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);
618 It is often useful to create objects that live in the
619 same space as some other object. This can be accomplished
620 by creating the new objects
621 (see L<Creating New Sets and Relations> or
622 L<Creating New (Piecewise) Quasipolynomials>) based on the space
623 of the original object.
626 __isl_give isl_space *isl_basic_set_get_space(
627 __isl_keep isl_basic_set *bset);
628 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
630 #include <isl/union_set.h>
631 __isl_give isl_space *isl_union_set_get_space(
632 __isl_keep isl_union_set *uset);
635 __isl_give isl_space *isl_basic_map_get_space(
636 __isl_keep isl_basic_map *bmap);
637 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
639 #include <isl/union_map.h>
640 __isl_give isl_space *isl_union_map_get_space(
641 __isl_keep isl_union_map *umap);
643 #include <isl/constraint.h>
644 __isl_give isl_space *isl_constraint_get_space(
645 __isl_keep isl_constraint *constraint);
647 #include <isl/polynomial.h>
648 __isl_give isl_space *isl_qpolynomial_get_domain_space(
649 __isl_keep isl_qpolynomial *qp);
650 __isl_give isl_space *isl_qpolynomial_get_space(
651 __isl_keep isl_qpolynomial *qp);
652 __isl_give isl_space *isl_qpolynomial_fold_get_space(
653 __isl_keep isl_qpolynomial_fold *fold);
654 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
655 __isl_keep isl_pw_qpolynomial *pwqp);
656 __isl_give isl_space *isl_pw_qpolynomial_get_space(
657 __isl_keep isl_pw_qpolynomial *pwqp);
658 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
659 __isl_keep isl_pw_qpolynomial_fold *pwf);
660 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
661 __isl_keep isl_pw_qpolynomial_fold *pwf);
662 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
663 __isl_keep isl_union_pw_qpolynomial *upwqp);
664 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
665 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
668 __isl_give isl_space *isl_aff_get_domain_space(
669 __isl_keep isl_aff *aff);
670 __isl_give isl_space *isl_aff_get_space(
671 __isl_keep isl_aff *aff);
672 __isl_give isl_space *isl_pw_aff_get_domain_space(
673 __isl_keep isl_pw_aff *pwaff);
674 __isl_give isl_space *isl_pw_aff_get_space(
675 __isl_keep isl_pw_aff *pwaff);
676 __isl_give isl_space *isl_multi_aff_get_domain_space(
677 __isl_keep isl_multi_aff *maff);
678 __isl_give isl_space *isl_multi_aff_get_space(
679 __isl_keep isl_multi_aff *maff);
680 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
681 __isl_keep isl_pw_multi_aff *pma);
682 __isl_give isl_space *isl_pw_multi_aff_get_space(
683 __isl_keep isl_pw_multi_aff *pma);
684 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
685 __isl_keep isl_union_pw_multi_aff *upma);
687 #include <isl/point.h>
688 __isl_give isl_space *isl_point_get_space(
689 __isl_keep isl_point *pnt);
691 The identifiers or names of the individual dimensions may be set or read off
692 using the following functions.
694 #include <isl/space.h>
695 __isl_give isl_space *isl_space_set_dim_id(
696 __isl_take isl_space *space,
697 enum isl_dim_type type, unsigned pos,
698 __isl_take isl_id *id);
699 int isl_space_has_dim_id(__isl_keep isl_space *space,
700 enum isl_dim_type type, unsigned pos);
701 __isl_give isl_id *isl_space_get_dim_id(
702 __isl_keep isl_space *space,
703 enum isl_dim_type type, unsigned pos);
704 __isl_give isl_space *isl_space_set_dim_name(
705 __isl_take isl_space *space,
706 enum isl_dim_type type, unsigned pos,
707 __isl_keep const char *name);
708 int isl_space_has_dim_name(__isl_keep isl_space *space,
709 enum isl_dim_type type, unsigned pos);
710 __isl_keep const char *isl_space_get_dim_name(
711 __isl_keep isl_space *space,
712 enum isl_dim_type type, unsigned pos);
714 Note that C<isl_space_get_name> returns a pointer to some internal
715 data structure, so the result can only be used while the
716 corresponding C<isl_space> is alive.
717 Also note that every function that operates on two sets or relations
718 requires that both arguments have the same parameters. This also
719 means that if one of the arguments has named parameters, then the
720 other needs to have named parameters too and the names need to match.
721 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
722 arguments may have different parameters (as long as they are named),
723 in which case the result will have as parameters the union of the parameters of
726 Given the identifier or name of a dimension (typically a parameter),
727 its position can be obtained from the following function.
729 #include <isl/space.h>
730 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
731 enum isl_dim_type type, __isl_keep isl_id *id);
732 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
733 enum isl_dim_type type, const char *name);
735 The identifiers or names of entire spaces may be set or read off
736 using the following functions.
738 #include <isl/space.h>
739 __isl_give isl_space *isl_space_set_tuple_id(
740 __isl_take isl_space *space,
741 enum isl_dim_type type, __isl_take isl_id *id);
742 __isl_give isl_space *isl_space_reset_tuple_id(
743 __isl_take isl_space *space, enum isl_dim_type type);
744 int isl_space_has_tuple_id(__isl_keep isl_space *space,
745 enum isl_dim_type type);
746 __isl_give isl_id *isl_space_get_tuple_id(
747 __isl_keep isl_space *space, enum isl_dim_type type);
748 __isl_give isl_space *isl_space_set_tuple_name(
749 __isl_take isl_space *space,
750 enum isl_dim_type type, const char *s);
751 int isl_space_has_tuple_name(__isl_keep isl_space *space,
752 enum isl_dim_type type);
753 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
754 enum isl_dim_type type);
756 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
757 or C<isl_dim_set>. As with C<isl_space_get_name>,
758 the C<isl_space_get_tuple_name> function returns a pointer to some internal
760 Binary operations require the corresponding spaces of their arguments
761 to have the same name.
763 Spaces can be nested. In particular, the domain of a set or
764 the domain or range of a relation can be a nested relation.
765 The following functions can be used to construct and deconstruct
768 #include <isl/space.h>
769 int isl_space_is_wrapping(__isl_keep isl_space *space);
770 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
771 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
773 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
774 be the space of a set, while that of
775 C<isl_space_wrap> should be the space of a relation.
776 Conversely, the output of C<isl_space_unwrap> is the space
777 of a relation, while that of C<isl_space_wrap> is the space of a set.
779 Spaces can be created from other spaces
780 using the following functions.
