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.
222 C<isl> is released under the MIT license.
226 Permission is hereby granted, free of charge, to any person obtaining a copy of
227 this software and associated documentation files (the "Software"), to deal in
228 the Software without restriction, including without limitation the rights to
229 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
230 of the Software, and to permit persons to whom the Software is furnished to do
231 so, subject to the following conditions:
233 The above copyright notice and this permission notice shall be included in all
234 copies or substantial portions of the Software.
236 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
237 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
238 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
239 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
240 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
241 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
246 Note that by default C<isl> requires C<GMP>, which is released
247 under the GNU Lesser General Public License (LGPL). This means
248 that code linked against C<isl> is also linked against LGPL code.
250 When configuring with C<--with-int=imath>, C<isl> will link against C<imath>, a
251 library for exact integer arithmetic released under the MIT license.
255 The source of C<isl> can be obtained either as a tarball
256 or from the git repository. Both are available from
257 L<http://freshmeat.net/projects/isl/>.
258 The installation process depends on how you obtained
261 =head2 Installation from the git repository
265 =item 1 Clone or update the repository
267 The first time the source is obtained, you need to clone
270 git clone git://repo.or.cz/isl.git
272 To obtain updates, you need to pull in the latest changes
276 =item 2 Optionally get C<imath> submodule
278 To build C<isl> with C<imath>, you need to obtain the C<imath>
279 submodule by running in the git source tree of C<isl>
284 This will fetch the required version of C<imath> in a subdirectory of C<isl>.
286 =item 2 Generate C<configure>
292 After performing the above steps, continue
293 with the L<Common installation instructions>.
295 =head2 Common installation instructions
299 =item 1 Obtain C<GMP>
301 By default, building C<isl> requires C<GMP>, including its headers files.
302 Your distribution may not provide these header files by default
303 and you may need to install a package called C<gmp-devel> or something
304 similar. Alternatively, C<GMP> can be built from
305 source, available from L<http://gmplib.org/>.
306 C<GMP> is not needed if you build C<isl> with C<imath>.
310 C<isl> uses the standard C<autoconf> C<configure> script.
315 optionally followed by some configure options.
316 A complete list of options can be obtained by running
320 Below we discuss some of the more common options.
326 Installation prefix for C<isl>
328 =item C<--with-int=[gmp|imath]>
330 Select the integer library to be used by C<isl>, the default is C<gmp>.
331 Note that C<isl> may run significantly slower if you use C<imath>.
333 =item C<--with-gmp-prefix>
335 Installation prefix for C<GMP> (architecture-independent files).
337 =item C<--with-gmp-exec-prefix>
339 Installation prefix for C<GMP> (architecture-dependent files).
347 =item 4 Install (optional)
353 =head1 Integer Set Library
355 =head2 Memory Management
357 Since a high-level operation on isl objects usually involves
358 several substeps and since the user is usually not interested in
359 the intermediate results, most functions that return a new object
360 will also release all the objects passed as arguments.
361 If the user still wants to use one or more of these arguments
362 after the function call, she should pass along a copy of the
363 object rather than the object itself.
364 The user is then responsible for making sure that the original
365 object gets used somewhere else or is explicitly freed.
367 The arguments and return values of all documented functions are
368 annotated to make clear which arguments are released and which
369 arguments are preserved. In particular, the following annotations
376 C<__isl_give> means that a new object is returned.
377 The user should make sure that the returned pointer is
378 used exactly once as a value for an C<__isl_take> argument.
379 In between, it can be used as a value for as many
380 C<__isl_keep> arguments as the user likes.
381 There is one exception, and that is the case where the
382 pointer returned is C<NULL>. Is this case, the user
383 is free to use it as an C<__isl_take> argument or not.
384 When applied to a C<char *>, the returned pointer needs to be
389 C<__isl_null> means that a C<NULL> value is returned.
393 C<__isl_take> means that the object the argument points to
394 is taken over by the function and may no longer be used
395 by the user as an argument to any other function.
396 The pointer value must be one returned by a function
397 returning an C<__isl_give> pointer.
398 If the user passes in a C<NULL> value, then this will
399 be treated as an error in the sense that the function will
400 not perform its usual operation. However, it will still
401 make sure that all the other C<__isl_take> arguments
406 C<__isl_keep> means that the function will only use the object
407 temporarily. After the function has finished, the user
408 can still use it as an argument to other functions.
409 A C<NULL> value will be treated in the same way as
410 a C<NULL> value for an C<__isl_take> argument.
411 This annotation may also be used on return values of
412 type C<const char *>, in which case the returned pointer should
413 not be freed by the user and is only valid until the object
414 from which it was derived is updated or freed.
418 =head2 Initialization
420 All manipulations of integer sets and relations occur within
421 the context of an C<isl_ctx>.
422 A given C<isl_ctx> can only be used within a single thread.
423 All arguments of a function are required to have been allocated
424 within the same context.
425 There are currently no functions available for moving an object
426 from one C<isl_ctx> to another C<isl_ctx>. This means that
427 there is currently no way of safely moving an object from one
428 thread to another, unless the whole C<isl_ctx> is moved.
430 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
431 freed using C<isl_ctx_free>.
432 All objects allocated within an C<isl_ctx> should be freed
433 before the C<isl_ctx> itself is freed.
435 isl_ctx *isl_ctx_alloc();
436 void isl_ctx_free(isl_ctx *ctx);
438 The user can impose a bound on the number of low-level I<operations>
439 that can be performed by an C<isl_ctx>. This bound can be set and
440 retrieved using the following functions. A bound of zero means that
441 no bound is imposed. The number of operations performed can be
442 reset using C<isl_ctx_reset_operations>. Note that the number
443 of low-level operations needed to perform a high-level computation
444 may differ significantly across different versions
445 of C<isl>, but it should be the same across different platforms
446 for the same version of C<isl>.
448 Warning: This feature is experimental. C<isl> has good support to abort and
449 bail out during the computation, but this feature may exercise error code paths
450 that are normally not used that much. Consequently, it is not unlikely that
451 hidden bugs will be exposed.
453 void isl_ctx_set_max_operations(isl_ctx *ctx,
454 unsigned long max_operations);
455 unsigned long isl_ctx_get_max_operations(isl_ctx *ctx);
456 void isl_ctx_reset_operations(isl_ctx *ctx);
458 In order to be able to create an object in the same context
459 as another object, most object types (described later in
460 this document) provide a function to obtain the context
461 in which the object was created.
464 isl_ctx *isl_val_get_ctx(__isl_keep isl_val *val);
465 isl_ctx *isl_multi_val_get_ctx(
466 __isl_keep isl_multi_val *mv);
469 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
471 #include <isl/local_space.h>
472 isl_ctx *isl_local_space_get_ctx(
473 __isl_keep isl_local_space *ls);
476 isl_ctx *isl_set_list_get_ctx(
477 __isl_keep isl_set_list *list);
480 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
481 isl_ctx *isl_multi_aff_get_ctx(
482 __isl_keep isl_multi_aff *maff);
483 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pa);
484 isl_ctx *isl_pw_multi_aff_get_ctx(
485 __isl_keep isl_pw_multi_aff *pma);
486 isl_ctx *isl_multi_pw_aff_get_ctx(
487 __isl_keep isl_multi_pw_aff *mpa);
488 isl_ctx *isl_union_pw_multi_aff_get_ctx(
489 __isl_keep isl_union_pw_multi_aff *upma);
491 #include <isl/id_to_ast_expr.h>
492 isl_ctx *isl_id_to_ast_expr_get_ctx(
493 __isl_keep id_to_ast_expr *id2expr);
495 #include <isl/point.h>
496 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
499 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
502 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
504 #include <isl/vertices.h>
505 isl_ctx *isl_vertices_get_ctx(
506 __isl_keep isl_vertices *vertices);
507 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
508 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
510 #include <isl/flow.h>
511 isl_ctx *isl_restriction_get_ctx(
512 __isl_keep isl_restriction *restr);
514 #include <isl/schedule.h>
515 isl_ctx *isl_schedule_constraints_get_ctx(
516 __isl_keep isl_schedule_constraints *sc);
518 #include <isl/band.h>
519 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
521 #include <isl/ast_build.h>
522 isl_ctx *isl_ast_build_get_ctx(
523 __isl_keep isl_ast_build *build);
526 isl_ctx *isl_ast_expr_get_ctx(
527 __isl_keep isl_ast_expr *expr);
528 isl_ctx *isl_ast_node_get_ctx(
529 __isl_keep isl_ast_node *node);
533 An C<isl_val> represents an integer value, a rational value
534 or one of three special values, infinity, negative infinity and NaN.
535 Some predefined values can be created using the following functions.
538 __isl_give isl_val *isl_val_zero(isl_ctx *ctx);
539 __isl_give isl_val *isl_val_one(isl_ctx *ctx);
540 __isl_give isl_val *isl_val_negone(isl_ctx *ctx);
541 __isl_give isl_val *isl_val_nan(isl_ctx *ctx);
542 __isl_give isl_val *isl_val_infty(isl_ctx *ctx);
543 __isl_give isl_val *isl_val_neginfty(isl_ctx *ctx);
545 Specific integer values can be created using the following functions.
548 __isl_give isl_val *isl_val_int_from_si(isl_ctx *ctx,
550 __isl_give isl_val *isl_val_int_from_ui(isl_ctx *ctx,
552 __isl_give isl_val *isl_val_int_from_chunks(isl_ctx *ctx,
553 size_t n, size_t size, const void *chunks);
555 The function C<isl_val_int_from_chunks> constructs an C<isl_val>
556 from the C<n> I<digits>, each consisting of C<size> bytes, stored at C<chunks>.
557 The least significant digit is assumed to be stored first.
559 Value objects can be copied and freed using the following functions.
562 __isl_give isl_val *isl_val_copy(__isl_keep isl_val *v);
563 __isl_null isl_val *isl_val_free(__isl_take isl_val *v);
565 They can be inspected using the following functions.
568 long isl_val_get_num_si(__isl_keep isl_val *v);
569 long isl_val_get_den_si(__isl_keep isl_val *v);
570 double isl_val_get_d(__isl_keep isl_val *v);
571 size_t isl_val_n_abs_num_chunks(__isl_keep isl_val *v,
573 int isl_val_get_abs_num_chunks(__isl_keep isl_val *v,
574 size_t size, void *chunks);
576 C<isl_val_n_abs_num_chunks> returns the number of I<digits>
577 of C<size> bytes needed to store the absolute value of the
579 C<isl_val_get_abs_num_chunks> stores these digits at C<chunks>,
580 which is assumed to have been preallocated by the caller.
581 The least significant digit is stored first.
582 Note that C<isl_val_get_num_si>, C<isl_val_get_den_si>,
583 C<isl_val_get_d>, C<isl_val_n_abs_num_chunks>
584 and C<isl_val_get_abs_num_chunks> can only be applied to rational values.
586 An C<isl_val> can be modified using the following function.
589 __isl_give isl_val *isl_val_set_si(__isl_take isl_val *v,
592 The following unary properties are defined on C<isl_val>s.
595 int isl_val_sgn(__isl_keep isl_val *v);
596 int isl_val_is_zero(__isl_keep isl_val *v);
597 int isl_val_is_one(__isl_keep isl_val *v);
598 int isl_val_is_negone(__isl_keep isl_val *v);
599 int isl_val_is_nonneg(__isl_keep isl_val *v);
600 int isl_val_is_nonpos(__isl_keep isl_val *v);
601 int isl_val_is_pos(__isl_keep isl_val *v);
602 int isl_val_is_neg(__isl_keep isl_val *v);
603 int isl_val_is_int(__isl_keep isl_val *v);
604 int isl_val_is_rat(__isl_keep isl_val *v);
605 int isl_val_is_nan(__isl_keep isl_val *v);
606 int isl_val_is_infty(__isl_keep isl_val *v);
607 int isl_val_is_neginfty(__isl_keep isl_val *v);
609 Note that the sign of NaN is undefined.
611 The following binary properties are defined on pairs of C<isl_val>s.
614 int isl_val_lt(__isl_keep isl_val *v1,
615 __isl_keep isl_val *v2);
616 int isl_val_le(__isl_keep isl_val *v1,
617 __isl_keep isl_val *v2);
618 int isl_val_gt(__isl_keep isl_val *v1,
619 __isl_keep isl_val *v2);
620 int isl_val_ge(__isl_keep isl_val *v1,
621 __isl_keep isl_val *v2);
622 int isl_val_eq(__isl_keep isl_val *v1,
623 __isl_keep isl_val *v2);
624 int isl_val_ne(__isl_keep isl_val *v1,
625 __isl_keep isl_val *v2);
626 int isl_val_abs_eq(__isl_keep isl_val *v1,
627 __isl_keep isl_val *v2);
629 The function C<isl_val_abs_eq> checks whether its two arguments
630 are equal in absolute value.
632 For integer C<isl_val>s we additionally have the following binary property.
635 int isl_val_is_divisible_by(__isl_keep isl_val *v1,
636 __isl_keep isl_val *v2);
638 An C<isl_val> can also be compared to an integer using the following
639 function. The result is undefined for NaN.
642 int isl_val_cmp_si(__isl_keep isl_val *v, long i);
644 The following unary operations are available on C<isl_val>s.
647 __isl_give isl_val *isl_val_abs(__isl_take isl_val *v);
648 __isl_give isl_val *isl_val_neg(__isl_take isl_val *v);
649 __isl_give isl_val *isl_val_floor(__isl_take isl_val *v);
650 __isl_give isl_val *isl_val_ceil(__isl_take isl_val *v);
651 __isl_give isl_val *isl_val_trunc(__isl_take isl_val *v);
652 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
654 The following binary operations are available on C<isl_val>s.
657 __isl_give isl_val *isl_val_min(__isl_take isl_val *v1,
658 __isl_take isl_val *v2);
659 __isl_give isl_val *isl_val_max(__isl_take isl_val *v1,
660 __isl_take isl_val *v2);
661 __isl_give isl_val *isl_val_add(__isl_take isl_val *v1,
662 __isl_take isl_val *v2);
663 __isl_give isl_val *isl_val_add_ui(__isl_take isl_val *v1,
665 __isl_give isl_val *isl_val_sub(__isl_take isl_val *v1,
666 __isl_take isl_val *v2);
667 __isl_give isl_val *isl_val_sub_ui(__isl_take isl_val *v1,
669 __isl_give isl_val *isl_val_mul(__isl_take isl_val *v1,
670 __isl_take isl_val *v2);
671 __isl_give isl_val *isl_val_mul_ui(__isl_take isl_val *v1,
673 __isl_give isl_val *isl_val_div(__isl_take isl_val *v1,
674 __isl_take isl_val *v2);
676 On integer values, we additionally have the following operations.
679 __isl_give isl_val *isl_val_2exp(__isl_take isl_val *v);
680 __isl_give isl_val *isl_val_mod(__isl_take isl_val *v1,
681 __isl_take isl_val *v2);
682 __isl_give isl_val *isl_val_gcd(__isl_take isl_val *v1,
683 __isl_take isl_val *v2);
684 __isl_give isl_val *isl_val_gcdext(__isl_take isl_val *v1,
685 __isl_take isl_val *v2, __isl_give isl_val **x,
686 __isl_give isl_val **y);
688 The function C<isl_val_gcdext> returns the greatest common divisor g
689 of C<v1> and C<v2> as well as two integers C<*x> and C<*y> such
690 that C<*x> * C<v1> + C<*y> * C<v2> = g.
692 =head3 GMP specific functions
694 These functions are only available if C<isl> has been compiled with C<GMP>
697 Specific integer and rational values can be created from C<GMP> values using
698 the following functions.
700 #include <isl/val_gmp.h>
701 __isl_give isl_val *isl_val_int_from_gmp(isl_ctx *ctx,
703 __isl_give isl_val *isl_val_from_gmp(isl_ctx *ctx,
704 const mpz_t n, const mpz_t d);
706 The numerator and denominator of a rational value can be extracted as
707 C<GMP> values using the following functions.
709 #include <isl/val_gmp.h>
710 int isl_val_get_num_gmp(__isl_keep isl_val *v, mpz_t z);
711 int isl_val_get_den_gmp(__isl_keep isl_val *v, mpz_t z);
713 =head2 Sets and Relations
715 C<isl> uses six types of objects for representing sets and relations,
716 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
717 C<isl_union_set> and C<isl_union_map>.
718 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
719 can be described as a conjunction of affine constraints, while
720 C<isl_set> and C<isl_map> represent unions of
721 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
722 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
723 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
724 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
725 where spaces are considered different if they have a different number
726 of dimensions and/or different names (see L<"Spaces">).
727 The difference between sets and relations (maps) is that sets have
728 one set of variables, while relations have two sets of variables,
729 input variables and output variables.
731 =head2 Error Handling
733 C<isl> supports different ways to react in case a runtime error is triggered.
734 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
735 with two maps that have incompatible spaces. There are three possible ways
736 to react on error: to warn, to continue or to abort.
738 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
739 the last error in the corresponding C<isl_ctx> and the function in which the
740 error was triggered returns C<NULL>. An error does not corrupt internal state,
741 such that isl can continue to be used. C<isl> also provides functions to
742 read the last error and to reset the memory that stores the last error. The
743 last error is only stored for information purposes. Its presence does not
744 change the behavior of C<isl>. Hence, resetting an error is not required to
745 continue to use isl, but only to observe new errors.
748 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
749 void isl_ctx_reset_error(isl_ctx *ctx);
751 Another option is to continue on error. This is similar to warn on error mode,
752 except that C<isl> does not print any warning. This allows a program to
753 implement its own error reporting.
755 The last option is to directly abort the execution of the program from within
756 the isl library. This makes it obviously impossible to recover from an error,
757 but it allows to directly spot the error location. By aborting on error,
758 debuggers break at the location the error occurred and can provide a stack
759 trace. Other tools that automatically provide stack traces on abort or that do
760 not want to continue execution after an error was triggered may also prefer to
763 The on error behavior of isl can be specified by calling
764 C<isl_options_set_on_error> or by setting the command line option
765 C<--isl-on-error>. Valid arguments for the function call are
766 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
767 choices for the command line option are C<warn>, C<continue> and C<abort>.
768 It is also possible to query the current error mode.
770 #include <isl/options.h>
771 int isl_options_set_on_error(isl_ctx *ctx, int val);
772 int isl_options_get_on_error(isl_ctx *ctx);
776 Identifiers are used to identify both individual dimensions
777 and tuples of dimensions. They consist of an optional name and an optional
778 user pointer. The name and the user pointer cannot both be C<NULL>, however.
779 Identifiers with the same name but different pointer values
780 are considered to be distinct.
781 Similarly, identifiers with different names but the same pointer value
782 are also considered to be distinct.
783 Equal identifiers are represented using the same object.
784 Pairs of identifiers can therefore be tested for equality using the
786 Identifiers can be constructed, copied, freed, inspected and printed
787 using the following functions.
790 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
791 __isl_keep const char *name, void *user);
792 __isl_give isl_id *isl_id_set_free_user(
793 __isl_take isl_id *id,
794 __isl_give void (*free_user)(void *user));
795 __isl_give isl_id *isl_id_copy(isl_id *id);
796 __isl_null isl_id *isl_id_free(__isl_take isl_id *id);
798 void *isl_id_get_user(__isl_keep isl_id *id);
799 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
801 __isl_give isl_printer *isl_printer_print_id(
802 __isl_take isl_printer *p, __isl_keep isl_id *id);
804 The callback set by C<isl_id_set_free_user> is called on the user
805 pointer when the last reference to the C<isl_id> is freed.
806 Note that C<isl_id_get_name> returns a pointer to some internal
807 data structure, so the result can only be used while the
808 corresponding C<isl_id> is alive.
812 Whenever a new set, relation or similar object is created from scratch,
813 the space in which it lives needs to be specified using an C<isl_space>.
814 Each space involves zero or more parameters and zero, one or two
815 tuples of set or input/output dimensions. The parameters and dimensions
816 are identified by an C<isl_dim_type> and a position.
817 The type C<isl_dim_param> refers to parameters,
818 the type C<isl_dim_set> refers to set dimensions (for spaces
819 with a single tuple of dimensions) and the types C<isl_dim_in>
820 and C<isl_dim_out> refer to input and output dimensions
821 (for spaces with two tuples of dimensions).
822 Local spaces (see L</"Local Spaces">) also contain dimensions
823 of type C<isl_dim_div>.
824 Note that parameters are only identified by their position within
825 a given object. Across different objects, parameters are (usually)
826 identified by their names or identifiers. Only unnamed parameters
827 are identified by their positions across objects. The use of unnamed
828 parameters is discouraged.
830 #include <isl/space.h>
831 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
832 unsigned nparam, unsigned n_in, unsigned n_out);
833 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
835 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
836 unsigned nparam, unsigned dim);
837 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
838 __isl_null isl_space *isl_space_free(__isl_take isl_space *space);
840 The space used for creating a parameter domain
841 needs to be created using C<isl_space_params_alloc>.
842 For other sets, the space
843 needs to be created using C<isl_space_set_alloc>, while
844 for a relation, the space
845 needs to be created using C<isl_space_alloc>.
847 To check whether a given space is that of a set or a map
848 or whether it is a parameter space, use these functions:
850 #include <isl/space.h>
851 int isl_space_is_params(__isl_keep isl_space *space);
852 int isl_space_is_set(__isl_keep isl_space *space);
853 int isl_space_is_map(__isl_keep isl_space *space);
855 Spaces can be compared using the following functions:
857 #include <isl/space.h>
858 int isl_space_is_equal(__isl_keep isl_space *space1,
859 __isl_keep isl_space *space2);
860 int isl_space_is_domain(__isl_keep isl_space *space1,
861 __isl_keep isl_space *space2);
862 int isl_space_is_range(__isl_keep isl_space *space1,
863 __isl_keep isl_space *space2);
864 int isl_space_tuple_is_equal(
865 __isl_keep isl_space *space1,
866 enum isl_dim_type type1,
867 __isl_keep isl_space *space2,
868 enum isl_dim_type type2);
870 C<isl_space_is_domain> checks whether the first argument is equal
871 to the domain of the second argument. This requires in particular that
872 the first argument is a set space and that the second argument
873 is a map space. C<isl_space_tuple_is_equal> checks whether the given
874 tuples (C<isl_dim_in>, C<isl_dim_out> or C<isl_dim_set>) of the given
875 spaces are the same. That is, it checks if they have the same
876 identifier (if any), the same dimension and the same internal structure
879 It is often useful to create objects that live in the
880 same space as some other object. This can be accomplished
881 by creating the new objects
882 (see L</"Creating New Sets and Relations"> or
883 L</"Functions">) based on the space
884 of the original object.
887 __isl_give isl_space *isl_basic_set_get_space(
888 __isl_keep isl_basic_set *bset);
889 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
891 #include <isl/union_set.h>
892 __isl_give isl_space *isl_union_set_get_space(
893 __isl_keep isl_union_set *uset);
896 __isl_give isl_space *isl_basic_map_get_space(
897 __isl_keep isl_basic_map *bmap);
898 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
900 #include <isl/union_map.h>
901 __isl_give isl_space *isl_union_map_get_space(
902 __isl_keep isl_union_map *umap);
904 #include <isl/constraint.h>
905 __isl_give isl_space *isl_constraint_get_space(
906 __isl_keep isl_constraint *constraint);
908 #include <isl/polynomial.h>
909 __isl_give isl_space *isl_qpolynomial_get_domain_space(
910 __isl_keep isl_qpolynomial *qp);
911 __isl_give isl_space *isl_qpolynomial_get_space(
912 __isl_keep isl_qpolynomial *qp);
913 __isl_give isl_space *isl_qpolynomial_fold_get_space(
914 __isl_keep isl_qpolynomial_fold *fold);
915 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
916 __isl_keep isl_pw_qpolynomial *pwqp);
917 __isl_give isl_space *isl_pw_qpolynomial_get_space(
918 __isl_keep isl_pw_qpolynomial *pwqp);
919 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
920 __isl_keep isl_pw_qpolynomial_fold *pwf);
921 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
922 __isl_keep isl_pw_qpolynomial_fold *pwf);
923 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
924 __isl_keep isl_union_pw_qpolynomial *upwqp);
925 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
926 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
929 __isl_give isl_space *isl_multi_val_get_space(
930 __isl_keep isl_multi_val *mv);
933 __isl_give isl_space *isl_aff_get_domain_space(
934 __isl_keep isl_aff *aff);
935 __isl_give isl_space *isl_aff_get_space(
936 __isl_keep isl_aff *aff);
937 __isl_give isl_space *isl_pw_aff_get_domain_space(
938 __isl_keep isl_pw_aff *pwaff);
939 __isl_give isl_space *isl_pw_aff_get_space(
940 __isl_keep isl_pw_aff *pwaff);
941 __isl_give isl_space *isl_multi_aff_get_domain_space(
942 __isl_keep isl_multi_aff *maff);
943 __isl_give isl_space *isl_multi_aff_get_space(
944 __isl_keep isl_multi_aff *maff);
945 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
946 __isl_keep isl_pw_multi_aff *pma);
947 __isl_give isl_space *isl_pw_multi_aff_get_space(
948 __isl_keep isl_pw_multi_aff *pma);
949 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
950 __isl_keep isl_union_pw_multi_aff *upma);
951 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
952 __isl_keep isl_multi_pw_aff *mpa);
953 __isl_give isl_space *isl_multi_pw_aff_get_space(
954 __isl_keep isl_multi_pw_aff *mpa);
956 #include <isl/point.h>
957 __isl_give isl_space *isl_point_get_space(
958 __isl_keep isl_point *pnt);
960 The number of dimensions of a given type of space
961 may be read off from a space or an object that lives
962 in a space using the following functions.
963 In case of C<isl_space_dim>, type may be
964 C<isl_dim_param>, C<isl_dim_in> (only for relations),
965 C<isl_dim_out> (only for relations), C<isl_dim_set>
966 (only for sets) or C<isl_dim_all>.
968 #include <isl/space.h>
969 unsigned isl_space_dim(__isl_keep isl_space *space,
970 enum isl_dim_type type);
972 #include <isl/local_space.h>
973 int isl_local_space_dim(__isl_keep isl_local_space *ls,
974 enum isl_dim_type type);
977 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
978 enum isl_dim_type type);
979 unsigned isl_set_dim(__isl_keep isl_set *set,
980 enum isl_dim_type type);
983 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
984 enum isl_dim_type type);
985 unsigned isl_map_dim(__isl_keep isl_map *map,
986 enum isl_dim_type type);
988 #include <isl/union_map.h>
989 unsigned isl_union_map_dim(__isl_keep isl_union_map *umap,
990 enum isl_dim_type type);
993 unsigned isl_multi_val_dim(__isl_keep isl_multi_val *mv,
994 enum isl_dim_type type);
997 int isl_aff_dim(__isl_keep isl_aff *aff,
998 enum isl_dim_type type);
999 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
1000 enum isl_dim_type type);
1001 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
1002 enum isl_dim_type type);
1003 unsigned isl_pw_multi_aff_dim(
1004 __isl_keep isl_pw_multi_aff *pma,
1005 enum isl_dim_type type);
1006 unsigned isl_multi_pw_aff_dim(
1007 __isl_keep isl_multi_pw_aff *mpa,
1008 enum isl_dim_type type);
1010 Note that an C<isl_union_map> only has parameters.
1012 The identifiers or names of the individual dimensions of spaces
1013 may be set or read off using the following functions on spaces
1014 or objects that live in spaces.
1015 These functions are mostly useful to obtain the identifiers, positions
1016 or names of the parameters. Identifiers of individual dimensions are
1017 essentially only useful for printing. They are ignored by all other
1018 operations and may not be preserved across those operations.
1020 #include <isl/space.h>
1021 __isl_give isl_space *isl_space_set_dim_id(
1022 __isl_take isl_space *space,
1023 enum isl_dim_type type, unsigned pos,
1024 __isl_take isl_id *id);
1025 int isl_space_has_dim_id(__isl_keep isl_space *space,
1026 enum isl_dim_type type, unsigned pos);
1027 __isl_give isl_id *isl_space_get_dim_id(
1028 __isl_keep isl_space *space,
1029 enum isl_dim_type type, unsigned pos);
1030 __isl_give isl_space *isl_space_set_dim_name(
1031 __isl_take isl_space *space,
1032 enum isl_dim_type type, unsigned pos,
1033 __isl_keep const char *name);
1034 int isl_space_has_dim_name(__isl_keep isl_space *space,
1035 enum isl_dim_type type, unsigned pos);
1036 __isl_keep const char *isl_space_get_dim_name(
1037 __isl_keep isl_space *space,
1038 enum isl_dim_type type, unsigned pos);
1040 #include <isl/local_space.h>
1041 __isl_give isl_local_space *isl_local_space_set_dim_id(
1042 __isl_take isl_local_space *ls,
1043 enum isl_dim_type type, unsigned pos,
1044 __isl_take isl_id *id);
1045 int isl_local_space_has_dim_id(
1046 __isl_keep isl_local_space *ls,
1047 enum isl_dim_type type, unsigned pos);
1048 __isl_give isl_id *isl_local_space_get_dim_id(
1049 __isl_keep isl_local_space *ls,
1050 enum isl_dim_type type, unsigned pos);
1051 __isl_give isl_local_space *isl_local_space_set_dim_name(
1052 __isl_take isl_local_space *ls,
1053 enum isl_dim_type type, unsigned pos, const char *s);
1054 int isl_local_space_has_dim_name(
1055 __isl_keep isl_local_space *ls,
1056 enum isl_dim_type type, unsigned pos)
1057 const char *isl_local_space_get_dim_name(
1058 __isl_keep isl_local_space *ls,
1059 enum isl_dim_type type, unsigned pos);
1061 #include <isl/constraint.h>
1062 const char *isl_constraint_get_dim_name(
1063 __isl_keep isl_constraint *constraint,
1064 enum isl_dim_type type, unsigned pos);
1066 #include <isl/set.h>
1067 __isl_give isl_id *isl_basic_set_get_dim_id(
1068 __isl_keep isl_basic_set *bset,
1069 enum isl_dim_type type, unsigned pos);
1070 __isl_give isl_set *isl_set_set_dim_id(
1071 __isl_take isl_set *set, enum isl_dim_type type,
1072 unsigned pos, __isl_take isl_id *id);
1073 int isl_set_has_dim_id(__isl_keep isl_set *set,
1074 enum isl_dim_type type, unsigned pos);
1075 __isl_give isl_id *isl_set_get_dim_id(
1076 __isl_keep isl_set *set, enum isl_dim_type type,
1078 const char *isl_basic_set_get_dim_name(
1079 __isl_keep isl_basic_set *bset,
1080 enum isl_dim_type type, unsigned pos);
1081 int isl_set_has_dim_name(__isl_keep isl_set *set,
1082 enum isl_dim_type type, unsigned pos);
1083 const char *isl_set_get_dim_name(
1084 __isl_keep isl_set *set,
1085 enum isl_dim_type type, unsigned pos);
1087 #include <isl/map.h>
1088 __isl_give isl_map *isl_map_set_dim_id(
1089 __isl_take isl_map *map, enum isl_dim_type type,
1090 unsigned pos, __isl_take isl_id *id);
1091 int isl_basic_map_has_dim_id(
1092 __isl_keep isl_basic_map *bmap,
1093 enum isl_dim_type type, unsigned pos);
1094 int isl_map_has_dim_id(__isl_keep isl_map *map,
1095 enum isl_dim_type type, unsigned pos);
1096 __isl_give isl_id *isl_map_get_dim_id(
1097 __isl_keep isl_map *map, enum isl_dim_type type,
1099 __isl_give isl_id *isl_union_map_get_dim_id(
1100 __isl_keep isl_union_map *umap,
1101 enum isl_dim_type type, unsigned pos);
1102 const char *isl_basic_map_get_dim_name(
1103 __isl_keep isl_basic_map *bmap,
1104 enum isl_dim_type type, unsigned pos);
1105 int isl_map_has_dim_name(__isl_keep isl_map *map,
1106 enum isl_dim_type type, unsigned pos);
1107 const char *isl_map_get_dim_name(
1108 __isl_keep isl_map *map,
1109 enum isl_dim_type type, unsigned pos);
1111 #include <isl/val.h>
1112 __isl_give isl_multi_val *isl_multi_val_set_dim_id(
1113 __isl_take isl_multi_val *mv,
1114 enum isl_dim_type type, unsigned pos,
1115 __isl_take isl_id *id);
1116 __isl_give isl_id *isl_multi_val_get_dim_id(
1117 __isl_keep isl_multi_val *mv,
1118 enum isl_dim_type type, unsigned pos);
1119 __isl_give isl_multi_val *isl_multi_val_set_dim_name(
1120 __isl_take isl_multi_val *mv,
1121 enum isl_dim_type type, unsigned pos, const char *s);
1123 #include <isl/aff.h>
1124 __isl_give isl_aff *isl_aff_set_dim_id(
1125 __isl_take isl_aff *aff, enum isl_dim_type type,
1126 unsigned pos, __isl_take isl_id *id);
1127 __isl_give isl_multi_aff *isl_multi_aff_set_dim_id(
1128 __isl_take isl_multi_aff *maff,
1129 enum isl_dim_type type, unsigned pos,
1130 __isl_take isl_id *id);
1131 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
1132 __isl_take isl_pw_aff *pma,
1133 enum isl_dim_type type, unsigned pos,
1134 __isl_take isl_id *id);
1135 __isl_give isl_multi_pw_aff *
1136 isl_multi_pw_aff_set_dim_id(
1137 __isl_take isl_multi_pw_aff *mpa,
1138 enum isl_dim_type type, unsigned pos,
1139 __isl_take isl_id *id);
1140 __isl_give isl_id *isl_multi_aff_get_dim_id(
1141 __isl_keep isl_multi_aff *ma,
1142 enum isl_dim_type type, unsigned pos);
1143 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
1144 enum isl_dim_type type, unsigned pos);
1145 __isl_give isl_id *isl_pw_aff_get_dim_id(
1146 __isl_keep isl_pw_aff *pa,
1147 enum isl_dim_type type, unsigned pos);
1148 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
1149 __isl_keep isl_pw_multi_aff *pma,
1150 enum isl_dim_type type, unsigned pos);
1151 __isl_give isl_id *isl_multi_pw_aff_get_dim_id(
1152 __isl_keep isl_multi_pw_aff *mpa,
1153 enum isl_dim_type type, unsigned pos);
1154 __isl_give isl_aff *isl_aff_set_dim_name(
1155 __isl_take isl_aff *aff, enum isl_dim_type type,
1156 unsigned pos, const char *s);
1157 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
1158 __isl_take isl_multi_aff *maff,
1159 enum isl_dim_type type, unsigned pos, const char *s);
1160 __isl_give isl_multi_pw_aff *
1161 isl_multi_pw_aff_set_dim_name(
1162 __isl_take isl_multi_pw_aff *mpa,
1163 enum isl_dim_type type, unsigned pos, const char *s);
1164 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
1165 enum isl_dim_type type, unsigned pos);
1166 const char *isl_pw_aff_get_dim_name(
1167 __isl_keep isl_pw_aff *pa,
1168 enum isl_dim_type type, unsigned pos);
1169 const char *isl_pw_multi_aff_get_dim_name(
1170 __isl_keep isl_pw_multi_aff *pma,
1171 enum isl_dim_type type, unsigned pos);
1173 #include <isl/polynomial.h>
1174 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1175 __isl_take isl_qpolynomial *qp,
1176 enum isl_dim_type type, unsigned pos,
1178 __isl_give isl_pw_qpolynomial *
1179 isl_pw_qpolynomial_set_dim_name(
1180 __isl_take isl_pw_qpolynomial *pwqp,
1181 enum isl_dim_type type, unsigned pos,
1183 __isl_give isl_pw_qpolynomial_fold *
1184 isl_pw_qpolynomial_fold_set_dim_name(
1185 __isl_take isl_pw_qpolynomial_fold *pwf,
1186 enum isl_dim_type type, unsigned pos,
1189 Note that C<isl_space_get_name> returns a pointer to some internal
1190 data structure, so the result can only be used while the
1191 corresponding C<isl_space> is alive.
1192 Also note that every function that operates on two sets or relations
1193 requires that both arguments have the same parameters. This also
1194 means that if one of the arguments has named parameters, then the
1195 other needs to have named parameters too and the names need to match.
1196 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
1197 arguments may have different parameters (as long as they are named),
1198 in which case the result will have as parameters the union of the parameters of
1201 Given the identifier or name of a dimension (typically a parameter),
1202 its position can be obtained from the following functions.
1204 #include <isl/space.h>
1205 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
1206 enum isl_dim_type type, __isl_keep isl_id *id);
1207 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
1208 enum isl_dim_type type, const char *name);
1210 #include <isl/val.h>
1211 int isl_multi_val_find_dim_by_id(
1212 __isl_keep isl_multi_val *mv,
1213 enum isl_dim_type type, __isl_keep isl_id *id);
1215 #include <isl/set.h>
1216 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1217 enum isl_dim_type type, __isl_keep isl_id *id);
1218 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1219 enum isl_dim_type type, const char *name);
1221 #include <isl/map.h>
1222 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1223 enum isl_dim_type type, __isl_keep isl_id *id);
1224 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1225 enum isl_dim_type type, const char *name);
1227 #include <isl/aff.h>
1228 int isl_multi_aff_find_dim_by_id(
1229 __isl_keep isl_multi_aff *ma,
1230 enum isl_dim_type type, __isl_keep isl_id *id);
1231 int isl_multi_pw_aff_find_dim_by_id(
1232 __isl_keep isl_multi_pw_aff *mpa,
1233 enum isl_dim_type type, __isl_keep isl_id *id);
1235 The identifiers or names of entire spaces may be set or read off
1236 using the following functions.
