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 const char *isl_local_space_get_dim_name(
834 __isl_keep isl_local_space *ls,
835 enum isl_dim_type type, unsigned pos);
836 __isl_give isl_local_space *isl_local_space_set_dim_name(
837 __isl_take isl_local_space *ls,
838 enum isl_dim_type type, unsigned pos, const char *s);
839 __isl_give isl_local_space *isl_local_space_set_dim_id(
840 __isl_take isl_local_space *ls,
841 enum isl_dim_type type, unsigned pos,
842 __isl_take isl_id *id);
843 __isl_give isl_space *isl_local_space_get_space(
844 __isl_keep isl_local_space *ls);
845 __isl_give isl_aff *isl_local_space_get_div(
846 __isl_keep isl_local_space *ls, int pos);
847 __isl_give isl_local_space *isl_local_space_copy(
848 __isl_keep isl_local_space *ls);
849 void *isl_local_space_free(__isl_take isl_local_space *ls);
851 Two local spaces can be compared using
853 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
854 __isl_keep isl_local_space *ls2);
856 Local spaces can be created from other local spaces
857 using the following functions.
859 __isl_give isl_local_space *isl_local_space_domain(
860 __isl_take isl_local_space *ls);
861 __isl_give isl_local_space *isl_local_space_range(
862 __isl_take isl_local_space *ls);
863 __isl_give isl_local_space *isl_local_space_from_domain(
864 __isl_take isl_local_space *ls);
865 __isl_give isl_local_space *isl_local_space_intersect(
866 __isl_take isl_local_space *ls1,
867 __isl_take isl_local_space *ls2);
868 __isl_give isl_local_space *isl_local_space_add_dims(
869 __isl_take isl_local_space *ls,
870 enum isl_dim_type type, unsigned n);
871 __isl_give isl_local_space *isl_local_space_insert_dims(
872 __isl_take isl_local_space *ls,
873 enum isl_dim_type type, unsigned first, unsigned n);
874 __isl_give isl_local_space *isl_local_space_drop_dims(
875 __isl_take isl_local_space *ls,
876 enum isl_dim_type type, unsigned first, unsigned n);
878 =head2 Input and Output
880 C<isl> supports its own input/output format, which is similar
881 to the C<Omega> format, but also supports the C<PolyLib> format
886 The C<isl> format is similar to that of C<Omega>, but has a different
887 syntax for describing the parameters and allows for the definition
888 of an existentially quantified variable as the integer division
889 of an affine expression.
890 For example, the set of integers C<i> between C<0> and C<n>
891 such that C<i % 10 <= 6> can be described as
893 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
896 A set or relation can have several disjuncts, separated
897 by the keyword C<or>. Each disjunct is either a conjunction
898 of constraints or a projection (C<exists>) of a conjunction
899 of constraints. The constraints are separated by the keyword
902 =head3 C<PolyLib> format
904 If the represented set is a union, then the first line
905 contains a single number representing the number of disjuncts.
906 Otherwise, a line containing the number C<1> is optional.
908 Each disjunct is represented by a matrix of constraints.
909 The first line contains two numbers representing
910 the number of rows and columns,
911 where the number of rows is equal to the number of constraints
912 and the number of columns is equal to two plus the number of variables.
913 The following lines contain the actual rows of the constraint matrix.
914 In each row, the first column indicates whether the constraint
915 is an equality (C<0>) or inequality (C<1>). The final column
916 corresponds to the constant term.
918 If the set is parametric, then the coefficients of the parameters
919 appear in the last columns before the constant column.
920 The coefficients of any existentially quantified variables appear
921 between those of the set variables and those of the parameters.
923 =head3 Extended C<PolyLib> format
925 The extended C<PolyLib> format is nearly identical to the
926 C<PolyLib> format. The only difference is that the line
927 containing the number of rows and columns of a constraint matrix
928 also contains four additional numbers:
929 the number of output dimensions, the number of input dimensions,
930 the number of local dimensions (i.e., the number of existentially
931 quantified variables) and the number of parameters.
932 For sets, the number of ``output'' dimensions is equal
933 to the number of set dimensions, while the number of ``input''
939 __isl_give isl_basic_set *isl_basic_set_read_from_file(
940 isl_ctx *ctx, FILE *input);
941 __isl_give isl_basic_set *isl_basic_set_read_from_str(
942 isl_ctx *ctx, const char *str);
943 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
945 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
949 __isl_give isl_basic_map *isl_basic_map_read_from_file(
950 isl_ctx *ctx, FILE *input);
951 __isl_give isl_basic_map *isl_basic_map_read_from_str(
952 isl_ctx *ctx, const char *str);
953 __isl_give isl_map *isl_map_read_from_file(
954 isl_ctx *ctx, FILE *input);
955 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
958 #include <isl/union_set.h>
959 __isl_give isl_union_set *isl_union_set_read_from_file(
960 isl_ctx *ctx, FILE *input);
961 __isl_give isl_union_set *isl_union_set_read_from_str(
962 isl_ctx *ctx, const char *str);
964 #include <isl/union_map.h>
965 __isl_give isl_union_map *isl_union_map_read_from_file(
966 isl_ctx *ctx, FILE *input);
967 __isl_give isl_union_map *isl_union_map_read_from_str(
968 isl_ctx *ctx, const char *str);
970 The input format is autodetected and may be either the C<PolyLib> format
971 or the C<isl> format.
975 Before anything can be printed, an C<isl_printer> needs to
978 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
980 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
981 void isl_printer_free(__isl_take isl_printer *printer);
982 __isl_give char *isl_printer_get_str(
983 __isl_keep isl_printer *printer);
985 The printer can be inspected using the following function.
987 FILE *isl_printer_get_file(
988 __isl_keep isl_printer *printer);
990 The behavior of the printer can be modified in various ways
992 __isl_give isl_printer *isl_printer_set_output_format(
993 __isl_take isl_printer *p, int output_format);
994 __isl_give isl_printer *isl_printer_set_indent(
995 __isl_take isl_printer *p, int indent);
996 __isl_give isl_printer *isl_printer_indent(
997 __isl_take isl_printer *p, int indent);
998 __isl_give isl_printer *isl_printer_set_prefix(
999 __isl_take isl_printer *p, const char *prefix);
1000 __isl_give isl_printer *isl_printer_set_suffix(
1001 __isl_take isl_printer *p, const char *suffix);
1003 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1004 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1005 and defaults to C<ISL_FORMAT_ISL>.
1006 Each line in the output is indented by C<indent> (set by
1007 C<isl_printer_set_indent>) spaces
1008 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1009 In the C<PolyLib> format output,
1010 the coefficients of the existentially quantified variables
1011 appear between those of the set variables and those
1013 The function C<isl_printer_indent> increases the indentation
1014 by the specified amount (which may be negative).
1016 To actually print something, use
1018 #include <isl/set.h>
1019 __isl_give isl_printer *isl_printer_print_basic_set(
1020 __isl_take isl_printer *printer,
1021 __isl_keep isl_basic_set *bset);
1022 __isl_give isl_printer *isl_printer_print_set(
1023 __isl_take isl_printer *printer,
1024 __isl_keep isl_set *set);
1026 #include <isl/map.h>
1027 __isl_give isl_printer *isl_printer_print_basic_map(
1028 __isl_take isl_printer *printer,
1029 __isl_keep isl_basic_map *bmap);
1030 __isl_give isl_printer *isl_printer_print_map(
1031 __isl_take isl_printer *printer,
1032 __isl_keep isl_map *map);
1034 #include <isl/union_set.h>
1035 __isl_give isl_printer *isl_printer_print_union_set(
1036 __isl_take isl_printer *p,
1037 __isl_keep isl_union_set *uset);
1039 #include <isl/union_map.h>
1040 __isl_give isl_printer *isl_printer_print_union_map(
1041 __isl_take isl_printer *p,
1042 __isl_keep isl_union_map *umap);
1044 When called on a file printer, the following function flushes
1045 the file. When called on a string printer, the buffer is cleared.
1047 __isl_give isl_printer *isl_printer_flush(
1048 __isl_take isl_printer *p);
1050 =head2 Creating New Sets and Relations
1052 C<isl> has functions for creating some standard sets and relations.
1056 =item * Empty sets and relations
1058 __isl_give isl_basic_set *isl_basic_set_empty(
1059 __isl_take isl_space *space);
1060 __isl_give isl_basic_map *isl_basic_map_empty(
1061 __isl_take isl_space *space);
1062 __isl_give isl_set *isl_set_empty(
1063 __isl_take isl_space *space);
1064 __isl_give isl_map *isl_map_empty(
1065 __isl_take isl_space *space);
1066 __isl_give isl_union_set *isl_union_set_empty(
1067 __isl_take isl_space *space);
1068 __isl_give isl_union_map *isl_union_map_empty(
1069 __isl_take isl_space *space);
1071 For C<isl_union_set>s and C<isl_union_map>s, the space
1072 is only used to specify the parameters.
1074 =item * Universe sets and relations
1076 __isl_give isl_basic_set *isl_basic_set_universe(
1077 __isl_take isl_space *space);
1078 __isl_give isl_basic_map *isl_basic_map_universe(
1079 __isl_take isl_space *space);
1080 __isl_give isl_set *isl_set_universe(
1081 __isl_take isl_space *space);
1082 __isl_give isl_map *isl_map_universe(
1083 __isl_take isl_space *space);
1084 __isl_give isl_union_set *isl_union_set_universe(
1085 __isl_take isl_union_set *uset);
1086 __isl_give isl_union_map *isl_union_map_universe(
1087 __isl_take isl_union_map *umap);
1089 The sets and relations constructed by the functions above
1090 contain all integer values, while those constructed by the
1091 functions below only contain non-negative values.
1093 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1094 __isl_take isl_space *space);
1095 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1096 __isl_take isl_space *space);
1097 __isl_give isl_set *isl_set_nat_universe(
1098 __isl_take isl_space *space);
1099 __isl_give isl_map *isl_map_nat_universe(
1100 __isl_take isl_space *space);
1102 =item * Identity relations
1104 __isl_give isl_basic_map *isl_basic_map_identity(
1105 __isl_take isl_space *space);
1106 __isl_give isl_map *isl_map_identity(
1107 __isl_take isl_space *space);
1109 The number of input and output dimensions in C<space> needs
1112 =item * Lexicographic order
1114 __isl_give isl_map *isl_map_lex_lt(
1115 __isl_take isl_space *set_space);
1116 __isl_give isl_map *isl_map_lex_le(
1117 __isl_take isl_space *set_space);
1118 __isl_give isl_map *isl_map_lex_gt(
1119 __isl_take isl_space *set_space);
1120 __isl_give isl_map *isl_map_lex_ge(
1121 __isl_take isl_space *set_space);
1122 __isl_give isl_map *isl_map_lex_lt_first(
1123 __isl_take isl_space *space, unsigned n);
1124 __isl_give isl_map *isl_map_lex_le_first(
1125 __isl_take isl_space *space, unsigned n);
1126 __isl_give isl_map *isl_map_lex_gt_first(
1127 __isl_take isl_space *space, unsigned n);
1128 __isl_give isl_map *isl_map_lex_ge_first(
1129 __isl_take isl_space *space, unsigned n);
1131 The first four functions take a space for a B<set>
1132 and return relations that express that the elements in the domain
1133 are lexicographically less
1134 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1135 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1136 than the elements in the range.
1137 The last four functions take a space for a map
1138 and return relations that express that the first C<n> dimensions
1139 in the domain are lexicographically less
1140 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1141 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1142 than the first C<n> dimensions in the range.
1146 A basic set or relation can be converted to a set or relation
1147 using the following functions.
1149 __isl_give isl_set *isl_set_from_basic_set(
1150 __isl_take isl_basic_set *bset);
1151 __isl_give isl_map *isl_map_from_basic_map(
1152 __isl_take isl_basic_map *bmap);
1154 Sets and relations can be converted to union sets and relations
1155 using the following functions.
1157 __isl_give isl_union_map *isl_union_map_from_map(
1158 __isl_take isl_map *map);
1159 __isl_give isl_union_set *isl_union_set_from_set(
1160 __isl_take isl_set *set);
1162 The inverse conversions below can only be used if the input
1163 union set or relation is known to contain elements in exactly one
1166 __isl_give isl_set *isl_set_from_union_set(
1167 __isl_take isl_union_set *uset);
1168 __isl_give isl_map *isl_map_from_union_map(
1169 __isl_take isl_union_map *umap);
1171 A zero-dimensional set can be constructed on a given parameter domain
1172 using the following function.
1174 __isl_give isl_set *isl_set_from_params(
1175 __isl_take isl_set *set);
1177 Sets and relations can be copied and freed again using the following
1180 __isl_give isl_basic_set *isl_basic_set_copy(
1181 __isl_keep isl_basic_set *bset);
1182 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1183 __isl_give isl_union_set *isl_union_set_copy(
1184 __isl_keep isl_union_set *uset);
1185 __isl_give isl_basic_map *isl_basic_map_copy(
1186 __isl_keep isl_basic_map *bmap);
1187 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1188 __isl_give isl_union_map *isl_union_map_copy(
1189 __isl_keep isl_union_map *umap);
1190 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1191 void isl_set_free(__isl_take isl_set *set);
1192 void *isl_union_set_free(__isl_take isl_union_set *uset);
1193 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1194 void isl_map_free(__isl_take isl_map *map);
1195 void *isl_union_map_free(__isl_take isl_union_map *umap);
1197 Other sets and relations can be constructed by starting
1198 from a universe set or relation, adding equality and/or
1199 inequality constraints and then projecting out the
1200 existentially quantified variables, if any.
1201 Constraints can be constructed, manipulated and
1202 added to (or removed from) (basic) sets and relations
1203 using the following functions.
1205 #include <isl/constraint.h>
1206 __isl_give isl_constraint *isl_equality_alloc(
1207 __isl_take isl_local_space *ls);
1208 __isl_give isl_constraint *isl_inequality_alloc(
1209 __isl_take isl_local_space *ls);
1210 __isl_give isl_constraint *isl_constraint_set_constant(
1211 __isl_take isl_constraint *constraint, isl_int v);
1212 __isl_give isl_constraint *isl_constraint_set_constant_si(
1213 __isl_take isl_constraint *constraint, int v);
1214 __isl_give isl_constraint *isl_constraint_set_coefficient(
1215 __isl_take isl_constraint *constraint,
1216 enum isl_dim_type type, int pos, isl_int v);
1217 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1218 __isl_take isl_constraint *constraint,
1219 enum isl_dim_type type, int pos, int v);
1220 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1221 __isl_take isl_basic_map *bmap,
1222 __isl_take isl_constraint *constraint);
1223 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1224 __isl_take isl_basic_set *bset,
1225 __isl_take isl_constraint *constraint);
1226 __isl_give isl_map *isl_map_add_constraint(
1227 __isl_take isl_map *map,
1228 __isl_take isl_constraint *constraint);
1229 __isl_give isl_set *isl_set_add_constraint(
1230 __isl_take isl_set *set,
1231 __isl_take isl_constraint *constraint);
1232 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1233 __isl_take isl_basic_set *bset,
1234 __isl_take isl_constraint *constraint);
1236 For example, to create a set containing the even integers
1237 between 10 and 42, you would use the following code.
1240 isl_local_space *ls;
1242 isl_basic_set *bset;
1244 space = isl_space_set_alloc(ctx, 0, 2);
1245 bset = isl_basic_set_universe(isl_space_copy(space));
1246 ls = isl_local_space_from_space(space);
1248 c = isl_equality_alloc(isl_local_space_copy(ls));
1249 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1250 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1251 bset = isl_basic_set_add_constraint(bset, c);
1253 c = isl_inequality_alloc(isl_local_space_copy(ls));
1254 c = isl_constraint_set_constant_si(c, -10);
1255 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1256 bset = isl_basic_set_add_constraint(bset, c);
1258 c = isl_inequality_alloc(ls);
1259 c = isl_constraint_set_constant_si(c, 42);
1260 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1261 bset = isl_basic_set_add_constraint(bset, c);
1263 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1267 isl_basic_set *bset;
1268 bset = isl_basic_set_read_from_str(ctx,
1269 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1271 A basic set or relation can also be constructed from two matrices
1272 describing the equalities and the inequalities.
1274 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1275 __isl_take isl_space *space,
1276 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1277 enum isl_dim_type c1,
1278 enum isl_dim_type c2, enum isl_dim_type c3,
1279 enum isl_dim_type c4);
1280 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1281 __isl_take isl_space *space,
1282 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1283 enum isl_dim_type c1,
1284 enum isl_dim_type c2, enum isl_dim_type c3,
1285 enum isl_dim_type c4, enum isl_dim_type c5);
1287 The C<isl_dim_type> arguments indicate the order in which
1288 different kinds of variables appear in the input matrices
1289 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1290 C<isl_dim_set> and C<isl_dim_div> for sets and
1291 of C<isl_dim_cst>, C<isl_dim_param>,
1292 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1294 A (basic or union) set or relation can also be constructed from a
1295 (union) (piecewise) (multiple) affine expression
1296 or a list of affine expressions
1297 (See L<"Piecewise Quasi Affine Expressions"> and
1298 L<"Piecewise Multiple Quasi Affine Expressions">).
1300 __isl_give isl_basic_map *isl_basic_map_from_aff(
1301 __isl_take isl_aff *aff);
1302 __isl_give isl_map *isl_map_from_aff(
1303 __isl_take isl_aff *aff);
1304 __isl_give isl_set *isl_set_from_pw_aff(
1305 __isl_take isl_pw_aff *pwaff);
1306 __isl_give isl_map *isl_map_from_pw_aff(
1307 __isl_take isl_pw_aff *pwaff);
1308 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1309 __isl_take isl_space *domain_space,
1310 __isl_take isl_aff_list *list);
1311 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1312 __isl_take isl_multi_aff *maff)
1313 __isl_give isl_map *isl_map_from_multi_aff(
1314 __isl_take isl_multi_aff *maff)
1315 __isl_give isl_set *isl_set_from_pw_multi_aff(
1316 __isl_take isl_pw_multi_aff *pma);
1317 __isl_give isl_map *isl_map_from_pw_multi_aff(
1318 __isl_take isl_pw_multi_aff *pma);
1319 __isl_give isl_union_map *
1320 isl_union_map_from_union_pw_multi_aff(
1321 __isl_take isl_union_pw_multi_aff *upma);
1323 The C<domain_dim> argument describes the domain of the resulting
1324 basic relation. It is required because the C<list> may consist
1325 of zero affine expressions.
