3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * Objects of type C<isl_union_pw_multi_aff> can no longer contain
216 two or more C<isl_pw_multi_aff> objects with the same domain space.
218 =item * The function C<isl_union_pw_multi_aff_add> now consistently
219 computes the sum on the shared definition domain.
220 The function C<isl_union_pw_multi_aff_union_add> has been added
221 to compute the sum on the union of definition domains.
222 The original behavior of C<isl_union_pw_multi_aff_add> was
223 confused and is no longer available.
229 C<isl> is released under the MIT license.
233 Permission is hereby granted, free of charge, to any person obtaining a copy of
234 this software and associated documentation files (the "Software"), to deal in
235 the Software without restriction, including without limitation the rights to
236 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
237 of the Software, and to permit persons to whom the Software is furnished to do
238 so, subject to the following conditions:
240 The above copyright notice and this permission notice shall be included in all
241 copies or substantial portions of the Software.
243 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
244 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
245 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
246 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
247 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
248 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
253 Note that by default C<isl> requires C<GMP>, which is released
254 under the GNU Lesser General Public License (LGPL). This means
255 that code linked against C<isl> is also linked against LGPL code.
257 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
258 library for exact integer arithmetic released under the MIT license.
262 The source of C<isl> can be obtained either as a tarball
263 or from the git repository. Both are available from
264 L<http://freshmeat.net/projects/isl/>.
265 The installation process depends on how you obtained
268 =head2 Installation from the git repository
272 =item 1 Clone or update the repository
274 The first time the source is obtained, you need to clone
277 git clone git://repo.or.cz/isl.git
279 To obtain updates, you need to pull in the latest changes
283 =item 2 Optionally get C<imath> submodule
285 To build C<isl> with C<imath>, you need to obtain the C<imath>
286 submodule by running in the git source tree of C<isl>
291 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
293 =item 2 Generate C<configure>
299 After performing the above steps, continue
300 with the L<Common installation instructions>.
302 =head2 Common installation instructions
306 =item 1 Obtain C<GMP>
308 By default, building C<isl> requires C<GMP>, including its headers files.
309 Your distribution may not provide these header files by default
310 and you may need to install a package called C<gmp-devel> or something
311 similar. Alternatively, C<GMP> can be built from
312 source, available from L<http://gmplib.org/>.
313 C<GMP> is not needed if you build C<isl> with C<imath>.
317 C<isl> uses the standard C<autoconf> C<configure> script.
322 optionally followed by some configure options.
323 A complete list of options can be obtained by running
327 Below we discuss some of the more common options.
333 Installation prefix for C<isl>
335 =item C<--with-int=[gmp|imath]>
337 Select the integer library to be used by C<isl>, the default is C<gmp>.
338 Note that C<isl> may run significantly slower if you use C<imath>.
340 =item C<--with-gmp-prefix>
342 Installation prefix for C<GMP> (architecture-independent files).
344 =item C<--with-gmp-exec-prefix>
346 Installation prefix for C<GMP> (architecture-dependent files).
354 =item 4 Install (optional)
360 =head1 Integer Set Library
362 =head2 Memory Management
364 Since a high-level operation on isl objects usually involves
365 several substeps and since the user is usually not interested in
366 the intermediate results, most functions that return a new object
367 will also release all the objects passed as arguments.
368 If the user still wants to use one or more of these arguments
369 after the function call, she should pass along a copy of the
370 object rather than the object itself.
371 The user is then responsible for making sure that the original
372 object gets used somewhere else or is explicitly freed.
374 The arguments and return values of all documented functions are
375 annotated to make clear which arguments are released and which
376 arguments are preserved. In particular, the following annotations
383 C<__isl_give> means that a new object is returned.
384 The user should make sure that the returned pointer is
385 used exactly once as a value for an C<__isl_take> argument.
386 In between, it can be used as a value for as many
387 C<__isl_keep> arguments as the user likes.
388 There is one exception, and that is the case where the
389 pointer returned is C<NULL>. Is this case, the user
390 is free to use it as an C<__isl_take> argument or not.
391 When applied to a C<char *>, the returned pointer needs to be
396 C<__isl_null> means that a C<NULL> value is returned.
400 C<__isl_take> means that the object the argument points to
401 is taken over by the function and may no longer be used
402 by the user as an argument to any other function.
403 The pointer value must be one returned by a function
404 returning an C<__isl_give> pointer.
405 If the user passes in a C<NULL> value, then this will
406 be treated as an error in the sense that the function will
407 not perform its usual operation. However, it will still
408 make sure that all the other C<__isl_take> arguments
413 C<__isl_keep> means that the function will only use the object
414 temporarily. After the function has finished, the user
415 can still use it as an argument to other functions.
416 A C<NULL> value will be treated in the same way as
417 a C<NULL> value for an C<__isl_take> argument.
418 This annotation may also be used on return values of
419 type C<const char *>, in which case the returned pointer should
420 not be freed by the user and is only valid until the object
421 from which it was derived is updated or freed.
425 =head2 Initialization
427 All manipulations of integer sets and relations occur within
428 the context of an C<isl_ctx>.
429 A given C<isl_ctx> can only be used within a single thread.
430 All arguments of a function are required to have been allocated
431 within the same context.
432 There are currently no functions available for moving an object
433 from one C<isl_ctx> to another C<isl_ctx>. This means that
434 there is currently no way of safely moving an object from one
435 thread to another, unless the whole C<isl_ctx> is moved.
437 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
438 freed using C<isl_ctx_free>.
439 All objects allocated within an C<isl_ctx> should be freed
440 before the C<isl_ctx> itself is freed.
442 isl_ctx *isl_ctx_alloc();
443 void isl_ctx_free(isl_ctx *ctx);
445 The user can impose a bound on the number of low-level I<operations>
446 that can be performed by an C<isl_ctx>. This bound can be set and
447 retrieved using the following functions. A bound of zero means that
448 no bound is imposed. The number of operations performed can be
449 reset using C<isl_ctx_reset_operations>. Note that the number
450 of low-level operations needed to perform a high-level computation
451 may differ significantly across different versions
452 of C<isl>, but it should be the same across different platforms
453 for the same version of C<isl>.
455 Warning: This feature is experimental. C<isl> has good support to abort and
456 bail out during the computation, but this feature may exercise error code paths
457 that are normally not used that much. Consequently, it is not unlikely that
458 hidden bugs will be exposed.
460 void isl_ctx_set_max_operations(isl_ctx *ctx,
461 unsigned long max_operations);
462 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
463 void isl_ctx_reset_operations(isl_ctx *ctx);
465 In order to be able to create an object in the same context
466 as another object, most object types (described later in
467 this document) provide a function to obtain the context
468 in which the object was created.
471 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
472 isl_ctx *isl_multi_val_get_ctx(
473 __isl_keep isl_multi_val *mv);
476 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
478 #include <isl/local_space.h>
479 isl_ctx *isl_local_space_get_ctx(
480 __isl_keep isl_local_space *ls);
483 isl_ctx *isl_set_list_get_ctx(
484 __isl_keep isl_set_list *list);
487 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
488 isl_ctx *isl_multi_aff_get_ctx(
489 __isl_keep isl_multi_aff *maff);
490 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
491 isl_ctx *isl_pw_multi_aff_get_ctx(
492 __isl_keep isl_pw_multi_aff *pma);
493 isl_ctx *isl_multi_pw_aff_get_ctx(
494 __isl_keep isl_multi_pw_aff *mpa);
495 isl_ctx *isl_union_pw_multi_aff_get_ctx(
496 __isl_keep isl_union_pw_multi_aff *upma);
498 #include <isl/id_to_ast_expr.h>
499 isl_ctx *isl_id_to_ast_expr_get_ctx(
500 __isl_keep id_to_ast_expr *id2expr);
502 #include <isl/point.h>
503 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
506 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
509 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
511 #include <isl/vertices.h>
512 isl_ctx *isl_vertices_get_ctx(
513 __isl_keep isl_vertices *vertices);
514 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
515 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
517 #include <isl/flow.h>
518 isl_ctx *isl_restriction_get_ctx(
519 __isl_keep isl_restriction *restr);
521 #include <isl/schedule.h>
522 isl_ctx *isl_schedule_constraints_get_ctx(
523 __isl_keep isl_schedule_constraints *sc);
525 #include <isl/band.h>
526 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
528 #include <isl/ast_build.h>
529 isl_ctx *isl_ast_build_get_ctx(
530 __isl_keep isl_ast_build *build);
533 isl_ctx *isl_ast_expr_get_ctx(
534 __isl_keep isl_ast_expr *expr);
535 isl_ctx *isl_ast_node_get_ctx(
536 __isl_keep isl_ast_node *node);
540 An C<isl_val> represents an integer value, a rational value
541 or one of three special values, infinity, negative infinity and NaN.
542 Some predefined values can be created using the following functions.
545 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
546 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
547 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
548 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
549 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
550 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
552 Specific integer values can be created using the following functions.
555 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
557 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
559 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
560 size_t n, size_t size, const void *chunks);
562 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
563 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
564 The least significant digit is assumed to be stored first.
566 Value objects can be copied and freed using the following functions.
569 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
570 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
572 They can be inspected using the following functions.
575 long isl_val_get_num_si(__isl_keep isl_val *v);
576 long isl_val_get_den_si(__isl_keep isl_val *v);
577 double isl_val_get_d(__isl_keep isl_val *v);
578 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
580 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
581 size_t size, void *chunks);
583 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
584 of C<size> bytes needed to store the absolute value of the
586 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
587 which is assumed to have been preallocated by the caller.
588 The least significant digit is stored first.
589 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
590 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
591 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
593 An C<isl_val> can be modified using the following function.
596 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
599 The following unary properties are defined on C<isl_val>s.
602 int isl_val_sgn(__isl_keep isl_val *v);
603 int isl_val_is_zero(__isl_keep isl_val *v);
604 int isl_val_is_one(__isl_keep isl_val *v);
605 int isl_val_is_negone(__isl_keep isl_val *v);
606 int isl_val_is_nonneg(__isl_keep isl_val *v);
607 int isl_val_is_nonpos(__isl_keep isl_val *v);
608 int isl_val_is_pos(__isl_keep isl_val *v);
609 int isl_val_is_neg(__isl_keep isl_val *v);
610 int isl_val_is_int(__isl_keep isl_val *v);
611 int isl_val_is_rat(__isl_keep isl_val *v);
612 int isl_val_is_nan(__isl_keep isl_val *v);
613 int isl_val_is_infty(__isl_keep isl_val *v);
614 int isl_val_is_neginfty(__isl_keep isl_val *v);
616 Note that the sign of NaN is undefined.
618 The following binary properties are defined on pairs of C<isl_val>s.
621 int isl_val_lt(__isl_keep isl_val *v1,
622 __isl_keep isl_val *v2);
623 int isl_val_le(__isl_keep isl_val *v1,
624 __isl_keep isl_val *v2);
625 int isl_val_gt(__isl_keep isl_val *v1,
626 __isl_keep isl_val *v2);
627 int isl_val_ge(__isl_keep isl_val *v1,
628 __isl_keep isl_val *v2);
629 int isl_val_eq(__isl_keep isl_val *v1,
630 __isl_keep isl_val *v2);
631 int isl_val_ne(__isl_keep isl_val *v1,
632 __isl_keep isl_val *v2);
633 int isl_val_abs_eq(__isl_keep isl_val *v1,
634 __isl_keep isl_val *v2);
636 The function C<isl_val_abs_eq> checks whether its two arguments
637 are equal in absolute value.
639 For integer C<isl_val>s we additionally have the following binary property.
642 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
643 __isl_keep isl_val *v2);
645 An C<isl_val> can also be compared to an integer using the following
646 function. The result is undefined for NaN.
649 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
651 The following unary operations are available on C<isl_val>s.
654 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
655 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
656 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
657 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
658 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
659 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
660 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
662 The following binary operations are available on C<isl_val>s.
665 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
666 __isl_take isl_val *v2);
667 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
668 __isl_take isl_val *v2);
669 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
670 __isl_take isl_val *v2);
671 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
673 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
674 __isl_take isl_val *v2);
675 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
677 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
678 __isl_take isl_val *v2);
679 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
681 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
682 __isl_take isl_val *v2);
684 On integer values, we additionally have the following operations.
687 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
688 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
689 __isl_take isl_val *v2);
690 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
691 __isl_take isl_val *v2);
692 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
693 __isl_take isl_val *v2, __isl_give isl_val **x,
694 __isl_give isl_val **y);
696 The function C<isl_val_gcdext> returns the greatest common divisor g
697 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
698 that C<*x> * C<v1> + C<*y> * C<v2> = g.
700 =head3 GMP specific functions
702 These functions are only available if C<isl> has been compiled with C<GMP>
705 Specific integer and rational values can be created from C<GMP> values using
706 the following functions.
708 #include <isl/val_gmp.h>
709 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
711 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
712 const mpz_t n, const mpz_t d);
714 The numerator and denominator of a rational value can be extracted as
715 C<GMP> values using the following functions.
717 #include <isl/val_gmp.h>
718 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
719 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
721 =head2 Sets and Relations
723 C<isl> uses six types of objects for representing sets and relations,
724 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
725 C<isl_union_set> and C<isl_union_map>.
726 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
727 can be described as a conjunction of affine constraints, while
728 C<isl_set> and C<isl_map> represent unions of
729 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
730 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
731 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
732 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
733 where spaces are considered different if they have a different number
734 of dimensions and/or different names (see L<"Spaces">).
735 The difference between sets and relations (maps) is that sets have
736 one set of variables, while relations have two sets of variables,
737 input variables and output variables.
739 =head2 Error Handling
741 C<isl> supports different ways to react in case a runtime error is triggered.
742 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
743 with two maps that have incompatible spaces. There are three possible ways
744 to react on error: to warn, to continue or to abort.
746 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
747 the last error in the corresponding C<isl_ctx> and the function in which the
748 error was triggered returns C<NULL>. An error does not corrupt internal state,
749 such that isl can continue to be used. C<isl> also provides functions to
750 read the last error and to reset the memory that stores the last error. The
751 last error is only stored for information purposes. Its presence does not
752 change the behavior of C<isl>. Hence, resetting an error is not required to
753 continue to use isl, but only to observe new errors.
756 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
757 void isl_ctx_reset_error(isl_ctx *ctx);
759 Another option is to continue on error. This is similar to warn on error mode,
760 except that C<isl> does not print any warning. This allows a program to
761 implement its own error reporting.
763 The last option is to directly abort the execution of the program from within
764 the isl library. This makes it obviously impossible to recover from an error,
765 but it allows to directly spot the error location. By aborting on error,
766 debuggers break at the location the error occurred and can provide a stack
767 trace. Other tools that automatically provide stack traces on abort or that do
768 not want to continue execution after an error was triggered may also prefer to
771 The on error behavior of isl can be specified by calling
772 C<isl_options_set_on_error> or by setting the command line option
773 C<--isl-on-error>. Valid arguments for the function call are
774 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
775 choices for the command line option are C<warn>, C<continue> and C<abort>.
776 It is also possible to query the current error mode.
778 #include <isl/options.h>
779 int isl_options_set_on_error(isl_ctx *ctx, int val);
780 int isl_options_get_on_error(isl_ctx *ctx);
784 Identifiers are used to identify both individual dimensions
785 and tuples of dimensions. They consist of an optional name and an optional
786 user pointer. The name and the user pointer cannot both be C<NULL>, however.
787 Identifiers with the same name but different pointer values
788 are considered to be distinct.
789 Similarly, identifiers with different names but the same pointer value
790 are also considered to be distinct.
791 Equal identifiers are represented using the same object.
792 Pairs of identifiers can therefore be tested for equality using the
794 Identifiers can be constructed, copied, freed, inspected and printed
795 using the following functions.
798 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
799 __isl_keep const char *name, void *user);
800 __isl_give isl_id *isl_id_set_free_user(
801 __isl_take isl_id *id,
802 __isl_give void (*free_user)(void *user));
803 __isl_give isl_id *isl_id_copy(isl_id *id);
804 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
806 void *isl_id_get_user(__isl_keep isl_id *id);
807 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
809 __isl_give isl_printer *isl_printer_print_id(
810 __isl_take isl_printer *p, __isl_keep isl_id *id);
812 The callback set by C<isl_id_set_free_user> is called on the user
813 pointer when the last reference to the C<isl_id> is freed.
814 Note that C<isl_id_get_name> returns a pointer to some internal
815 data structure, so the result can only be used while the
816 corresponding C<isl_id> is alive.
820 Whenever a new set, relation or similar object is created from scratch,
821 the space in which it lives needs to be specified using an C<isl_space>.
822 Each space involves zero or more parameters and zero, one or two
823 tuples of set or input/output dimensions. The parameters and dimensions
824 are identified by an C<isl_dim_type> and a position.
825 The type C<isl_dim_param> refers to parameters,
826 the type C<isl_dim_set> refers to set dimensions (for spaces
827 with a single tuple of dimensions) and the types C<isl_dim_in>
828 and C<isl_dim_out> refer to input and output dimensions
829 (for spaces with two tuples of dimensions).
830 Local spaces (see L</"Local Spaces">) also contain dimensions
831 of type C<isl_dim_div>.
832 Note that parameters are only identified by their position within
833 a given object. Across different objects, parameters are (usually)
834 identified by their names or identifiers. Only unnamed parameters
835 are identified by their positions across objects. The use of unnamed
836 parameters is discouraged.
838 #include <isl/space.h>
839 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
840 unsigned nparam, unsigned n_in, unsigned n_out);
841 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
843 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
844 unsigned nparam, unsigned dim);
845 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
846 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
848 The space used for creating a parameter domain
849 needs to be created using C<isl_space_params_alloc>.
850 For other sets, the space
851 needs to be created using C<isl_space_set_alloc>, while
852 for a relation, the space
853 needs to be created using C<isl_space_alloc>.
855 To check whether a given space is that of a set or a map
856 or whether it is a parameter space, use these functions:
858 #include <isl/space.h>
859 int isl_space_is_params(__isl_keep isl_space *space);
860 int isl_space_is_set(__isl_keep isl_space *space);
861 int isl_space_is_map(__isl_keep isl_space *space);
863 Spaces can be compared using the following functions:
865 #include <isl/space.h>
866 int isl_space_is_equal(__isl_keep isl_space *space1,
867 __isl_keep isl_space *space2);
868 int isl_space_is_domain(__isl_keep isl_space *space1,
869 __isl_keep isl_space *space2);
870 int isl_space_is_range(__isl_keep isl_space *space1,
871 __isl_keep isl_space *space2);
872 int isl_space_tuple_is_equal(
873 __isl_keep isl_space *space1,
874 enum isl_dim_type type1,
875 __isl_keep isl_space *space2,
876 enum isl_dim_type type2);
878 C<isl_space_is_domain> checks whether the first argument is equal
879 to the domain of the second argument. This requires in particular that
880 the first argument is a set space and that the second argument
881 is a map space. C<isl_space_tuple_is_equal> checks whether the given
882 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
883 spaces are the same. That is, it checks if they have the same
884 identifier (if any), the same dimension and the same internal structure
887 It is often useful to create objects that live in the
888 same space as some other object. This can be accomplished
889 by creating the new objects
890 (see L</"Creating New Sets and Relations"> or
891 L</"Functions">) based on the space
892 of the original object.
895 __isl_give isl_space *isl_basic_set_get_space(
896 __isl_keep isl_basic_set *bset);
897 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
899 #include <isl/union_set.h>
900 __isl_give isl_space *isl_union_set_get_space(
901 __isl_keep isl_union_set *uset);
904 __isl_give isl_space *isl_basic_map_get_space(
905 __isl_keep isl_basic_map *bmap);
906 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
908 #include <isl/union_map.h>
909 __isl_give isl_space *isl_union_map_get_space(
910 __isl_keep isl_union_map *umap);
912 #include <isl/constraint.h>
913 __isl_give isl_space *isl_constraint_get_space(
914 __isl_keep isl_constraint *constraint);
916 #include <isl/polynomial.h>
917 __isl_give isl_space *isl_qpolynomial_get_domain_space(
918 __isl_keep isl_qpolynomial *qp);
919 __isl_give isl_space *isl_qpolynomial_get_space(
920 __isl_keep isl_qpolynomial *qp);
921 __isl_give isl_space *isl_qpolynomial_fold_get_space(
922 __isl_keep isl_qpolynomial_fold *fold);
923 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
924 __isl_keep isl_pw_qpolynomial *pwqp);
925 __isl_give isl_space *isl_pw_qpolynomial_get_space(
926 __isl_keep isl_pw_qpolynomial *pwqp);
927 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
928 __isl_keep isl_pw_qpolynomial_fold *pwf);
929 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
930 __isl_keep isl_pw_qpolynomial_fold *pwf);
931 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
932 __isl_keep isl_union_pw_qpolynomial *upwqp);
933 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
934 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
937 __isl_give isl_space *isl_multi_val_get_space(
938 __isl_keep isl_multi_val *mv);
941 __isl_give isl_space *isl_aff_get_domain_space(
942 __isl_keep isl_aff *aff);
943 __isl_give isl_space *isl_aff_get_space(
944 __isl_keep isl_aff *aff);
945 __isl_give isl_space *isl_pw_aff_get_domain_space(
946 __isl_keep isl_pw_aff *pwaff);
947 __isl_give isl_space *isl_pw_aff_get_space(
948 __isl_keep isl_pw_aff *pwaff);
949 __isl_give isl_space *isl_multi_aff_get_domain_space(
950 __isl_keep isl_multi_aff *maff);
951 __isl_give isl_space *isl_multi_aff_get_space(
952 __isl_keep isl_multi_aff *maff);
953 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
954 __isl_keep isl_pw_multi_aff *pma);
955 __isl_give isl_space *isl_pw_multi_aff_get_space(
956 __isl_keep isl_pw_multi_aff *pma);
957 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
958 __isl_keep isl_union_pw_multi_aff *upma);
959 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
960 __isl_keep isl_multi_pw_aff *mpa);
961 __isl_give isl_space *isl_multi_pw_aff_get_space(
962 __isl_keep isl_multi_pw_aff *mpa);
964 #include <isl/point.h>
965 __isl_give isl_space *isl_point_get_space(
966 __isl_keep isl_point *pnt);
968 The number of dimensions of a given type of space
969 may be read off from a space or an object that lives
970 in a space using the following functions.
971 In case of C<isl_space_dim>, type may be
972 C<isl_dim_param>, C<isl_dim_in> (only for relations),
973 C<isl_dim_out> (only for relations), C<isl_dim_set>
974 (only for sets) or C<isl_dim_all>.
976 #include <isl/space.h>
977 unsigned isl_space_dim(__isl_keep isl_space *space,
978 enum isl_dim_type type);
980 #include <isl/local_space.h>
981 int isl_local_space_dim(__isl_keep isl_local_space *ls,
982 enum isl_dim_type type);
985 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
986 enum isl_dim_type type);
987 unsigned isl_set_dim(__isl_keep isl_set *set,
988 enum isl_dim_type type);
990 #include <isl/union_set.h>
991 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
992 enum isl_dim_type type);
995 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
996 enum isl_dim_type type);
997 unsigned isl_map_dim(__isl_keep isl_map *map,
998 enum isl_dim_type type);
1000 #include <isl/union_map.h>
1001 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1002 enum isl_dim_type type);
1004 #include <isl/val.h>
1005 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1006 enum isl_dim_type type);
1008 #include <isl/aff.h>
1009 int isl_aff_dim(__isl_keep isl_aff *aff,
1010 enum isl_dim_type type);
1011 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1012 enum isl_dim_type type);
1013 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1014 enum isl_dim_type type);
1015 unsigned isl_pw_multi_aff_dim(
1016 __isl_keep isl_pw_multi_aff *pma,
1017 enum isl_dim_type type);
1018 unsigned isl_multi_pw_aff_dim(
1019 __isl_keep isl_multi_pw_aff *mpa,
1020 enum isl_dim_type type);
1021 unsigned isl_union_pw_multi_aff_dim(
1022 __isl_keep isl_union_pw_multi_aff *upma,
1023 enum isl_dim_type type);
1025 #include <isl/polynomial.h>
1026 unsigned isl_union_pw_qpolynomial_dim(
1027 __isl_keep isl_union_pw_qpolynomial *upwqp,
1028 enum isl_dim_type type);
1029 unsigned isl_union_pw_qpolynomial_fold_dim(
1030 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1031 enum isl_dim_type type);
1033 Note that an C<isl_union_set>, an C<isl_union_map>,
1034 an C<isl_union_pw_multi_aff>,
1035 an C<isl_union_pw_qpolynomial> and
1036 an C<isl_union_pw_qpolynomial_fold>
1037 only have parameters.
1039 The identifiers or names of the individual dimensions of spaces
1040 may be set or read off using the following functions on spaces
1041 or objects that live in spaces.
1042 These functions are mostly useful to obtain the identifiers, positions
1043 or names of the parameters. Identifiers of individual dimensions are
1044 essentially only useful for printing. They are ignored by all other
1045 operations and may not be preserved across those operations.
1047 #include <isl/space.h>
1048 __isl_give isl_space *isl_space_set_dim_id(
1049 __isl_take isl_space *space,
1050 enum isl_dim_type type, unsigned pos,
1051 __isl_take isl_id *id);
1052 int isl_space_has_dim_id(__isl_keep isl_space *space,
1053 enum isl_dim_type type, unsigned pos);
1054 __isl_give isl_id *isl_space_get_dim_id(
1055 __isl_keep isl_space *space,
1056 enum isl_dim_type type, unsigned pos);
1057 __isl_give isl_space *isl_space_set_dim_name(
1058 __isl_take isl_space *space,
1059 enum isl_dim_type type, unsigned pos,
1060 __isl_keep const char *name);
1061 int isl_space_has_dim_name(__isl_keep isl_space *space,
1062 enum isl_dim_type type, unsigned pos);
1063 __isl_keep const char *isl_space_get_dim_name(
1064 __isl_keep isl_space *space,
1065 enum isl_dim_type type, unsigned pos);
1067 #include <isl/local_space.h>
1068 __isl_give isl_local_space *isl_local_space_set_dim_id(
1069 __isl_take isl_local_space *ls,
1070 enum isl_dim_type type, unsigned pos,
1071 __isl_take isl_id *id);
1072 int isl_local_space_has_dim_id(
1073 __isl_keep isl_local_space *ls,
1074 enum isl_dim_type type, unsigned pos);
1075 __isl_give isl_id *isl_local_space_get_dim_id(
1076 __isl_keep isl_local_space *ls,
1077 enum isl_dim_type type, unsigned pos);
1078 __isl_give isl_local_space *isl_local_space_set_dim_name(
1079 __isl_take isl_local_space *ls,
1080 enum isl_dim_type type, unsigned pos, const char *s);
1081 int isl_local_space_has_dim_name(
1082 __isl_keep isl_local_space *ls,
1083 enum isl_dim_type type, unsigned pos)
1084 const char *isl_local_space_get_dim_name(
1085 __isl_keep isl_local_space *ls,
1086 enum isl_dim_type type, unsigned pos);
1088 #include <isl/constraint.h>
1089 const char *isl_constraint_get_dim_name(
1090 __isl_keep isl_constraint *constraint,
1091 enum isl_dim_type type, unsigned pos);
1093 #include <isl/set.h>
1094 __isl_give isl_id *isl_basic_set_get_dim_id(
1095 __isl_keep isl_basic_set *bset,
1096 enum isl_dim_type type, unsigned pos);
1097 __isl_give isl_set *isl_set_set_dim_id(
1098 __isl_take isl_set *set, enum isl_dim_type type,
1099 unsigned pos, __isl_take isl_id *id);
1100 int isl_set_has_dim_id(__isl_keep isl_set *set,
1101 enum isl_dim_type type, unsigned pos);
1102 __isl_give isl_id *isl_set_get_dim_id(
1103 __isl_keep isl_set *set, enum isl_dim_type type,
1105 const char *isl_basic_set_get_dim_name(
1106 __isl_keep isl_basic_set *bset,
1107 enum isl_dim_type type, unsigned pos);
1108 int isl_set_has_dim_name(__isl_keep isl_set *set,
1109 enum isl_dim_type type, unsigned pos);
1110 const char *isl_set_get_dim_name(
1111 __isl_keep isl_set *set,
1112 enum isl_dim_type type, unsigned pos);
1114 #include <isl/map.h>
1115 __isl_give isl_map *isl_map_set_dim_id(
1116 __isl_take isl_map *map, enum isl_dim_type type,
1117 unsigned pos, __isl_take isl_id *id);
1118 int isl_basic_map_has_dim_id(
1119 __isl_keep isl_basic_map *bmap,
1120 enum isl_dim_type type, unsigned pos);
1121 int isl_map_has_dim_id(__isl_keep isl_map *map,
1122 enum isl_dim_type type, unsigned pos);
1123 __isl_give isl_id *isl_map_get_dim_id(
1124 __isl_keep isl_map *map, enum isl_dim_type type,
1126 __isl_give isl_id *isl_union_map_get_dim_id(
1127 __isl_keep isl_union_map *umap,
1128 enum isl_dim_type type, unsigned pos);
1129 const char *isl_basic_map_get_dim_name(
1130 __isl_keep isl_basic_map *bmap,
1131 enum isl_dim_type type, unsigned pos);
1132 int isl_map_has_dim_name(__isl_keep isl_map *map,
1133 enum isl_dim_type type, unsigned pos);
1134 const char *isl_map_get_dim_name(
1135 __isl_keep isl_map *map,
1136 enum isl_dim_type type, unsigned pos);
1138 #include <isl/val.h>
1139 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1140 __isl_take isl_multi_val *mv,
1141 enum isl_dim_type type, unsigned pos,
1142 __isl_take isl_id *id);
1143 __isl_give isl_id *isl_multi_val_get_dim_id(
1144 __isl_keep isl_multi_val *mv,
1145 enum isl_dim_type type, unsigned pos);
1146 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1147 __isl_take isl_multi_val *mv,
1148 enum isl_dim_type type, unsigned pos, const char *s);
1150 #include <isl/aff.h>
1151 __isl_give isl_aff *isl_aff_set_dim_id(
1152 __isl_take isl_aff *aff, enum isl_dim_type type,
1153 unsigned pos, __isl_take isl_id *id);
1154 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1155 __isl_take isl_multi_aff *maff,
1156 enum isl_dim_type type, unsigned pos,
1157 __isl_take isl_id *id);
1158 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1159 __isl_take isl_pw_aff *pma,
1160 enum isl_dim_type type, unsigned pos,
1161 __isl_take isl_id *id);
1162 __isl_give isl_multi_pw_aff *
1163 isl_multi_pw_aff_set_dim_id(
1164 __isl_take isl_multi_pw_aff *mpa,
1165 enum isl_dim_type type, unsigned pos,
1166 __isl_take isl_id *id);
1167 __isl_give isl_id *isl_multi_aff_get_dim_id(
1168 __isl_keep isl_multi_aff *ma,
1169 enum isl_dim_type type, unsigned pos);
1170 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1171 enum isl_dim_type type, unsigned pos);
1172 __isl_give isl_id *isl_pw_aff_get_dim_id(
1173 __isl_keep isl_pw_aff *pa,
1174 enum isl_dim_type type, unsigned pos);
1175 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1176 __isl_keep isl_pw_multi_aff *pma,
1177 enum isl_dim_type type, unsigned pos);
1178 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1179 __isl_keep isl_multi_pw_aff *mpa,
1180 enum isl_dim_type type, unsigned pos);
1181 __isl_give isl_aff *isl_aff_set_dim_name(
1182 __isl_take isl_aff *aff, enum isl_dim_type type,
1183 unsigned pos, const char *s);
1184 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1185 __isl_take isl_multi_aff *maff,
1186 enum isl_dim_type type, unsigned pos, const char *s);
1187 __isl_give isl_multi_pw_aff *
1188 isl_multi_pw_aff_set_dim_name(
1189 __isl_take isl_multi_pw_aff *mpa,
1190 enum isl_dim_type type, unsigned pos, const char *s);
1191 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1192 enum isl_dim_type type, unsigned pos);
1193 const char *isl_pw_aff_get_dim_name(
1194 __isl_keep isl_pw_aff *pa,
1195 enum isl_dim_type type, unsigned pos);
1196 const char *isl_pw_multi_aff_get_dim_name(
1197 __isl_keep isl_pw_multi_aff *pma,
1198 enum isl_dim_type type, unsigned pos);
1200 #include <isl/polynomial.h>
1201 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1202 __isl_take isl_qpolynomial *qp,
1203 enum isl_dim_type type, unsigned pos,
1205 __isl_give isl_pw_qpolynomial *
1206 isl_pw_qpolynomial_set_dim_name(
1207 __isl_take isl_pw_qpolynomial *pwqp,
1208 enum isl_dim_type type, unsigned pos,
1210 __isl_give isl_pw_qpolynomial_fold *
1211 isl_pw_qpolynomial_fold_set_dim_name(
1212 __isl_take isl_pw_qpolynomial_fold *pwf,
1213 enum isl_dim_type type, unsigned pos,
1216 Note that C<isl_space_get_name> returns a pointer to some internal
1217 data structure, so the result can only be used while the
1218 corresponding C<isl_space> is alive.
1219 Also note that every function that operates on two sets or relations
1220 requires that both arguments have the same parameters. This also
1221 means that if one of the arguments has named parameters, then the
1222 other needs to have named parameters too and the names need to match.
1223 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1224 arguments may have different parameters (as long as they are named),
1225 in which case the result will have as parameters the union of the parameters of
1228 Given the identifier or name of a dimension (typically a parameter),
1229 its position can be obtained from the following functions.
1231 #include <isl/space.h>
1232 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1233 enum isl_dim_type type, __isl_keep isl_id *id);
1234 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1235 enum isl_dim_type type, const char *name);
1237 #include <isl/local_space.h>
1238 int isl_local_space_find_dim_by_name(
1239 __isl_keep isl_local_space *ls,
1240 enum isl_dim_type type, const char *name);
1242 #include <isl/val.h>
1243 int isl_multi_val_find_dim_by_id(
1244 __isl_keep isl_multi_val *mv,
1245 enum isl_dim_type type, __isl_keep isl_id *id);
1246 int isl_multi_val_find_dim_by_name(
1247 __isl_keep isl_multi_val *mv,
1248 enum isl_dim_type type, const char *name);
1250 #include <isl/set.h>
1251 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1252 enum isl_dim_type type, __isl_keep isl_id *id);
1253 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1254 enum isl_dim_type type, const char *name);
1256 #include <isl/map.h>
1257 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1258 enum isl_dim_type type, __isl_keep isl_id *id);
1259 int isl_basic_map_find_dim_by_name(
1260 __isl_keep isl_basic_map *bmap,
1261 enum isl_dim_type type, const char *name);
1262 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1263 enum isl_dim_type type, const char *name);
1264 int isl_union_map_find_dim_by_name(
1265 __isl_keep isl_union_map *umap,
1266 enum isl_dim_type type, const char *name);
1268 #include <isl/aff.h>
1269 int isl_multi_aff_find_dim_by_id(
1270 __isl_keep isl_multi_aff *ma,
1271 enum isl_dim_type type, __isl_keep isl_id *id);
1272 int isl_multi_pw_aff_find_dim_by_id(
1273 __isl_keep isl_multi_pw_aff *mpa,
1274 enum isl_dim_type type, __isl_keep isl_id *id);
1275 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1276 enum isl_dim_type type, const char *name);
1277 int isl_multi_aff_find_dim_by_name(
1278 __isl_keep isl_multi_aff *ma,
1279 enum isl_dim_type type, const char *name);
1280 int isl_multi_pw_aff_find_dim_by_name(
1281 __isl_keep isl_multi_pw_aff *mpa,
1282 enum isl_dim_type type, const char *name);
1284 The identifiers or names of entire spaces may be set or read off
1285 using the following functions.