1238 #include <isl/space.h>
1239 __isl_give isl_space *isl_space_set_tuple_id(
1240 __isl_take isl_space *space,
1241 enum isl_dim_type type, __isl_take isl_id *id);
1242 __isl_give isl_space *isl_space_reset_tuple_id(
1243 __isl_take isl_space *space, enum isl_dim_type type);
1244 int isl_space_has_tuple_id(__isl_keep isl_space *space,
1245 enum isl_dim_type type);
1246 __isl_give isl_id *isl_space_get_tuple_id(
1247 __isl_keep isl_space *space, enum isl_dim_type type);
1248 __isl_give isl_space *isl_space_set_tuple_name(
1249 __isl_take isl_space *space,
1250 enum isl_dim_type type, const char *s);
1251 int isl_space_has_tuple_name(__isl_keep isl_space *space,
1252 enum isl_dim_type type);
1253 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
1254 enum isl_dim_type type);
1256 #include <isl/local_space.h>
1257 __isl_give isl_local_space *isl_local_space_set_tuple_id(
1258 __isl_take isl_local_space *ls,
1259 enum isl_dim_type type, __isl_take isl_id *id);
1261 #include <isl/set.h>
1262 __isl_give isl_basic_set *isl_basic_set_set_tuple_id(
1263 __isl_take isl_basic_set *bset,
1264 __isl_take isl_id *id);
1265 __isl_give isl_set *isl_set_set_tuple_id(
1266 __isl_take isl_set *set, __isl_take isl_id *id);
1267 __isl_give isl_set *isl_set_reset_tuple_id(
1268 __isl_take isl_set *set);
1269 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1270 __isl_give isl_id *isl_set_get_tuple_id(
1271 __isl_keep isl_set *set);
1272 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1273 __isl_take isl_basic_set *set, const char *s);
1274 __isl_give isl_set *isl_set_set_tuple_name(
1275 __isl_take isl_set *set, const char *s);
1276 const char *isl_basic_set_get_tuple_name(
1277 __isl_keep isl_basic_set *bset);
1278 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1279 const char *isl_set_get_tuple_name(
1280 __isl_keep isl_set *set);
1282 #include <isl/map.h>
1283 __isl_give isl_basic_map *isl_basic_map_set_tuple_id(
1284 __isl_take isl_basic_map *bmap,
1285 enum isl_dim_type type, __isl_take isl_id *id);
1286 __isl_give isl_map *isl_map_set_tuple_id(
1287 __isl_take isl_map *map, enum isl_dim_type type,
1288 __isl_take isl_id *id);
1289 __isl_give isl_map *isl_map_reset_tuple_id(
1290 __isl_take isl_map *map, enum isl_dim_type type);
1291 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1292 enum isl_dim_type type);
1293 __isl_give isl_id *isl_map_get_tuple_id(
1294 __isl_keep isl_map *map, enum isl_dim_type type);
1295 __isl_give isl_map *isl_map_set_tuple_name(
1296 __isl_take isl_map *map,
1297 enum isl_dim_type type, const char *s);
1298 const char *isl_basic_map_get_tuple_name(
1299 __isl_keep isl_basic_map *bmap,
1300 enum isl_dim_type type);
1301 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1302 __isl_take isl_basic_map *bmap,
1303 enum isl_dim_type type, const char *s);
1304 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1305 enum isl_dim_type type);
1306 const char *isl_map_get_tuple_name(
1307 __isl_keep isl_map *map,
1308 enum isl_dim_type type);
1310 #include <isl/val.h>
1311 __isl_give isl_multi_val *isl_multi_val_set_tuple_id(
1312 __isl_take isl_multi_val *mv,
1313 enum isl_dim_type type, __isl_take isl_id *id);
1314 __isl_give isl_multi_val *isl_multi_val_reset_tuple_id(
1315 __isl_take isl_multi_val *mv,
1316 enum isl_dim_type type);
1317 int isl_multi_val_has_tuple_id(__isl_keep isl_multi_val *mv,
1318 enum isl_dim_type type);
1319 __isl_give isl_id *isl_multi_val_get_tuple_id(
1320 __isl_keep isl_multi_val *mv,
1321 enum isl_dim_type type);
1322 __isl_give isl_multi_val *isl_multi_val_set_tuple_name(
1323 __isl_take isl_multi_val *mv,
1324 enum isl_dim_type type, const char *s);
1325 const char *isl_multi_val_get_tuple_name(
1326 __isl_keep isl_multi_val *mv,
1327 enum isl_dim_type type);
1329 #include <isl/aff.h>
1330 __isl_give isl_aff *isl_aff_set_tuple_id(
1331 __isl_take isl_aff *aff,
1332 enum isl_dim_type type, __isl_take isl_id *id);
1333 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
1334 __isl_take isl_multi_aff *maff,
1335 enum isl_dim_type type, __isl_take isl_id *id);
1336 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
1337 __isl_take isl_pw_aff *pwaff,
1338 enum isl_dim_type type, __isl_take isl_id *id);
1339 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
1340 __isl_take isl_pw_multi_aff *pma,
1341 enum isl_dim_type type, __isl_take isl_id *id);
1342 __isl_give isl_multi_aff *isl_multi_aff_reset_tuple_id(
1343 __isl_take isl_multi_aff *ma,
1344 enum isl_dim_type type);
1345 __isl_give isl_pw_aff *isl_pw_aff_reset_tuple_id(
1346 __isl_take isl_pw_aff *pa,
1347 enum isl_dim_type type);
1348 __isl_give isl_multi_pw_aff *
1349 isl_multi_pw_aff_reset_tuple_id(
1350 __isl_take isl_multi_pw_aff *mpa,
1351 enum isl_dim_type type);
1352 __isl_give isl_pw_multi_aff *
1353 isl_pw_multi_aff_reset_tuple_id(
1354 __isl_take isl_pw_multi_aff *pma,
1355 enum isl_dim_type type);
1356 int isl_multi_aff_has_tuple_id(__isl_keep isl_multi_aff *ma,
1357 enum isl_dim_type type);
1358 __isl_give isl_id *isl_multi_aff_get_tuple_id(
1359 __isl_keep isl_multi_aff *ma,
1360 enum isl_dim_type type);
1361 int isl_pw_aff_has_tuple_id(__isl_keep isl_pw_aff *pa,
1362 enum isl_dim_type type);
1363 __isl_give isl_id *isl_pw_aff_get_tuple_id(
1364 __isl_keep isl_pw_aff *pa,
1365 enum isl_dim_type type);
1366 int isl_pw_multi_aff_has_tuple_id(
1367 __isl_keep isl_pw_multi_aff *pma,
1368 enum isl_dim_type type);
1369 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
1370 __isl_keep isl_pw_multi_aff *pma,
1371 enum isl_dim_type type);
1372 int isl_multi_pw_aff_has_tuple_id(
1373 __isl_keep isl_multi_pw_aff *mpa,
1374 enum isl_dim_type type);
1375 __isl_give isl_id *isl_multi_pw_aff_get_tuple_id(
1376 __isl_keep isl_multi_pw_aff *mpa,
1377 enum isl_dim_type type);
1378 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
1379 __isl_take isl_multi_aff *maff,
1380 enum isl_dim_type type, const char *s);
1381 __isl_give isl_multi_pw_aff *
1382 isl_multi_pw_aff_set_tuple_name(
1383 __isl_take isl_multi_pw_aff *mpa,
1384 enum isl_dim_type type, const char *s);
1385 const char *isl_multi_aff_get_tuple_name(
1386 __isl_keep isl_multi_aff *multi,
1387 enum isl_dim_type type);
1388 int isl_pw_multi_aff_has_tuple_name(
1389 __isl_keep isl_pw_multi_aff *pma,
1390 enum isl_dim_type type);
1391 const char *isl_pw_multi_aff_get_tuple_name(
1392 __isl_keep isl_pw_multi_aff *pma,
1393 enum isl_dim_type type);
1395 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
1396 or C<isl_dim_set>. As with C<isl_space_get_name>,
1397 the C<isl_space_get_tuple_name> function returns a pointer to some internal
1399 Binary operations require the corresponding spaces of their arguments
1400 to have the same name.
1402 To keep the names of all parameters and tuples, but reset the user pointers
1403 of all the corresponding identifiers, use the following function.
1405 #include <isl/space.h>
1406 __isl_give isl_space *isl_space_reset_user(
1407 __isl_take isl_space *space);
1409 #include <isl/set.h>
1410 __isl_give isl_set *isl_set_reset_user(
1411 __isl_take isl_set *set);
1413 #include <isl/map.h>
1414 __isl_give isl_map *isl_map_reset_user(
1415 __isl_take isl_map *map);
1417 #include <isl/union_set.h>
1418 __isl_give isl_union_set *isl_union_set_reset_user(
1419 __isl_take isl_union_set *uset);
1421 #include <isl/union_map.h>
1422 __isl_give isl_union_map *isl_union_map_reset_user(
1423 __isl_take isl_union_map *umap);
1425 #include <isl/val.h>
1426 __isl_give isl_multi_val *isl_multi_val_reset_user(
1427 __isl_take isl_multi_val *mv);
1429 #include <isl/aff.h>
1430 __isl_give isl_multi_aff *isl_multi_aff_reset_user(
1431 __isl_take isl_multi_aff *ma);
1432 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_reset_user(
1433 __isl_take isl_multi_pw_aff *mpa);
1435 Spaces can be nested. In particular, the domain of a set or
1436 the domain or range of a relation can be a nested relation.
1437 This process is also called I<wrapping>.
1438 The functions for detecting, constructing and deconstructing
1439 such nested spaces can be found in the wrapping properties
1440 of L</"Unary Properties">, the wrapping operations
1441 of L</"Unary Operations"> and the Cartesian product operations
1442 of L</"Basic Operations">.
1444 Spaces can be created from other spaces
1445 using the functions described in L</"Unary Operations">
1446 and L</"Binary Operations">.
1450 A local space is essentially a space with
1451 zero or more existentially quantified variables.
1452 The local space of various objects can be obtained
1453 using the following functions.
1455 #include <isl/constraint.h>
1456 __isl_give isl_local_space *isl_constraint_get_local_space(
1457 __isl_keep isl_constraint *constraint);
1459 #include <isl/set.h>
1460 __isl_give isl_local_space *isl_basic_set_get_local_space(
1461 __isl_keep isl_basic_set *bset);
1463 #include <isl/map.h>
1464 __isl_give isl_local_space *isl_basic_map_get_local_space(
1465 __isl_keep isl_basic_map *bmap);
1467 #include <isl/aff.h>
1468 __isl_give isl_local_space *isl_aff_get_domain_local_space(
1469 __isl_keep isl_aff *aff);
1470 __isl_give isl_local_space *isl_aff_get_local_space(
1471 __isl_keep isl_aff *aff);
1473 A new local space can be created from a space using
1475 #include <isl/local_space.h>
1476 __isl_give isl_local_space *isl_local_space_from_space(
1477 __isl_take isl_space *space);
1479 They can be inspected, modified, copied and freed using the following functions.
1481 #include <isl/local_space.h>
1482 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
1483 __isl_give isl_space *isl_local_space_get_space(
1484 __isl_keep isl_local_space *ls);
1485 __isl_give isl_aff *isl_local_space_get_div(
1486 __isl_keep isl_local_space *ls, int pos);
1487 __isl_give isl_local_space *isl_local_space_copy(
1488 __isl_keep isl_local_space *ls);
1489 __isl_null isl_local_space *isl_local_space_free(
1490 __isl_take isl_local_space *ls);
1492 Note that C<isl_local_space_get_div> can only be used on local spaces
1495 Two local spaces can be compared using
1497 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
1498 __isl_keep isl_local_space *ls2);
1500 Local spaces can be created from other local spaces
1501 using the functions described in L</"Unary Operations">
1502 and L</"Binary Operations">.
1504 =head2 Creating New Sets and Relations
1506 C<isl> has functions for creating some standard sets and relations.
1510 =item * Empty sets and relations
1512 __isl_give isl_basic_set *isl_basic_set_empty(
1513 __isl_take isl_space *space);
1514 __isl_give isl_basic_map *isl_basic_map_empty(
1515 __isl_take isl_space *space);
1516 __isl_give isl_set *isl_set_empty(
1517 __isl_take isl_space *space);
1518 __isl_give isl_map *isl_map_empty(
1519 __isl_take isl_space *space);
1520 __isl_give isl_union_set *isl_union_set_empty(
1521 __isl_take isl_space *space);
1522 __isl_give isl_union_map *isl_union_map_empty(
1523 __isl_take isl_space *space);
1525 For C<isl_union_set>s and C<isl_union_map>s, the space
1526 is only used to specify the parameters.
1528 =item * Universe sets and relations
1530 __isl_give isl_basic_set *isl_basic_set_universe(
1531 __isl_take isl_space *space);
1532 __isl_give isl_basic_map *isl_basic_map_universe(
1533 __isl_take isl_space *space);
1534 __isl_give isl_set *isl_set_universe(
1535 __isl_take isl_space *space);
1536 __isl_give isl_map *isl_map_universe(
1537 __isl_take isl_space *space);
1538 __isl_give isl_union_set *isl_union_set_universe(
1539 __isl_take isl_union_set *uset);
1540 __isl_give isl_union_map *isl_union_map_universe(
1541 __isl_take isl_union_map *umap);
1543 The sets and relations constructed by the functions above
1544 contain all integer values, while those constructed by the
1545 functions below only contain non-negative values.
1547 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1548 __isl_take isl_space *space);
1549 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1550 __isl_take isl_space *space);
1551 __isl_give isl_set *isl_set_nat_universe(
1552 __isl_take isl_space *space);
1553 __isl_give isl_map *isl_map_nat_universe(
1554 __isl_take isl_space *space);
1556 =item * Identity relations
1558 __isl_give isl_basic_map *isl_basic_map_identity(
1559 __isl_take isl_space *space);
1560 __isl_give isl_map *isl_map_identity(
1561 __isl_take isl_space *space);
1563 The number of input and output dimensions in C<space> needs
1566 =item * Lexicographic order
1568 __isl_give isl_map *isl_map_lex_lt(
1569 __isl_take isl_space *set_space);
1570 __isl_give isl_map *isl_map_lex_le(
1571 __isl_take isl_space *set_space);
1572 __isl_give isl_map *isl_map_lex_gt(
1573 __isl_take isl_space *set_space);
1574 __isl_give isl_map *isl_map_lex_ge(
1575 __isl_take isl_space *set_space);
1576 __isl_give isl_map *isl_map_lex_lt_first(
1577 __isl_take isl_space *space, unsigned n);
1578 __isl_give isl_map *isl_map_lex_le_first(
1579 __isl_take isl_space *space, unsigned n);
1580 __isl_give isl_map *isl_map_lex_gt_first(
1581 __isl_take isl_space *space, unsigned n);
1582 __isl_give isl_map *isl_map_lex_ge_first(
1583 __isl_take isl_space *space, unsigned n);
1585 The first four functions take a space for a B<set>
1586 and return relations that express that the elements in the domain
1587 are lexicographically less
1588 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1589 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1590 than the elements in the range.
1591 The last four functions take a space for a map
1592 and return relations that express that the first C<n> dimensions
1593 in the domain are lexicographically less
1594 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1595 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1596 than the first C<n> dimensions in the range.
1600 A basic set or relation can be converted to a set or relation
1601 using the following functions.
1603 __isl_give isl_set *isl_set_from_basic_set(
1604 __isl_take isl_basic_set *bset);
1605 __isl_give isl_map *isl_map_from_basic_map(
1606 __isl_take isl_basic_map *bmap);
1608 Sets and relations can be converted to union sets and relations
1609 using the following functions.
1611 __isl_give isl_union_set *isl_union_set_from_basic_set(
1612 __isl_take isl_basic_set *bset);
1613 __isl_give isl_union_map *isl_union_map_from_basic_map(
1614 __isl_take isl_basic_map *bmap);
1615 __isl_give isl_union_set *isl_union_set_from_set(
1616 __isl_take isl_set *set);
1617 __isl_give isl_union_map *isl_union_map_from_map(
1618 __isl_take isl_map *map);
1620 The inverse conversions below can only be used if the input
1621 union set or relation is known to contain elements in exactly one
1624 __isl_give isl_set *isl_set_from_union_set(
1625 __isl_take isl_union_set *uset);
1626 __isl_give isl_map *isl_map_from_union_map(
1627 __isl_take isl_union_map *umap);
1629 Sets and relations can be copied and freed again using the following
1632 __isl_give isl_basic_set *isl_basic_set_copy(
1633 __isl_keep isl_basic_set *bset);
1634 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1635 __isl_give isl_union_set *isl_union_set_copy(
1636 __isl_keep isl_union_set *uset);
1637 __isl_give isl_basic_map *isl_basic_map_copy(
1638 __isl_keep isl_basic_map *bmap);
1639 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1640 __isl_give isl_union_map *isl_union_map_copy(
1641 __isl_keep isl_union_map *umap);
1642 __isl_null isl_basic_set *isl_basic_set_free(
1643 __isl_take isl_basic_set *bset);
1644 __isl_null isl_set *isl_set_free(__isl_take isl_set *set);
1645 __isl_null isl_union_set *isl_union_set_free(
1646 __isl_take isl_union_set *uset);
1647 __isl_null isl_basic_map *isl_basic_map_free(
1648 __isl_take isl_basic_map *bmap);
1649 __isl_null isl_map *isl_map_free(__isl_take isl_map *map);
1650 __isl_null isl_union_map *isl_union_map_free(
1651 __isl_take isl_union_map *umap);
1653 Other sets and relations can be constructed by starting
1654 from a universe set or relation, adding equality and/or
1655 inequality constraints and then projecting out the
1656 existentially quantified variables, if any.
1657 Constraints can be constructed, manipulated and
1658 added to (or removed from) (basic) sets and relations
1659 using the following functions.
1661 #include <isl/constraint.h>
1662 __isl_give isl_constraint *isl_equality_alloc(
1663 __isl_take isl_local_space *ls);
1664 __isl_give isl_constraint *isl_inequality_alloc(
1665 __isl_take isl_local_space *ls);
1666 __isl_give isl_constraint *isl_constraint_set_constant_si(
1667 __isl_take isl_constraint *constraint, int v);
1668 __isl_give isl_constraint *isl_constraint_set_constant_val(
1669 __isl_take isl_constraint *constraint,
1670 __isl_take isl_val *v);
1671 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1672 __isl_take isl_constraint *constraint,
1673 enum isl_dim_type type, int pos, int v);
1674 __isl_give isl_constraint *
1675 isl_constraint_set_coefficient_val(
1676 __isl_take isl_constraint *constraint,
1677 enum isl_dim_type type, int pos,
1678 __isl_take isl_val *v);
1679 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1680 __isl_take isl_basic_map *bmap,
1681 __isl_take isl_constraint *constraint);
1682 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1683 __isl_take isl_basic_set *bset,
1684 __isl_take isl_constraint *constraint);
1685 __isl_give isl_map *isl_map_add_constraint(
1686 __isl_take isl_map *map,
1687 __isl_take isl_constraint *constraint);
1688 __isl_give isl_set *isl_set_add_constraint(
1689 __isl_take isl_set *set,
1690 __isl_take isl_constraint *constraint);
1691 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1692 __isl_take isl_basic_set *bset,
1693 __isl_take isl_constraint *constraint);
1695 For example, to create a set containing the even integers
1696 between 10 and 42, you would use the following code.
1699 isl_local_space *ls;
1701 isl_basic_set *bset;
1703 space = isl_space_set_alloc(ctx, 0, 2);
1704 bset = isl_basic_set_universe(isl_space_copy(space));
1705 ls = isl_local_space_from_space(space);
1707 c = isl_equality_alloc(isl_local_space_copy(ls));
1708 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1709 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1710 bset = isl_basic_set_add_constraint(bset, c);
1712 c = isl_inequality_alloc(isl_local_space_copy(ls));
1713 c = isl_constraint_set_constant_si(c, -10);
1714 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1715 bset = isl_basic_set_add_constraint(bset, c);
1717 c = isl_inequality_alloc(ls);
1718 c = isl_constraint_set_constant_si(c, 42);
1719 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1720 bset = isl_basic_set_add_constraint(bset, c);
1722 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1726 isl_basic_set *bset;
1727 bset = isl_basic_set_read_from_str(ctx,
1728 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1730 A basic set or relation can also be constructed from two matrices
1731 describing the equalities and the inequalities.
1733 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1734 __isl_take isl_space *space,
1735 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1736 enum isl_dim_type c1,
1737 enum isl_dim_type c2, enum isl_dim_type c3,
1738 enum isl_dim_type c4);
1739 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1740 __isl_take isl_space *space,
1741 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1742 enum isl_dim_type c1,
1743 enum isl_dim_type c2, enum isl_dim_type c3,
1744 enum isl_dim_type c4, enum isl_dim_type c5);
1746 The C<isl_dim_type> arguments indicate the order in which
1747 different kinds of variables appear in the input matrices
1748 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1749 C<isl_dim_set> and C<isl_dim_div> for sets and
1750 of C<isl_dim_cst>, C<isl_dim_param>,
1751 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1753 A (basic or union) set or relation can also be constructed from a
1754 (union) (piecewise) (multiple) affine expression
1755 or a list of affine expressions
1756 (See L</"Functions">).
1758 __isl_give isl_basic_map *isl_basic_map_from_aff(
1759 __isl_take isl_aff *aff);
1760 __isl_give isl_map *isl_map_from_aff(
1761 __isl_take isl_aff *aff);
1762 __isl_give isl_set *isl_set_from_pw_aff(
1763 __isl_take isl_pw_aff *pwaff);
1764 __isl_give isl_map *isl_map_from_pw_aff(
1765 __isl_take isl_pw_aff *pwaff);
1766 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1767 __isl_take isl_space *domain_space,
1768 __isl_take isl_aff_list *list);
1769 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1770 __isl_take isl_multi_aff *maff)
1771 __isl_give isl_map *isl_map_from_multi_aff(
1772 __isl_take isl_multi_aff *maff)
1773 __isl_give isl_set *isl_set_from_pw_multi_aff(
1774 __isl_take isl_pw_multi_aff *pma);
1775 __isl_give isl_map *isl_map_from_pw_multi_aff(
1776 __isl_take isl_pw_multi_aff *pma);
1777 __isl_give isl_set *isl_set_from_multi_pw_aff(
1778 __isl_take isl_multi_pw_aff *mpa);
1779 __isl_give isl_map *isl_map_from_multi_pw_aff(
1780 __isl_take isl_multi_pw_aff *mpa);
1781 __isl_give isl_union_map *
1782 isl_union_map_from_union_pw_multi_aff(
1783 __isl_take isl_union_pw_multi_aff *upma);
1785 The C<domain_space> argument describes the domain of the resulting
1786 basic relation. It is required because the C<list> may consist
1787 of zero affine expressions.
1789 =head2 Inspecting Sets and Relations
1791 Usually, the user should not have to care about the actual constraints
1792 of the sets and maps, but should instead apply the abstract operations
1793 explained in the following sections.
1794 Occasionally, however, it may be required to inspect the individual
1795 coefficients of the constraints. This section explains how to do so.
1796 In these cases, it may also be useful to have C<isl> compute
1797 an explicit representation of the existentially quantified variables.
1799 __isl_give isl_set *isl_set_compute_divs(
1800 __isl_take isl_set *set);
1801 __isl_give isl_map *isl_map_compute_divs(
1802 __isl_take isl_map *map);
1803 __isl_give isl_union_set *isl_union_set_compute_divs(
1804 __isl_take isl_union_set *uset);
1805 __isl_give isl_union_map *isl_union_map_compute_divs(
1806 __isl_take isl_union_map *umap);
1808 This explicit representation defines the existentially quantified
1809 variables as integer divisions of the other variables, possibly
1810 including earlier existentially quantified variables.
1811 An explicitly represented existentially quantified variable therefore
1812 has a unique value when the values of the other variables are known.
1813 If, furthermore, the same existentials, i.e., existentials
1814 with the same explicit representations, should appear in the
1815 same order in each of the disjuncts of a set or map, then the user should call
1816 either of the following functions.
1818 __isl_give isl_set *isl_set_align_divs(
1819 __isl_take isl_set *set);
1820 __isl_give isl_map *isl_map_align_divs(
1821 __isl_take isl_map *map);
1823 Alternatively, the existentially quantified variables can be removed
1824 using the following functions, which compute an overapproximation.
1826 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1827 __isl_take isl_basic_set *bset);
1828 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1829 __isl_take isl_basic_map *bmap);
1830 __isl_give isl_set *isl_set_remove_divs(
1831 __isl_take isl_set *set);
1832 __isl_give isl_map *isl_map_remove_divs(
1833 __isl_take isl_map *map);
1835 It is also possible to only remove those divs that are defined
1836 in terms of a given range of dimensions or only those for which
1837 no explicit representation is known.
1839 __isl_give isl_basic_set *
1840 isl_basic_set_remove_divs_involving_dims(
1841 __isl_take isl_basic_set *bset,
1842 enum isl_dim_type type,
1843 unsigned first, unsigned n);
1844 __isl_give isl_basic_map *
1845 isl_basic_map_remove_divs_involving_dims(
1846 __isl_take isl_basic_map *bmap,
1847 enum isl_dim_type type,
1848 unsigned first, unsigned n);
1849 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1850 __isl_take isl_set *set, enum isl_dim_type type,
1851 unsigned first, unsigned n);
1852 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1853 __isl_take isl_map *map, enum isl_dim_type type,
1854 unsigned first, unsigned n);
1856 __isl_give isl_basic_set *
1857 isl_basic_set_remove_unknown_divs(
1858 __isl_take isl_basic_set *bset);
1859 __isl_give isl_set *isl_set_remove_unknown_divs(
1860 __isl_take isl_set *set);
1861 __isl_give isl_map *isl_map_remove_unknown_divs(
1862 __isl_take isl_map *map);
1864 To iterate over all the sets or maps in a union set or map, use
1866 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1867 int (*fn)(__isl_take isl_set *set, void *user),
1869 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1870 int (*fn)(__isl_take isl_map *map, void *user),
1873 The number of sets or maps in a union set or map can be obtained
1876 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1877 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1879 To extract the set or map in a given space from a union, use
1881 __isl_give isl_set *isl_union_set_extract_set(
1882 __isl_keep isl_union_set *uset,
1883 __isl_take isl_space *space);
1884 __isl_give isl_map *isl_union_map_extract_map(
1885 __isl_keep isl_union_map *umap,
1886 __isl_take isl_space *space);
1888 To iterate over all the basic sets or maps in a set or map, use
1890 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1891 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1893 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1894 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1897 The callback function C<fn> should return 0 if successful and
1898 -1 if an error occurs. In the latter case, or if any other error
1899 occurs, the above functions will return -1.
1901 It should be noted that C<isl> does not guarantee that
1902 the basic sets or maps passed to C<fn> are disjoint.
1903 If this is required, then the user should call one of
1904 the following functions first.
1906 __isl_give isl_set *isl_set_make_disjoint(
1907 __isl_take isl_set *set);
1908 __isl_give isl_map *isl_map_make_disjoint(
1909 __isl_take isl_map *map);
1911 The number of basic sets in a set can be obtained
1912 or the number of basic maps in a map can be obtained
1915 #include <isl/set.h>
1916 int isl_set_n_basic_set(__isl_keep isl_set *set);
1918 #include <isl/map.h>
1919 int isl_map_n_basic_map(__isl_keep isl_map *map);
1921 To iterate over the constraints of a basic set or map, use
1923 #include <isl/constraint.h>
1925 int isl_basic_set_n_constraint(
1926 __isl_keep isl_basic_set *bset);
1927 int isl_basic_set_foreach_constraint(
1928 __isl_keep isl_basic_set *bset,
1929 int (*fn)(__isl_take isl_constraint *c, void *user),
1931 int isl_basic_map_n_constraint(
1932 __isl_keep isl_basic_map *bmap);
1933 int isl_basic_map_foreach_constraint(
1934 __isl_keep isl_basic_map *bmap,
1935 int (*fn)(__isl_take isl_constraint *c, void *user),
1937 __isl_null isl_constraint *isl_constraint_free(
1938 __isl_take isl_constraint *c);
1940 Again, the callback function C<fn> should return 0 if successful and
1941 -1 if an error occurs. In the latter case, or if any other error
1942 occurs, the above functions will return -1.
1943 The constraint C<c> represents either an equality or an inequality.
1944 Use the following function to find out whether a constraint
1945 represents an equality. If not, it represents an inequality.
1947 int isl_constraint_is_equality(
1948 __isl_keep isl_constraint *constraint);
1950 It is also possible to obtain a list of constraints from a basic
1953 #include <isl/constraint.h>
1954 __isl_give isl_constraint_list *
1955 isl_basic_map_get_constraint_list(
1956 __isl_keep isl_basic_map *bmap);
1957 __isl_give isl_constraint_list *
1958 isl_basic_set_get_constraint_list(
1959 __isl_keep isl_basic_set *bset);
1961 These functions require that all existentially quantified variables
1962 have an explicit representation.
1963 The returned list can be manipulated using the functions in L<"Lists">.
1965 The coefficients of the constraints can be inspected using
1966 the following functions.
1968 int isl_constraint_is_lower_bound(
1969 __isl_keep isl_constraint *constraint,
1970 enum isl_dim_type type, unsigned pos);
1971 int isl_constraint_is_upper_bound(
1972 __isl_keep isl_constraint *constraint,
1973 enum isl_dim_type type, unsigned pos);
1974 __isl_give isl_val *isl_constraint_get_constant_val(
1975 __isl_keep isl_constraint *constraint);
1976 __isl_give isl_val *isl_constraint_get_coefficient_val(
1977 __isl_keep isl_constraint *constraint,
1978 enum isl_dim_type type, int pos);
1980 The explicit representations of the existentially quantified
1981 variables can be inspected using the following function.
1982 Note that the user is only allowed to use this function
1983 if the inspected set or map is the result of a call
1984 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1985 The existentially quantified variable is equal to the floor
1986 of the returned affine expression. The affine expression
1987 itself can be inspected using the functions in
1990 __isl_give isl_aff *isl_constraint_get_div(
1991 __isl_keep isl_constraint *constraint, int pos);
1993 To obtain the constraints of a basic set or map in matrix
1994 form, use the following functions.
1996 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1997 __isl_keep isl_basic_set *bset,
1998 enum isl_dim_type c1, enum isl_dim_type c2,
1999 enum isl_dim_type c3, enum isl_dim_type c4);
2000 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
2001 __isl_keep isl_basic_set *bset,
2002 enum isl_dim_type c1, enum isl_dim_type c2,
2003 enum isl_dim_type c3, enum isl_dim_type c4);
2004 __isl_give isl_mat *isl_basic_map_equalities_matrix(
2005 __isl_keep isl_basic_map *bmap,
2006 enum isl_dim_type c1,
2007 enum isl_dim_type c2, enum isl_dim_type c3,
2008 enum isl_dim_type c4, enum isl_dim_type c5);
2009 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
2010 __isl_keep isl_basic_map *bmap,
2011 enum isl_dim_type c1,
2012 enum isl_dim_type c2, enum isl_dim_type c3,
2013 enum isl_dim_type c4, enum isl_dim_type c5);
2015 The C<isl_dim_type> arguments dictate the order in which
2016 different kinds of variables appear in the resulting matrix.
2017 For set inputs, they should be a permutation of
2018 C<isl_dim_cst>, C<isl_dim_param>, C<isl_dim_set> and C<isl_dim_div>.
2019 For map inputs, they should be a permutation of
2020 C<isl_dim_cst>, C<isl_dim_param>,
2021 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
2025 Points are elements of a set. They can be used to construct
2026 simple sets (boxes) or they can be used to represent the
2027 individual elements of a set.
2028 The zero point (the origin) can be created using
2030 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
2032 The coordinates of a point can be inspected, set and changed
2035 __isl_give isl_val *isl_point_get_coordinate_val(
2036 __isl_keep isl_point *pnt,
2037 enum isl_dim_type type, int pos);
2038 __isl_give isl_point *isl_point_set_coordinate_val(
2039 __isl_take isl_point *pnt,
2040 enum isl_dim_type type, int pos,
2041 __isl_take isl_val *v);
2043 __isl_give isl_point *isl_point_add_ui(
2044 __isl_take isl_point *pnt,
2045 enum isl_dim_type type, int pos, unsigned val);
2046 __isl_give isl_point *isl_point_sub_ui(
2047 __isl_take isl_point *pnt,
2048 enum isl_dim_type type, int pos, unsigned val);
2050 Points can be copied or freed using
2052 __isl_give isl_point *isl_point_copy(
2053 __isl_keep isl_point *pnt);
2054 void isl_point_free(__isl_take isl_point *pnt);
2056 A singleton set can be created from a point using
2058 __isl_give isl_basic_set *isl_basic_set_from_point(
2059 __isl_take isl_point *pnt);
2060 __isl_give isl_set *isl_set_from_point(
2061 __isl_take isl_point *pnt);
2063 and a box can be created from two opposite extremal points using
2065 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2066 __isl_take isl_point *pnt1,
2067 __isl_take isl_point *pnt2);
2068 __isl_give isl_set *isl_set_box_from_points(
2069 __isl_take isl_point *pnt1,
2070 __isl_take isl_point *pnt2);
2072 All elements of a B<bounded> (union) set can be enumerated using
2073 the following functions.
2075 int isl_set_foreach_point(__isl_keep isl_set *set,
2076 int (*fn)(__isl_take isl_point *pnt, void *user),
2078 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2079 int (*fn)(__isl_take isl_point *pnt, void *user),
2082 The function C<fn> is called for each integer point in
2083 C<set> with as second argument the last argument of
2084 the C<isl_set_foreach_point> call. The function C<fn>
2085 should return C<0> on success and C<-1> on failure.
2086 In the latter case, C<isl_set_foreach_point> will stop
2087 enumerating and return C<-1> as well.
2088 If the enumeration is performed successfully and to completion,
2089 then C<isl_set_foreach_point> returns C<0>.
2091 To obtain a single point of a (basic) set, use
2093 __isl_give isl_point *isl_basic_set_sample_point(
2094 __isl_take isl_basic_set *bset);
2095 __isl_give isl_point *isl_set_sample_point(
2096 __isl_take isl_set *set);
2098 If C<set> does not contain any (integer) points, then the
2099 resulting point will be ``void'', a property that can be
2102 int isl_point_is_void(__isl_keep isl_point *pnt);
2106 Besides sets and relation, C<isl> also supports various types of functions.
2107 Each of these types is derived from the value type (see L</"Values">)
2108 or from one of two primitive function types
2109 through the application of zero or more type constructors.
2110 We first describe the primitive type and then we describe
2111 the types derived from these primitive types.
2113 =head3 Primitive Functions
2115 C<isl> support two primitive function types, quasi-affine
2116 expressions and quasipolynomials.
2117 A quasi-affine expression is defined either over a parameter
2118 space or over a set and is composed of integer constants,
2119 parameters and set variables, addition, subtraction and
2120 integer division by an integer constant.
2121 For example, the quasi-affine expression
2123 [n] -> { [x] -> [2*floor((4 n + x)/9] }
2125 maps C<x> to C<2*floor((4 n + x)/9>.
2126 A quasipolynomial is a polynomial expression in quasi-affine
2127 expression. That is, it additionally allows for multiplication.
2128 Note, though, that it is not allowed to construct an integer
2129 division of an expression involving multiplications.
2130 Here is an example of a quasipolynomial that is not
2131 quasi-affine expression
2133 [n] -> { [x] -> (n*floor((4 n + x)/9) }
2135 Note that the external representations of quasi-affine expressions
2136 and quasipolynomials are different. Quasi-affine expressions
2137 use a notation with square brackets just like binary relations,
2138 while quasipolynomials do not. This might change at some point.
2140 If a primitive function is defined over a parameter space,
2141 then the space of the function itself is that of a set.
2142 If it is defined over a set, then the space of the function
2143 is that of a relation. In both cases, the set space (or
2144 the output space) is single-dimensional, anonymous and unstructured.
2145 To create functions with multiple dimensions or with other kinds
2146 of set or output spaces, use multiple expressions
2147 (see L</"Multiple Expressions">).
2151 =item * Quasi-affine Expressions
2153 Besides the expressions described above, a quasi-affine
2154 expression can also be set to NaN. Such expressions
2155 typically represent a failure to represent a result
2156 as a quasi-affine expression.
2158 The zero quasi affine expression or the quasi affine expression
2159 that is equal to a given value or
2160 a specified dimension on a given domain can be created using
2162 #include <isl/aff.h>
2163 __isl_give isl_aff *isl_aff_zero_on_domain(
2164 __isl_take isl_local_space *ls);
2165 __isl_give isl_aff *isl_aff_val_on_domain(
2166 __isl_take isl_local_space *ls,
2167 __isl_take isl_val *val);
2168 __isl_give isl_aff *isl_aff_var_on_domain(
2169 __isl_take isl_local_space *ls,
2170 enum isl_dim_type type, unsigned pos);
2171 __isl_give isl_aff *isl_aff_nan_on_domain(
2172 __isl_take isl_local_space *ls);
2174 Quasi affine expressions can be copied and freed using
2176 #include <isl/aff.h>
2177 __isl_give isl_aff *isl_aff_copy(
2178 __isl_keep isl_aff *aff);
2179 __isl_null isl_aff *isl_aff_free(
2180 __isl_take isl_aff *aff);
2182 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2183 using the following function. The constraint is required to have
2184 a non-zero coefficient for the specified dimension.
