3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
8 using C<GMP> or C<imath>.
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
184 =head3 Changes since isl-0.12
188 =item * C<isl_int> has been replaced by C<isl_val>.
189 Some of the old functions are still available in C<isl/deprecated/*.h>
190 but they will be removed in the future.
192 =item * The functions C<isl_pw_qpolynomial_eval>,
193 C<isl_union_pw_qpolynomial_eval>, C<isl_pw_qpolynomial_fold_eval>
194 and C<isl_union_pw_qpolynomial_fold_eval> have been changed to return
195 an C<isl_val> instead of an C<isl_qpolynomial>.
197 =item * The function C<isl_band_member_is_zero_distance>
198 has been removed. Essentially the same functionality is available
199 through C<isl_band_member_is_coincident>, except that is requires
200 setting up coincidence constraints.
201 The option C<schedule_outer_zero_distance> has accordingly been
202 replaced by the option C<schedule_outer_coincidence>.
204 =item * The function C<isl_vertex_get_expr> has been changed
205 to return an C<isl_multi_aff> instead of a rational C<isl_basic_set>.
206 The function C<isl_vertex_get_domain> has been changed to return
207 a regular basic set, rather than a rational basic set.
211 =head3 Changes since isl-0.14
215 =item * Objects of type C<isl_union_pw_multi_aff> can no longer contain
216 two or more C<isl_pw_multi_aff> objects with the same domain space.
218 =item * The function C<isl_union_pw_multi_aff_add> now consistently
219 computes the sum on the shared definition domain.
220 The function C<isl_union_pw_multi_aff_union_add> has been added
221 to compute the sum on the union of definition domains.
222 The original behavior of C<isl_union_pw_multi_aff_add> was
223 confused and is no longer available.
229 C<isl> is released under the MIT license.
233 Permission is hereby granted, free of charge, to any person obtaining a copy of
234 this software and associated documentation files (the "Software"), to deal in
235 the Software without restriction, including without limitation the rights to
236 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
237 of the Software, and to permit persons to whom the Software is furnished to do
238 so, subject to the following conditions:
240 The above copyright notice and this permission notice shall be included in all
241 copies or substantial portions of the Software.
243 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
244 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
245 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
246 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
247 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
248 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
253 Note that by default C<isl> requires C<GMP>, which is released
254 under the GNU Lesser General Public License (LGPL). This means
255 that code linked against C<isl> is also linked against LGPL code.
257 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
258 library for exact integer arithmetic released under the MIT license.
262 The source of C<isl> can be obtained either as a tarball
263 or from the git repository. Both are available from
264 L<http://freshmeat.net/projects/isl/>.
265 The installation process depends on how you obtained
268 =head2 Installation from the git repository
272 =item 1 Clone or update the repository
274 The first time the source is obtained, you need to clone
277 git clone git://repo.or.cz/isl.git
279 To obtain updates, you need to pull in the latest changes
283 =item 2 Optionally get C<imath> submodule
285 To build C<isl> with C<imath>, you need to obtain the C<imath>
286 submodule by running in the git source tree of C<isl>
291 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
293 =item 2 Generate C<configure>
299 After performing the above steps, continue
300 with the L<Common installation instructions>.
302 =head2 Common installation instructions
306 =item 1 Obtain C<GMP>
308 By default, building C<isl> requires C<GMP>, including its headers files.
309 Your distribution may not provide these header files by default
310 and you may need to install a package called C<gmp-devel> or something
311 similar. Alternatively, C<GMP> can be built from
312 source, available from L<http://gmplib.org/>.
313 C<GMP> is not needed if you build C<isl> with C<imath>.
317 C<isl> uses the standard C<autoconf> C<configure> script.
322 optionally followed by some configure options.
323 A complete list of options can be obtained by running
327 Below we discuss some of the more common options.
333 Installation prefix for C<isl>
335 =item C<--with-int=[gmp|imath]>
337 Select the integer library to be used by C<isl>, the default is C<gmp>.
338 Note that C<isl> may run significantly slower if you use C<imath>.
340 =item C<--with-gmp-prefix>
342 Installation prefix for C<GMP> (architecture-independent files).
344 =item C<--with-gmp-exec-prefix>
346 Installation prefix for C<GMP> (architecture-dependent files).
354 =item 4 Install (optional)
360 =head1 Integer Set Library
362 =head2 Memory Management
364 Since a high-level operation on isl objects usually involves
365 several substeps and since the user is usually not interested in
366 the intermediate results, most functions that return a new object
367 will also release all the objects passed as arguments.
368 If the user still wants to use one or more of these arguments
369 after the function call, she should pass along a copy of the
370 object rather than the object itself.
371 The user is then responsible for making sure that the original
372 object gets used somewhere else or is explicitly freed.
374 The arguments and return values of all documented functions are
375 annotated to make clear which arguments are released and which
376 arguments are preserved. In particular, the following annotations
383 C<__isl_give> means that a new object is returned.
384 The user should make sure that the returned pointer is
385 used exactly once as a value for an C<__isl_take> argument.
386 In between, it can be used as a value for as many
387 C<__isl_keep> arguments as the user likes.
388 There is one exception, and that is the case where the
389 pointer returned is C<NULL>. Is this case, the user
390 is free to use it as an C<__isl_take> argument or not.
391 When applied to a C<char *>, the returned pointer needs to be
396 C<__isl_null> means that a C<NULL> value is returned.
400 C<__isl_take> means that the object the argument points to
401 is taken over by the function and may no longer be used
402 by the user as an argument to any other function.
403 The pointer value must be one returned by a function
404 returning an C<__isl_give> pointer.
405 If the user passes in a C<NULL> value, then this will
406 be treated as an error in the sense that the function will
407 not perform its usual operation. However, it will still
408 make sure that all the other C<__isl_take> arguments
413 C<__isl_keep> means that the function will only use the object
414 temporarily. After the function has finished, the user
415 can still use it as an argument to other functions.
416 A C<NULL> value will be treated in the same way as
417 a C<NULL> value for an C<__isl_take> argument.
418 This annotation may also be used on return values of
419 type C<const char *>, in which case the returned pointer should
420 not be freed by the user and is only valid until the object
421 from which it was derived is updated or freed.
425 =head2 Initialization
427 All manipulations of integer sets and relations occur within
428 the context of an C<isl_ctx>.
429 A given C<isl_ctx> can only be used within a single thread.
430 All arguments of a function are required to have been allocated
431 within the same context.
432 There are currently no functions available for moving an object
433 from one C<isl_ctx> to another C<isl_ctx>. This means that
434 there is currently no way of safely moving an object from one
435 thread to another, unless the whole C<isl_ctx> is moved.
437 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
438 freed using C<isl_ctx_free>.
439 All objects allocated within an C<isl_ctx> should be freed
440 before the C<isl_ctx> itself is freed.
442 isl_ctx *isl_ctx_alloc();
443 void isl_ctx_free(isl_ctx *ctx);
445 The user can impose a bound on the number of low-level I<operations>
446 that can be performed by an C<isl_ctx>. This bound can be set and
447 retrieved using the following functions. A bound of zero means that
448 no bound is imposed. The number of operations performed can be
449 reset using C<isl_ctx_reset_operations>. Note that the number
450 of low-level operations needed to perform a high-level computation
451 may differ significantly across different versions
452 of C<isl>, but it should be the same across different platforms
453 for the same version of C<isl>.
455 Warning: This feature is experimental. C<isl> has good support to abort and
456 bail out during the computation, but this feature may exercise error code paths
457 that are normally not used that much. Consequently, it is not unlikely that
458 hidden bugs will be exposed.
460 void isl_ctx_set_max_operations(isl_ctx *ctx,
461 unsigned long max_operations);
462 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
463 void isl_ctx_reset_operations(isl_ctx *ctx);
465 In order to be able to create an object in the same context
466 as another object, most object types (described later in
467 this document) provide a function to obtain the context
468 in which the object was created.
471 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
472 isl_ctx *isl_multi_val_get_ctx(
473 __isl_keep isl_multi_val *mv);
476 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
478 #include <isl/local_space.h>
479 isl_ctx *isl_local_space_get_ctx(
480 __isl_keep isl_local_space *ls);
483 isl_ctx *isl_set_list_get_ctx(
484 __isl_keep isl_set_list *list);
487 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
488 isl_ctx *isl_multi_aff_get_ctx(
489 __isl_keep isl_multi_aff *maff);
490 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
491 isl_ctx *isl_pw_multi_aff_get_ctx(
492 __isl_keep isl_pw_multi_aff *pma);
493 isl_ctx *isl_multi_pw_aff_get_ctx(
494 __isl_keep isl_multi_pw_aff *mpa);
495 isl_ctx *isl_union_pw_multi_aff_get_ctx(
496 __isl_keep isl_union_pw_multi_aff *upma);
498 #include <isl/id_to_ast_expr.h>
499 isl_ctx *isl_id_to_ast_expr_get_ctx(
500 __isl_keep id_to_ast_expr *id2expr);
502 #include <isl/point.h>
503 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
506 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
509 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
511 #include <isl/vertices.h>
512 isl_ctx *isl_vertices_get_ctx(
513 __isl_keep isl_vertices *vertices);
514 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
515 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
517 #include <isl/flow.h>
518 isl_ctx *isl_restriction_get_ctx(
519 __isl_keep isl_restriction *restr);
521 #include <isl/schedule.h>
522 isl_ctx *isl_schedule_constraints_get_ctx(
523 __isl_keep isl_schedule_constraints *sc);
525 #include <isl/band.h>
526 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
528 #include <isl/ast_build.h>
529 isl_ctx *isl_ast_build_get_ctx(
530 __isl_keep isl_ast_build *build);
533 isl_ctx *isl_ast_expr_get_ctx(
534 __isl_keep isl_ast_expr *expr);
535 isl_ctx *isl_ast_node_get_ctx(
536 __isl_keep isl_ast_node *node);
540 An C<isl_val> represents an integer value, a rational value
541 or one of three special values, infinity, negative infinity and NaN.
542 Some predefined values can be created using the following functions.
545 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
546 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
547 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
548 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
549 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
550 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
552 Specific integer values can be created using the following functions.
555 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
557 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
559 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
560 size_t n, size_t size, const void *chunks);
562 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
563 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
564 The least significant digit is assumed to be stored first.
566 Value objects can be copied and freed using the following functions.
569 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
570 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
572 They can be inspected using the following functions.
575 long isl_val_get_num_si(__isl_keep isl_val *v);
576 long isl_val_get_den_si(__isl_keep isl_val *v);
577 double isl_val_get_d(__isl_keep isl_val *v);
578 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
580 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
581 size_t size, void *chunks);
583 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
584 of C<size> bytes needed to store the absolute value of the
586 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
587 which is assumed to have been preallocated by the caller.
588 The least significant digit is stored first.
589 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
590 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
591 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
593 An C<isl_val> can be modified using the following function.
596 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
599 The following unary properties are defined on C<isl_val>s.
602 int isl_val_sgn(__isl_keep isl_val *v);
603 int isl_val_is_zero(__isl_keep isl_val *v);
604 int isl_val_is_one(__isl_keep isl_val *v);
605 int isl_val_is_negone(__isl_keep isl_val *v);
606 int isl_val_is_nonneg(__isl_keep isl_val *v);
607 int isl_val_is_nonpos(__isl_keep isl_val *v);
608 int isl_val_is_pos(__isl_keep isl_val *v);
609 int isl_val_is_neg(__isl_keep isl_val *v);
610 int isl_val_is_int(__isl_keep isl_val *v);
611 int isl_val_is_rat(__isl_keep isl_val *v);
612 int isl_val_is_nan(__isl_keep isl_val *v);
613 int isl_val_is_infty(__isl_keep isl_val *v);
614 int isl_val_is_neginfty(__isl_keep isl_val *v);
616 Note that the sign of NaN is undefined.
618 The following binary properties are defined on pairs of C<isl_val>s.
621 int isl_val_lt(__isl_keep isl_val *v1,
622 __isl_keep isl_val *v2);
623 int isl_val_le(__isl_keep isl_val *v1,
624 __isl_keep isl_val *v2);
625 int isl_val_gt(__isl_keep isl_val *v1,
626 __isl_keep isl_val *v2);
627 int isl_val_ge(__isl_keep isl_val *v1,
628 __isl_keep isl_val *v2);
629 int isl_val_eq(__isl_keep isl_val *v1,
630 __isl_keep isl_val *v2);
631 int isl_val_ne(__isl_keep isl_val *v1,
632 __isl_keep isl_val *v2);
633 int isl_val_abs_eq(__isl_keep isl_val *v1,
634 __isl_keep isl_val *v2);
636 The function C<isl_val_abs_eq> checks whether its two arguments
637 are equal in absolute value.
639 For integer C<isl_val>s we additionally have the following binary property.
642 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
643 __isl_keep isl_val *v2);
645 An C<isl_val> can also be compared to an integer using the following
646 function. The result is undefined for NaN.
649 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
651 The following unary operations are available on C<isl_val>s.
654 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
655 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
656 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
657 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
658 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
659 __isl_give isl_val *isl_val_inv(__isl_take isl_val *v);
660 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
662 The following binary operations are available on C<isl_val>s.
665 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
666 __isl_take isl_val *v2);
667 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
668 __isl_take isl_val *v2);
669 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
670 __isl_take isl_val *v2);
671 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
673 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
674 __isl_take isl_val *v2);
675 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
677 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
678 __isl_take isl_val *v2);
679 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
681 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
682 __isl_take isl_val *v2);
684 On integer values, we additionally have the following operations.
687 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
688 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
689 __isl_take isl_val *v2);
690 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
691 __isl_take isl_val *v2);
692 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
693 __isl_take isl_val *v2, __isl_give isl_val **x,
694 __isl_give isl_val **y);
696 The function C<isl_val_gcdext> returns the greatest common divisor g
697 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
698 that C<*x> * C<v1> + C<*y> * C<v2> = g.
700 =head3 GMP specific functions
702 These functions are only available if C<isl> has been compiled with C<GMP>
705 Specific integer and rational values can be created from C<GMP> values using
706 the following functions.
708 #include <isl/val_gmp.h>
709 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
711 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
712 const mpz_t n, const mpz_t d);
714 The numerator and denominator of a rational value can be extracted as
715 C<GMP> values using the following functions.
717 #include <isl/val_gmp.h>
718 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
719 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
721 =head2 Sets and Relations
723 C<isl> uses six types of objects for representing sets and relations,
724 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
725 C<isl_union_set> and C<isl_union_map>.
726 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
727 can be described as a conjunction of affine constraints, while
728 C<isl_set> and C<isl_map> represent unions of
729 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
730 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
731 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
732 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
733 where spaces are considered different if they have a different number
734 of dimensions and/or different names (see L<"Spaces">).
735 The difference between sets and relations (maps) is that sets have
736 one set of variables, while relations have two sets of variables,
737 input variables and output variables.
739 =head2 Error Handling
741 C<isl> supports different ways to react in case a runtime error is triggered.
742 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
743 with two maps that have incompatible spaces. There are three possible ways
744 to react on error: to warn, to continue or to abort.
746 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
747 the last error in the corresponding C<isl_ctx> and the function in which the
748 error was triggered returns C<NULL>. An error does not corrupt internal state,
749 such that isl can continue to be used. C<isl> also provides functions to
750 read the last error and to reset the memory that stores the last error. The
751 last error is only stored for information purposes. Its presence does not
752 change the behavior of C<isl>. Hence, resetting an error is not required to
753 continue to use isl, but only to observe new errors.
756 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
757 void isl_ctx_reset_error(isl_ctx *ctx);
759 Another option is to continue on error. This is similar to warn on error mode,
760 except that C<isl> does not print any warning. This allows a program to
761 implement its own error reporting.
763 The last option is to directly abort the execution of the program from within
764 the isl library. This makes it obviously impossible to recover from an error,
765 but it allows to directly spot the error location. By aborting on error,
766 debuggers break at the location the error occurred and can provide a stack
767 trace. Other tools that automatically provide stack traces on abort or that do
768 not want to continue execution after an error was triggered may also prefer to
771 The on error behavior of isl can be specified by calling
772 C<isl_options_set_on_error> or by setting the command line option
773 C<--isl-on-error>. Valid arguments for the function call are
774 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
775 choices for the command line option are C<warn>, C<continue> and C<abort>.
776 It is also possible to query the current error mode.
778 #include <isl/options.h>
779 int isl_options_set_on_error(isl_ctx *ctx, int val);
780 int isl_options_get_on_error(isl_ctx *ctx);
784 Identifiers are used to identify both individual dimensions
785 and tuples of dimensions. They consist of an optional name and an optional
786 user pointer. The name and the user pointer cannot both be C<NULL>, however.
787 Identifiers with the same name but different pointer values
788 are considered to be distinct.
789 Similarly, identifiers with different names but the same pointer value
790 are also considered to be distinct.
791 Equal identifiers are represented using the same object.
792 Pairs of identifiers can therefore be tested for equality using the
794 Identifiers can be constructed, copied, freed, inspected and printed
795 using the following functions.
798 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
799 __isl_keep const char *name, void *user);
800 __isl_give isl_id *isl_id_set_free_user(
801 __isl_take isl_id *id,
802 __isl_give void (*free_user)(void *user));
803 __isl_give isl_id *isl_id_copy(isl_id *id);
804 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
806 void *isl_id_get_user(__isl_keep isl_id *id);
807 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
809 __isl_give isl_printer *isl_printer_print_id(
810 __isl_take isl_printer *p, __isl_keep isl_id *id);
812 The callback set by C<isl_id_set_free_user> is called on the user
813 pointer when the last reference to the C<isl_id> is freed.
814 Note that C<isl_id_get_name> returns a pointer to some internal
815 data structure, so the result can only be used while the
816 corresponding C<isl_id> is alive.
820 Whenever a new set, relation or similar object is created from scratch,
821 the space in which it lives needs to be specified using an C<isl_space>.
822 Each space involves zero or more parameters and zero, one or two
823 tuples of set or input/output dimensions. The parameters and dimensions
824 are identified by an C<isl_dim_type> and a position.
825 The type C<isl_dim_param> refers to parameters,
826 the type C<isl_dim_set> refers to set dimensions (for spaces
827 with a single tuple of dimensions) and the types C<isl_dim_in>
828 and C<isl_dim_out> refer to input and output dimensions
829 (for spaces with two tuples of dimensions).
830 Local spaces (see L</"Local Spaces">) also contain dimensions
831 of type C<isl_dim_div>.
832 Note that parameters are only identified by their position within
833 a given object. Across different objects, parameters are (usually)
834 identified by their names or identifiers. Only unnamed parameters
835 are identified by their positions across objects. The use of unnamed
836 parameters is discouraged.
838 #include <isl/space.h>
839 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
840 unsigned nparam, unsigned n_in, unsigned n_out);
841 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
843 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
844 unsigned nparam, unsigned dim);
845 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
846 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
848 The space used for creating a parameter domain
849 needs to be created using C<isl_space_params_alloc>.
850 For other sets, the space
851 needs to be created using C<isl_space_set_alloc>, while
852 for a relation, the space
853 needs to be created using C<isl_space_alloc>.
855 To check whether a given space is that of a set or a map
856 or whether it is a parameter space, use these functions:
858 #include <isl/space.h>
859 int isl_space_is_params(__isl_keep isl_space *space);
860 int isl_space_is_set(__isl_keep isl_space *space);
861 int isl_space_is_map(__isl_keep isl_space *space);
863 Spaces can be compared using the following functions:
865 #include <isl/space.h>
866 int isl_space_is_equal(__isl_keep isl_space *space1,
867 __isl_keep isl_space *space2);
868 int isl_space_is_domain(__isl_keep isl_space *space1,
869 __isl_keep isl_space *space2);
870 int isl_space_is_range(__isl_keep isl_space *space1,
871 __isl_keep isl_space *space2);
872 int isl_space_tuple_is_equal(
873 __isl_keep isl_space *space1,
874 enum isl_dim_type type1,
875 __isl_keep isl_space *space2,
876 enum isl_dim_type type2);
878 C<isl_space_is_domain> checks whether the first argument is equal
879 to the domain of the second argument. This requires in particular that
880 the first argument is a set space and that the second argument
881 is a map space. C<isl_space_tuple_is_equal> checks whether the given
882 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
883 spaces are the same. That is, it checks if they have the same
884 identifier (if any), the same dimension and the same internal structure
887 It is often useful to create objects that live in the
888 same space as some other object. This can be accomplished
889 by creating the new objects
890 (see L</"Creating New Sets and Relations"> or
891 L</"Functions">) based on the space
892 of the original object.
895 __isl_give isl_space *isl_basic_set_get_space(
896 __isl_keep isl_basic_set *bset);
897 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
899 #include <isl/union_set.h>
900 __isl_give isl_space *isl_union_set_get_space(
901 __isl_keep isl_union_set *uset);
904 __isl_give isl_space *isl_basic_map_get_space(
905 __isl_keep isl_basic_map *bmap);
906 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
908 #include <isl/union_map.h>
909 __isl_give isl_space *isl_union_map_get_space(
910 __isl_keep isl_union_map *umap);
912 #include <isl/constraint.h>
913 __isl_give isl_space *isl_constraint_get_space(
914 __isl_keep isl_constraint *constraint);
916 #include <isl/polynomial.h>
917 __isl_give isl_space *isl_qpolynomial_get_domain_space(
918 __isl_keep isl_qpolynomial *qp);
919 __isl_give isl_space *isl_qpolynomial_get_space(
920 __isl_keep isl_qpolynomial *qp);
921 __isl_give isl_space *isl_qpolynomial_fold_get_space(
922 __isl_keep isl_qpolynomial_fold *fold);
923 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
924 __isl_keep isl_pw_qpolynomial *pwqp);
925 __isl_give isl_space *isl_pw_qpolynomial_get_space(
926 __isl_keep isl_pw_qpolynomial *pwqp);
927 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
928 __isl_keep isl_pw_qpolynomial_fold *pwf);
929 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
930 __isl_keep isl_pw_qpolynomial_fold *pwf);
931 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
932 __isl_keep isl_union_pw_qpolynomial *upwqp);
933 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
934 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
937 __isl_give isl_space *isl_multi_val_get_space(
938 __isl_keep isl_multi_val *mv);
941 __isl_give isl_space *isl_aff_get_domain_space(
942 __isl_keep isl_aff *aff);
943 __isl_give isl_space *isl_aff_get_space(
944 __isl_keep isl_aff *aff);
945 __isl_give isl_space *isl_pw_aff_get_domain_space(
946 __isl_keep isl_pw_aff *pwaff);
947 __isl_give isl_space *isl_pw_aff_get_space(
948 __isl_keep isl_pw_aff *pwaff);
949 __isl_give isl_space *isl_multi_aff_get_domain_space(
950 __isl_keep isl_multi_aff *maff);
951 __isl_give isl_space *isl_multi_aff_get_space(
952 __isl_keep isl_multi_aff *maff);
953 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
954 __isl_keep isl_pw_multi_aff *pma);
955 __isl_give isl_space *isl_pw_multi_aff_get_space(
956 __isl_keep isl_pw_multi_aff *pma);
957 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
958 __isl_keep isl_union_pw_multi_aff *upma);
959 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
960 __isl_keep isl_multi_pw_aff *mpa);
961 __isl_give isl_space *isl_multi_pw_aff_get_space(
962 __isl_keep isl_multi_pw_aff *mpa);
964 #include <isl/point.h>
965 __isl_give isl_space *isl_point_get_space(
966 __isl_keep isl_point *pnt);
968 The number of dimensions of a given type of space
969 may be read off from a space or an object that lives
970 in a space using the following functions.
971 In case of C<isl_space_dim>, type may be
972 C<isl_dim_param>, C<isl_dim_in> (only for relations),
973 C<isl_dim_out> (only for relations), C<isl_dim_set>
974 (only for sets) or C<isl_dim_all>.
976 #include <isl/space.h>
977 unsigned isl_space_dim(__isl_keep isl_space *space,
978 enum isl_dim_type type);
980 #include <isl/local_space.h>
981 int isl_local_space_dim(__isl_keep isl_local_space *ls,
982 enum isl_dim_type type);
985 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
986 enum isl_dim_type type);
987 unsigned isl_set_dim(__isl_keep isl_set *set,
988 enum isl_dim_type type);
990 #include <isl/union_set.h>
991 unsigned isl_union_set_dim(__isl_keep isl_union_set *uset,
992 enum isl_dim_type type);
995 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
996 enum isl_dim_type type);
997 unsigned isl_map_dim(__isl_keep isl_map *map,
998 enum isl_dim_type type);
1000 #include <isl/union_map.h>
1001 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
1002 enum isl_dim_type type);
1004 #include <isl/val.h>
1005 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
1006 enum isl_dim_type type);
1008 #include <isl/aff.h>
1009 int isl_aff_dim(__isl_keep isl_aff *aff,
1010 enum isl_dim_type type);
1011 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1012 enum isl_dim_type type);
1013 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1014 enum isl_dim_type type);
1015 unsigned isl_pw_multi_aff_dim(
1016 __isl_keep isl_pw_multi_aff *pma,
1017 enum isl_dim_type type);
1018 unsigned isl_multi_pw_aff_dim(
1019 __isl_keep isl_multi_pw_aff *mpa,
1020 enum isl_dim_type type);
1021 unsigned isl_union_pw_multi_aff_dim(
1022 __isl_keep isl_union_pw_multi_aff *upma,
1023 enum isl_dim_type type);
1025 #include <isl/polynomial.h>
1026 unsigned isl_union_pw_qpolynomial_dim(
1027 __isl_keep isl_union_pw_qpolynomial *upwqp,
1028 enum isl_dim_type type);
1029 unsigned isl_union_pw_qpolynomial_fold_dim(
1030 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1031 enum isl_dim_type type);
1033 Note that an C<isl_union_set>, an C<isl_union_map>,
1034 an C<isl_union_pw_multi_aff>,
1035 an C<isl_union_pw_qpolynomial> and
1036 an C<isl_union_pw_qpolynomial_fold>
1037 only have parameters.
1039 The identifiers or names of the individual dimensions of spaces
1040 may be set or read off using the following functions on spaces
1041 or objects that live in spaces.
1042 These functions are mostly useful to obtain the identifiers, positions
1043 or names of the parameters. Identifiers of individual dimensions are
1044 essentially only useful for printing. They are ignored by all other
1045 operations and may not be preserved across those operations.
1047 #include <isl/space.h>
1048 __isl_give isl_space *isl_space_set_dim_id(
1049 __isl_take isl_space *space,
1050 enum isl_dim_type type, unsigned pos,
1051 __isl_take isl_id *id);
1052 int isl_space_has_dim_id(__isl_keep isl_space *space,
1053 enum isl_dim_type type, unsigned pos);
1054 __isl_give isl_id *isl_space_get_dim_id(
1055 __isl_keep isl_space *space,
1056 enum isl_dim_type type, unsigned pos);
1057 __isl_give isl_space *isl_space_set_dim_name(
1058 __isl_take isl_space *space,
1059 enum isl_dim_type type, unsigned pos,
1060 __isl_keep const char *name);
1061 int isl_space_has_dim_name(__isl_keep isl_space *space,
1062 enum isl_dim_type type, unsigned pos);
1063 __isl_keep const char *isl_space_get_dim_name(
1064 __isl_keep isl_space *space,
1065 enum isl_dim_type type, unsigned pos);
1067 #include <isl/local_space.h>
1068 __isl_give isl_local_space *isl_local_space_set_dim_id(
1069 __isl_take isl_local_space *ls,
1070 enum isl_dim_type type, unsigned pos,
1071 __isl_take isl_id *id);
1072 int isl_local_space_has_dim_id(
1073 __isl_keep isl_local_space *ls,
1074 enum isl_dim_type type, unsigned pos);
1075 __isl_give isl_id *isl_local_space_get_dim_id(
1076 __isl_keep isl_local_space *ls,
1077 enum isl_dim_type type, unsigned pos);
1078 __isl_give isl_local_space *isl_local_space_set_dim_name(
1079 __isl_take isl_local_space *ls,
1080 enum isl_dim_type type, unsigned pos, const char *s);
1081 int isl_local_space_has_dim_name(
1082 __isl_keep isl_local_space *ls,
1083 enum isl_dim_type type, unsigned pos)
1084 const char *isl_local_space_get_dim_name(
1085 __isl_keep isl_local_space *ls,
1086 enum isl_dim_type type, unsigned pos);
1088 #include <isl/constraint.h>
1089 const char *isl_constraint_get_dim_name(
1090 __isl_keep isl_constraint *constraint,
1091 enum isl_dim_type type, unsigned pos);
1093 #include <isl/set.h>
1094 __isl_give isl_id *isl_basic_set_get_dim_id(
1095 __isl_keep isl_basic_set *bset,
1096 enum isl_dim_type type, unsigned pos);
1097 __isl_give isl_set *isl_set_set_dim_id(
1098 __isl_take isl_set *set, enum isl_dim_type type,
1099 unsigned pos, __isl_take isl_id *id);
1100 int isl_set_has_dim_id(__isl_keep isl_set *set,
1101 enum isl_dim_type type, unsigned pos);
1102 __isl_give isl_id *isl_set_get_dim_id(
1103 __isl_keep isl_set *set, enum isl_dim_type type,
1105 const char *isl_basic_set_get_dim_name(
1106 __isl_keep isl_basic_set *bset,
1107 enum isl_dim_type type, unsigned pos);
1108 int isl_set_has_dim_name(__isl_keep isl_set *set,
1109 enum isl_dim_type type, unsigned pos);
1110 const char *isl_set_get_dim_name(
1111 __isl_keep isl_set *set,
1112 enum isl_dim_type type, unsigned pos);
1114 #include <isl/map.h>
1115 __isl_give isl_map *isl_map_set_dim_id(
1116 __isl_take isl_map *map, enum isl_dim_type type,
1117 unsigned pos, __isl_take isl_id *id);
1118 int isl_basic_map_has_dim_id(
1119 __isl_keep isl_basic_map *bmap,
1120 enum isl_dim_type type, unsigned pos);
1121 int isl_map_has_dim_id(__isl_keep isl_map *map,
1122 enum isl_dim_type type, unsigned pos);
1123 __isl_give isl_id *isl_map_get_dim_id(
1124 __isl_keep isl_map *map, enum isl_dim_type type,
1126 __isl_give isl_id *isl_union_map_get_dim_id(
1127 __isl_keep isl_union_map *umap,
1128 enum isl_dim_type type, unsigned pos);
1129 const char *isl_basic_map_get_dim_name(
1130 __isl_keep isl_basic_map *bmap,
1131 enum isl_dim_type type, unsigned pos);
1132 int isl_map_has_dim_name(__isl_keep isl_map *map,
1133 enum isl_dim_type type, unsigned pos);
1134 const char *isl_map_get_dim_name(
1135 __isl_keep isl_map *map,
1136 enum isl_dim_type type, unsigned pos);
1138 #include <isl/val.h>
1139 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1140 __isl_take isl_multi_val *mv,
1141 enum isl_dim_type type, unsigned pos,
1142 __isl_take isl_id *id);
1143 __isl_give isl_id *isl_multi_val_get_dim_id(
1144 __isl_keep isl_multi_val *mv,
1145 enum isl_dim_type type, unsigned pos);
1146 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1147 __isl_take isl_multi_val *mv,
1148 enum isl_dim_type type, unsigned pos, const char *s);
1150 #include <isl/aff.h>
1151 __isl_give isl_aff *isl_aff_set_dim_id(
1152 __isl_take isl_aff *aff, enum isl_dim_type type,
1153 unsigned pos, __isl_take isl_id *id);
1154 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1155 __isl_take isl_multi_aff *maff,
1156 enum isl_dim_type type, unsigned pos,
1157 __isl_take isl_id *id);
1158 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1159 __isl_take isl_pw_aff *pma,
1160 enum isl_dim_type type, unsigned pos,
1161 __isl_take isl_id *id);
1162 __isl_give isl_multi_pw_aff *
1163 isl_multi_pw_aff_set_dim_id(
1164 __isl_take isl_multi_pw_aff *mpa,
1165 enum isl_dim_type type, unsigned pos,
1166 __isl_take isl_id *id);
1167 __isl_give isl_id *isl_multi_aff_get_dim_id(
1168 __isl_keep isl_multi_aff *ma,
1169 enum isl_dim_type type, unsigned pos);
1170 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1171 enum isl_dim_type type, unsigned pos);
1172 __isl_give isl_id *isl_pw_aff_get_dim_id(
1173 __isl_keep isl_pw_aff *pa,
1174 enum isl_dim_type type, unsigned pos);
1175 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1176 __isl_keep isl_pw_multi_aff *pma,
1177 enum isl_dim_type type, unsigned pos);
1178 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1179 __isl_keep isl_multi_pw_aff *mpa,
1180 enum isl_dim_type type, unsigned pos);
1181 __isl_give isl_aff *isl_aff_set_dim_name(
1182 __isl_take isl_aff *aff, enum isl_dim_type type,
1183 unsigned pos, const char *s);
1184 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1185 __isl_take isl_multi_aff *maff,
1186 enum isl_dim_type type, unsigned pos, const char *s);
1187 __isl_give isl_multi_pw_aff *
1188 isl_multi_pw_aff_set_dim_name(
1189 __isl_take isl_multi_pw_aff *mpa,
1190 enum isl_dim_type type, unsigned pos, const char *s);
1191 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1192 enum isl_dim_type type, unsigned pos);
1193 const char *isl_pw_aff_get_dim_name(
1194 __isl_keep isl_pw_aff *pa,
1195 enum isl_dim_type type, unsigned pos);
1196 const char *isl_pw_multi_aff_get_dim_name(
1197 __isl_keep isl_pw_multi_aff *pma,
1198 enum isl_dim_type type, unsigned pos);
1200 #include <isl/polynomial.h>
1201 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1202 __isl_take isl_qpolynomial *qp,
1203 enum isl_dim_type type, unsigned pos,
1205 __isl_give isl_pw_qpolynomial *
1206 isl_pw_qpolynomial_set_dim_name(
1207 __isl_take isl_pw_qpolynomial *pwqp,
1208 enum isl_dim_type type, unsigned pos,
1210 __isl_give isl_pw_qpolynomial_fold *
1211 isl_pw_qpolynomial_fold_set_dim_name(
1212 __isl_take isl_pw_qpolynomial_fold *pwf,
1213 enum isl_dim_type type, unsigned pos,
1216 Note that C<isl_space_get_name> returns a pointer to some internal
1217 data structure, so the result can only be used while the
1218 corresponding C<isl_space> is alive.
1219 Also note that every function that operates on two sets or relations
1220 requires that both arguments have the same parameters. This also
1221 means that if one of the arguments has named parameters, then the
1222 other needs to have named parameters too and the names need to match.
1223 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1224 arguments may have different parameters (as long as they are named),
1225 in which case the result will have as parameters the union of the parameters of
1228 Given the identifier or name of a dimension (typically a parameter),
1229 its position can be obtained from the following functions.
1231 #include <isl/space.h>
1232 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1233 enum isl_dim_type type, __isl_keep isl_id *id);
1234 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1235 enum isl_dim_type type, const char *name);
1237 #include <isl/local_space.h>
1238 int isl_local_space_find_dim_by_name(
1239 __isl_keep isl_local_space *ls,
1240 enum isl_dim_type type, const char *name);
1242 #include <isl/val.h>
1243 int isl_multi_val_find_dim_by_id(
1244 __isl_keep isl_multi_val *mv,
1245 enum isl_dim_type type, __isl_keep isl_id *id);
1246 int isl_multi_val_find_dim_by_name(
1247 __isl_keep isl_multi_val *mv,
1248 enum isl_dim_type type, const char *name);
1250 #include <isl/set.h>
1251 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1252 enum isl_dim_type type, __isl_keep isl_id *id);
1253 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1254 enum isl_dim_type type, const char *name);
1256 #include <isl/map.h>
1257 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1258 enum isl_dim_type type, __isl_keep isl_id *id);
1259 int isl_basic_map_find_dim_by_name(
1260 __isl_keep isl_basic_map *bmap,
1261 enum isl_dim_type type, const char *name);
1262 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1263 enum isl_dim_type type, const char *name);
1264 int isl_union_map_find_dim_by_name(
1265 __isl_keep isl_union_map *umap,
1266 enum isl_dim_type type, const char *name);
1268 #include <isl/aff.h>
1269 int isl_multi_aff_find_dim_by_id(
1270 __isl_keep isl_multi_aff *ma,
1271 enum isl_dim_type type, __isl_keep isl_id *id);
1272 int isl_multi_pw_aff_find_dim_by_id(
1273 __isl_keep isl_multi_pw_aff *mpa,
1274 enum isl_dim_type type, __isl_keep isl_id *id);
1275 int isl_aff_find_dim_by_name(__isl_keep isl_aff *aff,
1276 enum isl_dim_type type, const char *name);
1277 int isl_multi_aff_find_dim_by_name(
1278 __isl_keep isl_multi_aff *ma,
1279 enum isl_dim_type type, const char *name);
1280 int isl_pw_aff_find_dim_by_name(__isl_keep isl_pw_aff *pa,
1281 enum isl_dim_type type, const char *name);
1282 int isl_multi_pw_aff_find_dim_by_name(
1283 __isl_keep isl_multi_pw_aff *mpa,
1284 enum isl_dim_type type, const char *name);
1285 int isl_pw_multi_aff_find_dim_by_name(
1286 __isl_keep isl_pw_multi_aff *pma,
1287 enum isl_dim_type type, const char *name);
1288 int isl_union_pw_multi_aff_find_dim_by_name(
1289 __isl_keep isl_union_pw_multi_aff *upma,
1290 enum isl_dim_type type, const char *name);
1292 #include <isl/polynomial.h>
1293 int isl_pw_qpolynomial_find_dim_by_name(
1294 __isl_keep isl_pw_qpolynomial *pwqp,
1295 enum isl_dim_type type, const char *name);
1296 int isl_pw_qpolynomial_fold_find_dim_by_name(
1297 __isl_keep isl_pw_qpolynomial_fold *pwf,
1298 enum isl_dim_type type, const char *name);
1299 int isl_union_pw_qpolynomial_find_dim_by_name(
1300 __isl_keep isl_union_pw_qpolynomial *upwqp,
1301 enum isl_dim_type type, const char *name);
1302 int isl_union_pw_qpolynomial_fold_find_dim_by_name(
1303 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1304 enum isl_dim_type type, const char *name);
1306 The identifiers or names of entire spaces may be set or read off
1307 using the following functions.
