.h>
5792 __isl_give isl_map *isl_map_factor_domain(
5793 __isl_take isl_map *map);
5794 __isl_give isl_map *isl_map_factor_range(
5795 __isl_take isl_map *map);
5796 __isl_give isl_map *isl_map_domain_factor_domain(
5797 __isl_take isl_map *map);
5798 __isl_give isl_map *isl_map_domain_factor_range(
5799 __isl_take isl_map *map);
5800 __isl_give isl_map *isl_map_range_factor_domain(
5801 __isl_take isl_map *map);
5802 __isl_give isl_map *isl_map_range_factor_range(
5803 __isl_take isl_map *map);
5805 #include <isl/union_map.h>
5806 __isl_give isl_union_map *isl_union_map_factor_domain(
5807 __isl_take isl_union_map *umap);
5808 __isl_give isl_union_map *isl_union_map_factor_range(
5809 __isl_take isl_union_map *umap);
5810 __isl_give isl_union_map *
5811 isl_union_map_domain_factor_domain(
5812 __isl_take isl_union_map *umap);
5813 __isl_give isl_union_map *
5814 isl_union_map_domain_factor_range(
5815 __isl_take isl_union_map *umap);
5816 __isl_give isl_union_map *
5817 isl_union_map_range_factor_range(
5818 __isl_take isl_union_map *umap);
5820 #include <isl/val.h>
5821 __isl_give isl_multi_val *
5822 isl_multi_val_range_factor_domain(
5823 __isl_take isl_multi_val *mv);
5824 __isl_give isl_multi_val *
5825 isl_multi_val_range_factor_range(
5826 __isl_take isl_multi_val *mv);
5828 #include <isl/aff.h>
5829 __isl_give isl_multi_aff *
5830 isl_multi_aff_range_factor_domain(
5831 __isl_take isl_multi_aff *ma);
5832 __isl_give isl_multi_aff *
5833 isl_multi_aff_range_factor_range(
5834 __isl_take isl_multi_aff *ma);
5835 __isl_give isl_multi_pw_aff *
5836 isl_multi_pw_aff_range_factor_domain(
5837 __isl_take isl_multi_pw_aff *mpa);
5838 __isl_give isl_multi_pw_aff *
5839 isl_multi_pw_aff_range_factor_range(
5840 __isl_take isl_multi_pw_aff *mpa);
5842 The splice functions are a generalization of the flat product functions,
5843 where the second argument may be inserted at any position inside
5844 the first argument rather than being placed at the end.
5846 #include <isl/val.h>
5847 __isl_give isl_multi_val *isl_multi_val_range_splice(
5848 __isl_take isl_multi_val *mv1, unsigned pos,
5849 __isl_take isl_multi_val *mv2);
5851 #include <isl/aff.h>
5852 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
5853 __isl_take isl_multi_aff *ma1, unsigned pos,
5854 __isl_take isl_multi_aff *ma2);
5855 __isl_give isl_multi_aff *isl_multi_aff_splice(
5856 __isl_take isl_multi_aff *ma1,
5857 unsigned in_pos, unsigned out_pos,
5858 __isl_take isl_multi_aff *ma2);
5859 __isl_give isl_multi_pw_aff *
5860 isl_multi_pw_aff_range_splice(
5861 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
5862 __isl_take isl_multi_pw_aff *mpa2);
5863 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
5864 __isl_take isl_multi_pw_aff *mpa1,
5865 unsigned in_pos, unsigned out_pos,
5866 __isl_take isl_multi_pw_aff *mpa2);
5868 =item * Simplification
5870 When applied to a set or relation,
5871 the gist operation returns a set or relation that has the
5872 same intersection with the context as the input set or relation.
5873 Any implicit equality in the intersection is made explicit in the result,
5874 while all inequalities that are redundant with respect to the intersection
5876 In case of union sets and relations, the gist operation is performed
5879 When applied to a function,
5880 the gist operation applies the set gist operation to each of
5881 the cells in the domain of the input piecewise expression.
5882 The context is also exploited
5883 to simplify the expression associated to each cell.
5885 #include <isl/set.h>
5886 __isl_give isl_basic_set *isl_basic_set_gist(
5887 __isl_take isl_basic_set *bset,
5888 __isl_take isl_basic_set *context);
5889 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
5890 __isl_take isl_set *context);
5891 __isl_give isl_set *isl_set_gist_params(
5892 __isl_take isl_set *set,
5893 __isl_take isl_set *context);
5895 #include <isl/map.h>
5896 __isl_give isl_basic_map *isl_basic_map_gist(
5897 __isl_take isl_basic_map *bmap,
5898 __isl_take isl_basic_map *context);
5899 __isl_give isl_basic_map *isl_basic_map_gist_domain(
5900 __isl_take isl_basic_map *bmap,
5901 __isl_take isl_basic_set *context);
5902 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
5903 __isl_take isl_map *context);
5904 __isl_give isl_map *isl_map_gist_params(
5905 __isl_take isl_map *map,
5906 __isl_take isl_set *context);
5907 __isl_give isl_map *isl_map_gist_domain(
5908 __isl_take isl_map *map,
5909 __isl_take isl_set *context);
5910 __isl_give isl_map *isl_map_gist_range(
5911 __isl_take isl_map *map,
5912 __isl_take isl_set *context);
5914 #include <isl/union_set.h>
5915 __isl_give isl_union_set *isl_union_set_gist(
5916 __isl_take isl_union_set *uset,
5917 __isl_take isl_union_set *context);
5918 __isl_give isl_union_set *isl_union_set_gist_params(
5919 __isl_take isl_union_set *uset,
5920 __isl_take isl_set *set);
5922 #include <isl/union_map.h>
5923 __isl_give isl_union_map *isl_union_map_gist(
5924 __isl_take isl_union_map *umap,
5925 __isl_take isl_union_map *context);
5926 __isl_give isl_union_map *isl_union_map_gist_params(
5927 __isl_take isl_union_map *umap,
5928 __isl_take isl_set *set);
5929 __isl_give isl_union_map *isl_union_map_gist_domain(
5930 __isl_take isl_union_map *umap,
5931 __isl_take isl_union_set *uset);
5932 __isl_give isl_union_map *isl_union_map_gist_range(
5933 __isl_take isl_union_map *umap,
5934 __isl_take isl_union_set *uset);
5936 #include <isl/aff.h>
5937 __isl_give isl_aff *isl_aff_gist_params(
5938 __isl_take isl_aff *aff,
5939 __isl_take isl_set *context);
5940 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
5941 __isl_take isl_set *context);
5942 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
5943 __isl_take isl_multi_aff *maff,
5944 __isl_take isl_set *context);
5945 __isl_give isl_multi_aff *isl_multi_aff_gist(
5946 __isl_take isl_multi_aff *maff,
5947 __isl_take isl_set *context);
5948 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
5949 __isl_take isl_pw_aff *pwaff,
5950 __isl_take isl_set *context);
5951 __isl_give isl_pw_aff *isl_pw_aff_gist(
5952 __isl_take isl_pw_aff *pwaff,
5953 __isl_take isl_set *context);
5954 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
5955 __isl_take isl_pw_multi_aff *pma,
5956 __isl_take isl_set *set);
5957 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
5958 __isl_take isl_pw_multi_aff *pma,
5959 __isl_take isl_set *set);
5960 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
5961 __isl_take isl_multi_pw_aff *mpa,
5962 __isl_take isl_set *set);
5963 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
5964 __isl_take isl_multi_pw_aff *mpa,
5965 __isl_take isl_set *set);
5966 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist(
5967 __isl_take isl_union_pw_aff *upa,
5968 __isl_take isl_union_set *context);
5969 __isl_give isl_union_pw_aff *isl_union_pw_aff_gist_params(
5970 __isl_take isl_union_pw_aff *upa,
5971 __isl_take isl_set *context);
5972 __isl_give isl_union_pw_multi_aff *
5973 isl_union_pw_multi_aff_gist_params(
5974 __isl_take isl_union_pw_multi_aff *upma,
5975 __isl_take isl_set *context);
5976 __isl_give isl_union_pw_multi_aff *
5977 isl_union_pw_multi_aff_gist(
5978 __isl_take isl_union_pw_multi_aff *upma,
5979 __isl_take isl_union_set *context);
5981 #include <isl/polynomial.h>
5982 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5983 __isl_take isl_qpolynomial *qp,
5984 __isl_take isl_set *context);
5985 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5986 __isl_take isl_qpolynomial *qp,
5987 __isl_take isl_set *context);
5988 __isl_give isl_qpolynomial_fold *
5989 isl_qpolynomial_fold_gist_params(
5990 __isl_take isl_qpolynomial_fold *fold,
5991 __isl_take isl_set *context);
5992 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5993 __isl_take isl_qpolynomial_fold *fold,
5994 __isl_take isl_set *context);
5995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5996 __isl_take isl_pw_qpolynomial *pwqp,
5997 __isl_take isl_set *context);
5998 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5999 __isl_take isl_pw_qpolynomial *pwqp,
6000 __isl_take isl_set *context);
6001 __isl_give isl_pw_qpolynomial_fold *
6002 isl_pw_qpolynomial_fold_gist(
6003 __isl_take isl_pw_qpolynomial_fold *pwf,
6004 __isl_take isl_set *context);
6005 __isl_give isl_pw_qpolynomial_fold *
6006 isl_pw_qpolynomial_fold_gist_params(
6007 __isl_take isl_pw_qpolynomial_fold *pwf,
6008 __isl_take isl_set *context);
6009 __isl_give isl_union_pw_qpolynomial *
6010 isl_union_pw_qpolynomial_gist_params(
6011 __isl_take isl_union_pw_qpolynomial *upwqp,
6012 __isl_take isl_set *context);
6013 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
6014 __isl_take isl_union_pw_qpolynomial *upwqp,
6015 __isl_take isl_union_set *context);
6016 __isl_give isl_union_pw_qpolynomial_fold *
6017 isl_union_pw_qpolynomial_fold_gist(
6018 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6019 __isl_take isl_union_set *context);
6020 __isl_give isl_union_pw_qpolynomial_fold *
6021 isl_union_pw_qpolynomial_fold_gist_params(
6022 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6023 __isl_take isl_set *context);
6025 =item * Binary Arithmethic Operations
6027 #include <isl/val.h>
6028 __isl_give isl_multi_val *isl_multi_val_sub(
6029 __isl_take isl_multi_val *mv1,
6030 __isl_take isl_multi_val *mv2);
6032 #include <isl/aff.h>
6033 __isl_give isl_aff *isl_aff_add(
6034 __isl_take isl_aff *aff1,
6035 __isl_take isl_aff *aff2);
6036 __isl_give isl_multi_aff *isl_multi_aff_add(
6037 __isl_take isl_multi_aff *maff1,
6038 __isl_take isl_multi_aff *maff2);
6039 __isl_give isl_pw_aff *isl_pw_aff_add(
6040 __isl_take isl_pw_aff *pwaff1,
6041 __isl_take isl_pw_aff *pwaff2);
6042 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
6043 __isl_take isl_pw_multi_aff *pma1,
6044 __isl_take isl_pw_multi_aff *pma2);
6045 __isl_give isl_union_pw_aff *isl_union_pw_aff_add(
6046 __isl_take isl_union_pw_aff *upa1,
6047 __isl_take isl_union_pw_aff *upa2);
6048 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
6049 __isl_take isl_union_pw_multi_aff *upma1,
6050 __isl_take isl_union_pw_multi_aff *upma2);
6051 __isl_give isl_pw_aff *isl_pw_aff_min(
6052 __isl_take isl_pw_aff *pwaff1,
6053 __isl_take isl_pw_aff *pwaff2);
6054 __isl_give isl_pw_aff *isl_pw_aff_max(
6055 __isl_take isl_pw_aff *pwaff1,
6056 __isl_take isl_pw_aff *pwaff2);
6057 __isl_give isl_aff *isl_aff_sub(
6058 __isl_take isl_aff *aff1,
6059 __isl_take isl_aff *aff2);
6060 __isl_give isl_multi_aff *isl_multi_aff_sub(
6061 __isl_take isl_multi_aff *ma1,
6062 __isl_take isl_multi_aff *ma2);
6063 __isl_give isl_pw_aff *isl_pw_aff_sub(
6064 __isl_take isl_pw_aff *pwaff1,
6065 __isl_take isl_pw_aff *pwaff2);
6066 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_sub(
6067 __isl_take isl_multi_pw_aff *mpa1,
6068 __isl_take isl_multi_pw_aff *mpa2);
6069 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
6070 __isl_take isl_pw_multi_aff *pma1,
6071 __isl_take isl_pw_multi_aff *pma2);
6072 __isl_give isl_union_pw_aff *isl_union_pw_aff_sub(
6073 __isl_take isl_union_pw_aff *upa1,
6074 __isl_take isl_union_pw_aff *upa2);
6075 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
6076 __isl_take isl_union_pw_multi_aff *upma1,
6077 __isl_take isl_union_pw_multi_aff *upma2);