2186 #include <isl/constraint.h>
2187 __isl_give isl_aff *isl_constraint_get_bound(
2188 __isl_keep isl_constraint *constraint,
2189 enum isl_dim_type type, int pos);
2191 The entire affine expression of the constraint can also be extracted
2192 using the following function.
2194 #include <isl/constraint.h>
2195 __isl_give isl_aff *isl_constraint_get_aff(
2196 __isl_keep isl_constraint *constraint);
2198 Conversely, an equality constraint equating
2199 the affine expression to zero or an inequality constraint enforcing
2200 the affine expression to be non-negative, can be constructed using
2202 __isl_give isl_constraint *isl_equality_from_aff(
2203 __isl_take isl_aff *aff);
2204 __isl_give isl_constraint *isl_inequality_from_aff(
2205 __isl_take isl_aff *aff);
2207 The coefficients and the integer divisions of an affine expression
2208 can be inspected using the following functions.
2210 #include <isl/aff.h>
2211 __isl_give isl_val *isl_aff_get_constant_val(
2212 __isl_keep isl_aff *aff);
2213 __isl_give isl_val *isl_aff_get_coefficient_val(
2214 __isl_keep isl_aff *aff,
2215 enum isl_dim_type type, int pos);
2216 int isl_aff_coefficient_sgn(__isl_keep isl_aff *aff,
2217 enum isl_dim_type type, int pos);
2218 __isl_give isl_val *isl_aff_get_denominator_val(
2219 __isl_keep isl_aff *aff);
2220 __isl_give isl_aff *isl_aff_get_div(
2221 __isl_keep isl_aff *aff, int pos);
2223 They can be modified using the following functions.
2225 #include <isl/aff.h>
2226 __isl_give isl_aff *isl_aff_set_constant_si(
2227 __isl_take isl_aff *aff, int v);
2228 __isl_give isl_aff *isl_aff_set_constant_val(
2229 __isl_take isl_aff *aff, __isl_take isl_val *v);
2230 __isl_give isl_aff *isl_aff_set_coefficient_si(
2231 __isl_take isl_aff *aff,
2232 enum isl_dim_type type, int pos, int v);
2233 __isl_give isl_aff *isl_aff_set_coefficient_val(
2234 __isl_take isl_aff *aff,
2235 enum isl_dim_type type, int pos,
2236 __isl_take isl_val *v);
2238 __isl_give isl_aff *isl_aff_add_constant_si(
2239 __isl_take isl_aff *aff, int v);
2240 __isl_give isl_aff *isl_aff_add_constant_val(
2241 __isl_take isl_aff *aff, __isl_take isl_val *v);
2242 __isl_give isl_aff *isl_aff_add_constant_num_si(
2243 __isl_take isl_aff *aff, int v);
2244 __isl_give isl_aff *isl_aff_add_coefficient_si(
2245 __isl_take isl_aff *aff,
2246 enum isl_dim_type type, int pos, int v);
2247 __isl_give isl_aff *isl_aff_add_coefficient_val(
2248 __isl_take isl_aff *aff,
2249 enum isl_dim_type type, int pos,
2250 __isl_take isl_val *v);
2252 Note that C<isl_aff_set_constant_si> and C<isl_aff_set_coefficient_si>
2253 set the I<numerator> of the constant or coefficient, while
2254 C<isl_aff_set_constant_val> and C<isl_aff_set_coefficient_val> set
2255 the constant or coefficient as a whole.
2256 The C<add_constant> and C<add_coefficient> functions add an integer
2257 or rational value to
2258 the possibly rational constant or coefficient.
2259 The C<add_constant_num> functions add an integer value to
2262 =item * Quasipolynomials
2264 Some simple quasipolynomials can be created using the following functions.
2266 #include <isl/polynomial.h>
2267 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
2268 __isl_take isl_space *domain);
2269 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
2270 __isl_take isl_space *domain);
2271 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
2272 __isl_take isl_space *domain);
2273 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
2274 __isl_take isl_space *domain);
2275 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
2276 __isl_take isl_space *domain);
2277 __isl_give isl_qpolynomial *isl_qpolynomial_val_on_domain(
2278 __isl_take isl_space *domain,
2279 __isl_take isl_val *val);
2280 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
2281 __isl_take isl_space *domain,
2282 enum isl_dim_type type, unsigned pos);
2283 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
2284 __isl_take isl_aff *aff);
2286 Recall that the space in which a quasipolynomial lives is a map space
2287 with a one-dimensional range. The C<domain> argument in some of
2288 the functions above corresponds to the domain of this map space.
2290 Quasipolynomials can be copied and freed again using the following
2293 #include <isl/polynomial.h>
2294 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2295 __isl_keep isl_qpolynomial *qp);
2296 __isl_null isl_qpolynomial *isl_qpolynomial_free(
2297 __isl_take isl_qpolynomial *qp);
2299 The constant term of a quasipolynomial can be extracted using
2301 __isl_give isl_val *isl_qpolynomial_get_constant_val(
2302 __isl_keep isl_qpolynomial *qp);
2304 To iterate over all terms in a quasipolynomial,
2307 int isl_qpolynomial_foreach_term(
2308 __isl_keep isl_qpolynomial *qp,
2309 int (*fn)(__isl_take isl_term *term,
2310 void *user), void *user);
2312 The terms themselves can be inspected and freed using
2315 unsigned isl_term_dim(__isl_keep isl_term *term,
2316 enum isl_dim_type type);
2317 __isl_give isl_val *isl_term_get_coefficient_val(
2318 __isl_keep isl_term *term);
2319 int isl_term_get_exp(__isl_keep isl_term *term,
2320 enum isl_dim_type type, unsigned pos);
2321 __isl_give isl_aff *isl_term_get_div(
2322 __isl_keep isl_term *term, unsigned pos);
2323 void isl_term_free(__isl_take isl_term *term);
2325 Each term is a product of parameters, set variables and
2326 integer divisions. The function C<isl_term_get_exp>
2327 returns the exponent of a given dimensions in the given term.
2333 A reduction represents a maximum or a minimum of its
2335 The only reduction type defined by C<isl> is
2336 C<isl_qpolynomial_fold>.
2338 There are currently no functions to directly create such
2339 objects, but they do appear in the piecewise quasipolynomial
2340 reductions returned by the C<isl_pw_qpolynomial_bound> function.
2342 L</"Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions">.
2344 Reductions can be copied and freed using
2345 the following functions.
2347 #include <isl/polynomial.h>
2348 __isl_give isl_qpolynomial_fold *
2349 isl_qpolynomial_fold_copy(
2350 __isl_keep isl_qpolynomial_fold *fold);
2351 void isl_qpolynomial_fold_free(
2352 __isl_take isl_qpolynomial_fold *fold);
2354 To iterate over all quasipolynomials in a reduction, use
2356 int isl_qpolynomial_fold_foreach_qpolynomial(
2357 __isl_keep isl_qpolynomial_fold *fold,
2358 int (*fn)(__isl_take isl_qpolynomial *qp,
2359 void *user), void *user);
2361 =head3 Multiple Expressions
2363 A multiple expression represents a sequence of zero or
2364 more base expressions, all defined on the same domain space.
2365 The domain space of the multiple expression is the same
2366 as that of the base expressions, but the range space
2367 can be any space. In case the base expressions have
2368 a set space, the corresponding multiple expression
2369 also has a set space.
2370 Objects of the value type do not have an associated space.
2371 The space of a multiple value is therefore always a set space.
2373 The multiple expression types defined by C<isl>
2374 are C<isl_multi_val>, C<isl_multi_aff> and C<isl_multi_pw_aff>.
2376 A multiple expression with the value zero for
2377 each output (or set) dimension can be created
2378 using the following functions.
2380 #include <isl/val.h>
2381 __isl_give isl_multi_val *isl_multi_val_zero(
2382 __isl_take isl_space *space);
2384 #include <isl/aff.h>
2385 __isl_give isl_multi_aff *isl_multi_aff_zero(
2386 __isl_take isl_space *space);
2387 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
2388 __isl_take isl_space *space);
2390 An identity function can be created using the following
2391 functions. The space needs to be that of a relation
2392 with the same number of input and output dimensions.
2394 #include <isl/aff.h>
2395 __isl_give isl_multi_aff *isl_multi_aff_identity(
2396 __isl_take isl_space *space);
2397 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
2398 __isl_take isl_space *space);
2400 A function that performs a projection on a universe
2401 relation or set can be created using the following functions.
2402 See also the corresponding
2403 projection operations in L</"Unary Operations">.
2405 #include <isl/aff.h>
2406 __isl_give isl_multi_aff *isl_multi_aff_domain_map(
2407 __isl_take isl_space *space);
2408 __isl_give isl_multi_aff *isl_multi_aff_range_map(
2409 __isl_take isl_space *space);
2410 __isl_give isl_multi_aff *isl_multi_aff_project_out_map(
2411 __isl_take isl_space *space,
2412 enum isl_dim_type type,
2413 unsigned first, unsigned n);
2415 A multiple expression can be created from a single
2416 base expression using the following functions.
2417 The space of the created multiple expression is the same
2418 as that of the base expression.
2420 #include <isl/aff.h>
2421 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
2422 __isl_take isl_aff *aff);
2423 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
2424 __isl_take isl_pw_aff *pa);
2426 A multiple expression can be created from a list
2427 of base expression in a specified space.
2428 The domain of this space needs to be the same
2429 as the domains of the base expressions in the list.
2430 If the base expressions have a set space (or no associated space),
2431 then this space also needs to be a set space.
2433 #include <isl/val.h>
2434 __isl_give isl_multi_val *isl_multi_val_from_val_list(
2435 __isl_take isl_space *space,
2436 __isl_take isl_val_list *list);
2438 #include <isl/aff.h>
2439 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
2440 __isl_take isl_space *space,
2441 __isl_take isl_aff_list *list);
2443 As a convenience, a multiple piecewise expression can
2444 also be created from a multiple expression.
2445 Each piecewise expression in the result has a single
2448 #include <isl/aff.h>
2449 __isl_give isl_multi_pw_aff *
2450 isl_multi_pw_aff_from_multi_aff(
2451 __isl_take isl_multi_aff *ma);
2453 Multiple expressions can be copied and freed using
2454 the following functions.
2456 #include <isl/val.h>
2457 __isl_give isl_multi_val *isl_multi_val_copy(
2458 __isl_keep isl_multi_val *mv);
2459 __isl_null isl_multi_val *isl_multi_val_free(
2460 __isl_take isl_multi_val *mv);
2462 #include <isl/aff.h>
2463 __isl_give isl_multi_aff *isl_multi_aff_copy(
2464 __isl_keep isl_multi_aff *maff);
2465 __isl_null isl_multi_aff *isl_multi_aff_free(
2466 __isl_take isl_multi_aff *maff);
2467 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
2468 __isl_keep isl_multi_pw_aff *mpa);
2469 __isl_null isl_multi_pw_aff *isl_multi_pw_aff_free(
2470 __isl_take isl_multi_pw_aff *mpa);
2472 The base expression at a given position of a multiple
2473 expression can be extracted using the following functions.
2475 #include <isl/val.h>
2476 __isl_give isl_val *isl_multi_val_get_val(
2477 __isl_keep isl_multi_val *mv, int pos);
2479 #include <isl/aff.h>
2480 __isl_give isl_aff *isl_multi_aff_get_aff(
2481 __isl_keep isl_multi_aff *multi, int pos);
2482 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
2483 __isl_keep isl_multi_pw_aff *mpa, int pos);
2485 It can be replaced using the following functions.
2487 #include <isl/val.h>
2488 __isl_give isl_multi_val *isl_multi_val_set_val(
2489 __isl_take isl_multi_val *mv, int pos,
2490 __isl_take isl_val *val);
2492 #include <isl/aff.h>
2493 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
2494 __isl_take isl_multi_aff *multi, int pos,
2495 __isl_take isl_aff *aff);
2497 =head3 Piecewise Expressions
2499 A piecewise expression is an expression that is described
2500 using zero or more base expression defined over the same
2501 number of cells in the domain space of the base expressions.
2502 All base expressions are defined over the same
2503 domain space and the cells are disjoint.
2504 The space of a piecewise expression is the same as
2505 that of the base expressions.
2506 If the union of the cells is a strict subset of the domain
2507 space, then the value of the piecewise expression outside
2508 this union is different for types derived from quasi-affine
2509 expressions and those derived from quasipolynomials.
2510 Piecewise expressions derived from quasi-affine expressions
2511 are considered to be undefined outside the union of their cells.
2512 Piecewise expressions derived from quasipolynomials
2513 are considered to be zero outside the union of their cells.
2515 Piecewise quasipolynomials are mainly used by the C<barvinok>
2516 library for representing the number of elements in a parametric set or map.
2517 For example, the piecewise quasipolynomial
2519 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2521 represents the number of points in the map
2523 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2525 The piecewise expression types defined by C<isl>
2526 are C<isl_pw_aff>, C<isl_pw_multi_aff>,
2527 C<isl_pw_qpolynomial> and C<isl_pw_qpolynomial_fold>.
2529 A piecewise expression with no cells can be created using
2530 the following functions.
2532 #include <isl/aff.h>
2533 __isl_give isl_pw_aff *isl_pw_aff_empty(
2534 __isl_take isl_space *space);
2535 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
2536 __isl_take isl_space *space);
2538 A piecewise expression with a single universe cell can be
2539 created using the following functions.
2541 #include <isl/aff.h>
2542 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2543 __isl_take isl_aff *aff);
2544 __isl_give isl_pw_multi_aff *
2545 isl_pw_multi_aff_from_multi_aff(
2546 __isl_take isl_multi_aff *ma);
2548 #include <isl/polynomial.h>
2549 __isl_give isl_pw_qpolynomial *
2550 isl_pw_qpolynomial_from_qpolynomial(
2551 __isl_take isl_qpolynomial *qp);
2553 A piecewise expression with a single specified cell can be
2554 created using the following functions.
2556 #include <isl/aff.h>
2557 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2558 __isl_take isl_set *set, __isl_take isl_aff *aff);
2559 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
2560 __isl_take isl_set *set,
2561 __isl_take isl_multi_aff *maff);
2563 #include <isl/polynomial.h>
2564 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2565 __isl_take isl_set *set,
2566 __isl_take isl_qpolynomial *qp);
2568 The following convenience functions first create a base expression and
2569 then create a piecewise expression over a universe domain.
2571 #include <isl/aff.h>
2572 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
2573 __isl_take isl_local_space *ls);
2574 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
2575 __isl_take isl_local_space *ls,
2576 enum isl_dim_type type, unsigned pos);
2577 __isl_give isl_pw_aff *isl_pw_aff_nan_on_domain(
2578 __isl_take isl_local_space *ls);
2579 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_zero(
2580 __isl_take isl_space *space);
2581 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
2582 __isl_take isl_space *space);
2583 __isl_give isl_pw_multi_aff *
2584 isl_pw_multi_aff_project_out_map(
2585 __isl_take isl_space *space,
2586 enum isl_dim_type type,
2587 unsigned first, unsigned n);
2589 #include <isl/polynomial.h>
2590 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2591 __isl_take isl_space *space);
2593 As a convenience, a piecewise multiple expression can
2594 also be created from a piecewise expression.
2595 Each multiple expression in the result is derived
2596 from the corresponding base expression.
2598 #include <isl/aff.h>
2599 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_pw_aff(
2600 __isl_take isl_pw_aff *pa);
2602 Similarly, a piecewise quasipolynomial can be
2603 created from a piecewise quasi-affine expression using
2604 the following function.
2606 #include <isl/polynomial.h>
2607 __isl_give isl_pw_qpolynomial *
2608 isl_pw_qpolynomial_from_pw_aff(
2609 __isl_take isl_pw_aff *pwaff);
2611 Piecewise expressions can be copied and freed using the following functions.
2613 #include <isl/aff.h>
2614 __isl_give isl_pw_aff *isl_pw_aff_copy(
2615 __isl_keep isl_pw_aff *pwaff);
2616 __isl_null isl_pw_aff *isl_pw_aff_free(
2617 __isl_take isl_pw_aff *pwaff);
2618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
2619 __isl_keep isl_pw_multi_aff *pma);
2620 __isl_null isl_pw_multi_aff *isl_pw_multi_aff_free(
2621 __isl_take isl_pw_multi_aff *pma);
2623 #include <isl/polynomial.h>
2624 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2625 __isl_keep isl_pw_qpolynomial *pwqp);
2626 __isl_null isl_pw_qpolynomial *isl_pw_qpolynomial_free(
2627 __isl_take isl_pw_qpolynomial *pwqp);
2628 __isl_give isl_pw_qpolynomial_fold *
2629 isl_pw_qpolynomial_fold_copy(
2630 __isl_keep isl_pw_qpolynomial_fold *pwf);
2631 __isl_null isl_pw_qpolynomial_fold *
2632 isl_pw_qpolynomial_fold_free(
2633 __isl_take isl_pw_qpolynomial_fold *pwf);
2635 To iterate over the different cells of a piecewise expression,
2636 use the following functions.
2638 #include <isl/aff.h>
2639 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2640 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2641 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2642 int (*fn)(__isl_take isl_set *set,
2643 __isl_take isl_aff *aff,
2644 void *user), void *user);
2645 int isl_pw_multi_aff_foreach_piece(
2646 __isl_keep isl_pw_multi_aff *pma,
2647 int (*fn)(__isl_take isl_set *set,
2648 __isl_take isl_multi_aff *maff,
2649 void *user), void *user);
2651 #include <isl/polynomial.h>
2652 int isl_pw_qpolynomial_foreach_piece(
2653 __isl_keep isl_pw_qpolynomial *pwqp,
2654 int (*fn)(__isl_take isl_set *set,
2655 __isl_take isl_qpolynomial *qp,
2656 void *user), void *user);
2657 int isl_pw_qpolynomial_foreach_lifted_piece(
2658 __isl_keep isl_pw_qpolynomial *pwqp,
2659 int (*fn)(__isl_take isl_set *set,
2660 __isl_take isl_qpolynomial *qp,
2661 void *user), void *user);
2662 int isl_pw_qpolynomial_fold_foreach_piece(
2663 __isl_keep isl_pw_qpolynomial_fold *pwf,
2664 int (*fn)(__isl_take isl_set *set,
2665 __isl_take isl_qpolynomial_fold *fold,
2666 void *user), void *user);
2667 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2668 __isl_keep isl_pw_qpolynomial_fold *pwf,
2669 int (*fn)(__isl_take isl_set *set,
2670 __isl_take isl_qpolynomial_fold *fold,
2671 void *user), void *user);
2673 As usual, the function C<fn> should return C<0> on success
2674 and C<-1> on failure. The difference between
2675 C<isl_pw_qpolynomial_foreach_piece> and
2676 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2677 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2678 compute unique representations for all existentially quantified
2679 variables and then turn these existentially quantified variables
2680 into extra set variables, adapting the associated quasipolynomial
2681 accordingly. This means that the C<set> passed to C<fn>
2682 will not have any existentially quantified variables, but that
2683 the dimensions of the sets may be different for different
2684 invocations of C<fn>.
2685 Similarly for C<isl_pw_qpolynomial_fold_foreach_piece>
2686 and C<isl_pw_qpolynomial_fold_foreach_lifted_piece>.
2688 A piecewise expression consisting of the expressions at a given
2689 position of a piecewise multiple expression can be extracted
2690 using the following function.
2692 #include <isl/aff.h>
2693 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
2694 __isl_keep isl_pw_multi_aff *pma, int pos);
2696 These expressions can be replaced using the following function.
2698 #include <isl/aff.h>
2699 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
2700 __isl_take isl_pw_multi_aff *pma, unsigned pos,
2701 __isl_take isl_pw_aff *pa);
2703 Note that there is a difference between C<isl_multi_pw_aff> and
2704 C<isl_pw_multi_aff> objects. The first is a sequence of piecewise
2705 affine expressions, while the second is a piecewise sequence
2706 of affine expressions. In particular, each of the piecewise
2707 affine expressions in an C<isl_multi_pw_aff> may have a different
2708 domain, while all multiple expressions associated to a cell
2709 in an C<isl_pw_multi_aff> have the same domain.
2710 It is possible to convert between the two, but when converting
2711 an C<isl_multi_pw_aff> to an C<isl_pw_multi_aff>, the domain
2712 of the result is the intersection of the domains of the input.
2713 The reverse conversion is exact.
2715 #include <isl/aff.h>
2716 __isl_give isl_pw_multi_aff *
2717 isl_pw_multi_aff_from_multi_pw_aff(
2718 __isl_take isl_multi_pw_aff *mpa);
2719 __isl_give isl_multi_pw_aff *
2720 isl_multi_pw_aff_from_pw_multi_aff(
2721 __isl_take isl_pw_multi_aff *pma);
2723 =head3 Union Expressions
2725 A union expression collects base expressions defined
2726 over different domains. The space of a union expression
2727 is that of the shared parameter space.
2729 The union expression types defined by C<isl>
2730 are C<isl_union_pw_multi_aff>, C<isl_union_pw_qpolynomial> and
2731 C<isl_union_pw_qpolynomial_fold>.
2733 An empty union expression can be created using the following functions.
2735 #include <isl/aff.h>
2736 __isl_give isl_union_pw_multi_aff *
2737 isl_union_pw_multi_aff_empty(
2738 __isl_take isl_space *space);
2740 #include <isl/polynomial.h>
2741 __isl_give isl_union_pw_qpolynomial *
2742 isl_union_pw_qpolynomial_zero(
2743 __isl_take isl_space *space);
2745 A union expression containing a single base expression
2746 can be created using the following functions.
2748 #include <isl/aff.h>
2749 __isl_give isl_union_pw_multi_aff *
2750 isl_union_pw_multi_aff_from_pw_multi_aff(
2751 __isl_take isl_pw_multi_aff *pma);
2753 #include <isl/polynomial.h>
2754 __isl_give isl_union_pw_qpolynomial *
2755 isl_union_pw_qpolynomial_from_pw_qpolynomial(
2756 __isl_take isl_pw_qpolynomial *pwqp);
2758 A base expression can be added to a union expression using
2759 the following functions.
2761 #include <isl/aff.h>
2762 __isl_give isl_union_pw_multi_aff *
2763 isl_union_pw_multi_aff_add_pw_multi_aff(
2764 __isl_take isl_union_pw_multi_aff *upma,
2765 __isl_take isl_pw_multi_aff *pma);
2767 #include <isl/polynomial.h>
2768 __isl_give isl_union_pw_qpolynomial *
2769 isl_union_pw_qpolynomial_add_pw_qpolynomial(
2770 __isl_take isl_union_pw_qpolynomial *upwqp,
2771 __isl_take isl_pw_qpolynomial *pwqp);
2773 Union expressions can be copied and freed using
2774 the following functions.
2776 #include <isl/aff.h>
2777 __isl_give isl_union_pw_multi_aff *
2778 isl_union_pw_multi_aff_copy(
2779 __isl_keep isl_union_pw_multi_aff *upma);
2780 __isl_null isl_union_pw_multi_aff *
2781 isl_union_pw_multi_aff_free(
2782 __isl_take isl_union_pw_multi_aff *upma);
2784 #include <isl/polynomial.h>
2785 __isl_give isl_union_pw_qpolynomial *
2786 isl_union_pw_qpolynomial_copy(
2787 __isl_keep isl_union_pw_qpolynomial *upwqp);
2788 __isl_null isl_union_pw_qpolynomial *
2789 isl_union_pw_qpolynomial_free(
2790 __isl_take isl_union_pw_qpolynomial *upwqp);
2791 __isl_give isl_union_pw_qpolynomial_fold *
2792 isl_union_pw_qpolynomial_fold_copy(
2793 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2794 __isl_null isl_union_pw_qpolynomial_fold *
2795 isl_union_pw_qpolynomial_fold_free(
2796 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2798 To iterate over the base expressions in a union expression,
2799 use the following functions.
2801 #include <isl/aff.h>
2802 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
2803 __isl_keep isl_union_pw_multi_aff *upma,
2804 int (*fn)(__isl_take isl_pw_multi_aff *pma,
2805 void *user), void *user);
2807 #include <isl/polynomial.h>
2808 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2809 __isl_keep isl_union_pw_qpolynomial *upwqp,
2810 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp,
2811 void *user), void *user);
2812 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2813 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2814 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2815 void *user), void *user);
2817 To extract the base expression in a given space from a union, use
2818 the following functions.
2820 #include <isl/aff.h>
2821 __isl_give isl_pw_multi_aff *
2822 isl_union_pw_multi_aff_extract_pw_multi_aff(
2823 __isl_keep isl_union_pw_multi_aff *upma,
2824 __isl_take isl_space *space);
2826 #include <isl/polynomial.h>
2827 __isl_give isl_pw_qpolynomial *
2828 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2829 __isl_keep isl_union_pw_qpolynomial *upwqp,
2830 __isl_take isl_space *space);
2832 =head2 Input and Output
2834 For set and relation,
2835 C<isl> supports its own input/output format, which is similar
2836 to the C<Omega> format, but also supports the C<PolyLib> format
2838 For other object types, typically only an C<isl> format is supported.
2840 =head3 C<isl> format
2842 The C<isl> format is similar to that of C<Omega>, but has a different
2843 syntax for describing the parameters and allows for the definition
2844 of an existentially quantified variable as the integer division
2845 of an affine expression.
2846 For example, the set of integers C<i> between C<0> and C<n>
2847 such that C<i % 10 <= 6> can be described as
2849 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
2852 A set or relation can have several disjuncts, separated
2853 by the keyword C<or>. Each disjunct is either a conjunction
2854 of constraints or a projection (C<exists>) of a conjunction
2855 of constraints. The constraints are separated by the keyword
2858 =head3 C<PolyLib> format
2860 If the represented set is a union, then the first line
2861 contains a single number representing the number of disjuncts.
2862 Otherwise, a line containing the number C<1> is optional.
2864 Each disjunct is represented by a matrix of constraints.
2865 The first line contains two numbers representing
2866 the number of rows and columns,
2867 where the number of rows is equal to the number of constraints
2868 and the number of columns is equal to two plus the number of variables.
2869 The following lines contain the actual rows of the constraint matrix.
2870 In each row, the first column indicates whether the constraint
2871 is an equality (C<0>) or inequality (C<1>). The final column
2872 corresponds to the constant term.
2874 If the set is parametric, then the coefficients of the parameters
2875 appear in the last columns before the constant column.
2876 The coefficients of any existentially quantified variables appear
2877 between those of the set variables and those of the parameters.
2879 =head3 Extended C<PolyLib> format
2881 The extended C<PolyLib> format is nearly identical to the
2882 C<PolyLib> format. The only difference is that the line
2883 containing the number of rows and columns of a constraint matrix
2884 also contains four additional numbers:
2885 the number of output dimensions, the number of input dimensions,
2886 the number of local dimensions (i.e., the number of existentially
2887 quantified variables) and the number of parameters.
2888 For sets, the number of ``output'' dimensions is equal
2889 to the number of set dimensions, while the number of ``input''
2894 Objects can be read from input using the following functions.
2896 #include <isl/val.h>
2897 __isl_give isl_val *isl_val_read_from_str(isl_ctx *ctx,
2900 #include <isl/set.h>
2901 __isl_give isl_basic_set *isl_basic_set_read_from_file(
2902 isl_ctx *ctx, FILE *input);
2903 __isl_give isl_basic_set *isl_basic_set_read_from_str(
2904 isl_ctx *ctx, const char *str);
2905 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
2907 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
2910 #include <isl/map.h>
2911 __isl_give isl_basic_map *isl_basic_map_read_from_file(
2912 isl_ctx *ctx, FILE *input);
2913 __isl_give isl_basic_map *isl_basic_map_read_from_str(
2914 isl_ctx *ctx, const char *str);
2915 __isl_give isl_map *isl_map_read_from_file(
2916 isl_ctx *ctx, FILE *input);
2917 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
2920 #include <isl/union_set.h>
2921 __isl_give isl_union_set *isl_union_set_read_from_file(
2922 isl_ctx *ctx, FILE *input);
2923 __isl_give isl_union_set *isl_union_set_read_from_str(
2924 isl_ctx *ctx, const char *str);
2926 #include <isl/union_map.h>
2927 __isl_give isl_union_map *isl_union_map_read_from_file(
2928 isl_ctx *ctx, FILE *input);
2929 __isl_give isl_union_map *isl_union_map_read_from_str(
2930 isl_ctx *ctx, const char *str);
2932 #include <isl/aff.h>
2933 __isl_give isl_aff *isl_aff_read_from_str(
2934 isl_ctx *ctx, const char *str);
2935 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
2936 isl_ctx *ctx, const char *str);
2937 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
2938 isl_ctx *ctx, const char *str);
2939 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
2940 isl_ctx *ctx, const char *str);
2941 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_read_from_str(
2942 isl_ctx *ctx, const char *str);
2943 __isl_give isl_union_pw_multi_aff *
2944 isl_union_pw_multi_aff_read_from_str(
2945 isl_ctx *ctx, const char *str);
2947 #include <isl/polynomial.h>
2948 __isl_give isl_union_pw_qpolynomial *
2949 isl_union_pw_qpolynomial_read_from_str(
2950 isl_ctx *ctx, const char *str);
2952 For sets and relations,
2953 the input format is autodetected and may be either the C<PolyLib> format
2954 or the C<isl> format.
2958 Before anything can be printed, an C<isl_printer> needs to
2961 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
2963 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
2964 __isl_null isl_printer *isl_printer_free(
2965 __isl_take isl_printer *printer);
2966 __isl_give char *isl_printer_get_str(
2967 __isl_keep isl_printer *printer);
2969 The printer can be inspected using the following functions.
2971 FILE *isl_printer_get_file(
2972 __isl_keep isl_printer *printer);
2973 int isl_printer_get_output_format(
2974 __isl_keep isl_printer *p);
2976 The behavior of the printer can be modified in various ways
2978 __isl_give isl_printer *isl_printer_set_output_format(
2979 __isl_take isl_printer *p, int output_format);
2980 __isl_give isl_printer *isl_printer_set_indent(
2981 __isl_take isl_printer *p, int indent);
2982 __isl_give isl_printer *isl_printer_set_indent_prefix(
2983 __isl_take isl_printer *p, const char *prefix);
2984 __isl_give isl_printer *isl_printer_indent(
2985 __isl_take isl_printer *p, int indent);
2986 __isl_give isl_printer *isl_printer_set_prefix(
2987 __isl_take isl_printer *p, const char *prefix);
2988 __isl_give isl_printer *isl_printer_set_suffix(
2989 __isl_take isl_printer *p, const char *suffix);
2991 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
2992 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
2993 and defaults to C<ISL_FORMAT_ISL>.
2994 Each line in the output is prefixed by C<indent_prefix>,
2995 indented by C<indent> (set by C<isl_printer_set_indent>) spaces
2996 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
2997 In the C<PolyLib> format output,
2998 the coefficients of the existentially quantified variables
2999 appear between those of the set variables and those
3001 The function C<isl_printer_indent> increases the indentation
3002 by the specified amount (which may be negative).
3004 To actually print something, use
3006 #include <isl/printer.h>
3007 __isl_give isl_printer *isl_printer_print_double(
3008 __isl_take isl_printer *p, double d);
3010 #include <isl/val.h>
3011 __isl_give isl_printer *isl_printer_print_val(
3012 __isl_take isl_printer *p, __isl_keep isl_val *v);
3014 #include <isl/set.h>
3015 __isl_give isl_printer *isl_printer_print_basic_set(
3016 __isl_take isl_printer *printer,
3017 __isl_keep isl_basic_set *bset);
3018 __isl_give isl_printer *isl_printer_print_set(
3019 __isl_take isl_printer *printer,
3020 __isl_keep isl_set *set);
3022 #include <isl/map.h>
3023 __isl_give isl_printer *isl_printer_print_basic_map(
3024 __isl_take isl_printer *printer,
3025 __isl_keep isl_basic_map *bmap);
3026 __isl_give isl_printer *isl_printer_print_map(
3027 __isl_take isl_printer *printer,
3028 __isl_keep isl_map *map);
3030 #include <isl/union_set.h>
3031 __isl_give isl_printer *isl_printer_print_union_set(
3032 __isl_take isl_printer *p,
3033 __isl_keep isl_union_set *uset);
3035 #include <isl/union_map.h>
3036 __isl_give isl_printer *isl_printer_print_union_map(
3037 __isl_take isl_printer *p,
3038 __isl_keep isl_union_map *umap);
3040 #include <isl/val.h>
3041 __isl_give isl_printer *isl_printer_print_multi_val(
3042 __isl_take isl_printer *p,
3043 __isl_keep isl_multi_val *mv);
3045 #include <isl/aff.h>
3046 __isl_give isl_printer *isl_printer_print_aff(
3047 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3048 __isl_give isl_printer *isl_printer_print_multi_aff(
3049 __isl_take isl_printer *p,
3050 __isl_keep isl_multi_aff *maff);
3051 __isl_give isl_printer *isl_printer_print_pw_aff(
3052 __isl_take isl_printer *p,
3053 __isl_keep isl_pw_aff *pwaff);
3054 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3055 __isl_take isl_printer *p,
3056 __isl_keep isl_pw_multi_aff *pma);
3057 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
3058 __isl_take isl_printer *p,
3059 __isl_keep isl_multi_pw_aff *mpa);
3060 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3061 __isl_take isl_printer *p,
3062 __isl_keep isl_union_pw_multi_aff *upma);
3064 #include <isl/polynomial.h>
3065 __isl_give isl_printer *isl_printer_print_qpolynomial(
3066 __isl_take isl_printer *p,
3067 __isl_keep isl_qpolynomial *qp);
3068 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3069 __isl_take isl_printer *p,
3070 __isl_keep isl_pw_qpolynomial *pwqp);
3071 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3072 __isl_take isl_printer *p,
3073 __isl_keep isl_union_pw_qpolynomial *upwqp);
3075 __isl_give isl_printer *
3076 isl_printer_print_pw_qpolynomial_fold(
3077 __isl_take isl_printer *p,
3078 __isl_keep isl_pw_qpolynomial_fold *pwf);
3079 __isl_give isl_printer *
3080 isl_printer_print_union_pw_qpolynomial_fold(
3081 __isl_take isl_printer *p,
3082 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3084 For C<isl_printer_print_qpolynomial>,
3085 C<isl_printer_print_pw_qpolynomial> and
3086 C<isl_printer_print_pw_qpolynomial_fold>,
3087 the output format of the printer
3088 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3089 For C<isl_printer_print_union_pw_qpolynomial> and
3090 C<isl_printer_print_union_pw_qpolynomial_fold>, only C<ISL_FORMAT_ISL>
3092 In case of printing in C<ISL_FORMAT_C>, the user may want
3093 to set the names of all dimensions first.
3095 When called on a file printer, the following function flushes
3096 the file. When called on a string printer, the buffer is cleared.
3098 __isl_give isl_printer *isl_printer_flush(
3099 __isl_take isl_printer *p);
3101 Alternatively, a string representation can be obtained
3102 directly using the following functions, which always print
3105 #include <isl/space.h>
3106 __isl_give char *isl_space_to_str(
3107 __isl_keep isl_space *space);
3109 #include <isl/val.h>
3110 __isl_give char *isl_val_to_str(__isl_keep isl_val *v);
3111 __isl_give char *isl_multi_val_to_str(
3112 __isl_keep isl_multi_val *mv);
3114 #include <isl/set.h>
3115 __isl_give char *isl_set_to_str(
3116 __isl_keep isl_set *set);
3118 #include <isl/union_set.h>
3119 __isl_give char *isl_union_set_to_str(
3120 __isl_keep isl_union_set *uset);
3122 #include <isl/map.h>
3123 __isl_give char *isl_map_to_str(
3124 __isl_keep isl_map *map);
3126 #include <isl/union_map.h>
3127 __isl_give char *isl_union_map_to_str(
3128 __isl_keep isl_union_map *umap);
3130 #include <isl/aff.h>
3131 __isl_give char *isl_multi_aff_to_str(
3132 __isl_keep isl_multi_aff *aff);
3133 __isl_give char *isl_union_pw_multi_aff_to_str(
3134 __isl_keep isl_union_pw_multi_aff *upma);
3138 =head3 Unary Properties
3144 The following functions test whether the given set or relation
3145 contains any integer points. The ``plain'' variants do not perform
3146 any computations, but simply check if the given set or relation
3147 is already known to be empty.