1327 =head2 Inspecting Sets and Relations
1329 Usually, the user should not have to care about the actual constraints
1330 of the sets and maps, but should instead apply the abstract operations
1331 explained in the following sections.
1332 Occasionally, however, it may be required to inspect the individual
1333 coefficients of the constraints. This section explains how to do so.
1334 In these cases, it may also be useful to have C<isl> compute
1335 an explicit representation of the existentially quantified variables.
1337 __isl_give isl_set *isl_set_compute_divs(
1338 __isl_take isl_set *set);
1339 __isl_give isl_map *isl_map_compute_divs(
1340 __isl_take isl_map *map);
1341 __isl_give isl_union_set *isl_union_set_compute_divs(
1342 __isl_take isl_union_set *uset);
1343 __isl_give isl_union_map *isl_union_map_compute_divs(
1344 __isl_take isl_union_map *umap);
1346 This explicit representation defines the existentially quantified
1347 variables as integer divisions of the other variables, possibly
1348 including earlier existentially quantified variables.
1349 An explicitly represented existentially quantified variable therefore
1350 has a unique value when the values of the other variables are known.
1351 If, furthermore, the same existentials, i.e., existentials
1352 with the same explicit representations, should appear in the
1353 same order in each of the disjuncts of a set or map, then the user should call
1354 either of the following functions.
1356 __isl_give isl_set *isl_set_align_divs(
1357 __isl_take isl_set *set);
1358 __isl_give isl_map *isl_map_align_divs(
1359 __isl_take isl_map *map);
1361 Alternatively, the existentially quantified variables can be removed
1362 using the following functions, which compute an overapproximation.
1364 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1365 __isl_take isl_basic_set *bset);
1366 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1367 __isl_take isl_basic_map *bmap);
1368 __isl_give isl_set *isl_set_remove_divs(
1369 __isl_take isl_set *set);
1370 __isl_give isl_map *isl_map_remove_divs(
1371 __isl_take isl_map *map);
1373 To iterate over all the sets or maps in a union set or map, use
1375 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1376 int (*fn)(__isl_take isl_set *set, void *user),
1378 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1379 int (*fn)(__isl_take isl_map *map, void *user),
1382 The number of sets or maps in a union set or map can be obtained
1385 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1386 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1388 To extract the set or map in a given space from a union, use
1390 __isl_give isl_set *isl_union_set_extract_set(
1391 __isl_keep isl_union_set *uset,
1392 __isl_take isl_space *space);
1393 __isl_give isl_map *isl_union_map_extract_map(
1394 __isl_keep isl_union_map *umap,
1395 __isl_take isl_space *space);
1397 To iterate over all the basic sets or maps in a set or map, use
1399 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1400 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1402 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1403 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1406 The callback function C<fn> should return 0 if successful and
1407 -1 if an error occurs. In the latter case, or if any other error
1408 occurs, the above functions will return -1.
1410 It should be noted that C<isl> does not guarantee that
1411 the basic sets or maps passed to C<fn> are disjoint.
1412 If this is required, then the user should call one of
1413 the following functions first.
1415 __isl_give isl_set *isl_set_make_disjoint(
1416 __isl_take isl_set *set);
1417 __isl_give isl_map *isl_map_make_disjoint(
1418 __isl_take isl_map *map);
1420 The number of basic sets in a set can be obtained
1423 int isl_set_n_basic_set(__isl_keep isl_set *set);
1425 To iterate over the constraints of a basic set or map, use
1427 #include <isl/constraint.h>
1429 int isl_basic_set_n_constraint(
1430 __isl_keep isl_basic_set *bset);
1431 int isl_basic_set_foreach_constraint(
1432 __isl_keep isl_basic_set *bset,
1433 int (*fn)(__isl_take isl_constraint *c, void *user),
1435 int isl_basic_map_foreach_constraint(
1436 __isl_keep isl_basic_map *bmap,
1437 int (*fn)(__isl_take isl_constraint *c, void *user),
1439 void *isl_constraint_free(__isl_take isl_constraint *c);
1441 Again, the callback function C<fn> should return 0 if successful and
1442 -1 if an error occurs. In the latter case, or if any other error
1443 occurs, the above functions will return -1.
1444 The constraint C<c> represents either an equality or an inequality.
1445 Use the following function to find out whether a constraint
1446 represents an equality. If not, it represents an inequality.
1448 int isl_constraint_is_equality(
1449 __isl_keep isl_constraint *constraint);
1451 The coefficients of the constraints can be inspected using
1452 the following functions.
1454 int isl_constraint_is_lower_bound(
1455 __isl_keep isl_constraint *constraint,
1456 enum isl_dim_type type, unsigned pos);
1457 int isl_constraint_is_upper_bound(
1458 __isl_keep isl_constraint *constraint,
1459 enum isl_dim_type type, unsigned pos);
1460 void isl_constraint_get_constant(
1461 __isl_keep isl_constraint *constraint, isl_int *v);
1462 void isl_constraint_get_coefficient(
1463 __isl_keep isl_constraint *constraint,
1464 enum isl_dim_type type, int pos, isl_int *v);
1465 int isl_constraint_involves_dims(
1466 __isl_keep isl_constraint *constraint,
1467 enum isl_dim_type type, unsigned first, unsigned n);
1469 The explicit representations of the existentially quantified
1470 variables can be inspected using the following function.
1471 Note that the user is only allowed to use this function
1472 if the inspected set or map is the result of a call
1473 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1474 The existentially quantified variable is equal to the floor
1475 of the returned affine expression. The affine expression
1476 itself can be inspected using the functions in
1477 L<"Piecewise Quasi Affine Expressions">.
1479 __isl_give isl_aff *isl_constraint_get_div(
1480 __isl_keep isl_constraint *constraint, int pos);
1482 To obtain the constraints of a basic set or map in matrix
1483 form, use the following functions.
1485 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1486 __isl_keep isl_basic_set *bset,
1487 enum isl_dim_type c1, enum isl_dim_type c2,
1488 enum isl_dim_type c3, enum isl_dim_type c4);
1489 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1490 __isl_keep isl_basic_set *bset,
1491 enum isl_dim_type c1, enum isl_dim_type c2,
1492 enum isl_dim_type c3, enum isl_dim_type c4);
1493 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1494 __isl_keep isl_basic_map *bmap,
1495 enum isl_dim_type c1,
1496 enum isl_dim_type c2, enum isl_dim_type c3,
1497 enum isl_dim_type c4, enum isl_dim_type c5);
1498 __isl_give isl_mat *isl_basic_map_inequalities_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);
1504 The C<isl_dim_type> arguments dictate the order in which
1505 different kinds of variables appear in the resulting matrix
1506 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1507 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1509 The number of parameters, input, output or set dimensions can
1510 be obtained using the following functions.
1512 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1513 enum isl_dim_type type);
1514 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1515 enum isl_dim_type type);
1516 unsigned isl_set_dim(__isl_keep isl_set *set,
1517 enum isl_dim_type type);
1518 unsigned isl_map_dim(__isl_keep isl_map *map,
1519 enum isl_dim_type type);
1521 To check whether the description of a set or relation depends
1522 on one or more given dimensions, it is not necessary to iterate over all
1523 constraints. Instead the following functions can be used.
1525 int isl_basic_set_involves_dims(
1526 __isl_keep isl_basic_set *bset,
1527 enum isl_dim_type type, unsigned first, unsigned n);
1528 int isl_set_involves_dims(__isl_keep isl_set *set,
1529 enum isl_dim_type type, unsigned first, unsigned n);
1530 int isl_basic_map_involves_dims(
1531 __isl_keep isl_basic_map *bmap,
1532 enum isl_dim_type type, unsigned first, unsigned n);
1533 int isl_map_involves_dims(__isl_keep isl_map *map,
1534 enum isl_dim_type type, unsigned first, unsigned n);
1536 Similarly, the following functions can be used to check whether
1537 a given dimension is involved in any lower or upper bound.
1539 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1540 enum isl_dim_type type, unsigned pos);
1541 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1542 enum isl_dim_type type, unsigned pos);
1544 The identifiers or names of the domain and range spaces of a set
1545 or relation can be read off or set using the following functions.
1547 __isl_give isl_set *isl_set_set_tuple_id(
1548 __isl_take isl_set *set, __isl_take isl_id *id);
1549 __isl_give isl_set *isl_set_reset_tuple_id(
1550 __isl_take isl_set *set);
1551 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1552 __isl_give isl_id *isl_set_get_tuple_id(
1553 __isl_keep isl_set *set);
1554 __isl_give isl_map *isl_map_set_tuple_id(
1555 __isl_take isl_map *map, enum isl_dim_type type,
1556 __isl_take isl_id *id);
1557 __isl_give isl_map *isl_map_reset_tuple_id(
1558 __isl_take isl_map *map, enum isl_dim_type type);
1559 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1560 enum isl_dim_type type);
1561 __isl_give isl_id *isl_map_get_tuple_id(
1562 __isl_keep isl_map *map, enum isl_dim_type type);
1564 const char *isl_basic_set_get_tuple_name(
1565 __isl_keep isl_basic_set *bset);
1566 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1567 __isl_take isl_basic_set *set, const char *s);
1568 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1569 const char *isl_set_get_tuple_name(
1570 __isl_keep isl_set *set);
1571 const char *isl_basic_map_get_tuple_name(
1572 __isl_keep isl_basic_map *bmap,
1573 enum isl_dim_type type);
1574 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1575 __isl_take isl_basic_map *bmap,
1576 enum isl_dim_type type, const char *s);
1577 const char *isl_map_get_tuple_name(
1578 __isl_keep isl_map *map,
1579 enum isl_dim_type type);
1581 As with C<isl_space_get_tuple_name>, the value returned points to
1582 an internal data structure.
1583 The identifiers, positions or names of individual dimensions can be
1584 read off using the following functions.
1586 __isl_give isl_set *isl_set_set_dim_id(
1587 __isl_take isl_set *set, enum isl_dim_type type,
1588 unsigned pos, __isl_take isl_id *id);
1589 int isl_set_has_dim_id(__isl_keep isl_set *set,
1590 enum isl_dim_type type, unsigned pos);
1591 __isl_give isl_id *isl_set_get_dim_id(
1592 __isl_keep isl_set *set, enum isl_dim_type type,
1594 int isl_basic_map_has_dim_id(
1595 __isl_keep isl_basic_map *bmap,
1596 enum isl_dim_type type, unsigned pos);
1597 __isl_give isl_map *isl_map_set_dim_id(
1598 __isl_take isl_map *map, enum isl_dim_type type,
1599 unsigned pos, __isl_take isl_id *id);
1600 int isl_map_has_dim_id(__isl_keep isl_map *map,
1601 enum isl_dim_type type, unsigned pos);
1602 __isl_give isl_id *isl_map_get_dim_id(
1603 __isl_keep isl_map *map, enum isl_dim_type type,
1606 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1607 enum isl_dim_type type, __isl_keep isl_id *id);
1608 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1609 enum isl_dim_type type, __isl_keep isl_id *id);
1610 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1611 enum isl_dim_type type, const char *name);
1612 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1613 enum isl_dim_type type, const char *name);
1615 const char *isl_constraint_get_dim_name(
1616 __isl_keep isl_constraint *constraint,
1617 enum isl_dim_type type, unsigned pos);
1618 const char *isl_basic_set_get_dim_name(
1619 __isl_keep isl_basic_set *bset,
1620 enum isl_dim_type type, unsigned pos);
1621 int isl_set_has_dim_name(__isl_keep isl_set *set,
1622 enum isl_dim_type type, unsigned pos);
1623 const char *isl_set_get_dim_name(
1624 __isl_keep isl_set *set,
1625 enum isl_dim_type type, unsigned pos);
1626 const char *isl_basic_map_get_dim_name(
1627 __isl_keep isl_basic_map *bmap,
1628 enum isl_dim_type type, unsigned pos);
1629 const char *isl_map_get_dim_name(
1630 __isl_keep isl_map *map,
1631 enum isl_dim_type type, unsigned pos);
1633 These functions are mostly useful to obtain the identifiers, positions
1634 or names of the parameters. Identifiers of individual dimensions are
1635 essentially only useful for printing. They are ignored by all other
1636 operations and may not be preserved across those operations.
1640 =head3 Unary Properties
1646 The following functions test whether the given set or relation
1647 contains any integer points. The ``plain'' variants do not perform
1648 any computations, but simply check if the given set or relation
1649 is already known to be empty.
1651 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1652 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1653 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1654 int isl_set_is_empty(__isl_keep isl_set *set);
1655 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1656 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1657 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1658 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1659 int isl_map_is_empty(__isl_keep isl_map *map);
1660 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1662 =item * Universality
1664 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1665 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1666 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1668 =item * Single-valuedness
1670 int isl_map_plain_is_single_valued(
1671 __isl_keep isl_map *map);
1672 int isl_map_is_single_valued(__isl_keep isl_map *map);
1673 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1677 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1678 int isl_map_is_injective(__isl_keep isl_map *map);
1679 int isl_union_map_plain_is_injective(
1680 __isl_keep isl_union_map *umap);
1681 int isl_union_map_is_injective(
1682 __isl_keep isl_union_map *umap);
1686 int isl_map_is_bijective(__isl_keep isl_map *map);
1687 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1691 int isl_basic_map_plain_is_fixed(
1692 __isl_keep isl_basic_map *bmap,
1693 enum isl_dim_type type, unsigned pos,
1695 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1696 enum isl_dim_type type, unsigned pos,
1698 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1699 enum isl_dim_type type, unsigned pos,
1702 Check if the relation obviously lies on a hyperplane where the given dimension
1703 has a fixed value and if so, return that value in C<*val>.
1707 To check whether a set is a parameter domain, use this function:
1709 int isl_set_is_params(__isl_keep isl_set *set);
1710 int isl_union_set_is_params(
1711 __isl_keep isl_union_set *uset);
1715 The following functions check whether the domain of the given
1716 (basic) set is a wrapped relation.
1718 int isl_basic_set_is_wrapping(
1719 __isl_keep isl_basic_set *bset);
1720 int isl_set_is_wrapping(__isl_keep isl_set *set);
1722 =item * Internal Product
1724 int isl_basic_map_can_zip(
1725 __isl_keep isl_basic_map *bmap);
1726 int isl_map_can_zip(__isl_keep isl_map *map);
1728 Check whether the product of domain and range of the given relation
1730 i.e., whether both domain and range are nested relations.
