3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
173 The source of C<isl> can be obtained either as a tarball
174 or from the git repository. Both are available from
175 L<http://freshmeat.net/projects/isl/>.
176 The installation process depends on how you obtained
179 =head2 Installation from the git repository
183 =item 1 Clone or update the repository
185 The first time the source is obtained, you need to clone
188 git clone git://repo.or.cz/isl.git
190 To obtain updates, you need to pull in the latest changes
194 =item 2 Generate C<configure>
200 After performing the above steps, continue
201 with the L<Common installation instructions>.
203 =head2 Common installation instructions
207 =item 1 Obtain C<GMP>
209 Building C<isl> requires C<GMP>, including its headers files.
210 Your distribution may not provide these header files by default
211 and you may need to install a package called C<gmp-devel> or something
212 similar. Alternatively, C<GMP> can be built from
213 source, available from L<http://gmplib.org/>.
217 C<isl> uses the standard C<autoconf> C<configure> script.
222 optionally followed by some configure options.
223 A complete list of options can be obtained by running
227 Below we discuss some of the more common options.
229 C<isl> can optionally use C<piplib>, but no
230 C<piplib> functionality is currently used by default.
231 The C<--with-piplib> option can
232 be used to specify which C<piplib>
233 library to use, either an installed version (C<system>),
234 an externally built version (C<build>)
235 or no version (C<no>). The option C<build> is mostly useful
236 in C<configure> scripts of larger projects that bundle both C<isl>
243 Installation prefix for C<isl>
245 =item C<--with-gmp-prefix>
247 Installation prefix for C<GMP> (architecture-independent files).
249 =item C<--with-gmp-exec-prefix>
251 Installation prefix for C<GMP> (architecture-dependent files).
253 =item C<--with-piplib>
255 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
257 =item C<--with-piplib-prefix>
259 Installation prefix for C<system> C<piplib> (architecture-independent files).
261 =item C<--with-piplib-exec-prefix>
263 Installation prefix for C<system> C<piplib> (architecture-dependent files).
265 =item C<--with-piplib-builddir>
267 Location where C<build> C<piplib> was built.
275 =item 4 Install (optional)
283 =head2 Initialization
285 All manipulations of integer sets and relations occur within
286 the context of an C<isl_ctx>.
287 A given C<isl_ctx> can only be used within a single thread.
288 All arguments of a function are required to have been allocated
289 within the same context.
290 There are currently no functions available for moving an object
291 from one C<isl_ctx> to another C<isl_ctx>. This means that
292 there is currently no way of safely moving an object from one
293 thread to another, unless the whole C<isl_ctx> is moved.
295 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
296 freed using C<isl_ctx_free>.
297 All objects allocated within an C<isl_ctx> should be freed
298 before the C<isl_ctx> itself is freed.
300 isl_ctx *isl_ctx_alloc();
301 void isl_ctx_free(isl_ctx *ctx);
305 All operations on integers, mainly the coefficients
306 of the constraints describing the sets and relations,
307 are performed in exact integer arithmetic using C<GMP>.
308 However, to allow future versions of C<isl> to optionally
309 support fixed integer arithmetic, all calls to C<GMP>
310 are wrapped inside C<isl> specific macros.
311 The basic type is C<isl_int> and the operations below
312 are available on this type.
313 The meanings of these operations are essentially the same
314 as their C<GMP> C<mpz_> counterparts.
315 As always with C<GMP> types, C<isl_int>s need to be
316 initialized with C<isl_int_init> before they can be used
317 and they need to be released with C<isl_int_clear>
319 The user should not assume that an C<isl_int> is represented
320 as a C<mpz_t>, but should instead explicitly convert between
321 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
322 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
326 =item isl_int_init(i)
328 =item isl_int_clear(i)
330 =item isl_int_set(r,i)
332 =item isl_int_set_si(r,i)
334 =item isl_int_set_gmp(r,g)
336 =item isl_int_get_gmp(i,g)
338 =item isl_int_abs(r,i)
340 =item isl_int_neg(r,i)
342 =item isl_int_swap(i,j)
344 =item isl_int_swap_or_set(i,j)
346 =item isl_int_add_ui(r,i,j)
348 =item isl_int_sub_ui(r,i,j)
350 =item isl_int_add(r,i,j)
352 =item isl_int_sub(r,i,j)
354 =item isl_int_mul(r,i,j)
356 =item isl_int_mul_ui(r,i,j)
358 =item isl_int_addmul(r,i,j)
360 =item isl_int_submul(r,i,j)
362 =item isl_int_gcd(r,i,j)
364 =item isl_int_lcm(r,i,j)
366 =item isl_int_divexact(r,i,j)
368 =item isl_int_cdiv_q(r,i,j)
370 =item isl_int_fdiv_q(r,i,j)
372 =item isl_int_fdiv_r(r,i,j)
374 =item isl_int_fdiv_q_ui(r,i,j)
376 =item isl_int_read(r,s)
378 =item isl_int_print(out,i,width)
382 =item isl_int_cmp(i,j)
384 =item isl_int_cmp_si(i,si)
386 =item isl_int_eq(i,j)
388 =item isl_int_ne(i,j)
390 =item isl_int_lt(i,j)
392 =item isl_int_le(i,j)
394 =item isl_int_gt(i,j)
396 =item isl_int_ge(i,j)
398 =item isl_int_abs_eq(i,j)
400 =item isl_int_abs_ne(i,j)
402 =item isl_int_abs_lt(i,j)
404 =item isl_int_abs_gt(i,j)
406 =item isl_int_abs_ge(i,j)
408 =item isl_int_is_zero(i)
410 =item isl_int_is_one(i)
412 =item isl_int_is_negone(i)
414 =item isl_int_is_pos(i)
416 =item isl_int_is_neg(i)
418 =item isl_int_is_nonpos(i)
420 =item isl_int_is_nonneg(i)
422 =item isl_int_is_divisible_by(i,j)
426 =head2 Sets and Relations
428 C<isl> uses six types of objects for representing sets and relations,
429 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
430 C<isl_union_set> and C<isl_union_map>.
431 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
432 can be described as a conjunction of affine constraints, while
433 C<isl_set> and C<isl_map> represent unions of
434 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
435 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
436 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
437 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
438 where spaces are considered different if they have a different number
439 of dimensions and/or different names (see L<"Spaces">).
440 The difference between sets and relations (maps) is that sets have
441 one set of variables, while relations have two sets of variables,
442 input variables and output variables.
444 =head2 Memory Management
446 Since a high-level operation on sets and/or relations usually involves
447 several substeps and since the user is usually not interested in
448 the intermediate results, most functions that return a new object
449 will also release all the objects passed as arguments.
450 If the user still wants to use one or more of these arguments
451 after the function call, she should pass along a copy of the
452 object rather than the object itself.
453 The user is then responsible for making sure that the original
454 object gets used somewhere else or is explicitly freed.
456 The arguments and return values of all documented functions are
457 annotated to make clear which arguments are released and which
458 arguments are preserved. In particular, the following annotations
465 C<__isl_give> means that a new object is returned.
466 The user should make sure that the returned pointer is
467 used exactly once as a value for an C<__isl_take> argument.
468 In between, it can be used as a value for as many
469 C<__isl_keep> arguments as the user likes.
470 There is one exception, and that is the case where the
471 pointer returned is C<NULL>. Is this case, the user
472 is free to use it as an C<__isl_take> argument or not.
476 C<__isl_take> means that the object the argument points to
477 is taken over by the function and may no longer be used
478 by the user as an argument to any other function.
479 The pointer value must be one returned by a function
480 returning an C<__isl_give> pointer.
481 If the user passes in a C<NULL> value, then this will
482 be treated as an error in the sense that the function will
483 not perform its usual operation. However, it will still
484 make sure that all the other C<__isl_take> arguments
489 C<__isl_keep> means that the function will only use the object
490 temporarily. After the function has finished, the user
491 can still use it as an argument to other functions.
492 A C<NULL> value will be treated in the same way as
493 a C<NULL> value for an C<__isl_take> argument.
497 =head2 Error Handling
499 C<isl> supports different ways to react in case a runtime error is triggered.
500 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
501 with two maps that have incompatible spaces. There are three possible ways
502 to react on error: to warn, to continue or to abort.
504 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
505 the last error in the corresponding C<isl_ctx> and the function in which the
506 error was triggered returns C<NULL>. An error does not corrupt internal state,
507 such that isl can continue to be used. C<isl> also provides functions to
508 read the last error and to reset the memory that stores the last error. The
509 last error is only stored for information purposes. Its presence does not
510 change the behavior of C<isl>. Hence, resetting an error is not required to
511 continue to use isl, but only to observe new errors.
514 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
515 void isl_ctx_reset_error(isl_ctx *ctx);
517 Another option is to continue on error. This is similar to warn on error mode,
518 except that C<isl> does not print any warning. This allows a program to
519 implement its own error reporting.
521 The last option is to directly abort the execution of the program from within
522 the isl library. This makes it obviously impossible to recover from an error,
523 but it allows to directly spot the error location. By aborting on error,
524 debuggers break at the location the error occurred and can provide a stack
525 trace. Other tools that automatically provide stack traces on abort or that do
526 not want to continue execution after an error was triggered may also prefer to
529 The on error behavior of isl can be specified by calling
530 C<isl_options_set_on_error> or by setting the command line option
531 C<--isl-on-error>. Valid arguments for the function call are
532 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
533 choices for the command line option are C<warn>, C<continue> and C<abort>.
534 It is also possible to query the current error mode.
536 #include <isl/options.h>
537 int isl_options_set_on_error(isl_ctx *ctx, int val);
538 int isl_options_get_on_error(isl_ctx *ctx);
542 Identifiers are used to identify both individual dimensions
543 and tuples of dimensions. They consist of a name and an optional
544 pointer. Identifiers with the same name but different pointer values
545 are considered to be distinct.
546 Identifiers can be constructed, copied, freed, inspected and printed
547 using the following functions.
550 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
551 __isl_keep const char *name, void *user);
552 __isl_give isl_id *isl_id_copy(isl_id *id);
553 void *isl_id_free(__isl_take isl_id *id);
555 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
556 void *isl_id_get_user(__isl_keep isl_id *id);
557 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
559 __isl_give isl_printer *isl_printer_print_id(
560 __isl_take isl_printer *p, __isl_keep isl_id *id);
562 Note that C<isl_id_get_name> returns a pointer to some internal
563 data structure, so the result can only be used while the
564 corresponding C<isl_id> is alive.
568 Whenever a new set or relation is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
571 #include <isl/space.h>
572 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
573 unsigned nparam, unsigned n_in, unsigned n_out);
574 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
576 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
577 unsigned nparam, unsigned dim);
578 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
579 void isl_space_free(__isl_take isl_space *space);
580 unsigned isl_space_dim(__isl_keep isl_space *space,
581 enum isl_dim_type type);
583 The space used for creating a parameter domain
584 needs to be created using C<isl_space_params_alloc>.
585 For other sets, the space
586 needs to be created using C<isl_space_set_alloc>, while
587 for a relation, the space
588 needs to be created using C<isl_space_alloc>.
589 C<isl_space_dim> can be used
590 to find out the number of dimensions of each type in
591 a space, where type may be
592 C<isl_dim_param>, C<isl_dim_in> (only for relations),
593 C<isl_dim_out> (only for relations), C<isl_dim_set>
594 (only for sets) or C<isl_dim_all>.
596 To check whether a given space is that of a set or a map
597 or whether it is a parameter space, use these functions:
599 #include <isl/space.h>
600 int isl_space_is_params(__isl_keep isl_space *space);
601 int isl_space_is_set(__isl_keep isl_space *space);
603 It is often useful to create objects that live in the
604 same space as some other object. This can be accomplished
605 by creating the new objects
606 (see L<Creating New Sets and Relations> or
607 L<Creating New (Piecewise) Quasipolynomials>) based on the space
608 of the original object.
611 __isl_give isl_space *isl_basic_set_get_space(
612 __isl_keep isl_basic_set *bset);
613 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
615 #include <isl/union_set.h>
616 __isl_give isl_space *isl_union_set_get_space(
617 __isl_keep isl_union_set *uset);
620 __isl_give isl_space *isl_basic_map_get_space(
621 __isl_keep isl_basic_map *bmap);
622 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
624 #include <isl/union_map.h>
625 __isl_give isl_space *isl_union_map_get_space(
626 __isl_keep isl_union_map *umap);
628 #include <isl/constraint.h>
629 __isl_give isl_space *isl_constraint_get_space(
630 __isl_keep isl_constraint *constraint);
632 #include <isl/polynomial.h>
633 __isl_give isl_space *isl_qpolynomial_get_domain_space(
634 __isl_keep isl_qpolynomial *qp);
635 __isl_give isl_space *isl_qpolynomial_get_space(
636 __isl_keep isl_qpolynomial *qp);
637 __isl_give isl_space *isl_qpolynomial_fold_get_space(
638 __isl_keep isl_qpolynomial_fold *fold);
639 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
640 __isl_keep isl_pw_qpolynomial *pwqp);
641 __isl_give isl_space *isl_pw_qpolynomial_get_space(
642 __isl_keep isl_pw_qpolynomial *pwqp);
643 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
644 __isl_keep isl_pw_qpolynomial_fold *pwf);
645 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
646 __isl_keep isl_pw_qpolynomial_fold *pwf);
647 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
648 __isl_keep isl_union_pw_qpolynomial *upwqp);
649 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
650 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
653 __isl_give isl_space *isl_aff_get_domain_space(
654 __isl_keep isl_aff *aff);
655 __isl_give isl_space *isl_aff_get_space(
656 __isl_keep isl_aff *aff);
657 __isl_give isl_space *isl_pw_aff_get_domain_space(
658 __isl_keep isl_pw_aff *pwaff);
659 __isl_give isl_space *isl_pw_aff_get_space(
660 __isl_keep isl_pw_aff *pwaff);
661 __isl_give isl_space *isl_multi_aff_get_space(
662 __isl_keep isl_multi_aff *maff);
663 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
664 __isl_keep isl_pw_multi_aff *pma);
665 __isl_give isl_space *isl_pw_multi_aff_get_space(
666 __isl_keep isl_pw_multi_aff *pma);
667 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
668 __isl_keep isl_union_pw_multi_aff *upma);
670 #include <isl/point.h>
671 __isl_give isl_space *isl_point_get_space(
672 __isl_keep isl_point *pnt);
674 The identifiers or names of the individual dimensions may be set or read off
675 using the following functions.
677 #include <isl/space.h>
678 __isl_give isl_space *isl_space_set_dim_id(
679 __isl_take isl_space *space,
680 enum isl_dim_type type, unsigned pos,
681 __isl_take isl_id *id);
682 int isl_space_has_dim_id(__isl_keep isl_space *space,
683 enum isl_dim_type type, unsigned pos);
684 __isl_give isl_id *isl_space_get_dim_id(
685 __isl_keep isl_space *space,
686 enum isl_dim_type type, unsigned pos);
687 __isl_give isl_space *isl_space_set_dim_name(
688 __isl_take isl_space *space,
689 enum isl_dim_type type, unsigned pos,
690 __isl_keep const char *name);
691 int isl_space_has_dim_name(__isl_keep isl_space *space,
692 enum isl_dim_type type, unsigned pos);
693 __isl_keep const char *isl_space_get_dim_name(
694 __isl_keep isl_space *space,
695 enum isl_dim_type type, unsigned pos);
697 Note that C<isl_space_get_name> returns a pointer to some internal
698 data structure, so the result can only be used while the
699 corresponding C<isl_space> is alive.
700 Also note that every function that operates on two sets or relations
701 requires that both arguments have the same parameters. This also
702 means that if one of the arguments has named parameters, then the
703 other needs to have named parameters too and the names need to match.
704 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
705 arguments may have different parameters (as long as they are named),
706 in which case the result will have as parameters the union of the parameters of
709 Given the identifier or name of a dimension (typically a parameter),
710 its position can be obtained from the following function.
712 #include <isl/space.h>
713 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
714 enum isl_dim_type type, __isl_keep isl_id *id);
715 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
716 enum isl_dim_type type, const char *name);
718 The identifiers or names of entire spaces may be set or read off
719 using the following functions.
721 #include <isl/space.h>
722 __isl_give isl_space *isl_space_set_tuple_id(
723 __isl_take isl_space *space,
724 enum isl_dim_type type, __isl_take isl_id *id);
725 __isl_give isl_space *isl_space_reset_tuple_id(
726 __isl_take isl_space *space, enum isl_dim_type type);
727 int isl_space_has_tuple_id(__isl_keep isl_space *space,
728 enum isl_dim_type type);
729 __isl_give isl_id *isl_space_get_tuple_id(
730 __isl_keep isl_space *space, enum isl_dim_type type);
731 __isl_give isl_space *isl_space_set_tuple_name(
732 __isl_take isl_space *space,
733 enum isl_dim_type type, const char *s);
734 int isl_space_has_tuple_name(__isl_keep isl_space *space,
735 enum isl_dim_type type);
736 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
737 enum isl_dim_type type);
739 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
740 or C<isl_dim_set>. As with C<isl_space_get_name>,
741 the C<isl_space_get_tuple_name> function returns a pointer to some internal
743 Binary operations require the corresponding spaces of their arguments
744 to have the same name.
746 Spaces can be nested. In particular, the domain of a set or
747 the domain or range of a relation can be a nested relation.
748 The following functions can be used to construct and deconstruct
751 #include <isl/space.h>
752 int isl_space_is_wrapping(__isl_keep isl_space *space);
753 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
754 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
756 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
757 be the space of a set, while that of
758 C<isl_space_wrap> should be the space of a relation.
759 Conversely, the output of C<isl_space_unwrap> is the space
760 of a relation, while that of C<isl_space_wrap> is the space of a set.
762 Spaces can be created from other spaces
763 using the following functions.
765 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
766 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
767 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
768 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
769 __isl_give isl_space *isl_space_params(
770 __isl_take isl_space *space);
771 __isl_give isl_space *isl_space_set_from_params(
772 __isl_take isl_space *space);
773 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
774 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
775 __isl_take isl_space *right);
776 __isl_give isl_space *isl_space_align_params(
777 __isl_take isl_space *space1, __isl_take isl_space *space2)
778 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
779 enum isl_dim_type type, unsigned pos, unsigned n);
780 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
781 enum isl_dim_type type, unsigned n);
782 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
783 enum isl_dim_type type, unsigned first, unsigned n);
784 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
785 enum isl_dim_type dst_type, unsigned dst_pos,
786 enum isl_dim_type src_type, unsigned src_pos,
788 __isl_give isl_space *isl_space_map_from_set(
789 __isl_take isl_space *space);
790 __isl_give isl_space *isl_space_map_from_domain_and_range(
791 __isl_take isl_space *domain,
792 __isl_take isl_space *range);
793 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
794 __isl_give isl_space *isl_space_curry(
795 __isl_take isl_space *space);
797 Note that if dimensions are added or removed from a space, then
798 the name and the internal structure are lost.
802 A local space is essentially a space with
803 zero or more existentially quantified variables.
804 The local space of a (constraint of a) basic set or relation can be obtained
805 using the following functions.
807 #include <isl/constraint.h>
808 __isl_give isl_local_space *isl_constraint_get_local_space(
809 __isl_keep isl_constraint *constraint);
812 __isl_give isl_local_space *isl_basic_set_get_local_space(
813 __isl_keep isl_basic_set *bset);
816 __isl_give isl_local_space *isl_basic_map_get_local_space(
817 __isl_keep isl_basic_map *bmap);
819 A new local space can be created from a space using
821 #include <isl/local_space.h>
822 __isl_give isl_local_space *isl_local_space_from_space(
823 __isl_take isl_space *space);
825 They can be inspected, modified, copied and freed using the following functions.
827 #include <isl/local_space.h>
828 isl_ctx *isl_local_space_get_ctx(
829 __isl_keep isl_local_space *ls);
830 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
831 int isl_local_space_dim(__isl_keep isl_local_space *ls,
832 enum isl_dim_type type);
833 int isl_local_space_has_dim_name(
834 __isl_keep isl_local_space *ls,
835 enum isl_dim_type type, unsigned pos)
836 const char *isl_local_space_get_dim_name(
837 __isl_keep isl_local_space *ls,
838 enum isl_dim_type type, unsigned pos);
839 __isl_give isl_local_space *isl_local_space_set_dim_name(
840 __isl_take isl_local_space *ls,
841 enum isl_dim_type type, unsigned pos, const char *s);
842 __isl_give isl_local_space *isl_local_space_set_dim_id(
843 __isl_take isl_local_space *ls,
844 enum isl_dim_type type, unsigned pos,
845 __isl_take isl_id *id);
846 __isl_give isl_space *isl_local_space_get_space(
847 __isl_keep isl_local_space *ls);
848 __isl_give isl_aff *isl_local_space_get_div(
849 __isl_keep isl_local_space *ls, int pos);
850 __isl_give isl_local_space *isl_local_space_copy(
851 __isl_keep isl_local_space *ls);
852 void *isl_local_space_free(__isl_take isl_local_space *ls);
854 Two local spaces can be compared using
856 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
857 __isl_keep isl_local_space *ls2);
859 Local spaces can be created from other local spaces
860 using the following functions.