3149 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
3150 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
3151 int isl_set_plain_is_empty(__isl_keep isl_set *set);
3152 int isl_set_is_empty(__isl_keep isl_set *set);
3153 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
3154 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
3155 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
3156 int isl_map_plain_is_empty(__isl_keep isl_map *map);
3157 int isl_map_is_empty(__isl_keep isl_map *map);
3158 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
3160 =item * Universality
3162 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
3163 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
3164 int isl_set_plain_is_universe(__isl_keep isl_set *set);
3166 =item * Single-valuedness
3168 #include <isl/set.h>
3169 int isl_set_is_singleton(__isl_keep isl_set *set);
3171 #include <isl/map.h>
3172 int isl_basic_map_is_single_valued(
3173 __isl_keep isl_basic_map *bmap);
3174 int isl_map_plain_is_single_valued(
3175 __isl_keep isl_map *map);
3176 int isl_map_is_single_valued(__isl_keep isl_map *map);
3178 #include <isl/union_map.h>
3179 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
3183 int isl_map_plain_is_injective(__isl_keep isl_map *map);
3184 int isl_map_is_injective(__isl_keep isl_map *map);
3185 int isl_union_map_plain_is_injective(
3186 __isl_keep isl_union_map *umap);
3187 int isl_union_map_is_injective(
3188 __isl_keep isl_union_map *umap);
3192 int isl_map_is_bijective(__isl_keep isl_map *map);
3193 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
3197 __isl_give isl_val *
3198 isl_basic_map_plain_get_val_if_fixed(
3199 __isl_keep isl_basic_map *bmap,
3200 enum isl_dim_type type, unsigned pos);
3201 __isl_give isl_val *isl_set_plain_get_val_if_fixed(
3202 __isl_keep isl_set *set,
3203 enum isl_dim_type type, unsigned pos);
3204 __isl_give isl_val *isl_map_plain_get_val_if_fixed(
3205 __isl_keep isl_map *map,
3206 enum isl_dim_type type, unsigned pos);
3208 If the set or relation obviously lies on a hyperplane where the given dimension
3209 has a fixed value, then return that value.
3210 Otherwise return NaN.
3214 int isl_set_dim_residue_class_val(
3215 __isl_keep isl_set *set,
3216 int pos, __isl_give isl_val **modulo,
3217 __isl_give isl_val **residue);
3219 Check if the values of the given set dimension are equal to a fixed
3220 value modulo some integer value. If so, assign the modulo to C<*modulo>
3221 and the fixed value to C<*residue>. If the given dimension attains only
3222 a single value, then assign C<0> to C<*modulo> and the fixed value to
3224 If the dimension does not attain only a single value and if no modulo
3225 can be found then assign C<1> to C<*modulo> and C<1> to C<*residue>.
3229 To check whether the description of a set, relation or function depends
3230 on one or more given dimensions,
3231 the following functions can be used.
3233 #include <isl/constraint.h>
3234 int isl_constraint_involves_dims(
3235 __isl_keep isl_constraint *constraint,
3236 enum isl_dim_type type, unsigned first, unsigned n);
3238 #include <isl/set.h>
3239 int isl_basic_set_involves_dims(
3240 __isl_keep isl_basic_set *bset,
3241 enum isl_dim_type type, unsigned first, unsigned n);
3242 int isl_set_involves_dims(__isl_keep isl_set *set,
3243 enum isl_dim_type type, unsigned first, unsigned n);
3245 #include <isl/map.h>
3246 int isl_basic_map_involves_dims(
3247 __isl_keep isl_basic_map *bmap,
3248 enum isl_dim_type type, unsigned first, unsigned n);
3249 int isl_map_involves_dims(__isl_keep isl_map *map,
3250 enum isl_dim_type type, unsigned first, unsigned n);
3252 #include <isl/aff.h>
3253 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3254 enum isl_dim_type type, unsigned first, unsigned n);
3255 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3256 enum isl_dim_type type, unsigned first, unsigned n);
3257 int isl_multi_aff_involves_dims(
3258 __isl_keep isl_multi_aff *ma,
3259 enum isl_dim_type type, unsigned first, unsigned n);
3260 int isl_multi_pw_aff_involves_dims(
3261 __isl_keep isl_multi_pw_aff *mpa,
3262 enum isl_dim_type type, unsigned first, unsigned n);
3264 Similarly, the following functions can be used to check whether
3265 a given dimension is involved in any lower or upper bound.
3267 #include <isl/set.h>
3268 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
3269 enum isl_dim_type type, unsigned pos);
3270 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
3271 enum isl_dim_type type, unsigned pos);
3273 Note that these functions return true even if there is a bound on
3274 the dimension on only some of the basic sets of C<set>.
3275 To check if they have a bound for all of the basic sets in C<set>,
3276 use the following functions instead.
3278 #include <isl/set.h>
3279 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
3280 enum isl_dim_type type, unsigned pos);
3281 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
3282 enum isl_dim_type type, unsigned pos);
3286 To check whether a set is a parameter domain, use this function:
3288 int isl_set_is_params(__isl_keep isl_set *set);
3289 int isl_union_set_is_params(
3290 __isl_keep isl_union_set *uset);
3294 The following functions check whether the space of the given
3295 (basic) set or relation range is a wrapped relation.
3297 #include <isl/space.h>
3298 int isl_space_is_wrapping(
3299 __isl_keep isl_space *space);
3300 int isl_space_domain_is_wrapping(
3301 __isl_keep isl_space *space);
3302 int isl_space_range_is_wrapping(
3303 __isl_keep isl_space *space);
3305 #include <isl/set.h>
3306 int isl_basic_set_is_wrapping(
3307 __isl_keep isl_basic_set *bset);
3308 int isl_set_is_wrapping(__isl_keep isl_set *set);
3310 #include <isl/map.h>
3311 int isl_map_domain_is_wrapping(
3312 __isl_keep isl_map *map);
3313 int isl_map_range_is_wrapping(
3314 __isl_keep isl_map *map);
3316 #include <isl/val.h>
3317 int isl_multi_val_range_is_wrapping(
3318 __isl_keep isl_multi_val *mv);
3320 #include <isl/aff.h>
3321 int isl_multi_aff_range_is_wrapping(
3322 __isl_keep isl_multi_aff *ma);
3323 int isl_multi_pw_aff_range_is_wrapping(
3324 __isl_keep isl_multi_pw_aff *mpa);
3326 The input to C<isl_space_is_wrapping> should
3327 be the space of a set, while that of
3328 C<isl_space_domain_is_wrapping> and
3329 C<isl_space_range_is_wrapping> should be the space of a relation.
3331 =item * Internal Product
3333 int isl_basic_map_can_zip(
3334 __isl_keep isl_basic_map *bmap);
3335 int isl_map_can_zip(__isl_keep isl_map *map);
3337 Check whether the product of domain and range of the given relation
3339 i.e., whether both domain and range are nested relations.
3343 int isl_basic_map_can_curry(
3344 __isl_keep isl_basic_map *bmap);
3345 int isl_map_can_curry(__isl_keep isl_map *map);
3347 Check whether the domain of the (basic) relation is a wrapped relation.
3349 int isl_basic_map_can_uncurry(
3350 __isl_keep isl_basic_map *bmap);
3351 int isl_map_can_uncurry(__isl_keep isl_map *map);
3353 Check whether the range of the (basic) relation is a wrapped relation.
3355 =item * Special Values
3357 #include <isl/aff.h>
3358 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3359 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3361 Check whether the given expression is a constant.
3363 #include <isl/aff.h>
3364 int isl_aff_is_nan(__isl_keep isl_aff *aff);
3365 int isl_pw_aff_involves_nan(__isl_keep isl_pw_aff *pa);
3367 Check whether the given expression is equal to or involves NaN.
3369 #include <isl/aff.h>
3370 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3372 Check whether the affine expression is obviously zero.
3376 =head3 Binary Properties
3382 The following functions check whether two objects
3383 represent the same set, relation or function.
3384 The C<plain> variants only return true if the objects
3385 are obviously the same. That is, they may return false
3386 even if the objects are the same, but they will never
3387 return true if the objects are not the same.
3389 #include <isl/set.h>
3390 int isl_basic_set_plain_is_equal(
3391 __isl_keep isl_basic_set *bset1,
3392 __isl_keep isl_basic_set *bset2);
3393 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
3394 __isl_keep isl_set *set2);
3395 int isl_set_is_equal(__isl_keep isl_set *set1,
3396 __isl_keep isl_set *set2);
3398 #include <isl/map.h>
3399 int isl_basic_map_is_equal(
3400 __isl_keep isl_basic_map *bmap1,
3401 __isl_keep isl_basic_map *bmap2);
3402 int isl_map_is_equal(__isl_keep isl_map *map1,
3403 __isl_keep isl_map *map2);
3404 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
3405 __isl_keep isl_map *map2);
3407 #include <isl/union_set.h>
3408 int isl_union_set_is_equal(
3409 __isl_keep isl_union_set *uset1,
3410 __isl_keep isl_union_set *uset2);
3412 #include <isl/union_map.h>
3413 int isl_union_map_is_equal(
3414 __isl_keep isl_union_map *umap1,
3415 __isl_keep isl_union_map *umap2);
3417 #include <isl/aff.h>
3418 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3419 __isl_keep isl_aff *aff2);
3420 int isl_multi_aff_plain_is_equal(
3421 __isl_keep isl_multi_aff *maff1,
3422 __isl_keep isl_multi_aff *maff2);
3423 int isl_pw_aff_plain_is_equal(
3424 __isl_keep isl_pw_aff *pwaff1,
3425 __isl_keep isl_pw_aff *pwaff2);
3426 int isl_pw_multi_aff_plain_is_equal(
3427 __isl_keep isl_pw_multi_aff *pma1,
3428 __isl_keep isl_pw_multi_aff *pma2);
3429 int isl_multi_pw_aff_plain_is_equal(
3430 __isl_keep isl_multi_pw_aff *mpa1,
3431 __isl_keep isl_multi_pw_aff *mpa2);
3432 int isl_multi_pw_aff_is_equal(
3433 __isl_keep isl_multi_pw_aff *mpa1,
3434 __isl_keep isl_multi_pw_aff *mpa2);
3435 int isl_union_pw_multi_aff_plain_is_equal(
3436 __isl_keep isl_union_pw_multi_aff *upma1,
3437 __isl_keep isl_union_pw_multi_aff *upma2);
3439 #include <isl/polynomial.h>
3440 int isl_union_pw_qpolynomial_plain_is_equal(
3441 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3442 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3443 int isl_union_pw_qpolynomial_fold_plain_is_equal(
3444 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
3445 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
3447 =item * Disjointness
3449 int isl_basic_set_is_disjoint(
3450 __isl_keep isl_basic_set *bset1,
3451 __isl_keep isl_basic_set *bset2);
3452 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
3453 __isl_keep isl_set *set2);
3454 int isl_set_is_disjoint(__isl_keep isl_set *set1,
3455 __isl_keep isl_set *set2);
3456 int isl_basic_map_is_disjoint(
3457 __isl_keep isl_basic_map *bmap1,
3458 __isl_keep isl_basic_map *bmap2);
3459 int isl_map_is_disjoint(__isl_keep isl_map *map1,
3460 __isl_keep isl_map *map2);
3464 int isl_basic_set_is_subset(
3465 __isl_keep isl_basic_set *bset1,
3466 __isl_keep isl_basic_set *bset2);
3467 int isl_set_is_subset(__isl_keep isl_set *set1,
3468 __isl_keep isl_set *set2);
3469 int isl_set_is_strict_subset(
3470 __isl_keep isl_set *set1,
3471 __isl_keep isl_set *set2);
3472 int isl_union_set_is_subset(
3473 __isl_keep isl_union_set *uset1,
3474 __isl_keep isl_union_set *uset2);
3475 int isl_union_set_is_strict_subset(
3476 __isl_keep isl_union_set *uset1,
3477 __isl_keep isl_union_set *uset2);
3478 int isl_basic_map_is_subset(
3479 __isl_keep isl_basic_map *bmap1,
3480 __isl_keep isl_basic_map *bmap2);
3481 int isl_basic_map_is_strict_subset(
3482 __isl_keep isl_basic_map *bmap1,
3483 __isl_keep isl_basic_map *bmap2);
3484 int isl_map_is_subset(
3485 __isl_keep isl_map *map1,
3486 __isl_keep isl_map *map2);
3487 int isl_map_is_strict_subset(
3488 __isl_keep isl_map *map1,
3489 __isl_keep isl_map *map2);
3490 int isl_union_map_is_subset(
3491 __isl_keep isl_union_map *umap1,
3492 __isl_keep isl_union_map *umap2);
3493 int isl_union_map_is_strict_subset(
3494 __isl_keep isl_union_map *umap1,
3495 __isl_keep isl_union_map *umap2);
3497 Check whether the first argument is a (strict) subset of the
3502 Every comparison function returns a negative value if the first
3503 argument is considered smaller than the second, a positive value
3504 if the first argument is considered greater and zero if the two
3505 constraints are considered the same by the comparison criterion.
3507 #include <isl/constraint.h>
3508 int isl_constraint_plain_cmp(
3509 __isl_keep isl_constraint *c1,
3510 __isl_keep isl_constraint *c2);
3512 This function is useful for sorting C<isl_constraint>s.
3513 The order depends on the internal representation of the inputs.
3514 The order is fixed over different calls to the function (assuming
3515 the internal representation of the inputs has not changed), but may
3516 change over different versions of C<isl>.
3518 #include <isl/constraint.h>
3519 int isl_constraint_cmp_last_non_zero(
3520 __isl_keep isl_constraint *c1,
3521 __isl_keep isl_constraint *c2);
3523 This function can be used to sort constraints that live in the same
3524 local space. Constraints that involve ``earlier'' dimensions or
3525 that have a smaller coefficient for the shared latest dimension
3526 are considered smaller than other constraints.
3527 This function only defines a B<partial> order.
3529 #include <isl/set.h>
3530 int isl_set_plain_cmp(__isl_keep isl_set *set1,
3531 __isl_keep isl_set *set2);
3533 This function is useful for sorting C<isl_set>s.
3534 The order depends on the internal representation of the inputs.
3535 The order is fixed over different calls to the function (assuming
3536 the internal representation of the inputs has not changed), but may
3537 change over different versions of C<isl>.
3539 #include <isl/aff.h>
3540 int isl_pw_aff_plain_cmp(__isl_keep isl_pw_aff *pa1,
3541 __isl_keep isl_pw_aff *pa2);
3543 The function C<isl_pw_aff_plain_cmp> can be used to sort
3544 C<isl_pw_aff>s. The order is not strictly defined.
3545 The current order sorts expressions that only involve
3546 earlier dimensions before those that involve later dimensions.
3550 =head2 Unary Operations
3556 __isl_give isl_set *isl_set_complement(
3557 __isl_take isl_set *set);
3558 __isl_give isl_map *isl_map_complement(
3559 __isl_take isl_map *map);
3563 #include <isl/space.h>
3564 __isl_give isl_space *isl_space_reverse(
3565 __isl_take isl_space *space);
3567 #include <isl/map.h>
3568 __isl_give isl_basic_map *isl_basic_map_reverse(
3569 __isl_take isl_basic_map *bmap);
3570 __isl_give isl_map *isl_map_reverse(
3571 __isl_take isl_map *map);
3573 #include <isl/union_map.h>
3574 __isl_give isl_union_map *isl_union_map_reverse(
3575 __isl_take isl_union_map *umap);
3579 #include <isl/space.h>
3580 __isl_give isl_space *isl_space_domain(
3581 __isl_take isl_space *space);
3582 __isl_give isl_space *isl_space_range(
3583 __isl_take isl_space *space);
3584 __isl_give isl_space *isl_space_params(
3585 __isl_take isl_space *space);
3587 #include <isl/local_space.h>
3588 __isl_give isl_local_space *isl_local_space_domain(
3589 __isl_take isl_local_space *ls);
3590 __isl_give isl_local_space *isl_local_space_range(
3591 __isl_take isl_local_space *ls);
3593 #include <isl/set.h>
3594 __isl_give isl_basic_set *isl_basic_set_project_out(
3595 __isl_take isl_basic_set *bset,
3596 enum isl_dim_type type, unsigned first, unsigned n);
3597 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
3598 enum isl_dim_type type, unsigned first, unsigned n);
3599 __isl_give isl_basic_set *isl_basic_set_params(
3600 __isl_take isl_basic_set *bset);
3601 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
3603 #include <isl/map.h>
3604 __isl_give isl_basic_map *isl_basic_map_project_out(
3605 __isl_take isl_basic_map *bmap,
3606 enum isl_dim_type type, unsigned first, unsigned n);
3607 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
3608 enum isl_dim_type type, unsigned first, unsigned n);
3609 __isl_give isl_basic_set *isl_basic_map_domain(
3610 __isl_take isl_basic_map *bmap);
3611 __isl_give isl_basic_set *isl_basic_map_range(
3612 __isl_take isl_basic_map *bmap);
3613 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
3614 __isl_give isl_set *isl_map_domain(
3615 __isl_take isl_map *bmap);
3616 __isl_give isl_set *isl_map_range(
3617 __isl_take isl_map *map);
3619 #include <isl/union_set.h>
3620 __isl_give isl_set *isl_union_set_params(
3621 __isl_take isl_union_set *uset);
3623 #include <isl/union_map.h>
3624 __isl_give isl_union_map *isl_union_map_project_out(
3625 __isl_take isl_union_map *umap,
3626 enum isl_dim_type type, unsigned first, unsigned n);
3627 __isl_give isl_set *isl_union_map_params(
3628 __isl_take isl_union_map *umap);
3629 __isl_give isl_union_set *isl_union_map_domain(
3630 __isl_take isl_union_map *umap);
3631 __isl_give isl_union_set *isl_union_map_range(
3632 __isl_take isl_union_map *umap);
3634 The function C<isl_union_map_project_out> can only project out
3637 #include <isl/aff.h>
3638 __isl_give isl_aff *isl_aff_project_domain_on_params(
3639 __isl_take isl_aff *aff);
3640 __isl_give isl_pw_multi_aff *
3641 isl_pw_multi_aff_project_domain_on_params(
3642 __isl_take isl_pw_multi_aff *pma);
3643 __isl_give isl_set *isl_pw_aff_domain(
3644 __isl_take isl_pw_aff *pwaff);
3645 __isl_give isl_set *isl_pw_multi_aff_domain(
3646 __isl_take isl_pw_multi_aff *pma);
3647 __isl_give isl_set *isl_multi_pw_aff_domain(
3648 __isl_take isl_multi_pw_aff *mpa);
3649 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3650 __isl_take isl_union_pw_multi_aff *upma);
3651 __isl_give isl_set *isl_pw_aff_params(
3652 __isl_take isl_pw_aff *pwa);
3654 #include <isl/polynomial.h>
3655 __isl_give isl_qpolynomial *
3656 isl_qpolynomial_project_domain_on_params(
3657 __isl_take isl_qpolynomial *qp);
3658 __isl_give isl_pw_qpolynomial *
3659 isl_pw_qpolynomial_project_domain_on_params(
3660 __isl_take isl_pw_qpolynomial *pwqp);
3661 __isl_give isl_pw_qpolynomial_fold *
3662 isl_pw_qpolynomial_fold_project_domain_on_params(
3663 __isl_take isl_pw_qpolynomial_fold *pwf);
3664 __isl_give isl_set *isl_pw_qpolynomial_domain(
3665 __isl_take isl_pw_qpolynomial *pwqp);
3666 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
3667 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3668 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3669 __isl_take isl_union_pw_qpolynomial *upwqp);
3671 #include <isl/space.h>
3672 __isl_give isl_space *isl_space_domain_map(
3673 __isl_take isl_space *space);
3674 __isl_give isl_space *isl_space_range_map(
3675 __isl_take isl_space *space);
3677 #include <isl/map.h>
3678 __isl_give isl_basic_map *isl_basic_map_domain_map(
3679 __isl_take isl_basic_map *bmap);
3680 __isl_give isl_basic_map *isl_basic_map_range_map(
3681 __isl_take isl_basic_map *bmap);
3682 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
3683 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
3685 #include <isl/union_map.h>
3686 __isl_give isl_union_map *isl_union_map_domain_map(
3687 __isl_take isl_union_map *umap);
3688 __isl_give isl_union_map *isl_union_map_range_map(
3689 __isl_take isl_union_map *umap);
3691 The functions above construct a (basic, regular or union) relation
3692 that maps (a wrapped version of) the input relation to its domain or range.
3696 __isl_give isl_basic_set *isl_basic_set_eliminate(
3697 __isl_take isl_basic_set *bset,
3698 enum isl_dim_type type,
3699 unsigned first, unsigned n);
3700 __isl_give isl_set *isl_set_eliminate(
3701 __isl_take isl_set *set, enum isl_dim_type type,
3702 unsigned first, unsigned n);
3703 __isl_give isl_basic_map *isl_basic_map_eliminate(
3704 __isl_take isl_basic_map *bmap,
3705 enum isl_dim_type type,
3706 unsigned first, unsigned n);
3707 __isl_give isl_map *isl_map_eliminate(
3708 __isl_take isl_map *map, enum isl_dim_type type,
3709 unsigned first, unsigned n);
3711 Eliminate the coefficients for the given dimensions from the constraints,
3712 without removing the dimensions.
3714 =item * Constructing a set from a parameter domain
3716 A zero-dimensional space or (basic) set can be constructed
3717 on a given parameter domain using the following functions.
3719 #include <isl/space.h>
3720 __isl_give isl_space *isl_space_set_from_params(
3721 __isl_take isl_space *space);
3723 #include <isl/set.h>
3724 __isl_give isl_basic_set *isl_basic_set_from_params(
3725 __isl_take isl_basic_set *bset);
3726 __isl_give isl_set *isl_set_from_params(
3727 __isl_take isl_set *set);
3729 =item * Constructing a relation from a set
3731 Create a relation with the given set as domain or range.
3732 The range or domain of the created relation is a zero-dimensional
3733 flat anonymous space.
3735 #include <isl/space.h>
3736 __isl_give isl_space *isl_space_from_domain(
3737 __isl_take isl_space *space);
3738 __isl_give isl_space *isl_space_from_range(
3739 __isl_take isl_space *space);
3740 __isl_give isl_space *isl_space_map_from_set(
3741 __isl_take isl_space *space);
3742 __isl_give isl_space *isl_space_map_from_domain_and_range(
3743 __isl_take isl_space *domain,
3744 __isl_take isl_space *range);
3746 #include <isl/local_space.h>
3747 __isl_give isl_local_space *isl_local_space_from_domain(
3748 __isl_take isl_local_space *ls);
3750 #include <isl/map.h>
3751 __isl_give isl_map *isl_map_from_domain(
3752 __isl_take isl_set *set);
3753 __isl_give isl_map *isl_map_from_range(
3754 __isl_take isl_set *set);
3756 #include <isl/val.h>
3757 __isl_give isl_multi_val *isl_multi_val_from_range(
3758 __isl_take isl_multi_val *mv);
3760 #include <isl/aff.h>
3761 __isl_give isl_multi_aff *isl_multi_aff_from_range(
3762 __isl_take isl_multi_aff *ma);
3763 __isl_give isl_pw_aff *isl_pw_aff_from_range(
3764 __isl_take isl_pw_aff *pwa);
3765 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_range(
3766 __isl_take isl_multi_pw_aff *mpa);
3767 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3768 __isl_take isl_set *set);
3769 __isl_give isl_union_pw_multi_aff *
3770 isl_union_pw_multi_aff_from_domain(
3771 __isl_take isl_union_set *uset);
3775 #include <isl/set.h>
3776 __isl_give isl_basic_set *isl_basic_set_fix_si(
3777 __isl_take isl_basic_set *bset,
3778 enum isl_dim_type type, unsigned pos, int value);
3779 __isl_give isl_basic_set *isl_basic_set_fix_val(
3780 __isl_take isl_basic_set *bset,
3781 enum isl_dim_type type, unsigned pos,
3782 __isl_take isl_val *v);
3783 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
3784 enum isl_dim_type type, unsigned pos, int value);
3785 __isl_give isl_set *isl_set_fix_val(
3786 __isl_take isl_set *set,
3787 enum isl_dim_type type, unsigned pos,
3788 __isl_take isl_val *v);
3790 #include <isl/map.h>
3791 __isl_give isl_basic_map *isl_basic_map_fix_si(
3792 __isl_take isl_basic_map *bmap,
3793 enum isl_dim_type type, unsigned pos, int value);
3794 __isl_give isl_basic_map *isl_basic_map_fix_val(
3795 __isl_take isl_basic_map *bmap,
3796 enum isl_dim_type type, unsigned pos,
3797 __isl_take isl_val *v);
3798 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
3799 enum isl_dim_type type, unsigned pos, int value);
3800 __isl_give isl_map *isl_map_fix_val(
3801 __isl_take isl_map *map,
3802 enum isl_dim_type type, unsigned pos,
3803 __isl_take isl_val *v);
3805 #include <isl/aff.h>
3806 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_fix_si(
3807 __isl_take isl_pw_multi_aff *pma,
3808 enum isl_dim_type type, unsigned pos, int value);
3810 #include <isl/polynomial.h>
3811 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_fix_val(
3812 __isl_take isl_pw_qpolynomial *pwqp,
3813 enum isl_dim_type type, unsigned n,
3814 __isl_take isl_val *v);
3816 Intersect the set, relation or function domain
3817 with the hyperplane where the given
3818 dimension has the fixed given value.
3820 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
3821 __isl_take isl_basic_map *bmap,
3822 enum isl_dim_type type, unsigned pos, int value);
3823 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
3824 __isl_take isl_basic_map *bmap,
3825 enum isl_dim_type type, unsigned pos, int value);
3826 __isl_give isl_set *isl_set_lower_bound_si(
3827 __isl_take isl_set *set,
3828 enum isl_dim_type type, unsigned pos, int value);
3829 __isl_give isl_set *isl_set_lower_bound_val(
3830 __isl_take isl_set *set,
3831 enum isl_dim_type type, unsigned pos,
3832 __isl_take isl_val *value);
3833 __isl_give isl_map *isl_map_lower_bound_si(
3834 __isl_take isl_map *map,
3835 enum isl_dim_type type, unsigned pos, int value);
3836 __isl_give isl_set *isl_set_upper_bound_si(
3837 __isl_take isl_set *set,
3838 enum isl_dim_type type, unsigned pos, int value);
3839 __isl_give isl_set *isl_set_upper_bound_val(
3840 __isl_take isl_set *set,
3841 enum isl_dim_type type, unsigned pos,
3842 __isl_take isl_val *value);
3843 __isl_give isl_map *isl_map_upper_bound_si(
3844 __isl_take isl_map *map,
3845 enum isl_dim_type type, unsigned pos, int value);
3847 Intersect the set or relation with the half-space where the given
3848 dimension has a value bounded by the fixed given integer value.
3850 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
3851 enum isl_dim_type type1, int pos1,
3852 enum isl_dim_type type2, int pos2);
3853 __isl_give isl_basic_map *isl_basic_map_equate(
3854 __isl_take isl_basic_map *bmap,
3855 enum isl_dim_type type1, int pos1,
3856 enum isl_dim_type type2, int pos2);
3857 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
3858 enum isl_dim_type type1, int pos1,
3859 enum isl_dim_type type2, int pos2);
3861 Intersect the set or relation with the hyperplane where the given
3862 dimensions are equal to each other.
3864 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
3865 enum isl_dim_type type1, int pos1,
3866 enum isl_dim_type type2, int pos2);
3868 Intersect the relation with the hyperplane where the given
3869 dimensions have opposite values.
3871 __isl_give isl_map *isl_map_order_le(
3872 __isl_take isl_map *map,
3873 enum isl_dim_type type1, int pos1,
3874 enum isl_dim_type type2, int pos2);
3875 __isl_give isl_basic_map *isl_basic_map_order_ge(
3876 __isl_take isl_basic_map *bmap,
3877 enum isl_dim_type type1, int pos1,
3878 enum isl_dim_type type2, int pos2);
3879 __isl_give isl_map *isl_map_order_ge(
3880 __isl_take isl_map *map,
3881 enum isl_dim_type type1, int pos1,
3882 enum isl_dim_type type2, int pos2);
3883 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
3884 enum isl_dim_type type1, int pos1,
3885 enum isl_dim_type type2, int pos2);
3886 __isl_give isl_basic_map *isl_basic_map_order_gt(
3887 __isl_take isl_basic_map *bmap,
3888 enum isl_dim_type type1, int pos1,
3889 enum isl_dim_type type2, int pos2);
3890 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
3891 enum isl_dim_type type1, int pos1,
3892 enum isl_dim_type type2, int pos2);
3894 Intersect the relation with the half-space where the given
3895 dimensions satisfy the given ordering.
3899 #include <isl/aff.h>
3900 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3901 __isl_take isl_aff *aff);
3902 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3903 __isl_take isl_aff *aff);
3904 __isl_give isl_set *isl_pw_aff_nonneg_set(
3905 __isl_take isl_pw_aff *pwaff);
3906 __isl_give isl_set *isl_pw_aff_zero_set(
3907 __isl_take isl_pw_aff *pwaff);
3908 __isl_give isl_set *isl_pw_aff_non_zero_set(
3909 __isl_take isl_pw_aff *pwaff);
3911 The function C<isl_aff_neg_basic_set> returns a basic set
3912 containing those elements in the domain space
3913 of C<aff> where C<aff> is negative.
3914 The function C<isl_pw_aff_nonneg_set> returns a set
3915 containing those elements in the domain
3916 of C<pwaff> where C<pwaff> is non-negative.
3920 __isl_give isl_map *isl_set_identity(
3921 __isl_take isl_set *set);
3922 __isl_give isl_union_map *isl_union_set_identity(
3923 __isl_take isl_union_set *uset);
3925 Construct an identity relation on the given (union) set.
3927 =item * Function Extraction
3929 A piecewise quasi affine expression that is equal to 1 on a set
3930 and 0 outside the set can be created using the following function.
3932 #include <isl/aff.h>
3933 __isl_give isl_pw_aff *isl_set_indicator_function(
3934 __isl_take isl_set *set);
3936 A piecewise multiple quasi affine expression can be extracted
3937 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3938 and the C<isl_map> is single-valued.
3939 In case of a conversion from an C<isl_union_map>
3940 to an C<isl_union_pw_multi_aff>, these properties need to hold
3941 in each domain space.
3943 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3944 __isl_take isl_set *set);
3945 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3946 __isl_take isl_map *map);
3948 __isl_give isl_union_pw_multi_aff *
3949 isl_union_pw_multi_aff_from_union_set(
3950 __isl_take isl_union_set *uset);
3951 __isl_give isl_union_pw_multi_aff *
3952 isl_union_pw_multi_aff_from_union_map(
3953 __isl_take isl_union_map *umap);
3957 __isl_give isl_basic_set *isl_basic_map_deltas(
3958 __isl_take isl_basic_map *bmap);
3959 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
3960 __isl_give isl_union_set *isl_union_map_deltas(
3961 __isl_take isl_union_map *umap);
3963 These functions return a (basic) set containing the differences
3964 between image elements and corresponding domain elements in the input.
3966 __isl_give isl_basic_map *isl_basic_map_deltas_map(
3967 __isl_take isl_basic_map *bmap);
3968 __isl_give isl_map *isl_map_deltas_map(
3969 __isl_take isl_map *map);
3970 __isl_give isl_union_map *isl_union_map_deltas_map(
3971 __isl_take isl_union_map *umap);
3973 The functions above construct a (basic, regular or union) relation
3974 that maps (a wrapped version of) the input relation to its delta set.
3978 Simplify the representation of a set, relation or functions by trying
3979 to combine pairs of basic sets or relations into a single
3980 basic set or relation.
3982 #include <isl/set.h>
3983 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
3985 #include <isl/map.h>
3986 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
3988 #include <isl/union_set.h>
3989 __isl_give isl_union_set *isl_union_set_coalesce(
3990 __isl_take isl_union_set *uset);
3992 #include <isl/union_map.h>
3993 __isl_give isl_union_map *isl_union_map_coalesce(
3994 __isl_take isl_union_map *umap);
3996 #include <isl/aff.h>
3997 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3998 __isl_take isl_pw_aff *pwqp);
3999 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
4000 __isl_take isl_pw_multi_aff *pma);
4001 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_coalesce(
4002 __isl_take isl_multi_pw_aff *mpa);
4003 __isl_give isl_union_pw_multi_aff *
4004 isl_union_pw_multi_aff_coalesce(
4005 __isl_take isl_union_pw_multi_aff *upma);
4007 #include <isl/polynomial.h>
4008 __isl_give isl_pw_qpolynomial_fold *
4009 isl_pw_qpolynomial_fold_coalesce(
4010 __isl_take isl_pw_qpolynomial_fold *pwf);
4011 __isl_give isl_union_pw_qpolynomial *
4012 isl_union_pw_qpolynomial_coalesce(
4013 __isl_take isl_union_pw_qpolynomial *upwqp);
4014 __isl_give isl_union_pw_qpolynomial_fold *
4015 isl_union_pw_qpolynomial_fold_coalesce(
4016 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4018 One of the methods for combining pairs of basic sets or relations
4019 can result in coefficients that are much larger than those that appear
4020 in the constraints of the input. By default, the coefficients are
4021 not allowed to grow larger, but this can be changed by unsetting
4022 the following option.
4024 int isl_options_set_coalesce_bounded_wrapping(
4025 isl_ctx *ctx, int val);
4026 int isl_options_get_coalesce_bounded_wrapping(
4029 =item * Detecting equalities
4031 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
4032 __isl_take isl_basic_set *bset);
4033 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
4034 __isl_take isl_basic_map *bmap);
4035 __isl_give isl_set *isl_set_detect_equalities(
4036 __isl_take isl_set *set);
4037 __isl_give isl_map *isl_map_detect_equalities(
4038 __isl_take isl_map *map);
4039 __isl_give isl_union_set *isl_union_set_detect_equalities(
4040 __isl_take isl_union_set *uset);
4041 __isl_give isl_union_map *isl_union_map_detect_equalities(
4042 __isl_take isl_union_map *umap);
4044 Simplify the representation of a set or relation by detecting implicit
4047 =item * Removing redundant constraints
4049 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
4050 __isl_take isl_basic_set *bset);
4051 __isl_give isl_set *isl_set_remove_redundancies(
4052 __isl_take isl_set *set);
4053 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
4054 __isl_take isl_basic_map *bmap);
4055 __isl_give isl_map *isl_map_remove_redundancies(
4056 __isl_take isl_map *map);
4060 __isl_give isl_basic_set *isl_set_convex_hull(
4061 __isl_take isl_set *set);
4062 __isl_give isl_basic_map *isl_map_convex_hull(
4063 __isl_take isl_map *map);
4065 If the input set or relation has any existentially quantified
4066 variables, then the result of these operations is currently undefined.
4070 #include <isl/set.h>
4071 __isl_give isl_basic_set *
4072 isl_set_unshifted_simple_hull(
4073 __isl_take isl_set *set);
4074 __isl_give isl_basic_set *isl_set_simple_hull(
4075 __isl_take isl_set *set);
4076 __isl_give isl_basic_set *
4077 isl_set_unshifted_simple_hull_from_set_list(
4078 __isl_take isl_set *set,
4079 __isl_take isl_set_list *list);
4081 #include <isl/map.h>
4082 __isl_give isl_basic_map *
4083 isl_map_unshifted_simple_hull(
4084 __isl_take isl_map *map);
4085 __isl_give isl_basic_map *isl_map_simple_hull(
4086 __isl_take isl_map *map);
4088 #include <isl/union_map.h>
4089 __isl_give isl_union_map *isl_union_map_simple_hull(
4090 __isl_take isl_union_map *umap);
4092 These functions compute a single basic set or relation
4093 that contains the whole input set or relation.
4094 In particular, the output is described by translates
4095 of the constraints describing the basic sets or relations in the input.
4096 In case of C<isl_set_unshifted_simple_hull>, only the original
4097 constraints are used, without any translation.
4098 In case of C<isl_set_unshifted_simple_hull_from_set_list>, the
4099 constraints are taken from the elements of the second argument.
4103 (See \autoref{s:simple hull}.)
4109 __isl_give isl_basic_set *isl_basic_set_affine_hull(
4110 __isl_take isl_basic_set *bset);
4111 __isl_give isl_basic_set *isl_set_affine_hull(
4112 __isl_take isl_set *set);
4113 __isl_give isl_union_set *isl_union_set_affine_hull(
4114 __isl_take isl_union_set *uset);
4115 __isl_give isl_basic_map *isl_basic_map_affine_hull(
4116 __isl_take isl_basic_map *bmap);
4117 __isl_give isl_basic_map *isl_map_affine_hull(
4118 __isl_take isl_map *map);
4119 __isl_give isl_union_map *isl_union_map_affine_hull(
4120 __isl_take isl_union_map *umap);
4122 In case of union sets and relations, the affine hull is computed
4125 =item * Polyhedral hull
4127 __isl_give isl_basic_set *isl_set_polyhedral_hull(
4128 __isl_take isl_set *set);
4129 __isl_give isl_basic_map *isl_map_polyhedral_hull(
4130 __isl_take isl_map *map);
4131 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
4132 __isl_take isl_union_set *uset);
4133 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
4134 __isl_take isl_union_map *umap);
4136 These functions compute a single basic set or relation
4137 not involving any existentially quantified variables
4138 that contains the whole input set or relation.
