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
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 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)
173 The source of C<isl> can be obtained either as a tarball
174 or from the git repository. Both are available from
175 L<http://freshmeat.net/projects/isl/>.
176 The installation process depends on how you obtained
179 =head2 Installation from the git repository
183 =item 1 Clone or update the repository
185 The first time the source is obtained, you need to clone
188 git clone git://repo.or.cz/isl.git
190 To obtain updates, you need to pull in the latest changes
194 =item 2 Generate C<configure>
200 After performing the above steps, continue
201 with the L<Common installation instructions>.
203 =head2 Common installation instructions
207 =item 1 Obtain C<GMP>
209 Building C<isl> requires C<GMP>, including its headers files.
210 Your distribution may not provide these header files by default
211 and you may need to install a package called C<gmp-devel> or something
212 similar. Alternatively, C<GMP> can be built from
213 source, available from L<http://gmplib.org/>.
217 C<isl> uses the standard C<autoconf> C<configure> script.
222 optionally followed by some configure options.
223 A complete list of options can be obtained by running
227 Below we discuss some of the more common options.
229 C<isl> can optionally use C<piplib>, but no
230 C<piplib> functionality is currently used by default.
231 The C<--with-piplib> option can
232 be used to specify which C<piplib>
233 library to use, either an installed version (C<system>),
234 an externally built version (C<build>)
235 or no version (C<no>). The option C<build> is mostly useful
236 in C<configure> scripts of larger projects that bundle both C<isl>
243 Installation prefix for C<isl>
245 =item C<--with-gmp-prefix>
247 Installation prefix for C<GMP> (architecture-independent files).
249 =item C<--with-gmp-exec-prefix>
251 Installation prefix for C<GMP> (architecture-dependent files).
253 =item C<--with-piplib>
255 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
257 =item C<--with-piplib-prefix>
259 Installation prefix for C<system> C<piplib> (architecture-independent files).
261 =item C<--with-piplib-exec-prefix>
263 Installation prefix for C<system> C<piplib> (architecture-dependent files).
265 =item C<--with-piplib-builddir>
267 Location where C<build> C<piplib> was built.
275 =item 4 Install (optional)
283 =head2 Initialization
285 All manipulations of integer sets and relations occur within
286 the context of an C<isl_ctx>.
287 A given C<isl_ctx> can only be used within a single thread.
288 All arguments of a function are required to have been allocated
289 within the same context.
290 There are currently no functions available for moving an object
291 from one C<isl_ctx> to another C<isl_ctx>. This means that
292 there is currently no way of safely moving an object from one
293 thread to another, unless the whole C<isl_ctx> is moved.
295 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
296 freed using C<isl_ctx_free>.
297 All objects allocated within an C<isl_ctx> should be freed
298 before the C<isl_ctx> itself is freed.
300 isl_ctx *isl_ctx_alloc();
301 void isl_ctx_free(isl_ctx *ctx);
305 All operations on integers, mainly the coefficients
306 of the constraints describing the sets and relations,
307 are performed in exact integer arithmetic using C<GMP>.
308 However, to allow future versions of C<isl> to optionally
309 support fixed integer arithmetic, all calls to C<GMP>
310 are wrapped inside C<isl> specific macros.
311 The basic type is C<isl_int> and the operations below
312 are available on this type.
313 The meanings of these operations are essentially the same
314 as their C<GMP> C<mpz_> counterparts.
315 As always with C<GMP> types, C<isl_int>s need to be
316 initialized with C<isl_int_init> before they can be used
317 and they need to be released with C<isl_int_clear>
319 The user should not assume that an C<isl_int> is represented
320 as a C<mpz_t>, but should instead explicitly convert between
321 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
322 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
326 =item isl_int_init(i)
328 =item isl_int_clear(i)
330 =item isl_int_set(r,i)
332 =item isl_int_set_si(r,i)
334 =item isl_int_set_gmp(r,g)
336 =item isl_int_get_gmp(i,g)
338 =item isl_int_abs(r,i)
340 =item isl_int_neg(r,i)
342 =item isl_int_swap(i,j)
344 =item isl_int_swap_or_set(i,j)
346 =item isl_int_add_ui(r,i,j)
348 =item isl_int_sub_ui(r,i,j)
350 =item isl_int_add(r,i,j)
352 =item isl_int_sub(r,i,j)
354 =item isl_int_mul(r,i,j)
356 =item isl_int_mul_ui(r,i,j)
358 =item isl_int_addmul(r,i,j)
360 =item isl_int_submul(r,i,j)
362 =item isl_int_gcd(r,i,j)
364 =item isl_int_lcm(r,i,j)
366 =item isl_int_divexact(r,i,j)
368 =item isl_int_cdiv_q(r,i,j)
370 =item isl_int_fdiv_q(r,i,j)
372 =item isl_int_fdiv_r(r,i,j)
374 =item isl_int_fdiv_q_ui(r,i,j)
376 =item isl_int_read(r,s)
378 =item isl_int_print(out,i,width)
382 =item isl_int_cmp(i,j)
384 =item isl_int_cmp_si(i,si)
386 =item isl_int_eq(i,j)
388 =item isl_int_ne(i,j)
390 =item isl_int_lt(i,j)
392 =item isl_int_le(i,j)
394 =item isl_int_gt(i,j)
396 =item isl_int_ge(i,j)
398 =item isl_int_abs_eq(i,j)
400 =item isl_int_abs_ne(i,j)
402 =item isl_int_abs_lt(i,j)
404 =item isl_int_abs_gt(i,j)
406 =item isl_int_abs_ge(i,j)
408 =item isl_int_is_zero(i)
410 =item isl_int_is_one(i)
412 =item isl_int_is_negone(i)
414 =item isl_int_is_pos(i)
416 =item isl_int_is_neg(i)
418 =item isl_int_is_nonpos(i)
420 =item isl_int_is_nonneg(i)
422 =item isl_int_is_divisible_by(i,j)
426 =head2 Sets and Relations
428 C<isl> uses six types of objects for representing sets and relations,
429 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
430 C<isl_union_set> and C<isl_union_map>.
431 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
432 can be described as a conjunction of affine constraints, while
433 C<isl_set> and C<isl_map> represent unions of
434 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
435 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
436 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
437 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
438 where spaces are considered different if they have a different number
439 of dimensions and/or different names (see L<"Spaces">).
440 The difference between sets and relations (maps) is that sets have
441 one set of variables, while relations have two sets of variables,
442 input variables and output variables.
444 =head2 Memory Management
446 Since a high-level operation on sets and/or relations usually involves
447 several substeps and since the user is usually not interested in
448 the intermediate results, most functions that return a new object
449 will also release all the objects passed as arguments.
450 If the user still wants to use one or more of these arguments
451 after the function call, she should pass along a copy of the
452 object rather than the object itself.
453 The user is then responsible for making sure that the original
454 object gets used somewhere else or is explicitly freed.
456 The arguments and return values of all documented functions are
457 annotated to make clear which arguments are released and which
458 arguments are preserved. In particular, the following annotations
465 C<__isl_give> means that a new object is returned.
466 The user should make sure that the returned pointer is
467 used exactly once as a value for an C<__isl_take> argument.
468 In between, it can be used as a value for as many
469 C<__isl_keep> arguments as the user likes.
470 There is one exception, and that is the case where the
471 pointer returned is C<NULL>. Is this case, the user
472 is free to use it as an C<__isl_take> argument or not.
476 C<__isl_take> means that the object the argument points to
477 is taken over by the function and may no longer be used
478 by the user as an argument to any other function.
479 The pointer value must be one returned by a function
480 returning an C<__isl_give> pointer.
481 If the user passes in a C<NULL> value, then this will
482 be treated as an error in the sense that the function will
483 not perform its usual operation. However, it will still
484 make sure that all the other C<__isl_take> arguments
489 C<__isl_keep> means that the function will only use the object
490 temporarily. After the function has finished, the user
491 can still use it as an argument to other functions.
492 A C<NULL> value will be treated in the same way as
493 a C<NULL> value for an C<__isl_take> argument.
497 =head2 Error Handling
499 C<isl> supports different ways to react in case a runtime error is triggered.
500 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
501 with two maps that have incompatible spaces. There are three possible ways
502 to react on error: to warn, to continue or to abort.
504 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
505 the last error in the corresponding C<isl_ctx> and the function in which the
506 error was triggered returns C<NULL>. An error does not corrupt internal state,
507 such that isl can continue to be used. C<isl> also provides functions to
508 read the last error and to reset the memory that stores the last error. The
509 last error is only stored for information purposes. Its presence does not
510 change the behavior of C<isl>. Hence, resetting an error is not required to
511 continue to use isl, but only to observe new errors.
514 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
515 void isl_ctx_reset_error(isl_ctx *ctx);
517 Another option is to continue on error. This is similar to warn on error mode,
518 except that C<isl> does not print any warning. This allows a program to
519 implement its own error reporting.
521 The last option is to directly abort the execution of the program from within
522 the isl library. This makes it obviously impossible to recover from an error,
523 but it allows to directly spot the error location. By aborting on error,
524 debuggers break at the location the error occurred and can provide a stack
525 trace. Other tools that automatically provide stack traces on abort or that do
526 not want to continue execution after an error was triggered may also prefer to
529 The on error behavior of isl can be specified by calling
530 C<isl_options_set_on_error> or by setting the command line option
531 C<--isl-on-error>. Valid arguments for the function call are
532 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
533 choices for the command line option are C<warn>, C<continue> and C<abort>.
534 It is also possible to query the current error mode.
536 #include <isl/options.h>
537 int isl_options_set_on_error(isl_ctx *ctx, int val);
538 int isl_options_get_on_error(isl_ctx *ctx);
542 Identifiers are used to identify both individual dimensions
543 and tuples of dimensions. They consist of a name and an optional
544 pointer. Identifiers with the same name but different pointer values
545 are considered to be distinct.
546 Identifiers can be constructed, copied, freed, inspected and printed
547 using the following functions.
550 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
551 __isl_keep const char *name, void *user);
552 __isl_give isl_id *isl_id_copy(isl_id *id);
553 void *isl_id_free(__isl_take isl_id *id);
555 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
556 void *isl_id_get_user(__isl_keep isl_id *id);
557 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
559 __isl_give isl_printer *isl_printer_print_id(
560 __isl_take isl_printer *p, __isl_keep isl_id *id);
562 Note that C<isl_id_get_name> returns a pointer to some internal
563 data structure, so the result can only be used while the
564 corresponding C<isl_id> is alive.
568 Whenever a new set or relation is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
571 #include <isl/space.h>
572 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
573 unsigned nparam, unsigned n_in, unsigned n_out);
574 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
576 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
577 unsigned nparam, unsigned dim);
578 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
579 void isl_space_free(__isl_take isl_space *space);
580 unsigned isl_space_dim(__isl_keep isl_space *space,
581 enum isl_dim_type type);
583 The space used for creating a parameter domain
584 needs to be created using C<isl_space_params_alloc>.
585 For other sets, the space
586 needs to be created using C<isl_space_set_alloc>, while
587 for a relation, the space
588 needs to be created using C<isl_space_alloc>.
589 C<isl_space_dim> can be used
590 to find out the number of dimensions of each type in
591 a space, where type may be
592 C<isl_dim_param>, C<isl_dim_in> (only for relations),
593 C<isl_dim_out> (only for relations), C<isl_dim_set>
594 (only for sets) or C<isl_dim_all>.
596 To check whether a given space is that of a set or a map
597 or whether it is a parameter space, use these functions:
599 #include <isl/space.h>
600 int isl_space_is_params(__isl_keep isl_space *space);
601 int isl_space_is_set(__isl_keep isl_space *space);
603 It is often useful to create objects that live in the
604 same space as some other object. This can be accomplished
605 by creating the new objects
606 (see L<Creating New Sets and Relations> or
607 L<Creating New (Piecewise) Quasipolynomials>) based on the space
608 of the original object.
611 __isl_give isl_space *isl_basic_set_get_space(
612 __isl_keep isl_basic_set *bset);
613 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
615 #include <isl/union_set.h>
616 __isl_give isl_space *isl_union_set_get_space(
617 __isl_keep isl_union_set *uset);
620 __isl_give isl_space *isl_basic_map_get_space(
621 __isl_keep isl_basic_map *bmap);
622 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
624 #include <isl/union_map.h>
625 __isl_give isl_space *isl_union_map_get_space(
626 __isl_keep isl_union_map *umap);
628 #include <isl/constraint.h>
629 __isl_give isl_space *isl_constraint_get_space(
630 __isl_keep isl_constraint *constraint);
632 #include <isl/polynomial.h>
633 __isl_give isl_space *isl_qpolynomial_get_domain_space(
634 __isl_keep isl_qpolynomial *qp);
635 __isl_give isl_space *isl_qpolynomial_get_space(
636 __isl_keep isl_qpolynomial *qp);
637 __isl_give isl_space *isl_qpolynomial_fold_get_space(
638 __isl_keep isl_qpolynomial_fold *fold);
639 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
640 __isl_keep isl_pw_qpolynomial *pwqp);
641 __isl_give isl_space *isl_pw_qpolynomial_get_space(
642 __isl_keep isl_pw_qpolynomial *pwqp);
643 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
644 __isl_keep isl_pw_qpolynomial_fold *pwf);
645 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
646 __isl_keep isl_pw_qpolynomial_fold *pwf);
647 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
648 __isl_keep isl_union_pw_qpolynomial *upwqp);
649 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
650 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
653 __isl_give isl_space *isl_aff_get_domain_space(
654 __isl_keep isl_aff *aff);
655 __isl_give isl_space *isl_aff_get_space(
656 __isl_keep isl_aff *aff);
657 __isl_give isl_space *isl_pw_aff_get_domain_space(
658 __isl_keep isl_pw_aff *pwaff);
659 __isl_give isl_space *isl_pw_aff_get_space(
660 __isl_keep isl_pw_aff *pwaff);
661 __isl_give isl_space *isl_multi_aff_get_space(
662 __isl_keep isl_multi_aff *maff);
663 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
664 __isl_keep isl_pw_multi_aff *pma);
665 __isl_give isl_space *isl_pw_multi_aff_get_space(
666 __isl_keep isl_pw_multi_aff *pma);
667 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
668 __isl_keep isl_union_pw_multi_aff *upma);
670 #include <isl/point.h>
671 __isl_give isl_space *isl_point_get_space(
672 __isl_keep isl_point *pnt);
674 The identifiers or names of the individual dimensions may be set or read off
675 using the following functions.
677 #include <isl/space.h>
678 __isl_give isl_space *isl_space_set_dim_id(
679 __isl_take isl_space *space,
680 enum isl_dim_type type, unsigned pos,
681 __isl_take isl_id *id);
682 int isl_space_has_dim_id(__isl_keep isl_space *space,
683 enum isl_dim_type type, unsigned pos);
684 __isl_give isl_id *isl_space_get_dim_id(
685 __isl_keep isl_space *space,
686 enum isl_dim_type type, unsigned pos);
687 __isl_give isl_space *isl_space_set_dim_name(
688 __isl_take isl_space *space,
689 enum isl_dim_type type, unsigned pos,
690 __isl_keep const char *name);
691 int isl_space_has_dim_name(__isl_keep isl_space *space,
692 enum isl_dim_type type, unsigned pos);
693 __isl_keep const char *isl_space_get_dim_name(
694 __isl_keep isl_space *space,
695 enum isl_dim_type type, unsigned pos);
697 Note that C<isl_space_get_name> returns a pointer to some internal
698 data structure, so the result can only be used while the
699 corresponding C<isl_space> is alive.
700 Also note that every function that operates on two sets or relations
701 requires that both arguments have the same parameters. This also
702 means that if one of the arguments has named parameters, then the
703 other needs to have named parameters too and the names need to match.
704 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
705 arguments may have different parameters (as long as they are named),
706 in which case the result will have as parameters the union of the parameters of
709 Given the identifier or name of a dimension (typically a parameter),
710 its position can be obtained from the following function.
712 #include <isl/space.h>
713 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
714 enum isl_dim_type type, __isl_keep isl_id *id);
715 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
716 enum isl_dim_type type, const char *name);
718 The identifiers or names of entire spaces may be set or read off
719 using the following functions.
721 #include <isl/space.h>
722 __isl_give isl_space *isl_space_set_tuple_id(
723 __isl_take isl_space *space,
724 enum isl_dim_type type, __isl_take isl_id *id);
725 __isl_give isl_space *isl_space_reset_tuple_id(
726 __isl_take isl_space *space, enum isl_dim_type type);
727 int isl_space_has_tuple_id(__isl_keep isl_space *space,
728 enum isl_dim_type type);
729 __isl_give isl_id *isl_space_get_tuple_id(
730 __isl_keep isl_space *space, enum isl_dim_type type);
731 __isl_give isl_space *isl_space_set_tuple_name(
732 __isl_take isl_space *space,
733 enum isl_dim_type type, const char *s);
734 int isl_space_has_tuple_name(__isl_keep isl_space *space,
735 enum isl_dim_type type);
736 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
737 enum isl_dim_type type);
739 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
740 or C<isl_dim_set>. As with C<isl_space_get_name>,
741 the C<isl_space_get_tuple_name> function returns a pointer to some internal
743 Binary operations require the corresponding spaces of their arguments
744 to have the same name.
746 Spaces can be nested. In particular, the domain of a set or
747 the domain or range of a relation can be a nested relation.
748 The following functions can be used to construct and deconstruct
751 #include <isl/space.h>
752 int isl_space_is_wrapping(__isl_keep isl_space *space);
753 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
754 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
756 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
757 be the space of a set, while that of
758 C<isl_space_wrap> should be the space of a relation.
759 Conversely, the output of C<isl_space_unwrap> is the space
760 of a relation, while that of C<isl_space_wrap> is the space of a set.
762 Spaces can be created from other spaces
763 using the following functions.
765 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
766 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
767 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
768 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
769 __isl_give isl_space *isl_space_params(
770 __isl_take isl_space *space);
771 __isl_give isl_space *isl_space_set_from_params(
772 __isl_take isl_space *space);
773 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
774 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
775 __isl_take isl_space *right);
776 __isl_give isl_space *isl_space_align_params(
777 __isl_take isl_space *space1, __isl_take isl_space *space2)
778 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
779 enum isl_dim_type type, unsigned pos, unsigned n);
780 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
781 enum isl_dim_type type, unsigned n);
782 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
783 enum isl_dim_type type, unsigned first, unsigned n);
784 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
785 enum isl_dim_type dst_type, unsigned dst_pos,
786 enum isl_dim_type src_type, unsigned src_pos,
788 __isl_give isl_space *isl_space_map_from_set(
789 __isl_take isl_space *space);
790 __isl_give isl_space *isl_space_map_from_domain_and_range(
791 __isl_take isl_space *domain,
792 __isl_take isl_space *range);
793 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
794 __isl_give isl_space *isl_space_curry(
795 __isl_take isl_space *space);
797 Note that if dimensions are added or removed from a space, then
798 the name and the internal structure are lost.
802 A local space is essentially a space with
803 zero or more existentially quantified variables.
804 The local space of a (constraint of a) basic set or relation can be obtained
805 using the following functions.
807 #include <isl/constraint.h>
808 __isl_give isl_local_space *isl_constraint_get_local_space(
809 __isl_keep isl_constraint *constraint);
812 __isl_give isl_local_space *isl_basic_set_get_local_space(
813 __isl_keep isl_basic_set *bset);
816 __isl_give isl_local_space *isl_basic_map_get_local_space(
817 __isl_keep isl_basic_map *bmap);
819 A new local space can be created from a space using
821 #include <isl/local_space.h>
822 __isl_give isl_local_space *isl_local_space_from_space(
823 __isl_take isl_space *space);
825 They can be inspected, modified, copied and freed using the following functions.
827 #include <isl/local_space.h>
828 isl_ctx *isl_local_space_get_ctx(
829 __isl_keep isl_local_space *ls);
830 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
831 int isl_local_space_dim(__isl_keep isl_local_space *ls,
832 enum isl_dim_type type);
833 int isl_local_space_has_dim_name(
834 __isl_keep isl_local_space *ls,
835 enum isl_dim_type type, unsigned pos)
836 const char *isl_local_space_get_dim_name(
837 __isl_keep isl_local_space *ls,
838 enum isl_dim_type type, unsigned pos);
839 __isl_give isl_local_space *isl_local_space_set_dim_name(
840 __isl_take isl_local_space *ls,
841 enum isl_dim_type type, unsigned pos, const char *s);
842 __isl_give isl_local_space *isl_local_space_set_dim_id(
843 __isl_take isl_local_space *ls,
844 enum isl_dim_type type, unsigned pos,
845 __isl_take isl_id *id);
846 __isl_give isl_space *isl_local_space_get_space(
847 __isl_keep isl_local_space *ls);
848 __isl_give isl_aff *isl_local_space_get_div(
849 __isl_keep isl_local_space *ls, int pos);
850 __isl_give isl_local_space *isl_local_space_copy(
851 __isl_keep isl_local_space *ls);
852 void *isl_local_space_free(__isl_take isl_local_space *ls);
854 Two local spaces can be compared using
856 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
857 __isl_keep isl_local_space *ls2);
859 Local spaces can be created from other local spaces
860 using the following functions.