6079 C<isl_aff_sub> subtracts the second argument from the first.
6081 #include <isl/polynomial.h>
6082 __isl_give isl_qpolynomial *isl_qpolynomial_add(
6083 __isl_take isl_qpolynomial *qp1,
6084 __isl_take isl_qpolynomial *qp2);
6085 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
6086 __isl_take isl_pw_qpolynomial *pwqp1,
6087 __isl_take isl_pw_qpolynomial *pwqp2);
6088 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
6089 __isl_take isl_pw_qpolynomial *pwqp1,
6090 __isl_take isl_pw_qpolynomial *pwqp2);
6091 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
6092 __isl_take isl_pw_qpolynomial_fold *pwf1,
6093 __isl_take isl_pw_qpolynomial_fold *pwf2);
6094 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
6095 __isl_take isl_union_pw_qpolynomial *upwqp1,
6096 __isl_take isl_union_pw_qpolynomial *upwqp2);
6097 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
6098 __isl_take isl_qpolynomial *qp1,
6099 __isl_take isl_qpolynomial *qp2);
6100 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
6101 __isl_take isl_pw_qpolynomial *pwqp1,
6102 __isl_take isl_pw_qpolynomial *pwqp2);
6103 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
6104 __isl_take isl_union_pw_qpolynomial *upwqp1,
6105 __isl_take isl_union_pw_qpolynomial *upwqp2);
6106 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
6107 __isl_take isl_pw_qpolynomial_fold *pwf1,
6108 __isl_take isl_pw_qpolynomial_fold *pwf2);
6109 __isl_give isl_union_pw_qpolynomial_fold *
6110 isl_union_pw_qpolynomial_fold_fold(
6111 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
6112 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
6114 #include <isl/aff.h>
6115 __isl_give isl_pw_aff *isl_pw_aff_union_add(
6116 __isl_take isl_pw_aff *pwaff1,
6117 __isl_take isl_pw_aff *pwaff2);
6118 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
6119 __isl_take isl_pw_multi_aff *pma1,
6120 __isl_take isl_pw_multi_aff *pma2);
6121 __isl_give isl_union_pw_aff *isl_union_pw_aff_union_add(
6122 __isl_take isl_union_pw_aff *upa1,
6123 __isl_take isl_union_pw_aff *upa2);
6124 __isl_give isl_union_pw_multi_aff *
6125 isl_union_pw_multi_aff_union_add(
6126 __isl_take isl_union_pw_multi_aff *upma1,
6127 __isl_take isl_union_pw_multi_aff *upma2);
6128 __isl_give isl_pw_aff *isl_pw_aff_union_min(
6129 __isl_take isl_pw_aff *pwaff1,
6130 __isl_take isl_pw_aff *pwaff2);
6131 __isl_give isl_pw_aff *isl_pw_aff_union_max(
6132 __isl_take isl_pw_aff *pwaff1,
6133 __isl_take isl_pw_aff *pwaff2);
6135 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
6136 expression with a domain that is the union of those of C<pwaff1> and
6137 C<pwaff2> and such that on each cell, the quasi-affine expression is
6138 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
6139 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
6140 associated expression is the defined one.
6141 This in contrast to the C<isl_pw_aff_max> function, which is
6142 only defined on the shared definition domain of the arguments.
6144 #include <isl/val.h>
6145 __isl_give isl_multi_val *isl_multi_val_add_val(
6146 __isl_take isl_multi_val *mv,
6147 __isl_take isl_val *v);
6148 __isl_give isl_multi_val *isl_multi_val_mod_val(
6149 __isl_take isl_multi_val *mv,
6150 __isl_take isl_val *v);
6151 __isl_give isl_multi_val *isl_multi_val_scale_val(
6152 __isl_take isl_multi_val *mv,
6153 __isl_take isl_val *v);
6154 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
6155 __isl_take isl_multi_val *mv,
6156 __isl_take isl_val *v);
6158 #include <isl/aff.h>
6159 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
6160 __isl_take isl_val *mod);
6161 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
6162 __isl_take isl_pw_aff *pa,
6163 __isl_take isl_val *mod);
6164 __isl_give isl_union_pw_aff *isl_union_pw_aff_mod_val(
6165 __isl_take isl_union_pw_aff *upa,
6166 __isl_take isl_val *f);
6167 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
6168 __isl_take isl_val *v);
6169 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
6170 __isl_take isl_multi_aff *ma,
6171 __isl_take isl_val *v);
6172 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
6173 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
6174 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
6175 __isl_take isl_multi_pw_aff *mpa,
6176 __isl_take isl_val *v);
6177 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
6178 __isl_take isl_pw_multi_aff *pma,
6179 __isl_take isl_val *v);
6180 __isl_give isl_union_pw_multi_aff *
6181 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_val(
6182 __isl_take isl_union_pw_aff *upa,
6183 __isl_take isl_val *f);
6184 isl_union_pw_multi_aff_scale_val(
6185 __isl_take isl_union_pw_multi_aff *upma,
6186 __isl_take isl_val *val);
6187 __isl_give isl_aff *isl_aff_scale_down_ui(
6188 __isl_take isl_aff *aff, unsigned f);
6189 __isl_give isl_aff *isl_aff_scale_down_val(
6190 __isl_take isl_aff *aff, __isl_take isl_val *v);
6191 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
6192 __isl_take isl_multi_aff *ma,
6193 __isl_take isl_val *v);
6194 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
6195 __isl_take isl_pw_aff *pa,
6196 __isl_take isl_val *f);
6197 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
6198 __isl_take isl_multi_pw_aff *mpa,
6199 __isl_take isl_val *v);
6200 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
6201 __isl_take isl_pw_multi_aff *pma,
6202 __isl_take isl_val *v);
6203 __isl_give isl_union_pw_aff *isl_union_pw_aff_scale_down_val(
6204 __isl_take isl_union_pw_aff *upa,
6205 __isl_take isl_val *v);
6206 __isl_give isl_union_pw_multi_aff *
6207 isl_union_pw_multi_aff_scale_down_val(
6208 __isl_take isl_union_pw_multi_aff *upma,
6209 __isl_take isl_val *val);
6211 #include <isl/polynomial.h>
6212 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
6213 __isl_take isl_qpolynomial *qp,
6214 __isl_take isl_val *v);
6215 __isl_give isl_qpolynomial_fold *
6216 isl_qpolynomial_fold_scale_val(
6217 __isl_take isl_qpolynomial_fold *fold,
6218 __isl_take isl_val *v);
6219 __isl_give isl_pw_qpolynomial *
6220 isl_pw_qpolynomial_scale_val(
6221 __isl_take isl_pw_qpolynomial *pwqp,
6222 __isl_take isl_val *v);
6223 __isl_give isl_pw_qpolynomial_fold *
6224 isl_pw_qpolynomial_fold_scale_val(
6225 __isl_take isl_pw_qpolynomial_fold *pwf,
6226 __isl_take isl_val *v);
6227 __isl_give isl_union_pw_qpolynomial *
6228 isl_union_pw_qpolynomial_scale_val(
6229 __isl_take isl_union_pw_qpolynomial *upwqp,
6230 __isl_take isl_val *v);
6231 __isl_give isl_union_pw_qpolynomial_fold *
6232 isl_union_pw_qpolynomial_fold_scale_val(
6233 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6234 __isl_take isl_val *v);
6235 __isl_give isl_qpolynomial *
6236 isl_qpolynomial_scale_down_val(
6237 __isl_take isl_qpolynomial *qp,
6238 __isl_take isl_val *v);
6239 __isl_give isl_qpolynomial_fold *
6240 isl_qpolynomial_fold_scale_down_val(
6241 __isl_take isl_qpolynomial_fold *fold,
6242 __isl_take isl_val *v);
6243 __isl_give isl_pw_qpolynomial *
6244 isl_pw_qpolynomial_scale_down_val(
6245 __isl_take isl_pw_qpolynomial *pwqp,
6246 __isl_take isl_val *v);
6247 __isl_give isl_pw_qpolynomial_fold *
6248 isl_pw_qpolynomial_fold_scale_down_val(
6249 __isl_take isl_pw_qpolynomial_fold *pwf,
6250 __isl_take isl_val *v);
6251 __isl_give isl_union_pw_qpolynomial *
6252 isl_union_pw_qpolynomial_scale_down_val(
6253 __isl_take isl_union_pw_qpolynomial *upwqp,
6254 __isl_take isl_val *v);
6255 __isl_give isl_union_pw_qpolynomial_fold *
6256 isl_union_pw_qpolynomial_fold_scale_down_val(
6257 __isl_take isl_union_pw_qpolynomial_fold *upwf,
6258 __isl_take isl_val *v);
6260 #include <isl/val.h>
6261 __isl_give isl_multi_val *isl_multi_val_mod_multi_val(
6262 __isl_take isl_multi_val *mv1,
6263 __isl_take isl_multi_val *mv2);
6264 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
6265 __isl_take isl_multi_val *mv1,
6266 __isl_take isl_multi_val *mv2);
6267 __isl_give isl_multi_val *
6268 isl_multi_val_scale_down_multi_val(
6269 __isl_take isl_multi_val *mv1,
6270 __isl_take isl_multi_val *mv2);
6272 #include <isl/aff.h>
6273 __isl_give isl_multi_aff *isl_multi_aff_mod_multi_val(
6274 __isl_take isl_multi_aff *ma,
6275 __isl_take isl_multi_val *mv);
6276 __isl_give isl_multi_pw_aff *
6277 isl_multi_pw_aff_mod_multi_val(
6278 __isl_take isl_multi_pw_aff *mpa,
6279 __isl_take isl_multi_val *mv);
6280 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
6281 __isl_take isl_multi_aff *ma,
6282 __isl_take isl_multi_val *mv);
6283 __isl_give isl_pw_multi_aff *
6284 isl_pw_multi_aff_scale_multi_val(
6285 __isl_take isl_pw_multi_aff *pma,
6286 __isl_take isl_multi_val *mv);
6287 __isl_give isl_multi_pw_aff *
6288 isl_multi_pw_aff_scale_multi_val(
6289 __isl_take isl_multi_pw_aff *mpa,
6290 __isl_take isl_multi_val *mv);
6291 __isl_give isl_union_pw_multi_aff *
6292 isl_union_pw_multi_aff_scale_multi_val(
6293 __isl_take isl_union_pw_multi_aff *upma,
6294 __isl_take isl_multi_val *mv);
6295 __isl_give isl_multi_aff *
6296 isl_multi_aff_scale_down_multi_val(
6297 __isl_take isl_multi_aff *ma,
6298 __isl_take isl_multi_val *mv);
6299 __isl_give isl_multi_pw_aff *
6300 isl_multi_pw_aff_scale_down_multi_val(
6301 __isl_take isl_multi_pw_aff *mpa,
6302 __isl_take isl_multi_val *mv);
6304 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
6305 by the corresponding elements of C<mv>.
6307 #include <isl/aff.h>
6308 __isl_give isl_aff *isl_aff_mul(
6309 __isl_take isl_aff *aff1,
6310 __isl_take isl_aff *aff2);
6311 __isl_give isl_aff *isl_aff_div(
6312 __isl_take isl_aff *aff1,
6313 __isl_take isl_aff *aff2);
6314 __isl_give isl_pw_aff *isl_pw_aff_mul(
6315 __isl_take isl_pw_aff *pwaff1,
6316 __isl_take isl_pw_aff *pwaff2);
6317 __isl_give isl_pw_aff *isl_pw_aff_div(
6318 __isl_take isl_pw_aff *pa1,
6319 __isl_take isl_pw_aff *pa2);
6320 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
6321 __isl_take isl_pw_aff *pa1,
6322 __isl_take isl_pw_aff *pa2);
6323 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
6324 __isl_take isl_pw_aff *pa1,
6325 __isl_take isl_pw_aff *pa2);
6327 When multiplying two affine expressions, at least one of the two needs
6328 to be a constant. Similarly, when dividing an affine expression by another,
6329 the second expression needs to be a constant.