4139 In case of union sets and relations, the polyhedral hull is computed
4142 =item * Other approximations
4144 #include <isl/set.h>
4145 __isl_give isl_basic_set *
4146 isl_basic_set_drop_constraints_involving_dims(
4147 __isl_take isl_basic_set *bset,
4148 enum isl_dim_type type,
4149 unsigned first, unsigned n);
4150 __isl_give isl_basic_set *
4151 isl_basic_set_drop_constraints_not_involving_dims(
4152 __isl_take isl_basic_set *bset,
4153 enum isl_dim_type type,
4154 unsigned first, unsigned n);
4155 __isl_give isl_set *
4156 isl_set_drop_constraints_involving_dims(
4157 __isl_take isl_set *set,
4158 enum isl_dim_type type,
4159 unsigned first, unsigned n);
4161 #include <isl/map.h>
4162 __isl_give isl_basic_map *
4163 isl_basic_map_drop_constraints_involving_dims(
4164 __isl_take isl_basic_map *bmap,
4165 enum isl_dim_type type,
4166 unsigned first, unsigned n);
4167 __isl_give isl_map *
4168 isl_map_drop_constraints_involving_dims(
4169 __isl_take isl_map *map,
4170 enum isl_dim_type type,
4171 unsigned first, unsigned n);
4173 These functions drop any constraints (not) involving the specified dimensions.
4174 Note that the result depends on the representation of the input.
4176 #include <isl/polynomial.h>
4177 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4178 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4179 __isl_give isl_union_pw_qpolynomial *
4180 isl_union_pw_qpolynomial_to_polynomial(
4181 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4183 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4184 the polynomial will be an overapproximation. If C<sign> is negative,
4185 it will be an underapproximation. If C<sign> is zero, the approximation
4186 will lie somewhere in between.
4190 __isl_give isl_basic_set *isl_basic_set_sample(
4191 __isl_take isl_basic_set *bset);
4192 __isl_give isl_basic_set *isl_set_sample(
4193 __isl_take isl_set *set);
4194 __isl_give isl_basic_map *isl_basic_map_sample(
4195 __isl_take isl_basic_map *bmap);
4196 __isl_give isl_basic_map *isl_map_sample(
4197 __isl_take isl_map *map);
4199 If the input (basic) set or relation is non-empty, then return
4200 a singleton subset of the input. Otherwise, return an empty set.
4202 =item * Optimization
4204 #include <isl/ilp.h>
4205 __isl_give isl_val *isl_basic_set_max_val(
4206 __isl_keep isl_basic_set *bset,
4207 __isl_keep isl_aff *obj);
4208 __isl_give isl_val *isl_set_min_val(
4209 __isl_keep isl_set *set,
4210 __isl_keep isl_aff *obj);
4211 __isl_give isl_val *isl_set_max_val(
4212 __isl_keep isl_set *set,
4213 __isl_keep isl_aff *obj);
4215 Compute the minimum or maximum of the integer affine expression C<obj>
4216 over the points in C<set>, returning the result in C<opt>.
4217 The result is C<NULL> in case of an error, the optimal value in case
4218 there is one, negative infinity or infinity if the problem is unbounded and
4219 NaN if the problem is empty.
4221 =item * Parametric optimization
4223 __isl_give isl_pw_aff *isl_set_dim_min(
4224 __isl_take isl_set *set, int pos);
4225 __isl_give isl_pw_aff *isl_set_dim_max(
4226 __isl_take isl_set *set, int pos);
4227 __isl_give isl_pw_aff *isl_map_dim_max(
4228 __isl_take isl_map *map, int pos);
4230 Compute the minimum or maximum of the given set or output dimension
4231 as a function of the parameters (and input dimensions), but independently
4232 of the other set or output dimensions.
4233 For lexicographic optimization, see L<"Lexicographic Optimization">.
4237 The following functions compute either the set of (rational) coefficient
4238 values of valid constraints for the given set or the set of (rational)
4239 values satisfying the constraints with coefficients from the given set.
4240 Internally, these two sets of functions perform essentially the
4241 same operations, except that the set of coefficients is assumed to
4242 be a cone, while the set of values may be any polyhedron.
4243 The current implementation is based on the Farkas lemma and
4244 Fourier-Motzkin elimination, but this may change or be made optional
4245 in future. In particular, future implementations may use different
4246 dualization algorithms or skip the elimination step.
4248 __isl_give isl_basic_set *isl_basic_set_coefficients(
4249 __isl_take isl_basic_set *bset);
4250 __isl_give isl_basic_set *isl_set_coefficients(
4251 __isl_take isl_set *set);
4252 __isl_give isl_union_set *isl_union_set_coefficients(
4253 __isl_take isl_union_set *bset);
4254 __isl_give isl_basic_set *isl_basic_set_solutions(
4255 __isl_take isl_basic_set *bset);
4256 __isl_give isl_basic_set *isl_set_solutions(
4257 __isl_take isl_set *set);
4258 __isl_give isl_union_set *isl_union_set_solutions(
4259 __isl_take isl_union_set *bset);
4263 __isl_give isl_map *isl_map_fixed_power_val(
4264 __isl_take isl_map *map,
4265 __isl_take isl_val *exp);
4266 __isl_give isl_union_map *
4267 isl_union_map_fixed_power_val(
4268 __isl_take isl_union_map *umap,
4269 __isl_take isl_val *exp);
4271 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
4272 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
4273 of C<map> is computed.
4275 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
4277 __isl_give isl_union_map *isl_union_map_power(
4278 __isl_take isl_union_map *umap, int *exact);
4280 Compute a parametric representation for all positive powers I<k> of C<map>.
4281 The result maps I<k> to a nested relation corresponding to the
4282 I<k>th power of C<map>.
4283 The result may be an overapproximation. If the result is known to be exact,
4284 then C<*exact> is set to C<1>.
4286 =item * Transitive closure
4288 __isl_give isl_map *isl_map_transitive_closure(
4289 __isl_take isl_map *map, int *exact);
4290 __isl_give isl_union_map *isl_union_map_transitive_closure(
4291 __isl_take isl_union_map *umap, int *exact);
4293 Compute the transitive closure of C<map>.
4294 The result may be an overapproximation. If the result is known to be exact,
4295 then C<*exact> is set to C<1>.
4297 =item * Reaching path lengths
4299 __isl_give isl_map *isl_map_reaching_path_lengths(
4300 __isl_take isl_map *map, int *exact);
4302 Compute a relation that maps each element in the range of C<map>
4303 to the lengths of all paths composed of edges in C<map> that
4304 end up in the given element.
4305 The result may be an overapproximation. If the result is known to be exact,
4306 then C<*exact> is set to C<1>.
4307 To compute the I<maximal> path length, the resulting relation
4308 should be postprocessed by C<isl_map_lexmax>.
4309 In particular, if the input relation is a dependence relation
4310 (mapping sources to sinks), then the maximal path length corresponds
4311 to the free schedule.
4312 Note, however, that C<isl_map_lexmax> expects the maximum to be
4313 finite, so if the path lengths are unbounded (possibly due to
4314 the overapproximation), then you will get an error message.
4318 #include <isl/space.h>
4319 __isl_give isl_space *isl_space_wrap(
4320 __isl_take isl_space *space);
4321 __isl_give isl_space *isl_space_unwrap(
4322 __isl_take isl_space *space);
4324 #include <isl/set.h>
4325 __isl_give isl_basic_map *isl_basic_set_unwrap(
4326 __isl_take isl_basic_set *bset);
4327 __isl_give isl_map *isl_set_unwrap(
4328 __isl_take isl_set *set);
4330 #include <isl/map.h>
4331 __isl_give isl_basic_set *isl_basic_map_wrap(
4332 __isl_take isl_basic_map *bmap);
4333 __isl_give isl_set *isl_map_wrap(
4334 __isl_take isl_map *map);
4336 #include <isl/union_set.h>
4337 __isl_give isl_union_map *isl_union_set_unwrap(
4338 __isl_take isl_union_set *uset);
4340 #include <isl/union_map.h>
4341 __isl_give isl_union_set *isl_union_map_wrap(
4342 __isl_take isl_union_map *umap);
4344 The input to C<isl_space_unwrap> should
4345 be the space of a set, while that of
4346 C<isl_space_wrap> should be the space of a relation.
4347 Conversely, the output of C<isl_space_unwrap> is the space
4348 of a relation, while that of C<isl_space_wrap> is the space of a set.
4352 Remove any internal structure of domain (and range) of the given
4353 set or relation. If there is any such internal structure in the input,
4354 then the name of the space is also removed.
4356 #include <isl/local_space.h>
4357 __isl_give isl_local_space *
4358 isl_local_space_flatten_domain(
4359 __isl_take isl_local_space *ls);
4360 __isl_give isl_local_space *
4361 isl_local_space_flatten_range(
4362 __isl_take isl_local_space *ls);
4364 #include <isl/set.h>
4365 __isl_give isl_basic_set *isl_basic_set_flatten(
4366 __isl_take isl_basic_set *bset);
4367 __isl_give isl_set *isl_set_flatten(
4368 __isl_take isl_set *set);
4370 #include <isl/map.h>
4371 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
4372 __isl_take isl_basic_map *bmap);
4373 __isl_give isl_basic_map *isl_basic_map_flatten_range(
4374 __isl_take isl_basic_map *bmap);
4375 __isl_give isl_map *isl_map_flatten_range(
4376 __isl_take isl_map *map);
4377 __isl_give isl_map *isl_map_flatten_domain(
4378 __isl_take isl_map *map);
4379 __isl_give isl_basic_map *isl_basic_map_flatten(
4380 __isl_take isl_basic_map *bmap);
4381 __isl_give isl_map *isl_map_flatten(
4382 __isl_take isl_map *map);
4384 #include <isl/val.h>
4385 __isl_give isl_multi_val *isl_multi_val_flatten_range(
4386 __isl_take isl_multi_val *mv);
4388 #include <isl/aff.h>
4389 __isl_give isl_multi_aff *isl_multi_aff_flatten_domain(
4390 __isl_take isl_multi_aff *ma);
4391 __isl_give isl_multi_aff *isl_multi_aff_flatten_range(
4392 __isl_take isl_multi_aff *ma);
4393 __isl_give isl_multi_pw_aff *
4394 isl_multi_pw_aff_flatten_range(
4395 __isl_take isl_multi_pw_aff *mpa);
4397 #include <isl/map.h>
4398 __isl_give isl_map *isl_set_flatten_map(
4399 __isl_take isl_set *set);
4401 The function above constructs a relation
4402 that maps the input set to a flattened version of the set.
4406 Lift the input set to a space with extra dimensions corresponding
4407 to the existentially quantified variables in the input.
4408 In particular, the result lives in a wrapped map where the domain
4409 is the original space and the range corresponds to the original
4410 existentially quantified variables.
4412 #include <isl/set.h>
4413 __isl_give isl_basic_set *isl_basic_set_lift(
4414 __isl_take isl_basic_set *bset);
4415 __isl_give isl_set *isl_set_lift(
4416 __isl_take isl_set *set);
4417 __isl_give isl_union_set *isl_union_set_lift(
4418 __isl_take isl_union_set *uset);
4420 Given a local space that contains the existentially quantified
4421 variables of a set, a basic relation that, when applied to
4422 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
4423 can be constructed using the following function.
4425 #include <isl/local_space.h>
4426 __isl_give isl_basic_map *isl_local_space_lifting(
4427 __isl_take isl_local_space *ls);
4429 #include <isl/aff.h>
4430 __isl_give isl_multi_aff *isl_multi_aff_lift(
4431 __isl_take isl_multi_aff *maff,
4432 __isl_give isl_local_space **ls);
4434 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4435 then it is assigned the local space that lies at the basis of
4436 the lifting applied.
4438 =item * Internal Product
4440 #include <isl/space.h>
4441 __isl_give isl_space *isl_space_zip(
4442 __isl_take isl_space *space);
4444 #include <isl/map.h>
4445 __isl_give isl_basic_map *isl_basic_map_zip(
4446 __isl_take isl_basic_map *bmap);
4447 __isl_give isl_map *isl_map_zip(
4448 __isl_take isl_map *map);
4450 #include <isl/union_map.h>
4451 __isl_give isl_union_map *isl_union_map_zip(
4452 __isl_take isl_union_map *umap);
4454 Given a relation with nested relations for domain and range,
4455 interchange the range of the domain with the domain of the range.
4459 #include <isl/space.h>
4460 __isl_give isl_space *isl_space_curry(
4461 __isl_take isl_space *space);
4462 __isl_give isl_space *isl_space_uncurry(
4463 __isl_take isl_space *space);
4465 #include <isl/map.h>
4466 __isl_give isl_basic_map *isl_basic_map_curry(
4467 __isl_take isl_basic_map *bmap);
4468 __isl_give isl_basic_map *isl_basic_map_uncurry(
4469 __isl_take isl_basic_map *bmap);
4470 __isl_give isl_map *isl_map_curry(
4471 __isl_take isl_map *map);
4472 __isl_give isl_map *isl_map_uncurry(
4473 __isl_take isl_map *map);
4475 #include <isl/union_map.h>
4476 __isl_give isl_union_map *isl_union_map_curry(
4477 __isl_take isl_union_map *umap);
4478 __isl_give isl_union_map *isl_union_map_uncurry(
4479 __isl_take isl_union_map *umap);
4481 Given a relation with a nested relation for domain,
4482 the C<curry> functions
4483 move the range of the nested relation out of the domain
4484 and use it as the domain of a nested relation in the range,
4485 with the original range as range of this nested relation.
4486 The C<uncurry> functions perform the inverse operation.
4488 =item * Aligning parameters
4490 Change the order of the parameters of the given set, relation
4492 such that the first parameters match those of C<model>.
4493 This may involve the introduction of extra parameters.
4494 All parameters need to be named.
4496 #include <isl/space.h>
4497 __isl_give isl_space *isl_space_align_params(
4498 __isl_take isl_space *space1,
4499 __isl_take isl_space *space2)
4501 #include <isl/set.h>
4502 __isl_give isl_basic_set *isl_basic_set_align_params(
4503 __isl_take isl_basic_set *bset,
4504 __isl_take isl_space *model);
4505 __isl_give isl_set *isl_set_align_params(
4506 __isl_take isl_set *set,
4507 __isl_take isl_space *model);
4509 #include <isl/map.h>
4510 __isl_give isl_basic_map *isl_basic_map_align_params(
4511 __isl_take isl_basic_map *bmap,
4512 __isl_take isl_space *model);
4513 __isl_give isl_map *isl_map_align_params(
4514 __isl_take isl_map *map,
4515 __isl_take isl_space *model);
4517 #include <isl/val.h>
4518 __isl_give isl_multi_val *isl_multi_val_align_params(
4519 __isl_take isl_multi_val *mv,
4520 __isl_take isl_space *model);
4522 #include <isl/aff.h>
4523 __isl_give isl_aff *isl_aff_align_params(
4524 __isl_take isl_aff *aff,
4525 __isl_take isl_space *model);
4526 __isl_give isl_multi_aff *isl_multi_aff_align_params(
4527 __isl_take isl_multi_aff *multi,
4528 __isl_take isl_space *model);
4529 __isl_give isl_pw_aff *isl_pw_aff_align_params(
4530 __isl_take isl_pw_aff *pwaff,
4531 __isl_take isl_space *model);
4532 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
4533 __isl_take isl_pw_multi_aff *pma,
4534 __isl_take isl_space *model);
4535 __isl_give isl_union_pw_multi_aff *
4536 isl_union_pw_multi_aff_align_params(
4537 __isl_take isl_union_pw_multi_aff *upma,
4538 __isl_take isl_space *model);
4540 #include <isl/polynomial.h>
4541 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4542 __isl_take isl_qpolynomial *qp,
4543 __isl_take isl_space *model);
4545 =item * Unary Arithmethic Operations
4547 #include <isl/aff.h>
4548 __isl_give isl_aff *isl_aff_neg(
4549 __isl_take isl_aff *aff);
4550 __isl_give isl_pw_aff *isl_pw_aff_neg(
4551 __isl_take isl_pw_aff *pwaff);
4552 __isl_give isl_aff *isl_aff_ceil(
4553 __isl_take isl_aff *aff);
4554 __isl_give isl_pw_aff *isl_pw_aff_ceil(
4555 __isl_take isl_pw_aff *pwaff);
4556 __isl_give isl_aff *isl_aff_floor(
4557 __isl_take isl_aff *aff);
4558 __isl_give isl_multi_aff *isl_multi_aff_floor(
4559 __isl_take isl_multi_aff *ma);
4560 __isl_give isl_pw_aff *isl_pw_aff_floor(
4561 __isl_take isl_pw_aff *pwaff);
4563 #include <isl/aff.h>
4564 __isl_give isl_pw_aff *isl_pw_aff_list_min(
4565 __isl_take isl_pw_aff_list *list);
4566 __isl_give isl_pw_aff *isl_pw_aff_list_max(
4567 __isl_take isl_pw_aff_list *list);
4569 #include <isl/polynomial.h>
4570 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4571 __isl_take isl_qpolynomial *qp);
4572 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4573 __isl_take isl_pw_qpolynomial *pwqp);
4574 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4575 __isl_take isl_qpolynomial *qp,
4577 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4578 __isl_take isl_pw_qpolynomial *pwqp,
4583 The following functions evaluate a function in a point.
4585 #include <isl/polynomial.h>
4586 __isl_give isl_val *isl_pw_qpolynomial_eval(
4587 __isl_take isl_pw_qpolynomial *pwqp,
4588 __isl_take isl_point *pnt);
4589 __isl_give isl_val *isl_pw_qpolynomial_fold_eval(
4590 __isl_take isl_pw_qpolynomial_fold *pwf,
4591 __isl_take isl_point *pnt);
4592 __isl_give isl_val *isl_union_pw_qpolynomial_eval(
4593 __isl_take isl_union_pw_qpolynomial *upwqp,
4594 __isl_take isl_point *pnt);
4595 __isl_give isl_val *isl_union_pw_qpolynomial_fold_eval(
4596 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4597 __isl_take isl_point *pnt);
4599 =item * Dimension manipulation
4601 It is usually not advisable to directly change the (input or output)
4602 space of a set or a relation as this removes the name and the internal
4603 structure of the space. However, the functions below can be useful
4604 to add new parameters, assuming
4605 C<isl_set_align_params> and C<isl_map_align_params>
4608 #include <isl/space.h>
4609 __isl_give isl_space *isl_space_add_dims(
4610 __isl_take isl_space *space,
4611 enum isl_dim_type type, unsigned n);
4612 __isl_give isl_space *isl_space_insert_dims(
4613 __isl_take isl_space *space,
4614 enum isl_dim_type type, unsigned pos, unsigned n);
4615 __isl_give isl_space *isl_space_drop_dims(
4616 __isl_take isl_space *space,
4617 enum isl_dim_type type, unsigned first, unsigned n);
4618 __isl_give isl_space *isl_space_move_dims(
4619 __isl_take isl_space *space,
4620 enum isl_dim_type dst_type, unsigned dst_pos,
4621 enum isl_dim_type src_type, unsigned src_pos,
4624 #include <isl/local_space.h>
4625 __isl_give isl_local_space *isl_local_space_add_dims(
4626 __isl_take isl_local_space *ls,
4627 enum isl_dim_type type, unsigned n);
4628 __isl_give isl_local_space *isl_local_space_insert_dims(
4629 __isl_take isl_local_space *ls,
4630 enum isl_dim_type type, unsigned first, unsigned n);
4631 __isl_give isl_local_space *isl_local_space_drop_dims(
4632 __isl_take isl_local_space *ls,
4633 enum isl_dim_type type, unsigned first, unsigned n);
4635 #include <isl/set.h>
4636 __isl_give isl_basic_set *isl_basic_set_add_dims(
4637 __isl_take isl_basic_set *bset,
4638 enum isl_dim_type type, unsigned n);
4639 __isl_give isl_set *isl_set_add_dims(
4640 __isl_take isl_set *set,
4641 enum isl_dim_type type, unsigned n);
4642 __isl_give isl_basic_set *isl_basic_set_insert_dims(
4643 __isl_take isl_basic_set *bset,
4644 enum isl_dim_type type, unsigned pos,
4646 __isl_give isl_set *isl_set_insert_dims(
4647 __isl_take isl_set *set,
4648 enum isl_dim_type type, unsigned pos, unsigned n);
4649 __isl_give isl_basic_set *isl_basic_set_move_dims(
4650 __isl_take isl_basic_set *bset,
4651 enum isl_dim_type dst_type, unsigned dst_pos,
4652 enum isl_dim_type src_type, unsigned src_pos,
4654 __isl_give isl_set *isl_set_move_dims(
4655 __isl_take isl_set *set,
4656 enum isl_dim_type dst_type, unsigned dst_pos,
4657 enum isl_dim_type src_type, unsigned src_pos,
4660 #include <isl/map.h>
4661 __isl_give isl_map *isl_map_add_dims(
4662 __isl_take isl_map *map,
4663 enum isl_dim_type type, unsigned n);
4664 __isl_give isl_basic_map *isl_basic_map_insert_dims(
4665 __isl_take isl_basic_map *bmap,
4666 enum isl_dim_type type, unsigned pos,
4668 __isl_give isl_map *isl_map_insert_dims(
4669 __isl_take isl_map *map,
4670 enum isl_dim_type type, unsigned pos, unsigned n);
4671 __isl_give isl_basic_map *isl_basic_map_move_dims(
4672 __isl_take isl_basic_map *bmap,
4673 enum isl_dim_type dst_type, unsigned dst_pos,
4674 enum isl_dim_type src_type, unsigned src_pos,
4676 __isl_give isl_map *isl_map_move_dims(
4677 __isl_take isl_map *map,
4678 enum isl_dim_type dst_type, unsigned dst_pos,
4679 enum isl_dim_type src_type, unsigned src_pos,
4682 #include <isl/val.h>
4683 __isl_give isl_multi_val *isl_multi_val_insert_dims(
4684 __isl_take isl_multi_val *mv,
4685 enum isl_dim_type type, unsigned first, unsigned n);
4686 __isl_give isl_multi_val *isl_multi_val_add_dims(
4687 __isl_take isl_multi_val *mv,
4688 enum isl_dim_type type, unsigned n);
4689 __isl_give isl_multi_val *isl_multi_val_drop_dims(
4690 __isl_take isl_multi_val *mv,
4691 enum isl_dim_type type, unsigned first, unsigned n);
4693 #include <isl/aff.h>
4694 __isl_give isl_aff *isl_aff_insert_dims(
4695 __isl_take isl_aff *aff,
4696 enum isl_dim_type type, unsigned first, unsigned n);
4697 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
4698 __isl_take isl_multi_aff *ma,
4699 enum isl_dim_type type, unsigned first, unsigned n);
4700 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
4701 __isl_take isl_pw_aff *pwaff,
4702 enum isl_dim_type type, unsigned first, unsigned n);
4703 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
4704 __isl_take isl_multi_pw_aff *mpa,
4705 enum isl_dim_type type, unsigned first, unsigned n);
4706 __isl_give isl_aff *isl_aff_add_dims(
4707 __isl_take isl_aff *aff,
4708 enum isl_dim_type type, unsigned n);
4709 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
4710 __isl_take isl_multi_aff *ma,
4711 enum isl_dim_type type, unsigned n);
4712 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
4713 __isl_take isl_pw_aff *pwaff,
4714 enum isl_dim_type type, unsigned n);
4715 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
4716 __isl_take isl_multi_pw_aff *mpa,
4717 enum isl_dim_type type, unsigned n);
4718 __isl_give isl_aff *isl_aff_drop_dims(
4719 __isl_take isl_aff *aff,
4720 enum isl_dim_type type, unsigned first, unsigned n);
4721 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
4722 __isl_take isl_multi_aff *maff,
4723 enum isl_dim_type type, unsigned first, unsigned n);
4724 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
4725 __isl_take isl_pw_aff *pwaff,
4726 enum isl_dim_type type, unsigned first, unsigned n);
4727 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
4728 __isl_take isl_pw_multi_aff *pma,
4729 enum isl_dim_type type, unsigned first, unsigned n);
4730 __isl_give isl_aff *isl_aff_move_dims(
4731 __isl_take isl_aff *aff,
4732 enum isl_dim_type dst_type, unsigned dst_pos,
4733 enum isl_dim_type src_type, unsigned src_pos,
4735 __isl_give isl_multi_aff *isl_multi_aff_move_dims(
4736 __isl_take isl_multi_aff *ma,
4737 enum isl_dim_type dst_type, unsigned dst_pos,
4738 enum isl_dim_type src_type, unsigned src_pos,
4740 __isl_give isl_pw_aff *isl_pw_aff_move_dims(
4741 __isl_take isl_pw_aff *pa,
4742 enum isl_dim_type dst_type, unsigned dst_pos,
4743 enum isl_dim_type src_type, unsigned src_pos,
4745 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_move_dims(
4746 __isl_take isl_multi_pw_aff *pma,
4747 enum isl_dim_type dst_type, unsigned dst_pos,
4748 enum isl_dim_type src_type, unsigned src_pos,
4753 =head2 Binary Operations
4755 The two arguments of a binary operation not only need to live
4756 in the same C<isl_ctx>, they currently also need to have
4757 the same (number of) parameters.
4759 =head3 Basic Operations
4763 =item * Intersection
4765 #include <isl/local_space.h>
4766 __isl_give isl_local_space *isl_local_space_intersect(
4767 __isl_take isl_local_space *ls1,
4768 __isl_take isl_local_space *ls2);
4770 #include <isl/set.h>
4771 __isl_give isl_basic_set *isl_basic_set_intersect_params(
4772 __isl_take isl_basic_set *bset1,
4773 __isl_take isl_basic_set *bset2);
4774 __isl_give isl_basic_set *isl_basic_set_intersect(
4775 __isl_take isl_basic_set *bset1,
4776 __isl_take isl_basic_set *bset2);
4777 __isl_give isl_basic_set *isl_basic_set_list_intersect(
4778 __isl_take struct isl_basic_set_list *list);
4779 __isl_give isl_set *isl_set_intersect_params(
4780 __isl_take isl_set *set,
4781 __isl_take isl_set *params);
4782 __isl_give isl_set *isl_set_intersect(
4783 __isl_take isl_set *set1,
4784 __isl_take isl_set *set2);
4786 #include <isl/map.h>
4787 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
4788 __isl_take isl_basic_map *bmap,
4789 __isl_take isl_basic_set *bset);
4790 __isl_give isl_basic_map *isl_basic_map_intersect_range(
4791 __isl_take isl_basic_map *bmap,
4792 __isl_take isl_basic_set *bset);
4793 __isl_give isl_basic_map *isl_basic_map_intersect(
4794 __isl_take isl_basic_map *bmap1,
4795 __isl_take isl_basic_map *bmap2);
4796 __isl_give isl_map *isl_map_intersect_params(
4797 __isl_take isl_map *map,
4798 __isl_take isl_set *params);
4799 __isl_give isl_map *isl_map_intersect_domain(
4800 __isl_take isl_map *map,
4801 __isl_take isl_set *set);
4802 __isl_give isl_map *isl_map_intersect_range(
4803 __isl_take isl_map *map,
4804 __isl_take isl_set *set);
4805 __isl_give isl_map *isl_map_intersect(
4806 __isl_take isl_map *map1,
4807 __isl_take isl_map *map2);
4809 #include <isl/union_set.h>
4810 __isl_give isl_union_set *isl_union_set_intersect_params(
4811 __isl_take isl_union_set *uset,
4812 __isl_take isl_set *set);
4813 __isl_give isl_union_set *isl_union_set_intersect(
4814 __isl_take isl_union_set *uset1,
4815 __isl_take isl_union_set *uset2);
4817 #include <isl/union_map.h>
4818 __isl_give isl_union_map *isl_union_map_intersect_params(
4819 __isl_take isl_union_map *umap,
4820 __isl_take isl_set *set);
4821 __isl_give isl_union_map *isl_union_map_intersect_domain(
4822 __isl_take isl_union_map *umap,
4823 __isl_take isl_union_set *uset);
4824 __isl_give isl_union_map *isl_union_map_intersect_range(
4825 __isl_take isl_union_map *umap,
4826 __isl_take isl_union_set *uset);
4827 __isl_give isl_union_map *isl_union_map_intersect(
4828 __isl_take isl_union_map *umap1,
4829 __isl_take isl_union_map *umap2);
4831 #include <isl/aff.h>
4832 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
4833 __isl_take isl_pw_aff *pa,
4834 __isl_take isl_set *set);
4835 __isl_give isl_multi_pw_aff *
4836 isl_multi_pw_aff_intersect_domain(
4837 __isl_take isl_multi_pw_aff *mpa,
4838 __isl_take isl_set *domain);
4839 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
4840 __isl_take isl_pw_multi_aff *pma,
4841 __isl_take isl_set *set);
4842 __isl_give isl_union_pw_multi_aff *
4843 isl_union_pw_multi_aff_intersect_domain(
4844 __isl_take isl_union_pw_multi_aff *upma,
4845 __isl_take isl_union_set *uset);
4846 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
4847 __isl_take isl_pw_aff *pa,
4848 __isl_take isl_set *set);
4849 __isl_give isl_multi_pw_aff *
4850 isl_multi_pw_aff_intersect_params(
4851 __isl_take isl_multi_pw_aff *mpa,
4852 __isl_take isl_set *set);
4853 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
4854 __isl_take isl_pw_multi_aff *pma,
4855 __isl_take isl_set *set);
4857 #include <isl/polynomial.h>
4858 __isl_give isl_pw_qpolynomial *
4859 isl_pw_qpolynomial_intersect_domain(
4860 __isl_take isl_pw_qpolynomial *pwpq,
4861 __isl_take isl_set *set);
4862 __isl_give isl_union_pw_qpolynomial *
4863 isl_union_pw_qpolynomial_intersect_domain(
4864 __isl_take isl_union_pw_qpolynomial *upwpq,
4865 __isl_take isl_union_set *uset);
4866 __isl_give isl_union_pw_qpolynomial_fold *
4867 isl_union_pw_qpolynomial_fold_intersect_domain(
4868 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4869 __isl_take isl_union_set *uset);
4870 __isl_give isl_pw_qpolynomial *
4871 isl_pw_qpolynomial_intersect_params(
4872 __isl_take isl_pw_qpolynomial *pwpq,
4873 __isl_take isl_set *set);
4874 __isl_give isl_pw_qpolynomial_fold *
4875 isl_pw_qpolynomial_fold_intersect_params(
4876 __isl_take isl_pw_qpolynomial_fold *pwf,
4877 __isl_take isl_set *set);
4878 __isl_give isl_union_pw_qpolynomial *
4879 isl_union_pw_qpolynomial_intersect_params(
4880 __isl_take isl_union_pw_qpolynomial *upwpq,
4881 __isl_take isl_set *set);
4882 __isl_give isl_union_pw_qpolynomial_fold *
4883 isl_union_pw_qpolynomial_fold_intersect_params(
4884 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4885 __isl_take isl_set *set);
4887 The second argument to the C<_params> functions needs to be
4888 a parametric (basic) set. For the other functions, a parametric set
4889 for either argument is only allowed if the other argument is
4890 a parametric set as well.
4891 The list passed to C<isl_basic_set_list_intersect> needs to have
4892 at least one element and all elements need to live in the same space.
4896 __isl_give isl_set *isl_basic_set_union(
4897 __isl_take isl_basic_set *bset1,
4898 __isl_take isl_basic_set *bset2);
4899 __isl_give isl_map *isl_basic_map_union(
4900 __isl_take isl_basic_map *bmap1,
4901 __isl_take isl_basic_map *bmap2);
4902 __isl_give isl_set *isl_set_union(
4903 __isl_take isl_set *set1,
4904 __isl_take isl_set *set2);
4905 __isl_give isl_map *isl_map_union(
4906 __isl_take isl_map *map1,
4907 __isl_take isl_map *map2);
4908 __isl_give isl_union_set *isl_union_set_union(
4909 __isl_take isl_union_set *uset1,
4910 __isl_take isl_union_set *uset2);
4911 __isl_give isl_union_map *isl_union_map_union(
4912 __isl_take isl_union_map *umap1,
4913 __isl_take isl_union_map *umap2);
4915 =item * Set difference
4917 __isl_give isl_set *isl_set_subtract(
4918 __isl_take isl_set *set1,
4919 __isl_take isl_set *set2);
4920 __isl_give isl_map *isl_map_subtract(
4921 __isl_take isl_map *map1,
4922 __isl_take isl_map *map2);
4923 __isl_give isl_map *isl_map_subtract_domain(
4924 __isl_take isl_map *map,
4925 __isl_take isl_set *dom);
4926 __isl_give isl_map *isl_map_subtract_range(
4927 __isl_take isl_map *map,
4928 __isl_take isl_set *dom);
4929 __isl_give isl_union_set *isl_union_set_subtract(
4930 __isl_take isl_union_set *uset1,
4931 __isl_take isl_union_set *uset2);
4932 __isl_give isl_union_map *isl_union_map_subtract(
4933 __isl_take isl_union_map *umap1,
4934 __isl_take isl_union_map *umap2);
4935 __isl_give isl_union_map *isl_union_map_subtract_domain(
4936 __isl_take isl_union_map *umap,
4937 __isl_take isl_union_set *dom);
4938 __isl_give isl_union_map *isl_union_map_subtract_range(
4939 __isl_take isl_union_map *umap,
4940 __isl_take isl_union_set *dom);
4944 #include <isl/space.h>
4945 __isl_give isl_space *isl_space_join(
4946 __isl_take isl_space *left,
4947 __isl_take isl_space *right);
4949 #include <isl/map.h>
4950 __isl_give isl_basic_set *isl_basic_set_apply(
4951 __isl_take isl_basic_set *bset,
4952 __isl_take isl_basic_map *bmap);
4953 __isl_give isl_set *isl_set_apply(
4954 __isl_take isl_set *set,
4955 __isl_take isl_map *map);
4956 __isl_give isl_union_set *isl_union_set_apply(
4957 __isl_take isl_union_set *uset,
4958 __isl_take isl_union_map *umap);
4959 __isl_give isl_basic_map *isl_basic_map_apply_domain(
4960 __isl_take isl_basic_map *bmap1,
4961 __isl_take isl_basic_map *bmap2);
4962 __isl_give isl_basic_map *isl_basic_map_apply_range(
4963 __isl_take isl_basic_map *bmap1,
4964 __isl_take isl_basic_map *bmap2);
4965 __isl_give isl_map *isl_map_apply_domain(
4966 __isl_take isl_map *map1,
4967 __isl_take isl_map *map2);
4968 __isl_give isl_map *isl_map_apply_range(
4969 __isl_take isl_map *map1,
4970 __isl_take isl_map *map2);
4972 #include <isl/union_map.h>
4973 __isl_give isl_union_map *isl_union_map_apply_domain(
4974 __isl_take isl_union_map *umap1,
4975 __isl_take isl_union_map *umap2);
4976 __isl_give isl_union_map *isl_union_map_apply_range(
4977 __isl_take isl_union_map *umap1,
4978 __isl_take isl_union_map *umap2);
4980 #include <isl/polynomial.h>
4981 __isl_give isl_pw_qpolynomial_fold *
4982 isl_set_apply_pw_qpolynomial_fold(
4983 __isl_take isl_set *set,
4984 __isl_take isl_pw_qpolynomial_fold *pwf,
4986 __isl_give isl_pw_qpolynomial_fold *
4987 isl_map_apply_pw_qpolynomial_fold(
4988 __isl_take isl_map *map,
4989 __isl_take isl_pw_qpolynomial_fold *pwf,
4991 __isl_give isl_union_pw_qpolynomial_fold *
4992 isl_union_set_apply_union_pw_qpolynomial_fold(
4993 __isl_take isl_union_set *uset,
4994 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4996 __isl_give isl_union_pw_qpolynomial_fold *
4997 isl_union_map_apply_union_pw_qpolynomial_fold(
4998 __isl_take isl_union_map *umap,
4999 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5002 The functions taking a map
5003 compose the given map with the given piecewise quasipolynomial reduction.
5004 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
5005 over all elements in the intersection of the range of the map
5006 and the domain of the piecewise quasipolynomial reduction
5007 as a function of an element in the domain of the map.
5008 The functions taking a set compute a bound over all elements in the
5009 intersection of the set and the domain of the
5010 piecewise quasipolynomial reduction.