862 __isl_give isl_local_space *isl_local_space_domain(
863 __isl_take isl_local_space *ls);
864 __isl_give isl_local_space *isl_local_space_range(
865 __isl_take isl_local_space *ls);
866 __isl_give isl_local_space *isl_local_space_from_domain(
867 __isl_take isl_local_space *ls);
868 __isl_give isl_local_space *isl_local_space_intersect(
869 __isl_take isl_local_space *ls1,
870 __isl_take isl_local_space *ls2);
871 __isl_give isl_local_space *isl_local_space_add_dims(
872 __isl_take isl_local_space *ls,
873 enum isl_dim_type type, unsigned n);
874 __isl_give isl_local_space *isl_local_space_insert_dims(
875 __isl_take isl_local_space *ls,
876 enum isl_dim_type type, unsigned first, unsigned n);
877 __isl_give isl_local_space *isl_local_space_drop_dims(
878 __isl_take isl_local_space *ls,
879 enum isl_dim_type type, unsigned first, unsigned n);
881 =head2 Input and Output
883 C<isl> supports its own input/output format, which is similar
884 to the C<Omega> format, but also supports the C<PolyLib> format
889 The C<isl> format is similar to that of C<Omega>, but has a different
890 syntax for describing the parameters and allows for the definition
891 of an existentially quantified variable as the integer division
892 of an affine expression.
893 For example, the set of integers C<i> between C<0> and C<n>
894 such that C<i % 10 <= 6> can be described as
896 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
899 A set or relation can have several disjuncts, separated
900 by the keyword C<or>. Each disjunct is either a conjunction
901 of constraints or a projection (C<exists>) of a conjunction
902 of constraints. The constraints are separated by the keyword
905 =head3 C<PolyLib> format
907 If the represented set is a union, then the first line
908 contains a single number representing the number of disjuncts.
909 Otherwise, a line containing the number C<1> is optional.
911 Each disjunct is represented by a matrix of constraints.
912 The first line contains two numbers representing
913 the number of rows and columns,
914 where the number of rows is equal to the number of constraints
915 and the number of columns is equal to two plus the number of variables.
916 The following lines contain the actual rows of the constraint matrix.
917 In each row, the first column indicates whether the constraint
918 is an equality (C<0>) or inequality (C<1>). The final column
919 corresponds to the constant term.
921 If the set is parametric, then the coefficients of the parameters
922 appear in the last columns before the constant column.
923 The coefficients of any existentially quantified variables appear
924 between those of the set variables and those of the parameters.
926 =head3 Extended C<PolyLib> format
928 The extended C<PolyLib> format is nearly identical to the
929 C<PolyLib> format. The only difference is that the line
930 containing the number of rows and columns of a constraint matrix
931 also contains four additional numbers:
932 the number of output dimensions, the number of input dimensions,
933 the number of local dimensions (i.e., the number of existentially
934 quantified variables) and the number of parameters.
935 For sets, the number of ``output'' dimensions is equal
936 to the number of set dimensions, while the number of ``input''
942 __isl_give isl_basic_set *isl_basic_set_read_from_file(
943 isl_ctx *ctx, FILE *input);
944 __isl_give isl_basic_set *isl_basic_set_read_from_str(
945 isl_ctx *ctx, const char *str);
946 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
948 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
952 __isl_give isl_basic_map *isl_basic_map_read_from_file(
953 isl_ctx *ctx, FILE *input);
954 __isl_give isl_basic_map *isl_basic_map_read_from_str(
955 isl_ctx *ctx, const char *str);
956 __isl_give isl_map *isl_map_read_from_file(
957 isl_ctx *ctx, FILE *input);
958 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
961 #include <isl/union_set.h>
962 __isl_give isl_union_set *isl_union_set_read_from_file(
963 isl_ctx *ctx, FILE *input);
964 __isl_give isl_union_set *isl_union_set_read_from_str(
965 isl_ctx *ctx, const char *str);
967 #include <isl/union_map.h>
968 __isl_give isl_union_map *isl_union_map_read_from_file(
969 isl_ctx *ctx, FILE *input);
970 __isl_give isl_union_map *isl_union_map_read_from_str(
971 isl_ctx *ctx, const char *str);
973 The input format is autodetected and may be either the C<PolyLib> format
974 or the C<isl> format.
978 Before anything can be printed, an C<isl_printer> needs to
981 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
983 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
984 void isl_printer_free(__isl_take isl_printer *printer);
985 __isl_give char *isl_printer_get_str(
986 __isl_keep isl_printer *printer);
988 The printer can be inspected using the following functions.
990 FILE *isl_printer_get_file(
991 __isl_keep isl_printer *printer);
992 int isl_printer_get_output_format(
993 __isl_keep isl_printer *p);
995 The behavior of the printer can be modified in various ways
997 __isl_give isl_printer *isl_printer_set_output_format(
998 __isl_take isl_printer *p, int output_format);
999 __isl_give isl_printer *isl_printer_set_indent(
1000 __isl_take isl_printer *p, int indent);
1001 __isl_give isl_printer *isl_printer_indent(
1002 __isl_take isl_printer *p, int indent);
1003 __isl_give isl_printer *isl_printer_set_prefix(
1004 __isl_take isl_printer *p, const char *prefix);
1005 __isl_give isl_printer *isl_printer_set_suffix(
1006 __isl_take isl_printer *p, const char *suffix);
1008 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1009 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1010 and defaults to C<ISL_FORMAT_ISL>.
1011 Each line in the output is indented by C<indent> (set by
1012 C<isl_printer_set_indent>) spaces
1013 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1014 In the C<PolyLib> format output,
1015 the coefficients of the existentially quantified variables
1016 appear between those of the set variables and those
1018 The function C<isl_printer_indent> increases the indentation
1019 by the specified amount (which may be negative).
1021 To actually print something, use
1023 #include <isl/set.h>
1024 __isl_give isl_printer *isl_printer_print_basic_set(
1025 __isl_take isl_printer *printer,
1026 __isl_keep isl_basic_set *bset);
1027 __isl_give isl_printer *isl_printer_print_set(
1028 __isl_take isl_printer *printer,
1029 __isl_keep isl_set *set);
1031 #include <isl/map.h>
1032 __isl_give isl_printer *isl_printer_print_basic_map(
1033 __isl_take isl_printer *printer,
1034 __isl_keep isl_basic_map *bmap);
1035 __isl_give isl_printer *isl_printer_print_map(
1036 __isl_take isl_printer *printer,
1037 __isl_keep isl_map *map);
1039 #include <isl/union_set.h>
1040 __isl_give isl_printer *isl_printer_print_union_set(
1041 __isl_take isl_printer *p,
1042 __isl_keep isl_union_set *uset);
1044 #include <isl/union_map.h>
1045 __isl_give isl_printer *isl_printer_print_union_map(
1046 __isl_take isl_printer *p,
1047 __isl_keep isl_union_map *umap);
1049 When called on a file printer, the following function flushes
1050 the file. When called on a string printer, the buffer is cleared.
1052 __isl_give isl_printer *isl_printer_flush(
1053 __isl_take isl_printer *p);
1055 =head2 Creating New Sets and Relations
1057 C<isl> has functions for creating some standard sets and relations.
1061 =item * Empty sets and relations
1063 __isl_give isl_basic_set *isl_basic_set_empty(
1064 __isl_take isl_space *space);
1065 __isl_give isl_basic_map *isl_basic_map_empty(
1066 __isl_take isl_space *space);
1067 __isl_give isl_set *isl_set_empty(
1068 __isl_take isl_space *space);
1069 __isl_give isl_map *isl_map_empty(
1070 __isl_take isl_space *space);
1071 __isl_give isl_union_set *isl_union_set_empty(
1072 __isl_take isl_space *space);
1073 __isl_give isl_union_map *isl_union_map_empty(
1074 __isl_take isl_space *space);
1076 For C<isl_union_set>s and C<isl_union_map>s, the space
1077 is only used to specify the parameters.
1079 =item * Universe sets and relations
1081 __isl_give isl_basic_set *isl_basic_set_universe(
1082 __isl_take isl_space *space);
1083 __isl_give isl_basic_map *isl_basic_map_universe(
1084 __isl_take isl_space *space);
1085 __isl_give isl_set *isl_set_universe(
1086 __isl_take isl_space *space);
1087 __isl_give isl_map *isl_map_universe(
1088 __isl_take isl_space *space);
1089 __isl_give isl_union_set *isl_union_set_universe(
1090 __isl_take isl_union_set *uset);
1091 __isl_give isl_union_map *isl_union_map_universe(
1092 __isl_take isl_union_map *umap);
1094 The sets and relations constructed by the functions above
1095 contain all integer values, while those constructed by the
1096 functions below only contain non-negative values.
1098 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1099 __isl_take isl_space *space);
1100 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1101 __isl_take isl_space *space);
1102 __isl_give isl_set *isl_set_nat_universe(
1103 __isl_take isl_space *space);
1104 __isl_give isl_map *isl_map_nat_universe(
1105 __isl_take isl_space *space);
1107 =item * Identity relations
1109 __isl_give isl_basic_map *isl_basic_map_identity(
1110 __isl_take isl_space *space);
1111 __isl_give isl_map *isl_map_identity(
1112 __isl_take isl_space *space);
1114 The number of input and output dimensions in C<space> needs
1117 =item * Lexicographic order
1119 __isl_give isl_map *isl_map_lex_lt(
1120 __isl_take isl_space *set_space);
1121 __isl_give isl_map *isl_map_lex_le(
1122 __isl_take isl_space *set_space);
1123 __isl_give isl_map *isl_map_lex_gt(
1124 __isl_take isl_space *set_space);
1125 __isl_give isl_map *isl_map_lex_ge(
1126 __isl_take isl_space *set_space);
1127 __isl_give isl_map *isl_map_lex_lt_first(
1128 __isl_take isl_space *space, unsigned n);
1129 __isl_give isl_map *isl_map_lex_le_first(
1130 __isl_take isl_space *space, unsigned n);
1131 __isl_give isl_map *isl_map_lex_gt_first(
1132 __isl_take isl_space *space, unsigned n);
1133 __isl_give isl_map *isl_map_lex_ge_first(
1134 __isl_take isl_space *space, unsigned n);
1136 The first four functions take a space for a B<set>
1137 and return relations that express that the elements in the domain
1138 are lexicographically less
1139 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1140 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1141 than the elements in the range.
1142 The last four functions take a space for a map
1143 and return relations that express that the first C<n> dimensions
1144 in the domain are lexicographically less
1145 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1146 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1147 than the first C<n> dimensions in the range.
1151 A basic set or relation can be converted to a set or relation
1152 using the following functions.
1154 __isl_give isl_set *isl_set_from_basic_set(
1155 __isl_take isl_basic_set *bset);
1156 __isl_give isl_map *isl_map_from_basic_map(
1157 __isl_take isl_basic_map *bmap);
1159 Sets and relations can be converted to union sets and relations
1160 using the following functions.
1162 __isl_give isl_union_map *isl_union_map_from_map(
1163 __isl_take isl_map *map);
1164 __isl_give isl_union_set *isl_union_set_from_set(
1165 __isl_take isl_set *set);
1167 The inverse conversions below can only be used if the input
1168 union set or relation is known to contain elements in exactly one
1171 __isl_give isl_set *isl_set_from_union_set(
1172 __isl_take isl_union_set *uset);
1173 __isl_give isl_map *isl_map_from_union_map(
1174 __isl_take isl_union_map *umap);
1176 A zero-dimensional set can be constructed on a given parameter domain
1177 using the following function.
1179 __isl_give isl_set *isl_set_from_params(
1180 __isl_take isl_set *set);
1182 Sets and relations can be copied and freed again using the following
1185 __isl_give isl_basic_set *isl_basic_set_copy(
1186 __isl_keep isl_basic_set *bset);
1187 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1188 __isl_give isl_union_set *isl_union_set_copy(
1189 __isl_keep isl_union_set *uset);
1190 __isl_give isl_basic_map *isl_basic_map_copy(
1191 __isl_keep isl_basic_map *bmap);
1192 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1193 __isl_give isl_union_map *isl_union_map_copy(
1194 __isl_keep isl_union_map *umap);
1195 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1196 void isl_set_free(__isl_take isl_set *set);
1197 void *isl_union_set_free(__isl_take isl_union_set *uset);
1198 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1199 void isl_map_free(__isl_take isl_map *map);
1200 void *isl_union_map_free(__isl_take isl_union_map *umap);
1202 Other sets and relations can be constructed by starting
1203 from a universe set or relation, adding equality and/or
1204 inequality constraints and then projecting out the
1205 existentially quantified variables, if any.
1206 Constraints can be constructed, manipulated and
1207 added to (or removed from) (basic) sets and relations
1208 using the following functions.
1210 #include <isl/constraint.h>
1211 __isl_give isl_constraint *isl_equality_alloc(
1212 __isl_take isl_local_space *ls);
1213 __isl_give isl_constraint *isl_inequality_alloc(
1214 __isl_take isl_local_space *ls);
1215 __isl_give isl_constraint *isl_constraint_set_constant(
1216 __isl_take isl_constraint *constraint, isl_int v);
1217 __isl_give isl_constraint *isl_constraint_set_constant_si(
1218 __isl_take isl_constraint *constraint, int v);
1219 __isl_give isl_constraint *isl_constraint_set_coefficient(
1220 __isl_take isl_constraint *constraint,
1221 enum isl_dim_type type, int pos, isl_int v);
1222 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1223 __isl_take isl_constraint *constraint,
1224 enum isl_dim_type type, int pos, int v);
1225 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1226 __isl_take isl_basic_map *bmap,
1227 __isl_take isl_constraint *constraint);
1228 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1229 __isl_take isl_basic_set *bset,
1230 __isl_take isl_constraint *constraint);
1231 __isl_give isl_map *isl_map_add_constraint(
1232 __isl_take isl_map *map,
1233 __isl_take isl_constraint *constraint);
1234 __isl_give isl_set *isl_set_add_constraint(
1235 __isl_take isl_set *set,
1236 __isl_take isl_constraint *constraint);
1237 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1238 __isl_take isl_basic_set *bset,
1239 __isl_take isl_constraint *constraint);
1241 For example, to create a set containing the even integers
1242 between 10 and 42, you would use the following code.
1245 isl_local_space *ls;
1247 isl_basic_set *bset;
1249 space = isl_space_set_alloc(ctx, 0, 2);
1250 bset = isl_basic_set_universe(isl_space_copy(space));
1251 ls = isl_local_space_from_space(space);
1253 c = isl_equality_alloc(isl_local_space_copy(ls));
1254 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1255 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1256 bset = isl_basic_set_add_constraint(bset, c);
1258 c = isl_inequality_alloc(isl_local_space_copy(ls));
1259 c = isl_constraint_set_constant_si(c, -10);
1260 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1261 bset = isl_basic_set_add_constraint(bset, c);
1263 c = isl_inequality_alloc(ls);
1264 c = isl_constraint_set_constant_si(c, 42);
1265 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1266 bset = isl_basic_set_add_constraint(bset, c);
1268 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1272 isl_basic_set *bset;
1273 bset = isl_basic_set_read_from_str(ctx,
1274 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1276 A basic set or relation can also be constructed from two matrices
1277 describing the equalities and the inequalities.
1279 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1280 __isl_take isl_space *space,
1281 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1282 enum isl_dim_type c1,
1283 enum isl_dim_type c2, enum isl_dim_type c3,
1284 enum isl_dim_type c4);
1285 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1286 __isl_take isl_space *space,
1287 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1288 enum isl_dim_type c1,
1289 enum isl_dim_type c2, enum isl_dim_type c3,
1290 enum isl_dim_type c4, enum isl_dim_type c5);
1292 The C<isl_dim_type> arguments indicate the order in which
1293 different kinds of variables appear in the input matrices
1294 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1295 C<isl_dim_set> and C<isl_dim_div> for sets and
1296 of C<isl_dim_cst>, C<isl_dim_param>,
1297 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1299 A (basic or union) set or relation can also be constructed from a
1300 (union) (piecewise) (multiple) affine expression
1301 or a list of affine expressions
1302 (See L<"Piecewise Quasi Affine Expressions"> and
1303 L<"Piecewise Multiple Quasi Affine Expressions">).
1305 __isl_give isl_basic_map *isl_basic_map_from_aff(
1306 __isl_take isl_aff *aff);
1307 __isl_give isl_map *isl_map_from_aff(
1308 __isl_take isl_aff *aff);
1309 __isl_give isl_set *isl_set_from_pw_aff(
1310 __isl_take isl_pw_aff *pwaff);
1311 __isl_give isl_map *isl_map_from_pw_aff(
1312 __isl_take isl_pw_aff *pwaff);
1313 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1314 __isl_take isl_space *domain_space,
1315 __isl_take isl_aff_list *list);
1316 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1317 __isl_take isl_multi_aff *maff)
1318 __isl_give isl_map *isl_map_from_multi_aff(
1319 __isl_take isl_multi_aff *maff)
1320 __isl_give isl_set *isl_set_from_pw_multi_aff(
1321 __isl_take isl_pw_multi_aff *pma);
1322 __isl_give isl_map *isl_map_from_pw_multi_aff(
1323 __isl_take isl_pw_multi_aff *pma);
1324 __isl_give isl_union_map *
1325 isl_union_map_from_union_pw_multi_aff(
1326 __isl_take isl_union_pw_multi_aff *upma);
1328 The C<domain_dim> argument describes the domain of the resulting
1329 basic relation. It is required because the C<list> may consist
1330 of zero affine expressions.
1332 =head2 Inspecting Sets and Relations
1334 Usually, the user should not have to care about the actual constraints
1335 of the sets and maps, but should instead apply the abstract operations
1336 explained in the following sections.
1337 Occasionally, however, it may be required to inspect the individual
1338 coefficients of the constraints. This section explains how to do so.
1339 In these cases, it may also be useful to have C<isl> compute
1340 an explicit representation of the existentially quantified variables.
1342 __isl_give isl_set *isl_set_compute_divs(
1343 __isl_take isl_set *set);
1344 __isl_give isl_map *isl_map_compute_divs(
1345 __isl_take isl_map *map);
1346 __isl_give isl_union_set *isl_union_set_compute_divs(
1347 __isl_take isl_union_set *uset);
1348 __isl_give isl_union_map *isl_union_map_compute_divs(
1349 __isl_take isl_union_map *umap);
1351 This explicit representation defines the existentially quantified
1352 variables as integer divisions of the other variables, possibly
1353 including earlier existentially quantified variables.
1354 An explicitly represented existentially quantified variable therefore
1355 has a unique value when the values of the other variables are known.
1356 If, furthermore, the same existentials, i.e., existentials
1357 with the same explicit representations, should appear in the
1358 same order in each of the disjuncts of a set or map, then the user should call
1359 either of the following functions.
1361 __isl_give isl_set *isl_set_align_divs(
1362 __isl_take isl_set *set);
1363 __isl_give isl_map *isl_map_align_divs(
1364 __isl_take isl_map *map);
1366 Alternatively, the existentially quantified variables can be removed
1367 using the following functions, which compute an overapproximation.