782 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
783 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
784 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
785 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
786 __isl_give isl_space *isl_space_params(
787 __isl_take isl_space *space);
788 __isl_give isl_space *isl_space_set_from_params(
789 __isl_take isl_space *space);
790 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
791 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
792 __isl_take isl_space *right);
793 __isl_give isl_space *isl_space_align_params(
794 __isl_take isl_space *space1, __isl_take isl_space *space2)
795 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
796 enum isl_dim_type type, unsigned pos, unsigned n);
797 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
798 enum isl_dim_type type, unsigned n);
799 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
800 enum isl_dim_type type, unsigned first, unsigned n);
801 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
802 enum isl_dim_type dst_type, unsigned dst_pos,
803 enum isl_dim_type src_type, unsigned src_pos,
805 __isl_give isl_space *isl_space_map_from_set(
806 __isl_take isl_space *space);
807 __isl_give isl_space *isl_space_map_from_domain_and_range(
808 __isl_take isl_space *domain,
809 __isl_take isl_space *range);
810 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
811 __isl_give isl_space *isl_space_curry(
812 __isl_take isl_space *space);
814 Note that if dimensions are added or removed from a space, then
815 the name and the internal structure are lost.
819 A local space is essentially a space with
820 zero or more existentially quantified variables.
821 The local space of a (constraint of a) basic set or relation can be obtained
822 using the following functions.
824 #include <isl/constraint.h>
825 __isl_give isl_local_space *isl_constraint_get_local_space(
826 __isl_keep isl_constraint *constraint);
829 __isl_give isl_local_space *isl_basic_set_get_local_space(
830 __isl_keep isl_basic_set *bset);
833 __isl_give isl_local_space *isl_basic_map_get_local_space(
834 __isl_keep isl_basic_map *bmap);
836 A new local space can be created from a space using
838 #include <isl/local_space.h>
839 __isl_give isl_local_space *isl_local_space_from_space(
840 __isl_take isl_space *space);
842 They can be inspected, modified, copied and freed using the following functions.
844 #include <isl/local_space.h>
845 isl_ctx *isl_local_space_get_ctx(
846 __isl_keep isl_local_space *ls);
847 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
848 int isl_local_space_dim(__isl_keep isl_local_space *ls,
849 enum isl_dim_type type);
850 int isl_local_space_has_dim_id(
851 __isl_keep isl_local_space *ls,
852 enum isl_dim_type type, unsigned pos);
853 __isl_give isl_id *isl_local_space_get_dim_id(
854 __isl_keep isl_local_space *ls,
855 enum isl_dim_type type, unsigned pos);
856 int isl_local_space_has_dim_name(
857 __isl_keep isl_local_space *ls,
858 enum isl_dim_type type, unsigned pos)
859 const char *isl_local_space_get_dim_name(
860 __isl_keep isl_local_space *ls,
861 enum isl_dim_type type, unsigned pos);
862 __isl_give isl_local_space *isl_local_space_set_dim_name(
863 __isl_take isl_local_space *ls,
864 enum isl_dim_type type, unsigned pos, const char *s);
865 __isl_give isl_local_space *isl_local_space_set_dim_id(
866 __isl_take isl_local_space *ls,
867 enum isl_dim_type type, unsigned pos,
868 __isl_take isl_id *id);
869 __isl_give isl_space *isl_local_space_get_space(
870 __isl_keep isl_local_space *ls);
871 __isl_give isl_aff *isl_local_space_get_div(
872 __isl_keep isl_local_space *ls, int pos);
873 __isl_give isl_local_space *isl_local_space_copy(
874 __isl_keep isl_local_space *ls);
875 void *isl_local_space_free(__isl_take isl_local_space *ls);
877 Two local spaces can be compared using
879 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
880 __isl_keep isl_local_space *ls2);
882 Local spaces can be created from other local spaces
883 using the following functions.
885 __isl_give isl_local_space *isl_local_space_domain(
886 __isl_take isl_local_space *ls);
887 __isl_give isl_local_space *isl_local_space_range(
888 __isl_take isl_local_space *ls);
889 __isl_give isl_local_space *isl_local_space_from_domain(
890 __isl_take isl_local_space *ls);
891 __isl_give isl_local_space *isl_local_space_intersect(
892 __isl_take isl_local_space *ls1,
893 __isl_take isl_local_space *ls2);
894 __isl_give isl_local_space *isl_local_space_add_dims(
895 __isl_take isl_local_space *ls,
896 enum isl_dim_type type, unsigned n);
897 __isl_give isl_local_space *isl_local_space_insert_dims(
898 __isl_take isl_local_space *ls,
899 enum isl_dim_type type, unsigned first, unsigned n);
900 __isl_give isl_local_space *isl_local_space_drop_dims(
901 __isl_take isl_local_space *ls,
902 enum isl_dim_type type, unsigned first, unsigned n);
904 =head2 Input and Output
906 C<isl> supports its own input/output format, which is similar
907 to the C<Omega> format, but also supports the C<PolyLib> format
912 The C<isl> format is similar to that of C<Omega>, but has a different
913 syntax for describing the parameters and allows for the definition
914 of an existentially quantified variable as the integer division
915 of an affine expression.
916 For example, the set of integers C<i> between C<0> and C<n>
917 such that C<i % 10 <= 6> can be described as
919 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
922 A set or relation can have several disjuncts, separated
923 by the keyword C<or>. Each disjunct is either a conjunction
924 of constraints or a projection (C<exists>) of a conjunction
925 of constraints. The constraints are separated by the keyword
928 =head3 C<PolyLib> format
930 If the represented set is a union, then the first line
931 contains a single number representing the number of disjuncts.
932 Otherwise, a line containing the number C<1> is optional.
934 Each disjunct is represented by a matrix of constraints.
935 The first line contains two numbers representing
936 the number of rows and columns,
937 where the number of rows is equal to the number of constraints
938 and the number of columns is equal to two plus the number of variables.
939 The following lines contain the actual rows of the constraint matrix.
940 In each row, the first column indicates whether the constraint
941 is an equality (C<0>) or inequality (C<1>). The final column
942 corresponds to the constant term.
944 If the set is parametric, then the coefficients of the parameters
945 appear in the last columns before the constant column.
946 The coefficients of any existentially quantified variables appear
947 between those of the set variables and those of the parameters.
949 =head3 Extended C<PolyLib> format
951 The extended C<PolyLib> format is nearly identical to the
952 C<PolyLib> format. The only difference is that the line
953 containing the number of rows and columns of a constraint matrix
954 also contains four additional numbers:
955 the number of output dimensions, the number of input dimensions,
956 the number of local dimensions (i.e., the number of existentially
957 quantified variables) and the number of parameters.