862 __isl_give isl_local_space *isl_local_space_domain(
863 __isl_take isl_local_space *ls);
864 __isl_give isl_local_space *isl_local_space_range(
865 __isl_take isl_local_space *ls);
866 __isl_give isl_local_space *isl_local_space_from_domain(
867 __isl_take isl_local_space *ls);
868 __isl_give isl_local_space *isl_local_space_intersect(
869 __isl_take isl_local_space *ls1,
870 __isl_take isl_local_space *ls2);
871 __isl_give isl_local_space *isl_local_space_add_dims(
872 __isl_take isl_local_space *ls,
873 enum isl_dim_type type, unsigned n);
874 __isl_give isl_local_space *isl_local_space_insert_dims(
875 __isl_take isl_local_space *ls,
876 enum isl_dim_type type, unsigned first, unsigned n);
877 __isl_give isl_local_space *isl_local_space_drop_dims(
878 __isl_take isl_local_space *ls,
879 enum isl_dim_type type, unsigned first, unsigned n);
881 =head2 Input and Output
883 C<isl> supports its own input/output format, which is similar
884 to the C<Omega> format, but also supports the C<PolyLib> format
889 The C<isl> format is similar to that of C<Omega>, but has a different
890 syntax for describing the parameters and allows for the definition
891 of an existentially quantified variable as the integer division
892 of an affine expression.
893 For example, the set of integers C<i> between C<0> and C<n>
894 such that C<i % 10 <= 6> can be described as
896 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
899 A set or relation can have several disjuncts, separated
900 by the keyword C<or>. Each disjunct is either a conjunction
901 of constraints or a projection (C<exists>) of a conjunction
902 of constraints. The constraints are separated by the keyword
905 =head3 C<PolyLib> format
907 If the represented set is a union, then the first line
908 contains a single number representing the number of disjuncts.
909 Otherwise, a line containing the number C<1> is optional.
911 Each disjunct is represented by a matrix of constraints.
912 The first line contains two numbers representing
913 the number of rows and columns,
914 where the number of rows is equal to the number of constraints
915 and the number of columns is equal to two plus the number of variables.
916 The following lines contain the actual rows of the constraint matrix.
917 In each row, the first column indicates whether the constraint
918 is an equality (C<0>) or inequality (C<1>). The final column
919 corresponds to the constant term.
921 If the set is parametric, then the coefficients of the parameters
922 appear in the last columns before the constant column.
923 The coefficients of any existentially quantified variables appear
924 between those of the set variables and those of the parameters.
926 =head3 Extended C<PolyLib> format
928 The extended C<PolyLib> format is nearly identical to the
929 C<PolyLib> format. The only difference is that the line
930 containing the number of rows and columns of a constraint matrix
931 also contains four additional numbers:
932 the number of output dimensions, the number of input dimensions,
933 the number of local dimensions (i.e., the number of existentially
934 quantified variables) and the number of parameters.
935 For sets, the number of ``output'' dimensions is equal
936 to the number of set dimensions, while the number of ``input''
942 __isl_give isl_basic_set *isl_basic_set_read_from_file(
943 isl_ctx *ctx, FILE *input);
944 __isl_give isl_basic_set *isl_basic_set_read_from_str(
945 isl_ctx *ctx, const char *str);
946 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
948 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
952 __isl_give isl_basic_map *isl_basic_map_read_from_file(
953 isl_ctx *ctx, FILE *input);
954 __isl_give isl_basic_map *isl_basic_map_read_from_str(
955 isl_ctx *ctx, const char *str);
956 __isl_give isl_map *isl_map_read_from_file(
957 isl_ctx *ctx, FILE *input);
958 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
961 #include <isl/union_set.h>
962 __isl_give isl_union_set *isl_union_set_read_from_file(
963 isl_ctx *ctx, FILE *input);
964 __isl_give isl_union_set *isl_union_set_read_from_str(
965 isl_ctx *ctx, const char *str);
967 #include <isl/union_map.h>
968 __isl_give isl_union_map *isl_union_map_read_from_file(
969 isl_ctx *ctx, FILE *input);
970 __isl_give isl_union_map *isl_union_map_read_from_str(
971 isl_ctx *ctx, const char *str);
973 The input format is autodetected and may be either the C<PolyLib> format
974 or the C<isl> format.
978 Before anything can be printed, an C<isl_printer> needs to
981 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
983 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
984 void isl_printer_free(__isl_take isl_printer *printer);
985 __isl_give char *isl_printer_get_str(
986 __isl_keep isl_printer *printer);
988 The printer can be inspected using the following functions.
990 FILE *isl_printer_get_file(
991 __isl_keep isl_printer *printer);
992 int isl_printer_get_output_format(
993 __isl_keep isl_printer *p);
995 The behavior of the printer can be modified in various ways
997 __isl_give isl_printer *isl_printer_set_output_format(
998 __isl_take isl_printer *p, int output_format);
999 __isl_give isl_printer *isl_printer_set_indent(
1000 __isl_take isl_printer *p, int indent);
1001 __isl_give isl_printer *isl_printer_indent(
1002 __isl_take isl_printer *p, int indent);
1003 __isl_give isl_printer *isl_printer_set_prefix(
1004 __isl_take isl_printer *p, const char *prefix);
1005 __isl_give isl_printer *isl_printer_set_suffix(
1006 __isl_take isl_printer *p, const char *suffix);
1008 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1009 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1010 and defaults to C<ISL_FORMAT_ISL>.
1011 Each line in the output is indented by C<indent> (set by
1012 C<isl_printer_set_indent>) spaces
1013 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1014 In the C<PolyLib> format output,
1015 the coefficients of the existentially quantified variables
1016 appear between those of the set variables and those
1018 The function C<isl_printer_indent> increases the indentation
1019 by the specified amount (which may be negative).
1021 To actually print something, use
1023 #include <isl/set.h>
1024 __isl_give isl_printer *isl_printer_print_basic_set(
1025 __isl_take isl_printer *printer,
1026 __isl_keep isl_basic_set *bset);
1027 __isl_give isl_printer *isl_printer_print_set(
1028 __isl_take isl_printer *printer,
1029 __isl_keep isl_set *set);
1031 #include <isl/map.h>
1032 __isl_give isl_printer *isl_printer_print_basic_map(
1033 __isl_take isl_printer *printer,
1034 __isl_keep isl_basic_map *bmap);
1035 __isl_give isl_printer *isl_printer_print_map(
1036 __isl_take isl_printer *printer,
1037 __isl_keep isl_map *map);
1039 #include <isl/union_set.h>
1040 __isl_give isl_printer *isl_printer_print_union_set(
1041 __isl_take isl_printer *p,
1042 __isl_keep isl_union_set *uset);
1044 #include <isl/union_map.h>
1045 __isl_give isl_printer *isl_printer_print_union_map(
1046 __isl_take isl_printer *p,
1047 __isl_keep isl_union_map *umap);
1049 When called on a file printer, the following function flushes
1050 the file. When called on a string printer, the buffer is cleared.
1052 __isl_give isl_printer *isl_printer_flush(
1053 __isl_take isl_printer *p);
1055 =head2 Creating New Sets and Relations
1057 C<isl> has functions for creating some standard sets and relations.
1061 =item * Empty sets and relations
1063 __isl_give isl_basic_set *isl_basic_set_empty(
1064 __isl_take isl_space *space);
1065 __isl_give isl_basic_map *isl_basic_map_empty(
1066 __isl_take isl_space *space);
1067 __isl_give isl_set *isl_set_empty(
1068 __isl_take isl_space *space);
1069 __isl_give isl_map *isl_map_empty(
1070 __isl_take isl_space *space);
1071 __isl_give isl_union_set *isl_union_set_empty(
1072 __isl_take isl_space *space);
1073 __isl_give isl_union_map *isl_union_map_empty(
1074 __isl_take isl_space *space);
1076 For C<isl_union_set>s and C<isl_union_map>s, the space
1077 is only used to specify the parameters.
1079 =item * Universe sets and relations
1081 __isl_give isl_basic_set *isl_basic_set_universe(
1082 __isl_take isl_space *space);
1083 __isl_give isl_basic_map *isl_basic_map_universe(
1084 __isl_take isl_space *space);
1085 __isl_give isl_set *isl_set_universe(
1086 __isl_take isl_space *space);
1087 __isl_give isl_map *isl_map_universe(
1088 __isl_take isl_space *space);
1089 __isl_give isl_union_set *isl_union_set_universe(
1090 __isl_take isl_union_set *uset);
1091 __isl_give isl_union_map *isl_union_map_universe(
1092 __isl_take isl_union_map *umap);
1094 The sets and relations constructed by the functions above
1095 contain all integer values, while those constructed by the
1096 functions below only contain non-negative values.
1098 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1099 __isl_take isl_space *space);
1100 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1101 __isl_take isl_space *space);
1102 __isl_give isl_set *isl_set_nat_universe(
1103 __isl_take isl_space *space);
1104 __isl_give isl_map *isl_map_nat_universe(
1105 __isl_take isl_space *space);
1107 =item * Identity relations
1109 __isl_give isl_basic_map *isl_basic_map_identity(
1110 __isl_take isl_space *space);
1111 __isl_give isl_map *isl_map_identity(
1112 __isl_take isl_space *space);
1114 The number of input and output dimensions in C<space> needs
1117 =item * Lexicographic order
1119 __isl_give isl_map *isl_map_lex_lt(
1120 __isl_take isl_space *set_space);
1121 __isl_give isl_map *isl_map_lex_le(
1122 __isl_take isl_space *set_space);
1123 __isl_give isl_map *isl_map_lex_gt(
1124 __isl_take isl_space *set_space);
1125 __isl_give isl_map *isl_map_lex_ge(
1126 __isl_take isl_space *set_space);
1127 __isl_give isl_map *isl_map_lex_lt_first(
1128 __isl_take isl_space *space, unsigned n);
1129 __isl_give isl_map *isl_map_lex_le_first(
1130 __isl_take isl_space *space, unsigned n);
1131 __isl_give isl_map *isl_map_lex_gt_first(
1132 __isl_take isl_space *space, unsigned n);
1133 __isl_give isl_map *isl_map_lex_ge_first(
1134 __isl_take isl_space *space, unsigned n);
1136 The first four functions take a space for a B<set>
1137 and return relations that express that the elements in the domain
1138 are lexicographically less
1139 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1140 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1141 than the elements in the range.
1142 The last four functions take a space for a map
1143 and return relations that express that the first C<n> dimensions
1144 in the domain are lexicographically less
1145 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1146 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1147 than the first C<n> dimensions in the range.
1151 A basic set or relation can be converted to a set or relation
1152 using the following functions.
1154 __isl_give isl_set *isl_set_from_basic_set(
1155 __isl_take isl_basic_set *bset);
1156 __isl_give isl_map *isl_map_from_basic_map(
1157 __isl_take isl_basic_map *bmap);
1159 Sets and relations can be converted to union sets and relations
1160 using the following functions.
1162 __isl_give isl_union_map *isl_union_map_from_map(
1163 __isl_take isl_map *map);
1164 __isl_give isl_union_set *isl_union_set_from_set(
1165 __isl_take isl_set *set);
1167 The inverse conversions below can only be used if the input
1168 union set or relation is known to contain elements in exactly one
1171 __isl_give isl_set *isl_set_from_union_set(
1172 __isl_take isl_union_set *uset);
1173 __isl_give isl_map *isl_map_from_union_map(
1174 __isl_take isl_union_map *umap);
1176 A zero-dimensional set can be constructed on a given parameter domain
1177 using the following function.
1179 __isl_give isl_set *isl_set_from_params(
1180 __isl_take isl_set *set);
1182 Sets and relations can be copied and freed again using the following
1185 __isl_give isl_basic_set *isl_basic_set_copy(
1186 __isl_keep isl_basic_set *bset);
1187 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1188 __isl_give isl_union_set *isl_union_set_copy(
1189 __isl_keep isl_union_set *uset);
1190 __isl_give isl_basic_map *isl_basic_map_copy(
1191 __isl_keep isl_basic_map *bmap);
1192 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1193 __isl_give isl_union_map *isl_union_map_copy(
1194 __isl_keep isl_union_map *umap);
1195 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1196 void isl_set_free(__isl_take isl_set *set);
1197 void *isl_union_set_free(__isl_take isl_union_set *uset);
1198 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1199 void isl_map_free(__isl_take isl_map *map);
1200 void *isl_union_map_free(__isl_take isl_union_map *umap);
1202 Other sets and relations can be constructed by starting
1203 from a universe set or relation, adding equality and/or
1204 inequality constraints and then projecting out the
1205 existentially quantified variables, if any.
1206 Constraints can be constructed, manipulated and
1207 added to (or removed from) (basic) sets and relations
1208 using the following functions.
1210 #include <isl/constraint.h>
1211 __isl_give isl_constraint *isl_equality_alloc(
1212 __isl_take isl_local_space *ls);
1213 __isl_give isl_constraint *isl_inequality_alloc(
1214 __isl_take isl_local_space *ls);
1215 __isl_give isl_constraint *isl_constraint_set_constant(
1216 __isl_take isl_constraint *constraint, isl_int v);
1217 __isl_give isl_constraint *isl_constraint_set_constant_si(
1218 __isl_take isl_constraint *constraint, int v);
1219 __isl_give isl_constraint *isl_constraint_set_coefficient(
1220 __isl_take isl_constraint *constraint,
1221 enum isl_dim_type type, int pos, isl_int v);
1222 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1223 __isl_take isl_constraint *constraint,
1224 enum isl_dim_type type, int pos, int v);
1225 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1226 __isl_take isl_basic_map *bmap,
1227 __isl_take isl_constraint *constraint);
1228 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1229 __isl_take isl_basic_set *bset,
1230 __isl_take isl_constraint *constraint);
1231 __isl_give isl_map *isl_map_add_constraint(
1232 __isl_take isl_map *map,
1233 __isl_take isl_constraint *constraint);
1234 __isl_give isl_set *isl_set_add_constraint(
1235 __isl_take isl_set *set,
1236 __isl_take isl_constraint *constraint);
1237 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1238 __isl_take isl_basic_set *bset,
1239 __isl_take isl_constraint *constraint);
1241 For example, to create a set containing the even integers
1242 between 10 and 42, you would use the following code.
1245 isl_local_space *ls;
1247 isl_basic_set *bset;
1249 space = isl_space_set_alloc(ctx, 0, 2);
1250 bset = isl_basic_set_universe(isl_space_copy(space));
1251 ls = isl_local_space_from_space(space);
1253 c = isl_equality_alloc(isl_local_space_copy(ls));
1254 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1255 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1256 bset = isl_basic_set_add_constraint(bset, c);
1258 c = isl_inequality_alloc(isl_local_space_copy(ls));
1259 c = isl_constraint_set_constant_si(c, -10);
1260 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1261 bset = isl_basic_set_add_constraint(bset, c);
1263 c = isl_inequality_alloc(ls);
1264 c = isl_constraint_set_constant_si(c, 42);
1265 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1266 bset = isl_basic_set_add_constraint(bset, c);
1268 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1272 isl_basic_set *bset;
1273 bset = isl_basic_set_read_from_str(ctx,
1274 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1276 A basic set or relation can also be constructed from two matrices
1277 describing the equalities and the inequalities.
1279 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1280 __isl_take isl_space *space,
1281 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1282 enum isl_dim_type c1,
1283 enum isl_dim_type c2, enum isl_dim_type c3,
1284 enum isl_dim_type c4);
1285 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1286 __isl_take isl_space *space,
1287 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1288 enum isl_dim_type c1,
1289 enum isl_dim_type c2, enum isl_dim_type c3,
1290 enum isl_dim_type c4, enum isl_dim_type c5);
1292 The C<isl_dim_type> arguments indicate the order in which
1293 different kinds of variables appear in the input matrices
1294 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1295 C<isl_dim_set> and C<isl_dim_div> for sets and
1296 of C<isl_dim_cst>, C<isl_dim_param>,
1297 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1299 A (basic or union) set or relation can also be constructed from a
1300 (union) (piecewise) (multiple) affine expression
1301 or a list of affine expressions
1302 (See L<"Piecewise Quasi Affine Expressions"> and
1303 L<"Piecewise Multiple Quasi Affine Expressions">).
1305 __isl_give isl_basic_map *isl_basic_map_from_aff(
1306 __isl_take isl_aff *aff);
1307 __isl_give isl_map *isl_map_from_aff(
1308 __isl_take isl_aff *aff);
1309 __isl_give isl_set *isl_set_from_pw_aff(
1310 __isl_take isl_pw_aff *pwaff);
1311 __isl_give isl_map *isl_map_from_pw_aff(
1312 __isl_take isl_pw_aff *pwaff);
1313 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1314 __isl_take isl_space *domain_space,
1315 __isl_take isl_aff_list *list);
1316 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1317 __isl_take isl_multi_aff *maff)
1318 __isl_give isl_map *isl_map_from_multi_aff(
1319 __isl_take isl_multi_aff *maff)
1320 __isl_give isl_set *isl_set_from_pw_multi_aff(
1321 __isl_take isl_pw_multi_aff *pma);
1322 __isl_give isl_map *isl_map_from_pw_multi_aff(
1323 __isl_take isl_pw_multi_aff *pma);
1324 __isl_give isl_union_map *
1325 isl_union_map_from_union_pw_multi_aff(
1326 __isl_take isl_union_pw_multi_aff *upma);
1328 The C<domain_dim> argument describes the domain of the resulting
1329 basic relation. It is required because the C<list> may consist
1330 of zero affine expressions.
1332 =head2 Inspecting Sets and Relations
1334 Usually, the user should not have to care about the actual constraints
1335 of the sets and maps, but should instead apply the abstract operations
1336 explained in the following sections.
1337 Occasionally, however, it may be required to inspect the individual
1338 coefficients of the constraints. This section explains how to do so.
1339 In these cases, it may also be useful to have C<isl> compute
1340 an explicit representation of the existentially quantified variables.
1342 __isl_give isl_set *isl_set_compute_divs(
1343 __isl_take isl_set *set);
1344 __isl_give isl_map *isl_map_compute_divs(
1345 __isl_take isl_map *map);
1346 __isl_give isl_union_set *isl_union_set_compute_divs(
1347 __isl_take isl_union_set *uset);
1348 __isl_give isl_union_map *isl_union_map_compute_divs(
1349 __isl_take isl_union_map *umap);
1351 This explicit representation defines the existentially quantified
1352 variables as integer divisions of the other variables, possibly
1353 including earlier existentially quantified variables.
1354 An explicitly represented existentially quantified variable therefore
1355 has a unique value when the values of the other variables are known.
1356 If, furthermore, the same existentials, i.e., existentials
1357 with the same explicit representations, should appear in the
1358 same order in each of the disjuncts of a set or map, then the user should call
1359 either of the following functions.
1361 __isl_give isl_set *isl_set_align_divs(
1362 __isl_take isl_set *set);
1363 __isl_give isl_map *isl_map_align_divs(
1364 __isl_take isl_map *map);
1366 Alternatively, the existentially quantified variables can be removed
1367 using the following functions, which compute an overapproximation.
1369 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1370 __isl_take isl_basic_set *bset);
1371 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1372 __isl_take isl_basic_map *bmap);
1373 __isl_give isl_set *isl_set_remove_divs(
1374 __isl_take isl_set *set);
1375 __isl_give isl_map *isl_map_remove_divs(
1376 __isl_take isl_map *map);
1378 To iterate over all the sets or maps in a union set or map, use
1380 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1381 int (*fn)(__isl_take isl_set *set, void *user),
1383 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1384 int (*fn)(__isl_take isl_map *map, void *user),
1387 The number of sets or maps in a union set or map can be obtained
1390 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1391 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1393 To extract the set or map in a given space from a union, use
1395 __isl_give isl_set *isl_union_set_extract_set(
1396 __isl_keep isl_union_set *uset,
1397 __isl_take isl_space *space);
1398 __isl_give isl_map *isl_union_map_extract_map(
1399 __isl_keep isl_union_map *umap,
1400 __isl_take isl_space *space);
1402 To iterate over all the basic sets or maps in a set or map, use
1404 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1405 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1407 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1408 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1411 The callback function C<fn> should return 0 if successful and
1412 -1 if an error occurs. In the latter case, or if any other error
1413 occurs, the above functions will return -1.