1369 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1370 __isl_take isl_basic_set *bset);
1371 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1372 __isl_take isl_basic_map *bmap);
1373 __isl_give isl_set *isl_set_remove_divs(
1374 __isl_take isl_set *set);
1375 __isl_give isl_map *isl_map_remove_divs(
1376 __isl_take isl_map *map);
1378 To iterate over all the sets or maps in a union set or map, use
1380 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1381 int (*fn)(__isl_take isl_set *set, void *user),
1383 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1384 int (*fn)(__isl_take isl_map *map, void *user),
1387 The number of sets or maps in a union set or map can be obtained
1390 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1391 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1393 To extract the set or map in a given space from a union, use
1395 __isl_give isl_set *isl_union_set_extract_set(
1396 __isl_keep isl_union_set *uset,
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_union_map_extract_map(
1399 __isl_keep isl_union_map *umap,
1400 __isl_take isl_space *space);
1402 To iterate over all the basic sets or maps in a set or map, use
1404 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1405 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1407 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1408 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1411 The callback function C<fn> should return 0 if successful and
1412 -1 if an error occurs. In the latter case, or if any other error
1413 occurs, the above functions will return -1.
1415 It should be noted that C<isl> does not guarantee that
1416 the basic sets or maps passed to C<fn> are disjoint.
1417 If this is required, then the user should call one of
1418 the following functions first.
1420 __isl_give isl_set *isl_set_make_disjoint(
1421 __isl_take isl_set *set);
1422 __isl_give isl_map *isl_map_make_disjoint(
1423 __isl_take isl_map *map);
1425 The number of basic sets in a set can be obtained
1428 int isl_set_n_basic_set(__isl_keep isl_set *set);
1430 To iterate over the constraints of a basic set or map, use
1432 #include <isl/constraint.h>
1434 int isl_basic_set_n_constraint(
1435 __isl_keep isl_basic_set *bset);
1436 int isl_basic_set_foreach_constraint(
1437 __isl_keep isl_basic_set *bset,
1438 int (*fn)(__isl_take isl_constraint *c, void *user),
1440 int isl_basic_map_foreach_constraint(
1441 __isl_keep isl_basic_map *bmap,
1442 int (*fn)(__isl_take isl_constraint *c, void *user),
1444 void *isl_constraint_free(__isl_take isl_constraint *c);
1446 Again, the callback function C<fn> should return 0 if successful and
1447 -1 if an error occurs. In the latter case, or if any other error
1448 occurs, the above functions will return -1.
1449 The constraint C<c> represents either an equality or an inequality.
1450 Use the following function to find out whether a constraint
1451 represents an equality. If not, it represents an inequality.
1453 int isl_constraint_is_equality(
1454 __isl_keep isl_constraint *constraint);
1456 The coefficients of the constraints can be inspected using
1457 the following functions.
1459 int isl_constraint_is_lower_bound(
1460 __isl_keep isl_constraint *constraint,
1461 enum isl_dim_type type, unsigned pos);
1462 int isl_constraint_is_upper_bound(
1463 __isl_keep isl_constraint *constraint,
1464 enum isl_dim_type type, unsigned pos);
1465 void isl_constraint_get_constant(
1466 __isl_keep isl_constraint *constraint, isl_int *v);
1467 void isl_constraint_get_coefficient(
1468 __isl_keep isl_constraint *constraint,
1469 enum isl_dim_type type, int pos, isl_int *v);
1470 int isl_constraint_involves_dims(
1471 __isl_keep isl_constraint *constraint,
1472 enum isl_dim_type type, unsigned first, unsigned n);
1474 The explicit representations of the existentially quantified
1475 variables can be inspected using the following function.
1476 Note that the user is only allowed to use this function
1477 if the inspected set or map is the result of a call
1478 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1479 The existentially quantified variable is equal to the floor
1480 of the returned affine expression. The affine expression
1481 itself can be inspected using the functions in
1482 L<"Piecewise Quasi Affine Expressions">.
1484 __isl_give isl_aff *isl_constraint_get_div(
1485 __isl_keep isl_constraint *constraint, int pos);
1487 To obtain the constraints of a basic set or map in matrix
1488 form, use the following functions.
1490 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1491 __isl_keep isl_basic_set *bset,
1492 enum isl_dim_type c1, enum isl_dim_type c2,
1493 enum isl_dim_type c3, enum isl_dim_type c4);
1494 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1495 __isl_keep isl_basic_set *bset,
1496 enum isl_dim_type c1, enum isl_dim_type c2,
1497 enum isl_dim_type c3, enum isl_dim_type c4);
1498 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1499 __isl_keep isl_basic_map *bmap,
1500 enum isl_dim_type c1,
1501 enum isl_dim_type c2, enum isl_dim_type c3,
1502 enum isl_dim_type c4, enum isl_dim_type c5);
1503 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1504 __isl_keep isl_basic_map *bmap,
1505 enum isl_dim_type c1,
1506 enum isl_dim_type c2, enum isl_dim_type c3,
1507 enum isl_dim_type c4, enum isl_dim_type c5);
1509 The C<isl_dim_type> arguments dictate the order in which
1510 different kinds of variables appear in the resulting matrix
1511 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1512 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1514 The number of parameters, input, output or set dimensions can
1515 be obtained using the following functions.
1517 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1518 enum isl_dim_type type);
1519 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1520 enum isl_dim_type type);
1521 unsigned isl_set_dim(__isl_keep isl_set *set,
1522 enum isl_dim_type type);
1523 unsigned isl_map_dim(__isl_keep isl_map *map,
1524 enum isl_dim_type type);
1526 To check whether the description of a set or relation depends
1527 on one or more given dimensions, it is not necessary to iterate over all
1528 constraints. Instead the following functions can be used.
1530 int isl_basic_set_involves_dims(
1531 __isl_keep isl_basic_set *bset,
1532 enum isl_dim_type type, unsigned first, unsigned n);
1533 int isl_set_involves_dims(__isl_keep isl_set *set,
1534 enum isl_dim_type type, unsigned first, unsigned n);
1535 int isl_basic_map_involves_dims(
1536 __isl_keep isl_basic_map *bmap,
1537 enum isl_dim_type type, unsigned first, unsigned n);
1538 int isl_map_involves_dims(__isl_keep isl_map *map,
1539 enum isl_dim_type type, unsigned first, unsigned n);
1541 Similarly, the following functions can be used to check whether
1542 a given dimension is involved in any lower or upper bound.
1544 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1545 enum isl_dim_type type, unsigned pos);
1546 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1547 enum isl_dim_type type, unsigned pos);
1549 The identifiers or names of the domain and range spaces of a set
1550 or relation can be read off or set using the following functions.
1552 __isl_give isl_set *isl_set_set_tuple_id(
1553 __isl_take isl_set *set, __isl_take isl_id *id);
1554 __isl_give isl_set *isl_set_reset_tuple_id(
1555 __isl_take isl_set *set);
1556 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1557 __isl_give isl_id *isl_set_get_tuple_id(
1558 __isl_keep isl_set *set);
1559 __isl_give isl_map *isl_map_set_tuple_id(
1560 __isl_take isl_map *map, enum isl_dim_type type,
1561 __isl_take isl_id *id);
1562 __isl_give isl_map *isl_map_reset_tuple_id(
1563 __isl_take isl_map *map, enum isl_dim_type type);
1564 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1565 enum isl_dim_type type);
1566 __isl_give isl_id *isl_map_get_tuple_id(
1567 __isl_keep isl_map *map, enum isl_dim_type type);
1569 const char *isl_basic_set_get_tuple_name(
1570 __isl_keep isl_basic_set *bset);
1571 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1572 __isl_take isl_basic_set *set, const char *s);
1573 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1574 const char *isl_set_get_tuple_name(
1575 __isl_keep isl_set *set);
1576 const char *isl_basic_map_get_tuple_name(
1577 __isl_keep isl_basic_map *bmap,
1578 enum isl_dim_type type);
1579 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1580 __isl_take isl_basic_map *bmap,
1581 enum isl_dim_type type, const char *s);
1582 const char *isl_map_get_tuple_name(
1583 __isl_keep isl_map *map,
1584 enum isl_dim_type type);
1586 As with C<isl_space_get_tuple_name>, the value returned points to
1587 an internal data structure.
1588 The identifiers, positions or names of individual dimensions can be
1589 read off using the following functions.
1591 __isl_give isl_set *isl_set_set_dim_id(
1592 __isl_take isl_set *set, enum isl_dim_type type,
1593 unsigned pos, __isl_take isl_id *id);
1594 int isl_set_has_dim_id(__isl_keep isl_set *set,
1595 enum isl_dim_type type, unsigned pos);
1596 __isl_give isl_id *isl_set_get_dim_id(
1597 __isl_keep isl_set *set, enum isl_dim_type type,
1599 int isl_basic_map_has_dim_id(
1600 __isl_keep isl_basic_map *bmap,
1601 enum isl_dim_type type, unsigned pos);
1602 __isl_give isl_map *isl_map_set_dim_id(
1603 __isl_take isl_map *map, enum isl_dim_type type,
1604 unsigned pos, __isl_take isl_id *id);
1605 int isl_map_has_dim_id(__isl_keep isl_map *map,
1606 enum isl_dim_type type, unsigned pos);
1607 __isl_give isl_id *isl_map_get_dim_id(
1608 __isl_keep isl_map *map, enum isl_dim_type type,
1611 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1612 enum isl_dim_type type, __isl_keep isl_id *id);
1613 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1614 enum isl_dim_type type, __isl_keep isl_id *id);
1615 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1616 enum isl_dim_type type, const char *name);
1617 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1618 enum isl_dim_type type, const char *name);
1620 const char *isl_constraint_get_dim_name(
1621 __isl_keep isl_constraint *constraint,
1622 enum isl_dim_type type, unsigned pos);
1623 const char *isl_basic_set_get_dim_name(
1624 __isl_keep isl_basic_set *bset,
1625 enum isl_dim_type type, unsigned pos);
1626 int isl_set_has_dim_name(__isl_keep isl_set *set,
1627 enum isl_dim_type type, unsigned pos);
1628 const char *isl_set_get_dim_name(
1629 __isl_keep isl_set *set,
1630 enum isl_dim_type type, unsigned pos);
1631 const char *isl_basic_map_get_dim_name(
1632 __isl_keep isl_basic_map *bmap,
1633 enum isl_dim_type type, unsigned pos);
1634 const char *isl_map_get_dim_name(
1635 __isl_keep isl_map *map,
1636 enum isl_dim_type type, unsigned pos);
1638 These functions are mostly useful to obtain the identifiers, positions
1639 or names of the parameters. Identifiers of individual dimensions are
1640 essentially only useful for printing. They are ignored by all other
1641 operations and may not be preserved across those operations.
1645 =head3 Unary Properties
1651 The following functions test whether the given set or relation
1652 contains any integer points. The ``plain'' variants do not perform
1653 any computations, but simply check if the given set or relation
1654 is already known to be empty.
1656 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1657 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1658 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1659 int isl_set_is_empty(__isl_keep isl_set *set);
1660 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1661 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1662 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1663 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1664 int isl_map_is_empty(__isl_keep isl_map *map);
1665 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1667 =item * Universality
1669 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1670 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1671 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1673 =item * Single-valuedness
1675 int isl_map_plain_is_single_valued(
1676 __isl_keep isl_map *map);
1677 int isl_map_is_single_valued(__isl_keep isl_map *map);
1678 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1682 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1683 int isl_map_is_injective(__isl_keep isl_map *map);
1684 int isl_union_map_plain_is_injective(
1685 __isl_keep isl_union_map *umap);
1686 int isl_union_map_is_injective(
1687 __isl_keep isl_union_map *umap);
1691 int isl_map_is_bijective(__isl_keep isl_map *map);
1692 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1696 int isl_basic_map_plain_is_fixed(
1697 __isl_keep isl_basic_map *bmap,
1698 enum isl_dim_type type, unsigned pos,
1700 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1701 enum isl_dim_type type, unsigned pos,
1703 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1704 enum isl_dim_type type, unsigned pos,
1707 Check if the relation obviously lies on a hyperplane where the given dimension
1708 has a fixed value and if so, return that value in C<*val>.
1712 To check whether a set is a parameter domain, use this function:
1714 int isl_set_is_params(__isl_keep isl_set *set);
1715 int isl_union_set_is_params(
1716 __isl_keep isl_union_set *uset);
1720 The following functions check whether the domain of the given
1721 (basic) set is a wrapped relation.
1723 int isl_basic_set_is_wrapping(
1724 __isl_keep isl_basic_set *bset);
1725 int isl_set_is_wrapping(__isl_keep isl_set *set);
1727 =item * Internal Product
1729 int isl_basic_map_can_zip(
1730 __isl_keep isl_basic_map *bmap);
1731 int isl_map_can_zip(__isl_keep isl_map *map);
1733 Check whether the product of domain and range of the given relation
1735 i.e., whether both domain and range are nested relations.
1739 int isl_basic_map_can_curry(
1740 __isl_keep isl_basic_map *bmap);
1741 int isl_map_can_curry(__isl_keep isl_map *map);
1743 Check whether the domain of the (basic) relation is a wrapped relation.
1747 =head3 Binary Properties
1753 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1754 __isl_keep isl_set *set2);
1755 int isl_set_is_equal(__isl_keep isl_set *set1,
1756 __isl_keep isl_set *set2);
1757 int isl_union_set_is_equal(
1758 __isl_keep isl_union_set *uset1,
1759 __isl_keep isl_union_set *uset2);
1760 int isl_basic_map_is_equal(
1761 __isl_keep isl_basic_map *bmap1,
1762 __isl_keep isl_basic_map *bmap2);
1763 int isl_map_is_equal(__isl_keep isl_map *map1,
1764 __isl_keep isl_map *map2);
1765 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1766 __isl_keep isl_map *map2);
1767 int isl_union_map_is_equal(
1768 __isl_keep isl_union_map *umap1,
1769 __isl_keep isl_union_map *umap2);
1771 =item * Disjointness
1773 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1774 __isl_keep isl_set *set2);
1778 int isl_basic_set_is_subset(
1779 __isl_keep isl_basic_set *bset1,
1780 __isl_keep isl_basic_set *bset2);
1781 int isl_set_is_subset(__isl_keep isl_set *set1,
1782 __isl_keep isl_set *set2);
1783 int isl_set_is_strict_subset(
1784 __isl_keep isl_set *set1,
1785 __isl_keep isl_set *set2);
1786 int isl_union_set_is_subset(
1787 __isl_keep isl_union_set *uset1,
1788 __isl_keep isl_union_set *uset2);
1789 int isl_union_set_is_strict_subset(
1790 __isl_keep isl_union_set *uset1,
1791 __isl_keep isl_union_set *uset2);
1792 int isl_basic_map_is_subset(
1793 __isl_keep isl_basic_map *bmap1,
1794 __isl_keep isl_basic_map *bmap2);
1795 int isl_basic_map_is_strict_subset(
1796 __isl_keep isl_basic_map *bmap1,
1797 __isl_keep isl_basic_map *bmap2);
1798 int isl_map_is_subset(
1799 __isl_keep isl_map *map1,
1800 __isl_keep isl_map *map2);
1801 int isl_map_is_strict_subset(
1802 __isl_keep isl_map *map1,
1803 __isl_keep isl_map *map2);
1804 int isl_union_map_is_subset(
1805 __isl_keep isl_union_map *umap1,
1806 __isl_keep isl_union_map *umap2);
1807 int isl_union_map_is_strict_subset(
1808 __isl_keep isl_union_map *umap1,
1809 __isl_keep isl_union_map *umap2);
1813 =head2 Unary Operations
1819 __isl_give isl_set *isl_set_complement(
1820 __isl_take isl_set *set);
1821 __isl_give isl_map *isl_map_complement(
1822 __isl_take isl_map *map);
1826 __isl_give isl_basic_map *isl_basic_map_reverse(
1827 __isl_take isl_basic_map *bmap);
1828 __isl_give isl_map *isl_map_reverse(
1829 __isl_take isl_map *map);
1830 __isl_give isl_union_map *isl_union_map_reverse(
1831 __isl_take isl_union_map *umap);
1835 __isl_give isl_basic_set *isl_basic_set_project_out(
1836 __isl_take isl_basic_set *bset,
1837 enum isl_dim_type type, unsigned first, unsigned n);
1838 __isl_give isl_basic_map *isl_basic_map_project_out(
1839 __isl_take isl_basic_map *bmap,
1840 enum isl_dim_type type, unsigned first, unsigned n);
1841 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1842 enum isl_dim_type type, unsigned first, unsigned n);
1843 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1844 enum isl_dim_type type, unsigned first, unsigned n);
1845 __isl_give isl_basic_set *isl_basic_set_params(
1846 __isl_take isl_basic_set *bset);
1847 __isl_give isl_basic_set *isl_basic_map_domain(
1848 __isl_take isl_basic_map *bmap);
1849 __isl_give isl_basic_set *isl_basic_map_range(
1850 __isl_take isl_basic_map *bmap);
1851 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1852 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1853 __isl_give isl_set *isl_map_domain(
1854 __isl_take isl_map *bmap);
1855 __isl_give isl_set *isl_map_range(
1856 __isl_take isl_map *map);
1857 __isl_give isl_set *isl_union_set_params(
1858 __isl_take isl_union_set *uset);
1859 __isl_give isl_set *isl_union_map_params(
1860 __isl_take isl_union_map *umap);
1861 __isl_give isl_union_set *isl_union_map_domain(
1862 __isl_take isl_union_map *umap);
1863 __isl_give isl_union_set *isl_union_map_range(
1864 __isl_take isl_union_map *umap);
1866 __isl_give isl_basic_map *isl_basic_map_domain_map(
1867 __isl_take isl_basic_map *bmap);
1868 __isl_give isl_basic_map *isl_basic_map_range_map(
1869 __isl_take isl_basic_map *bmap);
1870 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1871 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1872 __isl_give isl_union_map *isl_union_map_domain_map(
1873 __isl_take isl_union_map *umap);
1874 __isl_give isl_union_map *isl_union_map_range_map(
1875 __isl_take isl_union_map *umap);
1877 The functions above construct a (basic, regular or union) relation
1878 that maps (a wrapped version of) the input relation to its domain or range.
1882 __isl_give isl_set *isl_set_eliminate(
1883 __isl_take isl_set *set, enum isl_dim_type type,
1884 unsigned first, unsigned n);
1885 __isl_give isl_basic_map *isl_basic_map_eliminate(
1886 __isl_take isl_basic_map *bmap,
1887 enum isl_dim_type type,
1888 unsigned first, unsigned n);
1889 __isl_give isl_map *isl_map_eliminate(
1890 __isl_take isl_map *map, enum isl_dim_type type,
1891 unsigned first, unsigned n);
1893 Eliminate the coefficients for the given dimensions from the constraints,
1894 without removing the dimensions.
1898 __isl_give isl_basic_set *isl_basic_set_fix(
1899 __isl_take isl_basic_set *bset,
1900 enum isl_dim_type type, unsigned pos,
1902 __isl_give isl_basic_set *isl_basic_set_fix_si(
1903 __isl_take isl_basic_set *bset,
1904 enum isl_dim_type type, unsigned pos, int value);
1905 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1906 enum isl_dim_type type, unsigned pos,
1908 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1909 enum isl_dim_type type, unsigned pos, int value);
1910 __isl_give isl_basic_map *isl_basic_map_fix_si(
1911 __isl_take isl_basic_map *bmap,
1912 enum isl_dim_type type, unsigned pos, int value);
1913 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1914 enum isl_dim_type type, unsigned pos, int value);
1916 Intersect the set or relation with the hyperplane where the given
1917 dimension has the fixed given value.
1919 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1920 __isl_take isl_basic_map *bmap,
1921 enum isl_dim_type type, unsigned pos, int value);
1922 __isl_give isl_set *isl_set_lower_bound(
1923 __isl_take isl_set *set,
1924 enum isl_dim_type type, unsigned pos,
1926 __isl_give isl_set *isl_set_lower_bound_si(
1927 __isl_take isl_set *set,
1928 enum isl_dim_type type, unsigned pos, int value);
1929 __isl_give isl_map *isl_map_lower_bound_si(
1930 __isl_take isl_map *map,
1931 enum isl_dim_type type, unsigned pos, int value);
1932 __isl_give isl_set *isl_set_upper_bound(
1933 __isl_take isl_set *set,
1934 enum isl_dim_type type, unsigned pos,
1936 __isl_give isl_set *isl_set_upper_bound_si(
1937 __isl_take isl_set *set,
1938 enum isl_dim_type type, unsigned pos, int value);
1939 __isl_give isl_map *isl_map_upper_bound_si(
1940 __isl_take isl_map *map,
1941 enum isl_dim_type type, unsigned pos, int value);
1943 Intersect the set or relation with the half-space where the given
1944 dimension has a value bounded by the fixed given value.