958 For sets, the number of ``output'' dimensions is equal
959 to the number of set dimensions, while the number of ``input''
965 __isl_give isl_basic_set *isl_basic_set_read_from_file(
966 isl_ctx *ctx, FILE *input);
967 __isl_give isl_basic_set *isl_basic_set_read_from_str(
968 isl_ctx *ctx, const char *str);
969 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
971 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
975 __isl_give isl_basic_map *isl_basic_map_read_from_file(
976 isl_ctx *ctx, FILE *input);
977 __isl_give isl_basic_map *isl_basic_map_read_from_str(
978 isl_ctx *ctx, const char *str);
979 __isl_give isl_map *isl_map_read_from_file(
980 isl_ctx *ctx, FILE *input);
981 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
984 #include <isl/union_set.h>
985 __isl_give isl_union_set *isl_union_set_read_from_file(
986 isl_ctx *ctx, FILE *input);
987 __isl_give isl_union_set *isl_union_set_read_from_str(
988 isl_ctx *ctx, const char *str);
990 #include <isl/union_map.h>
991 __isl_give isl_union_map *isl_union_map_read_from_file(
992 isl_ctx *ctx, FILE *input);
993 __isl_give isl_union_map *isl_union_map_read_from_str(
994 isl_ctx *ctx, const char *str);
996 The input format is autodetected and may be either the C<PolyLib> format
997 or the C<isl> format.
1001 Before anything can be printed, an C<isl_printer> needs to
1004 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1006 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1007 void *isl_printer_free(__isl_take isl_printer *printer);
1008 __isl_give char *isl_printer_get_str(
1009 __isl_keep isl_printer *printer);
1011 The printer can be inspected using the following functions.
1013 FILE *isl_printer_get_file(
1014 __isl_keep isl_printer *printer);
1015 int isl_printer_get_output_format(
1016 __isl_keep isl_printer *p);
1018 The behavior of the printer can be modified in various ways
1020 __isl_give isl_printer *isl_printer_set_output_format(
1021 __isl_take isl_printer *p, int output_format);
1022 __isl_give isl_printer *isl_printer_set_indent(
1023 __isl_take isl_printer *p, int indent);
1024 __isl_give isl_printer *isl_printer_indent(
1025 __isl_take isl_printer *p, int indent);
1026 __isl_give isl_printer *isl_printer_set_prefix(
1027 __isl_take isl_printer *p, const char *prefix);
1028 __isl_give isl_printer *isl_printer_set_suffix(
1029 __isl_take isl_printer *p, const char *suffix);
1031 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1032 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1033 and defaults to C<ISL_FORMAT_ISL>.
1034 Each line in the output is indented by C<indent> (set by
1035 C<isl_printer_set_indent>) spaces
1036 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1037 In the C<PolyLib> format output,
1038 the coefficients of the existentially quantified variables
1039 appear between those of the set variables and those
1041 The function C<isl_printer_indent> increases the indentation
1042 by the specified amount (which may be negative).
1044 To actually print something, use
1046 #include <isl/printer.h>
1047 __isl_give isl_printer *isl_printer_print_double(
1048 __isl_take isl_printer *p, double d);
1050 #include <isl/set.h>
1051 __isl_give isl_printer *isl_printer_print_basic_set(
1052 __isl_take isl_printer *printer,
1053 __isl_keep isl_basic_set *bset);
1054 __isl_give isl_printer *isl_printer_print_set(
1055 __isl_take isl_printer *printer,
1056 __isl_keep isl_set *set);
1058 #include <isl/map.h>
1059 __isl_give isl_printer *isl_printer_print_basic_map(
1060 __isl_take isl_printer *printer,
1061 __isl_keep isl_basic_map *bmap);
1062 __isl_give isl_printer *isl_printer_print_map(
1063 __isl_take isl_printer *printer,
1064 __isl_keep isl_map *map);
1066 #include <isl/union_set.h>
1067 __isl_give isl_printer *isl_printer_print_union_set(
1068 __isl_take isl_printer *p,
1069 __isl_keep isl_union_set *uset);
1071 #include <isl/union_map.h>
1072 __isl_give isl_printer *isl_printer_print_union_map(
1073 __isl_take isl_printer *p,
1074 __isl_keep isl_union_map *umap);
1076 When called on a file printer, the following function flushes
1077 the file. When called on a string printer, the buffer is cleared.
1079 __isl_give isl_printer *isl_printer_flush(
1080 __isl_take isl_printer *p);
1082 =head2 Creating New Sets and Relations
1084 C<isl> has functions for creating some standard sets and relations.
1088 =item * Empty sets and relations
1090 __isl_give isl_basic_set *isl_basic_set_empty(
1091 __isl_take isl_space *space);
1092 __isl_give isl_basic_map *isl_basic_map_empty(
1093 __isl_take isl_space *space);
1094 __isl_give isl_set *isl_set_empty(
1095 __isl_take isl_space *space);
1096 __isl_give isl_map *isl_map_empty(
1097 __isl_take isl_space *space);
1098 __isl_give isl_union_set *isl_union_set_empty(
1099 __isl_take isl_space *space);
1100 __isl_give isl_union_map *isl_union_map_empty(
1101 __isl_take isl_space *space);
1103 For C<isl_union_set>s and C<isl_union_map>s, the space
1104 is only used to specify the parameters.
1106 =item * Universe sets and relations
1108 __isl_give isl_basic_set *isl_basic_set_universe(
1109 __isl_take isl_space *space);
1110 __isl_give isl_basic_map *isl_basic_map_universe(
1111 __isl_take isl_space *space);
1112 __isl_give isl_set *isl_set_universe(
1113 __isl_take isl_space *space);
1114 __isl_give isl_map *isl_map_universe(
1115 __isl_take isl_space *space);
1116 __isl_give isl_union_set *isl_union_set_universe(
1117 __isl_take isl_union_set *uset);
1118 __isl_give isl_union_map *isl_union_map_universe(
1119 __isl_take isl_union_map *umap);
1121 The sets and relations constructed by the functions above
1122 contain all integer values, while those constructed by the
1123 functions below only contain non-negative values.
1125 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1126 __isl_take isl_space *space);
1127 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1128 __isl_take isl_space *space);
1129 __isl_give isl_set *isl_set_nat_universe(
1130 __isl_take isl_space *space);
1131 __isl_give isl_map *isl_map_nat_universe(
1132 __isl_take isl_space *space);
1134 =item * Identity relations
1136 __isl_give isl_basic_map *isl_basic_map_identity(
1137 __isl_take isl_space *space);
1138 __isl_give isl_map *isl_map_identity(
1139 __isl_take isl_space *space);
1141 The number of input and output dimensions in C<space> needs
1144 =item * Lexicographic order
1146 __isl_give isl_map *isl_map_lex_lt(
1147 __isl_take isl_space *set_space);
1148 __isl_give isl_map *isl_map_lex_le(
1149 __isl_take isl_space *set_space);
1150 __isl_give isl_map *isl_map_lex_gt(
1151 __isl_take isl_space *set_space);
1152 __isl_give isl_map *isl_map_lex_ge(
1153 __isl_take isl_space *set_space);
1154 __isl_give isl_map *isl_map_lex_lt_first(
1155 __isl_take isl_space *space, unsigned n);
1156 __isl_give isl_map *isl_map_lex_le_first(
1157 __isl_take isl_space *space, unsigned n);
1158 __isl_give isl_map *isl_map_lex_gt_first(
1159 __isl_take isl_space *space, unsigned n);
1160 __isl_give isl_map *isl_map_lex_ge_first(
1161 __isl_take isl_space *space, unsigned n);
1163 The first four functions take a space for a B<set>
1164 and return relations that express that the elements in the domain
1165 are lexicographically less
1166 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1167 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1168 than the elements in the range.
