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, relation or similiar object is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
570 Each space involves zero or more parameters and zero, one or two
571 tuples of set or input/output dimensions. The parameters and dimensions
572 are identified by an C<isl_dim_type> and a position.
573 The type C<isl_dim_param> refers to parameters,
574 the type C<isl_dim_set> refers to set dimensions (for spaces
575 with a single tuple of dimensions) and the types C<isl_dim_in>
576 and C<isl_dim_out> refer to input and output dimensions
577 (for spaces with two tuples of dimensions).
578 Local spaces (see L</"Local Spaces">) also contain dimensions
579 of type C<isl_dim_div>.
580 Note that parameters are only identified by their position within
581 a given object. Across different objects, parameters are (usually)
582 identified by their names or identifiers. Only unnamed parameters
583 are identified by their positions across objects. The use of unnamed
584 parameters is discouraged.
586 #include <isl/space.h>
587 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
588 unsigned nparam, unsigned n_in, unsigned n_out);
589 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
591 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
592 unsigned nparam, unsigned dim);
593 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
594 void isl_space_free(__isl_take isl_space *space);
595 unsigned isl_space_dim(__isl_keep isl_space *space,
596 enum isl_dim_type type);
598 The space used for creating a parameter domain
599 needs to be created using C<isl_space_params_alloc>.
600 For other sets, the space
601 needs to be created using C<isl_space_set_alloc>, while
602 for a relation, the space
603 needs to be created using C<isl_space_alloc>.
604 C<isl_space_dim> can be used
605 to find out the number of dimensions of each type in
606 a space, where type may be
607 C<isl_dim_param>, C<isl_dim_in> (only for relations),
608 C<isl_dim_out> (only for relations), C<isl_dim_set>
609 (only for sets) or C<isl_dim_all>.
611 To check whether a given space is that of a set or a map
612 or whether it is a parameter space, use these functions:
614 #include <isl/space.h>
615 int isl_space_is_params(__isl_keep isl_space *space);
616 int isl_space_is_set(__isl_keep isl_space *space);
617 int isl_space_is_map(__isl_keep isl_space *space);
619 It is often useful to create objects that live in the
620 same space as some other object. This can be accomplished
621 by creating the new objects
622 (see L<Creating New Sets and Relations> or
623 L<Creating New (Piecewise) Quasipolynomials>) based on the space
624 of the original object.
627 __isl_give isl_space *isl_basic_set_get_space(
628 __isl_keep isl_basic_set *bset);
629 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
631 #include <isl/union_set.h>
632 __isl_give isl_space *isl_union_set_get_space(
633 __isl_keep isl_union_set *uset);
636 __isl_give isl_space *isl_basic_map_get_space(
637 __isl_keep isl_basic_map *bmap);
638 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
640 #include <isl/union_map.h>
641 __isl_give isl_space *isl_union_map_get_space(
642 __isl_keep isl_union_map *umap);
644 #include <isl/constraint.h>
645 __isl_give isl_space *isl_constraint_get_space(
646 __isl_keep isl_constraint *constraint);
648 #include <isl/polynomial.h>
649 __isl_give isl_space *isl_qpolynomial_get_domain_space(
650 __isl_keep isl_qpolynomial *qp);
651 __isl_give isl_space *isl_qpolynomial_get_space(
652 __isl_keep isl_qpolynomial *qp);
653 __isl_give isl_space *isl_qpolynomial_fold_get_space(
654 __isl_keep isl_qpolynomial_fold *fold);
655 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
656 __isl_keep isl_pw_qpolynomial *pwqp);
657 __isl_give isl_space *isl_pw_qpolynomial_get_space(
658 __isl_keep isl_pw_qpolynomial *pwqp);
659 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
660 __isl_keep isl_pw_qpolynomial_fold *pwf);
661 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
662 __isl_keep isl_pw_qpolynomial_fold *pwf);
663 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
664 __isl_keep isl_union_pw_qpolynomial *upwqp);
665 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
666 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
669 __isl_give isl_space *isl_aff_get_domain_space(
670 __isl_keep isl_aff *aff);
671 __isl_give isl_space *isl_aff_get_space(
672 __isl_keep isl_aff *aff);
673 __isl_give isl_space *isl_pw_aff_get_domain_space(
674 __isl_keep isl_pw_aff *pwaff);
675 __isl_give isl_space *isl_pw_aff_get_space(
676 __isl_keep isl_pw_aff *pwaff);
677 __isl_give isl_space *isl_multi_aff_get_domain_space(
678 __isl_keep isl_multi_aff *maff);
679 __isl_give isl_space *isl_multi_aff_get_space(
680 __isl_keep isl_multi_aff *maff);
681 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
682 __isl_keep isl_pw_multi_aff *pma);
683 __isl_give isl_space *isl_pw_multi_aff_get_space(
684 __isl_keep isl_pw_multi_aff *pma);
685 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
686 __isl_keep isl_union_pw_multi_aff *upma);
688 #include <isl/point.h>
689 __isl_give isl_space *isl_point_get_space(
690 __isl_keep isl_point *pnt);
692 The identifiers or names of the individual dimensions may be set or read off
693 using the following functions.
695 #include <isl/space.h>
696 __isl_give isl_space *isl_space_set_dim_id(
697 __isl_take isl_space *space,
698 enum isl_dim_type type, unsigned pos,
699 __isl_take isl_id *id);
700 int isl_space_has_dim_id(__isl_keep isl_space *space,
701 enum isl_dim_type type, unsigned pos);
702 __isl_give isl_id *isl_space_get_dim_id(
703 __isl_keep isl_space *space,
704 enum isl_dim_type type, unsigned pos);
705 __isl_give isl_space *isl_space_set_dim_name(
706 __isl_take isl_space *space,
707 enum isl_dim_type type, unsigned pos,
708 __isl_keep const char *name);
709 int isl_space_has_dim_name(__isl_keep isl_space *space,
710 enum isl_dim_type type, unsigned pos);
711 __isl_keep const char *isl_space_get_dim_name(
712 __isl_keep isl_space *space,
713 enum isl_dim_type type, unsigned pos);
715 Note that C<isl_space_get_name> returns a pointer to some internal
716 data structure, so the result can only be used while the
717 corresponding C<isl_space> is alive.
718 Also note that every function that operates on two sets or relations
719 requires that both arguments have the same parameters. This also
720 means that if one of the arguments has named parameters, then the
721 other needs to have named parameters too and the names need to match.
722 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
723 arguments may have different parameters (as long as they are named),
724 in which case the result will have as parameters the union of the parameters of
727 Given the identifier or name of a dimension (typically a parameter),
728 its position can be obtained from the following function.
730 #include <isl/space.h>
731 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
732 enum isl_dim_type type, __isl_keep isl_id *id);
733 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
734 enum isl_dim_type type, const char *name);
736 The identifiers or names of entire spaces may be set or read off
737 using the following functions.
739 #include <isl/space.h>
740 __isl_give isl_space *isl_space_set_tuple_id(
741 __isl_take isl_space *space,
742 enum isl_dim_type type, __isl_take isl_id *id);
743 __isl_give isl_space *isl_space_reset_tuple_id(
744 __isl_take isl_space *space, enum isl_dim_type type);
745 int isl_space_has_tuple_id(__isl_keep isl_space *space,
746 enum isl_dim_type type);
747 __isl_give isl_id *isl_space_get_tuple_id(
748 __isl_keep isl_space *space, enum isl_dim_type type);
749 __isl_give isl_space *isl_space_set_tuple_name(
750 __isl_take isl_space *space,
751 enum isl_dim_type type, const char *s);
752 int isl_space_has_tuple_name(__isl_keep isl_space *space,
753 enum isl_dim_type type);
754 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
755 enum isl_dim_type type);
757 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
758 or C<isl_dim_set>. As with C<isl_space_get_name>,
759 the C<isl_space_get_tuple_name> function returns a pointer to some internal
761 Binary operations require the corresponding spaces of their arguments
762 to have the same name.
764 Spaces can be nested. In particular, the domain of a set or
765 the domain or range of a relation can be a nested relation.
766 The following functions can be used to construct and deconstruct
769 #include <isl/space.h>
770 int isl_space_is_wrapping(__isl_keep isl_space *space);
771 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
772 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
774 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
775 be the space of a set, while that of
776 C<isl_space_wrap> should be the space of a relation.
777 Conversely, the output of C<isl_space_unwrap> is the space
778 of a relation, while that of C<isl_space_wrap> is the space of a set.
780 Spaces can be created from other spaces
781 using the following functions.
783 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
784 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
785 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
786 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
787 __isl_give isl_space *isl_space_params(
788 __isl_take isl_space *space);
789 __isl_give isl_space *isl_space_set_from_params(
790 __isl_take isl_space *space);
791 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
792 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
793 __isl_take isl_space *right);
794 __isl_give isl_space *isl_space_align_params(
795 __isl_take isl_space *space1, __isl_take isl_space *space2)
796 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
797 enum isl_dim_type type, unsigned pos, unsigned n);
798 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
799 enum isl_dim_type type, unsigned n);
800 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
801 enum isl_dim_type type, unsigned first, unsigned n);
802 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
803 enum isl_dim_type dst_type, unsigned dst_pos,
804 enum isl_dim_type src_type, unsigned src_pos,
806 __isl_give isl_space *isl_space_map_from_set(
807 __isl_take isl_space *space);
808 __isl_give isl_space *isl_space_map_from_domain_and_range(
809 __isl_take isl_space *domain,
810 __isl_take isl_space *range);
811 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
812 __isl_give isl_space *isl_space_curry(
813 __isl_take isl_space *space);
815 Note that if dimensions are added or removed from a space, then
816 the name and the internal structure are lost.
820 A local space is essentially a space with
821 zero or more existentially quantified variables.
822 The local space of a (constraint of a) basic set or relation can be obtained
823 using the following functions.
825 #include <isl/constraint.h>
826 __isl_give isl_local_space *isl_constraint_get_local_space(
827 __isl_keep isl_constraint *constraint);
830 __isl_give isl_local_space *isl_basic_set_get_local_space(
831 __isl_keep isl_basic_set *bset);
834 __isl_give isl_local_space *isl_basic_map_get_local_space(
835 __isl_keep isl_basic_map *bmap);
837 A new local space can be created from a space using
839 #include <isl/local_space.h>
840 __isl_give isl_local_space *isl_local_space_from_space(
841 __isl_take isl_space *space);
843 They can be inspected, modified, copied and freed using the following functions.
845 #include <isl/local_space.h>
846 isl_ctx *isl_local_space_get_ctx(
847 __isl_keep isl_local_space *ls);
848 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
849 int isl_local_space_dim(__isl_keep isl_local_space *ls,
850 enum isl_dim_type type);
851 int isl_local_space_has_dim_id(
852 __isl_keep isl_local_space *ls,
853 enum isl_dim_type type, unsigned pos);
854 __isl_give isl_id *isl_local_space_get_dim_id(
855 __isl_keep isl_local_space *ls,
856 enum isl_dim_type type, unsigned pos);
857 int isl_local_space_has_dim_name(
858 __isl_keep isl_local_space *ls,
859 enum isl_dim_type type, unsigned pos)
860 const char *isl_local_space_get_dim_name(
861 __isl_keep isl_local_space *ls,
862 enum isl_dim_type type, unsigned pos);
863 __isl_give isl_local_space *isl_local_space_set_dim_name(
864 __isl_take isl_local_space *ls,
865 enum isl_dim_type type, unsigned pos, const char *s);
866 __isl_give isl_local_space *isl_local_space_set_dim_id(
867 __isl_take isl_local_space *ls,
868 enum isl_dim_type type, unsigned pos,
869 __isl_take isl_id *id);
870 __isl_give isl_space *isl_local_space_get_space(
871 __isl_keep isl_local_space *ls);
872 __isl_give isl_aff *isl_local_space_get_div(
873 __isl_keep isl_local_space *ls, int pos);
874 __isl_give isl_local_space *isl_local_space_copy(
875 __isl_keep isl_local_space *ls);
876 void *isl_local_space_free(__isl_take isl_local_space *ls);
878 Two local spaces can be compared using
880 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
881 __isl_keep isl_local_space *ls2);
883 Local spaces can be created from other local spaces
884 using the following functions.
886 __isl_give isl_local_space *isl_local_space_domain(
887 __isl_take isl_local_space *ls);
888 __isl_give isl_local_space *isl_local_space_range(
889 __isl_take isl_local_space *ls);
890 __isl_give isl_local_space *isl_local_space_from_domain(
891 __isl_take isl_local_space *ls);
892 __isl_give isl_local_space *isl_local_space_intersect(
893 __isl_take isl_local_space *ls1,
894 __isl_take isl_local_space *ls2);
895 __isl_give isl_local_space *isl_local_space_add_dims(
896 __isl_take isl_local_space *ls,
897 enum isl_dim_type type, unsigned n);
898 __isl_give isl_local_space *isl_local_space_insert_dims(
899 __isl_take isl_local_space *ls,
900 enum isl_dim_type type, unsigned first, unsigned n);
901 __isl_give isl_local_space *isl_local_space_drop_dims(
902 __isl_take isl_local_space *ls,
903 enum isl_dim_type type, unsigned first, unsigned n);
905 =head2 Input and Output
907 C<isl> supports its own input/output format, which is similar
908 to the C<Omega> format, but also supports the C<PolyLib> format
913 The C<isl> format is similar to that of C<Omega>, but has a different
914 syntax for describing the parameters and allows for the definition
915 of an existentially quantified variable as the integer division
916 of an affine expression.
917 For example, the set of integers C<i> between C<0> and C<n>
918 such that C<i % 10 <= 6> can be described as
920 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
923 A set or relation can have several disjuncts, separated
924 by the keyword C<or>. Each disjunct is either a conjunction
925 of constraints or a projection (C<exists>) of a conjunction
926 of constraints. The constraints are separated by the keyword
929 =head3 C<PolyLib> format
931 If the represented set is a union, then the first line
932 contains a single number representing the number of disjuncts.
933 Otherwise, a line containing the number C<1> is optional.
935 Each disjunct is represented by a matrix of constraints.
936 The first line contains two numbers representing
937 the number of rows and columns,
938 where the number of rows is equal to the number of constraints
939 and the number of columns is equal to two plus the number of variables.
940 The following lines contain the actual rows of the constraint matrix.
941 In each row, the first column indicates whether the constraint
942 is an equality (C<0>) or inequality (C<1>). The final column
943 corresponds to the constant term.
945 If the set is parametric, then the coefficients of the parameters
946 appear in the last columns before the constant column.
947 The coefficients of any existentially quantified variables appear
948 between those of the set variables and those of the parameters.
950 =head3 Extended C<PolyLib> format
952 The extended C<PolyLib> format is nearly identical to the
953 C<PolyLib> format. The only difference is that the line
954 containing the number of rows and columns of a constraint matrix
955 also contains four additional numbers:
956 the number of output dimensions, the number of input dimensions,
957 the number of local dimensions (i.e., the number of existentially
958 quantified variables) and the number of parameters.
959 For sets, the number of ``output'' dimensions is equal
960 to the number of set dimensions, while the number of ``input''
966 __isl_give isl_basic_set *isl_basic_set_read_from_file(
967 isl_ctx *ctx, FILE *input);
968 __isl_give isl_basic_set *isl_basic_set_read_from_str(
969 isl_ctx *ctx, const char *str);
970 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
972 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
976 __isl_give isl_basic_map *isl_basic_map_read_from_file(
977 isl_ctx *ctx, FILE *input);
978 __isl_give isl_basic_map *isl_basic_map_read_from_str(
979 isl_ctx *ctx, const char *str);
980 __isl_give isl_map *isl_map_read_from_file(
981 isl_ctx *ctx, FILE *input);
982 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
985 #include <isl/union_set.h>
986 __isl_give isl_union_set *isl_union_set_read_from_file(
987 isl_ctx *ctx, FILE *input);
988 __isl_give isl_union_set *isl_union_set_read_from_str(
989 isl_ctx *ctx, const char *str);
991 #include <isl/union_map.h>
992 __isl_give isl_union_map *isl_union_map_read_from_file(
993 isl_ctx *ctx, FILE *input);
994 __isl_give isl_union_map *isl_union_map_read_from_str(
995 isl_ctx *ctx, const char *str);
997 The input format is autodetected and may be either the C<PolyLib> format
998 or the C<isl> format.
1002 Before anything can be printed, an C<isl_printer> needs to
1005 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1007 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1008 void *isl_printer_free(__isl_take isl_printer *printer);
1009 __isl_give char *isl_printer_get_str(
1010 __isl_keep isl_printer *printer);
1012 The printer can be inspected using the following functions.
1014 FILE *isl_printer_get_file(
1015 __isl_keep isl_printer *printer);
1016 int isl_printer_get_output_format(
1017 __isl_keep isl_printer *p);
1019 The behavior of the printer can be modified in various ways
1021 __isl_give isl_printer *isl_printer_set_output_format(
1022 __isl_take isl_printer *p, int output_format);
1023 __isl_give isl_printer *isl_printer_set_indent(
1024 __isl_take isl_printer *p, int indent);
1025 __isl_give isl_printer *isl_printer_indent(
1026 __isl_take isl_printer *p, int indent);
1027 __isl_give isl_printer *isl_printer_set_prefix(
1028 __isl_take isl_printer *p, const char *prefix);
1029 __isl_give isl_printer *isl_printer_set_suffix(
1030 __isl_take isl_printer *p, const char *suffix);
1032 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1033 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1034 and defaults to C<ISL_FORMAT_ISL>.
1035 Each line in the output is indented by C<indent> (set by
1036 C<isl_printer_set_indent>) spaces
1037 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1038 In the C<PolyLib> format output,
1039 the coefficients of the existentially quantified variables
1040 appear between those of the set variables and those
1042 The function C<isl_printer_indent> increases the indentation
1043 by the specified amount (which may be negative).
1045 To actually print something, use
1047 #include <isl/printer.h>
1048 __isl_give isl_printer *isl_printer_print_double(
1049 __isl_take isl_printer *p, double d);
1051 #include <isl/set.h>
1052 __isl_give isl_printer *isl_printer_print_basic_set(
1053 __isl_take isl_printer *printer,
1054 __isl_keep isl_basic_set *bset);
1055 __isl_give isl_printer *isl_printer_print_set(
1056 __isl_take isl_printer *printer,
1057 __isl_keep isl_set *set);
1059 #include <isl/map.h>
1060 __isl_give isl_printer *isl_printer_print_basic_map(
1061 __isl_take isl_printer *printer,
1062 __isl_keep isl_basic_map *bmap);
1063 __isl_give isl_printer *isl_printer_print_map(
1064 __isl_take isl_printer *printer,
1065 __isl_keep isl_map *map);
1067 #include <isl/union_set.h>
1068 __isl_give isl_printer *isl_printer_print_union_set(
1069 __isl_take isl_printer *p,
1070 __isl_keep isl_union_set *uset);
1072 #include <isl/union_map.h>
1073 __isl_give isl_printer *isl_printer_print_union_map(
1074 __isl_take isl_printer *p,
1075 __isl_keep isl_union_map *umap);
1077 When called on a file printer, the following function flushes
1078 the file. When called on a string printer, the buffer is cleared.
1080 __isl_give isl_printer *isl_printer_flush(
1081 __isl_take isl_printer *p);
1083 =head2 Creating New Sets and Relations
1085 C<isl> has functions for creating some standard sets and relations.
1089 =item * Empty sets and relations
1091 __isl_give isl_basic_set *isl_basic_set_empty(
1092 __isl_take isl_space *space);
1093 __isl_give isl_basic_map *isl_basic_map_empty(
1094 __isl_take isl_space *space);
1095 __isl_give isl_set *isl_set_empty(
1096 __isl_take isl_space *space);
1097 __isl_give isl_map *isl_map_empty(
1098 __isl_take isl_space *space);
1099 __isl_give isl_union_set *isl_union_set_empty(
1100 __isl_take isl_space *space);
1101 __isl_give isl_union_map *isl_union_map_empty(
1102 __isl_take isl_space *space);
1104 For C<isl_union_set>s and C<isl_union_map>s, the space
1105 is only used to specify the parameters.