1946 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1947 enum isl_dim_type type1, int pos1,
1948 enum isl_dim_type type2, int pos2);
1949 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1950 enum isl_dim_type type1, int pos1,
1951 enum isl_dim_type type2, int pos2);
1953 Intersect the set or relation with the hyperplane where the given
1954 dimensions are equal to each other.
1956 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1957 enum isl_dim_type type1, int pos1,
1958 enum isl_dim_type type2, int pos2);
1960 Intersect the relation with the hyperplane where the given
1961 dimensions have opposite values.
1963 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1964 enum isl_dim_type type1, int pos1,
1965 enum isl_dim_type type2, int pos2);
1967 Intersect the relation with the half-space where the given
1968 dimensions satisfy the given ordering.
1972 __isl_give isl_map *isl_set_identity(
1973 __isl_take isl_set *set);
1974 __isl_give isl_union_map *isl_union_set_identity(
1975 __isl_take isl_union_set *uset);
1977 Construct an identity relation on the given (union) set.
1981 __isl_give isl_basic_set *isl_basic_map_deltas(
1982 __isl_take isl_basic_map *bmap);
1983 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1984 __isl_give isl_union_set *isl_union_map_deltas(
1985 __isl_take isl_union_map *umap);
1987 These functions return a (basic) set containing the differences
1988 between image elements and corresponding domain elements in the input.
1990 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1991 __isl_take isl_basic_map *bmap);
1992 __isl_give isl_map *isl_map_deltas_map(
1993 __isl_take isl_map *map);
1994 __isl_give isl_union_map *isl_union_map_deltas_map(
1995 __isl_take isl_union_map *umap);
1997 The functions above construct a (basic, regular or union) relation
1998 that maps (a wrapped version of) the input relation to its delta set.
2002 Simplify the representation of a set or relation by trying
2003 to combine pairs of basic sets or relations into a single
2004 basic set or relation.
2006 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2007 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2008 __isl_give isl_union_set *isl_union_set_coalesce(
2009 __isl_take isl_union_set *uset);
2010 __isl_give isl_union_map *isl_union_map_coalesce(
2011 __isl_take isl_union_map *umap);
2013 One of the methods for combining pairs of basic sets or relations
2014 can result in coefficients that are much larger than those that appear
2015 in the constraints of the input. By default, the coefficients are
2016 not allowed to grow larger, but this can be changed by unsetting
2017 the following option.
2019 int isl_options_set_coalesce_bounded_wrapping(
2020 isl_ctx *ctx, int val);
2021 int isl_options_get_coalesce_bounded_wrapping(
2024 =item * Detecting equalities
2026 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2027 __isl_take isl_basic_set *bset);
2028 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2029 __isl_take isl_basic_map *bmap);
2030 __isl_give isl_set *isl_set_detect_equalities(
2031 __isl_take isl_set *set);
2032 __isl_give isl_map *isl_map_detect_equalities(
2033 __isl_take isl_map *map);
2034 __isl_give isl_union_set *isl_union_set_detect_equalities(
2035 __isl_take isl_union_set *uset);
2036 __isl_give isl_union_map *isl_union_map_detect_equalities(
2037 __isl_take isl_union_map *umap);
2039 Simplify the representation of a set or relation by detecting implicit
2042 =item * Removing redundant constraints
2044 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2045 __isl_take isl_basic_set *bset);
2046 __isl_give isl_set *isl_set_remove_redundancies(
2047 __isl_take isl_set *set);
2048 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2049 __isl_take isl_basic_map *bmap);
2050 __isl_give isl_map *isl_map_remove_redundancies(
2051 __isl_take isl_map *map);
2055 __isl_give isl_basic_set *isl_set_convex_hull(
2056 __isl_take isl_set *set);
2057 __isl_give isl_basic_map *isl_map_convex_hull(
2058 __isl_take isl_map *map);
2060 If the input set or relation has any existentially quantified
2061 variables, then the result of these operations is currently undefined.
2065 __isl_give isl_basic_set *isl_set_simple_hull(
2066 __isl_take isl_set *set);
2067 __isl_give isl_basic_map *isl_map_simple_hull(
2068 __isl_take isl_map *map);
2069 __isl_give isl_union_map *isl_union_map_simple_hull(
2070 __isl_take isl_union_map *umap);
2072 These functions compute a single basic set or relation
2073 that contains the whole input set or relation.
2074 In particular, the output is described by translates
2075 of the constraints describing the basic sets or relations in the input.
2079 (See \autoref{s:simple hull}.)
2085 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2086 __isl_take isl_basic_set *bset);
2087 __isl_give isl_basic_set *isl_set_affine_hull(
2088 __isl_take isl_set *set);
2089 __isl_give isl_union_set *isl_union_set_affine_hull(
2090 __isl_take isl_union_set *uset);
2091 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2092 __isl_take isl_basic_map *bmap);
2093 __isl_give isl_basic_map *isl_map_affine_hull(
2094 __isl_take isl_map *map);
2095 __isl_give isl_union_map *isl_union_map_affine_hull(
2096 __isl_take isl_union_map *umap);
2098 In case of union sets and relations, the affine hull is computed
2101 =item * Polyhedral hull
2103 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2104 __isl_take isl_set *set);
2105 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2106 __isl_take isl_map *map);
2107 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2108 __isl_take isl_union_set *uset);
2109 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2110 __isl_take isl_union_map *umap);
2112 These functions compute a single basic set or relation
2113 not involving any existentially quantified variables
2114 that contains the whole input set or relation.
2115 In case of union sets and relations, the polyhedral hull is computed
2120 __isl_give isl_basic_set *isl_basic_set_sample(
2121 __isl_take isl_basic_set *bset);
2122 __isl_give isl_basic_set *isl_set_sample(
2123 __isl_take isl_set *set);
2124 __isl_give isl_basic_map *isl_basic_map_sample(
2125 __isl_take isl_basic_map *bmap);
2126 __isl_give isl_basic_map *isl_map_sample(
2127 __isl_take isl_map *map);
2129 If the input (basic) set or relation is non-empty, then return
2130 a singleton subset of the input. Otherwise, return an empty set.
2132 =item * Optimization
2134 #include <isl/ilp.h>
2135 enum isl_lp_result isl_basic_set_max(
2136 __isl_keep isl_basic_set *bset,
2137 __isl_keep isl_aff *obj, isl_int *opt)
2138 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2139 __isl_keep isl_aff *obj, isl_int *opt);
2140 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2141 __isl_keep isl_aff *obj, isl_int *opt);
2143 Compute the minimum or maximum of the integer affine expression C<obj>
2144 over the points in C<set>, returning the result in C<opt>.
2145 The return value may be one of C<isl_lp_error>,
2146 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2148 =item * Parametric optimization
2150 __isl_give isl_pw_aff *isl_set_dim_min(
2151 __isl_take isl_set *set, int pos);
2152 __isl_give isl_pw_aff *isl_set_dim_max(
2153 __isl_take isl_set *set, int pos);
2154 __isl_give isl_pw_aff *isl_map_dim_max(
2155 __isl_take isl_map *map, int pos);
2157 Compute the minimum or maximum of the given set or output dimension
2158 as a function of the parameters (and input dimensions), but independently
2159 of the other set or output dimensions.
2160 For lexicographic optimization, see L<"Lexicographic Optimization">.
2164 The following functions compute either the set of (rational) coefficient
2165 values of valid constraints for the given set or the set of (rational)
2166 values satisfying the constraints with coefficients from the given set.
2167 Internally, these two sets of functions perform essentially the
2168 same operations, except that the set of coefficients is assumed to
2169 be a cone, while the set of values may be any polyhedron.
2170 The current implementation is based on the Farkas lemma and
2171 Fourier-Motzkin elimination, but this may change or be made optional
2172 in future. In particular, future implementations may use different
2173 dualization algorithms or skip the elimination step.
2175 __isl_give isl_basic_set *isl_basic_set_coefficients(
2176 __isl_take isl_basic_set *bset);
2177 __isl_give isl_basic_set *isl_set_coefficients(
2178 __isl_take isl_set *set);
2179 __isl_give isl_union_set *isl_union_set_coefficients(
2180 __isl_take isl_union_set *bset);
2181 __isl_give isl_basic_set *isl_basic_set_solutions(
2182 __isl_take isl_basic_set *bset);
2183 __isl_give isl_basic_set *isl_set_solutions(
2184 __isl_take isl_set *set);
2185 __isl_give isl_union_set *isl_union_set_solutions(
2186 __isl_take isl_union_set *bset);
2190 __isl_give isl_map *isl_map_fixed_power(
2191 __isl_take isl_map *map, isl_int exp);
2192 __isl_give isl_union_map *isl_union_map_fixed_power(
2193 __isl_take isl_union_map *umap, isl_int exp);
2195 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2196 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2197 of C<map> is computed.
2199 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2201 __isl_give isl_union_map *isl_union_map_power(
2202 __isl_take isl_union_map *umap, int *exact);
2204 Compute a parametric representation for all positive powers I<k> of C<map>.
2205 The result maps I<k> to a nested relation corresponding to the
2206 I<k>th power of C<map>.
2207 The result may be an overapproximation. If the result is known to be exact,
2208 then C<*exact> is set to C<1>.
2210 =item * Transitive closure
2212 __isl_give isl_map *isl_map_transitive_closure(
2213 __isl_take isl_map *map, int *exact);
2214 __isl_give isl_union_map *isl_union_map_transitive_closure(
2215 __isl_take isl_union_map *umap, int *exact);
2217 Compute the transitive closure of C<map>.
2218 The result may be an overapproximation. If the result is known to be exact,
2219 then C<*exact> is set to C<1>.
2221 =item * Reaching path lengths
2223 __isl_give isl_map *isl_map_reaching_path_lengths(
2224 __isl_take isl_map *map, int *exact);
2226 Compute a relation that maps each element in the range of C<map>
2227 to the lengths of all paths composed of edges in C<map> that
2228 end up in the given element.
2229 The result may be an overapproximation. If the result is known to be exact,
2230 then C<*exact> is set to C<1>.
2231 To compute the I<maximal> path length, the resulting relation
2232 should be postprocessed by C<isl_map_lexmax>.
2233 In particular, if the input relation is a dependence relation
2234 (mapping sources to sinks), then the maximal path length corresponds
2235 to the free schedule.
2236 Note, however, that C<isl_map_lexmax> expects the maximum to be
2237 finite, so if the path lengths are unbounded (possibly due to
2238 the overapproximation), then you will get an error message.
2242 __isl_give isl_basic_set *isl_basic_map_wrap(
2243 __isl_take isl_basic_map *bmap);
2244 __isl_give isl_set *isl_map_wrap(
2245 __isl_take isl_map *map);
2246 __isl_give isl_union_set *isl_union_map_wrap(
2247 __isl_take isl_union_map *umap);
2248 __isl_give isl_basic_map *isl_basic_set_unwrap(
2249 __isl_take isl_basic_set *bset);
2250 __isl_give isl_map *isl_set_unwrap(
2251 __isl_take isl_set *set);
2252 __isl_give isl_union_map *isl_union_set_unwrap(
2253 __isl_take isl_union_set *uset);
2257 Remove any internal structure of domain (and range) of the given
2258 set or relation. If there is any such internal structure in the input,
2259 then the name of the space is also removed.
2261 __isl_give isl_basic_set *isl_basic_set_flatten(
2262 __isl_take isl_basic_set *bset);
2263 __isl_give isl_set *isl_set_flatten(
2264 __isl_take isl_set *set);
2265 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2266 __isl_take isl_basic_map *bmap);
2267 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2268 __isl_take isl_basic_map *bmap);
2269 __isl_give isl_map *isl_map_flatten_range(
2270 __isl_take isl_map *map);
2271 __isl_give isl_map *isl_map_flatten_domain(
2272 __isl_take isl_map *map);
2273 __isl_give isl_basic_map *isl_basic_map_flatten(
2274 __isl_take isl_basic_map *bmap);
2275 __isl_give isl_map *isl_map_flatten(
2276 __isl_take isl_map *map);
2278 __isl_give isl_map *isl_set_flatten_map(
2279 __isl_take isl_set *set);
2281 The function above constructs a relation
2282 that maps the input set to a flattened version of the set.
2286 Lift the input set to a space with extra dimensions corresponding
2287 to the existentially quantified variables in the input.
2288 In particular, the result lives in a wrapped map where the domain
2289 is the original space and the range corresponds to the original
2290 existentially quantified variables.
2292 __isl_give isl_basic_set *isl_basic_set_lift(
2293 __isl_take isl_basic_set *bset);
2294 __isl_give isl_set *isl_set_lift(
2295 __isl_take isl_set *set);
2296 __isl_give isl_union_set *isl_union_set_lift(
2297 __isl_take isl_union_set *uset);
2299 Given a local space that contains the existentially quantified
2300 variables of a set, a basic relation that, when applied to
2301 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2302 can be constructed using the following function.
2304 #include <isl/local_space.h>
2305 __isl_give isl_basic_map *isl_local_space_lifting(
2306 __isl_take isl_local_space *ls);
2308 =item * Internal Product
2310 __isl_give isl_basic_map *isl_basic_map_zip(
2311 __isl_take isl_basic_map *bmap);
2312 __isl_give isl_map *isl_map_zip(
2313 __isl_take isl_map *map);
2314 __isl_give isl_union_map *isl_union_map_zip(
2315 __isl_take isl_union_map *umap);
2317 Given a relation with nested relations for domain and range,
2318 interchange the range of the domain with the domain of the range.
2322 __isl_give isl_basic_map *isl_basic_map_curry(
2323 __isl_take isl_basic_map *bmap);
2324 __isl_give isl_map *isl_map_curry(
2325 __isl_take isl_map *map);
2326 __isl_give isl_union_map *isl_union_map_curry(
2327 __isl_take isl_union_map *umap);
2329 Given a relation with a nested relation for domain,
2330 move the range of the nested relation out of the domain
2331 and use it as the domain of a nested relation in the range,
2332 with the original range as range of this nested relation.
2334 =item * Aligning parameters
2336 __isl_give isl_set *isl_set_align_params(
2337 __isl_take isl_set *set,
2338 __isl_take isl_space *model);
2339 __isl_give isl_map *isl_map_align_params(
2340 __isl_take isl_map *map,
2341 __isl_take isl_space *model);
2343 Change the order of the parameters of the given set or relation
2344 such that the first parameters match those of C<model>.
2345 This may involve the introduction of extra parameters.
2346 All parameters need to be named.
2348 =item * Dimension manipulation
2350 __isl_give isl_set *isl_set_add_dims(
2351 __isl_take isl_set *set,
2352 enum isl_dim_type type, unsigned n);
2353 __isl_give isl_map *isl_map_add_dims(
2354 __isl_take isl_map *map,
2355 enum isl_dim_type type, unsigned n);
2356 __isl_give isl_set *isl_set_insert_dims(
2357 __isl_take isl_set *set,
2358 enum isl_dim_type type, unsigned pos, unsigned n);
2359 __isl_give isl_map *isl_map_insert_dims(
2360 __isl_take isl_map *map,
2361 enum isl_dim_type type, unsigned pos, unsigned n);
2362 __isl_give isl_basic_set *isl_basic_set_move_dims(
2363 __isl_take isl_basic_set *bset,
2364 enum isl_dim_type dst_type, unsigned dst_pos,
2365 enum isl_dim_type src_type, unsigned src_pos,
2367 __isl_give isl_basic_map *isl_basic_map_move_dims(
2368 __isl_take isl_basic_map *bmap,
2369 enum isl_dim_type dst_type, unsigned dst_pos,
2370 enum isl_dim_type src_type, unsigned src_pos,
2372 __isl_give isl_set *isl_set_move_dims(
2373 __isl_take isl_set *set,
2374 enum isl_dim_type dst_type, unsigned dst_pos,
2375 enum isl_dim_type src_type, unsigned src_pos,
2377 __isl_give isl_map *isl_map_move_dims(
2378 __isl_take isl_map *map,
2379 enum isl_dim_type dst_type, unsigned dst_pos,
2380 enum isl_dim_type src_type, unsigned src_pos,
2383 It is usually not advisable to directly change the (input or output)
2384 space of a set or a relation as this removes the name and the internal
2385 structure of the space. However, the above functions can be useful
2386 to add new parameters, assuming
2387 C<isl_set_align_params> and C<isl_map_align_params>
2392 =head2 Binary Operations
2394 The two arguments of a binary operation not only need to live
2395 in the same C<isl_ctx>, they currently also need to have
2396 the same (number of) parameters.