1169 The last four functions take a space for a map
1170 and return relations that express that the first C<n> dimensions
1171 in the domain are lexicographically less
1172 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1173 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1174 than the first C<n> dimensions in the range.
1178 A basic set or relation can be converted to a set or relation
1179 using the following functions.
1181 __isl_give isl_set *isl_set_from_basic_set(
1182 __isl_take isl_basic_set *bset);
1183 __isl_give isl_map *isl_map_from_basic_map(
1184 __isl_take isl_basic_map *bmap);
1186 Sets and relations can be converted to union sets and relations
1187 using the following functions.
1189 __isl_give isl_union_set *isl_union_set_from_basic_set(
1190 __isl_take isl_basic_set *bset);
1191 __isl_give isl_union_map *isl_union_map_from_basic_map(
1192 __isl_take isl_basic_map *bmap);
1193 __isl_give isl_union_set *isl_union_set_from_set(
1194 __isl_take isl_set *set);
1195 __isl_give isl_union_map *isl_union_map_from_map(
1196 __isl_take isl_map *map);
1198 The inverse conversions below can only be used if the input
1199 union set or relation is known to contain elements in exactly one
1202 __isl_give isl_set *isl_set_from_union_set(
1203 __isl_take isl_union_set *uset);
1204 __isl_give isl_map *isl_map_from_union_map(
1205 __isl_take isl_union_map *umap);
1207 A zero-dimensional set can be constructed on a given parameter domain
1208 using the following function.
1210 __isl_give isl_set *isl_set_from_params(
1211 __isl_take isl_set *set);
1213 Sets and relations can be copied and freed again using the following
1216 __isl_give isl_basic_set *isl_basic_set_copy(
1217 __isl_keep isl_basic_set *bset);
1218 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1219 __isl_give isl_union_set *isl_union_set_copy(
1220 __isl_keep isl_union_set *uset);
1221 __isl_give isl_basic_map *isl_basic_map_copy(
1222 __isl_keep isl_basic_map *bmap);
1223 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1224 __isl_give isl_union_map *isl_union_map_copy(
1225 __isl_keep isl_union_map *umap);
1226 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1227 void *isl_set_free(__isl_take isl_set *set);
1228 void *isl_union_set_free(__isl_take isl_union_set *uset);
1229 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1230 void isl_map_free(__isl_take isl_map *map);
1231 void *isl_union_map_free(__isl_take isl_union_map *umap);
1233 Other sets and relations can be constructed by starting
1234 from a universe set or relation, adding equality and/or
1235 inequality constraints and then projecting out the
1236 existentially quantified variables, if any.
1237 Constraints can be constructed, manipulated and
1238 added to (or removed from) (basic) sets and relations
1239 using the following functions.
1241 #include <isl/constraint.h>
1242 __isl_give isl_constraint *isl_equality_alloc(
1243 __isl_take isl_local_space *ls);
1244 __isl_give isl_constraint *isl_inequality_alloc(
1245 __isl_take isl_local_space *ls);
1246 __isl_give isl_constraint *isl_constraint_set_constant(
1247 __isl_take isl_constraint *constraint, isl_int v);
1248 __isl_give isl_constraint *isl_constraint_set_constant_si(
1249 __isl_take isl_constraint *constraint, int v);
1250 __isl_give isl_constraint *isl_constraint_set_coefficient(
1251 __isl_take isl_constraint *constraint,
1252 enum isl_dim_type type, int pos, isl_int v);
1253 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1254 __isl_take isl_constraint *constraint,
1255 enum isl_dim_type type, int pos, int v);
1256 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1257 __isl_take isl_basic_map *bmap,
1258 __isl_take isl_constraint *constraint);
1259 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1260 __isl_take isl_basic_set *bset,
1261 __isl_take isl_constraint *constraint);
1262 __isl_give isl_map *isl_map_add_constraint(
1263 __isl_take isl_map *map,
1264 __isl_take isl_constraint *constraint);
1265 __isl_give isl_set *isl_set_add_constraint(
1266 __isl_take isl_set *set,
1267 __isl_take isl_constraint *constraint);
1268 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1269 __isl_take isl_basic_set *bset,
1270 __isl_take isl_constraint *constraint);
1272 For example, to create a set containing the even integers
1273 between 10 and 42, you would use the following code.
1276 isl_local_space *ls;
1278 isl_basic_set *bset;
1280 space = isl_space_set_alloc(ctx, 0, 2);
1281 bset = isl_basic_set_universe(isl_space_copy(space));
1282 ls = isl_local_space_from_space(space);
1284 c = isl_equality_alloc(isl_local_space_copy(ls));
1285 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1286 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1287 bset = isl_basic_set_add_constraint(bset, c);
1289 c = isl_inequality_alloc(isl_local_space_copy(ls));
1290 c = isl_constraint_set_constant_si(c, -10);
1291 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1292 bset = isl_basic_set_add_constraint(bset, c);
1294 c = isl_inequality_alloc(ls);
1295 c = isl_constraint_set_constant_si(c, 42);
1296 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1297 bset = isl_basic_set_add_constraint(bset, c);
1299 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1303 isl_basic_set *bset;
1304 bset = isl_basic_set_read_from_str(ctx,
1305 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1307 A basic set or relation can also be constructed from two matrices
1308 describing the equalities and the inequalities.
1310 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1311 __isl_take isl_space *space,
1312 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1313 enum isl_dim_type c1,
1314 enum isl_dim_type c2, enum isl_dim_type c3,
1315 enum isl_dim_type c4);
1316 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1317 __isl_take isl_space *space,
1318 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1319 enum isl_dim_type c1,
1320 enum isl_dim_type c2, enum isl_dim_type c3,
1321 enum isl_dim_type c4, enum isl_dim_type c5);
1323 The C<isl_dim_type> arguments indicate the order in which
1324 different kinds of variables appear in the input matrices
1325 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1326 C<isl_dim_set> and C<isl_dim_div> for sets and
1327 of C<isl_dim_cst>, C<isl_dim_param>,
1328 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1330 A (basic or union) set or relation can also be constructed from a
1331 (union) (piecewise) (multiple) affine expression
1332 or a list of affine expressions
1333 (See L<"Piecewise Quasi Affine Expressions"> and
1334 L<"Piecewise Multiple Quasi Affine Expressions">).
1336 __isl_give isl_basic_map *isl_basic_map_from_aff(
1337 __isl_take isl_aff *aff);
1338 __isl_give isl_map *isl_map_from_aff(
1339 __isl_take isl_aff *aff);
1340 __isl_give isl_set *isl_set_from_pw_aff(
1341 __isl_take isl_pw_aff *pwaff);
1342 __isl_give isl_map *isl_map_from_pw_aff(
1343 __isl_take isl_pw_aff *pwaff);
1344 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1345 __isl_take isl_space *domain_space,
1346 __isl_take isl_aff_list *list);
1347 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1348 __isl_take isl_multi_aff *maff)
1349 __isl_give isl_map *isl_map_from_multi_aff(
1350 __isl_take isl_multi_aff *maff)
1351 __isl_give isl_set *isl_set_from_pw_multi_aff(
1352 __isl_take isl_pw_multi_aff *pma);
1353 __isl_give isl_map *isl_map_from_pw_multi_aff(
1354 __isl_take isl_pw_multi_aff *pma);
1355 __isl_give isl_union_map *
1356 isl_union_map_from_union_pw_multi_aff(
1357 __isl_take isl_union_pw_multi_aff *upma);
1359 The C<domain_dim> argument describes the domain of the resulting
1360 basic relation. It is required because the C<list> may consist
1361 of zero affine expressions.