5014 #include <isl/set.h>
5015 __isl_give isl_basic_set *
5016 isl_basic_set_preimage_multi_aff(
5017 __isl_take isl_basic_set *bset,
5018 __isl_take isl_multi_aff *ma);
5019 __isl_give isl_set *isl_set_preimage_multi_aff(
5020 __isl_take isl_set *set,
5021 __isl_take isl_multi_aff *ma);
5022 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
5023 __isl_take isl_set *set,
5024 __isl_take isl_pw_multi_aff *pma);
5025 __isl_give isl_set *isl_set_preimage_multi_pw_aff(
5026 __isl_take isl_set *set,
5027 __isl_take isl_multi_pw_aff *mpa);
5029 #include <isl/union_set.h>
5030 __isl_give isl_union_set *
5031 isl_union_set_preimage_multi_aff(
5032 __isl_take isl_union_set *uset,
5033 __isl_take isl_multi_aff *ma);
5034 __isl_give isl_union_set *
5035 isl_union_set_preimage_pw_multi_aff(
5036 __isl_take isl_union_set *uset,
5037 __isl_take isl_pw_multi_aff *pma);
5038 __isl_give isl_union_set *
5039 isl_union_set_preimage_union_pw_multi_aff(
5040 __isl_take isl_union_set *uset,
5041 __isl_take isl_union_pw_multi_aff *upma);
5043 #include <isl/map.h>
5044 __isl_give isl_basic_map *
5045 isl_basic_map_preimage_domain_multi_aff(
5046 __isl_take isl_basic_map *bmap,
5047 __isl_take isl_multi_aff *ma);
5048 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
5049 __isl_take isl_map *map,
5050 __isl_take isl_multi_aff *ma);
5051 __isl_give isl_map *isl_map_preimage_range_multi_aff(
5052 __isl_take isl_map *map,
5053 __isl_take isl_multi_aff *ma);
5054 __isl_give isl_map *
5055 isl_map_preimage_domain_pw_multi_aff(
5056 __isl_take isl_map *map,
5057 __isl_take isl_pw_multi_aff *pma);
5058 __isl_give isl_map *
5059 isl_map_preimage_range_pw_multi_aff(
5060 __isl_take isl_map *map,
5061 __isl_take isl_pw_multi_aff *pma);
5062 __isl_give isl_map *
5063 isl_map_preimage_domain_multi_pw_aff(
5064 __isl_take isl_map *map,
5065 __isl_take isl_multi_pw_aff *mpa);
5066 __isl_give isl_basic_map *
5067 isl_basic_map_preimage_range_multi_aff(
5068 __isl_take isl_basic_map *bmap,
5069 __isl_take isl_multi_aff *ma);
5071 #include <isl/union_map.h>
5072 __isl_give isl_union_map *
5073 isl_union_map_preimage_domain_multi_aff(
5074 __isl_take isl_union_map *umap,
5075 __isl_take isl_multi_aff *ma);
5076 __isl_give isl_union_map *
5077 isl_union_map_preimage_range_multi_aff(
5078 __isl_take isl_union_map *umap,
5079 __isl_take isl_multi_aff *ma);
5080 __isl_give isl_union_map *
5081 isl_union_map_preimage_domain_pw_multi_aff(
5082 __isl_take isl_union_map *umap,
5083 __isl_take isl_pw_multi_aff *pma);
5084 __isl_give isl_union_map *
5085 isl_union_map_preimage_range_pw_multi_aff(
5086 __isl_take isl_union_map *umap,
5087 __isl_take isl_pw_multi_aff *pma);
5088 __isl_give isl_union_map *
5089 isl_union_map_preimage_domain_union_pw_multi_aff(
5090 __isl_take isl_union_map *umap,
5091 __isl_take isl_union_pw_multi_aff *upma);
5092 __isl_give isl_union_map *
5093 isl_union_map_preimage_range_union_pw_multi_aff(
5094 __isl_take isl_union_map *umap,
5095 __isl_take isl_union_pw_multi_aff *upma);
5097 These functions compute the preimage of the given set or map domain/range under
5098 the given function. In other words, the expression is plugged
5099 into the set description or into the domain/range of the map.
5103 #include <isl/aff.h>
5104 __isl_give isl_aff *isl_aff_pullback_aff(
5105 __isl_take isl_aff *aff1,
5106 __isl_take isl_aff *aff2);
5107 __isl_give isl_aff *isl_aff_pullback_multi_aff(
5108 __isl_take isl_aff *aff,
5109 __isl_take isl_multi_aff *ma);
5110 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
5111 __isl_take isl_pw_aff *pa,
5112 __isl_take isl_multi_aff *ma);
5113 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
5114 __isl_take isl_pw_aff *pa,
5115 __isl_take isl_pw_multi_aff *pma);
5116 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_pw_aff(
5117 __isl_take isl_pw_aff *pa,
5118 __isl_take isl_multi_pw_aff *mpa);
5119 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
5120 __isl_take isl_multi_aff *ma1,
5121 __isl_take isl_multi_aff *ma2);
5122 __isl_give isl_pw_multi_aff *
5123 isl_pw_multi_aff_pullback_multi_aff(
5124 __isl_take isl_pw_multi_aff *pma,
5125 __isl_take isl_multi_aff *ma);
5126 __isl_give isl_multi_pw_aff *
5127 isl_multi_pw_aff_pullback_multi_aff(
5128 __isl_take isl_multi_pw_aff *mpa,
5129 __isl_take isl_multi_aff *ma);
5130 __isl_give isl_pw_multi_aff *
5131 isl_pw_multi_aff_pullback_pw_multi_aff(
5132 __isl_take isl_pw_multi_aff *pma1,
5133 __isl_take isl_pw_multi_aff *pma2);
5134 __isl_give isl_multi_pw_aff *
5135 isl_multi_pw_aff_pullback_pw_multi_aff(
5136 __isl_take isl_multi_pw_aff *mpa,
5137 __isl_take isl_pw_multi_aff *pma);
5138 __isl_give isl_multi_pw_aff *
5139 isl_multi_pw_aff_pullback_multi_pw_aff(
5140 __isl_take isl_multi_pw_aff *mpa1,
5141 __isl_take isl_multi_pw_aff *mpa2);
5143 These functions precompose the first expression by the second function.
5144 In other words, the second function is plugged
5145 into the first expression.
5149 #include <isl/aff.h>
5150 __isl_give isl_basic_set *isl_aff_le_basic_set(
5151 __isl_take isl_aff *aff1,
5152 __isl_take isl_aff *aff2);
5153 __isl_give isl_basic_set *isl_aff_ge_basic_set(
5154 __isl_take isl_aff *aff1,
5155 __isl_take isl_aff *aff2);
5156 __isl_give isl_set *isl_pw_aff_eq_set(
5157 __isl_take isl_pw_aff *pwaff1,
5158 __isl_take isl_pw_aff *pwaff2);
5159 __isl_give isl_set *isl_pw_aff_ne_set(
5160 __isl_take isl_pw_aff *pwaff1,
5161 __isl_take isl_pw_aff *pwaff2);
5162 __isl_give isl_set *isl_pw_aff_le_set(
5163 __isl_take isl_pw_aff *pwaff1,
5164 __isl_take isl_pw_aff *pwaff2);
5165 __isl_give isl_set *isl_pw_aff_lt_set(
5166 __isl_take isl_pw_aff *pwaff1,
5167 __isl_take isl_pw_aff *pwaff2);
5168 __isl_give isl_set *isl_pw_aff_ge_set(
5169 __isl_take isl_pw_aff *pwaff1,
5170 __isl_take isl_pw_aff *pwaff2);
5171 __isl_give isl_set *isl_pw_aff_gt_set(
5172 __isl_take isl_pw_aff *pwaff1,
5173 __isl_take isl_pw_aff *pwaff2);
5175 __isl_give isl_set *isl_multi_aff_lex_le_set(
5176 __isl_take isl_multi_aff *ma1,
5177 __isl_take isl_multi_aff *ma2);
5178 __isl_give isl_set *isl_multi_aff_lex_ge_set(
5179 __isl_take isl_multi_aff *ma1,
5180 __isl_take isl_multi_aff *ma2);
5182 __isl_give isl_set *isl_pw_aff_list_eq_set(
5183 __isl_take isl_pw_aff_list *list1,
5184 __isl_take isl_pw_aff_list *list2);
5185 __isl_give isl_set *isl_pw_aff_list_ne_set(
5186 __isl_take isl_pw_aff_list *list1,
5187 __isl_take isl_pw_aff_list *list2);
5188 __isl_give isl_set *isl_pw_aff_list_le_set(
5189 __isl_take isl_pw_aff_list *list1,
5190 __isl_take isl_pw_aff_list *list2);
5191 __isl_give isl_set *isl_pw_aff_list_lt_set(
5192 __isl_take isl_pw_aff_list *list1,
5193 __isl_take isl_pw_aff_list *list2);
5194 __isl_give isl_set *isl_pw_aff_list_ge_set(
5195 __isl_take isl_pw_aff_list *list1,
5196 __isl_take isl_pw_aff_list *list2);
5197 __isl_give isl_set *isl_pw_aff_list_gt_set(
5198 __isl_take isl_pw_aff_list *list1,
5199 __isl_take isl_pw_aff_list *list2);
5201 The function C<isl_aff_ge_basic_set> returns a basic set
5202 containing those elements in the shared space
5203 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
5204 The function C<isl_pw_aff_ge_set> returns a set
5205 containing those elements in the shared domain
5206 of C<pwaff1> and C<pwaff2> where C<pwaff1> is
5207 greater than or equal to C<pwaff2>.
5208 The function C<isl_multi_aff_lex_le_set> returns a set
5209 containing those elements in the shared domain space
5210 where C<ma1> is lexicographically smaller than or
5212 The functions operating on C<isl_pw_aff_list> apply the corresponding
5213 C<isl_pw_aff> function to each pair of elements in the two lists.
5215 =item * Cartesian Product
5217 #include <isl/space.h>
5218 __isl_give isl_space *isl_space_product(
5219 __isl_take isl_space *space1,
5220 __isl_take isl_space *space2);
5221 __isl_give isl_space *isl_space_domain_product(
5222 __isl_take isl_space *space1,
5223 __isl_take isl_space *space2);
5224 __isl_give isl_space *isl_space_range_product(
5225 __isl_take isl_space *space1,
5226 __isl_take isl_space *space2);
5229 C<isl_space_product>, C<isl_space_domain_product>
5230 and C<isl_space_range_product> take pairs or relation spaces and
5231 produce a single relations space, where either the domain, the range
5232 or both domain and range are wrapped spaces of relations between
5233 the domains and/or ranges of the input spaces.
5234 If the product is only constructed over the domain or the range
5235 then the ranges or the domains of the inputs should be the same.
5236 The function C<isl_space_product> also accepts a pair of set spaces,
5237 in which case it returns a wrapped space of a relation between the
5240 #include <isl/set.h>
5241 __isl_give isl_set *isl_set_product(
5242 __isl_take isl_set *set1,
5243 __isl_take isl_set *set2);
5245 #include <isl/map.h>
5246 __isl_give isl_basic_map *isl_basic_map_domain_product(
5247 __isl_take isl_basic_map *bmap1,
5248 __isl_take isl_basic_map *bmap2);
5249 __isl_give isl_basic_map *isl_basic_map_range_product(
5250 __isl_take isl_basic_map *bmap1,
5251 __isl_take isl_basic_map *bmap2);
5252 __isl_give isl_basic_map *isl_basic_map_product(
5253 __isl_take isl_basic_map *bmap1,
5254 __isl_take isl_basic_map *bmap2);
5255 __isl_give isl_map *isl_map_domain_product(
5256 __isl_take isl_map *map1,
5257 __isl_take isl_map *map2);
5258 __isl_give isl_map *isl_map_range_product(
5259 __isl_take isl_map *map1,
5260 __isl_take isl_map *map2);
5261 __isl_give isl_map *isl_map_product(
5262 __isl_take isl_map *map1,
5263 __isl_take isl_map *map2);
5265 #include <isl/union_set.h>
5266 __isl_give isl_union_set *isl_union_set_product(
5267 __isl_take isl_union_set *uset1,
5268 __isl_take isl_union_set *uset2);
5270 #include <isl/union_map.h>
5271 __isl_give isl_union_map *isl_union_map_domain_product(
5272 __isl_take isl_union_map *umap1,
5273 __isl_take isl_union_map *umap2);
5274 __isl_give isl_union_map *isl_union_map_range_product(
5275 __isl_take isl_union_map *umap1,
5276 __isl_take isl_union_map *umap2);
5277 __isl_give isl_union_map *isl_union_map_product(
5278 __isl_take isl_union_map *umap1,
5279 __isl_take isl_union_map *umap2);
5281 #include <isl/val.h>
5282 __isl_give isl_multi_val *isl_multi_val_range_product(
5283 __isl_take isl_multi_val *mv1,
5284 __isl_take isl_multi_val *mv2);
5285 __isl_give isl_multi_val *isl_multi_val_product(
5286 __isl_take isl_multi_val *mv1,
5287 __isl_take isl_multi_val *mv2);
5289 #include <isl/aff.h>
5290 __isl_give isl_multi_aff *isl_multi_aff_range_product(
5291 __isl_take isl_multi_aff *ma1,
5292 __isl_take isl_multi_aff *ma2);
5293 __isl_give isl_multi_aff *isl_multi_aff_product(
5294 __isl_take isl_multi_aff *ma1,
5295 __isl_take isl_multi_aff *ma2);
5296 __isl_give isl_multi_pw_aff *
5297 isl_multi_pw_aff_range_product(
5298 __isl_take isl_multi_pw_aff *mpa1,
5299 __isl_take isl_multi_pw_aff *mpa2);
5300 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_product(
5301 __isl_take isl_multi_pw_aff *mpa1,
5302 __isl_take isl_multi_pw_aff *mpa2);
5303 __isl_give isl_pw_multi_aff *
5304 isl_pw_multi_aff_range_product(
5305 __isl_take isl_pw_multi_aff *pma1,
5306 __isl_take isl_pw_multi_aff *pma2);
5307 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
5308 __isl_take isl_pw_multi_aff *pma1,
5309 __isl_take isl_pw_multi_aff *pma2);
5311 The above functions compute the cross product of the given
5312 sets, relations or functions. The domains and ranges of the results
5313 are wrapped maps between domains and ranges of the inputs.
5314 To obtain a ``flat'' product, use the following functions
5317 #include <isl/set.h>
5318 __isl_give isl_basic_set *isl_basic_set_flat_product(
5319 __isl_take isl_basic_set *bset1,
5320 __isl_take isl_basic_set *bset2);
5321 __isl_give isl_set *isl_set_flat_product(
5322 __isl_take isl_set *set1,
5323 __isl_take isl_set *set2);
5325 #include <isl/map.h>
5326 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
5327 __isl_take isl_basic_map *bmap1,
5328 __isl_take isl_basic_map *bmap2);
5329 __isl_give isl_map *isl_map_flat_domain_product(
5330 __isl_take isl_map *map1,
5331 __isl_take isl_map *map2);
5332 __isl_give isl_map *isl_map_flat_range_product(
5333 __isl_take isl_map *map1,
5334 __isl_take isl_map *map2);
5335 __isl_give isl_basic_map *isl_basic_map_flat_product(
5336 __isl_take isl_basic_map *bmap1,
5337 __isl_take isl_basic_map *bmap2);
5338 __isl_give isl_map *isl_map_flat_product(
5339 __isl_take isl_map *map1,
5340 __isl_take isl_map *map2);
5342 #include <isl/union_map.h>
5343 __isl_give isl_union_map *
5344 isl_union_map_flat_range_product(
5345 __isl_take isl_union_map *umap1,
5346 __isl_take isl_union_map *umap2);
5348 #include <isl/val.h>
5349 __isl_give isl_multi_val *isl_multi_val_flat_range_product(
5350 __isl_take isl_multi_val *mv1,
5351 __isl_take isl_multi_aff *mv2);
5353 #include <isl/aff.h>
5354 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
5355 __isl_take isl_multi_aff *ma1,
5356 __isl_take isl_multi_aff *ma2);
5357 __isl_give isl_pw_multi_aff *
5358 isl_pw_multi_aff_flat_range_product(
5359 __isl_take isl_pw_multi_aff *pma1,
5360 __isl_take isl_pw_multi_aff *pma2);
5361 __isl_give isl_multi_pw_aff *
5362 isl_multi_pw_aff_flat_range_product(
5363 __isl_take isl_multi_pw_aff *mpa1,
5364 __isl_take isl_multi_pw_aff *mpa2);
5365 __isl_give isl_union_pw_multi_aff *
5366 isl_union_pw_multi_aff_flat_range_product(
5367 __isl_take isl_union_pw_multi_aff *upma1,
5368 __isl_take isl_union_pw_multi_aff *upma2);
5370 #include <isl/space.h>
5371 __isl_give isl_space *isl_space_domain_factor_domain(
5372 __isl_take isl_space *space);
5373 __isl_give isl_space *isl_space_range_factor_domain(
5374 __isl_take isl_space *space);
5375 __isl_give isl_space *isl_space_range_factor_range(
5376 __isl_take isl_space *space);
5378 The functions C<isl_space_range_factor_domain> and
5379 C<isl_space_range_factor_range> extract the two arguments from
5380 the result of a call to C<isl_space_range_product>.
5382 The arguments of a call to C<isl_map_range_product> can be extracted
5383 from the result using the following two functions.
5385 #include <isl/map.h>
5386 __isl_give isl_map *isl_map_range_factor_domain(
5387 __isl_take isl_map *map);
5388 __isl_give isl_map *isl_map_range_factor_range(
5389 __isl_take isl_map *map);
5391 #include <isl/val.h>
5392 __isl_give isl_multi_val *
5393 isl_multi_val_range_factor_domain(
5394 __isl_take isl_multi_val *mv);
5395 __isl_give isl_multi_val *
5396 isl_multi_val_range_factor_range(
5397 __isl_take isl_multi_val *mv);
5399 #include <isl/aff.h>
5400 __isl_give isl_multi_aff *
5401 isl_multi_aff_range_factor_domain(
5402 __isl_take isl_multi_aff *ma);
5403 __isl_give isl_multi_aff *
5404 isl_multi_aff_range_factor_range(
5405 __isl_take isl_multi_aff *ma);
5406 __isl_give isl_multi_pw_aff *
5407 isl_multi_pw_aff_range_factor_domain(
5408 __isl_take isl_multi_pw_aff *mpa);
5409 __isl_give isl_multi_pw_aff *
5410 isl_multi_pw_aff_range_factor_range(
5411 __isl_take isl_multi_pw_aff *mpa);
5413 The splice functions are a generalization of the flat product functions,
5414 where the second argument may be inserted at any position inside
5415 the first argument rather than being placed at the end.
5417 #include <isl/val.h>
5418 __isl_give isl_multi_val *isl_multi_val_range_splice(
5419 __isl_take isl_multi_val *mv1, unsigned pos,
5420 __isl_take isl_multi_val *mv2);
5422 #include <isl/aff.h>
5423 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
5424 __isl_take isl_multi_aff *ma1, unsigned pos,
5425 __isl_take isl_multi_aff *ma2);
5426 __isl_give isl_multi_aff *isl_multi_aff_splice(
5427 __isl_take isl_multi_aff *ma1,
5428 unsigned in_pos, unsigned out_pos,
5429 __isl_take isl_multi_aff *ma2);
5430 __isl_give isl_multi_pw_aff *
5431 isl_multi_pw_aff_range_splice(
5432 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
5433 __isl_take isl_multi_pw_aff *mpa2);
5434 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
5435 __isl_take isl_multi_pw_aff *mpa1,
5436 unsigned in_pos, unsigned out_pos,
5437 __isl_take isl_multi_pw_aff *mpa2);
5439 =item * Simplification
5441 When applied to a set or relation,
5442 the gist operation returns a set or relation that has the
5443 same intersection with the context as the input set or relation.
5444 Any implicit equality in the intersection is made explicit in the result,
5445 while all inequalities that are redundant with respect to the intersection
5447 In case of union sets and relations, the gist operation is performed
5450 When applied to a function,
5451 the gist operation applies the set gist operation to each of
5452 the cells in the domain of the input piecewise expression.
5453 The context is also exploited
5454 to simplify the expression associated to each cell.
5456 #include <isl/set.h>
5457 __isl_give isl_basic_set *isl_basic_set_gist(
5458 __isl_take isl_basic_set *bset,
5459 __isl_take isl_basic_set *context);
5460 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
5461 __isl_take isl_set *context);
5462 __isl_give isl_set *isl_set_gist_params(
5463 __isl_take isl_set *set,
5464 __isl_take isl_set *context);
5466 #include <isl/map.h>
5467 __isl_give isl_basic_map *isl_basic_map_gist(
5468 __isl_take isl_basic_map *bmap,
5469 __isl_take isl_basic_map *context);
5470 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
5471 __isl_take isl_map *context);
5472 __isl_give isl_map *isl_map_gist_params(
5473 __isl_take isl_map *map,
5474 __isl_take isl_set *context);
5475 __isl_give isl_map *isl_map_gist_domain(
5476 __isl_take isl_map *map,
5477 __isl_take isl_set *context);
5478 __isl_give isl_map *isl_map_gist_range(
5479 __isl_take isl_map *map,
5480 __isl_take isl_set *context);
5482 #include <isl/union_set.h>
5483 __isl_give isl_union_set *isl_union_set_gist(
5484 __isl_take isl_union_set *uset,
5485 __isl_take isl_union_set *context);
5486 __isl_give isl_union_set *isl_union_set_gist_params(
5487 __isl_take isl_union_set *uset,
5488 __isl_take isl_set *set);
5490 #include <isl/union_map.h>
5491 __isl_give isl_union_map *isl_union_map_gist(
5492 __isl_take isl_union_map *umap,
5493 __isl_take isl_union_map *context);
5494 __isl_give isl_union_map *isl_union_map_gist_params(
5495 __isl_take isl_union_map *umap,
5496 __isl_take isl_set *set);
5497 __isl_give isl_union_map *isl_union_map_gist_domain(
5498 __isl_take isl_union_map *umap,
5499 __isl_take isl_union_set *uset);
5500 __isl_give isl_union_map *isl_union_map_gist_range(
5501 __isl_take isl_union_map *umap,
5502 __isl_take isl_union_set *uset);
5504 #include <isl/aff.h>
5505 __isl_give isl_aff *isl_aff_gist_params(
5506 __isl_take isl_aff *aff,
5507 __isl_take isl_set *context);
5508 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
5509 __isl_take isl_set *context);
5510 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
5511 __isl_take isl_multi_aff *maff,
5512 __isl_take isl_set *context);
5513 __isl_give isl_multi_aff *isl_multi_aff_gist(
5514 __isl_take isl_multi_aff *maff,
5515 __isl_take isl_set *context);
5516 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
5517 __isl_take isl_pw_aff *pwaff,
5518 __isl_take isl_set *context);
5519 __isl_give isl_pw_aff *isl_pw_aff_gist(
5520 __isl_take isl_pw_aff *pwaff,
5521 __isl_take isl_set *context);
5522 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
5523 __isl_take isl_pw_multi_aff *pma,
5524 __isl_take isl_set *set);
5525 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
5526 __isl_take isl_pw_multi_aff *pma,
5527 __isl_take isl_set *set);
5528 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist_params(
5529 __isl_take isl_multi_pw_aff *mpa,
5530 __isl_take isl_set *set);
5531 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_gist(
5532 __isl_take isl_multi_pw_aff *mpa,
5533 __isl_take isl_set *set);
5534 __isl_give isl_union_pw_multi_aff *
5535 isl_union_pw_multi_aff_gist_params(
5536 __isl_take isl_union_pw_multi_aff *upma,
5537 __isl_take isl_set *context);
5538 __isl_give isl_union_pw_multi_aff *
5539 isl_union_pw_multi_aff_gist(
5540 __isl_take isl_union_pw_multi_aff *upma,
5541 __isl_take isl_union_set *context);
5543 #include <isl/polynomial.h>
5544 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
5545 __isl_take isl_qpolynomial *qp,
5546 __isl_take isl_set *context);
5547 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
5548 __isl_take isl_qpolynomial *qp,
5549 __isl_take isl_set *context);
5550 __isl_give isl_qpolynomial_fold *
5551 isl_qpolynomial_fold_gist_params(
5552 __isl_take isl_qpolynomial_fold *fold,
5553 __isl_take isl_set *context);
5554 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
5555 __isl_take isl_qpolynomial_fold *fold,
5556 __isl_take isl_set *context);
5557 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
5558 __isl_take isl_pw_qpolynomial *pwqp,
5559 __isl_take isl_set *context);
5560 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
5561 __isl_take isl_pw_qpolynomial *pwqp,
5562 __isl_take isl_set *context);
5563 __isl_give isl_pw_qpolynomial_fold *
5564 isl_pw_qpolynomial_fold_gist(
5565 __isl_take isl_pw_qpolynomial_fold *pwf,
5566 __isl_take isl_set *context);
5567 __isl_give isl_pw_qpolynomial_fold *
5568 isl_pw_qpolynomial_fold_gist_params(
5569 __isl_take isl_pw_qpolynomial_fold *pwf,
5570 __isl_take isl_set *context);
5571 __isl_give isl_union_pw_qpolynomial *
5572 isl_union_pw_qpolynomial_gist_params(
5573 __isl_take isl_union_pw_qpolynomial *upwqp,
5574 __isl_take isl_set *context);
5575 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
5576 __isl_take isl_union_pw_qpolynomial *upwqp,
5577 __isl_take isl_union_set *context);
5578 __isl_give isl_union_pw_qpolynomial_fold *
5579 isl_union_pw_qpolynomial_fold_gist(
5580 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5581 __isl_take isl_union_set *context);
5582 __isl_give isl_union_pw_qpolynomial_fold *
5583 isl_union_pw_qpolynomial_fold_gist_params(
5584 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5585 __isl_take isl_set *context);
5587 =item * Binary Arithmethic Operations
5589 #include <isl/aff.h>
5590 __isl_give isl_aff *isl_aff_add(
5591 __isl_take isl_aff *aff1,
5592 __isl_take isl_aff *aff2);
5593 __isl_give isl_multi_aff *isl_multi_aff_add(
5594 __isl_take isl_multi_aff *maff1,
5595 __isl_take isl_multi_aff *maff2);
5596 __isl_give isl_pw_aff *isl_pw_aff_add(
5597 __isl_take isl_pw_aff *pwaff1,
5598 __isl_take isl_pw_aff *pwaff2);
5599 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
5600 __isl_take isl_pw_multi_aff *pma1,
5601 __isl_take isl_pw_multi_aff *pma2);
5602 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
5603 __isl_take isl_union_pw_multi_aff *upma1,
5604 __isl_take isl_union_pw_multi_aff *upma2);
5605 __isl_give isl_pw_aff *isl_pw_aff_min(
5606 __isl_take isl_pw_aff *pwaff1,
5607 __isl_take isl_pw_aff *pwaff2);
5608 __isl_give isl_pw_aff *isl_pw_aff_max(
5609 __isl_take isl_pw_aff *pwaff1,
5610 __isl_take isl_pw_aff *pwaff2);
5611 __isl_give isl_aff *isl_aff_sub(
5612 __isl_take isl_aff *aff1,
5613 __isl_take isl_aff *aff2);
5614 __isl_give isl_multi_aff *isl_multi_aff_sub(
5615 __isl_take isl_multi_aff *ma1,
5616 __isl_take isl_multi_aff *ma2);
5617 __isl_give isl_pw_aff *isl_pw_aff_sub(
5618 __isl_take isl_pw_aff *pwaff1,
5619 __isl_take isl_pw_aff *pwaff2);
5620 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
5621 __isl_take isl_pw_multi_aff *pma1,
5622 __isl_take isl_pw_multi_aff *pma2);
5623 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
5624 __isl_take isl_union_pw_multi_aff *upma1,
5625 __isl_take isl_union_pw_multi_aff *upma2);
5627 C<isl_aff_sub> subtracts the second argument from the first.
5629 #include <isl/polynomial.h>
5630 __isl_give isl_qpolynomial *isl_qpolynomial_add(
5631 __isl_take isl_qpolynomial *qp1,
5632 __isl_take isl_qpolynomial *qp2);
5633 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
5634 __isl_take isl_pw_qpolynomial *pwqp1,
5635 __isl_take isl_pw_qpolynomial *pwqp2);
5636 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
5637 __isl_take isl_pw_qpolynomial *pwqp1,
5638 __isl_take isl_pw_qpolynomial *pwqp2);
5639 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
5640 __isl_take isl_pw_qpolynomial_fold *pwf1,
5641 __isl_take isl_pw_qpolynomial_fold *pwf2);
5642 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
5643 __isl_take isl_union_pw_qpolynomial *upwqp1,
5644 __isl_take isl_union_pw_qpolynomial *upwqp2);
5645 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
5646 __isl_take isl_qpolynomial *qp1,
5647 __isl_take isl_qpolynomial *qp2);
5648 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
5649 __isl_take isl_pw_qpolynomial *pwqp1,
5650 __isl_take isl_pw_qpolynomial *pwqp2);
5651 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
5652 __isl_take isl_union_pw_qpolynomial *upwqp1,
5653 __isl_take isl_union_pw_qpolynomial *upwqp2);
5654 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
5655 __isl_take isl_pw_qpolynomial_fold *pwf1,
5656 __isl_take isl_pw_qpolynomial_fold *pwf2);
5657 __isl_give isl_union_pw_qpolynomial_fold *
5658 isl_union_pw_qpolynomial_fold_fold(
5659 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
5660 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
5662 #include <isl/aff.h>
5663 __isl_give isl_pw_aff *isl_pw_aff_union_add(
5664 __isl_take isl_pw_aff *pwaff1,
5665 __isl_take isl_pw_aff *pwaff2);
5666 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
5667 __isl_take isl_pw_multi_aff *pma1,
5668 __isl_take isl_pw_multi_aff *pma2);
5669 __isl_give isl_pw_aff *isl_pw_aff_union_min(
5670 __isl_take isl_pw_aff *pwaff1,
5671 __isl_take isl_pw_aff *pwaff2);
5672 __isl_give isl_pw_aff *isl_pw_aff_union_max(
5673 __isl_take isl_pw_aff *pwaff1,
5674 __isl_take isl_pw_aff *pwaff2);
5676 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
5677 expression with a domain that is the union of those of C<pwaff1> and
5678 C<pwaff2> and such that on each cell, the quasi-affine expression is
5679 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
5680 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
5681 associated expression is the defined one.
5682 This in contrast to the C<isl_pw_aff_max> function, which is
5683 only defined on the shared definition domain of the arguments.
5685 #include <isl/val.h>
5686 __isl_give isl_multi_val *isl_multi_val_add_val(
5687 __isl_take isl_multi_val *mv,
5688 __isl_take isl_val *v);
5689 __isl_give isl_multi_val *isl_multi_val_mod_val(
5690 __isl_take isl_multi_val *mv,
5691 __isl_take isl_val *v);
5692 __isl_give isl_multi_val *isl_multi_val_scale_val(
5693 __isl_take isl_multi_val *mv,
5694 __isl_take isl_val *v);
5696 #include <isl/aff.h>
5697 __isl_give isl_aff *isl_aff_mod_val(__isl_take isl_aff *aff,
5698 __isl_take isl_val *mod);
5699 __isl_give isl_pw_aff *isl_pw_aff_mod_val(
5700 __isl_take isl_pw_aff *pa,
5701 __isl_take isl_val *mod);
5702 __isl_give isl_aff *isl_aff_scale_val(__isl_take isl_aff *aff,
5703 __isl_take isl_val *v);
5704 __isl_give isl_multi_aff *isl_multi_aff_scale_val(
5705 __isl_take isl_multi_aff *ma,
5706 __isl_take isl_val *v);
5707 __isl_give isl_pw_aff *isl_pw_aff_scale_val(
5708 __isl_take isl_pw_aff *pa, __isl_take isl_val *v);
5709 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_scale_val(
5710 __isl_take isl_multi_pw_aff *mpa,
5711 __isl_take isl_val *v);
5712 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_val(
5713 __isl_take isl_pw_multi_aff *pma,
5714 __isl_take isl_val *v);
5715 __isl_give isl_union_pw_multi_aff *
5716 isl_union_pw_multi_aff_scale_val(
5717 __isl_take isl_union_pw_multi_aff *upma,
5718 __isl_take isl_val *val);
5719 __isl_give isl_aff *isl_aff_scale_down_ui(
5720 __isl_take isl_aff *aff, unsigned f);
5721 __isl_give isl_aff *isl_aff_scale_down_val(
5722 __isl_take isl_aff *aff, __isl_take isl_val *v);
5723 __isl_give isl_pw_aff *isl_pw_aff_scale_down_val(
5724 __isl_take isl_pw_aff *pa,
5725 __isl_take isl_val *f);
5727 #include <isl/polynomial.h>
5728 __isl_give isl_qpolynomial *isl_qpolynomial_scale_val(
5729 __isl_take isl_qpolynomial *qp,
5730 __isl_take isl_val *v);
5731 __isl_give isl_qpolynomial_fold *
5732 isl_qpolynomial_fold_scale_val(
5733 __isl_take isl_qpolynomial_fold *fold,
5734 __isl_take isl_val *v);
5735 __isl_give isl_pw_qpolynomial *
5736 isl_pw_qpolynomial_scale_val(
5737 __isl_take isl_pw_qpolynomial *pwqp,
5738 __isl_take isl_val *v);
5739 __isl_give isl_pw_qpolynomial_fold *
5740 isl_pw_qpolynomial_fold_scale_val(
5741 __isl_take isl_pw_qpolynomial_fold *pwf,
5742 __isl_take isl_val *v);
5743 __isl_give isl_union_pw_qpolynomial *
5744 isl_union_pw_qpolynomial_scale_val(
5745 __isl_take isl_union_pw_qpolynomial *upwqp,
5746 __isl_take isl_val *v);
5747 __isl_give isl_union_pw_qpolynomial_fold *
5748 isl_union_pw_qpolynomial_fold_scale_val(
5749 __isl_take isl_union_pw_qpolynomial_fold *upwf,
5750 __isl_take isl_val *v);
5752 #include <isl/val.h>
5753 __isl_give isl_multi_val *isl_multi_val_scale_multi_val(
5754 __isl_take isl_multi_val *mv1,
5755 __isl_take isl_multi_val *mv2);
5756 __isl_give isl_multi_val *
5757 isl_multi_val_scale_down_multi_val(
5758 __isl_take isl_multi_val *mv1,
5759 __isl_take isl_multi_val *mv2);
5761 #include <isl/aff.h>
5762 __isl_give isl_multi_aff *isl_multi_aff_scale_multi_val(
5763 __isl_take isl_multi_aff *ma,
5764 __isl_take isl_multi_val *mv);
5765 __isl_give isl_pw_multi_aff *
5766 isl_pw_multi_aff_scale_multi_val(
5767 __isl_take isl_pw_multi_aff *pma,
5768 __isl_take isl_multi_val *mv);
5769 __isl_give isl_multi_pw_aff *
5770 isl_multi_pw_aff_scale_multi_val(
5771 __isl_take isl_multi_pw_aff *mpa,
5772 __isl_take isl_multi_val *mv);
5773 __isl_give isl_union_pw_multi_aff *
5774 isl_union_pw_multi_aff_scale_multi_val(
5775 __isl_take isl_union_pw_multi_aff *upma,
5776 __isl_take isl_multi_val *mv);
5777 __isl_give isl_multi_aff *
5778 isl_multi_aff_scale_down_multi_val(
5779 __isl_take isl_multi_aff *ma,
5780 __isl_take isl_multi_val *mv);
5781 __isl_give isl_multi_pw_aff *
5782 isl_multi_pw_aff_scale_down_multi_val(
5783 __isl_take isl_multi_pw_aff *mpa,
5784 __isl_take isl_multi_val *mv);
5786 C<isl_multi_aff_scale_multi_val> scales the elements of C<ma>
5787 by the corresponding elements of C<mv>.
5789 #include <isl/aff.h>
5790 __isl_give isl_aff *isl_aff_mul(
5791 __isl_take isl_aff *aff1,
5792 __isl_take isl_aff *aff2);
5793 __isl_give isl_aff *isl_aff_div(
5794 __isl_take isl_aff *aff1,
5795 __isl_take isl_aff *aff2);
5796 __isl_give isl_pw_aff *isl_pw_aff_mul(
5797 __isl_take isl_pw_aff *pwaff1,
5798 __isl_take isl_pw_aff *pwaff2);
5799 __isl_give isl_pw_aff *isl_pw_aff_div(
5800 __isl_take isl_pw_aff *pa1,
5801 __isl_take isl_pw_aff *pa2);
5802 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
5803 __isl_take isl_pw_aff *pa1,
5804 __isl_take isl_pw_aff *pa2);
5805 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
5806 __isl_take isl_pw_aff *pa1,
5807 __isl_take isl_pw_aff *pa2);
5809 When multiplying two affine expressions, at least one of the two needs
5810 to be a constant. Similarly, when dividing an affine expression by another,
5811 the second expression needs to be a constant.
5812 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
5813 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
5816 #include <isl/polynomial.h>
5817 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
5818 __isl_take isl_qpolynomial *qp1,
5819 __isl_take isl_qpolynomial *qp2);
5820 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
5821 __isl_take isl_pw_qpolynomial *pwqp1,
5822 __isl_take isl_pw_qpolynomial *pwqp2);
5823 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
5824 __isl_take isl_union_pw_qpolynomial *upwqp1,
5825 __isl_take isl_union_pw_qpolynomial *upwqp2);
5829 =head3 Lexicographic Optimization
5831 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
5832 the following functions
5833 compute a set that contains the lexicographic minimum or maximum
5834 of the elements in C<set> (or C<bset>) for those values of the parameters
5835 that satisfy C<dom>.
5836 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
5837 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
5839 In other words, the union of the parameter values
5840 for which the result is non-empty and of C<*empty>
5843 #include <isl/set.h>
5844 __isl_give isl_set *isl_basic_set_partial_lexmin(
5845 __isl_take isl_basic_set *bset,
5846 __isl_take isl_basic_set *dom,
5847 __isl_give isl_set **empty);
5848 __isl_give isl_set *isl_basic_set_partial_lexmax(
5849 __isl_take isl_basic_set *bset,
5850 __isl_take isl_basic_set *dom,
5851 __isl_give isl_set **empty);
5852 __isl_give isl_set *isl_set_partial_lexmin(
5853 __isl_take isl_set *set, __isl_take isl_set *dom,
5854 __isl_give isl_set **empty);
5855 __isl_give isl_set *isl_set_partial_lexmax(
5856 __isl_take isl_set *set, __isl_take isl_set *dom,
5857 __isl_give isl_set **empty);
5859 Given a (basic) set C<set> (or C<bset>), the following functions simply
5860 return a set containing the lexicographic minimum or maximum
5861 of the elements in C<set> (or C<bset>).