1287 #include <isl/space.h>
1288 __isl_give isl_space *isl_space_set_tuple_id(
1289 __isl_take isl_space *space,
1290 enum isl_dim_type type, __isl_take isl_id *id);
1291 __isl_give isl_space *isl_space_reset_tuple_id(
1292 __isl_take isl_space *space, enum isl_dim_type type);
1293 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1294 enum isl_dim_type type);
1295 __isl_give isl_id *isl_space_get_tuple_id(
1296 __isl_keep isl_space *space, enum isl_dim_type type);
1297 __isl_give isl_space *isl_space_set_tuple_name(
1298 __isl_take isl_space *space,
1299 enum isl_dim_type type, const char *s);
1300 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1301 enum isl_dim_type type);
1302 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1303 enum isl_dim_type type);
1305 #include <isl/local_space.h>
1306 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1307 __isl_take isl_local_space *ls,
1308 enum isl_dim_type type, __isl_take isl_id *id);
1310 #include <isl/set.h>
1311 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1312 __isl_take isl_basic_set *bset,
1313 __isl_take isl_id *id);
1314 __isl_give isl_set *isl_set_set_tuple_id(
1315 __isl_take isl_set *set, __isl_take isl_id *id);
1316 __isl_give isl_set *isl_set_reset_tuple_id(
1317 __isl_take isl_set *set);
1318 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1319 __isl_give isl_id *isl_set_get_tuple_id(
1320 __isl_keep isl_set *set);
1321 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1322 __isl_take isl_basic_set *set, const char *s);
1323 __isl_give isl_set *isl_set_set_tuple_name(
1324 __isl_take isl_set *set, const char *s);
1325 const char *isl_basic_set_get_tuple_name(
1326 __isl_keep isl_basic_set *bset);
1327 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1328 const char *isl_set_get_tuple_name(
1329 __isl_keep isl_set *set);
1331 #include <isl/map.h>
1332 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1333 __isl_take isl_basic_map *bmap,
1334 enum isl_dim_type type, __isl_take isl_id *id);
1335 __isl_give isl_map *isl_map_set_tuple_id(
1336 __isl_take isl_map *map, enum isl_dim_type type,
1337 __isl_take isl_id *id);
1338 __isl_give isl_map *isl_map_reset_tuple_id(
1339 __isl_take isl_map *map, enum isl_dim_type type);
1340 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1341 enum isl_dim_type type);
1342 __isl_give isl_id *isl_map_get_tuple_id(
1343 __isl_keep isl_map *map, enum isl_dim_type type);
1344 __isl_give isl_map *isl_map_set_tuple_name(
1345 __isl_take isl_map *map,
1346 enum isl_dim_type type, const char *s);
1347 const char *isl_basic_map_get_tuple_name(
1348 __isl_keep isl_basic_map *bmap,
1349 enum isl_dim_type type);
1350 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1351 __isl_take isl_basic_map *bmap,
1352 enum isl_dim_type type, const char *s);
1353 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1354 enum isl_dim_type type);
1355 const char *isl_map_get_tuple_name(
1356 __isl_keep isl_map *map,
1357 enum isl_dim_type type);
1359 #include <isl/val.h>
1360 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1361 __isl_take isl_multi_val *mv,
1362 enum isl_dim_type type, __isl_take isl_id *id);
1363 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1364 __isl_take isl_multi_val *mv,
1365 enum isl_dim_type type);
1366 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1367 enum isl_dim_type type);
1368 __isl_give isl_id *isl_multi_val_get_tuple_id(
1369 __isl_keep isl_multi_val *mv,
1370 enum isl_dim_type type);
1371 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1372 __isl_take isl_multi_val *mv,
1373 enum isl_dim_type type, const char *s);
1374 const char *isl_multi_val_get_tuple_name(
1375 __isl_keep isl_multi_val *mv,
1376 enum isl_dim_type type);
1378 #include <isl/aff.h>
1379 __isl_give isl_aff *isl_aff_set_tuple_id(
1380 __isl_take isl_aff *aff,
1381 enum isl_dim_type type, __isl_take isl_id *id);
1382 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1383 __isl_take isl_multi_aff *maff,
1384 enum isl_dim_type type, __isl_take isl_id *id);
1385 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1386 __isl_take isl_pw_aff *pwaff,
1387 enum isl_dim_type type, __isl_take isl_id *id);
1388 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1389 __isl_take isl_pw_multi_aff *pma,
1390 enum isl_dim_type type, __isl_take isl_id *id);
1391 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1392 __isl_take isl_multi_aff *ma,
1393 enum isl_dim_type type);
1394 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1395 __isl_take isl_pw_aff *pa,
1396 enum isl_dim_type type);
1397 __isl_give isl_multi_pw_aff *
1398 isl_multi_pw_aff_reset_tuple_id(
1399 __isl_take isl_multi_pw_aff *mpa,
1400 enum isl_dim_type type);
1401 __isl_give isl_pw_multi_aff *
1402 isl_pw_multi_aff_reset_tuple_id(
1403 __isl_take isl_pw_multi_aff *pma,
1404 enum isl_dim_type type);
1405 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1406 enum isl_dim_type type);
1407 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1408 __isl_keep isl_multi_aff *ma,
1409 enum isl_dim_type type);
1410 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1411 enum isl_dim_type type);
1412 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1413 __isl_keep isl_pw_aff *pa,
1414 enum isl_dim_type type);
1415 int isl_pw_multi_aff_has_tuple_id(
1416 __isl_keep isl_pw_multi_aff *pma,
1417 enum isl_dim_type type);
1418 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1419 __isl_keep isl_pw_multi_aff *pma,
1420 enum isl_dim_type type);
1421 int isl_multi_pw_aff_has_tuple_id(
1422 __isl_keep isl_multi_pw_aff *mpa,
1423 enum isl_dim_type type);
1424 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1425 __isl_keep isl_multi_pw_aff *mpa,
1426 enum isl_dim_type type);
1427 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1428 __isl_take isl_multi_aff *maff,
1429 enum isl_dim_type type, const char *s);
1430 __isl_give isl_multi_pw_aff *
1431 isl_multi_pw_aff_set_tuple_name(
1432 __isl_take isl_multi_pw_aff *mpa,
1433 enum isl_dim_type type, const char *s);
1434 const char *isl_multi_aff_get_tuple_name(
1435 __isl_keep isl_multi_aff *multi,
1436 enum isl_dim_type type);
1437 int isl_pw_multi_aff_has_tuple_name(
1438 __isl_keep isl_pw_multi_aff *pma,
1439 enum isl_dim_type type);
1440 const char *isl_pw_multi_aff_get_tuple_name(
1441 __isl_keep isl_pw_multi_aff *pma,
1442 enum isl_dim_type type);
1444 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1445 or C<isl_dim_set>. As with C<isl_space_get_name>,
1446 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1448 Binary operations require the corresponding spaces of their arguments
1449 to have the same name.
1451 To keep the names of all parameters and tuples, but reset the user pointers
1452 of all the corresponding identifiers, use the following function.
1454 #include <isl/space.h>
1455 __isl_give isl_space *isl_space_reset_user(
1456 __isl_take isl_space *space);
1458 #include <isl/set.h>
1459 __isl_give isl_set *isl_set_reset_user(
1460 __isl_take isl_set *set);
1462 #include <isl/map.h>
1463 __isl_give isl_map *isl_map_reset_user(
1464 __isl_take isl_map *map);
1466 #include <isl/union_set.h>
1467 __isl_give isl_union_set *isl_union_set_reset_user(
1468 __isl_take isl_union_set *uset);
1470 #include <isl/union_map.h>
1471 __isl_give isl_union_map *isl_union_map_reset_user(
1472 __isl_take isl_union_map *umap);
1474 #include <isl/val.h>
1475 __isl_give isl_multi_val *isl_multi_val_reset_user(
1476 __isl_take isl_multi_val *mv);
1478 #include <isl/aff.h>
1479 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1480 __isl_take isl_multi_aff *ma);
1481 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1482 __isl_take isl_multi_pw_aff *mpa);
1484 Spaces can be nested. In particular, the domain of a set or
1485 the domain or range of a relation can be a nested relation.
1486 This process is also called I<wrapping>.
1487 The functions for detecting, constructing and deconstructing
1488 such nested spaces can be found in the wrapping properties
1489 of L</"Unary Properties">, the wrapping operations
1490 of L</"Unary Operations"> and the Cartesian product operations
1491 of L</"Basic Operations">.
1493 Spaces can be created from other spaces
1494 using the functions described in L</"Unary Operations">
1495 and L</"Binary Operations">.
1499 A local space is essentially a space with
1500 zero or more existentially quantified variables.
1501 The local space of various objects can be obtained
1502 using the following functions.
1504 #include <isl/constraint.h>
1505 __isl_give isl_local_space *isl_constraint_get_local_space(
1506 __isl_keep isl_constraint *constraint);
1508 #include <isl/set.h>
1509 __isl_give isl_local_space *isl_basic_set_get_local_space(
1510 __isl_keep isl_basic_set *bset);
1512 #include <isl/map.h>
1513 __isl_give isl_local_space *isl_basic_map_get_local_space(
1514 __isl_keep isl_basic_map *bmap);
1516 #include <isl/aff.h>
1517 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1518 __isl_keep isl_aff *aff);
1519 __isl_give isl_local_space *isl_aff_get_local_space(
1520 __isl_keep isl_aff *aff);
1522 A new local space can be created from a space using
1524 #include <isl/local_space.h>
1525 __isl_give isl_local_space *isl_local_space_from_space(
1526 __isl_take isl_space *space);
1528 They can be inspected, modified, copied and freed using the following functions.
1530 #include <isl/local_space.h>
1531 int isl_local_space_is_params(
1532 __isl_keep isl_local_space *ls);
1533 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1534 __isl_give isl_space *isl_local_space_get_space(
1535 __isl_keep isl_local_space *ls);
1536 __isl_give isl_aff *isl_local_space_get_div(
1537 __isl_keep isl_local_space *ls, int pos);
1538 __isl_give isl_local_space *isl_local_space_copy(
1539 __isl_keep isl_local_space *ls);
1540 __isl_null isl_local_space *isl_local_space_free(
1541 __isl_take isl_local_space *ls);
1543 Note that C<isl_local_space_get_div> can only be used on local spaces
1546 Two local spaces can be compared using
1548 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1549 __isl_keep isl_local_space *ls2);
1551 Local spaces can be created from other local spaces
1552 using the functions described in L</"Unary Operations">
1553 and L</"Binary Operations">.
1555 =head2 Creating New Sets and Relations
1557 C<isl> has functions for creating some standard sets and relations.
1561 =item * Empty sets and relations
1563 __isl_give isl_basic_set *isl_basic_set_empty(
1564 __isl_take isl_space *space);
1565 __isl_give isl_basic_map *isl_basic_map_empty(
1566 __isl_take isl_space *space);
1567 __isl_give isl_set *isl_set_empty(
1568 __isl_take isl_space *space);
1569 __isl_give isl_map *isl_map_empty(
1570 __isl_take isl_space *space);
1571 __isl_give isl_union_set *isl_union_set_empty(
1572 __isl_take isl_space *space);
1573 __isl_give isl_union_map *isl_union_map_empty(
1574 __isl_take isl_space *space);
1576 For C<isl_union_set>s and C<isl_union_map>s, the space
1577 is only used to specify the parameters.
1579 =item * Universe sets and relations
1581 __isl_give isl_basic_set *isl_basic_set_universe(
1582 __isl_take isl_space *space);
1583 __isl_give isl_basic_map *isl_basic_map_universe(
1584 __isl_take isl_space *space);
1585 __isl_give isl_set *isl_set_universe(
1586 __isl_take isl_space *space);
1587 __isl_give isl_map *isl_map_universe(
1588 __isl_take isl_space *space);
1589 __isl_give isl_union_set *isl_union_set_universe(
1590 __isl_take isl_union_set *uset);
1591 __isl_give isl_union_map *isl_union_map_universe(
1592 __isl_take isl_union_map *umap);
1594 The sets and relations constructed by the functions above
1595 contain all integer values, while those constructed by the
1596 functions below only contain non-negative values.
1598 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1599 __isl_take isl_space *space);
1600 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1601 __isl_take isl_space *space);
1602 __isl_give isl_set *isl_set_nat_universe(
1603 __isl_take isl_space *space);
1604 __isl_give isl_map *isl_map_nat_universe(
1605 __isl_take isl_space *space);
1607 =item * Identity relations
1609 __isl_give isl_basic_map *isl_basic_map_identity(
1610 __isl_take isl_space *space);
1611 __isl_give isl_map *isl_map_identity(
1612 __isl_take isl_space *space);
1614 The number of input and output dimensions in C<space> needs
1617 =item * Lexicographic order
1619 __isl_give isl_map *isl_map_lex_lt(
1620 __isl_take isl_space *set_space);
1621 __isl_give isl_map *isl_map_lex_le(
1622 __isl_take isl_space *set_space);
1623 __isl_give isl_map *isl_map_lex_gt(
1624 __isl_take isl_space *set_space);
1625 __isl_give isl_map *isl_map_lex_ge(
1626 __isl_take isl_space *set_space);
1627 __isl_give isl_map *isl_map_lex_lt_first(
1628 __isl_take isl_space *space, unsigned n);
1629 __isl_give isl_map *isl_map_lex_le_first(
1630 __isl_take isl_space *space, unsigned n);
1631 __isl_give isl_map *isl_map_lex_gt_first(
1632 __isl_take isl_space *space, unsigned n);
1633 __isl_give isl_map *isl_map_lex_ge_first(
1634 __isl_take isl_space *space, unsigned n);
1636 The first four functions take a space for a B<set>
1637 and return relations that express that the elements in the domain
1638 are lexicographically less
1639 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1640 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1641 than the elements in the range.
1642 The last four functions take a space for a map
1643 and return relations that express that the first C<n> dimensions
1644 in the domain are lexicographically less
1645 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1646 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1647 than the first C<n> dimensions in the range.
1651 A basic set or relation can be converted to a set or relation
1652 using the following functions.
1654 __isl_give isl_set *isl_set_from_basic_set(
1655 __isl_take isl_basic_set *bset);
1656 __isl_give isl_map *isl_map_from_basic_map(
1657 __isl_take isl_basic_map *bmap);
1659 Sets and relations can be converted to union sets and relations
1660 using the following functions.
1662 __isl_give isl_union_set *isl_union_set_from_basic_set(
1663 __isl_take isl_basic_set *bset);
1664 __isl_give isl_union_map *isl_union_map_from_basic_map(
1665 __isl_take isl_basic_map *bmap);
1666 __isl_give isl_union_set *isl_union_set_from_set(
1667 __isl_take isl_set *set);
1668 __isl_give isl_union_map *isl_union_map_from_map(
1669 __isl_take isl_map *map);
1671 The inverse conversions below can only be used if the input
1672 union set or relation is known to contain elements in exactly one
1675 __isl_give isl_set *isl_set_from_union_set(
1676 __isl_take isl_union_set *uset);
1677 __isl_give isl_map *isl_map_from_union_map(
1678 __isl_take isl_union_map *umap);
1680 Sets and relations can be copied and freed again using the following
1683 __isl_give isl_basic_set *isl_basic_set_copy(
1684 __isl_keep isl_basic_set *bset);
1685 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1686 __isl_give isl_union_set *isl_union_set_copy(
1687 __isl_keep isl_union_set *uset);
1688 __isl_give isl_basic_map *isl_basic_map_copy(
1689 __isl_keep isl_basic_map *bmap);
1690 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1691 __isl_give isl_union_map *isl_union_map_copy(
1692 __isl_keep isl_union_map *umap);
1693 __isl_null isl_basic_set *isl_basic_set_free(
1694 __isl_take isl_basic_set *bset);
1695 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1696 __isl_null isl_union_set *isl_union_set_free(
1697 __isl_take isl_union_set *uset);
1698 __isl_null isl_basic_map *isl_basic_map_free(
1699 __isl_take isl_basic_map *bmap);
1700 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1701 __isl_null isl_union_map *isl_union_map_free(
1702 __isl_take isl_union_map *umap);
1704 Other sets and relations can be constructed by starting
1705 from a universe set or relation, adding equality and/or
1706 inequality constraints and then projecting out the
1707 existentially quantified variables, if any.
1708 Constraints can be constructed, manipulated and
1709 added to (or removed from) (basic) sets and relations
1710 using the following functions.
1712 #include <isl/constraint.h>
1713 __isl_give isl_constraint *isl_equality_alloc(
1714 __isl_take isl_local_space *ls);
1715 __isl_give isl_constraint *isl_inequality_alloc(
1716 __isl_take isl_local_space *ls);
1717 __isl_give isl_constraint *isl_constraint_set_constant_si(
1718 __isl_take isl_constraint *constraint, int v);
1719 __isl_give isl_constraint *isl_constraint_set_constant_val(
1720 __isl_take isl_constraint *constraint,
1721 __isl_take isl_val *v);
1722 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1723 __isl_take isl_constraint *constraint,
1724 enum isl_dim_type type, int pos, int v);
1725 __isl_give isl_constraint *
1726 isl_constraint_set_coefficient_val(
1727 __isl_take isl_constraint *constraint,
1728 enum isl_dim_type type, int pos,
1729 __isl_take isl_val *v);
1730 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1731 __isl_take isl_basic_map *bmap,
1732 __isl_take isl_constraint *constraint);
1733 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1734 __isl_take isl_basic_set *bset,
1735 __isl_take isl_constraint *constraint);
1736 __isl_give isl_map *isl_map_add_constraint(
1737 __isl_take isl_map *map,
1738 __isl_take isl_constraint *constraint);
1739 __isl_give isl_set *isl_set_add_constraint(
1740 __isl_take isl_set *set,
1741 __isl_take isl_constraint *constraint);
1742 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1743 __isl_take isl_basic_set *bset,
1744 __isl_take isl_constraint *constraint);
1746 For example, to create a set containing the even integers
1747 between 10 and 42, you would use the following code.
1750 isl_local_space *ls;
1752 isl_basic_set *bset;
1754 space = isl_space_set_alloc(ctx, 0, 2);
1755 bset = isl_basic_set_universe(isl_space_copy(space));
1756 ls = isl_local_space_from_space(space);
1758 c = isl_equality_alloc(isl_local_space_copy(ls));
1759 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1760 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1761 bset = isl_basic_set_add_constraint(bset, c);
1763 c = isl_inequality_alloc(isl_local_space_copy(ls));
1764 c = isl_constraint_set_constant_si(c, -10);
1765 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1766 bset = isl_basic_set_add_constraint(bset, c);
1768 c = isl_inequality_alloc(ls);
1769 c = isl_constraint_set_constant_si(c, 42);
1770 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1771 bset = isl_basic_set_add_constraint(bset, c);
1773 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1777 isl_basic_set *bset;
1778 bset = isl_basic_set_read_from_str(ctx,
1779 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1781 A basic set or relation can also be constructed from two matrices
1782 describing the equalities and the inequalities.
1784 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1785 __isl_take isl_space *space,
1786 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1787 enum isl_dim_type c1,
1788 enum isl_dim_type c2, enum isl_dim_type c3,
1789 enum isl_dim_type c4);
1790 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1791 __isl_take isl_space *space,
1792 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1793 enum isl_dim_type c1,
1794 enum isl_dim_type c2, enum isl_dim_type c3,
1795 enum isl_dim_type c4, enum isl_dim_type c5);
1797 The C<isl_dim_type> arguments indicate the order in which
1798 different kinds of variables appear in the input matrices
1799 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1800 C<isl_dim_set> and C<isl_dim_div> for sets and
1801 of C<isl_dim_cst>, C<isl_dim_param>,
1802 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1804 A (basic or union) set or relation can also be constructed from a
1805 (union) (piecewise) (multiple) affine expression
1806 or a list of affine expressions
1807 (See L</"Functions">).
1809 __isl_give isl_basic_map *isl_basic_map_from_aff(
1810 __isl_take isl_aff *aff);
1811 __isl_give isl_map *isl_map_from_aff(
1812 __isl_take isl_aff *aff);
1813 __isl_give isl_set *isl_set_from_pw_aff(
1814 __isl_take isl_pw_aff *pwaff);
1815 __isl_give isl_map *isl_map_from_pw_aff(
1816 __isl_take isl_pw_aff *pwaff);
1817 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1818 __isl_take isl_space *domain_space,
1819 __isl_take isl_aff_list *list);
1820 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1821 __isl_take isl_multi_aff *maff)
1822 __isl_give isl_map *isl_map_from_multi_aff(
1823 __isl_take isl_multi_aff *maff)
1824 __isl_give isl_set *isl_set_from_pw_multi_aff(
1825 __isl_take isl_pw_multi_aff *pma);
1826 __isl_give isl_map *isl_map_from_pw_multi_aff(
1827 __isl_take isl_pw_multi_aff *pma);
1828 __isl_give isl_set *isl_set_from_multi_pw_aff(
1829 __isl_take isl_multi_pw_aff *mpa);
1830 __isl_give isl_map *isl_map_from_multi_pw_aff(
1831 __isl_take isl_multi_pw_aff *mpa);
1832 __isl_give isl_union_map *
1833 isl_union_map_from_union_pw_multi_aff(
1834 __isl_take isl_union_pw_multi_aff *upma);
1836 The C<domain_space> argument describes the domain of the resulting
1837 basic relation. It is required because the C<list> may consist
1838 of zero affine expressions.
1840 =head2 Inspecting Sets and Relations
1842 Usually, the user should not have to care about the actual constraints
1843 of the sets and maps, but should instead apply the abstract operations
1844 explained in the following sections.
1845 Occasionally, however, it may be required to inspect the individual
1846 coefficients of the constraints. This section explains how to do so.
1847 In these cases, it may also be useful to have C<isl> compute
1848 an explicit representation of the existentially quantified variables.
1850 __isl_give isl_set *isl_set_compute_divs(
1851 __isl_take isl_set *set);
1852 __isl_give isl_map *isl_map_compute_divs(
1853 __isl_take isl_map *map);
1854 __isl_give isl_union_set *isl_union_set_compute_divs(
1855 __isl_take isl_union_set *uset);
1856 __isl_give isl_union_map *isl_union_map_compute_divs(
1857 __isl_take isl_union_map *umap);
1859 This explicit representation defines the existentially quantified
1860 variables as integer divisions of the other variables, possibly
1861 including earlier existentially quantified variables.
1862 An explicitly represented existentially quantified variable therefore
1863 has a unique value when the values of the other variables are known.
1864 If, furthermore, the same existentials, i.e., existentials
1865 with the same explicit representations, should appear in the
1866 same order in each of the disjuncts of a set or map, then the user should call
1867 either of the following functions.
1869 __isl_give isl_set *isl_set_align_divs(
1870 __isl_take isl_set *set);
1871 __isl_give isl_map *isl_map_align_divs(
1872 __isl_take isl_map *map);
1874 Alternatively, the existentially quantified variables can be removed
1875 using the following functions, which compute an overapproximation.
1877 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1878 __isl_take isl_basic_set *bset);
1879 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1880 __isl_take isl_basic_map *bmap);
1881 __isl_give isl_set *isl_set_remove_divs(
1882 __isl_take isl_set *set);
1883 __isl_give isl_map *isl_map_remove_divs(
1884 __isl_take isl_map *map);
1886 It is also possible to only remove those divs that are defined
1887 in terms of a given range of dimensions or only those for which
1888 no explicit representation is known.
1890 __isl_give isl_basic_set *
1891 isl_basic_set_remove_divs_involving_dims(
1892 __isl_take isl_basic_set *bset,
1893 enum isl_dim_type type,
1894 unsigned first, unsigned n);
1895 __isl_give isl_basic_map *
1896 isl_basic_map_remove_divs_involving_dims(
1897 __isl_take isl_basic_map *bmap,
1898 enum isl_dim_type type,
1899 unsigned first, unsigned n);
1900 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1901 __isl_take isl_set *set, enum isl_dim_type type,
1902 unsigned first, unsigned n);
1903 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1904 __isl_take isl_map *map, enum isl_dim_type type,
1905 unsigned first, unsigned n);
1907 __isl_give isl_basic_set *
1908 isl_basic_set_remove_unknown_divs(
1909 __isl_take isl_basic_set *bset);
1910 __isl_give isl_set *isl_set_remove_unknown_divs(
1911 __isl_take isl_set *set);
1912 __isl_give isl_map *isl_map_remove_unknown_divs(
1913 __isl_take isl_map *map);
1915 To iterate over all the sets or maps in a union set or map, use
1917 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1918 int (*fn)(__isl_take isl_set *set, void *user),
1920 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1921 int (*fn)(__isl_take isl_map *map, void *user),
1924 The number of sets or maps in a union set or map can be obtained
1927 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1928 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1930 To extract the set or map in a given space from a union, use
1932 __isl_give isl_set *isl_union_set_extract_set(
1933 __isl_keep isl_union_set *uset,
1934 __isl_take isl_space *space);
1935 __isl_give isl_map *isl_union_map_extract_map(
1936 __isl_keep isl_union_map *umap,
1937 __isl_take isl_space *space);
1939 To iterate over all the basic sets or maps in a set or map, use
1941 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1942 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1944 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1945 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1948 The callback function C<fn> should return 0 if successful and
1949 -1 if an error occurs. In the latter case, or if any other error
1950 occurs, the above functions will return -1.
1952 It should be noted that C<isl> does not guarantee that
1953 the basic sets or maps passed to C<fn> are disjoint.
1954 If this is required, then the user should call one of
1955 the following functions first.
1957 __isl_give isl_set *isl_set_make_disjoint(
1958 __isl_take isl_set *set);
1959 __isl_give isl_map *isl_map_make_disjoint(
1960 __isl_take isl_map *map);
1962 The number of basic sets in a set can be obtained
1963 or the number of basic maps in a map can be obtained
1966 #include <isl/set.h>
1967 int isl_set_n_basic_set(__isl_keep isl_set *set);
1969 #include <isl/map.h>
1970 int isl_map_n_basic_map(__isl_keep isl_map *map);
1972 To iterate over the constraints of a basic set or map, use
1974 #include <isl/constraint.h>
1976 int isl_basic_set_n_constraint(
1977 __isl_keep isl_basic_set *bset);
1978 int isl_basic_set_foreach_constraint(
1979 __isl_keep isl_basic_set *bset,
1980 int (*fn)(__isl_take isl_constraint *c, void *user),
1982 int isl_basic_map_n_constraint(
1983 __isl_keep isl_basic_map *bmap);
1984 int isl_basic_map_foreach_constraint(
1985 __isl_keep isl_basic_map *bmap,
1986 int (*fn)(__isl_take isl_constraint *c, void *user),
1988 __isl_null isl_constraint *isl_constraint_free(
1989 __isl_take isl_constraint *c);
1991 Again, the callback function C<fn> should return 0 if successful and
1992 -1 if an error occurs. In the latter case, or if any other error
1993 occurs, the above functions will return -1.
1994 The constraint C<c> represents either an equality or an inequality.
1995 Use the following function to find out whether a constraint
1996 represents an equality. If not, it represents an inequality.
1998 int isl_constraint_is_equality(
1999 __isl_keep isl_constraint *constraint);
2001 It is also possible to obtain a list of constraints from a basic
2004 #include <isl/constraint.h>
2005 __isl_give isl_constraint_list *
2006 isl_basic_map_get_constraint_list(
2007 __isl_keep isl_basic_map *bmap);
2008 __isl_give isl_constraint_list *
2009 isl_basic_set_get_constraint_list(
2010 __isl_keep isl_basic_set *bset);
2012 These functions require that all existentially quantified variables
2013 have an explicit representation.
2014 The returned list can be manipulated using the functions in L<"Lists">.
2016 The coefficients of the constraints can be inspected using
2017 the following functions.
2019 int isl_constraint_is_lower_bound(
2020 __isl_keep isl_constraint *constraint,
2021 enum isl_dim_type type, unsigned pos);
2022 int isl_constraint_is_upper_bound(
2023 __isl_keep isl_constraint *constraint,
2024 enum isl_dim_type type, unsigned pos);
2025 __isl_give isl_val *isl_constraint_get_constant_val(
2026 __isl_keep isl_constraint *constraint);
2027 __isl_give isl_val *isl_constraint_get_coefficient_val(
2028 __isl_keep isl_constraint *constraint,
2029 enum isl_dim_type type, int pos);
2031 The explicit representations of the existentially quantified
2032 variables can be inspected using the following function.
2033 Note that the user is only allowed to use this function
2034 if the inspected set or map is the result of a call
2035 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2036 The existentially quantified variable is equal to the floor
2037 of the returned affine expression. The affine expression
2038 itself can be inspected using the functions in
2041 __isl_give isl_aff *isl_constraint_get_div(
2042 __isl_keep isl_constraint *constraint, int pos);
2044 To obtain the constraints of a basic set or map in matrix
2045 form, use the following functions.
2047 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2048 __isl_keep isl_basic_set *bset,
2049 enum isl_dim_type c1, enum isl_dim_type c2,
2050 enum isl_dim_type c3, enum isl_dim_type c4);
2051 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2052 __isl_keep isl_basic_set *bset,
2053 enum isl_dim_type c1, enum isl_dim_type c2,
2054 enum isl_dim_type c3, enum isl_dim_type c4);
2055 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2056 __isl_keep isl_basic_map *bmap,
2057 enum isl_dim_type c1,
2058 enum isl_dim_type c2, enum isl_dim_type c3,
2059 enum isl_dim_type c4, enum isl_dim_type c5);
2060 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2061 __isl_keep isl_basic_map *bmap,
2062 enum isl_dim_type c1,
2063 enum isl_dim_type c2, enum isl_dim_type c3,
2064 enum isl_dim_type c4, enum isl_dim_type c5);
2066 The C<isl_dim_type> arguments dictate the order in which
2067 different kinds of variables appear in the resulting matrix.
2068 For set inputs, they should be a permutation of
2069 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2070 For map inputs, they should be a permutation of
2071 C<isl_dim_cst>, C<isl_dim_param>,
2072 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2076 Points are elements of a set. They can be used to construct
2077 simple sets (boxes) or they can be used to represent the
2078 individual elements of a set.
2079 The zero point (the origin) can be created using
2081 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2083 The coordinates of a point can be inspected, set and changed
2086 __isl_give isl_val *isl_point_get_coordinate_val(
2087 __isl_keep isl_point *pnt,
2088 enum isl_dim_type type, int pos);
2089 __isl_give isl_point *isl_point_set_coordinate_val(
2090 __isl_take isl_point *pnt,
2091 enum isl_dim_type type, int pos,
2092 __isl_take isl_val *v);
2094 __isl_give isl_point *isl_point_add_ui(
2095 __isl_take isl_point *pnt,
2096 enum isl_dim_type type, int pos, unsigned val);
2097 __isl_give isl_point *isl_point_sub_ui(
2098 __isl_take isl_point *pnt,
2099 enum isl_dim_type type, int pos, unsigned val);
2101 Points can be copied or freed using
2103 __isl_give isl_point *isl_point_copy(
2104 __isl_keep isl_point *pnt);
2105 void isl_point_free(__isl_take isl_point *pnt);
2107 A singleton set can be created from a point using
2109 __isl_give isl_basic_set *isl_basic_set_from_point(
2110 __isl_take isl_point *pnt);
2111 __isl_give isl_set *isl_set_from_point(
2112 __isl_take isl_point *pnt);
2114 and a box can be created from two opposite extremal points using
2116 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2117 __isl_take isl_point *pnt1,
2118 __isl_take isl_point *pnt2);
2119 __isl_give isl_set *isl_set_box_from_points(
2120 __isl_take isl_point *pnt1,
2121 __isl_take isl_point *pnt2);
2123 All elements of a B<bounded> (union) set can be enumerated using
2124 the following functions.
2126 int isl_set_foreach_point(__isl_keep isl_set *set,
2127 int (*fn)(__isl_take isl_point *pnt, void *user),
2129 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2130 int (*fn)(__isl_take isl_point *pnt, void *user),
2133 The function C<fn> is called for each integer point in
2134 C<set> with as second argument the last argument of
2135 the C<isl_set_foreach_point> call. The function C<fn>
2136 should return C<0> on success and C<-1> on failure.
2137 In the latter case, C<isl_set_foreach_point> will stop
2138 enumerating and return C<-1> as well.
2139 If the enumeration is performed successfully and to completion,
2140 then C<isl_set_foreach_point> returns C<0>.
2142 To obtain a single point of a (basic) set, use
2144 __isl_give isl_point *isl_basic_set_sample_point(
2145 __isl_take isl_basic_set *bset);
2146 __isl_give isl_point *isl_set_sample_point(
2147 __isl_take isl_set *set);
2149 If C<set> does not contain any (integer) points, then the
2150 resulting point will be ``void'', a property that can be
2153 int isl_point_is_void(__isl_keep isl_point *pnt);
2157 Besides sets and relation, C<isl> also supports various types of functions.
2158 Each of these types is derived from the value type (see L</"Values">)
2159 or from one of two primitive function types
2160 through the application of zero or more type constructors.
2161 We first describe the primitive type and then we describe
2162 the types derived from these primitive types.
2164 =head3 Primitive Functions
2166 C<isl> support two primitive function types, quasi-affine
2167 expressions and quasipolynomials.
2168 A quasi-affine expression is defined either over a parameter
2169 space or over a set and is composed of integer constants,
2170 parameters and set variables, addition, subtraction and
2171 integer division by an integer constant.
2172 For example, the quasi-affine expression
2174 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2176 maps C<x> to C<2*floor((4 n + x)/9>.
2177 A quasipolynomial is a polynomial expression in quasi-affine
2178 expression. That is, it additionally allows for multiplication.
2179 Note, though, that it is not allowed to construct an integer
2180 division of an expression involving multiplications.
2181 Here is an example of a quasipolynomial that is not
2182 quasi-affine expression
2184 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2186 Note that the external representations of quasi-affine expressions
2187 and quasipolynomials are different. Quasi-affine expressions
2188 use a notation with square brackets just like binary relations,
2189 while quasipolynomials do not. This might change at some point.
2191 If a primitive function is defined over a parameter space,
2192 then the space of the function itself is that of a set.
2193 If it is defined over a set, then the space of the function
2194 is that of a relation. In both cases, the set space (or
2195 the output space) is single-dimensional, anonymous and unstructured.
2196 To create functions with multiple dimensions or with other kinds
2197 of set or output spaces, use multiple expressions
2198 (see L</"Multiple Expressions">).
2202 =item * Quasi-affine Expressions
2204 Besides the expressions described above, a quasi-affine
2205 expression can also be set to NaN. Such expressions
2206 typically represent a failure to represent a result
2207 as a quasi-affine expression.
2209 The zero quasi affine expression or the quasi affine expression
2210 that is equal to a given value or
2211 a specified dimension on a given domain can be created using
2213 #include <isl/aff.h>
2214 __isl_give isl_aff *isl_aff_zero_on_domain(
2215 __isl_take isl_local_space *ls);
2216 __isl_give isl_aff *isl_aff_val_on_domain(
2217 __isl_take isl_local_space *ls,
2218 __isl_take isl_val *val);
2219 __isl_give isl_aff *isl_aff_var_on_domain(
2220 __isl_take isl_local_space *ls,
2221 enum isl_dim_type type, unsigned pos);
2222 __isl_give isl_aff *isl_aff_nan_on_domain(
2223 __isl_take isl_local_space *ls);
2225 Quasi affine expressions can be copied and freed using
2227 #include <isl/aff.h>
2228 __isl_give isl_aff *isl_aff_copy(
2229 __isl_keep isl_aff *aff);
2230 __isl_null isl_aff *isl_aff_free(
2231 __isl_take isl_aff *aff);
2233 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2234 using the following function. The constraint is required to have
2235 a non-zero coefficient for the specified dimension.
2237 #include <isl/constraint.h>
2238 __isl_give isl_aff *isl_constraint_get_bound(
2239 __isl_keep isl_constraint *constraint,
2240 enum isl_dim_type type, int pos);
2242 The entire affine expression of the constraint can also be extracted
2243 using the following function.
2245 #include <isl/constraint.h>
2246 __isl_give isl_aff *isl_constraint_get_aff(
2247 __isl_keep isl_constraint *constraint);
2249 Conversely, an equality constraint equating
2250 the affine expression to zero or an inequality constraint enforcing
2251 the affine expression to be non-negative, can be constructed using
2253 __isl_give isl_constraint *isl_equality_from_aff(
2254 __isl_take isl_aff *aff);
2255 __isl_give isl_constraint *isl_inequality_from_aff(
2256 __isl_take isl_aff *aff);
2258 The coefficients and the integer divisions of an affine expression
2259 can be inspected using the following functions.