6330 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
6331 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
6334 #include <isl/polynomial.h>
6335 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
6336 __isl_take isl_qpolynomial *qp1,
6337 __isl_take isl_qpolynomial *qp2);
6338 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6339 __isl_take isl_pw_qpolynomial *pwqp1,
6340 __isl_take isl_pw_qpolynomial *pwqp2);
6341 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6342 __isl_take isl_union_pw_qpolynomial *upwqp1,
6343 __isl_take isl_union_pw_qpolynomial *upwqp2);
6347 =head3 Lexicographic Optimization
6349 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6350 the following functions
6351 compute a set that contains the lexicographic minimum or maximum
6352 of the elements in C<set> (or C<bset>) for those values of the parameters
6353 that satisfy C<dom>.
6354 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6355 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6357 In other words, the union of the parameter values
6358 for which the result is non-empty and of C<*empty>
6361 #include <isl/set.h>
6362 __isl_give isl_set *isl_basic_set_partial_lexmin(
6363 __isl_take isl_basic_set *bset,
6364 __isl_take isl_basic_set *dom,
6365 __isl_give isl_set **empty);
6366 __isl_give isl_set *isl_basic_set_partial_lexmax(
6367 __isl_take isl_basic_set *bset,
6368 __isl_take isl_basic_set *dom,
6369 __isl_give isl_set **empty);
6370 __isl_give isl_set *isl_set_partial_lexmin(
6371 __isl_take isl_set *set, __isl_take isl_set *dom,
6372 __isl_give isl_set **empty);
6373 __isl_give isl_set *isl_set_partial_lexmax(
6374 __isl_take isl_set *set, __isl_take isl_set *dom,
6375 __isl_give isl_set **empty);
6377 Given a (basic) set C<set> (or C<bset>), the following functions simply
6378 return a set containing the lexicographic minimum or maximum
6379 of the elements in C<set> (or C<bset>).
6380 In case of union sets, the optimum is computed per space.
6382 #include <isl/set.h>
6383 __isl_give isl_set *isl_basic_set_lexmin(
6384 __isl_take isl_basic_set *bset);
6385 __isl_give isl_set *isl_basic_set_lexmax(
6386 __isl_take isl_basic_set *bset);
6387 __isl_give isl_set *isl_set_lexmin(
6388 __isl_take isl_set *set);
6389 __isl_give isl_set *isl_set_lexmax(
6390 __isl_take isl_set *set);
6391 __isl_give isl_union_set *isl_union_set_lexmin(
6392 __isl_take isl_union_set *uset);
6393 __isl_give isl_union_set *isl_union_set_lexmax(
6394 __isl_take isl_union_set *uset);
6396 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6397 the following functions
6398 compute a relation that maps each element of C<dom>
6399 to the single lexicographic minimum or maximum
6400 of the elements that are associated to that same
6401 element in C<map> (or C<bmap>).
6402 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6403 that contains the elements in C<dom> that do not map
6404 to any elements in C<map> (or C<bmap>).
6405 In other words, the union of the domain of the result and of C<*empty>
6408 #include <isl/map.h>
6409 __isl_give isl_map *isl_basic_map_partial_lexmax(
6410 __isl_take isl_basic_map *bmap,
6411 __isl_take isl_basic_set *dom,
6412 __isl_give isl_set **empty);
6413 __isl_give isl_map *isl_basic_map_partial_lexmin(
6414 __isl_take isl_basic_map *bmap,
6415 __isl_take isl_basic_set *dom,
6416 __isl_give isl_set **empty);
6417 __isl_give isl_map *isl_map_partial_lexmax(
6418 __isl_take isl_map *map, __isl_take isl_set *dom,
6419 __isl_give isl_set **empty);
6420 __isl_give isl_map *isl_map_partial_lexmin(
6421 __isl_take isl_map *map, __isl_take isl_set *dom,
6422 __isl_give isl_set **empty);
6424 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6425 return a map mapping each element in the domain of
6426 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6427 of all elements associated to that element.
6428 In case of union relations, the optimum is computed per space.
6430 #include <isl/map.h>
6431 __isl_give isl_map *isl_basic_map_lexmin(
6432 __isl_take isl_basic_map *bmap);
6433 __isl_give isl_map *isl_basic_map_lexmax(
6434 __isl_take isl_basic_map *bmap);
6435 __isl_give isl_map *isl_map_lexmin(
6436 __isl_take isl_map *map);
6437 __isl_give isl_map *isl_map_lexmax(
6438 __isl_take isl_map *map);
6439 __isl_give isl_union_map *isl_union_map_lexmin(
6440 __isl_take isl_union_map *umap);
6441 __isl_give isl_union_map *isl_union_map_lexmax(
6442 __isl_take isl_union_map *umap);
6444 The following functions return their result in the form of
6445 a piecewise multi-affine expression,
6446 but are otherwise equivalent to the corresponding functions
6447 returning a basic set or relation.
6449 #include <isl/set.h>
6450 __isl_give isl_pw_multi_aff *
6451 isl_basic_set_partial_lexmin_pw_multi_aff(
6452 __isl_take isl_basic_set *bset,
6453 __isl_take isl_basic_set *dom,
6454 __isl_give isl_set **empty);
6455 __isl_give isl_pw_multi_aff *
6456 isl_basic_set_partial_lexmax_pw_multi_aff(
6457 __isl_take isl_basic_set *bset,
6458 __isl_take isl_basic_set *dom,
6459 __isl_give isl_set **empty);
6460 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6461 __isl_take isl_set *set);
6462 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6463 __isl_take isl_set *set);
6465 #include <isl/map.h>
6466 __isl_give isl_pw_multi_aff *
6467 isl_basic_map_lexmin_pw_multi_aff(
6468 __isl_take isl_basic_map *bmap);
6469 __isl_give isl_pw_multi_aff *
6470 isl_basic_map_partial_lexmin_pw_multi_aff(
6471 __isl_take isl_basic_map *bmap,
6472 __isl_take isl_basic_set *dom,
6473 __isl_give isl_set **empty);
6474 __isl_give isl_pw_multi_aff *
6475 isl_basic_map_partial_lexmax_pw_multi_aff(
6476 __isl_take isl_basic_map *bmap,
6477 __isl_take isl_basic_set *dom,
6478 __isl_give isl_set **empty);
6479 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6480 __isl_take isl_map *map);
6481 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6482 __isl_take isl_map *map);
6484 The following functions return the lexicographic minimum or maximum
6485 on the shared domain of the inputs and the single defined function
6486 on those parts of the domain where only a single function is defined.
6488 #include <isl/aff.h>
6489 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6490 __isl_take isl_pw_multi_aff *pma1,
6491 __isl_take isl_pw_multi_aff *pma2);
6492 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6493 __isl_take isl_pw_multi_aff *pma1,
6494 __isl_take isl_pw_multi_aff *pma2);
6496 =head2 Ternary Operations
6498 #include <isl/aff.h>
6499 __isl_give isl_pw_aff *isl_pw_aff_cond(
6500 __isl_take isl_pw_aff *cond,
6501 __isl_take isl_pw_aff *pwaff_true,
6502 __isl_take isl_pw_aff *pwaff_false);
6504 The function C<isl_pw_aff_cond> performs a conditional operator
6505 and returns an expression that is equal to C<pwaff_true>
6506 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6507 where C<cond> is zero.
6511 Lists are defined over several element types, including
6512 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_union_pw_aff>,
6513 C<isl_union_pw_multi_aff>, C<isl_constraint>,
6514 C<isl_basic_set>, C<isl_set>, C<isl_basic_map>, C<isl_map>, C<isl_union_set>,
6515 C<isl_union_map>, C<isl_ast_expr> and C<isl_ast_node>.
6516 Here we take lists of C<isl_set>s as an example.
6517 Lists can be created, copied, modified and freed using the following functions.
6519 #include <isl/set.h>
6520 __isl_give isl_set_list *isl_set_list_from_set(
6521 __isl_take isl_set *el);
6522 __isl_give isl_set_list *isl_set_list_alloc(
6523 isl_ctx *ctx, int n);
6524 __isl_give isl_set_list *isl_set_list_copy(
6525 __isl_keep isl_set_list *list);
6526 __isl_give isl_set_list *isl_set_list_insert(
6527 __isl_take isl_set_list *list, unsigned pos,
6528 __isl_take isl_set *el);
6529 __isl_give isl_set_list *isl_set_list_add(
6530 __isl_take isl_set_list *list,
6531 __isl_take isl_set *el);
6532 __isl_give isl_set_list *isl_set_list_drop(
6533 __isl_take isl_set_list *list,
6534 unsigned first, unsigned n);
6535 __isl_give isl_set_list *isl_set_list_set_set(
6536 __isl_take isl_set_list *list, int index,
6537 __isl_take isl_set *set);
6538 __isl_give isl_set_list *isl_set_list_concat(
6539 __isl_take isl_set_list *list1,
6540 __isl_take isl_set_list *list2);
6541 __isl_give isl_set_list *isl_set_list_sort(
6542 __isl_take isl_set_list *list,
6543 int (*cmp)(__isl_keep isl_set *a,
6544 __isl_keep isl_set *b, void *user),
6546 __isl_null isl_set_list *isl_set_list_free(
6547 __isl_take isl_set_list *list);
6549 C<isl_set_list_alloc> creates an empty list with an initial capacity
6550 for C<n> elements. C<isl_set_list_insert> and C<isl_set_list_add>
6551 add elements to a list, increasing its capacity as needed.
6552 C<isl_set_list_from_set> creates a list with a single element.
6554 Lists can be inspected using the following functions.
6556 #include <isl/set.h>
6557 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6558 __isl_give isl_set *isl_set_list_get_set(
6559 __isl_keep isl_set_list *list, int index);
6560 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6561 int (*fn)(__isl_take isl_set *el, void *user),
6563 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6564 int (*follows)(__isl_keep isl_set *a,
6565 __isl_keep isl_set *b, void *user),
6567 int (*fn)(__isl_take isl_set *el, void *user),
6570 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6571 strongly connected components of the graph with as vertices the elements
6572 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6573 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6574 should return C<-1> on error.
6576 Lists can be printed using
6578 #include <isl/set.h>
6579 __isl_give isl_printer *isl_printer_print_set_list(
6580 __isl_take isl_printer *p,
6581 __isl_keep isl_set_list *list);
6583 =head2 Associative arrays
6585 Associative arrays map isl objects of a specific type to isl objects
6586 of some (other) specific type. They are defined for several pairs
6587 of types, including (C<isl_map>, C<isl_basic_set>),
6588 (C<isl_id>, C<isl_ast_expr>) and.
6589 (C<isl_id>, C<isl_pw_aff>).
6590 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6593 Associative arrays can be created, copied and freed using
6594 the following functions.
6596 #include <isl/id_to_ast_expr.h>
6597 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6598 isl_ctx *ctx, int min_size);
6599 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6600 __isl_keep id_to_ast_expr *id2expr);
6601 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6602 __isl_take id_to_ast_expr *id2expr);
6604 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6605 to specify the expected size of the associative array.
6606 The associative array will be grown automatically as needed.
6608 Associative arrays can be inspected using the following functions.
6610 #include <isl/id_to_ast_expr.h>
6611 int isl_id_to_ast_expr_has(
6612 __isl_keep id_to_ast_expr *id2expr,
6613 __isl_keep isl_id *key);
6614 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6615 __isl_keep id_to_ast_expr *id2expr,
6616 __isl_take isl_id *key);
6617 int isl_id_to_ast_expr_foreach(
6618 __isl_keep id_to_ast_expr *id2expr,
6619 int (*fn)(__isl_take isl_id *key,
6620 __isl_take isl_ast_expr *val, void *user),
6623 They can be modified using the following function.
6625 #include <isl/id_to_ast_expr.h>
6626 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6627 __isl_take id_to_ast_expr *id2expr,
6628 __isl_take isl_id *key,
6629 __isl_take isl_ast_expr *val);
6630 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6631 __isl_take id_to_ast_expr *id2expr,
6632 __isl_take isl_id *key);
6634 Associative arrays can be printed using the following function.
6636 #include <isl/id_to_ast_expr.h>
6637 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6638 __isl_take isl_printer *p,
6639 __isl_keep id_to_ast_expr *id2expr);
6643 Vectors can be created, copied and freed using the following functions.
6645 #include <isl/vec.h>
6646 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6648 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6649 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6651 Note that the elements of a newly created vector may have arbitrary values.