1309 #include <isl/space.h>
1310 __isl_give isl_space *isl_space_set_tuple_id(
1311 __isl_take isl_space *space,
1312 enum isl_dim_type type, __isl_take isl_id *id);
1313 __isl_give isl_space *isl_space_reset_tuple_id(
1314 __isl_take isl_space *space, enum isl_dim_type type);
1315 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1316 enum isl_dim_type type);
1317 __isl_give isl_id *isl_space_get_tuple_id(
1318 __isl_keep isl_space *space, enum isl_dim_type type);
1319 __isl_give isl_space *isl_space_set_tuple_name(
1320 __isl_take isl_space *space,
1321 enum isl_dim_type type, const char *s);
1322 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1323 enum isl_dim_type type);
1324 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1325 enum isl_dim_type type);
1327 #include <isl/local_space.h>
1328 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1329 __isl_take isl_local_space *ls,
1330 enum isl_dim_type type, __isl_take isl_id *id);
1332 #include <isl/set.h>
1333 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1334 __isl_take isl_basic_set *bset,
1335 __isl_take isl_id *id);
1336 __isl_give isl_set *isl_set_set_tuple_id(
1337 __isl_take isl_set *set, __isl_take isl_id *id);
1338 __isl_give isl_set *isl_set_reset_tuple_id(
1339 __isl_take isl_set *set);
1340 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1341 __isl_give isl_id *isl_set_get_tuple_id(
1342 __isl_keep isl_set *set);
1343 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1344 __isl_take isl_basic_set *set, const char *s);
1345 __isl_give isl_set *isl_set_set_tuple_name(
1346 __isl_take isl_set *set, const char *s);
1347 const char *isl_basic_set_get_tuple_name(
1348 __isl_keep isl_basic_set *bset);
1349 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1350 const char *isl_set_get_tuple_name(
1351 __isl_keep isl_set *set);
1353 #include <isl/map.h>
1354 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1355 __isl_take isl_basic_map *bmap,
1356 enum isl_dim_type type, __isl_take isl_id *id);
1357 __isl_give isl_map *isl_map_set_tuple_id(
1358 __isl_take isl_map *map, enum isl_dim_type type,
1359 __isl_take isl_id *id);
1360 __isl_give isl_map *isl_map_reset_tuple_id(
1361 __isl_take isl_map *map, enum isl_dim_type type);
1362 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1363 enum isl_dim_type type);
1364 __isl_give isl_id *isl_map_get_tuple_id(
1365 __isl_keep isl_map *map, enum isl_dim_type type);
1366 __isl_give isl_map *isl_map_set_tuple_name(
1367 __isl_take isl_map *map,
1368 enum isl_dim_type type, const char *s);
1369 const char *isl_basic_map_get_tuple_name(
1370 __isl_keep isl_basic_map *bmap,
1371 enum isl_dim_type type);
1372 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1373 __isl_take isl_basic_map *bmap,
1374 enum isl_dim_type type, const char *s);
1375 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1376 enum isl_dim_type type);
1377 const char *isl_map_get_tuple_name(
1378 __isl_keep isl_map *map,
1379 enum isl_dim_type type);
1381 #include <isl/val.h>
1382 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1383 __isl_take isl_multi_val *mv,
1384 enum isl_dim_type type, __isl_take isl_id *id);
1385 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1386 __isl_take isl_multi_val *mv,
1387 enum isl_dim_type type);
1388 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1389 enum isl_dim_type type);
1390 __isl_give isl_id *isl_multi_val_get_tuple_id(
1391 __isl_keep isl_multi_val *mv,
1392 enum isl_dim_type type);
1393 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1394 __isl_take isl_multi_val *mv,
1395 enum isl_dim_type type, const char *s);
1396 const char *isl_multi_val_get_tuple_name(
1397 __isl_keep isl_multi_val *mv,
1398 enum isl_dim_type type);
1400 #include <isl/aff.h>
1401 __isl_give isl_aff *isl_aff_set_tuple_id(
1402 __isl_take isl_aff *aff,
1403 enum isl_dim_type type, __isl_take isl_id *id);
1404 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1405 __isl_take isl_multi_aff *maff,
1406 enum isl_dim_type type, __isl_take isl_id *id);
1407 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1408 __isl_take isl_pw_aff *pwaff,
1409 enum isl_dim_type type, __isl_take isl_id *id);
1410 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1411 __isl_take isl_pw_multi_aff *pma,
1412 enum isl_dim_type type, __isl_take isl_id *id);
1413 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1414 __isl_take isl_multi_aff *ma,
1415 enum isl_dim_type type);
1416 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1417 __isl_take isl_pw_aff *pa,
1418 enum isl_dim_type type);
1419 __isl_give isl_multi_pw_aff *
1420 isl_multi_pw_aff_reset_tuple_id(
1421 __isl_take isl_multi_pw_aff *mpa,
1422 enum isl_dim_type type);
1423 __isl_give isl_pw_multi_aff *
1424 isl_pw_multi_aff_reset_tuple_id(
1425 __isl_take isl_pw_multi_aff *pma,
1426 enum isl_dim_type type);
1427 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1428 enum isl_dim_type type);
1429 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1430 __isl_keep isl_multi_aff *ma,
1431 enum isl_dim_type type);
1432 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1433 enum isl_dim_type type);
1434 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1435 __isl_keep isl_pw_aff *pa,
1436 enum isl_dim_type type);
1437 int isl_pw_multi_aff_has_tuple_id(
1438 __isl_keep isl_pw_multi_aff *pma,
1439 enum isl_dim_type type);
1440 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1441 __isl_keep isl_pw_multi_aff *pma,
1442 enum isl_dim_type type);
1443 int isl_multi_pw_aff_has_tuple_id(
1444 __isl_keep isl_multi_pw_aff *mpa,
1445 enum isl_dim_type type);
1446 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1447 __isl_keep isl_multi_pw_aff *mpa,
1448 enum isl_dim_type type);
1449 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1450 __isl_take isl_multi_aff *maff,
1451 enum isl_dim_type type, const char *s);
1452 __isl_give isl_multi_pw_aff *
1453 isl_multi_pw_aff_set_tuple_name(
1454 __isl_take isl_multi_pw_aff *mpa,
1455 enum isl_dim_type type, const char *s);
1456 const char *isl_multi_aff_get_tuple_name(
1457 __isl_keep isl_multi_aff *multi,
1458 enum isl_dim_type type);
1459 int isl_pw_multi_aff_has_tuple_name(
1460 __isl_keep isl_pw_multi_aff *pma,
1461 enum isl_dim_type type);
1462 const char *isl_pw_multi_aff_get_tuple_name(
1463 __isl_keep isl_pw_multi_aff *pma,
1464 enum isl_dim_type type);
1466 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1467 or C<isl_dim_set>. As with C<isl_space_get_name>,
1468 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1470 Binary operations require the corresponding spaces of their arguments
1471 to have the same name.
1473 To keep the names of all parameters and tuples, but reset the user pointers
1474 of all the corresponding identifiers, use the following function.
1476 #include <isl/space.h>
1477 __isl_give isl_space *isl_space_reset_user(
1478 __isl_take isl_space *space);
1480 #include <isl/set.h>
1481 __isl_give isl_set *isl_set_reset_user(
1482 __isl_take isl_set *set);
1484 #include <isl/map.h>
1485 __isl_give isl_map *isl_map_reset_user(
1486 __isl_take isl_map *map);
1488 #include <isl/union_set.h>
1489 __isl_give isl_union_set *isl_union_set_reset_user(
1490 __isl_take isl_union_set *uset);
1492 #include <isl/union_map.h>
1493 __isl_give isl_union_map *isl_union_map_reset_user(
1494 __isl_take isl_union_map *umap);
1496 #include <isl/val.h>
1497 __isl_give isl_multi_val *isl_multi_val_reset_user(
1498 __isl_take isl_multi_val *mv);
1500 #include <isl/aff.h>
1501 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1502 __isl_take isl_multi_aff *ma);
1503 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1504 __isl_take isl_multi_pw_aff *mpa);
1506 Spaces can be nested. In particular, the domain of a set or
1507 the domain or range of a relation can be a nested relation.
1508 This process is also called I<wrapping>.
1509 The functions for detecting, constructing and deconstructing
1510 such nested spaces can be found in the wrapping properties
1511 of L</"Unary Properties">, the wrapping operations
1512 of L</"Unary Operations"> and the Cartesian product operations
1513 of L</"Basic Operations">.
1515 Spaces can be created from other spaces
1516 using the functions described in L</"Unary Operations">
1517 and L</"Binary Operations">.
1521 A local space is essentially a space with
1522 zero or more existentially quantified variables.
1523 The local space of various objects can be obtained
1524 using the following functions.
1526 #include <isl/constraint.h>
1527 __isl_give isl_local_space *isl_constraint_get_local_space(
1528 __isl_keep isl_constraint *constraint);
1530 #include <isl/set.h>
1531 __isl_give isl_local_space *isl_basic_set_get_local_space(
1532 __isl_keep isl_basic_set *bset);
1534 #include <isl/map.h>
1535 __isl_give isl_local_space *isl_basic_map_get_local_space(
1536 __isl_keep isl_basic_map *bmap);
1538 #include <isl/aff.h>
1539 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1540 __isl_keep isl_aff *aff);
1541 __isl_give isl_local_space *isl_aff_get_local_space(
1542 __isl_keep isl_aff *aff);
1544 A new local space can be created from a space using
1546 #include <isl/local_space.h>
1547 __isl_give isl_local_space *isl_local_space_from_space(
1548 __isl_take isl_space *space);
1550 They can be inspected, modified, copied and freed using the following functions.
1552 #include <isl/local_space.h>
1553 int isl_local_space_is_params(
1554 __isl_keep isl_local_space *ls);
1555 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1556 __isl_give isl_space *isl_local_space_get_space(
1557 __isl_keep isl_local_space *ls);
1558 __isl_give isl_aff *isl_local_space_get_div(
1559 __isl_keep isl_local_space *ls, int pos);
1560 __isl_give isl_local_space *isl_local_space_copy(
1561 __isl_keep isl_local_space *ls);
1562 __isl_null isl_local_space *isl_local_space_free(
1563 __isl_take isl_local_space *ls);
1565 Note that C<isl_local_space_get_div> can only be used on local spaces
1568 Two local spaces can be compared using
1570 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1571 __isl_keep isl_local_space *ls2);
1573 Local spaces can be created from other local spaces
1574 using the functions described in L</"Unary Operations">
1575 and L</"Binary Operations">.
1577 =head2 Creating New Sets and Relations
1579 C<isl> has functions for creating some standard sets and relations.
1583 =item * Empty sets and relations
1585 __isl_give isl_basic_set *isl_basic_set_empty(
1586 __isl_take isl_space *space);
1587 __isl_give isl_basic_map *isl_basic_map_empty(
1588 __isl_take isl_space *space);
1589 __isl_give isl_set *isl_set_empty(
1590 __isl_take isl_space *space);
1591 __isl_give isl_map *isl_map_empty(
1592 __isl_take isl_space *space);
1593 __isl_give isl_union_set *isl_union_set_empty(
1594 __isl_take isl_space *space);
1595 __isl_give isl_union_map *isl_union_map_empty(
1596 __isl_take isl_space *space);
1598 For C<isl_union_set>s and C<isl_union_map>s, the space
1599 is only used to specify the parameters.
1601 =item * Universe sets and relations
1603 __isl_give isl_basic_set *isl_basic_set_universe(
1604 __isl_take isl_space *space);
1605 __isl_give isl_basic_map *isl_basic_map_universe(
1606 __isl_take isl_space *space);
1607 __isl_give isl_set *isl_set_universe(
1608 __isl_take isl_space *space);
1609 __isl_give isl_map *isl_map_universe(
1610 __isl_take isl_space *space);
1611 __isl_give isl_union_set *isl_union_set_universe(
1612 __isl_take isl_union_set *uset);
1613 __isl_give isl_union_map *isl_union_map_universe(
1614 __isl_take isl_union_map *umap);
1616 The sets and relations constructed by the functions above
1617 contain all integer values, while those constructed by the
1618 functions below only contain non-negative values.
1620 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1621 __isl_take isl_space *space);
1622 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1623 __isl_take isl_space *space);
1624 __isl_give isl_set *isl_set_nat_universe(
1625 __isl_take isl_space *space);
1626 __isl_give isl_map *isl_map_nat_universe(
1627 __isl_take isl_space *space);
1629 =item * Identity relations
1631 __isl_give isl_basic_map *isl_basic_map_identity(
1632 __isl_take isl_space *space);
1633 __isl_give isl_map *isl_map_identity(
1634 __isl_take isl_space *space);
1636 The number of input and output dimensions in C<space> needs
1639 =item * Lexicographic order
1641 __isl_give isl_map *isl_map_lex_lt(
1642 __isl_take isl_space *set_space);
1643 __isl_give isl_map *isl_map_lex_le(
1644 __isl_take isl_space *set_space);
1645 __isl_give isl_map *isl_map_lex_gt(
1646 __isl_take isl_space *set_space);
1647 __isl_give isl_map *isl_map_lex_ge(
1648 __isl_take isl_space *set_space);
1649 __isl_give isl_map *isl_map_lex_lt_first(
1650 __isl_take isl_space *space, unsigned n);
1651 __isl_give isl_map *isl_map_lex_le_first(
1652 __isl_take isl_space *space, unsigned n);
1653 __isl_give isl_map *isl_map_lex_gt_first(
1654 __isl_take isl_space *space, unsigned n);
1655 __isl_give isl_map *isl_map_lex_ge_first(
1656 __isl_take isl_space *space, unsigned n);
1658 The first four functions take a space for a B<set>
1659 and return relations that express that the elements in the domain
1660 are lexicographically less
1661 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1662 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1663 than the elements in the range.
1664 The last four functions take a space for a map
1665 and return relations that express that the first C<n> dimensions
1666 in the domain are lexicographically less
1667 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1668 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1669 than the first C<n> dimensions in the range.
1673 A basic set or relation can be converted to a set or relation
1674 using the following functions.
1676 __isl_give isl_set *isl_set_from_basic_set(
1677 __isl_take isl_basic_set *bset);
1678 __isl_give isl_map *isl_map_from_basic_map(
1679 __isl_take isl_basic_map *bmap);
1681 Sets and relations can be converted to union sets and relations
1682 using the following functions.
1684 __isl_give isl_union_set *isl_union_set_from_basic_set(
1685 __isl_take isl_basic_set *bset);
1686 __isl_give isl_union_map *isl_union_map_from_basic_map(
1687 __isl_take isl_basic_map *bmap);
1688 __isl_give isl_union_set *isl_union_set_from_set(
1689 __isl_take isl_set *set);
1690 __isl_give isl_union_map *isl_union_map_from_map(
1691 __isl_take isl_map *map);
1693 The inverse conversions below can only be used if the input
1694 union set or relation is known to contain elements in exactly one
1697 __isl_give isl_set *isl_set_from_union_set(
1698 __isl_take isl_union_set *uset);
1699 __isl_give isl_map *isl_map_from_union_map(
1700 __isl_take isl_union_map *umap);
1702 Sets and relations can be copied and freed again using the following
1705 __isl_give isl_basic_set *isl_basic_set_copy(
1706 __isl_keep isl_basic_set *bset);
1707 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1708 __isl_give isl_union_set *isl_union_set_copy(
1709 __isl_keep isl_union_set *uset);
1710 __isl_give isl_basic_map *isl_basic_map_copy(
1711 __isl_keep isl_basic_map *bmap);
1712 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1713 __isl_give isl_union_map *isl_union_map_copy(
1714 __isl_keep isl_union_map *umap);
1715 __isl_null isl_basic_set *isl_basic_set_free(
1716 __isl_take isl_basic_set *bset);
1717 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1718 __isl_null isl_union_set *isl_union_set_free(
1719 __isl_take isl_union_set *uset);
1720 __isl_null isl_basic_map *isl_basic_map_free(
1721 __isl_take isl_basic_map *bmap);
1722 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1723 __isl_null isl_union_map *isl_union_map_free(
1724 __isl_take isl_union_map *umap);
1726 Other sets and relations can be constructed by starting
1727 from a universe set or relation, adding equality and/or
1728 inequality constraints and then projecting out the
1729 existentially quantified variables, if any.
1730 Constraints can be constructed, manipulated and
1731 added to (or removed from) (basic) sets and relations
1732 using the following functions.
1734 #include <isl/constraint.h>
1735 __isl_give isl_constraint *isl_equality_alloc(
1736 __isl_take isl_local_space *ls);
1737 __isl_give isl_constraint *isl_inequality_alloc(
1738 __isl_take isl_local_space *ls);
1739 __isl_give isl_constraint *isl_constraint_set_constant_si(
1740 __isl_take isl_constraint *constraint, int v);
1741 __isl_give isl_constraint *isl_constraint_set_constant_val(
1742 __isl_take isl_constraint *constraint,
1743 __isl_take isl_val *v);
1744 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1745 __isl_take isl_constraint *constraint,
1746 enum isl_dim_type type, int pos, int v);
1747 __isl_give isl_constraint *
1748 isl_constraint_set_coefficient_val(
1749 __isl_take isl_constraint *constraint,
1750 enum isl_dim_type type, int pos,
1751 __isl_take isl_val *v);
1752 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1753 __isl_take isl_basic_map *bmap,
1754 __isl_take isl_constraint *constraint);
1755 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1756 __isl_take isl_basic_set *bset,
1757 __isl_take isl_constraint *constraint);
1758 __isl_give isl_map *isl_map_add_constraint(
1759 __isl_take isl_map *map,
1760 __isl_take isl_constraint *constraint);
1761 __isl_give isl_set *isl_set_add_constraint(
1762 __isl_take isl_set *set,
1763 __isl_take isl_constraint *constraint);
1764 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1765 __isl_take isl_basic_set *bset,
1766 __isl_take isl_constraint *constraint);
1768 For example, to create a set containing the even integers
1769 between 10 and 42, you would use the following code.
1772 isl_local_space *ls;
1774 isl_basic_set *bset;
1776 space = isl_space_set_alloc(ctx, 0, 2);
1777 bset = isl_basic_set_universe(isl_space_copy(space));
1778 ls = isl_local_space_from_space(space);
1780 c = isl_equality_alloc(isl_local_space_copy(ls));
1781 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1782 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1783 bset = isl_basic_set_add_constraint(bset, c);
1785 c = isl_inequality_alloc(isl_local_space_copy(ls));
1786 c = isl_constraint_set_constant_si(c, -10);
1787 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1788 bset = isl_basic_set_add_constraint(bset, c);
1790 c = isl_inequality_alloc(ls);
1791 c = isl_constraint_set_constant_si(c, 42);
1792 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1793 bset = isl_basic_set_add_constraint(bset, c);
1795 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1799 isl_basic_set *bset;
1800 bset = isl_basic_set_read_from_str(ctx,
1801 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1803 A basic set or relation can also be constructed from two matrices
1804 describing the equalities and the inequalities.
1806 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1807 __isl_take isl_space *space,
1808 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1809 enum isl_dim_type c1,
1810 enum isl_dim_type c2, enum isl_dim_type c3,
1811 enum isl_dim_type c4);
1812 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1813 __isl_take isl_space *space,
1814 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1815 enum isl_dim_type c1,
1816 enum isl_dim_type c2, enum isl_dim_type c3,
1817 enum isl_dim_type c4, enum isl_dim_type c5);
1819 The C<isl_dim_type> arguments indicate the order in which
1820 different kinds of variables appear in the input matrices
1821 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1822 C<isl_dim_set> and C<isl_dim_div> for sets and
1823 of C<isl_dim_cst>, C<isl_dim_param>,
1824 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1826 A (basic or union) set or relation can also be constructed from a
1827 (union) (piecewise) (multiple) affine expression
1828 or a list of affine expressions
1829 (See L</"Functions">).
1831 __isl_give isl_basic_map *isl_basic_map_from_aff(
1832 __isl_take isl_aff *aff);
1833 __isl_give isl_map *isl_map_from_aff(
1834 __isl_take isl_aff *aff);
1835 __isl_give isl_set *isl_set_from_pw_aff(
1836 __isl_take isl_pw_aff *pwaff);
1837 __isl_give isl_map *isl_map_from_pw_aff(
1838 __isl_take isl_pw_aff *pwaff);
1839 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1840 __isl_take isl_space *domain_space,
1841 __isl_take isl_aff_list *list);
1842 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1843 __isl_take isl_multi_aff *maff)
1844 __isl_give isl_map *isl_map_from_multi_aff(
1845 __isl_take isl_multi_aff *maff)
1846 __isl_give isl_set *isl_set_from_pw_multi_aff(
1847 __isl_take isl_pw_multi_aff *pma);
1848 __isl_give isl_map *isl_map_from_pw_multi_aff(
1849 __isl_take isl_pw_multi_aff *pma);
1850 __isl_give isl_set *isl_set_from_multi_pw_aff(
1851 __isl_take isl_multi_pw_aff *mpa);
1852 __isl_give isl_map *isl_map_from_multi_pw_aff(
1853 __isl_take isl_multi_pw_aff *mpa);
1854 __isl_give isl_union_map *
1855 isl_union_map_from_union_pw_multi_aff(
1856 __isl_take isl_union_pw_multi_aff *upma);
1858 The C<domain_space> argument describes the domain of the resulting
1859 basic relation. It is required because the C<list> may consist
1860 of zero affine expressions.
1862 =head2 Inspecting Sets and Relations
1864 Usually, the user should not have to care about the actual constraints
1865 of the sets and maps, but should instead apply the abstract operations
1866 explained in the following sections.
1867 Occasionally, however, it may be required to inspect the individual
1868 coefficients of the constraints. This section explains how to do so.
1869 In these cases, it may also be useful to have C<isl> compute
1870 an explicit representation of the existentially quantified variables.
1872 __isl_give isl_set *isl_set_compute_divs(
1873 __isl_take isl_set *set);
1874 __isl_give isl_map *isl_map_compute_divs(
1875 __isl_take isl_map *map);
1876 __isl_give isl_union_set *isl_union_set_compute_divs(
1877 __isl_take isl_union_set *uset);
1878 __isl_give isl_union_map *isl_union_map_compute_divs(
1879 __isl_take isl_union_map *umap);
1881 This explicit representation defines the existentially quantified
1882 variables as integer divisions of the other variables, possibly
1883 including earlier existentially quantified variables.
1884 An explicitly represented existentially quantified variable therefore
1885 has a unique value when the values of the other variables are known.
1886 If, furthermore, the same existentials, i.e., existentials
1887 with the same explicit representations, should appear in the
1888 same order in each of the disjuncts of a set or map, then the user should call
1889 either of the following functions.
1891 __isl_give isl_set *isl_set_align_divs(
1892 __isl_take isl_set *set);
1893 __isl_give isl_map *isl_map_align_divs(
1894 __isl_take isl_map *map);
1896 Alternatively, the existentially quantified variables can be removed
1897 using the following functions, which compute an overapproximation.
1899 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1900 __isl_take isl_basic_set *bset);
1901 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1902 __isl_take isl_basic_map *bmap);
1903 __isl_give isl_set *isl_set_remove_divs(
1904 __isl_take isl_set *set);
1905 __isl_give isl_map *isl_map_remove_divs(
1906 __isl_take isl_map *map);
1908 It is also possible to only remove those divs that are defined
1909 in terms of a given range of dimensions or only those for which
1910 no explicit representation is known.
1912 __isl_give isl_basic_set *
1913 isl_basic_set_remove_divs_involving_dims(
1914 __isl_take isl_basic_set *bset,
1915 enum isl_dim_type type,
1916 unsigned first, unsigned n);
1917 __isl_give isl_basic_map *
1918 isl_basic_map_remove_divs_involving_dims(
1919 __isl_take isl_basic_map *bmap,
1920 enum isl_dim_type type,
1921 unsigned first, unsigned n);
1922 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1923 __isl_take isl_set *set, enum isl_dim_type type,
1924 unsigned first, unsigned n);
1925 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1926 __isl_take isl_map *map, enum isl_dim_type type,
1927 unsigned first, unsigned n);
1929 __isl_give isl_basic_set *
1930 isl_basic_set_remove_unknown_divs(
1931 __isl_take isl_basic_set *bset);
1932 __isl_give isl_set *isl_set_remove_unknown_divs(
1933 __isl_take isl_set *set);
1934 __isl_give isl_map *isl_map_remove_unknown_divs(
1935 __isl_take isl_map *map);
1937 To iterate over all the sets or maps in a union set or map, use
1939 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1940 int (*fn)(__isl_take isl_set *set, void *user),
1942 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1943 int (*fn)(__isl_take isl_map *map, void *user),
1946 The number of sets or maps in a union set or map can be obtained
1949 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1950 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1952 To extract the set or map in a given space from a union, use
1954 __isl_give isl_set *isl_union_set_extract_set(
1955 __isl_keep isl_union_set *uset,
1956 __isl_take isl_space *space);
1957 __isl_give isl_map *isl_union_map_extract_map(
1958 __isl_keep isl_union_map *umap,
1959 __isl_take isl_space *space);
1961 To iterate over all the basic sets or maps in a set or map, use
1963 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1964 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1966 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1967 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1970 The callback function C<fn> should return 0 if successful and
1971 -1 if an error occurs. In the latter case, or if any other error
1972 occurs, the above functions will return -1.
1974 It should be noted that C<isl> does not guarantee that
1975 the basic sets or maps passed to C<fn> are disjoint.
1976 If this is required, then the user should call one of
1977 the following functions first.
1979 __isl_give isl_set *isl_set_make_disjoint(
1980 __isl_take isl_set *set);
1981 __isl_give isl_map *isl_map_make_disjoint(
1982 __isl_take isl_map *map);
1984 The number of basic sets in a set can be obtained
1985 or the number of basic maps in a map can be obtained
1988 #include <isl/set.h>
1989 int isl_set_n_basic_set(__isl_keep isl_set *set);
1991 #include <isl/map.h>
1992 int isl_map_n_basic_map(__isl_keep isl_map *map);
1994 To iterate over the constraints of a basic set or map, use
1996 #include <isl/constraint.h>
1998 int isl_basic_set_n_constraint(
1999 __isl_keep isl_basic_set *bset);
2000 int isl_basic_set_foreach_constraint(
2001 __isl_keep isl_basic_set *bset,
2002 int (*fn)(__isl_take isl_constraint *c, void *user),
2004 int isl_basic_map_n_constraint(
2005 __isl_keep isl_basic_map *bmap);
2006 int isl_basic_map_foreach_constraint(
2007 __isl_keep isl_basic_map *bmap,
2008 int (*fn)(__isl_take isl_constraint *c, void *user),
2010 __isl_null isl_constraint *isl_constraint_free(
2011 __isl_take isl_constraint *c);
2013 Again, the callback function C<fn> should return 0 if successful and
2014 -1 if an error occurs. In the latter case, or if any other error
2015 occurs, the above functions will return -1.
2016 The constraint C<c> represents either an equality or an inequality.
2017 Use the following function to find out whether a constraint
2018 represents an equality. If not, it represents an inequality.
2020 int isl_constraint_is_equality(
2021 __isl_keep isl_constraint *constraint);
2023 It is also possible to obtain a list of constraints from a basic
2026 #include <isl/constraint.h>
2027 __isl_give isl_constraint_list *
2028 isl_basic_map_get_constraint_list(
2029 __isl_keep isl_basic_map *bmap);
2030 __isl_give isl_constraint_list *
2031 isl_basic_set_get_constraint_list(
2032 __isl_keep isl_basic_set *bset);
2034 These functions require that all existentially quantified variables
2035 have an explicit representation.
2036 The returned list can be manipulated using the functions in L<"Lists">.
2038 The coefficients of the constraints can be inspected using
2039 the following functions.
2041 int isl_constraint_is_lower_bound(
2042 __isl_keep isl_constraint *constraint,
2043 enum isl_dim_type type, unsigned pos);
2044 int isl_constraint_is_upper_bound(
2045 __isl_keep isl_constraint *constraint,
2046 enum isl_dim_type type, unsigned pos);
2047 __isl_give isl_val *isl_constraint_get_constant_val(
2048 __isl_keep isl_constraint *constraint);
2049 __isl_give isl_val *isl_constraint_get_coefficient_val(
2050 __isl_keep isl_constraint *constraint,
2051 enum isl_dim_type type, int pos);
2053 The explicit representations of the existentially quantified
2054 variables can be inspected using the following function.
2055 Note that the user is only allowed to use this function
2056 if the inspected set or map is the result of a call
2057 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
2058 The existentially quantified variable is equal to the floor
2059 of the returned affine expression. The affine expression
2060 itself can be inspected using the functions in
2063 __isl_give isl_aff *isl_constraint_get_div(
2064 __isl_keep isl_constraint *constraint, int pos);
2066 To obtain the constraints of a basic set or map in matrix
2067 form, use the following functions.
2069 __isl_give isl_mat *isl_basic_set_equalities_matrix(
2070 __isl_keep isl_basic_set *bset,
2071 enum isl_dim_type c1, enum isl_dim_type c2,
2072 enum isl_dim_type c3, enum isl_dim_type c4);
2073 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2074 __isl_keep isl_basic_set *bset,
2075 enum isl_dim_type c1, enum isl_dim_type c2,
2076 enum isl_dim_type c3, enum isl_dim_type c4);
2077 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2078 __isl_keep isl_basic_map *bmap,
2079 enum isl_dim_type c1,
2080 enum isl_dim_type c2, enum isl_dim_type c3,
2081 enum isl_dim_type c4, enum isl_dim_type c5);
2082 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2083 __isl_keep isl_basic_map *bmap,
2084 enum isl_dim_type c1,
2085 enum isl_dim_type c2, enum isl_dim_type c3,
2086 enum isl_dim_type c4, enum isl_dim_type c5);
2088 The C<isl_dim_type> arguments dictate the order in which
2089 different kinds of variables appear in the resulting matrix.
2090 For set inputs, they should be a permutation of
2091 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2092 For map inputs, they should be a permutation of
2093 C<isl_dim_cst>, C<isl_dim_param>,
2094 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2098 Points are elements of a set. They can be used to construct
2099 simple sets (boxes) or they can be used to represent the
2100 individual elements of a set.
2101 The zero point (the origin) can be created using
2103 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2105 The coordinates of a point can be inspected, set and changed
2108 __isl_give isl_val *isl_point_get_coordinate_val(
2109 __isl_keep isl_point *pnt,
2110 enum isl_dim_type type, int pos);
2111 __isl_give isl_point *isl_point_set_coordinate_val(
2112 __isl_take isl_point *pnt,
2113 enum isl_dim_type type, int pos,
2114 __isl_take isl_val *v);
2116 __isl_give isl_point *isl_point_add_ui(
2117 __isl_take isl_point *pnt,
2118 enum isl_dim_type type, int pos, unsigned val);
2119 __isl_give isl_point *isl_point_sub_ui(
2120 __isl_take isl_point *pnt,
2121 enum isl_dim_type type, int pos, unsigned val);
2123 Points can be copied or freed using
2125 __isl_give isl_point *isl_point_copy(
2126 __isl_keep isl_point *pnt);
2127 void isl_point_free(__isl_take isl_point *pnt);
2129 A singleton set can be created from a point using
2131 __isl_give isl_basic_set *isl_basic_set_from_point(
2132 __isl_take isl_point *pnt);
2133 __isl_give isl_set *isl_set_from_point(
2134 __isl_take isl_point *pnt);
2136 and a box can be created from two opposite extremal points using
2138 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2139 __isl_take isl_point *pnt1,
2140 __isl_take isl_point *pnt2);
2141 __isl_give isl_set *isl_set_box_from_points(
2142 __isl_take isl_point *pnt1,
2143 __isl_take isl_point *pnt2);
2145 All elements of a B<bounded> (union) set can be enumerated using
2146 the following functions.
2148 int isl_set_foreach_point(__isl_keep isl_set *set,
2149 int (*fn)(__isl_take isl_point *pnt, void *user),
2151 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2152 int (*fn)(__isl_take isl_point *pnt, void *user),
2155 The function C<fn> is called for each integer point in
2156 C<set> with as second argument the last argument of
2157 the C<isl_set_foreach_point> call. The function C<fn>
2158 should return C<0> on success and C<-1> on failure.
2159 In the latter case, C<isl_set_foreach_point> will stop
2160 enumerating and return C<-1> as well.
2161 If the enumeration is performed successfully and to completion,
2162 then C<isl_set_foreach_point> returns C<0>.
2164 To obtain a single point of a (basic) set, use
2166 __isl_give isl_point *isl_basic_set_sample_point(
2167 __isl_take isl_basic_set *bset);
2168 __isl_give isl_point *isl_set_sample_point(
2169 __isl_take isl_set *set);
2171 If C<set> does not contain any (integer) points, then the
2172 resulting point will be ``void'', a property that can be
2175 int isl_point_is_void(__isl_keep isl_point *pnt);
2179 Besides sets and relation, C<isl> also supports various types of functions.
2180 Each of these types is derived from the value type (see L</"Values">)
2181 or from one of two primitive function types
2182 through the application of zero or more type constructors.
2183 We first describe the primitive type and then we describe
2184 the types derived from these primitive types.
2186 =head3 Primitive Functions
2188 C<isl> support two primitive function types, quasi-affine
2189 expressions and quasipolynomials.
2190 A quasi-affine expression is defined either over a parameter
2191 space or over a set and is composed of integer constants,
2192 parameters and set variables, addition, subtraction and
2193 integer division by an integer constant.
2194 For example, the quasi-affine expression
2196 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2198 maps C<x> to C<2*floor((4 n + x)/9>.
2199 A quasipolynomial is a polynomial expression in quasi-affine
2200 expression. That is, it additionally allows for multiplication.
2201 Note, though, that it is not allowed to construct an integer
2202 division of an expression involving multiplications.
2203 Here is an example of a quasipolynomial that is not
2204 quasi-affine expression
2206 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2208 Note that the external representations of quasi-affine expressions
2209 and quasipolynomials are different. Quasi-affine expressions
2210 use a notation with square brackets just like binary relations,
2211 while quasipolynomials do not. This might change at some point.
2213 If a primitive function is defined over a parameter space,
2214 then the space of the function itself is that of a set.
2215 If it is defined over a set, then the space of the function
2216 is that of a relation. In both cases, the set space (or
2217 the output space) is single-dimensional, anonymous and unstructured.
2218 To create functions with multiple dimensions or with other kinds
2219 of set or output spaces, use multiple expressions
2220 (see L</"Multiple Expressions">).
2224 =item * Quasi-affine Expressions
2226 Besides the expressions described above, a quasi-affine
2227 expression can also be set to NaN. Such expressions
2228 typically represent a failure to represent a result
2229 as a quasi-affine expression.