1363 =head2 Inspecting Sets and Relations
1365 Usually, the user should not have to care about the actual constraints
1366 of the sets and maps, but should instead apply the abstract operations
1367 explained in the following sections.
1368 Occasionally, however, it may be required to inspect the individual
1369 coefficients of the constraints. This section explains how to do so.
1370 In these cases, it may also be useful to have C<isl> compute
1371 an explicit representation of the existentially quantified variables.
1373 __isl_give isl_set *isl_set_compute_divs(
1374 __isl_take isl_set *set);
1375 __isl_give isl_map *isl_map_compute_divs(
1376 __isl_take isl_map *map);
1377 __isl_give isl_union_set *isl_union_set_compute_divs(
1378 __isl_take isl_union_set *uset);
1379 __isl_give isl_union_map *isl_union_map_compute_divs(
1380 __isl_take isl_union_map *umap);
1382 This explicit representation defines the existentially quantified
1383 variables as integer divisions of the other variables, possibly
1384 including earlier existentially quantified variables.
1385 An explicitly represented existentially quantified variable therefore
1386 has a unique value when the values of the other variables are known.
1387 If, furthermore, the same existentials, i.e., existentials
1388 with the same explicit representations, should appear in the
1389 same order in each of the disjuncts of a set or map, then the user should call
1390 either of the following functions.
1392 __isl_give isl_set *isl_set_align_divs(
1393 __isl_take isl_set *set);
1394 __isl_give isl_map *isl_map_align_divs(
1395 __isl_take isl_map *map);
1397 Alternatively, the existentially quantified variables can be removed
1398 using the following functions, which compute an overapproximation.
1400 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1401 __isl_take isl_basic_set *bset);
1402 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1403 __isl_take isl_basic_map *bmap);
1404 __isl_give isl_set *isl_set_remove_divs(
1405 __isl_take isl_set *set);
1406 __isl_give isl_map *isl_map_remove_divs(
1407 __isl_take isl_map *map);
1409 It is also possible to only remove those divs that are defined
1410 in terms of a given range of dimensions or only those for which
1411 no explicit representation is known.
1413 __isl_give isl_basic_set *
1414 isl_basic_set_remove_divs_involving_dims(
1415 __isl_take isl_basic_set *bset,
1416 enum isl_dim_type type,
1417 unsigned first, unsigned n);
1418 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1419 __isl_take isl_set *set, enum isl_dim_type type,
1420 unsigned first, unsigned n);
1421 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1422 __isl_take isl_map *map, enum isl_dim_type type,
1423 unsigned first, unsigned n);
1425 __isl_give isl_set *isl_set_remove_unknown_divs(
1426 __isl_take isl_set *set);
1427 __isl_give isl_map *isl_map_remove_unknown_divs(
1428 __isl_take isl_map *map);
1430 To iterate over all the sets or maps in a union set or map, use
1432 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1433 int (*fn)(__isl_take isl_set *set, void *user),
1435 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1436 int (*fn)(__isl_take isl_map *map, void *user),
1439 The number of sets or maps in a union set or map can be obtained
1442 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1443 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1445 To extract the set or map in a given space from a union, use
1447 __isl_give isl_set *isl_union_set_extract_set(
1448 __isl_keep isl_union_set *uset,
1449 __isl_take isl_space *space);
1450 __isl_give isl_map *isl_union_map_extract_map(
1451 __isl_keep isl_union_map *umap,
1452 __isl_take isl_space *space);
1454 To iterate over all the basic sets or maps in a set or map, use
1456 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1457 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1459 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1460 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1463 The callback function C<fn> should return 0 if successful and
1464 -1 if an error occurs. In the latter case, or if any other error
1465 occurs, the above functions will return -1.
1467 It should be noted that C<isl> does not guarantee that
1468 the basic sets or maps passed to C<fn> are disjoint.
1469 If this is required, then the user should call one of
1470 the following functions first.
1472 __isl_give isl_set *isl_set_make_disjoint(
1473 __isl_take isl_set *set);
1474 __isl_give isl_map *isl_map_make_disjoint(
1475 __isl_take isl_map *map);
1477 The number of basic sets in a set can be obtained
1480 int isl_set_n_basic_set(__isl_keep isl_set *set);
1482 To iterate over the constraints of a basic set or map, use
1484 #include <isl/constraint.h>
1486 int isl_basic_set_n_constraint(
1487 __isl_keep isl_basic_set *bset);
1488 int isl_basic_set_foreach_constraint(
1489 __isl_keep isl_basic_set *bset,
1490 int (*fn)(__isl_take isl_constraint *c, void *user),
1492 int isl_basic_map_foreach_constraint(
1493 __isl_keep isl_basic_map *bmap,
1494 int (*fn)(__isl_take isl_constraint *c, void *user),
1496 void *isl_constraint_free(__isl_take isl_constraint *c);
1498 Again, the callback function C<fn> should return 0 if successful and
1499 -1 if an error occurs. In the latter case, or if any other error
1500 occurs, the above functions will return -1.
1501 The constraint C<c> represents either an equality or an inequality.
1502 Use the following function to find out whether a constraint
1503 represents an equality. If not, it represents an inequality.
1505 int isl_constraint_is_equality(
1506 __isl_keep isl_constraint *constraint);
1508 The coefficients of the constraints can be inspected using
1509 the following functions.
1511 int isl_constraint_is_lower_bound(
1512 __isl_keep isl_constraint *constraint,
1513 enum isl_dim_type type, unsigned pos);
1514 int isl_constraint_is_upper_bound(
1515 __isl_keep isl_constraint *constraint,
1516 enum isl_dim_type type, unsigned pos);
1517 void isl_constraint_get_constant(
1518 __isl_keep isl_constraint *constraint, isl_int *v);
1519 void isl_constraint_get_coefficient(
1520 __isl_keep isl_constraint *constraint,
1521 enum isl_dim_type type, int pos, isl_int *v);
1522 int isl_constraint_involves_dims(
1523 __isl_keep isl_constraint *constraint,
1524 enum isl_dim_type type, unsigned first, unsigned n);
1526 The explicit representations of the existentially quantified
1527 variables can be inspected using the following function.