1107 =item * Universe sets and relations
1109 __isl_give isl_basic_set *isl_basic_set_universe(
1110 __isl_take isl_space *space);
1111 __isl_give isl_basic_map *isl_basic_map_universe(
1112 __isl_take isl_space *space);
1113 __isl_give isl_set *isl_set_universe(
1114 __isl_take isl_space *space);
1115 __isl_give isl_map *isl_map_universe(
1116 __isl_take isl_space *space);
1117 __isl_give isl_union_set *isl_union_set_universe(
1118 __isl_take isl_union_set *uset);
1119 __isl_give isl_union_map *isl_union_map_universe(
1120 __isl_take isl_union_map *umap);
1122 The sets and relations constructed by the functions above
1123 contain all integer values, while those constructed by the
1124 functions below only contain non-negative values.
1126 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1127 __isl_take isl_space *space);
1128 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1129 __isl_take isl_space *space);
1130 __isl_give isl_set *isl_set_nat_universe(
1131 __isl_take isl_space *space);
1132 __isl_give isl_map *isl_map_nat_universe(
1133 __isl_take isl_space *space);
1135 =item * Identity relations
1137 __isl_give isl_basic_map *isl_basic_map_identity(
1138 __isl_take isl_space *space);
1139 __isl_give isl_map *isl_map_identity(
1140 __isl_take isl_space *space);
1142 The number of input and output dimensions in C<space> needs
1145 =item * Lexicographic order
1147 __isl_give isl_map *isl_map_lex_lt(
1148 __isl_take isl_space *set_space);
1149 __isl_give isl_map *isl_map_lex_le(
1150 __isl_take isl_space *set_space);
1151 __isl_give isl_map *isl_map_lex_gt(
1152 __isl_take isl_space *set_space);
1153 __isl_give isl_map *isl_map_lex_ge(
1154 __isl_take isl_space *set_space);
1155 __isl_give isl_map *isl_map_lex_lt_first(
1156 __isl_take isl_space *space, unsigned n);
1157 __isl_give isl_map *isl_map_lex_le_first(
1158 __isl_take isl_space *space, unsigned n);
1159 __isl_give isl_map *isl_map_lex_gt_first(
1160 __isl_take isl_space *space, unsigned n);
1161 __isl_give isl_map *isl_map_lex_ge_first(
1162 __isl_take isl_space *space, unsigned n);
1164 The first four functions take a space for a B<set>
1165 and return relations that express that the elements in the domain
1166 are lexicographically less
1167 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1168 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1169 than the elements in the range.
1170 The last four functions take a space for a map
1171 and return relations that express that the first C<n> dimensions
1172 in the domain are lexicographically less
1173 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1174 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1175 than the first C<n> dimensions in the range.
1179 A basic set or relation can be converted to a set or relation
1180 using the following functions.
1182 __isl_give isl_set *isl_set_from_basic_set(
1183 __isl_take isl_basic_set *bset);
1184 __isl_give isl_map *isl_map_from_basic_map(
1185 __isl_take isl_basic_map *bmap);
1187 Sets and relations can be converted to union sets and relations
1188 using the following functions.
1190 __isl_give isl_union_set *isl_union_set_from_basic_set(
1191 __isl_take isl_basic_set *bset);
1192 __isl_give isl_union_map *isl_union_map_from_basic_map(
1193 __isl_take isl_basic_map *bmap);
1194 __isl_give isl_union_set *isl_union_set_from_set(
1195 __isl_take isl_set *set);
1196 __isl_give isl_union_map *isl_union_map_from_map(
1197 __isl_take isl_map *map);
1199 The inverse conversions below can only be used if the input
1200 union set or relation is known to contain elements in exactly one
1203 __isl_give isl_set *isl_set_from_union_set(
1204 __isl_take isl_union_set *uset);
1205 __isl_give isl_map *isl_map_from_union_map(
1206 __isl_take isl_union_map *umap);
1208 A zero-dimensional set can be constructed on a given parameter domain
1209 using the following function.
1211 __isl_give isl_set *isl_set_from_params(
1212 __isl_take isl_set *set);
1214 Sets and relations can be copied and freed again using the following
1217 __isl_give isl_basic_set *isl_basic_set_copy(
1218 __isl_keep isl_basic_set *bset);
1219 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1220 __isl_give isl_union_set *isl_union_set_copy(
1221 __isl_keep isl_union_set *uset);
1222 __isl_give isl_basic_map *isl_basic_map_copy(
1223 __isl_keep isl_basic_map *bmap);
1224 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1225 __isl_give isl_union_map *isl_union_map_copy(
1226 __isl_keep isl_union_map *umap);
1227 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1228 void *isl_set_free(__isl_take isl_set *set);
1229 void *isl_union_set_free(__isl_take isl_union_set *uset);
1230 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1231 void isl_map_free(__isl_take isl_map *map);
1232 void *isl_union_map_free(__isl_take isl_union_map *umap);
1234 Other sets and relations can be constructed by starting
1235 from a universe set or relation, adding equality and/or
1236 inequality constraints and then projecting out the
1237 existentially quantified variables, if any.
1238 Constraints can be constructed, manipulated and
1239 added to (or removed from) (basic) sets and relations
1240 using the following functions.
1242 #include <isl/constraint.h>
1243 __isl_give isl_constraint *isl_equality_alloc(
1244 __isl_take isl_local_space *ls);
1245 __isl_give isl_constraint *isl_inequality_alloc(
1246 __isl_take isl_local_space *ls);
1247 __isl_give isl_constraint *isl_constraint_set_constant(
1248 __isl_take isl_constraint *constraint, isl_int v);
1249 __isl_give isl_constraint *isl_constraint_set_constant_si(
1250 __isl_take isl_constraint *constraint, int v);
1251 __isl_give isl_constraint *isl_constraint_set_coefficient(
1252 __isl_take isl_constraint *constraint,
1253 enum isl_dim_type type, int pos, isl_int v);
1254 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1255 __isl_take isl_constraint *constraint,
1256 enum isl_dim_type type, int pos, int v);
1257 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1258 __isl_take isl_basic_map *bmap,
1259 __isl_take isl_constraint *constraint);
1260 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1261 __isl_take isl_basic_set *bset,
1262 __isl_take isl_constraint *constraint);
1263 __isl_give isl_map *isl_map_add_constraint(
1264 __isl_take isl_map *map,
1265 __isl_take isl_constraint *constraint);
1266 __isl_give isl_set *isl_set_add_constraint(
1267 __isl_take isl_set *set,
1268 __isl_take isl_constraint *constraint);
1269 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1270 __isl_take isl_basic_set *bset,
1271 __isl_take isl_constraint *constraint);
1273 For example, to create a set containing the even integers
1274 between 10 and 42, you would use the following code.
1277 isl_local_space *ls;
1279 isl_basic_set *bset;
1281 space = isl_space_set_alloc(ctx, 0, 2);
1282 bset = isl_basic_set_universe(isl_space_copy(space));
1283 ls = isl_local_space_from_space(space);
1285 c = isl_equality_alloc(isl_local_space_copy(ls));
1286 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1287 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1288 bset = isl_basic_set_add_constraint(bset, c);
1290 c = isl_inequality_alloc(isl_local_space_copy(ls));
1291 c = isl_constraint_set_constant_si(c, -10);
1292 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1293 bset = isl_basic_set_add_constraint(bset, c);
1295 c = isl_inequality_alloc(ls);
1296 c = isl_constraint_set_constant_si(c, 42);
1297 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1298 bset = isl_basic_set_add_constraint(bset, c);
1300 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1304 isl_basic_set *bset;
1305 bset = isl_basic_set_read_from_str(ctx,
1306 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1308 A basic set or relation can also be constructed from two matrices
1309 describing the equalities and the inequalities.
1311 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1312 __isl_take isl_space *space,
1313 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1314 enum isl_dim_type c1,
1315 enum isl_dim_type c2, enum isl_dim_type c3,
1316 enum isl_dim_type c4);
1317 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1318 __isl_take isl_space *space,
1319 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1320 enum isl_dim_type c1,
1321 enum isl_dim_type c2, enum isl_dim_type c3,
1322 enum isl_dim_type c4, enum isl_dim_type c5);
1324 The C<isl_dim_type> arguments indicate the order in which
1325 different kinds of variables appear in the input matrices
1326 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1327 C<isl_dim_set> and C<isl_dim_div> for sets and
1328 of C<isl_dim_cst>, C<isl_dim_param>,
1329 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1331 A (basic or union) set or relation can also be constructed from a
1332 (union) (piecewise) (multiple) affine expression
1333 or a list of affine expressions
1334 (See L<"Piecewise Quasi Affine Expressions"> and
1335 L<"Piecewise Multiple Quasi Affine Expressions">).
1337 __isl_give isl_basic_map *isl_basic_map_from_aff(
1338 __isl_take isl_aff *aff);
1339 __isl_give isl_map *isl_map_from_aff(
1340 __isl_take isl_aff *aff);
1341 __isl_give isl_set *isl_set_from_pw_aff(
1342 __isl_take isl_pw_aff *pwaff);
1343 __isl_give isl_map *isl_map_from_pw_aff(
1344 __isl_take isl_pw_aff *pwaff);
1345 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1346 __isl_take isl_space *domain_space,
1347 __isl_take isl_aff_list *list);
1348 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1349 __isl_take isl_multi_aff *maff)
1350 __isl_give isl_map *isl_map_from_multi_aff(
1351 __isl_take isl_multi_aff *maff)
1352 __isl_give isl_set *isl_set_from_pw_multi_aff(
1353 __isl_take isl_pw_multi_aff *pma);
1354 __isl_give isl_map *isl_map_from_pw_multi_aff(
1355 __isl_take isl_pw_multi_aff *pma);
1356 __isl_give isl_union_map *
1357 isl_union_map_from_union_pw_multi_aff(
1358 __isl_take isl_union_pw_multi_aff *upma);
1360 The C<domain_dim> argument describes the domain of the resulting
1361 basic relation. It is required because the C<list> may consist
1362 of zero affine expressions.
1364 =head2 Inspecting Sets and Relations
1366 Usually, the user should not have to care about the actual constraints
1367 of the sets and maps, but should instead apply the abstract operations
1368 explained in the following sections.
1369 Occasionally, however, it may be required to inspect the individual
1370 coefficients of the constraints. This section explains how to do so.
1371 In these cases, it may also be useful to have C<isl> compute
1372 an explicit representation of the existentially quantified variables.
1374 __isl_give isl_set *isl_set_compute_divs(
1375 __isl_take isl_set *set);
1376 __isl_give isl_map *isl_map_compute_divs(
1377 __isl_take isl_map *map);
1378 __isl_give isl_union_set *isl_union_set_compute_divs(
1379 __isl_take isl_union_set *uset);
1380 __isl_give isl_union_map *isl_union_map_compute_divs(
1381 __isl_take isl_union_map *umap);
1383 This explicit representation defines the existentially quantified
1384 variables as integer divisions of the other variables, possibly
1385 including earlier existentially quantified variables.
1386 An explicitly represented existentially quantified variable therefore
1387 has a unique value when the values of the other variables are known.
1388 If, furthermore, the same existentials, i.e., existentials
1389 with the same explicit representations, should appear in the
1390 same order in each of the disjuncts of a set or map, then the user should call
1391 either of the following functions.
1393 __isl_give isl_set *isl_set_align_divs(
1394 __isl_take isl_set *set);
1395 __isl_give isl_map *isl_map_align_divs(
1396 __isl_take isl_map *map);
1398 Alternatively, the existentially quantified variables can be removed
1399 using the following functions, which compute an overapproximation.
1401 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1402 __isl_take isl_basic_set *bset);
1403 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1404 __isl_take isl_basic_map *bmap);
1405 __isl_give isl_set *isl_set_remove_divs(
1406 __isl_take isl_set *set);
1407 __isl_give isl_map *isl_map_remove_divs(
1408 __isl_take isl_map *map);
1410 It is also possible to only remove those divs that are defined
1411 in terms of a given range of dimensions or only those for which
1412 no explicit representation is known.
1414 __isl_give isl_basic_set *
1415 isl_basic_set_remove_divs_involving_dims(
1416 __isl_take isl_basic_set *bset,
1417 enum isl_dim_type type,
1418 unsigned first, unsigned n);
1419 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1420 __isl_take isl_set *set, enum isl_dim_type type,
1421 unsigned first, unsigned n);
1422 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1423 __isl_take isl_map *map, enum isl_dim_type type,
1424 unsigned first, unsigned n);
1426 __isl_give isl_set *isl_set_remove_unknown_divs(
1427 __isl_take isl_set *set);
1428 __isl_give isl_map *isl_map_remove_unknown_divs(
1429 __isl_take isl_map *map);
1431 To iterate over all the sets or maps in a union set or map, use
1433 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1434 int (*fn)(__isl_take isl_set *set, void *user),
1436 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1437 int (*fn)(__isl_take isl_map *map, void *user),
1440 The number of sets or maps in a union set or map can be obtained
1443 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1444 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1446 To extract the set or map in a given space from a union, use
1448 __isl_give isl_set *isl_union_set_extract_set(
1449 __isl_keep isl_union_set *uset,
1450 __isl_take isl_space *space);
1451 __isl_give isl_map *isl_union_map_extract_map(
1452 __isl_keep isl_union_map *umap,
1453 __isl_take isl_space *space);
1455 To iterate over all the basic sets or maps in a set or map, use
1457 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1458 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1460 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1461 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1464 The callback function C<fn> should return 0 if successful and
1465 -1 if an error occurs. In the latter case, or if any other error
1466 occurs, the above functions will return -1.
1468 It should be noted that C<isl> does not guarantee that
1469 the basic sets or maps passed to C<fn> are disjoint.
1470 If this is required, then the user should call one of
1471 the following functions first.
1473 __isl_give isl_set *isl_set_make_disjoint(
1474 __isl_take isl_set *set);
1475 __isl_give isl_map *isl_map_make_disjoint(
1476 __isl_take isl_map *map);
1478 The number of basic sets in a set can be obtained
1481 int isl_set_n_basic_set(__isl_keep isl_set *set);
1483 To iterate over the constraints of a basic set or map, use
1485 #include <isl/constraint.h>
1487 int isl_basic_set_n_constraint(
1488 __isl_keep isl_basic_set *bset);
1489 int isl_basic_set_foreach_constraint(
1490 __isl_keep isl_basic_set *bset,
1491 int (*fn)(__isl_take isl_constraint *c, void *user),
1493 int isl_basic_map_foreach_constraint(
1494 __isl_keep isl_basic_map *bmap,
1495 int (*fn)(__isl_take isl_constraint *c, void *user),
1497 void *isl_constraint_free(__isl_take isl_constraint *c);
1499 Again, the callback function C<fn> should return 0 if successful and
1500 -1 if an error occurs. In the latter case, or if any other error
1501 occurs, the above functions will return -1.
1502 The constraint C<c> represents either an equality or an inequality.
1503 Use the following function to find out whether a constraint
1504 represents an equality. If not, it represents an inequality.
1506 int isl_constraint_is_equality(
1507 __isl_keep isl_constraint *constraint);
1509 The coefficients of the constraints can be inspected using
1510 the following functions.
1512 int isl_constraint_is_lower_bound(
1513 __isl_keep isl_constraint *constraint,
1514 enum isl_dim_type type, unsigned pos);
1515 int isl_constraint_is_upper_bound(
1516 __isl_keep isl_constraint *constraint,
1517 enum isl_dim_type type, unsigned pos);
1518 void isl_constraint_get_constant(
1519 __isl_keep isl_constraint *constraint, isl_int *v);
1520 void isl_constraint_get_coefficient(
1521 __isl_keep isl_constraint *constraint,
1522 enum isl_dim_type type, int pos, isl_int *v);
1523 int isl_constraint_involves_dims(
1524 __isl_keep isl_constraint *constraint,
1525 enum isl_dim_type type, unsigned first, unsigned n);
1527 The explicit representations of the existentially quantified
1528 variables can be inspected using the following function.
1529 Note that the user is only allowed to use this function
1530 if the inspected set or map is the result of a call
1531 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1532 The existentially quantified variable is equal to the floor
1533 of the returned affine expression. The affine expression
1534 itself can be inspected using the functions in
1535 L<"Piecewise Quasi Affine Expressions">.
1537 __isl_give isl_aff *isl_constraint_get_div(
1538 __isl_keep isl_constraint *constraint, int pos);
1540 To obtain the constraints of a basic set or map in matrix
1541 form, use the following functions.
1543 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1544 __isl_keep isl_basic_set *bset,
1545 enum isl_dim_type c1, enum isl_dim_type c2,
1546 enum isl_dim_type c3, enum isl_dim_type c4);
1547 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1548 __isl_keep isl_basic_set *bset,
1549 enum isl_dim_type c1, enum isl_dim_type c2,
1550 enum isl_dim_type c3, enum isl_dim_type c4);
1551 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1552 __isl_keep isl_basic_map *bmap,
1553 enum isl_dim_type c1,
1554 enum isl_dim_type c2, enum isl_dim_type c3,
1555 enum isl_dim_type c4, enum isl_dim_type c5);
1556 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1557 __isl_keep isl_basic_map *bmap,
1558 enum isl_dim_type c1,
1559 enum isl_dim_type c2, enum isl_dim_type c3,
1560 enum isl_dim_type c4, enum isl_dim_type c5);
1562 The C<isl_dim_type> arguments dictate the order in which
1563 different kinds of variables appear in the resulting matrix
1564 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1565 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1567 The number of parameters, input, output or set dimensions can
1568 be obtained using the following functions.
1570 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1571 enum isl_dim_type type);
1572 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1573 enum isl_dim_type type);
1574 unsigned isl_set_dim(__isl_keep isl_set *set,
1575 enum isl_dim_type type);
1576 unsigned isl_map_dim(__isl_keep isl_map *map,
1577 enum isl_dim_type type);
1579 To check whether the description of a set or relation depends
1580 on one or more given dimensions, it is not necessary to iterate over all
1581 constraints. Instead the following functions can be used.
1583 int isl_basic_set_involves_dims(
1584 __isl_keep isl_basic_set *bset,
1585 enum isl_dim_type type, unsigned first, unsigned n);
1586 int isl_set_involves_dims(__isl_keep isl_set *set,
1587 enum isl_dim_type type, unsigned first, unsigned n);
1588 int isl_basic_map_involves_dims(
1589 __isl_keep isl_basic_map *bmap,
1590 enum isl_dim_type type, unsigned first, unsigned n);
1591 int isl_map_involves_dims(__isl_keep isl_map *map,
1592 enum isl_dim_type type, unsigned first, unsigned n);
1594 Similarly, the following functions can be used to check whether
1595 a given dimension is involved in any lower or upper bound.
1597 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1598 enum isl_dim_type type, unsigned pos);
1599 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1600 enum isl_dim_type type, unsigned pos);
1602 The identifiers or names of the domain and range spaces of a set
1603 or relation can be read off or set using the following functions.
1605 __isl_give isl_set *isl_set_set_tuple_id(
1606 __isl_take isl_set *set, __isl_take isl_id *id);
1607 __isl_give isl_set *isl_set_reset_tuple_id(
1608 __isl_take isl_set *set);
1609 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1610 __isl_give isl_id *isl_set_get_tuple_id(
1611 __isl_keep isl_set *set);
1612 __isl_give isl_map *isl_map_set_tuple_id(
1613 __isl_take isl_map *map, enum isl_dim_type type,
1614 __isl_take isl_id *id);
1615 __isl_give isl_map *isl_map_reset_tuple_id(
1616 __isl_take isl_map *map, enum isl_dim_type type);
1617 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1618 enum isl_dim_type type);
1619 __isl_give isl_id *isl_map_get_tuple_id(
1620 __isl_keep isl_map *map, enum isl_dim_type type);
1622 const char *isl_basic_set_get_tuple_name(
1623 __isl_keep isl_basic_set *bset);
1624 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1625 __isl_take isl_basic_set *set, const char *s);
1626 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1627 const char *isl_set_get_tuple_name(
1628 __isl_keep isl_set *set);
1629 const char *isl_basic_map_get_tuple_name(
1630 __isl_keep isl_basic_map *bmap,
1631 enum isl_dim_type type);
1632 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1633 __isl_take isl_basic_map *bmap,
1634 enum isl_dim_type type, const char *s);
1635 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1636 enum isl_dim_type type);
1637 const char *isl_map_get_tuple_name(
1638 __isl_keep isl_map *map,
1639 enum isl_dim_type type);
1641 As with C<isl_space_get_tuple_name>, the value returned points to
1642 an internal data structure.