1415 It should be noted that C<isl> does not guarantee that
1416 the basic sets or maps passed to C<fn> are disjoint.
1417 If this is required, then the user should call one of
1418 the following functions first.
1420 __isl_give isl_set *isl_set_make_disjoint(
1421 __isl_take isl_set *set);
1422 __isl_give isl_map *isl_map_make_disjoint(
1423 __isl_take isl_map *map);
1425 The number of basic sets in a set can be obtained
1428 int isl_set_n_basic_set(__isl_keep isl_set *set);
1430 To iterate over the constraints of a basic set or map, use
1432 #include <isl/constraint.h>
1434 int isl_basic_set_n_constraint(
1435 __isl_keep isl_basic_set *bset);
1436 int isl_basic_set_foreach_constraint(
1437 __isl_keep isl_basic_set *bset,
1438 int (*fn)(__isl_take isl_constraint *c, void *user),
1440 int isl_basic_map_foreach_constraint(
1441 __isl_keep isl_basic_map *bmap,
1442 int (*fn)(__isl_take isl_constraint *c, void *user),
1444 void *isl_constraint_free(__isl_take isl_constraint *c);
1446 Again, the callback function C<fn> should return 0 if successful and
1447 -1 if an error occurs. In the latter case, or if any other error
1448 occurs, the above functions will return -1.
1449 The constraint C<c> represents either an equality or an inequality.
1450 Use the following function to find out whether a constraint
1451 represents an equality. If not, it represents an inequality.
1453 int isl_constraint_is_equality(
1454 __isl_keep isl_constraint *constraint);
1456 The coefficients of the constraints can be inspected using
1457 the following functions.
1459 int isl_constraint_is_lower_bound(
1460 __isl_keep isl_constraint *constraint,
1461 enum isl_dim_type type, unsigned pos);
1462 int isl_constraint_is_upper_bound(
1463 __isl_keep isl_constraint *constraint,
1464 enum isl_dim_type type, unsigned pos);
1465 void isl_constraint_get_constant(
1466 __isl_keep isl_constraint *constraint, isl_int *v);
1467 void isl_constraint_get_coefficient(
1468 __isl_keep isl_constraint *constraint,
1469 enum isl_dim_type type, int pos, isl_int *v);
1470 int isl_constraint_involves_dims(
1471 __isl_keep isl_constraint *constraint,
1472 enum isl_dim_type type, unsigned first, unsigned n);
1474 The explicit representations of the existentially quantified
1475 variables can be inspected using the following function.
1476 Note that the user is only allowed to use this function
1477 if the inspected set or map is the result of a call
1478 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1479 The existentially quantified variable is equal to the floor
1480 of the returned affine expression. The affine expression
1481 itself can be inspected using the functions in
1482 L<"Piecewise Quasi Affine Expressions">.
1484 __isl_give isl_aff *isl_constraint_get_div(
1485 __isl_keep isl_constraint *constraint, int pos);
1487 To obtain the constraints of a basic set or map in matrix
1488 form, use the following functions.
1490 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1491 __isl_keep isl_basic_set *bset,
1492 enum isl_dim_type c1, enum isl_dim_type c2,
1493 enum isl_dim_type c3, enum isl_dim_type c4);
1494 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1495 __isl_keep isl_basic_set *bset,
1496 enum isl_dim_type c1, enum isl_dim_type c2,
1497 enum isl_dim_type c3, enum isl_dim_type c4);
1498 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1499 __isl_keep isl_basic_map *bmap,
1500 enum isl_dim_type c1,
1501 enum isl_dim_type c2, enum isl_dim_type c3,
1502 enum isl_dim_type c4, enum isl_dim_type c5);
1503 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1504 __isl_keep isl_basic_map *bmap,
1505 enum isl_dim_type c1,
1506 enum isl_dim_type c2, enum isl_dim_type c3,
1507 enum isl_dim_type c4, enum isl_dim_type c5);
1509 The C<isl_dim_type> arguments dictate the order in which
1510 different kinds of variables appear in the resulting matrix
1511 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1512 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1514 The number of parameters, input, output or set dimensions can
1515 be obtained using the following functions.
1517 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1518 enum isl_dim_type type);
1519 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1520 enum isl_dim_type type);
1521 unsigned isl_set_dim(__isl_keep isl_set *set,
1522 enum isl_dim_type type);
1523 unsigned isl_map_dim(__isl_keep isl_map *map,
1524 enum isl_dim_type type);
1526 To check whether the description of a set or relation depends
1527 on one or more given dimensions, it is not necessary to iterate over all
1528 constraints. Instead the following functions can be used.
1530 int isl_basic_set_involves_dims(
1531 __isl_keep isl_basic_set *bset,
1532 enum isl_dim_type type, unsigned first, unsigned n);
1533 int isl_set_involves_dims(__isl_keep isl_set *set,
1534 enum isl_dim_type type, unsigned first, unsigned n);
1535 int isl_basic_map_involves_dims(
1536 __isl_keep isl_basic_map *bmap,
1537 enum isl_dim_type type, unsigned first, unsigned n);
1538 int isl_map_involves_dims(__isl_keep isl_map *map,
1539 enum isl_dim_type type, unsigned first, unsigned n);
1541 Similarly, the following functions can be used to check whether
1542 a given dimension is involved in any lower or upper bound.
1544 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1545 enum isl_dim_type type, unsigned pos);
1546 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1547 enum isl_dim_type type, unsigned pos);
1549 The identifiers or names of the domain and range spaces of a set
1550 or relation can be read off or set using the following functions.
1552 __isl_give isl_set *isl_set_set_tuple_id(
1553 __isl_take isl_set *set, __isl_take isl_id *id);
1554 __isl_give isl_set *isl_set_reset_tuple_id(
1555 __isl_take isl_set *set);
1556 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1557 __isl_give isl_id *isl_set_get_tuple_id(
1558 __isl_keep isl_set *set);
1559 __isl_give isl_map *isl_map_set_tuple_id(
1560 __isl_take isl_map *map, enum isl_dim_type type,
1561 __isl_take isl_id *id);
1562 __isl_give isl_map *isl_map_reset_tuple_id(
1563 __isl_take isl_map *map, enum isl_dim_type type);
1564 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1565 enum isl_dim_type type);
1566 __isl_give isl_id *isl_map_get_tuple_id(
1567 __isl_keep isl_map *map, enum isl_dim_type type);
1569 const char *isl_basic_set_get_tuple_name(
1570 __isl_keep isl_basic_set *bset);
1571 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1572 __isl_take isl_basic_set *set, const char *s);
1573 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1574 const char *isl_set_get_tuple_name(
1575 __isl_keep isl_set *set);
1576 const char *isl_basic_map_get_tuple_name(
1577 __isl_keep isl_basic_map *bmap,
1578 enum isl_dim_type type);
1579 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1580 __isl_take isl_basic_map *bmap,
1581 enum isl_dim_type type, const char *s);
1582 const char *isl_map_get_tuple_name(
1583 __isl_keep isl_map *map,
1584 enum isl_dim_type type);
1586 As with C<isl_space_get_tuple_name>, the value returned points to
1587 an internal data structure.
1588 The identifiers, positions or names of individual dimensions can be
1589 read off using the following functions.
1591 __isl_give isl_id *isl_basic_set_get_dim_id(
1592 __isl_keep isl_basic_set *bset,
1593 enum isl_dim_type type, unsigned pos);
1594 __isl_give isl_set *isl_set_set_dim_id(
1595 __isl_take isl_set *set, enum isl_dim_type type,
1596 unsigned pos, __isl_take isl_id *id);
1597 int isl_set_has_dim_id(__isl_keep isl_set *set,
1598 enum isl_dim_type type, unsigned pos);
1599 __isl_give isl_id *isl_set_get_dim_id(
1600 __isl_keep isl_set *set, enum isl_dim_type type,
1602 int isl_basic_map_has_dim_id(
1603 __isl_keep isl_basic_map *bmap,
1604 enum isl_dim_type type, unsigned pos);
1605 __isl_give isl_map *isl_map_set_dim_id(
1606 __isl_take isl_map *map, enum isl_dim_type type,
1607 unsigned pos, __isl_take isl_id *id);
1608 int isl_map_has_dim_id(__isl_keep isl_map *map,
1609 enum isl_dim_type type, unsigned pos);
1610 __isl_give isl_id *isl_map_get_dim_id(
1611 __isl_keep isl_map *map, enum isl_dim_type type,
1614 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1615 enum isl_dim_type type, __isl_keep isl_id *id);
1616 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1617 enum isl_dim_type type, __isl_keep isl_id *id);
1618 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1619 enum isl_dim_type type, const char *name);
1620 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1621 enum isl_dim_type type, const char *name);
1623 const char *isl_constraint_get_dim_name(
1624 __isl_keep isl_constraint *constraint,
1625 enum isl_dim_type type, unsigned pos);
1626 const char *isl_basic_set_get_dim_name(
1627 __isl_keep isl_basic_set *bset,
1628 enum isl_dim_type type, unsigned pos);
1629 int isl_set_has_dim_name(__isl_keep isl_set *set,
1630 enum isl_dim_type type, unsigned pos);
1631 const char *isl_set_get_dim_name(
1632 __isl_keep isl_set *set,
1633 enum isl_dim_type type, unsigned pos);
1634 const char *isl_basic_map_get_dim_name(
1635 __isl_keep isl_basic_map *bmap,
1636 enum isl_dim_type type, unsigned pos);
1637 const char *isl_map_get_dim_name(
1638 __isl_keep isl_map *map,
1639 enum isl_dim_type type, unsigned pos);
1641 These functions are mostly useful to obtain the identifiers, positions
1642 or names of the parameters. Identifiers of individual dimensions are
1643 essentially only useful for printing. They are ignored by all other
1644 operations and may not be preserved across those operations.
1648 =head3 Unary Properties
1654 The following functions test whether the given set or relation
1655 contains any integer points. The ``plain'' variants do not perform
1656 any computations, but simply check if the given set or relation
1657 is already known to be empty.
1659 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1660 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1661 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1662 int isl_set_is_empty(__isl_keep isl_set *set);
1663 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1664 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1665 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1666 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1667 int isl_map_is_empty(__isl_keep isl_map *map);
1668 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1670 =item * Universality
1672 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1673 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1674 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1676 =item * Single-valuedness
1678 int isl_basic_map_is_single_valued(
1679 __isl_keep isl_basic_map *bmap);
1680 int isl_map_plain_is_single_valued(
1681 __isl_keep isl_map *map);
1682 int isl_map_is_single_valued(__isl_keep isl_map *map);
1683 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1687 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1688 int isl_map_is_injective(__isl_keep isl_map *map);
1689 int isl_union_map_plain_is_injective(
1690 __isl_keep isl_union_map *umap);
1691 int isl_union_map_is_injective(
1692 __isl_keep isl_union_map *umap);
1696 int isl_map_is_bijective(__isl_keep isl_map *map);
1697 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1701 int isl_basic_map_plain_is_fixed(
1702 __isl_keep isl_basic_map *bmap,
1703 enum isl_dim_type type, unsigned pos,
1705 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1706 enum isl_dim_type type, unsigned pos,
1708 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1709 enum isl_dim_type type, unsigned pos,
1712 Check if the relation obviously lies on a hyperplane where the given dimension
1713 has a fixed value and if so, return that value in C<*val>.
1717 To check whether a set is a parameter domain, use this function:
1719 int isl_set_is_params(__isl_keep isl_set *set);
1720 int isl_union_set_is_params(
1721 __isl_keep isl_union_set *uset);
1725 The following functions check whether the domain of the given
1726 (basic) set is a wrapped relation.
1728 int isl_basic_set_is_wrapping(
1729 __isl_keep isl_basic_set *bset);
1730 int isl_set_is_wrapping(__isl_keep isl_set *set);
1732 =item * Internal Product
1734 int isl_basic_map_can_zip(
1735 __isl_keep isl_basic_map *bmap);
1736 int isl_map_can_zip(__isl_keep isl_map *map);
1738 Check whether the product of domain and range of the given relation
1740 i.e., whether both domain and range are nested relations.
1744 int isl_basic_map_can_curry(
1745 __isl_keep isl_basic_map *bmap);
1746 int isl_map_can_curry(__isl_keep isl_map *map);
1748 Check whether the domain of the (basic) relation is a wrapped relation.
1752 =head3 Binary Properties
1758 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1759 __isl_keep isl_set *set2);
1760 int isl_set_is_equal(__isl_keep isl_set *set1,
1761 __isl_keep isl_set *set2);
1762 int isl_union_set_is_equal(
1763 __isl_keep isl_union_set *uset1,
1764 __isl_keep isl_union_set *uset2);
1765 int isl_basic_map_is_equal(
1766 __isl_keep isl_basic_map *bmap1,
1767 __isl_keep isl_basic_map *bmap2);
1768 int isl_map_is_equal(__isl_keep isl_map *map1,
1769 __isl_keep isl_map *map2);
1770 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1771 __isl_keep isl_map *map2);
1772 int isl_union_map_is_equal(
1773 __isl_keep isl_union_map *umap1,
1774 __isl_keep isl_union_map *umap2);
1776 =item * Disjointness
1778 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1779 __isl_keep isl_set *set2);
1783 int isl_basic_set_is_subset(
1784 __isl_keep isl_basic_set *bset1,
1785 __isl_keep isl_basic_set *bset2);
1786 int isl_set_is_subset(__isl_keep isl_set *set1,
1787 __isl_keep isl_set *set2);
1788 int isl_set_is_strict_subset(
1789 __isl_keep isl_set *set1,
1790 __isl_keep isl_set *set2);
1791 int isl_union_set_is_subset(
1792 __isl_keep isl_union_set *uset1,
1793 __isl_keep isl_union_set *uset2);
1794 int isl_union_set_is_strict_subset(
1795 __isl_keep isl_union_set *uset1,
1796 __isl_keep isl_union_set *uset2);
1797 int isl_basic_map_is_subset(
1798 __isl_keep isl_basic_map *bmap1,
1799 __isl_keep isl_basic_map *bmap2);
1800 int isl_basic_map_is_strict_subset(
1801 __isl_keep isl_basic_map *bmap1,
1802 __isl_keep isl_basic_map *bmap2);
1803 int isl_map_is_subset(
1804 __isl_keep isl_map *map1,
1805 __isl_keep isl_map *map2);
1806 int isl_map_is_strict_subset(
1807 __isl_keep isl_map *map1,
1808 __isl_keep isl_map *map2);
1809 int isl_union_map_is_subset(
1810 __isl_keep isl_union_map *umap1,
1811 __isl_keep isl_union_map *umap2);
1812 int isl_union_map_is_strict_subset(
1813 __isl_keep isl_union_map *umap1,
1814 __isl_keep isl_union_map *umap2);
1818 =head2 Unary Operations
1824 __isl_give isl_set *isl_set_complement(
1825 __isl_take isl_set *set);
1826 __isl_give isl_map *isl_map_complement(
1827 __isl_take isl_map *map);
1831 __isl_give isl_basic_map *isl_basic_map_reverse(
1832 __isl_take isl_basic_map *bmap);
1833 __isl_give isl_map *isl_map_reverse(
1834 __isl_take isl_map *map);
1835 __isl_give isl_union_map *isl_union_map_reverse(
1836 __isl_take isl_union_map *umap);
1840 __isl_give isl_basic_set *isl_basic_set_project_out(
1841 __isl_take isl_basic_set *bset,
1842 enum isl_dim_type type, unsigned first, unsigned n);
1843 __isl_give isl_basic_map *isl_basic_map_project_out(
1844 __isl_take isl_basic_map *bmap,
1845 enum isl_dim_type type, unsigned first, unsigned n);
1846 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1847 enum isl_dim_type type, unsigned first, unsigned n);
1848 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1849 enum isl_dim_type type, unsigned first, unsigned n);
1850 __isl_give isl_basic_set *isl_basic_set_params(
1851 __isl_take isl_basic_set *bset);
1852 __isl_give isl_basic_set *isl_basic_map_domain(
1853 __isl_take isl_basic_map *bmap);
1854 __isl_give isl_basic_set *isl_basic_map_range(
1855 __isl_take isl_basic_map *bmap);
1856 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1857 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1858 __isl_give isl_set *isl_map_domain(
1859 __isl_take isl_map *bmap);
1860 __isl_give isl_set *isl_map_range(
1861 __isl_take isl_map *map);
1862 __isl_give isl_set *isl_union_set_params(
1863 __isl_take isl_union_set *uset);
1864 __isl_give isl_set *isl_union_map_params(
1865 __isl_take isl_union_map *umap);
1866 __isl_give isl_union_set *isl_union_map_domain(
1867 __isl_take isl_union_map *umap);
1868 __isl_give isl_union_set *isl_union_map_range(
1869 __isl_take isl_union_map *umap);
1871 __isl_give isl_basic_map *isl_basic_map_domain_map(
1872 __isl_take isl_basic_map *bmap);
1873 __isl_give isl_basic_map *isl_basic_map_range_map(
1874 __isl_take isl_basic_map *bmap);
1875 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1876 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1877 __isl_give isl_union_map *isl_union_map_domain_map(
1878 __isl_take isl_union_map *umap);
1879 __isl_give isl_union_map *isl_union_map_range_map(
1880 __isl_take isl_union_map *umap);
1882 The functions above construct a (basic, regular or union) relation
1883 that maps (a wrapped version of) the input relation to its domain or range.
1887 __isl_give isl_set *isl_set_eliminate(
1888 __isl_take isl_set *set, enum isl_dim_type type,
1889 unsigned first, unsigned n);
1890 __isl_give isl_basic_map *isl_basic_map_eliminate(
1891 __isl_take isl_basic_map *bmap,
1892 enum isl_dim_type type,
1893 unsigned first, unsigned n);
1894 __isl_give isl_map *isl_map_eliminate(
1895 __isl_take isl_map *map, enum isl_dim_type type,
1896 unsigned first, unsigned n);
1898 Eliminate the coefficients for the given dimensions from the constraints,
1899 without removing the dimensions.
1903 __isl_give isl_basic_set *isl_basic_set_fix(
1904 __isl_take isl_basic_set *bset,
1905 enum isl_dim_type type, unsigned pos,
1907 __isl_give isl_basic_set *isl_basic_set_fix_si(
1908 __isl_take isl_basic_set *bset,
1909 enum isl_dim_type type, unsigned pos, int value);
1910 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1911 enum isl_dim_type type, unsigned pos,
1913 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1914 enum isl_dim_type type, unsigned pos, int value);
1915 __isl_give isl_basic_map *isl_basic_map_fix_si(
1916 __isl_take isl_basic_map *bmap,
1917 enum isl_dim_type type, unsigned pos, int value);
1918 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1919 enum isl_dim_type type, unsigned pos, int value);
1921 Intersect the set or relation with the hyperplane where the given
1922 dimension has the fixed given value.
1924 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1925 __isl_take isl_basic_map *bmap,
1926 enum isl_dim_type type, unsigned pos, int value);
1927 __isl_give isl_set *isl_set_lower_bound(
1928 __isl_take isl_set *set,
1929 enum isl_dim_type type, unsigned pos,
1931 __isl_give isl_set *isl_set_lower_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_lower_bound_si(
1935 __isl_take isl_map *map,
1936 enum isl_dim_type type, unsigned pos, int value);
1937 __isl_give isl_set *isl_set_upper_bound(
1938 __isl_take isl_set *set,
1939 enum isl_dim_type type, unsigned pos,
1941 __isl_give isl_set *isl_set_upper_bound_si(
1942 __isl_take isl_set *set,
1943 enum isl_dim_type type, unsigned pos, int value);
1944 __isl_give isl_map *isl_map_upper_bound_si(
1945 __isl_take isl_map *map,
1946 enum isl_dim_type type, unsigned pos, int value);
1948 Intersect the set or relation with the half-space where the given
1949 dimension has a value bounded by the fixed given value.