2261 #include <isl/aff.h>
2262 __isl_give isl_val *isl_aff_get_constant_val(
2263 __isl_keep isl_aff *aff);
2264 __isl_give isl_val *isl_aff_get_coefficient_val(
2265 __isl_keep isl_aff *aff,
2266 enum isl_dim_type type, int pos);
2267 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2268 enum isl_dim_type type, int pos);
2269 __isl_give isl_val *isl_aff_get_denominator_val(
2270 __isl_keep isl_aff *aff);
2271 __isl_give isl_aff *isl_aff_get_div(
2272 __isl_keep isl_aff *aff, int pos);
2274 They can be modified using the following functions.
2276 #include <isl/aff.h>
2277 __isl_give isl_aff *isl_aff_set_constant_si(
2278 __isl_take isl_aff *aff, int v);
2279 __isl_give isl_aff *isl_aff_set_constant_val(
2280 __isl_take isl_aff *aff, __isl_take isl_val *v);
2281 __isl_give isl_aff *isl_aff_set_coefficient_si(
2282 __isl_take isl_aff *aff,
2283 enum isl_dim_type type, int pos, int v);
2284 __isl_give isl_aff *isl_aff_set_coefficient_val(
2285 __isl_take isl_aff *aff,
2286 enum isl_dim_type type, int pos,
2287 __isl_take isl_val *v);
2289 __isl_give isl_aff *isl_aff_add_constant_si(
2290 __isl_take isl_aff *aff, int v);
2291 __isl_give isl_aff *isl_aff_add_constant_val(
2292 __isl_take isl_aff *aff, __isl_take isl_val *v);
2293 __isl_give isl_aff *isl_aff_add_constant_num_si(
2294 __isl_take isl_aff *aff, int v);
2295 __isl_give isl_aff *isl_aff_add_coefficient_si(
2296 __isl_take isl_aff *aff,
2297 enum isl_dim_type type, int pos, int v);
2298 __isl_give isl_aff *isl_aff_add_coefficient_val(
2299 __isl_take isl_aff *aff,
2300 enum isl_dim_type type, int pos,
2301 __isl_take isl_val *v);
2303 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2304 set the I<numerator> of the constant or coefficient, while
2305 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2306 the constant or coefficient as a whole.
2307 The C<add_constant> and C<add_coefficient> functions add an integer
2308 or rational value to
2309 the possibly rational constant or coefficient.
2310 The C<add_constant_num> functions add an integer value to
2313 =item * Quasipolynomials
2315 Some simple quasipolynomials can be created using the following functions.
2317 #include <isl/polynomial.h>
2318 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2319 __isl_take isl_space *domain);
2320 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2321 __isl_take isl_space *domain);
2322 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2323 __isl_take isl_space *domain);
2324 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2325 __isl_take isl_space *domain);
2326 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2327 __isl_take isl_space *domain);
2328 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2329 __isl_take isl_space *domain,
2330 __isl_take isl_val *val);
2331 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2332 __isl_take isl_space *domain,
2333 enum isl_dim_type type, unsigned pos);
2334 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2335 __isl_take isl_aff *aff);
2337 Recall that the space in which a quasipolynomial lives is a map space
2338 with a one-dimensional range. The C<domain> argument in some of
2339 the functions above corresponds to the domain of this map space.
2341 Quasipolynomials can be copied and freed again using the following
2344 #include <isl/polynomial.h>
2345 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2346 __isl_keep isl_qpolynomial *qp);
2347 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2348 __isl_take isl_qpolynomial *qp);
2350 The constant term of a quasipolynomial can be extracted using
2352 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2353 __isl_keep isl_qpolynomial *qp);
2355 To iterate over all terms in a quasipolynomial,
2358 int isl_qpolynomial_foreach_term(
2359 __isl_keep isl_qpolynomial *qp,
2360 int (*fn)(__isl_take isl_term *term,
2361 void *user), void *user);
2363 The terms themselves can be inspected and freed using
2366 unsigned isl_term_dim(__isl_keep isl_term *term,
2367 enum isl_dim_type type);
2368 __isl_give isl_val *isl_term_get_coefficient_val(
2369 __isl_keep isl_term *term);
2370 int isl_term_get_exp(__isl_keep isl_term *term,
2371 enum isl_dim_type type, unsigned pos);
2372 __isl_give isl_aff *isl_term_get_div(
2373 __isl_keep isl_term *term, unsigned pos);
2374 void isl_term_free(__isl_take isl_term *term);
2376 Each term is a product of parameters, set variables and
2377 integer divisions. The function C<isl_term_get_exp>
2378 returns the exponent of a given dimensions in the given term.
2384 A reduction represents a maximum or a minimum of its
2386 The only reduction type defined by C<isl> is
2387 C<isl_qpolynomial_fold>.
2389 There are currently no functions to directly create such
2390 objects, but they do appear in the piecewise quasipolynomial
2391 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2393 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2395 Reductions can be copied and freed using
2396 the following functions.
2398 #include <isl/polynomial.h>
2399 __isl_give isl_qpolynomial_fold *
2400 isl_qpolynomial_fold_copy(
2401 __isl_keep isl_qpolynomial_fold *fold);
2402 void isl_qpolynomial_fold_free(
2403 __isl_take isl_qpolynomial_fold *fold);
2405 To iterate over all quasipolynomials in a reduction, use
2407 int isl_qpolynomial_fold_foreach_qpolynomial(
2408 __isl_keep isl_qpolynomial_fold *fold,
2409 int (*fn)(__isl_take isl_qpolynomial *qp,
2410 void *user), void *user);
2412 =head3 Multiple Expressions
2414 A multiple expression represents a sequence of zero or
2415 more base expressions, all defined on the same domain space.
2416 The domain space of the multiple expression is the same
2417 as that of the base expressions, but the range space
2418 can be any space. In case the base expressions have
2419 a set space, the corresponding multiple expression
2420 also has a set space.
2421 Objects of the value type do not have an associated space.
2422 The space of a multiple value is therefore always a set space.
2424 The multiple expression types defined by C<isl>
2425 are C<isl_multi_val>, C<isl_multi_aff> and C<isl_multi_pw_aff>.
2427 A multiple expression with the value zero for
2428 each output (or set) dimension can be created
2429 using the following functions.
2431 #include <isl/val.h>
2432 __isl_give isl_multi_val *isl_multi_val_zero(
2433 __isl_take isl_space *space);
2435 #include <isl/aff.h>
2436 __isl_give isl_multi_aff *isl_multi_aff_zero(
2437 __isl_take isl_space *space);
2438 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2439 __isl_take isl_space *space);
2441 An identity function can be created using the following
2442 functions. The space needs to be that of a relation
2443 with the same number of input and output dimensions.
2445 #include <isl/aff.h>
2446 __isl_give isl_multi_aff *isl_multi_aff_identity(
2447 __isl_take isl_space *space);
2448 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2449 __isl_take isl_space *space);
2451 A function that performs a projection on a universe
2452 relation or set can be created using the following functions.
2453 See also the corresponding
2454 projection operations in L</"Unary Operations">.
2456 #include <isl/aff.h>
2457 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2458 __isl_take isl_space *space);
2459 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2460 __isl_take isl_space *space);
2461 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2462 __isl_take isl_space *space,
2463 enum isl_dim_type type,
2464 unsigned first, unsigned n);
2466 A multiple expression can be created from a single
2467 base expression using the following functions.
2468 The space of the created multiple expression is the same
2469 as that of the base expression.
2471 #include <isl/aff.h>
2472 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2473 __isl_take isl_aff *aff);
2474 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2475 __isl_take isl_pw_aff *pa);
2477 A multiple expression can be created from a list
2478 of base expression in a specified space.
2479 The domain of this space needs to be the same
2480 as the domains of the base expressions in the list.
2481 If the base expressions have a set space (or no associated space),
2482 then this space also needs to be a set space.
2484 #include <isl/val.h>
2485 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2486 __isl_take isl_space *space,
2487 __isl_take isl_val_list *list);
2489 #include <isl/aff.h>
2490 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2491 __isl_take isl_space *space,
2492 __isl_take isl_aff_list *list);
2494 As a convenience, a multiple piecewise expression can
2495 also be created from a multiple expression.
2496 Each piecewise expression in the result has a single
2499 #include <isl/aff.h>
2500 __isl_give isl_multi_pw_aff *
2501 isl_multi_pw_aff_from_multi_aff(
2502 __isl_take isl_multi_aff *ma);
2504 A multiple quasi-affine expression can be created from
2505 a multiple value with a given domain space using the following
2508 #include <isl/aff.h>
2509 __isl_give isl_multi_aff *
2510 isl_multi_aff_multi_val_on_space(
2511 __isl_take isl_space *space,
2512 __isl_take isl_multi_val *mv);
2514 Multiple expressions can be copied and freed using
2515 the following functions.
2517 #include <isl/val.h>
2518 __isl_give isl_multi_val *isl_multi_val_copy(
2519 __isl_keep isl_multi_val *mv);
2520 __isl_null isl_multi_val *isl_multi_val_free(
2521 __isl_take isl_multi_val *mv);
2523 #include <isl/aff.h>
2524 __isl_give isl_multi_aff *isl_multi_aff_copy(
2525 __isl_keep isl_multi_aff *maff);
2526 __isl_null isl_multi_aff *isl_multi_aff_free(
2527 __isl_take isl_multi_aff *maff);
2528 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2529 __isl_keep isl_multi_pw_aff *mpa);
2530 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2531 __isl_take isl_multi_pw_aff *mpa);
2533 The base expression at a given position of a multiple
2534 expression can be extracted using the following functions.
2536 #include <isl/val.h>
2537 __isl_give isl_val *isl_multi_val_get_val(
2538 __isl_keep isl_multi_val *mv, int pos);
2540 #include <isl/aff.h>
2541 __isl_give isl_aff *isl_multi_aff_get_aff(
2542 __isl_keep isl_multi_aff *multi, int pos);
2543 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2544 __isl_keep isl_multi_pw_aff *mpa, int pos);
2546 It can be replaced using the following functions.
2548 #include <isl/val.h>
2549 __isl_give isl_multi_val *isl_multi_val_set_val(
2550 __isl_take isl_multi_val *mv, int pos,
2551 __isl_take isl_val *val);
2553 #include <isl/aff.h>
2554 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2555 __isl_take isl_multi_aff *multi, int pos,
2556 __isl_take isl_aff *aff);
2558 =head3 Piecewise Expressions
2560 A piecewise expression is an expression that is described
2561 using zero or more base expression defined over the same
2562 number of cells in the domain space of the base expressions.
2563 All base expressions are defined over the same
2564 domain space and the cells are disjoint.
2565 The space of a piecewise expression is the same as
2566 that of the base expressions.
2567 If the union of the cells is a strict subset of the domain
2568 space, then the value of the piecewise expression outside
2569 this union is different for types derived from quasi-affine
2570 expressions and those derived from quasipolynomials.
2571 Piecewise expressions derived from quasi-affine expressions
2572 are considered to be undefined outside the union of their cells.
2573 Piecewise expressions derived from quasipolynomials
2574 are considered to be zero outside the union of their cells.
2576 Piecewise quasipolynomials are mainly used by the C<barvinok>
2577 library for representing the number of elements in a parametric set or map.
2578 For example, the piecewise quasipolynomial
2580 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2582 represents the number of points in the map
2584 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2586 The piecewise expression types defined by C<isl>
2587 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2588 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2590 A piecewise expression with no cells can be created using
2591 the following functions.
2593 #include <isl/aff.h>
2594 __isl_give isl_pw_aff *isl_pw_aff_empty(
2595 __isl_take isl_space *space);
2596 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2597 __isl_take isl_space *space);
2599 A piecewise expression with a single universe cell can be
2600 created using the following functions.
2602 #include <isl/aff.h>
2603 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2604 __isl_take isl_aff *aff);
2605 __isl_give isl_pw_multi_aff *
2606 isl_pw_multi_aff_from_multi_aff(
2607 __isl_take isl_multi_aff *ma);
2609 #include <isl/polynomial.h>
2610 __isl_give isl_pw_qpolynomial *
2611 isl_pw_qpolynomial_from_qpolynomial(
2612 __isl_take isl_qpolynomial *qp);
2614 A piecewise expression with a single specified cell can be
2615 created using the following functions.
2617 #include <isl/aff.h>
2618 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2619 __isl_take isl_set *set, __isl_take isl_aff *aff);
2620 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2621 __isl_take isl_set *set,
2622 __isl_take isl_multi_aff *maff);
2624 #include <isl/polynomial.h>
2625 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2626 __isl_take isl_set *set,
2627 __isl_take isl_qpolynomial *qp);
2629 The following convenience functions first create a base expression and
2630 then create a piecewise expression over a universe domain.
2632 #include <isl/aff.h>
2633 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2634 __isl_take isl_local_space *ls);
2635 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2636 __isl_take isl_local_space *ls,
2637 enum isl_dim_type type, unsigned pos);
2638 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2639 __isl_take isl_local_space *ls);
2640 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2641 __isl_take isl_space *space);
2642 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2643 __isl_take isl_space *space);
2644 __isl_give isl_pw_multi_aff *
2645 isl_pw_multi_aff_project_out_map(
2646 __isl_take isl_space *space,
2647 enum isl_dim_type type,
2648 unsigned first, unsigned n);
2650 #include <isl/polynomial.h>
2651 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2652 __isl_take isl_space *space);
2654 The following convenience functions first create a base expression and
2655 then create a piecewise expression over a given domain.
2657 #include <isl/aff.h>
2658 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2659 __isl_take isl_set *domain,
2660 __isl_take isl_val *v);
2661 __isl_give isl_pw_multi_aff *
2662 isl_pw_multi_aff_multi_val_on_domain(
2663 __isl_take isl_set *domain,
2664 __isl_take isl_multi_val *mv);
2666 As a convenience, a piecewise multiple expression can
2667 also be created from a piecewise expression.
2668 Each multiple expression in the result is derived
2669 from the corresponding base expression.
2671 #include <isl/aff.h>
2672 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2673 __isl_take isl_pw_aff *pa);
2675 Similarly, a piecewise quasipolynomial can be
2676 created from a piecewise quasi-affine expression using
2677 the following function.
2679 #include <isl/polynomial.h>
2680 __isl_give isl_pw_qpolynomial *
2681 isl_pw_qpolynomial_from_pw_aff(
2682 __isl_take isl_pw_aff *pwaff);
2684 Piecewise expressions can be copied and freed using the following functions.
2686 #include <isl/aff.h>
2687 __isl_give isl_pw_aff *isl_pw_aff_copy(
2688 __isl_keep isl_pw_aff *pwaff);
2689 __isl_null isl_pw_aff *isl_pw_aff_free(
2690 __isl_take isl_pw_aff *pwaff);
2691 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2692 __isl_keep isl_pw_multi_aff *pma);
2693 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2694 __isl_take isl_pw_multi_aff *pma);
2696 #include <isl/polynomial.h>
2697 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2698 __isl_keep isl_pw_qpolynomial *pwqp);
2699 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2700 __isl_take isl_pw_qpolynomial *pwqp);
2701 __isl_give isl_pw_qpolynomial_fold *
2702 isl_pw_qpolynomial_fold_copy(
2703 __isl_keep isl_pw_qpolynomial_fold *pwf);
2704 __isl_null isl_pw_qpolynomial_fold *
2705 isl_pw_qpolynomial_fold_free(
2706 __isl_take isl_pw_qpolynomial_fold *pwf);
2708 To iterate over the different cells of a piecewise expression,
2709 use the following functions.
2711 #include <isl/aff.h>
2712 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2713 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2714 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2715 int (*fn)(__isl_take isl_set *set,
2716 __isl_take isl_aff *aff,
2717 void *user), void *user);
2718 int isl_pw_multi_aff_foreach_piece(
2719 __isl_keep isl_pw_multi_aff *pma,
2720 int (*fn)(__isl_take isl_set *set,
2721 __isl_take isl_multi_aff *maff,
2722 void *user), void *user);
2724 #include <isl/polynomial.h>
2725 int isl_pw_qpolynomial_foreach_piece(
2726 __isl_keep isl_pw_qpolynomial *pwqp,
2727 int (*fn)(__isl_take isl_set *set,
2728 __isl_take isl_qpolynomial *qp,
2729 void *user), void *user);
2730 int isl_pw_qpolynomial_foreach_lifted_piece(
2731 __isl_keep isl_pw_qpolynomial *pwqp,
2732 int (*fn)(__isl_take isl_set *set,
2733 __isl_take isl_qpolynomial *qp,
2734 void *user), void *user);
2735 int isl_pw_qpolynomial_fold_foreach_piece(
2736 __isl_keep isl_pw_qpolynomial_fold *pwf,
2737 int (*fn)(__isl_take isl_set *set,
2738 __isl_take isl_qpolynomial_fold *fold,
2739 void *user), void *user);
2740 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2741 __isl_keep isl_pw_qpolynomial_fold *pwf,
2742 int (*fn)(__isl_take isl_set *set,
2743 __isl_take isl_qpolynomial_fold *fold,
2744 void *user), void *user);
2746 As usual, the function C<fn> should return C<0> on success
2747 and C<-1> on failure. The difference between
2748 C<isl_pw_qpolynomial_foreach_piece> and
2749 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2750 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2751 compute unique representations for all existentially quantified
2752 variables and then turn these existentially quantified variables
2753 into extra set variables, adapting the associated quasipolynomial
2754 accordingly. This means that the C<set> passed to C<fn>
2755 will not have any existentially quantified variables, but that
2756 the dimensions of the sets may be different for different
2757 invocations of C<fn>.
2758 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2759 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2761 A piecewise expression consisting of the expressions at a given
2762 position of a piecewise multiple expression can be extracted
2763 using the following function.
2765 #include <isl/aff.h>
2766 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2767 __isl_keep isl_pw_multi_aff *pma, int pos);
2769 These expressions can be replaced using the following function.
2771 #include <isl/aff.h>
2772 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2773 __isl_take isl_pw_multi_aff *pma, unsigned pos,
2774 __isl_take isl_pw_aff *pa);
2776 Note that there is a difference between C<isl_multi_pw_aff> and
2777 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
2778 affine expressions, while the second is a piecewise sequence
2779 of affine expressions. In particular, each of the piecewise
2780 affine expressions in an C<isl_multi_pw_aff> may have a different
2781 domain, while all multiple expressions associated to a cell
2782 in an C<isl_pw_multi_aff> have the same domain.
2783 It is possible to convert between the two, but when converting
2784 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
2785 of the result is the intersection of the domains of the input.
2786 The reverse conversion is exact.
2788 #include <isl/aff.h>
2789 __isl_give isl_pw_multi_aff *
2790 isl_pw_multi_aff_from_multi_pw_aff(
2791 __isl_take isl_multi_pw_aff *mpa);
2792 __isl_give isl_multi_pw_aff *
2793 isl_multi_pw_aff_from_pw_multi_aff(
2794 __isl_take isl_pw_multi_aff *pma);
2796 =head3 Union Expressions
2798 A union expression collects base expressions defined
2799 over different domains. The space of a union expression
2800 is that of the shared parameter space.
2802 The union expression types defined by C<isl>
2803 are C<isl_union_pw_multi_aff>, C<isl_union_pw_qpolynomial> and
2804 C<isl_union_pw_qpolynomial_fold>.
2806 An empty union expression can be created using the following functions.
2808 #include <isl/aff.h>
2809 __isl_give isl_union_pw_multi_aff *
2810 isl_union_pw_multi_aff_empty(
2811 __isl_take isl_space *space);
2813 #include <isl/polynomial.h>
2814 __isl_give isl_union_pw_qpolynomial *
2815 isl_union_pw_qpolynomial_zero(
2816 __isl_take isl_space *space);
2818 A union expression containing a single base expression
2819 can be created using the following functions.
2821 #include <isl/aff.h>
2822 __isl_give isl_union_pw_multi_aff *
2823 isl_union_pw_multi_aff_from_pw_multi_aff(
2824 __isl_take isl_pw_multi_aff *pma);
2826 #include <isl/polynomial.h>
2827 __isl_give isl_union_pw_qpolynomial *
2828 isl_union_pw_qpolynomial_from_pw_qpolynomial(
2829 __isl_take isl_pw_qpolynomial *pwqp);
2831 The following function creates a base expression on each
2832 of the sets in the union set and collects the results.
2834 #include <isl/aff.h>
2835 __isl_give isl_union_pw_multi_aff *
2836 isl_union_pw_multi_aff_multi_val_on_domain(
2837 __isl_take isl_union_set *domain,
2838 __isl_take isl_multi_val *mv);
2840 A base expression can be added to a union expression using
2841 the following functions.
2843 #include <isl/aff.h>
2844 __isl_give isl_union_pw_multi_aff *
2845 isl_union_pw_multi_aff_add_pw_multi_aff(
2846 __isl_take isl_union_pw_multi_aff *upma,
2847 __isl_take isl_pw_multi_aff *pma);
2849 #include <isl/polynomial.h>
2850 __isl_give isl_union_pw_qpolynomial *
2851 isl_union_pw_qpolynomial_add_pw_qpolynomial(
2852 __isl_take isl_union_pw_qpolynomial *upwqp,
2853 __isl_take isl_pw_qpolynomial *pwqp);
2855 Union expressions can be copied and freed using
2856 the following functions.
2858 #include <isl/aff.h>
2859 __isl_give isl_union_pw_multi_aff *
2860 isl_union_pw_multi_aff_copy(
2861 __isl_keep isl_union_pw_multi_aff *upma);
2862 __isl_null isl_union_pw_multi_aff *
2863 isl_union_pw_multi_aff_free(
2864 __isl_take isl_union_pw_multi_aff *upma);
2866 #include <isl/polynomial.h>
2867 __isl_give isl_union_pw_qpolynomial *
2868 isl_union_pw_qpolynomial_copy(
2869 __isl_keep isl_union_pw_qpolynomial *upwqp);
2870 __isl_null isl_union_pw_qpolynomial *
2871 isl_union_pw_qpolynomial_free(
2872 __isl_take isl_union_pw_qpolynomial *upwqp);
2873 __isl_give isl_union_pw_qpolynomial_fold *
2874 isl_union_pw_qpolynomial_fold_copy(
2875 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2876 __isl_null isl_union_pw_qpolynomial_fold *
2877 isl_union_pw_qpolynomial_fold_free(
2878 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2880 To iterate over the base expressions in a union expression,
2881 use the following functions.
2883 #include <isl/aff.h>
2884 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
2885 __isl_keep isl_union_pw_multi_aff *upma,
2886 int (*fn)(__isl_take isl_pw_multi_aff *pma,
2887 void *user), void *user);
2889 #include <isl/polynomial.h>
2890 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2891 __isl_keep isl_union_pw_qpolynomial *upwqp,
2892 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
2893 void *user), void *user);
2894 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2895 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2896 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2897 void *user), void *user);
2899 To extract the base expression in a given space from a union, use
2900 the following functions.
2902 #include <isl/aff.h>
2903 __isl_give isl_pw_multi_aff *
2904 isl_union_pw_multi_aff_extract_pw_multi_aff(
2905 __isl_keep isl_union_pw_multi_aff *upma,
2906 __isl_take isl_space *space);
2908 #include <isl/polynomial.h>
2909 __isl_give isl_pw_qpolynomial *
2910 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2911 __isl_keep isl_union_pw_qpolynomial *upwqp,
2912 __isl_take isl_space *space);
2914 =head2 Input and Output
2916 For set and relation,
2917 C<isl> supports its own input/output format, which is similar
2918 to the C<Omega> format, but also supports the C<PolyLib> format
2920 For other object types, typically only an C<isl> format is supported.
2922 =head3 C<isl> format
2924 The C<isl> format is similar to that of C<Omega>, but has a different
2925 syntax for describing the parameters and allows for the definition
2926 of an existentially quantified variable as the integer division
2927 of an affine expression.
2928 For example, the set of integers C<i> between C<0> and C<n>
2929 such that C<i % 10 <= 6> can be described as
2931 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
2934 A set or relation can have several disjuncts, separated
2935 by the keyword C<or>. Each disjunct is either a conjunction
2936 of constraints or a projection (C<exists>) of a conjunction
2937 of constraints. The constraints are separated by the keyword
2940 =head3 C<PolyLib> format
2942 If the represented set is a union, then the first line
2943 contains a single number representing the number of disjuncts.
2944 Otherwise, a line containing the number C<1> is optional.
2946 Each disjunct is represented by a matrix of constraints.
2947 The first line contains two numbers representing
2948 the number of rows and columns,
2949 where the number of rows is equal to the number of constraints
2950 and the number of columns is equal to two plus the number of variables.
2951 The following lines contain the actual rows of the constraint matrix.
2952 In each row, the first column indicates whether the constraint
2953 is an equality (C<0>) or inequality (C<1>). The final column
2954 corresponds to the constant term.
2956 If the set is parametric, then the coefficients of the parameters
2957 appear in the last columns before the constant column.
2958 The coefficients of any existentially quantified variables appear
2959 between those of the set variables and those of the parameters.
2961 =head3 Extended C<PolyLib> format
2963 The extended C<PolyLib> format is nearly identical to the
2964 C<PolyLib> format. The only difference is that the line
2965 containing the number of rows and columns of a constraint matrix
2966 also contains four additional numbers:
2967 the number of output dimensions, the number of input dimensions,
2968 the number of local dimensions (i.e., the number of existentially
2969 quantified variables) and the number of parameters.
2970 For sets, the number of ``output'' dimensions is equal
2971 to the number of set dimensions, while the number of ``input''
2976 Objects can be read from input using the following functions.
2978 #include <isl/val.h>
2979 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
2982 #include <isl/set.h>
2983 __isl_give isl_basic_set *isl_basic_set_read_from_file(
2984 isl_ctx *ctx, FILE *input);
2985 __isl_give isl_basic_set *isl_basic_set_read_from_str(
2986 isl_ctx *ctx, const char *str);
2987 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
2989 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
2992 #include <isl/map.h>
2993 __isl_give isl_basic_map *isl_basic_map_read_from_file(
2994 isl_ctx *ctx, FILE *input);
2995 __isl_give isl_basic_map *isl_basic_map_read_from_str(
2996 isl_ctx *ctx, const char *str);
2997 __isl_give isl_map *isl_map_read_from_file(
2998 isl_ctx *ctx, FILE *input);
2999 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3002 #include <isl/union_set.h>
3003 __isl_give isl_union_set *isl_union_set_read_from_file(
3004 isl_ctx *ctx, FILE *input);
3005 __isl_give isl_union_set *isl_union_set_read_from_str(
3006 isl_ctx *ctx, const char *str);
3008 #include <isl/union_map.h>
3009 __isl_give isl_union_map *isl_union_map_read_from_file(
3010 isl_ctx *ctx, FILE *input);
3011 __isl_give isl_union_map *isl_union_map_read_from_str(
3012 isl_ctx *ctx, const char *str);
3014 #include <isl/aff.h>
3015 __isl_give isl_aff *isl_aff_read_from_str(
3016 isl_ctx *ctx, const char *str);
3017 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3018 isl_ctx *ctx, const char *str);
3019 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3020 isl_ctx *ctx, const char *str);
3021 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3022 isl_ctx *ctx, const char *str);
3023 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3024 isl_ctx *ctx, const char *str);
3025 __isl_give isl_union_pw_multi_aff *
3026 isl_union_pw_multi_aff_read_from_str(
3027 isl_ctx *ctx, const char *str);
3029 #include <isl/polynomial.h>
3030 __isl_give isl_union_pw_qpolynomial *
3031 isl_union_pw_qpolynomial_read_from_str(
3032 isl_ctx *ctx, const char *str);
3034 For sets and relations,
3035 the input format is autodetected and may be either the C<PolyLib> format
3036 or the C<isl> format.
3040 Before anything can be printed, an C<isl_printer> needs to
3043 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3045 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3046 __isl_null isl_printer *isl_printer_free(
3047 __isl_take isl_printer *printer);
3048 __isl_give char *isl_printer_get_str(
3049 __isl_keep isl_printer *printer);
3051 The printer can be inspected using the following functions.
3053 FILE *isl_printer_get_file(
3054 __isl_keep isl_printer *printer);
3055 int isl_printer_get_output_format(
3056 __isl_keep isl_printer *p);
3058 The behavior of the printer can be modified in various ways
3060 __isl_give isl_printer *isl_printer_set_output_format(
3061 __isl_take isl_printer *p, int output_format);
3062 __isl_give isl_printer *isl_printer_set_indent(
3063 __isl_take isl_printer *p, int indent);
3064 __isl_give isl_printer *isl_printer_set_indent_prefix(
3065 __isl_take isl_printer *p, const char *prefix);
3066 __isl_give isl_printer *isl_printer_indent(
3067 __isl_take isl_printer *p, int indent);
3068 __isl_give isl_printer *isl_printer_set_prefix(
3069 __isl_take isl_printer *p, const char *prefix);
3070 __isl_give isl_printer *isl_printer_set_suffix(
3071 __isl_take isl_printer *p, const char *suffix);
3073 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3074 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3075 and defaults to C<ISL_FORMAT_ISL>.
3076 Each line in the output is prefixed by C<indent_prefix>,
3077 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3078 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3079 In the C<PolyLib> format output,
3080 the coefficients of the existentially quantified variables
3081 appear between those of the set variables and those
3083 The function C<isl_printer_indent> increases the indentation
3084 by the specified amount (which may be negative).
3086 To actually print something, use
3088 #include <isl/printer.h>
3089 __isl_give isl_printer *isl_printer_print_double(
3090 __isl_take isl_printer *p, double d);
3092 #include <isl/val.h>
3093 __isl_give isl_printer *isl_printer_print_val(
3094 __isl_take isl_printer *p, __isl_keep isl_val *v);
3096 #include <isl/set.h>
3097 __isl_give isl_printer *isl_printer_print_basic_set(
3098 __isl_take isl_printer *printer,
3099 __isl_keep isl_basic_set *bset);
3100 __isl_give isl_printer *isl_printer_print_set(
3101 __isl_take isl_printer *printer,
3102 __isl_keep isl_set *set);
3104 #include <isl/map.h>
3105 __isl_give isl_printer *isl_printer_print_basic_map(
3106 __isl_take isl_printer *printer,
3107 __isl_keep isl_basic_map *bmap);
3108 __isl_give isl_printer *isl_printer_print_map(
3109 __isl_take isl_printer *printer,
3110 __isl_keep isl_map *map);
3112 #include <isl/union_set.h>
3113 __isl_give isl_printer *isl_printer_print_union_set(
3114 __isl_take isl_printer *p,
3115 __isl_keep isl_union_set *uset);
3117 #include <isl/union_map.h>
3118 __isl_give isl_printer *isl_printer_print_union_map(
3119 __isl_take isl_printer *p,
3120 __isl_keep isl_union_map *umap);
3122 #include <isl/val.h>
3123 __isl_give isl_printer *isl_printer_print_multi_val(
3124 __isl_take isl_printer *p,
3125 __isl_keep isl_multi_val *mv);
3127 #include <isl/aff.h>
3128 __isl_give isl_printer *isl_printer_print_aff(
3129 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3130 __isl_give isl_printer *isl_printer_print_multi_aff(
3131 __isl_take isl_printer *p,
3132 __isl_keep isl_multi_aff *maff);
3133 __isl_give isl_printer *isl_printer_print_pw_aff(
3134 __isl_take isl_printer *p,
3135 __isl_keep isl_pw_aff *pwaff);
3136 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3137 __isl_take isl_printer *p,
3138 __isl_keep isl_pw_multi_aff *pma);
3139 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3140 __isl_take isl_printer *p,
3141 __isl_keep isl_multi_pw_aff *mpa);
3142 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3143 __isl_take isl_printer *p,
3144 __isl_keep isl_union_pw_multi_aff *upma);
3146 #include <isl/polynomial.h>
3147 __isl_give isl_printer *isl_printer_print_qpolynomial(
3148 __isl_take isl_printer *p,
3149 __isl_keep isl_qpolynomial *qp);
3150 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3151 __isl_take isl_printer *p,
3152 __isl_keep isl_pw_qpolynomial *pwqp);
3153 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3154 __isl_take isl_printer *p,
3155 __isl_keep isl_union_pw_qpolynomial *upwqp);
3157 __isl_give isl_printer *
3158 isl_printer_print_pw_qpolynomial_fold(
3159 __isl_take isl_printer *p,
3160 __isl_keep isl_pw_qpolynomial_fold *pwf);
3161 __isl_give isl_printer *
3162 isl_printer_print_union_pw_qpolynomial_fold(
3163 __isl_take isl_printer *p,
3164 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3166 For C<isl_printer_print_qpolynomial>,
3167 C<isl_printer_print_pw_qpolynomial> and
3168 C<isl_printer_print_pw_qpolynomial_fold>,
3169 the output format of the printer
3170 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3171 For C<isl_printer_print_union_pw_qpolynomial> and
3172 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3174 In case of printing in C<ISL_FORMAT_C>, the user may want
3175 to set the names of all dimensions first.
3177 When called on a file printer, the following function flushes
3178 the file. When called on a string printer, the buffer is cleared.
3180 __isl_give isl_printer *isl_printer_flush(
3181 __isl_take isl_printer *p);
3183 Alternatively, a string representation can be obtained
3184 directly using the following functions, which always print
3187 #include <isl/space.h>
3188 __isl_give char *isl_space_to_str(
3189 __isl_keep isl_space *space);
3191 #include <isl/val.h>
3192 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3193 __isl_give char *isl_multi_val_to_str(
3194 __isl_keep isl_multi_val *mv);
3196 #include <isl/set.h>
3197 __isl_give char *isl_set_to_str(
3198 __isl_keep isl_set *set);
3200 #include <isl/union_set.h>
3201 __isl_give char *isl_union_set_to_str(
3202 __isl_keep isl_union_set *uset);
3204 #include <isl/map.h>
3205 __isl_give char *isl_map_to_str(
3206 __isl_keep isl_map *map);
3208 #include <isl/union_map.h>
3209 __isl_give char *isl_union_map_to_str(
3210 __isl_keep isl_union_map *umap);
3212 #include <isl/aff.h>
3213 __isl_give char *isl_multi_aff_to_str(
3214 __isl_keep isl_multi_aff *aff);
3215 __isl_give char *isl_union_pw_multi_aff_to_str(
3216 __isl_keep isl_union_pw_multi_aff *upma);
3220 =head3 Unary Properties
3226 The following functions test whether the given set or relation
3227 contains any integer points. The ``plain'' variants do not perform
3228 any computations, but simply check if the given set or relation
3229 is already known to be empty.
3231 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3232 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3233 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3234 int isl_set_is_empty(__isl_keep isl_set *set);
3235 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3236 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3237 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3238 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3239 int isl_map_is_empty(__isl_keep isl_map *map);
3240 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3242 =item * Universality
3244 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3245 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3246 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3248 =item * Single-valuedness
3250 #include <isl/set.h>
3251 int isl_set_is_singleton(__isl_keep isl_set *set);
3253 #include <isl/map.h>
3254 int isl_basic_map_is_single_valued(
3255 __isl_keep isl_basic_map *bmap);
3256 int isl_map_plain_is_single_valued(
3257 __isl_keep isl_map *map);
3258 int isl_map_is_single_valued(__isl_keep isl_map *map);
3260 #include <isl/union_map.h>
3261 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3265 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3266 int isl_map_is_injective(__isl_keep isl_map *map);
3267 int isl_union_map_plain_is_injective(
3268 __isl_keep isl_union_map *umap);
3269 int isl_union_map_is_injective(
3270 __isl_keep isl_union_map *umap);
3274 int isl_map_is_bijective(__isl_keep isl_map *map);
3275 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3279 __isl_give isl_val *
3280 isl_basic_map_plain_get_val_if_fixed(
3281 __isl_keep isl_basic_map *bmap,
3282 enum isl_dim_type type, unsigned pos);
3283 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3284 __isl_keep isl_set *set,
3285 enum isl_dim_type type, unsigned pos);
3286 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3287 __isl_keep isl_map *map,
3288 enum isl_dim_type type, unsigned pos);
3290 If the set or relation obviously lies on a hyperplane where the given dimension
3291 has a fixed value, then return that value.