1734 int isl_basic_map_can_curry(
1735 __isl_keep isl_basic_map *bmap);
1736 int isl_map_can_curry(__isl_keep isl_map *map);
1738 Check whether the domain of the (basic) relation is a wrapped relation.
1742 =head3 Binary Properties
1748 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1749 __isl_keep isl_set *set2);
1750 int isl_set_is_equal(__isl_keep isl_set *set1,
1751 __isl_keep isl_set *set2);
1752 int isl_union_set_is_equal(
1753 __isl_keep isl_union_set *uset1,
1754 __isl_keep isl_union_set *uset2);
1755 int isl_basic_map_is_equal(
1756 __isl_keep isl_basic_map *bmap1,
1757 __isl_keep isl_basic_map *bmap2);
1758 int isl_map_is_equal(__isl_keep isl_map *map1,
1759 __isl_keep isl_map *map2);
1760 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1761 __isl_keep isl_map *map2);
1762 int isl_union_map_is_equal(
1763 __isl_keep isl_union_map *umap1,
1764 __isl_keep isl_union_map *umap2);
1766 =item * Disjointness
1768 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1769 __isl_keep isl_set *set2);
1773 int isl_basic_set_is_subset(
1774 __isl_keep isl_basic_set *bset1,
1775 __isl_keep isl_basic_set *bset2);
1776 int isl_set_is_subset(__isl_keep isl_set *set1,
1777 __isl_keep isl_set *set2);
1778 int isl_set_is_strict_subset(
1779 __isl_keep isl_set *set1,
1780 __isl_keep isl_set *set2);
1781 int isl_union_set_is_subset(
1782 __isl_keep isl_union_set *uset1,
1783 __isl_keep isl_union_set *uset2);
1784 int isl_union_set_is_strict_subset(
1785 __isl_keep isl_union_set *uset1,
1786 __isl_keep isl_union_set *uset2);
1787 int isl_basic_map_is_subset(
1788 __isl_keep isl_basic_map *bmap1,
1789 __isl_keep isl_basic_map *bmap2);
1790 int isl_basic_map_is_strict_subset(
1791 __isl_keep isl_basic_map *bmap1,
1792 __isl_keep isl_basic_map *bmap2);
1793 int isl_map_is_subset(
1794 __isl_keep isl_map *map1,
1795 __isl_keep isl_map *map2);
1796 int isl_map_is_strict_subset(
1797 __isl_keep isl_map *map1,
1798 __isl_keep isl_map *map2);
1799 int isl_union_map_is_subset(
1800 __isl_keep isl_union_map *umap1,
1801 __isl_keep isl_union_map *umap2);
1802 int isl_union_map_is_strict_subset(
1803 __isl_keep isl_union_map *umap1,
1804 __isl_keep isl_union_map *umap2);
1808 =head2 Unary Operations
1814 __isl_give isl_set *isl_set_complement(
1815 __isl_take isl_set *set);
1816 __isl_give isl_map *isl_map_complement(
1817 __isl_take isl_map *map);
1821 __isl_give isl_basic_map *isl_basic_map_reverse(
1822 __isl_take isl_basic_map *bmap);
1823 __isl_give isl_map *isl_map_reverse(
1824 __isl_take isl_map *map);
1825 __isl_give isl_union_map *isl_union_map_reverse(
1826 __isl_take isl_union_map *umap);
1830 __isl_give isl_basic_set *isl_basic_set_project_out(
1831 __isl_take isl_basic_set *bset,
1832 enum isl_dim_type type, unsigned first, unsigned n);
1833 __isl_give isl_basic_map *isl_basic_map_project_out(
1834 __isl_take isl_basic_map *bmap,
1835 enum isl_dim_type type, unsigned first, unsigned n);
1836 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1837 enum isl_dim_type type, unsigned first, unsigned n);
1838 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1839 enum isl_dim_type type, unsigned first, unsigned n);
1840 __isl_give isl_basic_set *isl_basic_set_params(
1841 __isl_take isl_basic_set *bset);
1842 __isl_give isl_basic_set *isl_basic_map_domain(
1843 __isl_take isl_basic_map *bmap);
1844 __isl_give isl_basic_set *isl_basic_map_range(
1845 __isl_take isl_basic_map *bmap);
1846 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1847 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1848 __isl_give isl_set *isl_map_domain(
1849 __isl_take isl_map *bmap);
1850 __isl_give isl_set *isl_map_range(
1851 __isl_take isl_map *map);
1852 __isl_give isl_set *isl_union_set_params(
1853 __isl_take isl_union_set *uset);
1854 __isl_give isl_set *isl_union_map_params(
1855 __isl_take isl_union_map *umap);
1856 __isl_give isl_union_set *isl_union_map_domain(
1857 __isl_take isl_union_map *umap);
1858 __isl_give isl_union_set *isl_union_map_range(
1859 __isl_take isl_union_map *umap);
1861 __isl_give isl_basic_map *isl_basic_map_domain_map(
1862 __isl_take isl_basic_map *bmap);
1863 __isl_give isl_basic_map *isl_basic_map_range_map(
1864 __isl_take isl_basic_map *bmap);
1865 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1866 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1867 __isl_give isl_union_map *isl_union_map_domain_map(
1868 __isl_take isl_union_map *umap);
1869 __isl_give isl_union_map *isl_union_map_range_map(
1870 __isl_take isl_union_map *umap);
1872 The functions above construct a (basic, regular or union) relation
1873 that maps (a wrapped version of) the input relation to its domain or range.
1877 __isl_give isl_set *isl_set_eliminate(
1878 __isl_take isl_set *set, enum isl_dim_type type,
1879 unsigned first, unsigned n);
1880 __isl_give isl_basic_map *isl_basic_map_eliminate(
1881 __isl_take isl_basic_map *bmap,
1882 enum isl_dim_type type,
1883 unsigned first, unsigned n);
1884 __isl_give isl_map *isl_map_eliminate(
1885 __isl_take isl_map *map, enum isl_dim_type type,
1886 unsigned first, unsigned n);
1888 Eliminate the coefficients for the given dimensions from the constraints,
1889 without removing the dimensions.
1893 __isl_give isl_basic_set *isl_basic_set_fix(
1894 __isl_take isl_basic_set *bset,
1895 enum isl_dim_type type, unsigned pos,
1897 __isl_give isl_basic_set *isl_basic_set_fix_si(
1898 __isl_take isl_basic_set *bset,
1899 enum isl_dim_type type, unsigned pos, int value);
1900 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1901 enum isl_dim_type type, unsigned pos,
1903 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1904 enum isl_dim_type type, unsigned pos, int value);
1905 __isl_give isl_basic_map *isl_basic_map_fix_si(
1906 __isl_take isl_basic_map *bmap,
1907 enum isl_dim_type type, unsigned pos, int value);
1908 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1909 enum isl_dim_type type, unsigned pos, int value);
1911 Intersect the set or relation with the hyperplane where the given
1912 dimension has the fixed given value.
1914 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1915 __isl_take isl_basic_map *bmap,
1916 enum isl_dim_type type, unsigned pos, int value);
1917 __isl_give isl_set *isl_set_lower_bound(
1918 __isl_take isl_set *set,
1919 enum isl_dim_type type, unsigned pos,
1921 __isl_give isl_set *isl_set_lower_bound_si(
1922 __isl_take isl_set *set,
1923 enum isl_dim_type type, unsigned pos, int value);
1924 __isl_give isl_map *isl_map_lower_bound_si(
1925 __isl_take isl_map *map,
1926 enum isl_dim_type type, unsigned pos, int value);
1927 __isl_give isl_set *isl_set_upper_bound(
1928 __isl_take isl_set *set,
1929 enum isl_dim_type type, unsigned pos,
1931 __isl_give isl_set *isl_set_upper_bound_si(
1932 __isl_take isl_set *set,
1933 enum isl_dim_type type, unsigned pos, int value);
1934 __isl_give isl_map *isl_map_upper_bound_si(
1935 __isl_take isl_map *map,
1936 enum isl_dim_type type, unsigned pos, int value);
1938 Intersect the set or relation with the half-space where the given
1939 dimension has a value bounded by the fixed given value.
1941 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1942 enum isl_dim_type type1, int pos1,
1943 enum isl_dim_type type2, int pos2);
1944 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1945 enum isl_dim_type type1, int pos1,
1946 enum isl_dim_type type2, int pos2);
1948 Intersect the set or relation with the hyperplane where the given
1949 dimensions are equal to each other.
1951 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1952 enum isl_dim_type type1, int pos1,
1953 enum isl_dim_type type2, int pos2);
1955 Intersect the relation with the hyperplane where the given
1956 dimensions have opposite values.
1958 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1959 enum isl_dim_type type1, int pos1,
1960 enum isl_dim_type type2, int pos2);
1962 Intersect the relation with the half-space where the given
1963 dimensions satisfy the given ordering.
1967 __isl_give isl_map *isl_set_identity(
1968 __isl_take isl_set *set);
1969 __isl_give isl_union_map *isl_union_set_identity(
1970 __isl_take isl_union_set *uset);
1972 Construct an identity relation on the given (union) set.
1976 __isl_give isl_basic_set *isl_basic_map_deltas(
1977 __isl_take isl_basic_map *bmap);
1978 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1979 __isl_give isl_union_set *isl_union_map_deltas(
1980 __isl_take isl_union_map *umap);
1982 These functions return a (basic) set containing the differences
1983 between image elements and corresponding domain elements in the input.
1985 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1986 __isl_take isl_basic_map *bmap);
1987 __isl_give isl_map *isl_map_deltas_map(
1988 __isl_take isl_map *map);
1989 __isl_give isl_union_map *isl_union_map_deltas_map(
1990 __isl_take isl_union_map *umap);
1992 The functions above construct a (basic, regular or union) relation
1993 that maps (a wrapped version of) the input relation to its delta set.
1997 Simplify the representation of a set or relation by trying
1998 to combine pairs of basic sets or relations into a single
1999 basic set or relation.
2001 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2002 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2003 __isl_give isl_union_set *isl_union_set_coalesce(
2004 __isl_take isl_union_set *uset);
2005 __isl_give isl_union_map *isl_union_map_coalesce(
2006 __isl_take isl_union_map *umap);
2008 One of the methods for combining pairs of basic sets or relations
2009 can result in coefficients that are much larger than those that appear
2010 in the constraints of the input. By default, the coefficients are
2011 not allowed to grow larger, but this can be changed by unsetting
2012 the following option.
2014 int isl_options_set_coalesce_bounded_wrapping(
2015 isl_ctx *ctx, int val);
2016 int isl_options_get_coalesce_bounded_wrapping(
2019 =item * Detecting equalities
2021 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2022 __isl_take isl_basic_set *bset);
2023 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2024 __isl_take isl_basic_map *bmap);
2025 __isl_give isl_set *isl_set_detect_equalities(
2026 __isl_take isl_set *set);
2027 __isl_give isl_map *isl_map_detect_equalities(
2028 __isl_take isl_map *map);
2029 __isl_give isl_union_set *isl_union_set_detect_equalities(
2030 __isl_take isl_union_set *uset);
2031 __isl_give isl_union_map *isl_union_map_detect_equalities(
2032 __isl_take isl_union_map *umap);
2034 Simplify the representation of a set or relation by detecting implicit
2037 =item * Removing redundant constraints
2039 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2040 __isl_take isl_basic_set *bset);
2041 __isl_give isl_set *isl_set_remove_redundancies(
2042 __isl_take isl_set *set);
2043 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2044 __isl_take isl_basic_map *bmap);
2045 __isl_give isl_map *isl_map_remove_redundancies(
2046 __isl_take isl_map *map);
2050 __isl_give isl_basic_set *isl_set_convex_hull(
2051 __isl_take isl_set *set);
2052 __isl_give isl_basic_map *isl_map_convex_hull(
2053 __isl_take isl_map *map);
2055 If the input set or relation has any existentially quantified
2056 variables, then the result of these operations is currently undefined.
2060 __isl_give isl_basic_set *isl_set_simple_hull(
2061 __isl_take isl_set *set);
2062 __isl_give isl_basic_map *isl_map_simple_hull(
2063 __isl_take isl_map *map);
2064 __isl_give isl_union_map *isl_union_map_simple_hull(
2065 __isl_take isl_union_map *umap);
2067 These functions compute a single basic set or relation
2068 that contains the whole input set or relation.
2069 In particular, the output is described by translates
2070 of the constraints describing the basic sets or relations in the input.
2074 (See \autoref{s:simple hull}.)
2080 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2081 __isl_take isl_basic_set *bset);
2082 __isl_give isl_basic_set *isl_set_affine_hull(
2083 __isl_take isl_set *set);
2084 __isl_give isl_union_set *isl_union_set_affine_hull(
2085 __isl_take isl_union_set *uset);
2086 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2087 __isl_take isl_basic_map *bmap);
2088 __isl_give isl_basic_map *isl_map_affine_hull(
2089 __isl_take isl_map *map);
2090 __isl_give isl_union_map *isl_union_map_affine_hull(
2091 __isl_take isl_union_map *umap);
2093 In case of union sets and relations, the affine hull is computed
2096 =item * Polyhedral hull
2098 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2099 __isl_take isl_set *set);
2100 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2101 __isl_take isl_map *map);
2102 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2103 __isl_take isl_union_set *uset);
2104 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2105 __isl_take isl_union_map *umap);
2107 These functions compute a single basic set or relation
2108 not involving any existentially quantified variables
2109 that contains the whole input set or relation.
2110 In case of union sets and relations, the polyhedral hull is computed
2115 __isl_give isl_basic_set *isl_basic_set_sample(
2116 __isl_take isl_basic_set *bset);
2117 __isl_give isl_basic_set *isl_set_sample(
2118 __isl_take isl_set *set);
2119 __isl_give isl_basic_map *isl_basic_map_sample(
2120 __isl_take isl_basic_map *bmap);
2121 __isl_give isl_basic_map *isl_map_sample(
2122 __isl_take isl_map *map);
2124 If the input (basic) set or relation is non-empty, then return
2125 a singleton subset of the input. Otherwise, return an empty set.
2127 =item * Optimization
2129 #include <isl/ilp.h>
2130 enum isl_lp_result isl_basic_set_max(
2131 __isl_keep isl_basic_set *bset,
2132 __isl_keep isl_aff *obj, isl_int *opt)
2133 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2134 __isl_keep isl_aff *obj, isl_int *opt);
2135 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2136 __isl_keep isl_aff *obj, isl_int *opt);
2138 Compute the minimum or maximum of the integer affine expression C<obj>
2139 over the points in C<set>, returning the result in C<opt>.
2140 The return value may be one of C<isl_lp_error>,
2141 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2143 =item * Parametric optimization
2145 __isl_give isl_pw_aff *isl_set_dim_min(
2146 __isl_take isl_set *set, int pos);
2147 __isl_give isl_pw_aff *isl_set_dim_max(
2148 __isl_take isl_set *set, int pos);
2149 __isl_give isl_pw_aff *isl_map_dim_max(
2150 __isl_take isl_map *map, int pos);
2152 Compute the minimum or maximum of the given set or output dimension
2153 as a function of the parameters (and input dimensions), but independently
2154 of the other set or output dimensions.
2155 For lexicographic optimization, see L<"Lexicographic Optimization">.
2159 The following functions compute either the set of (rational) coefficient
2160 values of valid constraints for the given set or the set of (rational)
2161 values satisfying the constraints with coefficients from the given set.
2162 Internally, these two sets of functions perform essentially the
2163 same operations, except that the set of coefficients is assumed to
2164 be a cone, while the set of values may be any polyhedron.
2165 The current implementation is based on the Farkas lemma and
2166 Fourier-Motzkin elimination, but this may change or be made optional
2167 in future. In particular, future implementations may use different
2168 dualization algorithms or skip the elimination step.
2170 __isl_give isl_basic_set *isl_basic_set_coefficients(
2171 __isl_take isl_basic_set *bset);
2172 __isl_give isl_basic_set *isl_set_coefficients(
2173 __isl_take isl_set *set);
2174 __isl_give isl_union_set *isl_union_set_coefficients(
2175 __isl_take isl_union_set *bset);
2176 __isl_give isl_basic_set *isl_basic_set_solutions(
2177 __isl_take isl_basic_set *bset);
2178 __isl_give isl_basic_set *isl_set_solutions(
2179 __isl_take isl_set *set);
2180 __isl_give isl_union_set *isl_union_set_solutions(
2181 __isl_take isl_union_set *bset);
2185 __isl_give isl_map *isl_map_fixed_power(
2186 __isl_take isl_map *map, isl_int exp);
2187 __isl_give isl_union_map *isl_union_map_fixed_power(
2188 __isl_take isl_union_map *umap, isl_int exp);
2190 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2191 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2192 of C<map> is computed.
2194 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2196 __isl_give isl_union_map *isl_union_map_power(
2197 __isl_take isl_union_map *umap, int *exact);
2199 Compute a parametric representation for all positive powers I<k> of C<map>.
2200 The result maps I<k> to a nested relation corresponding to the
2201 I<k>th power of C<map>.
2202 The result may be an overapproximation. If the result is known to be exact,
2203 then C<*exact> is set to C<1>.
2205 =item * Transitive closure
2207 __isl_give isl_map *isl_map_transitive_closure(
2208 __isl_take isl_map *map, int *exact);
2209 __isl_give isl_union_map *isl_union_map_transitive_closure(
2210 __isl_take isl_union_map *umap, int *exact);
2212 Compute the transitive closure of C<map>.
2213 The result may be an overapproximation. If the result is known to be exact,
2214 then C<*exact> is set to C<1>.
2216 =item * Reaching path lengths
2218 __isl_give isl_map *isl_map_reaching_path_lengths(
2219 __isl_take isl_map *map, int *exact);
2221 Compute a relation that maps each element in the range of C<map>
2222 to the lengths of all paths composed of edges in C<map> that
2223 end up in the given element.
2224 The result may be an overapproximation. If the result is known to be exact,
2225 then C<*exact> is set to C<1>.
2226 To compute the I<maximal> path length, the resulting relation
2227 should be postprocessed by C<isl_map_lexmax>.
2228 In particular, if the input relation is a dependence relation
2229 (mapping sources to sinks), then the maximal path length corresponds
2230 to the free schedule.
2231 Note, however, that C<isl_map_lexmax> expects the maximum to be
2232 finite, so if the path lengths are unbounded (possibly due to
2233 the overapproximation), then you will get an error message.
2237 __isl_give isl_basic_set *isl_basic_map_wrap(
2238 __isl_take isl_basic_map *bmap);
2239 __isl_give isl_set *isl_map_wrap(
2240 __isl_take isl_map *map);
2241 __isl_give isl_union_set *isl_union_map_wrap(
2242 __isl_take isl_union_map *umap);
2243 __isl_give isl_basic_map *isl_basic_set_unwrap(
2244 __isl_take isl_basic_set *bset);
2245 __isl_give isl_map *isl_set_unwrap(
2246 __isl_take isl_set *set);
2247 __isl_give isl_union_map *isl_union_set_unwrap(
2248 __isl_take isl_union_set *uset);
2252 Remove any internal structure of domain (and range) of the given
2253 set or relation. If there is any such internal structure in the input,
2254 then the name of the space is also removed.
2256 __isl_give isl_basic_set *isl_basic_set_flatten(
2257 __isl_take isl_basic_set *bset);
2258 __isl_give isl_set *isl_set_flatten(
2259 __isl_take isl_set *set);
2260 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2261 __isl_take isl_basic_map *bmap);
2262 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2263 __isl_take isl_basic_map *bmap);
2264 __isl_give isl_map *isl_map_flatten_range(
2265 __isl_take isl_map *map);
2266 __isl_give isl_map *isl_map_flatten_domain(
2267 __isl_take isl_map *map);
2268 __isl_give isl_basic_map *isl_basic_map_flatten(
2269 __isl_take isl_basic_map *bmap);
2270 __isl_give isl_map *isl_map_flatten(
2271 __isl_take isl_map *map);
2273 __isl_give isl_map *isl_set_flatten_map(
2274 __isl_take isl_set *set);
2276 The function above constructs a relation
2277 that maps the input set to a flattened version of the set.