6652 The elements can be changed and inspected using the following functions.
6654 int isl_vec_size(__isl_keep isl_vec *vec);
6655 __isl_give isl_val *isl_vec_get_element_val(
6656 __isl_keep isl_vec *vec, int pos);
6657 __isl_give isl_vec *isl_vec_set_element_si(
6658 __isl_take isl_vec *vec, int pos, int v);
6659 __isl_give isl_vec *isl_vec_set_element_val(
6660 __isl_take isl_vec *vec, int pos,
6661 __isl_take isl_val *v);
6662 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6664 __isl_give isl_vec *isl_vec_set_val(
6665 __isl_take isl_vec *vec, __isl_take isl_val *v);
6666 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6667 __isl_keep isl_vec *vec2, int pos);
6669 C<isl_vec_get_element> will return a negative value if anything went wrong.
6670 In that case, the value of C<*v> is undefined.
6672 The following function can be used to concatenate two vectors.
6674 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6675 __isl_take isl_vec *vec2);
6679 Matrices can be created, copied and freed using the following functions.
6681 #include <isl/mat.h>
6682 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6683 unsigned n_row, unsigned n_col);
6684 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6685 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6687 Note that the elements of a newly created matrix may have arbitrary values.
6688 The elements can be changed and inspected using the following functions.
6690 int isl_mat_rows(__isl_keep isl_mat *mat);
6691 int isl_mat_cols(__isl_keep isl_mat *mat);
6692 __isl_give isl_val *isl_mat_get_element_val(
6693 __isl_keep isl_mat *mat, int row, int col);
6694 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
6695 int row, int col, int v);
6696 __isl_give isl_mat *isl_mat_set_element_val(
6697 __isl_take isl_mat *mat, int row, int col,
6698 __isl_take isl_val *v);
6700 C<isl_mat_get_element> will return a negative value if anything went wrong.
6701 In that case, the value of C<*v> is undefined.
6703 The following function can be used to compute the (right) inverse
6704 of a matrix, i.e., a matrix such that the product of the original
6705 and the inverse (in that order) is a multiple of the identity matrix.
6706 The input matrix is assumed to be of full row-rank.
6708 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
6710 The following function can be used to compute the (right) kernel
6711 (or null space) of a matrix, i.e., a matrix such that the product of
6712 the original and the kernel (in that order) is the zero matrix.
6714 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
6716 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
6718 The following functions determine
6719 an upper or lower bound on a quasipolynomial over its domain.
6721 __isl_give isl_pw_qpolynomial_fold *
6722 isl_pw_qpolynomial_bound(
6723 __isl_take isl_pw_qpolynomial *pwqp,
6724 enum isl_fold type, int *tight);
6726 __isl_give isl_union_pw_qpolynomial_fold *
6727 isl_union_pw_qpolynomial_bound(
6728 __isl_take isl_union_pw_qpolynomial *upwqp,
6729 enum isl_fold type, int *tight);
6731 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
6732 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
6733 is the returned bound is known be tight, i.e., for each value
6734 of the parameters there is at least
6735 one element in the domain that reaches the bound.
6736 If the domain of C<pwqp> is not wrapping, then the bound is computed
6737 over all elements in that domain and the result has a purely parametric
6738 domain. If the domain of C<pwqp> is wrapping, then the bound is
6739 computed over the range of the wrapped relation. The domain of the
6740 wrapped relation becomes the domain of the result.
6742 =head2 Parametric Vertex Enumeration
6744 The parametric vertex enumeration described in this section
6745 is mainly intended to be used internally and by the C<barvinok>
6748 #include <isl/vertices.h>
6749 __isl_give isl_vertices *isl_basic_set_compute_vertices(
6750 __isl_keep isl_basic_set *bset);
6752 The function C<isl_basic_set_compute_vertices> performs the
6753 actual computation of the parametric vertices and the chamber
6754 decomposition and store the result in an C<isl_vertices> object.
6755 This information can be queried by either iterating over all
6756 the vertices or iterating over all the chambers or cells
6757 and then iterating over all vertices that are active on the chamber.
6759 int isl_vertices_foreach_vertex(
6760 __isl_keep isl_vertices *vertices,
6761 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6764 int isl_vertices_foreach_cell(
6765 __isl_keep isl_vertices *vertices,
6766 int (*fn)(__isl_take isl_cell *cell, void *user),
6768 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
6769 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6772 Other operations that can be performed on an C<isl_vertices> object are
6775 int isl_vertices_get_n_vertices(
6776 __isl_keep isl_vertices *vertices);
6777 void isl_vertices_free(__isl_take isl_vertices *vertices);
6779 Vertices can be inspected and destroyed using the following functions.
6781 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
6782 __isl_give isl_basic_set *isl_vertex_get_domain(
6783 __isl_keep isl_vertex *vertex);
6784 __isl_give isl_multi_aff *isl_vertex_get_expr(
6785 __isl_keep isl_vertex *vertex);
6786 void isl_vertex_free(__isl_take isl_vertex *vertex);
6788 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
6789 describing the vertex in terms of the parameters,
6790 while C<isl_vertex_get_domain> returns the activity domain
6793 Chambers can be inspected and destroyed using the following functions.
6795 __isl_give isl_basic_set *isl_cell_get_domain(
6796 __isl_keep isl_cell *cell);
6797 void isl_cell_free(__isl_take isl_cell *cell);
6799 =head1 Polyhedral Compilation Library
6801 This section collects functionality in C<isl> that has been specifically
6802 designed for use during polyhedral compilation.
6804 =head2 Dependence Analysis
6806 C<isl> contains specialized functionality for performing
6807 array dataflow analysis. That is, given a I<sink> access relation
6808 and a collection of possible I<source> access relations,
6809 C<isl> can compute relations that describe
6810 for each iteration of the sink access, which iteration
6811 of which of the source access relations was the last
6812 to access the same data element before the given iteration
6814 The resulting dependence relations map source iterations
6815 to the corresponding sink iterations.
6816 To compute standard flow dependences, the sink should be
6817 a read, while the sources should be writes.
6818 If any of the source accesses are marked as being I<may>
6819 accesses, then there will be a dependence from the last
6820 I<must> access B<and> from any I<may> access that follows
6821 this last I<must> access.
6822 In particular, if I<all> sources are I<may> accesses,
6823 then memory based dependence analysis is performed.
6824 If, on the other hand, all sources are I<must> accesses,
6825 then value based dependence analysis is performed.
6827 #include <isl/flow.h>
6829 typedef int (*isl_access_level_before)(void *first, void *second);
6831 __isl_give isl_access_info *isl_access_info_alloc(
6832 __isl_take isl_map *sink,
6833 void *sink_user, isl_access_level_before fn,
6835 __isl_give isl_access_info *isl_access_info_add_source(
6836 __isl_take isl_access_info *acc,
6837 __isl_take isl_map *source, int must,
6839 __isl_null isl_access_info *isl_access_info_free(
6840 __isl_take isl_access_info *acc);
6842 __isl_give isl_flow *isl_access_info_compute_flow(
6843 __isl_take isl_access_info *acc);
6845 int isl_flow_foreach(__isl_keep isl_flow *deps,
6846 int (*fn)(__isl_take isl_map *dep, int must,
6847 void *dep_user, void *user),
6849 __isl_give isl_map *isl_flow_get_no_source(
6850 __isl_keep isl_flow *deps, int must);
6851 void isl_flow_free(__isl_take isl_flow *deps);
6853 The function C<isl_access_info_compute_flow> performs the actual
6854 dependence analysis. The other functions are used to construct
6855 the input for this function or to read off the output.
6857 The input is collected in an C<isl_access_info>, which can
6858 be created through a call to C<isl_access_info_alloc>.
6859 The arguments to this functions are the sink access relation
6860 C<sink>, a token C<sink_user> used to identify the sink
6861 access to the user, a callback function for specifying the
6862 relative order of source and sink accesses, and the number
6863 of source access relations that will be added.
6864 The callback function has type C<int (*)(void *first, void *second)>.
6865 The function is called with two user supplied tokens identifying
6866 either a source or the sink and it should return the shared nesting
6867 level and the relative order of the two accesses.
6868 In particular, let I<n> be the number of loops shared by
6869 the two accesses. If C<first> precedes C<second> textually,
6870 then the function should return I<2 * n + 1>; otherwise,
6871 it should return I<2 * n>.
6872 The sources can be added to the C<isl_access_info> by performing
6873 (at most) C<max_source> calls to C<isl_access_info_add_source>.
6874 C<must> indicates whether the source is a I<must> access
6875 or a I<may> access. Note that a multi-valued access relation
6876 should only be marked I<must> if every iteration in the domain
6877 of the relation accesses I<all> elements in its image.
6878 The C<source_user> token is again used to identify
6879 the source access. The range of the source access relation
6880 C<source> should have the same dimension as the range
6881 of the sink access relation.
6882 The C<isl_access_info_free> function should usually not be
6883 called explicitly, because it is called implicitly by
6884 C<isl_access_info_compute_flow>.
6886 The result of the dependence analysis is collected in an
6887 C<isl_flow>. There may be elements of
6888 the sink access for which no preceding source access could be
6889 found or for which all preceding sources are I<may> accesses.
6890 The relations containing these elements can be obtained through
6891 calls to C<isl_flow_get_no_source>, the first with C<must> set
6892 and the second with C<must> unset.
6893 In the case of standard flow dependence analysis,
6894 with the sink a read and the sources I<must> writes,
6895 the first relation corresponds to the reads from uninitialized
6896 array elements and the second relation is empty.
6897 The actual flow dependences can be extracted using
6898 C<isl_flow_foreach>. This function will call the user-specified
6899 callback function C<fn> for each B<non-empty> dependence between
6900 a source and the sink. The callback function is called
6901 with four arguments, the actual flow dependence relation
6902 mapping source iterations to sink iterations, a boolean that
6903 indicates whether it is a I<must> or I<may> dependence, a token
6904 identifying the source and an additional C<void *> with value
6905 equal to the third argument of the C<isl_flow_foreach> call.
6906 A dependence is marked I<must> if it originates from a I<must>
6907 source and if it is not followed by any I<may> sources.
6909 After finishing with an C<isl_flow>, the user should call
6910 C<isl_flow_free> to free all associated memory.
6912 A higher-level interface to dependence analysis is provided
6913 by the following function.
6915 #include <isl/flow.h>
6917 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
6918 __isl_take isl_union_map *must_source,
6919 __isl_take isl_union_map *may_source,
6920 __isl_take isl_union_map *schedule,
6921 __isl_give isl_union_map **must_dep,
6922 __isl_give isl_union_map **may_dep,
6923 __isl_give isl_union_map **must_no_source,
6924 __isl_give isl_union_map **may_no_source);
6926 The arrays are identified by the tuple names of the ranges
6927 of the accesses. The iteration domains by the tuple names
6928 of the domains of the accesses and of the schedule.
6929 The relative order of the iteration domains is given by the
6930 schedule. The relations returned through C<must_no_source>
6931 and C<may_no_source> are subsets of C<sink>.
6932 Any of C<must_dep>, C<may_dep>, C<must_no_source>
6933 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
6934 any of the other arguments is treated as an error.
6936 =head3 Interaction with Dependence Analysis
6938 During the dependence analysis, we frequently need to perform
6939 the following operation. Given a relation between sink iterations
6940 and potential source iterations from a particular source domain,
6941 what is the last potential source iteration corresponding to each
6942 sink iteration. It can sometimes be convenient to adjust
6943 the set of potential source iterations before or after each such operation.
6944 The prototypical example is fuzzy array dataflow analysis,
6945 where we need to analyze if, based on data-dependent constraints,
6946 the sink iteration can ever be executed without one or more of
6947 the corresponding potential source iterations being executed.
6948 If so, we can introduce extra parameters and select an unknown
6949 but fixed source iteration from the potential source iterations.
6950 To be able to perform such manipulations, C<isl> provides the following
6953 #include <isl/flow.h>
6955 typedef __isl_give isl_restriction *(*isl_access_restrict)(
6956 __isl_keep isl_map *source_map,
6957 __isl_keep isl_set *sink, void *source_user,
6959 __isl_give isl_access_info *isl_access_info_set_restrict(
6960 __isl_take isl_access_info *acc,
6961 isl_access_restrict fn, void *user);
6963 The function C<isl_access_info_set_restrict> should be called
6964 before calling C<isl_access_info_compute_flow> and registers a callback function
6965 that will be called any time C<isl> is about to compute the last
6966 potential source. The first argument is the (reverse) proto-dependence,
6967 mapping sink iterations to potential source iterations.
6968 The second argument represents the sink iterations for which
6969 we want to compute the last source iteration.
6970 The third argument is the token corresponding to the source
6971 and the final argument is the token passed to C<isl_access_info_set_restrict>.