1951 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1952 enum isl_dim_type type1, int pos1,
1953 enum isl_dim_type type2, int pos2);
1954 __isl_give isl_basic_map *isl_basic_map_equate(
1955 __isl_take isl_basic_map *bmap,
1956 enum isl_dim_type type1, int pos1,
1957 enum isl_dim_type type2, int pos2);
1958 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1959 enum isl_dim_type type1, int pos1,
1960 enum isl_dim_type type2, int pos2);
1962 Intersect the set or relation with the hyperplane where the given
1963 dimensions are equal to each other.
1965 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1966 enum isl_dim_type type1, int pos1,
1967 enum isl_dim_type type2, int pos2);
1969 Intersect the relation with the hyperplane where the given
1970 dimensions have opposite values.
1972 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1973 enum isl_dim_type type1, int pos1,
1974 enum isl_dim_type type2, int pos2);
1976 Intersect the relation with the half-space where the given
1977 dimensions satisfy the given ordering.
1981 __isl_give isl_map *isl_set_identity(
1982 __isl_take isl_set *set);
1983 __isl_give isl_union_map *isl_union_set_identity(
1984 __isl_take isl_union_set *uset);
1986 Construct an identity relation on the given (union) set.
1990 __isl_give isl_basic_set *isl_basic_map_deltas(
1991 __isl_take isl_basic_map *bmap);
1992 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1993 __isl_give isl_union_set *isl_union_map_deltas(
1994 __isl_take isl_union_map *umap);
1996 These functions return a (basic) set containing the differences
1997 between image elements and corresponding domain elements in the input.
1999 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2000 __isl_take isl_basic_map *bmap);
2001 __isl_give isl_map *isl_map_deltas_map(
2002 __isl_take isl_map *map);
2003 __isl_give isl_union_map *isl_union_map_deltas_map(
2004 __isl_take isl_union_map *umap);
2006 The functions above construct a (basic, regular or union) relation
2007 that maps (a wrapped version of) the input relation to its delta set.
2011 Simplify the representation of a set or relation by trying
2012 to combine pairs of basic sets or relations into a single
2013 basic set or relation.
2015 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2016 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2017 __isl_give isl_union_set *isl_union_set_coalesce(
2018 __isl_take isl_union_set *uset);
2019 __isl_give isl_union_map *isl_union_map_coalesce(
2020 __isl_take isl_union_map *umap);
2022 One of the methods for combining pairs of basic sets or relations
2023 can result in coefficients that are much larger than those that appear
2024 in the constraints of the input. By default, the coefficients are
2025 not allowed to grow larger, but this can be changed by unsetting
2026 the following option.
2028 int isl_options_set_coalesce_bounded_wrapping(
2029 isl_ctx *ctx, int val);
2030 int isl_options_get_coalesce_bounded_wrapping(
2033 =item * Detecting equalities
2035 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2036 __isl_take isl_basic_set *bset);
2037 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2038 __isl_take isl_basic_map *bmap);
2039 __isl_give isl_set *isl_set_detect_equalities(
2040 __isl_take isl_set *set);
2041 __isl_give isl_map *isl_map_detect_equalities(
2042 __isl_take isl_map *map);
2043 __isl_give isl_union_set *isl_union_set_detect_equalities(
2044 __isl_take isl_union_set *uset);
2045 __isl_give isl_union_map *isl_union_map_detect_equalities(
2046 __isl_take isl_union_map *umap);
2048 Simplify the representation of a set or relation by detecting implicit
2051 =item * Removing redundant constraints
2053 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2054 __isl_take isl_basic_set *bset);
2055 __isl_give isl_set *isl_set_remove_redundancies(
2056 __isl_take isl_set *set);
2057 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2058 __isl_take isl_basic_map *bmap);
2059 __isl_give isl_map *isl_map_remove_redundancies(
2060 __isl_take isl_map *map);
2064 __isl_give isl_basic_set *isl_set_convex_hull(
2065 __isl_take isl_set *set);
2066 __isl_give isl_basic_map *isl_map_convex_hull(
2067 __isl_take isl_map *map);
2069 If the input set or relation has any existentially quantified
2070 variables, then the result of these operations is currently undefined.
2074 __isl_give isl_basic_set *isl_set_simple_hull(
2075 __isl_take isl_set *set);
2076 __isl_give isl_basic_map *isl_map_simple_hull(
2077 __isl_take isl_map *map);
2078 __isl_give isl_union_map *isl_union_map_simple_hull(
2079 __isl_take isl_union_map *umap);
2081 These functions compute a single basic set or relation
2082 that contains the whole input set or relation.
2083 In particular, the output is described by translates
2084 of the constraints describing the basic sets or relations in the input.
2088 (See \autoref{s:simple hull}.)
2094 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2095 __isl_take isl_basic_set *bset);
2096 __isl_give isl_basic_set *isl_set_affine_hull(
2097 __isl_take isl_set *set);
2098 __isl_give isl_union_set *isl_union_set_affine_hull(
2099 __isl_take isl_union_set *uset);
2100 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2101 __isl_take isl_basic_map *bmap);
2102 __isl_give isl_basic_map *isl_map_affine_hull(
2103 __isl_take isl_map *map);
2104 __isl_give isl_union_map *isl_union_map_affine_hull(
2105 __isl_take isl_union_map *umap);
2107 In case of union sets and relations, the affine hull is computed
2110 =item * Polyhedral hull
2112 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2113 __isl_take isl_set *set);
2114 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2115 __isl_take isl_map *map);
2116 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2117 __isl_take isl_union_set *uset);
2118 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2119 __isl_take isl_union_map *umap);
2121 These functions compute a single basic set or relation
2122 not involving any existentially quantified variables
2123 that contains the whole input set or relation.
2124 In case of union sets and relations, the polyhedral hull is computed
2129 __isl_give isl_basic_set *isl_basic_set_sample(
2130 __isl_take isl_basic_set *bset);
2131 __isl_give isl_basic_set *isl_set_sample(
2132 __isl_take isl_set *set);
2133 __isl_give isl_basic_map *isl_basic_map_sample(
2134 __isl_take isl_basic_map *bmap);
2135 __isl_give isl_basic_map *isl_map_sample(
2136 __isl_take isl_map *map);
2138 If the input (basic) set or relation is non-empty, then return
2139 a singleton subset of the input. Otherwise, return an empty set.
2141 =item * Optimization
2143 #include <isl/ilp.h>
2144 enum isl_lp_result isl_basic_set_max(
2145 __isl_keep isl_basic_set *bset,
2146 __isl_keep isl_aff *obj, isl_int *opt)
2147 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2148 __isl_keep isl_aff *obj, isl_int *opt);
2149 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2150 __isl_keep isl_aff *obj, isl_int *opt);
2152 Compute the minimum or maximum of the integer affine expression C<obj>
2153 over the points in C<set>, returning the result in C<opt>.
2154 The return value may be one of C<isl_lp_error>,
2155 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2157 =item * Parametric optimization
2159 __isl_give isl_pw_aff *isl_set_dim_min(
2160 __isl_take isl_set *set, int pos);
2161 __isl_give isl_pw_aff *isl_set_dim_max(
2162 __isl_take isl_set *set, int pos);
2163 __isl_give isl_pw_aff *isl_map_dim_max(
2164 __isl_take isl_map *map, int pos);
2166 Compute the minimum or maximum of the given set or output dimension
2167 as a function of the parameters (and input dimensions), but independently
2168 of the other set or output dimensions.
2169 For lexicographic optimization, see L<"Lexicographic Optimization">.
2173 The following functions compute either the set of (rational) coefficient
2174 values of valid constraints for the given set or the set of (rational)
2175 values satisfying the constraints with coefficients from the given set.
2176 Internally, these two sets of functions perform essentially the
2177 same operations, except that the set of coefficients is assumed to
2178 be a cone, while the set of values may be any polyhedron.
2179 The current implementation is based on the Farkas lemma and
2180 Fourier-Motzkin elimination, but this may change or be made optional
2181 in future. In particular, future implementations may use different
2182 dualization algorithms or skip the elimination step.
2184 __isl_give isl_basic_set *isl_basic_set_coefficients(
2185 __isl_take isl_basic_set *bset);
2186 __isl_give isl_basic_set *isl_set_coefficients(
2187 __isl_take isl_set *set);
2188 __isl_give isl_union_set *isl_union_set_coefficients(
2189 __isl_take isl_union_set *bset);
2190 __isl_give isl_basic_set *isl_basic_set_solutions(
2191 __isl_take isl_basic_set *bset);
2192 __isl_give isl_basic_set *isl_set_solutions(
2193 __isl_take isl_set *set);
2194 __isl_give isl_union_set *isl_union_set_solutions(
2195 __isl_take isl_union_set *bset);
2199 __isl_give isl_map *isl_map_fixed_power(
2200 __isl_take isl_map *map, isl_int exp);
2201 __isl_give isl_union_map *isl_union_map_fixed_power(
2202 __isl_take isl_union_map *umap, isl_int exp);
2204 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2205 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2206 of C<map> is computed.
2208 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2210 __isl_give isl_union_map *isl_union_map_power(
2211 __isl_take isl_union_map *umap, int *exact);
2213 Compute a parametric representation for all positive powers I<k> of C<map>.
2214 The result maps I<k> to a nested relation corresponding to the
2215 I<k>th power of C<map>.
2216 The result may be an overapproximation. If the result is known to be exact,
2217 then C<*exact> is set to C<1>.
2219 =item * Transitive closure
2221 __isl_give isl_map *isl_map_transitive_closure(
2222 __isl_take isl_map *map, int *exact);
2223 __isl_give isl_union_map *isl_union_map_transitive_closure(
2224 __isl_take isl_union_map *umap, int *exact);
2226 Compute the transitive closure of C<map>.
2227 The result may be an overapproximation. If the result is known to be exact,
2228 then C<*exact> is set to C<1>.
2230 =item * Reaching path lengths
2232 __isl_give isl_map *isl_map_reaching_path_lengths(
2233 __isl_take isl_map *map, int *exact);
2235 Compute a relation that maps each element in the range of C<map>
2236 to the lengths of all paths composed of edges in C<map> that
2237 end up in the given element.
2238 The result may be an overapproximation. If the result is known to be exact,
2239 then C<*exact> is set to C<1>.
2240 To compute the I<maximal> path length, the resulting relation
2241 should be postprocessed by C<isl_map_lexmax>.
2242 In particular, if the input relation is a dependence relation
2243 (mapping sources to sinks), then the maximal path length corresponds
2244 to the free schedule.
2245 Note, however, that C<isl_map_lexmax> expects the maximum to be
2246 finite, so if the path lengths are unbounded (possibly due to
2247 the overapproximation), then you will get an error message.
2251 __isl_give isl_basic_set *isl_basic_map_wrap(
2252 __isl_take isl_basic_map *bmap);
2253 __isl_give isl_set *isl_map_wrap(
2254 __isl_take isl_map *map);
2255 __isl_give isl_union_set *isl_union_map_wrap(
2256 __isl_take isl_union_map *umap);
2257 __isl_give isl_basic_map *isl_basic_set_unwrap(
2258 __isl_take isl_basic_set *bset);
2259 __isl_give isl_map *isl_set_unwrap(
2260 __isl_take isl_set *set);
2261 __isl_give isl_union_map *isl_union_set_unwrap(
2262 __isl_take isl_union_set *uset);
2266 Remove any internal structure of domain (and range) of the given
2267 set or relation. If there is any such internal structure in the input,
2268 then the name of the space is also removed.
2270 __isl_give isl_basic_set *isl_basic_set_flatten(
2271 __isl_take isl_basic_set *bset);
2272 __isl_give isl_set *isl_set_flatten(
2273 __isl_take isl_set *set);
2274 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2275 __isl_take isl_basic_map *bmap);
2276 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2277 __isl_take isl_basic_map *bmap);
2278 __isl_give isl_map *isl_map_flatten_range(
2279 __isl_take isl_map *map);
2280 __isl_give isl_map *isl_map_flatten_domain(
2281 __isl_take isl_map *map);
2282 __isl_give isl_basic_map *isl_basic_map_flatten(
2283 __isl_take isl_basic_map *bmap);
2284 __isl_give isl_map *isl_map_flatten(
2285 __isl_take isl_map *map);
2287 __isl_give isl_map *isl_set_flatten_map(
2288 __isl_take isl_set *set);
2290 The function above constructs a relation
2291 that maps the input set to a flattened version of the set.
2295 Lift the input set to a space with extra dimensions corresponding
2296 to the existentially quantified variables in the input.
2297 In particular, the result lives in a wrapped map where the domain
2298 is the original space and the range corresponds to the original
2299 existentially quantified variables.
2301 __isl_give isl_basic_set *isl_basic_set_lift(
2302 __isl_take isl_basic_set *bset);
2303 __isl_give isl_set *isl_set_lift(
2304 __isl_take isl_set *set);
2305 __isl_give isl_union_set *isl_union_set_lift(
2306 __isl_take isl_union_set *uset);
2308 Given a local space that contains the existentially quantified
2309 variables of a set, a basic relation that, when applied to
2310 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2311 can be constructed using the following function.
2313 #include <isl/local_space.h>
2314 __isl_give isl_basic_map *isl_local_space_lifting(
2315 __isl_take isl_local_space *ls);
2317 =item * Internal Product
2319 __isl_give isl_basic_map *isl_basic_map_zip(
2320 __isl_take isl_basic_map *bmap);
2321 __isl_give isl_map *isl_map_zip(
2322 __isl_take isl_map *map);
2323 __isl_give isl_union_map *isl_union_map_zip(
2324 __isl_take isl_union_map *umap);
2326 Given a relation with nested relations for domain and range,
2327 interchange the range of the domain with the domain of the range.
2331 __isl_give isl_basic_map *isl_basic_map_curry(
2332 __isl_take isl_basic_map *bmap);
2333 __isl_give isl_map *isl_map_curry(
2334 __isl_take isl_map *map);
2335 __isl_give isl_union_map *isl_union_map_curry(
2336 __isl_take isl_union_map *umap);
2338 Given a relation with a nested relation for domain,
2339 move the range of the nested relation out of the domain
2340 and use it as the domain of a nested relation in the range,
2341 with the original range as range of this nested relation.
2343 =item * Aligning parameters
2345 __isl_give isl_set *isl_set_align_params(
2346 __isl_take isl_set *set,
2347 __isl_take isl_space *model);
2348 __isl_give isl_map *isl_map_align_params(
2349 __isl_take isl_map *map,
2350 __isl_take isl_space *model);
2352 Change the order of the parameters of the given set or relation
2353 such that the first parameters match those of C<model>.
2354 This may involve the introduction of extra parameters.
2355 All parameters need to be named.
2357 =item * Dimension manipulation
2359 __isl_give isl_set *isl_set_add_dims(
2360 __isl_take isl_set *set,
2361 enum isl_dim_type type, unsigned n);
2362 __isl_give isl_map *isl_map_add_dims(
2363 __isl_take isl_map *map,
2364 enum isl_dim_type type, unsigned n);
2365 __isl_give isl_set *isl_set_insert_dims(
2366 __isl_take isl_set *set,
2367 enum isl_dim_type type, unsigned pos, unsigned n);
2368 __isl_give isl_map *isl_map_insert_dims(
2369 __isl_take isl_map *map,
2370 enum isl_dim_type type, unsigned pos, unsigned n);
2371 __isl_give isl_basic_set *isl_basic_set_move_dims(
2372 __isl_take isl_basic_set *bset,
2373 enum isl_dim_type dst_type, unsigned dst_pos,
2374 enum isl_dim_type src_type, unsigned src_pos,
2376 __isl_give isl_basic_map *isl_basic_map_move_dims(
2377 __isl_take isl_basic_map *bmap,
2378 enum isl_dim_type dst_type, unsigned dst_pos,
2379 enum isl_dim_type src_type, unsigned src_pos,
2381 __isl_give isl_set *isl_set_move_dims(
2382 __isl_take isl_set *set,
2383 enum isl_dim_type dst_type, unsigned dst_pos,
2384 enum isl_dim_type src_type, unsigned src_pos,
2386 __isl_give isl_map *isl_map_move_dims(
2387 __isl_take isl_map *map,
2388 enum isl_dim_type dst_type, unsigned dst_pos,
2389 enum isl_dim_type src_type, unsigned src_pos,
2392 It is usually not advisable to directly change the (input or output)
2393 space of a set or a relation as this removes the name and the internal
2394 structure of the space. However, the above functions can be useful
2395 to add new parameters, assuming
2396 C<isl_set_align_params> and C<isl_map_align_params>
2401 =head2 Binary Operations
2403 The two arguments of a binary operation not only need to live
2404 in the same C<isl_ctx>, they currently also need to have
2405 the same (number of) parameters.
2407 =head3 Basic Operations
2411 =item * Intersection
2413 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2414 __isl_take isl_basic_set *bset1,
2415 __isl_take isl_basic_set *bset2);
2416 __isl_give isl_basic_set *isl_basic_set_intersect(
2417 __isl_take isl_basic_set *bset1,
2418 __isl_take isl_basic_set *bset2);
2419 __isl_give isl_set *isl_set_intersect_params(
2420 __isl_take isl_set *set,
2421 __isl_take isl_set *params);
2422 __isl_give isl_set *isl_set_intersect(
2423 __isl_take isl_set *set1,
2424 __isl_take isl_set *set2);
2425 __isl_give isl_union_set *isl_union_set_intersect_params(
2426 __isl_take isl_union_set *uset,
2427 __isl_take isl_set *set);
2428 __isl_give isl_union_map *isl_union_map_intersect_params(
2429 __isl_take isl_union_map *umap,
2430 __isl_take isl_set *set);
2431 __isl_give isl_union_set *isl_union_set_intersect(
2432 __isl_take isl_union_set *uset1,
2433 __isl_take isl_union_set *uset2);
2434 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2435 __isl_take isl_basic_map *bmap,
2436 __isl_take isl_basic_set *bset);
2437 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2438 __isl_take isl_basic_map *bmap,
2439 __isl_take isl_basic_set *bset);
2440 __isl_give isl_basic_map *isl_basic_map_intersect(
2441 __isl_take isl_basic_map *bmap1,
2442 __isl_take isl_basic_map *bmap2);
2443 __isl_give isl_map *isl_map_intersect_params(
2444 __isl_take isl_map *map,
2445 __isl_take isl_set *params);
2446 __isl_give isl_map *isl_map_intersect_domain(
2447 __isl_take isl_map *map,
2448 __isl_take isl_set *set);
2449 __isl_give isl_map *isl_map_intersect_range(
2450 __isl_take isl_map *map,
2451 __isl_take isl_set *set);
2452 __isl_give isl_map *isl_map_intersect(
2453 __isl_take isl_map *map1,
2454 __isl_take isl_map *map2);
2455 __isl_give isl_union_map *isl_union_map_intersect_domain(
2456 __isl_take isl_union_map *umap,
2457 __isl_take isl_union_set *uset);
2458 __isl_give isl_union_map *isl_union_map_intersect_range(
2459 __isl_take isl_union_map *umap,
2460 __isl_take isl_union_set *uset);
2461 __isl_give isl_union_map *isl_union_map_intersect(
2462 __isl_take isl_union_map *umap1,
2463 __isl_take isl_union_map *umap2);
2467 __isl_give isl_set *isl_basic_set_union(
2468 __isl_take isl_basic_set *bset1,
2469 __isl_take isl_basic_set *bset2);
2470 __isl_give isl_map *isl_basic_map_union(
2471 __isl_take isl_basic_map *bmap1,
2472 __isl_take isl_basic_map *bmap2);
2473 __isl_give isl_set *isl_set_union(
2474 __isl_take isl_set *set1,
2475 __isl_take isl_set *set2);
2476 __isl_give isl_map *isl_map_union(
2477 __isl_take isl_map *map1,
2478 __isl_take isl_map *map2);
2479 __isl_give isl_union_set *isl_union_set_union(
2480 __isl_take isl_union_set *uset1,
2481 __isl_take isl_union_set *uset2);
2482 __isl_give isl_union_map *isl_union_map_union(
2483 __isl_take isl_union_map *umap1,
2484 __isl_take isl_union_map *umap2);
2486 =item * Set difference
2488 __isl_give isl_set *isl_set_subtract(
2489 __isl_take isl_set *set1,
2490 __isl_take isl_set *set2);
2491 __isl_give isl_map *isl_map_subtract(
2492 __isl_take isl_map *map1,
2493 __isl_take isl_map *map2);
2494 __isl_give isl_map *isl_map_subtract_domain(
2495 __isl_take isl_map *map,
2496 __isl_take isl_set *dom);
2497 __isl_give isl_map *isl_map_subtract_range(
2498 __isl_take isl_map *map,
2499 __isl_take isl_set *dom);
2500 __isl_give isl_union_set *isl_union_set_subtract(
2501 __isl_take isl_union_set *uset1,
2502 __isl_take isl_union_set *uset2);
2503 __isl_give isl_union_map *isl_union_map_subtract(
2504 __isl_take isl_union_map *umap1,
2505 __isl_take isl_union_map *umap2);
2509 __isl_give isl_basic_set *isl_basic_set_apply(
2510 __isl_take isl_basic_set *bset,
2511 __isl_take isl_basic_map *bmap);
2512 __isl_give isl_set *isl_set_apply(
2513 __isl_take isl_set *set,
2514 __isl_take isl_map *map);
2515 __isl_give isl_union_set *isl_union_set_apply(
2516 __isl_take isl_union_set *uset,
2517 __isl_take isl_union_map *umap);
2518 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2519 __isl_take isl_basic_map *bmap1,
2520 __isl_take isl_basic_map *bmap2);
2521 __isl_give isl_basic_map *isl_basic_map_apply_range(
2522 __isl_take isl_basic_map *bmap1,
2523 __isl_take isl_basic_map *bmap2);
2524 __isl_give isl_map *isl_map_apply_domain(
2525 __isl_take isl_map *map1,
2526 __isl_take isl_map *map2);
2527 __isl_give isl_union_map *isl_union_map_apply_domain(
2528 __isl_take isl_union_map *umap1,
2529 __isl_take isl_union_map *umap2);
2530 __isl_give isl_map *isl_map_apply_range(
2531 __isl_take isl_map *map1,
2532 __isl_take isl_map *map2);
2533 __isl_give isl_union_map *isl_union_map_apply_range(
2534 __isl_take isl_union_map *umap1,
2535 __isl_take isl_union_map *umap2);
2537 =item * Cartesian Product
2539 __isl_give isl_set *isl_set_product(
2540 __isl_take isl_set *set1,
2541 __isl_take isl_set *set2);
2542 __isl_give isl_union_set *isl_union_set_product(
2543 __isl_take isl_union_set *uset1,
2544 __isl_take isl_union_set *uset2);
2545 __isl_give isl_basic_map *isl_basic_map_domain_product(
2546 __isl_take isl_basic_map *bmap1,
2547 __isl_take isl_basic_map *bmap2);
2548 __isl_give isl_basic_map *isl_basic_map_range_product(
2549 __isl_take isl_basic_map *bmap1,
2550 __isl_take isl_basic_map *bmap2);
2551 __isl_give isl_map *isl_map_domain_product(
2552 __isl_take isl_map *map1,
2553 __isl_take isl_map *map2);
2554 __isl_give isl_map *isl_map_range_product(
2555 __isl_take isl_map *map1,
2556 __isl_take isl_map *map2);
2557 __isl_give isl_union_map *isl_union_map_range_product(
2558 __isl_take isl_union_map *umap1,
2559 __isl_take isl_union_map *umap2);
2560 __isl_give isl_map *isl_map_product(
2561 __isl_take isl_map *map1,
2562 __isl_take isl_map *map2);
2563 __isl_give isl_union_map *isl_union_map_product(
2564 __isl_take isl_union_map *umap1,
2565 __isl_take isl_union_map *umap2);
2567 The above functions compute the cross product of the given
2568 sets or relations. The domains and ranges of the results
2569 are wrapped maps between domains and ranges of the inputs.