2398 =head3 Basic Operations
2402 =item * Intersection
2404 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2405 __isl_take isl_basic_set *bset1,
2406 __isl_take isl_basic_set *bset2);
2407 __isl_give isl_basic_set *isl_basic_set_intersect(
2408 __isl_take isl_basic_set *bset1,
2409 __isl_take isl_basic_set *bset2);
2410 __isl_give isl_set *isl_set_intersect_params(
2411 __isl_take isl_set *set,
2412 __isl_take isl_set *params);
2413 __isl_give isl_set *isl_set_intersect(
2414 __isl_take isl_set *set1,
2415 __isl_take isl_set *set2);
2416 __isl_give isl_union_set *isl_union_set_intersect_params(
2417 __isl_take isl_union_set *uset,
2418 __isl_take isl_set *set);
2419 __isl_give isl_union_map *isl_union_map_intersect_params(
2420 __isl_take isl_union_map *umap,
2421 __isl_take isl_set *set);
2422 __isl_give isl_union_set *isl_union_set_intersect(
2423 __isl_take isl_union_set *uset1,
2424 __isl_take isl_union_set *uset2);
2425 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2426 __isl_take isl_basic_map *bmap,
2427 __isl_take isl_basic_set *bset);
2428 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2429 __isl_take isl_basic_map *bmap,
2430 __isl_take isl_basic_set *bset);
2431 __isl_give isl_basic_map *isl_basic_map_intersect(
2432 __isl_take isl_basic_map *bmap1,
2433 __isl_take isl_basic_map *bmap2);
2434 __isl_give isl_map *isl_map_intersect_params(
2435 __isl_take isl_map *map,
2436 __isl_take isl_set *params);
2437 __isl_give isl_map *isl_map_intersect_domain(
2438 __isl_take isl_map *map,
2439 __isl_take isl_set *set);
2440 __isl_give isl_map *isl_map_intersect_range(
2441 __isl_take isl_map *map,
2442 __isl_take isl_set *set);
2443 __isl_give isl_map *isl_map_intersect(
2444 __isl_take isl_map *map1,
2445 __isl_take isl_map *map2);
2446 __isl_give isl_union_map *isl_union_map_intersect_domain(
2447 __isl_take isl_union_map *umap,
2448 __isl_take isl_union_set *uset);
2449 __isl_give isl_union_map *isl_union_map_intersect_range(
2450 __isl_take isl_union_map *umap,
2451 __isl_take isl_union_set *uset);
2452 __isl_give isl_union_map *isl_union_map_intersect(
2453 __isl_take isl_union_map *umap1,
2454 __isl_take isl_union_map *umap2);
2458 __isl_give isl_set *isl_basic_set_union(
2459 __isl_take isl_basic_set *bset1,
2460 __isl_take isl_basic_set *bset2);
2461 __isl_give isl_map *isl_basic_map_union(
2462 __isl_take isl_basic_map *bmap1,
2463 __isl_take isl_basic_map *bmap2);
2464 __isl_give isl_set *isl_set_union(
2465 __isl_take isl_set *set1,
2466 __isl_take isl_set *set2);
2467 __isl_give isl_map *isl_map_union(
2468 __isl_take isl_map *map1,
2469 __isl_take isl_map *map2);
2470 __isl_give isl_union_set *isl_union_set_union(
2471 __isl_take isl_union_set *uset1,
2472 __isl_take isl_union_set *uset2);
2473 __isl_give isl_union_map *isl_union_map_union(
2474 __isl_take isl_union_map *umap1,
2475 __isl_take isl_union_map *umap2);
2477 =item * Set difference
2479 __isl_give isl_set *isl_set_subtract(
2480 __isl_take isl_set *set1,
2481 __isl_take isl_set *set2);
2482 __isl_give isl_map *isl_map_subtract(
2483 __isl_take isl_map *map1,
2484 __isl_take isl_map *map2);
2485 __isl_give isl_map *isl_map_subtract_domain(
2486 __isl_take isl_map *map,
2487 __isl_take isl_set *dom);
2488 __isl_give isl_map *isl_map_subtract_range(
2489 __isl_take isl_map *map,
2490 __isl_take isl_set *dom);
2491 __isl_give isl_union_set *isl_union_set_subtract(
2492 __isl_take isl_union_set *uset1,
2493 __isl_take isl_union_set *uset2);
2494 __isl_give isl_union_map *isl_union_map_subtract(
2495 __isl_take isl_union_map *umap1,
2496 __isl_take isl_union_map *umap2);
2500 __isl_give isl_basic_set *isl_basic_set_apply(
2501 __isl_take isl_basic_set *bset,
2502 __isl_take isl_basic_map *bmap);
2503 __isl_give isl_set *isl_set_apply(
2504 __isl_take isl_set *set,
2505 __isl_take isl_map *map);
2506 __isl_give isl_union_set *isl_union_set_apply(
2507 __isl_take isl_union_set *uset,
2508 __isl_take isl_union_map *umap);
2509 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2510 __isl_take isl_basic_map *bmap1,
2511 __isl_take isl_basic_map *bmap2);
2512 __isl_give isl_basic_map *isl_basic_map_apply_range(
2513 __isl_take isl_basic_map *bmap1,
2514 __isl_take isl_basic_map *bmap2);
2515 __isl_give isl_map *isl_map_apply_domain(
2516 __isl_take isl_map *map1,
2517 __isl_take isl_map *map2);
2518 __isl_give isl_union_map *isl_union_map_apply_domain(
2519 __isl_take isl_union_map *umap1,
2520 __isl_take isl_union_map *umap2);
2521 __isl_give isl_map *isl_map_apply_range(
2522 __isl_take isl_map *map1,
2523 __isl_take isl_map *map2);
2524 __isl_give isl_union_map *isl_union_map_apply_range(
2525 __isl_take isl_union_map *umap1,
2526 __isl_take isl_union_map *umap2);
2528 =item * Cartesian Product
2530 __isl_give isl_set *isl_set_product(
2531 __isl_take isl_set *set1,
2532 __isl_take isl_set *set2);
2533 __isl_give isl_union_set *isl_union_set_product(
2534 __isl_take isl_union_set *uset1,
2535 __isl_take isl_union_set *uset2);
2536 __isl_give isl_basic_map *isl_basic_map_domain_product(
2537 __isl_take isl_basic_map *bmap1,
2538 __isl_take isl_basic_map *bmap2);
2539 __isl_give isl_basic_map *isl_basic_map_range_product(
2540 __isl_take isl_basic_map *bmap1,
2541 __isl_take isl_basic_map *bmap2);
2542 __isl_give isl_map *isl_map_domain_product(
2543 __isl_take isl_map *map1,
2544 __isl_take isl_map *map2);
2545 __isl_give isl_map *isl_map_range_product(
2546 __isl_take isl_map *map1,
2547 __isl_take isl_map *map2);
2548 __isl_give isl_union_map *isl_union_map_range_product(
2549 __isl_take isl_union_map *umap1,
2550 __isl_take isl_union_map *umap2);
2551 __isl_give isl_map *isl_map_product(
2552 __isl_take isl_map *map1,
2553 __isl_take isl_map *map2);
2554 __isl_give isl_union_map *isl_union_map_product(
2555 __isl_take isl_union_map *umap1,
2556 __isl_take isl_union_map *umap2);
2558 The above functions compute the cross product of the given
2559 sets or relations. The domains and ranges of the results
2560 are wrapped maps between domains and ranges of the inputs.
2561 To obtain a ``flat'' product, use the following functions
2564 __isl_give isl_basic_set *isl_basic_set_flat_product(
2565 __isl_take isl_basic_set *bset1,
2566 __isl_take isl_basic_set *bset2);
2567 __isl_give isl_set *isl_set_flat_product(
2568 __isl_take isl_set *set1,
2569 __isl_take isl_set *set2);
2570 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2571 __isl_take isl_basic_map *bmap1,
2572 __isl_take isl_basic_map *bmap2);
2573 __isl_give isl_map *isl_map_flat_domain_product(
2574 __isl_take isl_map *map1,
2575 __isl_take isl_map *map2);
2576 __isl_give isl_map *isl_map_flat_range_product(
2577 __isl_take isl_map *map1,
2578 __isl_take isl_map *map2);
2579 __isl_give isl_union_map *isl_union_map_flat_range_product(
2580 __isl_take isl_union_map *umap1,
2581 __isl_take isl_union_map *umap2);
2582 __isl_give isl_basic_map *isl_basic_map_flat_product(
2583 __isl_take isl_basic_map *bmap1,
2584 __isl_take isl_basic_map *bmap2);
2585 __isl_give isl_map *isl_map_flat_product(
2586 __isl_take isl_map *map1,
2587 __isl_take isl_map *map2);
2589 =item * Simplification
2591 __isl_give isl_basic_set *isl_basic_set_gist(
2592 __isl_take isl_basic_set *bset,
2593 __isl_take isl_basic_set *context);
2594 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2595 __isl_take isl_set *context);
2596 __isl_give isl_set *isl_set_gist_params(
2597 __isl_take isl_set *set,
2598 __isl_take isl_set *context);
2599 __isl_give isl_union_set *isl_union_set_gist(
2600 __isl_take isl_union_set *uset,
2601 __isl_take isl_union_set *context);
2602 __isl_give isl_union_set *isl_union_set_gist_params(
2603 __isl_take isl_union_set *uset,
2604 __isl_take isl_set *set);
2605 __isl_give isl_basic_map *isl_basic_map_gist(
2606 __isl_take isl_basic_map *bmap,
2607 __isl_take isl_basic_map *context);
2608 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2609 __isl_take isl_map *context);
2610 __isl_give isl_map *isl_map_gist_params(
2611 __isl_take isl_map *map,
2612 __isl_take isl_set *context);
2613 __isl_give isl_map *isl_map_gist_domain(
2614 __isl_take isl_map *map,
2615 __isl_take isl_set *context);
2616 __isl_give isl_map *isl_map_gist_range(
2617 __isl_take isl_map *map,
2618 __isl_take isl_set *context);
2619 __isl_give isl_union_map *isl_union_map_gist(
2620 __isl_take isl_union_map *umap,
2621 __isl_take isl_union_map *context);
2622 __isl_give isl_union_map *isl_union_map_gist_params(
2623 __isl_take isl_union_map *umap,
2624 __isl_take isl_set *set);
2625 __isl_give isl_union_map *isl_union_map_gist_domain(
2626 __isl_take isl_union_map *umap,
2627 __isl_take isl_union_set *uset);
2628 __isl_give isl_union_map *isl_union_map_gist_range(
2629 __isl_take isl_union_map *umap,
2630 __isl_take isl_union_set *uset);
2632 The gist operation returns a set or relation that has the
2633 same intersection with the context as the input set or relation.
2634 Any implicit equality in the intersection is made explicit in the result,
2635 while all inequalities that are redundant with respect to the intersection
2637 In case of union sets and relations, the gist operation is performed
2642 =head3 Lexicographic Optimization
2644 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2645 the following functions
2646 compute a set that contains the lexicographic minimum or maximum
2647 of the elements in C<set> (or C<bset>) for those values of the parameters
2648 that satisfy C<dom>.
2649 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2650 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2652 In other words, the union of the parameter values
2653 for which the result is non-empty and of C<*empty>
2656 __isl_give isl_set *isl_basic_set_partial_lexmin(
2657 __isl_take isl_basic_set *bset,
2658 __isl_take isl_basic_set *dom,
2659 __isl_give isl_set **empty);
2660 __isl_give isl_set *isl_basic_set_partial_lexmax(
2661 __isl_take isl_basic_set *bset,
2662 __isl_take isl_basic_set *dom,
2663 __isl_give isl_set **empty);
2664 __isl_give isl_set *isl_set_partial_lexmin(
2665 __isl_take isl_set *set, __isl_take isl_set *dom,
2666 __isl_give isl_set **empty);
2667 __isl_give isl_set *isl_set_partial_lexmax(
2668 __isl_take isl_set *set, __isl_take isl_set *dom,
2669 __isl_give isl_set **empty);
2671 Given a (basic) set C<set> (or C<bset>), the following functions simply
2672 return a set containing the lexicographic minimum or maximum
2673 of the elements in C<set> (or C<bset>).
2674 In case of union sets, the optimum is computed per space.
2676 __isl_give isl_set *isl_basic_set_lexmin(
2677 __isl_take isl_basic_set *bset);
2678 __isl_give isl_set *isl_basic_set_lexmax(
2679 __isl_take isl_basic_set *bset);
2680 __isl_give isl_set *isl_set_lexmin(
2681 __isl_take isl_set *set);
2682 __isl_give isl_set *isl_set_lexmax(
2683 __isl_take isl_set *set);
2684 __isl_give isl_union_set *isl_union_set_lexmin(
2685 __isl_take isl_union_set *uset);
2686 __isl_give isl_union_set *isl_union_set_lexmax(
2687 __isl_take isl_union_set *uset);
2689 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2690 the following functions
2691 compute a relation that maps each element of C<dom>
2692 to the single lexicographic minimum or maximum
2693 of the elements that are associated to that same
2694 element in C<map> (or C<bmap>).
2695 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2696 that contains the elements in C<dom> that do not map
2697 to any elements in C<map> (or C<bmap>).
2698 In other words, the union of the domain of the result and of C<*empty>
2701 __isl_give isl_map *isl_basic_map_partial_lexmax(
2702 __isl_take isl_basic_map *bmap,
2703 __isl_take isl_basic_set *dom,
2704 __isl_give isl_set **empty);
2705 __isl_give isl_map *isl_basic_map_partial_lexmin(
2706 __isl_take isl_basic_map *bmap,
2707 __isl_take isl_basic_set *dom,
2708 __isl_give isl_set **empty);
2709 __isl_give isl_map *isl_map_partial_lexmax(
2710 __isl_take isl_map *map, __isl_take isl_set *dom,
2711 __isl_give isl_set **empty);
2712 __isl_give isl_map *isl_map_partial_lexmin(
2713 __isl_take isl_map *map, __isl_take isl_set *dom,
2714 __isl_give isl_set **empty);
2716 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2717 return a map mapping each element in the domain of
2718 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2719 of all elements associated to that element.
2720 In case of union relations, the optimum is computed per space.
2722 __isl_give isl_map *isl_basic_map_lexmin(
2723 __isl_take isl_basic_map *bmap);
2724 __isl_give isl_map *isl_basic_map_lexmax(
2725 __isl_take isl_basic_map *bmap);
2726 __isl_give isl_map *isl_map_lexmin(
2727 __isl_take isl_map *map);
2728 __isl_give isl_map *isl_map_lexmax(
2729 __isl_take isl_map *map);
2730 __isl_give isl_union_map *isl_union_map_lexmin(
2731 __isl_take isl_union_map *umap);
2732 __isl_give isl_union_map *isl_union_map_lexmax(
2733 __isl_take isl_union_map *umap);
2735 The following functions return their result in the form of
2736 a piecewise multi-affine expression
2737 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2738 but are otherwise equivalent to the corresponding functions
2739 returning a basic set or relation.
2741 __isl_give isl_pw_multi_aff *
2742 isl_basic_map_lexmin_pw_multi_aff(
2743 __isl_take isl_basic_map *bmap);
2744 __isl_give isl_pw_multi_aff *
2745 isl_basic_set_partial_lexmin_pw_multi_aff(
2746 __isl_take isl_basic_set *bset,
2747 __isl_take isl_basic_set *dom,
2748 __isl_give isl_set **empty);
2749 __isl_give isl_pw_multi_aff *
2750 isl_basic_set_partial_lexmax_pw_multi_aff(
2751 __isl_take isl_basic_set *bset,
2752 __isl_take isl_basic_set *dom,
2753 __isl_give isl_set **empty);
2754 __isl_give isl_pw_multi_aff *
2755 isl_basic_map_partial_lexmin_pw_multi_aff(
2756 __isl_take isl_basic_map *bmap,
2757 __isl_take isl_basic_set *dom,
2758 __isl_give isl_set **empty);
2759 __isl_give isl_pw_multi_aff *
2760 isl_basic_map_partial_lexmax_pw_multi_aff(
2761 __isl_take isl_basic_map *bmap,
2762 __isl_take isl_basic_set *dom,
2763 __isl_give isl_set **empty);
2767 Lists are defined over several element types, including
2768 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2769 Here we take lists of C<isl_set>s as an example.
2770 Lists can be created, copied and freed using the following functions.
2772 #include <isl/list.h>
2773 __isl_give isl_set_list *isl_set_list_from_set(
2774 __isl_take isl_set *el);
2775 __isl_give isl_set_list *isl_set_list_alloc(
2776 isl_ctx *ctx, int n);
2777 __isl_give isl_set_list *isl_set_list_copy(
2778 __isl_keep isl_set_list *list);
2779 __isl_give isl_set_list *isl_set_list_add(
2780 __isl_take isl_set_list *list,
2781 __isl_take isl_set *el);
2782 __isl_give isl_set_list *isl_set_list_concat(
2783 __isl_take isl_set_list *list1,
2784 __isl_take isl_set_list *list2);
2785 void *isl_set_list_free(__isl_take isl_set_list *list);
2787 C<isl_set_list_alloc> creates an empty list with a capacity for
2788 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2791 Lists can be inspected using the following functions.
2793 #include <isl/list.h>
2794 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2795 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2796 __isl_give isl_set *isl_set_list_get_set(
2797 __isl_keep isl_set_list *list, int index);
2798 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2799 int (*fn)(__isl_take isl_set *el, void *user),
2802 Lists can be printed using
2804 #include <isl/list.h>
2805 __isl_give isl_printer *isl_printer_print_set_list(
2806 __isl_take isl_printer *p,
2807 __isl_keep isl_set_list *list);
2811 Vectors can be created, copied and freed using the following functions.
2813 #include <isl/vec.h>
2814 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2816 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2817 void isl_vec_free(__isl_take isl_vec *vec);
2819 Note that the elements of a newly created vector may have arbitrary values.
2820 The elements can be changed and inspected using the following functions.
2822 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2823 int isl_vec_size(__isl_keep isl_vec *vec);
2824 int isl_vec_get_element(__isl_keep isl_vec *vec,
2825 int pos, isl_int *v);
2826 __isl_give isl_vec *isl_vec_set_element(
2827 __isl_take isl_vec *vec, int pos, isl_int v);
2828 __isl_give isl_vec *isl_vec_set_element_si(
2829 __isl_take isl_vec *vec, int pos, int v);
2830 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2832 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2835 C<isl_vec_get_element> will return a negative value if anything went wrong.
2836 In that case, the value of C<*v> is undefined.
2840 Matrices can be created, copied and freed using the following functions.
2842 #include <isl/mat.h>
2843 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2844 unsigned n_row, unsigned n_col);
2845 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2846 void isl_mat_free(__isl_take isl_mat *mat);
2848 Note that the elements of a newly created matrix may have arbitrary values.
2849 The elements can be changed and inspected using the following functions.
2851 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2852 int isl_mat_rows(__isl_keep isl_mat *mat);
2853 int isl_mat_cols(__isl_keep isl_mat *mat);
2854 int isl_mat_get_element(__isl_keep isl_mat *mat,
2855 int row, int col, isl_int *v);
2856 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2857 int row, int col, isl_int v);
2858 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2859 int row, int col, int v);
2861 C<isl_mat_get_element> will return a negative value if anything went wrong.
2862 In that case, the value of C<*v> is undefined.
2864 The following function can be used to compute the (right) inverse
2865 of a matrix, i.e., a matrix such that the product of the original
2866 and the inverse (in that order) is a multiple of the identity matrix.
2867 The input matrix is assumed to be of full row-rank.
2869 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2871 The following function can be used to compute the (right) kernel
2872 (or null space) of a matrix, i.e., a matrix such that the product of
2873 the original and the kernel (in that order) is the zero matrix.
2875 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2877 =head2 Piecewise Quasi Affine Expressions
2879 The zero quasi affine expression on a given domain can be created using
2881 __isl_give isl_aff *isl_aff_zero_on_domain(
2882 __isl_take isl_local_space *ls);
2884 Note that the space in which the resulting object lives is a map space
2885 with the given space as domain and a one-dimensional range.
2887 An empty piecewise quasi affine expression (one with no cells)
2888 or a piecewise quasi affine expression with a single cell can
2889 be created using the following functions.
2891 #include <isl/aff.h>
2892 __isl_give isl_pw_aff *isl_pw_aff_empty(
2893 __isl_take isl_space *space);
2894 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2895 __isl_take isl_set *set, __isl_take isl_aff *aff);
2896 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2897 __isl_take isl_aff *aff);
2899 A piecewise quasi affine expression that is equal to 1 on a set
2900 and 0 outside the set can be created using the following function.
2902 #include <isl/aff.h>
2903 __isl_give isl_pw_aff *isl_set_indicator_function(
2904 __isl_take isl_set *set);
2906 Quasi affine expressions can be copied and freed using
2908 #include <isl/aff.h>
2909 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2910 void *isl_aff_free(__isl_take isl_aff *aff);
2912 __isl_give isl_pw_aff *isl_pw_aff_copy(
2913 __isl_keep isl_pw_aff *pwaff);
2914 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2916 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2917 using the following function. The constraint is required to have
2918 a non-zero coefficient for the specified dimension.
2920 #include <isl/constraint.h>
2921 __isl_give isl_aff *isl_constraint_get_bound(
2922 __isl_keep isl_constraint *constraint,
2923 enum isl_dim_type type, int pos);
2925 The entire affine expression of the constraint can also be extracted
2926 using the following function.