6972 The callback is expected to return a restriction on either the input or
6973 the output of the operation computing the last potential source.
6974 If the input needs to be restricted then restrictions are needed
6975 for both the source and the sink iterations. The sink iterations
6976 and the potential source iterations will be intersected with these sets.
6977 If the output needs to be restricted then only a restriction on the source
6978 iterations is required.
6979 If any error occurs, the callback should return C<NULL>.
6980 An C<isl_restriction> object can be created, freed and inspected
6981 using the following functions.
6983 #include <isl/flow.h>
6985 __isl_give isl_restriction *isl_restriction_input(
6986 __isl_take isl_set *source_restr,
6987 __isl_take isl_set *sink_restr);
6988 __isl_give isl_restriction *isl_restriction_output(
6989 __isl_take isl_set *source_restr);
6990 __isl_give isl_restriction *isl_restriction_none(
6991 __isl_take isl_map *source_map);
6992 __isl_give isl_restriction *isl_restriction_empty(
6993 __isl_take isl_map *source_map);
6994 __isl_null isl_restriction *isl_restriction_free(
6995 __isl_take isl_restriction *restr);
6997 C<isl_restriction_none> and C<isl_restriction_empty> are special
6998 cases of C<isl_restriction_input>. C<isl_restriction_none>
6999 is essentially equivalent to
7001 isl_restriction_input(isl_set_universe(
7002 isl_space_range(isl_map_get_space(source_map))),
7004 isl_space_domain(isl_map_get_space(source_map))));
7006 whereas C<isl_restriction_empty> is essentially equivalent to
7008 isl_restriction_input(isl_set_empty(
7009 isl_space_range(isl_map_get_space(source_map))),
7011 isl_space_domain(isl_map_get_space(source_map))));
7015 B<The functionality described in this section is fairly new
7016 and may be subject to change.>
7018 #include <isl/schedule.h>
7019 __isl_give isl_schedule *
7020 isl_schedule_constraints_compute_schedule(
7021 __isl_take isl_schedule_constraints *sc);
7022 __isl_null isl_schedule *isl_schedule_free(
7023 __isl_take isl_schedule *sched);
7025 The function C<isl_schedule_constraints_compute_schedule> can be
7026 used to compute a schedule that satisfies the given schedule constraints.
7027 These schedule constraints include the iteration domain for which
7028 a schedule should be computed and dependences between pairs of
7029 iterations. In particular, these dependences include
7030 I<validity> dependences and I<proximity> dependences.
7031 By default, the algorithm used to construct the schedule is similar
7032 to that of C<Pluto>.
7033 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
7035 The generated schedule respects all validity dependences.
7036 That is, all dependence distances over these dependences in the
7037 scheduled space are lexicographically positive.
7038 The default algorithm tries to ensure that the dependence distances
7039 over coincidence constraints are zero and to minimize the
7040 dependence distances over proximity dependences.
7041 Moreover, it tries to obtain sequences (bands) of schedule dimensions
7042 for groups of domains where the dependence distances over validity
7043 dependences have only non-negative values.
7044 When using Feautrier's algorithm, the coincidence and proximity constraints
7045 are only taken into account during the extension to a
7046 full-dimensional schedule.
7048 An C<isl_schedule_constraints> object can be constructed
7049 and manipulated using the following functions.
7051 #include <isl/schedule.h>
7052 __isl_give isl_schedule_constraints *
7053 isl_schedule_constraints_copy(
7054 __isl_keep isl_schedule_constraints *sc);
7055 __isl_give isl_schedule_constraints *
7056 isl_schedule_constraints_on_domain(
7057 __isl_take isl_union_set *domain);
7058 __isl_give isl_schedule_constraints *
7059 isl_schedule_constraints_set_validity(
7060 __isl_take isl_schedule_constraints *sc,
7061 __isl_take isl_union_map *validity);
7062 __isl_give isl_schedule_constraints *
7063 isl_schedule_constraints_set_coincidence(
7064 __isl_take isl_schedule_constraints *sc,
7065 __isl_take isl_union_map *coincidence);
7066 __isl_give isl_schedule_constraints *
7067 isl_schedule_constraints_set_proximity(
7068 __isl_take isl_schedule_constraints *sc,
7069 __isl_take isl_union_map *proximity);
7070 __isl_give isl_schedule_constraints *
7071 isl_schedule_constraints_set_conditional_validity(
7072 __isl_take isl_schedule_constraints *sc,
7073 __isl_take isl_union_map *condition,
7074 __isl_take isl_union_map *validity);
7075 __isl_null isl_schedule_constraints *
7076 isl_schedule_constraints_free(
7077 __isl_take isl_schedule_constraints *sc);
7079 The initial C<isl_schedule_constraints> object created by
7080 C<isl_schedule_constraints_on_domain> does not impose any constraints.
7081 That is, it has an empty set of dependences.
7082 The function C<isl_schedule_constraints_set_validity> replaces the
7083 validity dependences, mapping domain elements I<i> to domain
7084 elements that should be scheduled after I<i>.
7085 The function C<isl_schedule_constraints_set_coincidence> replaces the
7086 coincidence dependences, mapping domain elements I<i> to domain
7087 elements that should be scheduled together with I<I>, if possible.
7088 The function C<isl_schedule_constraints_set_proximity> replaces the
7089 proximity dependences, mapping domain elements I<i> to domain
7090 elements that should be scheduled either before I<I>
7091 or as early as possible after I<i>.
7093 The function C<isl_schedule_constraints_set_conditional_validity>
7094 replaces the conditional validity constraints.
7095 A conditional validity constraint is only imposed when any of the corresponding
7096 conditions is satisfied, i.e., when any of them is non-zero.
7097 That is, the scheduler ensures that within each band if the dependence
7098 distances over the condition constraints are not all zero
7099 then all corresponding conditional validity constraints are respected.
7100 A conditional validity constraint corresponds to a condition
7101 if the two are adjacent, i.e., if the domain of one relation intersect
7102 the range of the other relation.
7103 The typical use case of conditional validity constraints is
7104 to allow order constraints between live ranges to be violated
7105 as long as the live ranges themselves are local to the band.
7106 To allow more fine-grained control over which conditions correspond
7107 to which conditional validity constraints, the domains and ranges
7108 of these relations may include I<tags>. That is, the domains and
7109 ranges of those relation may themselves be wrapped relations
7110 where the iteration domain appears in the domain of those wrapped relations
7111 and the range of the wrapped relations can be arbitrarily chosen
7112 by the user. Conditions and conditional validity constraints are only
7113 considered adjacent to each other if the entire wrapped relation matches.
7114 In particular, a relation with a tag will never be considered adjacent
7115 to a relation without a tag.
7117 The following function computes a schedule directly from
7118 an iteration domain and validity and proximity dependences
7119 and is implemented in terms of the functions described above.
7120 The use of C<isl_union_set_compute_schedule> is discouraged.
7122 #include <isl/schedule.h>
7123 __isl_give isl_schedule *isl_union_set_compute_schedule(
7124 __isl_take isl_union_set *domain,
7125 __isl_take isl_union_map *validity,
7126 __isl_take isl_union_map *proximity);
7128 A mapping from the domains to the scheduled space can be obtained
7129 from an C<isl_schedule> using the following function.
7131 __isl_give isl_union_map *isl_schedule_get_map(
7132 __isl_keep isl_schedule *sched);
7134 A representation of the schedule can be printed using
7136 __isl_give isl_printer *isl_printer_print_schedule(
7137 __isl_take isl_printer *p,
7138 __isl_keep isl_schedule *schedule);
7140 A representation of the schedule as a forest of bands can be obtained
7141 using the following function.
7143 __isl_give isl_band_list *isl_schedule_get_band_forest(
7144 __isl_keep isl_schedule *schedule);
7146 The individual bands can be visited in depth-first post-order
7147 using the following function.
7149 #include <isl/schedule.h>
7150 int isl_schedule_foreach_band(
7151 __isl_keep isl_schedule *sched,
7152 int (*fn)(__isl_keep isl_band *band, void *user),
7155 The list can be manipulated as explained in L<"Lists">.
7156 The bands inside the list can be copied and freed using the following
7159 #include <isl/band.h>
7160 __isl_give isl_band *isl_band_copy(
7161 __isl_keep isl_band *band);
7162 __isl_null isl_band *isl_band_free(
7163 __isl_take isl_band *band);
7165 Each band contains zero or more scheduling dimensions.
7166 These are referred to as the members of the band.
7167 The section of the schedule that corresponds to the band is
7168 referred to as the partial schedule of the band.
7169 For those nodes that participate in a band, the outer scheduling
7170 dimensions form the prefix schedule, while the inner scheduling
7171 dimensions form the suffix schedule.
7172 That is, if we take a cut of the band forest, then the union of
7173 the concatenations of the prefix, partial and suffix schedules of
7174 each band in the cut is equal to the entire schedule (modulo
7175 some possible padding at the end with zero scheduling dimensions).
7176 The properties of a band can be inspected using the following functions.
7178 #include <isl/band.h>
7179 int isl_band_has_children(__isl_keep isl_band *band);
7180 __isl_give isl_band_list *isl_band_get_children(
7181 __isl_keep isl_band *band);
7183 __isl_give isl_union_map *isl_band_get_prefix_schedule(
7184 __isl_keep isl_band *band);
7185 __isl_give isl_union_map *isl_band_get_partial_schedule(
7186 __isl_keep isl_band *band);
7187 __isl_give isl_union_map *isl_band_get_suffix_schedule(
7188 __isl_keep isl_band *band);
7190 int isl_band_n_member(__isl_keep isl_band *band);
7191 int isl_band_member_is_coincident(
7192 __isl_keep isl_band *band, int pos);
7194 int isl_band_list_foreach_band(
7195 __isl_keep isl_band_list *list,
7196 int (*fn)(__isl_keep isl_band *band, void *user),
7199 Note that a scheduling dimension is considered to be ``coincident''
7200 if it satisfies the coincidence constraints within its band.
7201 That is, if the dependence distances of the coincidence
7202 constraints are all zero in that direction (for fixed
7203 iterations of outer bands).
7204 Like C<isl_schedule_foreach_band>,
7205 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
7206 in depth-first post-order.
7208 A band can be tiled using the following function.
7210 #include <isl/band.h>
7211 int isl_band_tile(__isl_keep isl_band *band,
7212 __isl_take isl_vec *sizes);
7214 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
7216 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
7217 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
7219 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
7221 The C<isl_band_tile> function tiles the band using the given tile sizes
7222 inside its schedule.
7223 A new child band is created to represent the point loops and it is
7224 inserted between the modified band and its children.
7225 The C<tile_scale_tile_loops> option specifies whether the tile
7226 loops iterators should be scaled by the tile sizes.
7227 If the C<tile_shift_point_loops> option is set, then the point loops
7228 are shifted to start at zero.
7230 A band can be split into two nested bands using the following function.
7232 int isl_band_split(__isl_keep isl_band *band, int pos);
7234 The resulting outer band contains the first C<pos> dimensions of C<band>
7235 while the inner band contains the remaining dimensions.
7237 A representation of the band can be printed using
7239 #include <isl/band.h>
7240 __isl_give isl_printer *isl_printer_print_band(
7241 __isl_take isl_printer *p,
7242 __isl_keep isl_band *band);
7246 #include <isl/schedule.h>
7247 int isl_options_set_schedule_max_coefficient(
7248 isl_ctx *ctx, int val);
7249 int isl_options_get_schedule_max_coefficient(
7251 int isl_options_set_schedule_max_constant_term(
7252 isl_ctx *ctx, int val);
7253 int isl_options_get_schedule_max_constant_term(
7255 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
7256 int isl_options_get_schedule_fuse(isl_ctx *ctx);
7257 int isl_options_set_schedule_maximize_band_depth(
7258 isl_ctx *ctx, int val);
7259 int isl_options_get_schedule_maximize_band_depth(
7261 int isl_options_set_schedule_outer_coincidence(
7262 isl_ctx *ctx, int val);
7263 int isl_options_get_schedule_outer_coincidence(
7265 int isl_options_set_schedule_split_scaled(
7266 isl_ctx *ctx, int val);
7267 int isl_options_get_schedule_split_scaled(
7269 int isl_options_set_schedule_algorithm(
7270 isl_ctx *ctx, int val);
7271 int isl_options_get_schedule_algorithm(
7273 int isl_options_set_schedule_separate_components(
7274 isl_ctx *ctx, int val);
7275 int isl_options_get_schedule_separate_components(
7280 =item * schedule_max_coefficient
7282 This option enforces that the coefficients for variable and parameter
7283 dimensions in the calculated schedule are not larger than the specified value.