1643 The identifiers, positions or names of individual dimensions can be
1644 read off using the following functions.
1646 __isl_give isl_id *isl_basic_set_get_dim_id(
1647 __isl_keep isl_basic_set *bset,
1648 enum isl_dim_type type, unsigned pos);
1649 __isl_give isl_set *isl_set_set_dim_id(
1650 __isl_take isl_set *set, enum isl_dim_type type,
1651 unsigned pos, __isl_take isl_id *id);
1652 int isl_set_has_dim_id(__isl_keep isl_set *set,
1653 enum isl_dim_type type, unsigned pos);
1654 __isl_give isl_id *isl_set_get_dim_id(
1655 __isl_keep isl_set *set, enum isl_dim_type type,
1657 int isl_basic_map_has_dim_id(
1658 __isl_keep isl_basic_map *bmap,
1659 enum isl_dim_type type, unsigned pos);
1660 __isl_give isl_map *isl_map_set_dim_id(
1661 __isl_take isl_map *map, enum isl_dim_type type,
1662 unsigned pos, __isl_take isl_id *id);
1663 int isl_map_has_dim_id(__isl_keep isl_map *map,
1664 enum isl_dim_type type, unsigned pos);
1665 __isl_give isl_id *isl_map_get_dim_id(
1666 __isl_keep isl_map *map, enum isl_dim_type type,
1669 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1670 enum isl_dim_type type, __isl_keep isl_id *id);
1671 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1672 enum isl_dim_type type, __isl_keep isl_id *id);
1673 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1674 enum isl_dim_type type, const char *name);
1675 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1676 enum isl_dim_type type, const char *name);
1678 const char *isl_constraint_get_dim_name(
1679 __isl_keep isl_constraint *constraint,
1680 enum isl_dim_type type, unsigned pos);
1681 const char *isl_basic_set_get_dim_name(
1682 __isl_keep isl_basic_set *bset,
1683 enum isl_dim_type type, unsigned pos);
1684 int isl_set_has_dim_name(__isl_keep isl_set *set,
1685 enum isl_dim_type type, unsigned pos);
1686 const char *isl_set_get_dim_name(
1687 __isl_keep isl_set *set,
1688 enum isl_dim_type type, unsigned pos);
1689 const char *isl_basic_map_get_dim_name(
1690 __isl_keep isl_basic_map *bmap,
1691 enum isl_dim_type type, unsigned pos);
1692 int isl_map_has_dim_name(__isl_keep isl_map *map,
1693 enum isl_dim_type type, unsigned pos);
1694 const char *isl_map_get_dim_name(
1695 __isl_keep isl_map *map,
1696 enum isl_dim_type type, unsigned pos);
1698 These functions are mostly useful to obtain the identifiers, positions
1699 or names of the parameters. Identifiers of individual dimensions are
1700 essentially only useful for printing. They are ignored by all other
1701 operations and may not be preserved across those operations.
1705 =head3 Unary Properties
1711 The following functions test whether the given set or relation
1712 contains any integer points. The ``plain'' variants do not perform
1713 any computations, but simply check if the given set or relation
1714 is already known to be empty.
1716 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1717 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1718 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1719 int isl_set_is_empty(__isl_keep isl_set *set);
1720 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1721 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1722 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1723 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1724 int isl_map_is_empty(__isl_keep isl_map *map);
1725 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1727 =item * Universality
1729 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1730 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1731 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1733 =item * Single-valuedness
1735 int isl_basic_map_is_single_valued(
1736 __isl_keep isl_basic_map *bmap);
1737 int isl_map_plain_is_single_valued(
1738 __isl_keep isl_map *map);
1739 int isl_map_is_single_valued(__isl_keep isl_map *map);
1740 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1744 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1745 int isl_map_is_injective(__isl_keep isl_map *map);
1746 int isl_union_map_plain_is_injective(
1747 __isl_keep isl_union_map *umap);
1748 int isl_union_map_is_injective(
1749 __isl_keep isl_union_map *umap);
1753 int isl_map_is_bijective(__isl_keep isl_map *map);
1754 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1758 int isl_basic_map_plain_is_fixed(
1759 __isl_keep isl_basic_map *bmap,
1760 enum isl_dim_type type, unsigned pos,
1762 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1763 enum isl_dim_type type, unsigned pos,
1765 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1766 enum isl_dim_type type, unsigned pos,
1769 Check if the relation obviously lies on a hyperplane where the given dimension
1770 has a fixed value and if so, return that value in C<*val>.
1774 To check whether a set is a parameter domain, use this function:
1776 int isl_set_is_params(__isl_keep isl_set *set);
1777 int isl_union_set_is_params(
1778 __isl_keep isl_union_set *uset);
1782 The following functions check whether the domain of the given
1783 (basic) set is a wrapped relation.
1785 int isl_basic_set_is_wrapping(
1786 __isl_keep isl_basic_set *bset);
1787 int isl_set_is_wrapping(__isl_keep isl_set *set);
1789 =item * Internal Product
1791 int isl_basic_map_can_zip(
1792 __isl_keep isl_basic_map *bmap);
1793 int isl_map_can_zip(__isl_keep isl_map *map);
1795 Check whether the product of domain and range of the given relation
1797 i.e., whether both domain and range are nested relations.
1801 int isl_basic_map_can_curry(
1802 __isl_keep isl_basic_map *bmap);
1803 int isl_map_can_curry(__isl_keep isl_map *map);
1805 Check whether the domain of the (basic) relation is a wrapped relation.
1809 =head3 Binary Properties
1815 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1816 __isl_keep isl_set *set2);
1817 int isl_set_is_equal(__isl_keep isl_set *set1,
1818 __isl_keep isl_set *set2);
1819 int isl_union_set_is_equal(
1820 __isl_keep isl_union_set *uset1,
1821 __isl_keep isl_union_set *uset2);
1822 int isl_basic_map_is_equal(
1823 __isl_keep isl_basic_map *bmap1,
1824 __isl_keep isl_basic_map *bmap2);
1825 int isl_map_is_equal(__isl_keep isl_map *map1,
1826 __isl_keep isl_map *map2);
1827 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1828 __isl_keep isl_map *map2);
1829 int isl_union_map_is_equal(
1830 __isl_keep isl_union_map *umap1,
1831 __isl_keep isl_union_map *umap2);
1833 =item * Disjointness
1835 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1836 __isl_keep isl_set *set2);
1840 int isl_basic_set_is_subset(
1841 __isl_keep isl_basic_set *bset1,
1842 __isl_keep isl_basic_set *bset2);
1843 int isl_set_is_subset(__isl_keep isl_set *set1,
1844 __isl_keep isl_set *set2);
1845 int isl_set_is_strict_subset(
1846 __isl_keep isl_set *set1,
1847 __isl_keep isl_set *set2);
1848 int isl_union_set_is_subset(
1849 __isl_keep isl_union_set *uset1,
1850 __isl_keep isl_union_set *uset2);
1851 int isl_union_set_is_strict_subset(
1852 __isl_keep isl_union_set *uset1,
1853 __isl_keep isl_union_set *uset2);
1854 int isl_basic_map_is_subset(
1855 __isl_keep isl_basic_map *bmap1,
1856 __isl_keep isl_basic_map *bmap2);
1857 int isl_basic_map_is_strict_subset(
1858 __isl_keep isl_basic_map *bmap1,
1859 __isl_keep isl_basic_map *bmap2);
1860 int isl_map_is_subset(
1861 __isl_keep isl_map *map1,
1862 __isl_keep isl_map *map2);
1863 int isl_map_is_strict_subset(
1864 __isl_keep isl_map *map1,
1865 __isl_keep isl_map *map2);
1866 int isl_union_map_is_subset(
1867 __isl_keep isl_union_map *umap1,
1868 __isl_keep isl_union_map *umap2);
1869 int isl_union_map_is_strict_subset(
1870 __isl_keep isl_union_map *umap1,
1871 __isl_keep isl_union_map *umap2);
1873 Check whether the first argument is a (strict) subset of the
1878 =head2 Unary Operations
1884 __isl_give isl_set *isl_set_complement(
1885 __isl_take isl_set *set);
1886 __isl_give isl_map *isl_map_complement(
1887 __isl_take isl_map *map);
1891 __isl_give isl_basic_map *isl_basic_map_reverse(
1892 __isl_take isl_basic_map *bmap);
1893 __isl_give isl_map *isl_map_reverse(
1894 __isl_take isl_map *map);
1895 __isl_give isl_union_map *isl_union_map_reverse(
1896 __isl_take isl_union_map *umap);
1900 __isl_give isl_basic_set *isl_basic_set_project_out(
1901 __isl_take isl_basic_set *bset,
1902 enum isl_dim_type type, unsigned first, unsigned n);
1903 __isl_give isl_basic_map *isl_basic_map_project_out(
1904 __isl_take isl_basic_map *bmap,
1905 enum isl_dim_type type, unsigned first, unsigned n);
1906 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1907 enum isl_dim_type type, unsigned first, unsigned n);
1908 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1909 enum isl_dim_type type, unsigned first, unsigned n);
1910 __isl_give isl_basic_set *isl_basic_set_params(
1911 __isl_take isl_basic_set *bset);
1912 __isl_give isl_basic_set *isl_basic_map_domain(
1913 __isl_take isl_basic_map *bmap);
1914 __isl_give isl_basic_set *isl_basic_map_range(
1915 __isl_take isl_basic_map *bmap);
1916 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1917 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1918 __isl_give isl_set *isl_map_domain(
1919 __isl_take isl_map *bmap);
1920 __isl_give isl_set *isl_map_range(
1921 __isl_take isl_map *map);
1922 __isl_give isl_set *isl_union_set_params(
1923 __isl_take isl_union_set *uset);
1924 __isl_give isl_set *isl_union_map_params(
1925 __isl_take isl_union_map *umap);
1926 __isl_give isl_union_set *isl_union_map_domain(
1927 __isl_take isl_union_map *umap);
1928 __isl_give isl_union_set *isl_union_map_range(
1929 __isl_take isl_union_map *umap);
1931 __isl_give isl_basic_map *isl_basic_map_domain_map(
1932 __isl_take isl_basic_map *bmap);
1933 __isl_give isl_basic_map *isl_basic_map_range_map(
1934 __isl_take isl_basic_map *bmap);
1935 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1936 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1937 __isl_give isl_union_map *isl_union_map_domain_map(
1938 __isl_take isl_union_map *umap);
1939 __isl_give isl_union_map *isl_union_map_range_map(
1940 __isl_take isl_union_map *umap);
1942 The functions above construct a (basic, regular or union) relation
1943 that maps (a wrapped version of) the input relation to its domain or range.
1947 __isl_give isl_basic_set *isl_basic_set_eliminate(
1948 __isl_take isl_basic_set *bset,
1949 enum isl_dim_type type,
1950 unsigned first, unsigned n);
1951 __isl_give isl_set *isl_set_eliminate(
1952 __isl_take isl_set *set, enum isl_dim_type type,
1953 unsigned first, unsigned n);
1954 __isl_give isl_basic_map *isl_basic_map_eliminate(
1955 __isl_take isl_basic_map *bmap,
1956 enum isl_dim_type type,
1957 unsigned first, unsigned n);
1958 __isl_give isl_map *isl_map_eliminate(
1959 __isl_take isl_map *map, enum isl_dim_type type,
1960 unsigned first, unsigned n);
1962 Eliminate the coefficients for the given dimensions from the constraints,
1963 without removing the dimensions.
1967 __isl_give isl_basic_set *isl_basic_set_fix(
1968 __isl_take isl_basic_set *bset,
1969 enum isl_dim_type type, unsigned pos,
1971 __isl_give isl_basic_set *isl_basic_set_fix_si(
1972 __isl_take isl_basic_set *bset,
1973 enum isl_dim_type type, unsigned pos, int value);
1974 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1975 enum isl_dim_type type, unsigned pos,
1977 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1978 enum isl_dim_type type, unsigned pos, int value);
1979 __isl_give isl_basic_map *isl_basic_map_fix_si(
1980 __isl_take isl_basic_map *bmap,
1981 enum isl_dim_type type, unsigned pos, int value);
1982 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1983 enum isl_dim_type type, unsigned pos, int value);
1985 Intersect the set or relation with the hyperplane where the given
1986 dimension has the fixed given value.
1988 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1989 __isl_take isl_basic_map *bmap,
1990 enum isl_dim_type type, unsigned pos, int value);
1991 __isl_give isl_set *isl_set_lower_bound(
1992 __isl_take isl_set *set,
1993 enum isl_dim_type type, unsigned pos,
1995 __isl_give isl_set *isl_set_lower_bound_si(
1996 __isl_take isl_set *set,
1997 enum isl_dim_type type, unsigned pos, int value);
1998 __isl_give isl_map *isl_map_lower_bound_si(
1999 __isl_take isl_map *map,
2000 enum isl_dim_type type, unsigned pos, int value);
2001 __isl_give isl_set *isl_set_upper_bound(
2002 __isl_take isl_set *set,
2003 enum isl_dim_type type, unsigned pos,
2005 __isl_give isl_set *isl_set_upper_bound_si(
2006 __isl_take isl_set *set,
2007 enum isl_dim_type type, unsigned pos, int value);
2008 __isl_give isl_map *isl_map_upper_bound_si(
2009 __isl_take isl_map *map,
2010 enum isl_dim_type type, unsigned pos, int value);
2012 Intersect the set or relation with the half-space where the given
2013 dimension has a value bounded by the fixed given value.
2015 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2016 enum isl_dim_type type1, int pos1,
2017 enum isl_dim_type type2, int pos2);
2018 __isl_give isl_basic_map *isl_basic_map_equate(
2019 __isl_take isl_basic_map *bmap,
2020 enum isl_dim_type type1, int pos1,
2021 enum isl_dim_type type2, int pos2);
2022 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2023 enum isl_dim_type type1, int pos1,
2024 enum isl_dim_type type2, int pos2);
2026 Intersect the set or relation with the hyperplane where the given
2027 dimensions are equal to each other.
2029 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2030 enum isl_dim_type type1, int pos1,
2031 enum isl_dim_type type2, int pos2);
2033 Intersect the relation with the hyperplane where the given
2034 dimensions have opposite values.
2036 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2037 enum isl_dim_type type1, int pos1,
2038 enum isl_dim_type type2, int pos2);
2039 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2040 enum isl_dim_type type1, int pos1,
2041 enum isl_dim_type type2, int pos2);
2043 Intersect the relation with the half-space where the given
2044 dimensions satisfy the given ordering.
2048 __isl_give isl_map *isl_set_identity(
2049 __isl_take isl_set *set);
2050 __isl_give isl_union_map *isl_union_set_identity(
2051 __isl_take isl_union_set *uset);
2053 Construct an identity relation on the given (union) set.
2057 __isl_give isl_basic_set *isl_basic_map_deltas(
2058 __isl_take isl_basic_map *bmap);
2059 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2060 __isl_give isl_union_set *isl_union_map_deltas(
2061 __isl_take isl_union_map *umap);
2063 These functions return a (basic) set containing the differences
2064 between image elements and corresponding domain elements in the input.
2066 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2067 __isl_take isl_basic_map *bmap);
2068 __isl_give isl_map *isl_map_deltas_map(
2069 __isl_take isl_map *map);
2070 __isl_give isl_union_map *isl_union_map_deltas_map(
2071 __isl_take isl_union_map *umap);
2073 The functions above construct a (basic, regular or union) relation
2074 that maps (a wrapped version of) the input relation to its delta set.
2078 Simplify the representation of a set or relation by trying
2079 to combine pairs of basic sets or relations into a single
2080 basic set or relation.
2082 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2083 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2084 __isl_give isl_union_set *isl_union_set_coalesce(
2085 __isl_take isl_union_set *uset);
2086 __isl_give isl_union_map *isl_union_map_coalesce(
2087 __isl_take isl_union_map *umap);
2089 One of the methods for combining pairs of basic sets or relations
2090 can result in coefficients that are much larger than those that appear
2091 in the constraints of the input. By default, the coefficients are
2092 not allowed to grow larger, but this can be changed by unsetting
2093 the following option.
2095 int isl_options_set_coalesce_bounded_wrapping(
2096 isl_ctx *ctx, int val);
2097 int isl_options_get_coalesce_bounded_wrapping(
2100 =item * Detecting equalities
2102 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2103 __isl_take isl_basic_set *bset);
2104 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2105 __isl_take isl_basic_map *bmap);
2106 __isl_give isl_set *isl_set_detect_equalities(
2107 __isl_take isl_set *set);
2108 __isl_give isl_map *isl_map_detect_equalities(
2109 __isl_take isl_map *map);
2110 __isl_give isl_union_set *isl_union_set_detect_equalities(
2111 __isl_take isl_union_set *uset);
2112 __isl_give isl_union_map *isl_union_map_detect_equalities(
2113 __isl_take isl_union_map *umap);
2115 Simplify the representation of a set or relation by detecting implicit
2118 =item * Removing redundant constraints
2120 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2121 __isl_take isl_basic_set *bset);
2122 __isl_give isl_set *isl_set_remove_redundancies(
2123 __isl_take isl_set *set);
2124 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2125 __isl_take isl_basic_map *bmap);
2126 __isl_give isl_map *isl_map_remove_redundancies(
2127 __isl_take isl_map *map);
2131 __isl_give isl_basic_set *isl_set_convex_hull(
2132 __isl_take isl_set *set);
2133 __isl_give isl_basic_map *isl_map_convex_hull(
2134 __isl_take isl_map *map);
2136 If the input set or relation has any existentially quantified
2137 variables, then the result of these operations is currently undefined.
2141 __isl_give isl_basic_set *isl_set_simple_hull(
2142 __isl_take isl_set *set);
2143 __isl_give isl_basic_map *isl_map_simple_hull(
2144 __isl_take isl_map *map);
2145 __isl_give isl_union_map *isl_union_map_simple_hull(
2146 __isl_take isl_union_map *umap);
2148 These functions compute a single basic set or relation
2149 that contains the whole input set or relation.
2150 In particular, the output is described by translates
2151 of the constraints describing the basic sets or relations in the input.
2155 (See \autoref{s:simple hull}.)
2161 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2162 __isl_take isl_basic_set *bset);
2163 __isl_give isl_basic_set *isl_set_affine_hull(
2164 __isl_take isl_set *set);
2165 __isl_give isl_union_set *isl_union_set_affine_hull(
2166 __isl_take isl_union_set *uset);
2167 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2168 __isl_take isl_basic_map *bmap);
2169 __isl_give isl_basic_map *isl_map_affine_hull(
2170 __isl_take isl_map *map);
2171 __isl_give isl_union_map *isl_union_map_affine_hull(
2172 __isl_take isl_union_map *umap);
2174 In case of union sets and relations, the affine hull is computed
2177 =item * Polyhedral hull
2179 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2180 __isl_take isl_set *set);
2181 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2182 __isl_take isl_map *map);
2183 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2184 __isl_take isl_union_set *uset);
2185 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2186 __isl_take isl_union_map *umap);
2188 These functions compute a single basic set or relation
2189 not involving any existentially quantified variables
2190 that contains the whole input set or relation.
2191 In case of union sets and relations, the polyhedral hull is computed
2196 __isl_give isl_basic_set *isl_basic_set_sample(
2197 __isl_take isl_basic_set *bset);
2198 __isl_give isl_basic_set *isl_set_sample(
2199 __isl_take isl_set *set);
2200 __isl_give isl_basic_map *isl_basic_map_sample(
2201 __isl_take isl_basic_map *bmap);
2202 __isl_give isl_basic_map *isl_map_sample(
2203 __isl_take isl_map *map);
2205 If the input (basic) set or relation is non-empty, then return
2206 a singleton subset of the input. Otherwise, return an empty set.