1528 Note that the user is only allowed to use this function
1529 if the inspected set or map is the result of a call
1530 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1531 The existentially quantified variable is equal to the floor
1532 of the returned affine expression. The affine expression
1533 itself can be inspected using the functions in
1534 L<"Piecewise Quasi Affine Expressions">.
1536 __isl_give isl_aff *isl_constraint_get_div(
1537 __isl_keep isl_constraint *constraint, int pos);
1539 To obtain the constraints of a basic set or map in matrix
1540 form, use the following functions.
1542 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1543 __isl_keep isl_basic_set *bset,
1544 enum isl_dim_type c1, enum isl_dim_type c2,
1545 enum isl_dim_type c3, enum isl_dim_type c4);
1546 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1547 __isl_keep isl_basic_set *bset,
1548 enum isl_dim_type c1, enum isl_dim_type c2,
1549 enum isl_dim_type c3, enum isl_dim_type c4);
1550 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1551 __isl_keep isl_basic_map *bmap,
1552 enum isl_dim_type c1,
1553 enum isl_dim_type c2, enum isl_dim_type c3,
1554 enum isl_dim_type c4, enum isl_dim_type c5);
1555 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1556 __isl_keep isl_basic_map *bmap,
1557 enum isl_dim_type c1,
1558 enum isl_dim_type c2, enum isl_dim_type c3,
1559 enum isl_dim_type c4, enum isl_dim_type c5);
1561 The C<isl_dim_type> arguments dictate the order in which
1562 different kinds of variables appear in the resulting matrix
1563 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1564 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1566 The number of parameters, input, output or set dimensions can
1567 be obtained using the following functions.
1569 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1570 enum isl_dim_type type);
1571 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1572 enum isl_dim_type type);
1573 unsigned isl_set_dim(__isl_keep isl_set *set,
1574 enum isl_dim_type type);
1575 unsigned isl_map_dim(__isl_keep isl_map *map,
1576 enum isl_dim_type type);
1578 To check whether the description of a set or relation depends
1579 on one or more given dimensions, it is not necessary to iterate over all
1580 constraints. Instead the following functions can be used.
1582 int isl_basic_set_involves_dims(
1583 __isl_keep isl_basic_set *bset,
1584 enum isl_dim_type type, unsigned first, unsigned n);
1585 int isl_set_involves_dims(__isl_keep isl_set *set,
1586 enum isl_dim_type type, unsigned first, unsigned n);
1587 int isl_basic_map_involves_dims(
1588 __isl_keep isl_basic_map *bmap,
1589 enum isl_dim_type type, unsigned first, unsigned n);
1590 int isl_map_involves_dims(__isl_keep isl_map *map,
1591 enum isl_dim_type type, unsigned first, unsigned n);
1593 Similarly, the following functions can be used to check whether
1594 a given dimension is involved in any lower or upper bound.
1596 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1597 enum isl_dim_type type, unsigned pos);
1598 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1599 enum isl_dim_type type, unsigned pos);
1601 The identifiers or names of the domain and range spaces of a set
1602 or relation can be read off or set using the following functions.
1604 __isl_give isl_set *isl_set_set_tuple_id(
1605 __isl_take isl_set *set, __isl_take isl_id *id);
1606 __isl_give isl_set *isl_set_reset_tuple_id(
1607 __isl_take isl_set *set);
1608 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1609 __isl_give isl_id *isl_set_get_tuple_id(
1610 __isl_keep isl_set *set);
1611 __isl_give isl_map *isl_map_set_tuple_id(
1612 __isl_take isl_map *map, enum isl_dim_type type,
1613 __isl_take isl_id *id);
1614 __isl_give isl_map *isl_map_reset_tuple_id(
1615 __isl_take isl_map *map, enum isl_dim_type type);
1616 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1617 enum isl_dim_type type);
1618 __isl_give isl_id *isl_map_get_tuple_id(
1619 __isl_keep isl_map *map, enum isl_dim_type type);
1621 const char *isl_basic_set_get_tuple_name(
1622 __isl_keep isl_basic_set *bset);
1623 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1624 __isl_take isl_basic_set *set, const char *s);
1625 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1626 const char *isl_set_get_tuple_name(
1627 __isl_keep isl_set *set);
1628 const char *isl_basic_map_get_tuple_name(
1629 __isl_keep isl_basic_map *bmap,
1630 enum isl_dim_type type);
1631 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1632 __isl_take isl_basic_map *bmap,
1633 enum isl_dim_type type, const char *s);
1634 const char *isl_map_get_tuple_name(
1635 __isl_keep isl_map *map,
1636 enum isl_dim_type type);
1638 As with C<isl_space_get_tuple_name>, the value returned points to
1639 an internal data structure.
1640 The identifiers, positions or names of individual dimensions can be
1641 read off using the following functions.
1643 __isl_give isl_id *isl_basic_set_get_dim_id(
1644 __isl_keep isl_basic_set *bset,
1645 enum isl_dim_type type, unsigned pos);
1646 __isl_give isl_set *isl_set_set_dim_id(
1647 __isl_take isl_set *set, enum isl_dim_type type,
1648 unsigned pos, __isl_take isl_id *id);
1649 int isl_set_has_dim_id(__isl_keep isl_set *set,
1650 enum isl_dim_type type, unsigned pos);
1651 __isl_give isl_id *isl_set_get_dim_id(
1652 __isl_keep isl_set *set, enum isl_dim_type type,
1654 int isl_basic_map_has_dim_id(
1655 __isl_keep isl_basic_map *bmap,
1656 enum isl_dim_type type, unsigned pos);
1657 __isl_give isl_map *isl_map_set_dim_id(
1658 __isl_take isl_map *map, enum isl_dim_type type,
1659 unsigned pos, __isl_take isl_id *id);
1660 int isl_map_has_dim_id(__isl_keep isl_map *map,
1661 enum isl_dim_type type, unsigned pos);
1662 __isl_give isl_id *isl_map_get_dim_id(
1663 __isl_keep isl_map *map, enum isl_dim_type type,
1666 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1667 enum isl_dim_type type, __isl_keep isl_id *id);
1668 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1669 enum isl_dim_type type, __isl_keep isl_id *id);
1670 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1671 enum isl_dim_type type, const char *name);
1672 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1673 enum isl_dim_type type, const char *name);
1675 const char *isl_constraint_get_dim_name(
1676 __isl_keep isl_constraint *constraint,
1677 enum isl_dim_type type, unsigned pos);
1678 const char *isl_basic_set_get_dim_name(
1679 __isl_keep isl_basic_set *bset,
1680 enum isl_dim_type type, unsigned pos);
1681 int isl_set_has_dim_name(__isl_keep isl_set *set,
1682 enum isl_dim_type type, unsigned pos);
1683 const char *isl_set_get_dim_name(
1684 __isl_keep isl_set *set,
1685 enum isl_dim_type type, unsigned pos);
1686 const char *isl_basic_map_get_dim_name(
1687 __isl_keep isl_basic_map *bmap,
1688 enum isl_dim_type type, unsigned pos);
1689 int isl_map_has_dim_name(__isl_keep isl_map *map,
1690 enum isl_dim_type type, unsigned pos);
1691 const char *isl_map_get_dim_name(
1692 __isl_keep isl_map *map,
1693 enum isl_dim_type type, unsigned pos);
1695 These functions are mostly useful to obtain the identifiers, positions
1696 or names of the parameters. Identifiers of individual dimensions are
1697 essentially only useful for printing. They are ignored by all other
1698 operations and may not be preserved across those operations.