2281 Lift the input set to a space with extra dimensions corresponding
2282 to the existentially quantified variables in the input.
2283 In particular, the result lives in a wrapped map where the domain
2284 is the original space and the range corresponds to the original
2285 existentially quantified variables.
2287 __isl_give isl_basic_set *isl_basic_set_lift(
2288 __isl_take isl_basic_set *bset);
2289 __isl_give isl_set *isl_set_lift(
2290 __isl_take isl_set *set);
2291 __isl_give isl_union_set *isl_union_set_lift(
2292 __isl_take isl_union_set *uset);
2294 Given a local space that contains the existentially quantified
2295 variables of a set, a basic relation that, when applied to
2296 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2297 can be constructed using the following function.
2299 #include <isl/local_space.h>
2300 __isl_give isl_basic_map *isl_local_space_lifting(
2301 __isl_take isl_local_space *ls);
2303 =item * Internal Product
2305 __isl_give isl_basic_map *isl_basic_map_zip(
2306 __isl_take isl_basic_map *bmap);
2307 __isl_give isl_map *isl_map_zip(
2308 __isl_take isl_map *map);
2309 __isl_give isl_union_map *isl_union_map_zip(
2310 __isl_take isl_union_map *umap);
2312 Given a relation with nested relations for domain and range,
2313 interchange the range of the domain with the domain of the range.
2317 __isl_give isl_basic_map *isl_basic_map_curry(
2318 __isl_take isl_basic_map *bmap);
2319 __isl_give isl_map *isl_map_curry(
2320 __isl_take isl_map *map);
2321 __isl_give isl_union_map *isl_union_map_curry(
2322 __isl_take isl_union_map *umap);
2324 Given a relation with a nested relation for domain,
2325 move the range of the nested relation out of the domain
2326 and use it as the domain of a nested relation in the range,
2327 with the original range as range of this nested relation.
2329 =item * Aligning parameters
2331 __isl_give isl_set *isl_set_align_params(
2332 __isl_take isl_set *set,
2333 __isl_take isl_space *model);
2334 __isl_give isl_map *isl_map_align_params(
2335 __isl_take isl_map *map,
2336 __isl_take isl_space *model);
2338 Change the order of the parameters of the given set or relation
2339 such that the first parameters match those of C<model>.
2340 This may involve the introduction of extra parameters.
2341 All parameters need to be named.
2343 =item * Dimension manipulation
2345 __isl_give isl_set *isl_set_add_dims(
2346 __isl_take isl_set *set,
2347 enum isl_dim_type type, unsigned n);
2348 __isl_give isl_map *isl_map_add_dims(
2349 __isl_take isl_map *map,
2350 enum isl_dim_type type, unsigned n);
2351 __isl_give isl_set *isl_set_insert_dims(
2352 __isl_take isl_set *set,
2353 enum isl_dim_type type, unsigned pos, unsigned n);
2354 __isl_give isl_map *isl_map_insert_dims(
2355 __isl_take isl_map *map,
2356 enum isl_dim_type type, unsigned pos, unsigned n);
2357 __isl_give isl_basic_set *isl_basic_set_move_dims(
2358 __isl_take isl_basic_set *bset,
2359 enum isl_dim_type dst_type, unsigned dst_pos,
2360 enum isl_dim_type src_type, unsigned src_pos,
2362 __isl_give isl_basic_map *isl_basic_map_move_dims(
2363 __isl_take isl_basic_map *bmap,
2364 enum isl_dim_type dst_type, unsigned dst_pos,
2365 enum isl_dim_type src_type, unsigned src_pos,
2367 __isl_give isl_set *isl_set_move_dims(
2368 __isl_take isl_set *set,
2369 enum isl_dim_type dst_type, unsigned dst_pos,
2370 enum isl_dim_type src_type, unsigned src_pos,
2372 __isl_give isl_map *isl_map_move_dims(
2373 __isl_take isl_map *map,
2374 enum isl_dim_type dst_type, unsigned dst_pos,
2375 enum isl_dim_type src_type, unsigned src_pos,
2378 It is usually not advisable to directly change the (input or output)
2379 space of a set or a relation as this removes the name and the internal
2380 structure of the space. However, the above functions can be useful
2381 to add new parameters, assuming
2382 C<isl_set_align_params> and C<isl_map_align_params>
2387 =head2 Binary Operations
2389 The two arguments of a binary operation not only need to live
2390 in the same C<isl_ctx>, they currently also need to have
2391 the same (number of) parameters.
2393 =head3 Basic Operations
2397 =item * Intersection
2399 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2400 __isl_take isl_basic_set *bset1,
2401 __isl_take isl_basic_set *bset2);
2402 __isl_give isl_basic_set *isl_basic_set_intersect(
2403 __isl_take isl_basic_set *bset1,
2404 __isl_take isl_basic_set *bset2);
2405 __isl_give isl_set *isl_set_intersect_params(
2406 __isl_take isl_set *set,
2407 __isl_take isl_set *params);
2408 __isl_give isl_set *isl_set_intersect(
2409 __isl_take isl_set *set1,
2410 __isl_take isl_set *set2);
2411 __isl_give isl_union_set *isl_union_set_intersect_params(
2412 __isl_take isl_union_set *uset,
2413 __isl_take isl_set *set);
2414 __isl_give isl_union_map *isl_union_map_intersect_params(
2415 __isl_take isl_union_map *umap,
2416 __isl_take isl_set *set);
2417 __isl_give isl_union_set *isl_union_set_intersect(
2418 __isl_take isl_union_set *uset1,
2419 __isl_take isl_union_set *uset2);
2420 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2421 __isl_take isl_basic_map *bmap,
2422 __isl_take isl_basic_set *bset);
2423 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2424 __isl_take isl_basic_map *bmap,
2425 __isl_take isl_basic_set *bset);
2426 __isl_give isl_basic_map *isl_basic_map_intersect(
2427 __isl_take isl_basic_map *bmap1,
2428 __isl_take isl_basic_map *bmap2);
2429 __isl_give isl_map *isl_map_intersect_params(
2430 __isl_take isl_map *map,
2431 __isl_take isl_set *params);
2432 __isl_give isl_map *isl_map_intersect_domain(
2433 __isl_take isl_map *map,
2434 __isl_take isl_set *set);
2435 __isl_give isl_map *isl_map_intersect_range(
2436 __isl_take isl_map *map,
2437 __isl_take isl_set *set);
2438 __isl_give isl_map *isl_map_intersect(
2439 __isl_take isl_map *map1,
2440 __isl_take isl_map *map2);
2441 __isl_give isl_union_map *isl_union_map_intersect_domain(
2442 __isl_take isl_union_map *umap,
2443 __isl_take isl_union_set *uset);
2444 __isl_give isl_union_map *isl_union_map_intersect_range(
2445 __isl_take isl_union_map *umap,
2446 __isl_take isl_union_set *uset);
2447 __isl_give isl_union_map *isl_union_map_intersect(
2448 __isl_take isl_union_map *umap1,
2449 __isl_take isl_union_map *umap2);
2453 __isl_give isl_set *isl_basic_set_union(
2454 __isl_take isl_basic_set *bset1,
2455 __isl_take isl_basic_set *bset2);
2456 __isl_give isl_map *isl_basic_map_union(
2457 __isl_take isl_basic_map *bmap1,
2458 __isl_take isl_basic_map *bmap2);
2459 __isl_give isl_set *isl_set_union(
2460 __isl_take isl_set *set1,
2461 __isl_take isl_set *set2);
2462 __isl_give isl_map *isl_map_union(
2463 __isl_take isl_map *map1,
2464 __isl_take isl_map *map2);
2465 __isl_give isl_union_set *isl_union_set_union(
2466 __isl_take isl_union_set *uset1,
2467 __isl_take isl_union_set *uset2);
2468 __isl_give isl_union_map *isl_union_map_union(
2469 __isl_take isl_union_map *umap1,
2470 __isl_take isl_union_map *umap2);
2472 =item * Set difference
2474 __isl_give isl_set *isl_set_subtract(
2475 __isl_take isl_set *set1,
2476 __isl_take isl_set *set2);
2477 __isl_give isl_map *isl_map_subtract(
2478 __isl_take isl_map *map1,
2479 __isl_take isl_map *map2);
2480 __isl_give isl_map *isl_map_subtract_domain(
2481 __isl_take isl_map *map,
2482 __isl_take isl_set *dom);
2483 __isl_give isl_map *isl_map_subtract_range(
2484 __isl_take isl_map *map,
2485 __isl_take isl_set *dom);
2486 __isl_give isl_union_set *isl_union_set_subtract(
2487 __isl_take isl_union_set *uset1,
2488 __isl_take isl_union_set *uset2);
2489 __isl_give isl_union_map *isl_union_map_subtract(
2490 __isl_take isl_union_map *umap1,
2491 __isl_take isl_union_map *umap2);
2495 __isl_give isl_basic_set *isl_basic_set_apply(
2496 __isl_take isl_basic_set *bset,
2497 __isl_take isl_basic_map *bmap);
2498 __isl_give isl_set *isl_set_apply(
2499 __isl_take isl_set *set,
2500 __isl_take isl_map *map);
2501 __isl_give isl_union_set *isl_union_set_apply(
2502 __isl_take isl_union_set *uset,
2503 __isl_take isl_union_map *umap);
2504 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2505 __isl_take isl_basic_map *bmap1,
2506 __isl_take isl_basic_map *bmap2);
2507 __isl_give isl_basic_map *isl_basic_map_apply_range(
2508 __isl_take isl_basic_map *bmap1,
2509 __isl_take isl_basic_map *bmap2);
2510 __isl_give isl_map *isl_map_apply_domain(
2511 __isl_take isl_map *map1,
2512 __isl_take isl_map *map2);
2513 __isl_give isl_union_map *isl_union_map_apply_domain(
2514 __isl_take isl_union_map *umap1,
2515 __isl_take isl_union_map *umap2);
2516 __isl_give isl_map *isl_map_apply_range(
2517 __isl_take isl_map *map1,
2518 __isl_take isl_map *map2);
2519 __isl_give isl_union_map *isl_union_map_apply_range(
2520 __isl_take isl_union_map *umap1,
2521 __isl_take isl_union_map *umap2);
2523 =item * Cartesian Product
2525 __isl_give isl_set *isl_set_product(
2526 __isl_take isl_set *set1,
2527 __isl_take isl_set *set2);
2528 __isl_give isl_union_set *isl_union_set_product(
2529 __isl_take isl_union_set *uset1,
2530 __isl_take isl_union_set *uset2);
2531 __isl_give isl_basic_map *isl_basic_map_domain_product(
2532 __isl_take isl_basic_map *bmap1,
2533 __isl_take isl_basic_map *bmap2);
2534 __isl_give isl_basic_map *isl_basic_map_range_product(
2535 __isl_take isl_basic_map *bmap1,
2536 __isl_take isl_basic_map *bmap2);
2537 __isl_give isl_map *isl_map_domain_product(
2538 __isl_take isl_map *map1,
2539 __isl_take isl_map *map2);
2540 __isl_give isl_map *isl_map_range_product(
2541 __isl_take isl_map *map1,
2542 __isl_take isl_map *map2);
2543 __isl_give isl_union_map *isl_union_map_range_product(
2544 __isl_take isl_union_map *umap1,
2545 __isl_take isl_union_map *umap2);
2546 __isl_give isl_map *isl_map_product(
2547 __isl_take isl_map *map1,
2548 __isl_take isl_map *map2);
2549 __isl_give isl_union_map *isl_union_map_product(
2550 __isl_take isl_union_map *umap1,
2551 __isl_take isl_union_map *umap2);
2553 The above functions compute the cross product of the given
2554 sets or relations. The domains and ranges of the results
2555 are wrapped maps between domains and ranges of the inputs.
2556 To obtain a ``flat'' product, use the following functions
2559 __isl_give isl_basic_set *isl_basic_set_flat_product(
2560 __isl_take isl_basic_set *bset1,
2561 __isl_take isl_basic_set *bset2);
2562 __isl_give isl_set *isl_set_flat_product(
2563 __isl_take isl_set *set1,
2564 __isl_take isl_set *set2);
2565 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2566 __isl_take isl_basic_map *bmap1,
2567 __isl_take isl_basic_map *bmap2);
2568 __isl_give isl_map *isl_map_flat_domain_product(
2569 __isl_take isl_map *map1,
2570 __isl_take isl_map *map2);
2571 __isl_give isl_map *isl_map_flat_range_product(
2572 __isl_take isl_map *map1,
2573 __isl_take isl_map *map2);
2574 __isl_give isl_union_map *isl_union_map_flat_range_product(
2575 __isl_take isl_union_map *umap1,
2576 __isl_take isl_union_map *umap2);
2577 __isl_give isl_basic_map *isl_basic_map_flat_product(
2578 __isl_take isl_basic_map *bmap1,
2579 __isl_take isl_basic_map *bmap2);
2580 __isl_give isl_map *isl_map_flat_product(
2581 __isl_take isl_map *map1,
2582 __isl_take isl_map *map2);
2584 =item * Simplification
2586 __isl_give isl_basic_set *isl_basic_set_gist(
2587 __isl_take isl_basic_set *bset,
2588 __isl_take isl_basic_set *context);
2589 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2590 __isl_take isl_set *context);
2591 __isl_give isl_set *isl_set_gist_params(
2592 __isl_take isl_set *set,
2593 __isl_take isl_set *context);
2594 __isl_give isl_union_set *isl_union_set_gist(
2595 __isl_take isl_union_set *uset,
2596 __isl_take isl_union_set *context);
2597 __isl_give isl_union_set *isl_union_set_gist_params(
2598 __isl_take isl_union_set *uset,
2599 __isl_take isl_set *set);
2600 __isl_give isl_basic_map *isl_basic_map_gist(
2601 __isl_take isl_basic_map *bmap,
2602 __isl_take isl_basic_map *context);
2603 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2604 __isl_take isl_map *context);
2605 __isl_give isl_map *isl_map_gist_params(
2606 __isl_take isl_map *map,
2607 __isl_take isl_set *context);
2608 __isl_give isl_map *isl_map_gist_domain(
2609 __isl_take isl_map *map,
2610 __isl_take isl_set *context);
2611 __isl_give isl_map *isl_map_gist_range(
2612 __isl_take isl_map *map,
2613 __isl_take isl_set *context);
2614 __isl_give isl_union_map *isl_union_map_gist(
2615 __isl_take isl_union_map *umap,
2616 __isl_take isl_union_map *context);
2617 __isl_give isl_union_map *isl_union_map_gist_params(
2618 __isl_take isl_union_map *umap,
2619 __isl_take isl_set *set);
2620 __isl_give isl_union_map *isl_union_map_gist_domain(
2621 __isl_take isl_union_map *umap,
2622 __isl_take isl_union_set *uset);
2623 __isl_give isl_union_map *isl_union_map_gist_range(
2624 __isl_take isl_union_map *umap,
2625 __isl_take isl_union_set *uset);
2627 The gist operation returns a set or relation that has the
2628 same intersection with the context as the input set or relation.
2629 Any implicit equality in the intersection is made explicit in the result,
2630 while all inequalities that are redundant with respect to the intersection
2632 In case of union sets and relations, the gist operation is performed
2637 =head3 Lexicographic Optimization
2639 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2640 the following functions
2641 compute a set that contains the lexicographic minimum or maximum
2642 of the elements in C<set> (or C<bset>) for those values of the parameters
2643 that satisfy C<dom>.
2644 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2645 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2647 In other words, the union of the parameter values
2648 for which the result is non-empty and of C<*empty>
2651 __isl_give isl_set *isl_basic_set_partial_lexmin(
2652 __isl_take isl_basic_set *bset,
2653 __isl_take isl_basic_set *dom,
2654 __isl_give isl_set **empty);
2655 __isl_give isl_set *isl_basic_set_partial_lexmax(
2656 __isl_take isl_basic_set *bset,
2657 __isl_take isl_basic_set *dom,
2658 __isl_give isl_set **empty);
2659 __isl_give isl_set *isl_set_partial_lexmin(
2660 __isl_take isl_set *set, __isl_take isl_set *dom,
2661 __isl_give isl_set **empty);
2662 __isl_give isl_set *isl_set_partial_lexmax(
2663 __isl_take isl_set *set, __isl_take isl_set *dom,
2664 __isl_give isl_set **empty);
2666 Given a (basic) set C<set> (or C<bset>), the following functions simply
2667 return a set containing the lexicographic minimum or maximum
2668 of the elements in C<set> (or C<bset>).
2669 In case of union sets, the optimum is computed per space.
2671 __isl_give isl_set *isl_basic_set_lexmin(
2672 __isl_take isl_basic_set *bset);
2673 __isl_give isl_set *isl_basic_set_lexmax(
2674 __isl_take isl_basic_set *bset);
2675 __isl_give isl_set *isl_set_lexmin(
2676 __isl_take isl_set *set);
2677 __isl_give isl_set *isl_set_lexmax(
2678 __isl_take isl_set *set);
2679 __isl_give isl_union_set *isl_union_set_lexmin(
2680 __isl_take isl_union_set *uset);
2681 __isl_give isl_union_set *isl_union_set_lexmax(
2682 __isl_take isl_union_set *uset);
2684 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2685 the following functions
2686 compute a relation that maps each element of C<dom>
2687 to the single lexicographic minimum or maximum
2688 of the elements that are associated to that same
2689 element in C<map> (or C<bmap>).
2690 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2691 that contains the elements in C<dom> that do not map
2692 to any elements in C<map> (or C<bmap>).