2208 =item * Optimization
2210 #include <isl/ilp.h>
2211 enum isl_lp_result isl_basic_set_max(
2212 __isl_keep isl_basic_set *bset,
2213 __isl_keep isl_aff *obj, isl_int *opt)
2214 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2215 __isl_keep isl_aff *obj, isl_int *opt);
2216 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2217 __isl_keep isl_aff *obj, isl_int *opt);
2219 Compute the minimum or maximum of the integer affine expression C<obj>
2220 over the points in C<set>, returning the result in C<opt>.
2221 The return value may be one of C<isl_lp_error>,
2222 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2224 =item * Parametric optimization
2226 __isl_give isl_pw_aff *isl_set_dim_min(
2227 __isl_take isl_set *set, int pos);
2228 __isl_give isl_pw_aff *isl_set_dim_max(
2229 __isl_take isl_set *set, int pos);
2230 __isl_give isl_pw_aff *isl_map_dim_max(
2231 __isl_take isl_map *map, int pos);
2233 Compute the minimum or maximum of the given set or output dimension
2234 as a function of the parameters (and input dimensions), but independently
2235 of the other set or output dimensions.
2236 For lexicographic optimization, see L<"Lexicographic Optimization">.
2240 The following functions compute either the set of (rational) coefficient
2241 values of valid constraints for the given set or the set of (rational)
2242 values satisfying the constraints with coefficients from the given set.
2243 Internally, these two sets of functions perform essentially the
2244 same operations, except that the set of coefficients is assumed to
2245 be a cone, while the set of values may be any polyhedron.
2246 The current implementation is based on the Farkas lemma and
2247 Fourier-Motzkin elimination, but this may change or be made optional
2248 in future. In particular, future implementations may use different
2249 dualization algorithms or skip the elimination step.
2251 __isl_give isl_basic_set *isl_basic_set_coefficients(
2252 __isl_take isl_basic_set *bset);
2253 __isl_give isl_basic_set *isl_set_coefficients(
2254 __isl_take isl_set *set);
2255 __isl_give isl_union_set *isl_union_set_coefficients(
2256 __isl_take isl_union_set *bset);
2257 __isl_give isl_basic_set *isl_basic_set_solutions(
2258 __isl_take isl_basic_set *bset);
2259 __isl_give isl_basic_set *isl_set_solutions(
2260 __isl_take isl_set *set);
2261 __isl_give isl_union_set *isl_union_set_solutions(
2262 __isl_take isl_union_set *bset);
2266 __isl_give isl_map *isl_map_fixed_power(
2267 __isl_take isl_map *map, isl_int exp);
2268 __isl_give isl_union_map *isl_union_map_fixed_power(
2269 __isl_take isl_union_map *umap, isl_int exp);
2271 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2272 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2273 of C<map> is computed.
2275 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2277 __isl_give isl_union_map *isl_union_map_power(
2278 __isl_take isl_union_map *umap, int *exact);
2280 Compute a parametric representation for all positive powers I<k> of C<map>.
2281 The result maps I<k> to a nested relation corresponding to the
2282 I<k>th power of C<map>.
2283 The result may be an overapproximation. If the result is known to be exact,
2284 then C<*exact> is set to C<1>.
2286 =item * Transitive closure
2288 __isl_give isl_map *isl_map_transitive_closure(
2289 __isl_take isl_map *map, int *exact);
2290 __isl_give isl_union_map *isl_union_map_transitive_closure(
2291 __isl_take isl_union_map *umap, int *exact);
2293 Compute the transitive closure of C<map>.
2294 The result may be an overapproximation. If the result is known to be exact,
2295 then C<*exact> is set to C<1>.
2297 =item * Reaching path lengths
2299 __isl_give isl_map *isl_map_reaching_path_lengths(
2300 __isl_take isl_map *map, int *exact);
2302 Compute a relation that maps each element in the range of C<map>
2303 to the lengths of all paths composed of edges in C<map> that
2304 end up in the given element.
2305 The result may be an overapproximation. If the result is known to be exact,
2306 then C<*exact> is set to C<1>.
2307 To compute the I<maximal> path length, the resulting relation
2308 should be postprocessed by C<isl_map_lexmax>.
2309 In particular, if the input relation is a dependence relation
2310 (mapping sources to sinks), then the maximal path length corresponds
2311 to the free schedule.
2312 Note, however, that C<isl_map_lexmax> expects the maximum to be
2313 finite, so if the path lengths are unbounded (possibly due to
2314 the overapproximation), then you will get an error message.
2318 __isl_give isl_basic_set *isl_basic_map_wrap(
2319 __isl_take isl_basic_map *bmap);
2320 __isl_give isl_set *isl_map_wrap(
2321 __isl_take isl_map *map);
2322 __isl_give isl_union_set *isl_union_map_wrap(
2323 __isl_take isl_union_map *umap);
2324 __isl_give isl_basic_map *isl_basic_set_unwrap(
2325 __isl_take isl_basic_set *bset);
2326 __isl_give isl_map *isl_set_unwrap(
2327 __isl_take isl_set *set);
2328 __isl_give isl_union_map *isl_union_set_unwrap(
2329 __isl_take isl_union_set *uset);
2333 Remove any internal structure of domain (and range) of the given
2334 set or relation. If there is any such internal structure in the input,
2335 then the name of the space is also removed.
2337 __isl_give isl_basic_set *isl_basic_set_flatten(
2338 __isl_take isl_basic_set *bset);
2339 __isl_give isl_set *isl_set_flatten(
2340 __isl_take isl_set *set);
2341 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2342 __isl_take isl_basic_map *bmap);
2343 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2344 __isl_take isl_basic_map *bmap);
2345 __isl_give isl_map *isl_map_flatten_range(
2346 __isl_take isl_map *map);
2347 __isl_give isl_map *isl_map_flatten_domain(
2348 __isl_take isl_map *map);
2349 __isl_give isl_basic_map *isl_basic_map_flatten(
2350 __isl_take isl_basic_map *bmap);
2351 __isl_give isl_map *isl_map_flatten(
2352 __isl_take isl_map *map);
2354 __isl_give isl_map *isl_set_flatten_map(
2355 __isl_take isl_set *set);
2357 The function above constructs a relation
2358 that maps the input set to a flattened version of the set.
2362 Lift the input set to a space with extra dimensions corresponding
2363 to the existentially quantified variables in the input.
2364 In particular, the result lives in a wrapped map where the domain
2365 is the original space and the range corresponds to the original
2366 existentially quantified variables.
2368 __isl_give isl_basic_set *isl_basic_set_lift(
2369 __isl_take isl_basic_set *bset);
2370 __isl_give isl_set *isl_set_lift(
2371 __isl_take isl_set *set);
2372 __isl_give isl_union_set *isl_union_set_lift(
2373 __isl_take isl_union_set *uset);
2375 Given a local space that contains the existentially quantified
2376 variables of a set, a basic relation that, when applied to
2377 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2378 can be constructed using the following function.
2380 #include <isl/local_space.h>
2381 __isl_give isl_basic_map *isl_local_space_lifting(
2382 __isl_take isl_local_space *ls);
2384 =item * Internal Product
2386 __isl_give isl_basic_map *isl_basic_map_zip(
2387 __isl_take isl_basic_map *bmap);
2388 __isl_give isl_map *isl_map_zip(
2389 __isl_take isl_map *map);
2390 __isl_give isl_union_map *isl_union_map_zip(
2391 __isl_take isl_union_map *umap);
2393 Given a relation with nested relations for domain and range,
2394 interchange the range of the domain with the domain of the range.
2398 __isl_give isl_basic_map *isl_basic_map_curry(
2399 __isl_take isl_basic_map *bmap);
2400 __isl_give isl_map *isl_map_curry(
2401 __isl_take isl_map *map);
2402 __isl_give isl_union_map *isl_union_map_curry(
2403 __isl_take isl_union_map *umap);
2405 Given a relation with a nested relation for domain,
2406 move the range of the nested relation out of the domain
2407 and use it as the domain of a nested relation in the range,
2408 with the original range as range of this nested relation.
2410 =item * Aligning parameters
2412 __isl_give isl_basic_set *isl_basic_set_align_params(
2413 __isl_take isl_basic_set *bset,
2414 __isl_take isl_space *model);
2415 __isl_give isl_set *isl_set_align_params(
2416 __isl_take isl_set *set,
2417 __isl_take isl_space *model);
2418 __isl_give isl_basic_map *isl_basic_map_align_params(
2419 __isl_take isl_basic_map *bmap,
2420 __isl_take isl_space *model);
2421 __isl_give isl_map *isl_map_align_params(
2422 __isl_take isl_map *map,
2423 __isl_take isl_space *model);
2425 Change the order of the parameters of the given set or relation
2426 such that the first parameters match those of C<model>.
2427 This may involve the introduction of extra parameters.
2428 All parameters need to be named.
2430 =item * Dimension manipulation
2432 __isl_give isl_set *isl_set_add_dims(
2433 __isl_take isl_set *set,
2434 enum isl_dim_type type, unsigned n);
2435 __isl_give isl_map *isl_map_add_dims(
2436 __isl_take isl_map *map,
2437 enum isl_dim_type type, unsigned n);
2438 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2439 __isl_take isl_basic_set *bset,
2440 enum isl_dim_type type, unsigned pos,
2442 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2443 __isl_take isl_basic_map *bmap,
2444 enum isl_dim_type type, unsigned pos,
2446 __isl_give isl_set *isl_set_insert_dims(
2447 __isl_take isl_set *set,
2448 enum isl_dim_type type, unsigned pos, unsigned n);
2449 __isl_give isl_map *isl_map_insert_dims(
2450 __isl_take isl_map *map,
2451 enum isl_dim_type type, unsigned pos, unsigned n);
2452 __isl_give isl_basic_set *isl_basic_set_move_dims(
2453 __isl_take isl_basic_set *bset,
2454 enum isl_dim_type dst_type, unsigned dst_pos,
2455 enum isl_dim_type src_type, unsigned src_pos,
2457 __isl_give isl_basic_map *isl_basic_map_move_dims(
2458 __isl_take isl_basic_map *bmap,
2459 enum isl_dim_type dst_type, unsigned dst_pos,
2460 enum isl_dim_type src_type, unsigned src_pos,
2462 __isl_give isl_set *isl_set_move_dims(
2463 __isl_take isl_set *set,
2464 enum isl_dim_type dst_type, unsigned dst_pos,
2465 enum isl_dim_type src_type, unsigned src_pos,
2467 __isl_give isl_map *isl_map_move_dims(
2468 __isl_take isl_map *map,
2469 enum isl_dim_type dst_type, unsigned dst_pos,
2470 enum isl_dim_type src_type, unsigned src_pos,
2473 It is usually not advisable to directly change the (input or output)
2474 space of a set or a relation as this removes the name and the internal
2475 structure of the space. However, the above functions can be useful
2476 to add new parameters, assuming
2477 C<isl_set_align_params> and C<isl_map_align_params>
2482 =head2 Binary Operations
2484 The two arguments of a binary operation not only need to live
2485 in the same C<isl_ctx>, they currently also need to have
2486 the same (number of) parameters.
2488 =head3 Basic Operations
2492 =item * Intersection
2494 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2495 __isl_take isl_basic_set *bset1,
2496 __isl_take isl_basic_set *bset2);
2497 __isl_give isl_basic_set *isl_basic_set_intersect(
2498 __isl_take isl_basic_set *bset1,
2499 __isl_take isl_basic_set *bset2);
2500 __isl_give isl_set *isl_set_intersect_params(
2501 __isl_take isl_set *set,
2502 __isl_take isl_set *params);
2503 __isl_give isl_set *isl_set_intersect(
2504 __isl_take isl_set *set1,
2505 __isl_take isl_set *set2);
2506 __isl_give isl_union_set *isl_union_set_intersect_params(
2507 __isl_take isl_union_set *uset,
2508 __isl_take isl_set *set);
2509 __isl_give isl_union_map *isl_union_map_intersect_params(
2510 __isl_take isl_union_map *umap,
2511 __isl_take isl_set *set);
2512 __isl_give isl_union_set *isl_union_set_intersect(
2513 __isl_take isl_union_set *uset1,
2514 __isl_take isl_union_set *uset2);
2515 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2516 __isl_take isl_basic_map *bmap,
2517 __isl_take isl_basic_set *bset);
2518 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2519 __isl_take isl_basic_map *bmap,
2520 __isl_take isl_basic_set *bset);
2521 __isl_give isl_basic_map *isl_basic_map_intersect(
2522 __isl_take isl_basic_map *bmap1,
2523 __isl_take isl_basic_map *bmap2);
2524 __isl_give isl_map *isl_map_intersect_params(
2525 __isl_take isl_map *map,
2526 __isl_take isl_set *params);
2527 __isl_give isl_map *isl_map_intersect_domain(
2528 __isl_take isl_map *map,
2529 __isl_take isl_set *set);
2530 __isl_give isl_map *isl_map_intersect_range(
2531 __isl_take isl_map *map,
2532 __isl_take isl_set *set);
2533 __isl_give isl_map *isl_map_intersect(
2534 __isl_take isl_map *map1,
2535 __isl_take isl_map *map2);
2536 __isl_give isl_union_map *isl_union_map_intersect_domain(
2537 __isl_take isl_union_map *umap,
2538 __isl_take isl_union_set *uset);
2539 __isl_give isl_union_map *isl_union_map_intersect_range(
2540 __isl_take isl_union_map *umap,
2541 __isl_take isl_union_set *uset);
2542 __isl_give isl_union_map *isl_union_map_intersect(
2543 __isl_take isl_union_map *umap1,
2544 __isl_take isl_union_map *umap2);
2546 The second argument to the C<_params> functions needs to be
2547 a parametric (basic) set. For the other functions, a parametric set
2548 for either argument is only allowed if the other argument is
2549 a parametric set as well.
2553 __isl_give isl_set *isl_basic_set_union(
2554 __isl_take isl_basic_set *bset1,
2555 __isl_take isl_basic_set *bset2);
2556 __isl_give isl_map *isl_basic_map_union(
2557 __isl_take isl_basic_map *bmap1,
2558 __isl_take isl_basic_map *bmap2);
2559 __isl_give isl_set *isl_set_union(
2560 __isl_take isl_set *set1,
2561 __isl_take isl_set *set2);
2562 __isl_give isl_map *isl_map_union(
2563 __isl_take isl_map *map1,
2564 __isl_take isl_map *map2);
2565 __isl_give isl_union_set *isl_union_set_union(
2566 __isl_take isl_union_set *uset1,
2567 __isl_take isl_union_set *uset2);
2568 __isl_give isl_union_map *isl_union_map_union(
2569 __isl_take isl_union_map *umap1,
2570 __isl_take isl_union_map *umap2);
2572 =item * Set difference
2574 __isl_give isl_set *isl_set_subtract(
2575 __isl_take isl_set *set1,
2576 __isl_take isl_set *set2);
2577 __isl_give isl_map *isl_map_subtract(
2578 __isl_take isl_map *map1,
2579 __isl_take isl_map *map2);
2580 __isl_give isl_map *isl_map_subtract_domain(
2581 __isl_take isl_map *map,
2582 __isl_take isl_set *dom);
2583 __isl_give isl_map *isl_map_subtract_range(
2584 __isl_take isl_map *map,
2585 __isl_take isl_set *dom);
2586 __isl_give isl_union_set *isl_union_set_subtract(
2587 __isl_take isl_union_set *uset1,
2588 __isl_take isl_union_set *uset2);
2589 __isl_give isl_union_map *isl_union_map_subtract(
2590 __isl_take isl_union_map *umap1,
2591 __isl_take isl_union_map *umap2);
2595 __isl_give isl_basic_set *isl_basic_set_apply(
2596 __isl_take isl_basic_set *bset,
2597 __isl_take isl_basic_map *bmap);
2598 __isl_give isl_set *isl_set_apply(
2599 __isl_take isl_set *set,
2600 __isl_take isl_map *map);
2601 __isl_give isl_union_set *isl_union_set_apply(
2602 __isl_take isl_union_set *uset,
2603 __isl_take isl_union_map *umap);
2604 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2605 __isl_take isl_basic_map *bmap1,
2606 __isl_take isl_basic_map *bmap2);
2607 __isl_give isl_basic_map *isl_basic_map_apply_range(
2608 __isl_take isl_basic_map *bmap1,
2609 __isl_take isl_basic_map *bmap2);
2610 __isl_give isl_map *isl_map_apply_domain(
2611 __isl_take isl_map *map1,
2612 __isl_take isl_map *map2);
2613 __isl_give isl_union_map *isl_union_map_apply_domain(
2614 __isl_take isl_union_map *umap1,
2615 __isl_take isl_union_map *umap2);
2616 __isl_give isl_map *isl_map_apply_range(
2617 __isl_take isl_map *map1,
2618 __isl_take isl_map *map2);
2619 __isl_give isl_union_map *isl_union_map_apply_range(
2620 __isl_take isl_union_map *umap1,
2621 __isl_take isl_union_map *umap2);
2623 =item * Cartesian Product
2625 __isl_give isl_set *isl_set_product(
2626 __isl_take isl_set *set1,
2627 __isl_take isl_set *set2);
2628 __isl_give isl_union_set *isl_union_set_product(
2629 __isl_take isl_union_set *uset1,
2630 __isl_take isl_union_set *uset2);
2631 __isl_give isl_basic_map *isl_basic_map_domain_product(
2632 __isl_take isl_basic_map *bmap1,
2633 __isl_take isl_basic_map *bmap2);
2634 __isl_give isl_basic_map *isl_basic_map_range_product(
2635 __isl_take isl_basic_map *bmap1,
2636 __isl_take isl_basic_map *bmap2);
2637 __isl_give isl_basic_map *isl_basic_map_product(
2638 __isl_take isl_basic_map *bmap1,
2639 __isl_take isl_basic_map *bmap2);
2640 __isl_give isl_map *isl_map_domain_product(
2641 __isl_take isl_map *map1,
2642 __isl_take isl_map *map2);
2643 __isl_give isl_map *isl_map_range_product(
2644 __isl_take isl_map *map1,
2645 __isl_take isl_map *map2);
2646 __isl_give isl_union_map *isl_union_map_domain_product(
2647 __isl_take isl_union_map *umap1,
2648 __isl_take isl_union_map *umap2);
2649 __isl_give isl_union_map *isl_union_map_range_product(
2650 __isl_take isl_union_map *umap1,
2651 __isl_take isl_union_map *umap2);
2652 __isl_give isl_map *isl_map_product(
2653 __isl_take isl_map *map1,
2654 __isl_take isl_map *map2);
2655 __isl_give isl_union_map *isl_union_map_product(
2656 __isl_take isl_union_map *umap1,
2657 __isl_take isl_union_map *umap2);
2659 The above functions compute the cross product of the given
2660 sets or relations. The domains and ranges of the results
2661 are wrapped maps between domains and ranges of the inputs.