5862 In case of union sets, the optimum is computed per space.
5864 #include <isl/set.h>
5865 __isl_give isl_set *isl_basic_set_lexmin(
5866 __isl_take isl_basic_set *bset);
5867 __isl_give isl_set *isl_basic_set_lexmax(
5868 __isl_take isl_basic_set *bset);
5869 __isl_give isl_set *isl_set_lexmin(
5870 __isl_take isl_set *set);
5871 __isl_give isl_set *isl_set_lexmax(
5872 __isl_take isl_set *set);
5873 __isl_give isl_union_set *isl_union_set_lexmin(
5874 __isl_take isl_union_set *uset);
5875 __isl_give isl_union_set *isl_union_set_lexmax(
5876 __isl_take isl_union_set *uset);
5878 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
5879 the following functions
5880 compute a relation that maps each element of C<dom>
5881 to the single lexicographic minimum or maximum
5882 of the elements that are associated to that same
5883 element in C<map> (or C<bmap>).
5884 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
5885 that contains the elements in C<dom> that do not map
5886 to any elements in C<map> (or C<bmap>).
5887 In other words, the union of the domain of the result and of C<*empty>
5890 #include <isl/map.h>
5891 __isl_give isl_map *isl_basic_map_partial_lexmax(
5892 __isl_take isl_basic_map *bmap,
5893 __isl_take isl_basic_set *dom,
5894 __isl_give isl_set **empty);
5895 __isl_give isl_map *isl_basic_map_partial_lexmin(
5896 __isl_take isl_basic_map *bmap,
5897 __isl_take isl_basic_set *dom,
5898 __isl_give isl_set **empty);
5899 __isl_give isl_map *isl_map_partial_lexmax(
5900 __isl_take isl_map *map, __isl_take isl_set *dom,
5901 __isl_give isl_set **empty);
5902 __isl_give isl_map *isl_map_partial_lexmin(
5903 __isl_take isl_map *map, __isl_take isl_set *dom,
5904 __isl_give isl_set **empty);
5906 Given a (basic) map C<map> (or C<bmap>), the following functions simply
5907 return a map mapping each element in the domain of
5908 C<map> (or C<bmap>) to the lexicographic minimum or maximum
5909 of all elements associated to that element.
5910 In case of union relations, the optimum is computed per space.
5912 #include <isl/map.h>
5913 __isl_give isl_map *isl_basic_map_lexmin(
5914 __isl_take isl_basic_map *bmap);
5915 __isl_give isl_map *isl_basic_map_lexmax(
5916 __isl_take isl_basic_map *bmap);
5917 __isl_give isl_map *isl_map_lexmin(
5918 __isl_take isl_map *map);
5919 __isl_give isl_map *isl_map_lexmax(
5920 __isl_take isl_map *map);
5921 __isl_give isl_union_map *isl_union_map_lexmin(
5922 __isl_take isl_union_map *umap);
5923 __isl_give isl_union_map *isl_union_map_lexmax(
5924 __isl_take isl_union_map *umap);
5926 The following functions return their result in the form of
5927 a piecewise multi-affine expression,
5928 but are otherwise equivalent to the corresponding functions
5929 returning a basic set or relation.
5931 #include <isl/set.h>
5932 __isl_give isl_pw_multi_aff *
5933 isl_basic_set_partial_lexmin_pw_multi_aff(
5934 __isl_take isl_basic_set *bset,
5935 __isl_take isl_basic_set *dom,
5936 __isl_give isl_set **empty);
5937 __isl_give isl_pw_multi_aff *
5938 isl_basic_set_partial_lexmax_pw_multi_aff(
5939 __isl_take isl_basic_set *bset,
5940 __isl_take isl_basic_set *dom,
5941 __isl_give isl_set **empty);
5942 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
5943 __isl_take isl_set *set);
5944 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
5945 __isl_take isl_set *set);
5947 #include <isl/map.h>
5948 __isl_give isl_pw_multi_aff *
5949 isl_basic_map_lexmin_pw_multi_aff(
5950 __isl_take isl_basic_map *bmap);
5951 __isl_give isl_pw_multi_aff *
5952 isl_basic_map_partial_lexmin_pw_multi_aff(
5953 __isl_take isl_basic_map *bmap,
5954 __isl_take isl_basic_set *dom,
5955 __isl_give isl_set **empty);
5956 __isl_give isl_pw_multi_aff *
5957 isl_basic_map_partial_lexmax_pw_multi_aff(
5958 __isl_take isl_basic_map *bmap,
5959 __isl_take isl_basic_set *dom,
5960 __isl_give isl_set **empty);
5961 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
5962 __isl_take isl_map *map);
5963 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
5964 __isl_take isl_map *map);
5966 The following functions return the lexicographic minimum or maximum
5967 on the shared domain of the inputs and the single defined function
5968 on those parts of the domain where only a single function is defined.
5970 #include <isl/aff.h>
5971 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
5972 __isl_take isl_pw_multi_aff *pma1,
5973 __isl_take isl_pw_multi_aff *pma2);
5974 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
5975 __isl_take isl_pw_multi_aff *pma1,
5976 __isl_take isl_pw_multi_aff *pma2);
5978 =head2 Ternary Operations
5980 #include <isl/aff.h>
5981 __isl_give isl_pw_aff *isl_pw_aff_cond(
5982 __isl_take isl_pw_aff *cond,
5983 __isl_take isl_pw_aff *pwaff_true,
5984 __isl_take isl_pw_aff *pwaff_false);
5986 The function C<isl_pw_aff_cond> performs a conditional operator
5987 and returns an expression that is equal to C<pwaff_true>
5988 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
5989 where C<cond> is zero.
5993 Lists are defined over several element types, including
5994 C<isl_val>, C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
5995 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
5996 Here we take lists of C<isl_set>s as an example.
5997 Lists can be created, copied, modified and freed using the following functions.
5999 #include <isl/set.h>
6000 __isl_give isl_set_list *isl_set_list_from_set(
6001 __isl_take isl_set *el);
6002 __isl_give isl_set_list *isl_set_list_alloc(
6003 isl_ctx *ctx, int n);
6004 __isl_give isl_set_list *isl_set_list_copy(
6005 __isl_keep isl_set_list *list);
6006 __isl_give isl_set_list *isl_set_list_insert(
6007 __isl_take isl_set_list *list, unsigned pos,
6008 __isl_take isl_set *el);
6009 __isl_give isl_set_list *isl_set_list_add(
6010 __isl_take isl_set_list *list,
6011 __isl_take isl_set *el);
6012 __isl_give isl_set_list *isl_set_list_drop(
6013 __isl_take isl_set_list *list,
6014 unsigned first, unsigned n);
6015 __isl_give isl_set_list *isl_set_list_set_set(
6016 __isl_take isl_set_list *list, int index,
6017 __isl_take isl_set *set);
6018 __isl_give isl_set_list *isl_set_list_concat(
6019 __isl_take isl_set_list *list1,
6020 __isl_take isl_set_list *list2);
6021 __isl_give isl_set_list *isl_set_list_sort(
6022 __isl_take isl_set_list *list,
6023 int (*cmp)(__isl_keep isl_set *a,
6024 __isl_keep isl_set *b, void *user),
6026 __isl_null isl_set_list *isl_set_list_free(
6027 __isl_take isl_set_list *list);
6029 C<isl_set_list_alloc> creates an empty list with a capacity for
6030 C<n> elements. C<isl_set_list_from_set> creates a list with a single
6033 Lists can be inspected using the following functions.
6035 #include <isl/set.h>
6036 int isl_set_list_n_set(__isl_keep isl_set_list *list);
6037 __isl_give isl_set *isl_set_list_get_set(
6038 __isl_keep isl_set_list *list, int index);
6039 int isl_set_list_foreach(__isl_keep isl_set_list *list,
6040 int (*fn)(__isl_take isl_set *el, void *user),
6042 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
6043 int (*follows)(__isl_keep isl_set *a,
6044 __isl_keep isl_set *b, void *user),
6046 int (*fn)(__isl_take isl_set *el, void *user),
6049 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
6050 strongly connected components of the graph with as vertices the elements
6051 of C<list> and a directed edge from vertex C<b> to vertex C<a>
6052 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
6053 should return C<-1> on error.
6055 Lists can be printed using
6057 #include <isl/set.h>
6058 __isl_give isl_printer *isl_printer_print_set_list(
6059 __isl_take isl_printer *p,
6060 __isl_keep isl_set_list *list);
6062 =head2 Associative arrays
6064 Associative arrays map isl objects of a specific type to isl objects
6065 of some (other) specific type. They are defined for several pairs
6066 of types, including (C<isl_map>, C<isl_basic_set>),
6067 (C<isl_id>, C<isl_ast_expr>) and.
6068 (C<isl_id>, C<isl_pw_aff>).
6069 Here, we take associative arrays that map C<isl_id>s to C<isl_ast_expr>s
6072 Associative arrays can be created, copied and freed using
6073 the following functions.
6075 #include <isl/id_to_ast_expr.h>
6076 __isl_give id_to_ast_expr *isl_id_to_ast_expr_alloc(
6077 isl_ctx *ctx, int min_size);
6078 __isl_give id_to_ast_expr *isl_id_to_ast_expr_copy(
6079 __isl_keep id_to_ast_expr *id2expr);
6080 __isl_null id_to_ast_expr *isl_id_to_ast_expr_free(
6081 __isl_take id_to_ast_expr *id2expr);
6083 The C<min_size> argument to C<isl_id_to_ast_expr_alloc> can be used
6084 to specify the expected size of the associative array.
6085 The associative array will be grown automatically as needed.
6087 Associative arrays can be inspected using the following functions.
6089 #include <isl/id_to_ast_expr.h>
6090 int isl_id_to_ast_expr_has(
6091 __isl_keep id_to_ast_expr *id2expr,
6092 __isl_keep isl_id *key);
6093 __isl_give isl_ast_expr *isl_id_to_ast_expr_get(
6094 __isl_keep id_to_ast_expr *id2expr,
6095 __isl_take isl_id *key);
6096 int isl_id_to_ast_expr_foreach(
6097 __isl_keep id_to_ast_expr *id2expr,
6098 int (*fn)(__isl_take isl_id *key,
6099 __isl_take isl_ast_expr *val, void *user),
6102 They can be modified using the following function.
6104 #include <isl/id_to_ast_expr.h>
6105 __isl_give id_to_ast_expr *isl_id_to_ast_expr_set(
6106 __isl_take id_to_ast_expr *id2expr,
6107 __isl_take isl_id *key,
6108 __isl_take isl_ast_expr *val);
6109 __isl_give id_to_ast_expr *isl_id_to_ast_expr_drop(
6110 __isl_take id_to_ast_expr *id2expr,
6111 __isl_take isl_id *key);
6113 Associative arrays can be printed using the following function.
6115 #include <isl/id_to_ast_expr.h>
6116 __isl_give isl_printer *isl_printer_print_id_to_ast_expr(
6117 __isl_take isl_printer *p,
6118 __isl_keep id_to_ast_expr *id2expr);
6122 Vectors can be created, copied and freed using the following functions.
6124 #include <isl/vec.h>
6125 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
6127 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
6128 __isl_null isl_vec *isl_vec_free(__isl_take isl_vec *vec);
6130 Note that the elements of a newly created vector may have arbitrary values.
6131 The elements can be changed and inspected using the following functions.
6133 int isl_vec_size(__isl_keep isl_vec *vec);
6134 __isl_give isl_val *isl_vec_get_element_val(
6135 __isl_keep isl_vec *vec, int pos);
6136 __isl_give isl_vec *isl_vec_set_element_si(
6137 __isl_take isl_vec *vec, int pos, int v);
6138 __isl_give isl_vec *isl_vec_set_element_val(
6139 __isl_take isl_vec *vec, int pos,
6140 __isl_take isl_val *v);
6141 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
6143 __isl_give isl_vec *isl_vec_set_val(
6144 __isl_take isl_vec *vec, __isl_take isl_val *v);
6145 int isl_vec_cmp_element(__isl_keep isl_vec *vec1,
6146 __isl_keep isl_vec *vec2, int pos);
6148 C<isl_vec_get_element> will return a negative value if anything went wrong.
6149 In that case, the value of C<*v> is undefined.
6151 The following function can be used to concatenate two vectors.
6153 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
6154 __isl_take isl_vec *vec2);
6158 Matrices can be created, copied and freed using the following functions.
6160 #include <isl/mat.h>
6161 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
6162 unsigned n_row, unsigned n_col);
6163 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
6164 __isl_null isl_mat *isl_mat_free(__isl_take isl_mat *mat);
6166 Note that the elements of a newly created matrix may have arbitrary values.
6167 The elements can be changed and inspected using the following functions.
6169 int isl_mat_rows(__isl_keep isl_mat *mat);
6170 int isl_mat_cols(__isl_keep isl_mat *mat);
6171 __isl_give isl_val *isl_mat_get_element_val(
6172 __isl_keep isl_mat *mat, int row, int col);
6173 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
6174 int row, int col, int v);
6175 __isl_give isl_mat *isl_mat_set_element_val(
6176 __isl_take isl_mat *mat, int row, int col,
6177 __isl_take isl_val *v);
6179 C<isl_mat_get_element> will return a negative value if anything went wrong.
6180 In that case, the value of C<*v> is undefined.
6182 The following function can be used to compute the (right) inverse
6183 of a matrix, i.e., a matrix such that the product of the original
6184 and the inverse (in that order) is a multiple of the identity matrix.
6185 The input matrix is assumed to be of full row-rank.
6187 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
6189 The following function can be used to compute the (right) kernel
6190 (or null space) of a matrix, i.e., a matrix such that the product of
6191 the original and the kernel (in that order) is the zero matrix.
6193 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
6195 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
6197 The following functions determine
6198 an upper or lower bound on a quasipolynomial over its domain.
6200 __isl_give isl_pw_qpolynomial_fold *
6201 isl_pw_qpolynomial_bound(
6202 __isl_take isl_pw_qpolynomial *pwqp,
6203 enum isl_fold type, int *tight);
6205 __isl_give isl_union_pw_qpolynomial_fold *
6206 isl_union_pw_qpolynomial_bound(
6207 __isl_take isl_union_pw_qpolynomial *upwqp,
6208 enum isl_fold type, int *tight);
6210 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
6211 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
6212 is the returned bound is known be tight, i.e., for each value
6213 of the parameters there is at least
6214 one element in the domain that reaches the bound.
6215 If the domain of C<pwqp> is not wrapping, then the bound is computed
6216 over all elements in that domain and the result has a purely parametric
6217 domain. If the domain of C<pwqp> is wrapping, then the bound is
6218 computed over the range of the wrapped relation. The domain of the
6219 wrapped relation becomes the domain of the result.
6221 =head2 Parametric Vertex Enumeration
6223 The parametric vertex enumeration described in this section
6224 is mainly intended to be used internally and by the C<barvinok>
6227 #include <isl/vertices.h>
6228 __isl_give isl_vertices *isl_basic_set_compute_vertices(
6229 __isl_keep isl_basic_set *bset);
6231 The function C<isl_basic_set_compute_vertices> performs the
6232 actual computation of the parametric vertices and the chamber
6233 decomposition and store the result in an C<isl_vertices> object.
6234 This information can be queried by either iterating over all
6235 the vertices or iterating over all the chambers or cells
6236 and then iterating over all vertices that are active on the chamber.
6238 int isl_vertices_foreach_vertex(
6239 __isl_keep isl_vertices *vertices,
6240 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6243 int isl_vertices_foreach_cell(
6244 __isl_keep isl_vertices *vertices,
6245 int (*fn)(__isl_take isl_cell *cell, void *user),
6247 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
6248 int (*fn)(__isl_take isl_vertex *vertex, void *user),
6251 Other operations that can be performed on an C<isl_vertices> object are
6254 int isl_vertices_get_n_vertices(
6255 __isl_keep isl_vertices *vertices);
6256 void isl_vertices_free(__isl_take isl_vertices *vertices);
6258 Vertices can be inspected and destroyed using the following functions.
6260 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
6261 __isl_give isl_basic_set *isl_vertex_get_domain(
6262 __isl_keep isl_vertex *vertex);
6263 __isl_give isl_multi_aff *isl_vertex_get_expr(
6264 __isl_keep isl_vertex *vertex);
6265 void isl_vertex_free(__isl_take isl_vertex *vertex);
6267 C<isl_vertex_get_expr> returns a multiple quasi-affine expression
6268 describing the vertex in terms of the parameters,
6269 while C<isl_vertex_get_domain> returns the activity domain
6272 Chambers can be inspected and destroyed using the following functions.
6274 __isl_give isl_basic_set *isl_cell_get_domain(
6275 __isl_keep isl_cell *cell);
6276 void isl_cell_free(__isl_take isl_cell *cell);
6278 =head1 Polyhedral Compilation Library
6280 This section collects functionality in C<isl> that has been specifically
6281 designed for use during polyhedral compilation.
6283 =head2 Dependence Analysis
6285 C<isl> contains specialized functionality for performing
6286 array dataflow analysis. That is, given a I<sink> access relation
6287 and a collection of possible I<source> access relations,
6288 C<isl> can compute relations that describe
6289 for each iteration of the sink access, which iteration
6290 of which of the source access relations was the last
6291 to access the same data element before the given iteration
6293 The resulting dependence relations map source iterations
6294 to the corresponding sink iterations.
6295 To compute standard flow dependences, the sink should be
6296 a read, while the sources should be writes.
6297 If any of the source accesses are marked as being I<may>
6298 accesses, then there will be a dependence from the last
6299 I<must> access B<and> from any I<may> access that follows
6300 this last I<must> access.
6301 In particular, if I<all> sources are I<may> accesses,
6302 then memory based dependence analysis is performed.
6303 If, on the other hand, all sources are I<must> accesses,
6304 then value based dependence analysis is performed.
6306 #include <isl/flow.h>
6308 typedef int (*isl_access_level_before)(void *first, void *second);
6310 __isl_give isl_access_info *isl_access_info_alloc(
6311 __isl_take isl_map *sink,
6312 void *sink_user, isl_access_level_before fn,
6314 __isl_give isl_access_info *isl_access_info_add_source(
6315 __isl_take isl_access_info *acc,
6316 __isl_take isl_map *source, int must,
6318 __isl_null isl_access_info *isl_access_info_free(
6319 __isl_take isl_access_info *acc);
6321 __isl_give isl_flow *isl_access_info_compute_flow(
6322 __isl_take isl_access_info *acc);
6324 int isl_flow_foreach(__isl_keep isl_flow *deps,
6325 int (*fn)(__isl_take isl_map *dep, int must,
6326 void *dep_user, void *user),
6328 __isl_give isl_map *isl_flow_get_no_source(
6329 __isl_keep isl_flow *deps, int must);
6330 void isl_flow_free(__isl_take isl_flow *deps);
6332 The function C<isl_access_info_compute_flow> performs the actual
6333 dependence analysis. The other functions are used to construct
6334 the input for this function or to read off the output.
6336 The input is collected in an C<isl_access_info>, which can
6337 be created through a call to C<isl_access_info_alloc>.
6338 The arguments to this functions are the sink access relation
6339 C<sink>, a token C<sink_user> used to identify the sink
6340 access to the user, a callback function for specifying the
6341 relative order of source and sink accesses, and the number
6342 of source access relations that will be added.
6343 The callback function has type C<int (*)(void *first, void *second)>.
6344 The function is called with two user supplied tokens identifying
6345 either a source or the sink and it should return the shared nesting
6346 level and the relative order of the two accesses.
6347 In particular, let I<n> be the number of loops shared by
6348 the two accesses. If C<first> precedes C<second> textually,
6349 then the function should return I<2 * n + 1>; otherwise,
6350 it should return I<2 * n>.
6351 The sources can be added to the C<isl_access_info> by performing
6352 (at most) C<max_source> calls to C<isl_access_info_add_source>.
6353 C<must> indicates whether the source is a I<must> access
6354 or a I<may> access. Note that a multi-valued access relation
6355 should only be marked I<must> if every iteration in the domain
6356 of the relation accesses I<all> elements in its image.
6357 The C<source_user> token is again used to identify
6358 the source access. The range of the source access relation
6359 C<source> should have the same dimension as the range
6360 of the sink access relation.
6361 The C<isl_access_info_free> function should usually not be
6362 called explicitly, because it is called implicitly by
6363 C<isl_access_info_compute_flow>.
6365 The result of the dependence analysis is collected in an
6366 C<isl_flow>. There may be elements of
6367 the sink access for which no preceding source access could be
6368 found or for which all preceding sources are I<may> accesses.
6369 The relations containing these elements can be obtained through
6370 calls to C<isl_flow_get_no_source>, the first with C<must> set
6371 and the second with C<must> unset.
6372 In the case of standard flow dependence analysis,
6373 with the sink a read and the sources I<must> writes,
6374 the first relation corresponds to the reads from uninitialized
6375 array elements and the second relation is empty.
6376 The actual flow dependences can be extracted using
6377 C<isl_flow_foreach>. This function will call the user-specified
6378 callback function C<fn> for each B<non-empty> dependence between
6379 a source and the sink. The callback function is called
6380 with four arguments, the actual flow dependence relation
6381 mapping source iterations to sink iterations, a boolean that
6382 indicates whether it is a I<must> or I<may> dependence, a token
6383 identifying the source and an additional C<void *> with value
6384 equal to the third argument of the C<isl_flow_foreach> call.
6385 A dependence is marked I<must> if it originates from a I<must>
6386 source and if it is not followed by any I<may> sources.
6388 After finishing with an C<isl_flow>, the user should call
6389 C<isl_flow_free> to free all associated memory.
6391 A higher-level interface to dependence analysis is provided
6392 by the following function.
6394 #include <isl/flow.h>
6396 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
6397 __isl_take isl_union_map *must_source,
6398 __isl_take isl_union_map *may_source,
6399 __isl_take isl_union_map *schedule,
6400 __isl_give isl_union_map **must_dep,
6401 __isl_give isl_union_map **may_dep,
6402 __isl_give isl_union_map **must_no_source,
6403 __isl_give isl_union_map **may_no_source);
6405 The arrays are identified by the tuple names of the ranges
6406 of the accesses. The iteration domains by the tuple names
6407 of the domains of the accesses and of the schedule.
6408 The relative order of the iteration domains is given by the
6409 schedule. The relations returned through C<must_no_source>
6410 and C<may_no_source> are subsets of C<sink>.
6411 Any of C<must_dep>, C<may_dep>, C<must_no_source>
6412 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
6413 any of the other arguments is treated as an error.
6415 =head3 Interaction with Dependence Analysis
6417 During the dependence analysis, we frequently need to perform
6418 the following operation. Given a relation between sink iterations
6419 and potential source iterations from a particular source domain,
6420 what is the last potential source iteration corresponding to each
6421 sink iteration. It can sometimes be convenient to adjust
6422 the set of potential source iterations before or after each such operation.
6423 The prototypical example is fuzzy array dataflow analysis,
6424 where we need to analyze if, based on data-dependent constraints,
6425 the sink iteration can ever be executed without one or more of
6426 the corresponding potential source iterations being executed.
6427 If so, we can introduce extra parameters and select an unknown
6428 but fixed source iteration from the potential source iterations.
6429 To be able to perform such manipulations, C<isl> provides the following
6432 #include <isl/flow.h>
6434 typedef __isl_give isl_restriction *(*isl_access_restrict)(
6435 __isl_keep isl_map *source_map,
6436 __isl_keep isl_set *sink, void *source_user,
6438 __isl_give isl_access_info *isl_access_info_set_restrict(
6439 __isl_take isl_access_info *acc,
6440 isl_access_restrict fn, void *user);
6442 The function C<isl_access_info_set_restrict> should be called
6443 before calling C<isl_access_info_compute_flow> and registers a callback function
6444 that will be called any time C<isl> is about to compute the last
6445 potential source. The first argument is the (reverse) proto-dependence,
6446 mapping sink iterations to potential source iterations.
6447 The second argument represents the sink iterations for which
6448 we want to compute the last source iteration.
6449 The third argument is the token corresponding to the source
6450 and the final argument is the token passed to C<isl_access_info_set_restrict>.
6451 The callback is expected to return a restriction on either the input or
6452 the output of the operation computing the last potential source.
6453 If the input needs to be restricted then restrictions are needed
6454 for both the source and the sink iterations. The sink iterations
6455 and the potential source iterations will be intersected with these sets.
6456 If the output needs to be restricted then only a restriction on the source
6457 iterations is required.
6458 If any error occurs, the callback should return C<NULL>.
6459 An C<isl_restriction> object can be created, freed and inspected
6460 using the following functions.
6462 #include <isl/flow.h>
6464 __isl_give isl_restriction *isl_restriction_input(
6465 __isl_take isl_set *source_restr,
6466 __isl_take isl_set *sink_restr);
6467 __isl_give isl_restriction *isl_restriction_output(
6468 __isl_take isl_set *source_restr);
6469 __isl_give isl_restriction *isl_restriction_none(
6470 __isl_take isl_map *source_map);
6471 __isl_give isl_restriction *isl_restriction_empty(
6472 __isl_take isl_map *source_map);
6473 __isl_null isl_restriction *isl_restriction_free(
6474 __isl_take isl_restriction *restr);
6476 C<isl_restriction_none> and C<isl_restriction_empty> are special
6477 cases of C<isl_restriction_input>. C<isl_restriction_none>
6478 is essentially equivalent to
6480 isl_restriction_input(isl_set_universe(
6481 isl_space_range(isl_map_get_space(source_map))),
6483 isl_space_domain(isl_map_get_space(source_map))));
6485 whereas C<isl_restriction_empty> is essentially equivalent to
6487 isl_restriction_input(isl_set_empty(
6488 isl_space_range(isl_map_get_space(source_map))),
6490 isl_space_domain(isl_map_get_space(source_map))));
6494 B<The functionality described in this section is fairly new
6495 and may be subject to change.>
6497 #include <isl/schedule.h>
6498 __isl_give isl_schedule *
6499 isl_schedule_constraints_compute_schedule(
6500 __isl_take isl_schedule_constraints *sc);
6501 __isl_null isl_schedule *isl_schedule_free(
6502 __isl_take isl_schedule *sched);
6504 The function C<isl_schedule_constraints_compute_schedule> can be
6505 used to compute a schedule that satisfies the given schedule constraints.
6506 These schedule constraints include the iteration domain for which
6507 a schedule should be computed and dependences between pairs of
6508 iterations. In particular, these dependences include
6509 I<validity> dependences and I<proximity> dependences.
6510 By default, the algorithm used to construct the schedule is similar
6511 to that of C<Pluto>.
6512 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
6514 The generated schedule respects all validity dependences.
6515 That is, all dependence distances over these dependences in the
6516 scheduled space are lexicographically positive.
6517 The default algorithm tries to ensure that the dependence distances
6518 over coincidence constraints are zero and to minimize the
6519 dependence distances over proximity dependences.
6520 Moreover, it tries to obtain sequences (bands) of schedule dimensions
6521 for groups of domains where the dependence distances over validity
6522 dependences have only non-negative values.
6523 When using Feautrier's algorithm, the coincidence and proximity constraints
6524 are only taken into account during the extension to a
6525 full-dimensional schedule.
6527 An C<isl_schedule_constraints> object can be constructed
6528 and manipulated using the following functions.
6530 #include <isl/schedule.h>
6531 __isl_give isl_schedule_constraints *
6532 isl_schedule_constraints_copy(
6533 __isl_keep isl_schedule_constraints *sc);
6534 __isl_give isl_schedule_constraints *
6535 isl_schedule_constraints_on_domain(
6536 __isl_take isl_union_set *domain);
6537 __isl_give isl_schedule_constraints *
6538 isl_schedule_constraints_set_validity(
6539 __isl_take isl_schedule_constraints *sc,
6540 __isl_take isl_union_map *validity);
6541 __isl_give isl_schedule_constraints *
6542 isl_schedule_constraints_set_coincidence(
6543 __isl_take isl_schedule_constraints *sc,
6544 __isl_take isl_union_map *coincidence);
6545 __isl_give isl_schedule_constraints *
6546 isl_schedule_constraints_set_proximity(
6547 __isl_take isl_schedule_constraints *sc,
6548 __isl_take isl_union_map *proximity);
6549 __isl_give isl_schedule_constraints *
6550 isl_schedule_constraints_set_conditional_validity(
6551 __isl_take isl_schedule_constraints *sc,
6552 __isl_take isl_union_map *condition,
6553 __isl_take isl_union_map *validity);
6554 __isl_null isl_schedule_constraints *
6555 isl_schedule_constraints_free(
6556 __isl_take isl_schedule_constraints *sc);
6558 The initial C<isl_schedule_constraints> object created by
6559 C<isl_schedule_constraints_on_domain> does not impose any constraints.
6560 That is, it has an empty set of dependences.
6561 The function C<isl_schedule_constraints_set_validity> replaces the
6562 validity dependences, mapping domain elements I<i> to domain
6563 elements that should be scheduled after I<i>.
6564 The function C<isl_schedule_constraints_set_coincidence> replaces the
6565 coincidence dependences, mapping domain elements I<i> to domain
6566 elements that should be scheduled together with I<I>, if possible.
6567 The function C<isl_schedule_constraints_set_proximity> replaces the
6568 proximity dependences, mapping domain elements I<i> to domain
6569 elements that should be scheduled either before I<I>
6570 or as early as possible after I<i>.
6572 The function C<isl_schedule_constraints_set_conditional_validity>
6573 replaces the conditional validity constraints.
6574 A conditional validity constraint is only imposed when any of the corresponding
6575 conditions is satisfied, i.e., when any of them is non-zero.
6576 That is, the scheduler ensures that within each band if the dependence
6577 distances over the condition constraints are not all zero
6578 then all corresponding conditional validity constraints are respected.
6579 A conditional validity constraint corresponds to a condition
6580 if the two are adjacent, i.e., if the domain of one relation intersect
6581 the range of the other relation.
6582 The typical use case of conditional validity constraints is
6583 to allow order constraints between live ranges to be violated
6584 as long as the live ranges themselves are local to the band.
6585 To allow more fine-grained control over which conditions correspond
6586 to which conditional validity constraints, the domains and ranges
6587 of these relations may include I<tags>. That is, the domains and
6588 ranges of those relation may themselves be wrapped relations
6589 where the iteration domain appears in the domain of those wrapped relations
6590 and the range of the wrapped relations can be arbitrarily chosen
6591 by the user. Conditions and conditional validity constraints are only
6592 considered adjacent to each other if the entire wrapped relation matches.
6593 In particular, a relation with a tag will never be considered adjacent
6594 to a relation without a tag.
6596 The following function computes a schedule directly from
6597 an iteration domain and validity and proximity dependences
6598 and is implemented in terms of the functions described above.
6599 The use of C<isl_union_set_compute_schedule> is discouraged.
6601 #include <isl/schedule.h>
6602 __isl_give isl_schedule *isl_union_set_compute_schedule(
6603 __isl_take isl_union_set *domain,
6604 __isl_take isl_union_map *validity,
6605 __isl_take isl_union_map *proximity);
6607 A mapping from the domains to the scheduled space can be obtained
6608 from an C<isl_schedule> using the following function.
6610 __isl_give isl_union_map *isl_schedule_get_map(
6611 __isl_keep isl_schedule *sched);
6613 A representation of the schedule can be printed using
6615 __isl_give isl_printer *isl_printer_print_schedule(
6616 __isl_take isl_printer *p,
6617 __isl_keep isl_schedule *schedule);
6619 A representation of the schedule as a forest of bands can be obtained
6620 using the following function.
6622 __isl_give isl_band_list *isl_schedule_get_band_forest(
6623 __isl_keep isl_schedule *schedule);
6625 The individual bands can be visited in depth-first post-order
6626 using the following function.
6628 #include <isl/schedule.h>
6629 int isl_schedule_foreach_band(
6630 __isl_keep isl_schedule *sched,
6631 int (*fn)(__isl_keep isl_band *band, void *user),
6634 The list can be manipulated as explained in L<"Lists">.
6635 The bands inside the list can be copied and freed using the following
6638 #include <isl/band.h>
6639 __isl_give isl_band *isl_band_copy(
6640 __isl_keep isl_band *band);
6641 __isl_null isl_band *isl_band_free(
6642 __isl_take isl_band *band);
6644 Each band contains zero or more scheduling dimensions.
6645 These are referred to as the members of the band.
6646 The section of the schedule that corresponds to the band is
6647 referred to as the partial schedule of the band.
6648 For those nodes that participate in a band, the outer scheduling
6649 dimensions form the prefix schedule, while the inner scheduling
6650 dimensions form the suffix schedule.
6651 That is, if we take a cut of the band forest, then the union of
6652 the concatenations of the prefix, partial and suffix schedules of
6653 each band in the cut is equal to the entire schedule (modulo
6654 some possible padding at the end with zero scheduling dimensions).
6655 The properties of a band can be inspected using the following functions.
6657 #include <isl/band.h>
6658 int isl_band_has_children(__isl_keep isl_band *band);
6659 __isl_give isl_band_list *isl_band_get_children(
6660 __isl_keep isl_band *band);
6662 __isl_give isl_union_map *isl_band_get_prefix_schedule(
6663 __isl_keep isl_band *band);
6664 __isl_give isl_union_map *isl_band_get_partial_schedule(
6665 __isl_keep isl_band *band);
6666 __isl_give isl_union_map *isl_band_get_suffix_schedule(
6667 __isl_keep isl_band *band);
6669 int isl_band_n_member(__isl_keep isl_band *band);
6670 int isl_band_member_is_coincident(
6671 __isl_keep isl_band *band, int pos);
6673 int isl_band_list_foreach_band(
6674 __isl_keep isl_band_list *list,
6675 int (*fn)(__isl_keep isl_band *band, void *user),
6678 Note that a scheduling dimension is considered to be ``coincident''
6679 if it satisfies the coincidence constraints within its band.
6680 That is, if the dependence distances of the coincidence
6681 constraints are all zero in that direction (for fixed
6682 iterations of outer bands).
6683 Like C<isl_schedule_foreach_band>,
6684 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
6685 in depth-first post-order.
6687 A band can be tiled using the following function.
6689 #include <isl/band.h>
6690 int isl_band_tile(__isl_keep isl_band *band,
6691 __isl_take isl_vec *sizes);
6693 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
6695 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
6696 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
6698 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
6700 The C<isl_band_tile> function tiles the band using the given tile sizes
6701 inside its schedule.
6702 A new child band is created to represent the point loops and it is
6703 inserted between the modified band and its children.
6704 The C<tile_scale_tile_loops> option specifies whether the tile
6705 loops iterators should be scaled by the tile sizes.
6706 If the C<tile_shift_point_loops> option is set, then the point loops
6707 are shifted to start at zero.
6709 A band can be split into two nested bands using the following function.
6711 int isl_band_split(__isl_keep isl_band *band, int pos);
6713 The resulting outer band contains the first C<pos> dimensions of C<band>
6714 while the inner band contains the remaining dimensions.
6716 A representation of the band can be printed using
6718 #include <isl/band.h>
6719 __isl_give isl_printer *isl_printer_print_band(
6720 __isl_take isl_printer *p,
6721 __isl_keep isl_band *band);
6725 #include <isl/schedule.h>
6726 int isl_options_set_schedule_max_coefficient(
6727 isl_ctx *ctx, int val);
6728 int isl_options_get_schedule_max_coefficient(
6730 int isl_options_set_schedule_max_constant_term(
6731 isl_ctx *ctx, int val);
6732 int isl_options_get_schedule_max_constant_term(
6734 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
6735 int isl_options_get_schedule_fuse(isl_ctx *ctx);
6736 int isl_options_set_schedule_maximize_band_depth(
6737 isl_ctx *ctx, int val);
6738 int isl_options_get_schedule_maximize_band_depth(
6740 int isl_options_set_schedule_outer_coincidence(
6741 isl_ctx *ctx, int val);
6742 int isl_options_get_schedule_outer_coincidence(
6744 int isl_options_set_schedule_split_scaled(
6745 isl_ctx *ctx, int val);
6746 int isl_options_get_schedule_split_scaled(
6748 int isl_options_set_schedule_algorithm(
6749 isl_ctx *ctx, int val);
6750 int isl_options_get_schedule_algorithm(
6752 int isl_options_set_schedule_separate_components(
6753 isl_ctx *ctx, int val);
6754 int isl_options_get_schedule_separate_components(
6759 =item * schedule_max_coefficient
6761 This option enforces that the coefficients for variable and parameter
6762 dimensions in the calculated schedule are not larger than the specified value.
6763 This option can significantly increase the speed of the scheduling calculation
6764 and may also prevent fusing of unrelated dimensions. A value of -1 means that
6765 this option does not introduce bounds on the variable or parameter
6768 =item * schedule_max_constant_term
6770 This option enforces that the constant coefficients in the calculated schedule
6771 are not larger than the maximal constant term. This option can significantly
6772 increase the speed of the scheduling calculation and may also prevent fusing of
6773 unrelated dimensions. A value of -1 means that this option does not introduce
6774 bounds on the constant coefficients.
6776 =item * schedule_fuse
6778 This option controls the level of fusion.
6779 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
6780 resulting schedule will be distributed as much as possible.