2693 In other words, the union of the domain of the result and of C<*empty>
2696 __isl_give isl_map *isl_basic_map_partial_lexmax(
2697 __isl_take isl_basic_map *bmap,
2698 __isl_take isl_basic_set *dom,
2699 __isl_give isl_set **empty);
2700 __isl_give isl_map *isl_basic_map_partial_lexmin(
2701 __isl_take isl_basic_map *bmap,
2702 __isl_take isl_basic_set *dom,
2703 __isl_give isl_set **empty);
2704 __isl_give isl_map *isl_map_partial_lexmax(
2705 __isl_take isl_map *map, __isl_take isl_set *dom,
2706 __isl_give isl_set **empty);
2707 __isl_give isl_map *isl_map_partial_lexmin(
2708 __isl_take isl_map *map, __isl_take isl_set *dom,
2709 __isl_give isl_set **empty);
2711 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2712 return a map mapping each element in the domain of
2713 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2714 of all elements associated to that element.
2715 In case of union relations, the optimum is computed per space.
2717 __isl_give isl_map *isl_basic_map_lexmin(
2718 __isl_take isl_basic_map *bmap);
2719 __isl_give isl_map *isl_basic_map_lexmax(
2720 __isl_take isl_basic_map *bmap);
2721 __isl_give isl_map *isl_map_lexmin(
2722 __isl_take isl_map *map);
2723 __isl_give isl_map *isl_map_lexmax(
2724 __isl_take isl_map *map);
2725 __isl_give isl_union_map *isl_union_map_lexmin(
2726 __isl_take isl_union_map *umap);
2727 __isl_give isl_union_map *isl_union_map_lexmax(
2728 __isl_take isl_union_map *umap);
2730 The following functions return their result in the form of
2731 a piecewise multi-affine expression
2732 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2733 but are otherwise equivalent to the corresponding functions
2734 returning a basic set or relation.
2736 __isl_give isl_pw_multi_aff *
2737 isl_basic_map_lexmin_pw_multi_aff(
2738 __isl_take isl_basic_map *bmap);
2739 __isl_give isl_pw_multi_aff *
2740 isl_basic_set_partial_lexmin_pw_multi_aff(
2741 __isl_take isl_basic_set *bset,
2742 __isl_take isl_basic_set *dom,
2743 __isl_give isl_set **empty);
2744 __isl_give isl_pw_multi_aff *
2745 isl_basic_set_partial_lexmax_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_map_partial_lexmin_pw_multi_aff(
2751 __isl_take isl_basic_map *bmap,
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_lexmax_pw_multi_aff(
2756 __isl_take isl_basic_map *bmap,
2757 __isl_take isl_basic_set *dom,
2758 __isl_give isl_set **empty);
2762 Lists are defined over several element types, including
2763 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2764 Here we take lists of C<isl_set>s as an example.
2765 Lists can be created, copied and freed using the following functions.
2767 #include <isl/list.h>
2768 __isl_give isl_set_list *isl_set_list_from_set(
2769 __isl_take isl_set *el);
2770 __isl_give isl_set_list *isl_set_list_alloc(
2771 isl_ctx *ctx, int n);
2772 __isl_give isl_set_list *isl_set_list_copy(
2773 __isl_keep isl_set_list *list);
2774 __isl_give isl_set_list *isl_set_list_add(
2775 __isl_take isl_set_list *list,
2776 __isl_take isl_set *el);
2777 __isl_give isl_set_list *isl_set_list_concat(
2778 __isl_take isl_set_list *list1,
2779 __isl_take isl_set_list *list2);
2780 void *isl_set_list_free(__isl_take isl_set_list *list);
2782 C<isl_set_list_alloc> creates an empty list with a capacity for
2783 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2786 Lists can be inspected using the following functions.
2788 #include <isl/list.h>
2789 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2790 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2791 __isl_give isl_set *isl_set_list_get_set(
2792 __isl_keep isl_set_list *list, int index);
2793 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2794 int (*fn)(__isl_take isl_set *el, void *user),
2797 Lists can be printed using
2799 #include <isl/list.h>
2800 __isl_give isl_printer *isl_printer_print_set_list(
2801 __isl_take isl_printer *p,
2802 __isl_keep isl_set_list *list);
2806 Vectors can be created, copied and freed using the following functions.
2808 #include <isl/vec.h>
2809 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2811 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2812 void isl_vec_free(__isl_take isl_vec *vec);
2814 Note that the elements of a newly created vector may have arbitrary values.
2815 The elements can be changed and inspected using the following functions.
2817 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2818 int isl_vec_size(__isl_keep isl_vec *vec);
2819 int isl_vec_get_element(__isl_keep isl_vec *vec,
2820 int pos, isl_int *v);
2821 __isl_give isl_vec *isl_vec_set_element(
2822 __isl_take isl_vec *vec, int pos, isl_int v);
2823 __isl_give isl_vec *isl_vec_set_element_si(
2824 __isl_take isl_vec *vec, int pos, int v);
2825 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2827 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2830 C<isl_vec_get_element> will return a negative value if anything went wrong.
2831 In that case, the value of C<*v> is undefined.
2835 Matrices can be created, copied and freed using the following functions.
2837 #include <isl/mat.h>
2838 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2839 unsigned n_row, unsigned n_col);
2840 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2841 void isl_mat_free(__isl_take isl_mat *mat);
2843 Note that the elements of a newly created matrix may have arbitrary values.
2844 The elements can be changed and inspected using the following functions.
2846 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2847 int isl_mat_rows(__isl_keep isl_mat *mat);
2848 int isl_mat_cols(__isl_keep isl_mat *mat);
2849 int isl_mat_get_element(__isl_keep isl_mat *mat,
2850 int row, int col, isl_int *v);
2851 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2852 int row, int col, isl_int v);
2853 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2854 int row, int col, int v);
2856 C<isl_mat_get_element> will return a negative value if anything went wrong.
2857 In that case, the value of C<*v> is undefined.
2859 The following function can be used to compute the (right) inverse
2860 of a matrix, i.e., a matrix such that the product of the original
2861 and the inverse (in that order) is a multiple of the identity matrix.
2862 The input matrix is assumed to be of full row-rank.
2864 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2866 The following function can be used to compute the (right) kernel
2867 (or null space) of a matrix, i.e., a matrix such that the product of
2868 the original and the kernel (in that order) is the zero matrix.
2870 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2872 =head2 Piecewise Quasi Affine Expressions
2874 The zero quasi affine expression on a given domain can be created using
2876 __isl_give isl_aff *isl_aff_zero_on_domain(
2877 __isl_take isl_local_space *ls);
2879 Note that the space in which the resulting object lives is a map space
2880 with the given space as domain and a one-dimensional range.
2882 An empty piecewise quasi affine expression (one with no cells)
2883 or a piecewise quasi affine expression with a single cell can
2884 be created using the following functions.
2886 #include <isl/aff.h>
2887 __isl_give isl_pw_aff *isl_pw_aff_empty(
2888 __isl_take isl_space *space);
2889 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2890 __isl_take isl_set *set, __isl_take isl_aff *aff);
2891 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2892 __isl_take isl_aff *aff);
2894 A piecewise quasi affine expression that is equal to 1 on a set
2895 and 0 outside the set can be created using the following function.
2897 #include <isl/aff.h>
2898 __isl_give isl_pw_aff *isl_set_indicator_function(
2899 __isl_take isl_set *set);
2901 Quasi affine expressions can be copied and freed using
2903 #include <isl/aff.h>
2904 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2905 void *isl_aff_free(__isl_take isl_aff *aff);
2907 __isl_give isl_pw_aff *isl_pw_aff_copy(
2908 __isl_keep isl_pw_aff *pwaff);
2909 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2911 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2912 using the following function. The constraint is required to have
2913 a non-zero coefficient for the specified dimension.
2915 #include <isl/constraint.h>
2916 __isl_give isl_aff *isl_constraint_get_bound(
2917 __isl_keep isl_constraint *constraint,
2918 enum isl_dim_type type, int pos);
2920 The entire affine expression of the constraint can also be extracted
2921 using the following function.
2923 #include <isl/constraint.h>
2924 __isl_give isl_aff *isl_constraint_get_aff(
2925 __isl_keep isl_constraint *constraint);
2927 Conversely, an equality constraint equating
2928 the affine expression to zero or an inequality constraint enforcing
2929 the affine expression to be non-negative, can be constructed using
2931 __isl_give isl_constraint *isl_equality_from_aff(
2932 __isl_take isl_aff *aff);
2933 __isl_give isl_constraint *isl_inequality_from_aff(
2934 __isl_take isl_aff *aff);
2936 The expression can be inspected using
2938 #include <isl/aff.h>
2939 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2940 int isl_aff_dim(__isl_keep isl_aff *aff,
2941 enum isl_dim_type type);
2942 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2943 __isl_keep isl_aff *aff);
2944 __isl_give isl_local_space *isl_aff_get_local_space(
2945 __isl_keep isl_aff *aff);
2946 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2947 enum isl_dim_type type, unsigned pos);
2948 const char *isl_pw_aff_get_dim_name(
2949 __isl_keep isl_pw_aff *pa,
2950 enum isl_dim_type type, unsigned pos);
2951 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2952 enum isl_dim_type type, unsigned pos);
2953 __isl_give isl_id *isl_pw_aff_get_dim_id(
2954 __isl_keep isl_pw_aff *pa,
2955 enum isl_dim_type type, unsigned pos);
2956 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2958 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2959 enum isl_dim_type type, int pos, isl_int *v);
2960 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2962 __isl_give isl_aff *isl_aff_get_div(
2963 __isl_keep isl_aff *aff, int pos);
2965 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2966 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2967 int (*fn)(__isl_take isl_set *set,
2968 __isl_take isl_aff *aff,
2969 void *user), void *user);
2971 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2972 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2974 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2975 enum isl_dim_type type, unsigned first, unsigned n);
2976 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2977 enum isl_dim_type type, unsigned first, unsigned n);
2979 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2980 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2981 enum isl_dim_type type);
2982 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2984 It can be modified using
2986 #include <isl/aff.h>
2987 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
2988 __isl_take isl_pw_aff *pwaff,
2989 enum isl_dim_type type, __isl_take isl_id *id);
2990 __isl_give isl_aff *isl_aff_set_dim_name(
2991 __isl_take isl_aff *aff, enum isl_dim_type type,
2992 unsigned pos, const char *s);
2993 __isl_give isl_aff *isl_aff_set_dim_id(
2994 __isl_take isl_aff *aff, enum isl_dim_type type,
2995 unsigned pos, __isl_take isl_id *id);
2996 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
2997 __isl_take isl_pw_aff *pma,
2998 enum isl_dim_type type, unsigned pos,
2999 __isl_take isl_id *id);
3000 __isl_give isl_aff *isl_aff_set_constant(
3001 __isl_take isl_aff *aff, isl_int v);
3002 __isl_give isl_aff *isl_aff_set_constant_si(
3003 __isl_take isl_aff *aff, int v);
3004 __isl_give isl_aff *isl_aff_set_coefficient(
3005 __isl_take isl_aff *aff,
3006 enum isl_dim_type type, int pos, isl_int v);
3007 __isl_give isl_aff *isl_aff_set_coefficient_si(
3008 __isl_take isl_aff *aff,
3009 enum isl_dim_type type, int pos, int v);
3010 __isl_give isl_aff *isl_aff_set_denominator(
3011 __isl_take isl_aff *aff, isl_int v);
3013 __isl_give isl_aff *isl_aff_add_constant(
3014 __isl_take isl_aff *aff, isl_int v);
3015 __isl_give isl_aff *isl_aff_add_constant_si(
3016 __isl_take isl_aff *aff, int v);
3017 __isl_give isl_aff *isl_aff_add_coefficient(
3018 __isl_take isl_aff *aff,
3019 enum isl_dim_type type, int pos, isl_int v);
3020 __isl_give isl_aff *isl_aff_add_coefficient_si(
3021 __isl_take isl_aff *aff,
3022 enum isl_dim_type type, int pos, int v);
3024 __isl_give isl_aff *isl_aff_insert_dims(
3025 __isl_take isl_aff *aff,
3026 enum isl_dim_type type, unsigned first, unsigned n);
3027 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3028 __isl_take isl_pw_aff *pwaff,
3029 enum isl_dim_type type, unsigned first, unsigned n);
3030 __isl_give isl_aff *isl_aff_add_dims(
3031 __isl_take isl_aff *aff,
3032 enum isl_dim_type type, unsigned n);
3033 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3034 __isl_take isl_pw_aff *pwaff,
3035 enum isl_dim_type type, unsigned n);
3036 __isl_give isl_aff *isl_aff_drop_dims(
3037 __isl_take isl_aff *aff,
3038 enum isl_dim_type type, unsigned first, unsigned n);
3039 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3040 __isl_take isl_pw_aff *pwaff,
3041 enum isl_dim_type type, unsigned first, unsigned n);
3043 Note that the C<set_constant> and C<set_coefficient> functions
3044 set the I<numerator> of the constant or coefficient, while
3045 C<add_constant> and C<add_coefficient> add an integer value to
3046 the possibly rational constant or coefficient.
3048 To check whether an affine expressions is obviously zero
3049 or obviously equal to some other affine expression, use
3051 #include <isl/aff.h>
3052 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3053 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3054 __isl_keep isl_aff *aff2);
3055 int isl_pw_aff_plain_is_equal(
3056 __isl_keep isl_pw_aff *pwaff1,
3057 __isl_keep isl_pw_aff *pwaff2);
3061 #include <isl/aff.h>
3062 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3063 __isl_take isl_aff *aff2);
3064 __isl_give isl_pw_aff *isl_pw_aff_add(
3065 __isl_take isl_pw_aff *pwaff1,
3066 __isl_take isl_pw_aff *pwaff2);
3067 __isl_give isl_pw_aff *isl_pw_aff_min(
3068 __isl_take isl_pw_aff *pwaff1,
3069 __isl_take isl_pw_aff *pwaff2);
3070 __isl_give isl_pw_aff *isl_pw_aff_max(
3071 __isl_take isl_pw_aff *pwaff1,
3072 __isl_take isl_pw_aff *pwaff2);
3073 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3074 __isl_take isl_aff *aff2);
3075 __isl_give isl_pw_aff *isl_pw_aff_sub(
3076 __isl_take isl_pw_aff *pwaff1,
3077 __isl_take isl_pw_aff *pwaff2);
3078 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3079 __isl_give isl_pw_aff *isl_pw_aff_neg(
3080 __isl_take isl_pw_aff *pwaff);
3081 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3082 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3083 __isl_take isl_pw_aff *pwaff);
3084 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3085 __isl_give isl_pw_aff *isl_pw_aff_floor(
3086 __isl_take isl_pw_aff *pwaff);
3087 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3089 __isl_give isl_pw_aff *isl_pw_aff_mod(
3090 __isl_take isl_pw_aff *pwaff, isl_int mod);
3091 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3093 __isl_give isl_pw_aff *isl_pw_aff_scale(
3094 __isl_take isl_pw_aff *pwaff, isl_int f);
3095 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3097 __isl_give isl_aff *isl_aff_scale_down_ui(
3098 __isl_take isl_aff *aff, unsigned f);
3099 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3100 __isl_take isl_pw_aff *pwaff, isl_int f);
3102 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3103 __isl_take isl_pw_aff_list *list);
3104 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3105 __isl_take isl_pw_aff_list *list);
3107 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3108 __isl_take isl_pw_aff *pwqp);
3110 __isl_give isl_aff *isl_aff_align_params(
3111 __isl_take isl_aff *aff,
3112 __isl_take isl_space *model);
3113 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3114 __isl_take isl_pw_aff *pwaff,
3115 __isl_take isl_space *model);
3117 __isl_give isl_aff *isl_aff_project_domain_on_params(
3118 __isl_take isl_aff *aff);
3120 __isl_give isl_aff *isl_aff_gist_params(
3121 __isl_take isl_aff *aff,
3122 __isl_take isl_set *context);
3123 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3124 __isl_take isl_set *context);
3125 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3126 __isl_take isl_pw_aff *pwaff,
3127 __isl_take isl_set *context);
3128 __isl_give isl_pw_aff *isl_pw_aff_gist(
3129 __isl_take isl_pw_aff *pwaff,
3130 __isl_take isl_set *context);
3132 __isl_give isl_set *isl_pw_aff_domain(
3133 __isl_take isl_pw_aff *pwaff);
3134 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3135 __isl_take isl_pw_aff *pa,
3136 __isl_take isl_set *set);
3137 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3138 __isl_take isl_pw_aff *pa,
3139 __isl_take isl_set *set);
3141 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3142 __isl_take isl_aff *aff2);
3143 __isl_give isl_pw_aff *isl_pw_aff_mul(
3144 __isl_take isl_pw_aff *pwaff1,
3145 __isl_take isl_pw_aff *pwaff2);
3147 When multiplying two affine expressions, at least one of the two needs
3150 #include <isl/aff.h>
3151 __isl_give isl_basic_set *isl_aff_le_basic_set(
3152 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3153 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3154 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3155 __isl_give isl_set *isl_pw_aff_eq_set(
3156 __isl_take isl_pw_aff *pwaff1,
3157 __isl_take isl_pw_aff *pwaff2);
3158 __isl_give isl_set *isl_pw_aff_ne_set(
3159 __isl_take isl_pw_aff *pwaff1,
3160 __isl_take isl_pw_aff *pwaff2);
3161 __isl_give isl_set *isl_pw_aff_le_set(
3162 __isl_take isl_pw_aff *pwaff1,
3163 __isl_take isl_pw_aff *pwaff2);
3164 __isl_give isl_set *isl_pw_aff_lt_set(
3165 __isl_take isl_pw_aff *pwaff1,
3166 __isl_take isl_pw_aff *pwaff2);
3167 __isl_give isl_set *isl_pw_aff_ge_set(
3168 __isl_take isl_pw_aff *pwaff1,
3169 __isl_take isl_pw_aff *pwaff2);
3170 __isl_give isl_set *isl_pw_aff_gt_set(
3171 __isl_take isl_pw_aff *pwaff1,
3172 __isl_take isl_pw_aff *pwaff2);
3174 __isl_give isl_set *isl_pw_aff_list_eq_set(
3175 __isl_take isl_pw_aff_list *list1,
3176 __isl_take isl_pw_aff_list *list2);
3177 __isl_give isl_set *isl_pw_aff_list_ne_set(
3178 __isl_take isl_pw_aff_list *list1,
3179 __isl_take isl_pw_aff_list *list2);
3180 __isl_give isl_set *isl_pw_aff_list_le_set(
3181 __isl_take isl_pw_aff_list *list1,
3182 __isl_take isl_pw_aff_list *list2);
3183 __isl_give isl_set *isl_pw_aff_list_lt_set(
3184 __isl_take isl_pw_aff_list *list1,
3185 __isl_take isl_pw_aff_list *list2);
3186 __isl_give isl_set *isl_pw_aff_list_ge_set(
3187 __isl_take isl_pw_aff_list *list1,
3188 __isl_take isl_pw_aff_list *list2);
3189 __isl_give isl_set *isl_pw_aff_list_gt_set(
3190 __isl_take isl_pw_aff_list *list1,
3191 __isl_take isl_pw_aff_list *list2);
3193 The function C<isl_aff_ge_basic_set> returns a basic set
3194 containing those elements in the shared space
3195 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3196 The function C<isl_aff_ge_set> returns a set
3197 containing those elements in the shared domain
3198 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3199 The functions operating on C<isl_pw_aff_list> apply the corresponding
3200 C<isl_pw_aff> function to each pair of elements in the two lists.
3202 #include <isl/aff.h>
3203 __isl_give isl_set *isl_pw_aff_nonneg_set(
3204 __isl_take isl_pw_aff *pwaff);
3205 __isl_give isl_set *isl_pw_aff_zero_set(
3206 __isl_take isl_pw_aff *pwaff);
3207 __isl_give isl_set *isl_pw_aff_non_zero_set(
3208 __isl_take isl_pw_aff *pwaff);
3210 The function C<isl_pw_aff_nonneg_set> returns a set
3211 containing those elements in the domain
3212 of C<pwaff> where C<pwaff> is non-negative.