2928 #include <isl/constraint.h>
2929 __isl_give isl_aff *isl_constraint_get_aff(
2930 __isl_keep isl_constraint *constraint);
2932 Conversely, an equality constraint equating
2933 the affine expression to zero or an inequality constraint enforcing
2934 the affine expression to be non-negative, can be constructed using
2936 __isl_give isl_constraint *isl_equality_from_aff(
2937 __isl_take isl_aff *aff);
2938 __isl_give isl_constraint *isl_inequality_from_aff(
2939 __isl_take isl_aff *aff);
2941 The expression can be inspected using
2943 #include <isl/aff.h>
2944 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2945 int isl_aff_dim(__isl_keep isl_aff *aff,
2946 enum isl_dim_type type);
2947 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2948 __isl_keep isl_aff *aff);
2949 __isl_give isl_local_space *isl_aff_get_local_space(
2950 __isl_keep isl_aff *aff);
2951 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2952 enum isl_dim_type type, unsigned pos);
2953 const char *isl_pw_aff_get_dim_name(
2954 __isl_keep isl_pw_aff *pa,
2955 enum isl_dim_type type, unsigned pos);
2956 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2957 enum isl_dim_type type, unsigned pos);
2958 __isl_give isl_id *isl_pw_aff_get_dim_id(
2959 __isl_keep isl_pw_aff *pa,
2960 enum isl_dim_type type, unsigned pos);
2961 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2963 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2964 enum isl_dim_type type, int pos, isl_int *v);
2965 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2967 __isl_give isl_aff *isl_aff_get_div(
2968 __isl_keep isl_aff *aff, int pos);
2970 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2971 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2972 int (*fn)(__isl_take isl_set *set,
2973 __isl_take isl_aff *aff,
2974 void *user), void *user);
2976 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2977 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2979 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2980 enum isl_dim_type type, unsigned first, unsigned n);
2981 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2982 enum isl_dim_type type, unsigned first, unsigned n);
2984 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2985 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2986 enum isl_dim_type type);
2987 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2989 It can be modified using
2991 #include <isl/aff.h>
2992 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2993 __isl_take isl_pw_aff *pwaff,
2994 enum isl_dim_type type, __isl_take isl_id *id);
2995 __isl_give isl_aff *isl_aff_set_dim_name(
2996 __isl_take isl_aff *aff, enum isl_dim_type type,
2997 unsigned pos, const char *s);
2998 __isl_give isl_aff *isl_aff_set_dim_id(
2999 __isl_take isl_aff *aff, enum isl_dim_type type,
3000 unsigned pos, __isl_take isl_id *id);
3001 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3002 __isl_take isl_pw_aff *pma,
3003 enum isl_dim_type type, unsigned pos,
3004 __isl_take isl_id *id);
3005 __isl_give isl_aff *isl_aff_set_constant(
3006 __isl_take isl_aff *aff, isl_int v);
3007 __isl_give isl_aff *isl_aff_set_constant_si(
3008 __isl_take isl_aff *aff, int v);
3009 __isl_give isl_aff *isl_aff_set_coefficient(
3010 __isl_take isl_aff *aff,
3011 enum isl_dim_type type, int pos, isl_int v);
3012 __isl_give isl_aff *isl_aff_set_coefficient_si(
3013 __isl_take isl_aff *aff,
3014 enum isl_dim_type type, int pos, int v);
3015 __isl_give isl_aff *isl_aff_set_denominator(
3016 __isl_take isl_aff *aff, isl_int v);
3018 __isl_give isl_aff *isl_aff_add_constant(
3019 __isl_take isl_aff *aff, isl_int v);
3020 __isl_give isl_aff *isl_aff_add_constant_si(
3021 __isl_take isl_aff *aff, int v);
3022 __isl_give isl_aff *isl_aff_add_coefficient(
3023 __isl_take isl_aff *aff,
3024 enum isl_dim_type type, int pos, isl_int v);
3025 __isl_give isl_aff *isl_aff_add_coefficient_si(
3026 __isl_take isl_aff *aff,
3027 enum isl_dim_type type, int pos, int v);
3029 __isl_give isl_aff *isl_aff_insert_dims(
3030 __isl_take isl_aff *aff,
3031 enum isl_dim_type type, unsigned first, unsigned n);
3032 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3033 __isl_take isl_pw_aff *pwaff,
3034 enum isl_dim_type type, unsigned first, unsigned n);
3035 __isl_give isl_aff *isl_aff_add_dims(
3036 __isl_take isl_aff *aff,
3037 enum isl_dim_type type, unsigned n);
3038 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3039 __isl_take isl_pw_aff *pwaff,
3040 enum isl_dim_type type, unsigned n);
3041 __isl_give isl_aff *isl_aff_drop_dims(
3042 __isl_take isl_aff *aff,
3043 enum isl_dim_type type, unsigned first, unsigned n);
3044 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3045 __isl_take isl_pw_aff *pwaff,
3046 enum isl_dim_type type, unsigned first, unsigned n);
3048 Note that the C<set_constant> and C<set_coefficient> functions
3049 set the I<numerator> of the constant or coefficient, while
3050 C<add_constant> and C<add_coefficient> add an integer value to
3051 the possibly rational constant or coefficient.
3053 To check whether an affine expressions is obviously zero
3054 or obviously equal to some other affine expression, use
3056 #include <isl/aff.h>
3057 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3058 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3059 __isl_keep isl_aff *aff2);
3060 int isl_pw_aff_plain_is_equal(
3061 __isl_keep isl_pw_aff *pwaff1,
3062 __isl_keep isl_pw_aff *pwaff2);
3066 #include <isl/aff.h>
3067 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3068 __isl_take isl_aff *aff2);
3069 __isl_give isl_pw_aff *isl_pw_aff_add(
3070 __isl_take isl_pw_aff *pwaff1,
3071 __isl_take isl_pw_aff *pwaff2);
3072 __isl_give isl_pw_aff *isl_pw_aff_min(
3073 __isl_take isl_pw_aff *pwaff1,
3074 __isl_take isl_pw_aff *pwaff2);
3075 __isl_give isl_pw_aff *isl_pw_aff_max(
3076 __isl_take isl_pw_aff *pwaff1,
3077 __isl_take isl_pw_aff *pwaff2);
3078 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3079 __isl_take isl_aff *aff2);
3080 __isl_give isl_pw_aff *isl_pw_aff_sub(
3081 __isl_take isl_pw_aff *pwaff1,
3082 __isl_take isl_pw_aff *pwaff2);
3083 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3084 __isl_give isl_pw_aff *isl_pw_aff_neg(
3085 __isl_take isl_pw_aff *pwaff);
3086 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3087 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3088 __isl_take isl_pw_aff *pwaff);
3089 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3090 __isl_give isl_pw_aff *isl_pw_aff_floor(
3091 __isl_take isl_pw_aff *pwaff);
3092 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3094 __isl_give isl_pw_aff *isl_pw_aff_mod(
3095 __isl_take isl_pw_aff *pwaff, isl_int mod);
3096 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3098 __isl_give isl_pw_aff *isl_pw_aff_scale(
3099 __isl_take isl_pw_aff *pwaff, isl_int f);
3100 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3102 __isl_give isl_aff *isl_aff_scale_down_ui(
3103 __isl_take isl_aff *aff, unsigned f);
3104 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3105 __isl_take isl_pw_aff *pwaff, isl_int f);
3107 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3108 __isl_take isl_pw_aff_list *list);
3109 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3110 __isl_take isl_pw_aff_list *list);
3112 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3113 __isl_take isl_pw_aff *pwqp);
3115 __isl_give isl_aff *isl_aff_align_params(
3116 __isl_take isl_aff *aff,
3117 __isl_take isl_space *model);
3118 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3119 __isl_take isl_pw_aff *pwaff,
3120 __isl_take isl_space *model);
3122 __isl_give isl_aff *isl_aff_project_domain_on_params(
3123 __isl_take isl_aff *aff);
3125 __isl_give isl_aff *isl_aff_gist_params(
3126 __isl_take isl_aff *aff,
3127 __isl_take isl_set *context);
3128 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3129 __isl_take isl_set *context);
3130 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3131 __isl_take isl_pw_aff *pwaff,
3132 __isl_take isl_set *context);
3133 __isl_give isl_pw_aff *isl_pw_aff_gist(
3134 __isl_take isl_pw_aff *pwaff,
3135 __isl_take isl_set *context);
3137 __isl_give isl_set *isl_pw_aff_domain(
3138 __isl_take isl_pw_aff *pwaff);
3139 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3140 __isl_take isl_pw_aff *pa,
3141 __isl_take isl_set *set);
3142 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3143 __isl_take isl_pw_aff *pa,
3144 __isl_take isl_set *set);
3146 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3147 __isl_take isl_aff *aff2);
3148 __isl_give isl_pw_aff *isl_pw_aff_mul(
3149 __isl_take isl_pw_aff *pwaff1,
3150 __isl_take isl_pw_aff *pwaff2);
3152 When multiplying two affine expressions, at least one of the two needs
3155 #include <isl/aff.h>
3156 __isl_give isl_basic_set *isl_aff_le_basic_set(
3157 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3158 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3159 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3160 __isl_give isl_set *isl_pw_aff_eq_set(
3161 __isl_take isl_pw_aff *pwaff1,
3162 __isl_take isl_pw_aff *pwaff2);
3163 __isl_give isl_set *isl_pw_aff_ne_set(
3164 __isl_take isl_pw_aff *pwaff1,
3165 __isl_take isl_pw_aff *pwaff2);
3166 __isl_give isl_set *isl_pw_aff_le_set(
3167 __isl_take isl_pw_aff *pwaff1,
3168 __isl_take isl_pw_aff *pwaff2);
3169 __isl_give isl_set *isl_pw_aff_lt_set(
3170 __isl_take isl_pw_aff *pwaff1,
3171 __isl_take isl_pw_aff *pwaff2);
3172 __isl_give isl_set *isl_pw_aff_ge_set(
3173 __isl_take isl_pw_aff *pwaff1,
3174 __isl_take isl_pw_aff *pwaff2);
3175 __isl_give isl_set *isl_pw_aff_gt_set(
3176 __isl_take isl_pw_aff *pwaff1,
3177 __isl_take isl_pw_aff *pwaff2);
3179 __isl_give isl_set *isl_pw_aff_list_eq_set(
3180 __isl_take isl_pw_aff_list *list1,
3181 __isl_take isl_pw_aff_list *list2);
3182 __isl_give isl_set *isl_pw_aff_list_ne_set(
3183 __isl_take isl_pw_aff_list *list1,
3184 __isl_take isl_pw_aff_list *list2);
3185 __isl_give isl_set *isl_pw_aff_list_le_set(
3186 __isl_take isl_pw_aff_list *list1,
3187 __isl_take isl_pw_aff_list *list2);
3188 __isl_give isl_set *isl_pw_aff_list_lt_set(
3189 __isl_take isl_pw_aff_list *list1,
3190 __isl_take isl_pw_aff_list *list2);
3191 __isl_give isl_set *isl_pw_aff_list_ge_set(
3192 __isl_take isl_pw_aff_list *list1,
3193 __isl_take isl_pw_aff_list *list2);
3194 __isl_give isl_set *isl_pw_aff_list_gt_set(
3195 __isl_take isl_pw_aff_list *list1,
3196 __isl_take isl_pw_aff_list *list2);
3198 The function C<isl_aff_ge_basic_set> returns a basic set
3199 containing those elements in the shared space
3200 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3201 The function C<isl_aff_ge_set> returns a set
3202 containing those elements in the shared domain
3203 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3204 The functions operating on C<isl_pw_aff_list> apply the corresponding
3205 C<isl_pw_aff> function to each pair of elements in the two lists.
3207 #include <isl/aff.h>
3208 __isl_give isl_set *isl_pw_aff_nonneg_set(
3209 __isl_take isl_pw_aff *pwaff);
3210 __isl_give isl_set *isl_pw_aff_zero_set(
3211 __isl_take isl_pw_aff *pwaff);
3212 __isl_give isl_set *isl_pw_aff_non_zero_set(
3213 __isl_take isl_pw_aff *pwaff);
3215 The function C<isl_pw_aff_nonneg_set> returns a set
3216 containing those elements in the domain
3217 of C<pwaff> where C<pwaff> is non-negative.
3219 #include <isl/aff.h>
3220 __isl_give isl_pw_aff *isl_pw_aff_cond(
3221 __isl_take isl_pw_aff *cond,
3222 __isl_take isl_pw_aff *pwaff_true,
3223 __isl_take isl_pw_aff *pwaff_false);
3225 The function C<isl_pw_aff_cond> performs a conditional operator
3226 and returns an expression that is equal to C<pwaff_true>
3227 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3228 where C<cond> is zero.
3230 #include <isl/aff.h>
3231 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3232 __isl_take isl_pw_aff *pwaff1,
3233 __isl_take isl_pw_aff *pwaff2);
3234 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3235 __isl_take isl_pw_aff *pwaff1,
3236 __isl_take isl_pw_aff *pwaff2);
3237 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3238 __isl_take isl_pw_aff *pwaff1,
3239 __isl_take isl_pw_aff *pwaff2);
3241 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3242 expression with a domain that is the union of those of C<pwaff1> and
3243 C<pwaff2> and such that on each cell, the quasi-affine expression is
3244 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3245 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3246 associated expression is the defined one.
3248 An expression can be read from input using
3250 #include <isl/aff.h>
3251 __isl_give isl_aff *isl_aff_read_from_str(
3252 isl_ctx *ctx, const char *str);
3253 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3254 isl_ctx *ctx, const char *str);
3256 An expression can be printed using
3258 #include <isl/aff.h>
3259 __isl_give isl_printer *isl_printer_print_aff(
3260 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3262 __isl_give isl_printer *isl_printer_print_pw_aff(
3263 __isl_take isl_printer *p,
3264 __isl_keep isl_pw_aff *pwaff);
3266 =head2 Piecewise Multiple Quasi Affine Expressions
3268 An C<isl_multi_aff> object represents a sequence of
3269 zero or more affine expressions, all defined on the same domain space.
3271 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3274 #include <isl/aff.h>
3275 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3276 __isl_take isl_space *space,
3277 __isl_take isl_aff_list *list);
3279 An empty piecewise multiple quasi affine expression (one with no cells),
3280 the zero piecewise multiple quasi affine expression (with value zero
3281 for each output dimension),
3282 a piecewise multiple quasi affine expression with a single cell (with
3283 either a universe or a specified domain) or
3284 a zero-dimensional piecewise multiple quasi affine expression
3286 can be created using the following functions.
3288 #include <isl/aff.h>
3289 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3290 __isl_take isl_space *space);
3291 __isl_give isl_multi_aff *isl_multi_aff_zero(
3292 __isl_take isl_space *space);
3293 __isl_give isl_pw_multi_aff *
3294 isl_pw_multi_aff_from_multi_aff(
3295 __isl_take isl_multi_aff *ma);
3296 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3297 __isl_take isl_set *set,
3298 __isl_take isl_multi_aff *maff);
3299 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3300 __isl_take isl_set *set);
3302 __isl_give isl_union_pw_multi_aff *
3303 isl_union_pw_multi_aff_empty(
3304 __isl_take isl_space *space);
3305 __isl_give isl_union_pw_multi_aff *
3306 isl_union_pw_multi_aff_add_pw_multi_aff(
3307 __isl_take isl_union_pw_multi_aff *upma,
3308 __isl_take isl_pw_multi_aff *pma);
3309 __isl_give isl_union_pw_multi_aff *
3310 isl_union_pw_multi_aff_from_domain(
3311 __isl_take isl_union_set *uset);
3313 A piecewise multiple quasi affine expression can also be initialized
3314 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3315 and the C<isl_map> is single-valued.
3317 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3318 __isl_take isl_set *set);
3319 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3320 __isl_take isl_map *map);
3322 Multiple quasi affine expressions can be copied and freed using
3324 #include <isl/aff.h>
3325 __isl_give isl_multi_aff *isl_multi_aff_copy(
3326 __isl_keep isl_multi_aff *maff);
3327 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3329 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3330 __isl_keep isl_pw_multi_aff *pma);
3331 void *isl_pw_multi_aff_free(
3332 __isl_take isl_pw_multi_aff *pma);
3334 __isl_give isl_union_pw_multi_aff *
3335 isl_union_pw_multi_aff_copy(
3336 __isl_keep isl_union_pw_multi_aff *upma);
3337 void *isl_union_pw_multi_aff_free(
3338 __isl_take isl_union_pw_multi_aff *upma);
3340 The expression can be inspected using
3342 #include <isl/aff.h>
3343 isl_ctx *isl_multi_aff_get_ctx(
3344 __isl_keep isl_multi_aff *maff);
3345 isl_ctx *isl_pw_multi_aff_get_ctx(
3346 __isl_keep isl_pw_multi_aff *pma);
3347 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3348 __isl_keep isl_union_pw_multi_aff *upma);
3349 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3350 enum isl_dim_type type);
3351 unsigned isl_pw_multi_aff_dim(
3352 __isl_keep isl_pw_multi_aff *pma,
3353 enum isl_dim_type type);
3354 __isl_give isl_aff *isl_multi_aff_get_aff(
3355 __isl_keep isl_multi_aff *multi, int pos);
3356 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3357 __isl_keep isl_pw_multi_aff *pma, int pos);
3358 const char *isl_pw_multi_aff_get_dim_name(
3359 __isl_keep isl_pw_multi_aff *pma,
3360 enum isl_dim_type type, unsigned pos);
3361 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3362 __isl_keep isl_pw_multi_aff *pma,
3363 enum isl_dim_type type, unsigned pos);
3364 const char *isl_multi_aff_get_tuple_name(
3365 __isl_keep isl_multi_aff *multi,
3366 enum isl_dim_type type);
3367 const char *isl_pw_multi_aff_get_tuple_name(
3368 __isl_keep isl_pw_multi_aff *pma,
3369 enum isl_dim_type type);
3370 int isl_pw_multi_aff_has_tuple_id(
3371 __isl_keep isl_pw_multi_aff *pma,
3372 enum isl_dim_type type);
3373 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3374 __isl_keep isl_pw_multi_aff *pma,
3375 enum isl_dim_type type);
3377 int isl_pw_multi_aff_foreach_piece(
3378 __isl_keep isl_pw_multi_aff *pma,
3379 int (*fn)(__isl_take isl_set *set,
3380 __isl_take isl_multi_aff *maff,
3381 void *user), void *user);
3383 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3384 __isl_keep isl_union_pw_multi_aff *upma,
3385 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3386 void *user), void *user);
3388 It can be modified using
3390 #include <isl/aff.h>
3391 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3392 __isl_take isl_multi_aff *multi, int pos,
3393 __isl_take isl_aff *aff);
3394 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3395 __isl_take isl_multi_aff *maff,
3396 enum isl_dim_type type, unsigned pos, const char *s);
3397 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3398 __isl_take isl_multi_aff *maff,
3399 enum isl_dim_type type, __isl_take isl_id *id);
3400 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3401 __isl_take isl_pw_multi_aff *pma,
3402 enum isl_dim_type type, __isl_take isl_id *id);
3404 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3405 __isl_take isl_multi_aff *maff,
3406 enum isl_dim_type type, unsigned first, unsigned n);
3408 To check whether two multiple affine expressions are
3409 obviously equal to each other, use
3411 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3412 __isl_keep isl_multi_aff *maff2);
3413 int isl_pw_multi_aff_plain_is_equal(
3414 __isl_keep isl_pw_multi_aff *pma1,
3415 __isl_keep isl_pw_multi_aff *pma2);
3419 #include <isl/aff.h>
3420 __isl_give isl_multi_aff *isl_multi_aff_add(
3421 __isl_take isl_multi_aff *maff1,
3422 __isl_take isl_multi_aff *maff2);
3423 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3424 __isl_take isl_pw_multi_aff *pma1,
3425 __isl_take isl_pw_multi_aff *pma2);
3426 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3427 __isl_take isl_union_pw_multi_aff *upma1,
3428 __isl_take isl_union_pw_multi_aff *upma2);
3429 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3430 __isl_take isl_pw_multi_aff *pma1,
3431 __isl_take isl_pw_multi_aff *pma2);
3432 __isl_give isl_multi_aff *isl_multi_aff_scale(
3433 __isl_take isl_multi_aff *maff,
3435 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3436 __isl_take isl_pw_multi_aff *pma,
3437 __isl_take isl_set *set);
3438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3439 __isl_take isl_pw_multi_aff *pma,
3440 __isl_take isl_set *set);
3441 __isl_give isl_multi_aff *isl_multi_aff_lift(
3442 __isl_take isl_multi_aff *maff,
3443 __isl_give isl_local_space **ls);
3444 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3445 __isl_take isl_pw_multi_aff *pma);
3446 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3447 __isl_take isl_multi_aff *maff,
3448 __isl_take isl_set *context);
3449 __isl_give isl_multi_aff *isl_multi_aff_gist(
3450 __isl_take isl_multi_aff *maff,
3451 __isl_take isl_set *context);
3452 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3453 __isl_take isl_pw_multi_aff *pma,
3454 __isl_take isl_set *set);
3455 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3456 __isl_take isl_pw_multi_aff *pma,
3457 __isl_take isl_set *set);
3458 __isl_give isl_set *isl_pw_multi_aff_domain(
3459 __isl_take isl_pw_multi_aff *pma);
3460 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3461 __isl_take isl_union_pw_multi_aff *upma);
3462 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3463 __isl_take isl_multi_aff *ma1,
3464 __isl_take isl_multi_aff *ma2);
3465 __isl_give isl_pw_multi_aff *
3466 isl_pw_multi_aff_flat_range_product(
3467 __isl_take isl_pw_multi_aff *pma1,
3468 __isl_take isl_pw_multi_aff *pma2);
3469 __isl_give isl_union_pw_multi_aff *
3470 isl_union_pw_multi_aff_flat_range_product(
3471 __isl_take isl_union_pw_multi_aff *upma1,
3472 __isl_take isl_union_pw_multi_aff *upma2);
3474 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3475 then it is assigned the local space that lies at the basis of
3476 the lifting applied.
3478 An expression can be read from input using
3480 #include <isl/aff.h>
3481 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3482 isl_ctx *ctx, const char *str);
3483 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3484 isl_ctx *ctx, const char *str);
3486 An expression can be printed using
3488 #include <isl/aff.h>
3489 __isl_give isl_printer *isl_printer_print_multi_aff(
3490 __isl_take isl_printer *p,
3491 __isl_keep isl_multi_aff *maff);
3492 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3493 __isl_take isl_printer *p,
3494 __isl_keep isl_pw_multi_aff *pma);
3495 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3496 __isl_take isl_printer *p,
3497 __isl_keep isl_union_pw_multi_aff *upma);
3501 Points are elements of a set. They can be used to construct
3502 simple sets (boxes) or they can be used to represent the
3503 individual elements of a set.