3292 Otherwise return NaN.
3296 int isl_set_dim_residue_class_val(
3297 __isl_keep isl_set *set,
3298 int pos, __isl_give isl_val **modulo,
3299 __isl_give isl_val **residue);
3301 Check if the values of the given set dimension are equal to a fixed
3302 value modulo some integer value. If so, assign the modulo to C<*modulo>
3303 and the fixed value to C<*residue>. If the given dimension attains only
3304 a single value, then assign C<0> to C<*modulo> and the fixed value to
3306 If the dimension does not attain only a single value and if no modulo
3307 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3311 To check whether the description of a set, relation or function depends
3312 on one or more given dimensions,
3313 the following functions can be used.
3315 #include <isl/constraint.h>
3316 int isl_constraint_involves_dims(
3317 __isl_keep isl_constraint *constraint,
3318 enum isl_dim_type type, unsigned first, unsigned n);
3320 #include <isl/set.h>
3321 int isl_basic_set_involves_dims(
3322 __isl_keep isl_basic_set *bset,
3323 enum isl_dim_type type, unsigned first, unsigned n);
3324 int isl_set_involves_dims(__isl_keep isl_set *set,
3325 enum isl_dim_type type, unsigned first, unsigned n);
3327 #include <isl/map.h>
3328 int isl_basic_map_involves_dims(
3329 __isl_keep isl_basic_map *bmap,
3330 enum isl_dim_type type, unsigned first, unsigned n);
3331 int isl_map_involves_dims(__isl_keep isl_map *map,
3332 enum isl_dim_type type, unsigned first, unsigned n);
3334 #include <isl/aff.h>
3335 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3336 enum isl_dim_type type, unsigned first, unsigned n);
3337 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3338 enum isl_dim_type type, unsigned first, unsigned n);
3339 int isl_multi_aff_involves_dims(
3340 __isl_keep isl_multi_aff *ma,
3341 enum isl_dim_type type, unsigned first, unsigned n);
3342 int isl_multi_pw_aff_involves_dims(
3343 __isl_keep isl_multi_pw_aff *mpa,
3344 enum isl_dim_type type, unsigned first, unsigned n);
3346 Similarly, the following functions can be used to check whether
3347 a given dimension is involved in any lower or upper bound.
3349 #include <isl/set.h>
3350 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3351 enum isl_dim_type type, unsigned pos);
3352 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3353 enum isl_dim_type type, unsigned pos);
3355 Note that these functions return true even if there is a bound on
3356 the dimension on only some of the basic sets of C<set>.
3357 To check if they have a bound for all of the basic sets in C<set>,
3358 use the following functions instead.
3360 #include <isl/set.h>
3361 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3362 enum isl_dim_type type, unsigned pos);
3363 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3364 enum isl_dim_type type, unsigned pos);
3368 To check whether a set is a parameter domain, use this function:
3370 int isl_set_is_params(__isl_keep isl_set *set);
3371 int isl_union_set_is_params(
3372 __isl_keep isl_union_set *uset);
3376 The following functions check whether the space of the given
3377 (basic) set or relation range is a wrapped relation.
3379 #include <isl/space.h>
3380 int isl_space_is_wrapping(
3381 __isl_keep isl_space *space);
3382 int isl_space_domain_is_wrapping(
3383 __isl_keep isl_space *space);
3384 int isl_space_range_is_wrapping(
3385 __isl_keep isl_space *space);
3387 #include <isl/set.h>
3388 int isl_basic_set_is_wrapping(
3389 __isl_keep isl_basic_set *bset);
3390 int isl_set_is_wrapping(__isl_keep isl_set *set);
3392 #include <isl/map.h>
3393 int isl_map_domain_is_wrapping(
3394 __isl_keep isl_map *map);
3395 int isl_map_range_is_wrapping(
3396 __isl_keep isl_map *map);
3398 #include <isl/val.h>
3399 int isl_multi_val_range_is_wrapping(
3400 __isl_keep isl_multi_val *mv);
3402 #include <isl/aff.h>
3403 int isl_multi_aff_range_is_wrapping(
3404 __isl_keep isl_multi_aff *ma);
3405 int isl_multi_pw_aff_range_is_wrapping(
3406 __isl_keep isl_multi_pw_aff *mpa);
3408 The input to C<isl_space_is_wrapping> should
3409 be the space of a set, while that of
3410 C<isl_space_domain_is_wrapping> and
3411 C<isl_space_range_is_wrapping> should be the space of a relation.
3413 =item * Internal Product
3415 int isl_basic_map_can_zip(
3416 __isl_keep isl_basic_map *bmap);
3417 int isl_map_can_zip(__isl_keep isl_map *map);
3419 Check whether the product of domain and range of the given relation
3421 i.e., whether both domain and range are nested relations.
3425 int isl_basic_map_can_curry(
3426 __isl_keep isl_basic_map *bmap);
3427 int isl_map_can_curry(__isl_keep isl_map *map);
3429 Check whether the domain of the (basic) relation is a wrapped relation.
3431 int isl_basic_map_can_uncurry(
3432 __isl_keep isl_basic_map *bmap);
3433 int isl_map_can_uncurry(__isl_keep isl_map *map);
3435 Check whether the range of the (basic) relation is a wrapped relation.
3437 =item * Special Values
3439 #include <isl/aff.h>
3440 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3441 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3443 Check whether the given expression is a constant.
3445 #include <isl/aff.h>
3446 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3447 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3449 Check whether the given expression is equal to or involves NaN.
3451 #include <isl/aff.h>
3452 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3454 Check whether the affine expression is obviously zero.
3458 =head3 Binary Properties
3464 The following functions check whether two objects
3465 represent the same set, relation or function.
3466 The C<plain> variants only return true if the objects
3467 are obviously the same. That is, they may return false
3468 even if the objects are the same, but they will never
3469 return true if the objects are not the same.
3471 #include <isl/set.h>
3472 int isl_basic_set_plain_is_equal(
3473 __isl_keep isl_basic_set *bset1,
3474 __isl_keep isl_basic_set *bset2);
3475 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3476 __isl_keep isl_set *set2);
3477 int isl_set_is_equal(__isl_keep isl_set *set1,
3478 __isl_keep isl_set *set2);
3480 #include <isl/map.h>
3481 int isl_basic_map_is_equal(
3482 __isl_keep isl_basic_map *bmap1,
3483 __isl_keep isl_basic_map *bmap2);
3484 int isl_map_is_equal(__isl_keep isl_map *map1,
3485 __isl_keep isl_map *map2);
3486 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3487 __isl_keep isl_map *map2);
3489 #include <isl/union_set.h>
3490 int isl_union_set_is_equal(
3491 __isl_keep isl_union_set *uset1,
3492 __isl_keep isl_union_set *uset2);
3494 #include <isl/union_map.h>
3495 int isl_union_map_is_equal(
3496 __isl_keep isl_union_map *umap1,
3497 __isl_keep isl_union_map *umap2);
3499 #include <isl/aff.h>
3500 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3501 __isl_keep isl_aff *aff2);
3502 int isl_multi_aff_plain_is_equal(
3503 __isl_keep isl_multi_aff *maff1,
3504 __isl_keep isl_multi_aff *maff2);
3505 int isl_pw_aff_plain_is_equal(
3506 __isl_keep isl_pw_aff *pwaff1,
3507 __isl_keep isl_pw_aff *pwaff2);
3508 int isl_pw_multi_aff_plain_is_equal(
3509 __isl_keep isl_pw_multi_aff *pma1,
3510 __isl_keep isl_pw_multi_aff *pma2);
3511 int isl_multi_pw_aff_plain_is_equal(
3512 __isl_keep isl_multi_pw_aff *mpa1,
3513 __isl_keep isl_multi_pw_aff *mpa2);
3514 int isl_multi_pw_aff_is_equal(
3515 __isl_keep isl_multi_pw_aff *mpa1,
3516 __isl_keep isl_multi_pw_aff *mpa2);
3517 int isl_union_pw_multi_aff_plain_is_equal(
3518 __isl_keep isl_union_pw_multi_aff *upma1,
3519 __isl_keep isl_union_pw_multi_aff *upma2);
3521 #include <isl/polynomial.h>
3522 int isl_union_pw_qpolynomial_plain_is_equal(
3523 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3524 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3525 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3526 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3527 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3529 =item * Disjointness
3531 int isl_basic_set_is_disjoint(
3532 __isl_keep isl_basic_set *bset1,
3533 __isl_keep isl_basic_set *bset2);
3534 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3535 __isl_keep isl_set *set2);
3536 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3537 __isl_keep isl_set *set2);
3538 int isl_basic_map_is_disjoint(
3539 __isl_keep isl_basic_map *bmap1,
3540 __isl_keep isl_basic_map *bmap2);
3541 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3542 __isl_keep isl_map *map2);
3546 int isl_basic_set_is_subset(
3547 __isl_keep isl_basic_set *bset1,
3548 __isl_keep isl_basic_set *bset2);
3549 int isl_set_is_subset(__isl_keep isl_set *set1,
3550 __isl_keep isl_set *set2);
3551 int isl_set_is_strict_subset(
3552 __isl_keep isl_set *set1,
3553 __isl_keep isl_set *set2);
3554 int isl_union_set_is_subset(
3555 __isl_keep isl_union_set *uset1,
3556 __isl_keep isl_union_set *uset2);
3557 int isl_union_set_is_strict_subset(
3558 __isl_keep isl_union_set *uset1,
3559 __isl_keep isl_union_set *uset2);
3560 int isl_basic_map_is_subset(
3561 __isl_keep isl_basic_map *bmap1,
3562 __isl_keep isl_basic_map *bmap2);
3563 int isl_basic_map_is_strict_subset(
3564 __isl_keep isl_basic_map *bmap1,
3565 __isl_keep isl_basic_map *bmap2);
3566 int isl_map_is_subset(
3567 __isl_keep isl_map *map1,
3568 __isl_keep isl_map *map2);
3569 int isl_map_is_strict_subset(
3570 __isl_keep isl_map *map1,
3571 __isl_keep isl_map *map2);
3572 int isl_union_map_is_subset(
3573 __isl_keep isl_union_map *umap1,
3574 __isl_keep isl_union_map *umap2);
3575 int isl_union_map_is_strict_subset(
3576 __isl_keep isl_union_map *umap1,
3577 __isl_keep isl_union_map *umap2);
3579 Check whether the first argument is a (strict) subset of the
3584 Every comparison function returns a negative value if the first
3585 argument is considered smaller than the second, a positive value
3586 if the first argument is considered greater and zero if the two
3587 constraints are considered the same by the comparison criterion.
3589 #include <isl/constraint.h>
3590 int isl_constraint_plain_cmp(
3591 __isl_keep isl_constraint *c1,
3592 __isl_keep isl_constraint *c2);
3594 This function is useful for sorting C<isl_constraint>s.
3595 The order depends on the internal representation of the inputs.
3596 The order is fixed over different calls to the function (assuming
3597 the internal representation of the inputs has not changed), but may
3598 change over different versions of C<isl>.
3600 #include <isl/constraint.h>
3601 int isl_constraint_cmp_last_non_zero(
3602 __isl_keep isl_constraint *c1,
3603 __isl_keep isl_constraint *c2);
3605 This function can be used to sort constraints that live in the same
3606 local space. Constraints that involve ``earlier'' dimensions or
3607 that have a smaller coefficient for the shared latest dimension
3608 are considered smaller than other constraints.
3609 This function only defines a B<partial> order.
3611 #include <isl/set.h>
3612 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3613 __isl_keep isl_set *set2);
3615 This function is useful for sorting C<isl_set>s.
3616 The order depends on the internal representation of the inputs.
3617 The order is fixed over different calls to the function (assuming
3618 the internal representation of the inputs has not changed), but may
3619 change over different versions of C<isl>.
3621 #include <isl/aff.h>
3622 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3623 __isl_keep isl_pw_aff *pa2);
3625 The function C<isl_pw_aff_plain_cmp> can be used to sort
3626 C<isl_pw_aff>s. The order is not strictly defined.
3627 The current order sorts expressions that only involve
3628 earlier dimensions before those that involve later dimensions.
3632 =head2 Unary Operations
3638 __isl_give isl_set *isl_set_complement(
3639 __isl_take isl_set *set);
3640 __isl_give isl_map *isl_map_complement(
3641 __isl_take isl_map *map);
3645 #include <isl/space.h>
3646 __isl_give isl_space *isl_space_reverse(
3647 __isl_take isl_space *space);
3649 #include <isl/map.h>
3650 __isl_give isl_basic_map *isl_basic_map_reverse(
3651 __isl_take isl_basic_map *bmap);
3652 __isl_give isl_map *isl_map_reverse(
3653 __isl_take isl_map *map);
3655 #include <isl/union_map.h>
3656 __isl_give isl_union_map *isl_union_map_reverse(
3657 __isl_take isl_union_map *umap);
3661 #include <isl/space.h>
3662 __isl_give isl_space *isl_space_domain(
3663 __isl_take isl_space *space);
3664 __isl_give isl_space *isl_space_range(
3665 __isl_take isl_space *space);
3666 __isl_give isl_space *isl_space_params(
3667 __isl_take isl_space *space);
3669 #include <isl/local_space.h>
3670 __isl_give isl_local_space *isl_local_space_domain(
3671 __isl_take isl_local_space *ls);
3672 __isl_give isl_local_space *isl_local_space_range(
3673 __isl_take isl_local_space *ls);
3675 #include <isl/set.h>
3676 __isl_give isl_basic_set *isl_basic_set_project_out(
3677 __isl_take isl_basic_set *bset,
3678 enum isl_dim_type type, unsigned first, unsigned n);
3679 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3680 enum isl_dim_type type, unsigned first, unsigned n);
3681 __isl_give isl_basic_set *isl_basic_set_params(
3682 __isl_take isl_basic_set *bset);
3683 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
3685 #include <isl/map.h>
3686 __isl_give isl_basic_map *isl_basic_map_project_out(
3687 __isl_take isl_basic_map *bmap,
3688 enum isl_dim_type type, unsigned first, unsigned n);
3689 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3690 enum isl_dim_type type, unsigned first, unsigned n);
3691 __isl_give isl_basic_set *isl_basic_map_domain(
3692 __isl_take isl_basic_map *bmap);
3693 __isl_give isl_basic_set *isl_basic_map_range(
3694 __isl_take isl_basic_map *bmap);
3695 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
3696 __isl_give isl_set *isl_map_domain(
3697 __isl_take isl_map *bmap);
3698 __isl_give isl_set *isl_map_range(
3699 __isl_take isl_map *map);
3701 #include <isl/union_set.h>
3702 __isl_give isl_set *isl_union_set_params(
3703 __isl_take isl_union_set *uset);
3705 #include <isl/union_map.h>
3706 __isl_give isl_union_map *isl_union_map_project_out(
3707 __isl_take isl_union_map *umap,
3708 enum isl_dim_type type, unsigned first, unsigned n);
3709 __isl_give isl_set *isl_union_map_params(
3710 __isl_take isl_union_map *umap);
3711 __isl_give isl_union_set *isl_union_map_domain(
3712 __isl_take isl_union_map *umap);
3713 __isl_give isl_union_set *isl_union_map_range(
3714 __isl_take isl_union_map *umap);
3716 The function C<isl_union_map_project_out> can only project out
3719 #include <isl/aff.h>
3720 __isl_give isl_aff *isl_aff_project_domain_on_params(
3721 __isl_take isl_aff *aff);
3722 __isl_give isl_pw_multi_aff *
3723 isl_pw_multi_aff_project_domain_on_params(
3724 __isl_take isl_pw_multi_aff *pma);
3725 __isl_give isl_set *isl_pw_aff_domain(
3726 __isl_take isl_pw_aff *pwaff);
3727 __isl_give isl_set *isl_pw_multi_aff_domain(
3728 __isl_take isl_pw_multi_aff *pma);
3729 __isl_give isl_set *isl_multi_pw_aff_domain(
3730 __isl_take isl_multi_pw_aff *mpa);
3731 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3732 __isl_take isl_union_pw_multi_aff *upma);
3733 __isl_give isl_set *isl_pw_aff_params(
3734 __isl_take isl_pw_aff *pwa);
3736 #include <isl/polynomial.h>
3737 __isl_give isl_qpolynomial *
3738 isl_qpolynomial_project_domain_on_params(
3739 __isl_take isl_qpolynomial *qp);
3740 __isl_give isl_pw_qpolynomial *
3741 isl_pw_qpolynomial_project_domain_on_params(
3742 __isl_take isl_pw_qpolynomial *pwqp);
3743 __isl_give isl_pw_qpolynomial_fold *
3744 isl_pw_qpolynomial_fold_project_domain_on_params(
3745 __isl_take isl_pw_qpolynomial_fold *pwf);
3746 __isl_give isl_set *isl_pw_qpolynomial_domain(
3747 __isl_take isl_pw_qpolynomial *pwqp);
3748 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3749 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3750 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3751 __isl_take isl_union_pw_qpolynomial *upwqp);
3753 #include <isl/space.h>
3754 __isl_give isl_space *isl_space_domain_map(
3755 __isl_take isl_space *space);
3756 __isl_give isl_space *isl_space_range_map(
3757 __isl_take isl_space *space);
3759 #include <isl/map.h>
3760 __isl_give isl_basic_map *isl_basic_map_domain_map(
3761 __isl_take isl_basic_map *bmap);
3762 __isl_give isl_basic_map *isl_basic_map_range_map(
3763 __isl_take isl_basic_map *bmap);
3764 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
3765 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
3767 #include <isl/union_map.h>
3768 __isl_give isl_union_map *isl_union_map_domain_map(
3769 __isl_take isl_union_map *umap);
3770 __isl_give isl_union_map *isl_union_map_range_map(
3771 __isl_take isl_union_map *umap);
3773 The functions above construct a (basic, regular or union) relation
3774 that maps (a wrapped version of) the input relation to its domain or range.
3778 __isl_give isl_basic_set *isl_basic_set_eliminate(
3779 __isl_take isl_basic_set *bset,
3780 enum isl_dim_type type,
3781 unsigned first, unsigned n);
3782 __isl_give isl_set *isl_set_eliminate(
3783 __isl_take isl_set *set, enum isl_dim_type type,
3784 unsigned first, unsigned n);
3785 __isl_give isl_basic_map *isl_basic_map_eliminate(
3786 __isl_take isl_basic_map *bmap,
3787 enum isl_dim_type type,
3788 unsigned first, unsigned n);
3789 __isl_give isl_map *isl_map_eliminate(
3790 __isl_take isl_map *map, enum isl_dim_type type,
3791 unsigned first, unsigned n);
3793 Eliminate the coefficients for the given dimensions from the constraints,
3794 without removing the dimensions.
3796 =item * Constructing a set from a parameter domain
3798 A zero-dimensional space or (basic) set can be constructed
3799 on a given parameter domain using the following functions.
3801 #include <isl/space.h>
3802 __isl_give isl_space *isl_space_set_from_params(
3803 __isl_take isl_space *space);
3805 #include <isl/set.h>
3806 __isl_give isl_basic_set *isl_basic_set_from_params(
3807 __isl_take isl_basic_set *bset);
3808 __isl_give isl_set *isl_set_from_params(
3809 __isl_take isl_set *set);
3811 =item * Constructing a relation from a set
3813 Create a relation with the given set as domain or range.
3814 The range or domain of the created relation is a zero-dimensional
3815 flat anonymous space.
3817 #include <isl/space.h>
3818 __isl_give isl_space *isl_space_from_domain(
3819 __isl_take isl_space *space);
3820 __isl_give isl_space *isl_space_from_range(
3821 __isl_take isl_space *space);
3822 __isl_give isl_space *isl_space_map_from_set(
3823 __isl_take isl_space *space);
3824 __isl_give isl_space *isl_space_map_from_domain_and_range(
3825 __isl_take isl_space *domain,
3826 __isl_take isl_space *range);
3828 #include <isl/local_space.h>
3829 __isl_give isl_local_space *isl_local_space_from_domain(
3830 __isl_take isl_local_space *ls);
3832 #include <isl/map.h>
3833 __isl_give isl_map *isl_map_from_domain(
3834 __isl_take isl_set *set);
3835 __isl_give isl_map *isl_map_from_range(
3836 __isl_take isl_set *set);
3838 #include <isl/val.h>
3839 __isl_give isl_multi_val *isl_multi_val_from_range(
3840 __isl_take isl_multi_val *mv);
3842 #include <isl/aff.h>
3843 __isl_give isl_multi_aff *isl_multi_aff_from_range(
3844 __isl_take isl_multi_aff *ma);
3845 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3846 __isl_take isl_pw_aff *pwa);
3847 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
3848 __isl_take isl_multi_pw_aff *mpa);
3849 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3850 __isl_take isl_set *set);
3851 __isl_give isl_union_pw_multi_aff *
3852 isl_union_pw_multi_aff_from_domain(
3853 __isl_take isl_union_set *uset);
3857 #include <isl/set.h>
3858 __isl_give isl_basic_set *isl_basic_set_fix_si(
3859 __isl_take isl_basic_set *bset,
3860 enum isl_dim_type type, unsigned pos, int value);
3861 __isl_give isl_basic_set *isl_basic_set_fix_val(
3862 __isl_take isl_basic_set *bset,
3863 enum isl_dim_type type, unsigned pos,
3864 __isl_take isl_val *v);
3865 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
3866 enum isl_dim_type type, unsigned pos, int value);
3867 __isl_give isl_set *isl_set_fix_val(
3868 __isl_take isl_set *set,
3869 enum isl_dim_type type, unsigned pos,
3870 __isl_take isl_val *v);
3872 #include <isl/map.h>
3873 __isl_give isl_basic_map *isl_basic_map_fix_si(
3874 __isl_take isl_basic_map *bmap,
3875 enum isl_dim_type type, unsigned pos, int value);
3876 __isl_give isl_basic_map *isl_basic_map_fix_val(
3877 __isl_take isl_basic_map *bmap,
3878 enum isl_dim_type type, unsigned pos,
3879 __isl_take isl_val *v);
3880 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
3881 enum isl_dim_type type, unsigned pos, int value);
3882 __isl_give isl_map *isl_map_fix_val(
3883 __isl_take isl_map *map,
3884 enum isl_dim_type type, unsigned pos,
3885 __isl_take isl_val *v);
3887 #include <isl/aff.h>
3888 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
3889 __isl_take isl_pw_multi_aff *pma,
3890 enum isl_dim_type type, unsigned pos, int value);
3892 #include <isl/polynomial.h>
3893 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
3894 __isl_take isl_pw_qpolynomial *pwqp,
3895 enum isl_dim_type type, unsigned n,
3896 __isl_take isl_val *v);
3898 Intersect the set, relation or function domain
3899 with the hyperplane where the given
3900 dimension has the fixed given value.
3902 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
3903 __isl_take isl_basic_map *bmap,
3904 enum isl_dim_type type, unsigned pos, int value);
3905 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
3906 __isl_take isl_basic_map *bmap,
3907 enum isl_dim_type type, unsigned pos, int value);
3908 __isl_give isl_set *isl_set_lower_bound_si(
3909 __isl_take isl_set *set,
3910 enum isl_dim_type type, unsigned pos, int value);
3911 __isl_give isl_set *isl_set_lower_bound_val(
3912 __isl_take isl_set *set,
3913 enum isl_dim_type type, unsigned pos,
3914 __isl_take isl_val *value);
3915 __isl_give isl_map *isl_map_lower_bound_si(
3916 __isl_take isl_map *map,
3917 enum isl_dim_type type, unsigned pos, int value);
3918 __isl_give isl_set *isl_set_upper_bound_si(
3919 __isl_take isl_set *set,
3920 enum isl_dim_type type, unsigned pos, int value);
3921 __isl_give isl_set *isl_set_upper_bound_val(
3922 __isl_take isl_set *set,
3923 enum isl_dim_type type, unsigned pos,
3924 __isl_take isl_val *value);
3925 __isl_give isl_map *isl_map_upper_bound_si(
3926 __isl_take isl_map *map,
3927 enum isl_dim_type type, unsigned pos, int value);
3929 Intersect the set or relation with the half-space where the given
3930 dimension has a value bounded by the fixed given integer value.
3932 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
3933 enum isl_dim_type type1, int pos1,
3934 enum isl_dim_type type2, int pos2);
3935 __isl_give isl_basic_map *isl_basic_map_equate(
3936 __isl_take isl_basic_map *bmap,
3937 enum isl_dim_type type1, int pos1,
3938 enum isl_dim_type type2, int pos2);
3939 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
3940 enum isl_dim_type type1, int pos1,
3941 enum isl_dim_type type2, int pos2);
3943 Intersect the set or relation with the hyperplane where the given
3944 dimensions are equal to each other.
3946 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
3947 enum isl_dim_type type1, int pos1,
3948 enum isl_dim_type type2, int pos2);
3950 Intersect the relation with the hyperplane where the given
3951 dimensions have opposite values.
3953 __isl_give isl_map *isl_map_order_le(
3954 __isl_take isl_map *map,
3955 enum isl_dim_type type1, int pos1,
3956 enum isl_dim_type type2, int pos2);
3957 __isl_give isl_basic_map *isl_basic_map_order_ge(
3958 __isl_take isl_basic_map *bmap,
3959 enum isl_dim_type type1, int pos1,
3960 enum isl_dim_type type2, int pos2);
3961 __isl_give isl_map *isl_map_order_ge(
3962 __isl_take isl_map *map,
3963 enum isl_dim_type type1, int pos1,
3964 enum isl_dim_type type2, int pos2);
3965 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
3966 enum isl_dim_type type1, int pos1,
3967 enum isl_dim_type type2, int pos2);
3968 __isl_give isl_basic_map *isl_basic_map_order_gt(
3969 __isl_take isl_basic_map *bmap,
3970 enum isl_dim_type type1, int pos1,
3971 enum isl_dim_type type2, int pos2);
3972 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
3973 enum isl_dim_type type1, int pos1,
3974 enum isl_dim_type type2, int pos2);
3976 Intersect the relation with the half-space where the given
3977 dimensions satisfy the given ordering.
3981 #include <isl/aff.h>
3982 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3983 __isl_take isl_aff *aff);
3984 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3985 __isl_take isl_aff *aff);
3986 __isl_give isl_set *isl_pw_aff_nonneg_set(
3987 __isl_take isl_pw_aff *pwaff);
3988 __isl_give isl_set *isl_pw_aff_zero_set(
3989 __isl_take isl_pw_aff *pwaff);
3990 __isl_give isl_set *isl_pw_aff_non_zero_set(
3991 __isl_take isl_pw_aff *pwaff);
3993 The function C<isl_aff_neg_basic_set> returns a basic set
3994 containing those elements in the domain space
3995 of C<aff> where C<aff> is negative.
3996 The function C<isl_pw_aff_nonneg_set> returns a set
3997 containing those elements in the domain
3998 of C<pwaff> where C<pwaff> is non-negative.
4002 __isl_give isl_map *isl_set_identity(
4003 __isl_take isl_set *set);
4004 __isl_give isl_union_map *isl_union_set_identity(
4005 __isl_take isl_union_set *uset);
4007 Construct an identity relation on the given (union) set.
4009 =item * Function Extraction
4011 A piecewise quasi affine expression that is equal to 1 on a set
4012 and 0 outside the set can be created using the following function.
4014 #include <isl/aff.h>
4015 __isl_give isl_pw_aff *isl_set_indicator_function(
4016 __isl_take isl_set *set);
4018 A piecewise multiple quasi affine expression can be extracted
4019 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4020 and the C<isl_map> is single-valued.
4021 In case of a conversion from an C<isl_union_map>
4022 to an C<isl_union_pw_multi_aff>, these properties need to hold
4023 in each domain space.
4025 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4026 __isl_take isl_set *set);
4027 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4028 __isl_take isl_map *map);
4030 __isl_give isl_union_pw_multi_aff *
4031 isl_union_pw_multi_aff_from_union_set(
4032 __isl_take isl_union_set *uset);
4033 __isl_give isl_union_pw_multi_aff *
4034 isl_union_pw_multi_aff_from_union_map(
4035 __isl_take isl_union_map *umap);
4039 __isl_give isl_basic_set *isl_basic_map_deltas(
4040 __isl_take isl_basic_map *bmap);
4041 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4042 __isl_give isl_union_set *isl_union_map_deltas(
4043 __isl_take isl_union_map *umap);
4045 These functions return a (basic) set containing the differences
4046 between image elements and corresponding domain elements in the input.
4048 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4049 __isl_take isl_basic_map *bmap);
4050 __isl_give isl_map *isl_map_deltas_map(
4051 __isl_take isl_map *map);
4052 __isl_give isl_union_map *isl_union_map_deltas_map(
4053 __isl_take isl_union_map *umap);
4055 The functions above construct a (basic, regular or union) relation
4056 that maps (a wrapped version of) the input relation to its delta set.
4060 Simplify the representation of a set, relation or functions by trying
4061 to combine pairs of basic sets or relations into a single
4062 basic set or relation.
4064 #include <isl/set.h>
4065 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4067 #include <isl/map.h>
4068 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4070 #include <isl/union_set.h>
4071 __isl_give isl_union_set *isl_union_set_coalesce(
4072 __isl_take isl_union_set *uset);
4074 #include <isl/union_map.h>
4075 __isl_give isl_union_map *isl_union_map_coalesce(
4076 __isl_take isl_union_map *umap);
4078 #include <isl/aff.h>
4079 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4080 __isl_take isl_pw_aff *pwqp);
4081 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4082 __isl_take isl_pw_multi_aff *pma);
4083 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4084 __isl_take isl_multi_pw_aff *mpa);
4085 __isl_give isl_union_pw_multi_aff *
4086 isl_union_pw_multi_aff_coalesce(
4087 __isl_take isl_union_pw_multi_aff *upma);
4089 #include <isl/polynomial.h>
4090 __isl_give isl_pw_qpolynomial_fold *
4091 isl_pw_qpolynomial_fold_coalesce(
4092 __isl_take isl_pw_qpolynomial_fold *pwf);
4093 __isl_give isl_union_pw_qpolynomial *
4094 isl_union_pw_qpolynomial_coalesce(
4095 __isl_take isl_union_pw_qpolynomial *upwqp);
4096 __isl_give isl_union_pw_qpolynomial_fold *
4097 isl_union_pw_qpolynomial_fold_coalesce(
4098 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4100 One of the methods for combining pairs of basic sets or relations
4101 can result in coefficients that are much larger than those that appear
4102 in the constraints of the input. By default, the coefficients are
4103 not allowed to grow larger, but this can be changed by unsetting
4104 the following option.
4106 int isl_options_set_coalesce_bounded_wrapping(
4107 isl_ctx *ctx, int val);
4108 int isl_options_get_coalesce_bounded_wrapping(
4111 =item * Detecting equalities
4113 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4114 __isl_take isl_basic_set *bset);
4115 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4116 __isl_take isl_basic_map *bmap);
4117 __isl_give isl_set *isl_set_detect_equalities(
4118 __isl_take isl_set *set);
4119 __isl_give isl_map *isl_map_detect_equalities(
4120 __isl_take isl_map *map);
4121 __isl_give isl_union_set *isl_union_set_detect_equalities(
4122 __isl_take isl_union_set *uset);
4123 __isl_give isl_union_map *isl_union_map_detect_equalities(
4124 __isl_take isl_union_map *umap);
4126 Simplify the representation of a set or relation by detecting implicit
4129 =item * Removing redundant constraints
4131 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4132 __isl_take isl_basic_set *bset);
4133 __isl_give isl_set *isl_set_remove_redundancies(
4134 __isl_take isl_set *set);
4135 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4136 __isl_take isl_basic_map *bmap);
4137 __isl_give isl_map *isl_map_remove_redundancies(
4138 __isl_take isl_map *map);
4142 __isl_give isl_basic_set *isl_set_convex_hull(
4143 __isl_take isl_set *set);
4144 __isl_give isl_basic_map *isl_map_convex_hull(
4145 __isl_take isl_map *map);
4147 If the input set or relation has any existentially quantified
4148 variables, then the result of these operations is currently undefined.
4152 #include <isl/set.h>
4153 __isl_give isl_basic_set *
4154 isl_set_unshifted_simple_hull(
4155 __isl_take isl_set *set);
4156 __isl_give isl_basic_set *isl_set_simple_hull(
4157 __isl_take isl_set *set);
4158 __isl_give isl_basic_set *
4159 isl_set_unshifted_simple_hull_from_set_list(
4160 __isl_take isl_set *set,
4161 __isl_take isl_set_list *list);
4163 #include <isl/map.h>
4164 __isl_give isl_basic_map *
4165 isl_map_unshifted_simple_hull(
4166 __isl_take isl_map *map);
4167 __isl_give isl_basic_map *isl_map_simple_hull(
4168 __isl_take isl_map *map);
4170 #include <isl/union_map.h>
4171 __isl_give isl_union_map *isl_union_map_simple_hull(
4172 __isl_take isl_union_map *umap);
4174 These functions compute a single basic set or relation
4175 that contains the whole input set or relation.
4176 In particular, the output is described by translates
4177 of the constraints describing the basic sets or relations in the input.
4178 In case of C<isl_set_unshifted_simple_hull>, only the original
4179 constraints are used, without any translation.
4180 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
4181 constraints are taken from the elements of the second argument.
4185 (See \autoref{s:simple hull}.)
4191 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4192 __isl_take isl_basic_set *bset);
4193 __isl_give isl_basic_set *isl_set_affine_hull(
4194 __isl_take isl_set *set);
4195 __isl_give isl_union_set *isl_union_set_affine_hull(
4196 __isl_take isl_union_set *uset);
4197 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4198 __isl_take isl_basic_map *bmap);
4199 __isl_give isl_basic_map *isl_map_affine_hull(
4200 __isl_take isl_map *map);
4201 __isl_give isl_union_map *isl_union_map_affine_hull(
4202 __isl_take isl_union_map *umap);
4204 In case of union sets and relations, the affine hull is computed
4207 =item * Polyhedral hull
4209 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4210 __isl_take isl_set *set);
4211 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4212 __isl_take isl_map *map);
4213 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4214 __isl_take isl_union_set *uset);
4215 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4216 __isl_take isl_union_map *umap);
4218 These functions compute a single basic set or relation
4219 not involving any existentially quantified variables
4220 that contains the whole input set or relation.
4221 In case of union sets and relations, the polyhedral hull is computed
4224 =item * Other approximations
4226 #include <isl/set.h>
4227 __isl_give isl_basic_set *
4228 isl_basic_set_drop_constraints_involving_dims(
4229 __isl_take isl_basic_set *bset,
4230 enum isl_dim_type type,
4231 unsigned first, unsigned n);
4232 __isl_give isl_basic_set *
4233 isl_basic_set_drop_constraints_not_involving_dims(
4234 __isl_take isl_basic_set *bset,
4235 enum isl_dim_type type,
4236 unsigned first, unsigned n);
4237 __isl_give isl_set *
4238 isl_set_drop_constraints_involving_dims(
4239 __isl_take isl_set *set,
4240 enum isl_dim_type type,
4241 unsigned first, unsigned n);
4243 #include <isl/map.h>
4244 __isl_give isl_basic_map *
4245 isl_basic_map_drop_constraints_involving_dims(
4246 __isl_take isl_basic_map *bmap,
4247 enum isl_dim_type type,
4248 unsigned first, unsigned n);
4249 __isl_give isl_map *
4250 isl_map_drop_constraints_involving_dims(
4251 __isl_take isl_map *map,
4252 enum isl_dim_type type,
4253 unsigned first, unsigned n);
4255 These functions drop any constraints (not) involving the specified dimensions.
4256 Note that the result depends on the representation of the input.
4258 #include <isl/polynomial.h>
4259 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4260 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4261 __isl_give isl_union_pw_qpolynomial *
4262 isl_union_pw_qpolynomial_to_polynomial(
4263 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4265 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4266 the polynomial will be an overapproximation. If C<sign> is negative,
4267 it will be an underapproximation. If C<sign> is zero, the approximation
4268 will lie somewhere in between.