2662 To obtain a ``flat'' product, use the following functions
2665 __isl_give isl_basic_set *isl_basic_set_flat_product(
2666 __isl_take isl_basic_set *bset1,
2667 __isl_take isl_basic_set *bset2);
2668 __isl_give isl_set *isl_set_flat_product(
2669 __isl_take isl_set *set1,
2670 __isl_take isl_set *set2);
2671 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2672 __isl_take isl_basic_map *bmap1,
2673 __isl_take isl_basic_map *bmap2);
2674 __isl_give isl_map *isl_map_flat_domain_product(
2675 __isl_take isl_map *map1,
2676 __isl_take isl_map *map2);
2677 __isl_give isl_map *isl_map_flat_range_product(
2678 __isl_take isl_map *map1,
2679 __isl_take isl_map *map2);
2680 __isl_give isl_union_map *isl_union_map_flat_range_product(
2681 __isl_take isl_union_map *umap1,
2682 __isl_take isl_union_map *umap2);
2683 __isl_give isl_basic_map *isl_basic_map_flat_product(
2684 __isl_take isl_basic_map *bmap1,
2685 __isl_take isl_basic_map *bmap2);
2686 __isl_give isl_map *isl_map_flat_product(
2687 __isl_take isl_map *map1,
2688 __isl_take isl_map *map2);
2690 =item * Simplification
2692 __isl_give isl_basic_set *isl_basic_set_gist(
2693 __isl_take isl_basic_set *bset,
2694 __isl_take isl_basic_set *context);
2695 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2696 __isl_take isl_set *context);
2697 __isl_give isl_set *isl_set_gist_params(
2698 __isl_take isl_set *set,
2699 __isl_take isl_set *context);
2700 __isl_give isl_union_set *isl_union_set_gist(
2701 __isl_take isl_union_set *uset,
2702 __isl_take isl_union_set *context);
2703 __isl_give isl_union_set *isl_union_set_gist_params(
2704 __isl_take isl_union_set *uset,
2705 __isl_take isl_set *set);
2706 __isl_give isl_basic_map *isl_basic_map_gist(
2707 __isl_take isl_basic_map *bmap,
2708 __isl_take isl_basic_map *context);
2709 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2710 __isl_take isl_map *context);
2711 __isl_give isl_map *isl_map_gist_params(
2712 __isl_take isl_map *map,
2713 __isl_take isl_set *context);
2714 __isl_give isl_map *isl_map_gist_domain(
2715 __isl_take isl_map *map,
2716 __isl_take isl_set *context);
2717 __isl_give isl_map *isl_map_gist_range(
2718 __isl_take isl_map *map,
2719 __isl_take isl_set *context);
2720 __isl_give isl_union_map *isl_union_map_gist(
2721 __isl_take isl_union_map *umap,
2722 __isl_take isl_union_map *context);
2723 __isl_give isl_union_map *isl_union_map_gist_params(
2724 __isl_take isl_union_map *umap,
2725 __isl_take isl_set *set);
2726 __isl_give isl_union_map *isl_union_map_gist_domain(
2727 __isl_take isl_union_map *umap,
2728 __isl_take isl_union_set *uset);
2729 __isl_give isl_union_map *isl_union_map_gist_range(
2730 __isl_take isl_union_map *umap,
2731 __isl_take isl_union_set *uset);
2733 The gist operation returns a set or relation that has the
2734 same intersection with the context as the input set or relation.
2735 Any implicit equality in the intersection is made explicit in the result,
2736 while all inequalities that are redundant with respect to the intersection
2738 In case of union sets and relations, the gist operation is performed
2743 =head3 Lexicographic Optimization
2745 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2746 the following functions
2747 compute a set that contains the lexicographic minimum or maximum
2748 of the elements in C<set> (or C<bset>) for those values of the parameters
2749 that satisfy C<dom>.
2750 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2751 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2753 In other words, the union of the parameter values
2754 for which the result is non-empty and of C<*empty>
2757 __isl_give isl_set *isl_basic_set_partial_lexmin(
2758 __isl_take isl_basic_set *bset,
2759 __isl_take isl_basic_set *dom,
2760 __isl_give isl_set **empty);
2761 __isl_give isl_set *isl_basic_set_partial_lexmax(
2762 __isl_take isl_basic_set *bset,
2763 __isl_take isl_basic_set *dom,
2764 __isl_give isl_set **empty);
2765 __isl_give isl_set *isl_set_partial_lexmin(
2766 __isl_take isl_set *set, __isl_take isl_set *dom,
2767 __isl_give isl_set **empty);
2768 __isl_give isl_set *isl_set_partial_lexmax(
2769 __isl_take isl_set *set, __isl_take isl_set *dom,
2770 __isl_give isl_set **empty);
2772 Given a (basic) set C<set> (or C<bset>), the following functions simply
2773 return a set containing the lexicographic minimum or maximum
2774 of the elements in C<set> (or C<bset>).
2775 In case of union sets, the optimum is computed per space.
2777 __isl_give isl_set *isl_basic_set_lexmin(
2778 __isl_take isl_basic_set *bset);
2779 __isl_give isl_set *isl_basic_set_lexmax(
2780 __isl_take isl_basic_set *bset);
2781 __isl_give isl_set *isl_set_lexmin(
2782 __isl_take isl_set *set);
2783 __isl_give isl_set *isl_set_lexmax(
2784 __isl_take isl_set *set);
2785 __isl_give isl_union_set *isl_union_set_lexmin(
2786 __isl_take isl_union_set *uset);
2787 __isl_give isl_union_set *isl_union_set_lexmax(
2788 __isl_take isl_union_set *uset);
2790 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2791 the following functions
2792 compute a relation that maps each element of C<dom>
2793 to the single lexicographic minimum or maximum
2794 of the elements that are associated to that same
2795 element in C<map> (or C<bmap>).
2796 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2797 that contains the elements in C<dom> that do not map
2798 to any elements in C<map> (or C<bmap>).
2799 In other words, the union of the domain of the result and of C<*empty>
2802 __isl_give isl_map *isl_basic_map_partial_lexmax(
2803 __isl_take isl_basic_map *bmap,
2804 __isl_take isl_basic_set *dom,
2805 __isl_give isl_set **empty);
2806 __isl_give isl_map *isl_basic_map_partial_lexmin(
2807 __isl_take isl_basic_map *bmap,
2808 __isl_take isl_basic_set *dom,
2809 __isl_give isl_set **empty);
2810 __isl_give isl_map *isl_map_partial_lexmax(
2811 __isl_take isl_map *map, __isl_take isl_set *dom,
2812 __isl_give isl_set **empty);
2813 __isl_give isl_map *isl_map_partial_lexmin(
2814 __isl_take isl_map *map, __isl_take isl_set *dom,
2815 __isl_give isl_set **empty);
2817 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2818 return a map mapping each element in the domain of
2819 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2820 of all elements associated to that element.
2821 In case of union relations, the optimum is computed per space.
2823 __isl_give isl_map *isl_basic_map_lexmin(
2824 __isl_take isl_basic_map *bmap);
2825 __isl_give isl_map *isl_basic_map_lexmax(
2826 __isl_take isl_basic_map *bmap);
2827 __isl_give isl_map *isl_map_lexmin(
2828 __isl_take isl_map *map);
2829 __isl_give isl_map *isl_map_lexmax(
2830 __isl_take isl_map *map);
2831 __isl_give isl_union_map *isl_union_map_lexmin(
2832 __isl_take isl_union_map *umap);
2833 __isl_give isl_union_map *isl_union_map_lexmax(
2834 __isl_take isl_union_map *umap);
2836 The following functions return their result in the form of
2837 a piecewise multi-affine expression
2838 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2839 but are otherwise equivalent to the corresponding functions
2840 returning a basic set or relation.
2842 __isl_give isl_pw_multi_aff *
2843 isl_basic_map_lexmin_pw_multi_aff(
2844 __isl_take isl_basic_map *bmap);
2845 __isl_give isl_pw_multi_aff *
2846 isl_basic_set_partial_lexmin_pw_multi_aff(
2847 __isl_take isl_basic_set *bset,
2848 __isl_take isl_basic_set *dom,
2849 __isl_give isl_set **empty);
2850 __isl_give isl_pw_multi_aff *
2851 isl_basic_set_partial_lexmax_pw_multi_aff(
2852 __isl_take isl_basic_set *bset,
2853 __isl_take isl_basic_set *dom,
2854 __isl_give isl_set **empty);
2855 __isl_give isl_pw_multi_aff *
2856 isl_basic_map_partial_lexmin_pw_multi_aff(
2857 __isl_take isl_basic_map *bmap,
2858 __isl_take isl_basic_set *dom,
2859 __isl_give isl_set **empty);
2860 __isl_give isl_pw_multi_aff *
2861 isl_basic_map_partial_lexmax_pw_multi_aff(
2862 __isl_take isl_basic_map *bmap,
2863 __isl_take isl_basic_set *dom,
2864 __isl_give isl_set **empty);
2865 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2866 __isl_take isl_map *map);
2867 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2868 __isl_take isl_map *map);
2872 Lists are defined over several element types, including
2873 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2874 Here we take lists of C<isl_set>s as an example.
2875 Lists can be created, copied, modified and freed using the following functions.
2877 #include <isl/list.h>
2878 __isl_give isl_set_list *isl_set_list_from_set(
2879 __isl_take isl_set *el);
2880 __isl_give isl_set_list *isl_set_list_alloc(
2881 isl_ctx *ctx, int n);
2882 __isl_give isl_set_list *isl_set_list_copy(
2883 __isl_keep isl_set_list *list);
2884 __isl_give isl_set_list *isl_set_list_add(
2885 __isl_take isl_set_list *list,
2886 __isl_take isl_set *el);
2887 __isl_give isl_set_list *isl_set_list_set_set(
2888 __isl_take isl_set_list *list, int index,
2889 __isl_take isl_set *set);
2890 __isl_give isl_set_list *isl_set_list_concat(
2891 __isl_take isl_set_list *list1,
2892 __isl_take isl_set_list *list2);
2893 void *isl_set_list_free(__isl_take isl_set_list *list);
2895 C<isl_set_list_alloc> creates an empty list with a capacity for
2896 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2899 Lists can be inspected using the following functions.
2901 #include <isl/list.h>
2902 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2903 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2904 __isl_give isl_set *isl_set_list_get_set(
2905 __isl_keep isl_set_list *list, int index);
2906 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2907 int (*fn)(__isl_take isl_set *el, void *user),
2910 Lists can be printed using
2912 #include <isl/list.h>
2913 __isl_give isl_printer *isl_printer_print_set_list(
2914 __isl_take isl_printer *p,
2915 __isl_keep isl_set_list *list);
2919 Vectors can be created, copied and freed using the following functions.
2921 #include <isl/vec.h>
2922 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2924 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2925 void isl_vec_free(__isl_take isl_vec *vec);
2927 Note that the elements of a newly created vector may have arbitrary values.
2928 The elements can be changed and inspected using the following functions.
2930 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2931 int isl_vec_size(__isl_keep isl_vec *vec);
2932 int isl_vec_get_element(__isl_keep isl_vec *vec,
2933 int pos, isl_int *v);
2934 __isl_give isl_vec *isl_vec_set_element(
2935 __isl_take isl_vec *vec, int pos, isl_int v);
2936 __isl_give isl_vec *isl_vec_set_element_si(
2937 __isl_take isl_vec *vec, int pos, int v);
2938 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2940 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2943 C<isl_vec_get_element> will return a negative value if anything went wrong.
2944 In that case, the value of C<*v> is undefined.
2948 Matrices can be created, copied and freed using the following functions.
2950 #include <isl/mat.h>
2951 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2952 unsigned n_row, unsigned n_col);
2953 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2954 void isl_mat_free(__isl_take isl_mat *mat);
2956 Note that the elements of a newly created matrix may have arbitrary values.
2957 The elements can be changed and inspected using the following functions.
2959 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2960 int isl_mat_rows(__isl_keep isl_mat *mat);
2961 int isl_mat_cols(__isl_keep isl_mat *mat);
2962 int isl_mat_get_element(__isl_keep isl_mat *mat,
2963 int row, int col, isl_int *v);
2964 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2965 int row, int col, isl_int v);
2966 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2967 int row, int col, int v);
2969 C<isl_mat_get_element> will return a negative value if anything went wrong.
2970 In that case, the value of C<*v> is undefined.
2972 The following function can be used to compute the (right) inverse
2973 of a matrix, i.e., a matrix such that the product of the original
2974 and the inverse (in that order) is a multiple of the identity matrix.
2975 The input matrix is assumed to be of full row-rank.
2977 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2979 The following function can be used to compute the (right) kernel
2980 (or null space) of a matrix, i.e., a matrix such that the product of
2981 the original and the kernel (in that order) is the zero matrix.
2983 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2985 =head2 Piecewise Quasi Affine Expressions
2987 The zero quasi affine expression on a given domain can be created using
2989 __isl_give isl_aff *isl_aff_zero_on_domain(
2990 __isl_take isl_local_space *ls);
2992 Note that the space in which the resulting object lives is a map space
2993 with the given space as domain and a one-dimensional range.
2995 An empty piecewise quasi affine expression (one with no cells)
2996 or a piecewise quasi affine expression with a single cell can
2997 be created using the following functions.
2999 #include <isl/aff.h>
3000 __isl_give isl_pw_aff *isl_pw_aff_empty(
3001 __isl_take isl_space *space);
3002 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3003 __isl_take isl_set *set, __isl_take isl_aff *aff);
3004 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3005 __isl_take isl_aff *aff);
3007 A piecewise quasi affine expression that is equal to 1 on a set
3008 and 0 outside the set can be created using the following function.
3010 #include <isl/aff.h>
3011 __isl_give isl_pw_aff *isl_set_indicator_function(
3012 __isl_take isl_set *set);
3014 Quasi affine expressions can be copied and freed using
3016 #include <isl/aff.h>
3017 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3018 void *isl_aff_free(__isl_take isl_aff *aff);
3020 __isl_give isl_pw_aff *isl_pw_aff_copy(
3021 __isl_keep isl_pw_aff *pwaff);
3022 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3024 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3025 using the following function. The constraint is required to have
3026 a non-zero coefficient for the specified dimension.
3028 #include <isl/constraint.h>
3029 __isl_give isl_aff *isl_constraint_get_bound(
3030 __isl_keep isl_constraint *constraint,
3031 enum isl_dim_type type, int pos);
3033 The entire affine expression of the constraint can also be extracted
3034 using the following function.
3036 #include <isl/constraint.h>
3037 __isl_give isl_aff *isl_constraint_get_aff(
3038 __isl_keep isl_constraint *constraint);
3040 Conversely, an equality constraint equating
3041 the affine expression to zero or an inequality constraint enforcing
3042 the affine expression to be non-negative, can be constructed using
3044 __isl_give isl_constraint *isl_equality_from_aff(
3045 __isl_take isl_aff *aff);
3046 __isl_give isl_constraint *isl_inequality_from_aff(
3047 __isl_take isl_aff *aff);
3049 The expression can be inspected using
3051 #include <isl/aff.h>
3052 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3053 int isl_aff_dim(__isl_keep isl_aff *aff,
3054 enum isl_dim_type type);
3055 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3056 __isl_keep isl_aff *aff);
3057 __isl_give isl_local_space *isl_aff_get_local_space(
3058 __isl_keep isl_aff *aff);
3059 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3060 enum isl_dim_type type, unsigned pos);
3061 const char *isl_pw_aff_get_dim_name(
3062 __isl_keep isl_pw_aff *pa,
3063 enum isl_dim_type type, unsigned pos);
3064 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3065 enum isl_dim_type type, unsigned pos);
3066 __isl_give isl_id *isl_pw_aff_get_dim_id(
3067 __isl_keep isl_pw_aff *pa,
3068 enum isl_dim_type type, unsigned pos);
3069 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3070 __isl_keep isl_pw_aff *pa,
3071 enum isl_dim_type type);
3072 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3074 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3075 enum isl_dim_type type, int pos, isl_int *v);
3076 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3078 __isl_give isl_aff *isl_aff_get_div(
3079 __isl_keep isl_aff *aff, int pos);
3081 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3082 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3083 int (*fn)(__isl_take isl_set *set,
3084 __isl_take isl_aff *aff,
3085 void *user), void *user);
3087 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3088 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3090 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3091 enum isl_dim_type type, unsigned first, unsigned n);
3092 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3093 enum isl_dim_type type, unsigned first, unsigned n);
3095 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3096 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3097 enum isl_dim_type type);
3098 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3100 It can be modified using
3102 #include <isl/aff.h>
3103 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3104 __isl_take isl_pw_aff *pwaff,
3105 enum isl_dim_type type, __isl_take isl_id *id);
3106 __isl_give isl_aff *isl_aff_set_dim_name(
3107 __isl_take isl_aff *aff, enum isl_dim_type type,
3108 unsigned pos, const char *s);
3109 __isl_give isl_aff *isl_aff_set_dim_id(
3110 __isl_take isl_aff *aff, enum isl_dim_type type,
3111 unsigned pos, __isl_take isl_id *id);
3112 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3113 __isl_take isl_pw_aff *pma,
3114 enum isl_dim_type type, unsigned pos,
3115 __isl_take isl_id *id);
3116 __isl_give isl_aff *isl_aff_set_constant(
3117 __isl_take isl_aff *aff, isl_int v);
3118 __isl_give isl_aff *isl_aff_set_constant_si(
3119 __isl_take isl_aff *aff, int v);
3120 __isl_give isl_aff *isl_aff_set_coefficient(
3121 __isl_take isl_aff *aff,
3122 enum isl_dim_type type, int pos, isl_int v);
3123 __isl_give isl_aff *isl_aff_set_coefficient_si(
3124 __isl_take isl_aff *aff,
3125 enum isl_dim_type type, int pos, int v);
3126 __isl_give isl_aff *isl_aff_set_denominator(
3127 __isl_take isl_aff *aff, isl_int v);
3129 __isl_give isl_aff *isl_aff_add_constant(
3130 __isl_take isl_aff *aff, isl_int v);
3131 __isl_give isl_aff *isl_aff_add_constant_si(
3132 __isl_take isl_aff *aff, int v);
3133 __isl_give isl_aff *isl_aff_add_constant_num(
3134 __isl_take isl_aff *aff, isl_int v);
3135 __isl_give isl_aff *isl_aff_add_constant_num_si(
3136 __isl_take isl_aff *aff, int v);
3137 __isl_give isl_aff *isl_aff_add_coefficient(
3138 __isl_take isl_aff *aff,
3139 enum isl_dim_type type, int pos, isl_int v);
3140 __isl_give isl_aff *isl_aff_add_coefficient_si(
3141 __isl_take isl_aff *aff,
3142 enum isl_dim_type type, int pos, int v);
3144 __isl_give isl_aff *isl_aff_insert_dims(
3145 __isl_take isl_aff *aff,
3146 enum isl_dim_type type, unsigned first, unsigned n);
3147 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3148 __isl_take isl_pw_aff *pwaff,
3149 enum isl_dim_type type, unsigned first, unsigned n);
3150 __isl_give isl_aff *isl_aff_add_dims(
3151 __isl_take isl_aff *aff,
3152 enum isl_dim_type type, unsigned n);
3153 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3154 __isl_take isl_pw_aff *pwaff,
3155 enum isl_dim_type type, unsigned n);
3156 __isl_give isl_aff *isl_aff_drop_dims(
3157 __isl_take isl_aff *aff,
3158 enum isl_dim_type type, unsigned first, unsigned n);
3159 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3160 __isl_take isl_pw_aff *pwaff,
3161 enum isl_dim_type type, unsigned first, unsigned n);
3163 Note that the C<set_constant> and C<set_coefficient> functions
3164 set the I<numerator> of the constant or coefficient, while
3165 C<add_constant> and C<add_coefficient> add an integer value to
3166 the possibly rational constant or coefficient.