7284 This option can significantly increase the speed of the scheduling calculation
7285 and may also prevent fusing of unrelated dimensions. A value of -1 means that
7286 this option does not introduce bounds on the variable or parameter
7289 =item * schedule_max_constant_term
7291 This option enforces that the constant coefficients in the calculated schedule
7292 are not larger than the maximal constant term. This option can significantly
7293 increase the speed of the scheduling calculation and may also prevent fusing of
7294 unrelated dimensions. A value of -1 means that this option does not introduce
7295 bounds on the constant coefficients.
7297 =item * schedule_fuse
7299 This option controls the level of fusion.
7300 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
7301 resulting schedule will be distributed as much as possible.
7302 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
7303 try to fuse loops in the resulting schedule.
7305 =item * schedule_maximize_band_depth
7307 If this option is set, we do not split bands at the point
7308 where we detect splitting is necessary. Instead, we
7309 backtrack and split bands as early as possible. This
7310 reduces the number of splits and maximizes the width of
7311 the bands. Wider bands give more possibilities for tiling.
7312 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
7313 then bands will be split as early as possible, even if there is no need.
7314 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
7316 =item * schedule_outer_coincidence
7318 If this option is set, then we try to construct schedules
7319 where the outermost scheduling dimension in each band
7320 satisfies the coincidence constraints.
7322 =item * schedule_split_scaled
7324 If this option is set, then we try to construct schedules in which the
7325 constant term is split off from the linear part if the linear parts of
7326 the scheduling rows for all nodes in the graphs have a common non-trivial
7328 The constant term is then placed in a separate band and the linear
7331 =item * schedule_algorithm
7333 Selects the scheduling algorithm to be used.
7334 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
7335 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
7337 =item * schedule_separate_components
7339 If at any point the dependence graph contains any (weakly connected) components,
7340 then these components are scheduled separately.
7341 If this option is not set, then some iterations of the domains
7342 in these components may be scheduled together.
7343 If this option is set, then the components are given consecutive
7348 =head2 AST Generation
7350 This section describes the C<isl> functionality for generating
7351 ASTs that visit all the elements
7352 in a domain in an order specified by a schedule.
7353 In particular, given a C<isl_union_map>, an AST is generated
7354 that visits all the elements in the domain of the C<isl_union_map>
7355 according to the lexicographic order of the corresponding image
7356 element(s). If the range of the C<isl_union_map> consists of
7357 elements in more than one space, then each of these spaces is handled
7358 separately in an arbitrary order.
7359 It should be noted that the image elements only specify the I<order>
7360 in which the corresponding domain elements should be visited.
7361 No direct relation between the image elements and the loop iterators
7362 in the generated AST should be assumed.
7364 Each AST is generated within a build. The initial build
7365 simply specifies the constraints on the parameters (if any)
7366 and can be created, inspected, copied and freed using the following functions.
7368 #include <isl/ast_build.h>
7369 __isl_give isl_ast_build *isl_ast_build_from_context(
7370 __isl_take isl_set *set);
7371 __isl_give isl_ast_build *isl_ast_build_copy(
7372 __isl_keep isl_ast_build *build);
7373 __isl_null isl_ast_build *isl_ast_build_free(
7374 __isl_take isl_ast_build *build);
7376 The C<set> argument is usually a parameter set with zero or more parameters.
7377 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
7378 and L</"Fine-grained Control over AST Generation">.
7379 Finally, the AST itself can be constructed using the following
7382 #include <isl/ast_build.h>
7383 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
7384 __isl_keep isl_ast_build *build,
7385 __isl_take isl_union_map *schedule);
7387 =head3 Inspecting the AST
7389 The basic properties of an AST node can be obtained as follows.
7391 #include <isl/ast.h>
7392 enum isl_ast_node_type isl_ast_node_get_type(
7393 __isl_keep isl_ast_node *node);
7395 The type of an AST node is one of
7396 C<isl_ast_node_for>,
7398 C<isl_ast_node_block> or
7399 C<isl_ast_node_user>.
7400 An C<isl_ast_node_for> represents a for node.
7401 An C<isl_ast_node_if> represents an if node.
7402 An C<isl_ast_node_block> represents a compound node.
7403 An C<isl_ast_node_user> represents an expression statement.
7404 An expression statement typically corresponds to a domain element, i.e.,
7405 one of the elements that is visited by the AST.
7407 Each type of node has its own additional properties.
7409 #include <isl/ast.h>
7410 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7411 __isl_keep isl_ast_node *node);
7412 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7413 __isl_keep isl_ast_node *node);
7414 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7415 __isl_keep isl_ast_node *node);
7416 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7417 __isl_keep isl_ast_node *node);
7418 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7419 __isl_keep isl_ast_node *node);
7420 int isl_ast_node_for_is_degenerate(
7421 __isl_keep isl_ast_node *node);
7423 An C<isl_ast_for> is considered degenerate if it is known to execute
7426 #include <isl/ast.h>
7427 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7428 __isl_keep isl_ast_node *node);
7429 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7430 __isl_keep isl_ast_node *node);
7431 int isl_ast_node_if_has_else(
7432 __isl_keep isl_ast_node *node);
7433 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7434 __isl_keep isl_ast_node *node);
7436 __isl_give isl_ast_node_list *
7437 isl_ast_node_block_get_children(
7438 __isl_keep isl_ast_node *node);
7440 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7441 __isl_keep isl_ast_node *node);
7443 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7444 the following functions.
7446 #include <isl/ast.h>
7447 enum isl_ast_expr_type isl_ast_expr_get_type(
7448 __isl_keep isl_ast_expr *expr);
7450 The type of an AST expression is one of
7452 C<isl_ast_expr_id> or
7453 C<isl_ast_expr_int>.
7454 An C<isl_ast_expr_op> represents the result of an operation.
7455 An C<isl_ast_expr_id> represents an identifier.
7456 An C<isl_ast_expr_int> represents an integer value.
7458 Each type of expression has its own additional properties.
7460 #include <isl/ast.h>
7461 enum isl_ast_op_type isl_ast_expr_get_op_type(
7462 __isl_keep isl_ast_expr *expr);
7463 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7464 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7465 __isl_keep isl_ast_expr *expr, int pos);
7466 int isl_ast_node_foreach_ast_op_type(
7467 __isl_keep isl_ast_node *node,
7468 int (*fn)(enum isl_ast_op_type type, void *user),
7471 C<isl_ast_expr_get_op_type> returns the type of the operation
7472 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7473 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7475 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7476 C<isl_ast_op_type> that appears in C<node>.
7477 The operation type is one of the following.
7481 =item C<isl_ast_op_and>
7483 Logical I<and> of two arguments.
7484 Both arguments can be evaluated.
7486 =item C<isl_ast_op_and_then>
7488 Logical I<and> of two arguments.
7489 The second argument can only be evaluated if the first evaluates to true.
7491 =item C<isl_ast_op_or>
7493 Logical I<or> of two arguments.
7494 Both arguments can be evaluated.
7496 =item C<isl_ast_op_or_else>
7498 Logical I<or> of two arguments.
7499 The second argument can only be evaluated if the first evaluates to false.
7501 =item C<isl_ast_op_max>
7503 Maximum of two or more arguments.
7505 =item C<isl_ast_op_min>
7507 Minimum of two or more arguments.
7509 =item C<isl_ast_op_minus>
7513 =item C<isl_ast_op_add>
7515 Sum of two arguments.
7517 =item C<isl_ast_op_sub>
7519 Difference of two arguments.
7521 =item C<isl_ast_op_mul>
7523 Product of two arguments.
7525 =item C<isl_ast_op_div>
7527 Exact division. That is, the result is known to be an integer.
7529 =item C<isl_ast_op_fdiv_q>
7531 Result of integer division, rounded towards negative
7534 =item C<isl_ast_op_pdiv_q>
7536 Result of integer division, where dividend is known to be non-negative.
7538 =item C<isl_ast_op_pdiv_r>
7540 Remainder of integer division, where dividend is known to be non-negative.
7542 =item C<isl_ast_op_zdiv_r>
7544 Equal to zero iff the remainder on integer division is zero.
7546 =item C<isl_ast_op_cond>
7548 Conditional operator defined on three arguments.
7549 If the first argument evaluates to true, then the result
7550 is equal to the second argument. Otherwise, the result
7551 is equal to the third argument.
7552 The second and third argument may only be evaluated if
7553 the first argument evaluates to true and false, respectively.
7554 Corresponds to C<a ? b : c> in C.
7556 =item C<isl_ast_op_select>
7558 Conditional operator defined on three arguments.
7559 If the first argument evaluates to true, then the result
7560 is equal to the second argument. Otherwise, the result
7561 is equal to the third argument.
7562 The second and third argument may be evaluated independently
7563 of the value of the first argument.
7564 Corresponds to C<a * b + (1 - a) * c> in C.
7566 =item C<isl_ast_op_eq>
7570 =item C<isl_ast_op_le>
7572 Less than or equal relation.
7574 =item C<isl_ast_op_lt>
7578 =item C<isl_ast_op_ge>
7580 Greater than or equal relation.
7582 =item C<isl_ast_op_gt>
7584 Greater than relation.
7586 =item C<isl_ast_op_call>
7589 The number of arguments of the C<isl_ast_expr> is one more than
7590 the number of arguments in the function call, the first argument
7591 representing the function being called.
7593 =item C<isl_ast_op_access>
7596 The number of arguments of the C<isl_ast_expr> is one more than
7597 the number of index expressions in the array access, the first argument
7598 representing the array being accessed.
7600 =item C<isl_ast_op_member>
7603 This operation has two arguments, a structure and the name of
7604 the member of the structure being accessed.
7608 #include <isl/ast.h>
7609 __isl_give isl_id *isl_ast_expr_get_id(
7610 __isl_keep isl_ast_expr *expr);
7612 Return the identifier represented by the AST expression.
7614 #include <isl/ast.h>
7615 __isl_give isl_val *isl_ast_expr_get_val(
7616 __isl_keep isl_ast_expr *expr);
7618 Return the integer represented by the AST expression.
7620 =head3 Properties of ASTs
7622 #include <isl/ast.h>
7623 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7624 __isl_keep isl_ast_expr *expr2);
7626 Check if two C<isl_ast_expr>s are equal to each other.
7628 =head3 Manipulating and printing the AST
7630 AST nodes can be copied and freed using the following functions.
7632 #include <isl/ast.h>
7633 __isl_give isl_ast_node *isl_ast_node_copy(
7634 __isl_keep isl_ast_node *node);
7635 __isl_null isl_ast_node *isl_ast_node_free(
7636 __isl_take isl_ast_node *node);
7638 AST expressions can be copied and freed using the following functions.
7640 #include <isl/ast.h>
7641 __isl_give isl_ast_expr *isl_ast_expr_copy(
7642 __isl_keep isl_ast_expr *expr);
7643 __isl_null isl_ast_expr *isl_ast_expr_free(
7644 __isl_take isl_ast_expr *expr);
7646 New AST expressions can be created either directly or within
7647 the context of an C<isl_ast_build>.
7649 #include <isl/ast.h>
7650 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7651 __isl_take isl_val *v);
7652 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7653 __isl_take isl_id *id);
7654 __isl_give isl_ast_expr *isl_ast_expr_neg(
7655 __isl_take isl_ast_expr *expr);
7656 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7657 __isl_take isl_ast_expr *expr);
7658 __isl_give isl_ast_expr *isl_ast_expr_add(
7659 __isl_take isl_ast_expr *expr1,
7660 __isl_take isl_ast_expr *expr2);
7661 __isl_give isl_ast_expr *isl_ast_expr_sub(
7662 __isl_take isl_ast_expr *expr1,
7663 __isl_take isl_ast_expr *expr2);
7664 __isl_give isl_ast_expr *isl_ast_expr_mul(
7665 __isl_take isl_ast_expr *expr1,
7666 __isl_take isl_ast_expr *expr2);
7667 __isl_give isl_ast_expr *isl_ast_expr_div(
7668 __isl_take isl_ast_expr *expr1,
7669 __isl_take isl_ast_expr *expr2);
7670 __isl_give isl_ast_expr *isl_ast_expr_and(
7671 __isl_take isl_ast_expr *expr1,
7672 __isl_take isl_ast_expr *expr2)
7673 __isl_give isl_ast_expr *isl_ast_expr_or(
7674 __isl_take isl_ast_expr *expr1,
7675 __isl_take isl_ast_expr *expr2)
7676 __isl_give isl_ast_expr *isl_ast_expr_eq(
7677 __isl_take isl_ast_expr *expr1,
7678 __isl_take isl_ast_expr *expr2);
7679 __isl_give isl_ast_expr *isl_ast_expr_le(
7680 __isl_take isl_ast_expr *expr1,
7681 __isl_take isl_ast_expr *expr2);
7682 __isl_give isl_ast_expr *isl_ast_expr_lt(
7683 __isl_take isl_ast_expr *expr1,
7684 __isl_take isl_ast_expr *expr2);
7685 __isl_give isl_ast_expr *isl_ast_expr_ge(
7686 __isl_take isl_ast_expr *expr1,
7687 __isl_take isl_ast_expr *expr2);
7688 __isl_give isl_ast_expr *isl_ast_expr_gt(
7689 __isl_take isl_ast_expr *expr1,
7690 __isl_take isl_ast_expr *expr2);
7691 __isl_give isl_ast_expr *isl_ast_expr_access(
7692 __isl_take isl_ast_expr *array,
7693 __isl_take isl_ast_expr_list *indices);
7695 The function C<isl_ast_expr_address_of> can be applied to an
7696 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
7697 to represent the address of the C<isl_ast_expr_access>.