4272 __isl_give isl_basic_set *isl_basic_set_sample(
4273 __isl_take isl_basic_set *bset);
4274 __isl_give isl_basic_set *isl_set_sample(
4275 __isl_take isl_set *set);
4276 __isl_give isl_basic_map *isl_basic_map_sample(
4277 __isl_take isl_basic_map *bmap);
4278 __isl_give isl_basic_map *isl_map_sample(
4279 __isl_take isl_map *map);
4281 If the input (basic) set or relation is non-empty, then return
4282 a singleton subset of the input. Otherwise, return an empty set.
4284 =item * Optimization
4286 #include <isl/ilp.h>
4287 __isl_give isl_val *isl_basic_set_max_val(
4288 __isl_keep isl_basic_set *bset,
4289 __isl_keep isl_aff *obj);
4290 __isl_give isl_val *isl_set_min_val(
4291 __isl_keep isl_set *set,
4292 __isl_keep isl_aff *obj);
4293 __isl_give isl_val *isl_set_max_val(
4294 __isl_keep isl_set *set,
4295 __isl_keep isl_aff *obj);
4297 Compute the minimum or maximum of the integer affine expression C<obj>
4298 over the points in C<set>, returning the result in C<opt>.
4299 The result is C<NULL> in case of an error, the optimal value in case
4300 there is one, negative infinity or infinity if the problem is unbounded and
4301 NaN if the problem is empty.
4303 =item * Parametric optimization
4305 __isl_give isl_pw_aff *isl_set_dim_min(
4306 __isl_take isl_set *set, int pos);
4307 __isl_give isl_pw_aff *isl_set_dim_max(
4308 __isl_take isl_set *set, int pos);
4309 __isl_give isl_pw_aff *isl_map_dim_max(
4310 __isl_take isl_map *map, int pos);
4312 Compute the minimum or maximum of the given set or output dimension
4313 as a function of the parameters (and input dimensions), but independently
4314 of the other set or output dimensions.
4315 For lexicographic optimization, see L<"Lexicographic Optimization">.
4319 The following functions compute either the set of (rational) coefficient
4320 values of valid constraints for the given set or the set of (rational)
4321 values satisfying the constraints with coefficients from the given set.
4322 Internally, these two sets of functions perform essentially the
4323 same operations, except that the set of coefficients is assumed to
4324 be a cone, while the set of values may be any polyhedron.
4325 The current implementation is based on the Farkas lemma and
4326 Fourier-Motzkin elimination, but this may change or be made optional
4327 in future. In particular, future implementations may use different
4328 dualization algorithms or skip the elimination step.
4330 __isl_give isl_basic_set *isl_basic_set_coefficients(
4331 __isl_take isl_basic_set *bset);
4332 __isl_give isl_basic_set *isl_set_coefficients(
4333 __isl_take isl_set *set);
4334 __isl_give isl_union_set *isl_union_set_coefficients(
4335 __isl_take isl_union_set *bset);
4336 __isl_give isl_basic_set *isl_basic_set_solutions(
4337 __isl_take isl_basic_set *bset);
4338 __isl_give isl_basic_set *isl_set_solutions(
4339 __isl_take isl_set *set);
4340 __isl_give isl_union_set *isl_union_set_solutions(
4341 __isl_take isl_union_set *bset);
4345 __isl_give isl_map *isl_map_fixed_power_val(
4346 __isl_take isl_map *map,
4347 __isl_take isl_val *exp);
4348 __isl_give isl_union_map *
4349 isl_union_map_fixed_power_val(
4350 __isl_take isl_union_map *umap,
4351 __isl_take isl_val *exp);
4353 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4354 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4355 of C<map> is computed.
4357 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4359 __isl_give isl_union_map *isl_union_map_power(
4360 __isl_take isl_union_map *umap, int *exact);
4362 Compute a parametric representation for all positive powers I<k> of C<map>.
4363 The result maps I<k> to a nested relation corresponding to the
4364 I<k>th power of C<map>.
4365 The result may be an overapproximation. If the result is known to be exact,
4366 then C<*exact> is set to C<1>.
4368 =item * Transitive closure
4370 __isl_give isl_map *isl_map_transitive_closure(
4371 __isl_take isl_map *map, int *exact);
4372 __isl_give isl_union_map *isl_union_map_transitive_closure(
4373 __isl_take isl_union_map *umap, int *exact);
4375 Compute the transitive closure of C<map>.
4376 The result may be an overapproximation. If the result is known to be exact,
4377 then C<*exact> is set to C<1>.
4379 =item * Reaching path lengths
4381 __isl_give isl_map *isl_map_reaching_path_lengths(
4382 __isl_take isl_map *map, int *exact);
4384 Compute a relation that maps each element in the range of C<map>
4385 to the lengths of all paths composed of edges in C<map> that
4386 end up in the given element.
4387 The result may be an overapproximation. If the result is known to be exact,
4388 then C<*exact> is set to C<1>.
4389 To compute the I<maximal> path length, the resulting relation
4390 should be postprocessed by C<isl_map_lexmax>.
4391 In particular, if the input relation is a dependence relation
4392 (mapping sources to sinks), then the maximal path length corresponds
4393 to the free schedule.
4394 Note, however, that C<isl_map_lexmax> expects the maximum to be
4395 finite, so if the path lengths are unbounded (possibly due to
4396 the overapproximation), then you will get an error message.
4400 #include <isl/space.h>
4401 __isl_give isl_space *isl_space_wrap(
4402 __isl_take isl_space *space);
4403 __isl_give isl_space *isl_space_unwrap(
4404 __isl_take isl_space *space);
4406 #include <isl/set.h>
4407 __isl_give isl_basic_map *isl_basic_set_unwrap(
4408 __isl_take isl_basic_set *bset);
4409 __isl_give isl_map *isl_set_unwrap(
4410 __isl_take isl_set *set);
4412 #include <isl/map.h>
4413 __isl_give isl_basic_set *isl_basic_map_wrap(
4414 __isl_take isl_basic_map *bmap);
4415 __isl_give isl_set *isl_map_wrap(
4416 __isl_take isl_map *map);
4418 #include <isl/union_set.h>
4419 __isl_give isl_union_map *isl_union_set_unwrap(
4420 __isl_take isl_union_set *uset);
4422 #include <isl/union_map.h>
4423 __isl_give isl_union_set *isl_union_map_wrap(
4424 __isl_take isl_union_map *umap);
4426 The input to C<isl_space_unwrap> should
4427 be the space of a set, while that of
4428 C<isl_space_wrap> should be the space of a relation.
4429 Conversely, the output of C<isl_space_unwrap> is the space
4430 of a relation, while that of C<isl_space_wrap> is the space of a set.
4434 Remove any internal structure of domain (and range) of the given
4435 set or relation. If there is any such internal structure in the input,
4436 then the name of the space is also removed.
4438 #include <isl/local_space.h>
4439 __isl_give isl_local_space *
4440 isl_local_space_flatten_domain(
4441 __isl_take isl_local_space *ls);
4442 __isl_give isl_local_space *
4443 isl_local_space_flatten_range(
4444 __isl_take isl_local_space *ls);
4446 #include <isl/set.h>
4447 __isl_give isl_basic_set *isl_basic_set_flatten(
4448 __isl_take isl_basic_set *bset);
4449 __isl_give isl_set *isl_set_flatten(
4450 __isl_take isl_set *set);
4452 #include <isl/map.h>
4453 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4454 __isl_take isl_basic_map *bmap);
4455 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4456 __isl_take isl_basic_map *bmap);
4457 __isl_give isl_map *isl_map_flatten_range(
4458 __isl_take isl_map *map);
4459 __isl_give isl_map *isl_map_flatten_domain(
4460 __isl_take isl_map *map);
4461 __isl_give isl_basic_map *isl_basic_map_flatten(
4462 __isl_take isl_basic_map *bmap);
4463 __isl_give isl_map *isl_map_flatten(
4464 __isl_take isl_map *map);
4466 #include <isl/val.h>
4467 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4468 __isl_take isl_multi_val *mv);
4470 #include <isl/aff.h>
4471 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4472 __isl_take isl_multi_aff *ma);
4473 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4474 __isl_take isl_multi_aff *ma);
4475 __isl_give isl_multi_pw_aff *
4476 isl_multi_pw_aff_flatten_range(
4477 __isl_take isl_multi_pw_aff *mpa);
4479 #include <isl/map.h>
4480 __isl_give isl_map *isl_set_flatten_map(
4481 __isl_take isl_set *set);
4483 The function above constructs a relation
4484 that maps the input set to a flattened version of the set.
4488 Lift the input set to a space with extra dimensions corresponding
4489 to the existentially quantified variables in the input.
4490 In particular, the result lives in a wrapped map where the domain
4491 is the original space and the range corresponds to the original
4492 existentially quantified variables.
4494 #include <isl/set.h>
4495 __isl_give isl_basic_set *isl_basic_set_lift(
4496 __isl_take isl_basic_set *bset);
4497 __isl_give isl_set *isl_set_lift(
4498 __isl_take isl_set *set);
4499 __isl_give isl_union_set *isl_union_set_lift(
4500 __isl_take isl_union_set *uset);
4502 Given a local space that contains the existentially quantified
4503 variables of a set, a basic relation that, when applied to
4504 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4505 can be constructed using the following function.
4507 #include <isl/local_space.h>
4508 __isl_give isl_basic_map *isl_local_space_lifting(
4509 __isl_take isl_local_space *ls);
4511 #include <isl/aff.h>
4512 __isl_give isl_multi_aff *isl_multi_aff_lift(
4513 __isl_take isl_multi_aff *maff,
4514 __isl_give isl_local_space **ls);
4516 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4517 then it is assigned the local space that lies at the basis of
4518 the lifting applied.
4520 =item * Internal Product
4522 #include <isl/space.h>
4523 __isl_give isl_space *isl_space_zip(
4524 __isl_take isl_space *space);
4526 #include <isl/map.h>
4527 __isl_give isl_basic_map *isl_basic_map_zip(
4528 __isl_take isl_basic_map *bmap);
4529 __isl_give isl_map *isl_map_zip(
4530 __isl_take isl_map *map);
4532 #include <isl/union_map.h>
4533 __isl_give isl_union_map *isl_union_map_zip(
4534 __isl_take isl_union_map *umap);
4536 Given a relation with nested relations for domain and range,
4537 interchange the range of the domain with the domain of the range.
4541 #include <isl/space.h>
4542 __isl_give isl_space *isl_space_curry(
4543 __isl_take isl_space *space);
4544 __isl_give isl_space *isl_space_uncurry(
4545 __isl_take isl_space *space);
4547 #include <isl/map.h>
4548 __isl_give isl_basic_map *isl_basic_map_curry(
4549 __isl_take isl_basic_map *bmap);
4550 __isl_give isl_basic_map *isl_basic_map_uncurry(
4551 __isl_take isl_basic_map *bmap);
4552 __isl_give isl_map *isl_map_curry(
4553 __isl_take isl_map *map);
4554 __isl_give isl_map *isl_map_uncurry(
4555 __isl_take isl_map *map);
4557 #include <isl/union_map.h>
4558 __isl_give isl_union_map *isl_union_map_curry(
4559 __isl_take isl_union_map *umap);
4560 __isl_give isl_union_map *isl_union_map_uncurry(
4561 __isl_take isl_union_map *umap);
4563 Given a relation with a nested relation for domain,
4564 the C<curry> functions
4565 move the range of the nested relation out of the domain
4566 and use it as the domain of a nested relation in the range,
4567 with the original range as range of this nested relation.
4568 The C<uncurry> functions perform the inverse operation.
4570 =item * Aligning parameters
4572 Change the order of the parameters of the given set, relation
4574 such that the first parameters match those of C<model>.
4575 This may involve the introduction of extra parameters.
4576 All parameters need to be named.
4578 #include <isl/space.h>
4579 __isl_give isl_space *isl_space_align_params(
4580 __isl_take isl_space *space1,
4581 __isl_take isl_space *space2)
4583 #include <isl/set.h>
4584 __isl_give isl_basic_set *isl_basic_set_align_params(
4585 __isl_take isl_basic_set *bset,
4586 __isl_take isl_space *model);
4587 __isl_give isl_set *isl_set_align_params(
4588 __isl_take isl_set *set,
4589 __isl_take isl_space *model);
4591 #include <isl/map.h>
4592 __isl_give isl_basic_map *isl_basic_map_align_params(
4593 __isl_take isl_basic_map *bmap,
4594 __isl_take isl_space *model);
4595 __isl_give isl_map *isl_map_align_params(
4596 __isl_take isl_map *map,
4597 __isl_take isl_space *model);
4599 #include <isl/val.h>
4600 __isl_give isl_multi_val *isl_multi_val_align_params(
4601 __isl_take isl_multi_val *mv,
4602 __isl_take isl_space *model);
4604 #include <isl/aff.h>
4605 __isl_give isl_aff *isl_aff_align_params(
4606 __isl_take isl_aff *aff,
4607 __isl_take isl_space *model);
4608 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4609 __isl_take isl_multi_aff *multi,
4610 __isl_take isl_space *model);
4611 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4612 __isl_take isl_pw_aff *pwaff,
4613 __isl_take isl_space *model);
4614 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4615 __isl_take isl_pw_multi_aff *pma,
4616 __isl_take isl_space *model);
4617 __isl_give isl_union_pw_multi_aff *
4618 isl_union_pw_multi_aff_align_params(
4619 __isl_take isl_union_pw_multi_aff *upma,
4620 __isl_take isl_space *model);
4622 #include <isl/polynomial.h>
4623 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4624 __isl_take isl_qpolynomial *qp,
4625 __isl_take isl_space *model);
4627 =item * Unary Arithmethic Operations
4629 #include <isl/aff.h>
4630 __isl_give isl_aff *isl_aff_neg(
4631 __isl_take isl_aff *aff);
4632 __isl_give isl_pw_aff *isl_pw_aff_neg(
4633 __isl_take isl_pw_aff *pwaff);
4634 __isl_give isl_aff *isl_aff_ceil(
4635 __isl_take isl_aff *aff);
4636 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4637 __isl_take isl_pw_aff *pwaff);
4638 __isl_give isl_aff *isl_aff_floor(
4639 __isl_take isl_aff *aff);
4640 __isl_give isl_multi_aff *isl_multi_aff_floor(
4641 __isl_take isl_multi_aff *ma);
4642 __isl_give isl_pw_aff *isl_pw_aff_floor(
4643 __isl_take isl_pw_aff *pwaff);
4645 #include <isl/aff.h>
4646 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4647 __isl_take isl_pw_aff_list *list);
4648 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4649 __isl_take isl_pw_aff_list *list);
4651 #include <isl/polynomial.h>
4652 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4653 __isl_take isl_qpolynomial *qp);
4654 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4655 __isl_take isl_pw_qpolynomial *pwqp);
4656 __isl_give isl_union_pw_qpolynomial *
4657 isl_union_pw_qpolynomial_neg(
4658 __isl_take isl_union_pw_qpolynomial *upwqp);
4659 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4660 __isl_take isl_qpolynomial *qp,
4662 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4663 __isl_take isl_pw_qpolynomial *pwqp,
4668 The following functions evaluate a function in a point.
4670 #include <isl/polynomial.h>
4671 __isl_give isl_val *isl_pw_qpolynomial_eval(
4672 __isl_take isl_pw_qpolynomial *pwqp,
4673 __isl_take isl_point *pnt);
4674 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
4675 __isl_take isl_pw_qpolynomial_fold *pwf,
4676 __isl_take isl_point *pnt);
4677 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4678 __isl_take isl_union_pw_qpolynomial *upwqp,
4679 __isl_take isl_point *pnt);
4680 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
4681 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4682 __isl_take isl_point *pnt);
4684 =item * Dimension manipulation
4686 It is usually not advisable to directly change the (input or output)
4687 space of a set or a relation as this removes the name and the internal
4688 structure of the space. However, the functions below can be useful
4689 to add new parameters, assuming
4690 C<isl_set_align_params> and C<isl_map_align_params>
4693 #include <isl/space.h>
4694 __isl_give isl_space *isl_space_add_dims(
4695 __isl_take isl_space *space,
4696 enum isl_dim_type type, unsigned n);
4697 __isl_give isl_space *isl_space_insert_dims(
4698 __isl_take isl_space *space,
4699 enum isl_dim_type type, unsigned pos, unsigned n);
4700 __isl_give isl_space *isl_space_drop_dims(
4701 __isl_take isl_space *space,
4702 enum isl_dim_type type, unsigned first, unsigned n);
4703 __isl_give isl_space *isl_space_move_dims(
4704 __isl_take isl_space *space,
4705 enum isl_dim_type dst_type, unsigned dst_pos,
4706 enum isl_dim_type src_type, unsigned src_pos,
4709 #include <isl/local_space.h>
4710 __isl_give isl_local_space *isl_local_space_add_dims(
4711 __isl_take isl_local_space *ls,
4712 enum isl_dim_type type, unsigned n);
4713 __isl_give isl_local_space *isl_local_space_insert_dims(
4714 __isl_take isl_local_space *ls,
4715 enum isl_dim_type type, unsigned first, unsigned n);
4716 __isl_give isl_local_space *isl_local_space_drop_dims(
4717 __isl_take isl_local_space *ls,
4718 enum isl_dim_type type, unsigned first, unsigned n);
4720 #include <isl/set.h>
4721 __isl_give isl_basic_set *isl_basic_set_add_dims(
4722 __isl_take isl_basic_set *bset,
4723 enum isl_dim_type type, unsigned n);
4724 __isl_give isl_set *isl_set_add_dims(
4725 __isl_take isl_set *set,
4726 enum isl_dim_type type, unsigned n);
4727 __isl_give isl_basic_set *isl_basic_set_insert_dims(
4728 __isl_take isl_basic_set *bset,
4729 enum isl_dim_type type, unsigned pos,
4731 __isl_give isl_set *isl_set_insert_dims(
4732 __isl_take isl_set *set,
4733 enum isl_dim_type type, unsigned pos, unsigned n);
4734 __isl_give isl_basic_set *isl_basic_set_move_dims(
4735 __isl_take isl_basic_set *bset,
4736 enum isl_dim_type dst_type, unsigned dst_pos,
4737 enum isl_dim_type src_type, unsigned src_pos,
4739 __isl_give isl_set *isl_set_move_dims(
4740 __isl_take isl_set *set,
4741 enum isl_dim_type dst_type, unsigned dst_pos,
4742 enum isl_dim_type src_type, unsigned src_pos,
4745 #include <isl/map.h>
4746 __isl_give isl_map *isl_map_add_dims(
4747 __isl_take isl_map *map,
4748 enum isl_dim_type type, unsigned n);
4749 __isl_give isl_basic_map *isl_basic_map_insert_dims(
4750 __isl_take isl_basic_map *bmap,
4751 enum isl_dim_type type, unsigned pos,
4753 __isl_give isl_map *isl_map_insert_dims(
4754 __isl_take isl_map *map,
4755 enum isl_dim_type type, unsigned pos, unsigned n);
4756 __isl_give isl_basic_map *isl_basic_map_move_dims(
4757 __isl_take isl_basic_map *bmap,
4758 enum isl_dim_type dst_type, unsigned dst_pos,
4759 enum isl_dim_type src_type, unsigned src_pos,
4761 __isl_give isl_map *isl_map_move_dims(
4762 __isl_take isl_map *map,
4763 enum isl_dim_type dst_type, unsigned dst_pos,
4764 enum isl_dim_type src_type, unsigned src_pos,
4767 #include <isl/val.h>
4768 __isl_give isl_multi_val *isl_multi_val_insert_dims(
4769 __isl_take isl_multi_val *mv,
4770 enum isl_dim_type type, unsigned first, unsigned n);
4771 __isl_give isl_multi_val *isl_multi_val_add_dims(
4772 __isl_take isl_multi_val *mv,
4773 enum isl_dim_type type, unsigned n);
4774 __isl_give isl_multi_val *isl_multi_val_drop_dims(
4775 __isl_take isl_multi_val *mv,
4776 enum isl_dim_type type, unsigned first, unsigned n);
4778 #include <isl/aff.h>
4779 __isl_give isl_aff *isl_aff_insert_dims(
4780 __isl_take isl_aff *aff,
4781 enum isl_dim_type type, unsigned first, unsigned n);
4782 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4783 __isl_take isl_multi_aff *ma,
4784 enum isl_dim_type type, unsigned first, unsigned n);
4785 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4786 __isl_take isl_pw_aff *pwaff,
4787 enum isl_dim_type type, unsigned first, unsigned n);
4788 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4789 __isl_take isl_multi_pw_aff *mpa,
4790 enum isl_dim_type type, unsigned first, unsigned n);
4791 __isl_give isl_aff *isl_aff_add_dims(
4792 __isl_take isl_aff *aff,
4793 enum isl_dim_type type, unsigned n);
4794 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4795 __isl_take isl_multi_aff *ma,
4796 enum isl_dim_type type, unsigned n);
4797 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4798 __isl_take isl_pw_aff *pwaff,
4799 enum isl_dim_type type, unsigned n);
4800 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4801 __isl_take isl_multi_pw_aff *mpa,
4802 enum isl_dim_type type, unsigned n);
4803 __isl_give isl_aff *isl_aff_drop_dims(
4804 __isl_take isl_aff *aff,
4805 enum isl_dim_type type, unsigned first, unsigned n);
4806 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4807 __isl_take isl_multi_aff *maff,
4808 enum isl_dim_type type, unsigned first, unsigned n);
4809 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4810 __isl_take isl_pw_aff *pwaff,
4811 enum isl_dim_type type, unsigned first, unsigned n);
4812 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4813 __isl_take isl_pw_multi_aff *pma,
4814 enum isl_dim_type type, unsigned first, unsigned n);
4815 __isl_give isl_aff *isl_aff_move_dims(
4816 __isl_take isl_aff *aff,
4817 enum isl_dim_type dst_type, unsigned dst_pos,
4818 enum isl_dim_type src_type, unsigned src_pos,
4820 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
4821 __isl_take isl_multi_aff *ma,
4822 enum isl_dim_type dst_type, unsigned dst_pos,
4823 enum isl_dim_type src_type, unsigned src_pos,
4825 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4826 __isl_take isl_pw_aff *pa,
4827 enum isl_dim_type dst_type, unsigned dst_pos,
4828 enum isl_dim_type src_type, unsigned src_pos,
4830 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4831 __isl_take isl_multi_pw_aff *pma,
4832 enum isl_dim_type dst_type, unsigned dst_pos,
4833 enum isl_dim_type src_type, unsigned src_pos,
4838 =head2 Binary Operations
4840 The two arguments of a binary operation not only need to live
4841 in the same C<isl_ctx>, they currently also need to have
4842 the same (number of) parameters.
4844 =head3 Basic Operations
4848 =item * Intersection
4850 #include <isl/local_space.h>
4851 __isl_give isl_local_space *isl_local_space_intersect(
4852 __isl_take isl_local_space *ls1,
4853 __isl_take isl_local_space *ls2);
4855 #include <isl/set.h>
4856 __isl_give isl_basic_set *isl_basic_set_intersect_params(
4857 __isl_take isl_basic_set *bset1,
4858 __isl_take isl_basic_set *bset2);
4859 __isl_give isl_basic_set *isl_basic_set_intersect(
4860 __isl_take isl_basic_set *bset1,
4861 __isl_take isl_basic_set *bset2);
4862 __isl_give isl_basic_set *isl_basic_set_list_intersect(
4863 __isl_take struct isl_basic_set_list *list);
4864 __isl_give isl_set *isl_set_intersect_params(
4865 __isl_take isl_set *set,
4866 __isl_take isl_set *params);
4867 __isl_give isl_set *isl_set_intersect(
4868 __isl_take isl_set *set1,
4869 __isl_take isl_set *set2);
4871 #include <isl/map.h>
4872 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
4873 __isl_take isl_basic_map *bmap,
4874 __isl_take isl_basic_set *bset);
4875 __isl_give isl_basic_map *isl_basic_map_intersect_range(
4876 __isl_take isl_basic_map *bmap,
4877 __isl_take isl_basic_set *bset);
4878 __isl_give isl_basic_map *isl_basic_map_intersect(
4879 __isl_take isl_basic_map *bmap1,
4880 __isl_take isl_basic_map *bmap2);
4881 __isl_give isl_map *isl_map_intersect_params(
4882 __isl_take isl_map *map,
4883 __isl_take isl_set *params);
4884 __isl_give isl_map *isl_map_intersect_domain(
4885 __isl_take isl_map *map,
4886 __isl_take isl_set *set);
4887 __isl_give isl_map *isl_map_intersect_range(
4888 __isl_take isl_map *map,
4889 __isl_take isl_set *set);
4890 __isl_give isl_map *isl_map_intersect(
4891 __isl_take isl_map *map1,
4892 __isl_take isl_map *map2);
4894 #include <isl/union_set.h>
4895 __isl_give isl_union_set *isl_union_set_intersect_params(
4896 __isl_take isl_union_set *uset,
4897 __isl_take isl_set *set);
4898 __isl_give isl_union_set *isl_union_set_intersect(
4899 __isl_take isl_union_set *uset1,
4900 __isl_take isl_union_set *uset2);
4902 #include <isl/union_map.h>
4903 __isl_give isl_union_map *isl_union_map_intersect_params(
4904 __isl_take isl_union_map *umap,
4905 __isl_take isl_set *set);
4906 __isl_give isl_union_map *isl_union_map_intersect_domain(
4907 __isl_take isl_union_map *umap,
4908 __isl_take isl_union_set *uset);
4909 __isl_give isl_union_map *isl_union_map_intersect_range(
4910 __isl_take isl_union_map *umap,
4911 __isl_take isl_union_set *uset);
4912 __isl_give isl_union_map *isl_union_map_intersect(
4913 __isl_take isl_union_map *umap1,
4914 __isl_take isl_union_map *umap2);
4916 #include <isl/aff.h>
4917 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4918 __isl_take isl_pw_aff *pa,
4919 __isl_take isl_set *set);
4920 __isl_give isl_multi_pw_aff *
4921 isl_multi_pw_aff_intersect_domain(
4922 __isl_take isl_multi_pw_aff *mpa,
4923 __isl_take isl_set *domain);
4924 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4925 __isl_take isl_pw_multi_aff *pma,
4926 __isl_take isl_set *set);
4927 __isl_give isl_union_pw_multi_aff *
4928 isl_union_pw_multi_aff_intersect_domain(
4929 __isl_take isl_union_pw_multi_aff *upma,
4930 __isl_take isl_union_set *uset);
4931 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4932 __isl_take isl_pw_aff *pa,
4933 __isl_take isl_set *set);
4934 __isl_give isl_multi_pw_aff *
4935 isl_multi_pw_aff_intersect_params(
4936 __isl_take isl_multi_pw_aff *mpa,
4937 __isl_take isl_set *set);
4938 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4939 __isl_take isl_pw_multi_aff *pma,
4940 __isl_take isl_set *set);
4941 __isl_give isl_union_pw_multi_aff *
4942 isl_union_pw_multi_aff_intersect_params(
4943 __isl_take isl_union_pw_multi_aff *upma,
4944 __isl_take isl_set *set);
4946 #include <isl/polynomial.h>
4947 __isl_give isl_pw_qpolynomial *
4948 isl_pw_qpolynomial_intersect_domain(
4949 __isl_take isl_pw_qpolynomial *pwpq,
4950 __isl_take isl_set *set);
4951 __isl_give isl_union_pw_qpolynomial *
4952 isl_union_pw_qpolynomial_intersect_domain(
4953 __isl_take isl_union_pw_qpolynomial *upwpq,
4954 __isl_take isl_union_set *uset);
4955 __isl_give isl_union_pw_qpolynomial_fold *
4956 isl_union_pw_qpolynomial_fold_intersect_domain(
4957 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4958 __isl_take isl_union_set *uset);
4959 __isl_give isl_pw_qpolynomial *
4960 isl_pw_qpolynomial_intersect_params(
4961 __isl_take isl_pw_qpolynomial *pwpq,
4962 __isl_take isl_set *set);
4963 __isl_give isl_pw_qpolynomial_fold *
4964 isl_pw_qpolynomial_fold_intersect_params(
4965 __isl_take isl_pw_qpolynomial_fold *pwf,
4966 __isl_take isl_set *set);
4967 __isl_give isl_union_pw_qpolynomial *
4968 isl_union_pw_qpolynomial_intersect_params(
4969 __isl_take isl_union_pw_qpolynomial *upwpq,
4970 __isl_take isl_set *set);
4971 __isl_give isl_union_pw_qpolynomial_fold *
4972 isl_union_pw_qpolynomial_fold_intersect_params(
4973 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4974 __isl_take isl_set *set);
4976 The second argument to the C<_params> functions needs to be
4977 a parametric (basic) set. For the other functions, a parametric set
4978 for either argument is only allowed if the other argument is
4979 a parametric set as well.
4980 The list passed to C<isl_basic_set_list_intersect> needs to have
4981 at least one element and all elements need to live in the same space.
4985 __isl_give isl_set *isl_basic_set_union(
4986 __isl_take isl_basic_set *bset1,
4987 __isl_take isl_basic_set *bset2);
4988 __isl_give isl_map *isl_basic_map_union(
4989 __isl_take isl_basic_map *bmap1,
4990 __isl_take isl_basic_map *bmap2);
4991 __isl_give isl_set *isl_set_union(
4992 __isl_take isl_set *set1,
4993 __isl_take isl_set *set2);
4994 __isl_give isl_map *isl_map_union(
4995 __isl_take isl_map *map1,
4996 __isl_take isl_map *map2);
4997 __isl_give isl_union_set *isl_union_set_union(
4998 __isl_take isl_union_set *uset1,
4999 __isl_take isl_union_set *uset2);
5000 __isl_give isl_union_map *isl_union_map_union(
5001 __isl_take isl_union_map *umap1,
5002 __isl_take isl_union_map *umap2);
5004 =item * Set difference
5006 __isl_give isl_set *isl_set_subtract(
5007 __isl_take isl_set *set1,
5008 __isl_take isl_set *set2);
5009 __isl_give isl_map *isl_map_subtract(
5010 __isl_take isl_map *map1,
5011 __isl_take isl_map *map2);
5012 __isl_give isl_map *isl_map_subtract_domain(
5013 __isl_take isl_map *map,
5014 __isl_take isl_set *dom);
5015 __isl_give isl_map *isl_map_subtract_range(
5016 __isl_take isl_map *map,
5017 __isl_take isl_set *dom);
5018 __isl_give isl_union_set *isl_union_set_subtract(
5019 __isl_take isl_union_set *uset1,
5020 __isl_take isl_union_set *uset2);
5021 __isl_give isl_union_map *isl_union_map_subtract(
5022 __isl_take isl_union_map *umap1,
5023 __isl_take isl_union_map *umap2);
5024 __isl_give isl_union_map *isl_union_map_subtract_domain(
5025 __isl_take isl_union_map *umap,
5026 __isl_take isl_union_set *dom);
5027 __isl_give isl_union_map *isl_union_map_subtract_range(
5028 __isl_take isl_union_map *umap,
5029 __isl_take isl_union_set *dom);
5033 #include <isl/space.h>
5034 __isl_give isl_space *isl_space_join(
5035 __isl_take isl_space *left,
5036 __isl_take isl_space *right);
5038 #include <isl/map.h>
5039 __isl_give isl_basic_set *isl_basic_set_apply(
5040 __isl_take isl_basic_set *bset,
5041 __isl_take isl_basic_map *bmap);
5042 __isl_give isl_set *isl_set_apply(
5043 __isl_take isl_set *set,
5044 __isl_take isl_map *map);
5045 __isl_give isl_union_set *isl_union_set_apply(
5046 __isl_take isl_union_set *uset,
5047 __isl_take isl_union_map *umap);
5048 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5049 __isl_take isl_basic_map *bmap1,
5050 __isl_take isl_basic_map *bmap2);
5051 __isl_give isl_basic_map *isl_basic_map_apply_range(
5052 __isl_take isl_basic_map *bmap1,
5053 __isl_take isl_basic_map *bmap2);
5054 __isl_give isl_map *isl_map_apply_domain(
5055 __isl_take isl_map *map1,
5056 __isl_take isl_map *map2);
5057 __isl_give isl_map *isl_map_apply_range(
5058 __isl_take isl_map *map1,
5059 __isl_take isl_map *map2);
5061 #include <isl/union_map.h>
5062 __isl_give isl_union_map *isl_union_map_apply_domain(
5063 __isl_take isl_union_map *umap1,
5064 __isl_take isl_union_map *umap2);
5065 __isl_give isl_union_map *isl_union_map_apply_range(
5066 __isl_take isl_union_map *umap1,
5067 __isl_take isl_union_map *umap2);
5069 #include <isl/polynomial.h>
5070 __isl_give isl_pw_qpolynomial_fold *
5071 isl_set_apply_pw_qpolynomial_fold(
5072 __isl_take isl_set *set,
5073 __isl_take isl_pw_qpolynomial_fold *pwf,
5075 __isl_give isl_pw_qpolynomial_fold *
5076 isl_map_apply_pw_qpolynomial_fold(
5077 __isl_take isl_map *map,
5078 __isl_take isl_pw_qpolynomial_fold *pwf,
5080 __isl_give isl_union_pw_qpolynomial_fold *
5081 isl_union_set_apply_union_pw_qpolynomial_fold(
5082 __isl_take isl_union_set *uset,
5083 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5085 __isl_give isl_union_pw_qpolynomial_fold *
5086 isl_union_map_apply_union_pw_qpolynomial_fold(
5087 __isl_take isl_union_map *umap,
5088 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5091 The functions taking a map
5092 compose the given map with the given piecewise quasipolynomial reduction.
5093 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5094 over all elements in the intersection of the range of the map
5095 and the domain of the piecewise quasipolynomial reduction
5096 as a function of an element in the domain of the map.
5097 The functions taking a set compute a bound over all elements in the
5098 intersection of the set and the domain of the
5099 piecewise quasipolynomial reduction.
5103 #include <isl/set.h>
5104 __isl_give isl_basic_set *
5105 isl_basic_set_preimage_multi_aff(
5106 __isl_take isl_basic_set *bset,
5107 __isl_take isl_multi_aff *ma);
5108 __isl_give isl_set *isl_set_preimage_multi_aff(
5109 __isl_take isl_set *set,
5110 __isl_take isl_multi_aff *ma);
5111 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5112 __isl_take isl_set *set,
5113 __isl_take isl_pw_multi_aff *pma);
5114 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5115 __isl_take isl_set *set,
5116 __isl_take isl_multi_pw_aff *mpa);
5118 #include <isl/union_set.h>
5119 __isl_give isl_union_set *
5120 isl_union_set_preimage_multi_aff(
5121 __isl_take isl_union_set *uset,
5122 __isl_take isl_multi_aff *ma);
5123 __isl_give isl_union_set *
5124 isl_union_set_preimage_pw_multi_aff(
5125 __isl_take isl_union_set *uset,
5126 __isl_take isl_pw_multi_aff *pma);
5127 __isl_give isl_union_set *
5128 isl_union_set_preimage_union_pw_multi_aff(
5129 __isl_take isl_union_set *uset,
5130 __isl_take isl_union_pw_multi_aff *upma);
5132 #include <isl/map.h>
5133 __isl_give isl_basic_map *
5134 isl_basic_map_preimage_domain_multi_aff(
5135 __isl_take isl_basic_map *bmap,
5136 __isl_take isl_multi_aff *ma);
5137 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5138 __isl_take isl_map *map,
5139 __isl_take isl_multi_aff *ma);
5140 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5141 __isl_take isl_map *map,
5142 __isl_take isl_multi_aff *ma);
5143 __isl_give isl_map *
5144 isl_map_preimage_domain_pw_multi_aff(
5145 __isl_take isl_map *map,
5146 __isl_take isl_pw_multi_aff *pma);
5147 __isl_give isl_map *
5148 isl_map_preimage_range_pw_multi_aff(
5149 __isl_take isl_map *map,
5150 __isl_take isl_pw_multi_aff *pma);
5151 __isl_give isl_map *
5152 isl_map_preimage_domain_multi_pw_aff(
5153 __isl_take isl_map *map,
5154 __isl_take isl_multi_pw_aff *mpa);
5155 __isl_give isl_basic_map *
5156 isl_basic_map_preimage_range_multi_aff(
5157 __isl_take isl_basic_map *bmap,
5158 __isl_take isl_multi_aff *ma);
5160 #include <isl/union_map.h>
5161 __isl_give isl_union_map *
5162 isl_union_map_preimage_domain_multi_aff(
5163 __isl_take isl_union_map *umap,
5164 __isl_take isl_multi_aff *ma);
5165 __isl_give isl_union_map *
5166 isl_union_map_preimage_range_multi_aff(
5167 __isl_take isl_union_map *umap,
5168 __isl_take isl_multi_aff *ma);
5169 __isl_give isl_union_map *
5170 isl_union_map_preimage_domain_pw_multi_aff(
5171 __isl_take isl_union_map *umap,
5172 __isl_take isl_pw_multi_aff *pma);
5173 __isl_give isl_union_map *
5174 isl_union_map_preimage_range_pw_multi_aff(
5175 __isl_take isl_union_map *umap,
5176 __isl_take isl_pw_multi_aff *pma);
5177 __isl_give isl_union_map *
5178 isl_union_map_preimage_domain_union_pw_multi_aff(
5179 __isl_take isl_union_map *umap,
5180 __isl_take isl_union_pw_multi_aff *upma);
5181 __isl_give isl_union_map *
5182 isl_union_map_preimage_range_union_pw_multi_aff(
5183 __isl_take isl_union_map *umap,
5184 __isl_take isl_union_pw_multi_aff *upma);
5186 These functions compute the preimage of the given set or map domain/range under
5187 the given function. In other words, the expression is plugged
5188 into the set description or into the domain/range of the map.