2231 The zero quasi affine expression or the quasi affine expression
2232 that is equal to a given value or
2233 a specified dimension on a given domain can be created using
2235 #include <isl/aff.h>
2236 __isl_give isl_aff *isl_aff_zero_on_domain(
2237 __isl_take isl_local_space *ls);
2238 __isl_give isl_aff *isl_aff_val_on_domain(
2239 __isl_take isl_local_space *ls,
2240 __isl_take isl_val *val);
2241 __isl_give isl_aff *isl_aff_var_on_domain(
2242 __isl_take isl_local_space *ls,
2243 enum isl_dim_type type, unsigned pos);
2244 __isl_give isl_aff *isl_aff_nan_on_domain(
2245 __isl_take isl_local_space *ls);
2247 Quasi affine expressions can be copied and freed using
2249 #include <isl/aff.h>
2250 __isl_give isl_aff *isl_aff_copy(
2251 __isl_keep isl_aff *aff);
2252 __isl_null isl_aff *isl_aff_free(
2253 __isl_take isl_aff *aff);
2255 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2256 using the following function. The constraint is required to have
2257 a non-zero coefficient for the specified dimension.
2259 #include <isl/constraint.h>
2260 __isl_give isl_aff *isl_constraint_get_bound(
2261 __isl_keep isl_constraint *constraint,
2262 enum isl_dim_type type, int pos);
2264 The entire affine expression of the constraint can also be extracted
2265 using the following function.
2267 #include <isl/constraint.h>
2268 __isl_give isl_aff *isl_constraint_get_aff(
2269 __isl_keep isl_constraint *constraint);
2271 Conversely, an equality constraint equating
2272 the affine expression to zero or an inequality constraint enforcing
2273 the affine expression to be non-negative, can be constructed using
2275 __isl_give isl_constraint *isl_equality_from_aff(
2276 __isl_take isl_aff *aff);
2277 __isl_give isl_constraint *isl_inequality_from_aff(
2278 __isl_take isl_aff *aff);
2280 The coefficients and the integer divisions of an affine expression
2281 can be inspected using the following functions.
2283 #include <isl/aff.h>
2284 __isl_give isl_val *isl_aff_get_constant_val(
2285 __isl_keep isl_aff *aff);
2286 __isl_give isl_val *isl_aff_get_coefficient_val(
2287 __isl_keep isl_aff *aff,
2288 enum isl_dim_type type, int pos);
2289 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2290 enum isl_dim_type type, int pos);
2291 __isl_give isl_val *isl_aff_get_denominator_val(
2292 __isl_keep isl_aff *aff);
2293 __isl_give isl_aff *isl_aff_get_div(
2294 __isl_keep isl_aff *aff, int pos);
2296 They can be modified using the following functions.
2298 #include <isl/aff.h>
2299 __isl_give isl_aff *isl_aff_set_constant_si(
2300 __isl_take isl_aff *aff, int v);
2301 __isl_give isl_aff *isl_aff_set_constant_val(
2302 __isl_take isl_aff *aff, __isl_take isl_val *v);
2303 __isl_give isl_aff *isl_aff_set_coefficient_si(
2304 __isl_take isl_aff *aff,
2305 enum isl_dim_type type, int pos, int v);
2306 __isl_give isl_aff *isl_aff_set_coefficient_val(
2307 __isl_take isl_aff *aff,
2308 enum isl_dim_type type, int pos,
2309 __isl_take isl_val *v);
2311 __isl_give isl_aff *isl_aff_add_constant_si(
2312 __isl_take isl_aff *aff, int v);
2313 __isl_give isl_aff *isl_aff_add_constant_val(
2314 __isl_take isl_aff *aff, __isl_take isl_val *v);
2315 __isl_give isl_aff *isl_aff_add_constant_num_si(
2316 __isl_take isl_aff *aff, int v);
2317 __isl_give isl_aff *isl_aff_add_coefficient_si(
2318 __isl_take isl_aff *aff,
2319 enum isl_dim_type type, int pos, int v);
2320 __isl_give isl_aff *isl_aff_add_coefficient_val(
2321 __isl_take isl_aff *aff,
2322 enum isl_dim_type type, int pos,
2323 __isl_take isl_val *v);
2325 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2326 set the I<numerator> of the constant or coefficient, while
2327 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2328 the constant or coefficient as a whole.
2329 The C<add_constant> and C<add_coefficient> functions add an integer
2330 or rational value to
2331 the possibly rational constant or coefficient.
2332 The C<add_constant_num> functions add an integer value to
2335 =item * Quasipolynomials
2337 Some simple quasipolynomials can be created using the following functions.
2339 #include <isl/polynomial.h>
2340 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2341 __isl_take isl_space *domain);
2342 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2343 __isl_take isl_space *domain);
2344 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2345 __isl_take isl_space *domain);
2346 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2347 __isl_take isl_space *domain);
2348 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2349 __isl_take isl_space *domain);
2350 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2351 __isl_take isl_space *domain,
2352 __isl_take isl_val *val);
2353 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2354 __isl_take isl_space *domain,
2355 enum isl_dim_type type, unsigned pos);
2356 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2357 __isl_take isl_aff *aff);
2359 Recall that the space in which a quasipolynomial lives is a map space
2360 with a one-dimensional range. The C<domain> argument in some of
2361 the functions above corresponds to the domain of this map space.
2363 Quasipolynomials can be copied and freed again using the following
2366 #include <isl/polynomial.h>
2367 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2368 __isl_keep isl_qpolynomial *qp);
2369 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2370 __isl_take isl_qpolynomial *qp);
2372 The constant term of a quasipolynomial can be extracted using
2374 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2375 __isl_keep isl_qpolynomial *qp);
2377 To iterate over all terms in a quasipolynomial,
2380 int isl_qpolynomial_foreach_term(
2381 __isl_keep isl_qpolynomial *qp,
2382 int (*fn)(__isl_take isl_term *term,
2383 void *user), void *user);
2385 The terms themselves can be inspected and freed using
2388 unsigned isl_term_dim(__isl_keep isl_term *term,
2389 enum isl_dim_type type);
2390 __isl_give isl_val *isl_term_get_coefficient_val(
2391 __isl_keep isl_term *term);
2392 int isl_term_get_exp(__isl_keep isl_term *term,
2393 enum isl_dim_type type, unsigned pos);
2394 __isl_give isl_aff *isl_term_get_div(
2395 __isl_keep isl_term *term, unsigned pos);
2396 void isl_term_free(__isl_take isl_term *term);
2398 Each term is a product of parameters, set variables and
2399 integer divisions. The function C<isl_term_get_exp>
2400 returns the exponent of a given dimensions in the given term.
2406 A reduction represents a maximum or a minimum of its
2408 The only reduction type defined by C<isl> is
2409 C<isl_qpolynomial_fold>.
2411 There are currently no functions to directly create such
2412 objects, but they do appear in the piecewise quasipolynomial
2413 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2415 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2417 Reductions can be copied and freed using
2418 the following functions.
2420 #include <isl/polynomial.h>
2421 __isl_give isl_qpolynomial_fold *
2422 isl_qpolynomial_fold_copy(
2423 __isl_keep isl_qpolynomial_fold *fold);
2424 void isl_qpolynomial_fold_free(
2425 __isl_take isl_qpolynomial_fold *fold);
2427 To iterate over all quasipolynomials in a reduction, use
2429 int isl_qpolynomial_fold_foreach_qpolynomial(
2430 __isl_keep isl_qpolynomial_fold *fold,
2431 int (*fn)(__isl_take isl_qpolynomial *qp,
2432 void *user), void *user);
2434 =head3 Multiple Expressions
2436 A multiple expression represents a sequence of zero or
2437 more base expressions, all defined on the same domain space.
2438 The domain space of the multiple expression is the same
2439 as that of the base expressions, but the range space
2440 can be any space. In case the base expressions have
2441 a set space, the corresponding multiple expression
2442 also has a set space.
2443 Objects of the value type do not have an associated space.
2444 The space of a multiple value is therefore always a set space.
2446 The multiple expression types defined by C<isl>
2447 are C<isl_multi_val>, C<isl_multi_aff> and C<isl_multi_pw_aff>.
2449 A multiple expression with the value zero for
2450 each output (or set) dimension can be created
2451 using the following functions.
2453 #include <isl/val.h>
2454 __isl_give isl_multi_val *isl_multi_val_zero(
2455 __isl_take isl_space *space);
2457 #include <isl/aff.h>
2458 __isl_give isl_multi_aff *isl_multi_aff_zero(
2459 __isl_take isl_space *space);
2460 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2461 __isl_take isl_space *space);
2463 An identity function can be created using the following
2464 functions. The space needs to be that of a relation
2465 with the same number of input and output dimensions.
2467 #include <isl/aff.h>
2468 __isl_give isl_multi_aff *isl_multi_aff_identity(
2469 __isl_take isl_space *space);
2470 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2471 __isl_take isl_space *space);
2473 A function that performs a projection on a universe
2474 relation or set can be created using the following functions.
2475 See also the corresponding
2476 projection operations in L</"Unary Operations">.
2478 #include <isl/aff.h>
2479 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2480 __isl_take isl_space *space);
2481 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2482 __isl_take isl_space *space);
2483 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2484 __isl_take isl_space *space,
2485 enum isl_dim_type type,
2486 unsigned first, unsigned n);
2488 A multiple expression can be created from a single
2489 base expression using the following functions.
2490 The space of the created multiple expression is the same
2491 as that of the base expression.
2493 #include <isl/aff.h>
2494 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2495 __isl_take isl_aff *aff);
2496 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2497 __isl_take isl_pw_aff *pa);
2499 A multiple expression can be created from a list
2500 of base expression in a specified space.
2501 The domain of this space needs to be the same
2502 as the domains of the base expressions in the list.
2503 If the base expressions have a set space (or no associated space),
2504 then this space also needs to be a set space.
2506 #include <isl/val.h>
2507 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2508 __isl_take isl_space *space,
2509 __isl_take isl_val_list *list);
2511 #include <isl/aff.h>
2512 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2513 __isl_take isl_space *space,
2514 __isl_take isl_aff_list *list);
2516 As a convenience, a multiple piecewise expression can
2517 also be created from a multiple expression.
2518 Each piecewise expression in the result has a single
2521 #include <isl/aff.h>
2522 __isl_give isl_multi_pw_aff *
2523 isl_multi_pw_aff_from_multi_aff(
2524 __isl_take isl_multi_aff *ma);
2526 A multiple quasi-affine expression can be created from
2527 a multiple value with a given domain space using the following
2530 #include <isl/aff.h>
2531 __isl_give isl_multi_aff *
2532 isl_multi_aff_multi_val_on_space(
2533 __isl_take isl_space *space,
2534 __isl_take isl_multi_val *mv);
2536 Multiple expressions can be copied and freed using
2537 the following functions.
2539 #include <isl/val.h>
2540 __isl_give isl_multi_val *isl_multi_val_copy(
2541 __isl_keep isl_multi_val *mv);
2542 __isl_null isl_multi_val *isl_multi_val_free(
2543 __isl_take isl_multi_val *mv);
2545 #include <isl/aff.h>
2546 __isl_give isl_multi_aff *isl_multi_aff_copy(
2547 __isl_keep isl_multi_aff *maff);
2548 __isl_null isl_multi_aff *isl_multi_aff_free(
2549 __isl_take isl_multi_aff *maff);
2550 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2551 __isl_keep isl_multi_pw_aff *mpa);
2552 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2553 __isl_take isl_multi_pw_aff *mpa);
2555 The base expression at a given position of a multiple
2556 expression can be extracted using the following functions.
2558 #include <isl/val.h>
2559 __isl_give isl_val *isl_multi_val_get_val(
2560 __isl_keep isl_multi_val *mv, int pos);
2562 #include <isl/aff.h>
2563 __isl_give isl_aff *isl_multi_aff_get_aff(
2564 __isl_keep isl_multi_aff *multi, int pos);
2565 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2566 __isl_keep isl_multi_pw_aff *mpa, int pos);
2568 It can be replaced using the following functions.
2570 #include <isl/val.h>
2571 __isl_give isl_multi_val *isl_multi_val_set_val(
2572 __isl_take isl_multi_val *mv, int pos,
2573 __isl_take isl_val *val);
2575 #include <isl/aff.h>
2576 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2577 __isl_take isl_multi_aff *multi, int pos,
2578 __isl_take isl_aff *aff);
2580 =head3 Piecewise Expressions
2582 A piecewise expression is an expression that is described
2583 using zero or more base expression defined over the same
2584 number of cells in the domain space of the base expressions.
2585 All base expressions are defined over the same
2586 domain space and the cells are disjoint.
2587 The space of a piecewise expression is the same as
2588 that of the base expressions.
2589 If the union of the cells is a strict subset of the domain
2590 space, then the value of the piecewise expression outside
2591 this union is different for types derived from quasi-affine
2592 expressions and those derived from quasipolynomials.
2593 Piecewise expressions derived from quasi-affine expressions
2594 are considered to be undefined outside the union of their cells.
2595 Piecewise expressions derived from quasipolynomials
2596 are considered to be zero outside the union of their cells.
2598 Piecewise quasipolynomials are mainly used by the C<barvinok>
2599 library for representing the number of elements in a parametric set or map.
2600 For example, the piecewise quasipolynomial
2602 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2604 represents the number of points in the map
2606 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2608 The piecewise expression types defined by C<isl>
2609 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2610 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2612 A piecewise expression with no cells can be created using
2613 the following functions.
2615 #include <isl/aff.h>
2616 __isl_give isl_pw_aff *isl_pw_aff_empty(
2617 __isl_take isl_space *space);
2618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2619 __isl_take isl_space *space);
2621 A piecewise expression with a single universe cell can be
2622 created using the following functions.
2624 #include <isl/aff.h>
2625 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2626 __isl_take isl_aff *aff);
2627 __isl_give isl_pw_multi_aff *
2628 isl_pw_multi_aff_from_multi_aff(
2629 __isl_take isl_multi_aff *ma);
2631 #include <isl/polynomial.h>
2632 __isl_give isl_pw_qpolynomial *
2633 isl_pw_qpolynomial_from_qpolynomial(
2634 __isl_take isl_qpolynomial *qp);
2636 A piecewise expression with a single specified cell can be
2637 created using the following functions.
2639 #include <isl/aff.h>
2640 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2641 __isl_take isl_set *set, __isl_take isl_aff *aff);
2642 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2643 __isl_take isl_set *set,
2644 __isl_take isl_multi_aff *maff);
2646 #include <isl/polynomial.h>
2647 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2648 __isl_take isl_set *set,
2649 __isl_take isl_qpolynomial *qp);
2651 The following convenience functions first create a base expression and
2652 then create a piecewise expression over a universe domain.
2654 #include <isl/aff.h>
2655 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2656 __isl_take isl_local_space *ls);
2657 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2658 __isl_take isl_local_space *ls,
2659 enum isl_dim_type type, unsigned pos);
2660 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2661 __isl_take isl_local_space *ls);
2662 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2663 __isl_take isl_space *space);
2664 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2665 __isl_take isl_space *space);
2666 __isl_give isl_pw_multi_aff *
2667 isl_pw_multi_aff_project_out_map(
2668 __isl_take isl_space *space,
2669 enum isl_dim_type type,
2670 unsigned first, unsigned n);
2672 #include <isl/polynomial.h>
2673 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2674 __isl_take isl_space *space);
2676 The following convenience functions first create a base expression and
2677 then create a piecewise expression over a given domain.
2679 #include <isl/aff.h>
2680 __isl_give isl_pw_aff *isl_pw_aff_val_on_domain(
2681 __isl_take isl_set *domain,
2682 __isl_take isl_val *v);
2683 __isl_give isl_pw_multi_aff *
2684 isl_pw_multi_aff_multi_val_on_domain(
2685 __isl_take isl_set *domain,
2686 __isl_take isl_multi_val *mv);
2688 As a convenience, a piecewise multiple expression can
2689 also be created from a piecewise expression.
2690 Each multiple expression in the result is derived
2691 from the corresponding base expression.
2693 #include <isl/aff.h>
2694 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2695 __isl_take isl_pw_aff *pa);
2697 Similarly, a piecewise quasipolynomial can be
2698 created from a piecewise quasi-affine expression using
2699 the following function.
2701 #include <isl/polynomial.h>
2702 __isl_give isl_pw_qpolynomial *
2703 isl_pw_qpolynomial_from_pw_aff(
2704 __isl_take isl_pw_aff *pwaff);
2706 Piecewise expressions can be copied and freed using the following functions.
2708 #include <isl/aff.h>
2709 __isl_give isl_pw_aff *isl_pw_aff_copy(
2710 __isl_keep isl_pw_aff *pwaff);
2711 __isl_null isl_pw_aff *isl_pw_aff_free(
2712 __isl_take isl_pw_aff *pwaff);
2713 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2714 __isl_keep isl_pw_multi_aff *pma);
2715 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2716 __isl_take isl_pw_multi_aff *pma);
2718 #include <isl/polynomial.h>
2719 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2720 __isl_keep isl_pw_qpolynomial *pwqp);
2721 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2722 __isl_take isl_pw_qpolynomial *pwqp);
2723 __isl_give isl_pw_qpolynomial_fold *
2724 isl_pw_qpolynomial_fold_copy(
2725 __isl_keep isl_pw_qpolynomial_fold *pwf);
2726 __isl_null isl_pw_qpolynomial_fold *
2727 isl_pw_qpolynomial_fold_free(
2728 __isl_take isl_pw_qpolynomial_fold *pwf);
2730 To iterate over the different cells of a piecewise expression,
2731 use the following functions.
2733 #include <isl/aff.h>
2734 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2735 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2736 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2737 int (*fn)(__isl_take isl_set *set,
2738 __isl_take isl_aff *aff,
2739 void *user), void *user);
2740 int isl_pw_multi_aff_foreach_piece(
2741 __isl_keep isl_pw_multi_aff *pma,
2742 int (*fn)(__isl_take isl_set *set,
2743 __isl_take isl_multi_aff *maff,
2744 void *user), void *user);
2746 #include <isl/polynomial.h>
2747 int isl_pw_qpolynomial_foreach_piece(
2748 __isl_keep isl_pw_qpolynomial *pwqp,
2749 int (*fn)(__isl_take isl_set *set,
2750 __isl_take isl_qpolynomial *qp,
2751 void *user), void *user);
2752 int isl_pw_qpolynomial_foreach_lifted_piece(
2753 __isl_keep isl_pw_qpolynomial *pwqp,
2754 int (*fn)(__isl_take isl_set *set,
2755 __isl_take isl_qpolynomial *qp,
2756 void *user), void *user);
2757 int isl_pw_qpolynomial_fold_foreach_piece(
2758 __isl_keep isl_pw_qpolynomial_fold *pwf,
2759 int (*fn)(__isl_take isl_set *set,
2760 __isl_take isl_qpolynomial_fold *fold,
2761 void *user), void *user);
2762 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2763 __isl_keep isl_pw_qpolynomial_fold *pwf,
2764 int (*fn)(__isl_take isl_set *set,
2765 __isl_take isl_qpolynomial_fold *fold,
2766 void *user), void *user);
2768 As usual, the function C<fn> should return C<0> on success
2769 and C<-1> on failure. The difference between
2770 C<isl_pw_qpolynomial_foreach_piece> and
2771 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2772 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2773 compute unique representations for all existentially quantified
2774 variables and then turn these existentially quantified variables
2775 into extra set variables, adapting the associated quasipolynomial
2776 accordingly. This means that the C<set> passed to C<fn>
2777 will not have any existentially quantified variables, but that
2778 the dimensions of the sets may be different for different
2779 invocations of C<fn>.
2780 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2781 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2783 A piecewise expression consisting of the expressions at a given
2784 position of a piecewise multiple expression can be extracted
2785 using the following function.
2787 #include <isl/aff.h>
2788 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2789 __isl_keep isl_pw_multi_aff *pma, int pos);
2791 These expressions can be replaced using the following function.
2793 #include <isl/aff.h>
2794 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2795 __isl_take isl_pw_multi_aff *pma, unsigned pos,
2796 __isl_take isl_pw_aff *pa);
2798 Note that there is a difference between C<isl_multi_pw_aff> and
2799 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
2800 affine expressions, while the second is a piecewise sequence
2801 of affine expressions. In particular, each of the piecewise
2802 affine expressions in an C<isl_multi_pw_aff> may have a different
2803 domain, while all multiple expressions associated to a cell
2804 in an C<isl_pw_multi_aff> have the same domain.
2805 It is possible to convert between the two, but when converting
2806 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
2807 of the result is the intersection of the domains of the input.
2808 The reverse conversion is exact.
2810 #include <isl/aff.h>
2811 __isl_give isl_pw_multi_aff *
2812 isl_pw_multi_aff_from_multi_pw_aff(
2813 __isl_take isl_multi_pw_aff *mpa);
2814 __isl_give isl_multi_pw_aff *
2815 isl_multi_pw_aff_from_pw_multi_aff(
2816 __isl_take isl_pw_multi_aff *pma);
2818 =head3 Union Expressions
2820 A union expression collects base expressions defined
2821 over different domains. The space of a union expression
2822 is that of the shared parameter space.
2824 The union expression types defined by C<isl>
2825 are C<isl_union_pw_multi_aff>, C<isl_union_pw_qpolynomial> and
2826 C<isl_union_pw_qpolynomial_fold>.
2828 An empty union expression can be created using the following functions.
2830 #include <isl/aff.h>
2831 __isl_give isl_union_pw_multi_aff *
2832 isl_union_pw_multi_aff_empty(
2833 __isl_take isl_space *space);
2835 #include <isl/polynomial.h>
2836 __isl_give isl_union_pw_qpolynomial *
2837 isl_union_pw_qpolynomial_zero(
2838 __isl_take isl_space *space);
2840 A union expression containing a single base expression
2841 can be created using the following functions.
2843 #include <isl/aff.h>
2844 __isl_give isl_union_pw_multi_aff *
2845 isl_union_pw_multi_aff_from_pw_multi_aff(
2846 __isl_take isl_pw_multi_aff *pma);
2848 #include <isl/polynomial.h>
2849 __isl_give isl_union_pw_qpolynomial *
2850 isl_union_pw_qpolynomial_from_pw_qpolynomial(
2851 __isl_take isl_pw_qpolynomial *pwqp);
2853 The following function creates a base expression on each
2854 of the sets in the union set and collects the results.
2856 #include <isl/aff.h>
2857 __isl_give isl_union_pw_multi_aff *
2858 isl_union_pw_multi_aff_multi_val_on_domain(
2859 __isl_take isl_union_set *domain,
2860 __isl_take isl_multi_val *mv);
2862 A base expression can be added to a union expression using
2863 the following functions.
2865 #include <isl/aff.h>
2866 __isl_give isl_union_pw_multi_aff *
2867 isl_union_pw_multi_aff_add_pw_multi_aff(
2868 __isl_take isl_union_pw_multi_aff *upma,
2869 __isl_take isl_pw_multi_aff *pma);
2871 #include <isl/polynomial.h>
2872 __isl_give isl_union_pw_qpolynomial *
2873 isl_union_pw_qpolynomial_add_pw_qpolynomial(
2874 __isl_take isl_union_pw_qpolynomial *upwqp,
2875 __isl_take isl_pw_qpolynomial *pwqp);
2877 Union expressions can be copied and freed using
2878 the following functions.
2880 #include <isl/aff.h>
2881 __isl_give isl_union_pw_multi_aff *
2882 isl_union_pw_multi_aff_copy(
2883 __isl_keep isl_union_pw_multi_aff *upma);
2884 __isl_null isl_union_pw_multi_aff *
2885 isl_union_pw_multi_aff_free(
2886 __isl_take isl_union_pw_multi_aff *upma);
2888 #include <isl/polynomial.h>
2889 __isl_give isl_union_pw_qpolynomial *
2890 isl_union_pw_qpolynomial_copy(
2891 __isl_keep isl_union_pw_qpolynomial *upwqp);
2892 __isl_null isl_union_pw_qpolynomial *
2893 isl_union_pw_qpolynomial_free(
2894 __isl_take isl_union_pw_qpolynomial *upwqp);
2895 __isl_give isl_union_pw_qpolynomial_fold *
2896 isl_union_pw_qpolynomial_fold_copy(
2897 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2898 __isl_null isl_union_pw_qpolynomial_fold *
2899 isl_union_pw_qpolynomial_fold_free(
2900 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2902 To iterate over the base expressions in a union expression,
2903 use the following functions.
2905 #include <isl/aff.h>
2906 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
2907 __isl_keep isl_union_pw_multi_aff *upma,
2908 int (*fn)(__isl_take isl_pw_multi_aff *pma,
2909 void *user), void *user);
2911 #include <isl/polynomial.h>
2912 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2913 __isl_keep isl_union_pw_qpolynomial *upwqp,
2914 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
2915 void *user), void *user);
2916 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2917 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2918 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2919 void *user), void *user);
2921 To extract the base expression in a given space from a union, use
2922 the following functions.
2924 #include <isl/aff.h>
2925 __isl_give isl_pw_multi_aff *
2926 isl_union_pw_multi_aff_extract_pw_multi_aff(
2927 __isl_keep isl_union_pw_multi_aff *upma,
2928 __isl_take isl_space *space);
2930 #include <isl/polynomial.h>
2931 __isl_give isl_pw_qpolynomial *
2932 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2933 __isl_keep isl_union_pw_qpolynomial *upwqp,
2934 __isl_take isl_space *space);
2936 =head2 Input and Output
2938 For set and relation,
2939 C<isl> supports its own input/output format, which is similar
2940 to the C<Omega> format, but also supports the C<PolyLib> format
2942 For other object types, typically only an C<isl> format is supported.
2944 =head3 C<isl> format
2946 The C<isl> format is similar to that of C<Omega>, but has a different
2947 syntax for describing the parameters and allows for the definition
2948 of an existentially quantified variable as the integer division
2949 of an affine expression.
2950 For example, the set of integers C<i> between C<0> and C<n>
2951 such that C<i % 10 <= 6> can be described as
2953 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
2956 A set or relation can have several disjuncts, separated
2957 by the keyword C<or>. Each disjunct is either a conjunction
2958 of constraints or a projection (C<exists>) of a conjunction
2959 of constraints. The constraints are separated by the keyword
2962 =head3 C<PolyLib> format
2964 If the represented set is a union, then the first line
2965 contains a single number representing the number of disjuncts.
2966 Otherwise, a line containing the number C<1> is optional.
2968 Each disjunct is represented by a matrix of constraints.
2969 The first line contains two numbers representing
2970 the number of rows and columns,
2971 where the number of rows is equal to the number of constraints
2972 and the number of columns is equal to two plus the number of variables.
2973 The following lines contain the actual rows of the constraint matrix.
2974 In each row, the first column indicates whether the constraint
2975 is an equality (C<0>) or inequality (C<1>). The final column
2976 corresponds to the constant term.
2978 If the set is parametric, then the coefficients of the parameters
2979 appear in the last columns before the constant column.
2980 The coefficients of any existentially quantified variables appear
2981 between those of the set variables and those of the parameters.
2983 =head3 Extended C<PolyLib> format
2985 The extended C<PolyLib> format is nearly identical to the
2986 C<PolyLib> format. The only difference is that the line
2987 containing the number of rows and columns of a constraint matrix
2988 also contains four additional numbers:
2989 the number of output dimensions, the number of input dimensions,
2990 the number of local dimensions (i.e., the number of existentially
2991 quantified variables) and the number of parameters.
2992 For sets, the number of ``output'' dimensions is equal
2993 to the number of set dimensions, while the number of ``input''
2998 Objects can be read from input using the following functions.
3000 #include <isl/val.h>
3001 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
3004 #include <isl/set.h>
3005 __isl_give isl_basic_set *isl_basic_set_read_from_file(
3006 isl_ctx *ctx, FILE *input);
3007 __isl_give isl_basic_set *isl_basic_set_read_from_str(
3008 isl_ctx *ctx, const char *str);
3009 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
3011 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
3014 #include <isl/map.h>
3015 __isl_give isl_basic_map *isl_basic_map_read_from_file(
3016 isl_ctx *ctx, FILE *input);
3017 __isl_give isl_basic_map *isl_basic_map_read_from_str(
3018 isl_ctx *ctx, const char *str);
3019 __isl_give isl_map *isl_map_read_from_file(
3020 isl_ctx *ctx, FILE *input);
3021 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
3024 #include <isl/union_set.h>
3025 __isl_give isl_union_set *isl_union_set_read_from_file(
3026 isl_ctx *ctx, FILE *input);
3027 __isl_give isl_union_set *isl_union_set_read_from_str(
3028 isl_ctx *ctx, const char *str);
3030 #include <isl/union_map.h>
3031 __isl_give isl_union_map *isl_union_map_read_from_file(
3032 isl_ctx *ctx, FILE *input);
3033 __isl_give isl_union_map *isl_union_map_read_from_str(
3034 isl_ctx *ctx, const char *str);
3036 #include <isl/aff.h>
3037 __isl_give isl_aff *isl_aff_read_from_str(
3038 isl_ctx *ctx, const char *str);
3039 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3040 isl_ctx *ctx, const char *str);
3041 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3042 isl_ctx *ctx, const char *str);
3043 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3044 isl_ctx *ctx, const char *str);
3045 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
3046 isl_ctx *ctx, const char *str);
3047 __isl_give isl_union_pw_multi_aff *
3048 isl_union_pw_multi_aff_read_from_str(
3049 isl_ctx *ctx, const char *str);
3051 #include <isl/polynomial.h>
3052 __isl_give isl_union_pw_qpolynomial *
3053 isl_union_pw_qpolynomial_read_from_str(
3054 isl_ctx *ctx, const char *str);
3056 For sets and relations,
3057 the input format is autodetected and may be either the C<PolyLib> format
3058 or the C<isl> format.
3062 Before anything can be printed, an C<isl_printer> needs to
3065 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
3067 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
3068 __isl_null isl_printer *isl_printer_free(
3069 __isl_take isl_printer *printer);
3070 __isl_give char *isl_printer_get_str(
3071 __isl_keep isl_printer *printer);
3073 The printer can be inspected using the following functions.
3075 FILE *isl_printer_get_file(
3076 __isl_keep isl_printer *printer);
3077 int isl_printer_get_output_format(
3078 __isl_keep isl_printer *p);
3080 The behavior of the printer can be modified in various ways
3082 __isl_give isl_printer *isl_printer_set_output_format(
3083 __isl_take isl_printer *p, int output_format);
3084 __isl_give isl_printer *isl_printer_set_indent(
3085 __isl_take isl_printer *p, int indent);
3086 __isl_give isl_printer *isl_printer_set_indent_prefix(
3087 __isl_take isl_printer *p, const char *prefix);
3088 __isl_give isl_printer *isl_printer_indent(
3089 __isl_take isl_printer *p, int indent);
3090 __isl_give isl_printer *isl_printer_set_prefix(
3091 __isl_take isl_printer *p, const char *prefix);
3092 __isl_give isl_printer *isl_printer_set_suffix(
3093 __isl_take isl_printer *p, const char *suffix);
3095 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
3096 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
3097 and defaults to C<ISL_FORMAT_ISL>.
3098 Each line in the output is prefixed by C<indent_prefix>,
3099 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
3100 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
3101 In the C<PolyLib> format output,
3102 the coefficients of the existentially quantified variables
3103 appear between those of the set variables and those
3105 The function C<isl_printer_indent> increases the indentation
3106 by the specified amount (which may be negative).
3108 To actually print something, use
3110 #include <isl/printer.h>
3111 __isl_give isl_printer *isl_printer_print_double(
3112 __isl_take isl_printer *p, double d);
3114 #include <isl/val.h>
3115 __isl_give isl_printer *isl_printer_print_val(
3116 __isl_take isl_printer *p, __isl_keep isl_val *v);
3118 #include <isl/set.h>
3119 __isl_give isl_printer *isl_printer_print_basic_set(
3120 __isl_take isl_printer *printer,
3121 __isl_keep isl_basic_set *bset);
3122 __isl_give isl_printer *isl_printer_print_set(
3123 __isl_take isl_printer *printer,
3124 __isl_keep isl_set *set);
3126 #include <isl/map.h>
3127 __isl_give isl_printer *isl_printer_print_basic_map(
3128 __isl_take isl_printer *printer,
3129 __isl_keep isl_basic_map *bmap);
3130 __isl_give isl_printer *isl_printer_print_map(
3131 __isl_take isl_printer *printer,
3132 __isl_keep isl_map *map);
3134 #include <isl/union_set.h>
3135 __isl_give isl_printer *isl_printer_print_union_set(
3136 __isl_take isl_printer *p,
3137 __isl_keep isl_union_set *uset);
3139 #include <isl/union_map.h>
3140 __isl_give isl_printer *isl_printer_print_union_map(
3141 __isl_take isl_printer *p,
3142 __isl_keep isl_union_map *umap);
3144 #include <isl/val.h>
3145 __isl_give isl_printer *isl_printer_print_multi_val(
3146 __isl_take isl_printer *p,
3147 __isl_keep isl_multi_val *mv);
3149 #include <isl/aff.h>
3150 __isl_give isl_printer *isl_printer_print_aff(
3151 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3152 __isl_give isl_printer *isl_printer_print_multi_aff(
3153 __isl_take isl_printer *p,
3154 __isl_keep isl_multi_aff *maff);
3155 __isl_give isl_printer *isl_printer_print_pw_aff(
3156 __isl_take isl_printer *p,
3157 __isl_keep isl_pw_aff *pwaff);
3158 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3159 __isl_take isl_printer *p,
3160 __isl_keep isl_pw_multi_aff *pma);
3161 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3162 __isl_take isl_printer *p,
3163 __isl_keep isl_multi_pw_aff *mpa);
3164 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3165 __isl_take isl_printer *p,
3166 __isl_keep isl_union_pw_multi_aff *upma);
3168 #include <isl/polynomial.h>
3169 __isl_give isl_printer *isl_printer_print_qpolynomial(
3170 __isl_take isl_printer *p,
3171 __isl_keep isl_qpolynomial *qp);
3172 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3173 __isl_take isl_printer *p,
3174 __isl_keep isl_pw_qpolynomial *pwqp);
3175 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3176 __isl_take isl_printer *p,
3177 __isl_keep isl_union_pw_qpolynomial *upwqp);
3179 __isl_give isl_printer *
3180 isl_printer_print_pw_qpolynomial_fold(
3181 __isl_take isl_printer *p,
3182 __isl_keep isl_pw_qpolynomial_fold *pwf);
3183 __isl_give isl_printer *
3184 isl_printer_print_union_pw_qpolynomial_fold(
3185 __isl_take isl_printer *p,
3186 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3188 For C<isl_printer_print_qpolynomial>,
3189 C<isl_printer_print_pw_qpolynomial> and
3190 C<isl_printer_print_pw_qpolynomial_fold>,
3191 the output format of the printer
3192 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3193 For C<isl_printer_print_union_pw_qpolynomial> and
3194 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3196 In case of printing in C<ISL_FORMAT_C>, the user may want
3197 to set the names of all dimensions first.
3199 When called on a file printer, the following function flushes
3200 the file. When called on a string printer, the buffer is cleared.
3202 __isl_give isl_printer *isl_printer_flush(
3203 __isl_take isl_printer *p);
3205 Alternatively, a string representation can be obtained
3206 directly using the following functions, which always print
3209 #include <isl/space.h>
3210 __isl_give char *isl_space_to_str(
3211 __isl_keep isl_space *space);
3213 #include <isl/val.h>
3214 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3215 __isl_give char *isl_multi_val_to_str(
3216 __isl_keep isl_multi_val *mv);
3218 #include <isl/set.h>
3219 __isl_give char *isl_set_to_str(
3220 __isl_keep isl_set *set);
3222 #include <isl/union_set.h>
3223 __isl_give char *isl_union_set_to_str(
3224 __isl_keep isl_union_set *uset);
3226 #include <isl/map.h>
3227 __isl_give char *isl_map_to_str(
3228 __isl_keep isl_map *map);
3230 #include <isl/union_map.h>
3231 __isl_give char *isl_union_map_to_str(
3232 __isl_keep isl_union_map *umap);
3234 #include <isl/aff.h>
3235 __isl_give char *isl_multi_aff_to_str(
3236 __isl_keep isl_multi_aff *aff);
3237 __isl_give char *isl_union_pw_multi_aff_to_str(
3238 __isl_keep isl_union_pw_multi_aff *upma);
3242 =head3 Unary Properties
3248 The following functions test whether the given set or relation
3249 contains any integer points. The ``plain'' variants do not perform
3250 any computations, but simply check if the given set or relation
3251 is already known to be empty.