7699 #include <isl/ast_build.h>
7700 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
7701 __isl_keep isl_ast_build *build,
7702 __isl_take isl_pw_aff *pa);
7703 __isl_give isl_ast_expr *
7704 isl_ast_build_access_from_pw_multi_aff(
7705 __isl_keep isl_ast_build *build,
7706 __isl_take isl_pw_multi_aff *pma);
7707 __isl_give isl_ast_expr *
7708 isl_ast_build_access_from_multi_pw_aff(
7709 __isl_keep isl_ast_build *build,
7710 __isl_take isl_multi_pw_aff *mpa);
7711 __isl_give isl_ast_expr *
7712 isl_ast_build_call_from_pw_multi_aff(
7713 __isl_keep isl_ast_build *build,
7714 __isl_take isl_pw_multi_aff *pma);
7715 __isl_give isl_ast_expr *
7716 isl_ast_build_call_from_multi_pw_aff(
7717 __isl_keep isl_ast_build *build,
7718 __isl_take isl_multi_pw_aff *mpa);
7720 The domains of C<pa>, C<mpa> and C<pma> should correspond
7721 to the schedule space of C<build>.
7722 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
7723 the function being called.
7724 If the accessed space is a nested relation, then it is taken
7725 to represent an access of the member specified by the range
7726 of this nested relation of the structure specified by the domain
7727 of the nested relation.
7729 The following functions can be used to modify an C<isl_ast_expr>.
7731 #include <isl/ast.h>
7732 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
7733 __isl_take isl_ast_expr *expr, int pos,
7734 __isl_take isl_ast_expr *arg);
7736 Replace the argument of C<expr> at position C<pos> by C<arg>.
7738 #include <isl/ast.h>
7739 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
7740 __isl_take isl_ast_expr *expr,
7741 __isl_take isl_id_to_ast_expr *id2expr);
7743 The function C<isl_ast_expr_substitute_ids> replaces the
7744 subexpressions of C<expr> of type C<isl_ast_expr_id>
7745 by the corresponding expression in C<id2expr>, if there is any.
7748 User specified data can be attached to an C<isl_ast_node> and obtained
7749 from the same C<isl_ast_node> using the following functions.
7751 #include <isl/ast.h>
7752 __isl_give isl_ast_node *isl_ast_node_set_annotation(
7753 __isl_take isl_ast_node *node,
7754 __isl_take isl_id *annotation);
7755 __isl_give isl_id *isl_ast_node_get_annotation(
7756 __isl_keep isl_ast_node *node);
7758 Basic printing can be performed using the following functions.
7760 #include <isl/ast.h>
7761 __isl_give isl_printer *isl_printer_print_ast_expr(
7762 __isl_take isl_printer *p,
7763 __isl_keep isl_ast_expr *expr);
7764 __isl_give isl_printer *isl_printer_print_ast_node(
7765 __isl_take isl_printer *p,
7766 __isl_keep isl_ast_node *node);
7767 __isl_give char *isl_ast_expr_to_str(
7768 __isl_keep isl_ast_expr *expr);
7770 More advanced printing can be performed using the following functions.
7772 #include <isl/ast.h>
7773 __isl_give isl_printer *isl_ast_op_type_print_macro(
7774 enum isl_ast_op_type type,
7775 __isl_take isl_printer *p);
7776 __isl_give isl_printer *isl_ast_node_print_macros(
7777 __isl_keep isl_ast_node *node,
7778 __isl_take isl_printer *p);
7779 __isl_give isl_printer *isl_ast_node_print(
7780 __isl_keep isl_ast_node *node,
7781 __isl_take isl_printer *p,
7782 __isl_take isl_ast_print_options *options);
7783 __isl_give isl_printer *isl_ast_node_for_print(
7784 __isl_keep isl_ast_node *node,
7785 __isl_take isl_printer *p,
7786 __isl_take isl_ast_print_options *options);
7787 __isl_give isl_printer *isl_ast_node_if_print(
7788 __isl_keep isl_ast_node *node,
7789 __isl_take isl_printer *p,
7790 __isl_take isl_ast_print_options *options);
7792 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
7793 C<isl> may print out an AST that makes use of macros such
7794 as C<floord>, C<min> and C<max>.
7795 C<isl_ast_op_type_print_macro> prints out the macro
7796 corresponding to a specific C<isl_ast_op_type>.
7797 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
7798 for expressions where these macros would be used and prints
7799 out the required macro definitions.
7800 Essentially, C<isl_ast_node_print_macros> calls
7801 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
7802 as function argument.
7803 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
7804 C<isl_ast_node_if_print> print an C<isl_ast_node>
7805 in C<ISL_FORMAT_C>, but allow for some extra control
7806 through an C<isl_ast_print_options> object.
7807 This object can be created using the following functions.
7809 #include <isl/ast.h>
7810 __isl_give isl_ast_print_options *
7811 isl_ast_print_options_alloc(isl_ctx *ctx);
7812 __isl_give isl_ast_print_options *
7813 isl_ast_print_options_copy(
7814 __isl_keep isl_ast_print_options *options);
7815 __isl_null isl_ast_print_options *
7816 isl_ast_print_options_free(
7817 __isl_take isl_ast_print_options *options);
7819 __isl_give isl_ast_print_options *
7820 isl_ast_print_options_set_print_user(
7821 __isl_take isl_ast_print_options *options,
7822 __isl_give isl_printer *(*print_user)(
7823 __isl_take isl_printer *p,
7824 __isl_take isl_ast_print_options *options,
7825 __isl_keep isl_ast_node *node, void *user),
7827 __isl_give isl_ast_print_options *
7828 isl_ast_print_options_set_print_for(
7829 __isl_take isl_ast_print_options *options,
7830 __isl_give isl_printer *(*print_for)(
7831 __isl_take isl_printer *p,
7832 __isl_take isl_ast_print_options *options,
7833 __isl_keep isl_ast_node *node, void *user),
7836 The callback set by C<isl_ast_print_options_set_print_user>
7837 is called whenever a node of type C<isl_ast_node_user> needs to
7839 The callback set by C<isl_ast_print_options_set_print_for>
7840 is called whenever a node of type C<isl_ast_node_for> needs to
7842 Note that C<isl_ast_node_for_print> will I<not> call the
7843 callback set by C<isl_ast_print_options_set_print_for> on the node
7844 on which C<isl_ast_node_for_print> is called, but only on nested
7845 nodes of type C<isl_ast_node_for>. It is therefore safe to
7846 call C<isl_ast_node_for_print> from within the callback set by
7847 C<isl_ast_print_options_set_print_for>.
7849 The following option determines the type to be used for iterators
7850 while printing the AST.
7852 int isl_options_set_ast_iterator_type(
7853 isl_ctx *ctx, const char *val);
7854 const char *isl_options_get_ast_iterator_type(
7857 The AST printer only prints body nodes as blocks if these
7858 blocks cannot be safely omitted.
7859 For example, a C<for> node with one body node will not be
7860 surrounded with braces in C<ISL_FORMAT_C>.
7861 A block will always be printed by setting the following option.
7863 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
7865 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
7869 #include <isl/ast_build.h>
7870 int isl_options_set_ast_build_atomic_upper_bound(
7871 isl_ctx *ctx, int val);
7872 int isl_options_get_ast_build_atomic_upper_bound(
7874 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
7876 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
7877 int isl_options_set_ast_build_exploit_nested_bounds(
7878 isl_ctx *ctx, int val);
7879 int isl_options_get_ast_build_exploit_nested_bounds(
7881 int isl_options_set_ast_build_group_coscheduled(
7882 isl_ctx *ctx, int val);
7883 int isl_options_get_ast_build_group_coscheduled(
7885 int isl_options_set_ast_build_scale_strides(
7886 isl_ctx *ctx, int val);
7887 int isl_options_get_ast_build_scale_strides(
7889 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
7891 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
7892 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
7894 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
7898 =item * ast_build_atomic_upper_bound
7900 Generate loop upper bounds that consist of the current loop iterator,
7901 an operator and an expression not involving the iterator.
7902 If this option is not set, then the current loop iterator may appear
7903 several times in the upper bound.
7904 For example, when this option is turned off, AST generation
7907 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
7911 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
7914 When the option is turned on, the following AST is generated
7916 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
7919 =item * ast_build_prefer_pdiv
7921 If this option is turned off, then the AST generation will
7922 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
7923 operators, but no C<isl_ast_op_pdiv_q> or
7924 C<isl_ast_op_pdiv_r> operators.
7925 If this options is turned on, then C<isl> will try to convert
7926 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
7927 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
7929 =item * ast_build_exploit_nested_bounds
7931 Simplify conditions based on bounds of nested for loops.
7932 In particular, remove conditions that are implied by the fact
7933 that one or more nested loops have at least one iteration,
7934 meaning that the upper bound is at least as large as the lower bound.
7935 For example, when this option is turned off, AST generation
7938 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
7944 for (int c0 = 0; c0 <= N; c0 += 1)
7945 for (int c1 = 0; c1 <= M; c1 += 1)
7948 When the option is turned on, the following AST is generated
7950 for (int c0 = 0; c0 <= N; c0 += 1)
7951 for (int c1 = 0; c1 <= M; c1 += 1)
7954 =item * ast_build_group_coscheduled
7956 If two domain elements are assigned the same schedule point, then
7957 they may be executed in any order and they may even appear in different
7958 loops. If this options is set, then the AST generator will make
7959 sure that coscheduled domain elements do not appear in separate parts
7960 of the AST. This is useful in case of nested AST generation
7961 if the outer AST generation is given only part of a schedule
7962 and the inner AST generation should handle the domains that are
7963 coscheduled by this initial part of the schedule together.
7964 For example if an AST is generated for a schedule
7966 { A[i] -> [0]; B[i] -> [0] }
7968 then the C<isl_ast_build_set_create_leaf> callback described
7969 below may get called twice, once for each domain.
7970 Setting this option ensures that the callback is only called once
7971 on both domains together.
7973 =item * ast_build_separation_bounds
7975 This option specifies which bounds to use during separation.
7976 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
7977 then all (possibly implicit) bounds on the current dimension will
7978 be used during separation.
7979 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
7980 then only those bounds that are explicitly available will
7981 be used during separation.
7983 =item * ast_build_scale_strides
7985 This option specifies whether the AST generator is allowed
7986 to scale down iterators of strided loops.
7988 =item * ast_build_allow_else
7990 This option specifies whether the AST generator is allowed
7991 to construct if statements with else branches.
7993 =item * ast_build_allow_or
7995 This option specifies whether the AST generator is allowed
7996 to construct if conditions with disjunctions.
8000 =head3 Fine-grained Control over AST Generation
8002 Besides specifying the constraints on the parameters,
8003 an C<isl_ast_build> object can be used to control
8004 various aspects of the AST generation process.
8005 The most prominent way of control is through ``options'',
8006 which can be set using the following function.
8008 #include <isl/ast_build.h>
8009 __isl_give isl_ast_build *
8010 isl_ast_build_set_options(
8011 __isl_take isl_ast_build *control,
8012 __isl_take isl_union_map *options);
8014 The options are encoded in an C<isl_union_map>.
8015 The domain of this union relation refers to the schedule domain,
8016 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
8017 In the case of nested AST generation (see L</"Nested AST Generation">),
8018 the domain of C<options> should refer to the extra piece of the schedule.