5192 #include <isl/aff.h>
5193 __isl_give isl_aff *isl_aff_pullback_aff(
5194 __isl_take isl_aff *aff1,
5195 __isl_take isl_aff *aff2);
5196 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5197 __isl_take isl_aff *aff,
5198 __isl_take isl_multi_aff *ma);
5199 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5200 __isl_take isl_pw_aff *pa,
5201 __isl_take isl_multi_aff *ma);
5202 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5203 __isl_take isl_pw_aff *pa,
5204 __isl_take isl_pw_multi_aff *pma);
5205 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5206 __isl_take isl_pw_aff *pa,
5207 __isl_take isl_multi_pw_aff *mpa);
5208 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5209 __isl_take isl_multi_aff *ma1,
5210 __isl_take isl_multi_aff *ma2);
5211 __isl_give isl_pw_multi_aff *
5212 isl_pw_multi_aff_pullback_multi_aff(
5213 __isl_take isl_pw_multi_aff *pma,
5214 __isl_take isl_multi_aff *ma);
5215 __isl_give isl_multi_pw_aff *
5216 isl_multi_pw_aff_pullback_multi_aff(
5217 __isl_take isl_multi_pw_aff *mpa,
5218 __isl_take isl_multi_aff *ma);
5219 __isl_give isl_pw_multi_aff *
5220 isl_pw_multi_aff_pullback_pw_multi_aff(
5221 __isl_take isl_pw_multi_aff *pma1,
5222 __isl_take isl_pw_multi_aff *pma2);
5223 __isl_give isl_multi_pw_aff *
5224 isl_multi_pw_aff_pullback_pw_multi_aff(
5225 __isl_take isl_multi_pw_aff *mpa,
5226 __isl_take isl_pw_multi_aff *pma);
5227 __isl_give isl_multi_pw_aff *
5228 isl_multi_pw_aff_pullback_multi_pw_aff(
5229 __isl_take isl_multi_pw_aff *mpa1,
5230 __isl_take isl_multi_pw_aff *mpa2);
5232 These functions precompose the first expression by the second function.
5233 In other words, the second function is plugged
5234 into the first expression.
5238 #include <isl/aff.h>
5239 __isl_give isl_basic_set *isl_aff_le_basic_set(
5240 __isl_take isl_aff *aff1,
5241 __isl_take isl_aff *aff2);
5242 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5243 __isl_take isl_aff *aff1,
5244 __isl_take isl_aff *aff2);
5245 __isl_give isl_set *isl_pw_aff_eq_set(
5246 __isl_take isl_pw_aff *pwaff1,
5247 __isl_take isl_pw_aff *pwaff2);
5248 __isl_give isl_set *isl_pw_aff_ne_set(
5249 __isl_take isl_pw_aff *pwaff1,
5250 __isl_take isl_pw_aff *pwaff2);
5251 __isl_give isl_set *isl_pw_aff_le_set(
5252 __isl_take isl_pw_aff *pwaff1,
5253 __isl_take isl_pw_aff *pwaff2);
5254 __isl_give isl_set *isl_pw_aff_lt_set(
5255 __isl_take isl_pw_aff *pwaff1,
5256 __isl_take isl_pw_aff *pwaff2);
5257 __isl_give isl_set *isl_pw_aff_ge_set(
5258 __isl_take isl_pw_aff *pwaff1,
5259 __isl_take isl_pw_aff *pwaff2);
5260 __isl_give isl_set *isl_pw_aff_gt_set(
5261 __isl_take isl_pw_aff *pwaff1,
5262 __isl_take isl_pw_aff *pwaff2);
5264 __isl_give isl_set *isl_multi_aff_lex_le_set(
5265 __isl_take isl_multi_aff *ma1,
5266 __isl_take isl_multi_aff *ma2);
5267 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5268 __isl_take isl_multi_aff *ma1,
5269 __isl_take isl_multi_aff *ma2);
5271 __isl_give isl_set *isl_pw_aff_list_eq_set(
5272 __isl_take isl_pw_aff_list *list1,
5273 __isl_take isl_pw_aff_list *list2);
5274 __isl_give isl_set *isl_pw_aff_list_ne_set(
5275 __isl_take isl_pw_aff_list *list1,
5276 __isl_take isl_pw_aff_list *list2);
5277 __isl_give isl_set *isl_pw_aff_list_le_set(
5278 __isl_take isl_pw_aff_list *list1,
5279 __isl_take isl_pw_aff_list *list2);
5280 __isl_give isl_set *isl_pw_aff_list_lt_set(
5281 __isl_take isl_pw_aff_list *list1,
5282 __isl_take isl_pw_aff_list *list2);
5283 __isl_give isl_set *isl_pw_aff_list_ge_set(
5284 __isl_take isl_pw_aff_list *list1,
5285 __isl_take isl_pw_aff_list *list2);
5286 __isl_give isl_set *isl_pw_aff_list_gt_set(
5287 __isl_take isl_pw_aff_list *list1,
5288 __isl_take isl_pw_aff_list *list2);
5290 The function C<isl_aff_ge_basic_set> returns a basic set
5291 containing those elements in the shared space
5292 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5293 The function C<isl_pw_aff_ge_set> returns a set
5294 containing those elements in the shared domain
5295 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5296 greater than or equal to C<pwaff2>.
5297 The function C<isl_multi_aff_lex_le_set> returns a set
5298 containing those elements in the shared domain space
5299 where C<ma1> is lexicographically smaller than or
5301 The functions operating on C<isl_pw_aff_list> apply the corresponding
5302 C<isl_pw_aff> function to each pair of elements in the two lists.
5304 =item * Cartesian Product
5306 #include <isl/space.h>
5307 __isl_give isl_space *isl_space_product(
5308 __isl_take isl_space *space1,
5309 __isl_take isl_space *space2);
5310 __isl_give isl_space *isl_space_domain_product(
5311 __isl_take isl_space *space1,
5312 __isl_take isl_space *space2);
5313 __isl_give isl_space *isl_space_range_product(
5314 __isl_take isl_space *space1,
5315 __isl_take isl_space *space2);
5318 C<isl_space_product>, C<isl_space_domain_product>
5319 and C<isl_space_range_product> take pairs or relation spaces and
5320 produce a single relations space, where either the domain, the range
5321 or both domain and range are wrapped spaces of relations between
5322 the domains and/or ranges of the input spaces.
5323 If the product is only constructed over the domain or the range
5324 then the ranges or the domains of the inputs should be the same.
5325 The function C<isl_space_product> also accepts a pair of set spaces,
5326 in which case it returns a wrapped space of a relation between the
5329 #include <isl/set.h>
5330 __isl_give isl_set *isl_set_product(
5331 __isl_take isl_set *set1,
5332 __isl_take isl_set *set2);
5334 #include <isl/map.h>
5335 __isl_give isl_basic_map *isl_basic_map_domain_product(
5336 __isl_take isl_basic_map *bmap1,
5337 __isl_take isl_basic_map *bmap2);
5338 __isl_give isl_basic_map *isl_basic_map_range_product(
5339 __isl_take isl_basic_map *bmap1,
5340 __isl_take isl_basic_map *bmap2);
5341 __isl_give isl_basic_map *isl_basic_map_product(
5342 __isl_take isl_basic_map *bmap1,
5343 __isl_take isl_basic_map *bmap2);
5344 __isl_give isl_map *isl_map_domain_product(
5345 __isl_take isl_map *map1,
5346 __isl_take isl_map *map2);
5347 __isl_give isl_map *isl_map_range_product(
5348 __isl_take isl_map *map1,
5349 __isl_take isl_map *map2);
5350 __isl_give isl_map *isl_map_product(
5351 __isl_take isl_map *map1,
5352 __isl_take isl_map *map2);
5354 #include <isl/union_set.h>
5355 __isl_give isl_union_set *isl_union_set_product(
5356 __isl_take isl_union_set *uset1,
5357 __isl_take isl_union_set *uset2);
5359 #include <isl/union_map.h>
5360 __isl_give isl_union_map *isl_union_map_domain_product(
5361 __isl_take isl_union_map *umap1,
5362 __isl_take isl_union_map *umap2);
5363 __isl_give isl_union_map *isl_union_map_range_product(
5364 __isl_take isl_union_map *umap1,
5365 __isl_take isl_union_map *umap2);
5366 __isl_give isl_union_map *isl_union_map_product(
5367 __isl_take isl_union_map *umap1,
5368 __isl_take isl_union_map *umap2);
5370 #include <isl/val.h>
5371 __isl_give isl_multi_val *isl_multi_val_range_product(
5372 __isl_take isl_multi_val *mv1,
5373 __isl_take isl_multi_val *mv2);
5374 __isl_give isl_multi_val *isl_multi_val_product(
5375 __isl_take isl_multi_val *mv1,
5376 __isl_take isl_multi_val *mv2);
5378 #include <isl/aff.h>
5379 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5380 __isl_take isl_multi_aff *ma1,
5381 __isl_take isl_multi_aff *ma2);
5382 __isl_give isl_multi_aff *isl_multi_aff_product(
5383 __isl_take isl_multi_aff *ma1,
5384 __isl_take isl_multi_aff *ma2);
5385 __isl_give isl_multi_pw_aff *
5386 isl_multi_pw_aff_range_product(
5387 __isl_take isl_multi_pw_aff *mpa1,
5388 __isl_take isl_multi_pw_aff *mpa2);
5389 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5390 __isl_take isl_multi_pw_aff *mpa1,
5391 __isl_take isl_multi_pw_aff *mpa2);
5392 __isl_give isl_pw_multi_aff *
5393 isl_pw_multi_aff_range_product(
5394 __isl_take isl_pw_multi_aff *pma1,
5395 __isl_take isl_pw_multi_aff *pma2);
5396 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5397 __isl_take isl_pw_multi_aff *pma1,
5398 __isl_take isl_pw_multi_aff *pma2);
5400 The above functions compute the cross product of the given
5401 sets, relations or functions. The domains and ranges of the results
5402 are wrapped maps between domains and ranges of the inputs.
5403 To obtain a ``flat'' product, use the following functions
5406 #include <isl/set.h>
5407 __isl_give isl_basic_set *isl_basic_set_flat_product(
5408 __isl_take isl_basic_set *bset1,
5409 __isl_take isl_basic_set *bset2);
5410 __isl_give isl_set *isl_set_flat_product(
5411 __isl_take isl_set *set1,
5412 __isl_take isl_set *set2);
5414 #include <isl/map.h>
5415 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5416 __isl_take isl_basic_map *bmap1,
5417 __isl_take isl_basic_map *bmap2);
5418 __isl_give isl_map *isl_map_flat_domain_product(
5419 __isl_take isl_map *map1,
5420 __isl_take isl_map *map2);
5421 __isl_give isl_map *isl_map_flat_range_product(
5422 __isl_take isl_map *map1,
5423 __isl_take isl_map *map2);
5424 __isl_give isl_basic_map *isl_basic_map_flat_product(
5425 __isl_take isl_basic_map *bmap1,
5426 __isl_take isl_basic_map *bmap2);
5427 __isl_give isl_map *isl_map_flat_product(
5428 __isl_take isl_map *map1,
5429 __isl_take isl_map *map2);
5431 #include <isl/union_map.h>
5432 __isl_give isl_union_map *
5433 isl_union_map_flat_range_product(
5434 __isl_take isl_union_map *umap1,
5435 __isl_take isl_union_map *umap2);
5437 #include <isl/val.h>
5438 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
5439 __isl_take isl_multi_val *mv1,
5440 __isl_take isl_multi_aff *mv2);
5442 #include <isl/aff.h>
5443 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
5444 __isl_take isl_multi_aff *ma1,
5445 __isl_take isl_multi_aff *ma2);
5446 __isl_give isl_pw_multi_aff *
5447 isl_pw_multi_aff_flat_range_product(
5448 __isl_take isl_pw_multi_aff *pma1,
5449 __isl_take isl_pw_multi_aff *pma2);
5450 __isl_give isl_multi_pw_aff *
5451 isl_multi_pw_aff_flat_range_product(
5452 __isl_take isl_multi_pw_aff *mpa1,
5453 __isl_take isl_multi_pw_aff *mpa2);
5454 __isl_give isl_union_pw_multi_aff *
5455 isl_union_pw_multi_aff_flat_range_product(
5456 __isl_take isl_union_pw_multi_aff *upma1,
5457 __isl_take isl_union_pw_multi_aff *upma2);
5459 #include <isl/space.h>
5460 __isl_give isl_space *isl_space_domain_factor_domain(
5461 __isl_take isl_space *space);
5462 __isl_give isl_space *isl_space_range_factor_domain(
5463 __isl_take isl_space *space);
5464 __isl_give isl_space *isl_space_range_factor_range(
5465 __isl_take isl_space *space);
5467 The functions C<isl_space_range_factor_domain> and
5468 C<isl_space_range_factor_range> extract the two arguments from
5469 the result of a call to C<isl_space_range_product>.
5471 The arguments of a call to C<isl_map_range_product> can be extracted
5472 from the result using the following two functions.
5474 #include <isl/map.h>
5475 __isl_give isl_map *isl_map_range_factor_domain(
5476 __isl_take isl_map *map);
5477 __isl_give isl_map *isl_map_range_factor_range(
5478 __isl_take isl_map *map);
5480 #include <isl/val.h>
5481 __isl_give isl_multi_val *
5482 isl_multi_val_range_factor_domain(
5483 __isl_take isl_multi_val *mv);
5484 __isl_give isl_multi_val *
5485 isl_multi_val_range_factor_range(
5486 __isl_take isl_multi_val *mv);
5488 #include <isl/aff.h>
5489 __isl_give isl_multi_aff *
5490 isl_multi_aff_range_factor_domain(
5491 __isl_take isl_multi_aff *ma);
5492 __isl_give isl_multi_aff *
5493 isl_multi_aff_range_factor_range(
5494 __isl_take isl_multi_aff *ma);
5495 __isl_give isl_multi_pw_aff *
5496 isl_multi_pw_aff_range_factor_domain(
5497 __isl_take isl_multi_pw_aff *mpa);
5498 __isl_give isl_multi_pw_aff *
5499 isl_multi_pw_aff_range_factor_range(
5500 __isl_take isl_multi_pw_aff *mpa);
5502 The splice functions are a generalization of the flat product functions,
5503 where the second argument may be inserted at any position inside
5504 the first argument rather than being placed at the end.
5506 #include <isl/val.h>
5507 __isl_give isl_multi_val *isl_multi_val_range_splice(
5508 __isl_take isl_multi_val *mv1, unsigned pos,
5509 __isl_take isl_multi_val *mv2);
5511 #include <isl/aff.h>
5512 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
5513 __isl_take isl_multi_aff *ma1, unsigned pos,
5514 __isl_take isl_multi_aff *ma2);
5515 __isl_give isl_multi_aff *isl_multi_aff_splice(
5516 __isl_take isl_multi_aff *ma1,
5517 unsigned in_pos, unsigned out_pos,
5518 __isl_take isl_multi_aff *ma2);
5519 __isl_give isl_multi_pw_aff *
5520 isl_multi_pw_aff_range_splice(
5521 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
5522 __isl_take isl_multi_pw_aff *mpa2);
5523 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
5524 __isl_take isl_multi_pw_aff *mpa1,
5525 unsigned in_pos, unsigned out_pos,
5526 __isl_take isl_multi_pw_aff *mpa2);
5528 =item * Simplification
5530 When applied to a set or relation,
5531 the gist operation returns a set or relation that has the
5532 same intersection with the context as the input set or relation.
5533 Any implicit equality in the intersection is made explicit in the result,
5534 while all inequalities that are redundant with respect to the intersection
5536 In case of union sets and relations, the gist operation is performed
5539 When applied to a function,
5540 the gist operation applies the set gist operation to each of
5541 the cells in the domain of the input piecewise expression.
5542 The context is also exploited
5543 to simplify the expression associated to each cell.
5545 #include <isl/set.h>
5546 __isl_give isl_basic_set *isl_basic_set_gist(
5547 __isl_take isl_basic_set *bset,
5548 __isl_take isl_basic_set *context);
5549 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
5550 __isl_take isl_set *context);
5551 __isl_give isl_set *isl_set_gist_params(
5552 __isl_take isl_set *set,
5553 __isl_take isl_set *context);
5555 #include <isl/map.h>
5556 __isl_give isl_basic_map *isl_basic_map_gist(
5557 __isl_take isl_basic_map *bmap,
5558 __isl_take isl_basic_map *context);
5559 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
5560 __isl_take isl_map *context);
5561 __isl_give isl_map *isl_map_gist_params(
5562 __isl_take isl_map *map,
5563 __isl_take isl_set *context);
5564 __isl_give isl_map *isl_map_gist_domain(
5565 __isl_take isl_map *map,
5566 __isl_take isl_set *context);
5567 __isl_give isl_map *isl_map_gist_range(
5568 __isl_take isl_map *map,
5569 __isl_take isl_set *context);
5571 #include <isl/union_set.h>
5572 __isl_give isl_union_set *isl_union_set_gist(
5573 __isl_take isl_union_set *uset,
5574 __isl_take isl_union_set *context);
5575 __isl_give isl_union_set *isl_union_set_gist_params(
5576 __isl_take isl_union_set *uset,
5577 __isl_take isl_set *set);
5579 #include <isl/union_map.h>
5580 __isl_give isl_union_map *isl_union_map_gist(
5581 __isl_take isl_union_map *umap,
5582 __isl_take isl_union_map *context);
5583 __isl_give isl_union_map *isl_union_map_gist_params(
5584 __isl_take isl_union_map *umap,
5585 __isl_take isl_set *set);
5586 __isl_give isl_union_map *isl_union_map_gist_domain(
5587 __isl_take isl_union_map *umap,
5588 __isl_take isl_union_set *uset);
5589 __isl_give isl_union_map *isl_union_map_gist_range(
5590 __isl_take isl_union_map *umap,
5591 __isl_take isl_union_set *uset);
5593 #include <isl/aff.h>
5594 __isl_give isl_aff *isl_aff_gist_params(
5595 __isl_take isl_aff *aff,
5596 __isl_take isl_set *context);
5597 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
5598 __isl_take isl_set *context);
5599 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
5600 __isl_take isl_multi_aff *maff,
5601 __isl_take isl_set *context);
5602 __isl_give isl_multi_aff *isl_multi_aff_gist(
5603 __isl_take isl_multi_aff *maff,
5604 __isl_take isl_set *context);
5605 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
5606 __isl_take isl_pw_aff *pwaff,
5607 __isl_take isl_set *context);
5608 __isl_give isl_pw_aff *isl_pw_aff_gist(
5609 __isl_take isl_pw_aff *pwaff,
5610 __isl_take isl_set *context);
5611 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
5612 __isl_take isl_pw_multi_aff *pma,
5613 __isl_take isl_set *set);
5614 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
5615 __isl_take isl_pw_multi_aff *pma,
5616 __isl_take isl_set *set);
5617 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
5618 __isl_take isl_multi_pw_aff *mpa,
5619 __isl_take isl_set *set);
5620 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
5621 __isl_take isl_multi_pw_aff *mpa,
5622 __isl_take isl_set *set);
5623 __isl_give isl_union_pw_multi_aff *
5624 isl_union_pw_multi_aff_gist_params(
5625 __isl_take isl_union_pw_multi_aff *upma,
5626 __isl_take isl_set *context);
5627 __isl_give isl_union_pw_multi_aff *
5628 isl_union_pw_multi_aff_gist(
5629 __isl_take isl_union_pw_multi_aff *upma,
5630 __isl_take isl_union_set *context);
5632 #include <isl/polynomial.h>
5633 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5634 __isl_take isl_qpolynomial *qp,
5635 __isl_take isl_set *context);
5636 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5637 __isl_take isl_qpolynomial *qp,
5638 __isl_take isl_set *context);
5639 __isl_give isl_qpolynomial_fold *
5640 isl_qpolynomial_fold_gist_params(
5641 __isl_take isl_qpolynomial_fold *fold,
5642 __isl_take isl_set *context);
5643 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5644 __isl_take isl_qpolynomial_fold *fold,
5645 __isl_take isl_set *context);
5646 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5647 __isl_take isl_pw_qpolynomial *pwqp,
5648 __isl_take isl_set *context);
5649 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5650 __isl_take isl_pw_qpolynomial *pwqp,
5651 __isl_take isl_set *context);
5652 __isl_give isl_pw_qpolynomial_fold *
5653 isl_pw_qpolynomial_fold_gist(
5654 __isl_take isl_pw_qpolynomial_fold *pwf,
5655 __isl_take isl_set *context);
5656 __isl_give isl_pw_qpolynomial_fold *
5657 isl_pw_qpolynomial_fold_gist_params(
5658 __isl_take isl_pw_qpolynomial_fold *pwf,
5659 __isl_take isl_set *context);
5660 __isl_give isl_union_pw_qpolynomial *
5661 isl_union_pw_qpolynomial_gist_params(
5662 __isl_take isl_union_pw_qpolynomial *upwqp,
5663 __isl_take isl_set *context);
5664 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5665 __isl_take isl_union_pw_qpolynomial *upwqp,
5666 __isl_take isl_union_set *context);
5667 __isl_give isl_union_pw_qpolynomial_fold *
5668 isl_union_pw_qpolynomial_fold_gist(
5669 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5670 __isl_take isl_union_set *context);
5671 __isl_give isl_union_pw_qpolynomial_fold *
5672 isl_union_pw_qpolynomial_fold_gist_params(
5673 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5674 __isl_take isl_set *context);
5676 =item * Binary Arithmethic Operations
5678 #include <isl/aff.h>
5679 __isl_give isl_aff *isl_aff_add(
5680 __isl_take isl_aff *aff1,
5681 __isl_take isl_aff *aff2);
5682 __isl_give isl_multi_aff *isl_multi_aff_add(
5683 __isl_take isl_multi_aff *maff1,
5684 __isl_take isl_multi_aff *maff2);
5685 __isl_give isl_pw_aff *isl_pw_aff_add(
5686 __isl_take isl_pw_aff *pwaff1,
5687 __isl_take isl_pw_aff *pwaff2);
5688 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
5689 __isl_take isl_pw_multi_aff *pma1,
5690 __isl_take isl_pw_multi_aff *pma2);
5691 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
5692 __isl_take isl_union_pw_multi_aff *upma1,
5693 __isl_take isl_union_pw_multi_aff *upma2);
5694 __isl_give isl_pw_aff *isl_pw_aff_min(
5695 __isl_take isl_pw_aff *pwaff1,
5696 __isl_take isl_pw_aff *pwaff2);
5697 __isl_give isl_pw_aff *isl_pw_aff_max(
5698 __isl_take isl_pw_aff *pwaff1,
5699 __isl_take isl_pw_aff *pwaff2);
5700 __isl_give isl_aff *isl_aff_sub(
5701 __isl_take isl_aff *aff1,
5702 __isl_take isl_aff *aff2);
5703 __isl_give isl_multi_aff *isl_multi_aff_sub(
5704 __isl_take isl_multi_aff *ma1,
5705 __isl_take isl_multi_aff *ma2);
5706 __isl_give isl_pw_aff *isl_pw_aff_sub(
5707 __isl_take isl_pw_aff *pwaff1,
5708 __isl_take isl_pw_aff *pwaff2);
5709 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
5710 __isl_take isl_pw_multi_aff *pma1,
5711 __isl_take isl_pw_multi_aff *pma2);
5712 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
5713 __isl_take isl_union_pw_multi_aff *upma1,
5714 __isl_take isl_union_pw_multi_aff *upma2);
5716 C<isl_aff_sub> subtracts the second argument from the first.
5718 #include <isl/polynomial.h>
5719 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5720 __isl_take isl_qpolynomial *qp1,
5721 __isl_take isl_qpolynomial *qp2);
5722 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5723 __isl_take isl_pw_qpolynomial *pwqp1,
5724 __isl_take isl_pw_qpolynomial *pwqp2);
5725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5726 __isl_take isl_pw_qpolynomial *pwqp1,
5727 __isl_take isl_pw_qpolynomial *pwqp2);
5728 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5729 __isl_take isl_pw_qpolynomial_fold *pwf1,
5730 __isl_take isl_pw_qpolynomial_fold *pwf2);
5731 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5732 __isl_take isl_union_pw_qpolynomial *upwqp1,
5733 __isl_take isl_union_pw_qpolynomial *upwqp2);
5734 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5735 __isl_take isl_qpolynomial *qp1,
5736 __isl_take isl_qpolynomial *qp2);
5737 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5738 __isl_take isl_pw_qpolynomial *pwqp1,
5739 __isl_take isl_pw_qpolynomial *pwqp2);
5740 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5741 __isl_take isl_union_pw_qpolynomial *upwqp1,
5742 __isl_take isl_union_pw_qpolynomial *upwqp2);
5743 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5744 __isl_take isl_pw_qpolynomial_fold *pwf1,
5745 __isl_take isl_pw_qpolynomial_fold *pwf2);
5746 __isl_give isl_union_pw_qpolynomial_fold *
5747 isl_union_pw_qpolynomial_fold_fold(
5748 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5749 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5751 #include <isl/aff.h>
5752 __isl_give isl_pw_aff *isl_pw_aff_union_add(
5753 __isl_take isl_pw_aff *pwaff1,
5754 __isl_take isl_pw_aff *pwaff2);
5755 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
5756 __isl_take isl_pw_multi_aff *pma1,
5757 __isl_take isl_pw_multi_aff *pma2);
5758 __isl_give isl_union_pw_multi_aff *
5759 isl_union_pw_multi_aff_union_add(
5760 __isl_take isl_union_pw_multi_aff *upma1,
5761 __isl_take isl_union_pw_multi_aff *upma2);
5762 __isl_give isl_pw_aff *isl_pw_aff_union_min(
5763 __isl_take isl_pw_aff *pwaff1,
5764 __isl_take isl_pw_aff *pwaff2);
5765 __isl_give isl_pw_aff *isl_pw_aff_union_max(
5766 __isl_take isl_pw_aff *pwaff1,
5767 __isl_take isl_pw_aff *pwaff2);
5769 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
5770 expression with a domain that is the union of those of C<pwaff1> and
5771 C<pwaff2> and such that on each cell, the quasi-affine expression is
5772 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
5773 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
5774 associated expression is the defined one.
5775 This in contrast to the C<isl_pw_aff_max> function, which is
5776 only defined on the shared definition domain of the arguments.
5778 #include <isl/val.h>
5779 __isl_give isl_multi_val *isl_multi_val_add_val(
5780 __isl_take isl_multi_val *mv,
5781 __isl_take isl_val *v);
5782 __isl_give isl_multi_val *isl_multi_val_mod_val(
5783 __isl_take isl_multi_val *mv,
5784 __isl_take isl_val *v);
5785 __isl_give isl_multi_val *isl_multi_val_scale_val(
5786 __isl_take isl_multi_val *mv,
5787 __isl_take isl_val *v);
5788 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
5789 __isl_take isl_multi_val *mv,
5790 __isl_take isl_val *v);
5792 #include <isl/aff.h>
5793 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
5794 __isl_take isl_val *mod);
5795 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
5796 __isl_take isl_pw_aff *pa,
5797 __isl_take isl_val *mod);
5798 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
5799 __isl_take isl_val *v);
5800 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
5801 __isl_take isl_multi_aff *ma,
5802 __isl_take isl_val *v);
5803 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
5804 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
5805 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
5806 __isl_take isl_multi_pw_aff *mpa,
5807 __isl_take isl_val *v);
5808 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
5809 __isl_take isl_pw_multi_aff *pma,
5810 __isl_take isl_val *v);
5811 __isl_give isl_union_pw_multi_aff *
5812 isl_union_pw_multi_aff_scale_val(
5813 __isl_take isl_union_pw_multi_aff *upma,
5814 __isl_take isl_val *val);
5815 __isl_give isl_aff *isl_aff_scale_down_ui(
5816 __isl_take isl_aff *aff, unsigned f);
5817 __isl_give isl_aff *isl_aff_scale_down_val(
5818 __isl_take isl_aff *aff, __isl_take isl_val *v);
5819 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
5820 __isl_take isl_multi_aff *ma,
5821 __isl_take isl_val *v);
5822 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
5823 __isl_take isl_pw_aff *pa,
5824 __isl_take isl_val *f);
5825 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
5826 __isl_take isl_multi_pw_aff *mpa,
5827 __isl_take isl_val *v);
5828 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
5829 __isl_take isl_pw_multi_aff *pma,
5830 __isl_take isl_val *v);
5831 __isl_give isl_union_pw_multi_aff *
5832 isl_union_pw_multi_aff_scale_down_val(
5833 __isl_take isl_union_pw_multi_aff *upma,
5834 __isl_take isl_val *val);
5836 #include <isl/polynomial.h>
5837 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5838 __isl_take isl_qpolynomial *qp,
5839 __isl_take isl_val *v);
5840 __isl_give isl_qpolynomial_fold *
5841 isl_qpolynomial_fold_scale_val(
5842 __isl_take isl_qpolynomial_fold *fold,
5843 __isl_take isl_val *v);
5844 __isl_give isl_pw_qpolynomial *
5845 isl_pw_qpolynomial_scale_val(
5846 __isl_take isl_pw_qpolynomial *pwqp,
5847 __isl_take isl_val *v);
5848 __isl_give isl_pw_qpolynomial_fold *
5849 isl_pw_qpolynomial_fold_scale_val(
5850 __isl_take isl_pw_qpolynomial_fold *pwf,
5851 __isl_take isl_val *v);
5852 __isl_give isl_union_pw_qpolynomial *
5853 isl_union_pw_qpolynomial_scale_val(
5854 __isl_take isl_union_pw_qpolynomial *upwqp,
5855 __isl_take isl_val *v);
5856 __isl_give isl_union_pw_qpolynomial_fold *
5857 isl_union_pw_qpolynomial_fold_scale_val(
5858 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5859 __isl_take isl_val *v);
5860 __isl_give isl_qpolynomial *
5861 isl_qpolynomial_scale_down_val(
5862 __isl_take isl_qpolynomial *qp,
5863 __isl_take isl_val *v);
5864 __isl_give isl_qpolynomial_fold *
5865 isl_qpolynomial_fold_scale_down_val(
5866 __isl_take isl_qpolynomial_fold *fold,
5867 __isl_take isl_val *v);
5868 __isl_give isl_pw_qpolynomial *
5869 isl_pw_qpolynomial_scale_down_val(
5870 __isl_take isl_pw_qpolynomial *pwqp,
5871 __isl_take isl_val *v);
5872 __isl_give isl_pw_qpolynomial_fold *
5873 isl_pw_qpolynomial_fold_scale_down_val(
5874 __isl_take isl_pw_qpolynomial_fold *pwf,
5875 __isl_take isl_val *v);
5876 __isl_give isl_union_pw_qpolynomial *
5877 isl_union_pw_qpolynomial_scale_down_val(
5878 __isl_take isl_union_pw_qpolynomial *upwqp,
5879 __isl_take isl_val *v);
5880 __isl_give isl_union_pw_qpolynomial_fold *
5881 isl_union_pw_qpolynomial_fold_scale_down_val(
5882 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5883 __isl_take isl_val *v);
5885 #include <isl/val.h>
5886 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
5887 __isl_take isl_multi_val *mv1,
5888 __isl_take isl_multi_val *mv2);
5889 __isl_give isl_multi_val *
5890 isl_multi_val_scale_down_multi_val(
5891 __isl_take isl_multi_val *mv1,
5892 __isl_take isl_multi_val *mv2);
5894 #include <isl/aff.h>
5895 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
5896 __isl_take isl_multi_aff *ma,
5897 __isl_take isl_multi_val *mv);
5898 __isl_give isl_pw_multi_aff *
5899 isl_pw_multi_aff_scale_multi_val(
5900 __isl_take isl_pw_multi_aff *pma,
5901 __isl_take isl_multi_val *mv);
5902 __isl_give isl_multi_pw_aff *
5903 isl_multi_pw_aff_scale_multi_val(
5904 __isl_take isl_multi_pw_aff *mpa,
5905 __isl_take isl_multi_val *mv);
5906 __isl_give isl_union_pw_multi_aff *
5907 isl_union_pw_multi_aff_scale_multi_val(
5908 __isl_take isl_union_pw_multi_aff *upma,
5909 __isl_take isl_multi_val *mv);
5910 __isl_give isl_multi_aff *
5911 isl_multi_aff_scale_down_multi_val(
5912 __isl_take isl_multi_aff *ma,
5913 __isl_take isl_multi_val *mv);
5914 __isl_give isl_multi_pw_aff *
5915 isl_multi_pw_aff_scale_down_multi_val(
5916 __isl_take isl_multi_pw_aff *mpa,
5917 __isl_take isl_multi_val *mv);
5919 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
5920 by the corresponding elements of C<mv>.
5922 #include <isl/aff.h>
5923 __isl_give isl_aff *isl_aff_mul(
5924 __isl_take isl_aff *aff1,
5925 __isl_take isl_aff *aff2);
5926 __isl_give isl_aff *isl_aff_div(
5927 __isl_take isl_aff *aff1,
5928 __isl_take isl_aff *aff2);
5929 __isl_give isl_pw_aff *isl_pw_aff_mul(
5930 __isl_take isl_pw_aff *pwaff1,
5931 __isl_take isl_pw_aff *pwaff2);
5932 __isl_give isl_pw_aff *isl_pw_aff_div(
5933 __isl_take isl_pw_aff *pa1,
5934 __isl_take isl_pw_aff *pa2);
5935 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
5936 __isl_take isl_pw_aff *pa1,
5937 __isl_take isl_pw_aff *pa2);
5938 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
5939 __isl_take isl_pw_aff *pa1,
5940 __isl_take isl_pw_aff *pa2);
5942 When multiplying two affine expressions, at least one of the two needs
5943 to be a constant. Similarly, when dividing an affine expression by another,
5944 the second expression needs to be a constant.
5945 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
5946 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
5949 #include <isl/polynomial.h>
5950 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5951 __isl_take isl_qpolynomial *qp1,
5952 __isl_take isl_qpolynomial *qp2);
5953 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5954 __isl_take isl_pw_qpolynomial *pwqp1,
5955 __isl_take isl_pw_qpolynomial *pwqp2);
5956 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5957 __isl_take isl_union_pw_qpolynomial *upwqp1,
5958 __isl_take isl_union_pw_qpolynomial *upwqp2);
5962 =head3 Lexicographic Optimization
5964 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
5965 the following functions
5966 compute a set that contains the lexicographic minimum or maximum
5967 of the elements in C<set> (or C<bset>) for those values of the parameters
5968 that satisfy C<dom>.