3504 The zero point (the origin) can be created using
3506 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3508 The coordinates of a point can be inspected, set and changed
3511 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3512 enum isl_dim_type type, int pos, isl_int *v);
3513 __isl_give isl_point *isl_point_set_coordinate(
3514 __isl_take isl_point *pnt,
3515 enum isl_dim_type type, int pos, isl_int v);
3517 __isl_give isl_point *isl_point_add_ui(
3518 __isl_take isl_point *pnt,
3519 enum isl_dim_type type, int pos, unsigned val);
3520 __isl_give isl_point *isl_point_sub_ui(
3521 __isl_take isl_point *pnt,
3522 enum isl_dim_type type, int pos, unsigned val);
3524 Other properties can be obtained using
3526 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3528 Points can be copied or freed using
3530 __isl_give isl_point *isl_point_copy(
3531 __isl_keep isl_point *pnt);
3532 void isl_point_free(__isl_take isl_point *pnt);
3534 A singleton set can be created from a point using
3536 __isl_give isl_basic_set *isl_basic_set_from_point(
3537 __isl_take isl_point *pnt);
3538 __isl_give isl_set *isl_set_from_point(
3539 __isl_take isl_point *pnt);
3541 and a box can be created from two opposite extremal points using
3543 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3544 __isl_take isl_point *pnt1,
3545 __isl_take isl_point *pnt2);
3546 __isl_give isl_set *isl_set_box_from_points(
3547 __isl_take isl_point *pnt1,
3548 __isl_take isl_point *pnt2);
3550 All elements of a B<bounded> (union) set can be enumerated using
3551 the following functions.
3553 int isl_set_foreach_point(__isl_keep isl_set *set,
3554 int (*fn)(__isl_take isl_point *pnt, void *user),
3556 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3557 int (*fn)(__isl_take isl_point *pnt, void *user),
3560 The function C<fn> is called for each integer point in
3561 C<set> with as second argument the last argument of
3562 the C<isl_set_foreach_point> call. The function C<fn>
3563 should return C<0> on success and C<-1> on failure.
3564 In the latter case, C<isl_set_foreach_point> will stop
3565 enumerating and return C<-1> as well.
3566 If the enumeration is performed successfully and to completion,
3567 then C<isl_set_foreach_point> returns C<0>.
3569 To obtain a single point of a (basic) set, use
3571 __isl_give isl_point *isl_basic_set_sample_point(
3572 __isl_take isl_basic_set *bset);
3573 __isl_give isl_point *isl_set_sample_point(
3574 __isl_take isl_set *set);
3576 If C<set> does not contain any (integer) points, then the
3577 resulting point will be ``void'', a property that can be
3580 int isl_point_is_void(__isl_keep isl_point *pnt);
3582 =head2 Piecewise Quasipolynomials
3584 A piecewise quasipolynomial is a particular kind of function that maps
3585 a parametric point to a rational value.
3586 More specifically, a quasipolynomial is a polynomial expression in greatest
3587 integer parts of affine expressions of parameters and variables.
3588 A piecewise quasipolynomial is a subdivision of a given parametric
3589 domain into disjoint cells with a quasipolynomial associated to
3590 each cell. The value of the piecewise quasipolynomial at a given
3591 point is the value of the quasipolynomial associated to the cell
3592 that contains the point. Outside of the union of cells,
3593 the value is assumed to be zero.
3594 For example, the piecewise quasipolynomial
3596 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3598 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3599 A given piecewise quasipolynomial has a fixed domain dimension.
3600 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3601 defined over different domains.
3602 Piecewise quasipolynomials are mainly used by the C<barvinok>
3603 library for representing the number of elements in a parametric set or map.
3604 For example, the piecewise quasipolynomial above represents
3605 the number of points in the map
3607 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3609 =head3 Input and Output
3611 Piecewise quasipolynomials can be read from input using
3613 __isl_give isl_union_pw_qpolynomial *
3614 isl_union_pw_qpolynomial_read_from_str(
3615 isl_ctx *ctx, const char *str);
3617 Quasipolynomials and piecewise quasipolynomials can be printed
3618 using the following functions.
3620 __isl_give isl_printer *isl_printer_print_qpolynomial(
3621 __isl_take isl_printer *p,
3622 __isl_keep isl_qpolynomial *qp);
3624 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3625 __isl_take isl_printer *p,
3626 __isl_keep isl_pw_qpolynomial *pwqp);
3628 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3629 __isl_take isl_printer *p,
3630 __isl_keep isl_union_pw_qpolynomial *upwqp);
3632 The output format of the printer
3633 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3634 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3636 In case of printing in C<ISL_FORMAT_C>, the user may want
3637 to set the names of all dimensions
3639 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3640 __isl_take isl_qpolynomial *qp,
3641 enum isl_dim_type type, unsigned pos,
3643 __isl_give isl_pw_qpolynomial *
3644 isl_pw_qpolynomial_set_dim_name(
3645 __isl_take isl_pw_qpolynomial *pwqp,
3646 enum isl_dim_type type, unsigned pos,
3649 =head3 Creating New (Piecewise) Quasipolynomials
3651 Some simple quasipolynomials can be created using the following functions.
3652 More complicated quasipolynomials can be created by applying
3653 operations such as addition and multiplication
3654 on the resulting quasipolynomials
3656 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3657 __isl_take isl_space *domain);
3658 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3659 __isl_take isl_space *domain);
3660 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3661 __isl_take isl_space *domain);
3662 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3663 __isl_take isl_space *domain);
3664 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3665 __isl_take isl_space *domain);
3666 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3667 __isl_take isl_space *domain,
3668 const isl_int n, const isl_int d);
3669 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3670 __isl_take isl_space *domain,
3671 enum isl_dim_type type, unsigned pos);
3672 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3673 __isl_take isl_aff *aff);
3675 Note that the space in which a quasipolynomial lives is a map space
3676 with a one-dimensional range. The C<domain> argument in some of
3677 the functions above corresponds to the domain of this map space.
3679 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3680 with a single cell can be created using the following functions.
3681 Multiple of these single cell piecewise quasipolynomials can
3682 be combined to create more complicated piecewise quasipolynomials.
3684 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3685 __isl_take isl_space *space);
3686 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3687 __isl_take isl_set *set,
3688 __isl_take isl_qpolynomial *qp);
3689 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3690 __isl_take isl_qpolynomial *qp);
3691 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3692 __isl_take isl_pw_aff *pwaff);
3694 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3695 __isl_take isl_space *space);
3696 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3697 __isl_take isl_pw_qpolynomial *pwqp);
3698 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3699 __isl_take isl_union_pw_qpolynomial *upwqp,
3700 __isl_take isl_pw_qpolynomial *pwqp);
3702 Quasipolynomials can be copied and freed again using the following
3705 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3706 __isl_keep isl_qpolynomial *qp);
3707 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3709 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3710 __isl_keep isl_pw_qpolynomial *pwqp);
3711 void *isl_pw_qpolynomial_free(
3712 __isl_take isl_pw_qpolynomial *pwqp);
3714 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3715 __isl_keep isl_union_pw_qpolynomial *upwqp);
3716 void *isl_union_pw_qpolynomial_free(
3717 __isl_take isl_union_pw_qpolynomial *upwqp);
3719 =head3 Inspecting (Piecewise) Quasipolynomials
3721 To iterate over all piecewise quasipolynomials in a union
3722 piecewise quasipolynomial, use the following function
3724 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3725 __isl_keep isl_union_pw_qpolynomial *upwqp,
3726 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3729 To extract the piecewise quasipolynomial in a given space from a union, use
3731 __isl_give isl_pw_qpolynomial *
3732 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3733 __isl_keep isl_union_pw_qpolynomial *upwqp,
3734 __isl_take isl_space *space);
3736 To iterate over the cells in a piecewise quasipolynomial,
3737 use either of the following two functions
3739 int isl_pw_qpolynomial_foreach_piece(
3740 __isl_keep isl_pw_qpolynomial *pwqp,
3741 int (*fn)(__isl_take isl_set *set,
3742 __isl_take isl_qpolynomial *qp,
3743 void *user), void *user);
3744 int isl_pw_qpolynomial_foreach_lifted_piece(
3745 __isl_keep isl_pw_qpolynomial *pwqp,
3746 int (*fn)(__isl_take isl_set *set,
3747 __isl_take isl_qpolynomial *qp,
3748 void *user), void *user);
3750 As usual, the function C<fn> should return C<0> on success
3751 and C<-1> on failure. The difference between
3752 C<isl_pw_qpolynomial_foreach_piece> and
3753 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3754 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3755 compute unique representations for all existentially quantified
3756 variables and then turn these existentially quantified variables
3757 into extra set variables, adapting the associated quasipolynomial
3758 accordingly. This means that the C<set> passed to C<fn>
3759 will not have any existentially quantified variables, but that
3760 the dimensions of the sets may be different for different
3761 invocations of C<fn>.
3763 To iterate over all terms in a quasipolynomial,
3766 int isl_qpolynomial_foreach_term(
3767 __isl_keep isl_qpolynomial *qp,
3768 int (*fn)(__isl_take isl_term *term,
3769 void *user), void *user);
3771 The terms themselves can be inspected and freed using
3774 unsigned isl_term_dim(__isl_keep isl_term *term,
3775 enum isl_dim_type type);
3776 void isl_term_get_num(__isl_keep isl_term *term,
3778 void isl_term_get_den(__isl_keep isl_term *term,
3780 int isl_term_get_exp(__isl_keep isl_term *term,
3781 enum isl_dim_type type, unsigned pos);
3782 __isl_give isl_aff *isl_term_get_div(
3783 __isl_keep isl_term *term, unsigned pos);
3784 void isl_term_free(__isl_take isl_term *term);
3786 Each term is a product of parameters, set variables and
3787 integer divisions. The function C<isl_term_get_exp>
3788 returns the exponent of a given dimensions in the given term.
3789 The C<isl_int>s in the arguments of C<isl_term_get_num>
3790 and C<isl_term_get_den> need to have been initialized
3791 using C<isl_int_init> before calling these functions.
3793 =head3 Properties of (Piecewise) Quasipolynomials
3795 To check whether a quasipolynomial is actually a constant,
3796 use the following function.
3798 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3799 isl_int *n, isl_int *d);
3801 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3802 then the numerator and denominator of the constant
3803 are returned in C<*n> and C<*d>, respectively.
3805 To check whether two union piecewise quasipolynomials are
3806 obviously equal, use
3808 int isl_union_pw_qpolynomial_plain_is_equal(
3809 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3810 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3812 =head3 Operations on (Piecewise) Quasipolynomials
3814 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3815 __isl_take isl_qpolynomial *qp, isl_int v);
3816 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3817 __isl_take isl_qpolynomial *qp);
3818 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3819 __isl_take isl_qpolynomial *qp1,
3820 __isl_take isl_qpolynomial *qp2);
3821 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3822 __isl_take isl_qpolynomial *qp1,
3823 __isl_take isl_qpolynomial *qp2);
3824 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3825 __isl_take isl_qpolynomial *qp1,
3826 __isl_take isl_qpolynomial *qp2);
3827 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3828 __isl_take isl_qpolynomial *qp, unsigned exponent);
3830 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3831 __isl_take isl_pw_qpolynomial *pwqp1,
3832 __isl_take isl_pw_qpolynomial *pwqp2);
3833 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3834 __isl_take isl_pw_qpolynomial *pwqp1,
3835 __isl_take isl_pw_qpolynomial *pwqp2);
3836 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3837 __isl_take isl_pw_qpolynomial *pwqp1,
3838 __isl_take isl_pw_qpolynomial *pwqp2);
3839 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3840 __isl_take isl_pw_qpolynomial *pwqp);
3841 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3842 __isl_take isl_pw_qpolynomial *pwqp1,
3843 __isl_take isl_pw_qpolynomial *pwqp2);
3844 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3845 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3847 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3848 __isl_take isl_union_pw_qpolynomial *upwqp1,
3849 __isl_take isl_union_pw_qpolynomial *upwqp2);
3850 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3851 __isl_take isl_union_pw_qpolynomial *upwqp1,
3852 __isl_take isl_union_pw_qpolynomial *upwqp2);
3853 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3854 __isl_take isl_union_pw_qpolynomial *upwqp1,
3855 __isl_take isl_union_pw_qpolynomial *upwqp2);
3857 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3858 __isl_take isl_pw_qpolynomial *pwqp,
3859 __isl_take isl_point *pnt);
3861 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3862 __isl_take isl_union_pw_qpolynomial *upwqp,
3863 __isl_take isl_point *pnt);
3865 __isl_give isl_set *isl_pw_qpolynomial_domain(
3866 __isl_take isl_pw_qpolynomial *pwqp);
3867 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3868 __isl_take isl_pw_qpolynomial *pwpq,
3869 __isl_take isl_set *set);
3870 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3871 __isl_take isl_pw_qpolynomial *pwpq,
3872 __isl_take isl_set *set);
3874 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3875 __isl_take isl_union_pw_qpolynomial *upwqp);
3876 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3877 __isl_take isl_union_pw_qpolynomial *upwpq,
3878 __isl_take isl_union_set *uset);
3879 __isl_give isl_union_pw_qpolynomial *
3880 isl_union_pw_qpolynomial_intersect_params(
3881 __isl_take isl_union_pw_qpolynomial *upwpq,
3882 __isl_take isl_set *set);
3884 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3885 __isl_take isl_qpolynomial *qp,
3886 __isl_take isl_space *model);
3888 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3889 __isl_take isl_qpolynomial *qp);
3890 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3891 __isl_take isl_pw_qpolynomial *pwqp);
3893 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3894 __isl_take isl_union_pw_qpolynomial *upwqp);
3896 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3897 __isl_take isl_qpolynomial *qp,
3898 __isl_take isl_set *context);
3899 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3900 __isl_take isl_qpolynomial *qp,
3901 __isl_take isl_set *context);
3903 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3904 __isl_take isl_pw_qpolynomial *pwqp,
3905 __isl_take isl_set *context);
3906 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3907 __isl_take isl_pw_qpolynomial *pwqp,
3908 __isl_take isl_set *context);
3910 __isl_give isl_union_pw_qpolynomial *
3911 isl_union_pw_qpolynomial_gist_params(
3912 __isl_take isl_union_pw_qpolynomial *upwqp,
3913 __isl_take isl_set *context);
3914 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3915 __isl_take isl_union_pw_qpolynomial *upwqp,
3916 __isl_take isl_union_set *context);
3918 The gist operation applies the gist operation to each of
3919 the cells in the domain of the input piecewise quasipolynomial.
3920 The context is also exploited
3921 to simplify the quasipolynomials associated to each cell.
3923 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3924 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3925 __isl_give isl_union_pw_qpolynomial *
3926 isl_union_pw_qpolynomial_to_polynomial(
3927 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3929 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3930 the polynomial will be an overapproximation. If C<sign> is negative,
3931 it will be an underapproximation. If C<sign> is zero, the approximation
3932 will lie somewhere in between.
3934 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3936 A piecewise quasipolynomial reduction is a piecewise
3937 reduction (or fold) of quasipolynomials.
3938 In particular, the reduction can be maximum or a minimum.
3939 The objects are mainly used to represent the result of
3940 an upper or lower bound on a quasipolynomial over its domain,
3941 i.e., as the result of the following function.
3943 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3944 __isl_take isl_pw_qpolynomial *pwqp,
3945 enum isl_fold type, int *tight);
3947 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3948 __isl_take isl_union_pw_qpolynomial *upwqp,
3949 enum isl_fold type, int *tight);
3951 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3952 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3953 is the returned bound is known be tight, i.e., for each value
3954 of the parameters there is at least
3955 one element in the domain that reaches the bound.
3956 If the domain of C<pwqp> is not wrapping, then the bound is computed
3957 over all elements in that domain and the result has a purely parametric
3958 domain. If the domain of C<pwqp> is wrapping, then the bound is
3959 computed over the range of the wrapped relation. The domain of the
3960 wrapped relation becomes the domain of the result.
3962 A (piecewise) quasipolynomial reduction can be copied or freed using the
3963 following functions.
3965 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3966 __isl_keep isl_qpolynomial_fold *fold);
3967 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3968 __isl_keep isl_pw_qpolynomial_fold *pwf);
3969 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3970 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3971 void isl_qpolynomial_fold_free(
3972 __isl_take isl_qpolynomial_fold *fold);
3973 void *isl_pw_qpolynomial_fold_free(
3974 __isl_take isl_pw_qpolynomial_fold *pwf);
3975 void *isl_union_pw_qpolynomial_fold_free(
3976 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3978 =head3 Printing Piecewise Quasipolynomial Reductions
3980 Piecewise quasipolynomial reductions can be printed
3981 using the following function.
3983 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3984 __isl_take isl_printer *p,
3985 __isl_keep isl_pw_qpolynomial_fold *pwf);
3986 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3987 __isl_take isl_printer *p,
3988 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3990 For C<isl_printer_print_pw_qpolynomial_fold>,
3991 output format of the printer
3992 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3993 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3994 output format of the printer
3995 needs to be set to C<ISL_FORMAT_ISL>.
3996 In case of printing in C<ISL_FORMAT_C>, the user may want
3997 to set the names of all dimensions
3999 __isl_give isl_pw_qpolynomial_fold *
4000 isl_pw_qpolynomial_fold_set_dim_name(
4001 __isl_take isl_pw_qpolynomial_fold *pwf,
4002 enum isl_dim_type type, unsigned pos,
4005 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4007 To iterate over all piecewise quasipolynomial reductions in a union
4008 piecewise quasipolynomial reduction, use the following function
4010 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4011 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4012 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4013 void *user), void *user);
4015 To iterate over the cells in a piecewise quasipolynomial reduction,
4016 use either of the following two functions
4018 int isl_pw_qpolynomial_fold_foreach_piece(
4019 __isl_keep isl_pw_qpolynomial_fold *pwf,
4020 int (*fn)(__isl_take isl_set *set,
4021 __isl_take isl_qpolynomial_fold *fold,
4022 void *user), void *user);
4023 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4024 __isl_keep isl_pw_qpolynomial_fold *pwf,
4025 int (*fn)(__isl_take isl_set *set,
4026 __isl_take isl_qpolynomial_fold *fold,
4027 void *user), void *user);
4029 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4030 of the difference between these two functions.
4032 To iterate over all quasipolynomials in a reduction, use
4034 int isl_qpolynomial_fold_foreach_qpolynomial(
4035 __isl_keep isl_qpolynomial_fold *fold,
4036 int (*fn)(__isl_take isl_qpolynomial *qp,
4037 void *user), void *user);
4039 =head3 Properties of Piecewise Quasipolynomial Reductions
4041 To check whether two union piecewise quasipolynomial reductions are
4042 obviously equal, use
4044 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4045 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4046 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4048 =head3 Operations on Piecewise Quasipolynomial Reductions
4050 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4051 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4053 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4054 __isl_take isl_pw_qpolynomial_fold *pwf1,
4055 __isl_take isl_pw_qpolynomial_fold *pwf2);
4057 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4058 __isl_take isl_pw_qpolynomial_fold *pwf1,
4059 __isl_take isl_pw_qpolynomial_fold *pwf2);
4061 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4062 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4063 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4065 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4066 __isl_take isl_pw_qpolynomial_fold *pwf,
4067 __isl_take isl_point *pnt);
4069 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4070 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4071 __isl_take isl_point *pnt);
4073 __isl_give isl_pw_qpolynomial_fold *
4074 sl_pw_qpolynomial_fold_intersect_params(
4075 __isl_take isl_pw_qpolynomial_fold *pwf,
4076 __isl_take isl_set *set);
4078 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4079 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4080 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4081 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4082 __isl_take isl_union_set *uset);
4083 __isl_give isl_union_pw_qpolynomial_fold *
4084 isl_union_pw_qpolynomial_fold_intersect_params(
4085 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4086 __isl_take isl_set *set);
4088 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4089 __isl_take isl_pw_qpolynomial_fold *pwf);
4091 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4092 __isl_take isl_pw_qpolynomial_fold *pwf);
4094 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4095 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4097 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4098 __isl_take isl_qpolynomial_fold *fold,
4099 __isl_take isl_set *context);
4100 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4101 __isl_take isl_qpolynomial_fold *fold,
4102 __isl_take isl_set *context);
4104 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4105 __isl_take isl_pw_qpolynomial_fold *pwf,
4106 __isl_take isl_set *context);
4107 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4108 __isl_take isl_pw_qpolynomial_fold *pwf,
4109 __isl_take isl_set *context);
4111 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4112 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4113 __isl_take isl_union_set *context);
4114 __isl_give isl_union_pw_qpolynomial_fold *
4115 isl_union_pw_qpolynomial_fold_gist_params(
4116 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4117 __isl_take isl_set *context);
4119 The gist operation applies the gist operation to each of
4120 the cells in the domain of the input piecewise quasipolynomial reduction.