1702 =head3 Unary Properties
1708 The following functions test whether the given set or relation
1709 contains any integer points. The ``plain'' variants do not perform
1710 any computations, but simply check if the given set or relation
1711 is already known to be empty.
1713 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1714 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1715 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1716 int isl_set_is_empty(__isl_keep isl_set *set);
1717 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1718 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1719 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1720 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1721 int isl_map_is_empty(__isl_keep isl_map *map);
1722 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1724 =item * Universality
1726 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1727 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1728 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1730 =item * Single-valuedness
1732 int isl_basic_map_is_single_valued(
1733 __isl_keep isl_basic_map *bmap);
1734 int isl_map_plain_is_single_valued(
1735 __isl_keep isl_map *map);
1736 int isl_map_is_single_valued(__isl_keep isl_map *map);
1737 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1741 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1742 int isl_map_is_injective(__isl_keep isl_map *map);
1743 int isl_union_map_plain_is_injective(
1744 __isl_keep isl_union_map *umap);
1745 int isl_union_map_is_injective(
1746 __isl_keep isl_union_map *umap);
1750 int isl_map_is_bijective(__isl_keep isl_map *map);
1751 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1755 int isl_basic_map_plain_is_fixed(
1756 __isl_keep isl_basic_map *bmap,
1757 enum isl_dim_type type, unsigned pos,
1759 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1760 enum isl_dim_type type, unsigned pos,
1762 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1763 enum isl_dim_type type, unsigned pos,
1766 Check if the relation obviously lies on a hyperplane where the given dimension
1767 has a fixed value and if so, return that value in C<*val>.
1771 To check whether a set is a parameter domain, use this function:
1773 int isl_set_is_params(__isl_keep isl_set *set);
1774 int isl_union_set_is_params(
1775 __isl_keep isl_union_set *uset);
1779 The following functions check whether the domain of the given
1780 (basic) set is a wrapped relation.
1782 int isl_basic_set_is_wrapping(
1783 __isl_keep isl_basic_set *bset);
1784 int isl_set_is_wrapping(__isl_keep isl_set *set);
1786 =item * Internal Product
1788 int isl_basic_map_can_zip(
1789 __isl_keep isl_basic_map *bmap);
1790 int isl_map_can_zip(__isl_keep isl_map *map);
1792 Check whether the product of domain and range of the given relation
1794 i.e., whether both domain and range are nested relations.
1798 int isl_basic_map_can_curry(
1799 __isl_keep isl_basic_map *bmap);
1800 int isl_map_can_curry(__isl_keep isl_map *map);
1802 Check whether the domain of the (basic) relation is a wrapped relation.
1806 =head3 Binary Properties
1812 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1813 __isl_keep isl_set *set2);
1814 int isl_set_is_equal(__isl_keep isl_set *set1,
1815 __isl_keep isl_set *set2);
1816 int isl_union_set_is_equal(
1817 __isl_keep isl_union_set *uset1,
1818 __isl_keep isl_union_set *uset2);
1819 int isl_basic_map_is_equal(
1820 __isl_keep isl_basic_map *bmap1,
1821 __isl_keep isl_basic_map *bmap2);
1822 int isl_map_is_equal(__isl_keep isl_map *map1,
1823 __isl_keep isl_map *map2);
1824 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1825 __isl_keep isl_map *map2);
1826 int isl_union_map_is_equal(
1827 __isl_keep isl_union_map *umap1,
1828 __isl_keep isl_union_map *umap2);
1830 =item * Disjointness
1832 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1833 __isl_keep isl_set *set2);
1837 int isl_basic_set_is_subset(
1838 __isl_keep isl_basic_set *bset1,
1839 __isl_keep isl_basic_set *bset2);
1840 int isl_set_is_subset(__isl_keep isl_set *set1,
1841 __isl_keep isl_set *set2);
1842 int isl_set_is_strict_subset(
1843 __isl_keep isl_set *set1,
1844 __isl_keep isl_set *set2);
1845 int isl_union_set_is_subset(
1846 __isl_keep isl_union_set *uset1,
1847 __isl_keep isl_union_set *uset2);
1848 int isl_union_set_is_strict_subset(
1849 __isl_keep isl_union_set *uset1,
1850 __isl_keep isl_union_set *uset2);
1851 int isl_basic_map_is_subset(
1852 __isl_keep isl_basic_map *bmap1,
1853 __isl_keep isl_basic_map *bmap2);
1854 int isl_basic_map_is_strict_subset(
1855 __isl_keep isl_basic_map *bmap1,
1856 __isl_keep isl_basic_map *bmap2);
1857 int isl_map_is_subset(
1858 __isl_keep isl_map *map1,
1859 __isl_keep isl_map *map2);
1860 int isl_map_is_strict_subset(
1861 __isl_keep isl_map *map1,
1862 __isl_keep isl_map *map2);
1863 int isl_union_map_is_subset(
1864 __isl_keep isl_union_map *umap1,
1865 __isl_keep isl_union_map *umap2);
1866 int isl_union_map_is_strict_subset(
1867 __isl_keep isl_union_map *umap1,
1868 __isl_keep isl_union_map *umap2);
1870 Check whether the first argument is a (strict) subset of the
1875 =head2 Unary Operations
1881 __isl_give isl_set *isl_set_complement(
1882 __isl_take isl_set *set);
1883 __isl_give isl_map *isl_map_complement(
1884 __isl_take isl_map *map);
1888 __isl_give isl_basic_map *isl_basic_map_reverse(
1889 __isl_take isl_basic_map *bmap);
1890 __isl_give isl_map *isl_map_reverse(
1891 __isl_take isl_map *map);
1892 __isl_give isl_union_map *isl_union_map_reverse(
1893 __isl_take isl_union_map *umap);
1897 __isl_give isl_basic_set *isl_basic_set_project_out(
1898 __isl_take isl_basic_set *bset,
1899 enum isl_dim_type type, unsigned first, unsigned n);
1900 __isl_give isl_basic_map *isl_basic_map_project_out(
1901 __isl_take isl_basic_map *bmap,
1902 enum isl_dim_type type, unsigned first, unsigned n);
1903 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1904 enum isl_dim_type type, unsigned first, unsigned n);
1905 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1906 enum isl_dim_type type, unsigned first, unsigned n);
1907 __isl_give isl_basic_set *isl_basic_set_params(
1908 __isl_take isl_basic_set *bset);
1909 __isl_give isl_basic_set *isl_basic_map_domain(
1910 __isl_take isl_basic_map *bmap);
1911 __isl_give isl_basic_set *isl_basic_map_range(
1912 __isl_take isl_basic_map *bmap);
1913 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1914 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1915 __isl_give isl_set *isl_map_domain(
1916 __isl_take isl_map *bmap);
1917 __isl_give isl_set *isl_map_range(
1918 __isl_take isl_map *map);
1919 __isl_give isl_set *isl_union_set_params(
1920 __isl_take isl_union_set *uset);
1921 __isl_give isl_set *isl_union_map_params(
1922 __isl_take isl_union_map *umap);
1923 __isl_give isl_union_set *isl_union_map_domain(
1924 __isl_take isl_union_map *umap);
1925 __isl_give isl_union_set *isl_union_map_range(
1926 __isl_take isl_union_map *umap);
1928 __isl_give isl_basic_map *isl_basic_map_domain_map(
1929 __isl_take isl_basic_map *bmap);
1930 __isl_give isl_basic_map *isl_basic_map_range_map(
1931 __isl_take isl_basic_map *bmap);
1932 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1933 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1934 __isl_give isl_union_map *isl_union_map_domain_map(
1935 __isl_take isl_union_map *umap);
1936 __isl_give isl_union_map *isl_union_map_range_map(
1937 __isl_take isl_union_map *umap);
1939 The functions above construct a (basic, regular or union) relation
1940 that maps (a wrapped version of) the input relation to its domain or range.