3167 The C<add_constant_num> functions add an integer value to
3170 To check whether an affine expressions is obviously zero
3171 or obviously equal to some other affine expression, use
3173 #include <isl/aff.h>
3174 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3175 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3176 __isl_keep isl_aff *aff2);
3177 int isl_pw_aff_plain_is_equal(
3178 __isl_keep isl_pw_aff *pwaff1,
3179 __isl_keep isl_pw_aff *pwaff2);
3183 #include <isl/aff.h>
3184 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3185 __isl_take isl_aff *aff2);
3186 __isl_give isl_pw_aff *isl_pw_aff_add(
3187 __isl_take isl_pw_aff *pwaff1,
3188 __isl_take isl_pw_aff *pwaff2);
3189 __isl_give isl_pw_aff *isl_pw_aff_min(
3190 __isl_take isl_pw_aff *pwaff1,
3191 __isl_take isl_pw_aff *pwaff2);
3192 __isl_give isl_pw_aff *isl_pw_aff_max(
3193 __isl_take isl_pw_aff *pwaff1,
3194 __isl_take isl_pw_aff *pwaff2);
3195 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3196 __isl_take isl_aff *aff2);
3197 __isl_give isl_pw_aff *isl_pw_aff_sub(
3198 __isl_take isl_pw_aff *pwaff1,
3199 __isl_take isl_pw_aff *pwaff2);
3200 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3201 __isl_give isl_pw_aff *isl_pw_aff_neg(
3202 __isl_take isl_pw_aff *pwaff);
3203 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3204 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3205 __isl_take isl_pw_aff *pwaff);
3206 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3207 __isl_give isl_pw_aff *isl_pw_aff_floor(
3208 __isl_take isl_pw_aff *pwaff);
3209 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3211 __isl_give isl_pw_aff *isl_pw_aff_mod(
3212 __isl_take isl_pw_aff *pwaff, isl_int mod);
3213 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3215 __isl_give isl_pw_aff *isl_pw_aff_scale(
3216 __isl_take isl_pw_aff *pwaff, isl_int f);
3217 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3219 __isl_give isl_aff *isl_aff_scale_down_ui(
3220 __isl_take isl_aff *aff, unsigned f);
3221 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3222 __isl_take isl_pw_aff *pwaff, isl_int f);
3224 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3225 __isl_take isl_pw_aff_list *list);
3226 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3227 __isl_take isl_pw_aff_list *list);
3229 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3230 __isl_take isl_pw_aff *pwqp);
3232 __isl_give isl_aff *isl_aff_align_params(
3233 __isl_take isl_aff *aff,
3234 __isl_take isl_space *model);
3235 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3236 __isl_take isl_pw_aff *pwaff,
3237 __isl_take isl_space *model);
3239 __isl_give isl_aff *isl_aff_project_domain_on_params(
3240 __isl_take isl_aff *aff);
3242 __isl_give isl_aff *isl_aff_gist_params(
3243 __isl_take isl_aff *aff,
3244 __isl_take isl_set *context);
3245 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3246 __isl_take isl_set *context);
3247 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3248 __isl_take isl_pw_aff *pwaff,
3249 __isl_take isl_set *context);
3250 __isl_give isl_pw_aff *isl_pw_aff_gist(
3251 __isl_take isl_pw_aff *pwaff,
3252 __isl_take isl_set *context);
3254 __isl_give isl_set *isl_pw_aff_domain(
3255 __isl_take isl_pw_aff *pwaff);
3256 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3257 __isl_take isl_pw_aff *pa,
3258 __isl_take isl_set *set);
3259 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3260 __isl_take isl_pw_aff *pa,
3261 __isl_take isl_set *set);
3263 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3264 __isl_take isl_aff *aff2);
3265 __isl_give isl_pw_aff *isl_pw_aff_mul(
3266 __isl_take isl_pw_aff *pwaff1,
3267 __isl_take isl_pw_aff *pwaff2);
3269 When multiplying two affine expressions, at least one of the two needs
3272 #include <isl/aff.h>
3273 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3274 __isl_take isl_aff *aff);
3275 __isl_give isl_basic_set *isl_aff_le_basic_set(
3276 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3277 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3278 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3279 __isl_give isl_set *isl_pw_aff_eq_set(
3280 __isl_take isl_pw_aff *pwaff1,
3281 __isl_take isl_pw_aff *pwaff2);
3282 __isl_give isl_set *isl_pw_aff_ne_set(
3283 __isl_take isl_pw_aff *pwaff1,
3284 __isl_take isl_pw_aff *pwaff2);
3285 __isl_give isl_set *isl_pw_aff_le_set(
3286 __isl_take isl_pw_aff *pwaff1,
3287 __isl_take isl_pw_aff *pwaff2);
3288 __isl_give isl_set *isl_pw_aff_lt_set(
3289 __isl_take isl_pw_aff *pwaff1,
3290 __isl_take isl_pw_aff *pwaff2);
3291 __isl_give isl_set *isl_pw_aff_ge_set(
3292 __isl_take isl_pw_aff *pwaff1,
3293 __isl_take isl_pw_aff *pwaff2);
3294 __isl_give isl_set *isl_pw_aff_gt_set(
3295 __isl_take isl_pw_aff *pwaff1,
3296 __isl_take isl_pw_aff *pwaff2);
3298 __isl_give isl_set *isl_pw_aff_list_eq_set(
3299 __isl_take isl_pw_aff_list *list1,
3300 __isl_take isl_pw_aff_list *list2);
3301 __isl_give isl_set *isl_pw_aff_list_ne_set(
3302 __isl_take isl_pw_aff_list *list1,
3303 __isl_take isl_pw_aff_list *list2);
3304 __isl_give isl_set *isl_pw_aff_list_le_set(
3305 __isl_take isl_pw_aff_list *list1,
3306 __isl_take isl_pw_aff_list *list2);
3307 __isl_give isl_set *isl_pw_aff_list_lt_set(
3308 __isl_take isl_pw_aff_list *list1,
3309 __isl_take isl_pw_aff_list *list2);
3310 __isl_give isl_set *isl_pw_aff_list_ge_set(
3311 __isl_take isl_pw_aff_list *list1,
3312 __isl_take isl_pw_aff_list *list2);
3313 __isl_give isl_set *isl_pw_aff_list_gt_set(
3314 __isl_take isl_pw_aff_list *list1,
3315 __isl_take isl_pw_aff_list *list2);
3317 The function C<isl_aff_neg_basic_set> returns a basic set
3318 containing those elements in the domain space
3319 of C<aff> where C<aff> is negative.
3320 The function C<isl_aff_ge_basic_set> returns a basic set
3321 containing those elements in the shared space
3322 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3323 The function C<isl_pw_aff_ge_set> returns a set
3324 containing those elements in the shared domain
3325 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3326 The functions operating on C<isl_pw_aff_list> apply the corresponding
3327 C<isl_pw_aff> function to each pair of elements in the two lists.
3329 #include <isl/aff.h>
3330 __isl_give isl_set *isl_pw_aff_nonneg_set(
3331 __isl_take isl_pw_aff *pwaff);
3332 __isl_give isl_set *isl_pw_aff_zero_set(
3333 __isl_take isl_pw_aff *pwaff);
3334 __isl_give isl_set *isl_pw_aff_non_zero_set(
3335 __isl_take isl_pw_aff *pwaff);
3337 The function C<isl_pw_aff_nonneg_set> returns a set
3338 containing those elements in the domain
3339 of C<pwaff> where C<pwaff> is non-negative.
3341 #include <isl/aff.h>
3342 __isl_give isl_pw_aff *isl_pw_aff_cond(
3343 __isl_take isl_pw_aff *cond,
3344 __isl_take isl_pw_aff *pwaff_true,
3345 __isl_take isl_pw_aff *pwaff_false);
3347 The function C<isl_pw_aff_cond> performs a conditional operator
3348 and returns an expression that is equal to C<pwaff_true>
3349 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3350 where C<cond> is zero.
3352 #include <isl/aff.h>
3353 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3354 __isl_take isl_pw_aff *pwaff1,
3355 __isl_take isl_pw_aff *pwaff2);
3356 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3357 __isl_take isl_pw_aff *pwaff1,
3358 __isl_take isl_pw_aff *pwaff2);
3359 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3360 __isl_take isl_pw_aff *pwaff1,
3361 __isl_take isl_pw_aff *pwaff2);
3363 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3364 expression with a domain that is the union of those of C<pwaff1> and
3365 C<pwaff2> and such that on each cell, the quasi-affine expression is
3366 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3367 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3368 associated expression is the defined one.
3370 An expression can be read from input using
3372 #include <isl/aff.h>
3373 __isl_give isl_aff *isl_aff_read_from_str(
3374 isl_ctx *ctx, const char *str);
3375 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3376 isl_ctx *ctx, const char *str);
3378 An expression can be printed using
3380 #include <isl/aff.h>
3381 __isl_give isl_printer *isl_printer_print_aff(
3382 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3384 __isl_give isl_printer *isl_printer_print_pw_aff(
3385 __isl_take isl_printer *p,
3386 __isl_keep isl_pw_aff *pwaff);
3388 =head2 Piecewise Multiple Quasi Affine Expressions
3390 An C<isl_multi_aff> object represents a sequence of
3391 zero or more affine expressions, all defined on the same domain space.
3393 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3396 #include <isl/aff.h>
3397 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3398 __isl_take isl_space *space,
3399 __isl_take isl_aff_list *list);
3401 An empty piecewise multiple quasi affine expression (one with no cells),
3402 the zero piecewise multiple quasi affine expression (with value zero
3403 for each output dimension),
3404 a piecewise multiple quasi affine expression with a single cell (with
3405 either a universe or a specified domain) or
3406 a zero-dimensional piecewise multiple quasi affine expression
3408 can be created using the following functions.
3410 #include <isl/aff.h>
3411 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3412 __isl_take isl_space *space);
3413 __isl_give isl_multi_aff *isl_multi_aff_zero(
3414 __isl_take isl_space *space);
3415 __isl_give isl_multi_aff *isl_multi_aff_identity(
3416 __isl_take isl_space *space);
3417 __isl_give isl_pw_multi_aff *
3418 isl_pw_multi_aff_from_multi_aff(
3419 __isl_take isl_multi_aff *ma);
3420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3421 __isl_take isl_set *set,
3422 __isl_take isl_multi_aff *maff);
3423 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3424 __isl_take isl_set *set);
3426 __isl_give isl_union_pw_multi_aff *
3427 isl_union_pw_multi_aff_empty(
3428 __isl_take isl_space *space);
3429 __isl_give isl_union_pw_multi_aff *
3430 isl_union_pw_multi_aff_add_pw_multi_aff(
3431 __isl_take isl_union_pw_multi_aff *upma,
3432 __isl_take isl_pw_multi_aff *pma);
3433 __isl_give isl_union_pw_multi_aff *
3434 isl_union_pw_multi_aff_from_domain(
3435 __isl_take isl_union_set *uset);
3437 A piecewise multiple quasi affine expression can also be initialized
3438 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3439 and the C<isl_map> is single-valued.
3441 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3442 __isl_take isl_set *set);
3443 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3444 __isl_take isl_map *map);
3446 Multiple quasi affine expressions can be copied and freed using
3448 #include <isl/aff.h>
3449 __isl_give isl_multi_aff *isl_multi_aff_copy(
3450 __isl_keep isl_multi_aff *maff);
3451 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3453 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3454 __isl_keep isl_pw_multi_aff *pma);
3455 void *isl_pw_multi_aff_free(
3456 __isl_take isl_pw_multi_aff *pma);
3458 __isl_give isl_union_pw_multi_aff *
3459 isl_union_pw_multi_aff_copy(
3460 __isl_keep isl_union_pw_multi_aff *upma);
3461 void *isl_union_pw_multi_aff_free(
3462 __isl_take isl_union_pw_multi_aff *upma);
3464 The expression can be inspected using
3466 #include <isl/aff.h>
3467 isl_ctx *isl_multi_aff_get_ctx(
3468 __isl_keep isl_multi_aff *maff);
3469 isl_ctx *isl_pw_multi_aff_get_ctx(
3470 __isl_keep isl_pw_multi_aff *pma);
3471 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3472 __isl_keep isl_union_pw_multi_aff *upma);
3473 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3474 enum isl_dim_type type);
3475 unsigned isl_pw_multi_aff_dim(
3476 __isl_keep isl_pw_multi_aff *pma,
3477 enum isl_dim_type type);
3478 __isl_give isl_aff *isl_multi_aff_get_aff(
3479 __isl_keep isl_multi_aff *multi, int pos);
3480 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3481 __isl_keep isl_pw_multi_aff *pma, int pos);
3482 const char *isl_pw_multi_aff_get_dim_name(
3483 __isl_keep isl_pw_multi_aff *pma,
3484 enum isl_dim_type type, unsigned pos);
3485 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3486 __isl_keep isl_pw_multi_aff *pma,
3487 enum isl_dim_type type, unsigned pos);
3488 const char *isl_multi_aff_get_tuple_name(
3489 __isl_keep isl_multi_aff *multi,
3490 enum isl_dim_type type);
3491 int isl_pw_multi_aff_has_tuple_name(
3492 __isl_keep isl_pw_multi_aff *pma,
3493 enum isl_dim_type type);
3494 const char *isl_pw_multi_aff_get_tuple_name(
3495 __isl_keep isl_pw_multi_aff *pma,
3496 enum isl_dim_type type);
3497 int isl_pw_multi_aff_has_tuple_id(
3498 __isl_keep isl_pw_multi_aff *pma,
3499 enum isl_dim_type type);
3500 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3501 __isl_keep isl_pw_multi_aff *pma,
3502 enum isl_dim_type type);
3504 int isl_pw_multi_aff_foreach_piece(
3505 __isl_keep isl_pw_multi_aff *pma,
3506 int (*fn)(__isl_take isl_set *set,
3507 __isl_take isl_multi_aff *maff,
3508 void *user), void *user);
3510 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3511 __isl_keep isl_union_pw_multi_aff *upma,
3512 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3513 void *user), void *user);
3515 It can be modified using
3517 #include <isl/aff.h>
3518 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3519 __isl_take isl_multi_aff *multi, int pos,
3520 __isl_take isl_aff *aff);
3521 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3522 __isl_take isl_multi_aff *maff,
3523 enum isl_dim_type type, unsigned pos, const char *s);
3524 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3525 __isl_take isl_multi_aff *maff,
3526 enum isl_dim_type type, __isl_take isl_id *id);
3527 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3528 __isl_take isl_pw_multi_aff *pma,
3529 enum isl_dim_type type, __isl_take isl_id *id);
3531 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3532 __isl_take isl_multi_aff *maff,
3533 enum isl_dim_type type, unsigned first, unsigned n);
3534 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3535 __isl_take isl_pw_multi_aff *pma,
3536 enum isl_dim_type type, unsigned first, unsigned n);
3538 To check whether two multiple affine expressions are
3539 obviously equal to each other, use
3541 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3542 __isl_keep isl_multi_aff *maff2);
3543 int isl_pw_multi_aff_plain_is_equal(
3544 __isl_keep isl_pw_multi_aff *pma1,
3545 __isl_keep isl_pw_multi_aff *pma2);
3549 #include <isl/aff.h>
3550 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3551 __isl_take isl_pw_multi_aff *pma1,
3552 __isl_take isl_pw_multi_aff *pma2);
3553 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3554 __isl_take isl_pw_multi_aff *pma1,
3555 __isl_take isl_pw_multi_aff *pma2);
3556 __isl_give isl_multi_aff *isl_multi_aff_add(
3557 __isl_take isl_multi_aff *maff1,
3558 __isl_take isl_multi_aff *maff2);
3559 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3560 __isl_take isl_pw_multi_aff *pma1,
3561 __isl_take isl_pw_multi_aff *pma2);
3562 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3563 __isl_take isl_union_pw_multi_aff *upma1,
3564 __isl_take isl_union_pw_multi_aff *upma2);
3565 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3566 __isl_take isl_pw_multi_aff *pma1,
3567 __isl_take isl_pw_multi_aff *pma2);
3568 __isl_give isl_multi_aff *isl_multi_aff_scale(
3569 __isl_take isl_multi_aff *maff,
3571 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3572 __isl_take isl_pw_multi_aff *pma,
3573 __isl_take isl_set *set);
3574 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3575 __isl_take isl_pw_multi_aff *pma,
3576 __isl_take isl_set *set);
3577 __isl_give isl_multi_aff *isl_multi_aff_lift(
3578 __isl_take isl_multi_aff *maff,
3579 __isl_give isl_local_space **ls);
3580 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3581 __isl_take isl_pw_multi_aff *pma);
3582 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3583 __isl_take isl_multi_aff *multi,
3584 __isl_take isl_space *model);
3585 __isl_give isl_pw_multi_aff *
3586 isl_pw_multi_aff_project_domain_on_params(
3587 __isl_take isl_pw_multi_aff *pma);
3588 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3589 __isl_take isl_multi_aff *maff,
3590 __isl_take isl_set *context);
3591 __isl_give isl_multi_aff *isl_multi_aff_gist(
3592 __isl_take isl_multi_aff *maff,
3593 __isl_take isl_set *context);
3594 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3595 __isl_take isl_pw_multi_aff *pma,
3596 __isl_take isl_set *set);
3597 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3598 __isl_take isl_pw_multi_aff *pma,
3599 __isl_take isl_set *set);
3600 __isl_give isl_set *isl_pw_multi_aff_domain(
3601 __isl_take isl_pw_multi_aff *pma);
3602 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3603 __isl_take isl_union_pw_multi_aff *upma);
3604 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3605 __isl_take isl_multi_aff *ma1,
3606 __isl_take isl_multi_aff *ma2);
3607 __isl_give isl_multi_aff *isl_multi_aff_product(
3608 __isl_take isl_multi_aff *ma1,
3609 __isl_take isl_multi_aff *ma2);
3610 __isl_give isl_pw_multi_aff *
3611 isl_pw_multi_aff_flat_range_product(
3612 __isl_take isl_pw_multi_aff *pma1,
3613 __isl_take isl_pw_multi_aff *pma2);
3614 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3615 __isl_take isl_pw_multi_aff *pma1,
3616 __isl_take isl_pw_multi_aff *pma2);
3617 __isl_give isl_union_pw_multi_aff *
3618 isl_union_pw_multi_aff_flat_range_product(
3619 __isl_take isl_union_pw_multi_aff *upma1,
3620 __isl_take isl_union_pw_multi_aff *upma2);
3622 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3623 then it is assigned the local space that lies at the basis of
3624 the lifting applied.
3626 __isl_give isl_set *isl_multi_aff_lex_le_set(
3627 __isl_take isl_multi_aff *ma1,
3628 __isl_take isl_multi_aff *ma2);
3629 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3630 __isl_take isl_multi_aff *ma1,
3631 __isl_take isl_multi_aff *ma2);
3633 The function C<isl_multi_aff_lex_le_set> returns a set
3634 containing those elements in the shared domain space
3635 where C<ma1> is lexicographically smaller than or
3638 An expression can be read from input using
3640 #include <isl/aff.h>
3641 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3642 isl_ctx *ctx, const char *str);
3643 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3644 isl_ctx *ctx, const char *str);
3646 An expression can be printed using
3648 #include <isl/aff.h>
3649 __isl_give isl_printer *isl_printer_print_multi_aff(
3650 __isl_take isl_printer *p,
3651 __isl_keep isl_multi_aff *maff);
3652 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3653 __isl_take isl_printer *p,
3654 __isl_keep isl_pw_multi_aff *pma);
3655 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3656 __isl_take isl_printer *p,
3657 __isl_keep isl_union_pw_multi_aff *upma);
3661 Points are elements of a set. They can be used to construct
3662 simple sets (boxes) or they can be used to represent the
3663 individual elements of a set.
3664 The zero point (the origin) can be created using
3666 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3668 The coordinates of a point can be inspected, set and changed
3671 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3672 enum isl_dim_type type, int pos, isl_int *v);
3673 __isl_give isl_point *isl_point_set_coordinate(
3674 __isl_take isl_point *pnt,
3675 enum isl_dim_type type, int pos, isl_int v);
3677 __isl_give isl_point *isl_point_add_ui(
3678 __isl_take isl_point *pnt,
3679 enum isl_dim_type type, int pos, unsigned val);
3680 __isl_give isl_point *isl_point_sub_ui(
3681 __isl_take isl_point *pnt,
3682 enum isl_dim_type type, int pos, unsigned val);
3684 Other properties can be obtained using
3686 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3688 Points can be copied or freed using
3690 __isl_give isl_point *isl_point_copy(
3691 __isl_keep isl_point *pnt);
3692 void isl_point_free(__isl_take isl_point *pnt);
3694 A singleton set can be created from a point using
3696 __isl_give isl_basic_set *isl_basic_set_from_point(
3697 __isl_take isl_point *pnt);
3698 __isl_give isl_set *isl_set_from_point(
3699 __isl_take isl_point *pnt);
3701 and a box can be created from two opposite extremal points using
3703 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3704 __isl_take isl_point *pnt1,
3705 __isl_take isl_point *pnt2);
3706 __isl_give isl_set *isl_set_box_from_points(
3707 __isl_take isl_point *pnt1,
3708 __isl_take isl_point *pnt2);
3710 All elements of a B<bounded> (union) set can be enumerated using
3711 the following functions.
3713 int isl_set_foreach_point(__isl_keep isl_set *set,
3714 int (*fn)(__isl_take isl_point *pnt, void *user),
3716 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3717 int (*fn)(__isl_take isl_point *pnt, void *user),
3720 The function C<fn> is called for each integer point in
3721 C<set> with as second argument the last argument of
3722 the C<isl_set_foreach_point> call. The function C<fn>
3723 should return C<0> on success and C<-1> on failure.