2570 To obtain a ``flat'' product, use the following functions
2573 __isl_give isl_basic_set *isl_basic_set_flat_product(
2574 __isl_take isl_basic_set *bset1,
2575 __isl_take isl_basic_set *bset2);
2576 __isl_give isl_set *isl_set_flat_product(
2577 __isl_take isl_set *set1,
2578 __isl_take isl_set *set2);
2579 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2580 __isl_take isl_basic_map *bmap1,
2581 __isl_take isl_basic_map *bmap2);
2582 __isl_give isl_map *isl_map_flat_domain_product(
2583 __isl_take isl_map *map1,
2584 __isl_take isl_map *map2);
2585 __isl_give isl_map *isl_map_flat_range_product(
2586 __isl_take isl_map *map1,
2587 __isl_take isl_map *map2);
2588 __isl_give isl_union_map *isl_union_map_flat_range_product(
2589 __isl_take isl_union_map *umap1,
2590 __isl_take isl_union_map *umap2);
2591 __isl_give isl_basic_map *isl_basic_map_flat_product(
2592 __isl_take isl_basic_map *bmap1,
2593 __isl_take isl_basic_map *bmap2);
2594 __isl_give isl_map *isl_map_flat_product(
2595 __isl_take isl_map *map1,
2596 __isl_take isl_map *map2);
2598 =item * Simplification
2600 __isl_give isl_basic_set *isl_basic_set_gist(
2601 __isl_take isl_basic_set *bset,
2602 __isl_take isl_basic_set *context);
2603 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2604 __isl_take isl_set *context);
2605 __isl_give isl_set *isl_set_gist_params(
2606 __isl_take isl_set *set,
2607 __isl_take isl_set *context);
2608 __isl_give isl_union_set *isl_union_set_gist(
2609 __isl_take isl_union_set *uset,
2610 __isl_take isl_union_set *context);
2611 __isl_give isl_union_set *isl_union_set_gist_params(
2612 __isl_take isl_union_set *uset,
2613 __isl_take isl_set *set);
2614 __isl_give isl_basic_map *isl_basic_map_gist(
2615 __isl_take isl_basic_map *bmap,
2616 __isl_take isl_basic_map *context);
2617 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2618 __isl_take isl_map *context);
2619 __isl_give isl_map *isl_map_gist_params(
2620 __isl_take isl_map *map,
2621 __isl_take isl_set *context);
2622 __isl_give isl_map *isl_map_gist_domain(
2623 __isl_take isl_map *map,
2624 __isl_take isl_set *context);
2625 __isl_give isl_map *isl_map_gist_range(
2626 __isl_take isl_map *map,
2627 __isl_take isl_set *context);
2628 __isl_give isl_union_map *isl_union_map_gist(
2629 __isl_take isl_union_map *umap,
2630 __isl_take isl_union_map *context);
2631 __isl_give isl_union_map *isl_union_map_gist_params(
2632 __isl_take isl_union_map *umap,
2633 __isl_take isl_set *set);
2634 __isl_give isl_union_map *isl_union_map_gist_domain(
2635 __isl_take isl_union_map *umap,
2636 __isl_take isl_union_set *uset);
2637 __isl_give isl_union_map *isl_union_map_gist_range(
2638 __isl_take isl_union_map *umap,
2639 __isl_take isl_union_set *uset);
2641 The gist operation returns a set or relation that has the
2642 same intersection with the context as the input set or relation.
2643 Any implicit equality in the intersection is made explicit in the result,
2644 while all inequalities that are redundant with respect to the intersection
2646 In case of union sets and relations, the gist operation is performed
2651 =head3 Lexicographic Optimization
2653 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2654 the following functions
2655 compute a set that contains the lexicographic minimum or maximum
2656 of the elements in C<set> (or C<bset>) for those values of the parameters
2657 that satisfy C<dom>.
2658 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2659 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2661 In other words, the union of the parameter values
2662 for which the result is non-empty and of C<*empty>
2665 __isl_give isl_set *isl_basic_set_partial_lexmin(
2666 __isl_take isl_basic_set *bset,
2667 __isl_take isl_basic_set *dom,
2668 __isl_give isl_set **empty);
2669 __isl_give isl_set *isl_basic_set_partial_lexmax(
2670 __isl_take isl_basic_set *bset,
2671 __isl_take isl_basic_set *dom,
2672 __isl_give isl_set **empty);
2673 __isl_give isl_set *isl_set_partial_lexmin(
2674 __isl_take isl_set *set, __isl_take isl_set *dom,
2675 __isl_give isl_set **empty);
2676 __isl_give isl_set *isl_set_partial_lexmax(
2677 __isl_take isl_set *set, __isl_take isl_set *dom,
2678 __isl_give isl_set **empty);
2680 Given a (basic) set C<set> (or C<bset>), the following functions simply
2681 return a set containing the lexicographic minimum or maximum
2682 of the elements in C<set> (or C<bset>).
2683 In case of union sets, the optimum is computed per space.
2685 __isl_give isl_set *isl_basic_set_lexmin(
2686 __isl_take isl_basic_set *bset);
2687 __isl_give isl_set *isl_basic_set_lexmax(
2688 __isl_take isl_basic_set *bset);
2689 __isl_give isl_set *isl_set_lexmin(
2690 __isl_take isl_set *set);
2691 __isl_give isl_set *isl_set_lexmax(
2692 __isl_take isl_set *set);
2693 __isl_give isl_union_set *isl_union_set_lexmin(
2694 __isl_take isl_union_set *uset);
2695 __isl_give isl_union_set *isl_union_set_lexmax(
2696 __isl_take isl_union_set *uset);
2698 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2699 the following functions
2700 compute a relation that maps each element of C<dom>
2701 to the single lexicographic minimum or maximum
2702 of the elements that are associated to that same
2703 element in C<map> (or C<bmap>).
2704 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2705 that contains the elements in C<dom> that do not map
2706 to any elements in C<map> (or C<bmap>).
2707 In other words, the union of the domain of the result and of C<*empty>
2710 __isl_give isl_map *isl_basic_map_partial_lexmax(
2711 __isl_take isl_basic_map *bmap,
2712 __isl_take isl_basic_set *dom,
2713 __isl_give isl_set **empty);
2714 __isl_give isl_map *isl_basic_map_partial_lexmin(
2715 __isl_take isl_basic_map *bmap,
2716 __isl_take isl_basic_set *dom,
2717 __isl_give isl_set **empty);
2718 __isl_give isl_map *isl_map_partial_lexmax(
2719 __isl_take isl_map *map, __isl_take isl_set *dom,
2720 __isl_give isl_set **empty);
2721 __isl_give isl_map *isl_map_partial_lexmin(
2722 __isl_take isl_map *map, __isl_take isl_set *dom,
2723 __isl_give isl_set **empty);
2725 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2726 return a map mapping each element in the domain of
2727 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2728 of all elements associated to that element.
2729 In case of union relations, the optimum is computed per space.
2731 __isl_give isl_map *isl_basic_map_lexmin(
2732 __isl_take isl_basic_map *bmap);
2733 __isl_give isl_map *isl_basic_map_lexmax(
2734 __isl_take isl_basic_map *bmap);
2735 __isl_give isl_map *isl_map_lexmin(
2736 __isl_take isl_map *map);
2737 __isl_give isl_map *isl_map_lexmax(
2738 __isl_take isl_map *map);
2739 __isl_give isl_union_map *isl_union_map_lexmin(
2740 __isl_take isl_union_map *umap);
2741 __isl_give isl_union_map *isl_union_map_lexmax(
2742 __isl_take isl_union_map *umap);
2744 The following functions return their result in the form of
2745 a piecewise multi-affine expression
2746 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2747 but are otherwise equivalent to the corresponding functions
2748 returning a basic set or relation.
2750 __isl_give isl_pw_multi_aff *
2751 isl_basic_map_lexmin_pw_multi_aff(
2752 __isl_take isl_basic_map *bmap);
2753 __isl_give isl_pw_multi_aff *
2754 isl_basic_set_partial_lexmin_pw_multi_aff(
2755 __isl_take isl_basic_set *bset,
2756 __isl_take isl_basic_set *dom,
2757 __isl_give isl_set **empty);
2758 __isl_give isl_pw_multi_aff *
2759 isl_basic_set_partial_lexmax_pw_multi_aff(
2760 __isl_take isl_basic_set *bset,
2761 __isl_take isl_basic_set *dom,
2762 __isl_give isl_set **empty);
2763 __isl_give isl_pw_multi_aff *
2764 isl_basic_map_partial_lexmin_pw_multi_aff(
2765 __isl_take isl_basic_map *bmap,
2766 __isl_take isl_basic_set *dom,
2767 __isl_give isl_set **empty);
2768 __isl_give isl_pw_multi_aff *
2769 isl_basic_map_partial_lexmax_pw_multi_aff(
2770 __isl_take isl_basic_map *bmap,
2771 __isl_take isl_basic_set *dom,
2772 __isl_give isl_set **empty);
2776 Lists are defined over several element types, including
2777 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2778 Here we take lists of C<isl_set>s as an example.
2779 Lists can be created, copied and freed using the following functions.
2781 #include <isl/list.h>
2782 __isl_give isl_set_list *isl_set_list_from_set(
2783 __isl_take isl_set *el);
2784 __isl_give isl_set_list *isl_set_list_alloc(
2785 isl_ctx *ctx, int n);
2786 __isl_give isl_set_list *isl_set_list_copy(
2787 __isl_keep isl_set_list *list);
2788 __isl_give isl_set_list *isl_set_list_add(
2789 __isl_take isl_set_list *list,
2790 __isl_take isl_set *el);
2791 __isl_give isl_set_list *isl_set_list_concat(
2792 __isl_take isl_set_list *list1,
2793 __isl_take isl_set_list *list2);
2794 void *isl_set_list_free(__isl_take isl_set_list *list);
2796 C<isl_set_list_alloc> creates an empty list with a capacity for
2797 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2800 Lists can be inspected using the following functions.
2802 #include <isl/list.h>
2803 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2804 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2805 __isl_give isl_set *isl_set_list_get_set(
2806 __isl_keep isl_set_list *list, int index);
2807 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2808 int (*fn)(__isl_take isl_set *el, void *user),
2811 Lists can be printed using
2813 #include <isl/list.h>
2814 __isl_give isl_printer *isl_printer_print_set_list(
2815 __isl_take isl_printer *p,
2816 __isl_keep isl_set_list *list);
2820 Vectors can be created, copied and freed using the following functions.
2822 #include <isl/vec.h>
2823 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2825 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2826 void isl_vec_free(__isl_take isl_vec *vec);
2828 Note that the elements of a newly created vector may have arbitrary values.
2829 The elements can be changed and inspected using the following functions.
2831 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2832 int isl_vec_size(__isl_keep isl_vec *vec);
2833 int isl_vec_get_element(__isl_keep isl_vec *vec,
2834 int pos, isl_int *v);
2835 __isl_give isl_vec *isl_vec_set_element(
2836 __isl_take isl_vec *vec, int pos, isl_int v);
2837 __isl_give isl_vec *isl_vec_set_element_si(
2838 __isl_take isl_vec *vec, int pos, int v);
2839 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2841 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2844 C<isl_vec_get_element> will return a negative value if anything went wrong.
2845 In that case, the value of C<*v> is undefined.
2849 Matrices can be created, copied and freed using the following functions.
2851 #include <isl/mat.h>
2852 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2853 unsigned n_row, unsigned n_col);
2854 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2855 void isl_mat_free(__isl_take isl_mat *mat);
2857 Note that the elements of a newly created matrix may have arbitrary values.
2858 The elements can be changed and inspected using the following functions.
2860 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2861 int isl_mat_rows(__isl_keep isl_mat *mat);
2862 int isl_mat_cols(__isl_keep isl_mat *mat);
2863 int isl_mat_get_element(__isl_keep isl_mat *mat,
2864 int row, int col, isl_int *v);
2865 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2866 int row, int col, isl_int v);
2867 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2868 int row, int col, int v);
2870 C<isl_mat_get_element> will return a negative value if anything went wrong.
2871 In that case, the value of C<*v> is undefined.
2873 The following function can be used to compute the (right) inverse
2874 of a matrix, i.e., a matrix such that the product of the original
2875 and the inverse (in that order) is a multiple of the identity matrix.
2876 The input matrix is assumed to be of full row-rank.
2878 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2880 The following function can be used to compute the (right) kernel
2881 (or null space) of a matrix, i.e., a matrix such that the product of
2882 the original and the kernel (in that order) is the zero matrix.
2884 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2886 =head2 Piecewise Quasi Affine Expressions
2888 The zero quasi affine expression on a given domain can be created using
2890 __isl_give isl_aff *isl_aff_zero_on_domain(
2891 __isl_take isl_local_space *ls);
2893 Note that the space in which the resulting object lives is a map space
2894 with the given space as domain and a one-dimensional range.
2896 An empty piecewise quasi affine expression (one with no cells)
2897 or a piecewise quasi affine expression with a single cell can
2898 be created using the following functions.
2900 #include <isl/aff.h>
2901 __isl_give isl_pw_aff *isl_pw_aff_empty(
2902 __isl_take isl_space *space);
2903 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2904 __isl_take isl_set *set, __isl_take isl_aff *aff);
2905 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2906 __isl_take isl_aff *aff);
2908 A piecewise quasi affine expression that is equal to 1 on a set
2909 and 0 outside the set can be created using the following function.
2911 #include <isl/aff.h>
2912 __isl_give isl_pw_aff *isl_set_indicator_function(
2913 __isl_take isl_set *set);
2915 Quasi affine expressions can be copied and freed using
2917 #include <isl/aff.h>
2918 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2919 void *isl_aff_free(__isl_take isl_aff *aff);
2921 __isl_give isl_pw_aff *isl_pw_aff_copy(
2922 __isl_keep isl_pw_aff *pwaff);
2923 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2925 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2926 using the following function. The constraint is required to have
2927 a non-zero coefficient for the specified dimension.
2929 #include <isl/constraint.h>
2930 __isl_give isl_aff *isl_constraint_get_bound(
2931 __isl_keep isl_constraint *constraint,
2932 enum isl_dim_type type, int pos);
2934 The entire affine expression of the constraint can also be extracted
2935 using the following function.
2937 #include <isl/constraint.h>
2938 __isl_give isl_aff *isl_constraint_get_aff(
2939 __isl_keep isl_constraint *constraint);
2941 Conversely, an equality constraint equating
2942 the affine expression to zero or an inequality constraint enforcing
2943 the affine expression to be non-negative, can be constructed using
2945 __isl_give isl_constraint *isl_equality_from_aff(
2946 __isl_take isl_aff *aff);
2947 __isl_give isl_constraint *isl_inequality_from_aff(
2948 __isl_take isl_aff *aff);
2950 The expression can be inspected using
2952 #include <isl/aff.h>
2953 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2954 int isl_aff_dim(__isl_keep isl_aff *aff,
2955 enum isl_dim_type type);
2956 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2957 __isl_keep isl_aff *aff);
2958 __isl_give isl_local_space *isl_aff_get_local_space(
2959 __isl_keep isl_aff *aff);
2960 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2961 enum isl_dim_type type, unsigned pos);
2962 const char *isl_pw_aff_get_dim_name(
2963 __isl_keep isl_pw_aff *pa,
2964 enum isl_dim_type type, unsigned pos);
2965 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2966 enum isl_dim_type type, unsigned pos);
2967 __isl_give isl_id *isl_pw_aff_get_dim_id(
2968 __isl_keep isl_pw_aff *pa,
2969 enum isl_dim_type type, unsigned pos);
2970 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2972 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2973 enum isl_dim_type type, int pos, isl_int *v);
2974 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
2976 __isl_give isl_aff *isl_aff_get_div(
2977 __isl_keep isl_aff *aff, int pos);
2979 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
2980 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
2981 int (*fn)(__isl_take isl_set *set,
2982 __isl_take isl_aff *aff,
2983 void *user), void *user);
2985 int isl_aff_is_cst(__isl_keep isl_aff *aff);
2986 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
2988 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
2989 enum isl_dim_type type, unsigned first, unsigned n);
2990 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
2991 enum isl_dim_type type, unsigned first, unsigned n);
2993 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
2994 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
2995 enum isl_dim_type type);
2996 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
2998 It can be modified using
3000 #include <isl/aff.h>
3001 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3002 __isl_take isl_pw_aff *pwaff,
3003 enum isl_dim_type type, __isl_take isl_id *id);
3004 __isl_give isl_aff *isl_aff_set_dim_name(
3005 __isl_take isl_aff *aff, enum isl_dim_type type,
3006 unsigned pos, const char *s);
3007 __isl_give isl_aff *isl_aff_set_dim_id(
3008 __isl_take isl_aff *aff, enum isl_dim_type type,
3009 unsigned pos, __isl_take isl_id *id);
3010 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3011 __isl_take isl_pw_aff *pma,
3012 enum isl_dim_type type, unsigned pos,
3013 __isl_take isl_id *id);
3014 __isl_give isl_aff *isl_aff_set_constant(
3015 __isl_take isl_aff *aff, isl_int v);
3016 __isl_give isl_aff *isl_aff_set_constant_si(
3017 __isl_take isl_aff *aff, int v);
3018 __isl_give isl_aff *isl_aff_set_coefficient(
3019 __isl_take isl_aff *aff,
3020 enum isl_dim_type type, int pos, isl_int v);
3021 __isl_give isl_aff *isl_aff_set_coefficient_si(
3022 __isl_take isl_aff *aff,
3023 enum isl_dim_type type, int pos, int v);
3024 __isl_give isl_aff *isl_aff_set_denominator(
3025 __isl_take isl_aff *aff, isl_int v);
3027 __isl_give isl_aff *isl_aff_add_constant(
3028 __isl_take isl_aff *aff, isl_int v);
3029 __isl_give isl_aff *isl_aff_add_constant_si(
3030 __isl_take isl_aff *aff, int v);
3031 __isl_give isl_aff *isl_aff_add_coefficient(
3032 __isl_take isl_aff *aff,
3033 enum isl_dim_type type, int pos, isl_int v);
3034 __isl_give isl_aff *isl_aff_add_coefficient_si(
3035 __isl_take isl_aff *aff,
3036 enum isl_dim_type type, int pos, int v);
3038 __isl_give isl_aff *isl_aff_insert_dims(
3039 __isl_take isl_aff *aff,
3040 enum isl_dim_type type, unsigned first, unsigned n);
3041 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3042 __isl_take isl_pw_aff *pwaff,
3043 enum isl_dim_type type, unsigned first, unsigned n);
3044 __isl_give isl_aff *isl_aff_add_dims(
3045 __isl_take isl_aff *aff,
3046 enum isl_dim_type type, unsigned n);
3047 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3048 __isl_take isl_pw_aff *pwaff,
3049 enum isl_dim_type type, unsigned n);
3050 __isl_give isl_aff *isl_aff_drop_dims(
3051 __isl_take isl_aff *aff,
3052 enum isl_dim_type type, unsigned first, unsigned n);
3053 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3054 __isl_take isl_pw_aff *pwaff,
3055 enum isl_dim_type type, unsigned first, unsigned n);
3057 Note that the C<set_constant> and C<set_coefficient> functions
3058 set the I<numerator> of the constant or coefficient, while
3059 C<add_constant> and C<add_coefficient> add an integer value to
3060 the possibly rational constant or coefficient.