4121 In future, the operation will also exploit the context
4122 to simplify the quasipolynomial reductions associated to each cell.
4124 __isl_give isl_pw_qpolynomial_fold *
4125 isl_set_apply_pw_qpolynomial_fold(
4126 __isl_take isl_set *set,
4127 __isl_take isl_pw_qpolynomial_fold *pwf,
4129 __isl_give isl_pw_qpolynomial_fold *
4130 isl_map_apply_pw_qpolynomial_fold(
4131 __isl_take isl_map *map,
4132 __isl_take isl_pw_qpolynomial_fold *pwf,
4134 __isl_give isl_union_pw_qpolynomial_fold *
4135 isl_union_set_apply_union_pw_qpolynomial_fold(
4136 __isl_take isl_union_set *uset,
4137 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4139 __isl_give isl_union_pw_qpolynomial_fold *
4140 isl_union_map_apply_union_pw_qpolynomial_fold(
4141 __isl_take isl_union_map *umap,
4142 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4145 The functions taking a map
4146 compose the given map with the given piecewise quasipolynomial reduction.
4147 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4148 over all elements in the intersection of the range of the map
4149 and the domain of the piecewise quasipolynomial reduction
4150 as a function of an element in the domain of the map.
4151 The functions taking a set compute a bound over all elements in the
4152 intersection of the set and the domain of the
4153 piecewise quasipolynomial reduction.
4155 =head2 Dependence Analysis
4157 C<isl> contains specialized functionality for performing
4158 array dataflow analysis. That is, given a I<sink> access relation
4159 and a collection of possible I<source> access relations,
4160 C<isl> can compute relations that describe
4161 for each iteration of the sink access, which iteration
4162 of which of the source access relations was the last
4163 to access the same data element before the given iteration
4165 The resulting dependence relations map source iterations
4166 to the corresponding sink iterations.
4167 To compute standard flow dependences, the sink should be
4168 a read, while the sources should be writes.
4169 If any of the source accesses are marked as being I<may>
4170 accesses, then there will be a dependence from the last
4171 I<must> access B<and> from any I<may> access that follows
4172 this last I<must> access.
4173 In particular, if I<all> sources are I<may> accesses,
4174 then memory based dependence analysis is performed.
4175 If, on the other hand, all sources are I<must> accesses,
4176 then value based dependence analysis is performed.
4178 #include <isl/flow.h>
4180 typedef int (*isl_access_level_before)(void *first, void *second);
4182 __isl_give isl_access_info *isl_access_info_alloc(
4183 __isl_take isl_map *sink,
4184 void *sink_user, isl_access_level_before fn,
4186 __isl_give isl_access_info *isl_access_info_add_source(
4187 __isl_take isl_access_info *acc,
4188 __isl_take isl_map *source, int must,
4190 void isl_access_info_free(__isl_take isl_access_info *acc);
4192 __isl_give isl_flow *isl_access_info_compute_flow(
4193 __isl_take isl_access_info *acc);
4195 int isl_flow_foreach(__isl_keep isl_flow *deps,
4196 int (*fn)(__isl_take isl_map *dep, int must,
4197 void *dep_user, void *user),
4199 __isl_give isl_map *isl_flow_get_no_source(
4200 __isl_keep isl_flow *deps, int must);
4201 void isl_flow_free(__isl_take isl_flow *deps);
4203 The function C<isl_access_info_compute_flow> performs the actual
4204 dependence analysis. The other functions are used to construct
4205 the input for this function or to read off the output.
4207 The input is collected in an C<isl_access_info>, which can
4208 be created through a call to C<isl_access_info_alloc>.
4209 The arguments to this functions are the sink access relation
4210 C<sink>, a token C<sink_user> used to identify the sink
4211 access to the user, a callback function for specifying the
4212 relative order of source and sink accesses, and the number
4213 of source access relations that will be added.
4214 The callback function has type C<int (*)(void *first, void *second)>.
4215 The function is called with two user supplied tokens identifying
4216 either a source or the sink and it should return the shared nesting
4217 level and the relative order of the two accesses.
4218 In particular, let I<n> be the number of loops shared by
4219 the two accesses. If C<first> precedes C<second> textually,
4220 then the function should return I<2 * n + 1>; otherwise,
4221 it should return I<2 * n>.
4222 The sources can be added to the C<isl_access_info> by performing
4223 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4224 C<must> indicates whether the source is a I<must> access
4225 or a I<may> access. Note that a multi-valued access relation
4226 should only be marked I<must> if every iteration in the domain
4227 of the relation accesses I<all> elements in its image.
4228 The C<source_user> token is again used to identify
4229 the source access. The range of the source access relation
4230 C<source> should have the same dimension as the range
4231 of the sink access relation.
4232 The C<isl_access_info_free> function should usually not be
4233 called explicitly, because it is called implicitly by
4234 C<isl_access_info_compute_flow>.
4236 The result of the dependence analysis is collected in an
4237 C<isl_flow>. There may be elements of
4238 the sink access for which no preceding source access could be
4239 found or for which all preceding sources are I<may> accesses.
4240 The relations containing these elements can be obtained through
4241 calls to C<isl_flow_get_no_source>, the first with C<must> set
4242 and the second with C<must> unset.
4243 In the case of standard flow dependence analysis,
4244 with the sink a read and the sources I<must> writes,
4245 the first relation corresponds to the reads from uninitialized
4246 array elements and the second relation is empty.
4247 The actual flow dependences can be extracted using
4248 C<isl_flow_foreach>. This function will call the user-specified
4249 callback function C<fn> for each B<non-empty> dependence between
4250 a source and the sink. The callback function is called
4251 with four arguments, the actual flow dependence relation
4252 mapping source iterations to sink iterations, a boolean that
4253 indicates whether it is a I<must> or I<may> dependence, a token
4254 identifying the source and an additional C<void *> with value
4255 equal to the third argument of the C<isl_flow_foreach> call.
4256 A dependence is marked I<must> if it originates from a I<must>
4257 source and if it is not followed by any I<may> sources.
4259 After finishing with an C<isl_flow>, the user should call
4260 C<isl_flow_free> to free all associated memory.
4262 A higher-level interface to dependence analysis is provided
4263 by the following function.
4265 #include <isl/flow.h>
4267 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4268 __isl_take isl_union_map *must_source,
4269 __isl_take isl_union_map *may_source,
4270 __isl_take isl_union_map *schedule,
4271 __isl_give isl_union_map **must_dep,
4272 __isl_give isl_union_map **may_dep,
4273 __isl_give isl_union_map **must_no_source,
4274 __isl_give isl_union_map **may_no_source);
4276 The arrays are identified by the tuple names of the ranges
4277 of the accesses. The iteration domains by the tuple names
4278 of the domains of the accesses and of the schedule.
4279 The relative order of the iteration domains is given by the
4280 schedule. The relations returned through C<must_no_source>
4281 and C<may_no_source> are subsets of C<sink>.
4282 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4283 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4284 any of the other arguments is treated as an error.
4286 =head3 Interaction with Dependence Analysis
4288 During the dependence analysis, we frequently need to perform
4289 the following operation. Given a relation between sink iterations
4290 and potential soure iterations from a particular source domain,
4291 what is the last potential source iteration corresponding to each
4292 sink iteration. It can sometimes be convenient to adjust
4293 the set of potential source iterations before or after each such operation.
4294 The prototypical example is fuzzy array dataflow analysis,
4295 where we need to analyze if, based on data-dependent constraints,
4296 the sink iteration can ever be executed without one or more of
4297 the corresponding potential source iterations being executed.
4298 If so, we can introduce extra parameters and select an unknown
4299 but fixed source iteration from the potential source iterations.
4300 To be able to perform such manipulations, C<isl> provides the following
4303 #include <isl/flow.h>
4305 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4306 __isl_keep isl_map *source_map,
4307 __isl_keep isl_set *sink, void *source_user,
4309 __isl_give isl_access_info *isl_access_info_set_restrict(
4310 __isl_take isl_access_info *acc,
4311 isl_access_restrict fn, void *user);
4313 The function C<isl_access_info_set_restrict> should be called
4314 before calling C<isl_access_info_compute_flow> and registers a callback function
4315 that will be called any time C<isl> is about to compute the last
4316 potential source. The first argument is the (reverse) proto-dependence,
4317 mapping sink iterations to potential source iterations.
4318 The second argument represents the sink iterations for which
4319 we want to compute the last source iteration.
4320 The third argument is the token corresponding to the source
4321 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4322 The callback is expected to return a restriction on either the input or
4323 the output of the operation computing the last potential source.
4324 If the input needs to be restricted then restrictions are needed
4325 for both the source and the sink iterations. The sink iterations
4326 and the potential source iterations will be intersected with these sets.
4327 If the output needs to be restricted then only a restriction on the source
4328 iterations is required.
4329 If any error occurs, the callback should return C<NULL>.
4330 An C<isl_restriction> object can be created and freed using the following
4333 #include <isl/flow.h>
4335 __isl_give isl_restriction *isl_restriction_input(
4336 __isl_take isl_set *source_restr,
4337 __isl_take isl_set *sink_restr);
4338 __isl_give isl_restriction *isl_restriction_output(
4339 __isl_take isl_set *source_restr);
4340 __isl_give isl_restriction *isl_restriction_none(
4341 __isl_keep isl_map *source_map);
4342 __isl_give isl_restriction *isl_restriction_empty(
4343 __isl_keep isl_map *source_map);
4344 void *isl_restriction_free(
4345 __isl_take isl_restriction *restr);
4347 C<isl_restriction_none> and C<isl_restriction_empty> are special
4348 cases of C<isl_restriction_input>. C<isl_restriction_none>
4349 is essentially equivalent to
4351 isl_restriction_input(isl_set_universe(
4352 isl_space_range(isl_map_get_space(source_map))),
4354 isl_space_domain(isl_map_get_space(source_map))));
4356 whereas C<isl_restriction_empty> is essentially equivalent to
4358 isl_restriction_input(isl_set_empty(
4359 isl_space_range(isl_map_get_space(source_map))),
4361 isl_space_domain(isl_map_get_space(source_map))));
4365 B<The functionality described in this section is fairly new
4366 and may be subject to change.>
4368 The following function can be used to compute a schedule
4369 for a union of domains.
4370 By default, the algorithm used to construct the schedule is similar
4371 to that of C<Pluto>.
4372 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4374 The generated schedule respects all C<validity> dependences.
4375 That is, all dependence distances over these dependences in the
4376 scheduled space are lexicographically positive.
4377 The default algorithm tries to minimize the dependence distances over
4378 C<proximity> dependences.
4379 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4380 for groups of domains where the dependence distances have only
4381 non-negative values.
4382 When using Feautrier's algorithm, the C<proximity> dependence
4383 distances are only minimized during the extension to a
4384 full-dimensional schedule.
4386 #include <isl/schedule.h>
4387 __isl_give isl_schedule *isl_union_set_compute_schedule(
4388 __isl_take isl_union_set *domain,
4389 __isl_take isl_union_map *validity,
4390 __isl_take isl_union_map *proximity);
4391 void *isl_schedule_free(__isl_take isl_schedule *sched);
4393 A mapping from the domains to the scheduled space can be obtained
4394 from an C<isl_schedule> using the following function.
4396 __isl_give isl_union_map *isl_schedule_get_map(
4397 __isl_keep isl_schedule *sched);
4399 A representation of the schedule can be printed using
4401 __isl_give isl_printer *isl_printer_print_schedule(
4402 __isl_take isl_printer *p,
4403 __isl_keep isl_schedule *schedule);
4405 A representation of the schedule as a forest of bands can be obtained
4406 using the following function.
4408 __isl_give isl_band_list *isl_schedule_get_band_forest(
4409 __isl_keep isl_schedule *schedule);
4411 The list can be manipulated as explained in L<"Lists">.
4412 The bands inside the list can be copied and freed using the following
4415 #include <isl/band.h>
4416 __isl_give isl_band *isl_band_copy(
4417 __isl_keep isl_band *band);
4418 void *isl_band_free(__isl_take isl_band *band);
4420 Each band contains zero or more scheduling dimensions.
4421 These are referred to as the members of the band.
4422 The section of the schedule that corresponds to the band is
4423 referred to as the partial schedule of the band.
4424 For those nodes that participate in a band, the outer scheduling
4425 dimensions form the prefix schedule, while the inner scheduling
4426 dimensions form the suffix schedule.
4427 That is, if we take a cut of the band forest, then the union of
4428 the concatenations of the prefix, partial and suffix schedules of
4429 each band in the cut is equal to the entire schedule (modulo
4430 some possible padding at the end with zero scheduling dimensions).
4431 The properties of a band can be inspected using the following functions.
4433 #include <isl/band.h>
4434 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4436 int isl_band_has_children(__isl_keep isl_band *band);
4437 __isl_give isl_band_list *isl_band_get_children(
4438 __isl_keep isl_band *band);
4440 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4441 __isl_keep isl_band *band);
4442 __isl_give isl_union_map *isl_band_get_partial_schedule(
4443 __isl_keep isl_band *band);
4444 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4445 __isl_keep isl_band *band);
4447 int isl_band_n_member(__isl_keep isl_band *band);
4448 int isl_band_member_is_zero_distance(
4449 __isl_keep isl_band *band, int pos);
4451 Note that a scheduling dimension is considered to be ``zero
4452 distance'' if it does not carry any proximity dependences
4454 That is, if the dependence distances of the proximity
4455 dependences are all zero in that direction (for fixed
4456 iterations of outer bands).
4458 A representation of the band can be printed using
4460 #include <isl/band.h>
4461 __isl_give isl_printer *isl_printer_print_band(
4462 __isl_take isl_printer *p,
4463 __isl_keep isl_band *band);
4467 #include <isl/schedule.h>
4468 int isl_options_set_schedule_max_coefficient(
4469 isl_ctx *ctx, int val);
4470 int isl_options_get_schedule_max_coefficient(
4472 int isl_options_set_schedule_max_constant_term(
4473 isl_ctx *ctx, int val);
4474 int isl_options_get_schedule_max_constant_term(
4476 int isl_options_set_schedule_maximize_band_depth(
4477 isl_ctx *ctx, int val);
4478 int isl_options_get_schedule_maximize_band_depth(
4480 int isl_options_set_schedule_outer_zero_distance(
4481 isl_ctx *ctx, int val);
4482 int isl_options_get_schedule_outer_zero_distance(
4484 int isl_options_set_schedule_split_scaled(
4485 isl_ctx *ctx, int val);
4486 int isl_options_get_schedule_split_scaled(
4488 int isl_options_set_schedule_algorithm(
4489 isl_ctx *ctx, int val);
4490 int isl_options_get_schedule_algorithm(
4496 =item * schedule_max_coefficient
4498 This option enforces that the coefficients for variable and parameter
4499 dimensions in the calculated schedule are not larger than the specified value.
4500 This option can significantly increase the speed of the scheduling calculation
4501 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4502 this option does not introduce bounds on the variable or parameter
4505 =item * schedule_max_constant_term
4507 This option enforces that the constant coefficients in the calculated schedule
4508 are not larger than the maximal constant term. This option can significantly
4509 increase the speed of the scheduling calculation and may also prevent fusing of
4510 unrelated dimensions. A value of -1 means that this option does not introduce
4511 bounds on the constant coefficients.
4513 =item * schedule_maximize_band_depth
4515 If this option is set, we do not split bands at the point
4516 where we detect splitting is necessary. Instead, we
4517 backtrack and split bands as early as possible. This
4518 reduces the number of splits and maximizes the width of
4519 the bands. Wider bands give more possibilities for tiling.
4521 =item * schedule_outer_zero_distance
4523 If this option is set, then we try to construct schedules
4524 where the outermost scheduling dimension in each band
4525 results in a zero dependence distance over the proximity
4528 =item * schedule_split_scaled
4530 If this option is set, then we try to construct schedules in which the
4531 constant term is split off from the linear part if the linear parts of
4532 the scheduling rows for all nodes in the graphs have a common non-trivial
4534 The constant term is then placed in a separate band and the linear
4537 =item * schedule_algorithm
4539 Selects the scheduling algorithm to be used.
4540 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4541 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4545 =head2 Parametric Vertex Enumeration
4547 The parametric vertex enumeration described in this section
4548 is mainly intended to be used internally and by the C<barvinok>
4551 #include <isl/vertices.h>
4552 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4553 __isl_keep isl_basic_set *bset);
4555 The function C<isl_basic_set_compute_vertices> performs the
4556 actual computation of the parametric vertices and the chamber
4557 decomposition and store the result in an C<isl_vertices> object.
4558 This information can be queried by either iterating over all
4559 the vertices or iterating over all the chambers or cells
4560 and then iterating over all vertices that are active on the chamber.
4562 int isl_vertices_foreach_vertex(
4563 __isl_keep isl_vertices *vertices,
4564 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4567 int isl_vertices_foreach_cell(
4568 __isl_keep isl_vertices *vertices,
4569 int (*fn)(__isl_take isl_cell *cell, void *user),
4571 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4572 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4575 Other operations that can be performed on an C<isl_vertices> object are
4578 isl_ctx *isl_vertices_get_ctx(
4579 __isl_keep isl_vertices *vertices);
4580 int isl_vertices_get_n_vertices(
4581 __isl_keep isl_vertices *vertices);
4582 void isl_vertices_free(__isl_take isl_vertices *vertices);
4584 Vertices can be inspected and destroyed using the following functions.
4586 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4587 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4588 __isl_give isl_basic_set *isl_vertex_get_domain(
4589 __isl_keep isl_vertex *vertex);
4590 __isl_give isl_basic_set *isl_vertex_get_expr(
4591 __isl_keep isl_vertex *vertex);
4592 void isl_vertex_free(__isl_take isl_vertex *vertex);
4594 C<isl_vertex_get_expr> returns a singleton parametric set describing
4595 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4597 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4598 B<rational> basic sets, so they should mainly be used for inspection
4599 and should not be mixed with integer sets.
4601 Chambers can be inspected and destroyed using the following functions.
4603 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4604 __isl_give isl_basic_set *isl_cell_get_domain(
4605 __isl_keep isl_cell *cell);
4606 void isl_cell_free(__isl_take isl_cell *cell);
4610 Although C<isl> is mainly meant to be used as a library,
4611 it also contains some basic applications that use some
4612 of the functionality of C<isl>.
4613 The input may be specified in either the L<isl format>
4614 or the L<PolyLib format>.
4616 =head2 C<isl_polyhedron_sample>
4618 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4619 an integer element of the polyhedron, if there is any.
4620 The first column in the output is the denominator and is always
4621 equal to 1. If the polyhedron contains no integer points,
4622 then a vector of length zero is printed.
4626 C<isl_pip> takes the same input as the C<example> program
4627 from the C<piplib> distribution, i.e., a set of constraints
4628 on the parameters, a line containing only -1 and finally a set
4629 of constraints on a parametric polyhedron.
4630 The coefficients of the parameters appear in the last columns
4631 (but before the final constant column).
4632 The output is the lexicographic minimum of the parametric polyhedron.
4633 As C<isl> currently does not have its own output format, the output
4634 is just a dump of the internal state.
4636 =head2 C<isl_polyhedron_minimize>
4638 C<isl_polyhedron_minimize> computes the minimum of some linear
4639 or affine objective function over the integer points in a polyhedron.
4640 If an affine objective function
4641 is given, then the constant should appear in the last column.
4643 =head2 C<isl_polytope_scan>
4645 Given a polytope, C<isl_polytope_scan> prints
4646 all integer points in the polytope.