3214 #include <isl/aff.h>
3215 __isl_give isl_pw_aff *isl_pw_aff_cond(
3216 __isl_take isl_pw_aff *cond,
3217 __isl_take isl_pw_aff *pwaff_true,
3218 __isl_take isl_pw_aff *pwaff_false);
3220 The function C<isl_pw_aff_cond> performs a conditional operator
3221 and returns an expression that is equal to C<pwaff_true>
3222 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3223 where C<cond> is zero.
3225 #include <isl/aff.h>
3226 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3227 __isl_take isl_pw_aff *pwaff1,
3228 __isl_take isl_pw_aff *pwaff2);
3229 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3230 __isl_take isl_pw_aff *pwaff1,
3231 __isl_take isl_pw_aff *pwaff2);
3232 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3233 __isl_take isl_pw_aff *pwaff1,
3234 __isl_take isl_pw_aff *pwaff2);
3236 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3237 expression with a domain that is the union of those of C<pwaff1> and
3238 C<pwaff2> and such that on each cell, the quasi-affine expression is
3239 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3240 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3241 associated expression is the defined one.
3243 An expression can be read from input using
3245 #include <isl/aff.h>
3246 __isl_give isl_aff *isl_aff_read_from_str(
3247 isl_ctx *ctx, const char *str);
3248 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3249 isl_ctx *ctx, const char *str);
3251 An expression can be printed using
3253 #include <isl/aff.h>
3254 __isl_give isl_printer *isl_printer_print_aff(
3255 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3257 __isl_give isl_printer *isl_printer_print_pw_aff(
3258 __isl_take isl_printer *p,
3259 __isl_keep isl_pw_aff *pwaff);
3261 =head2 Piecewise Multiple Quasi Affine Expressions
3263 An C<isl_multi_aff> object represents a sequence of
3264 zero or more affine expressions, all defined on the same domain space.
3266 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3269 #include <isl/aff.h>
3270 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3271 __isl_take isl_space *space,
3272 __isl_take isl_aff_list *list);
3274 An empty piecewise multiple quasi affine expression (one with no cells),
3275 the zero piecewise multiple quasi affine expression (with value zero
3276 for each output dimension),
3277 a piecewise multiple quasi affine expression with a single cell (with
3278 either a universe or a specified domain) or
3279 a zero-dimensional piecewise multiple quasi affine expression
3281 can be created using the following functions.
3283 #include <isl/aff.h>
3284 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3285 __isl_take isl_space *space);
3286 __isl_give isl_multi_aff *isl_multi_aff_zero(
3287 __isl_take isl_space *space);
3288 __isl_give isl_pw_multi_aff *
3289 isl_pw_multi_aff_from_multi_aff(
3290 __isl_take isl_multi_aff *ma);
3291 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3292 __isl_take isl_set *set,
3293 __isl_take isl_multi_aff *maff);
3294 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3295 __isl_take isl_set *set);
3297 __isl_give isl_union_pw_multi_aff *
3298 isl_union_pw_multi_aff_empty(
3299 __isl_take isl_space *space);
3300 __isl_give isl_union_pw_multi_aff *
3301 isl_union_pw_multi_aff_add_pw_multi_aff(
3302 __isl_take isl_union_pw_multi_aff *upma,
3303 __isl_take isl_pw_multi_aff *pma);
3304 __isl_give isl_union_pw_multi_aff *
3305 isl_union_pw_multi_aff_from_domain(
3306 __isl_take isl_union_set *uset);
3308 A piecewise multiple quasi affine expression can also be initialized
3309 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3310 and the C<isl_map> is single-valued.
3312 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3313 __isl_take isl_set *set);
3314 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3315 __isl_take isl_map *map);
3317 Multiple quasi affine expressions can be copied and freed using
3319 #include <isl/aff.h>
3320 __isl_give isl_multi_aff *isl_multi_aff_copy(
3321 __isl_keep isl_multi_aff *maff);
3322 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3324 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3325 __isl_keep isl_pw_multi_aff *pma);
3326 void *isl_pw_multi_aff_free(
3327 __isl_take isl_pw_multi_aff *pma);
3329 __isl_give isl_union_pw_multi_aff *
3330 isl_union_pw_multi_aff_copy(
3331 __isl_keep isl_union_pw_multi_aff *upma);
3332 void *isl_union_pw_multi_aff_free(
3333 __isl_take isl_union_pw_multi_aff *upma);
3335 The expression can be inspected using
3337 #include <isl/aff.h>
3338 isl_ctx *isl_multi_aff_get_ctx(
3339 __isl_keep isl_multi_aff *maff);
3340 isl_ctx *isl_pw_multi_aff_get_ctx(
3341 __isl_keep isl_pw_multi_aff *pma);
3342 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3343 __isl_keep isl_union_pw_multi_aff *upma);
3344 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3345 enum isl_dim_type type);
3346 unsigned isl_pw_multi_aff_dim(
3347 __isl_keep isl_pw_multi_aff *pma,
3348 enum isl_dim_type type);
3349 __isl_give isl_aff *isl_multi_aff_get_aff(
3350 __isl_keep isl_multi_aff *multi, int pos);
3351 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3352 __isl_keep isl_pw_multi_aff *pma, int pos);
3353 const char *isl_pw_multi_aff_get_dim_name(
3354 __isl_keep isl_pw_multi_aff *pma,
3355 enum isl_dim_type type, unsigned pos);
3356 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3357 __isl_keep isl_pw_multi_aff *pma,
3358 enum isl_dim_type type, unsigned pos);
3359 const char *isl_multi_aff_get_tuple_name(
3360 __isl_keep isl_multi_aff *multi,
3361 enum isl_dim_type type);
3362 const char *isl_pw_multi_aff_get_tuple_name(
3363 __isl_keep isl_pw_multi_aff *pma,
3364 enum isl_dim_type type);
3365 int isl_pw_multi_aff_has_tuple_id(
3366 __isl_keep isl_pw_multi_aff *pma,
3367 enum isl_dim_type type);
3368 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3369 __isl_keep isl_pw_multi_aff *pma,
3370 enum isl_dim_type type);
3372 int isl_pw_multi_aff_foreach_piece(
3373 __isl_keep isl_pw_multi_aff *pma,
3374 int (*fn)(__isl_take isl_set *set,
3375 __isl_take isl_multi_aff *maff,
3376 void *user), void *user);
3378 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3379 __isl_keep isl_union_pw_multi_aff *upma,
3380 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3381 void *user), void *user);
3383 It can be modified using
3385 #include <isl/aff.h>
3386 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3387 __isl_take isl_multi_aff *multi, int pos,
3388 __isl_take isl_aff *aff);
3389 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3390 __isl_take isl_multi_aff *maff,
3391 enum isl_dim_type type, unsigned pos, const char *s);
3392 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3393 __isl_take isl_multi_aff *maff,
3394 enum isl_dim_type type, __isl_take isl_id *id);
3395 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3396 __isl_take isl_pw_multi_aff *pma,
3397 enum isl_dim_type type, __isl_take isl_id *id);
3399 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3400 __isl_take isl_multi_aff *maff,
3401 enum isl_dim_type type, unsigned first, unsigned n);
3403 To check whether two multiple affine expressions are
3404 obviously equal to each other, use
3406 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3407 __isl_keep isl_multi_aff *maff2);
3408 int isl_pw_multi_aff_plain_is_equal(
3409 __isl_keep isl_pw_multi_aff *pma1,
3410 __isl_keep isl_pw_multi_aff *pma2);
3414 #include <isl/aff.h>
3415 __isl_give isl_multi_aff *isl_multi_aff_add(
3416 __isl_take isl_multi_aff *maff1,
3417 __isl_take isl_multi_aff *maff2);
3418 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3419 __isl_take isl_pw_multi_aff *pma1,
3420 __isl_take isl_pw_multi_aff *pma2);
3421 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3422 __isl_take isl_union_pw_multi_aff *upma1,
3423 __isl_take isl_union_pw_multi_aff *upma2);
3424 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3425 __isl_take isl_pw_multi_aff *pma1,
3426 __isl_take isl_pw_multi_aff *pma2);
3427 __isl_give isl_multi_aff *isl_multi_aff_scale(
3428 __isl_take isl_multi_aff *maff,
3430 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3431 __isl_take isl_pw_multi_aff *pma,
3432 __isl_take isl_set *set);
3433 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3434 __isl_take isl_pw_multi_aff *pma,
3435 __isl_take isl_set *set);
3436 __isl_give isl_multi_aff *isl_multi_aff_lift(
3437 __isl_take isl_multi_aff *maff,
3438 __isl_give isl_local_space **ls);
3439 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3440 __isl_take isl_pw_multi_aff *pma);
3441 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3442 __isl_take isl_multi_aff *maff,
3443 __isl_take isl_set *context);
3444 __isl_give isl_multi_aff *isl_multi_aff_gist(
3445 __isl_take isl_multi_aff *maff,
3446 __isl_take isl_set *context);
3447 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3448 __isl_take isl_pw_multi_aff *pma,
3449 __isl_take isl_set *set);
3450 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3451 __isl_take isl_pw_multi_aff *pma,
3452 __isl_take isl_set *set);
3453 __isl_give isl_set *isl_pw_multi_aff_domain(
3454 __isl_take isl_pw_multi_aff *pma);
3455 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3456 __isl_take isl_union_pw_multi_aff *upma);
3457 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3458 __isl_take isl_multi_aff *ma1,
3459 __isl_take isl_multi_aff *ma2);
3460 __isl_give isl_pw_multi_aff *
3461 isl_pw_multi_aff_flat_range_product(
3462 __isl_take isl_pw_multi_aff *pma1,
3463 __isl_take isl_pw_multi_aff *pma2);
3464 __isl_give isl_union_pw_multi_aff *
3465 isl_union_pw_multi_aff_flat_range_product(
3466 __isl_take isl_union_pw_multi_aff *upma1,
3467 __isl_take isl_union_pw_multi_aff *upma2);
3469 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3470 then it is assigned the local space that lies at the basis of
3471 the lifting applied.
3473 An expression can be read from input using
3475 #include <isl/aff.h>
3476 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3477 isl_ctx *ctx, const char *str);
3478 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3479 isl_ctx *ctx, const char *str);
3481 An expression can be printed using
3483 #include <isl/aff.h>
3484 __isl_give isl_printer *isl_printer_print_multi_aff(
3485 __isl_take isl_printer *p,
3486 __isl_keep isl_multi_aff *maff);
3487 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3488 __isl_take isl_printer *p,
3489 __isl_keep isl_pw_multi_aff *pma);
3490 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3491 __isl_take isl_printer *p,
3492 __isl_keep isl_union_pw_multi_aff *upma);
3496 Points are elements of a set. They can be used to construct
3497 simple sets (boxes) or they can be used to represent the
3498 individual elements of a set.
3499 The zero point (the origin) can be created using
3501 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3503 The coordinates of a point can be inspected, set and changed
3506 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3507 enum isl_dim_type type, int pos, isl_int *v);
3508 __isl_give isl_point *isl_point_set_coordinate(
3509 __isl_take isl_point *pnt,
3510 enum isl_dim_type type, int pos, isl_int v);
3512 __isl_give isl_point *isl_point_add_ui(
3513 __isl_take isl_point *pnt,
3514 enum isl_dim_type type, int pos, unsigned val);
3515 __isl_give isl_point *isl_point_sub_ui(
3516 __isl_take isl_point *pnt,
3517 enum isl_dim_type type, int pos, unsigned val);
3519 Other properties can be obtained using
3521 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3523 Points can be copied or freed using
3525 __isl_give isl_point *isl_point_copy(
3526 __isl_keep isl_point *pnt);
3527 void isl_point_free(__isl_take isl_point *pnt);
3529 A singleton set can be created from a point using
3531 __isl_give isl_basic_set *isl_basic_set_from_point(
3532 __isl_take isl_point *pnt);
3533 __isl_give isl_set *isl_set_from_point(
3534 __isl_take isl_point *pnt);
3536 and a box can be created from two opposite extremal points using
3538 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3539 __isl_take isl_point *pnt1,
3540 __isl_take isl_point *pnt2);
3541 __isl_give isl_set *isl_set_box_from_points(
3542 __isl_take isl_point *pnt1,
3543 __isl_take isl_point *pnt2);
3545 All elements of a B<bounded> (union) set can be enumerated using
3546 the following functions.
3548 int isl_set_foreach_point(__isl_keep isl_set *set,
3549 int (*fn)(__isl_take isl_point *pnt, void *user),
3551 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3552 int (*fn)(__isl_take isl_point *pnt, void *user),
3555 The function C<fn> is called for each integer point in
3556 C<set> with as second argument the last argument of
3557 the C<isl_set_foreach_point> call. The function C<fn>
3558 should return C<0> on success and C<-1> on failure.
3559 In the latter case, C<isl_set_foreach_point> will stop
3560 enumerating and return C<-1> as well.
3561 If the enumeration is performed successfully and to completion,
3562 then C<isl_set_foreach_point> returns C<0>.
3564 To obtain a single point of a (basic) set, use
3566 __isl_give isl_point *isl_basic_set_sample_point(
3567 __isl_take isl_basic_set *bset);
3568 __isl_give isl_point *isl_set_sample_point(
3569 __isl_take isl_set *set);
3571 If C<set> does not contain any (integer) points, then the
3572 resulting point will be ``void'', a property that can be
3575 int isl_point_is_void(__isl_keep isl_point *pnt);
3577 =head2 Piecewise Quasipolynomials
3579 A piecewise quasipolynomial is a particular kind of function that maps
3580 a parametric point to a rational value.
3581 More specifically, a quasipolynomial is a polynomial expression in greatest
3582 integer parts of affine expressions of parameters and variables.
3583 A piecewise quasipolynomial is a subdivision of a given parametric
3584 domain into disjoint cells with a quasipolynomial associated to
3585 each cell. The value of the piecewise quasipolynomial at a given
3586 point is the value of the quasipolynomial associated to the cell
3587 that contains the point. Outside of the union of cells,
3588 the value is assumed to be zero.
3589 For example, the piecewise quasipolynomial
3591 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3593 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3594 A given piecewise quasipolynomial has a fixed domain dimension.
3595 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3596 defined over different domains.
3597 Piecewise quasipolynomials are mainly used by the C<barvinok>
3598 library for representing the number of elements in a parametric set or map.
3599 For example, the piecewise quasipolynomial above represents
3600 the number of points in the map
3602 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3604 =head3 Input and Output
3606 Piecewise quasipolynomials can be read from input using
3608 __isl_give isl_union_pw_qpolynomial *
3609 isl_union_pw_qpolynomial_read_from_str(
3610 isl_ctx *ctx, const char *str);
3612 Quasipolynomials and piecewise quasipolynomials can be printed
3613 using the following functions.