5969 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
5970 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
5972 In other words, the union of the parameter values
5973 for which the result is non-empty and of C<*empty>
5976 #include <isl/set.h>
5977 __isl_give isl_set *isl_basic_set_partial_lexmin(
5978 __isl_take isl_basic_set *bset,
5979 __isl_take isl_basic_set *dom,
5980 __isl_give isl_set **empty);
5981 __isl_give isl_set *isl_basic_set_partial_lexmax(
5982 __isl_take isl_basic_set *bset,
5983 __isl_take isl_basic_set *dom,
5984 __isl_give isl_set **empty);
5985 __isl_give isl_set *isl_set_partial_lexmin(
5986 __isl_take isl_set *set, __isl_take isl_set *dom,
5987 __isl_give isl_set **empty);
5988 __isl_give isl_set *isl_set_partial_lexmax(
5989 __isl_take isl_set *set, __isl_take isl_set *dom,
5990 __isl_give isl_set **empty);
5992 Given a (basic) set C<set> (or C<bset>), the following functions simply
5993 return a set containing the lexicographic minimum or maximum
5994 of the elements in C<set> (or C<bset>).
5995 In case of union sets, the optimum is computed per space.
5997 #include <isl/set.h>
5998 __isl_give isl_set *isl_basic_set_lexmin(
5999 __isl_take isl_basic_set *bset);
6000 __isl_give isl_set *isl_basic_set_lexmax(
6001 __isl_take isl_basic_set *bset);
6002 __isl_give isl_set *isl_set_lexmin(
6003 __isl_take isl_set *set);
6004 __isl_give isl_set *isl_set_lexmax(
6005 __isl_take isl_set *set);
6006 __isl_give isl_union_set *isl_union_set_lexmin(
6007 __isl_take isl_union_set *uset);
6008 __isl_give isl_union_set *isl_union_set_lexmax(
6009 __isl_take isl_union_set *uset);
6011 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6012 the following functions
6013 compute a relation that maps each element of C<dom>
6014 to the single lexicographic minimum or maximum
6015 of the elements that are associated to that same
6016 element in C<map> (or C<bmap>).
6017 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6018 that contains the elements in C<dom> that do not map
6019 to any elements in C<map> (or C<bmap>).
6020 In other words, the union of the domain of the result and of C<*empty>
6023 #include <isl/map.h>
6024 __isl_give isl_map *isl_basic_map_partial_lexmax(
6025 __isl_take isl_basic_map *bmap,
6026 __isl_take isl_basic_set *dom,
6027 __isl_give isl_set **empty);
6028 __isl_give isl_map *isl_basic_map_partial_lexmin(
6029 __isl_take isl_basic_map *bmap,
6030 __isl_take isl_basic_set *dom,
6031 __isl_give isl_set **empty);
6032 __isl_give isl_map *isl_map_partial_lexmax(
6033 __isl_take isl_map *map, __isl_take isl_set *dom,
6034 __isl_give isl_set **empty);
6035 __isl_give isl_map *isl_map_partial_lexmin(
6036 __isl_take isl_map *map, __isl_take isl_set *dom,
6037 __isl_give isl_set **empty);
6039 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6040 return a map mapping each element in the domain of
6041 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6042 of all elements associated to that element.
6043 In case of union relations, the optimum is computed per space.
6045 #include <isl/map.h>
6046 __isl_give isl_map *isl_basic_map_lexmin(
6047 __isl_take isl_basic_map *bmap);
6048 __isl_give isl_map *isl_basic_map_lexmax(
6049 __isl_take isl_basic_map *bmap);
6050 __isl_give isl_map *isl_map_lexmin(
6051 __isl_take isl_map *map);
6052 __isl_give isl_map *isl_map_lexmax(
6053 __isl_take isl_map *map);
6054 __isl_give isl_union_map *isl_union_map_lexmin(
6055 __isl_take isl_union_map *umap);
6056 __isl_give isl_union_map *isl_union_map_lexmax(
6057 __isl_take isl_union_map *umap);
6059 The following functions return their result in the form of
6060 a piecewise multi-affine expression,
6061 but are otherwise equivalent to the corresponding functions
6062 returning a basic set or relation.
6064 #include <isl/set.h>
6065 __isl_give isl_pw_multi_aff *
6066 isl_basic_set_partial_lexmin_pw_multi_aff(
6067 __isl_take isl_basic_set *bset,
6068 __isl_take isl_basic_set *dom,
6069 __isl_give isl_set **empty);
6070 __isl_give isl_pw_multi_aff *
6071 isl_basic_set_partial_lexmax_pw_multi_aff(
6072 __isl_take isl_basic_set *bset,
6073 __isl_take isl_basic_set *dom,
6074 __isl_give isl_set **empty);
6075 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6076 __isl_take isl_set *set);
6077 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6078 __isl_take isl_set *set);
6080 #include <isl/map.h>
6081 __isl_give isl_pw_multi_aff *
6082 isl_basic_map_lexmin_pw_multi_aff(
6083 __isl_take isl_basic_map *bmap);
6084 __isl_give isl_pw_multi_aff *
6085 isl_basic_map_partial_lexmin_pw_multi_aff(
6086 __isl_take isl_basic_map *bmap,
6087 __isl_take isl_basic_set *dom,
6088 __isl_give isl_set **empty);
6089 __isl_give isl_pw_multi_aff *
6090 isl_basic_map_partial_lexmax_pw_multi_aff(
6091 __isl_take isl_basic_map *bmap,
6092 __isl_take isl_basic_set *dom,
6093 __isl_give isl_set **empty);
6094 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6095 __isl_take isl_map *map);
6096 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6097 __isl_take isl_map *map);
6099 The following functions return the lexicographic minimum or maximum
6100 on the shared domain of the inputs and the single defined function
6101 on those parts of the domain where only a single function is defined.
6103 #include <isl/aff.h>
6104 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6105 __isl_take isl_pw_multi_aff *pma1,
6106 __isl_take isl_pw_multi_aff *pma2);
6107 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6108 __isl_take isl_pw_multi_aff *pma1,
6109 __isl_take isl_pw_multi_aff *pma2);
6111 =head2 Ternary Operations
6113 #include <isl/aff.h>
6114 __isl_give isl_pw_aff *isl_pw_aff_cond(
6115 __isl_take isl_pw_aff *cond,
6116 __isl_take isl_pw_aff *pwaff_true,
6117 __isl_take isl_pw_aff *pwaff_false);
6119 The function C<isl_pw_aff_cond> performs a conditional operator
6120 and returns an expression that is equal to C<pwaff_true>
6121 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6122 where C<cond> is zero.
6126 Lists are defined over several element types, including
6127 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
6128 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
6129 Here we take lists of C<isl_set>s as an example.
6130 Lists can be created, copied, modified and freed using the following functions.
6132 #include <isl/set.h>
6133 __isl_give isl_set_list *isl_set_list_from_set(
6134 __isl_take isl_set *el);
6135 __isl_give isl_set_list *isl_set_list_alloc(
6136 isl_ctx *ctx, int n);
6137 __isl_give isl_set_list *isl_set_list_copy(
6138 __isl_keep isl_set_list *list);
6139 __isl_give isl_set_list *isl_set_list_insert(
6140 __isl_take isl_set_list *list, unsigned pos,
6141 __isl_take isl_set *el);
6142 __isl_give isl_set_list *isl_set_list_add(
6143 __isl_take isl_set_list *list,
6144 __isl_take isl_set *el);
6145 __isl_give isl_set_list *isl_set_list_drop(
6146 __isl_take isl_set_list *list,
6147 unsigned first, unsigned n);
6148 __isl_give isl_set_list *isl_set_list_set_set(
6149 __isl_take isl_set_list *list, int index,
6150 __isl_take isl_set *set);
6151 __isl_give isl_set_list *isl_set_list_concat(
6152 __isl_take isl_set_list *list1,
6153 __isl_take isl_set_list *list2);
6154 __isl_give isl_set_list *isl_set_list_sort(
6155 __isl_take isl_set_list *list,
6156 int (*cmp)(__isl_keep isl_set *a,
6157 __isl_keep isl_set *b, void *user),
6159 __isl_null isl_set_list *isl_set_list_free(
6160 __isl_take isl_set_list *list);
6162 C<isl_set_list_alloc> creates an empty list with a capacity for
6163 C<n> elements. C<isl_set_list_from_set> creates a list with a single
6166 Lists can be inspected using the following functions.
6168 #include <isl/set.h>
6169 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6170 __isl_give isl_set *isl_set_list_get_set(
6171 __isl_keep isl_set_list *list, int index);
6172 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6173 int (*fn)(__isl_take isl_set *el, void *user),
6175 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6176 int (*follows)(__isl_keep isl_set *a,
6177 __isl_keep isl_set *b, void *user),
6179 int (*fn)(__isl_take isl_set *el, void *user),
6182 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6183 strongly connected components of the graph with as vertices the elements
6184 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6185 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6186 should return C<-1> on error.
6188 Lists can be printed using
6190 #include <isl/set.h>
6191 __isl_give isl_printer *isl_printer_print_set_list(
6192 __isl_take isl_printer *p,
6193 __isl_keep isl_set_list *list);
6195 =head2 Associative arrays
6197 Associative arrays map isl objects of a specific type to isl objects
6198 of some (other) specific type. They are defined for several pairs
6199 of types, including (C<isl_map>, C<isl_basic_set>),
6200 (C<isl_id>, C<isl_ast_expr>) and.
6201 (C<isl_id>, C<isl_pw_aff>).
6202 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6205 Associative arrays can be created, copied and freed using
6206 the following functions.
6208 #include <isl/id_to_ast_expr.h>
6209 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6210 isl_ctx *ctx, int min_size);
6211 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6212 __isl_keep id_to_ast_expr *id2expr);
6213 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6214 __isl_take id_to_ast_expr *id2expr);
6216 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6217 to specify the expected size of the associative array.
6218 The associative array will be grown automatically as needed.
6220 Associative arrays can be inspected using the following functions.
6222 #include <isl/id_to_ast_expr.h>
6223 int isl_id_to_ast_expr_has(
6224 __isl_keep id_to_ast_expr *id2expr,
6225 __isl_keep isl_id *key);
6226 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6227 __isl_keep id_to_ast_expr *id2expr,
6228 __isl_take isl_id *key);
6229 int isl_id_to_ast_expr_foreach(
6230 __isl_keep id_to_ast_expr *id2expr,
6231 int (*fn)(__isl_take isl_id *key,
6232 __isl_take isl_ast_expr *val, void *user),
6235 They can be modified using the following function.
6237 #include <isl/id_to_ast_expr.h>
6238 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6239 __isl_take id_to_ast_expr *id2expr,
6240 __isl_take isl_id *key,
6241 __isl_take isl_ast_expr *val);
6242 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6243 __isl_take id_to_ast_expr *id2expr,
6244 __isl_take isl_id *key);
6246 Associative arrays can be printed using the following function.
6248 #include <isl/id_to_ast_expr.h>
6249 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6250 __isl_take isl_printer *p,
6251 __isl_keep id_to_ast_expr *id2expr);
6255 Vectors can be created, copied and freed using the following functions.
6257 #include <isl/vec.h>
6258 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6260 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6261 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6263 Note that the elements of a newly created vector may have arbitrary values.
6264 The elements can be changed and inspected using the following functions.
6266 int isl_vec_size(__isl_keep isl_vec *vec);
6267 __isl_give isl_val *isl_vec_get_element_val(
6268 __isl_keep isl_vec *vec, int pos);
6269 __isl_give isl_vec *isl_vec_set_element_si(
6270 __isl_take isl_vec *vec, int pos, int v);
6271 __isl_give isl_vec *isl_vec_set_element_val(
6272 __isl_take isl_vec *vec, int pos,
6273 __isl_take isl_val *v);
6274 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6276 __isl_give isl_vec *isl_vec_set_val(
6277 __isl_take isl_vec *vec, __isl_take isl_val *v);
6278 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6279 __isl_keep isl_vec *vec2, int pos);
6281 C<isl_vec_get_element> will return a negative value if anything went wrong.
6282 In that case, the value of C<*v> is undefined.
6284 The following function can be used to concatenate two vectors.
6286 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6287 __isl_take isl_vec *vec2);
6291 Matrices can be created, copied and freed using the following functions.
6293 #include <isl/mat.h>
6294 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6295 unsigned n_row, unsigned n_col);
6296 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6297 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6299 Note that the elements of a newly created matrix may have arbitrary values.
6300 The elements can be changed and inspected using the following functions.
6302 int isl_mat_rows(__isl_keep isl_mat *mat);
6303 int isl_mat_cols(__isl_keep isl_mat *mat);
6304 __isl_give isl_val *isl_mat_get_element_val(
6305 __isl_keep isl_mat *mat, int row, int col);
6306 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
6307 int row, int col, int v);
6308 __isl_give isl_mat *isl_mat_set_element_val(
6309 __isl_take isl_mat *mat, int row, int col,
6310 __isl_take isl_val *v);
6312 C<isl_mat_get_element> will return a negative value if anything went wrong.
6313 In that case, the value of C<*v> is undefined.
6315 The following function can be used to compute the (right) inverse
6316 of a matrix, i.e., a matrix such that the product of the original
6317 and the inverse (in that order) is a multiple of the identity matrix.
6318 The input matrix is assumed to be of full row-rank.
6320 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
6322 The following function can be used to compute the (right) kernel
6323 (or null space) of a matrix, i.e., a matrix such that the product of
6324 the original and the kernel (in that order) is the zero matrix.
6326 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
6328 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
6330 The following functions determine
6331 an upper or lower bound on a quasipolynomial over its domain.
6333 __isl_give isl_pw_qpolynomial_fold *
6334 isl_pw_qpolynomial_bound(
6335 __isl_take isl_pw_qpolynomial *pwqp,
6336 enum isl_fold type, int *tight);
6338 __isl_give isl_union_pw_qpolynomial_fold *
6339 isl_union_pw_qpolynomial_bound(
6340 __isl_take isl_union_pw_qpolynomial *upwqp,
6341 enum isl_fold type, int *tight);
6343 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
6344 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
6345 is the returned bound is known be tight, i.e., for each value
6346 of the parameters there is at least
6347 one element in the domain that reaches the bound.
6348 If the domain of C<pwqp> is not wrapping, then the bound is computed
6349 over all elements in that domain and the result has a purely parametric
6350 domain. If the domain of C<pwqp> is wrapping, then the bound is
6351 computed over the range of the wrapped relation. The domain of the
6352 wrapped relation becomes the domain of the result.
6354 =head2 Parametric Vertex Enumeration
6356 The parametric vertex enumeration described in this section
6357 is mainly intended to be used internally and by the C<barvinok>
6360 #include <isl/vertices.h>
6361 __isl_give isl_vertices *isl_basic_set_compute_vertices(
6362 __isl_keep isl_basic_set *bset);
6364 The function C<isl_basic_set_compute_vertices> performs the
6365 actual computation of the parametric vertices and the chamber
6366 decomposition and store the result in an C<isl_vertices> object.
6367 This information can be queried by either iterating over all
6368 the vertices or iterating over all the chambers or cells
6369 and then iterating over all vertices that are active on the chamber.
6371 int isl_vertices_foreach_vertex(
6372 __isl_keep isl_vertices *vertices,
6373 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6376 int isl_vertices_foreach_cell(
6377 __isl_keep isl_vertices *vertices,
6378 int (*fn)(__isl_take isl_cell *cell, void *user),
6380 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
6381 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6384 Other operations that can be performed on an C<isl_vertices> object are
6387 int isl_vertices_get_n_vertices(
6388 __isl_keep isl_vertices *vertices);
6389 void isl_vertices_free(__isl_take isl_vertices *vertices);
6391 Vertices can be inspected and destroyed using the following functions.
6393 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
6394 __isl_give isl_basic_set *isl_vertex_get_domain(
6395 __isl_keep isl_vertex *vertex);
6396 __isl_give isl_multi_aff *isl_vertex_get_expr(
6397 __isl_keep isl_vertex *vertex);
6398 void isl_vertex_free(__isl_take isl_vertex *vertex);
6400 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
6401 describing the vertex in terms of the parameters,
6402 while C<isl_vertex_get_domain> returns the activity domain
6405 Chambers can be inspected and destroyed using the following functions.
6407 __isl_give isl_basic_set *isl_cell_get_domain(
6408 __isl_keep isl_cell *cell);
6409 void isl_cell_free(__isl_take isl_cell *cell);
6411 =head1 Polyhedral Compilation Library
6413 This section collects functionality in C<isl> that has been specifically
6414 designed for use during polyhedral compilation.
6416 =head2 Dependence Analysis
6418 C<isl> contains specialized functionality for performing
6419 array dataflow analysis. That is, given a I<sink> access relation
6420 and a collection of possible I<source> access relations,
6421 C<isl> can compute relations that describe
6422 for each iteration of the sink access, which iteration
6423 of which of the source access relations was the last
6424 to access the same data element before the given iteration
6426 The resulting dependence relations map source iterations
6427 to the corresponding sink iterations.
6428 To compute standard flow dependences, the sink should be
6429 a read, while the sources should be writes.
6430 If any of the source accesses are marked as being I<may>
6431 accesses, then there will be a dependence from the last
6432 I<must> access B<and> from any I<may> access that follows
6433 this last I<must> access.
6434 In particular, if I<all> sources are I<may> accesses,
6435 then memory based dependence analysis is performed.
6436 If, on the other hand, all sources are I<must> accesses,
6437 then value based dependence analysis is performed.
6439 #include <isl/flow.h>
6441 typedef int (*isl_access_level_before)(void *first, void *second);
6443 __isl_give isl_access_info *isl_access_info_alloc(
6444 __isl_take isl_map *sink,
6445 void *sink_user, isl_access_level_before fn,
6447 __isl_give isl_access_info *isl_access_info_add_source(
6448 __isl_take isl_access_info *acc,
6449 __isl_take isl_map *source, int must,
6451 __isl_null isl_access_info *isl_access_info_free(
6452 __isl_take isl_access_info *acc);
6454 __isl_give isl_flow *isl_access_info_compute_flow(
6455 __isl_take isl_access_info *acc);
6457 int isl_flow_foreach(__isl_keep isl_flow *deps,
6458 int (*fn)(__isl_take isl_map *dep, int must,
6459 void *dep_user, void *user),
6461 __isl_give isl_map *isl_flow_get_no_source(
6462 __isl_keep isl_flow *deps, int must);
6463 void isl_flow_free(__isl_take isl_flow *deps);
6465 The function C<isl_access_info_compute_flow> performs the actual
6466 dependence analysis. The other functions are used to construct
6467 the input for this function or to read off the output.
6469 The input is collected in an C<isl_access_info>, which can
6470 be created through a call to C<isl_access_info_alloc>.
6471 The arguments to this functions are the sink access relation
6472 C<sink>, a token C<sink_user> used to identify the sink
6473 access to the user, a callback function for specifying the
6474 relative order of source and sink accesses, and the number
6475 of source access relations that will be added.
6476 The callback function has type C<int (*)(void *first, void *second)>.
6477 The function is called with two user supplied tokens identifying
6478 either a source or the sink and it should return the shared nesting
6479 level and the relative order of the two accesses.
6480 In particular, let I<n> be the number of loops shared by
6481 the two accesses. If C<first> precedes C<second> textually,
6482 then the function should return I<2 * n + 1>; otherwise,
6483 it should return I<2 * n>.
6484 The sources can be added to the C<isl_access_info> by performing
6485 (at most) C<max_source> calls to C<isl_access_info_add_source>.
6486 C<must> indicates whether the source is a I<must> access
6487 or a I<may> access. Note that a multi-valued access relation
6488 should only be marked I<must> if every iteration in the domain
6489 of the relation accesses I<all> elements in its image.
6490 The C<source_user> token is again used to identify
6491 the source access. The range of the source access relation
6492 C<source> should have the same dimension as the range
6493 of the sink access relation.
6494 The C<isl_access_info_free> function should usually not be
6495 called explicitly, because it is called implicitly by
6496 C<isl_access_info_compute_flow>.
6498 The result of the dependence analysis is collected in an
6499 C<isl_flow>. There may be elements of
6500 the sink access for which no preceding source access could be
6501 found or for which all preceding sources are I<may> accesses.
6502 The relations containing these elements can be obtained through
6503 calls to C<isl_flow_get_no_source>, the first with C<must> set
6504 and the second with C<must> unset.
6505 In the case of standard flow dependence analysis,
6506 with the sink a read and the sources I<must> writes,
6507 the first relation corresponds to the reads from uninitialized
6508 array elements and the second relation is empty.
6509 The actual flow dependences can be extracted using
6510 C<isl_flow_foreach>. This function will call the user-specified
6511 callback function C<fn> for each B<non-empty> dependence between
6512 a source and the sink. The callback function is called
6513 with four arguments, the actual flow dependence relation
6514 mapping source iterations to sink iterations, a boolean that
6515 indicates whether it is a I<must> or I<may> dependence, a token
6516 identifying the source and an additional C<void *> with value
6517 equal to the third argument of the C<isl_flow_foreach> call.
6518 A dependence is marked I<must> if it originates from a I<must>
6519 source and if it is not followed by any I<may> sources.
6521 After finishing with an C<isl_flow>, the user should call
6522 C<isl_flow_free> to free all associated memory.
6524 A higher-level interface to dependence analysis is provided
6525 by the following function.
6527 #include <isl/flow.h>
6529 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
6530 __isl_take isl_union_map *must_source,
6531 __isl_take isl_union_map *may_source,
6532 __isl_take isl_union_map *schedule,
6533 __isl_give isl_union_map **must_dep,
6534 __isl_give isl_union_map **may_dep,
6535 __isl_give isl_union_map **must_no_source,
6536 __isl_give isl_union_map **may_no_source);
6538 The arrays are identified by the tuple names of the ranges
6539 of the accesses. The iteration domains by the tuple names
6540 of the domains of the accesses and of the schedule.
6541 The relative order of the iteration domains is given by the
6542 schedule. The relations returned through C<must_no_source>
6543 and C<may_no_source> are subsets of C<sink>.
6544 Any of C<must_dep>, C<may_dep>, C<must_no_source>
6545 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
6546 any of the other arguments is treated as an error.
6548 =head3 Interaction with Dependence Analysis
6550 During the dependence analysis, we frequently need to perform
6551 the following operation. Given a relation between sink iterations
6552 and potential source iterations from a particular source domain,
6553 what is the last potential source iteration corresponding to each
6554 sink iteration. It can sometimes be convenient to adjust
6555 the set of potential source iterations before or after each such operation.
6556 The prototypical example is fuzzy array dataflow analysis,
6557 where we need to analyze if, based on data-dependent constraints,
6558 the sink iteration can ever be executed without one or more of
6559 the corresponding potential source iterations being executed.
6560 If so, we can introduce extra parameters and select an unknown
6561 but fixed source iteration from the potential source iterations.
6562 To be able to perform such manipulations, C<isl> provides the following
6565 #include <isl/flow.h>
6567 typedef __isl_give isl_restriction *(*isl_access_restrict)(
6568 __isl_keep isl_map *source_map,
6569 __isl_keep isl_set *sink, void *source_user,
6571 __isl_give isl_access_info *isl_access_info_set_restrict(
6572 __isl_take isl_access_info *acc,
6573 isl_access_restrict fn, void *user);
6575 The function C<isl_access_info_set_restrict> should be called
6576 before calling C<isl_access_info_compute_flow> and registers a callback function
6577 that will be called any time C<isl> is about to compute the last
6578 potential source. The first argument is the (reverse) proto-dependence,
6579 mapping sink iterations to potential source iterations.
6580 The second argument represents the sink iterations for which
6581 we want to compute the last source iteration.
6582 The third argument is the token corresponding to the source
6583 and the final argument is the token passed to C<isl_access_info_set_restrict>.
6584 The callback is expected to return a restriction on either the input or
6585 the output of the operation computing the last potential source.
6586 If the input needs to be restricted then restrictions are needed
6587 for both the source and the sink iterations. The sink iterations
6588 and the potential source iterations will be intersected with these sets.
6589 If the output needs to be restricted then only a restriction on the source
6590 iterations is required.
6591 If any error occurs, the callback should return C<NULL>.
6592 An C<isl_restriction> object can be created, freed and inspected
6593 using the following functions.
6595 #include <isl/flow.h>
6597 __isl_give isl_restriction *isl_restriction_input(
6598 __isl_take isl_set *source_restr,
6599 __isl_take isl_set *sink_restr);
6600 __isl_give isl_restriction *isl_restriction_output(
6601 __isl_take isl_set *source_restr);
6602 __isl_give isl_restriction *isl_restriction_none(
6603 __isl_take isl_map *source_map);
6604 __isl_give isl_restriction *isl_restriction_empty(
6605 __isl_take isl_map *source_map);
6606 __isl_null isl_restriction *isl_restriction_free(
6607 __isl_take isl_restriction *restr);
6609 C<isl_restriction_none> and C<isl_restriction_empty> are special
6610 cases of C<isl_restriction_input>. C<isl_restriction_none>
6611 is essentially equivalent to
6613 isl_restriction_input(isl_set_universe(
6614 isl_space_range(isl_map_get_space(source_map))),
6616 isl_space_domain(isl_map_get_space(source_map))));
6618 whereas C<isl_restriction_empty> is essentially equivalent to
6620 isl_restriction_input(isl_set_empty(
6621 isl_space_range(isl_map_get_space(source_map))),
6623 isl_space_domain(isl_map_get_space(source_map))));
6627 B<The functionality described in this section is fairly new
6628 and may be subject to change.>
6630 #include <isl/schedule.h>
6631 __isl_give isl_schedule *
6632 isl_schedule_constraints_compute_schedule(
6633 __isl_take isl_schedule_constraints *sc);
6634 __isl_null isl_schedule *isl_schedule_free(
6635 __isl_take isl_schedule *sched);
6637 The function C<isl_schedule_constraints_compute_schedule> can be
6638 used to compute a schedule that satisfies the given schedule constraints.
6639 These schedule constraints include the iteration domain for which
6640 a schedule should be computed and dependences between pairs of
6641 iterations. In particular, these dependences include
6642 I<validity> dependences and I<proximity> dependences.
6643 By default, the algorithm used to construct the schedule is similar
6644 to that of C<Pluto>.
6645 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6647 The generated schedule respects all validity dependences.
6648 That is, all dependence distances over these dependences in the
6649 scheduled space are lexicographically positive.
6650 The default algorithm tries to ensure that the dependence distances
6651 over coincidence constraints are zero and to minimize the
6652 dependence distances over proximity dependences.
6653 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6654 for groups of domains where the dependence distances over validity
6655 dependences have only non-negative values.
6656 When using Feautrier's algorithm, the coincidence and proximity constraints
6657 are only taken into account during the extension to a
6658 full-dimensional schedule.
6660 An C<isl_schedule_constraints> object can be constructed
6661 and manipulated using the following functions.
6663 #include <isl/schedule.h>
6664 __isl_give isl_schedule_constraints *
6665 isl_schedule_constraints_copy(
6666 __isl_keep isl_schedule_constraints *sc);
6667 __isl_give isl_schedule_constraints *
6668 isl_schedule_constraints_on_domain(
6669 __isl_take isl_union_set *domain);
6670 __isl_give isl_schedule_constraints *
6671 isl_schedule_constraints_set_validity(
6672 __isl_take isl_schedule_constraints *sc,
6673 __isl_take isl_union_map *validity);
6674 __isl_give isl_schedule_constraints *
6675 isl_schedule_constraints_set_coincidence(
6676 __isl_take isl_schedule_constraints *sc,
6677 __isl_take isl_union_map *coincidence);
6678 __isl_give isl_schedule_constraints *
6679 isl_schedule_constraints_set_proximity(
6680 __isl_take isl_schedule_constraints *sc,
6681 __isl_take isl_union_map *proximity);
6682 __isl_give isl_schedule_constraints *
6683 isl_schedule_constraints_set_conditional_validity(
6684 __isl_take isl_schedule_constraints *sc,
6685 __isl_take isl_union_map *condition,
6686 __isl_take isl_union_map *validity);
6687 __isl_null isl_schedule_constraints *
6688 isl_schedule_constraints_free(
6689 __isl_take isl_schedule_constraints *sc);
6691 The initial C<isl_schedule_constraints> object created by
6692 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6693 That is, it has an empty set of dependences.
6694 The function C<isl_schedule_constraints_set_validity> replaces the
6695 validity dependences, mapping domain elements I<i> to domain
6696 elements that should be scheduled after I<i>.
6697 The function C<isl_schedule_constraints_set_coincidence> replaces the
6698 coincidence dependences, mapping domain elements I<i> to domain
6699 elements that should be scheduled together with I<I>, if possible.
6700 The function C<isl_schedule_constraints_set_proximity> replaces the
6701 proximity dependences, mapping domain elements I<i> to domain
6702 elements that should be scheduled either before I<I>
6703 or as early as possible after I<i>.
6705 The function C<isl_schedule_constraints_set_conditional_validity>
6706 replaces the conditional validity constraints.
6707 A conditional validity constraint is only imposed when any of the corresponding
6708 conditions is satisfied, i.e., when any of them is non-zero.
6709 That is, the scheduler ensures that within each band if the dependence
6710 distances over the condition constraints are not all zero
6711 then all corresponding conditional validity constraints are respected.
6712 A conditional validity constraint corresponds to a condition
6713 if the two are adjacent, i.e., if the domain of one relation intersect
6714 the range of the other relation.
6715 The typical use case of conditional validity constraints is
6716 to allow order constraints between live ranges to be violated
6717 as long as the live ranges themselves are local to the band.
6718 To allow more fine-grained control over which conditions correspond
6719 to which conditional validity constraints, the domains and ranges
6720 of these relations may include I<tags>. That is, the domains and
6721 ranges of those relation may themselves be wrapped relations
6722 where the iteration domain appears in the domain of those wrapped relations
6723 and the range of the wrapped relations can be arbitrarily chosen
6724 by the user. Conditions and conditional validity constraints are only
6725 considered adjacent to each other if the entire wrapped relation matches.
6726 In particular, a relation with a tag will never be considered adjacent
6727 to a relation without a tag.
6729 The following function computes a schedule directly from
6730 an iteration domain and validity and proximity dependences
6731 and is implemented in terms of the functions described above.
6732 The use of C<isl_union_set_compute_schedule> is discouraged.
6734 #include <isl/schedule.h>
6735 __isl_give isl_schedule *isl_union_set_compute_schedule(
6736 __isl_take isl_union_set *domain,
6737 __isl_take isl_union_map *validity,
6738 __isl_take isl_union_map *proximity);
6740 A mapping from the domains to the scheduled space can be obtained
6741 from an C<isl_schedule> using the following function.
6743 __isl_give isl_union_map *isl_schedule_get_map(
6744 __isl_keep isl_schedule *sched);
6746 A representation of the schedule can be printed using
6748 __isl_give isl_printer *isl_printer_print_schedule(
6749 __isl_take isl_printer *p,
6750 __isl_keep isl_schedule *schedule);
6752 A representation of the schedule as a forest of bands can be obtained
6753 using the following function.
6755 __isl_give isl_band_list *isl_schedule_get_band_forest(
6756 __isl_keep isl_schedule *schedule);
6758 The individual bands can be visited in depth-first post-order
6759 using the following function.
6761 #include <isl/schedule.h>
6762 int isl_schedule_foreach_band(
6763 __isl_keep isl_schedule *sched,
6764 int (*fn)(__isl_keep isl_band *band, void *user),
6767 The list can be manipulated as explained in L<"Lists">.
6768 The bands inside the list can be copied and freed using the following
6771 #include <isl/band.h>
6772 __isl_give isl_band *isl_band_copy(
6773 __isl_keep isl_band *band);
6774 __isl_null isl_band *isl_band_free(
6775 __isl_take isl_band *band);
6777 Each band contains zero or more scheduling dimensions.
6778 These are referred to as the members of the band.
6779 The section of the schedule that corresponds to the band is
6780 referred to as the partial schedule of the band.
6781 For those nodes that participate in a band, the outer scheduling
6782 dimensions form the prefix schedule, while the inner scheduling
6783 dimensions form the suffix schedule.
6784 That is, if we take a cut of the band forest, then the union of
6785 the concatenations of the prefix, partial and suffix schedules of
6786 each band in the cut is equal to the entire schedule (modulo
6787 some possible padding at the end with zero scheduling dimensions).
6788 The properties of a band can be inspected using the following functions.
6790 #include <isl/band.h>
6791 int isl_band_has_children(__isl_keep isl_band *band);
6792 __isl_give isl_band_list *isl_band_get_children(
6793 __isl_keep isl_band *band);
6795 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6796 __isl_keep isl_band *band);
6797 __isl_give isl_union_map *isl_band_get_partial_schedule(
6798 __isl_keep isl_band *band);
6799 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6800 __isl_keep isl_band *band);
6802 int isl_band_n_member(__isl_keep isl_band *band);
6803 int isl_band_member_is_coincident(
6804 __isl_keep isl_band *band, int pos);
6806 int isl_band_list_foreach_band(
6807 __isl_keep isl_band_list *list,
6808 int (*fn)(__isl_keep isl_band *band, void *user),
6811 Note that a scheduling dimension is considered to be ``coincident''
6812 if it satisfies the coincidence constraints within its band.
6813 That is, if the dependence distances of the coincidence
6814 constraints are all zero in that direction (for fixed
6815 iterations of outer bands).
6816 Like C<isl_schedule_foreach_band>,
6817 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6818 in depth-first post-order.
6820 A band can be tiled using the following function.
6822 #include <isl/band.h>
6823 int isl_band_tile(__isl_keep isl_band *band,
6824 __isl_take isl_vec *sizes);
6826 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6828 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6829 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6831 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6833 The C<isl_band_tile> function tiles the band using the given tile sizes
6834 inside its schedule.
6835 A new child band is created to represent the point loops and it is
6836 inserted between the modified band and its children.
6837 The C<tile_scale_tile_loops> option specifies whether the tile
6838 loops iterators should be scaled by the tile sizes.
6839 If the C<tile_shift_point_loops> option is set, then the point loops
6840 are shifted to start at zero.
6842 A band can be split into two nested bands using the following function.
6844 int isl_band_split(__isl_keep isl_band *band, int pos);
6846 The resulting outer band contains the first C<pos> dimensions of C<band>
6847 while the inner band contains the remaining dimensions.
6849 A representation of the band can be printed using
6851 #include <isl/band.h>
6852 __isl_give isl_printer *isl_printer_print_band(
6853 __isl_take isl_printer *p,
6854 __isl_keep isl_band *band);
6858 #include <isl/schedule.h>
6859 int isl_options_set_schedule_max_coefficient(
6860 isl_ctx *ctx, int val);
6861 int isl_options_get_schedule_max_coefficient(
6863 int isl_options_set_schedule_max_constant_term(
6864 isl_ctx *ctx, int val);
6865 int isl_options_get_schedule_max_constant_term(
6867 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6868 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6869 int isl_options_set_schedule_maximize_band_depth(
6870 isl_ctx *ctx, int val);
6871 int isl_options_get_schedule_maximize_band_depth(
6873 int isl_options_set_schedule_outer_coincidence(
6874 isl_ctx *ctx, int val);
6875 int isl_options_get_schedule_outer_coincidence(
6877 int isl_options_set_schedule_split_scaled(
6878 isl_ctx *ctx, int val);
6879 int isl_options_get_schedule_split_scaled(
6881 int isl_options_set_schedule_algorithm(
6882 isl_ctx *ctx, int val);
6883 int isl_options_get_schedule_algorithm(
6885 int isl_options_set_schedule_separate_components(
6886 isl_ctx *ctx, int val);
6887 int isl_options_get_schedule_separate_components(
6892 =item * schedule_max_coefficient
6894 This option enforces that the coefficients for variable and parameter
6895 dimensions in the calculated schedule are not larger than the specified value.
6896 This option can significantly increase the speed of the scheduling calculation
6897 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6898 this option does not introduce bounds on the variable or parameter
6901 =item * schedule_max_constant_term
6903 This option enforces that the constant coefficients in the calculated schedule
6904 are not larger than the maximal constant term. This option can significantly
6905 increase the speed of the scheduling calculation and may also prevent fusing of
6906 unrelated dimensions. A value of -1 means that this option does not introduce
6907 bounds on the constant coefficients.