8019 That is, it should be equal to the range of the wrapped relation in the
8020 range of the schedule.
8021 The range of the options can consist of elements in one or more spaces,
8022 the names of which determine the effect of the option.
8023 The values of the range typically also refer to the schedule dimension
8024 to which the option applies. In case of nested AST generation
8025 (see L</"Nested AST Generation">), these values refer to the position
8026 of the schedule dimension within the innermost AST generation.
8027 The constraints on the domain elements of
8028 the option should only refer to this dimension and earlier dimensions.
8029 We consider the following spaces.
8033 =item C<separation_class>
8035 This space is a wrapped relation between two one dimensional spaces.
8036 The input space represents the schedule dimension to which the option
8037 applies and the output space represents the separation class.
8038 While constructing a loop corresponding to the specified schedule
8039 dimension(s), the AST generator will try to generate separate loops
8040 for domain elements that are assigned different classes.
8041 If only some of the elements are assigned a class, then those elements
8042 that are not assigned any class will be treated as belonging to a class
8043 that is separate from the explicitly assigned classes.
8044 The typical use case for this option is to separate full tiles from
8046 The other options, described below, are applied after the separation
8049 As an example, consider the separation into full and partial tiles
8050 of a tiling of a triangular domain.
8051 Take, for example, the domain
8053 { A[i,j] : 0 <= i,j and i + j <= 100 }
8055 and a tiling into tiles of 10 by 10. The input to the AST generator
8056 is then the schedule
8058 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
8061 Without any options, the following AST is generated
8063 for (int c0 = 0; c0 <= 10; c0 += 1)
8064 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8065 for (int c2 = 10 * c0;
8066 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8068 for (int c3 = 10 * c1;
8069 c3 <= min(10 * c1 + 9, -c2 + 100);
8073 Separation into full and partial tiles can be obtained by assigning
8074 a class, say C<0>, to the full tiles. The full tiles are represented by those
8075 values of the first and second schedule dimensions for which there are
8076 values of the third and fourth dimensions to cover an entire tile.
8077 That is, we need to specify the following option
8079 { [a,b,c,d] -> separation_class[[0]->[0]] :
8080 exists b': 0 <= 10a,10b' and
8081 10a+9+10b'+9 <= 100;
8082 [a,b,c,d] -> separation_class[[1]->[0]] :
8083 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
8087 { [a, b, c, d] -> separation_class[[1] -> [0]] :
8088 a >= 0 and b >= 0 and b <= 8 - a;
8089 [a, b, c, d] -> separation_class[[0] -> [0]] :
8092 With this option, the generated AST is as follows
8095 for (int c0 = 0; c0 <= 8; c0 += 1) {
8096 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
8097 for (int c2 = 10 * c0;
8098 c2 <= 10 * c0 + 9; c2 += 1)
8099 for (int c3 = 10 * c1;
8100 c3 <= 10 * c1 + 9; c3 += 1)
8102 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
8103 for (int c2 = 10 * c0;
8104 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8106 for (int c3 = 10 * c1;
8107 c3 <= min(-c2 + 100, 10 * c1 + 9);
8111 for (int c0 = 9; c0 <= 10; c0 += 1)
8112 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
8113 for (int c2 = 10 * c0;
8114 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
8116 for (int c3 = 10 * c1;
8117 c3 <= min(10 * c1 + 9, -c2 + 100);
8124 This is a single-dimensional space representing the schedule dimension(s)
8125 to which ``separation'' should be applied. Separation tries to split
8126 a loop into several pieces if this can avoid the generation of guards
8128 See also the C<atomic> option.
8132 This is a single-dimensional space representing the schedule dimension(s)
8133 for which the domains should be considered ``atomic''. That is, the
8134 AST generator will make sure that any given domain space will only appear
8135 in a single loop at the specified level.
8137 Consider the following schedule
8139 { a[i] -> [i] : 0 <= i < 10;
8140 b[i] -> [i+1] : 0 <= i < 10 }
8142 If the following option is specified
8144 { [i] -> separate[x] }
8146 then the following AST will be generated
8150 for (int c0 = 1; c0 <= 9; c0 += 1) {
8157 If, on the other hand, the following option is specified
8159 { [i] -> atomic[x] }
8161 then the following AST will be generated
8163 for (int c0 = 0; c0 <= 10; c0 += 1) {
8170 If neither C<atomic> nor C<separate> is specified, then the AST generator
8171 may produce either of these two results or some intermediate form.
8175 This is a single-dimensional space representing the schedule dimension(s)
8176 that should be I<completely> unrolled.
8177 To obtain a partial unrolling, the user should apply an additional
8178 strip-mining to the schedule and fully unroll the inner loop.
8182 Additional control is available through the following functions.
8184 #include <isl/ast_build.h>
8185 __isl_give isl_ast_build *
8186 isl_ast_build_set_iterators(
8187 __isl_take isl_ast_build *control,
8188 __isl_take isl_id_list *iterators);
8190 The function C<isl_ast_build_set_iterators> allows the user to
8191 specify a list of iterator C<isl_id>s to be used as iterators.
8192 If the input schedule is injective, then
8193 the number of elements in this list should be as large as the dimension
8194 of the schedule space, but no direct correspondence should be assumed
8195 between dimensions and elements.
8196 If the input schedule is not injective, then an additional number
8197 of C<isl_id>s equal to the largest dimension of the input domains
8199 If the number of provided C<isl_id>s is insufficient, then additional
8200 names are automatically generated.
8202 #include <isl/ast_build.h>
8203 __isl_give isl_ast_build *
8204 isl_ast_build_set_create_leaf(
8205 __isl_take isl_ast_build *control,
8206 __isl_give isl_ast_node *(*fn)(
8207 __isl_take isl_ast_build *build,
8208 void *user), void *user);
8211 C<isl_ast_build_set_create_leaf> function allows for the
8212 specification of a callback that should be called whenever the AST
8213 generator arrives at an element of the schedule domain.
8214 The callback should return an AST node that should be inserted
8215 at the corresponding position of the AST. The default action (when
8216 the callback is not set) is to continue generating parts of the AST to scan
8217 all the domain elements associated to the schedule domain element
8218 and to insert user nodes, ``calling'' the domain element, for each of them.
8219 The C<build> argument contains the current state of the C<isl_ast_build>.
8220 To ease nested AST generation (see L</"Nested AST Generation">),
8221 all control information that is
8222 specific to the current AST generation such as the options and
8223 the callbacks has been removed from this C<isl_ast_build>.
8224 The callback would typically return the result of a nested
8226 user defined node created using the following function.
8228 #include <isl/ast.h>
8229 __isl_give isl_ast_node *isl_ast_node_alloc_user(
8230 __isl_take isl_ast_expr *expr);
8232 #include <isl/ast_build.h>
8233 __isl_give isl_ast_build *
8234 isl_ast_build_set_at_each_domain(
8235 __isl_take isl_ast_build *build,
8236 __isl_give isl_ast_node *(*fn)(
8237 __isl_take isl_ast_node *node,
8238 __isl_keep isl_ast_build *build,
8239 void *user), void *user);
8240 __isl_give isl_ast_build *
8241 isl_ast_build_set_before_each_for(
8242 __isl_take isl_ast_build *build,
8243 __isl_give isl_id *(*fn)(
8244 __isl_keep isl_ast_build *build,
8245 void *user), void *user);
8246 __isl_give isl_ast_build *
8247 isl_ast_build_set_after_each_for(
8248 __isl_take isl_ast_build *build,
8249 __isl_give isl_ast_node *(*fn)(
8250 __isl_take isl_ast_node *node,
8251 __isl_keep isl_ast_build *build,
8252 void *user), void *user);
8254 The callback set by C<isl_ast_build_set_at_each_domain> will
8255 be called for each domain AST node.
8256 The callbacks set by C<isl_ast_build_set_before_each_for>
8257 and C<isl_ast_build_set_after_each_for> will be called
8258 for each for AST node. The first will be called in depth-first
8259 pre-order, while the second will be called in depth-first post-order.
8260 Since C<isl_ast_build_set_before_each_for> is called before the for
8261 node is actually constructed, it is only passed an C<isl_ast_build>.
8262 The returned C<isl_id> will be added as an annotation (using
8263 C<isl_ast_node_set_annotation>) to the constructed for node.
8264 In particular, if the user has also specified an C<after_each_for>
8265 callback, then the annotation can be retrieved from the node passed to
8266 that callback using C<isl_ast_node_get_annotation>.
8267 All callbacks should C<NULL> on failure.
8268 The given C<isl_ast_build> can be used to create new
8269 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
8270 or C<isl_ast_build_call_from_pw_multi_aff>.
8272 =head3 Nested AST Generation
8274 C<isl> allows the user to create an AST within the context
8275 of another AST. These nested ASTs are created using the
8276 same C<isl_ast_build_ast_from_schedule> function that is used to create the
8277 outer AST. The C<build> argument should be an C<isl_ast_build>
8278 passed to a callback set by
8279 C<isl_ast_build_set_create_leaf>.
8280 The space of the range of the C<schedule> argument should refer
8281 to this build. In particular, the space should be a wrapped
8282 relation and the domain of this wrapped relation should be the
8283 same as that of the range of the schedule returned by
8284 C<isl_ast_build_get_schedule> below.
8285 In practice, the new schedule is typically
8286 created by calling C<isl_union_map_range_product> on the old schedule
8287 and some extra piece of the schedule.
8288 The space of the schedule domain is also available from
8289 the C<isl_ast_build>.
8291 #include <isl/ast_build.h>
8292 __isl_give isl_union_map *isl_ast_build_get_schedule(
8293 __isl_keep isl_ast_build *build);
8294 __isl_give isl_space *isl_ast_build_get_schedule_space(
8295 __isl_keep isl_ast_build *build);
8296 __isl_give isl_ast_build *isl_ast_build_restrict(
8297 __isl_take isl_ast_build *build,
8298 __isl_take isl_set *set);
8300 The C<isl_ast_build_get_schedule> function returns a (partial)
8301 schedule for the domains elements for which part of the AST still needs to
8302 be generated in the current build.
8303 In particular, the domain elements are mapped to those iterations of the loops
8304 enclosing the current point of the AST generation inside which
8305 the domain elements are executed.
8306 No direct correspondence between
8307 the input schedule and this schedule should be assumed.
8308 The space obtained from C<isl_ast_build_get_schedule_space> can be used
8309 to create a set for C<isl_ast_build_restrict> to intersect
8310 with the current build. In particular, the set passed to
8311 C<isl_ast_build_restrict> can have additional parameters.
8312 The ids of the set dimensions in the space returned by
8313 C<isl_ast_build_get_schedule_space> correspond to the
8314 iterators of the already generated loops.
8315 The user should not rely on the ids of the output dimensions
8316 of the relations in the union relation returned by
8317 C<isl_ast_build_get_schedule> having any particular value.
8321 Although C<isl> is mainly meant to be used as a library,
8322 it also contains some basic applications that use some
8323 of the functionality of C<isl>.
8324 The input may be specified in either the L<isl format>
8325 or the L<PolyLib format>.
8327 =head2 C<isl_polyhedron_sample>
8329 C<isl_polyhedron_sample> takes a polyhedron as input and prints
8330 an integer element of the polyhedron, if there is any.
8331 The first column in the output is the denominator and is always
8332 equal to 1. If the polyhedron contains no integer points,
8333 then a vector of length zero is printed.
8337 C<isl_pip> takes the same input as the C<example> program
8338 from the C<piplib> distribution, i.e., a set of constraints
8339 on the parameters, a line containing only -1 and finally a set
8340 of constraints on a parametric polyhedron.
8341 The coefficients of the parameters appear in the last columns
8342 (but before the final constant column).
8343 The output is the lexicographic minimum of the parametric polyhedron.
8344 As C<isl> currently does not have its own output format, the output
8345 is just a dump of the internal state.
8347 =head2 C<isl_polyhedron_minimize>
8349 C<isl_polyhedron_minimize> computes the minimum of some linear
8350 or affine objective function over the integer points in a polyhedron.
8351 If an affine objective function
8352 is given, then the constant should appear in the last column.
8354 =head2 C<isl_polytope_scan>
8356 Given a polytope, C<isl_polytope_scan> prints
8357 all integer points in the polytope.
8359 =head2 C<isl_codegen>
8361 Given a schedule, a context set and an options relation,
8362 C<isl_codegen> prints out an AST that scans the domain elements
8363 of the schedule in the order of their image(s) taking into account
8364 the constraints in the context set.