3724 In the latter case, C<isl_set_foreach_point> will stop
3725 enumerating and return C<-1> as well.
3726 If the enumeration is performed successfully and to completion,
3727 then C<isl_set_foreach_point> returns C<0>.
3729 To obtain a single point of a (basic) set, use
3731 __isl_give isl_point *isl_basic_set_sample_point(
3732 __isl_take isl_basic_set *bset);
3733 __isl_give isl_point *isl_set_sample_point(
3734 __isl_take isl_set *set);
3736 If C<set> does not contain any (integer) points, then the
3737 resulting point will be ``void'', a property that can be
3740 int isl_point_is_void(__isl_keep isl_point *pnt);
3742 =head2 Piecewise Quasipolynomials
3744 A piecewise quasipolynomial is a particular kind of function that maps
3745 a parametric point to a rational value.
3746 More specifically, a quasipolynomial is a polynomial expression in greatest
3747 integer parts of affine expressions of parameters and variables.
3748 A piecewise quasipolynomial is a subdivision of a given parametric
3749 domain into disjoint cells with a quasipolynomial associated to
3750 each cell. The value of the piecewise quasipolynomial at a given
3751 point is the value of the quasipolynomial associated to the cell
3752 that contains the point. Outside of the union of cells,
3753 the value is assumed to be zero.
3754 For example, the piecewise quasipolynomial
3756 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3758 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3759 A given piecewise quasipolynomial has a fixed domain dimension.
3760 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3761 defined over different domains.
3762 Piecewise quasipolynomials are mainly used by the C<barvinok>
3763 library for representing the number of elements in a parametric set or map.
3764 For example, the piecewise quasipolynomial above represents
3765 the number of points in the map
3767 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3769 =head3 Input and Output
3771 Piecewise quasipolynomials can be read from input using
3773 __isl_give isl_union_pw_qpolynomial *
3774 isl_union_pw_qpolynomial_read_from_str(
3775 isl_ctx *ctx, const char *str);
3777 Quasipolynomials and piecewise quasipolynomials can be printed
3778 using the following functions.
3780 __isl_give isl_printer *isl_printer_print_qpolynomial(
3781 __isl_take isl_printer *p,
3782 __isl_keep isl_qpolynomial *qp);
3784 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3785 __isl_take isl_printer *p,
3786 __isl_keep isl_pw_qpolynomial *pwqp);
3788 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3789 __isl_take isl_printer *p,
3790 __isl_keep isl_union_pw_qpolynomial *upwqp);
3792 The output format of the printer
3793 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3794 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3796 In case of printing in C<ISL_FORMAT_C>, the user may want
3797 to set the names of all dimensions
3799 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3800 __isl_take isl_qpolynomial *qp,
3801 enum isl_dim_type type, unsigned pos,
3803 __isl_give isl_pw_qpolynomial *
3804 isl_pw_qpolynomial_set_dim_name(
3805 __isl_take isl_pw_qpolynomial *pwqp,
3806 enum isl_dim_type type, unsigned pos,
3809 =head3 Creating New (Piecewise) Quasipolynomials
3811 Some simple quasipolynomials can be created using the following functions.
3812 More complicated quasipolynomials can be created by applying
3813 operations such as addition and multiplication
3814 on the resulting quasipolynomials
3816 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3817 __isl_take isl_space *domain);
3818 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3819 __isl_take isl_space *domain);
3820 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3821 __isl_take isl_space *domain);
3822 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3823 __isl_take isl_space *domain);
3824 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3825 __isl_take isl_space *domain);
3826 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3827 __isl_take isl_space *domain,
3828 const isl_int n, const isl_int d);
3829 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3830 __isl_take isl_space *domain,
3831 enum isl_dim_type type, unsigned pos);
3832 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3833 __isl_take isl_aff *aff);
3835 Note that the space in which a quasipolynomial lives is a map space
3836 with a one-dimensional range. The C<domain> argument in some of
3837 the functions above corresponds to the domain of this map space.
3839 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3840 with a single cell can be created using the following functions.
3841 Multiple of these single cell piecewise quasipolynomials can
3842 be combined to create more complicated piecewise quasipolynomials.
3844 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3845 __isl_take isl_space *space);
3846 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3847 __isl_take isl_set *set,
3848 __isl_take isl_qpolynomial *qp);
3849 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3850 __isl_take isl_qpolynomial *qp);
3851 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3852 __isl_take isl_pw_aff *pwaff);
3854 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3855 __isl_take isl_space *space);
3856 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3857 __isl_take isl_pw_qpolynomial *pwqp);
3858 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3859 __isl_take isl_union_pw_qpolynomial *upwqp,
3860 __isl_take isl_pw_qpolynomial *pwqp);
3862 Quasipolynomials can be copied and freed again using the following
3865 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3866 __isl_keep isl_qpolynomial *qp);
3867 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3869 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3870 __isl_keep isl_pw_qpolynomial *pwqp);
3871 void *isl_pw_qpolynomial_free(
3872 __isl_take isl_pw_qpolynomial *pwqp);
3874 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3875 __isl_keep isl_union_pw_qpolynomial *upwqp);
3876 void *isl_union_pw_qpolynomial_free(
3877 __isl_take isl_union_pw_qpolynomial *upwqp);
3879 =head3 Inspecting (Piecewise) Quasipolynomials
3881 To iterate over all piecewise quasipolynomials in a union
3882 piecewise quasipolynomial, use the following function
3884 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3885 __isl_keep isl_union_pw_qpolynomial *upwqp,
3886 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3889 To extract the piecewise quasipolynomial in a given space from a union, use
3891 __isl_give isl_pw_qpolynomial *
3892 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3893 __isl_keep isl_union_pw_qpolynomial *upwqp,
3894 __isl_take isl_space *space);
3896 To iterate over the cells in a piecewise quasipolynomial,
3897 use either of the following two functions
3899 int isl_pw_qpolynomial_foreach_piece(
3900 __isl_keep isl_pw_qpolynomial *pwqp,
3901 int (*fn)(__isl_take isl_set *set,
3902 __isl_take isl_qpolynomial *qp,
3903 void *user), void *user);
3904 int isl_pw_qpolynomial_foreach_lifted_piece(
3905 __isl_keep isl_pw_qpolynomial *pwqp,
3906 int (*fn)(__isl_take isl_set *set,
3907 __isl_take isl_qpolynomial *qp,
3908 void *user), void *user);
3910 As usual, the function C<fn> should return C<0> on success
3911 and C<-1> on failure. The difference between
3912 C<isl_pw_qpolynomial_foreach_piece> and
3913 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3914 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3915 compute unique representations for all existentially quantified
3916 variables and then turn these existentially quantified variables
3917 into extra set variables, adapting the associated quasipolynomial
3918 accordingly. This means that the C<set> passed to C<fn>
3919 will not have any existentially quantified variables, but that
3920 the dimensions of the sets may be different for different
3921 invocations of C<fn>.
3923 To iterate over all terms in a quasipolynomial,
3926 int isl_qpolynomial_foreach_term(
3927 __isl_keep isl_qpolynomial *qp,
3928 int (*fn)(__isl_take isl_term *term,
3929 void *user), void *user);
3931 The terms themselves can be inspected and freed using
3934 unsigned isl_term_dim(__isl_keep isl_term *term,
3935 enum isl_dim_type type);
3936 void isl_term_get_num(__isl_keep isl_term *term,
3938 void isl_term_get_den(__isl_keep isl_term *term,
3940 int isl_term_get_exp(__isl_keep isl_term *term,
3941 enum isl_dim_type type, unsigned pos);
3942 __isl_give isl_aff *isl_term_get_div(
3943 __isl_keep isl_term *term, unsigned pos);
3944 void isl_term_free(__isl_take isl_term *term);
3946 Each term is a product of parameters, set variables and
3947 integer divisions. The function C<isl_term_get_exp>
3948 returns the exponent of a given dimensions in the given term.
3949 The C<isl_int>s in the arguments of C<isl_term_get_num>
3950 and C<isl_term_get_den> need to have been initialized
3951 using C<isl_int_init> before calling these functions.
3953 =head3 Properties of (Piecewise) Quasipolynomials
3955 To check whether a quasipolynomial is actually a constant,
3956 use the following function.
3958 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3959 isl_int *n, isl_int *d);
3961 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3962 then the numerator and denominator of the constant
3963 are returned in C<*n> and C<*d>, respectively.
3965 To check whether two union piecewise quasipolynomials are
3966 obviously equal, use
3968 int isl_union_pw_qpolynomial_plain_is_equal(
3969 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3970 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3972 =head3 Operations on (Piecewise) Quasipolynomials
3974 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3975 __isl_take isl_qpolynomial *qp, isl_int v);
3976 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3977 __isl_take isl_qpolynomial *qp);
3978 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3979 __isl_take isl_qpolynomial *qp1,
3980 __isl_take isl_qpolynomial *qp2);
3981 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3982 __isl_take isl_qpolynomial *qp1,
3983 __isl_take isl_qpolynomial *qp2);
3984 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3985 __isl_take isl_qpolynomial *qp1,
3986 __isl_take isl_qpolynomial *qp2);
3987 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3988 __isl_take isl_qpolynomial *qp, unsigned exponent);
3990 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3991 __isl_take isl_pw_qpolynomial *pwqp1,
3992 __isl_take isl_pw_qpolynomial *pwqp2);
3993 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3994 __isl_take isl_pw_qpolynomial *pwqp1,
3995 __isl_take isl_pw_qpolynomial *pwqp2);
3996 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3997 __isl_take isl_pw_qpolynomial *pwqp1,
3998 __isl_take isl_pw_qpolynomial *pwqp2);
3999 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4000 __isl_take isl_pw_qpolynomial *pwqp);
4001 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4002 __isl_take isl_pw_qpolynomial *pwqp1,
4003 __isl_take isl_pw_qpolynomial *pwqp2);
4004 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4005 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4007 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4008 __isl_take isl_union_pw_qpolynomial *upwqp1,
4009 __isl_take isl_union_pw_qpolynomial *upwqp2);
4010 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4011 __isl_take isl_union_pw_qpolynomial *upwqp1,
4012 __isl_take isl_union_pw_qpolynomial *upwqp2);
4013 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4014 __isl_take isl_union_pw_qpolynomial *upwqp1,
4015 __isl_take isl_union_pw_qpolynomial *upwqp2);
4017 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4018 __isl_take isl_pw_qpolynomial *pwqp,
4019 __isl_take isl_point *pnt);
4021 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4022 __isl_take isl_union_pw_qpolynomial *upwqp,
4023 __isl_take isl_point *pnt);
4025 __isl_give isl_set *isl_pw_qpolynomial_domain(
4026 __isl_take isl_pw_qpolynomial *pwqp);
4027 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4028 __isl_take isl_pw_qpolynomial *pwpq,
4029 __isl_take isl_set *set);
4030 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4031 __isl_take isl_pw_qpolynomial *pwpq,
4032 __isl_take isl_set *set);
4034 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4035 __isl_take isl_union_pw_qpolynomial *upwqp);
4036 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4037 __isl_take isl_union_pw_qpolynomial *upwpq,
4038 __isl_take isl_union_set *uset);
4039 __isl_give isl_union_pw_qpolynomial *
4040 isl_union_pw_qpolynomial_intersect_params(
4041 __isl_take isl_union_pw_qpolynomial *upwpq,
4042 __isl_take isl_set *set);
4044 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4045 __isl_take isl_qpolynomial *qp,
4046 __isl_take isl_space *model);
4048 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4049 __isl_take isl_qpolynomial *qp);
4050 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4051 __isl_take isl_pw_qpolynomial *pwqp);
4053 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4054 __isl_take isl_union_pw_qpolynomial *upwqp);
4056 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4057 __isl_take isl_qpolynomial *qp,
4058 __isl_take isl_set *context);
4059 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4060 __isl_take isl_qpolynomial *qp,
4061 __isl_take isl_set *context);
4063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4064 __isl_take isl_pw_qpolynomial *pwqp,
4065 __isl_take isl_set *context);
4066 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4067 __isl_take isl_pw_qpolynomial *pwqp,
4068 __isl_take isl_set *context);
4070 __isl_give isl_union_pw_qpolynomial *
4071 isl_union_pw_qpolynomial_gist_params(
4072 __isl_take isl_union_pw_qpolynomial *upwqp,
4073 __isl_take isl_set *context);
4074 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4075 __isl_take isl_union_pw_qpolynomial *upwqp,
4076 __isl_take isl_union_set *context);
4078 The gist operation applies the gist operation to each of
4079 the cells in the domain of the input piecewise quasipolynomial.
4080 The context is also exploited
4081 to simplify the quasipolynomials associated to each cell.
4083 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4084 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4085 __isl_give isl_union_pw_qpolynomial *
4086 isl_union_pw_qpolynomial_to_polynomial(
4087 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4089 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4090 the polynomial will be an overapproximation. If C<sign> is negative,
4091 it will be an underapproximation. If C<sign> is zero, the approximation
4092 will lie somewhere in between.
4094 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4096 A piecewise quasipolynomial reduction is a piecewise
4097 reduction (or fold) of quasipolynomials.
4098 In particular, the reduction can be maximum or a minimum.
4099 The objects are mainly used to represent the result of
4100 an upper or lower bound on a quasipolynomial over its domain,
4101 i.e., as the result of the following function.
4103 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4104 __isl_take isl_pw_qpolynomial *pwqp,
4105 enum isl_fold type, int *tight);
4107 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4108 __isl_take isl_union_pw_qpolynomial *upwqp,
4109 enum isl_fold type, int *tight);
4111 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4112 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4113 is the returned bound is known be tight, i.e., for each value
4114 of the parameters there is at least
4115 one element in the domain that reaches the bound.
4116 If the domain of C<pwqp> is not wrapping, then the bound is computed
4117 over all elements in that domain and the result has a purely parametric
4118 domain. If the domain of C<pwqp> is wrapping, then the bound is
4119 computed over the range of the wrapped relation. The domain of the
4120 wrapped relation becomes the domain of the result.
4122 A (piecewise) quasipolynomial reduction can be copied or freed using the
4123 following functions.
4125 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4126 __isl_keep isl_qpolynomial_fold *fold);
4127 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4128 __isl_keep isl_pw_qpolynomial_fold *pwf);
4129 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4130 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4131 void isl_qpolynomial_fold_free(
4132 __isl_take isl_qpolynomial_fold *fold);
4133 void *isl_pw_qpolynomial_fold_free(
4134 __isl_take isl_pw_qpolynomial_fold *pwf);
4135 void *isl_union_pw_qpolynomial_fold_free(
4136 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4138 =head3 Printing Piecewise Quasipolynomial Reductions
4140 Piecewise quasipolynomial reductions can be printed
4141 using the following function.
4143 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4144 __isl_take isl_printer *p,
4145 __isl_keep isl_pw_qpolynomial_fold *pwf);
4146 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4147 __isl_take isl_printer *p,
4148 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4150 For C<isl_printer_print_pw_qpolynomial_fold>,
4151 output format of the printer
4152 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4153 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4154 output format of the printer
4155 needs to be set to C<ISL_FORMAT_ISL>.
4156 In case of printing in C<ISL_FORMAT_C>, the user may want
4157 to set the names of all dimensions
4159 __isl_give isl_pw_qpolynomial_fold *
4160 isl_pw_qpolynomial_fold_set_dim_name(
4161 __isl_take isl_pw_qpolynomial_fold *pwf,
4162 enum isl_dim_type type, unsigned pos,
4165 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4167 To iterate over all piecewise quasipolynomial reductions in a union
4168 piecewise quasipolynomial reduction, use the following function
4170 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4171 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4172 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4173 void *user), void *user);
4175 To iterate over the cells in a piecewise quasipolynomial reduction,
4176 use either of the following two functions
4178 int isl_pw_qpolynomial_fold_foreach_piece(
4179 __isl_keep isl_pw_qpolynomial_fold *pwf,
4180 int (*fn)(__isl_take isl_set *set,
4181 __isl_take isl_qpolynomial_fold *fold,
4182 void *user), void *user);
4183 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4184 __isl_keep isl_pw_qpolynomial_fold *pwf,
4185 int (*fn)(__isl_take isl_set *set,
4186 __isl_take isl_qpolynomial_fold *fold,
4187 void *user), void *user);
4189 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4190 of the difference between these two functions.
4192 To iterate over all quasipolynomials in a reduction, use
4194 int isl_qpolynomial_fold_foreach_qpolynomial(
4195 __isl_keep isl_qpolynomial_fold *fold,
4196 int (*fn)(__isl_take isl_qpolynomial *qp,
4197 void *user), void *user);
4199 =head3 Properties of Piecewise Quasipolynomial Reductions
4201 To check whether two union piecewise quasipolynomial reductions are
4202 obviously equal, use
4204 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4205 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4206 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4208 =head3 Operations on Piecewise Quasipolynomial Reductions
4210 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4211 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4213 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4214 __isl_take isl_pw_qpolynomial_fold *pwf1,
4215 __isl_take isl_pw_qpolynomial_fold *pwf2);
4217 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4218 __isl_take isl_pw_qpolynomial_fold *pwf1,
4219 __isl_take isl_pw_qpolynomial_fold *pwf2);
4221 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4222 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4223 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4225 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4226 __isl_take isl_pw_qpolynomial_fold *pwf,
4227 __isl_take isl_point *pnt);
4229 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4230 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4231 __isl_take isl_point *pnt);
4233 __isl_give isl_pw_qpolynomial_fold *
4234 isl_pw_qpolynomial_fold_intersect_params(
4235 __isl_take isl_pw_qpolynomial_fold *pwf,
4236 __isl_take isl_set *set);
4238 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4239 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4240 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4241 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4242 __isl_take isl_union_set *uset);
4243 __isl_give isl_union_pw_qpolynomial_fold *
4244 isl_union_pw_qpolynomial_fold_intersect_params(
4245 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4246 __isl_take isl_set *set);
4248 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4249 __isl_take isl_pw_qpolynomial_fold *pwf);
4251 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4252 __isl_take isl_pw_qpolynomial_fold *pwf);
4254 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4255 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4257 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4258 __isl_take isl_qpolynomial_fold *fold,
4259 __isl_take isl_set *context);
4260 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4261 __isl_take isl_qpolynomial_fold *fold,
4262 __isl_take isl_set *context);
4264 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4265 __isl_take isl_pw_qpolynomial_fold *pwf,
4266 __isl_take isl_set *context);
4267 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4268 __isl_take isl_pw_qpolynomial_fold *pwf,
4269 __isl_take isl_set *context);
4271 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4272 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4273 __isl_take isl_union_set *context);
4274 __isl_give isl_union_pw_qpolynomial_fold *
4275 isl_union_pw_qpolynomial_fold_gist_params(
4276 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4277 __isl_take isl_set *context);
4279 The gist operation applies the gist operation to each of
4280 the cells in the domain of the input piecewise quasipolynomial reduction.
4281 In future, the operation will also exploit the context
4282 to simplify the quasipolynomial reductions associated to each cell.
4284 __isl_give isl_pw_qpolynomial_fold *
4285 isl_set_apply_pw_qpolynomial_fold(
4286 __isl_take isl_set *set,
4287 __isl_take isl_pw_qpolynomial_fold *pwf,
4289 __isl_give isl_pw_qpolynomial_fold *
4290 isl_map_apply_pw_qpolynomial_fold(
4291 __isl_take isl_map *map,
4292 __isl_take isl_pw_qpolynomial_fold *pwf,
4294 __isl_give isl_union_pw_qpolynomial_fold *
4295 isl_union_set_apply_union_pw_qpolynomial_fold(
4296 __isl_take isl_union_set *uset,
4297 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4299 __isl_give isl_union_pw_qpolynomial_fold *
4300 isl_union_map_apply_union_pw_qpolynomial_fold(
4301 __isl_take isl_union_map *umap,
4302 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4305 The functions taking a map
4306 compose the given map with the given piecewise quasipolynomial reduction.
4307 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4308 over all elements in the intersection of the range of the map
4309 and the domain of the piecewise quasipolynomial reduction
4310 as a function of an element in the domain of the map.