3253 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3254 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3255 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3256 int isl_set_is_empty(__isl_keep isl_set *set);
3257 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3258 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3259 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3260 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3261 int isl_map_is_empty(__isl_keep isl_map *map);
3262 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3264 =item * Universality
3266 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3267 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3268 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3270 =item * Single-valuedness
3272 #include <isl/set.h>
3273 int isl_set_is_singleton(__isl_keep isl_set *set);
3275 #include <isl/map.h>
3276 int isl_basic_map_is_single_valued(
3277 __isl_keep isl_basic_map *bmap);
3278 int isl_map_plain_is_single_valued(
3279 __isl_keep isl_map *map);
3280 int isl_map_is_single_valued(__isl_keep isl_map *map);
3282 #include <isl/union_map.h>
3283 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3287 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3288 int isl_map_is_injective(__isl_keep isl_map *map);
3289 int isl_union_map_plain_is_injective(
3290 __isl_keep isl_union_map *umap);
3291 int isl_union_map_is_injective(
3292 __isl_keep isl_union_map *umap);
3296 int isl_map_is_bijective(__isl_keep isl_map *map);
3297 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3301 __isl_give isl_val *
3302 isl_basic_map_plain_get_val_if_fixed(
3303 __isl_keep isl_basic_map *bmap,
3304 enum isl_dim_type type, unsigned pos);
3305 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3306 __isl_keep isl_set *set,
3307 enum isl_dim_type type, unsigned pos);
3308 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3309 __isl_keep isl_map *map,
3310 enum isl_dim_type type, unsigned pos);
3312 If the set or relation obviously lies on a hyperplane where the given dimension
3313 has a fixed value, then return that value.
3314 Otherwise return NaN.
3318 int isl_set_dim_residue_class_val(
3319 __isl_keep isl_set *set,
3320 int pos, __isl_give isl_val **modulo,
3321 __isl_give isl_val **residue);
3323 Check if the values of the given set dimension are equal to a fixed
3324 value modulo some integer value. If so, assign the modulo to C<*modulo>
3325 and the fixed value to C<*residue>. If the given dimension attains only
3326 a single value, then assign C<0> to C<*modulo> and the fixed value to
3328 If the dimension does not attain only a single value and if no modulo
3329 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3333 To check whether the description of a set, relation or function depends
3334 on one or more given dimensions,
3335 the following functions can be used.
3337 #include <isl/constraint.h>
3338 int isl_constraint_involves_dims(
3339 __isl_keep isl_constraint *constraint,
3340 enum isl_dim_type type, unsigned first, unsigned n);
3342 #include <isl/set.h>
3343 int isl_basic_set_involves_dims(
3344 __isl_keep isl_basic_set *bset,
3345 enum isl_dim_type type, unsigned first, unsigned n);
3346 int isl_set_involves_dims(__isl_keep isl_set *set,
3347 enum isl_dim_type type, unsigned first, unsigned n);
3349 #include <isl/map.h>
3350 int isl_basic_map_involves_dims(
3351 __isl_keep isl_basic_map *bmap,
3352 enum isl_dim_type type, unsigned first, unsigned n);
3353 int isl_map_involves_dims(__isl_keep isl_map *map,
3354 enum isl_dim_type type, unsigned first, unsigned n);
3356 #include <isl/union_map.h>
3357 int isl_union_map_involves_dims(
3358 __isl_keep isl_union_map *umap,
3359 enum isl_dim_type type, unsigned first, unsigned n);
3361 #include <isl/aff.h>
3362 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3363 enum isl_dim_type type, unsigned first, unsigned n);
3364 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3365 enum isl_dim_type type, unsigned first, unsigned n);
3366 int isl_multi_aff_involves_dims(
3367 __isl_keep isl_multi_aff *ma,
3368 enum isl_dim_type type, unsigned first, unsigned n);
3369 int isl_multi_pw_aff_involves_dims(
3370 __isl_keep isl_multi_pw_aff *mpa,
3371 enum isl_dim_type type, unsigned first, unsigned n);
3373 Similarly, the following functions can be used to check whether
3374 a given dimension is involved in any lower or upper bound.
3376 #include <isl/set.h>
3377 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3378 enum isl_dim_type type, unsigned pos);
3379 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3380 enum isl_dim_type type, unsigned pos);
3382 Note that these functions return true even if there is a bound on
3383 the dimension on only some of the basic sets of C<set>.
3384 To check if they have a bound for all of the basic sets in C<set>,
3385 use the following functions instead.
3387 #include <isl/set.h>
3388 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3389 enum isl_dim_type type, unsigned pos);
3390 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3391 enum isl_dim_type type, unsigned pos);
3395 To check whether a set is a parameter domain, use this function:
3397 int isl_set_is_params(__isl_keep isl_set *set);
3398 int isl_union_set_is_params(
3399 __isl_keep isl_union_set *uset);
3403 The following functions check whether the space of the given
3404 (basic) set or relation range is a wrapped relation.
3406 #include <isl/space.h>
3407 int isl_space_is_wrapping(
3408 __isl_keep isl_space *space);
3409 int isl_space_domain_is_wrapping(
3410 __isl_keep isl_space *space);
3411 int isl_space_range_is_wrapping(
3412 __isl_keep isl_space *space);
3414 #include <isl/set.h>
3415 int isl_basic_set_is_wrapping(
3416 __isl_keep isl_basic_set *bset);
3417 int isl_set_is_wrapping(__isl_keep isl_set *set);
3419 #include <isl/map.h>
3420 int isl_map_domain_is_wrapping(
3421 __isl_keep isl_map *map);
3422 int isl_map_range_is_wrapping(
3423 __isl_keep isl_map *map);
3425 #include <isl/val.h>
3426 int isl_multi_val_range_is_wrapping(
3427 __isl_keep isl_multi_val *mv);
3429 #include <isl/aff.h>
3430 int isl_multi_aff_range_is_wrapping(
3431 __isl_keep isl_multi_aff *ma);
3432 int isl_multi_pw_aff_range_is_wrapping(
3433 __isl_keep isl_multi_pw_aff *mpa);
3435 The input to C<isl_space_is_wrapping> should
3436 be the space of a set, while that of
3437 C<isl_space_domain_is_wrapping> and
3438 C<isl_space_range_is_wrapping> should be the space of a relation.
3440 =item * Internal Product
3442 int isl_basic_map_can_zip(
3443 __isl_keep isl_basic_map *bmap);
3444 int isl_map_can_zip(__isl_keep isl_map *map);
3446 Check whether the product of domain and range of the given relation
3448 i.e., whether both domain and range are nested relations.
3452 int isl_basic_map_can_curry(
3453 __isl_keep isl_basic_map *bmap);
3454 int isl_map_can_curry(__isl_keep isl_map *map);
3456 Check whether the domain of the (basic) relation is a wrapped relation.
3458 int isl_basic_map_can_uncurry(
3459 __isl_keep isl_basic_map *bmap);
3460 int isl_map_can_uncurry(__isl_keep isl_map *map);
3462 Check whether the range of the (basic) relation is a wrapped relation.
3464 =item * Special Values
3466 #include <isl/aff.h>
3467 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3468 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3470 Check whether the given expression is a constant.
3472 #include <isl/aff.h>
3473 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3474 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3476 Check whether the given expression is equal to or involves NaN.
3478 #include <isl/aff.h>
3479 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3481 Check whether the affine expression is obviously zero.
3485 =head3 Binary Properties
3491 The following functions check whether two objects
3492 represent the same set, relation or function.
3493 The C<plain> variants only return true if the objects
3494 are obviously the same. That is, they may return false
3495 even if the objects are the same, but they will never
3496 return true if the objects are not the same.
3498 #include <isl/set.h>
3499 int isl_basic_set_plain_is_equal(
3500 __isl_keep isl_basic_set *bset1,
3501 __isl_keep isl_basic_set *bset2);
3502 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3503 __isl_keep isl_set *set2);
3504 int isl_set_is_equal(__isl_keep isl_set *set1,
3505 __isl_keep isl_set *set2);
3507 #include <isl/map.h>
3508 int isl_basic_map_is_equal(
3509 __isl_keep isl_basic_map *bmap1,
3510 __isl_keep isl_basic_map *bmap2);
3511 int isl_map_is_equal(__isl_keep isl_map *map1,
3512 __isl_keep isl_map *map2);
3513 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3514 __isl_keep isl_map *map2);
3516 #include <isl/union_set.h>
3517 int isl_union_set_is_equal(
3518 __isl_keep isl_union_set *uset1,
3519 __isl_keep isl_union_set *uset2);
3521 #include <isl/union_map.h>
3522 int isl_union_map_is_equal(
3523 __isl_keep isl_union_map *umap1,
3524 __isl_keep isl_union_map *umap2);
3526 #include <isl/aff.h>
3527 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3528 __isl_keep isl_aff *aff2);
3529 int isl_multi_aff_plain_is_equal(
3530 __isl_keep isl_multi_aff *maff1,
3531 __isl_keep isl_multi_aff *maff2);
3532 int isl_pw_aff_plain_is_equal(
3533 __isl_keep isl_pw_aff *pwaff1,
3534 __isl_keep isl_pw_aff *pwaff2);
3535 int isl_pw_multi_aff_plain_is_equal(
3536 __isl_keep isl_pw_multi_aff *pma1,
3537 __isl_keep isl_pw_multi_aff *pma2);
3538 int isl_multi_pw_aff_plain_is_equal(
3539 __isl_keep isl_multi_pw_aff *mpa1,
3540 __isl_keep isl_multi_pw_aff *mpa2);
3541 int isl_multi_pw_aff_is_equal(
3542 __isl_keep isl_multi_pw_aff *mpa1,
3543 __isl_keep isl_multi_pw_aff *mpa2);
3544 int isl_union_pw_multi_aff_plain_is_equal(
3545 __isl_keep isl_union_pw_multi_aff *upma1,
3546 __isl_keep isl_union_pw_multi_aff *upma2);
3548 #include <isl/polynomial.h>
3549 int isl_union_pw_qpolynomial_plain_is_equal(
3550 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3551 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3552 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3553 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3554 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3556 =item * Disjointness
3558 int isl_basic_set_is_disjoint(
3559 __isl_keep isl_basic_set *bset1,
3560 __isl_keep isl_basic_set *bset2);
3561 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3562 __isl_keep isl_set *set2);
3563 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3564 __isl_keep isl_set *set2);
3565 int isl_basic_map_is_disjoint(
3566 __isl_keep isl_basic_map *bmap1,
3567 __isl_keep isl_basic_map *bmap2);
3568 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3569 __isl_keep isl_map *map2);
3573 int isl_basic_set_is_subset(
3574 __isl_keep isl_basic_set *bset1,
3575 __isl_keep isl_basic_set *bset2);
3576 int isl_set_is_subset(__isl_keep isl_set *set1,
3577 __isl_keep isl_set *set2);
3578 int isl_set_is_strict_subset(
3579 __isl_keep isl_set *set1,
3580 __isl_keep isl_set *set2);
3581 int isl_union_set_is_subset(
3582 __isl_keep isl_union_set *uset1,
3583 __isl_keep isl_union_set *uset2);
3584 int isl_union_set_is_strict_subset(
3585 __isl_keep isl_union_set *uset1,
3586 __isl_keep isl_union_set *uset2);
3587 int isl_basic_map_is_subset(
3588 __isl_keep isl_basic_map *bmap1,
3589 __isl_keep isl_basic_map *bmap2);
3590 int isl_basic_map_is_strict_subset(
3591 __isl_keep isl_basic_map *bmap1,
3592 __isl_keep isl_basic_map *bmap2);
3593 int isl_map_is_subset(
3594 __isl_keep isl_map *map1,
3595 __isl_keep isl_map *map2);
3596 int isl_map_is_strict_subset(
3597 __isl_keep isl_map *map1,
3598 __isl_keep isl_map *map2);
3599 int isl_union_map_is_subset(
3600 __isl_keep isl_union_map *umap1,
3601 __isl_keep isl_union_map *umap2);
3602 int isl_union_map_is_strict_subset(
3603 __isl_keep isl_union_map *umap1,
3604 __isl_keep isl_union_map *umap2);
3606 Check whether the first argument is a (strict) subset of the
3611 Every comparison function returns a negative value if the first
3612 argument is considered smaller than the second, a positive value
3613 if the first argument is considered greater and zero if the two
3614 constraints are considered the same by the comparison criterion.
3616 #include <isl/constraint.h>
3617 int isl_constraint_plain_cmp(
3618 __isl_keep isl_constraint *c1,
3619 __isl_keep isl_constraint *c2);
3621 This function is useful for sorting C<isl_constraint>s.
3622 The order depends on the internal representation of the inputs.
3623 The order is fixed over different calls to the function (assuming
3624 the internal representation of the inputs has not changed), but may
3625 change over different versions of C<isl>.
3627 #include <isl/constraint.h>
3628 int isl_constraint_cmp_last_non_zero(
3629 __isl_keep isl_constraint *c1,
3630 __isl_keep isl_constraint *c2);
3632 This function can be used to sort constraints that live in the same
3633 local space. Constraints that involve ``earlier'' dimensions or
3634 that have a smaller coefficient for the shared latest dimension
3635 are considered smaller than other constraints.
3636 This function only defines a B<partial> order.
3638 #include <isl/set.h>
3639 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3640 __isl_keep isl_set *set2);
3642 This function is useful for sorting C<isl_set>s.
3643 The order depends on the internal representation of the inputs.
3644 The order is fixed over different calls to the function (assuming
3645 the internal representation of the inputs has not changed), but may
3646 change over different versions of C<isl>.
3648 #include <isl/aff.h>
3649 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3650 __isl_keep isl_pw_aff *pa2);
3652 The function C<isl_pw_aff_plain_cmp> can be used to sort
3653 C<isl_pw_aff>s. The order is not strictly defined.
3654 The current order sorts expressions that only involve
3655 earlier dimensions before those that involve later dimensions.
3659 =head2 Unary Operations
3665 __isl_give isl_set *isl_set_complement(
3666 __isl_take isl_set *set);
3667 __isl_give isl_map *isl_map_complement(
3668 __isl_take isl_map *map);
3672 #include <isl/space.h>
3673 __isl_give isl_space *isl_space_reverse(
3674 __isl_take isl_space *space);
3676 #include <isl/map.h>
3677 __isl_give isl_basic_map *isl_basic_map_reverse(
3678 __isl_take isl_basic_map *bmap);
3679 __isl_give isl_map *isl_map_reverse(
3680 __isl_take isl_map *map);
3682 #include <isl/union_map.h>
3683 __isl_give isl_union_map *isl_union_map_reverse(
3684 __isl_take isl_union_map *umap);
3688 #include <isl/space.h>
3689 __isl_give isl_space *isl_space_domain(
3690 __isl_take isl_space *space);
3691 __isl_give isl_space *isl_space_range(
3692 __isl_take isl_space *space);
3693 __isl_give isl_space *isl_space_params(
3694 __isl_take isl_space *space);
3696 #include <isl/local_space.h>
3697 __isl_give isl_local_space *isl_local_space_domain(
3698 __isl_take isl_local_space *ls);
3699 __isl_give isl_local_space *isl_local_space_range(
3700 __isl_take isl_local_space *ls);
3702 #include <isl/set.h>
3703 __isl_give isl_basic_set *isl_basic_set_project_out(
3704 __isl_take isl_basic_set *bset,
3705 enum isl_dim_type type, unsigned first, unsigned n);
3706 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3707 enum isl_dim_type type, unsigned first, unsigned n);
3708 __isl_give isl_basic_set *isl_basic_set_params(
3709 __isl_take isl_basic_set *bset);
3710 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
3712 #include <isl/map.h>
3713 __isl_give isl_basic_map *isl_basic_map_project_out(
3714 __isl_take isl_basic_map *bmap,
3715 enum isl_dim_type type, unsigned first, unsigned n);
3716 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3717 enum isl_dim_type type, unsigned first, unsigned n);
3718 __isl_give isl_basic_set *isl_basic_map_domain(
3719 __isl_take isl_basic_map *bmap);
3720 __isl_give isl_basic_set *isl_basic_map_range(
3721 __isl_take isl_basic_map *bmap);
3722 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
3723 __isl_give isl_set *isl_map_domain(
3724 __isl_take isl_map *bmap);
3725 __isl_give isl_set *isl_map_range(
3726 __isl_take isl_map *map);
3728 #include <isl/union_set.h>
3729 __isl_give isl_set *isl_union_set_params(
3730 __isl_take isl_union_set *uset);
3732 #include <isl/union_map.h>
3733 __isl_give isl_union_map *isl_union_map_project_out(
3734 __isl_take isl_union_map *umap,
3735 enum isl_dim_type type, unsigned first, unsigned n);
3736 __isl_give isl_set *isl_union_map_params(
3737 __isl_take isl_union_map *umap);
3738 __isl_give isl_union_set *isl_union_map_domain(
3739 __isl_take isl_union_map *umap);
3740 __isl_give isl_union_set *isl_union_map_range(
3741 __isl_take isl_union_map *umap);
3743 The function C<isl_union_map_project_out> can only project out
3746 #include <isl/aff.h>
3747 __isl_give isl_aff *isl_aff_project_domain_on_params(
3748 __isl_take isl_aff *aff);
3749 __isl_give isl_pw_multi_aff *
3750 isl_pw_multi_aff_project_domain_on_params(
3751 __isl_take isl_pw_multi_aff *pma);
3752 __isl_give isl_set *isl_pw_aff_domain(
3753 __isl_take isl_pw_aff *pwaff);
3754 __isl_give isl_set *isl_pw_multi_aff_domain(
3755 __isl_take isl_pw_multi_aff *pma);
3756 __isl_give isl_set *isl_multi_pw_aff_domain(
3757 __isl_take isl_multi_pw_aff *mpa);
3758 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3759 __isl_take isl_union_pw_multi_aff *upma);
3760 __isl_give isl_set *isl_pw_aff_params(
3761 __isl_take isl_pw_aff *pwa);
3763 #include <isl/polynomial.h>
3764 __isl_give isl_qpolynomial *
3765 isl_qpolynomial_project_domain_on_params(
3766 __isl_take isl_qpolynomial *qp);
3767 __isl_give isl_pw_qpolynomial *
3768 isl_pw_qpolynomial_project_domain_on_params(
3769 __isl_take isl_pw_qpolynomial *pwqp);
3770 __isl_give isl_pw_qpolynomial_fold *
3771 isl_pw_qpolynomial_fold_project_domain_on_params(
3772 __isl_take isl_pw_qpolynomial_fold *pwf);
3773 __isl_give isl_set *isl_pw_qpolynomial_domain(
3774 __isl_take isl_pw_qpolynomial *pwqp);
3775 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3776 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3777 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3778 __isl_take isl_union_pw_qpolynomial *upwqp);
3780 #include <isl/space.h>
3781 __isl_give isl_space *isl_space_domain_map(
3782 __isl_take isl_space *space);
3783 __isl_give isl_space *isl_space_range_map(
3784 __isl_take isl_space *space);
3786 #include <isl/map.h>
3787 __isl_give isl_map *isl_set_wrapped_domain_map(
3788 __isl_take isl_set *set);
3789 __isl_give isl_basic_map *isl_basic_map_domain_map(
3790 __isl_take isl_basic_map *bmap);
3791 __isl_give isl_basic_map *isl_basic_map_range_map(
3792 __isl_take isl_basic_map *bmap);
3793 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
3794 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
3796 #include <isl/union_map.h>
3797 __isl_give isl_union_map *isl_union_map_domain_map(
3798 __isl_take isl_union_map *umap);
3799 __isl_give isl_union_map *isl_union_map_range_map(
3800 __isl_take isl_union_map *umap);
3801 __isl_give isl_union_map *
3802 isl_union_set_wrapped_domain_map(
3803 __isl_take isl_union_set *uset);
3805 The functions above construct a (basic, regular or union) relation
3806 that maps (a wrapped version of) the input relation to its domain or range.
3807 C<isl_set_wrapped_domain_map> maps the input set to the domain
3808 of its wrapped relation.
3812 __isl_give isl_basic_set *isl_basic_set_eliminate(
3813 __isl_take isl_basic_set *bset,
3814 enum isl_dim_type type,
3815 unsigned first, unsigned n);
3816 __isl_give isl_set *isl_set_eliminate(
3817 __isl_take isl_set *set, enum isl_dim_type type,
3818 unsigned first, unsigned n);
3819 __isl_give isl_basic_map *isl_basic_map_eliminate(
3820 __isl_take isl_basic_map *bmap,
3821 enum isl_dim_type type,
3822 unsigned first, unsigned n);
3823 __isl_give isl_map *isl_map_eliminate(
3824 __isl_take isl_map *map, enum isl_dim_type type,
3825 unsigned first, unsigned n);
3827 Eliminate the coefficients for the given dimensions from the constraints,
3828 without removing the dimensions.
3830 =item * Constructing a set from a parameter domain
3832 A zero-dimensional space or (basic) set can be constructed
3833 on a given parameter domain using the following functions.
3835 #include <isl/space.h>
3836 __isl_give isl_space *isl_space_set_from_params(
3837 __isl_take isl_space *space);
3839 #include <isl/set.h>
3840 __isl_give isl_basic_set *isl_basic_set_from_params(
3841 __isl_take isl_basic_set *bset);
3842 __isl_give isl_set *isl_set_from_params(
3843 __isl_take isl_set *set);
3845 =item * Constructing a relation from a set
3847 Create a relation with the given set as domain or range.
3848 The range or domain of the created relation is a zero-dimensional
3849 flat anonymous space.
3851 #include <isl/space.h>
3852 __isl_give isl_space *isl_space_from_domain(
3853 __isl_take isl_space *space);
3854 __isl_give isl_space *isl_space_from_range(
3855 __isl_take isl_space *space);
3856 __isl_give isl_space *isl_space_map_from_set(
3857 __isl_take isl_space *space);
3858 __isl_give isl_space *isl_space_map_from_domain_and_range(
3859 __isl_take isl_space *domain,
3860 __isl_take isl_space *range);
3862 #include <isl/local_space.h>
3863 __isl_give isl_local_space *isl_local_space_from_domain(
3864 __isl_take isl_local_space *ls);
3866 #include <isl/map.h>
3867 __isl_give isl_map *isl_map_from_domain(
3868 __isl_take isl_set *set);
3869 __isl_give isl_map *isl_map_from_range(
3870 __isl_take isl_set *set);
3872 #include <isl/val.h>
3873 __isl_give isl_multi_val *isl_multi_val_from_range(
3874 __isl_take isl_multi_val *mv);
3876 #include <isl/aff.h>
3877 __isl_give isl_multi_aff *isl_multi_aff_from_range(
3878 __isl_take isl_multi_aff *ma);
3879 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3880 __isl_take isl_pw_aff *pwa);
3881 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
3882 __isl_take isl_multi_pw_aff *mpa);
3883 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3884 __isl_take isl_set *set);
3885 __isl_give isl_union_pw_multi_aff *
3886 isl_union_pw_multi_aff_from_domain(
3887 __isl_take isl_union_set *uset);
3891 #include <isl/set.h>
3892 __isl_give isl_basic_set *isl_basic_set_fix_si(
3893 __isl_take isl_basic_set *bset,
3894 enum isl_dim_type type, unsigned pos, int value);
3895 __isl_give isl_basic_set *isl_basic_set_fix_val(
3896 __isl_take isl_basic_set *bset,
3897 enum isl_dim_type type, unsigned pos,
3898 __isl_take isl_val *v);
3899 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
3900 enum isl_dim_type type, unsigned pos, int value);
3901 __isl_give isl_set *isl_set_fix_val(
3902 __isl_take isl_set *set,
3903 enum isl_dim_type type, unsigned pos,
3904 __isl_take isl_val *v);
3906 #include <isl/map.h>
3907 __isl_give isl_basic_map *isl_basic_map_fix_si(
3908 __isl_take isl_basic_map *bmap,
3909 enum isl_dim_type type, unsigned pos, int value);
3910 __isl_give isl_basic_map *isl_basic_map_fix_val(
3911 __isl_take isl_basic_map *bmap,
3912 enum isl_dim_type type, unsigned pos,
3913 __isl_take isl_val *v);
3914 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
3915 enum isl_dim_type type, unsigned pos, int value);
3916 __isl_give isl_map *isl_map_fix_val(
3917 __isl_take isl_map *map,
3918 enum isl_dim_type type, unsigned pos,
3919 __isl_take isl_val *v);
3921 #include <isl/aff.h>
3922 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
3923 __isl_take isl_pw_multi_aff *pma,
3924 enum isl_dim_type type, unsigned pos, int value);
3926 #include <isl/polynomial.h>
3927 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
3928 __isl_take isl_pw_qpolynomial *pwqp,
3929 enum isl_dim_type type, unsigned n,
3930 __isl_take isl_val *v);
3932 Intersect the set, relation or function domain
3933 with the hyperplane where the given
3934 dimension has the fixed given value.
3936 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
3937 __isl_take isl_basic_map *bmap,
3938 enum isl_dim_type type, unsigned pos, int value);
3939 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
3940 __isl_take isl_basic_map *bmap,
3941 enum isl_dim_type type, unsigned pos, int value);
3942 __isl_give isl_set *isl_set_lower_bound_si(
3943 __isl_take isl_set *set,
3944 enum isl_dim_type type, unsigned pos, int value);
3945 __isl_give isl_set *isl_set_lower_bound_val(
3946 __isl_take isl_set *set,
3947 enum isl_dim_type type, unsigned pos,
3948 __isl_take isl_val *value);
3949 __isl_give isl_map *isl_map_lower_bound_si(
3950 __isl_take isl_map *map,
3951 enum isl_dim_type type, unsigned pos, int value);
3952 __isl_give isl_set *isl_set_upper_bound_si(
3953 __isl_take isl_set *set,
3954 enum isl_dim_type type, unsigned pos, int value);
3955 __isl_give isl_set *isl_set_upper_bound_val(
3956 __isl_take isl_set *set,
3957 enum isl_dim_type type, unsigned pos,
3958 __isl_take isl_val *value);
3959 __isl_give isl_map *isl_map_upper_bound_si(
3960 __isl_take isl_map *map,
3961 enum isl_dim_type type, unsigned pos, int value);
3963 Intersect the set or relation with the half-space where the given
3964 dimension has a value bounded by the fixed given integer value.
3966 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
3967 enum isl_dim_type type1, int pos1,
3968 enum isl_dim_type type2, int pos2);
3969 __isl_give isl_basic_map *isl_basic_map_equate(
3970 __isl_take isl_basic_map *bmap,
3971 enum isl_dim_type type1, int pos1,
3972 enum isl_dim_type type2, int pos2);
3973 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
3974 enum isl_dim_type type1, int pos1,
3975 enum isl_dim_type type2, int pos2);
3977 Intersect the set or relation with the hyperplane where the given
3978 dimensions are equal to each other.
3980 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
3981 enum isl_dim_type type1, int pos1,
3982 enum isl_dim_type type2, int pos2);
3984 Intersect the relation with the hyperplane where the given
3985 dimensions have opposite values.
3987 __isl_give isl_map *isl_map_order_le(
3988 __isl_take isl_map *map,
3989 enum isl_dim_type type1, int pos1,
3990 enum isl_dim_type type2, int pos2);
3991 __isl_give isl_basic_map *isl_basic_map_order_ge(
3992 __isl_take isl_basic_map *bmap,
3993 enum isl_dim_type type1, int pos1,
3994 enum isl_dim_type type2, int pos2);
3995 __isl_give isl_map *isl_map_order_ge(
3996 __isl_take isl_map *map,
3997 enum isl_dim_type type1, int pos1,
3998 enum isl_dim_type type2, int pos2);
3999 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
4000 enum isl_dim_type type1, int pos1,
4001 enum isl_dim_type type2, int pos2);
4002 __isl_give isl_basic_map *isl_basic_map_order_gt(
4003 __isl_take isl_basic_map *bmap,
4004 enum isl_dim_type type1, int pos1,
4005 enum isl_dim_type type2, int pos2);
4006 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
4007 enum isl_dim_type type1, int pos1,
4008 enum isl_dim_type type2, int pos2);
4010 Intersect the relation with the half-space where the given
4011 dimensions satisfy the given ordering.
4015 #include <isl/aff.h>
4016 __isl_give isl_basic_set *isl_aff_zero_basic_set(
4017 __isl_take isl_aff *aff);
4018 __isl_give isl_basic_set *isl_aff_neg_basic_set(
4019 __isl_take isl_aff *aff);
4020 __isl_give isl_set *isl_pw_aff_nonneg_set(
4021 __isl_take isl_pw_aff *pwaff);
4022 __isl_give isl_set *isl_pw_aff_zero_set(
4023 __isl_take isl_pw_aff *pwaff);
4024 __isl_give isl_set *isl_pw_aff_non_zero_set(
4025 __isl_take isl_pw_aff *pwaff);
4027 The function C<isl_aff_neg_basic_set> returns a basic set
4028 containing those elements in the domain space
4029 of C<aff> where C<aff> is negative.
4030 The function C<isl_pw_aff_nonneg_set> returns a set
4031 containing those elements in the domain
4032 of C<pwaff> where C<pwaff> is non-negative.
4036 __isl_give isl_map *isl_set_identity(
4037 __isl_take isl_set *set);
4038 __isl_give isl_union_map *isl_union_set_identity(
4039 __isl_take isl_union_set *uset);
4041 Construct an identity relation on the given (union) set.
4043 =item * Function Extraction
4045 A piecewise quasi affine expression that is equal to 1 on a set
4046 and 0 outside the set can be created using the following function.
4048 #include <isl/aff.h>
4049 __isl_give isl_pw_aff *isl_set_indicator_function(
4050 __isl_take isl_set *set);
4052 A piecewise multiple quasi affine expression can be extracted
4053 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
4054 and the C<isl_map> is single-valued.
4055 In case of a conversion from an C<isl_union_map>
4056 to an C<isl_union_pw_multi_aff>, these properties need to hold
4057 in each domain space.
4059 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
4060 __isl_take isl_set *set);
4061 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
4062 __isl_take isl_map *map);
4064 __isl_give isl_union_pw_multi_aff *
4065 isl_union_pw_multi_aff_from_union_set(
4066 __isl_take isl_union_set *uset);
4067 __isl_give isl_union_pw_multi_aff *
4068 isl_union_pw_multi_aff_from_union_map(
4069 __isl_take isl_union_map *umap);
4073 __isl_give isl_basic_set *isl_basic_map_deltas(
4074 __isl_take isl_basic_map *bmap);
4075 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
4076 __isl_give isl_union_set *isl_union_map_deltas(
4077 __isl_take isl_union_map *umap);
4079 These functions return a (basic) set containing the differences
4080 between image elements and corresponding domain elements in the input.
4082 __isl_give isl_basic_map *isl_basic_map_deltas_map(
4083 __isl_take isl_basic_map *bmap);
4084 __isl_give isl_map *isl_map_deltas_map(
4085 __isl_take isl_map *map);
4086 __isl_give isl_union_map *isl_union_map_deltas_map(
4087 __isl_take isl_union_map *umap);
4089 The functions above construct a (basic, regular or union) relation
4090 that maps (a wrapped version of) the input relation to its delta set.
4094 Simplify the representation of a set, relation or functions by trying
4095 to combine pairs of basic sets or relations into a single
4096 basic set or relation.
4098 #include <isl/set.h>
4099 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
4101 #include <isl/map.h>
4102 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
4104 #include <isl/union_set.h>
4105 __isl_give isl_union_set *isl_union_set_coalesce(
4106 __isl_take isl_union_set *uset);
4108 #include <isl/union_map.h>
4109 __isl_give isl_union_map *isl_union_map_coalesce(
4110 __isl_take isl_union_map *umap);
4112 #include <isl/aff.h>
4113 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
4114 __isl_take isl_pw_aff *pwqp);
4115 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4116 __isl_take isl_pw_multi_aff *pma);
4117 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4118 __isl_take isl_multi_pw_aff *mpa);
4119 __isl_give isl_union_pw_multi_aff *
4120 isl_union_pw_multi_aff_coalesce(
4121 __isl_take isl_union_pw_multi_aff *upma);
4123 #include <isl/polynomial.h>
4124 __isl_give isl_pw_qpolynomial_fold *
4125 isl_pw_qpolynomial_fold_coalesce(
4126 __isl_take isl_pw_qpolynomial_fold *pwf);
4127 __isl_give isl_union_pw_qpolynomial *
4128 isl_union_pw_qpolynomial_coalesce(
4129 __isl_take isl_union_pw_qpolynomial *upwqp);
4130 __isl_give isl_union_pw_qpolynomial_fold *
4131 isl_union_pw_qpolynomial_fold_coalesce(
4132 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4134 One of the methods for combining pairs of basic sets or relations
4135 can result in coefficients that are much larger than those that appear
4136 in the constraints of the input. By default, the coefficients are
4137 not allowed to grow larger, but this can be changed by unsetting
4138 the following option.
4140 int isl_options_set_coalesce_bounded_wrapping(
4141 isl_ctx *ctx, int val);
4142 int isl_options_get_coalesce_bounded_wrapping(
4145 =item * Detecting equalities
4147 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4148 __isl_take isl_basic_set *bset);
4149 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4150 __isl_take isl_basic_map *bmap);
4151 __isl_give isl_set *isl_set_detect_equalities(
4152 __isl_take isl_set *set);
4153 __isl_give isl_map *isl_map_detect_equalities(
4154 __isl_take isl_map *map);
4155 __isl_give isl_union_set *isl_union_set_detect_equalities(
4156 __isl_take isl_union_set *uset);
4157 __isl_give isl_union_map *isl_union_map_detect_equalities(
4158 __isl_take isl_union_map *umap);
4160 Simplify the representation of a set or relation by detecting implicit
4163 =item * Removing redundant constraints
4165 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4166 __isl_take isl_basic_set *bset);
4167 __isl_give isl_set *isl_set_remove_redundancies(
4168 __isl_take isl_set *set);
4169 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4170 __isl_take isl_basic_map *bmap);
4171 __isl_give isl_map *isl_map_remove_redundancies(
4172 __isl_take isl_map *map);
4176 __isl_give isl_basic_set *isl_set_convex_hull(
4177 __isl_take isl_set *set);
4178 __isl_give isl_basic_map *isl_map_convex_hull(
4179 __isl_take isl_map *map);
4181 If the input set or relation has any existentially quantified
4182 variables, then the result of these operations is currently undefined.
4186 #include <isl/set.h>
4187 __isl_give isl_basic_set *
4188 isl_set_unshifted_simple_hull(
4189 __isl_take isl_set *set);
4190 __isl_give isl_basic_set *isl_set_simple_hull(
4191 __isl_take isl_set *set);
4192 __isl_give isl_basic_set *
4193 isl_set_unshifted_simple_hull_from_set_list(
4194 __isl_take isl_set *set,
4195 __isl_take isl_set_list *list);
4197 #include <isl/map.h>
4198 __isl_give isl_basic_map *
4199 isl_map_unshifted_simple_hull(
4200 __isl_take isl_map *map);
4201 __isl_give isl_basic_map *isl_map_simple_hull(
4202 __isl_take isl_map *map);
4204 #include <isl/union_map.h>
4205 __isl_give isl_union_map *isl_union_map_simple_hull(
4206 __isl_take isl_union_map *umap);
4208 These functions compute a single basic set or relation
4209 that contains the whole input set or relation.
4210 In particular, the output is described by translates
4211 of the constraints describing the basic sets or relations in the input.
4212 In case of C<isl_set_unshifted_simple_hull>, only the original
4213 constraints are used, without any translation.
4214 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
4215 constraints are taken from the elements of the second argument.
4219 (See \autoref{s:simple hull}.)
4225 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4226 __isl_take isl_basic_set *bset);
4227 __isl_give isl_basic_set *isl_set_affine_hull(
4228 __isl_take isl_set *set);
4229 __isl_give isl_union_set *isl_union_set_affine_hull(
4230 __isl_take isl_union_set *uset);
4231 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4232 __isl_take isl_basic_map *bmap);
4233 __isl_give isl_basic_map *isl_map_affine_hull(
4234 __isl_take isl_map *map);
4235 __isl_give isl_union_map *isl_union_map_affine_hull(
4236 __isl_take isl_union_map *umap);
4238 In case of union sets and relations, the affine hull is computed
4241 =item * Polyhedral hull
4243 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4244 __isl_take isl_set *set);
4245 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4246 __isl_take isl_map *map);
4247 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4248 __isl_take isl_union_set *uset);
4249 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4250 __isl_take isl_union_map *umap);
4252 These functions compute a single basic set or relation
4253 not involving any existentially quantified variables
4254 that contains the whole input set or relation.