3062 To check whether an affine expressions is obviously zero
3063 or obviously equal to some other affine expression, use
3065 #include <isl/aff.h>
3066 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3067 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3068 __isl_keep isl_aff *aff2);
3069 int isl_pw_aff_plain_is_equal(
3070 __isl_keep isl_pw_aff *pwaff1,
3071 __isl_keep isl_pw_aff *pwaff2);
3075 #include <isl/aff.h>
3076 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3077 __isl_take isl_aff *aff2);
3078 __isl_give isl_pw_aff *isl_pw_aff_add(
3079 __isl_take isl_pw_aff *pwaff1,
3080 __isl_take isl_pw_aff *pwaff2);
3081 __isl_give isl_pw_aff *isl_pw_aff_min(
3082 __isl_take isl_pw_aff *pwaff1,
3083 __isl_take isl_pw_aff *pwaff2);
3084 __isl_give isl_pw_aff *isl_pw_aff_max(
3085 __isl_take isl_pw_aff *pwaff1,
3086 __isl_take isl_pw_aff *pwaff2);
3087 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3088 __isl_take isl_aff *aff2);
3089 __isl_give isl_pw_aff *isl_pw_aff_sub(
3090 __isl_take isl_pw_aff *pwaff1,
3091 __isl_take isl_pw_aff *pwaff2);
3092 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3093 __isl_give isl_pw_aff *isl_pw_aff_neg(
3094 __isl_take isl_pw_aff *pwaff);
3095 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3096 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3097 __isl_take isl_pw_aff *pwaff);
3098 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3099 __isl_give isl_pw_aff *isl_pw_aff_floor(
3100 __isl_take isl_pw_aff *pwaff);
3101 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3103 __isl_give isl_pw_aff *isl_pw_aff_mod(
3104 __isl_take isl_pw_aff *pwaff, isl_int mod);
3105 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3107 __isl_give isl_pw_aff *isl_pw_aff_scale(
3108 __isl_take isl_pw_aff *pwaff, isl_int f);
3109 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3111 __isl_give isl_aff *isl_aff_scale_down_ui(
3112 __isl_take isl_aff *aff, unsigned f);
3113 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3114 __isl_take isl_pw_aff *pwaff, isl_int f);
3116 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3117 __isl_take isl_pw_aff_list *list);
3118 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3119 __isl_take isl_pw_aff_list *list);
3121 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3122 __isl_take isl_pw_aff *pwqp);
3124 __isl_give isl_aff *isl_aff_align_params(
3125 __isl_take isl_aff *aff,
3126 __isl_take isl_space *model);
3127 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3128 __isl_take isl_pw_aff *pwaff,
3129 __isl_take isl_space *model);
3131 __isl_give isl_aff *isl_aff_project_domain_on_params(
3132 __isl_take isl_aff *aff);
3134 __isl_give isl_aff *isl_aff_gist_params(
3135 __isl_take isl_aff *aff,
3136 __isl_take isl_set *context);
3137 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3138 __isl_take isl_set *context);
3139 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3140 __isl_take isl_pw_aff *pwaff,
3141 __isl_take isl_set *context);
3142 __isl_give isl_pw_aff *isl_pw_aff_gist(
3143 __isl_take isl_pw_aff *pwaff,
3144 __isl_take isl_set *context);
3146 __isl_give isl_set *isl_pw_aff_domain(
3147 __isl_take isl_pw_aff *pwaff);
3148 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3149 __isl_take isl_pw_aff *pa,
3150 __isl_take isl_set *set);
3151 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3152 __isl_take isl_pw_aff *pa,
3153 __isl_take isl_set *set);
3155 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3156 __isl_take isl_aff *aff2);
3157 __isl_give isl_pw_aff *isl_pw_aff_mul(
3158 __isl_take isl_pw_aff *pwaff1,
3159 __isl_take isl_pw_aff *pwaff2);
3161 When multiplying two affine expressions, at least one of the two needs
3164 #include <isl/aff.h>
3165 __isl_give isl_basic_set *isl_aff_le_basic_set(
3166 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3167 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3168 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3169 __isl_give isl_set *isl_pw_aff_eq_set(
3170 __isl_take isl_pw_aff *pwaff1,
3171 __isl_take isl_pw_aff *pwaff2);
3172 __isl_give isl_set *isl_pw_aff_ne_set(
3173 __isl_take isl_pw_aff *pwaff1,
3174 __isl_take isl_pw_aff *pwaff2);
3175 __isl_give isl_set *isl_pw_aff_le_set(
3176 __isl_take isl_pw_aff *pwaff1,
3177 __isl_take isl_pw_aff *pwaff2);
3178 __isl_give isl_set *isl_pw_aff_lt_set(
3179 __isl_take isl_pw_aff *pwaff1,
3180 __isl_take isl_pw_aff *pwaff2);
3181 __isl_give isl_set *isl_pw_aff_ge_set(
3182 __isl_take isl_pw_aff *pwaff1,
3183 __isl_take isl_pw_aff *pwaff2);
3184 __isl_give isl_set *isl_pw_aff_gt_set(
3185 __isl_take isl_pw_aff *pwaff1,
3186 __isl_take isl_pw_aff *pwaff2);
3188 __isl_give isl_set *isl_pw_aff_list_eq_set(
3189 __isl_take isl_pw_aff_list *list1,
3190 __isl_take isl_pw_aff_list *list2);
3191 __isl_give isl_set *isl_pw_aff_list_ne_set(
3192 __isl_take isl_pw_aff_list *list1,
3193 __isl_take isl_pw_aff_list *list2);
3194 __isl_give isl_set *isl_pw_aff_list_le_set(
3195 __isl_take isl_pw_aff_list *list1,
3196 __isl_take isl_pw_aff_list *list2);
3197 __isl_give isl_set *isl_pw_aff_list_lt_set(
3198 __isl_take isl_pw_aff_list *list1,
3199 __isl_take isl_pw_aff_list *list2);
3200 __isl_give isl_set *isl_pw_aff_list_ge_set(
3201 __isl_take isl_pw_aff_list *list1,
3202 __isl_take isl_pw_aff_list *list2);
3203 __isl_give isl_set *isl_pw_aff_list_gt_set(
3204 __isl_take isl_pw_aff_list *list1,
3205 __isl_take isl_pw_aff_list *list2);
3207 The function C<isl_aff_ge_basic_set> returns a basic set
3208 containing those elements in the shared space
3209 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3210 The function C<isl_aff_ge_set> returns a set
3211 containing those elements in the shared domain
3212 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3213 The functions operating on C<isl_pw_aff_list> apply the corresponding
3214 C<isl_pw_aff> function to each pair of elements in the two lists.
3216 #include <isl/aff.h>
3217 __isl_give isl_set *isl_pw_aff_nonneg_set(
3218 __isl_take isl_pw_aff *pwaff);
3219 __isl_give isl_set *isl_pw_aff_zero_set(
3220 __isl_take isl_pw_aff *pwaff);
3221 __isl_give isl_set *isl_pw_aff_non_zero_set(
3222 __isl_take isl_pw_aff *pwaff);
3224 The function C<isl_pw_aff_nonneg_set> returns a set
3225 containing those elements in the domain
3226 of C<pwaff> where C<pwaff> is non-negative.
3228 #include <isl/aff.h>
3229 __isl_give isl_pw_aff *isl_pw_aff_cond(
3230 __isl_take isl_pw_aff *cond,
3231 __isl_take isl_pw_aff *pwaff_true,
3232 __isl_take isl_pw_aff *pwaff_false);
3234 The function C<isl_pw_aff_cond> performs a conditional operator
3235 and returns an expression that is equal to C<pwaff_true>
3236 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3237 where C<cond> is zero.
3239 #include <isl/aff.h>
3240 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3241 __isl_take isl_pw_aff *pwaff1,
3242 __isl_take isl_pw_aff *pwaff2);
3243 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3244 __isl_take isl_pw_aff *pwaff1,
3245 __isl_take isl_pw_aff *pwaff2);
3246 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3247 __isl_take isl_pw_aff *pwaff1,
3248 __isl_take isl_pw_aff *pwaff2);
3250 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3251 expression with a domain that is the union of those of C<pwaff1> and
3252 C<pwaff2> and such that on each cell, the quasi-affine expression is
3253 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3254 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3255 associated expression is the defined one.
3257 An expression can be read from input using
3259 #include <isl/aff.h>
3260 __isl_give isl_aff *isl_aff_read_from_str(
3261 isl_ctx *ctx, const char *str);
3262 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3263 isl_ctx *ctx, const char *str);
3265 An expression can be printed using
3267 #include <isl/aff.h>
3268 __isl_give isl_printer *isl_printer_print_aff(
3269 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3271 __isl_give isl_printer *isl_printer_print_pw_aff(
3272 __isl_take isl_printer *p,
3273 __isl_keep isl_pw_aff *pwaff);
3275 =head2 Piecewise Multiple Quasi Affine Expressions
3277 An C<isl_multi_aff> object represents a sequence of
3278 zero or more affine expressions, all defined on the same domain space.
3280 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3283 #include <isl/aff.h>
3284 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3285 __isl_take isl_space *space,
3286 __isl_take isl_aff_list *list);
3288 An empty piecewise multiple quasi affine expression (one with no cells),
3289 the zero piecewise multiple quasi affine expression (with value zero
3290 for each output dimension),
3291 a piecewise multiple quasi affine expression with a single cell (with
3292 either a universe or a specified domain) or
3293 a zero-dimensional piecewise multiple quasi affine expression
3295 can be created using the following functions.
3297 #include <isl/aff.h>
3298 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3299 __isl_take isl_space *space);
3300 __isl_give isl_multi_aff *isl_multi_aff_zero(
3301 __isl_take isl_space *space);
3302 __isl_give isl_pw_multi_aff *
3303 isl_pw_multi_aff_from_multi_aff(
3304 __isl_take isl_multi_aff *ma);
3305 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3306 __isl_take isl_set *set,
3307 __isl_take isl_multi_aff *maff);
3308 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3309 __isl_take isl_set *set);
3311 __isl_give isl_union_pw_multi_aff *
3312 isl_union_pw_multi_aff_empty(
3313 __isl_take isl_space *space);
3314 __isl_give isl_union_pw_multi_aff *
3315 isl_union_pw_multi_aff_add_pw_multi_aff(
3316 __isl_take isl_union_pw_multi_aff *upma,
3317 __isl_take isl_pw_multi_aff *pma);
3318 __isl_give isl_union_pw_multi_aff *
3319 isl_union_pw_multi_aff_from_domain(
3320 __isl_take isl_union_set *uset);
3322 A piecewise multiple quasi affine expression can also be initialized
3323 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3324 and the C<isl_map> is single-valued.
3326 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3327 __isl_take isl_set *set);
3328 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3329 __isl_take isl_map *map);
3331 Multiple quasi affine expressions can be copied and freed using
3333 #include <isl/aff.h>
3334 __isl_give isl_multi_aff *isl_multi_aff_copy(
3335 __isl_keep isl_multi_aff *maff);
3336 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3338 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3339 __isl_keep isl_pw_multi_aff *pma);
3340 void *isl_pw_multi_aff_free(
3341 __isl_take isl_pw_multi_aff *pma);
3343 __isl_give isl_union_pw_multi_aff *
3344 isl_union_pw_multi_aff_copy(
3345 __isl_keep isl_union_pw_multi_aff *upma);
3346 void *isl_union_pw_multi_aff_free(
3347 __isl_take isl_union_pw_multi_aff *upma);
3349 The expression can be inspected using
3351 #include <isl/aff.h>
3352 isl_ctx *isl_multi_aff_get_ctx(
3353 __isl_keep isl_multi_aff *maff);
3354 isl_ctx *isl_pw_multi_aff_get_ctx(
3355 __isl_keep isl_pw_multi_aff *pma);
3356 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3357 __isl_keep isl_union_pw_multi_aff *upma);
3358 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3359 enum isl_dim_type type);
3360 unsigned isl_pw_multi_aff_dim(
3361 __isl_keep isl_pw_multi_aff *pma,
3362 enum isl_dim_type type);
3363 __isl_give isl_aff *isl_multi_aff_get_aff(
3364 __isl_keep isl_multi_aff *multi, int pos);
3365 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3366 __isl_keep isl_pw_multi_aff *pma, int pos);
3367 const char *isl_pw_multi_aff_get_dim_name(
3368 __isl_keep isl_pw_multi_aff *pma,
3369 enum isl_dim_type type, unsigned pos);
3370 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3371 __isl_keep isl_pw_multi_aff *pma,
3372 enum isl_dim_type type, unsigned pos);
3373 const char *isl_multi_aff_get_tuple_name(
3374 __isl_keep isl_multi_aff *multi,
3375 enum isl_dim_type type);
3376 const char *isl_pw_multi_aff_get_tuple_name(
3377 __isl_keep isl_pw_multi_aff *pma,
3378 enum isl_dim_type type);
3379 int isl_pw_multi_aff_has_tuple_id(
3380 __isl_keep isl_pw_multi_aff *pma,
3381 enum isl_dim_type type);
3382 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3383 __isl_keep isl_pw_multi_aff *pma,
3384 enum isl_dim_type type);
3386 int isl_pw_multi_aff_foreach_piece(
3387 __isl_keep isl_pw_multi_aff *pma,
3388 int (*fn)(__isl_take isl_set *set,
3389 __isl_take isl_multi_aff *maff,
3390 void *user), void *user);
3392 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3393 __isl_keep isl_union_pw_multi_aff *upma,
3394 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3395 void *user), void *user);
3397 It can be modified using
3399 #include <isl/aff.h>
3400 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3401 __isl_take isl_multi_aff *multi, int pos,
3402 __isl_take isl_aff *aff);
3403 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3404 __isl_take isl_multi_aff *maff,
3405 enum isl_dim_type type, unsigned pos, const char *s);
3406 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3407 __isl_take isl_multi_aff *maff,
3408 enum isl_dim_type type, __isl_take isl_id *id);
3409 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3410 __isl_take isl_pw_multi_aff *pma,
3411 enum isl_dim_type type, __isl_take isl_id *id);
3413 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3414 __isl_take isl_multi_aff *maff,
3415 enum isl_dim_type type, unsigned first, unsigned n);
3417 To check whether two multiple affine expressions are
3418 obviously equal to each other, use
3420 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3421 __isl_keep isl_multi_aff *maff2);
3422 int isl_pw_multi_aff_plain_is_equal(
3423 __isl_keep isl_pw_multi_aff *pma1,
3424 __isl_keep isl_pw_multi_aff *pma2);
3428 #include <isl/aff.h>
3429 __isl_give isl_multi_aff *isl_multi_aff_add(
3430 __isl_take isl_multi_aff *maff1,
3431 __isl_take isl_multi_aff *maff2);
3432 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3433 __isl_take isl_pw_multi_aff *pma1,
3434 __isl_take isl_pw_multi_aff *pma2);
3435 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3436 __isl_take isl_union_pw_multi_aff *upma1,
3437 __isl_take isl_union_pw_multi_aff *upma2);
3438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3439 __isl_take isl_pw_multi_aff *pma1,
3440 __isl_take isl_pw_multi_aff *pma2);
3441 __isl_give isl_multi_aff *isl_multi_aff_scale(
3442 __isl_take isl_multi_aff *maff,
3444 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3445 __isl_take isl_pw_multi_aff *pma,
3446 __isl_take isl_set *set);
3447 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3448 __isl_take isl_pw_multi_aff *pma,
3449 __isl_take isl_set *set);
3450 __isl_give isl_multi_aff *isl_multi_aff_lift(
3451 __isl_take isl_multi_aff *maff,
3452 __isl_give isl_local_space **ls);
3453 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3454 __isl_take isl_pw_multi_aff *pma);
3455 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3456 __isl_take isl_multi_aff *maff,
3457 __isl_take isl_set *context);
3458 __isl_give isl_multi_aff *isl_multi_aff_gist(
3459 __isl_take isl_multi_aff *maff,
3460 __isl_take isl_set *context);
3461 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3462 __isl_take isl_pw_multi_aff *pma,
3463 __isl_take isl_set *set);
3464 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3465 __isl_take isl_pw_multi_aff *pma,
3466 __isl_take isl_set *set);
3467 __isl_give isl_set *isl_pw_multi_aff_domain(
3468 __isl_take isl_pw_multi_aff *pma);
3469 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3470 __isl_take isl_union_pw_multi_aff *upma);
3471 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3472 __isl_take isl_multi_aff *ma1,
3473 __isl_take isl_multi_aff *ma2);
3474 __isl_give isl_pw_multi_aff *
3475 isl_pw_multi_aff_flat_range_product(
3476 __isl_take isl_pw_multi_aff *pma1,
3477 __isl_take isl_pw_multi_aff *pma2);
3478 __isl_give isl_union_pw_multi_aff *
3479 isl_union_pw_multi_aff_flat_range_product(
3480 __isl_take isl_union_pw_multi_aff *upma1,
3481 __isl_take isl_union_pw_multi_aff *upma2);
3483 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3484 then it is assigned the local space that lies at the basis of
3485 the lifting applied.
3487 An expression can be read from input using
3489 #include <isl/aff.h>
3490 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3491 isl_ctx *ctx, const char *str);
3492 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3493 isl_ctx *ctx, const char *str);
3495 An expression can be printed using
3497 #include <isl/aff.h>
3498 __isl_give isl_printer *isl_printer_print_multi_aff(
3499 __isl_take isl_printer *p,
3500 __isl_keep isl_multi_aff *maff);
3501 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3502 __isl_take isl_printer *p,
3503 __isl_keep isl_pw_multi_aff *pma);
3504 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3505 __isl_take isl_printer *p,
3506 __isl_keep isl_union_pw_multi_aff *upma);
3510 Points are elements of a set. They can be used to construct
3511 simple sets (boxes) or they can be used to represent the
3512 individual elements of a set.