3615 __isl_give isl_printer *isl_printer_print_qpolynomial(
3616 __isl_take isl_printer *p,
3617 __isl_keep isl_qpolynomial *qp);
3619 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3620 __isl_take isl_printer *p,
3621 __isl_keep isl_pw_qpolynomial *pwqp);
3623 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3624 __isl_take isl_printer *p,
3625 __isl_keep isl_union_pw_qpolynomial *upwqp);
3627 The output format of the printer
3628 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3629 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3631 In case of printing in C<ISL_FORMAT_C>, the user may want
3632 to set the names of all dimensions
3634 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3635 __isl_take isl_qpolynomial *qp,
3636 enum isl_dim_type type, unsigned pos,
3638 __isl_give isl_pw_qpolynomial *
3639 isl_pw_qpolynomial_set_dim_name(
3640 __isl_take isl_pw_qpolynomial *pwqp,
3641 enum isl_dim_type type, unsigned pos,
3644 =head3 Creating New (Piecewise) Quasipolynomials
3646 Some simple quasipolynomials can be created using the following functions.
3647 More complicated quasipolynomials can be created by applying
3648 operations such as addition and multiplication
3649 on the resulting quasipolynomials
3651 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3652 __isl_take isl_space *domain);
3653 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3654 __isl_take isl_space *domain);
3655 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3656 __isl_take isl_space *domain);
3657 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3658 __isl_take isl_space *domain);
3659 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3660 __isl_take isl_space *domain);
3661 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3662 __isl_take isl_space *domain,
3663 const isl_int n, const isl_int d);
3664 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3665 __isl_take isl_space *domain,
3666 enum isl_dim_type type, unsigned pos);
3667 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3668 __isl_take isl_aff *aff);
3670 Note that the space in which a quasipolynomial lives is a map space
3671 with a one-dimensional range. The C<domain> argument in some of
3672 the functions above corresponds to the domain of this map space.
3674 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3675 with a single cell can be created using the following functions.
3676 Multiple of these single cell piecewise quasipolynomials can
3677 be combined to create more complicated piecewise quasipolynomials.
3679 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3680 __isl_take isl_space *space);
3681 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3682 __isl_take isl_set *set,
3683 __isl_take isl_qpolynomial *qp);
3684 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3685 __isl_take isl_qpolynomial *qp);
3686 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3687 __isl_take isl_pw_aff *pwaff);
3689 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3690 __isl_take isl_space *space);
3691 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3692 __isl_take isl_pw_qpolynomial *pwqp);
3693 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3694 __isl_take isl_union_pw_qpolynomial *upwqp,
3695 __isl_take isl_pw_qpolynomial *pwqp);
3697 Quasipolynomials can be copied and freed again using the following
3700 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3701 __isl_keep isl_qpolynomial *qp);
3702 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3704 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3705 __isl_keep isl_pw_qpolynomial *pwqp);
3706 void *isl_pw_qpolynomial_free(
3707 __isl_take isl_pw_qpolynomial *pwqp);
3709 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3710 __isl_keep isl_union_pw_qpolynomial *upwqp);
3711 void *isl_union_pw_qpolynomial_free(
3712 __isl_take isl_union_pw_qpolynomial *upwqp);
3714 =head3 Inspecting (Piecewise) Quasipolynomials
3716 To iterate over all piecewise quasipolynomials in a union
3717 piecewise quasipolynomial, use the following function
3719 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3720 __isl_keep isl_union_pw_qpolynomial *upwqp,
3721 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3724 To extract the piecewise quasipolynomial in a given space from a union, use
3726 __isl_give isl_pw_qpolynomial *
3727 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3728 __isl_keep isl_union_pw_qpolynomial *upwqp,
3729 __isl_take isl_space *space);
3731 To iterate over the cells in a piecewise quasipolynomial,
3732 use either of the following two functions
3734 int isl_pw_qpolynomial_foreach_piece(
3735 __isl_keep isl_pw_qpolynomial *pwqp,
3736 int (*fn)(__isl_take isl_set *set,
3737 __isl_take isl_qpolynomial *qp,
3738 void *user), void *user);
3739 int isl_pw_qpolynomial_foreach_lifted_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);
3745 As usual, the function C<fn> should return C<0> on success
3746 and C<-1> on failure. The difference between
3747 C<isl_pw_qpolynomial_foreach_piece> and
3748 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3749 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3750 compute unique representations for all existentially quantified
3751 variables and then turn these existentially quantified variables
3752 into extra set variables, adapting the associated quasipolynomial
3753 accordingly. This means that the C<set> passed to C<fn>
3754 will not have any existentially quantified variables, but that
3755 the dimensions of the sets may be different for different
3756 invocations of C<fn>.
3758 To iterate over all terms in a quasipolynomial,
3761 int isl_qpolynomial_foreach_term(
3762 __isl_keep isl_qpolynomial *qp,
3763 int (*fn)(__isl_take isl_term *term,
3764 void *user), void *user);
3766 The terms themselves can be inspected and freed using
3769 unsigned isl_term_dim(__isl_keep isl_term *term,
3770 enum isl_dim_type type);
3771 void isl_term_get_num(__isl_keep isl_term *term,
3773 void isl_term_get_den(__isl_keep isl_term *term,
3775 int isl_term_get_exp(__isl_keep isl_term *term,
3776 enum isl_dim_type type, unsigned pos);
3777 __isl_give isl_aff *isl_term_get_div(
3778 __isl_keep isl_term *term, unsigned pos);
3779 void isl_term_free(__isl_take isl_term *term);
3781 Each term is a product of parameters, set variables and
3782 integer divisions. The function C<isl_term_get_exp>
3783 returns the exponent of a given dimensions in the given term.
3784 The C<isl_int>s in the arguments of C<isl_term_get_num>
3785 and C<isl_term_get_den> need to have been initialized
3786 using C<isl_int_init> before calling these functions.
3788 =head3 Properties of (Piecewise) Quasipolynomials
3790 To check whether a quasipolynomial is actually a constant,
3791 use the following function.
3793 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3794 isl_int *n, isl_int *d);
3796 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3797 then the numerator and denominator of the constant
3798 are returned in C<*n> and C<*d>, respectively.
3800 To check whether two union piecewise quasipolynomials are
3801 obviously equal, use
3803 int isl_union_pw_qpolynomial_plain_is_equal(
3804 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3805 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3807 =head3 Operations on (Piecewise) Quasipolynomials
3809 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3810 __isl_take isl_qpolynomial *qp, isl_int v);
3811 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3812 __isl_take isl_qpolynomial *qp);
3813 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3814 __isl_take isl_qpolynomial *qp1,
3815 __isl_take isl_qpolynomial *qp2);
3816 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3817 __isl_take isl_qpolynomial *qp1,
3818 __isl_take isl_qpolynomial *qp2);
3819 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3820 __isl_take isl_qpolynomial *qp1,
3821 __isl_take isl_qpolynomial *qp2);
3822 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3823 __isl_take isl_qpolynomial *qp, unsigned exponent);
3825 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3826 __isl_take isl_pw_qpolynomial *pwqp1,
3827 __isl_take isl_pw_qpolynomial *pwqp2);
3828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3829 __isl_take isl_pw_qpolynomial *pwqp1,
3830 __isl_take isl_pw_qpolynomial *pwqp2);
3831 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3832 __isl_take isl_pw_qpolynomial *pwqp1,
3833 __isl_take isl_pw_qpolynomial *pwqp2);
3834 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3835 __isl_take isl_pw_qpolynomial *pwqp);
3836 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3837 __isl_take isl_pw_qpolynomial *pwqp1,
3838 __isl_take isl_pw_qpolynomial *pwqp2);
3839 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3840 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3842 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3843 __isl_take isl_union_pw_qpolynomial *upwqp1,
3844 __isl_take isl_union_pw_qpolynomial *upwqp2);
3845 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3846 __isl_take isl_union_pw_qpolynomial *upwqp1,
3847 __isl_take isl_union_pw_qpolynomial *upwqp2);
3848 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3849 __isl_take isl_union_pw_qpolynomial *upwqp1,
3850 __isl_take isl_union_pw_qpolynomial *upwqp2);
3852 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3853 __isl_take isl_pw_qpolynomial *pwqp,
3854 __isl_take isl_point *pnt);
3856 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3857 __isl_take isl_union_pw_qpolynomial *upwqp,
3858 __isl_take isl_point *pnt);
3860 __isl_give isl_set *isl_pw_qpolynomial_domain(
3861 __isl_take isl_pw_qpolynomial *pwqp);
3862 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3863 __isl_take isl_pw_qpolynomial *pwpq,
3864 __isl_take isl_set *set);
3865 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3866 __isl_take isl_pw_qpolynomial *pwpq,
3867 __isl_take isl_set *set);
3869 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3870 __isl_take isl_union_pw_qpolynomial *upwqp);
3871 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3872 __isl_take isl_union_pw_qpolynomial *upwpq,
3873 __isl_take isl_union_set *uset);
3874 __isl_give isl_union_pw_qpolynomial *
3875 isl_union_pw_qpolynomial_intersect_params(
3876 __isl_take isl_union_pw_qpolynomial *upwpq,
3877 __isl_take isl_set *set);
3879 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3880 __isl_take isl_qpolynomial *qp,
3881 __isl_take isl_space *model);
3883 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3884 __isl_take isl_qpolynomial *qp);
3885 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3886 __isl_take isl_pw_qpolynomial *pwqp);
3888 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3889 __isl_take isl_union_pw_qpolynomial *upwqp);
3891 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3892 __isl_take isl_qpolynomial *qp,
3893 __isl_take isl_set *context);
3894 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3895 __isl_take isl_qpolynomial *qp,
3896 __isl_take isl_set *context);
3898 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3899 __isl_take isl_pw_qpolynomial *pwqp,
3900 __isl_take isl_set *context);
3901 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3902 __isl_take isl_pw_qpolynomial *pwqp,
3903 __isl_take isl_set *context);
3905 __isl_give isl_union_pw_qpolynomial *
3906 isl_union_pw_qpolynomial_gist_params(
3907 __isl_take isl_union_pw_qpolynomial *upwqp,
3908 __isl_take isl_set *context);
3909 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3910 __isl_take isl_union_pw_qpolynomial *upwqp,
3911 __isl_take isl_union_set *context);
3913 The gist operation applies the gist operation to each of
3914 the cells in the domain of the input piecewise quasipolynomial.
3915 The context is also exploited
3916 to simplify the quasipolynomials associated to each cell.
3918 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3919 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3920 __isl_give isl_union_pw_qpolynomial *
3921 isl_union_pw_qpolynomial_to_polynomial(
3922 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3924 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3925 the polynomial will be an overapproximation. If C<sign> is negative,
3926 it will be an underapproximation. If C<sign> is zero, the approximation
3927 will lie somewhere in between.
3929 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3931 A piecewise quasipolynomial reduction is a piecewise
3932 reduction (or fold) of quasipolynomials.
3933 In particular, the reduction can be maximum or a minimum.
3934 The objects are mainly used to represent the result of
3935 an upper or lower bound on a quasipolynomial over its domain,
3936 i.e., as the result of the following function.
3938 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3939 __isl_take isl_pw_qpolynomial *pwqp,
3940 enum isl_fold type, int *tight);
3942 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3943 __isl_take isl_union_pw_qpolynomial *upwqp,
3944 enum isl_fold type, int *tight);
3946 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3947 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3948 is the returned bound is known be tight, i.e., for each value
3949 of the parameters there is at least
3950 one element in the domain that reaches the bound.
3951 If the domain of C<pwqp> is not wrapping, then the bound is computed
3952 over all elements in that domain and the result has a purely parametric
3953 domain. If the domain of C<pwqp> is wrapping, then the bound is
3954 computed over the range of the wrapped relation. The domain of the
3955 wrapped relation becomes the domain of the result.
3957 A (piecewise) quasipolynomial reduction can be copied or freed using the
3958 following functions.
3960 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3961 __isl_keep isl_qpolynomial_fold *fold);
3962 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3963 __isl_keep isl_pw_qpolynomial_fold *pwf);
3964 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3965 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3966 void isl_qpolynomial_fold_free(
3967 __isl_take isl_qpolynomial_fold *fold);
3968 void *isl_pw_qpolynomial_fold_free(
3969 __isl_take isl_pw_qpolynomial_fold *pwf);
3970 void *isl_union_pw_qpolynomial_fold_free(
3971 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3973 =head3 Printing Piecewise Quasipolynomial Reductions
3975 Piecewise quasipolynomial reductions can be printed
3976 using the following function.
3978 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3979 __isl_take isl_printer *p,
3980 __isl_keep isl_pw_qpolynomial_fold *pwf);
3981 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3982 __isl_take isl_printer *p,
3983 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3985 For C<isl_printer_print_pw_qpolynomial_fold>,
3986 output format of the printer
3987 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3988 For C<isl_printer_print_union_pw_qpolynomial_fold>,
3989 output format of the printer
3990 needs to be set to C<ISL_FORMAT_ISL>.
3991 In case of printing in C<ISL_FORMAT_C>, the user may want
3992 to set the names of all dimensions
3994 __isl_give isl_pw_qpolynomial_fold *
3995 isl_pw_qpolynomial_fold_set_dim_name(
3996 __isl_take isl_pw_qpolynomial_fold *pwf,
3997 enum isl_dim_type type, unsigned pos,
4000 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4002 To iterate over all piecewise quasipolynomial reductions in a union
4003 piecewise quasipolynomial reduction, use the following function
4005 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4006 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4007 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4008 void *user), void *user);
4010 To iterate over the cells in a piecewise quasipolynomial reduction,
4011 use either of the following two functions
4013 int isl_pw_qpolynomial_fold_foreach_piece(
4014 __isl_keep isl_pw_qpolynomial_fold *pwf,
4015 int (*fn)(__isl_take isl_set *set,
4016 __isl_take isl_qpolynomial_fold *fold,
4017 void *user), void *user);
4018 int isl_pw_qpolynomial_fold_foreach_lifted_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);
4024 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4025 of the difference between these two functions.
4027 To iterate over all quasipolynomials in a reduction, use
4029 int isl_qpolynomial_fold_foreach_qpolynomial(
4030 __isl_keep isl_qpolynomial_fold *fold,
4031 int (*fn)(__isl_take isl_qpolynomial *qp,
4032 void *user), void *user);
4034 =head3 Properties of Piecewise Quasipolynomial Reductions
4036 To check whether two union piecewise quasipolynomial reductions are
4037 obviously equal, use
4039 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4040 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4041 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4043 =head3 Operations on Piecewise Quasipolynomial Reductions
4045 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4046 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4048 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4049 __isl_take isl_pw_qpolynomial_fold *pwf1,
4050 __isl_take isl_pw_qpolynomial_fold *pwf2);
4052 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4053 __isl_take isl_pw_qpolynomial_fold *pwf1,
4054 __isl_take isl_pw_qpolynomial_fold *pwf2);
4056 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4057 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4058 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4060 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4061 __isl_take isl_pw_qpolynomial_fold *pwf,
4062 __isl_take isl_point *pnt);
4064 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4065 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4066 __isl_take isl_point *pnt);
4068 __isl_give isl_pw_qpolynomial_fold *
4069 sl_pw_qpolynomial_fold_intersect_params(
4070 __isl_take isl_pw_qpolynomial_fold *pwf,
4071 __isl_take isl_set *set);
4073 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4074 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4075 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4076 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4077 __isl_take isl_union_set *uset);
4078 __isl_give isl_union_pw_qpolynomial_fold *
4079 isl_union_pw_qpolynomial_fold_intersect_params(
4080 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4081 __isl_take isl_set *set);
4083 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4084 __isl_take isl_pw_qpolynomial_fold *pwf);
4086 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4087 __isl_take isl_pw_qpolynomial_fold *pwf);
4089 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4090 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4092 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4093 __isl_take isl_qpolynomial_fold *fold,
4094 __isl_take isl_set *context);
4095 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4096 __isl_take isl_qpolynomial_fold *fold,
4097 __isl_take isl_set *context);
4099 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4100 __isl_take isl_pw_qpolynomial_fold *pwf,
4101 __isl_take isl_set *context);
4102 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4103 __isl_take isl_pw_qpolynomial_fold *pwf,
4104 __isl_take isl_set *context);
4106 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4107 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4108 __isl_take isl_union_set *context);
4109 __isl_give isl_union_pw_qpolynomial_fold *
4110 isl_union_pw_qpolynomial_fold_gist_params(
4111 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4112 __isl_take isl_set *context);
4114 The gist operation applies the gist operation to each of
4115 the cells in the domain of the input piecewise quasipolynomial reduction.
4116 In future, the operation will also exploit the context
4117 to simplify the quasipolynomial reductions associated to each cell.
4119 __isl_give isl_pw_qpolynomial_fold *
4120 isl_set_apply_pw_qpolynomial_fold(
4121 __isl_take isl_set *set,
4122 __isl_take isl_pw_qpolynomial_fold *pwf,
4124 __isl_give isl_pw_qpolynomial_fold *
4125 isl_map_apply_pw_qpolynomial_fold(
4126 __isl_take isl_map *map,
4127 __isl_take isl_pw_qpolynomial_fold *pwf,
4129 __isl_give isl_union_pw_qpolynomial_fold *
4130 isl_union_set_apply_union_pw_qpolynomial_fold(
4131 __isl_take isl_union_set *uset,
4132 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4134 __isl_give isl_union_pw_qpolynomial_fold *
4135 isl_union_map_apply_union_pw_qpolynomial_fold(
4136 __isl_take isl_union_map *umap,
4137 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4140 The functions taking a map
4141 compose the given map with the given piecewise quasipolynomial reduction.
4142 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4143 over all elements in the intersection of the range of the map
4144 and the domain of the piecewise quasipolynomial reduction
4145 as a function of an element in the domain of the map.
4146 The functions taking a set compute a bound over all elements in the
4147 intersection of the set and the domain of the
4148 piecewise quasipolynomial reduction.
4150 =head2 Dependence Analysis
4152 C<isl> contains specialized functionality for performing
4153 array dataflow analysis. That is, given a I<sink> access relation
4154 and a collection of possible I<source> access relations,
4155 C<isl> can compute relations that describe
4156 for each iteration of the sink access, which iteration
4157 of which of the source access relations was the last
4158 to access the same data element before the given iteration
4160 The resulting dependence relations map source iterations
4161 to the corresponding sink iterations.