4255 In case of union sets and relations, the polyhedral hull is computed
4258 =item * Other approximations
4260 #include <isl/set.h>
4261 __isl_give isl_basic_set *
4262 isl_basic_set_drop_constraints_involving_dims(
4263 __isl_take isl_basic_set *bset,
4264 enum isl_dim_type type,
4265 unsigned first, unsigned n);
4266 __isl_give isl_basic_set *
4267 isl_basic_set_drop_constraints_not_involving_dims(
4268 __isl_take isl_basic_set *bset,
4269 enum isl_dim_type type,
4270 unsigned first, unsigned n);
4271 __isl_give isl_set *
4272 isl_set_drop_constraints_involving_dims(
4273 __isl_take isl_set *set,
4274 enum isl_dim_type type,
4275 unsigned first, unsigned n);
4277 #include <isl/map.h>
4278 __isl_give isl_basic_map *
4279 isl_basic_map_drop_constraints_involving_dims(
4280 __isl_take isl_basic_map *bmap,
4281 enum isl_dim_type type,
4282 unsigned first, unsigned n);
4283 __isl_give isl_map *
4284 isl_map_drop_constraints_involving_dims(
4285 __isl_take isl_map *map,
4286 enum isl_dim_type type,
4287 unsigned first, unsigned n);
4289 These functions drop any constraints (not) involving the specified dimensions.
4290 Note that the result depends on the representation of the input.
4292 #include <isl/polynomial.h>
4293 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4294 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4295 __isl_give isl_union_pw_qpolynomial *
4296 isl_union_pw_qpolynomial_to_polynomial(
4297 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4299 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4300 the polynomial will be an overapproximation. If C<sign> is negative,
4301 it will be an underapproximation. If C<sign> is zero, the approximation
4302 will lie somewhere in between.
4306 __isl_give isl_basic_set *isl_basic_set_sample(
4307 __isl_take isl_basic_set *bset);
4308 __isl_give isl_basic_set *isl_set_sample(
4309 __isl_take isl_set *set);
4310 __isl_give isl_basic_map *isl_basic_map_sample(
4311 __isl_take isl_basic_map *bmap);
4312 __isl_give isl_basic_map *isl_map_sample(
4313 __isl_take isl_map *map);
4315 If the input (basic) set or relation is non-empty, then return
4316 a singleton subset of the input. Otherwise, return an empty set.
4318 =item * Optimization
4320 #include <isl/ilp.h>
4321 __isl_give isl_val *isl_basic_set_max_val(
4322 __isl_keep isl_basic_set *bset,
4323 __isl_keep isl_aff *obj);
4324 __isl_give isl_val *isl_set_min_val(
4325 __isl_keep isl_set *set,
4326 __isl_keep isl_aff *obj);
4327 __isl_give isl_val *isl_set_max_val(
4328 __isl_keep isl_set *set,
4329 __isl_keep isl_aff *obj);
4331 Compute the minimum or maximum of the integer affine expression C<obj>
4332 over the points in C<set>, returning the result in C<opt>.
4333 The result is C<NULL> in case of an error, the optimal value in case
4334 there is one, negative infinity or infinity if the problem is unbounded and
4335 NaN if the problem is empty.
4337 =item * Parametric optimization
4339 __isl_give isl_pw_aff *isl_set_dim_min(
4340 __isl_take isl_set *set, int pos);
4341 __isl_give isl_pw_aff *isl_set_dim_max(
4342 __isl_take isl_set *set, int pos);
4343 __isl_give isl_pw_aff *isl_map_dim_max(
4344 __isl_take isl_map *map, int pos);
4346 Compute the minimum or maximum of the given set or output dimension
4347 as a function of the parameters (and input dimensions), but independently
4348 of the other set or output dimensions.
4349 For lexicographic optimization, see L<"Lexicographic Optimization">.
4353 The following functions compute either the set of (rational) coefficient
4354 values of valid constraints for the given set or the set of (rational)
4355 values satisfying the constraints with coefficients from the given set.
4356 Internally, these two sets of functions perform essentially the
4357 same operations, except that the set of coefficients is assumed to
4358 be a cone, while the set of values may be any polyhedron.
4359 The current implementation is based on the Farkas lemma and
4360 Fourier-Motzkin elimination, but this may change or be made optional
4361 in future. In particular, future implementations may use different
4362 dualization algorithms or skip the elimination step.
4364 __isl_give isl_basic_set *isl_basic_set_coefficients(
4365 __isl_take isl_basic_set *bset);
4366 __isl_give isl_basic_set *isl_set_coefficients(
4367 __isl_take isl_set *set);
4368 __isl_give isl_union_set *isl_union_set_coefficients(
4369 __isl_take isl_union_set *bset);
4370 __isl_give isl_basic_set *isl_basic_set_solutions(
4371 __isl_take isl_basic_set *bset);
4372 __isl_give isl_basic_set *isl_set_solutions(
4373 __isl_take isl_set *set);
4374 __isl_give isl_union_set *isl_union_set_solutions(
4375 __isl_take isl_union_set *bset);
4379 __isl_give isl_map *isl_map_fixed_power_val(
4380 __isl_take isl_map *map,
4381 __isl_take isl_val *exp);
4382 __isl_give isl_union_map *
4383 isl_union_map_fixed_power_val(
4384 __isl_take isl_union_map *umap,
4385 __isl_take isl_val *exp);
4387 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4388 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4389 of C<map> is computed.
4391 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4393 __isl_give isl_union_map *isl_union_map_power(
4394 __isl_take isl_union_map *umap, int *exact);
4396 Compute a parametric representation for all positive powers I<k> of C<map>.
4397 The result maps I<k> to a nested relation corresponding to the
4398 I<k>th power of C<map>.
4399 The result may be an overapproximation. If the result is known to be exact,
4400 then C<*exact> is set to C<1>.
4402 =item * Transitive closure
4404 __isl_give isl_map *isl_map_transitive_closure(
4405 __isl_take isl_map *map, int *exact);
4406 __isl_give isl_union_map *isl_union_map_transitive_closure(
4407 __isl_take isl_union_map *umap, int *exact);
4409 Compute the transitive closure of C<map>.
4410 The result may be an overapproximation. If the result is known to be exact,
4411 then C<*exact> is set to C<1>.
4413 =item * Reaching path lengths
4415 __isl_give isl_map *isl_map_reaching_path_lengths(
4416 __isl_take isl_map *map, int *exact);
4418 Compute a relation that maps each element in the range of C<map>
4419 to the lengths of all paths composed of edges in C<map> that
4420 end up in the given element.
4421 The result may be an overapproximation. If the result is known to be exact,
4422 then C<*exact> is set to C<1>.
4423 To compute the I<maximal> path length, the resulting relation
4424 should be postprocessed by C<isl_map_lexmax>.
4425 In particular, if the input relation is a dependence relation
4426 (mapping sources to sinks), then the maximal path length corresponds
4427 to the free schedule.
4428 Note, however, that C<isl_map_lexmax> expects the maximum to be
4429 finite, so if the path lengths are unbounded (possibly due to
4430 the overapproximation), then you will get an error message.
4434 #include <isl/space.h>
4435 __isl_give isl_space *isl_space_wrap(
4436 __isl_take isl_space *space);
4437 __isl_give isl_space *isl_space_unwrap(
4438 __isl_take isl_space *space);
4440 #include <isl/set.h>
4441 __isl_give isl_basic_map *isl_basic_set_unwrap(
4442 __isl_take isl_basic_set *bset);
4443 __isl_give isl_map *isl_set_unwrap(
4444 __isl_take isl_set *set);
4446 #include <isl/map.h>
4447 __isl_give isl_basic_set *isl_basic_map_wrap(
4448 __isl_take isl_basic_map *bmap);
4449 __isl_give isl_set *isl_map_wrap(
4450 __isl_take isl_map *map);
4452 #include <isl/union_set.h>
4453 __isl_give isl_union_map *isl_union_set_unwrap(
4454 __isl_take isl_union_set *uset);
4456 #include <isl/union_map.h>
4457 __isl_give isl_union_set *isl_union_map_wrap(
4458 __isl_take isl_union_map *umap);
4460 The input to C<isl_space_unwrap> should
4461 be the space of a set, while that of
4462 C<isl_space_wrap> should be the space of a relation.
4463 Conversely, the output of C<isl_space_unwrap> is the space
4464 of a relation, while that of C<isl_space_wrap> is the space of a set.
4468 Remove any internal structure of domain (and range) of the given
4469 set or relation. If there is any such internal structure in the input,
4470 then the name of the space is also removed.
4472 #include <isl/local_space.h>
4473 __isl_give isl_local_space *
4474 isl_local_space_flatten_domain(
4475 __isl_take isl_local_space *ls);
4476 __isl_give isl_local_space *
4477 isl_local_space_flatten_range(
4478 __isl_take isl_local_space *ls);
4480 #include <isl/set.h>
4481 __isl_give isl_basic_set *isl_basic_set_flatten(
4482 __isl_take isl_basic_set *bset);
4483 __isl_give isl_set *isl_set_flatten(
4484 __isl_take isl_set *set);
4486 #include <isl/map.h>
4487 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4488 __isl_take isl_basic_map *bmap);
4489 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4490 __isl_take isl_basic_map *bmap);
4491 __isl_give isl_map *isl_map_flatten_range(
4492 __isl_take isl_map *map);
4493 __isl_give isl_map *isl_map_flatten_domain(
4494 __isl_take isl_map *map);
4495 __isl_give isl_basic_map *isl_basic_map_flatten(
4496 __isl_take isl_basic_map *bmap);
4497 __isl_give isl_map *isl_map_flatten(
4498 __isl_take isl_map *map);
4500 #include <isl/val.h>
4501 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4502 __isl_take isl_multi_val *mv);
4504 #include <isl/aff.h>
4505 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4506 __isl_take isl_multi_aff *ma);
4507 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4508 __isl_take isl_multi_aff *ma);
4509 __isl_give isl_multi_pw_aff *
4510 isl_multi_pw_aff_flatten_range(
4511 __isl_take isl_multi_pw_aff *mpa);
4513 #include <isl/map.h>
4514 __isl_give isl_map *isl_set_flatten_map(
4515 __isl_take isl_set *set);
4517 The function above constructs a relation
4518 that maps the input set to a flattened version of the set.
4522 Lift the input set to a space with extra dimensions corresponding
4523 to the existentially quantified variables in the input.
4524 In particular, the result lives in a wrapped map where the domain
4525 is the original space and the range corresponds to the original
4526 existentially quantified variables.
4528 #include <isl/set.h>
4529 __isl_give isl_basic_set *isl_basic_set_lift(
4530 __isl_take isl_basic_set *bset);
4531 __isl_give isl_set *isl_set_lift(
4532 __isl_take isl_set *set);
4533 __isl_give isl_union_set *isl_union_set_lift(
4534 __isl_take isl_union_set *uset);
4536 Given a local space that contains the existentially quantified
4537 variables of a set, a basic relation that, when applied to
4538 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4539 can be constructed using the following function.
4541 #include <isl/local_space.h>
4542 __isl_give isl_basic_map *isl_local_space_lifting(
4543 __isl_take isl_local_space *ls);
4545 #include <isl/aff.h>
4546 __isl_give isl_multi_aff *isl_multi_aff_lift(
4547 __isl_take isl_multi_aff *maff,
4548 __isl_give isl_local_space **ls);
4550 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4551 then it is assigned the local space that lies at the basis of
4552 the lifting applied.
4554 =item * Internal Product
4556 #include <isl/space.h>
4557 __isl_give isl_space *isl_space_zip(
4558 __isl_take isl_space *space);
4560 #include <isl/map.h>
4561 __isl_give isl_basic_map *isl_basic_map_zip(
4562 __isl_take isl_basic_map *bmap);
4563 __isl_give isl_map *isl_map_zip(
4564 __isl_take isl_map *map);
4566 #include <isl/union_map.h>
4567 __isl_give isl_union_map *isl_union_map_zip(
4568 __isl_take isl_union_map *umap);
4570 Given a relation with nested relations for domain and range,
4571 interchange the range of the domain with the domain of the range.
4575 #include <isl/space.h>
4576 __isl_give isl_space *isl_space_curry(
4577 __isl_take isl_space *space);
4578 __isl_give isl_space *isl_space_uncurry(
4579 __isl_take isl_space *space);
4581 #include <isl/map.h>
4582 __isl_give isl_basic_map *isl_basic_map_curry(
4583 __isl_take isl_basic_map *bmap);
4584 __isl_give isl_basic_map *isl_basic_map_uncurry(
4585 __isl_take isl_basic_map *bmap);
4586 __isl_give isl_map *isl_map_curry(
4587 __isl_take isl_map *map);
4588 __isl_give isl_map *isl_map_uncurry(
4589 __isl_take isl_map *map);
4591 #include <isl/union_map.h>
4592 __isl_give isl_union_map *isl_union_map_curry(
4593 __isl_take isl_union_map *umap);
4594 __isl_give isl_union_map *isl_union_map_uncurry(
4595 __isl_take isl_union_map *umap);
4597 Given a relation with a nested relation for domain,
4598 the C<curry> functions
4599 move the range of the nested relation out of the domain
4600 and use it as the domain of a nested relation in the range,
4601 with the original range as range of this nested relation.
4602 The C<uncurry> functions perform the inverse operation.
4604 =item * Aligning parameters
4606 Change the order of the parameters of the given set, relation
4608 such that the first parameters match those of C<model>.
4609 This may involve the introduction of extra parameters.
4610 All parameters need to be named.
4612 #include <isl/space.h>
4613 __isl_give isl_space *isl_space_align_params(
4614 __isl_take isl_space *space1,
4615 __isl_take isl_space *space2)
4617 #include <isl/set.h>
4618 __isl_give isl_basic_set *isl_basic_set_align_params(
4619 __isl_take isl_basic_set *bset,
4620 __isl_take isl_space *model);
4621 __isl_give isl_set *isl_set_align_params(
4622 __isl_take isl_set *set,
4623 __isl_take isl_space *model);
4625 #include <isl/map.h>
4626 __isl_give isl_basic_map *isl_basic_map_align_params(
4627 __isl_take isl_basic_map *bmap,
4628 __isl_take isl_space *model);
4629 __isl_give isl_map *isl_map_align_params(
4630 __isl_take isl_map *map,
4631 __isl_take isl_space *model);
4633 #include <isl/val.h>
4634 __isl_give isl_multi_val *isl_multi_val_align_params(
4635 __isl_take isl_multi_val *mv,
4636 __isl_take isl_space *model);
4638 #include <isl/aff.h>
4639 __isl_give isl_aff *isl_aff_align_params(
4640 __isl_take isl_aff *aff,
4641 __isl_take isl_space *model);
4642 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4643 __isl_take isl_multi_aff *multi,
4644 __isl_take isl_space *model);
4645 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4646 __isl_take isl_pw_aff *pwaff,
4647 __isl_take isl_space *model);
4648 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4649 __isl_take isl_pw_multi_aff *pma,
4650 __isl_take isl_space *model);
4651 __isl_give isl_union_pw_multi_aff *
4652 isl_union_pw_multi_aff_align_params(
4653 __isl_take isl_union_pw_multi_aff *upma,
4654 __isl_take isl_space *model);
4656 #include <isl/polynomial.h>
4657 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4658 __isl_take isl_qpolynomial *qp,
4659 __isl_take isl_space *model);
4661 =item * Unary Arithmethic Operations
4663 #include <isl/aff.h>
4664 __isl_give isl_aff *isl_aff_neg(
4665 __isl_take isl_aff *aff);
4666 __isl_give isl_pw_aff *isl_pw_aff_neg(
4667 __isl_take isl_pw_aff *pwaff);
4668 __isl_give isl_aff *isl_aff_ceil(
4669 __isl_take isl_aff *aff);
4670 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4671 __isl_take isl_pw_aff *pwaff);
4672 __isl_give isl_aff *isl_aff_floor(
4673 __isl_take isl_aff *aff);
4674 __isl_give isl_multi_aff *isl_multi_aff_floor(
4675 __isl_take isl_multi_aff *ma);
4676 __isl_give isl_pw_aff *isl_pw_aff_floor(
4677 __isl_take isl_pw_aff *pwaff);
4679 #include <isl/aff.h>
4680 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4681 __isl_take isl_pw_aff_list *list);
4682 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4683 __isl_take isl_pw_aff_list *list);
4685 #include <isl/polynomial.h>
4686 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4687 __isl_take isl_qpolynomial *qp);
4688 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4689 __isl_take isl_pw_qpolynomial *pwqp);
4690 __isl_give isl_union_pw_qpolynomial *
4691 isl_union_pw_qpolynomial_neg(
4692 __isl_take isl_union_pw_qpolynomial *upwqp);
4693 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4694 __isl_take isl_qpolynomial *qp,
4696 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4697 __isl_take isl_pw_qpolynomial *pwqp,
4702 The following functions evaluate a function in a point.
4704 #include <isl/polynomial.h>
4705 __isl_give isl_val *isl_pw_qpolynomial_eval(
4706 __isl_take isl_pw_qpolynomial *pwqp,
4707 __isl_take isl_point *pnt);
4708 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
4709 __isl_take isl_pw_qpolynomial_fold *pwf,
4710 __isl_take isl_point *pnt);
4711 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4712 __isl_take isl_union_pw_qpolynomial *upwqp,
4713 __isl_take isl_point *pnt);
4714 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
4715 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4716 __isl_take isl_point *pnt);
4718 =item * Dimension manipulation
4720 It is usually not advisable to directly change the (input or output)
4721 space of a set or a relation as this removes the name and the internal
4722 structure of the space. However, the functions below can be useful
4723 to add new parameters, assuming
4724 C<isl_set_align_params> and C<isl_map_align_params>
4727 #include <isl/space.h>
4728 __isl_give isl_space *isl_space_add_dims(
4729 __isl_take isl_space *space,
4730 enum isl_dim_type type, unsigned n);
4731 __isl_give isl_space *isl_space_insert_dims(
4732 __isl_take isl_space *space,
4733 enum isl_dim_type type, unsigned pos, unsigned n);
4734 __isl_give isl_space *isl_space_drop_dims(
4735 __isl_take isl_space *space,
4736 enum isl_dim_type type, unsigned first, unsigned n);
4737 __isl_give isl_space *isl_space_move_dims(
4738 __isl_take isl_space *space,
4739 enum isl_dim_type dst_type, unsigned dst_pos,
4740 enum isl_dim_type src_type, unsigned src_pos,
4743 #include <isl/local_space.h>
4744 __isl_give isl_local_space *isl_local_space_add_dims(
4745 __isl_take isl_local_space *ls,
4746 enum isl_dim_type type, unsigned n);
4747 __isl_give isl_local_space *isl_local_space_insert_dims(
4748 __isl_take isl_local_space *ls,
4749 enum isl_dim_type type, unsigned first, unsigned n);
4750 __isl_give isl_local_space *isl_local_space_drop_dims(
4751 __isl_take isl_local_space *ls,
4752 enum isl_dim_type type, unsigned first, unsigned n);
4754 #include <isl/set.h>
4755 __isl_give isl_basic_set *isl_basic_set_add_dims(
4756 __isl_take isl_basic_set *bset,
4757 enum isl_dim_type type, unsigned n);
4758 __isl_give isl_set *isl_set_add_dims(
4759 __isl_take isl_set *set,
4760 enum isl_dim_type type, unsigned n);
4761 __isl_give isl_basic_set *isl_basic_set_insert_dims(
4762 __isl_take isl_basic_set *bset,
4763 enum isl_dim_type type, unsigned pos,
4765 __isl_give isl_set *isl_set_insert_dims(
4766 __isl_take isl_set *set,
4767 enum isl_dim_type type, unsigned pos, unsigned n);
4768 __isl_give isl_basic_set *isl_basic_set_move_dims(
4769 __isl_take isl_basic_set *bset,
4770 enum isl_dim_type dst_type, unsigned dst_pos,
4771 enum isl_dim_type src_type, unsigned src_pos,
4773 __isl_give isl_set *isl_set_move_dims(
4774 __isl_take isl_set *set,
4775 enum isl_dim_type dst_type, unsigned dst_pos,
4776 enum isl_dim_type src_type, unsigned src_pos,
4779 #include <isl/map.h>
4780 __isl_give isl_map *isl_map_add_dims(
4781 __isl_take isl_map *map,
4782 enum isl_dim_type type, unsigned n);
4783 __isl_give isl_basic_map *isl_basic_map_insert_dims(
4784 __isl_take isl_basic_map *bmap,
4785 enum isl_dim_type type, unsigned pos,
4787 __isl_give isl_map *isl_map_insert_dims(
4788 __isl_take isl_map *map,
4789 enum isl_dim_type type, unsigned pos, unsigned n);
4790 __isl_give isl_basic_map *isl_basic_map_move_dims(
4791 __isl_take isl_basic_map *bmap,
4792 enum isl_dim_type dst_type, unsigned dst_pos,
4793 enum isl_dim_type src_type, unsigned src_pos,
4795 __isl_give isl_map *isl_map_move_dims(
4796 __isl_take isl_map *map,
4797 enum isl_dim_type dst_type, unsigned dst_pos,
4798 enum isl_dim_type src_type, unsigned src_pos,
4801 #include <isl/val.h>
4802 __isl_give isl_multi_val *isl_multi_val_insert_dims(
4803 __isl_take isl_multi_val *mv,
4804 enum isl_dim_type type, unsigned first, unsigned n);
4805 __isl_give isl_multi_val *isl_multi_val_add_dims(
4806 __isl_take isl_multi_val *mv,
4807 enum isl_dim_type type, unsigned n);
4808 __isl_give isl_multi_val *isl_multi_val_drop_dims(
4809 __isl_take isl_multi_val *mv,
4810 enum isl_dim_type type, unsigned first, unsigned n);
4812 #include <isl/aff.h>
4813 __isl_give isl_aff *isl_aff_insert_dims(
4814 __isl_take isl_aff *aff,
4815 enum isl_dim_type type, unsigned first, unsigned n);
4816 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4817 __isl_take isl_multi_aff *ma,
4818 enum isl_dim_type type, unsigned first, unsigned n);
4819 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4820 __isl_take isl_pw_aff *pwaff,
4821 enum isl_dim_type type, unsigned first, unsigned n);
4822 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4823 __isl_take isl_multi_pw_aff *mpa,
4824 enum isl_dim_type type, unsigned first, unsigned n);
4825 __isl_give isl_aff *isl_aff_add_dims(
4826 __isl_take isl_aff *aff,
4827 enum isl_dim_type type, unsigned n);
4828 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4829 __isl_take isl_multi_aff *ma,
4830 enum isl_dim_type type, unsigned n);
4831 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4832 __isl_take isl_pw_aff *pwaff,
4833 enum isl_dim_type type, unsigned n);
4834 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4835 __isl_take isl_multi_pw_aff *mpa,
4836 enum isl_dim_type type, unsigned n);
4837 __isl_give isl_aff *isl_aff_drop_dims(
4838 __isl_take isl_aff *aff,
4839 enum isl_dim_type type, unsigned first, unsigned n);
4840 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4841 __isl_take isl_multi_aff *maff,
4842 enum isl_dim_type type, unsigned first, unsigned n);
4843 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4844 __isl_take isl_pw_aff *pwaff,
4845 enum isl_dim_type type, unsigned first, unsigned n);
4846 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4847 __isl_take isl_pw_multi_aff *pma,
4848 enum isl_dim_type type, unsigned first, unsigned n);
4849 __isl_give isl_aff *isl_aff_move_dims(
4850 __isl_take isl_aff *aff,
4851 enum isl_dim_type dst_type, unsigned dst_pos,
4852 enum isl_dim_type src_type, unsigned src_pos,
4854 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
4855 __isl_take isl_multi_aff *ma,
4856 enum isl_dim_type dst_type, unsigned dst_pos,
4857 enum isl_dim_type src_type, unsigned src_pos,
4859 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4860 __isl_take isl_pw_aff *pa,
4861 enum isl_dim_type dst_type, unsigned dst_pos,
4862 enum isl_dim_type src_type, unsigned src_pos,
4864 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4865 __isl_take isl_multi_pw_aff *pma,
4866 enum isl_dim_type dst_type, unsigned dst_pos,
4867 enum isl_dim_type src_type, unsigned src_pos,
4872 =head2 Binary Operations
4874 The two arguments of a binary operation not only need to live
4875 in the same C<isl_ctx>, they currently also need to have
4876 the same (number of) parameters.
4878 =head3 Basic Operations
4882 =item * Intersection
4884 #include <isl/local_space.h>
4885 __isl_give isl_local_space *isl_local_space_intersect(
4886 __isl_take isl_local_space *ls1,
4887 __isl_take isl_local_space *ls2);
4889 #include <isl/set.h>
4890 __isl_give isl_basic_set *isl_basic_set_intersect_params(
4891 __isl_take isl_basic_set *bset1,
4892 __isl_take isl_basic_set *bset2);
4893 __isl_give isl_basic_set *isl_basic_set_intersect(
4894 __isl_take isl_basic_set *bset1,
4895 __isl_take isl_basic_set *bset2);
4896 __isl_give isl_basic_set *isl_basic_set_list_intersect(
4897 __isl_take struct isl_basic_set_list *list);
4898 __isl_give isl_set *isl_set_intersect_params(
4899 __isl_take isl_set *set,
4900 __isl_take isl_set *params);
4901 __isl_give isl_set *isl_set_intersect(
4902 __isl_take isl_set *set1,
4903 __isl_take isl_set *set2);
4905 #include <isl/map.h>
4906 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
4907 __isl_take isl_basic_map *bmap,
4908 __isl_take isl_basic_set *bset);
4909 __isl_give isl_basic_map *isl_basic_map_intersect_range(
4910 __isl_take isl_basic_map *bmap,
4911 __isl_take isl_basic_set *bset);
4912 __isl_give isl_basic_map *isl_basic_map_intersect(
4913 __isl_take isl_basic_map *bmap1,
4914 __isl_take isl_basic_map *bmap2);
4915 __isl_give isl_map *isl_map_intersect_params(
4916 __isl_take isl_map *map,
4917 __isl_take isl_set *params);
4918 __isl_give isl_map *isl_map_intersect_domain(
4919 __isl_take isl_map *map,
4920 __isl_take isl_set *set);
4921 __isl_give isl_map *isl_map_intersect_range(
4922 __isl_take isl_map *map,
4923 __isl_take isl_set *set);
4924 __isl_give isl_map *isl_map_intersect(
4925 __isl_take isl_map *map1,
4926 __isl_take isl_map *map2);
4928 #include <isl/union_set.h>
4929 __isl_give isl_union_set *isl_union_set_intersect_params(
4930 __isl_take isl_union_set *uset,
4931 __isl_take isl_set *set);
4932 __isl_give isl_union_set *isl_union_set_intersect(
4933 __isl_take isl_union_set *uset1,
4934 __isl_take isl_union_set *uset2);
4936 #include <isl/union_map.h>
4937 __isl_give isl_union_map *isl_union_map_intersect_params(
4938 __isl_take isl_union_map *umap,
4939 __isl_take isl_set *set);
4940 __isl_give isl_union_map *isl_union_map_intersect_domain(
4941 __isl_take isl_union_map *umap,
4942 __isl_take isl_union_set *uset);
4943 __isl_give isl_union_map *isl_union_map_intersect_range(
4944 __isl_take isl_union_map *umap,
4945 __isl_take isl_union_set *uset);
4946 __isl_give isl_union_map *isl_union_map_intersect(
4947 __isl_take isl_union_map *umap1,
4948 __isl_take isl_union_map *umap2);
4950 #include <isl/aff.h>
4951 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4952 __isl_take isl_pw_aff *pa,
4953 __isl_take isl_set *set);
4954 __isl_give isl_multi_pw_aff *
4955 isl_multi_pw_aff_intersect_domain(
4956 __isl_take isl_multi_pw_aff *mpa,
4957 __isl_take isl_set *domain);
4958 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4959 __isl_take isl_pw_multi_aff *pma,
4960 __isl_take isl_set *set);
4961 __isl_give isl_union_pw_multi_aff *
4962 isl_union_pw_multi_aff_intersect_domain(
4963 __isl_take isl_union_pw_multi_aff *upma,
4964 __isl_take isl_union_set *uset);
4965 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4966 __isl_take isl_pw_aff *pa,
4967 __isl_take isl_set *set);
4968 __isl_give isl_multi_pw_aff *
4969 isl_multi_pw_aff_intersect_params(
4970 __isl_take isl_multi_pw_aff *mpa,
4971 __isl_take isl_set *set);
4972 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4973 __isl_take isl_pw_multi_aff *pma,
4974 __isl_take isl_set *set);
4975 __isl_give isl_union_pw_multi_aff *
4976 isl_union_pw_multi_aff_intersect_params(
4977 __isl_take isl_union_pw_multi_aff *upma,
4978 __isl_take isl_set *set);
4980 #include <isl/polynomial.h>
4981 __isl_give isl_pw_qpolynomial *
4982 isl_pw_qpolynomial_intersect_domain(
4983 __isl_take isl_pw_qpolynomial *pwpq,
4984 __isl_take isl_set *set);
4985 __isl_give isl_union_pw_qpolynomial *
4986 isl_union_pw_qpolynomial_intersect_domain(
4987 __isl_take isl_union_pw_qpolynomial *upwpq,
4988 __isl_take isl_union_set *uset);
4989 __isl_give isl_union_pw_qpolynomial_fold *
4990 isl_union_pw_qpolynomial_fold_intersect_domain(
4991 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4992 __isl_take isl_union_set *uset);
4993 __isl_give isl_pw_qpolynomial *
4994 isl_pw_qpolynomial_intersect_params(
4995 __isl_take isl_pw_qpolynomial *pwpq,
4996 __isl_take isl_set *set);
4997 __isl_give isl_pw_qpolynomial_fold *
4998 isl_pw_qpolynomial_fold_intersect_params(
4999 __isl_take isl_pw_qpolynomial_fold *pwf,
5000 __isl_take isl_set *set);
5001 __isl_give isl_union_pw_qpolynomial *
5002 isl_union_pw_qpolynomial_intersect_params(
5003 __isl_take isl_union_pw_qpolynomial *upwpq,
5004 __isl_take isl_set *set);
5005 __isl_give isl_union_pw_qpolynomial_fold *
5006 isl_union_pw_qpolynomial_fold_intersect_params(
5007 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5008 __isl_take isl_set *set);
5010 The second argument to the C<_params> functions needs to be
5011 a parametric (basic) set. For the other functions, a parametric set
5012 for either argument is only allowed if the other argument is
5013 a parametric set as well.
5014 The list passed to C<isl_basic_set_list_intersect> needs to have
5015 at least one element and all elements need to live in the same space.
5019 __isl_give isl_set *isl_basic_set_union(
5020 __isl_take isl_basic_set *bset1,
5021 __isl_take isl_basic_set *bset2);
5022 __isl_give isl_map *isl_basic_map_union(
5023 __isl_take isl_basic_map *bmap1,
5024 __isl_take isl_basic_map *bmap2);
5025 __isl_give isl_set *isl_set_union(
5026 __isl_take isl_set *set1,
5027 __isl_take isl_set *set2);
5028 __isl_give isl_map *isl_map_union(
5029 __isl_take isl_map *map1,
5030 __isl_take isl_map *map2);
5031 __isl_give isl_union_set *isl_union_set_union(
5032 __isl_take isl_union_set *uset1,
5033 __isl_take isl_union_set *uset2);
5034 __isl_give isl_union_map *isl_union_map_union(
5035 __isl_take isl_union_map *umap1,
5036 __isl_take isl_union_map *umap2);
5038 =item * Set difference
5040 __isl_give isl_set *isl_set_subtract(
5041 __isl_take isl_set *set1,
5042 __isl_take isl_set *set2);
5043 __isl_give isl_map *isl_map_subtract(
5044 __isl_take isl_map *map1,
5045 __isl_take isl_map *map2);
5046 __isl_give isl_map *isl_map_subtract_domain(
5047 __isl_take isl_map *map,
5048 __isl_take isl_set *dom);
5049 __isl_give isl_map *isl_map_subtract_range(
5050 __isl_take isl_map *map,
5051 __isl_take isl_set *dom);
5052 __isl_give isl_union_set *isl_union_set_subtract(
5053 __isl_take isl_union_set *uset1,
5054 __isl_take isl_union_set *uset2);
5055 __isl_give isl_union_map *isl_union_map_subtract(
5056 __isl_take isl_union_map *umap1,
5057 __isl_take isl_union_map *umap2);
5058 __isl_give isl_union_map *isl_union_map_subtract_domain(
5059 __isl_take isl_union_map *umap,
5060 __isl_take isl_union_set *dom);
5061 __isl_give isl_union_map *isl_union_map_subtract_range(
5062 __isl_take isl_union_map *umap,
5063 __isl_take isl_union_set *dom);
5067 #include <isl/space.h>
5068 __isl_give isl_space *isl_space_join(
5069 __isl_take isl_space *left,
5070 __isl_take isl_space *right);
5072 #include <isl/map.h>
5073 __isl_give isl_basic_set *isl_basic_set_apply(
5074 __isl_take isl_basic_set *bset,
5075 __isl_take isl_basic_map *bmap);
5076 __isl_give isl_set *isl_set_apply(
5077 __isl_take isl_set *set,
5078 __isl_take isl_map *map);
5079 __isl_give isl_union_set *isl_union_set_apply(
5080 __isl_take isl_union_set *uset,
5081 __isl_take isl_union_map *umap);
5082 __isl_give isl_basic_map *isl_basic_map_apply_domain(
5083 __isl_take isl_basic_map *bmap1,
5084 __isl_take isl_basic_map *bmap2);
5085 __isl_give isl_basic_map *isl_basic_map_apply_range(
5086 __isl_take isl_basic_map *bmap1,
5087 __isl_take isl_basic_map *bmap2);
5088 __isl_give isl_map *isl_map_apply_domain(
5089 __isl_take isl_map *map1,
5090 __isl_take isl_map *map2);
5091 __isl_give isl_map *isl_map_apply_range(
5092 __isl_take isl_map *map1,
5093 __isl_take isl_map *map2);
5095 #include <isl/union_map.h>
5096 __isl_give isl_union_map *isl_union_map_apply_domain(
5097 __isl_take isl_union_map *umap1,
5098 __isl_take isl_union_map *umap2);
5099 __isl_give isl_union_map *isl_union_map_apply_range(
5100 __isl_take isl_union_map *umap1,
5101 __isl_take isl_union_map *umap2);
5103 #include <isl/polynomial.h>
5104 __isl_give isl_pw_qpolynomial_fold *
5105 isl_set_apply_pw_qpolynomial_fold(
5106 __isl_take isl_set *set,
5107 __isl_take isl_pw_qpolynomial_fold *pwf,
5109 __isl_give isl_pw_qpolynomial_fold *
5110 isl_map_apply_pw_qpolynomial_fold(
5111 __isl_take isl_map *map,
5112 __isl_take isl_pw_qpolynomial_fold *pwf,
5114 __isl_give isl_union_pw_qpolynomial_fold *
5115 isl_union_set_apply_union_pw_qpolynomial_fold(
5116 __isl_take isl_union_set *uset,
5117 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5119 __isl_give isl_union_pw_qpolynomial_fold *
5120 isl_union_map_apply_union_pw_qpolynomial_fold(
5121 __isl_take isl_union_map *umap,
5122 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5125 The functions taking a map
5126 compose the given map with the given piecewise quasipolynomial reduction.
5127 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5128 over all elements in the intersection of the range of the map
5129 and the domain of the piecewise quasipolynomial reduction
5130 as a function of an element in the domain of the map.
5131 The functions taking a set compute a bound over all elements in the
5132 intersection of the set and the domain of the
5133 piecewise quasipolynomial reduction.