3513 The zero point (the origin) can be created using
3515 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3517 The coordinates of a point can be inspected, set and changed
3520 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3521 enum isl_dim_type type, int pos, isl_int *v);
3522 __isl_give isl_point *isl_point_set_coordinate(
3523 __isl_take isl_point *pnt,
3524 enum isl_dim_type type, int pos, isl_int v);
3526 __isl_give isl_point *isl_point_add_ui(
3527 __isl_take isl_point *pnt,
3528 enum isl_dim_type type, int pos, unsigned val);
3529 __isl_give isl_point *isl_point_sub_ui(
3530 __isl_take isl_point *pnt,
3531 enum isl_dim_type type, int pos, unsigned val);
3533 Other properties can be obtained using
3535 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3537 Points can be copied or freed using
3539 __isl_give isl_point *isl_point_copy(
3540 __isl_keep isl_point *pnt);
3541 void isl_point_free(__isl_take isl_point *pnt);
3543 A singleton set can be created from a point using
3545 __isl_give isl_basic_set *isl_basic_set_from_point(
3546 __isl_take isl_point *pnt);
3547 __isl_give isl_set *isl_set_from_point(
3548 __isl_take isl_point *pnt);
3550 and a box can be created from two opposite extremal points using
3552 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3553 __isl_take isl_point *pnt1,
3554 __isl_take isl_point *pnt2);
3555 __isl_give isl_set *isl_set_box_from_points(
3556 __isl_take isl_point *pnt1,
3557 __isl_take isl_point *pnt2);
3559 All elements of a B<bounded> (union) set can be enumerated using
3560 the following functions.
3562 int isl_set_foreach_point(__isl_keep isl_set *set,
3563 int (*fn)(__isl_take isl_point *pnt, void *user),
3565 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3566 int (*fn)(__isl_take isl_point *pnt, void *user),
3569 The function C<fn> is called for each integer point in
3570 C<set> with as second argument the last argument of
3571 the C<isl_set_foreach_point> call. The function C<fn>
3572 should return C<0> on success and C<-1> on failure.
3573 In the latter case, C<isl_set_foreach_point> will stop
3574 enumerating and return C<-1> as well.
3575 If the enumeration is performed successfully and to completion,
3576 then C<isl_set_foreach_point> returns C<0>.
3578 To obtain a single point of a (basic) set, use
3580 __isl_give isl_point *isl_basic_set_sample_point(
3581 __isl_take isl_basic_set *bset);
3582 __isl_give isl_point *isl_set_sample_point(
3583 __isl_take isl_set *set);
3585 If C<set> does not contain any (integer) points, then the
3586 resulting point will be ``void'', a property that can be
3589 int isl_point_is_void(__isl_keep isl_point *pnt);
3591 =head2 Piecewise Quasipolynomials
3593 A piecewise quasipolynomial is a particular kind of function that maps
3594 a parametric point to a rational value.
3595 More specifically, a quasipolynomial is a polynomial expression in greatest
3596 integer parts of affine expressions of parameters and variables.
3597 A piecewise quasipolynomial is a subdivision of a given parametric
3598 domain into disjoint cells with a quasipolynomial associated to
3599 each cell. The value of the piecewise quasipolynomial at a given
3600 point is the value of the quasipolynomial associated to the cell
3601 that contains the point. Outside of the union of cells,
3602 the value is assumed to be zero.
3603 For example, the piecewise quasipolynomial
3605 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3607 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3608 A given piecewise quasipolynomial has a fixed domain dimension.
3609 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3610 defined over different domains.
3611 Piecewise quasipolynomials are mainly used by the C<barvinok>
3612 library for representing the number of elements in a parametric set or map.
3613 For example, the piecewise quasipolynomial above represents
3614 the number of points in the map
3616 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3618 =head3 Input and Output
3620 Piecewise quasipolynomials can be read from input using
3622 __isl_give isl_union_pw_qpolynomial *
3623 isl_union_pw_qpolynomial_read_from_str(
3624 isl_ctx *ctx, const char *str);
3626 Quasipolynomials and piecewise quasipolynomials can be printed
3627 using the following functions.
3629 __isl_give isl_printer *isl_printer_print_qpolynomial(
3630 __isl_take isl_printer *p,
3631 __isl_keep isl_qpolynomial *qp);
3633 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3634 __isl_take isl_printer *p,
3635 __isl_keep isl_pw_qpolynomial *pwqp);
3637 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3638 __isl_take isl_printer *p,
3639 __isl_keep isl_union_pw_qpolynomial *upwqp);
3641 The output format of the printer
3642 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3643 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3645 In case of printing in C<ISL_FORMAT_C>, the user may want
3646 to set the names of all dimensions
3648 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3649 __isl_take isl_qpolynomial *qp,
3650 enum isl_dim_type type, unsigned pos,
3652 __isl_give isl_pw_qpolynomial *
3653 isl_pw_qpolynomial_set_dim_name(
3654 __isl_take isl_pw_qpolynomial *pwqp,
3655 enum isl_dim_type type, unsigned pos,
3658 =head3 Creating New (Piecewise) Quasipolynomials
3660 Some simple quasipolynomials can be created using the following functions.
3661 More complicated quasipolynomials can be created by applying
3662 operations such as addition and multiplication
3663 on the resulting quasipolynomials
3665 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3666 __isl_take isl_space *domain);
3667 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3668 __isl_take isl_space *domain);
3669 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3670 __isl_take isl_space *domain);
3671 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3672 __isl_take isl_space *domain);
3673 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3674 __isl_take isl_space *domain);
3675 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3676 __isl_take isl_space *domain,
3677 const isl_int n, const isl_int d);
3678 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3679 __isl_take isl_space *domain,
3680 enum isl_dim_type type, unsigned pos);
3681 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3682 __isl_take isl_aff *aff);
3684 Note that the space in which a quasipolynomial lives is a map space
3685 with a one-dimensional range. The C<domain> argument in some of
3686 the functions above corresponds to the domain of this map space.
3688 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3689 with a single cell can be created using the following functions.
3690 Multiple of these single cell piecewise quasipolynomials can
3691 be combined to create more complicated piecewise quasipolynomials.
3693 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3694 __isl_take isl_space *space);
3695 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3696 __isl_take isl_set *set,
3697 __isl_take isl_qpolynomial *qp);
3698 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3699 __isl_take isl_qpolynomial *qp);
3700 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3701 __isl_take isl_pw_aff *pwaff);
3703 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3704 __isl_take isl_space *space);
3705 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3706 __isl_take isl_pw_qpolynomial *pwqp);
3707 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3708 __isl_take isl_union_pw_qpolynomial *upwqp,
3709 __isl_take isl_pw_qpolynomial *pwqp);
3711 Quasipolynomials can be copied and freed again using the following
3714 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3715 __isl_keep isl_qpolynomial *qp);
3716 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3718 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3719 __isl_keep isl_pw_qpolynomial *pwqp);
3720 void *isl_pw_qpolynomial_free(
3721 __isl_take isl_pw_qpolynomial *pwqp);
3723 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3724 __isl_keep isl_union_pw_qpolynomial *upwqp);
3725 void *isl_union_pw_qpolynomial_free(
3726 __isl_take isl_union_pw_qpolynomial *upwqp);
3728 =head3 Inspecting (Piecewise) Quasipolynomials
3730 To iterate over all piecewise quasipolynomials in a union
3731 piecewise quasipolynomial, use the following function
3733 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3734 __isl_keep isl_union_pw_qpolynomial *upwqp,
3735 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3738 To extract the piecewise quasipolynomial in a given space from a union, use
3740 __isl_give isl_pw_qpolynomial *
3741 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3742 __isl_keep isl_union_pw_qpolynomial *upwqp,
3743 __isl_take isl_space *space);
3745 To iterate over the cells in a piecewise quasipolynomial,
3746 use either of the following two functions
3748 int isl_pw_qpolynomial_foreach_piece(
3749 __isl_keep isl_pw_qpolynomial *pwqp,
3750 int (*fn)(__isl_take isl_set *set,
3751 __isl_take isl_qpolynomial *qp,
3752 void *user), void *user);
3753 int isl_pw_qpolynomial_foreach_lifted_piece(
3754 __isl_keep isl_pw_qpolynomial *pwqp,
3755 int (*fn)(__isl_take isl_set *set,
3756 __isl_take isl_qpolynomial *qp,
3757 void *user), void *user);
3759 As usual, the function C<fn> should return C<0> on success
3760 and C<-1> on failure. The difference between
3761 C<isl_pw_qpolynomial_foreach_piece> and
3762 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3763 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3764 compute unique representations for all existentially quantified
3765 variables and then turn these existentially quantified variables
3766 into extra set variables, adapting the associated quasipolynomial
3767 accordingly. This means that the C<set> passed to C<fn>
3768 will not have any existentially quantified variables, but that
3769 the dimensions of the sets may be different for different
3770 invocations of C<fn>.
3772 To iterate over all terms in a quasipolynomial,
3775 int isl_qpolynomial_foreach_term(
3776 __isl_keep isl_qpolynomial *qp,
3777 int (*fn)(__isl_take isl_term *term,
3778 void *user), void *user);
3780 The terms themselves can be inspected and freed using
3783 unsigned isl_term_dim(__isl_keep isl_term *term,
3784 enum isl_dim_type type);
3785 void isl_term_get_num(__isl_keep isl_term *term,
3787 void isl_term_get_den(__isl_keep isl_term *term,
3789 int isl_term_get_exp(__isl_keep isl_term *term,
3790 enum isl_dim_type type, unsigned pos);
3791 __isl_give isl_aff *isl_term_get_div(
3792 __isl_keep isl_term *term, unsigned pos);
3793 void isl_term_free(__isl_take isl_term *term);
3795 Each term is a product of parameters, set variables and
3796 integer divisions. The function C<isl_term_get_exp>
3797 returns the exponent of a given dimensions in the given term.
3798 The C<isl_int>s in the arguments of C<isl_term_get_num>
3799 and C<isl_term_get_den> need to have been initialized
3800 using C<isl_int_init> before calling these functions.
3802 =head3 Properties of (Piecewise) Quasipolynomials
3804 To check whether a quasipolynomial is actually a constant,
3805 use the following function.
3807 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3808 isl_int *n, isl_int *d);
3810 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3811 then the numerator and denominator of the constant
3812 are returned in C<*n> and C<*d>, respectively.
3814 To check whether two union piecewise quasipolynomials are
3815 obviously equal, use
3817 int isl_union_pw_qpolynomial_plain_is_equal(
3818 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3819 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3821 =head3 Operations on (Piecewise) Quasipolynomials
3823 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3824 __isl_take isl_qpolynomial *qp, isl_int v);
3825 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3826 __isl_take isl_qpolynomial *qp);
3827 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3828 __isl_take isl_qpolynomial *qp1,
3829 __isl_take isl_qpolynomial *qp2);
3830 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3831 __isl_take isl_qpolynomial *qp1,
3832 __isl_take isl_qpolynomial *qp2);
3833 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3834 __isl_take isl_qpolynomial *qp1,
3835 __isl_take isl_qpolynomial *qp2);
3836 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3837 __isl_take isl_qpolynomial *qp, unsigned exponent);
3839 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3840 __isl_take isl_pw_qpolynomial *pwqp1,
3841 __isl_take isl_pw_qpolynomial *pwqp2);
3842 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3843 __isl_take isl_pw_qpolynomial *pwqp1,
3844 __isl_take isl_pw_qpolynomial *pwqp2);
3845 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3846 __isl_take isl_pw_qpolynomial *pwqp1,
3847 __isl_take isl_pw_qpolynomial *pwqp2);
3848 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3849 __isl_take isl_pw_qpolynomial *pwqp);
3850 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3851 __isl_take isl_pw_qpolynomial *pwqp1,
3852 __isl_take isl_pw_qpolynomial *pwqp2);
3853 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3854 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3856 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3857 __isl_take isl_union_pw_qpolynomial *upwqp1,
3858 __isl_take isl_union_pw_qpolynomial *upwqp2);
3859 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3860 __isl_take isl_union_pw_qpolynomial *upwqp1,
3861 __isl_take isl_union_pw_qpolynomial *upwqp2);
3862 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3863 __isl_take isl_union_pw_qpolynomial *upwqp1,
3864 __isl_take isl_union_pw_qpolynomial *upwqp2);
3866 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3867 __isl_take isl_pw_qpolynomial *pwqp,
3868 __isl_take isl_point *pnt);
3870 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3871 __isl_take isl_union_pw_qpolynomial *upwqp,
3872 __isl_take isl_point *pnt);
3874 __isl_give isl_set *isl_pw_qpolynomial_domain(
3875 __isl_take isl_pw_qpolynomial *pwqp);
3876 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3877 __isl_take isl_pw_qpolynomial *pwpq,
3878 __isl_take isl_set *set);
3879 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3880 __isl_take isl_pw_qpolynomial *pwpq,
3881 __isl_take isl_set *set);
3883 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3884 __isl_take isl_union_pw_qpolynomial *upwqp);
3885 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3886 __isl_take isl_union_pw_qpolynomial *upwpq,
3887 __isl_take isl_union_set *uset);
3888 __isl_give isl_union_pw_qpolynomial *
3889 isl_union_pw_qpolynomial_intersect_params(
3890 __isl_take isl_union_pw_qpolynomial *upwpq,
3891 __isl_take isl_set *set);
3893 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3894 __isl_take isl_qpolynomial *qp,
3895 __isl_take isl_space *model);
3897 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3898 __isl_take isl_qpolynomial *qp);
3899 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3900 __isl_take isl_pw_qpolynomial *pwqp);
3902 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3903 __isl_take isl_union_pw_qpolynomial *upwqp);
3905 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3906 __isl_take isl_qpolynomial *qp,
3907 __isl_take isl_set *context);
3908 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3909 __isl_take isl_qpolynomial *qp,
3910 __isl_take isl_set *context);
3912 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3913 __isl_take isl_pw_qpolynomial *pwqp,
3914 __isl_take isl_set *context);
3915 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3916 __isl_take isl_pw_qpolynomial *pwqp,
3917 __isl_take isl_set *context);
3919 __isl_give isl_union_pw_qpolynomial *
3920 isl_union_pw_qpolynomial_gist_params(
3921 __isl_take isl_union_pw_qpolynomial *upwqp,
3922 __isl_take isl_set *context);
3923 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3924 __isl_take isl_union_pw_qpolynomial *upwqp,
3925 __isl_take isl_union_set *context);
3927 The gist operation applies the gist operation to each of
3928 the cells in the domain of the input piecewise quasipolynomial.
3929 The context is also exploited
3930 to simplify the quasipolynomials associated to each cell.
3932 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3933 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3934 __isl_give isl_union_pw_qpolynomial *
3935 isl_union_pw_qpolynomial_to_polynomial(
3936 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3938 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3939 the polynomial will be an overapproximation. If C<sign> is negative,
3940 it will be an underapproximation. If C<sign> is zero, the approximation
3941 will lie somewhere in between.
3943 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3945 A piecewise quasipolynomial reduction is a piecewise
3946 reduction (or fold) of quasipolynomials.
3947 In particular, the reduction can be maximum or a minimum.
3948 The objects are mainly used to represent the result of
3949 an upper or lower bound on a quasipolynomial over its domain,
3950 i.e., as the result of the following function.
3952 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3953 __isl_take isl_pw_qpolynomial *pwqp,
3954 enum isl_fold type, int *tight);
3956 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3957 __isl_take isl_union_pw_qpolynomial *upwqp,
3958 enum isl_fold type, int *tight);
3960 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3961 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3962 is the returned bound is known be tight, i.e., for each value
3963 of the parameters there is at least
3964 one element in the domain that reaches the bound.
3965 If the domain of C<pwqp> is not wrapping, then the bound is computed
3966 over all elements in that domain and the result has a purely parametric
3967 domain. If the domain of C<pwqp> is wrapping, then the bound is
3968 computed over the range of the wrapped relation. The domain of the
3969 wrapped relation becomes the domain of the result.
3971 A (piecewise) quasipolynomial reduction can be copied or freed using the
3972 following functions.
3974 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
3975 __isl_keep isl_qpolynomial_fold *fold);
3976 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
3977 __isl_keep isl_pw_qpolynomial_fold *pwf);
3978 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
3979 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3980 void isl_qpolynomial_fold_free(
3981 __isl_take isl_qpolynomial_fold *fold);
3982 void *isl_pw_qpolynomial_fold_free(
3983 __isl_take isl_pw_qpolynomial_fold *pwf);
3984 void *isl_union_pw_qpolynomial_fold_free(
3985 __isl_take isl_union_pw_qpolynomial_fold *upwf);
3987 =head3 Printing Piecewise Quasipolynomial Reductions
3989 Piecewise quasipolynomial reductions can be printed
3990 using the following function.
3992 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
3993 __isl_take isl_printer *p,
3994 __isl_keep isl_pw_qpolynomial_fold *pwf);
3995 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
3996 __isl_take isl_printer *p,
3997 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
3999 For C<isl_printer_print_pw_qpolynomial_fold>,
4000 output format of the printer
4001 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4002 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4003 output format of the printer
4004 needs to be set to C<ISL_FORMAT_ISL>.
4005 In case of printing in C<ISL_FORMAT_C>, the user may want
4006 to set the names of all dimensions
4008 __isl_give isl_pw_qpolynomial_fold *
4009 isl_pw_qpolynomial_fold_set_dim_name(
4010 __isl_take isl_pw_qpolynomial_fold *pwf,
4011 enum isl_dim_type type, unsigned pos,
4014 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4016 To iterate over all piecewise quasipolynomial reductions in a union
4017 piecewise quasipolynomial reduction, use the following function
4019 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4020 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4021 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4022 void *user), void *user);
4024 To iterate over the cells in a piecewise quasipolynomial reduction,
4025 use either of the following two functions
4027 int isl_pw_qpolynomial_fold_foreach_piece(
4028 __isl_keep isl_pw_qpolynomial_fold *pwf,
4029 int (*fn)(__isl_take isl_set *set,
4030 __isl_take isl_qpolynomial_fold *fold,
4031 void *user), void *user);
4032 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4033 __isl_keep isl_pw_qpolynomial_fold *pwf,
4034 int (*fn)(__isl_take isl_set *set,
4035 __isl_take isl_qpolynomial_fold *fold,
4036 void *user), void *user);
4038 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4039 of the difference between these two functions.
4041 To iterate over all quasipolynomials in a reduction, use
4043 int isl_qpolynomial_fold_foreach_qpolynomial(
4044 __isl_keep isl_qpolynomial_fold *fold,
4045 int (*fn)(__isl_take isl_qpolynomial *qp,
4046 void *user), void *user);
4048 =head3 Properties of Piecewise Quasipolynomial Reductions
4050 To check whether two union piecewise quasipolynomial reductions are
4051 obviously equal, use
4053 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4054 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4055 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4057 =head3 Operations on Piecewise Quasipolynomial Reductions
4059 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4060 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4062 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4063 __isl_take isl_pw_qpolynomial_fold *pwf1,
4064 __isl_take isl_pw_qpolynomial_fold *pwf2);
4066 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4067 __isl_take isl_pw_qpolynomial_fold *pwf1,
4068 __isl_take isl_pw_qpolynomial_fold *pwf2);
4070 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4071 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4072 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4074 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4075 __isl_take isl_pw_qpolynomial_fold *pwf,
4076 __isl_take isl_point *pnt);
4078 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4079 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4080 __isl_take isl_point *pnt);
4082 __isl_give isl_pw_qpolynomial_fold *
4083 sl_pw_qpolynomial_fold_intersect_params(
4084 __isl_take isl_pw_qpolynomial_fold *pwf,
4085 __isl_take isl_set *set);
4087 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4088 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4089 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4090 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4091 __isl_take isl_union_set *uset);
4092 __isl_give isl_union_pw_qpolynomial_fold *
4093 isl_union_pw_qpolynomial_fold_intersect_params(
4094 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4095 __isl_take isl_set *set);
4097 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4098 __isl_take isl_pw_qpolynomial_fold *pwf);
4100 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4101 __isl_take isl_pw_qpolynomial_fold *pwf);
4103 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4104 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4106 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4107 __isl_take isl_qpolynomial_fold *fold,
4108 __isl_take isl_set *context);
4109 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4110 __isl_take isl_qpolynomial_fold *fold,
4111 __isl_take isl_set *context);
4113 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4114 __isl_take isl_pw_qpolynomial_fold *pwf,
4115 __isl_take isl_set *context);
4116 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4117 __isl_take isl_pw_qpolynomial_fold *pwf,
4118 __isl_take isl_set *context);
4120 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4121 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4122 __isl_take isl_union_set *context);
4123 __isl_give isl_union_pw_qpolynomial_fold *
4124 isl_union_pw_qpolynomial_fold_gist_params(
4125 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4126 __isl_take isl_set *context);
4128 The gist operation applies the gist operation to each of
4129 the cells in the domain of the input piecewise quasipolynomial reduction.