4311 The functions taking a set compute a bound over all elements in the
4312 intersection of the set and the domain of the
4313 piecewise quasipolynomial reduction.
4315 =head2 Dependence Analysis
4317 C<isl> contains specialized functionality for performing
4318 array dataflow analysis. That is, given a I<sink> access relation
4319 and a collection of possible I<source> access relations,
4320 C<isl> can compute relations that describe
4321 for each iteration of the sink access, which iteration
4322 of which of the source access relations was the last
4323 to access the same data element before the given iteration
4325 The resulting dependence relations map source iterations
4326 to the corresponding sink iterations.
4327 To compute standard flow dependences, the sink should be
4328 a read, while the sources should be writes.
4329 If any of the source accesses are marked as being I<may>
4330 accesses, then there will be a dependence from the last
4331 I<must> access B<and> from any I<may> access that follows
4332 this last I<must> access.
4333 In particular, if I<all> sources are I<may> accesses,
4334 then memory based dependence analysis is performed.
4335 If, on the other hand, all sources are I<must> accesses,
4336 then value based dependence analysis is performed.
4338 #include <isl/flow.h>
4340 typedef int (*isl_access_level_before)(void *first, void *second);
4342 __isl_give isl_access_info *isl_access_info_alloc(
4343 __isl_take isl_map *sink,
4344 void *sink_user, isl_access_level_before fn,
4346 __isl_give isl_access_info *isl_access_info_add_source(
4347 __isl_take isl_access_info *acc,
4348 __isl_take isl_map *source, int must,
4350 void *isl_access_info_free(__isl_take isl_access_info *acc);
4352 __isl_give isl_flow *isl_access_info_compute_flow(
4353 __isl_take isl_access_info *acc);
4355 int isl_flow_foreach(__isl_keep isl_flow *deps,
4356 int (*fn)(__isl_take isl_map *dep, int must,
4357 void *dep_user, void *user),
4359 __isl_give isl_map *isl_flow_get_no_source(
4360 __isl_keep isl_flow *deps, int must);
4361 void isl_flow_free(__isl_take isl_flow *deps);
4363 The function C<isl_access_info_compute_flow> performs the actual
4364 dependence analysis. The other functions are used to construct
4365 the input for this function or to read off the output.
4367 The input is collected in an C<isl_access_info>, which can
4368 be created through a call to C<isl_access_info_alloc>.
4369 The arguments to this functions are the sink access relation
4370 C<sink>, a token C<sink_user> used to identify the sink
4371 access to the user, a callback function for specifying the
4372 relative order of source and sink accesses, and the number
4373 of source access relations that will be added.
4374 The callback function has type C<int (*)(void *first, void *second)>.
4375 The function is called with two user supplied tokens identifying
4376 either a source or the sink and it should return the shared nesting
4377 level and the relative order of the two accesses.
4378 In particular, let I<n> be the number of loops shared by
4379 the two accesses. If C<first> precedes C<second> textually,
4380 then the function should return I<2 * n + 1>; otherwise,
4381 it should return I<2 * n>.
4382 The sources can be added to the C<isl_access_info> by performing
4383 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4384 C<must> indicates whether the source is a I<must> access
4385 or a I<may> access. Note that a multi-valued access relation
4386 should only be marked I<must> if every iteration in the domain
4387 of the relation accesses I<all> elements in its image.
4388 The C<source_user> token is again used to identify
4389 the source access. The range of the source access relation
4390 C<source> should have the same dimension as the range
4391 of the sink access relation.
4392 The C<isl_access_info_free> function should usually not be
4393 called explicitly, because it is called implicitly by
4394 C<isl_access_info_compute_flow>.
4396 The result of the dependence analysis is collected in an
4397 C<isl_flow>. There may be elements of
4398 the sink access for which no preceding source access could be
4399 found or for which all preceding sources are I<may> accesses.
4400 The relations containing these elements can be obtained through
4401 calls to C<isl_flow_get_no_source>, the first with C<must> set
4402 and the second with C<must> unset.
4403 In the case of standard flow dependence analysis,
4404 with the sink a read and the sources I<must> writes,
4405 the first relation corresponds to the reads from uninitialized
4406 array elements and the second relation is empty.
4407 The actual flow dependences can be extracted using
4408 C<isl_flow_foreach>. This function will call the user-specified
4409 callback function C<fn> for each B<non-empty> dependence between
4410 a source and the sink. The callback function is called
4411 with four arguments, the actual flow dependence relation
4412 mapping source iterations to sink iterations, a boolean that
4413 indicates whether it is a I<must> or I<may> dependence, a token
4414 identifying the source and an additional C<void *> with value
4415 equal to the third argument of the C<isl_flow_foreach> call.
4416 A dependence is marked I<must> if it originates from a I<must>
4417 source and if it is not followed by any I<may> sources.
4419 After finishing with an C<isl_flow>, the user should call
4420 C<isl_flow_free> to free all associated memory.
4422 A higher-level interface to dependence analysis is provided
4423 by the following function.
4425 #include <isl/flow.h>
4427 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4428 __isl_take isl_union_map *must_source,
4429 __isl_take isl_union_map *may_source,
4430 __isl_take isl_union_map *schedule,
4431 __isl_give isl_union_map **must_dep,
4432 __isl_give isl_union_map **may_dep,
4433 __isl_give isl_union_map **must_no_source,
4434 __isl_give isl_union_map **may_no_source);
4436 The arrays are identified by the tuple names of the ranges
4437 of the accesses. The iteration domains by the tuple names
4438 of the domains of the accesses and of the schedule.
4439 The relative order of the iteration domains is given by the
4440 schedule. The relations returned through C<must_no_source>
4441 and C<may_no_source> are subsets of C<sink>.
4442 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4443 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4444 any of the other arguments is treated as an error.
4446 =head3 Interaction with Dependence Analysis
4448 During the dependence analysis, we frequently need to perform
4449 the following operation. Given a relation between sink iterations
4450 and potential source iterations from a particular source domain,
4451 what is the last potential source iteration corresponding to each
4452 sink iteration. It can sometimes be convenient to adjust
4453 the set of potential source iterations before or after each such operation.
4454 The prototypical example is fuzzy array dataflow analysis,
4455 where we need to analyze if, based on data-dependent constraints,
4456 the sink iteration can ever be executed without one or more of
4457 the corresponding potential source iterations being executed.
4458 If so, we can introduce extra parameters and select an unknown
4459 but fixed source iteration from the potential source iterations.
4460 To be able to perform such manipulations, C<isl> provides the following
4463 #include <isl/flow.h>
4465 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4466 __isl_keep isl_map *source_map,
4467 __isl_keep isl_set *sink, void *source_user,
4469 __isl_give isl_access_info *isl_access_info_set_restrict(
4470 __isl_take isl_access_info *acc,
4471 isl_access_restrict fn, void *user);
4473 The function C<isl_access_info_set_restrict> should be called
4474 before calling C<isl_access_info_compute_flow> and registers a callback function
4475 that will be called any time C<isl> is about to compute the last
4476 potential source. The first argument is the (reverse) proto-dependence,
4477 mapping sink iterations to potential source iterations.
4478 The second argument represents the sink iterations for which
4479 we want to compute the last source iteration.
4480 The third argument is the token corresponding to the source
4481 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4482 The callback is expected to return a restriction on either the input or
4483 the output of the operation computing the last potential source.
4484 If the input needs to be restricted then restrictions are needed
4485 for both the source and the sink iterations. The sink iterations
4486 and the potential source iterations will be intersected with these sets.
4487 If the output needs to be restricted then only a restriction on the source
4488 iterations is required.
4489 If any error occurs, the callback should return C<NULL>.
4490 An C<isl_restriction> object can be created, freed and inspected
4491 using the following functions.
4493 #include <isl/flow.h>
4495 __isl_give isl_restriction *isl_restriction_input(
4496 __isl_take isl_set *source_restr,
4497 __isl_take isl_set *sink_restr);
4498 __isl_give isl_restriction *isl_restriction_output(
4499 __isl_take isl_set *source_restr);
4500 __isl_give isl_restriction *isl_restriction_none(
4501 __isl_take isl_map *source_map);
4502 __isl_give isl_restriction *isl_restriction_empty(
4503 __isl_take isl_map *source_map);
4504 void *isl_restriction_free(
4505 __isl_take isl_restriction *restr);
4506 isl_ctx *isl_restriction_get_ctx(
4507 __isl_keep isl_restriction *restr);
4509 C<isl_restriction_none> and C<isl_restriction_empty> are special
4510 cases of C<isl_restriction_input>. C<isl_restriction_none>
4511 is essentially equivalent to
4513 isl_restriction_input(isl_set_universe(
4514 isl_space_range(isl_map_get_space(source_map))),
4516 isl_space_domain(isl_map_get_space(source_map))));
4518 whereas C<isl_restriction_empty> is essentially equivalent to
4520 isl_restriction_input(isl_set_empty(
4521 isl_space_range(isl_map_get_space(source_map))),
4523 isl_space_domain(isl_map_get_space(source_map))));
4527 B<The functionality described in this section is fairly new
4528 and may be subject to change.>
4530 The following function can be used to compute a schedule
4531 for a union of domains.
4532 By default, the algorithm used to construct the schedule is similar
4533 to that of C<Pluto>.
4534 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4536 The generated schedule respects all C<validity> dependences.
4537 That is, all dependence distances over these dependences in the
4538 scheduled space are lexicographically positive.
4539 The default algorithm tries to minimize the dependence distances over
4540 C<proximity> dependences.
4541 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4542 for groups of domains where the dependence distances have only
4543 non-negative values.
4544 When using Feautrier's algorithm, the C<proximity> dependence
4545 distances are only minimized during the extension to a
4546 full-dimensional schedule.
4548 #include <isl/schedule.h>
4549 __isl_give isl_schedule *isl_union_set_compute_schedule(
4550 __isl_take isl_union_set *domain,
4551 __isl_take isl_union_map *validity,
4552 __isl_take isl_union_map *proximity);
4553 void *isl_schedule_free(__isl_take isl_schedule *sched);
4555 A mapping from the domains to the scheduled space can be obtained
4556 from an C<isl_schedule> using the following function.
4558 __isl_give isl_union_map *isl_schedule_get_map(
4559 __isl_keep isl_schedule *sched);
4561 A representation of the schedule can be printed using
4563 __isl_give isl_printer *isl_printer_print_schedule(
4564 __isl_take isl_printer *p,
4565 __isl_keep isl_schedule *schedule);
4567 A representation of the schedule as a forest of bands can be obtained
4568 using the following function.
4570 __isl_give isl_band_list *isl_schedule_get_band_forest(
4571 __isl_keep isl_schedule *schedule);
4573 The individual bands can be visited in depth-first post-order
4574 using the following function.
4576 #include <isl/schedule.h>
4577 int isl_schedule_foreach_band(
4578 __isl_keep isl_schedule *sched,
4579 int (*fn)(__isl_keep isl_band *band, void *user),
4582 The list can be manipulated as explained in L<"Lists">.
4583 The bands inside the list can be copied and freed using the following
4586 #include <isl/band.h>
4587 __isl_give isl_band *isl_band_copy(
4588 __isl_keep isl_band *band);
4589 void *isl_band_free(__isl_take isl_band *band);
4591 Each band contains zero or more scheduling dimensions.
4592 These are referred to as the members of the band.
4593 The section of the schedule that corresponds to the band is
4594 referred to as the partial schedule of the band.
4595 For those nodes that participate in a band, the outer scheduling
4596 dimensions form the prefix schedule, while the inner scheduling
4597 dimensions form the suffix schedule.
4598 That is, if we take a cut of the band forest, then the union of
4599 the concatenations of the prefix, partial and suffix schedules of
4600 each band in the cut is equal to the entire schedule (modulo
4601 some possible padding at the end with zero scheduling dimensions).
4602 The properties of a band can be inspected using the following functions.
4604 #include <isl/band.h>
4605 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4607 int isl_band_has_children(__isl_keep isl_band *band);
4608 __isl_give isl_band_list *isl_band_get_children(
4609 __isl_keep isl_band *band);
4611 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4612 __isl_keep isl_band *band);
4613 __isl_give isl_union_map *isl_band_get_partial_schedule(
4614 __isl_keep isl_band *band);
4615 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4616 __isl_keep isl_band *band);
4618 int isl_band_n_member(__isl_keep isl_band *band);
4619 int isl_band_member_is_zero_distance(
4620 __isl_keep isl_band *band, int pos);
4622 int isl_band_list_foreach_band(
4623 __isl_keep isl_band_list *list,
4624 int (*fn)(__isl_keep isl_band *band, void *user),
4627 Note that a scheduling dimension is considered to be ``zero
4628 distance'' if it does not carry any proximity dependences
4630 That is, if the dependence distances of the proximity
4631 dependences are all zero in that direction (for fixed
4632 iterations of outer bands).
4633 Like C<isl_schedule_foreach_band>,
4634 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4635 in depth-first post-order.
4637 A band can be tiled using the following function.
4639 #include <isl/band.h>
4640 int isl_band_tile(__isl_keep isl_band *band,
4641 __isl_take isl_vec *sizes);
4643 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4645 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4647 The C<isl_band_tile> function tiles the band using the given tile sizes
4648 inside its schedule.
4649 A new child band is created to represent the point loops and it is
4650 inserted between the modified band and its children.
4651 The C<tile_scale_tile_loops> option specifies whether the tile
4652 loops iterators should be scaled by the tile sizes.
4654 A representation of the band can be printed using
4656 #include <isl/band.h>
4657 __isl_give isl_printer *isl_printer_print_band(
4658 __isl_take isl_printer *p,
4659 __isl_keep isl_band *band);
4663 #include <isl/schedule.h>
4664 int isl_options_set_schedule_max_coefficient(
4665 isl_ctx *ctx, int val);
4666 int isl_options_get_schedule_max_coefficient(
4668 int isl_options_set_schedule_max_constant_term(
4669 isl_ctx *ctx, int val);
4670 int isl_options_get_schedule_max_constant_term(
4672 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4673 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4674 int isl_options_set_schedule_maximize_band_depth(
4675 isl_ctx *ctx, int val);
4676 int isl_options_get_schedule_maximize_band_depth(
4678 int isl_options_set_schedule_outer_zero_distance(
4679 isl_ctx *ctx, int val);
4680 int isl_options_get_schedule_outer_zero_distance(
4682 int isl_options_set_schedule_split_scaled(
4683 isl_ctx *ctx, int val);
4684 int isl_options_get_schedule_split_scaled(
4686 int isl_options_set_schedule_algorithm(
4687 isl_ctx *ctx, int val);
4688 int isl_options_get_schedule_algorithm(
4690 int isl_options_set_schedule_separate_components(
4691 isl_ctx *ctx, int val);
4692 int isl_options_get_schedule_separate_components(
4697 =item * schedule_max_coefficient
4699 This option enforces that the coefficients for variable and parameter
4700 dimensions in the calculated schedule are not larger than the specified value.
4701 This option can significantly increase the speed of the scheduling calculation
4702 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4703 this option does not introduce bounds on the variable or parameter
4706 =item * schedule_max_constant_term
4708 This option enforces that the constant coefficients in the calculated schedule
4709 are not larger than the maximal constant term. This option can significantly
4710 increase the speed of the scheduling calculation and may also prevent fusing of
4711 unrelated dimensions. A value of -1 means that this option does not introduce
4712 bounds on the constant coefficients.
4714 =item * schedule_fuse
4716 This option controls the level of fusion.
4717 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4718 resulting schedule will be distributed as much as possible.
4719 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4720 try to fuse loops in the resulting schedule.
4722 =item * schedule_maximize_band_depth
4724 If this option is set, we do not split bands at the point
4725 where we detect splitting is necessary. Instead, we
4726 backtrack and split bands as early as possible. This
4727 reduces the number of splits and maximizes the width of
4728 the bands. Wider bands give more possibilities for tiling.
4729 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4730 then bands will be split as early as possible, even if there is no need.
4731 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4733 =item * schedule_outer_zero_distance
4735 If this option is set, then we try to construct schedules
4736 where the outermost scheduling dimension in each band
4737 results in a zero dependence distance over the proximity
4740 =item * schedule_split_scaled
4742 If this option is set, then we try to construct schedules in which the
4743 constant term is split off from the linear part if the linear parts of
4744 the scheduling rows for all nodes in the graphs have a common non-trivial
4746 The constant term is then placed in a separate band and the linear
4749 =item * schedule_algorithm
4751 Selects the scheduling algorithm to be used.
4752 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4753 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4755 =item * schedule_separate_components
4757 If at any point the dependence graph contains any (weakly connected) components,
4758 then these components are scheduled separately.
4759 If this option is not set, then some iterations of the domains
4760 in these components may be scheduled together.
4761 If this option is set, then the components are given consecutive
4766 =head2 Parametric Vertex Enumeration
4768 The parametric vertex enumeration described in this section
4769 is mainly intended to be used internally and by the C<barvinok>
4772 #include <isl/vertices.h>
4773 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4774 __isl_keep isl_basic_set *bset);
4776 The function C<isl_basic_set_compute_vertices> performs the
4777 actual computation of the parametric vertices and the chamber
4778 decomposition and store the result in an C<isl_vertices> object.
4779 This information can be queried by either iterating over all
4780 the vertices or iterating over all the chambers or cells
4781 and then iterating over all vertices that are active on the chamber.
4783 int isl_vertices_foreach_vertex(
4784 __isl_keep isl_vertices *vertices,
4785 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4788 int isl_vertices_foreach_cell(
4789 __isl_keep isl_vertices *vertices,
4790 int (*fn)(__isl_take isl_cell *cell, void *user),
4792 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4793 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4796 Other operations that can be performed on an C<isl_vertices> object are
4799 isl_ctx *isl_vertices_get_ctx(
4800 __isl_keep isl_vertices *vertices);
4801 int isl_vertices_get_n_vertices(
4802 __isl_keep isl_vertices *vertices);
4803 void isl_vertices_free(__isl_take isl_vertices *vertices);
4805 Vertices can be inspected and destroyed using the following functions.
4807 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4808 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4809 __isl_give isl_basic_set *isl_vertex_get_domain(
4810 __isl_keep isl_vertex *vertex);
4811 __isl_give isl_basic_set *isl_vertex_get_expr(
4812 __isl_keep isl_vertex *vertex);
4813 void isl_vertex_free(__isl_take isl_vertex *vertex);
4815 C<isl_vertex_get_expr> returns a singleton parametric set describing
4816 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4818 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4819 B<rational> basic sets, so they should mainly be used for inspection
4820 and should not be mixed with integer sets.
4822 Chambers can be inspected and destroyed using the following functions.
4824 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4825 __isl_give isl_basic_set *isl_cell_get_domain(
4826 __isl_keep isl_cell *cell);
4827 void isl_cell_free(__isl_take isl_cell *cell);
4831 Although C<isl> is mainly meant to be used as a library,
4832 it also contains some basic applications that use some
4833 of the functionality of C<isl>.
4834 The input may be specified in either the L<isl format>
4835 or the L<PolyLib format>.
4837 =head2 C<isl_polyhedron_sample>
4839 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4840 an integer element of the polyhedron, if there is any.
4841 The first column in the output is the denominator and is always
4842 equal to 1. If the polyhedron contains no integer points,
4843 then a vector of length zero is printed.
4847 C<isl_pip> takes the same input as the C<example> program
4848 from the C<piplib> distribution, i.e., a set of constraints
4849 on the parameters, a line containing only -1 and finally a set
4850 of constraints on a parametric polyhedron.
4851 The coefficients of the parameters appear in the last columns
4852 (but before the final constant column).
4853 The output is the lexicographic minimum of the parametric polyhedron.
4854 As C<isl> currently does not have its own output format, the output
4855 is just a dump of the internal state.
4857 =head2 C<isl_polyhedron_minimize>
4859 C<isl_polyhedron_minimize> computes the minimum of some linear
4860 or affine objective function over the integer points in a polyhedron.
4861 If an affine objective function
4862 is given, then the constant should appear in the last column.
4864 =head2 C<isl_polytope_scan>
4866 Given a polytope, C<isl_polytope_scan> prints
4867 all integer points in the polytope.