5137 #include <isl/set.h>
5138 __isl_give isl_basic_set *
5139 isl_basic_set_preimage_multi_aff(
5140 __isl_take isl_basic_set *bset,
5141 __isl_take isl_multi_aff *ma);
5142 __isl_give isl_set *isl_set_preimage_multi_aff(
5143 __isl_take isl_set *set,
5144 __isl_take isl_multi_aff *ma);
5145 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5146 __isl_take isl_set *set,
5147 __isl_take isl_pw_multi_aff *pma);
5148 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5149 __isl_take isl_set *set,
5150 __isl_take isl_multi_pw_aff *mpa);
5152 #include <isl/union_set.h>
5153 __isl_give isl_union_set *
5154 isl_union_set_preimage_multi_aff(
5155 __isl_take isl_union_set *uset,
5156 __isl_take isl_multi_aff *ma);
5157 __isl_give isl_union_set *
5158 isl_union_set_preimage_pw_multi_aff(
5159 __isl_take isl_union_set *uset,
5160 __isl_take isl_pw_multi_aff *pma);
5161 __isl_give isl_union_set *
5162 isl_union_set_preimage_union_pw_multi_aff(
5163 __isl_take isl_union_set *uset,
5164 __isl_take isl_union_pw_multi_aff *upma);
5166 #include <isl/map.h>
5167 __isl_give isl_basic_map *
5168 isl_basic_map_preimage_domain_multi_aff(
5169 __isl_take isl_basic_map *bmap,
5170 __isl_take isl_multi_aff *ma);
5171 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5172 __isl_take isl_map *map,
5173 __isl_take isl_multi_aff *ma);
5174 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5175 __isl_take isl_map *map,
5176 __isl_take isl_multi_aff *ma);
5177 __isl_give isl_map *
5178 isl_map_preimage_domain_pw_multi_aff(
5179 __isl_take isl_map *map,
5180 __isl_take isl_pw_multi_aff *pma);
5181 __isl_give isl_map *
5182 isl_map_preimage_range_pw_multi_aff(
5183 __isl_take isl_map *map,
5184 __isl_take isl_pw_multi_aff *pma);
5185 __isl_give isl_map *
5186 isl_map_preimage_domain_multi_pw_aff(
5187 __isl_take isl_map *map,
5188 __isl_take isl_multi_pw_aff *mpa);
5189 __isl_give isl_basic_map *
5190 isl_basic_map_preimage_range_multi_aff(
5191 __isl_take isl_basic_map *bmap,
5192 __isl_take isl_multi_aff *ma);
5194 #include <isl/union_map.h>
5195 __isl_give isl_union_map *
5196 isl_union_map_preimage_domain_multi_aff(
5197 __isl_take isl_union_map *umap,
5198 __isl_take isl_multi_aff *ma);
5199 __isl_give isl_union_map *
5200 isl_union_map_preimage_range_multi_aff(
5201 __isl_take isl_union_map *umap,
5202 __isl_take isl_multi_aff *ma);
5203 __isl_give isl_union_map *
5204 isl_union_map_preimage_domain_pw_multi_aff(
5205 __isl_take isl_union_map *umap,
5206 __isl_take isl_pw_multi_aff *pma);
5207 __isl_give isl_union_map *
5208 isl_union_map_preimage_range_pw_multi_aff(
5209 __isl_take isl_union_map *umap,
5210 __isl_take isl_pw_multi_aff *pma);
5211 __isl_give isl_union_map *
5212 isl_union_map_preimage_domain_union_pw_multi_aff(
5213 __isl_take isl_union_map *umap,
5214 __isl_take isl_union_pw_multi_aff *upma);
5215 __isl_give isl_union_map *
5216 isl_union_map_preimage_range_union_pw_multi_aff(
5217 __isl_take isl_union_map *umap,
5218 __isl_take isl_union_pw_multi_aff *upma);
5220 These functions compute the preimage of the given set or map domain/range under
5221 the given function. In other words, the expression is plugged
5222 into the set description or into the domain/range of the map.
5226 #include <isl/aff.h>
5227 __isl_give isl_aff *isl_aff_pullback_aff(
5228 __isl_take isl_aff *aff1,
5229 __isl_take isl_aff *aff2);
5230 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5231 __isl_take isl_aff *aff,
5232 __isl_take isl_multi_aff *ma);
5233 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5234 __isl_take isl_pw_aff *pa,
5235 __isl_take isl_multi_aff *ma);
5236 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5237 __isl_take isl_pw_aff *pa,
5238 __isl_take isl_pw_multi_aff *pma);
5239 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5240 __isl_take isl_pw_aff *pa,
5241 __isl_take isl_multi_pw_aff *mpa);
5242 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5243 __isl_take isl_multi_aff *ma1,
5244 __isl_take isl_multi_aff *ma2);
5245 __isl_give isl_pw_multi_aff *
5246 isl_pw_multi_aff_pullback_multi_aff(
5247 __isl_take isl_pw_multi_aff *pma,
5248 __isl_take isl_multi_aff *ma);
5249 __isl_give isl_multi_pw_aff *
5250 isl_multi_pw_aff_pullback_multi_aff(
5251 __isl_take isl_multi_pw_aff *mpa,
5252 __isl_take isl_multi_aff *ma);
5253 __isl_give isl_pw_multi_aff *
5254 isl_pw_multi_aff_pullback_pw_multi_aff(
5255 __isl_take isl_pw_multi_aff *pma1,
5256 __isl_take isl_pw_multi_aff *pma2);
5257 __isl_give isl_multi_pw_aff *
5258 isl_multi_pw_aff_pullback_pw_multi_aff(
5259 __isl_take isl_multi_pw_aff *mpa,
5260 __isl_take isl_pw_multi_aff *pma);
5261 __isl_give isl_multi_pw_aff *
5262 isl_multi_pw_aff_pullback_multi_pw_aff(
5263 __isl_take isl_multi_pw_aff *mpa1,
5264 __isl_take isl_multi_pw_aff *mpa2);
5266 These functions precompose the first expression by the second function.
5267 In other words, the second function is plugged
5268 into the first expression.
5272 #include <isl/aff.h>
5273 __isl_give isl_basic_set *isl_aff_le_basic_set(
5274 __isl_take isl_aff *aff1,
5275 __isl_take isl_aff *aff2);
5276 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5277 __isl_take isl_aff *aff1,
5278 __isl_take isl_aff *aff2);
5279 __isl_give isl_set *isl_pw_aff_eq_set(
5280 __isl_take isl_pw_aff *pwaff1,
5281 __isl_take isl_pw_aff *pwaff2);
5282 __isl_give isl_set *isl_pw_aff_ne_set(
5283 __isl_take isl_pw_aff *pwaff1,
5284 __isl_take isl_pw_aff *pwaff2);
5285 __isl_give isl_set *isl_pw_aff_le_set(
5286 __isl_take isl_pw_aff *pwaff1,
5287 __isl_take isl_pw_aff *pwaff2);
5288 __isl_give isl_set *isl_pw_aff_lt_set(
5289 __isl_take isl_pw_aff *pwaff1,
5290 __isl_take isl_pw_aff *pwaff2);
5291 __isl_give isl_set *isl_pw_aff_ge_set(
5292 __isl_take isl_pw_aff *pwaff1,
5293 __isl_take isl_pw_aff *pwaff2);
5294 __isl_give isl_set *isl_pw_aff_gt_set(
5295 __isl_take isl_pw_aff *pwaff1,
5296 __isl_take isl_pw_aff *pwaff2);
5298 __isl_give isl_set *isl_multi_aff_lex_le_set(
5299 __isl_take isl_multi_aff *ma1,
5300 __isl_take isl_multi_aff *ma2);
5301 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5302 __isl_take isl_multi_aff *ma1,
5303 __isl_take isl_multi_aff *ma2);
5305 __isl_give isl_set *isl_pw_aff_list_eq_set(
5306 __isl_take isl_pw_aff_list *list1,
5307 __isl_take isl_pw_aff_list *list2);
5308 __isl_give isl_set *isl_pw_aff_list_ne_set(
5309 __isl_take isl_pw_aff_list *list1,
5310 __isl_take isl_pw_aff_list *list2);
5311 __isl_give isl_set *isl_pw_aff_list_le_set(
5312 __isl_take isl_pw_aff_list *list1,
5313 __isl_take isl_pw_aff_list *list2);
5314 __isl_give isl_set *isl_pw_aff_list_lt_set(
5315 __isl_take isl_pw_aff_list *list1,
5316 __isl_take isl_pw_aff_list *list2);
5317 __isl_give isl_set *isl_pw_aff_list_ge_set(
5318 __isl_take isl_pw_aff_list *list1,
5319 __isl_take isl_pw_aff_list *list2);
5320 __isl_give isl_set *isl_pw_aff_list_gt_set(
5321 __isl_take isl_pw_aff_list *list1,
5322 __isl_take isl_pw_aff_list *list2);
5324 The function C<isl_aff_ge_basic_set> returns a basic set
5325 containing those elements in the shared space
5326 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5327 The function C<isl_pw_aff_ge_set> returns a set
5328 containing those elements in the shared domain
5329 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5330 greater than or equal to C<pwaff2>.
5331 The function C<isl_multi_aff_lex_le_set> returns a set
5332 containing those elements in the shared domain space
5333 where C<ma1> is lexicographically smaller than or
5335 The functions operating on C<isl_pw_aff_list> apply the corresponding
5336 C<isl_pw_aff> function to each pair of elements in the two lists.
5338 =item * Cartesian Product
5340 #include <isl/space.h>
5341 __isl_give isl_space *isl_space_product(
5342 __isl_take isl_space *space1,
5343 __isl_take isl_space *space2);
5344 __isl_give isl_space *isl_space_domain_product(
5345 __isl_take isl_space *space1,
5346 __isl_take isl_space *space2);
5347 __isl_give isl_space *isl_space_range_product(
5348 __isl_take isl_space *space1,
5349 __isl_take isl_space *space2);
5352 C<isl_space_product>, C<isl_space_domain_product>
5353 and C<isl_space_range_product> take pairs or relation spaces and
5354 produce a single relations space, where either the domain, the range
5355 or both domain and range are wrapped spaces of relations between
5356 the domains and/or ranges of the input spaces.
5357 If the product is only constructed over the domain or the range
5358 then the ranges or the domains of the inputs should be the same.
5359 The function C<isl_space_product> also accepts a pair of set spaces,
5360 in which case it returns a wrapped space of a relation between the
5363 #include <isl/set.h>
5364 __isl_give isl_set *isl_set_product(
5365 __isl_take isl_set *set1,
5366 __isl_take isl_set *set2);
5368 #include <isl/map.h>
5369 __isl_give isl_basic_map *isl_basic_map_domain_product(
5370 __isl_take isl_basic_map *bmap1,
5371 __isl_take isl_basic_map *bmap2);
5372 __isl_give isl_basic_map *isl_basic_map_range_product(
5373 __isl_take isl_basic_map *bmap1,
5374 __isl_take isl_basic_map *bmap2);
5375 __isl_give isl_basic_map *isl_basic_map_product(
5376 __isl_take isl_basic_map *bmap1,
5377 __isl_take isl_basic_map *bmap2);
5378 __isl_give isl_map *isl_map_domain_product(
5379 __isl_take isl_map *map1,
5380 __isl_take isl_map *map2);
5381 __isl_give isl_map *isl_map_range_product(
5382 __isl_take isl_map *map1,
5383 __isl_take isl_map *map2);
5384 __isl_give isl_map *isl_map_product(
5385 __isl_take isl_map *map1,
5386 __isl_take isl_map *map2);
5388 #include <isl/union_set.h>
5389 __isl_give isl_union_set *isl_union_set_product(
5390 __isl_take isl_union_set *uset1,
5391 __isl_take isl_union_set *uset2);
5393 #include <isl/union_map.h>
5394 __isl_give isl_union_map *isl_union_map_domain_product(
5395 __isl_take isl_union_map *umap1,
5396 __isl_take isl_union_map *umap2);
5397 __isl_give isl_union_map *isl_union_map_range_product(
5398 __isl_take isl_union_map *umap1,
5399 __isl_take isl_union_map *umap2);
5400 __isl_give isl_union_map *isl_union_map_product(
5401 __isl_take isl_union_map *umap1,
5402 __isl_take isl_union_map *umap2);
5404 #include <isl/val.h>
5405 __isl_give isl_multi_val *isl_multi_val_range_product(
5406 __isl_take isl_multi_val *mv1,
5407 __isl_take isl_multi_val *mv2);
5408 __isl_give isl_multi_val *isl_multi_val_product(
5409 __isl_take isl_multi_val *mv1,
5410 __isl_take isl_multi_val *mv2);
5412 #include <isl/aff.h>
5413 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5414 __isl_take isl_multi_aff *ma1,
5415 __isl_take isl_multi_aff *ma2);
5416 __isl_give isl_multi_aff *isl_multi_aff_product(
5417 __isl_take isl_multi_aff *ma1,
5418 __isl_take isl_multi_aff *ma2);
5419 __isl_give isl_multi_pw_aff *
5420 isl_multi_pw_aff_range_product(
5421 __isl_take isl_multi_pw_aff *mpa1,
5422 __isl_take isl_multi_pw_aff *mpa2);
5423 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5424 __isl_take isl_multi_pw_aff *mpa1,
5425 __isl_take isl_multi_pw_aff *mpa2);
5426 __isl_give isl_pw_multi_aff *
5427 isl_pw_multi_aff_range_product(
5428 __isl_take isl_pw_multi_aff *pma1,
5429 __isl_take isl_pw_multi_aff *pma2);
5430 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5431 __isl_take isl_pw_multi_aff *pma1,
5432 __isl_take isl_pw_multi_aff *pma2);
5434 The above functions compute the cross product of the given
5435 sets, relations or functions. The domains and ranges of the results
5436 are wrapped maps between domains and ranges of the inputs.
5437 To obtain a ``flat'' product, use the following functions
5440 #include <isl/set.h>
5441 __isl_give isl_basic_set *isl_basic_set_flat_product(
5442 __isl_take isl_basic_set *bset1,
5443 __isl_take isl_basic_set *bset2);
5444 __isl_give isl_set *isl_set_flat_product(
5445 __isl_take isl_set *set1,
5446 __isl_take isl_set *set2);
5448 #include <isl/map.h>
5449 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5450 __isl_take isl_basic_map *bmap1,
5451 __isl_take isl_basic_map *bmap2);
5452 __isl_give isl_map *isl_map_flat_domain_product(
5453 __isl_take isl_map *map1,
5454 __isl_take isl_map *map2);
5455 __isl_give isl_map *isl_map_flat_range_product(
5456 __isl_take isl_map *map1,
5457 __isl_take isl_map *map2);
5458 __isl_give isl_basic_map *isl_basic_map_flat_product(
5459 __isl_take isl_basic_map *bmap1,
5460 __isl_take isl_basic_map *bmap2);
5461 __isl_give isl_map *isl_map_flat_product(
5462 __isl_take isl_map *map1,
5463 __isl_take isl_map *map2);
5465 #include <isl/union_map.h>
5466 __isl_give isl_union_map *
5467 isl_union_map_flat_range_product(
5468 __isl_take isl_union_map *umap1,
5469 __isl_take isl_union_map *umap2);
5471 #include <isl/val.h>
5472 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
5473 __isl_take isl_multi_val *mv1,
5474 __isl_take isl_multi_aff *mv2);
5476 #include <isl/aff.h>
5477 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
5478 __isl_take isl_multi_aff *ma1,
5479 __isl_take isl_multi_aff *ma2);
5480 __isl_give isl_pw_multi_aff *
5481 isl_pw_multi_aff_flat_range_product(
5482 __isl_take isl_pw_multi_aff *pma1,
5483 __isl_take isl_pw_multi_aff *pma2);
5484 __isl_give isl_multi_pw_aff *
5485 isl_multi_pw_aff_flat_range_product(
5486 __isl_take isl_multi_pw_aff *mpa1,
5487 __isl_take isl_multi_pw_aff *mpa2);
5488 __isl_give isl_union_pw_multi_aff *
5489 isl_union_pw_multi_aff_flat_range_product(
5490 __isl_take isl_union_pw_multi_aff *upma1,
5491 __isl_take isl_union_pw_multi_aff *upma2);
5493 #include <isl/space.h>
5494 __isl_give isl_space *isl_space_factor_domain(
5495 __isl_take isl_space *space);
5496 __isl_give isl_space *isl_space_factor_range(
5497 __isl_take isl_space *space);
5498 __isl_give isl_space *isl_space_domain_factor_domain(
5499 __isl_take isl_space *space);
5500 __isl_give isl_space *isl_space_domain_factor_range(
5501 __isl_take isl_space *space);
5502 __isl_give isl_space *isl_space_range_factor_domain(
5503 __isl_take isl_space *space);
5504 __isl_give isl_space *isl_space_range_factor_range(
5505 __isl_take isl_space *space);
5507 The functions C<isl_space_range_factor_domain> and
5508 C<isl_space_range_factor_range> extract the two arguments from
5509 the result of a call to C<isl_space_range_product>.
5511 The arguments of a call to C<isl_map_range_product> can be extracted
5512 from the result using the following functions.
5514 #include <isl/map.h>
5515 __isl_give isl_map *isl_map_factor_range(
5516 __isl_take isl_map *map);
5517 __isl_give isl_map *isl_map_domain_factor_domain(
5518 __isl_take isl_map *map);
5519 __isl_give isl_map *isl_map_domain_factor_range(
5520 __isl_take isl_map *map);
5521 __isl_give isl_map *isl_map_range_factor_domain(
5522 __isl_take isl_map *map);
5523 __isl_give isl_map *isl_map_range_factor_range(
5524 __isl_take isl_map *map);
5526 #include <isl/val.h>
5527 __isl_give isl_multi_val *
5528 isl_multi_val_range_factor_domain(
5529 __isl_take isl_multi_val *mv);
5530 __isl_give isl_multi_val *
5531 isl_multi_val_range_factor_range(
5532 __isl_take isl_multi_val *mv);
5534 #include <isl/aff.h>
5535 __isl_give isl_multi_aff *
5536 isl_multi_aff_range_factor_domain(
5537 __isl_take isl_multi_aff *ma);
5538 __isl_give isl_multi_aff *
5539 isl_multi_aff_range_factor_range(
5540 __isl_take isl_multi_aff *ma);
5541 __isl_give isl_multi_pw_aff *
5542 isl_multi_pw_aff_range_factor_domain(
5543 __isl_take isl_multi_pw_aff *mpa);
5544 __isl_give isl_multi_pw_aff *
5545 isl_multi_pw_aff_range_factor_range(
5546 __isl_take isl_multi_pw_aff *mpa);
5548 The splice functions are a generalization of the flat product functions,
5549 where the second argument may be inserted at any position inside
5550 the first argument rather than being placed at the end.
5552 #include <isl/val.h>
5553 __isl_give isl_multi_val *isl_multi_val_range_splice(
5554 __isl_take isl_multi_val *mv1, unsigned pos,
5555 __isl_take isl_multi_val *mv2);
5557 #include <isl/aff.h>
5558 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
5559 __isl_take isl_multi_aff *ma1, unsigned pos,
5560 __isl_take isl_multi_aff *ma2);
5561 __isl_give isl_multi_aff *isl_multi_aff_splice(
5562 __isl_take isl_multi_aff *ma1,
5563 unsigned in_pos, unsigned out_pos,
5564 __isl_take isl_multi_aff *ma2);
5565 __isl_give isl_multi_pw_aff *
5566 isl_multi_pw_aff_range_splice(
5567 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
5568 __isl_take isl_multi_pw_aff *mpa2);
5569 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
5570 __isl_take isl_multi_pw_aff *mpa1,
5571 unsigned in_pos, unsigned out_pos,
5572 __isl_take isl_multi_pw_aff *mpa2);
5574 =item * Simplification
5576 When applied to a set or relation,
5577 the gist operation returns a set or relation that has the
5578 same intersection with the context as the input set or relation.
5579 Any implicit equality in the intersection is made explicit in the result,
5580 while all inequalities that are redundant with respect to the intersection
5582 In case of union sets and relations, the gist operation is performed
5585 When applied to a function,
5586 the gist operation applies the set gist operation to each of
5587 the cells in the domain of the input piecewise expression.
5588 The context is also exploited
5589 to simplify the expression associated to each cell.
5591 #include <isl/set.h>
5592 __isl_give isl_basic_set *isl_basic_set_gist(
5593 __isl_take isl_basic_set *bset,
5594 __isl_take isl_basic_set *context);
5595 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
5596 __isl_take isl_set *context);
5597 __isl_give isl_set *isl_set_gist_params(
5598 __isl_take isl_set *set,
5599 __isl_take isl_set *context);
5601 #include <isl/map.h>
5602 __isl_give isl_basic_map *isl_basic_map_gist(
5603 __isl_take isl_basic_map *bmap,
5604 __isl_take isl_basic_map *context);
5605 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
5606 __isl_take isl_map *context);
5607 __isl_give isl_map *isl_map_gist_params(
5608 __isl_take isl_map *map,
5609 __isl_take isl_set *context);
5610 __isl_give isl_map *isl_map_gist_domain(
5611 __isl_take isl_map *map,
5612 __isl_take isl_set *context);
5613 __isl_give isl_map *isl_map_gist_range(
5614 __isl_take isl_map *map,
5615 __isl_take isl_set *context);
5617 #include <isl/union_set.h>
5618 __isl_give isl_union_set *isl_union_set_gist(
5619 __isl_take isl_union_set *uset,
5620 __isl_take isl_union_set *context);
5621 __isl_give isl_union_set *isl_union_set_gist_params(
5622 __isl_take isl_union_set *uset,
5623 __isl_take isl_set *set);
5625 #include <isl/union_map.h>
5626 __isl_give isl_union_map *isl_union_map_gist(
5627 __isl_take isl_union_map *umap,
5628 __isl_take isl_union_map *context);
5629 __isl_give isl_union_map *isl_union_map_gist_params(
5630 __isl_take isl_union_map *umap,
5631 __isl_take isl_set *set);
5632 __isl_give isl_union_map *isl_union_map_gist_domain(
5633 __isl_take isl_union_map *umap,
5634 __isl_take isl_union_set *uset);
5635 __isl_give isl_union_map *isl_union_map_gist_range(
5636 __isl_take isl_union_map *umap,
5637 __isl_take isl_union_set *uset);
5639 #include <isl/aff.h>
5640 __isl_give isl_aff *isl_aff_gist_params(
5641 __isl_take isl_aff *aff,
5642 __isl_take isl_set *context);
5643 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
5644 __isl_take isl_set *context);
5645 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
5646 __isl_take isl_multi_aff *maff,
5647 __isl_take isl_set *context);
5648 __isl_give isl_multi_aff *isl_multi_aff_gist(
5649 __isl_take isl_multi_aff *maff,
5650 __isl_take isl_set *context);
5651 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
5652 __isl_take isl_pw_aff *pwaff,
5653 __isl_take isl_set *context);
5654 __isl_give isl_pw_aff *isl_pw_aff_gist(
5655 __isl_take isl_pw_aff *pwaff,
5656 __isl_take isl_set *context);
5657 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
5658 __isl_take isl_pw_multi_aff *pma,
5659 __isl_take isl_set *set);
5660 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
5661 __isl_take isl_pw_multi_aff *pma,
5662 __isl_take isl_set *set);
5663 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
5664 __isl_take isl_multi_pw_aff *mpa,
5665 __isl_take isl_set *set);
5666 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
5667 __isl_take isl_multi_pw_aff *mpa,
5668 __isl_take isl_set *set);
5669 __isl_give isl_union_pw_multi_aff *
5670 isl_union_pw_multi_aff_gist_params(
5671 __isl_take isl_union_pw_multi_aff *upma,
5672 __isl_take isl_set *context);
5673 __isl_give isl_union_pw_multi_aff *
5674 isl_union_pw_multi_aff_gist(
5675 __isl_take isl_union_pw_multi_aff *upma,
5676 __isl_take isl_union_set *context);
5678 #include <isl/polynomial.h>
5679 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5680 __isl_take isl_qpolynomial *qp,
5681 __isl_take isl_set *context);
5682 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5683 __isl_take isl_qpolynomial *qp,
5684 __isl_take isl_set *context);
5685 __isl_give isl_qpolynomial_fold *
5686 isl_qpolynomial_fold_gist_params(
5687 __isl_take isl_qpolynomial_fold *fold,
5688 __isl_take isl_set *context);
5689 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5690 __isl_take isl_qpolynomial_fold *fold,
5691 __isl_take isl_set *context);
5692 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5693 __isl_take isl_pw_qpolynomial *pwqp,
5694 __isl_take isl_set *context);
5695 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5696 __isl_take isl_pw_qpolynomial *pwqp,
5697 __isl_take isl_set *context);
5698 __isl_give isl_pw_qpolynomial_fold *
5699 isl_pw_qpolynomial_fold_gist(
5700 __isl_take isl_pw_qpolynomial_fold *pwf,
5701 __isl_take isl_set *context);
5702 __isl_give isl_pw_qpolynomial_fold *
5703 isl_pw_qpolynomial_fold_gist_params(
5704 __isl_take isl_pw_qpolynomial_fold *pwf,
5705 __isl_take isl_set *context);
5706 __isl_give isl_union_pw_qpolynomial *
5707 isl_union_pw_qpolynomial_gist_params(
5708 __isl_take isl_union_pw_qpolynomial *upwqp,
5709 __isl_take isl_set *context);
5710 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5711 __isl_take isl_union_pw_qpolynomial *upwqp,
5712 __isl_take isl_union_set *context);
5713 __isl_give isl_union_pw_qpolynomial_fold *
5714 isl_union_pw_qpolynomial_fold_gist(
5715 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5716 __isl_take isl_union_set *context);
5717 __isl_give isl_union_pw_qpolynomial_fold *
5718 isl_union_pw_qpolynomial_fold_gist_params(
5719 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5720 __isl_take isl_set *context);
5722 =item * Binary Arithmethic Operations
5724 #include <isl/aff.h>
5725 __isl_give isl_aff *isl_aff_add(
5726 __isl_take isl_aff *aff1,
5727 __isl_take isl_aff *aff2);
5728 __isl_give isl_multi_aff *isl_multi_aff_add(
5729 __isl_take isl_multi_aff *maff1,
5730 __isl_take isl_multi_aff *maff2);
5731 __isl_give isl_pw_aff *isl_pw_aff_add(
5732 __isl_take isl_pw_aff *pwaff1,
5733 __isl_take isl_pw_aff *pwaff2);
5734 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
5735 __isl_take isl_pw_multi_aff *pma1,
5736 __isl_take isl_pw_multi_aff *pma2);
5737 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
5738 __isl_take isl_union_pw_multi_aff *upma1,
5739 __isl_take isl_union_pw_multi_aff *upma2);
5740 __isl_give isl_pw_aff *isl_pw_aff_min(
5741 __isl_take isl_pw_aff *pwaff1,
5742 __isl_take isl_pw_aff *pwaff2);
5743 __isl_give isl_pw_aff *isl_pw_aff_max(
5744 __isl_take isl_pw_aff *pwaff1,
5745 __isl_take isl_pw_aff *pwaff2);
5746 __isl_give isl_aff *isl_aff_sub(
5747 __isl_take isl_aff *aff1,
5748 __isl_take isl_aff *aff2);
5749 __isl_give isl_multi_aff *isl_multi_aff_sub(
5750 __isl_take isl_multi_aff *ma1,
5751 __isl_take isl_multi_aff *ma2);
5752 __isl_give isl_pw_aff *isl_pw_aff_sub(
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_sub(
5756 __isl_take isl_pw_multi_aff *pma1,
5757 __isl_take isl_pw_multi_aff *pma2);
5758 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
5759 __isl_take isl_union_pw_multi_aff *upma1,
5760 __isl_take isl_union_pw_multi_aff *upma2);
5762 C<isl_aff_sub> subtracts the second argument from the first.
5764 #include <isl/polynomial.h>
5765 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5766 __isl_take isl_qpolynomial *qp1,
5767 __isl_take isl_qpolynomial *qp2);
5768 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5769 __isl_take isl_pw_qpolynomial *pwqp1,
5770 __isl_take isl_pw_qpolynomial *pwqp2);
5771 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5772 __isl_take isl_pw_qpolynomial *pwqp1,
5773 __isl_take isl_pw_qpolynomial *pwqp2);
5774 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5775 __isl_take isl_pw_qpolynomial_fold *pwf1,
5776 __isl_take isl_pw_qpolynomial_fold *pwf2);
5777 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5778 __isl_take isl_union_pw_qpolynomial *upwqp1,
5779 __isl_take isl_union_pw_qpolynomial *upwqp2);
5780 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5781 __isl_take isl_qpolynomial *qp1,
5782 __isl_take isl_qpolynomial *qp2);
5783 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5784 __isl_take isl_pw_qpolynomial *pwqp1,
5785 __isl_take isl_pw_qpolynomial *pwqp2);
5786 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5787 __isl_take isl_union_pw_qpolynomial *upwqp1,
5788 __isl_take isl_union_pw_qpolynomial *upwqp2);
5789 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5790 __isl_take isl_pw_qpolynomial_fold *pwf1,
5791 __isl_take isl_pw_qpolynomial_fold *pwf2);
5792 __isl_give isl_union_pw_qpolynomial_fold *
5793 isl_union_pw_qpolynomial_fold_fold(
5794 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5795 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5797 #include <isl/aff.h>
5798 __isl_give isl_pw_aff *isl_pw_aff_union_add(
5799 __isl_take isl_pw_aff *pwaff1,
5800 __isl_take isl_pw_aff *pwaff2);
5801 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
5802 __isl_take isl_pw_multi_aff *pma1,
5803 __isl_take isl_pw_multi_aff *pma2);
5804 __isl_give isl_union_pw_multi_aff *
5805 isl_union_pw_multi_aff_union_add(
5806 __isl_take isl_union_pw_multi_aff *upma1,
5807 __isl_take isl_union_pw_multi_aff *upma2);
5808 __isl_give isl_pw_aff *isl_pw_aff_union_min(
5809 __isl_take isl_pw_aff *pwaff1,
5810 __isl_take isl_pw_aff *pwaff2);
5811 __isl_give isl_pw_aff *isl_pw_aff_union_max(
5812 __isl_take isl_pw_aff *pwaff1,
5813 __isl_take isl_pw_aff *pwaff2);
5815 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
5816 expression with a domain that is the union of those of C<pwaff1> and
5817 C<pwaff2> and such that on each cell, the quasi-affine expression is
5818 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
5819 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
5820 associated expression is the defined one.
5821 This in contrast to the C<isl_pw_aff_max> function, which is
5822 only defined on the shared definition domain of the arguments.
5824 #include <isl/val.h>
5825 __isl_give isl_multi_val *isl_multi_val_add_val(
5826 __isl_take isl_multi_val *mv,
5827 __isl_take isl_val *v);
5828 __isl_give isl_multi_val *isl_multi_val_mod_val(
5829 __isl_take isl_multi_val *mv,
5830 __isl_take isl_val *v);
5831 __isl_give isl_multi_val *isl_multi_val_scale_val(
5832 __isl_take isl_multi_val *mv,
5833 __isl_take isl_val *v);
5834 __isl_give isl_multi_val *isl_multi_val_scale_down_val(
5835 __isl_take isl_multi_val *mv,
5836 __isl_take isl_val *v);
5838 #include <isl/aff.h>
5839 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
5840 __isl_take isl_val *mod);
5841 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
5842 __isl_take isl_pw_aff *pa,
5843 __isl_take isl_val *mod);
5844 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
5845 __isl_take isl_val *v);
5846 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
5847 __isl_take isl_multi_aff *ma,
5848 __isl_take isl_val *v);
5849 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
5850 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
5851 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
5852 __isl_take isl_multi_pw_aff *mpa,
5853 __isl_take isl_val *v);
5854 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
5855 __isl_take isl_pw_multi_aff *pma,
5856 __isl_take isl_val *v);
5857 __isl_give isl_union_pw_multi_aff *
5858 isl_union_pw_multi_aff_scale_val(
5859 __isl_take isl_union_pw_multi_aff *upma,
5860 __isl_take isl_val *val);
5861 __isl_give isl_aff *isl_aff_scale_down_ui(
5862 __isl_take isl_aff *aff, unsigned f);
5863 __isl_give isl_aff *isl_aff_scale_down_val(
5864 __isl_take isl_aff *aff, __isl_take isl_val *v);
5865 __isl_give isl_multi_aff *isl_multi_aff_scale_down_val(
5866 __isl_take isl_multi_aff *ma,
5867 __isl_take isl_val *v);
5868 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
5869 __isl_take isl_pw_aff *pa,
5870 __isl_take isl_val *f);
5871 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_down_val(
5872 __isl_take isl_multi_pw_aff *mpa,
5873 __isl_take isl_val *v);
5874 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_down_val(
5875 __isl_take isl_pw_multi_aff *pma,
5876 __isl_take isl_val *v);
5877 __isl_give isl_union_pw_multi_aff *
5878 isl_union_pw_multi_aff_scale_down_val(
5879 __isl_take isl_union_pw_multi_aff *upma,
5880 __isl_take isl_val *val);
5882 #include <isl/polynomial.h>
5883 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5884 __isl_take isl_qpolynomial *qp,
5885 __isl_take isl_val *v);
5886 __isl_give isl_qpolynomial_fold *
5887 isl_qpolynomial_fold_scale_val(
5888 __isl_take isl_qpolynomial_fold *fold,
5889 __isl_take isl_val *v);
5890 __isl_give isl_pw_qpolynomial *
5891 isl_pw_qpolynomial_scale_val(
5892 __isl_take isl_pw_qpolynomial *pwqp,
5893 __isl_take isl_val *v);
5894 __isl_give isl_pw_qpolynomial_fold *
5895 isl_pw_qpolynomial_fold_scale_val(
5896 __isl_take isl_pw_qpolynomial_fold *pwf,
5897 __isl_take isl_val *v);
5898 __isl_give isl_union_pw_qpolynomial *
5899 isl_union_pw_qpolynomial_scale_val(
5900 __isl_take isl_union_pw_qpolynomial *upwqp,
5901 __isl_take isl_val *v);
5902 __isl_give isl_union_pw_qpolynomial_fold *
5903 isl_union_pw_qpolynomial_fold_scale_val(
5904 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5905 __isl_take isl_val *v);
5906 __isl_give isl_qpolynomial *
5907 isl_qpolynomial_scale_down_val(
5908 __isl_take isl_qpolynomial *qp,
5909 __isl_take isl_val *v);
5910 __isl_give isl_qpolynomial_fold *
5911 isl_qpolynomial_fold_scale_down_val(
5912 __isl_take isl_qpolynomial_fold *fold,
5913 __isl_take isl_val *v);
5914 __isl_give isl_pw_qpolynomial *
5915 isl_pw_qpolynomial_scale_down_val(
5916 __isl_take isl_pw_qpolynomial *pwqp,
5917 __isl_take isl_val *v);
5918 __isl_give isl_pw_qpolynomial_fold *
5919 isl_pw_qpolynomial_fold_scale_down_val(
5920 __isl_take isl_pw_qpolynomial_fold *pwf,
5921 __isl_take isl_val *v);
5922 __isl_give isl_union_pw_qpolynomial *
5923 isl_union_pw_qpolynomial_scale_down_val(
5924 __isl_take isl_union_pw_qpolynomial *upwqp,
5925 __isl_take isl_val *v);
5926 __isl_give isl_union_pw_qpolynomial_fold *
5927 isl_union_pw_qpolynomial_fold_scale_down_val(
5928 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5929 __isl_take isl_val *v);
5931 #include <isl/val.h>
5932 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
5933 __isl_take isl_multi_val *mv1,
5934 __isl_take isl_multi_val *mv2);
5935 __isl_give isl_multi_val *
5936 isl_multi_val_scale_down_multi_val(
5937 __isl_take isl_multi_val *mv1,
5938 __isl_take isl_multi_val *mv2);
5940 #include <isl/aff.h>
5941 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
5942 __isl_take isl_multi_aff *ma,
5943 __isl_take isl_multi_val *mv);
5944 __isl_give isl_pw_multi_aff *
5945 isl_pw_multi_aff_scale_multi_val(
5946 __isl_take isl_pw_multi_aff *pma,
5947 __isl_take isl_multi_val *mv);
5948 __isl_give isl_multi_pw_aff *
5949 isl_multi_pw_aff_scale_multi_val(
5950 __isl_take isl_multi_pw_aff *mpa,
5951 __isl_take isl_multi_val *mv);
5952 __isl_give isl_union_pw_multi_aff *
5953 isl_union_pw_multi_aff_scale_multi_val(
5954 __isl_take isl_union_pw_multi_aff *upma,
5955 __isl_take isl_multi_val *mv);
5956 __isl_give isl_multi_aff *
5957 isl_multi_aff_scale_down_multi_val(
5958 __isl_take isl_multi_aff *ma,
5959 __isl_take isl_multi_val *mv);
5960 __isl_give isl_multi_pw_aff *
5961 isl_multi_pw_aff_scale_down_multi_val(
5962 __isl_take isl_multi_pw_aff *mpa,
5963 __isl_take isl_multi_val *mv);
5965 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
5966 by the corresponding elements of C<mv>.
5968 #include <isl/aff.h>
5969 __isl_give isl_aff *isl_aff_mul(
5970 __isl_take isl_aff *aff1,
5971 __isl_take isl_aff *aff2);
5972 __isl_give isl_aff *isl_aff_div(
5973 __isl_take isl_aff *aff1,
5974 __isl_take isl_aff *aff2);
5975 __isl_give isl_pw_aff *isl_pw_aff_mul(
5976 __isl_take isl_pw_aff *pwaff1,
5977 __isl_take isl_pw_aff *pwaff2);
5978 __isl_give isl_pw_aff *isl_pw_aff_div(
5979 __isl_take isl_pw_aff *pa1,
5980 __isl_take isl_pw_aff *pa2);
5981 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
5982 __isl_take isl_pw_aff *pa1,
5983 __isl_take isl_pw_aff *pa2);
5984 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
5985 __isl_take isl_pw_aff *pa1,
5986 __isl_take isl_pw_aff *pa2);
5988 When multiplying two affine expressions, at least one of the two needs
5989 to be a constant. Similarly, when dividing an affine expression by another,
5990 the second expression needs to be a constant.