6781 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
6782 try to fuse loops in the resulting schedule.
6784 =item * schedule_maximize_band_depth
6786 If this option is set, we do not split bands at the point
6787 where we detect splitting is necessary. Instead, we
6788 backtrack and split bands as early as possible. This
6789 reduces the number of splits and maximizes the width of
6790 the bands. Wider bands give more possibilities for tiling.
6791 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
6792 then bands will be split as early as possible, even if there is no need.
6793 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
6795 =item * schedule_outer_coincidence
6797 If this option is set, then we try to construct schedules
6798 where the outermost scheduling dimension in each band
6799 satisfies the coincidence constraints.
6801 =item * schedule_split_scaled
6803 If this option is set, then we try to construct schedules in which the
6804 constant term is split off from the linear part if the linear parts of
6805 the scheduling rows for all nodes in the graphs have a common non-trivial
6807 The constant term is then placed in a separate band and the linear
6810 =item * schedule_algorithm
6812 Selects the scheduling algorithm to be used.
6813 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
6814 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
6816 =item * schedule_separate_components
6818 If at any point the dependence graph contains any (weakly connected) components,
6819 then these components are scheduled separately.
6820 If this option is not set, then some iterations of the domains
6821 in these components may be scheduled together.
6822 If this option is set, then the components are given consecutive
6827 =head2 AST Generation
6829 This section describes the C<isl> functionality for generating
6830 ASTs that visit all the elements
6831 in a domain in an order specified by a schedule.
6832 In particular, given a C<isl_union_map>, an AST is generated
6833 that visits all the elements in the domain of the C<isl_union_map>
6834 according to the lexicographic order of the corresponding image
6835 element(s). If the range of the C<isl_union_map> consists of
6836 elements in more than one space, then each of these spaces is handled
6837 separately in an arbitrary order.
6838 It should be noted that the image elements only specify the I<order>
6839 in which the corresponding domain elements should be visited.
6840 No direct relation between the image elements and the loop iterators
6841 in the generated AST should be assumed.
6843 Each AST is generated within a build. The initial build
6844 simply specifies the constraints on the parameters (if any)
6845 and can be created, inspected, copied and freed using the following functions.
6847 #include <isl/ast_build.h>
6848 __isl_give isl_ast_build *isl_ast_build_from_context(
6849 __isl_take isl_set *set);
6850 __isl_give isl_ast_build *isl_ast_build_copy(
6851 __isl_keep isl_ast_build *build);
6852 __isl_null isl_ast_build *isl_ast_build_free(
6853 __isl_take isl_ast_build *build);
6855 The C<set> argument is usually a parameter set with zero or more parameters.
6856 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
6857 and L</"Fine-grained Control over AST Generation">.
6858 Finally, the AST itself can be constructed using the following
6861 #include <isl/ast_build.h>
6862 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
6863 __isl_keep isl_ast_build *build,
6864 __isl_take isl_union_map *schedule);
6866 =head3 Inspecting the AST
6868 The basic properties of an AST node can be obtained as follows.
6870 #include <isl/ast.h>
6871 enum isl_ast_node_type isl_ast_node_get_type(
6872 __isl_keep isl_ast_node *node);
6874 The type of an AST node is one of
6875 C<isl_ast_node_for>,
6877 C<isl_ast_node_block> or
6878 C<isl_ast_node_user>.
6879 An C<isl_ast_node_for> represents a for node.
6880 An C<isl_ast_node_if> represents an if node.
6881 An C<isl_ast_node_block> represents a compound node.
6882 An C<isl_ast_node_user> represents an expression statement.
6883 An expression statement typically corresponds to a domain element, i.e.,
6884 one of the elements that is visited by the AST.
6886 Each type of node has its own additional properties.
6888 #include <isl/ast.h>
6889 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
6890 __isl_keep isl_ast_node *node);
6891 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
6892 __isl_keep isl_ast_node *node);
6893 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
6894 __isl_keep isl_ast_node *node);
6895 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
6896 __isl_keep isl_ast_node *node);
6897 __isl_give isl_ast_node *isl_ast_node_for_get_body(
6898 __isl_keep isl_ast_node *node);
6899 int isl_ast_node_for_is_degenerate(
6900 __isl_keep isl_ast_node *node);
6902 An C<isl_ast_for> is considered degenerate if it is known to execute
6905 #include <isl/ast.h>
6906 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
6907 __isl_keep isl_ast_node *node);
6908 __isl_give isl_ast_node *isl_ast_node_if_get_then(
6909 __isl_keep isl_ast_node *node);
6910 int isl_ast_node_if_has_else(
6911 __isl_keep isl_ast_node *node);
6912 __isl_give isl_ast_node *isl_ast_node_if_get_else(
6913 __isl_keep isl_ast_node *node);
6915 __isl_give isl_ast_node_list *
6916 isl_ast_node_block_get_children(
6917 __isl_keep isl_ast_node *node);
6919 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
6920 __isl_keep isl_ast_node *node);
6922 Each of the returned C<isl_ast_expr>s can in turn be inspected using
6923 the following functions.
6925 #include <isl/ast.h>
6926 enum isl_ast_expr_type isl_ast_expr_get_type(
6927 __isl_keep isl_ast_expr *expr);
6929 The type of an AST expression is one of
6931 C<isl_ast_expr_id> or
6932 C<isl_ast_expr_int>.
6933 An C<isl_ast_expr_op> represents the result of an operation.
6934 An C<isl_ast_expr_id> represents an identifier.
6935 An C<isl_ast_expr_int> represents an integer value.
6937 Each type of expression has its own additional properties.
6939 #include <isl/ast.h>
6940 enum isl_ast_op_type isl_ast_expr_get_op_type(
6941 __isl_keep isl_ast_expr *expr);
6942 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
6943 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
6944 __isl_keep isl_ast_expr *expr, int pos);
6945 int isl_ast_node_foreach_ast_op_type(
6946 __isl_keep isl_ast_node *node,
6947 int (*fn)(enum isl_ast_op_type type, void *user),
6950 C<isl_ast_expr_get_op_type> returns the type of the operation
6951 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
6952 arguments. C<isl_ast_expr_get_op_arg> returns the specified
6954 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
6955 C<isl_ast_op_type> that appears in C<node>.
6956 The operation type is one of the following.
6960 =item C<isl_ast_op_and>
6962 Logical I<and> of two arguments.
6963 Both arguments can be evaluated.
6965 =item C<isl_ast_op_and_then>
6967 Logical I<and> of two arguments.
6968 The second argument can only be evaluated if the first evaluates to true.
6970 =item C<isl_ast_op_or>
6972 Logical I<or> of two arguments.
6973 Both arguments can be evaluated.
6975 =item C<isl_ast_op_or_else>
6977 Logical I<or> of two arguments.
6978 The second argument can only be evaluated if the first evaluates to false.
6980 =item C<isl_ast_op_max>
6982 Maximum of two or more arguments.
6984 =item C<isl_ast_op_min>
6986 Minimum of two or more arguments.
6988 =item C<isl_ast_op_minus>
6992 =item C<isl_ast_op_add>
6994 Sum of two arguments.
6996 =item C<isl_ast_op_sub>
6998 Difference of two arguments.
7000 =item C<isl_ast_op_mul>
7002 Product of two arguments.
7004 =item C<isl_ast_op_div>
7006 Exact division. That is, the result is known to be an integer.
7008 =item C<isl_ast_op_fdiv_q>
7010 Result of integer division, rounded towards negative
7013 =item C<isl_ast_op_pdiv_q>
7015 Result of integer division, where dividend is known to be non-negative.
7017 =item C<isl_ast_op_pdiv_r>
7019 Remainder of integer division, where dividend is known to be non-negative.
7021 =item C<isl_ast_op_zdiv_r>
7023 Equal to zero iff the remainder on integer division is zero.
7025 =item C<isl_ast_op_cond>
7027 Conditional operator defined on three arguments.
7028 If the first argument evaluates to true, then the result
7029 is equal to the second argument. Otherwise, the result
7030 is equal to the third argument.
7031 The second and third argument may only be evaluated if
7032 the first argument evaluates to true and false, respectively.
7033 Corresponds to C<a ? b : c> in C.
7035 =item C<isl_ast_op_select>
7037 Conditional operator defined on three arguments.
7038 If the first argument evaluates to true, then the result
7039 is equal to the second argument. Otherwise, the result
7040 is equal to the third argument.
7041 The second and third argument may be evaluated independently
7042 of the value of the first argument.
7043 Corresponds to C<a * b + (1 - a) * c> in C.
7045 =item C<isl_ast_op_eq>
7049 =item C<isl_ast_op_le>
7051 Less than or equal relation.
7053 =item C<isl_ast_op_lt>
7057 =item C<isl_ast_op_ge>
7059 Greater than or equal relation.
7061 =item C<isl_ast_op_gt>
7063 Greater than relation.
7065 =item C<isl_ast_op_call>
7068 The number of arguments of the C<isl_ast_expr> is one more than
7069 the number of arguments in the function call, the first argument
7070 representing the function being called.
7072 =item C<isl_ast_op_access>
7075 The number of arguments of the C<isl_ast_expr> is one more than
7076 the number of index expressions in the array access, the first argument
7077 representing the array being accessed.
7079 =item C<isl_ast_op_member>
7082 This operation has two arguments, a structure and the name of
7083 the member of the structure being accessed.
7087 #include <isl/ast.h>
7088 __isl_give isl_id *isl_ast_expr_get_id(
7089 __isl_keep isl_ast_expr *expr);
7091 Return the identifier represented by the AST expression.
7093 #include <isl/ast.h>
7094 __isl_give isl_val *isl_ast_expr_get_val(
7095 __isl_keep isl_ast_expr *expr);
7097 Return the integer represented by the AST expression.
7099 =head3 Properties of ASTs
7101 #include <isl/ast.h>
7102 int isl_ast_expr_is_equal(__isl_keep isl_ast_expr *expr1,
7103 __isl_keep isl_ast_expr *expr2);
7105 Check if two C<isl_ast_expr>s are equal to each other.
7107 =head3 Manipulating and printing the AST
7109 AST nodes can be copied and freed using the following functions.
7111 #include <isl/ast.h>
7112 __isl_give isl_ast_node *isl_ast_node_copy(
7113 __isl_keep isl_ast_node *node);
7114 __isl_null isl_ast_node *isl_ast_node_free(
7115 __isl_take isl_ast_node *node);
7117 AST expressions can be copied and freed using the following functions.
7119 #include <isl/ast.h>
7120 __isl_give isl_ast_expr *isl_ast_expr_copy(
7121 __isl_keep isl_ast_expr *expr);
7122 __isl_null isl_ast_expr *isl_ast_expr_free(
7123 __isl_take isl_ast_expr *expr);
7125 New AST expressions can be created either directly or within
7126 the context of an C<isl_ast_build>.
7128 #include <isl/ast.h>
7129 __isl_give isl_ast_expr *isl_ast_expr_from_val(
7130 __isl_take isl_val *v);
7131 __isl_give isl_ast_expr *isl_ast_expr_from_id(
7132 __isl_take isl_id *id);
7133 __isl_give isl_ast_expr *isl_ast_expr_neg(
7134 __isl_take isl_ast_expr *expr);
7135 __isl_give isl_ast_expr *isl_ast_expr_address_of(
7136 __isl_take isl_ast_expr *expr);
7137 __isl_give isl_ast_expr *isl_ast_expr_add(
7138 __isl_take isl_ast_expr *expr1,
7139 __isl_take isl_ast_expr *expr2);
7140 __isl_give isl_ast_expr *isl_ast_expr_sub(
7141 __isl_take isl_ast_expr *expr1,
7142 __isl_take isl_ast_expr *expr2);
7143 __isl_give isl_ast_expr *isl_ast_expr_mul(
7144 __isl_take isl_ast_expr *expr1,
7145 __isl_take isl_ast_expr *expr2);
7146 __isl_give isl_ast_expr *isl_ast_expr_div(
7147 __isl_take isl_ast_expr *expr1,
7148 __isl_take isl_ast_expr *expr2);
7149 __isl_give isl_ast_expr *isl_ast_expr_and(
7150 __isl_take isl_ast_expr *expr1,
7151 __isl_take isl_ast_expr *expr2)
7152 __isl_give isl_ast_expr *isl_ast_expr_or(
7153 __isl_take isl_ast_expr *expr1,
7154 __isl_take isl_ast_expr *expr2)
7155 __isl_give isl_ast_expr *isl_ast_expr_eq(
7156 __isl_take isl_ast_expr *expr1,
7157 __isl_take isl_ast_expr *expr2);
7158 __isl_give isl_ast_expr *isl_ast_expr_le(
7159 __isl_take isl_ast_expr *expr1,
7160 __isl_take isl_ast_expr *expr2);
7161 __isl_give isl_ast_expr *isl_ast_expr_lt(
7162 __isl_take isl_ast_expr *expr1,
7163 __isl_take isl_ast_expr *expr2);
7164 __isl_give isl_ast_expr *isl_ast_expr_ge(
7165 __isl_take isl_ast_expr *expr1,
7166 __isl_take isl_ast_expr *expr2);
7167 __isl_give isl_ast_expr *isl_ast_expr_gt(
7168 __isl_take isl_ast_expr *expr1,
7169 __isl_take isl_ast_expr *expr2);
7170 __isl_give isl_ast_expr *isl_ast_expr_access(
7171 __isl_take isl_ast_expr *array,
7172 __isl_take isl_ast_expr_list *indices);
7174 The function C<isl_ast_expr_address_of> can be applied to an
7175 C<isl_ast_expr> of type C<isl_ast_op_access> only. It is meant
7176 to represent the address of the C<isl_ast_expr_access>.
7178 #include <isl/ast_build.h>
7179 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
7180 __isl_keep isl_ast_build *build,
7181 __isl_take isl_pw_aff *pa);
7182 __isl_give isl_ast_expr *
7183 isl_ast_build_access_from_pw_multi_aff(
7184 __isl_keep isl_ast_build *build,
7185 __isl_take isl_pw_multi_aff *pma);
7186 __isl_give isl_ast_expr *
7187 isl_ast_build_access_from_multi_pw_aff(
7188 __isl_keep isl_ast_build *build,
7189 __isl_take isl_multi_pw_aff *mpa);
7190 __isl_give isl_ast_expr *
7191 isl_ast_build_call_from_pw_multi_aff(
7192 __isl_keep isl_ast_build *build,
7193 __isl_take isl_pw_multi_aff *pma);
7194 __isl_give isl_ast_expr *
7195 isl_ast_build_call_from_multi_pw_aff(
7196 __isl_keep isl_ast_build *build,
7197 __isl_take isl_multi_pw_aff *mpa);
7199 The domains of C<pa>, C<mpa> and C<pma> should correspond
7200 to the schedule space of C<build>.
7201 The tuple id of C<mpa> or C<pma> is used as the array being accessed or
7202 the function being called.
7203 If the accessed space is a nested relation, then it is taken
7204 to represent an access of the member specified by the range
7205 of this nested relation of the structure specified by the domain
7206 of the nested relation.
7208 The following functions can be used to modify an C<isl_ast_expr>.
7210 #include <isl/ast.h>
7211 __isl_give isl_ast_expr *isl_ast_expr_set_op_arg(
7212 __isl_take isl_ast_expr *expr, int pos,
7213 __isl_take isl_ast_expr *arg);
7215 Replace the argument of C<expr> at position C<pos> by C<arg>.
7217 #include <isl/ast.h>
7218 __isl_give isl_ast_expr *isl_ast_expr_substitute_ids(
7219 __isl_take isl_ast_expr *expr,
7220 __isl_take isl_id_to_ast_expr *id2expr);
7222 The function C<isl_ast_expr_substitute_ids> replaces the
7223 subexpressions of C<expr> of type C<isl_ast_expr_id>
7224 by the corresponding expression in C<id2expr>, if there is any.
7227 User specified data can be attached to an C<isl_ast_node> and obtained
7228 from the same C<isl_ast_node> using the following functions.
7230 #include <isl/ast.h>
7231 __isl_give isl_ast_node *isl_ast_node_set_annotation(
7232 __isl_take isl_ast_node *node,
7233 __isl_take isl_id *annotation);
7234 __isl_give isl_id *isl_ast_node_get_annotation(
7235 __isl_keep isl_ast_node *node);
7237 Basic printing can be performed using the following functions.
7239 #include <isl/ast.h>
7240 __isl_give isl_printer *isl_printer_print_ast_expr(
7241 __isl_take isl_printer *p,
7242 __isl_keep isl_ast_expr *expr);
7243 __isl_give isl_printer *isl_printer_print_ast_node(
7244 __isl_take isl_printer *p,
7245 __isl_keep isl_ast_node *node);
7246 __isl_give char *isl_ast_expr_to_str(
7247 __isl_keep isl_ast_expr *expr);
7249 More advanced printing can be performed using the following functions.
7251 #include <isl/ast.h>
7252 __isl_give isl_printer *isl_ast_op_type_print_macro(
7253 enum isl_ast_op_type type,
7254 __isl_take isl_printer *p);
7255 __isl_give isl_printer *isl_ast_node_print_macros(
7256 __isl_keep isl_ast_node *node,
7257 __isl_take isl_printer *p);
7258 __isl_give isl_printer *isl_ast_node_print(
7259 __isl_keep isl_ast_node *node,
7260 __isl_take isl_printer *p,
7261 __isl_take isl_ast_print_options *options);
7262 __isl_give isl_printer *isl_ast_node_for_print(
7263 __isl_keep isl_ast_node *node,
7264 __isl_take isl_printer *p,
7265 __isl_take isl_ast_print_options *options);
7266 __isl_give isl_printer *isl_ast_node_if_print(
7267 __isl_keep isl_ast_node *node,
7268 __isl_take isl_printer *p,
7269 __isl_take isl_ast_print_options *options);
7271 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
7272 C<isl> may print out an AST that makes use of macros such
7273 as C<floord>, C<min> and C<max>.
7274 C<isl_ast_op_type_print_macro> prints out the macro
7275 corresponding to a specific C<isl_ast_op_type>.
7276 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
7277 for expressions where these macros would be used and prints
7278 out the required macro definitions.
7279 Essentially, C<isl_ast_node_print_macros> calls
7280 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
7281 as function argument.
7282 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
7283 C<isl_ast_node_if_print> print an C<isl_ast_node>
7284 in C<ISL_FORMAT_C>, but allow for some extra control
7285 through an C<isl_ast_print_options> object.
7286 This object can be created using the following functions.
7288 #include <isl/ast.h>
7289 __isl_give isl_ast_print_options *
7290 isl_ast_print_options_alloc(isl_ctx *ctx);
7291 __isl_give isl_ast_print_options *
7292 isl_ast_print_options_copy(
7293 __isl_keep isl_ast_print_options *options);
7294 __isl_null isl_ast_print_options *
7295 isl_ast_print_options_free(
7296 __isl_take isl_ast_print_options *options);
7298 __isl_give isl_ast_print_options *
7299 isl_ast_print_options_set_print_user(
7300 __isl_take isl_ast_print_options *options,
7301 __isl_give isl_printer *(*print_user)(
7302 __isl_take isl_printer *p,
7303 __isl_take isl_ast_print_options *options,
7304 __isl_keep isl_ast_node *node, void *user),
7306 __isl_give isl_ast_print_options *
7307 isl_ast_print_options_set_print_for(
7308 __isl_take isl_ast_print_options *options,
7309 __isl_give isl_printer *(*print_for)(
7310 __isl_take isl_printer *p,
7311 __isl_take isl_ast_print_options *options,
7312 __isl_keep isl_ast_node *node, void *user),
7315 The callback set by C<isl_ast_print_options_set_print_user>
7316 is called whenever a node of type C<isl_ast_node_user> needs to
7318 The callback set by C<isl_ast_print_options_set_print_for>
7319 is called whenever a node of type C<isl_ast_node_for> needs to
7321 Note that C<isl_ast_node_for_print> will I<not> call the
7322 callback set by C<isl_ast_print_options_set_print_for> on the node
7323 on which C<isl_ast_node_for_print> is called, but only on nested
7324 nodes of type C<isl_ast_node_for>. It is therefore safe to
7325 call C<isl_ast_node_for_print> from within the callback set by
7326 C<isl_ast_print_options_set_print_for>.
7328 The following option determines the type to be used for iterators
7329 while printing the AST.
7331 int isl_options_set_ast_iterator_type(
7332 isl_ctx *ctx, const char *val);
7333 const char *isl_options_get_ast_iterator_type(
7336 The AST printer only prints body nodes as blocks if these
7337 blocks cannot be safely omitted.
7338 For example, a C<for> node with one body node will not be
7339 surrounded with braces in C<ISL_FORMAT_C>.
7340 A block will always be printed by setting the following option.
7342 int isl_options_set_ast_always_print_block(isl_ctx *ctx,
7344 int isl_options_get_ast_always_print_block(isl_ctx *ctx);
7348 #include <isl/ast_build.h>
7349 int isl_options_set_ast_build_atomic_upper_bound(
7350 isl_ctx *ctx, int val);
7351 int isl_options_get_ast_build_atomic_upper_bound(
7353 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
7355 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
7356 int isl_options_set_ast_build_exploit_nested_bounds(
7357 isl_ctx *ctx, int val);
7358 int isl_options_get_ast_build_exploit_nested_bounds(
7360 int isl_options_set_ast_build_group_coscheduled(
7361 isl_ctx *ctx, int val);
7362 int isl_options_get_ast_build_group_coscheduled(
7364 int isl_options_set_ast_build_scale_strides(
7365 isl_ctx *ctx, int val);
7366 int isl_options_get_ast_build_scale_strides(
7368 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
7370 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
7371 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
7373 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
7377 =item * ast_build_atomic_upper_bound
7379 Generate loop upper bounds that consist of the current loop iterator,
7380 an operator and an expression not involving the iterator.
7381 If this option is not set, then the current loop iterator may appear
7382 several times in the upper bound.
7383 For example, when this option is turned off, AST generation
7386 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
7390 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
7393 When the option is turned on, the following AST is generated
7395 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
7398 =item * ast_build_prefer_pdiv
7400 If this option is turned off, then the AST generation will
7401 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
7402 operators, but no C<isl_ast_op_pdiv_q> or
7403 C<isl_ast_op_pdiv_r> operators.
7404 If this options is turned on, then C<isl> will try to convert
7405 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
7406 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
7408 =item * ast_build_exploit_nested_bounds
7410 Simplify conditions based on bounds of nested for loops.
7411 In particular, remove conditions that are implied by the fact
7412 that one or more nested loops have at least one iteration,
7413 meaning that the upper bound is at least as large as the lower bound.
7414 For example, when this option is turned off, AST generation
7417 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
7423 for (int c0 = 0; c0 <= N; c0 += 1)
7424 for (int c1 = 0; c1 <= M; c1 += 1)
7427 When the option is turned on, the following AST is generated
7429 for (int c0 = 0; c0 <= N; c0 += 1)
7430 for (int c1 = 0; c1 <= M; c1 += 1)
7433 =item * ast_build_group_coscheduled
7435 If two domain elements are assigned the same schedule point, then
7436 they may be executed in any order and they may even appear in different
7437 loops. If this options is set, then the AST generator will make
7438 sure that coscheduled domain elements do not appear in separate parts
7439 of the AST. This is useful in case of nested AST generation
7440 if the outer AST generation is given only part of a schedule
7441 and the inner AST generation should handle the domains that are
7442 coscheduled by this initial part of the schedule together.
7443 For example if an AST is generated for a schedule
7445 { A[i] -> [0]; B[i] -> [0] }
7447 then the C<isl_ast_build_set_create_leaf> callback described
7448 below may get called twice, once for each domain.
7449 Setting this option ensures that the callback is only called once
7450 on both domains together.
7452 =item * ast_build_separation_bounds
7454 This option specifies which bounds to use during separation.
7455 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
7456 then all (possibly implicit) bounds on the current dimension will
7457 be used during separation.
7458 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
7459 then only those bounds that are explicitly available will
7460 be used during separation.
7462 =item * ast_build_scale_strides
7464 This option specifies whether the AST generator is allowed
7465 to scale down iterators of strided loops.
7467 =item * ast_build_allow_else
7469 This option specifies whether the AST generator is allowed
7470 to construct if statements with else branches.
7472 =item * ast_build_allow_or
7474 This option specifies whether the AST generator is allowed
7475 to construct if conditions with disjunctions.
7479 =head3 Fine-grained Control over AST Generation
7481 Besides specifying the constraints on the parameters,
7482 an C<isl_ast_build> object can be used to control
7483 various aspects of the AST generation process.
7484 The most prominent way of control is through ``options'',
7485 which can be set using the following function.
7487 #include <isl/ast_build.h>
7488 __isl_give isl_ast_build *
7489 isl_ast_build_set_options(
7490 __isl_take isl_ast_build *control,
7491 __isl_take isl_union_map *options);
7493 The options are encoded in an C<isl_union_map>.
7494 The domain of this union relation refers to the schedule domain,
7495 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
7496 In the case of nested AST generation (see L</"Nested AST Generation">),
7497 the domain of C<options> should refer to the extra piece of the schedule.
7498 That is, it should be equal to the range of the wrapped relation in the
7499 range of the schedule.
7500 The range of the options can consist of elements in one or more spaces,
7501 the names of which determine the effect of the option.
7502 The values of the range typically also refer to the schedule dimension
7503 to which the option applies. In case of nested AST generation
7504 (see L</"Nested AST Generation">), these values refer to the position
7505 of the schedule dimension within the innermost AST generation.
7506 The constraints on the domain elements of
7507 the option should only refer to this dimension and earlier dimensions.
7508 We consider the following spaces.
7512 =item C<separation_class>
7514 This space is a wrapped relation between two one dimensional spaces.
7515 The input space represents the schedule dimension to which the option
7516 applies and the output space represents the separation class.
7517 While constructing a loop corresponding to the specified schedule
7518 dimension(s), the AST generator will try to generate separate loops
7519 for domain elements that are assigned different classes.
7520 If only some of the elements are assigned a class, then those elements
7521 that are not assigned any class will be treated as belonging to a class
7522 that is separate from the explicitly assigned classes.
7523 The typical use case for this option is to separate full tiles from
7525 The other options, described below, are applied after the separation
7528 As an example, consider the separation into full and partial tiles
7529 of a tiling of a triangular domain.
7530 Take, for example, the domain
7532 { A[i,j] : 0 <= i,j and i + j <= 100 }
7534 and a tiling into tiles of 10 by 10. The input to the AST generator
7535 is then the schedule
7537 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
7540 Without any options, the following AST is generated
7542 for (int c0 = 0; c0 <= 10; c0 += 1)
7543 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7544 for (int c2 = 10 * c0;
7545 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7547 for (int c3 = 10 * c1;
7548 c3 <= min(10 * c1 + 9, -c2 + 100);
7552 Separation into full and partial tiles can be obtained by assigning
7553 a class, say C<0>, to the full tiles. The full tiles are represented by those
7554 values of the first and second schedule dimensions for which there are
7555 values of the third and fourth dimensions to cover an entire tile.
7556 That is, we need to specify the following option
7558 { [a,b,c,d] -> separation_class[[0]->[0]] :
7559 exists b': 0 <= 10a,10b' and
7560 10a+9+10b'+9 <= 100;
7561 [a,b,c,d] -> separation_class[[1]->[0]] :
7562 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
7566 { [a, b, c, d] -> separation_class[[1] -> [0]] :
7567 a >= 0 and b >= 0 and b <= 8 - a;
7568 [a, b, c, d] -> separation_class[[0] -> [0]] :
7571 With this option, the generated AST is as follows
7574 for (int c0 = 0; c0 <= 8; c0 += 1) {
7575 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
7576 for (int c2 = 10 * c0;
7577 c2 <= 10 * c0 + 9; c2 += 1)
7578 for (int c3 = 10 * c1;
7579 c3 <= 10 * c1 + 9; c3 += 1)
7581 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
7582 for (int c2 = 10 * c0;
7583 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7585 for (int c3 = 10 * c1;
7586 c3 <= min(-c2 + 100, 10 * c1 + 9);
7590 for (int c0 = 9; c0 <= 10; c0 += 1)
7591 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
7592 for (int c2 = 10 * c0;
7593 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
7595 for (int c3 = 10 * c1;
7596 c3 <= min(10 * c1 + 9, -c2 + 100);
7603 This is a single-dimensional space representing the schedule dimension(s)
7604 to which ``separation'' should be applied. Separation tries to split
7605 a loop into several pieces if this can avoid the generation of guards
7607 See also the C<atomic> option.
7611 This is a single-dimensional space representing the schedule dimension(s)
7612 for which the domains should be considered ``atomic''. That is, the
7613 AST generator will make sure that any given domain space will only appear
7614 in a single loop at the specified level.
7616 Consider the following schedule
7618 { a[i] -> [i] : 0 <= i < 10;
7619 b[i] -> [i+1] : 0 <= i < 10 }
7621 If the following option is specified
7623 { [i] -> separate[x] }
7625 then the following AST will be generated
7629 for (int c0 = 1; c0 <= 9; c0 += 1) {
7636 If, on the other hand, the following option is specified
7638 { [i] -> atomic[x] }
7640 then the following AST will be generated
7642 for (int c0 = 0; c0 <= 10; c0 += 1) {
7649 If neither C<atomic> nor C<separate> is specified, then the AST generator
7650 may produce either of these two results or some intermediate form.
7654 This is a single-dimensional space representing the schedule dimension(s)
7655 that should be I<completely> unrolled.
7656 To obtain a partial unrolling, the user should apply an additional
7657 strip-mining to the schedule and fully unroll the inner loop.
7661 Additional control is available through the following functions.
7663 #include <isl/ast_build.h>
7664 __isl_give isl_ast_build *
7665 isl_ast_build_set_iterators(
7666 __isl_take isl_ast_build *control,
7667 __isl_take isl_id_list *iterators);
7669 The function C<isl_ast_build_set_iterators> allows the user to
7670 specify a list of iterator C<isl_id>s to be used as iterators.
7671 If the input schedule is injective, then
7672 the number of elements in this list should be as large as the dimension
7673 of the schedule space, but no direct correspondence should be assumed
7674 between dimensions and elements.
7675 If the input schedule is not injective, then an additional number
7676 of C<isl_id>s equal to the largest dimension of the input domains
7678 If the number of provided C<isl_id>s is insufficient, then additional
7679 names are automatically generated.
7681 #include <isl/ast_build.h>
7682 __isl_give isl_ast_build *
7683 isl_ast_build_set_create_leaf(
7684 __isl_take isl_ast_build *control,
7685 __isl_give isl_ast_node *(*fn)(
7686 __isl_take isl_ast_build *build,
7687 void *user), void *user);
7690 C<isl_ast_build_set_create_leaf> function allows for the
7691 specification of a callback that should be called whenever the AST
7692 generator arrives at an element of the schedule domain.
7693 The callback should return an AST node that should be inserted
7694 at the corresponding position of the AST. The default action (when
7695 the callback is not set) is to continue generating parts of the AST to scan
7696 all the domain elements associated to the schedule domain element
7697 and to insert user nodes, ``calling'' the domain element, for each of them.
7698 The C<build> argument contains the current state of the C<isl_ast_build>.
7699 To ease nested AST generation (see L</"Nested AST Generation">),
7700 all control information that is
7701 specific to the current AST generation such as the options and
7702 the callbacks has been removed from this C<isl_ast_build>.
7703 The callback would typically return the result of a nested
7705 user defined node created using the following function.
7707 #include <isl/ast.h>
7708 __isl_give isl_ast_node *isl_ast_node_alloc_user(
7709 __isl_take isl_ast_expr *expr);
7711 #include <isl/ast_build.h>
7712 __isl_give isl_ast_build *
7713 isl_ast_build_set_at_each_domain(
7714 __isl_take isl_ast_build *build,
7715 __isl_give isl_ast_node *(*fn)(
7716 __isl_take isl_ast_node *node,
7717 __isl_keep isl_ast_build *build,
7718 void *user), void *user);
7719 __isl_give isl_ast_build *
7720 isl_ast_build_set_before_each_for(
7721 __isl_take isl_ast_build *build,
7722 __isl_give isl_id *(*fn)(
7723 __isl_keep isl_ast_build *build,
7724 void *user), void *user);
7725 __isl_give isl_ast_build *
7726 isl_ast_build_set_after_each_for(
7727 __isl_take isl_ast_build *build,
7728 __isl_give isl_ast_node *(*fn)(
7729 __isl_take isl_ast_node *node,
7730 __isl_keep isl_ast_build *build,
7731 void *user), void *user);
7733 The callback set by C<isl_ast_build_set_at_each_domain> will
7734 be called for each domain AST node.
7735 The callbacks set by C<isl_ast_build_set_before_each_for>
7736 and C<isl_ast_build_set_after_each_for> will be called
7737 for each for AST node. The first will be called in depth-first
7738 pre-order, while the second will be called in depth-first post-order.
7739 Since C<isl_ast_build_set_before_each_for> is called before the for
7740 node is actually constructed, it is only passed an C<isl_ast_build>.
7741 The returned C<isl_id> will be added as an annotation (using
7742 C<isl_ast_node_set_annotation>) to the constructed for node.
7743 In particular, if the user has also specified an C<after_each_for>
7744 callback, then the annotation can be retrieved from the node passed to
7745 that callback using C<isl_ast_node_get_annotation>.
7746 All callbacks should C<NULL> on failure.
7747 The given C<isl_ast_build> can be used to create new
7748 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
7749 or C<isl_ast_build_call_from_pw_multi_aff>.
7751 =head3 Nested AST Generation
7753 C<isl> allows the user to create an AST within the context
7754 of another AST. These nested ASTs are created using the
7755 same C<isl_ast_build_ast_from_schedule> function that is used to create the
7756 outer AST. The C<build> argument should be an C<isl_ast_build>
7757 passed to a callback set by
7758 C<isl_ast_build_set_create_leaf>.
7759 The space of the range of the C<schedule> argument should refer
7760 to this build. In particular, the space should be a wrapped
7761 relation and the domain of this wrapped relation should be the
7762 same as that of the range of the schedule returned by
7763 C<isl_ast_build_get_schedule> below.
7764 In practice, the new schedule is typically
7765 created by calling C<isl_union_map_range_product> on the old schedule
7766 and some extra piece of the schedule.
7767 The space of the schedule domain is also available from
7768 the C<isl_ast_build>.
7770 #include <isl/ast_build.h>
7771 __isl_give isl_union_map *isl_ast_build_get_schedule(
7772 __isl_keep isl_ast_build *build);
7773 __isl_give isl_space *isl_ast_build_get_schedule_space(
7774 __isl_keep isl_ast_build *build);
7775 __isl_give isl_ast_build *isl_ast_build_restrict(
7776 __isl_take isl_ast_build *build,
7777 __isl_take isl_set *set);
7779 The C<isl_ast_build_get_schedule> function returns a (partial)
7780 schedule for the domains elements for which part of the AST still needs to
7781 be generated in the current build.
7782 In particular, the domain elements are mapped to those iterations of the loops
7783 enclosing the current point of the AST generation inside which
7784 the domain elements are executed.
7785 No direct correspondence between
7786 the input schedule and this schedule should be assumed.
7787 The space obtained from C<isl_ast_build_get_schedule_space> can be used
7788 to create a set for C<isl_ast_build_restrict> to intersect
7789 with the current build. In particular, the set passed to
7790 C<isl_ast_build_restrict> can have additional parameters.
7791 The ids of the set dimensions in the space returned by
7792 C<isl_ast_build_get_schedule_space> correspond to the
7793 iterators of the already generated loops.
7794 The user should not rely on the ids of the output dimensions
7795 of the relations in the union relation returned by
7796 C<isl_ast_build_get_schedule> having any particular value.
7800 Although C<isl> is mainly meant to be used as a library,
7801 it also contains some basic applications that use some
7802 of the functionality of C<isl>.
7803 The input may be specified in either the L<isl format>
7804 or the L<PolyLib format>.
7806 =head2 C<isl_polyhedron_sample>
7808 C<isl_polyhedron_sample> takes a polyhedron as input and prints
7809 an integer element of the polyhedron, if there is any.
7810 The first column in the output is the denominator and is always
7811 equal to 1. If the polyhedron contains no integer points,
7812 then a vector of length zero is printed.
7816 C<isl_pip> takes the same input as the C<example> program
7817 from the C<piplib> distribution, i.e., a set of constraints
7818 on the parameters, a line containing only -1 and finally a set
7819 of constraints on a parametric polyhedron.
7820 The coefficients of the parameters appear in the last columns
7821 (but before the final constant column).
7822 The output is the lexicographic minimum of the parametric polyhedron.
7823 As C<isl> currently does not have its own output format, the output
7824 is just a dump of the internal state.
7826 =head2 C<isl_polyhedron_minimize>
7828 C<isl_polyhedron_minimize> computes the minimum of some linear
7829 or affine objective function over the integer points in a polyhedron.
7830 If an affine objective function
7831 is given, then the constant should appear in the last column.
7833 =head2 C<isl_polytope_scan>
7835 Given a polytope, C<isl_polytope_scan> prints
7836 all integer points in the polytope.
7838 =head2 C<isl_codegen>
7840 Given a schedule, a context set and an options relation,
7841 C<isl_codegen> prints out an AST that scans the domain elements
7842 of the schedule in the order of their image(s) taking into account
7843 the constraints in the context set.