4162 To compute standard flow dependences, the sink should be
4163 a read, while the sources should be writes.
4164 If any of the source accesses are marked as being I<may>
4165 accesses, then there will be a dependence from the last
4166 I<must> access B<and> from any I<may> access that follows
4167 this last I<must> access.
4168 In particular, if I<all> sources are I<may> accesses,
4169 then memory based dependence analysis is performed.
4170 If, on the other hand, all sources are I<must> accesses,
4171 then value based dependence analysis is performed.
4173 #include <isl/flow.h>
4175 typedef int (*isl_access_level_before)(void *first, void *second);
4177 __isl_give isl_access_info *isl_access_info_alloc(
4178 __isl_take isl_map *sink,
4179 void *sink_user, isl_access_level_before fn,
4181 __isl_give isl_access_info *isl_access_info_add_source(
4182 __isl_take isl_access_info *acc,
4183 __isl_take isl_map *source, int must,
4185 void isl_access_info_free(__isl_take isl_access_info *acc);
4187 __isl_give isl_flow *isl_access_info_compute_flow(
4188 __isl_take isl_access_info *acc);
4190 int isl_flow_foreach(__isl_keep isl_flow *deps,
4191 int (*fn)(__isl_take isl_map *dep, int must,
4192 void *dep_user, void *user),
4194 __isl_give isl_map *isl_flow_get_no_source(
4195 __isl_keep isl_flow *deps, int must);
4196 void isl_flow_free(__isl_take isl_flow *deps);
4198 The function C<isl_access_info_compute_flow> performs the actual
4199 dependence analysis. The other functions are used to construct
4200 the input for this function or to read off the output.
4202 The input is collected in an C<isl_access_info>, which can
4203 be created through a call to C<isl_access_info_alloc>.
4204 The arguments to this functions are the sink access relation
4205 C<sink>, a token C<sink_user> used to identify the sink
4206 access to the user, a callback function for specifying the
4207 relative order of source and sink accesses, and the number
4208 of source access relations that will be added.
4209 The callback function has type C<int (*)(void *first, void *second)>.
4210 The function is called with two user supplied tokens identifying
4211 either a source or the sink and it should return the shared nesting
4212 level and the relative order of the two accesses.
4213 In particular, let I<n> be the number of loops shared by
4214 the two accesses. If C<first> precedes C<second> textually,
4215 then the function should return I<2 * n + 1>; otherwise,
4216 it should return I<2 * n>.
4217 The sources can be added to the C<isl_access_info> by performing
4218 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4219 C<must> indicates whether the source is a I<must> access
4220 or a I<may> access. Note that a multi-valued access relation
4221 should only be marked I<must> if every iteration in the domain
4222 of the relation accesses I<all> elements in its image.
4223 The C<source_user> token is again used to identify
4224 the source access. The range of the source access relation
4225 C<source> should have the same dimension as the range
4226 of the sink access relation.
4227 The C<isl_access_info_free> function should usually not be
4228 called explicitly, because it is called implicitly by
4229 C<isl_access_info_compute_flow>.
4231 The result of the dependence analysis is collected in an
4232 C<isl_flow>. There may be elements of
4233 the sink access for which no preceding source access could be
4234 found or for which all preceding sources are I<may> accesses.
4235 The relations containing these elements can be obtained through
4236 calls to C<isl_flow_get_no_source>, the first with C<must> set
4237 and the second with C<must> unset.
4238 In the case of standard flow dependence analysis,
4239 with the sink a read and the sources I<must> writes,
4240 the first relation corresponds to the reads from uninitialized
4241 array elements and the second relation is empty.
4242 The actual flow dependences can be extracted using
4243 C<isl_flow_foreach>. This function will call the user-specified
4244 callback function C<fn> for each B<non-empty> dependence between
4245 a source and the sink. The callback function is called
4246 with four arguments, the actual flow dependence relation
4247 mapping source iterations to sink iterations, a boolean that
4248 indicates whether it is a I<must> or I<may> dependence, a token
4249 identifying the source and an additional C<void *> with value
4250 equal to the third argument of the C<isl_flow_foreach> call.
4251 A dependence is marked I<must> if it originates from a I<must>
4252 source and if it is not followed by any I<may> sources.
4254 After finishing with an C<isl_flow>, the user should call
4255 C<isl_flow_free> to free all associated memory.
4257 A higher-level interface to dependence analysis is provided
4258 by the following function.
4260 #include <isl/flow.h>
4262 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4263 __isl_take isl_union_map *must_source,
4264 __isl_take isl_union_map *may_source,
4265 __isl_take isl_union_map *schedule,
4266 __isl_give isl_union_map **must_dep,
4267 __isl_give isl_union_map **may_dep,
4268 __isl_give isl_union_map **must_no_source,
4269 __isl_give isl_union_map **may_no_source);
4271 The arrays are identified by the tuple names of the ranges
4272 of the accesses. The iteration domains by the tuple names
4273 of the domains of the accesses and of the schedule.
4274 The relative order of the iteration domains is given by the
4275 schedule. The relations returned through C<must_no_source>
4276 and C<may_no_source> are subsets of C<sink>.
4277 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4278 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4279 any of the other arguments is treated as an error.
4281 =head3 Interaction with Dependence Analysis
4283 During the dependence analysis, we frequently need to perform
4284 the following operation. Given a relation between sink iterations
4285 and potential soure iterations from a particular source domain,
4286 what is the last potential source iteration corresponding to each
4287 sink iteration. It can sometimes be convenient to adjust
4288 the set of potential source iterations before or after each such operation.
4289 The prototypical example is fuzzy array dataflow analysis,
4290 where we need to analyze if, based on data-dependent constraints,
4291 the sink iteration can ever be executed without one or more of
4292 the corresponding potential source iterations being executed.
4293 If so, we can introduce extra parameters and select an unknown
4294 but fixed source iteration from the potential source iterations.
4295 To be able to perform such manipulations, C<isl> provides the following
4298 #include <isl/flow.h>
4300 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4301 __isl_keep isl_map *source_map,
4302 __isl_keep isl_set *sink, void *source_user,
4304 __isl_give isl_access_info *isl_access_info_set_restrict(
4305 __isl_take isl_access_info *acc,
4306 isl_access_restrict fn, void *user);
4308 The function C<isl_access_info_set_restrict> should be called
4309 before calling C<isl_access_info_compute_flow> and registers a callback function
4310 that will be called any time C<isl> is about to compute the last
4311 potential source. The first argument is the (reverse) proto-dependence,
4312 mapping sink iterations to potential source iterations.
4313 The second argument represents the sink iterations for which
4314 we want to compute the last source iteration.
4315 The third argument is the token corresponding to the source
4316 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4317 The callback is expected to return a restriction on either the input or
4318 the output of the operation computing the last potential source.
4319 If the input needs to be restricted then restrictions are needed
4320 for both the source and the sink iterations. The sink iterations
4321 and the potential source iterations will be intersected with these sets.
4322 If the output needs to be restricted then only a restriction on the source
4323 iterations is required.
4324 If any error occurs, the callback should return C<NULL>.
4325 An C<isl_restriction> object can be created and freed using the following
4328 #include <isl/flow.h>
4330 __isl_give isl_restriction *isl_restriction_input(
4331 __isl_take isl_set *source_restr,
4332 __isl_take isl_set *sink_restr);
4333 __isl_give isl_restriction *isl_restriction_output(
4334 __isl_take isl_set *source_restr);
4335 __isl_give isl_restriction *isl_restriction_none(
4336 __isl_keep isl_map *source_map);
4337 __isl_give isl_restriction *isl_restriction_empty(
4338 __isl_keep isl_map *source_map);
4339 void *isl_restriction_free(
4340 __isl_take isl_restriction *restr);
4342 C<isl_restriction_none> and C<isl_restriction_empty> are special
4343 cases of C<isl_restriction_input>. C<isl_restriction_none>
4344 is essentially equivalent to
4346 isl_restriction_input(isl_set_universe(
4347 isl_space_range(isl_map_get_space(source_map))),
4349 isl_space_domain(isl_map_get_space(source_map))));
4351 whereas C<isl_restriction_empty> is essentially equivalent to
4353 isl_restriction_input(isl_set_empty(
4354 isl_space_range(isl_map_get_space(source_map))),
4356 isl_space_domain(isl_map_get_space(source_map))));
4360 B<The functionality described in this section is fairly new
4361 and may be subject to change.>
4363 The following function can be used to compute a schedule
4364 for a union of domains.
4365 By default, the algorithm used to construct the schedule is similar
4366 to that of C<Pluto>.
4367 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4369 The generated schedule respects all C<validity> dependences.
4370 That is, all dependence distances over these dependences in the
4371 scheduled space are lexicographically positive.
4372 The default algorithm tries to minimize the dependence distances over
4373 C<proximity> dependences.
4374 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4375 for groups of domains where the dependence distances have only
4376 non-negative values.
4377 When using Feautrier's algorithm, the C<proximity> dependence
4378 distances are only minimized during the extension to a
4379 full-dimensional schedule.
4381 #include <isl/schedule.h>
4382 __isl_give isl_schedule *isl_union_set_compute_schedule(
4383 __isl_take isl_union_set *domain,
4384 __isl_take isl_union_map *validity,
4385 __isl_take isl_union_map *proximity);
4386 void *isl_schedule_free(__isl_take isl_schedule *sched);
4388 A mapping from the domains to the scheduled space can be obtained
4389 from an C<isl_schedule> using the following function.
4391 __isl_give isl_union_map *isl_schedule_get_map(
4392 __isl_keep isl_schedule *sched);
4394 A representation of the schedule can be printed using
4396 __isl_give isl_printer *isl_printer_print_schedule(
4397 __isl_take isl_printer *p,
4398 __isl_keep isl_schedule *schedule);
4400 A representation of the schedule as a forest of bands can be obtained
4401 using the following function.
4403 __isl_give isl_band_list *isl_schedule_get_band_forest(
4404 __isl_keep isl_schedule *schedule);
4406 The list can be manipulated as explained in L<"Lists">.
4407 The bands inside the list can be copied and freed using the following
4410 #include <isl/band.h>
4411 __isl_give isl_band *isl_band_copy(
4412 __isl_keep isl_band *band);
4413 void *isl_band_free(__isl_take isl_band *band);
4415 Each band contains zero or more scheduling dimensions.
4416 These are referred to as the members of the band.
4417 The section of the schedule that corresponds to the band is
4418 referred to as the partial schedule of the band.
4419 For those nodes that participate in a band, the outer scheduling
4420 dimensions form the prefix schedule, while the inner scheduling
4421 dimensions form the suffix schedule.
4422 That is, if we take a cut of the band forest, then the union of
4423 the concatenations of the prefix, partial and suffix schedules of
4424 each band in the cut is equal to the entire schedule (modulo
4425 some possible padding at the end with zero scheduling dimensions).
4426 The properties of a band can be inspected using the following functions.
4428 #include <isl/band.h>
4429 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4431 int isl_band_has_children(__isl_keep isl_band *band);
4432 __isl_give isl_band_list *isl_band_get_children(
4433 __isl_keep isl_band *band);
4435 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4436 __isl_keep isl_band *band);
4437 __isl_give isl_union_map *isl_band_get_partial_schedule(
4438 __isl_keep isl_band *band);
4439 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4440 __isl_keep isl_band *band);
4442 int isl_band_n_member(__isl_keep isl_band *band);
4443 int isl_band_member_is_zero_distance(
4444 __isl_keep isl_band *band, int pos);
4446 Note that a scheduling dimension is considered to be ``zero
4447 distance'' if it does not carry any proximity dependences
4449 That is, if the dependence distances of the proximity
4450 dependences are all zero in that direction (for fixed
4451 iterations of outer bands).
4453 A representation of the band can be printed using
4455 #include <isl/band.h>
4456 __isl_give isl_printer *isl_printer_print_band(
4457 __isl_take isl_printer *p,
4458 __isl_keep isl_band *band);
4462 #include <isl/schedule.h>
4463 int isl_options_set_schedule_max_coefficient(
4464 isl_ctx *ctx, int val);
4465 int isl_options_get_schedule_max_coefficient(
4467 int isl_options_set_schedule_max_constant_term(
4468 isl_ctx *ctx, int val);
4469 int isl_options_get_schedule_max_constant_term(
4471 int isl_options_set_schedule_maximize_band_depth(
4472 isl_ctx *ctx, int val);
4473 int isl_options_get_schedule_maximize_band_depth(
4475 int isl_options_set_schedule_outer_zero_distance(
4476 isl_ctx *ctx, int val);
4477 int isl_options_get_schedule_outer_zero_distance(
4479 int isl_options_set_schedule_split_scaled(
4480 isl_ctx *ctx, int val);
4481 int isl_options_get_schedule_split_scaled(
4483 int isl_options_set_schedule_algorithm(
4484 isl_ctx *ctx, int val);
4485 int isl_options_get_schedule_algorithm(
4491 =item * schedule_max_coefficient
4493 This option enforces that the coefficients for variable and parameter
4494 dimensions in the calculated schedule are not larger than the specified value.
4495 This option can significantly increase the speed of the scheduling calculation
4496 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4497 this option does not introduce bounds on the variable or parameter
4500 =item * schedule_max_constant_term
4502 This option enforces that the constant coefficients in the calculated schedule
4503 are not larger than the maximal constant term. This option can significantly
4504 increase the speed of the scheduling calculation and may also prevent fusing of
4505 unrelated dimensions. A value of -1 means that this option does not introduce
4506 bounds on the constant coefficients.
4508 =item * schedule_maximize_band_depth
4510 If this option is set, we do not split bands at the point
4511 where we detect splitting is necessary. Instead, we
4512 backtrack and split bands as early as possible. This
4513 reduces the number of splits and maximizes the width of
4514 the bands. Wider bands give more possibilities for tiling.
4516 =item * schedule_outer_zero_distance
4518 If this option is set, then we try to construct schedules
4519 where the outermost scheduling dimension in each band
4520 results in a zero dependence distance over the proximity
4523 =item * schedule_split_scaled
4525 If this option is set, then we try to construct schedules in which the
4526 constant term is split off from the linear part if the linear parts of
4527 the scheduling rows for all nodes in the graphs have a common non-trivial
4529 The constant term is then placed in a separate band and the linear
4532 =item * schedule_algorithm
4534 Selects the scheduling algorithm to be used.
4535 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4536 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4540 =head2 Parametric Vertex Enumeration
4542 The parametric vertex enumeration described in this section
4543 is mainly intended to be used internally and by the C<barvinok>
4546 #include <isl/vertices.h>
4547 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4548 __isl_keep isl_basic_set *bset);
4550 The function C<isl_basic_set_compute_vertices> performs the
4551 actual computation of the parametric vertices and the chamber
4552 decomposition and store the result in an C<isl_vertices> object.
4553 This information can be queried by either iterating over all
4554 the vertices or iterating over all the chambers or cells
4555 and then iterating over all vertices that are active on the chamber.
4557 int isl_vertices_foreach_vertex(
4558 __isl_keep isl_vertices *vertices,
4559 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4562 int isl_vertices_foreach_cell(
4563 __isl_keep isl_vertices *vertices,
4564 int (*fn)(__isl_take isl_cell *cell, void *user),
4566 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4567 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4570 Other operations that can be performed on an C<isl_vertices> object are
4573 isl_ctx *isl_vertices_get_ctx(
4574 __isl_keep isl_vertices *vertices);
4575 int isl_vertices_get_n_vertices(
4576 __isl_keep isl_vertices *vertices);
4577 void isl_vertices_free(__isl_take isl_vertices *vertices);
4579 Vertices can be inspected and destroyed using the following functions.
4581 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4582 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4583 __isl_give isl_basic_set *isl_vertex_get_domain(
4584 __isl_keep isl_vertex *vertex);
4585 __isl_give isl_basic_set *isl_vertex_get_expr(
4586 __isl_keep isl_vertex *vertex);
4587 void isl_vertex_free(__isl_take isl_vertex *vertex);
4589 C<isl_vertex_get_expr> returns a singleton parametric set describing
4590 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4592 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4593 B<rational> basic sets, so they should mainly be used for inspection
4594 and should not be mixed with integer sets.
4596 Chambers can be inspected and destroyed using the following functions.
4598 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4599 __isl_give isl_basic_set *isl_cell_get_domain(
4600 __isl_keep isl_cell *cell);
4601 void isl_cell_free(__isl_take isl_cell *cell);
4605 Although C<isl> is mainly meant to be used as a library,
4606 it also contains some basic applications that use some
4607 of the functionality of C<isl>.
4608 The input may be specified in either the L<isl format>
4609 or the L<PolyLib format>.
4611 =head2 C<isl_polyhedron_sample>
4613 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4614 an integer element of the polyhedron, if there is any.
4615 The first column in the output is the denominator and is always
4616 equal to 1. If the polyhedron contains no integer points,
4617 then a vector of length zero is printed.
4621 C<isl_pip> takes the same input as the C<example> program
4622 from the C<piplib> distribution, i.e., a set of constraints
4623 on the parameters, a line containing only -1 and finally a set
4624 of constraints on a parametric polyhedron.
4625 The coefficients of the parameters appear in the last columns
4626 (but before the final constant column).
4627 The output is the lexicographic minimum of the parametric polyhedron.
4628 As C<isl> currently does not have its own output format, the output
4629 is just a dump of the internal state.
4631 =head2 C<isl_polyhedron_minimize>
4633 C<isl_polyhedron_minimize> computes the minimum of some linear
4634 or affine objective function over the integer points in a polyhedron.
4635 If an affine objective function
4636 is given, then the constant should appear in the last column.
4638 =head2 C<isl_polytope_scan>
4640 Given a polytope, C<isl_polytope_scan> prints
4641 all integer points in the polytope.