6909 =item * schedule_fuse
6911 This option controls the level of fusion.
6912 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6913 resulting schedule will be distributed as much as possible.
6914 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6915 try to fuse loops in the resulting schedule.
6917 =item * schedule_maximize_band_depth
6919 If this option is set, we do not split bands at the point
6920 where we detect splitting is necessary. Instead, we
6921 backtrack and split bands as early as possible. This
6922 reduces the number of splits and maximizes the width of
6923 the bands. Wider bands give more possibilities for tiling.
6924 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6925 then bands will be split as early as possible, even if there is no need.
6926 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6928 =item * schedule_outer_coincidence
6930 If this option is set, then we try to construct schedules
6931 where the outermost scheduling dimension in each band
6932 satisfies the coincidence constraints.
6934 =item * schedule_split_scaled
6936 If this option is set, then we try to construct schedules in which the
6937 constant term is split off from the linear part if the linear parts of
6938 the scheduling rows for all nodes in the graphs have a common non-trivial
6940 The constant term is then placed in a separate band and the linear
6943 =item * schedule_algorithm
6945 Selects the scheduling algorithm to be used.
6946 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6947 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6949 =item * schedule_separate_components
6951 If at any point the dependence graph contains any (weakly connected) components,
6952 then these components are scheduled separately.
6953 If this option is not set, then some iterations of the domains
6954 in these components may be scheduled together.
6955 If this option is set, then the components are given consecutive
6960 =head2 AST Generation
6962 This section describes the C<isl> functionality for generating
6963 ASTs that visit all the elements
6964 in a domain in an order specified by a schedule.
6965 In particular, given a C<isl_union_map>, an AST is generated
6966 that visits all the elements in the domain of the C<isl_union_map>
6967 according to the lexicographic order of the corresponding image
6968 element(s). If the range of the C<isl_union_map> consists of
6969 elements in more than one space, then each of these spaces is handled
6970 separately in an arbitrary order.
6971 It should be noted that the image elements only specify the I<order>
6972 in which the corresponding domain elements should be visited.
6973 No direct relation between the image elements and the loop iterators
6974 in the generated AST should be assumed.
6976 Each AST is generated within a build. The initial build
6977 simply specifies the constraints on the parameters (if any)
6978 and can be created, inspected, copied and freed using the following functions.
6980 #include <isl/ast_build.h>
6981 __isl_give isl_ast_build *isl_ast_build_from_context(
6982 __isl_take isl_set *set);
6983 __isl_give isl_ast_build *isl_ast_build_copy(
6984 __isl_keep isl_ast_build *build);
6985 __isl_null isl_ast_build *isl_ast_build_free(
6986 __isl_take isl_ast_build *build);
6988 The C<set> argument is usually a parameter set with zero or more parameters.
6989 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6990 and L</"Fine-grained Control over AST Generation">.
6991 Finally, the AST itself can be constructed using the following
6994 #include <isl/ast_build.h>
6995 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6996 __isl_keep isl_ast_build *build,
6997 __isl_take isl_union_map *schedule);
6999 =head3 Inspecting the AST
7001 The basic properties of an AST node can be obtained as follows.
7003 #include <isl/ast.h>
7004 enum isl_ast_node_type isl_ast_node_get_type(
7005 __isl_keep isl_ast_node *node);
7007 The type of an AST node is one of
7008 C<isl_ast_node_for>,
7010 C<isl_ast_node_block> or
7011 C<isl_ast_node_user>.
7012 An C<isl_ast_node_for> represents a for node.
7013 An C<isl_ast_node_if> represents an if node.
7014 An C<isl_ast_node_block> represents a compound node.
7015 An C<isl_ast_node_user> represents an expression statement.
7016 An expression statement typically corresponds to a domain element, i.e.,
7017 one of the elements that is visited by the AST.
7019 Each type of node has its own additional properties.
7021 #include <isl/ast.h>
7022 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7023 __isl_keep isl_ast_node *node);
7024 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7025 __isl_keep isl_ast_node *node);
7026 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7027 __isl_keep isl_ast_node *node);
7028 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7029 __isl_keep isl_ast_node *node);
7030 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7031 __isl_keep isl_ast_node *node);
7032 int isl_ast_node_for_is_degenerate(
7033 __isl_keep isl_ast_node *node);
7035 An C<isl_ast_for> is considered degenerate if it is known to execute
7038 #include <isl/ast.h>
7039 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7040 __isl_keep isl_ast_node *node);
7041 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7042 __isl_keep isl_ast_node *node);
7043 int isl_ast_node_if_has_else(
7044 __isl_keep isl_ast_node *node);
7045 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7046 __isl_keep isl_ast_node *node);
7048 __isl_give isl_ast_node_list *
7049 isl_ast_node_block_get_children(
7050 __isl_keep isl_ast_node *node);
7052 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7053 __isl_keep isl_ast_node *node);
7055 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7056 the following functions.
7058 #include <isl/ast.h>
7059 enum isl_ast_expr_type isl_ast_expr_get_type(
7060 __isl_keep isl_ast_expr *expr);
7062 The type of an AST expression is one of
7064 C<isl_ast_expr_id> or
7065 C<isl_ast_expr_int>.
7066 An C<isl_ast_expr_op> represents the result of an operation.
7067 An C<isl_ast_expr_id> represents an identifier.
7068 An C<isl_ast_expr_int> represents an integer value.
7070 Each type of expression has its own additional properties.
7072 #include <isl/ast.h>
7073 enum isl_ast_op_type isl_ast_expr_get_op_type(
7074 __isl_keep isl_ast_expr *expr);
7075 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7076 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7077 __isl_keep isl_ast_expr *expr, int pos);
7078 int isl_ast_node_foreach_ast_op_type(
7079 __isl_keep isl_ast_node *node,
7080 int (*fn)(enum isl_ast_op_type type, void *user),
7083 C<isl_ast_expr_get_op_type> returns the type of the operation
7084 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7085 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7087 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7088 C<isl_ast_op_type> that appears in C<node>.
7089 The operation type is one of the following.
7093 =item C<isl_ast_op_and>
7095 Logical I<and> of two arguments.
7096 Both arguments can be evaluated.
7098 =item C<isl_ast_op_and_then>
7100 Logical I<and> of two arguments.
7101 The second argument can only be evaluated if the first evaluates to true.
7103 =item C<isl_ast_op_or>
7105 Logical I<or> of two arguments.
7106 Both arguments can be evaluated.
7108 =item C<isl_ast_op_or_else>
7110 Logical I<or> of two arguments.
7111 The second argument can only be evaluated if the first evaluates to false.
7113 =item C<isl_ast_op_max>
7115 Maximum of two or more arguments.
7117 =item C<isl_ast_op_min>
7119 Minimum of two or more arguments.
7121 =item C<isl_ast_op_minus>
7125 =item C<isl_ast_op_add>
7127 Sum of two arguments.
7129 =item C<isl_ast_op_sub>
7131 Difference of two arguments.
7133 =item C<isl_ast_op_mul>
7135 Product of two arguments.
7137 =item C<isl_ast_op_div>
7139 Exact division. That is, the result is known to be an integer.
7141 =item C<isl_ast_op_fdiv_q>
7143 Result of integer division, rounded towards negative
7146 =item C<isl_ast_op_pdiv_q>
7148 Result of integer division, where dividend is known to be non-negative.
7150 =item C<isl_ast_op_pdiv_r>
7152 Remainder of integer division, where dividend is known to be non-negative.
7154 =item C<isl_ast_op_zdiv_r>
7156 Equal to zero iff the remainder on integer division is zero.
7158 =item C<isl_ast_op_cond>
7160 Conditional operator defined on three arguments.
7161 If the first argument evaluates to true, then the result
7162 is equal to the second argument. Otherwise, the result
7163 is equal to the third argument.
7164 The second and third argument may only be evaluated if
7165 the first argument evaluates to true and false, respectively.
7166 Corresponds to C<a ? b : c> in C.
7168 =item C<isl_ast_op_select>
7170 Conditional operator defined on three arguments.
7171 If the first argument evaluates to true, then the result
7172 is equal to the second argument. Otherwise, the result
7173 is equal to the third argument.
7174 The second and third argument may be evaluated independently
7175 of the value of the first argument.
7176 Corresponds to C<a * b + (1 - a) * c> in C.
7178 =item C<isl_ast_op_eq>
7182 =item C<isl_ast_op_le>
7184 Less than or equal relation.
7186 =item C<isl_ast_op_lt>
7190 =item C<isl_ast_op_ge>
7192 Greater than or equal relation.
7194 =item C<isl_ast_op_gt>
7196 Greater than relation.
7198 =item C<isl_ast_op_call>
7201 The number of arguments of the C<isl_ast_expr> is one more than
7202 the number of arguments in the function call, the first argument
7203 representing the function being called.
7205 =item C<isl_ast_op_access>
7208 The number of arguments of the C<isl_ast_expr> is one more than
7209 the number of index expressions in the array access, the first argument
7210 representing the array being accessed.
7212 =item C<isl_ast_op_member>
7215 This operation has two arguments, a structure and the name of
7216 the member of the structure being accessed.
7220 #include <isl/ast.h>
7221 __isl_give isl_id *isl_ast_expr_get_id(
7222 __isl_keep isl_ast_expr *expr);
7224 Return the identifier represented by the AST expression.
7226 #include <isl/ast.h>
7227 __isl_give isl_val *isl_ast_expr_get_val(
7228 __isl_keep isl_ast_expr *expr);
7230 Return the integer represented by the AST expression.
7232 =head3 Properties of ASTs
7234 #include <isl/ast.h>
7235 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7236 __isl_keep isl_ast_expr *expr2);
7238 Check if two C<isl_ast_expr>s are equal to each other.
7240 =head3 Manipulating and printing the AST
7242 AST nodes can be copied and freed using the following functions.
7244 #include <isl/ast.h>
7245 __isl_give isl_ast_node *isl_ast_node_copy(
7246 __isl_keep isl_ast_node *node);
7247 __isl_null isl_ast_node *isl_ast_node_free(
7248 __isl_take isl_ast_node *node);
7250 AST expressions can be copied and freed using the following functions.
7252 #include <isl/ast.h>
7253 __isl_give isl_ast_expr *isl_ast_expr_copy(
7254 __isl_keep isl_ast_expr *expr);
7255 __isl_null isl_ast_expr *isl_ast_expr_free(
7256 __isl_take isl_ast_expr *expr);
7258 New AST expressions can be created either directly or within
7259 the context of an C<isl_ast_build>.
7261 #include <isl/ast.h>
7262 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7263 __isl_take isl_val *v);
7264 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7265 __isl_take isl_id *id);
7266 __isl_give isl_ast_expr *isl_ast_expr_neg(
7267 __isl_take isl_ast_expr *expr);
7268 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7269 __isl_take isl_ast_expr *expr);
7270 __isl_give isl_ast_expr *isl_ast_expr_add(
7271 __isl_take isl_ast_expr *expr1,
7272 __isl_take isl_ast_expr *expr2);
7273 __isl_give isl_ast_expr *isl_ast_expr_sub(
7274 __isl_take isl_ast_expr *expr1,
7275 __isl_take isl_ast_expr *expr2);
7276 __isl_give isl_ast_expr *isl_ast_expr_mul(
7277 __isl_take isl_ast_expr *expr1,
7278 __isl_take isl_ast_expr *expr2);
7279 __isl_give isl_ast_expr *isl_ast_expr_div(
7280 __isl_take isl_ast_expr *expr1,
7281 __isl_take isl_ast_expr *expr2);
7282 __isl_give isl_ast_expr *isl_ast_expr_and(
7283 __isl_take isl_ast_expr *expr1,
7284 __isl_take isl_ast_expr *expr2)
7285 __isl_give isl_ast_expr *isl_ast_expr_or(
7286 __isl_take isl_ast_expr *expr1,
7287 __isl_take isl_ast_expr *expr2)
7288 __isl_give isl_ast_expr *isl_ast_expr_eq(
7289 __isl_take isl_ast_expr *expr1,
7290 __isl_take isl_ast_expr *expr2);
7291 __isl_give isl_ast_expr *isl_ast_expr_le(
7292 __isl_take isl_ast_expr *expr1,
7293 __isl_take isl_ast_expr *expr2);
7294 __isl_give isl_ast_expr *isl_ast_expr_lt(
7295 __isl_take isl_ast_expr *expr1,
7296 __isl_take isl_ast_expr *expr2);
7297 __isl_give isl_ast_expr *isl_ast_expr_ge(
7298 __isl_take isl_ast_expr *expr1,
7299 __isl_take isl_ast_expr *expr2);
7300 __isl_give isl_ast_expr *isl_ast_expr_gt(
7301 __isl_take isl_ast_expr *expr1,
7302 __isl_take isl_ast_expr *expr2);
7303 __isl_give isl_ast_expr *isl_ast_expr_access(
7304 __isl_take isl_ast_expr *array,
7305 __isl_take isl_ast_expr_list *indices);
7307 The function C<isl_ast_expr_address_of> can be applied to an
7308 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
7309 to represent the address of the C<isl_ast_expr_access>.
7311 #include <isl/ast_build.h>
7312 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
7313 __isl_keep isl_ast_build *build,
7314 __isl_take isl_pw_aff *pa);
7315 __isl_give isl_ast_expr *
7316 isl_ast_build_access_from_pw_multi_aff(
7317 __isl_keep isl_ast_build *build,
7318 __isl_take isl_pw_multi_aff *pma);
7319 __isl_give isl_ast_expr *
7320 isl_ast_build_access_from_multi_pw_aff(
7321 __isl_keep isl_ast_build *build,
7322 __isl_take isl_multi_pw_aff *mpa);
7323 __isl_give isl_ast_expr *
7324 isl_ast_build_call_from_pw_multi_aff(
7325 __isl_keep isl_ast_build *build,
7326 __isl_take isl_pw_multi_aff *pma);
7327 __isl_give isl_ast_expr *
7328 isl_ast_build_call_from_multi_pw_aff(
7329 __isl_keep isl_ast_build *build,
7330 __isl_take isl_multi_pw_aff *mpa);
7332 The domains of C<pa>, C<mpa> and C<pma> should correspond
7333 to the schedule space of C<build>.
7334 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
7335 the function being called.
7336 If the accessed space is a nested relation, then it is taken
7337 to represent an access of the member specified by the range
7338 of this nested relation of the structure specified by the domain
7339 of the nested relation.
7341 The following functions can be used to modify an C<isl_ast_expr>.
7343 #include <isl/ast.h>
7344 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
7345 __isl_take isl_ast_expr *expr, int pos,
7346 __isl_take isl_ast_expr *arg);
7348 Replace the argument of C<expr> at position C<pos> by C<arg>.
7350 #include <isl/ast.h>
7351 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
7352 __isl_take isl_ast_expr *expr,
7353 __isl_take isl_id_to_ast_expr *id2expr);
7355 The function C<isl_ast_expr_substitute_ids> replaces the
7356 subexpressions of C<expr> of type C<isl_ast_expr_id>
7357 by the corresponding expression in C<id2expr>, if there is any.
7360 User specified data can be attached to an C<isl_ast_node> and obtained
7361 from the same C<isl_ast_node> using the following functions.
7363 #include <isl/ast.h>
7364 __isl_give isl_ast_node *isl_ast_node_set_annotation(
7365 __isl_take isl_ast_node *node,
7366 __isl_take isl_id *annotation);
7367 __isl_give isl_id *isl_ast_node_get_annotation(
7368 __isl_keep isl_ast_node *node);
7370 Basic printing can be performed using the following functions.
7372 #include <isl/ast.h>
7373 __isl_give isl_printer *isl_printer_print_ast_expr(
7374 __isl_take isl_printer *p,
7375 __isl_keep isl_ast_expr *expr);
7376 __isl_give isl_printer *isl_printer_print_ast_node(
7377 __isl_take isl_printer *p,
7378 __isl_keep isl_ast_node *node);
7379 __isl_give char *isl_ast_expr_to_str(
7380 __isl_keep isl_ast_expr *expr);
7382 More advanced printing can be performed using the following functions.
7384 #include <isl/ast.h>
7385 __isl_give isl_printer *isl_ast_op_type_print_macro(
7386 enum isl_ast_op_type type,
7387 __isl_take isl_printer *p);
7388 __isl_give isl_printer *isl_ast_node_print_macros(
7389 __isl_keep isl_ast_node *node,
7390 __isl_take isl_printer *p);
7391 __isl_give isl_printer *isl_ast_node_print(
7392 __isl_keep isl_ast_node *node,
7393 __isl_take isl_printer *p,
7394 __isl_take isl_ast_print_options *options);
7395 __isl_give isl_printer *isl_ast_node_for_print(
7396 __isl_keep isl_ast_node *node,
7397 __isl_take isl_printer *p,
7398 __isl_take isl_ast_print_options *options);
7399 __isl_give isl_printer *isl_ast_node_if_print(
7400 __isl_keep isl_ast_node *node,
7401 __isl_take isl_printer *p,
7402 __isl_take isl_ast_print_options *options);
7404 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
7405 C<isl> may print out an AST that makes use of macros such
7406 as C<floord>, C<min> and C<max>.
7407 C<isl_ast_op_type_print_macro> prints out the macro
7408 corresponding to a specific C<isl_ast_op_type>.
7409 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
7410 for expressions where these macros would be used and prints
7411 out the required macro definitions.
7412 Essentially, C<isl_ast_node_print_macros> calls
7413 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
7414 as function argument.
7415 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
7416 C<isl_ast_node_if_print> print an C<isl_ast_node>
7417 in C<ISL_FORMAT_C>, but allow for some extra control
7418 through an C<isl_ast_print_options> object.
7419 This object can be created using the following functions.
7421 #include <isl/ast.h>
7422 __isl_give isl_ast_print_options *
7423 isl_ast_print_options_alloc(isl_ctx *ctx);
7424 __isl_give isl_ast_print_options *
7425 isl_ast_print_options_copy(
7426 __isl_keep isl_ast_print_options *options);
7427 __isl_null isl_ast_print_options *
7428 isl_ast_print_options_free(
7429 __isl_take isl_ast_print_options *options);
7431 __isl_give isl_ast_print_options *
7432 isl_ast_print_options_set_print_user(
7433 __isl_take isl_ast_print_options *options,
7434 __isl_give isl_printer *(*print_user)(
7435 __isl_take isl_printer *p,
7436 __isl_take isl_ast_print_options *options,
7437 __isl_keep isl_ast_node *node, void *user),
7439 __isl_give isl_ast_print_options *
7440 isl_ast_print_options_set_print_for(
7441 __isl_take isl_ast_print_options *options,
7442 __isl_give isl_printer *(*print_for)(
7443 __isl_take isl_printer *p,
7444 __isl_take isl_ast_print_options *options,
7445 __isl_keep isl_ast_node *node, void *user),
7448 The callback set by C<isl_ast_print_options_set_print_user>
7449 is called whenever a node of type C<isl_ast_node_user> needs to
7451 The callback set by C<isl_ast_print_options_set_print_for>
7452 is called whenever a node of type C<isl_ast_node_for> needs to
7454 Note that C<isl_ast_node_for_print> will I<not> call the
7455 callback set by C<isl_ast_print_options_set_print_for> on the node
7456 on which C<isl_ast_node_for_print> is called, but only on nested
7457 nodes of type C<isl_ast_node_for>. It is therefore safe to
7458 call C<isl_ast_node_for_print> from within the callback set by
7459 C<isl_ast_print_options_set_print_for>.
7461 The following option determines the type to be used for iterators
7462 while printing the AST.
7464 int isl_options_set_ast_iterator_type(
7465 isl_ctx *ctx, const char *val);
7466 const char *isl_options_get_ast_iterator_type(
7469 The AST printer only prints body nodes as blocks if these
7470 blocks cannot be safely omitted.
7471 For example, a C<for> node with one body node will not be
7472 surrounded with braces in C<ISL_FORMAT_C>.
7473 A block will always be printed by setting the following option.
7475 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
7477 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
7481 #include <isl/ast_build.h>
7482 int isl_options_set_ast_build_atomic_upper_bound(
7483 isl_ctx *ctx, int val);
7484 int isl_options_get_ast_build_atomic_upper_bound(
7486 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
7488 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
7489 int isl_options_set_ast_build_exploit_nested_bounds(
7490 isl_ctx *ctx, int val);
7491 int isl_options_get_ast_build_exploit_nested_bounds(
7493 int isl_options_set_ast_build_group_coscheduled(
7494 isl_ctx *ctx, int val);
7495 int isl_options_get_ast_build_group_coscheduled(
7497 int isl_options_set_ast_build_scale_strides(
7498 isl_ctx *ctx, int val);
7499 int isl_options_get_ast_build_scale_strides(
7501 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
7503 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
7504 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
7506 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
7510 =item * ast_build_atomic_upper_bound
7512 Generate loop upper bounds that consist of the current loop iterator,
7513 an operator and an expression not involving the iterator.
7514 If this option is not set, then the current loop iterator may appear
7515 several times in the upper bound.
7516 For example, when this option is turned off, AST generation
7519 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
7523 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
7526 When the option is turned on, the following AST is generated
7528 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
7531 =item * ast_build_prefer_pdiv
7533 If this option is turned off, then the AST generation will
7534 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
7535 operators, but no C<isl_ast_op_pdiv_q> or
7536 C<isl_ast_op_pdiv_r> operators.
7537 If this options is turned on, then C<isl> will try to convert
7538 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
7539 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
7541 =item * ast_build_exploit_nested_bounds
7543 Simplify conditions based on bounds of nested for loops.
7544 In particular, remove conditions that are implied by the fact
7545 that one or more nested loops have at least one iteration,
7546 meaning that the upper bound is at least as large as the lower bound.
7547 For example, when this option is turned off, AST generation
7550 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
7556 for (int c0 = 0; c0 <= N; c0 += 1)
7557 for (int c1 = 0; c1 <= M; c1 += 1)
7560 When the option is turned on, the following AST is generated
7562 for (int c0 = 0; c0 <= N; c0 += 1)
7563 for (int c1 = 0; c1 <= M; c1 += 1)
7566 =item * ast_build_group_coscheduled
7568 If two domain elements are assigned the same schedule point, then
7569 they may be executed in any order and they may even appear in different
7570 loops. If this options is set, then the AST generator will make
7571 sure that coscheduled domain elements do not appear in separate parts
7572 of the AST. This is useful in case of nested AST generation
7573 if the outer AST generation is given only part of a schedule
7574 and the inner AST generation should handle the domains that are
7575 coscheduled by this initial part of the schedule together.
7576 For example if an AST is generated for a schedule
7578 { A[i] -> [0]; B[i] -> [0] }
7580 then the C<isl_ast_build_set_create_leaf> callback described
7581 below may get called twice, once for each domain.
7582 Setting this option ensures that the callback is only called once
7583 on both domains together.
7585 =item * ast_build_separation_bounds
7587 This option specifies which bounds to use during separation.
7588 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
7589 then all (possibly implicit) bounds on the current dimension will
7590 be used during separation.
7591 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
7592 then only those bounds that are explicitly available will
7593 be used during separation.
7595 =item * ast_build_scale_strides
7597 This option specifies whether the AST generator is allowed
7598 to scale down iterators of strided loops.
7600 =item * ast_build_allow_else
7602 This option specifies whether the AST generator is allowed
7603 to construct if statements with else branches.
7605 =item * ast_build_allow_or
7607 This option specifies whether the AST generator is allowed
7608 to construct if conditions with disjunctions.
7612 =head3 Fine-grained Control over AST Generation
7614 Besides specifying the constraints on the parameters,
7615 an C<isl_ast_build> object can be used to control
7616 various aspects of the AST generation process.
7617 The most prominent way of control is through ``options'',
7618 which can be set using the following function.
7620 #include <isl/ast_build.h>
7621 __isl_give isl_ast_build *
7622 isl_ast_build_set_options(
7623 __isl_take isl_ast_build *control,
7624 __isl_take isl_union_map *options);
7626 The options are encoded in an C<isl_union_map>.
7627 The domain of this union relation refers to the schedule domain,
7628 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
7629 In the case of nested AST generation (see L</"Nested AST Generation">),
7630 the domain of C<options> should refer to the extra piece of the schedule.
7631 That is, it should be equal to the range of the wrapped relation in the
7632 range of the schedule.
7633 The range of the options can consist of elements in one or more spaces,
7634 the names of which determine the effect of the option.
7635 The values of the range typically also refer to the schedule dimension
7636 to which the option applies. In case of nested AST generation
7637 (see L</"Nested AST Generation">), these values refer to the position
7638 of the schedule dimension within the innermost AST generation.
7639 The constraints on the domain elements of
7640 the option should only refer to this dimension and earlier dimensions.
7641 We consider the following spaces.
7645 =item C<separation_class>
7647 This space is a wrapped relation between two one dimensional spaces.
7648 The input space represents the schedule dimension to which the option
7649 applies and the output space represents the separation class.
7650 While constructing a loop corresponding to the specified schedule
7651 dimension(s), the AST generator will try to generate separate loops
7652 for domain elements that are assigned different classes.
7653 If only some of the elements are assigned a class, then those elements
7654 that are not assigned any class will be treated as belonging to a class
7655 that is separate from the explicitly assigned classes.
7656 The typical use case for this option is to separate full tiles from
7658 The other options, described below, are applied after the separation
7661 As an example, consider the separation into full and partial tiles
7662 of a tiling of a triangular domain.
7663 Take, for example, the domain
7665 { A[i,j] : 0 <= i,j and i + j <= 100 }
7667 and a tiling into tiles of 10 by 10. The input to the AST generator
7668 is then the schedule
7670 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7673 Without any options, the following AST is generated
7675 for (int c0 = 0; c0 <= 10; c0 += 1)
7676 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7677 for (int c2 = 10 * c0;
7678 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7680 for (int c3 = 10 * c1;
7681 c3 <= min(10 * c1 + 9, -c2 + 100);
7685 Separation into full and partial tiles can be obtained by assigning
7686 a class, say C<0>, to the full tiles. The full tiles are represented by those
7687 values of the first and second schedule dimensions for which there are
7688 values of the third and fourth dimensions to cover an entire tile.
7689 That is, we need to specify the following option
7691 { [a,b,c,d] -> separation_class[[0]->[0]] :
7692 exists b': 0 <= 10a,10b' and
7693 10a+9+10b'+9 <= 100;
7694 [a,b,c,d] -> separation_class[[1]->[0]] :
7695 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7699 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7700 a >= 0 and b >= 0 and b <= 8 - a;
7701 [a, b, c, d] -> separation_class[[0] -> [0]] :
7704 With this option, the generated AST is as follows
7707 for (int c0 = 0; c0 <= 8; c0 += 1) {
7708 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7709 for (int c2 = 10 * c0;
7710 c2 <= 10 * c0 + 9; c2 += 1)
7711 for (int c3 = 10 * c1;
7712 c3 <= 10 * c1 + 9; c3 += 1)
7714 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7715 for (int c2 = 10 * c0;
7716 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7718 for (int c3 = 10 * c1;
7719 c3 <= min(-c2 + 100, 10 * c1 + 9);
7723 for (int c0 = 9; c0 <= 10; c0 += 1)
7724 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7725 for (int c2 = 10 * c0;
7726 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7728 for (int c3 = 10 * c1;
7729 c3 <= min(10 * c1 + 9, -c2 + 100);
7736 This is a single-dimensional space representing the schedule dimension(s)
7737 to which ``separation'' should be applied. Separation tries to split
7738 a loop into several pieces if this can avoid the generation of guards
7740 See also the C<atomic> option.
7744 This is a single-dimensional space representing the schedule dimension(s)
7745 for which the domains should be considered ``atomic''. That is, the
7746 AST generator will make sure that any given domain space will only appear
7747 in a single loop at the specified level.
7749 Consider the following schedule
7751 { a[i] -> [i] : 0 <= i < 10;
7752 b[i] -> [i+1] : 0 <= i < 10 }
7754 If the following option is specified
7756 { [i] -> separate[x] }
7758 then the following AST will be generated
7762 for (int c0 = 1; c0 <= 9; c0 += 1) {
7769 If, on the other hand, the following option is specified
7771 { [i] -> atomic[x] }
7773 then the following AST will be generated
7775 for (int c0 = 0; c0 <= 10; c0 += 1) {
7782 If neither C<atomic> nor C<separate> is specified, then the AST generator
7783 may produce either of these two results or some intermediate form.
7787 This is a single-dimensional space representing the schedule dimension(s)
7788 that should be I<completely> unrolled.
7789 To obtain a partial unrolling, the user should apply an additional
7790 strip-mining to the schedule and fully unroll the inner loop.
7794 Additional control is available through the following functions.
7796 #include <isl/ast_build.h>
7797 __isl_give isl_ast_build *
7798 isl_ast_build_set_iterators(
7799 __isl_take isl_ast_build *control,
7800 __isl_take isl_id_list *iterators);
7802 The function C<isl_ast_build_set_iterators> allows the user to
7803 specify a list of iterator C<isl_id>s to be used as iterators.
7804 If the input schedule is injective, then
7805 the number of elements in this list should be as large as the dimension
7806 of the schedule space, but no direct correspondence should be assumed
7807 between dimensions and elements.
7808 If the input schedule is not injective, then an additional number
7809 of C<isl_id>s equal to the largest dimension of the input domains
7811 If the number of provided C<isl_id>s is insufficient, then additional
7812 names are automatically generated.
7814 #include <isl/ast_build.h>
7815 __isl_give isl_ast_build *
7816 isl_ast_build_set_create_leaf(
7817 __isl_take isl_ast_build *control,
7818 __isl_give isl_ast_node *(*fn)(
7819 __isl_take isl_ast_build *build,
7820 void *user), void *user);
7823 C<isl_ast_build_set_create_leaf> function allows for the
7824 specification of a callback that should be called whenever the AST
7825 generator arrives at an element of the schedule domain.
7826 The callback should return an AST node that should be inserted
7827 at the corresponding position of the AST. The default action (when
7828 the callback is not set) is to continue generating parts of the AST to scan
7829 all the domain elements associated to the schedule domain element
7830 and to insert user nodes, ``calling'' the domain element, for each of them.
7831 The C<build> argument contains the current state of the C<isl_ast_build>.
7832 To ease nested AST generation (see L</"Nested AST Generation">),
7833 all control information that is
7834 specific to the current AST generation such as the options and
7835 the callbacks has been removed from this C<isl_ast_build>.
7836 The callback would typically return the result of a nested
7838 user defined node created using the following function.
7840 #include <isl/ast.h>
7841 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7842 __isl_take isl_ast_expr *expr);
7844 #include <isl/ast_build.h>
7845 __isl_give isl_ast_build *
7846 isl_ast_build_set_at_each_domain(
7847 __isl_take isl_ast_build *build,
7848 __isl_give isl_ast_node *(*fn)(
7849 __isl_take isl_ast_node *node,
7850 __isl_keep isl_ast_build *build,
7851 void *user), void *user);
7852 __isl_give isl_ast_build *
7853 isl_ast_build_set_before_each_for(
7854 __isl_take isl_ast_build *build,
7855 __isl_give isl_id *(*fn)(
7856 __isl_keep isl_ast_build *build,
7857 void *user), void *user);
7858 __isl_give isl_ast_build *
7859 isl_ast_build_set_after_each_for(
7860 __isl_take isl_ast_build *build,
7861 __isl_give isl_ast_node *(*fn)(
7862 __isl_take isl_ast_node *node,
7863 __isl_keep isl_ast_build *build,
7864 void *user), void *user);
7866 The callback set by C<isl_ast_build_set_at_each_domain> will
7867 be called for each domain AST node.
7868 The callbacks set by C<isl_ast_build_set_before_each_for>
7869 and C<isl_ast_build_set_after_each_for> will be called
7870 for each for AST node. The first will be called in depth-first
7871 pre-order, while the second will be called in depth-first post-order.
7872 Since C<isl_ast_build_set_before_each_for> is called before the for
7873 node is actually constructed, it is only passed an C<isl_ast_build>.
7874 The returned C<isl_id> will be added as an annotation (using
7875 C<isl_ast_node_set_annotation>) to the constructed for node.
7876 In particular, if the user has also specified an C<after_each_for>
7877 callback, then the annotation can be retrieved from the node passed to
7878 that callback using C<isl_ast_node_get_annotation>.
7879 All callbacks should C<NULL> on failure.
7880 The given C<isl_ast_build> can be used to create new
7881 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7882 or C<isl_ast_build_call_from_pw_multi_aff>.
7884 =head3 Nested AST Generation
7886 C<isl> allows the user to create an AST within the context
7887 of another AST. These nested ASTs are created using the
7888 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7889 outer AST. The C<build> argument should be an C<isl_ast_build>
7890 passed to a callback set by
7891 C<isl_ast_build_set_create_leaf>.
7892 The space of the range of the C<schedule> argument should refer
7893 to this build. In particular, the space should be a wrapped
7894 relation and the domain of this wrapped relation should be the
7895 same as that of the range of the schedule returned by
7896 C<isl_ast_build_get_schedule> below.
7897 In practice, the new schedule is typically
7898 created by calling C<isl_union_map_range_product> on the old schedule
7899 and some extra piece of the schedule.
7900 The space of the schedule domain is also available from
7901 the C<isl_ast_build>.
7903 #include <isl/ast_build.h>
7904 __isl_give isl_union_map *isl_ast_build_get_schedule(
7905 __isl_keep isl_ast_build *build);
7906 __isl_give isl_space *isl_ast_build_get_schedule_space(
7907 __isl_keep isl_ast_build *build);
7908 __isl_give isl_ast_build *isl_ast_build_restrict(
7909 __isl_take isl_ast_build *build,
7910 __isl_take isl_set *set);
7912 The C<isl_ast_build_get_schedule> function returns a (partial)
7913 schedule for the domains elements for which part of the AST still needs to
7914 be generated in the current build.
7915 In particular, the domain elements are mapped to those iterations of the loops
7916 enclosing the current point of the AST generation inside which
7917 the domain elements are executed.
7918 No direct correspondence between
7919 the input schedule and this schedule should be assumed.
7920 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7921 to create a set for C<isl_ast_build_restrict> to intersect
7922 with the current build. In particular, the set passed to
7923 C<isl_ast_build_restrict> can have additional parameters.
7924 The ids of the set dimensions in the space returned by
7925 C<isl_ast_build_get_schedule_space> correspond to the
7926 iterators of the already generated loops.
7927 The user should not rely on the ids of the output dimensions
7928 of the relations in the union relation returned by
7929 C<isl_ast_build_get_schedule> having any particular value.
7933 Although C<isl> is mainly meant to be used as a library,
7934 it also contains some basic applications that use some
7935 of the functionality of C<isl>.
7936 The input may be specified in either the L<isl format>
7937 or the L<PolyLib format>.
7939 =head2 C<isl_polyhedron_sample>
7941 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7942 an integer element of the polyhedron, if there is any.
7943 The first column in the output is the denominator and is always
7944 equal to 1. If the polyhedron contains no integer points,
7945 then a vector of length zero is printed.
7949 C<isl_pip> takes the same input as the C<example> program
7950 from the C<piplib> distribution, i.e., a set of constraints
7951 on the parameters, a line containing only -1 and finally a set
7952 of constraints on a parametric polyhedron.
7953 The coefficients of the parameters appear in the last columns
7954 (but before the final constant column).
7955 The output is the lexicographic minimum of the parametric polyhedron.
7956 As C<isl> currently does not have its own output format, the output
7957 is just a dump of the internal state.
7959 =head2 C<isl_polyhedron_minimize>
7961 C<isl_polyhedron_minimize> computes the minimum of some linear
7962 or affine objective function over the integer points in a polyhedron.
7963 If an affine objective function
7964 is given, then the constant should appear in the last column.
7966 =head2 C<isl_polytope_scan>
7968 Given a polytope, C<isl_polytope_scan> prints
7969 all integer points in the polytope.
7971 =head2 C<isl_codegen>
7973 Given a schedule, a context set and an options relation,
7974 C<isl_codegen> prints out an AST that scans the domain elements
7975 of the schedule in the order of their image(s) taking into account
7976 the constraints in the context set.