5991 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
5992 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
5995 #include <isl/polynomial.h>
5996 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5997 __isl_take isl_qpolynomial *qp1,
5998 __isl_take isl_qpolynomial *qp2);
5999 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
6000 __isl_take isl_pw_qpolynomial *pwqp1,
6001 __isl_take isl_pw_qpolynomial *pwqp2);
6002 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
6003 __isl_take isl_union_pw_qpolynomial *upwqp1,
6004 __isl_take isl_union_pw_qpolynomial *upwqp2);
6008 =head3 Lexicographic Optimization
6010 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
6011 the following functions
6012 compute a set that contains the lexicographic minimum or maximum
6013 of the elements in C<set> (or C<bset>) for those values of the parameters
6014 that satisfy C<dom>.
6015 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6016 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
6018 In other words, the union of the parameter values
6019 for which the result is non-empty and of C<*empty>
6022 #include <isl/set.h>
6023 __isl_give isl_set *isl_basic_set_partial_lexmin(
6024 __isl_take isl_basic_set *bset,
6025 __isl_take isl_basic_set *dom,
6026 __isl_give isl_set **empty);
6027 __isl_give isl_set *isl_basic_set_partial_lexmax(
6028 __isl_take isl_basic_set *bset,
6029 __isl_take isl_basic_set *dom,
6030 __isl_give isl_set **empty);
6031 __isl_give isl_set *isl_set_partial_lexmin(
6032 __isl_take isl_set *set, __isl_take isl_set *dom,
6033 __isl_give isl_set **empty);
6034 __isl_give isl_set *isl_set_partial_lexmax(
6035 __isl_take isl_set *set, __isl_take isl_set *dom,
6036 __isl_give isl_set **empty);
6038 Given a (basic) set C<set> (or C<bset>), the following functions simply
6039 return a set containing the lexicographic minimum or maximum
6040 of the elements in C<set> (or C<bset>).
6041 In case of union sets, the optimum is computed per space.
6043 #include <isl/set.h>
6044 __isl_give isl_set *isl_basic_set_lexmin(
6045 __isl_take isl_basic_set *bset);
6046 __isl_give isl_set *isl_basic_set_lexmax(
6047 __isl_take isl_basic_set *bset);
6048 __isl_give isl_set *isl_set_lexmin(
6049 __isl_take isl_set *set);
6050 __isl_give isl_set *isl_set_lexmax(
6051 __isl_take isl_set *set);
6052 __isl_give isl_union_set *isl_union_set_lexmin(
6053 __isl_take isl_union_set *uset);
6054 __isl_give isl_union_set *isl_union_set_lexmax(
6055 __isl_take isl_union_set *uset);
6057 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
6058 the following functions
6059 compute a relation that maps each element of C<dom>
6060 to the single lexicographic minimum or maximum
6061 of the elements that are associated to that same
6062 element in C<map> (or C<bmap>).
6063 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
6064 that contains the elements in C<dom> that do not map
6065 to any elements in C<map> (or C<bmap>).
6066 In other words, the union of the domain of the result and of C<*empty>
6069 #include <isl/map.h>
6070 __isl_give isl_map *isl_basic_map_partial_lexmax(
6071 __isl_take isl_basic_map *bmap,
6072 __isl_take isl_basic_set *dom,
6073 __isl_give isl_set **empty);
6074 __isl_give isl_map *isl_basic_map_partial_lexmin(
6075 __isl_take isl_basic_map *bmap,
6076 __isl_take isl_basic_set *dom,
6077 __isl_give isl_set **empty);
6078 __isl_give isl_map *isl_map_partial_lexmax(
6079 __isl_take isl_map *map, __isl_take isl_set *dom,
6080 __isl_give isl_set **empty);
6081 __isl_give isl_map *isl_map_partial_lexmin(
6082 __isl_take isl_map *map, __isl_take isl_set *dom,
6083 __isl_give isl_set **empty);
6085 Given a (basic) map C<map> (or C<bmap>), the following functions simply
6086 return a map mapping each element in the domain of
6087 C<map> (or C<bmap>) to the lexicographic minimum or maximum
6088 of all elements associated to that element.
6089 In case of union relations, the optimum is computed per space.
6091 #include <isl/map.h>
6092 __isl_give isl_map *isl_basic_map_lexmin(
6093 __isl_take isl_basic_map *bmap);
6094 __isl_give isl_map *isl_basic_map_lexmax(
6095 __isl_take isl_basic_map *bmap);
6096 __isl_give isl_map *isl_map_lexmin(
6097 __isl_take isl_map *map);
6098 __isl_give isl_map *isl_map_lexmax(
6099 __isl_take isl_map *map);
6100 __isl_give isl_union_map *isl_union_map_lexmin(
6101 __isl_take isl_union_map *umap);
6102 __isl_give isl_union_map *isl_union_map_lexmax(
6103 __isl_take isl_union_map *umap);
6105 The following functions return their result in the form of
6106 a piecewise multi-affine expression,
6107 but are otherwise equivalent to the corresponding functions
6108 returning a basic set or relation.
6110 #include <isl/set.h>
6111 __isl_give isl_pw_multi_aff *
6112 isl_basic_set_partial_lexmin_pw_multi_aff(
6113 __isl_take isl_basic_set *bset,
6114 __isl_take isl_basic_set *dom,
6115 __isl_give isl_set **empty);
6116 __isl_give isl_pw_multi_aff *
6117 isl_basic_set_partial_lexmax_pw_multi_aff(
6118 __isl_take isl_basic_set *bset,
6119 __isl_take isl_basic_set *dom,
6120 __isl_give isl_set **empty);
6121 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
6122 __isl_take isl_set *set);
6123 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
6124 __isl_take isl_set *set);
6126 #include <isl/map.h>
6127 __isl_give isl_pw_multi_aff *
6128 isl_basic_map_lexmin_pw_multi_aff(
6129 __isl_take isl_basic_map *bmap);
6130 __isl_give isl_pw_multi_aff *
6131 isl_basic_map_partial_lexmin_pw_multi_aff(
6132 __isl_take isl_basic_map *bmap,
6133 __isl_take isl_basic_set *dom,
6134 __isl_give isl_set **empty);
6135 __isl_give isl_pw_multi_aff *
6136 isl_basic_map_partial_lexmax_pw_multi_aff(
6137 __isl_take isl_basic_map *bmap,
6138 __isl_take isl_basic_set *dom,
6139 __isl_give isl_set **empty);
6140 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
6141 __isl_take isl_map *map);
6142 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
6143 __isl_take isl_map *map);
6145 The following functions return the lexicographic minimum or maximum
6146 on the shared domain of the inputs and the single defined function
6147 on those parts of the domain where only a single function is defined.
6149 #include <isl/aff.h>
6150 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
6151 __isl_take isl_pw_multi_aff *pma1,
6152 __isl_take isl_pw_multi_aff *pma2);
6153 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
6154 __isl_take isl_pw_multi_aff *pma1,
6155 __isl_take isl_pw_multi_aff *pma2);
6157 =head2 Ternary Operations
6159 #include <isl/aff.h>
6160 __isl_give isl_pw_aff *isl_pw_aff_cond(
6161 __isl_take isl_pw_aff *cond,
6162 __isl_take isl_pw_aff *pwaff_true,
6163 __isl_take isl_pw_aff *pwaff_false);
6165 The function C<isl_pw_aff_cond> performs a conditional operator
6166 and returns an expression that is equal to C<pwaff_true>
6167 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
6168 where C<cond> is zero.
6172 Lists are defined over several element types, including
6173 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
6174 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
6175 Here we take lists of C<isl_set>s as an example.
6176 Lists can be created, copied, modified and freed using the following functions.
6178 #include <isl/set.h>
6179 __isl_give isl_set_list *isl_set_list_from_set(
6180 __isl_take isl_set *el);
6181 __isl_give isl_set_list *isl_set_list_alloc(
6182 isl_ctx *ctx, int n);
6183 __isl_give isl_set_list *isl_set_list_copy(
6184 __isl_keep isl_set_list *list);
6185 __isl_give isl_set_list *isl_set_list_insert(
6186 __isl_take isl_set_list *list, unsigned pos,
6187 __isl_take isl_set *el);
6188 __isl_give isl_set_list *isl_set_list_add(
6189 __isl_take isl_set_list *list,
6190 __isl_take isl_set *el);
6191 __isl_give isl_set_list *isl_set_list_drop(
6192 __isl_take isl_set_list *list,
6193 unsigned first, unsigned n);
6194 __isl_give isl_set_list *isl_set_list_set_set(
6195 __isl_take isl_set_list *list, int index,
6196 __isl_take isl_set *set);
6197 __isl_give isl_set_list *isl_set_list_concat(
6198 __isl_take isl_set_list *list1,
6199 __isl_take isl_set_list *list2);
6200 __isl_give isl_set_list *isl_set_list_sort(
6201 __isl_take isl_set_list *list,
6202 int (*cmp)(__isl_keep isl_set *a,
6203 __isl_keep isl_set *b, void *user),
6205 __isl_null isl_set_list *isl_set_list_free(
6206 __isl_take isl_set_list *list);
6208 C<isl_set_list_alloc> creates an empty list with a capacity for
6209 C<n> elements. C<isl_set_list_from_set> creates a list with a single
6212 Lists can be inspected using the following functions.
6214 #include <isl/set.h>
6215 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6216 __isl_give isl_set *isl_set_list_get_set(
6217 __isl_keep isl_set_list *list, int index);
6218 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6219 int (*fn)(__isl_take isl_set *el, void *user),
6221 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6222 int (*follows)(__isl_keep isl_set *a,
6223 __isl_keep isl_set *b, void *user),
6225 int (*fn)(__isl_take isl_set *el, void *user),
6228 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6229 strongly connected components of the graph with as vertices the elements
6230 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6231 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6232 should return C<-1> on error.
6234 Lists can be printed using
6236 #include <isl/set.h>
6237 __isl_give isl_printer *isl_printer_print_set_list(
6238 __isl_take isl_printer *p,
6239 __isl_keep isl_set_list *list);
6241 =head2 Associative arrays
6243 Associative arrays map isl objects of a specific type to isl objects
6244 of some (other) specific type. They are defined for several pairs
6245 of types, including (C<isl_map>, C<isl_basic_set>),
6246 (C<isl_id>, C<isl_ast_expr>) and.
6247 (C<isl_id>, C<isl_pw_aff>).
6248 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6251 Associative arrays can be created, copied and freed using
6252 the following functions.
6254 #include <isl/id_to_ast_expr.h>
6255 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6256 isl_ctx *ctx, int min_size);
6257 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6258 __isl_keep id_to_ast_expr *id2expr);
6259 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6260 __isl_take id_to_ast_expr *id2expr);
6262 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6263 to specify the expected size of the associative array.
6264 The associative array will be grown automatically as needed.
6266 Associative arrays can be inspected using the following functions.
6268 #include <isl/id_to_ast_expr.h>
6269 int isl_id_to_ast_expr_has(
6270 __isl_keep id_to_ast_expr *id2expr,
6271 __isl_keep isl_id *key);
6272 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6273 __isl_keep id_to_ast_expr *id2expr,
6274 __isl_take isl_id *key);
6275 int isl_id_to_ast_expr_foreach(
6276 __isl_keep id_to_ast_expr *id2expr,
6277 int (*fn)(__isl_take isl_id *key,
6278 __isl_take isl_ast_expr *val, void *user),
6281 They can be modified using the following function.
6283 #include <isl/id_to_ast_expr.h>
6284 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6285 __isl_take id_to_ast_expr *id2expr,
6286 __isl_take isl_id *key,
6287 __isl_take isl_ast_expr *val);
6288 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6289 __isl_take id_to_ast_expr *id2expr,
6290 __isl_take isl_id *key);
6292 Associative arrays can be printed using the following function.
6294 #include <isl/id_to_ast_expr.h>
6295 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6296 __isl_take isl_printer *p,
6297 __isl_keep id_to_ast_expr *id2expr);
6301 Vectors can be created, copied and freed using the following functions.
6303 #include <isl/vec.h>
6304 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6306 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6307 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6309 Note that the elements of a newly created vector may have arbitrary values.
6310 The elements can be changed and inspected using the following functions.
6312 int isl_vec_size(__isl_keep isl_vec *vec);
6313 __isl_give isl_val *isl_vec_get_element_val(
6314 __isl_keep isl_vec *vec, int pos);
6315 __isl_give isl_vec *isl_vec_set_element_si(
6316 __isl_take isl_vec *vec, int pos, int v);
6317 __isl_give isl_vec *isl_vec_set_element_val(
6318 __isl_take isl_vec *vec, int pos,
6319 __isl_take isl_val *v);
6320 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6322 __isl_give isl_vec *isl_vec_set_val(
6323 __isl_take isl_vec *vec, __isl_take isl_val *v);
6324 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6325 __isl_keep isl_vec *vec2, int pos);
6327 C<isl_vec_get_element> will return a negative value if anything went wrong.
6328 In that case, the value of C<*v> is undefined.
6330 The following function can be used to concatenate two vectors.
6332 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6333 __isl_take isl_vec *vec2);
6337 Matrices can be created, copied and freed using the following functions.
6339 #include <isl/mat.h>
6340 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6341 unsigned n_row, unsigned n_col);
6342 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6343 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6345 Note that the elements of a newly created matrix may have arbitrary values.
6346 The elements can be changed and inspected using the following functions.
6348 int isl_mat_rows(__isl_keep isl_mat *mat);
6349 int isl_mat_cols(__isl_keep isl_mat *mat);
6350 __isl_give isl_val *isl_mat_get_element_val(
6351 __isl_keep isl_mat *mat, int row, int col);
6352 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
6353 int row, int col, int v);
6354 __isl_give isl_mat *isl_mat_set_element_val(
6355 __isl_take isl_mat *mat, int row, int col,
6356 __isl_take isl_val *v);
6358 C<isl_mat_get_element> will return a negative value if anything went wrong.
6359 In that case, the value of C<*v> is undefined.
6361 The following function can be used to compute the (right) inverse
6362 of a matrix, i.e., a matrix such that the product of the original
6363 and the inverse (in that order) is a multiple of the identity matrix.
6364 The input matrix is assumed to be of full row-rank.
6366 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
6368 The following function can be used to compute the (right) kernel
6369 (or null space) of a matrix, i.e., a matrix such that the product of
6370 the original and the kernel (in that order) is the zero matrix.
6372 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
6374 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
6376 The following functions determine
6377 an upper or lower bound on a quasipolynomial over its domain.
6379 __isl_give isl_pw_qpolynomial_fold *
6380 isl_pw_qpolynomial_bound(
6381 __isl_take isl_pw_qpolynomial *pwqp,
6382 enum isl_fold type, int *tight);
6384 __isl_give isl_union_pw_qpolynomial_fold *
6385 isl_union_pw_qpolynomial_bound(
6386 __isl_take isl_union_pw_qpolynomial *upwqp,
6387 enum isl_fold type, int *tight);
6389 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
6390 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
6391 is the returned bound is known be tight, i.e., for each value
6392 of the parameters there is at least
6393 one element in the domain that reaches the bound.
6394 If the domain of C<pwqp> is not wrapping, then the bound is computed
6395 over all elements in that domain and the result has a purely parametric
6396 domain. If the domain of C<pwqp> is wrapping, then the bound is
6397 computed over the range of the wrapped relation. The domain of the
6398 wrapped relation becomes the domain of the result.
6400 =head2 Parametric Vertex Enumeration
6402 The parametric vertex enumeration described in this section
6403 is mainly intended to be used internally and by the C<barvinok>
6406 #include <isl/vertices.h>
6407 __isl_give isl_vertices *isl_basic_set_compute_vertices(
6408 __isl_keep isl_basic_set *bset);
6410 The function C<isl_basic_set_compute_vertices> performs the
6411 actual computation of the parametric vertices and the chamber
6412 decomposition and store the result in an C<isl_vertices> object.
6413 This information can be queried by either iterating over all
6414 the vertices or iterating over all the chambers or cells
6415 and then iterating over all vertices that are active on the chamber.
6417 int isl_vertices_foreach_vertex(
6418 __isl_keep isl_vertices *vertices,
6419 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6422 int isl_vertices_foreach_cell(
6423 __isl_keep isl_vertices *vertices,
6424 int (*fn)(__isl_take isl_cell *cell, void *user),
6426 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
6427 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6430 Other operations that can be performed on an C<isl_vertices> object are
6433 int isl_vertices_get_n_vertices(
6434 __isl_keep isl_vertices *vertices);
6435 void isl_vertices_free(__isl_take isl_vertices *vertices);
6437 Vertices can be inspected and destroyed using the following functions.
6439 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
6440 __isl_give isl_basic_set *isl_vertex_get_domain(
6441 __isl_keep isl_vertex *vertex);
6442 __isl_give isl_multi_aff *isl_vertex_get_expr(
6443 __isl_keep isl_vertex *vertex);
6444 void isl_vertex_free(__isl_take isl_vertex *vertex);
6446 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
6447 describing the vertex in terms of the parameters,
6448 while C<isl_vertex_get_domain> returns the activity domain
6451 Chambers can be inspected and destroyed using the following functions.
6453 __isl_give isl_basic_set *isl_cell_get_domain(
6454 __isl_keep isl_cell *cell);
6455 void isl_cell_free(__isl_take isl_cell *cell);
6457 =head1 Polyhedral Compilation Library
6459 This section collects functionality in C<isl> that has been specifically
6460 designed for use during polyhedral compilation.
6462 =head2 Dependence Analysis
6464 C<isl> contains specialized functionality for performing
6465 array dataflow analysis. That is, given a I<sink> access relation
6466 and a collection of possible I<source> access relations,
6467 C<isl> can compute relations that describe
6468 for each iteration of the sink access, which iteration
6469 of which of the source access relations was the last
6470 to access the same data element before the given iteration
6472 The resulting dependence relations map source iterations
6473 to the corresponding sink iterations.
6474 To compute standard flow dependences, the sink should be
6475 a read, while the sources should be writes.
6476 If any of the source accesses are marked as being I<may>
6477 accesses, then there will be a dependence from the last
6478 I<must> access B<and> from any I<may> access that follows
6479 this last I<must> access.
6480 In particular, if I<all> sources are I<may> accesses,
6481 then memory based dependence analysis is performed.
6482 If, on the other hand, all sources are I<must> accesses,
6483 then value based dependence analysis is performed.
6485 #include <isl/flow.h>
6487 typedef int (*isl_access_level_before)(void *first, void *second);
6489 __isl_give isl_access_info *isl_access_info_alloc(
6490 __isl_take isl_map *sink,
6491 void *sink_user, isl_access_level_before fn,
6493 __isl_give isl_access_info *isl_access_info_add_source(
6494 __isl_take isl_access_info *acc,
6495 __isl_take isl_map *source, int must,
6497 __isl_null isl_access_info *isl_access_info_free(
6498 __isl_take isl_access_info *acc);
6500 __isl_give isl_flow *isl_access_info_compute_flow(
6501 __isl_take isl_access_info *acc);
6503 int isl_flow_foreach(__isl_keep isl_flow *deps,
6504 int (*fn)(__isl_take isl_map *dep, int must,
6505 void *dep_user, void *user),
6507 __isl_give isl_map *isl_flow_get_no_source(
6508 __isl_keep isl_flow *deps, int must);
6509 void isl_flow_free(__isl_take isl_flow *deps);
6511 The function C<isl_access_info_compute_flow> performs the actual
6512 dependence analysis. The other functions are used to construct
6513 the input for this function or to read off the output.
6515 The input is collected in an C<isl_access_info>, which can
6516 be created through a call to C<isl_access_info_alloc>.
6517 The arguments to this functions are the sink access relation
6518 C<sink>, a token C<sink_user> used to identify the sink
6519 access to the user, a callback function for specifying the
6520 relative order of source and sink accesses, and the number
6521 of source access relations that will be added.
6522 The callback function has type C<int (*)(void *first, void *second)>.
6523 The function is called with two user supplied tokens identifying
6524 either a source or the sink and it should return the shared nesting
6525 level and the relative order of the two accesses.
6526 In particular, let I<n> be the number of loops shared by
6527 the two accesses. If C<first> precedes C<second> textually,
6528 then the function should return I<2 * n + 1>; otherwise,
6529 it should return I<2 * n>.
6530 The sources can be added to the C<isl_access_info> by performing
6531 (at most) C<max_source> calls to C<isl_access_info_add_source>.
6532 C<must> indicates whether the source is a I<must> access
6533 or a I<may> access. Note that a multi-valued access relation
6534 should only be marked I<must> if every iteration in the domain
6535 of the relation accesses I<all> elements in its image.
6536 The C<source_user> token is again used to identify
6537 the source access. The range of the source access relation
6538 C<source> should have the same dimension as the range
6539 of the sink access relation.
6540 The C<isl_access_info_free> function should usually not be
6541 called explicitly, because it is called implicitly by
6542 C<isl_access_info_compute_flow>.
6544 The result of the dependence analysis is collected in an
6545 C<isl_flow>. There may be elements of
6546 the sink access for which no preceding source access could be
6547 found or for which all preceding sources are I<may> accesses.
6548 The relations containing these elements can be obtained through
6549 calls to C<isl_flow_get_no_source>, the first with C<must> set
6550 and the second with C<must> unset.
6551 In the case of standard flow dependence analysis,
6552 with the sink a read and the sources I<must> writes,
6553 the first relation corresponds to the reads from uninitialized
6554 array elements and the second relation is empty.
6555 The actual flow dependences can be extracted using
6556 C<isl_flow_foreach>. This function will call the user-specified
6557 callback function C<fn> for each B<non-empty> dependence between
6558 a source and the sink. The callback function is called
6559 with four arguments, the actual flow dependence relation
6560 mapping source iterations to sink iterations, a boolean that
6561 indicates whether it is a I<must> or I<may> dependence, a token
6562 identifying the source and an additional C<void *> with value
6563 equal to the third argument of the C<isl_flow_foreach> call.
6564 A dependence is marked I<must> if it originates from a I<must>
6565 source and if it is not followed by any I<may> sources.
6567 After finishing with an C<isl_flow>, the user should call
6568 C<isl_flow_free> to free all associated memory.
6570 A higher-level interface to dependence analysis is provided
6571 by the following function.
6573 #include <isl/flow.h>
6575 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
6576 __isl_take isl_union_map *must_source,
6577 __isl_take isl_union_map *may_source,
6578 __isl_take isl_union_map *schedule,
6579 __isl_give isl_union_map **must_dep,
6580 __isl_give isl_union_map **may_dep,
6581 __isl_give isl_union_map **must_no_source,
6582 __isl_give isl_union_map **may_no_source);
6584 The arrays are identified by the tuple names of the ranges
6585 of the accesses. The iteration domains by the tuple names
6586 of the domains of the accesses and of the schedule.
6587 The relative order of the iteration domains is given by the
6588 schedule. The relations returned through C<must_no_source>
6589 and C<may_no_source> are subsets of C<sink>.
6590 Any of C<must_dep>, C<may_dep>, C<must_no_source>
6591 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
6592 any of the other arguments is treated as an error.
6594 =head3 Interaction with Dependence Analysis
6596 During the dependence analysis, we frequently need to perform
6597 the following operation. Given a relation between sink iterations
6598 and potential source iterations from a particular source domain,
6599 what is the last potential source iteration corresponding to each
6600 sink iteration. It can sometimes be convenient to adjust
6601 the set of potential source iterations before or after each such operation.
6602 The prototypical example is fuzzy array dataflow analysis,
6603 where we need to analyze if, based on data-dependent constraints,
6604 the sink iteration can ever be executed without one or more of
6605 the corresponding potential source iterations being executed.
6606 If so, we can introduce extra parameters and select an unknown
6607 but fixed source iteration from the potential source iterations.
6608 To be able to perform such manipulations, C<isl> provides the following
6611 #include <isl/flow.h>
6613 typedef __isl_give isl_restriction *(*isl_access_restrict)(
6614 __isl_keep isl_map *source_map,
6615 __isl_keep isl_set *sink, void *source_user,
6617 __isl_give isl_access_info *isl_access_info_set_restrict(
6618 __isl_take isl_access_info *acc,
6619 isl_access_restrict fn, void *user);
6621 The function C<isl_access_info_set_restrict> should be called
6622 before calling C<isl_access_info_compute_flow> and registers a callback function
6623 that will be called any time C<isl> is about to compute the last
6624 potential source. The first argument is the (reverse) proto-dependence,
6625 mapping sink iterations to potential source iterations.
6626 The second argument represents the sink iterations for which
6627 we want to compute the last source iteration.
6628 The third argument is the token corresponding to the source
6629 and the final argument is the token passed to C<isl_access_info_set_restrict>.
6630 The callback is expected to return a restriction on either the input or
6631 the output of the operation computing the last potential source.
6632 If the input needs to be restricted then restrictions are needed
6633 for both the source and the sink iterations. The sink iterations
6634 and the potential source iterations will be intersected with these sets.
6635 If the output needs to be restricted then only a restriction on the source
6636 iterations is required.
6637 If any error occurs, the callback should return C<NULL>.
6638 An C<isl_restriction> object can be created, freed and inspected
6639 using the following functions.
6641 #include <isl/flow.h>
6643 __isl_give isl_restriction *isl_restriction_input(
6644 __isl_take isl_set *source_restr,
6645 __isl_take isl_set *sink_restr);
6646 __isl_give isl_restriction *isl_restriction_output(
6647 __isl_take isl_set *source_restr);
6648 __isl_give isl_restriction *isl_restriction_none(
6649 __isl_take isl_map *source_map);
6650 __isl_give isl_restriction *isl_restriction_empty(
6651 __isl_take isl_map *source_map);
6652 __isl_null isl_restriction *isl_restriction_free(
6653 __isl_take isl_restriction *restr);
6655 C<isl_restriction_none> and C<isl_restriction_empty> are special
6656 cases of C<isl_restriction_input>. C<isl_restriction_none>
6657 is essentially equivalent to
6659 isl_restriction_input(isl_set_universe(
6660 isl_space_range(isl_map_get_space(source_map))),
6662 isl_space_domain(isl_map_get_space(source_map))));
6664 whereas C<isl_restriction_empty> is essentially equivalent to
6666 isl_restriction_input(isl_set_empty(
6667 isl_space_range(isl_map_get_space(source_map))),
6669 isl_space_domain(isl_map_get_space(source_map))));
6673 B<The functionality described in this section is fairly new
6674 and may be subject to change.>
6676 #include <isl/schedule.h>
6677 __isl_give isl_schedule *
6678 isl_schedule_constraints_compute_schedule(
6679 __isl_take isl_schedule_constraints *sc);
6680 __isl_null isl_schedule *isl_schedule_free(
6681 __isl_take isl_schedule *sched);
6683 The function C<isl_schedule_constraints_compute_schedule> can be
6684 used to compute a schedule that satisfies the given schedule constraints.
6685 These schedule constraints include the iteration domain for which
6686 a schedule should be computed and dependences between pairs of
6687 iterations. In particular, these dependences include
6688 I<validity> dependences and I<proximity> dependences.
6689 By default, the algorithm used to construct the schedule is similar
6690 to that of C<Pluto>.
6691 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6693 The generated schedule respects all validity dependences.
6694 That is, all dependence distances over these dependences in the
6695 scheduled space are lexicographically positive.
6696 The default algorithm tries to ensure that the dependence distances
6697 over coincidence constraints are zero and to minimize the
6698 dependence distances over proximity dependences.
6699 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6700 for groups of domains where the dependence distances over validity
6701 dependences have only non-negative values.
6702 When using Feautrier's algorithm, the coincidence and proximity constraints
6703 are only taken into account during the extension to a
6704 full-dimensional schedule.
6706 An C<isl_schedule_constraints> object can be constructed
6707 and manipulated using the following functions.
6709 #include <isl/schedule.h>
6710 __isl_give isl_schedule_constraints *
6711 isl_schedule_constraints_copy(
6712 __isl_keep isl_schedule_constraints *sc);
6713 __isl_give isl_schedule_constraints *
6714 isl_schedule_constraints_on_domain(
6715 __isl_take isl_union_set *domain);
6716 __isl_give isl_schedule_constraints *
6717 isl_schedule_constraints_set_validity(
6718 __isl_take isl_schedule_constraints *sc,
6719 __isl_take isl_union_map *validity);
6720 __isl_give isl_schedule_constraints *
6721 isl_schedule_constraints_set_coincidence(
6722 __isl_take isl_schedule_constraints *sc,
6723 __isl_take isl_union_map *coincidence);
6724 __isl_give isl_schedule_constraints *
6725 isl_schedule_constraints_set_proximity(
6726 __isl_take isl_schedule_constraints *sc,
6727 __isl_take isl_union_map *proximity);
6728 __isl_give isl_schedule_constraints *
6729 isl_schedule_constraints_set_conditional_validity(
6730 __isl_take isl_schedule_constraints *sc,
6731 __isl_take isl_union_map *condition,
6732 __isl_take isl_union_map *validity);
6733 __isl_null isl_schedule_constraints *
6734 isl_schedule_constraints_free(
6735 __isl_take isl_schedule_constraints *sc);
6737 The initial C<isl_schedule_constraints> object created by
6738 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6739 That is, it has an empty set of dependences.
6740 The function C<isl_schedule_constraints_set_validity> replaces the
6741 validity dependences, mapping domain elements I<i> to domain
6742 elements that should be scheduled after I<i>.
6743 The function C<isl_schedule_constraints_set_coincidence> replaces the
6744 coincidence dependences, mapping domain elements I<i> to domain
6745 elements that should be scheduled together with I<I>, if possible.
6746 The function C<isl_schedule_constraints_set_proximity> replaces the
6747 proximity dependences, mapping domain elements I<i> to domain
6748 elements that should be scheduled either before I<I>
6749 or as early as possible after I<i>.
6751 The function C<isl_schedule_constraints_set_conditional_validity>
6752 replaces the conditional validity constraints.
6753 A conditional validity constraint is only imposed when any of the corresponding
6754 conditions is satisfied, i.e., when any of them is non-zero.
6755 That is, the scheduler ensures that within each band if the dependence
6756 distances over the condition constraints are not all zero
6757 then all corresponding conditional validity constraints are respected.
6758 A conditional validity constraint corresponds to a condition
6759 if the two are adjacent, i.e., if the domain of one relation intersect
6760 the range of the other relation.
6761 The typical use case of conditional validity constraints is
6762 to allow order constraints between live ranges to be violated
6763 as long as the live ranges themselves are local to the band.
6764 To allow more fine-grained control over which conditions correspond
6765 to which conditional validity constraints, the domains and ranges
6766 of these relations may include I<tags>. That is, the domains and
6767 ranges of those relation may themselves be wrapped relations
6768 where the iteration domain appears in the domain of those wrapped relations
6769 and the range of the wrapped relations can be arbitrarily chosen
6770 by the user. Conditions and conditional validity constraints are only
6771 considered adjacent to each other if the entire wrapped relation matches.
6772 In particular, a relation with a tag will never be considered adjacent
6773 to a relation without a tag.
6775 The following function computes a schedule directly from
6776 an iteration domain and validity and proximity dependences
6777 and is implemented in terms of the functions described above.
6778 The use of C<isl_union_set_compute_schedule> is discouraged.
6780 #include <isl/schedule.h>
6781 __isl_give isl_schedule *isl_union_set_compute_schedule(
6782 __isl_take isl_union_set *domain,
6783 __isl_take isl_union_map *validity,
6784 __isl_take isl_union_map *proximity);
6786 A mapping from the domains to the scheduled space can be obtained
6787 from an C<isl_schedule> using the following function.
6789 __isl_give isl_union_map *isl_schedule_get_map(
6790 __isl_keep isl_schedule *sched);
6792 A representation of the schedule can be printed using
6794 __isl_give isl_printer *isl_printer_print_schedule(
6795 __isl_take isl_printer *p,
6796 __isl_keep isl_schedule *schedule);
6798 A representation of the schedule as a forest of bands can be obtained
6799 using the following function.
6801 __isl_give isl_band_list *isl_schedule_get_band_forest(
6802 __isl_keep isl_schedule *schedule);
6804 The individual bands can be visited in depth-first post-order
6805 using the following function.
6807 #include <isl/schedule.h>
6808 int isl_schedule_foreach_band(
6809 __isl_keep isl_schedule *sched,
6810 int (*fn)(__isl_keep isl_band *band, void *user),
6813 The list can be manipulated as explained in L<"Lists">.
6814 The bands inside the list can be copied and freed using the following
6817 #include <isl/band.h>
6818 __isl_give isl_band *isl_band_copy(
6819 __isl_keep isl_band *band);
6820 __isl_null isl_band *isl_band_free(
6821 __isl_take isl_band *band);
6823 Each band contains zero or more scheduling dimensions.
6824 These are referred to as the members of the band.
6825 The section of the schedule that corresponds to the band is
6826 referred to as the partial schedule of the band.
6827 For those nodes that participate in a band, the outer scheduling
6828 dimensions form the prefix schedule, while the inner scheduling
6829 dimensions form the suffix schedule.
6830 That is, if we take a cut of the band forest, then the union of
6831 the concatenations of the prefix, partial and suffix schedules of
6832 each band in the cut is equal to the entire schedule (modulo
6833 some possible padding at the end with zero scheduling dimensions).
6834 The properties of a band can be inspected using the following functions.
6836 #include <isl/band.h>
6837 int isl_band_has_children(__isl_keep isl_band *band);
6838 __isl_give isl_band_list *isl_band_get_children(
6839 __isl_keep isl_band *band);
6841 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6842 __isl_keep isl_band *band);
6843 __isl_give isl_union_map *isl_band_get_partial_schedule(
6844 __isl_keep isl_band *band);
6845 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6846 __isl_keep isl_band *band);
6848 int isl_band_n_member(__isl_keep isl_band *band);
6849 int isl_band_member_is_coincident(
6850 __isl_keep isl_band *band, int pos);
6852 int isl_band_list_foreach_band(
6853 __isl_keep isl_band_list *list,
6854 int (*fn)(__isl_keep isl_band *band, void *user),
6857 Note that a scheduling dimension is considered to be ``coincident''
6858 if it satisfies the coincidence constraints within its band.
6859 That is, if the dependence distances of the coincidence
6860 constraints are all zero in that direction (for fixed
6861 iterations of outer bands).
6862 Like C<isl_schedule_foreach_band>,
6863 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6864 in depth-first post-order.
6866 A band can be tiled using the following function.
6868 #include <isl/band.h>
6869 int isl_band_tile(__isl_keep isl_band *band,
6870 __isl_take isl_vec *sizes);
6872 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6874 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6875 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6877 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6879 The C<isl_band_tile> function tiles the band using the given tile sizes
6880 inside its schedule.
6881 A new child band is created to represent the point loops and it is
6882 inserted between the modified band and its children.
6883 The C<tile_scale_tile_loops> option specifies whether the tile
6884 loops iterators should be scaled by the tile sizes.
6885 If the C<tile_shift_point_loops> option is set, then the point loops
6886 are shifted to start at zero.
6888 A band can be split into two nested bands using the following function.
6890 int isl_band_split(__isl_keep isl_band *band, int pos);
6892 The resulting outer band contains the first C<pos> dimensions of C<band>
6893 while the inner band contains the remaining dimensions.
6895 A representation of the band can be printed using
6897 #include <isl/band.h>
6898 __isl_give isl_printer *isl_printer_print_band(
6899 __isl_take isl_printer *p,
6900 __isl_keep isl_band *band);
6904 #include <isl/schedule.h>
6905 int isl_options_set_schedule_max_coefficient(
6906 isl_ctx *ctx, int val);
6907 int isl_options_get_schedule_max_coefficient(
6909 int isl_options_set_schedule_max_constant_term(
6910 isl_ctx *ctx, int val);
6911 int isl_options_get_schedule_max_constant_term(
6913 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6914 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6915 int isl_options_set_schedule_maximize_band_depth(
6916 isl_ctx *ctx, int val);
6917 int isl_options_get_schedule_maximize_band_depth(
6919 int isl_options_set_schedule_outer_coincidence(
6920 isl_ctx *ctx, int val);
6921 int isl_options_get_schedule_outer_coincidence(
6923 int isl_options_set_schedule_split_scaled(
6924 isl_ctx *ctx, int val);
6925 int isl_options_get_schedule_split_scaled(
6927 int isl_options_set_schedule_algorithm(
6928 isl_ctx *ctx, int val);
6929 int isl_options_get_schedule_algorithm(
6931 int isl_options_set_schedule_separate_components(
6932 isl_ctx *ctx, int val);
6933 int isl_options_get_schedule_separate_components(
6938 =item * schedule_max_coefficient
6940 This option enforces that the coefficients for variable and parameter
6941 dimensions in the calculated schedule are not larger than the specified value.