4130 In future, the operation will also exploit the context
4131 to simplify the quasipolynomial reductions associated to each cell.
4133 __isl_give isl_pw_qpolynomial_fold *
4134 isl_set_apply_pw_qpolynomial_fold(
4135 __isl_take isl_set *set,
4136 __isl_take isl_pw_qpolynomial_fold *pwf,
4138 __isl_give isl_pw_qpolynomial_fold *
4139 isl_map_apply_pw_qpolynomial_fold(
4140 __isl_take isl_map *map,
4141 __isl_take isl_pw_qpolynomial_fold *pwf,
4143 __isl_give isl_union_pw_qpolynomial_fold *
4144 isl_union_set_apply_union_pw_qpolynomial_fold(
4145 __isl_take isl_union_set *uset,
4146 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4148 __isl_give isl_union_pw_qpolynomial_fold *
4149 isl_union_map_apply_union_pw_qpolynomial_fold(
4150 __isl_take isl_union_map *umap,
4151 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4154 The functions taking a map
4155 compose the given map with the given piecewise quasipolynomial reduction.
4156 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4157 over all elements in the intersection of the range of the map
4158 and the domain of the piecewise quasipolynomial reduction
4159 as a function of an element in the domain of the map.
4160 The functions taking a set compute a bound over all elements in the
4161 intersection of the set and the domain of the
4162 piecewise quasipolynomial reduction.
4164 =head2 Dependence Analysis
4166 C<isl> contains specialized functionality for performing
4167 array dataflow analysis. That is, given a I<sink> access relation
4168 and a collection of possible I<source> access relations,
4169 C<isl> can compute relations that describe
4170 for each iteration of the sink access, which iteration
4171 of which of the source access relations was the last
4172 to access the same data element before the given iteration
4174 The resulting dependence relations map source iterations
4175 to the corresponding sink iterations.
4176 To compute standard flow dependences, the sink should be
4177 a read, while the sources should be writes.
4178 If any of the source accesses are marked as being I<may>
4179 accesses, then there will be a dependence from the last
4180 I<must> access B<and> from any I<may> access that follows
4181 this last I<must> access.
4182 In particular, if I<all> sources are I<may> accesses,
4183 then memory based dependence analysis is performed.
4184 If, on the other hand, all sources are I<must> accesses,
4185 then value based dependence analysis is performed.
4187 #include <isl/flow.h>
4189 typedef int (*isl_access_level_before)(void *first, void *second);
4191 __isl_give isl_access_info *isl_access_info_alloc(
4192 __isl_take isl_map *sink,
4193 void *sink_user, isl_access_level_before fn,
4195 __isl_give isl_access_info *isl_access_info_add_source(
4196 __isl_take isl_access_info *acc,
4197 __isl_take isl_map *source, int must,
4199 void isl_access_info_free(__isl_take isl_access_info *acc);
4201 __isl_give isl_flow *isl_access_info_compute_flow(
4202 __isl_take isl_access_info *acc);
4204 int isl_flow_foreach(__isl_keep isl_flow *deps,
4205 int (*fn)(__isl_take isl_map *dep, int must,
4206 void *dep_user, void *user),
4208 __isl_give isl_map *isl_flow_get_no_source(
4209 __isl_keep isl_flow *deps, int must);
4210 void isl_flow_free(__isl_take isl_flow *deps);
4212 The function C<isl_access_info_compute_flow> performs the actual
4213 dependence analysis. The other functions are used to construct
4214 the input for this function or to read off the output.
4216 The input is collected in an C<isl_access_info>, which can
4217 be created through a call to C<isl_access_info_alloc>.
4218 The arguments to this functions are the sink access relation
4219 C<sink>, a token C<sink_user> used to identify the sink
4220 access to the user, a callback function for specifying the
4221 relative order of source and sink accesses, and the number
4222 of source access relations that will be added.
4223 The callback function has type C<int (*)(void *first, void *second)>.
4224 The function is called with two user supplied tokens identifying
4225 either a source or the sink and it should return the shared nesting
4226 level and the relative order of the two accesses.
4227 In particular, let I<n> be the number of loops shared by
4228 the two accesses. If C<first> precedes C<second> textually,
4229 then the function should return I<2 * n + 1>; otherwise,
4230 it should return I<2 * n>.
4231 The sources can be added to the C<isl_access_info> by performing
4232 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4233 C<must> indicates whether the source is a I<must> access
4234 or a I<may> access. Note that a multi-valued access relation
4235 should only be marked I<must> if every iteration in the domain
4236 of the relation accesses I<all> elements in its image.
4237 The C<source_user> token is again used to identify
4238 the source access. The range of the source access relation
4239 C<source> should have the same dimension as the range
4240 of the sink access relation.
4241 The C<isl_access_info_free> function should usually not be
4242 called explicitly, because it is called implicitly by
4243 C<isl_access_info_compute_flow>.
4245 The result of the dependence analysis is collected in an
4246 C<isl_flow>. There may be elements of
4247 the sink access for which no preceding source access could be
4248 found or for which all preceding sources are I<may> accesses.
4249 The relations containing these elements can be obtained through
4250 calls to C<isl_flow_get_no_source>, the first with C<must> set
4251 and the second with C<must> unset.
4252 In the case of standard flow dependence analysis,
4253 with the sink a read and the sources I<must> writes,
4254 the first relation corresponds to the reads from uninitialized
4255 array elements and the second relation is empty.
4256 The actual flow dependences can be extracted using
4257 C<isl_flow_foreach>. This function will call the user-specified
4258 callback function C<fn> for each B<non-empty> dependence between
4259 a source and the sink. The callback function is called
4260 with four arguments, the actual flow dependence relation
4261 mapping source iterations to sink iterations, a boolean that
4262 indicates whether it is a I<must> or I<may> dependence, a token
4263 identifying the source and an additional C<void *> with value
4264 equal to the third argument of the C<isl_flow_foreach> call.
4265 A dependence is marked I<must> if it originates from a I<must>
4266 source and if it is not followed by any I<may> sources.
4268 After finishing with an C<isl_flow>, the user should call
4269 C<isl_flow_free> to free all associated memory.
4271 A higher-level interface to dependence analysis is provided
4272 by the following function.
4274 #include <isl/flow.h>
4276 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4277 __isl_take isl_union_map *must_source,
4278 __isl_take isl_union_map *may_source,
4279 __isl_take isl_union_map *schedule,
4280 __isl_give isl_union_map **must_dep,
4281 __isl_give isl_union_map **may_dep,
4282 __isl_give isl_union_map **must_no_source,
4283 __isl_give isl_union_map **may_no_source);
4285 The arrays are identified by the tuple names of the ranges
4286 of the accesses. The iteration domains by the tuple names
4287 of the domains of the accesses and of the schedule.
4288 The relative order of the iteration domains is given by the
4289 schedule. The relations returned through C<must_no_source>
4290 and C<may_no_source> are subsets of C<sink>.
4291 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4292 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4293 any of the other arguments is treated as an error.
4295 =head3 Interaction with Dependence Analysis
4297 During the dependence analysis, we frequently need to perform
4298 the following operation. Given a relation between sink iterations
4299 and potential soure iterations from a particular source domain,
4300 what is the last potential source iteration corresponding to each
4301 sink iteration. It can sometimes be convenient to adjust
4302 the set of potential source iterations before or after each such operation.
4303 The prototypical example is fuzzy array dataflow analysis,
4304 where we need to analyze if, based on data-dependent constraints,
4305 the sink iteration can ever be executed without one or more of
4306 the corresponding potential source iterations being executed.
4307 If so, we can introduce extra parameters and select an unknown
4308 but fixed source iteration from the potential source iterations.
4309 To be able to perform such manipulations, C<isl> provides the following
4312 #include <isl/flow.h>
4314 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4315 __isl_keep isl_map *source_map,
4316 __isl_keep isl_set *sink, void *source_user,
4318 __isl_give isl_access_info *isl_access_info_set_restrict(
4319 __isl_take isl_access_info *acc,
4320 isl_access_restrict fn, void *user);
4322 The function C<isl_access_info_set_restrict> should be called
4323 before calling C<isl_access_info_compute_flow> and registers a callback function
4324 that will be called any time C<isl> is about to compute the last
4325 potential source. The first argument is the (reverse) proto-dependence,
4326 mapping sink iterations to potential source iterations.
4327 The second argument represents the sink iterations for which
4328 we want to compute the last source iteration.
4329 The third argument is the token corresponding to the source
4330 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4331 The callback is expected to return a restriction on either the input or
4332 the output of the operation computing the last potential source.
4333 If the input needs to be restricted then restrictions are needed
4334 for both the source and the sink iterations. The sink iterations
4335 and the potential source iterations will be intersected with these sets.
4336 If the output needs to be restricted then only a restriction on the source
4337 iterations is required.
4338 If any error occurs, the callback should return C<NULL>.
4339 An C<isl_restriction> object can be created and freed using the following
4342 #include <isl/flow.h>
4344 __isl_give isl_restriction *isl_restriction_input(
4345 __isl_take isl_set *source_restr,
4346 __isl_take isl_set *sink_restr);
4347 __isl_give isl_restriction *isl_restriction_output(
4348 __isl_take isl_set *source_restr);
4349 __isl_give isl_restriction *isl_restriction_none(
4350 __isl_keep isl_map *source_map);
4351 __isl_give isl_restriction *isl_restriction_empty(
4352 __isl_keep isl_map *source_map);
4353 void *isl_restriction_free(
4354 __isl_take isl_restriction *restr);
4356 C<isl_restriction_none> and C<isl_restriction_empty> are special
4357 cases of C<isl_restriction_input>. C<isl_restriction_none>
4358 is essentially equivalent to
4360 isl_restriction_input(isl_set_universe(
4361 isl_space_range(isl_map_get_space(source_map))),
4363 isl_space_domain(isl_map_get_space(source_map))));
4365 whereas C<isl_restriction_empty> is essentially equivalent to
4367 isl_restriction_input(isl_set_empty(
4368 isl_space_range(isl_map_get_space(source_map))),
4370 isl_space_domain(isl_map_get_space(source_map))));
4374 B<The functionality described in this section is fairly new
4375 and may be subject to change.>
4377 The following function can be used to compute a schedule
4378 for a union of domains.
4379 By default, the algorithm used to construct the schedule is similar
4380 to that of C<Pluto>.
4381 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4383 The generated schedule respects all C<validity> dependences.
4384 That is, all dependence distances over these dependences in the
4385 scheduled space are lexicographically positive.
4386 The default algorithm tries to minimize the dependence distances over
4387 C<proximity> dependences.
4388 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4389 for groups of domains where the dependence distances have only
4390 non-negative values.
4391 When using Feautrier's algorithm, the C<proximity> dependence
4392 distances are only minimized during the extension to a
4393 full-dimensional schedule.
4395 #include <isl/schedule.h>
4396 __isl_give isl_schedule *isl_union_set_compute_schedule(
4397 __isl_take isl_union_set *domain,
4398 __isl_take isl_union_map *validity,
4399 __isl_take isl_union_map *proximity);
4400 void *isl_schedule_free(__isl_take isl_schedule *sched);
4402 A mapping from the domains to the scheduled space can be obtained
4403 from an C<isl_schedule> using the following function.
4405 __isl_give isl_union_map *isl_schedule_get_map(
4406 __isl_keep isl_schedule *sched);
4408 A representation of the schedule can be printed using
4410 __isl_give isl_printer *isl_printer_print_schedule(
4411 __isl_take isl_printer *p,
4412 __isl_keep isl_schedule *schedule);
4414 A representation of the schedule as a forest of bands can be obtained
4415 using the following function.
4417 __isl_give isl_band_list *isl_schedule_get_band_forest(
4418 __isl_keep isl_schedule *schedule);
4420 The individual bands can be visited in depth-first post-order
4421 using the following function.
4423 #include <isl/schedule.h>
4424 int isl_schedule_foreach_band(
4425 __isl_keep isl_schedule *sched,
4426 int (*fn)(__isl_keep isl_band *band, void *user),
4429 The list can be manipulated as explained in L<"Lists">.
4430 The bands inside the list can be copied and freed using the following
4433 #include <isl/band.h>
4434 __isl_give isl_band *isl_band_copy(
4435 __isl_keep isl_band *band);
4436 void *isl_band_free(__isl_take isl_band *band);
4438 Each band contains zero or more scheduling dimensions.
4439 These are referred to as the members of the band.
4440 The section of the schedule that corresponds to the band is
4441 referred to as the partial schedule of the band.
4442 For those nodes that participate in a band, the outer scheduling
4443 dimensions form the prefix schedule, while the inner scheduling
4444 dimensions form the suffix schedule.
4445 That is, if we take a cut of the band forest, then the union of
4446 the concatenations of the prefix, partial and suffix schedules of
4447 each band in the cut is equal to the entire schedule (modulo
4448 some possible padding at the end with zero scheduling dimensions).
4449 The properties of a band can be inspected using the following functions.
4451 #include <isl/band.h>
4452 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4454 int isl_band_has_children(__isl_keep isl_band *band);
4455 __isl_give isl_band_list *isl_band_get_children(
4456 __isl_keep isl_band *band);
4458 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4459 __isl_keep isl_band *band);
4460 __isl_give isl_union_map *isl_band_get_partial_schedule(
4461 __isl_keep isl_band *band);
4462 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4463 __isl_keep isl_band *band);
4465 int isl_band_n_member(__isl_keep isl_band *band);
4466 int isl_band_member_is_zero_distance(
4467 __isl_keep isl_band *band, int pos);
4469 int isl_band_list_foreach_band(
4470 __isl_keep isl_band_list *list,
4471 int (*fn)(__isl_keep isl_band *band, void *user),
4474 Note that a scheduling dimension is considered to be ``zero
4475 distance'' if it does not carry any proximity dependences
4477 That is, if the dependence distances of the proximity
4478 dependences are all zero in that direction (for fixed
4479 iterations of outer bands).
4480 Like C<isl_schedule_foreach_band>,
4481 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4482 in depth-first post-order.
4484 A band can be tiled using the following function.
4486 #include <isl/band.h>
4487 int isl_band_tile(__isl_keep isl_band *band,
4488 __isl_take isl_vec *sizes);
4490 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4492 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4494 The C<isl_band_tile> function tiles the band using the given tile sizes
4495 inside its schedule.
4496 A new child band is created to represent the point loops and it is
4497 inserted between the modified band and its children.
4498 The C<tile_scale_tile_loops> option specifies whether the tile
4499 loops iterators should be scaled by the tile sizes.
4501 A representation of the band can be printed using
4503 #include <isl/band.h>
4504 __isl_give isl_printer *isl_printer_print_band(
4505 __isl_take isl_printer *p,
4506 __isl_keep isl_band *band);
4510 #include <isl/schedule.h>
4511 int isl_options_set_schedule_max_coefficient(
4512 isl_ctx *ctx, int val);
4513 int isl_options_get_schedule_max_coefficient(
4515 int isl_options_set_schedule_max_constant_term(
4516 isl_ctx *ctx, int val);
4517 int isl_options_get_schedule_max_constant_term(
4519 int isl_options_set_schedule_maximize_band_depth(
4520 isl_ctx *ctx, int val);
4521 int isl_options_get_schedule_maximize_band_depth(
4523 int isl_options_set_schedule_outer_zero_distance(
4524 isl_ctx *ctx, int val);
4525 int isl_options_get_schedule_outer_zero_distance(
4527 int isl_options_set_schedule_split_scaled(
4528 isl_ctx *ctx, int val);
4529 int isl_options_get_schedule_split_scaled(
4531 int isl_options_set_schedule_algorithm(
4532 isl_ctx *ctx, int val);
4533 int isl_options_get_schedule_algorithm(
4539 =item * schedule_max_coefficient
4541 This option enforces that the coefficients for variable and parameter
4542 dimensions in the calculated schedule are not larger than the specified value.
4543 This option can significantly increase the speed of the scheduling calculation
4544 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4545 this option does not introduce bounds on the variable or parameter
4548 =item * schedule_max_constant_term
4550 This option enforces that the constant coefficients in the calculated schedule
4551 are not larger than the maximal constant term. This option can significantly
4552 increase the speed of the scheduling calculation and may also prevent fusing of
4553 unrelated dimensions. A value of -1 means that this option does not introduce
4554 bounds on the constant coefficients.
4556 =item * schedule_maximize_band_depth
4558 If this option is set, we do not split bands at the point
4559 where we detect splitting is necessary. Instead, we
4560 backtrack and split bands as early as possible. This
4561 reduces the number of splits and maximizes the width of
4562 the bands. Wider bands give more possibilities for tiling.
4564 =item * schedule_outer_zero_distance
4566 If this option is set, then we try to construct schedules
4567 where the outermost scheduling dimension in each band
4568 results in a zero dependence distance over the proximity
4571 =item * schedule_split_scaled
4573 If this option is set, then we try to construct schedules in which the
4574 constant term is split off from the linear part if the linear parts of
4575 the scheduling rows for all nodes in the graphs have a common non-trivial
4577 The constant term is then placed in a separate band and the linear
4580 =item * schedule_algorithm
4582 Selects the scheduling algorithm to be used.
4583 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4584 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4588 =head2 Parametric Vertex Enumeration
4590 The parametric vertex enumeration described in this section
4591 is mainly intended to be used internally and by the C<barvinok>
4594 #include <isl/vertices.h>
4595 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4596 __isl_keep isl_basic_set *bset);
4598 The function C<isl_basic_set_compute_vertices> performs the
4599 actual computation of the parametric vertices and the chamber
4600 decomposition and store the result in an C<isl_vertices> object.
4601 This information can be queried by either iterating over all
4602 the vertices or iterating over all the chambers or cells
4603 and then iterating over all vertices that are active on the chamber.
4605 int isl_vertices_foreach_vertex(
4606 __isl_keep isl_vertices *vertices,
4607 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4610 int isl_vertices_foreach_cell(
4611 __isl_keep isl_vertices *vertices,
4612 int (*fn)(__isl_take isl_cell *cell, void *user),
4614 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4615 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4618 Other operations that can be performed on an C<isl_vertices> object are
4621 isl_ctx *isl_vertices_get_ctx(
4622 __isl_keep isl_vertices *vertices);
4623 int isl_vertices_get_n_vertices(
4624 __isl_keep isl_vertices *vertices);
4625 void isl_vertices_free(__isl_take isl_vertices *vertices);
4627 Vertices can be inspected and destroyed using the following functions.
4629 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4630 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4631 __isl_give isl_basic_set *isl_vertex_get_domain(
4632 __isl_keep isl_vertex *vertex);
4633 __isl_give isl_basic_set *isl_vertex_get_expr(
4634 __isl_keep isl_vertex *vertex);
4635 void isl_vertex_free(__isl_take isl_vertex *vertex);
4637 C<isl_vertex_get_expr> returns a singleton parametric set describing
4638 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4640 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4641 B<rational> basic sets, so they should mainly be used for inspection
4642 and should not be mixed with integer sets.
4644 Chambers can be inspected and destroyed using the following functions.
4646 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4647 __isl_give isl_basic_set *isl_cell_get_domain(
4648 __isl_keep isl_cell *cell);
4649 void isl_cell_free(__isl_take isl_cell *cell);
4653 Although C<isl> is mainly meant to be used as a library,
4654 it also contains some basic applications that use some
4655 of the functionality of C<isl>.
4656 The input may be specified in either the L<isl format>
4657 or the L<PolyLib format>.
4659 =head2 C<isl_polyhedron_sample>
4661 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4662 an integer element of the polyhedron, if there is any.
4663 The first column in the output is the denominator and is always
4664 equal to 1. If the polyhedron contains no integer points,
4665 then a vector of length zero is printed.
4669 C<isl_pip> takes the same input as the C<example> program
4670 from the C<piplib> distribution, i.e., a set of constraints
4671 on the parameters, a line containing only -1 and finally a set
4672 of constraints on a parametric polyhedron.
4673 The coefficients of the parameters appear in the last columns
4674 (but before the final constant column).
4675 The output is the lexicographic minimum of the parametric polyhedron.
4676 As C<isl> currently does not have its own output format, the output
4677 is just a dump of the internal state.
4679 =head2 C<isl_polyhedron_minimize>
4681 C<isl_polyhedron_minimize> computes the minimum of some linear
4682 or affine objective function over the integer points in a polyhedron.
4683 If an affine objective function
4684 is given, then the constant should appear in the last column.
4686 =head2 C<isl_polytope_scan>
4688 Given a polytope, C<isl_polytope_scan> prints
4689 all integer points in the polytope.