6942 This option can significantly increase the speed of the scheduling calculation
6943 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6944 this option does not introduce bounds on the variable or parameter
6947 =item * schedule_max_constant_term
6949 This option enforces that the constant coefficients in the calculated schedule
6950 are not larger than the maximal constant term. This option can significantly
6951 increase the speed of the scheduling calculation and may also prevent fusing of
6952 unrelated dimensions. A value of -1 means that this option does not introduce
6953 bounds on the constant coefficients.
6955 =item * schedule_fuse
6957 This option controls the level of fusion.
6958 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6959 resulting schedule will be distributed as much as possible.
6960 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6961 try to fuse loops in the resulting schedule.
6963 =item * schedule_maximize_band_depth
6965 If this option is set, we do not split bands at the point
6966 where we detect splitting is necessary. Instead, we
6967 backtrack and split bands as early as possible. This
6968 reduces the number of splits and maximizes the width of
6969 the bands. Wider bands give more possibilities for tiling.
6970 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6971 then bands will be split as early as possible, even if there is no need.
6972 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6974 =item * schedule_outer_coincidence
6976 If this option is set, then we try to construct schedules
6977 where the outermost scheduling dimension in each band
6978 satisfies the coincidence constraints.
6980 =item * schedule_split_scaled
6982 If this option is set, then we try to construct schedules in which the
6983 constant term is split off from the linear part if the linear parts of
6984 the scheduling rows for all nodes in the graphs have a common non-trivial
6986 The constant term is then placed in a separate band and the linear
6989 =item * schedule_algorithm
6991 Selects the scheduling algorithm to be used.
6992 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6993 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6995 =item * schedule_separate_components
6997 If at any point the dependence graph contains any (weakly connected) components,
6998 then these components are scheduled separately.
6999 If this option is not set, then some iterations of the domains
7000 in these components may be scheduled together.
7001 If this option is set, then the components are given consecutive
7006 =head2 AST Generation
7008 This section describes the C<isl> functionality for generating
7009 ASTs that visit all the elements
7010 in a domain in an order specified by a schedule.
7011 In particular, given a C<isl_union_map>, an AST is generated
7012 that visits all the elements in the domain of the C<isl_union_map>
7013 according to the lexicographic order of the corresponding image
7014 element(s). If the range of the C<isl_union_map> consists of
7015 elements in more than one space, then each of these spaces is handled
7016 separately in an arbitrary order.
7017 It should be noted that the image elements only specify the I<order>
7018 in which the corresponding domain elements should be visited.
7019 No direct relation between the image elements and the loop iterators
7020 in the generated AST should be assumed.
7022 Each AST is generated within a build. The initial build
7023 simply specifies the constraints on the parameters (if any)
7024 and can be created, inspected, copied and freed using the following functions.
7026 #include <isl/ast_build.h>
7027 __isl_give isl_ast_build *isl_ast_build_from_context(
7028 __isl_take isl_set *set);
7029 __isl_give isl_ast_build *isl_ast_build_copy(
7030 __isl_keep isl_ast_build *build);
7031 __isl_null isl_ast_build *isl_ast_build_free(
7032 __isl_take isl_ast_build *build);
7034 The C<set> argument is usually a parameter set with zero or more parameters.
7035 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
7036 and L</"Fine-grained Control over AST Generation">.
7037 Finally, the AST itself can be constructed using the following
7040 #include <isl/ast_build.h>
7041 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
7042 __isl_keep isl_ast_build *build,
7043 __isl_take isl_union_map *schedule);
7045 =head3 Inspecting the AST
7047 The basic properties of an AST node can be obtained as follows.
7049 #include <isl/ast.h>
7050 enum isl_ast_node_type isl_ast_node_get_type(
7051 __isl_keep isl_ast_node *node);
7053 The type of an AST node is one of
7054 C<isl_ast_node_for>,
7056 C<isl_ast_node_block> or
7057 C<isl_ast_node_user>.
7058 An C<isl_ast_node_for> represents a for node.
7059 An C<isl_ast_node_if> represents an if node.
7060 An C<isl_ast_node_block> represents a compound node.
7061 An C<isl_ast_node_user> represents an expression statement.
7062 An expression statement typically corresponds to a domain element, i.e.,
7063 one of the elements that is visited by the AST.
7065 Each type of node has its own additional properties.
7067 #include <isl/ast.h>
7068 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
7069 __isl_keep isl_ast_node *node);
7070 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
7071 __isl_keep isl_ast_node *node);
7072 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
7073 __isl_keep isl_ast_node *node);
7074 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
7075 __isl_keep isl_ast_node *node);
7076 __isl_give isl_ast_node *isl_ast_node_for_get_body(
7077 __isl_keep isl_ast_node *node);
7078 int isl_ast_node_for_is_degenerate(
7079 __isl_keep isl_ast_node *node);
7081 An C<isl_ast_for> is considered degenerate if it is known to execute
7084 #include <isl/ast.h>
7085 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
7086 __isl_keep isl_ast_node *node);
7087 __isl_give isl_ast_node *isl_ast_node_if_get_then(
7088 __isl_keep isl_ast_node *node);
7089 int isl_ast_node_if_has_else(
7090 __isl_keep isl_ast_node *node);
7091 __isl_give isl_ast_node *isl_ast_node_if_get_else(
7092 __isl_keep isl_ast_node *node);
7094 __isl_give isl_ast_node_list *
7095 isl_ast_node_block_get_children(
7096 __isl_keep isl_ast_node *node);
7098 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
7099 __isl_keep isl_ast_node *node);
7101 Each of the returned C<isl_ast_expr>s can in turn be inspected using
7102 the following functions.
7104 #include <isl/ast.h>
7105 enum isl_ast_expr_type isl_ast_expr_get_type(
7106 __isl_keep isl_ast_expr *expr);
7108 The type of an AST expression is one of
7110 C<isl_ast_expr_id> or
7111 C<isl_ast_expr_int>.
7112 An C<isl_ast_expr_op> represents the result of an operation.
7113 An C<isl_ast_expr_id> represents an identifier.
7114 An C<isl_ast_expr_int> represents an integer value.
7116 Each type of expression has its own additional properties.
7118 #include <isl/ast.h>
7119 enum isl_ast_op_type isl_ast_expr_get_op_type(
7120 __isl_keep isl_ast_expr *expr);
7121 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
7122 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
7123 __isl_keep isl_ast_expr *expr, int pos);
7124 int isl_ast_node_foreach_ast_op_type(
7125 __isl_keep isl_ast_node *node,
7126 int (*fn)(enum isl_ast_op_type type, void *user),
7129 C<isl_ast_expr_get_op_type> returns the type of the operation
7130 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
7131 arguments. C<isl_ast_expr_get_op_arg> returns the specified
7133 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
7134 C<isl_ast_op_type> that appears in C<node>.
7135 The operation type is one of the following.
7139 =item C<isl_ast_op_and>
7141 Logical I<and> of two arguments.
7142 Both arguments can be evaluated.
7144 =item C<isl_ast_op_and_then>
7146 Logical I<and> of two arguments.
7147 The second argument can only be evaluated if the first evaluates to true.
7149 =item C<isl_ast_op_or>
7151 Logical I<or> of two arguments.
7152 Both arguments can be evaluated.
7154 =item C<isl_ast_op_or_else>
7156 Logical I<or> of two arguments.
7157 The second argument can only be evaluated if the first evaluates to false.
7159 =item C<isl_ast_op_max>
7161 Maximum of two or more arguments.
7163 =item C<isl_ast_op_min>
7165 Minimum of two or more arguments.
7167 =item C<isl_ast_op_minus>
7171 =item C<isl_ast_op_add>
7173 Sum of two arguments.
7175 =item C<isl_ast_op_sub>
7177 Difference of two arguments.
7179 =item C<isl_ast_op_mul>
7181 Product of two arguments.
7183 =item C<isl_ast_op_div>
7185 Exact division. That is, the result is known to be an integer.
7187 =item C<isl_ast_op_fdiv_q>
7189 Result of integer division, rounded towards negative
7192 =item C<isl_ast_op_pdiv_q>
7194 Result of integer division, where dividend is known to be non-negative.
7196 =item C<isl_ast_op_pdiv_r>
7198 Remainder of integer division, where dividend is known to be non-negative.
7200 =item C<isl_ast_op_zdiv_r>
7202 Equal to zero iff the remainder on integer division is zero.
7204 =item C<isl_ast_op_cond>
7206 Conditional operator defined on three arguments.
7207 If the first argument evaluates to true, then the result
7208 is equal to the second argument. Otherwise, the result
7209 is equal to the third argument.
7210 The second and third argument may only be evaluated if
7211 the first argument evaluates to true and false, respectively.
7212 Corresponds to C<a ? b : c> in C.
7214 =item C<isl_ast_op_select>
7216 Conditional operator defined on three arguments.
7217 If the first argument evaluates to true, then the result
7218 is equal to the second argument. Otherwise, the result
7219 is equal to the third argument.
7220 The second and third argument may be evaluated independently
7221 of the value of the first argument.
7222 Corresponds to C<a * b + (1 - a) * c> in C.
7224 =item C<isl_ast_op_eq>
7228 =item C<isl_ast_op_le>
7230 Less than or equal relation.
7232 =item C<isl_ast_op_lt>
7236 =item C<isl_ast_op_ge>
7238 Greater than or equal relation.
7240 =item C<isl_ast_op_gt>
7242 Greater than relation.
7244 =item C<isl_ast_op_call>
7247 The number of arguments of the C<isl_ast_expr> is one more than
7248 the number of arguments in the function call, the first argument
7249 representing the function being called.
7251 =item C<isl_ast_op_access>
7254 The number of arguments of the C<isl_ast_expr> is one more than
7255 the number of index expressions in the array access, the first argument
7256 representing the array being accessed.
7258 =item C<isl_ast_op_member>
7261 This operation has two arguments, a structure and the name of
7262 the member of the structure being accessed.
7266 #include <isl/ast.h>
7267 __isl_give isl_id *isl_ast_expr_get_id(
7268 __isl_keep isl_ast_expr *expr);
7270 Return the identifier represented by the AST expression.
7272 #include <isl/ast.h>
7273 __isl_give isl_val *isl_ast_expr_get_val(
7274 __isl_keep isl_ast_expr *expr);
7276 Return the integer represented by the AST expression.
7278 =head3 Properties of ASTs
7280 #include <isl/ast.h>
7281 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7282 __isl_keep isl_ast_expr *expr2);
7284 Check if two C<isl_ast_expr>s are equal to each other.
7286 =head3 Manipulating and printing the AST
7288 AST nodes can be copied and freed using the following functions.
7290 #include <isl/ast.h>
7291 __isl_give isl_ast_node *isl_ast_node_copy(
7292 __isl_keep isl_ast_node *node);
7293 __isl_null isl_ast_node *isl_ast_node_free(
7294 __isl_take isl_ast_node *node);
7296 AST expressions can be copied and freed using the following functions.
7298 #include <isl/ast.h>
7299 __isl_give isl_ast_expr *isl_ast_expr_copy(
7300 __isl_keep isl_ast_expr *expr);
7301 __isl_null isl_ast_expr *isl_ast_expr_free(
7302 __isl_take isl_ast_expr *expr);
7304 New AST expressions can be created either directly or within
7305 the context of an C<isl_ast_build>.
7307 #include <isl/ast.h>
7308 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7309 __isl_take isl_val *v);
7310 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7311 __isl_take isl_id *id);
7312 __isl_give isl_ast_expr *isl_ast_expr_neg(
7313 __isl_take isl_ast_expr *expr);
7314 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7315 __isl_take isl_ast_expr *expr);
7316 __isl_give isl_ast_expr *isl_ast_expr_add(
7317 __isl_take isl_ast_expr *expr1,
7318 __isl_take isl_ast_expr *expr2);
7319 __isl_give isl_ast_expr *isl_ast_expr_sub(
7320 __isl_take isl_ast_expr *expr1,
7321 __isl_take isl_ast_expr *expr2);
7322 __isl_give isl_ast_expr *isl_ast_expr_mul(
7323 __isl_take isl_ast_expr *expr1,
7324 __isl_take isl_ast_expr *expr2);
7325 __isl_give isl_ast_expr *isl_ast_expr_div(
7326 __isl_take isl_ast_expr *expr1,
7327 __isl_take isl_ast_expr *expr2);
7328 __isl_give isl_ast_expr *isl_ast_expr_and(
7329 __isl_take isl_ast_expr *expr1,
7330 __isl_take isl_ast_expr *expr2)
7331 __isl_give isl_ast_expr *isl_ast_expr_or(
7332 __isl_take isl_ast_expr *expr1,
7333 __isl_take isl_ast_expr *expr2)
7334 __isl_give isl_ast_expr *isl_ast_expr_eq(
7335 __isl_take isl_ast_expr *expr1,
7336 __isl_take isl_ast_expr *expr2);
7337 __isl_give isl_ast_expr *isl_ast_expr_le(
7338 __isl_take isl_ast_expr *expr1,
7339 __isl_take isl_ast_expr *expr2);
7340 __isl_give isl_ast_expr *isl_ast_expr_lt(
7341 __isl_take isl_ast_expr *expr1,
7342 __isl_take isl_ast_expr *expr2);
7343 __isl_give isl_ast_expr *isl_ast_expr_ge(
7344 __isl_take isl_ast_expr *expr1,
7345 __isl_take isl_ast_expr *expr2);
7346 __isl_give isl_ast_expr *isl_ast_expr_gt(
7347 __isl_take isl_ast_expr *expr1,
7348 __isl_take isl_ast_expr *expr2);
7349 __isl_give isl_ast_expr *isl_ast_expr_access(
7350 __isl_take isl_ast_expr *array,
7351 __isl_take isl_ast_expr_list *indices);
7353 The function C<isl_ast_expr_address_of> can be applied to an
7354 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
7355 to represent the address of the C<isl_ast_expr_access>.
7357 #include <isl/ast_build.h>
7358 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
7359 __isl_keep isl_ast_build *build,
7360 __isl_take isl_pw_aff *pa);
7361 __isl_give isl_ast_expr *
7362 isl_ast_build_access_from_pw_multi_aff(
7363 __isl_keep isl_ast_build *build,
7364 __isl_take isl_pw_multi_aff *pma);
7365 __isl_give isl_ast_expr *
7366 isl_ast_build_access_from_multi_pw_aff(
7367 __isl_keep isl_ast_build *build,
7368 __isl_take isl_multi_pw_aff *mpa);
7369 __isl_give isl_ast_expr *
7370 isl_ast_build_call_from_pw_multi_aff(
7371 __isl_keep isl_ast_build *build,
7372 __isl_take isl_pw_multi_aff *pma);
7373 __isl_give isl_ast_expr *
7374 isl_ast_build_call_from_multi_pw_aff(
7375 __isl_keep isl_ast_build *build,
7376 __isl_take isl_multi_pw_aff *mpa);
7378 The domains of C<pa>, C<mpa> and C<pma> should correspond
7379 to the schedule space of C<build>.
7380 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
7381 the function being called.
7382 If the accessed space is a nested relation, then it is taken
7383 to represent an access of the member specified by the range
7384 of this nested relation of the structure specified by the domain
7385 of the nested relation.
7387 The following functions can be used to modify an C<isl_ast_expr>.
7389 #include <isl/ast.h>
7390 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
7391 __isl_take isl_ast_expr *expr, int pos,
7392 __isl_take isl_ast_expr *arg);
7394 Replace the argument of C<expr> at position C<pos> by C<arg>.
7396 #include <isl/ast.h>
7397 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
7398 __isl_take isl_ast_expr *expr,
7399 __isl_take isl_id_to_ast_expr *id2expr);
7401 The function C<isl_ast_expr_substitute_ids> replaces the
7402 subexpressions of C<expr> of type C<isl_ast_expr_id>
7403 by the corresponding expression in C<id2expr>, if there is any.
7406 User specified data can be attached to an C<isl_ast_node> and obtained
7407 from the same C<isl_ast_node> using the following functions.
7409 #include <isl/ast.h>
7410 __isl_give isl_ast_node *isl_ast_node_set_annotation(
7411 __isl_take isl_ast_node *node,
7412 __isl_take isl_id *annotation);
7413 __isl_give isl_id *isl_ast_node_get_annotation(
7414 __isl_keep isl_ast_node *node);
7416 Basic printing can be performed using the following functions.
7418 #include <isl/ast.h>
7419 __isl_give isl_printer *isl_printer_print_ast_expr(
7420 __isl_take isl_printer *p,
7421 __isl_keep isl_ast_expr *expr);
7422 __isl_give isl_printer *isl_printer_print_ast_node(
7423 __isl_take isl_printer *p,
7424 __isl_keep isl_ast_node *node);
7425 __isl_give char *isl_ast_expr_to_str(
7426 __isl_keep isl_ast_expr *expr);
7428 More advanced printing can be performed using the following functions.
7430 #include <isl/ast.h>
7431 __isl_give isl_printer *isl_ast_op_type_print_macro(
7432 enum isl_ast_op_type type,
7433 __isl_take isl_printer *p);
7434 __isl_give isl_printer *isl_ast_node_print_macros(
7435 __isl_keep isl_ast_node *node,
7436 __isl_take isl_printer *p);
7437 __isl_give isl_printer *isl_ast_node_print(
7438 __isl_keep isl_ast_node *node,
7439 __isl_take isl_printer *p,
7440 __isl_take isl_ast_print_options *options);
7441 __isl_give isl_printer *isl_ast_node_for_print(
7442 __isl_keep isl_ast_node *node,
7443 __isl_take isl_printer *p,
7444 __isl_take isl_ast_print_options *options);
7445 __isl_give isl_printer *isl_ast_node_if_print(
7446 __isl_keep isl_ast_node *node,
7447 __isl_take isl_printer *p,
7448 __isl_take isl_ast_print_options *options);
7450 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
7451 C<isl> may print out an AST that makes use of macros such
7452 as C<floord>, C<min> and C<max>.
7453 C<isl_ast_op_type_print_macro> prints out the macro
7454 corresponding to a specific C<isl_ast_op_type>.
7455 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
7456 for expressions where these macros would be used and prints
7457 out the required macro definitions.
7458 Essentially, C<isl_ast_node_print_macros> calls
7459 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
7460 as function argument.
7461 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
7462 C<isl_ast_node_if_print> print an C<isl_ast_node>
7463 in C<ISL_FORMAT_C>, but allow for some extra control
7464 through an C<isl_ast_print_options> object.
7465 This object can be created using the following functions.
7467 #include <isl/ast.h>
7468 __isl_give isl_ast_print_options *
7469 isl_ast_print_options_alloc(isl_ctx *ctx);
7470 __isl_give isl_ast_print_options *
7471 isl_ast_print_options_copy(
7472 __isl_keep isl_ast_print_options *options);
7473 __isl_null isl_ast_print_options *
7474 isl_ast_print_options_free(
7475 __isl_take isl_ast_print_options *options);
7477 __isl_give isl_ast_print_options *
7478 isl_ast_print_options_set_print_user(
7479 __isl_take isl_ast_print_options *options,
7480 __isl_give isl_printer *(*print_user)(
7481 __isl_take isl_printer *p,
7482 __isl_take isl_ast_print_options *options,
7483 __isl_keep isl_ast_node *node, void *user),
7485 __isl_give isl_ast_print_options *
7486 isl_ast_print_options_set_print_for(
7487 __isl_take isl_ast_print_options *options,
7488 __isl_give isl_printer *(*print_for)(
7489 __isl_take isl_printer *p,
7490 __isl_take isl_ast_print_options *options,
7491 __isl_keep isl_ast_node *node, void *user),
7494 The callback set by C<isl_ast_print_options_set_print_user>
7495 is called whenever a node of type C<isl_ast_node_user> needs to
7497 The callback set by C<isl_ast_print_options_set_print_for>
7498 is called whenever a node of type C<isl_ast_node_for> needs to
7500 Note that C<isl_ast_node_for_print> will I<not> call the
7501 callback set by C<isl_ast_print_options_set_print_for> on the node
7502 on which C<isl_ast_node_for_print> is called, but only on nested
7503 nodes of type C<isl_ast_node_for>. It is therefore safe to
7504 call C<isl_ast_node_for_print> from within the callback set by
7505 C<isl_ast_print_options_set_print_for>.
7507 The following option determines the type to be used for iterators
7508 while printing the AST.
7510 int isl_options_set_ast_iterator_type(
7511 isl_ctx *ctx, const char *val);
7512 const char *isl_options_get_ast_iterator_type(
7515 The AST printer only prints body nodes as blocks if these
7516 blocks cannot be safely omitted.
7517 For example, a C<for> node with one body node will not be
7518 surrounded with braces in C<ISL_FORMAT_C>.
7519 A block will always be printed by setting the following option.
7521 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
7523 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
7527 #include <isl/ast_build.h>
7528 int isl_options_set_ast_build_atomic_upper_bound(
7529 isl_ctx *ctx, int val);
7530 int isl_options_get_ast_build_atomic_upper_bound(
7532 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
7534 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
7535 int isl_options_set_ast_build_exploit_nested_bounds(
7536 isl_ctx *ctx, int val);
7537 int isl_options_get_ast_build_exploit_nested_bounds(
7539 int isl_options_set_ast_build_group_coscheduled(
7540 isl_ctx *ctx, int val);
7541 int isl_options_get_ast_build_group_coscheduled(
7543 int isl_options_set_ast_build_scale_strides(
7544 isl_ctx *ctx, int val);
7545 int isl_options_get_ast_build_scale_strides(
7547 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
7549 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
7550 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
7552 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
7556 =item * ast_build_atomic_upper_bound
7558 Generate loop upper bounds that consist of the current loop iterator,
7559 an operator and an expression not involving the iterator.
7560 If this option is not set, then the current loop iterator may appear
7561 several times in the upper bound.
7562 For example, when this option is turned off, AST generation
7565 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
7569 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
7572 When the option is turned on, the following AST is generated
7574 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
7577 =item * ast_build_prefer_pdiv
7579 If this option is turned off, then the AST generation will
7580 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
7581 operators, but no C<isl_ast_op_pdiv_q> or
7582 C<isl_ast_op_pdiv_r> operators.
7583 If this options is turned on, then C<isl> will try to convert
7584 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
7585 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
7587 =item * ast_build_exploit_nested_bounds
7589 Simplify conditions based on bounds of nested for loops.
7590 In particular, remove conditions that are implied by the fact
7591 that one or more nested loops have at least one iteration,
7592 meaning that the upper bound is at least as large as the lower bound.
7593 For example, when this option is turned off, AST generation
7596 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
7602 for (int c0 = 0; c0 <= N; c0 += 1)
7603 for (int c1 = 0; c1 <= M; c1 += 1)
7606 When the option is turned on, the following AST is generated
7608 for (int c0 = 0; c0 <= N; c0 += 1)
7609 for (int c1 = 0; c1 <= M; c1 += 1)
7612 =item * ast_build_group_coscheduled
7614 If two domain elements are assigned the same schedule point, then
7615 they may be executed in any order and they may even appear in different
7616 loops. If this options is set, then the AST generator will make
7617 sure that coscheduled domain elements do not appear in separate parts
7618 of the AST. This is useful in case of nested AST generation
7619 if the outer AST generation is given only part of a schedule
7620 and the inner AST generation should handle the domains that are
7621 coscheduled by this initial part of the schedule together.
7622 For example if an AST is generated for a schedule
7624 { A[i] -> [0]; B[i] -> [0] }
7626 then the C<isl_ast_build_set_create_leaf> callback described
7627 below may get called twice, once for each domain.
7628 Setting this option ensures that the callback is only called once
7629 on both domains together.
7631 =item * ast_build_separation_bounds
7633 This option specifies which bounds to use during separation.
7634 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
7635 then all (possibly implicit) bounds on the current dimension will
7636 be used during separation.
7637 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
7638 then only those bounds that are explicitly available will
7639 be used during separation.
7641 =item * ast_build_scale_strides
7643 This option specifies whether the AST generator is allowed
7644 to scale down iterators of strided loops.
7646 =item * ast_build_allow_else
7648 This option specifies whether the AST generator is allowed
7649 to construct if statements with else branches.
7651 =item * ast_build_allow_or
7653 This option specifies whether the AST generator is allowed
7654 to construct if conditions with disjunctions.
7658 =head3 Fine-grained Control over AST Generation
7660 Besides specifying the constraints on the parameters,
7661 an C<isl_ast_build> object can be used to control
7662 various aspects of the AST generation process.
7663 The most prominent way of control is through ``options'',
7664 which can be set using the following function.
7666 #include <isl/ast_build.h>
7667 __isl_give isl_ast_build *
7668 isl_ast_build_set_options(
7669 __isl_take isl_ast_build *control,
7670 __isl_take isl_union_map *options);
7672 The options are encoded in an C<isl_union_map>.
7673 The domain of this union relation refers to the schedule domain,
7674 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
7675 In the case of nested AST generation (see L</"Nested AST Generation">),
7676 the domain of C<options> should refer to the extra piece of the schedule.
7677 That is, it should be equal to the range of the wrapped relation in the
7678 range of the schedule.
7679 The range of the options can consist of elements in one or more spaces,
7680 the names of which determine the effect of the option.
7681 The values of the range typically also refer to the schedule dimension
7682 to which the option applies. In case of nested AST generation
7683 (see L</"Nested AST Generation">), these values refer to the position
7684 of the schedule dimension within the innermost AST generation.
7685 The constraints on the domain elements of
7686 the option should only refer to this dimension and earlier dimensions.
7687 We consider the following spaces.
7691 =item C<separation_class>
7693 This space is a wrapped relation between two one dimensional spaces.
7694 The input space represents the schedule dimension to which the option
7695 applies and the output space represents the separation class.
7696 While constructing a loop corresponding to the specified schedule
7697 dimension(s), the AST generator will try to generate separate loops
7698 for domain elements that are assigned different classes.
7699 If only some of the elements are assigned a class, then those elements
7700 that are not assigned any class will be treated as belonging to a class
7701 that is separate from the explicitly assigned classes.
7702 The typical use case for this option is to separate full tiles from
7704 The other options, described below, are applied after the separation
7707 As an example, consider the separation into full and partial tiles
7708 of a tiling of a triangular domain.
7709 Take, for example, the domain
7711 { A[i,j] : 0 <= i,j and i + j <= 100 }
7713 and a tiling into tiles of 10 by 10. The input to the AST generator
7714 is then the schedule
7716 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7719 Without any options, the following AST is generated
7721 for (int c0 = 0; c0 <= 10; c0 += 1)
7722 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7723 for (int c2 = 10 * c0;
7724 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7726 for (int c3 = 10 * c1;
7727 c3 <= min(10 * c1 + 9, -c2 + 100);
7731 Separation into full and partial tiles can be obtained by assigning
7732 a class, say C<0>, to the full tiles. The full tiles are represented by those
7733 values of the first and second schedule dimensions for which there are
7734 values of the third and fourth dimensions to cover an entire tile.
7735 That is, we need to specify the following option
7737 { [a,b,c,d] -> separation_class[[0]->[0]] :
7738 exists b': 0 <= 10a,10b' and
7739 10a+9+10b'+9 <= 100;
7740 [a,b,c,d] -> separation_class[[1]->[0]] :
7741 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7745 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7746 a >= 0 and b >= 0 and b <= 8 - a;
7747 [a, b, c, d] -> separation_class[[0] -> [0]] :
7750 With this option, the generated AST is as follows
7753 for (int c0 = 0; c0 <= 8; c0 += 1) {
7754 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7755 for (int c2 = 10 * c0;
7756 c2 <= 10 * c0 + 9; c2 += 1)
7757 for (int c3 = 10 * c1;
7758 c3 <= 10 * c1 + 9; c3 += 1)
7760 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7761 for (int c2 = 10 * c0;
7762 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7764 for (int c3 = 10 * c1;
7765 c3 <= min(-c2 + 100, 10 * c1 + 9);
7769 for (int c0 = 9; c0 <= 10; c0 += 1)
7770 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7771 for (int c2 = 10 * c0;
7772 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7774 for (int c3 = 10 * c1;
7775 c3 <= min(10 * c1 + 9, -c2 + 100);
7782 This is a single-dimensional space representing the schedule dimension(s)
7783 to which ``separation'' should be applied. Separation tries to split
7784 a loop into several pieces if this can avoid the generation of guards
7786 See also the C<atomic> option.
7790 This is a single-dimensional space representing the schedule dimension(s)
7791 for which the domains should be considered ``atomic''. That is, the
7792 AST generator will make sure that any given domain space will only appear
7793 in a single loop at the specified level.
7795 Consider the following schedule
7797 { a[i] -> [i] : 0 <= i < 10;
7798 b[i] -> [i+1] : 0 <= i < 10 }
7800 If the following option is specified
7802 { [i] -> separate[x] }
7804 then the following AST will be generated
7808 for (int c0 = 1; c0 <= 9; c0 += 1) {
7815 If, on the other hand, the following option is specified
7817 { [i] -> atomic[x] }
7819 then the following AST will be generated
7821 for (int c0 = 0; c0 <= 10; c0 += 1) {
7828 If neither C<atomic> nor C<separate> is specified, then the AST generator
7829 may produce either of these two results or some intermediate form.
7833 This is a single-dimensional space representing the schedule dimension(s)
7834 that should be I<completely> unrolled.
7835 To obtain a partial unrolling, the user should apply an additional
7836 strip-mining to the schedule and fully unroll the inner loop.
7840 Additional control is available through the following functions.
7842 #include <isl/ast_build.h>
7843 __isl_give isl_ast_build *
7844 isl_ast_build_set_iterators(
7845 __isl_take isl_ast_build *control,
7846 __isl_take isl_id_list *iterators);
7848 The function C<isl_ast_build_set_iterators> allows the user to
7849 specify a list of iterator C<isl_id>s to be used as iterators.
7850 If the input schedule is injective, then
7851 the number of elements in this list should be as large as the dimension
7852 of the schedule space, but no direct correspondence should be assumed
7853 between dimensions and elements.
7854 If the input schedule is not injective, then an additional number
7855 of C<isl_id>s equal to the largest dimension of the input domains
7857 If the number of provided C<isl_id>s is insufficient, then additional
7858 names are automatically generated.
7860 #include <isl/ast_build.h>
7861 __isl_give isl_ast_build *
7862 isl_ast_build_set_create_leaf(
7863 __isl_take isl_ast_build *control,
7864 __isl_give isl_ast_node *(*fn)(
7865 __isl_take isl_ast_build *build,
7866 void *user), void *user);
7869 C<isl_ast_build_set_create_leaf> function allows for the
7870 specification of a callback that should be called whenever the AST
7871 generator arrives at an element of the schedule domain.
7872 The callback should return an AST node that should be inserted
7873 at the corresponding position of the AST. The default action (when
7874 the callback is not set) is to continue generating parts of the AST to scan
7875 all the domain elements associated to the schedule domain element
7876 and to insert user nodes, ``calling'' the domain element, for each of them.
7877 The C<build> argument contains the current state of the C<isl_ast_build>.
7878 To ease nested AST generation (see L</"Nested AST Generation">),
7879 all control information that is
7880 specific to the current AST generation such as the options and
7881 the callbacks has been removed from this C<isl_ast_build>.
7882 The callback would typically return the result of a nested
7884 user defined node created using the following function.
7886 #include <isl/ast.h>
7887 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7888 __isl_take isl_ast_expr *expr);
7890 #include <isl/ast_build.h>
7891 __isl_give isl_ast_build *
7892 isl_ast_build_set_at_each_domain(
7893 __isl_take isl_ast_build *build,
7894 __isl_give isl_ast_node *(*fn)(
7895 __isl_take isl_ast_node *node,
7896 __isl_keep isl_ast_build *build,
7897 void *user), void *user);
7898 __isl_give isl_ast_build *
7899 isl_ast_build_set_before_each_for(
7900 __isl_take isl_ast_build *build,
7901 __isl_give isl_id *(*fn)(
7902 __isl_keep isl_ast_build *build,
7903 void *user), void *user);
7904 __isl_give isl_ast_build *
7905 isl_ast_build_set_after_each_for(
7906 __isl_take isl_ast_build *build,
7907 __isl_give isl_ast_node *(*fn)(
7908 __isl_take isl_ast_node *node,
7909 __isl_keep isl_ast_build *build,
7910 void *user), void *user);
7912 The callback set by C<isl_ast_build_set_at_each_domain> will
7913 be called for each domain AST node.
7914 The callbacks set by C<isl_ast_build_set_before_each_for>
7915 and C<isl_ast_build_set_after_each_for> will be called
7916 for each for AST node. The first will be called in depth-first
7917 pre-order, while the second will be called in depth-first post-order.
7918 Since C<isl_ast_build_set_before_each_for> is called before the for
7919 node is actually constructed, it is only passed an C<isl_ast_build>.
7920 The returned C<isl_id> will be added as an annotation (using
7921 C<isl_ast_node_set_annotation>) to the constructed for node.
7922 In particular, if the user has also specified an C<after_each_for>
7923 callback, then the annotation can be retrieved from the node passed to
7924 that callback using C<isl_ast_node_get_annotation>.
7925 All callbacks should C<NULL> on failure.
7926 The given C<isl_ast_build> can be used to create new
7927 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7928 or C<isl_ast_build_call_from_pw_multi_aff>.
7930 =head3 Nested AST Generation
7932 C<isl> allows the user to create an AST within the context
7933 of another AST. These nested ASTs are created using the
7934 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7935 outer AST. The C<build> argument should be an C<isl_ast_build>
7936 passed to a callback set by
7937 C<isl_ast_build_set_create_leaf>.
7938 The space of the range of the C<schedule> argument should refer
7939 to this build. In particular, the space should be a wrapped
7940 relation and the domain of this wrapped relation should be the
7941 same as that of the range of the schedule returned by
7942 C<isl_ast_build_get_schedule> below.
7943 In practice, the new schedule is typically
7944 created by calling C<isl_union_map_range_product> on the old schedule
7945 and some extra piece of the schedule.
7946 The space of the schedule domain is also available from
7947 the C<isl_ast_build>.
7949 #include <isl/ast_build.h>
7950 __isl_give isl_union_map *isl_ast_build_get_schedule(
7951 __isl_keep isl_ast_build *build);
7952 __isl_give isl_space *isl_ast_build_get_schedule_space(
7953 __isl_keep isl_ast_build *build);
7954 __isl_give isl_ast_build *isl_ast_build_restrict(
7955 __isl_take isl_ast_build *build,
7956 __isl_take isl_set *set);
7958 The C<isl_ast_build_get_schedule> function returns a (partial)
7959 schedule for the domains elements for which part of the AST still needs to
7960 be generated in the current build.
7961 In particular, the domain elements are mapped to those iterations of the loops
7962 enclosing the current point of the AST generation inside which
7963 the domain elements are executed.
7964 No direct correspondence between
7965 the input schedule and this schedule should be assumed.
7966 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7967 to create a set for C<isl_ast_build_restrict> to intersect
7968 with the current build. In particular, the set passed to
7969 C<isl_ast_build_restrict> can have additional parameters.
7970 The ids of the set dimensions in the space returned by
7971 C<isl_ast_build_get_schedule_space> correspond to the
7972 iterators of the already generated loops.
7973 The user should not rely on the ids of the output dimensions
7974 of the relations in the union relation returned by
7975 C<isl_ast_build_get_schedule> having any particular value.
7979 Although C<isl> is mainly meant to be used as a library,
7980 it also contains some basic applications that use some
7981 of the functionality of C<isl>.
7982 The input may be specified in either the L<isl format>
7983 or the L<PolyLib format>.
7985 =head2 C<isl_polyhedron_sample>
7987 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7988 an integer element of the polyhedron, if there is any.
7989 The first column in the output is the denominator and is always
7990 equal to 1. If the polyhedron contains no integer points,
7991 then a vector of length zero is printed.
7995 C<isl_pip> takes the same input as the C<example> program
7996 from the C<piplib> distribution, i.e., a set of constraints
7997 on the parameters, a line containing only -1 and finally a set
7998 of constraints on a parametric polyhedron.
7999 The coefficients of the parameters appear in the last columns
8000 (but before the final constant column).
8001 The output is the lexicographic minimum of the parametric polyhedron.
8002 As C<isl> currently does not have its own output format, the output
8003 is just a dump of the internal state.
8005 =head2 C<isl_polyhedron_minimize>
8007 C<isl_polyhedron_minimize> computes the minimum of some linear
8008 or affine objective function over the integer points in a polyhedron.
8009 If an affine objective function
8010 is given, then the constant should appear in the last column.
8012 =head2 C<isl_polytope_scan>
8014 Given a polytope, C<isl_polytope_scan> prints
8015 all integer points in the polytope.
8017 =head2 C<isl_codegen>
8019 Given a schedule, a context set and an options relation,
8020 C<isl_codegen> prints out an AST that scans the domain elements
8021 of the schedule in the order of their image(s) taking into account
8022 the constraints in the context set.