1944 __isl_give isl_basic_set *isl_basic_set_eliminate(
1945 __isl_take isl_basic_set *bset,
1946 enum isl_dim_type type,
1947 unsigned first, unsigned n);
1948 __isl_give isl_set *isl_set_eliminate(
1949 __isl_take isl_set *set, enum isl_dim_type type,
1950 unsigned first, unsigned n);
1951 __isl_give isl_basic_map *isl_basic_map_eliminate(
1952 __isl_take isl_basic_map *bmap,
1953 enum isl_dim_type type,
1954 unsigned first, unsigned n);
1955 __isl_give isl_map *isl_map_eliminate(
1956 __isl_take isl_map *map, enum isl_dim_type type,
1957 unsigned first, unsigned n);
1959 Eliminate the coefficients for the given dimensions from the constraints,
1960 without removing the dimensions.
1964 __isl_give isl_basic_set *isl_basic_set_fix(
1965 __isl_take isl_basic_set *bset,
1966 enum isl_dim_type type, unsigned pos,
1968 __isl_give isl_basic_set *isl_basic_set_fix_si(
1969 __isl_take isl_basic_set *bset,
1970 enum isl_dim_type type, unsigned pos, int value);
1971 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1972 enum isl_dim_type type, unsigned pos,
1974 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1975 enum isl_dim_type type, unsigned pos, int value);
1976 __isl_give isl_basic_map *isl_basic_map_fix_si(
1977 __isl_take isl_basic_map *bmap,
1978 enum isl_dim_type type, unsigned pos, int value);
1979 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1980 enum isl_dim_type type, unsigned pos, int value);
1982 Intersect the set or relation with the hyperplane where the given
1983 dimension has the fixed given value.
1985 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1986 __isl_take isl_basic_map *bmap,
1987 enum isl_dim_type type, unsigned pos, int value);
1988 __isl_give isl_set *isl_set_lower_bound(
1989 __isl_take isl_set *set,
1990 enum isl_dim_type type, unsigned pos,
1992 __isl_give isl_set *isl_set_lower_bound_si(
1993 __isl_take isl_set *set,
1994 enum isl_dim_type type, unsigned pos, int value);
1995 __isl_give isl_map *isl_map_lower_bound_si(
1996 __isl_take isl_map *map,
1997 enum isl_dim_type type, unsigned pos, int value);
1998 __isl_give isl_set *isl_set_upper_bound(
1999 __isl_take isl_set *set,
2000 enum isl_dim_type type, unsigned pos,
2002 __isl_give isl_set *isl_set_upper_bound_si(
2003 __isl_take isl_set *set,
2004 enum isl_dim_type type, unsigned pos, int value);
2005 __isl_give isl_map *isl_map_upper_bound_si(
2006 __isl_take isl_map *map,
2007 enum isl_dim_type type, unsigned pos, int value);
2009 Intersect the set or relation with the half-space where the given
2010 dimension has a value bounded by the fixed given value.
2012 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2013 enum isl_dim_type type1, int pos1,
2014 enum isl_dim_type type2, int pos2);
2015 __isl_give isl_basic_map *isl_basic_map_equate(
2016 __isl_take isl_basic_map *bmap,
2017 enum isl_dim_type type1, int pos1,
2018 enum isl_dim_type type2, int pos2);
2019 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2020 enum isl_dim_type type1, int pos1,
2021 enum isl_dim_type type2, int pos2);
2023 Intersect the set or relation with the hyperplane where the given
2024 dimensions are equal to each other.
2026 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2027 enum isl_dim_type type1, int pos1,
2028 enum isl_dim_type type2, int pos2);
2030 Intersect the relation with the hyperplane where the given
2031 dimensions have opposite values.
2033 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2034 enum isl_dim_type type1, int pos1,
2035 enum isl_dim_type type2, int pos2);
2036 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2037 enum isl_dim_type type1, int pos1,
2038 enum isl_dim_type type2, int pos2);
2040 Intersect the relation with the half-space where the given
2041 dimensions satisfy the given ordering.
2045 __isl_give isl_map *isl_set_identity(
2046 __isl_take isl_set *set);
2047 __isl_give isl_union_map *isl_union_set_identity(
2048 __isl_take isl_union_set *uset);
2050 Construct an identity relation on the given (union) set.
2054 __isl_give isl_basic_set *isl_basic_map_deltas(
2055 __isl_take isl_basic_map *bmap);
2056 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2057 __isl_give isl_union_set *isl_union_map_deltas(
2058 __isl_take isl_union_map *umap);
2060 These functions return a (basic) set containing the differences
2061 between image elements and corresponding domain elements in the input.
2063 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2064 __isl_take isl_basic_map *bmap);
2065 __isl_give isl_map *isl_map_deltas_map(
2066 __isl_take isl_map *map);
2067 __isl_give isl_union_map *isl_union_map_deltas_map(
2068 __isl_take isl_union_map *umap);
2070 The functions above construct a (basic, regular or union) relation
2071 that maps (a wrapped version of) the input relation to its delta set.
2075 Simplify the representation of a set or relation by trying
2076 to combine pairs of basic sets or relations into a single
2077 basic set or relation.
2079 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2080 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2081 __isl_give isl_union_set *isl_union_set_coalesce(
2082 __isl_take isl_union_set *uset);
2083 __isl_give isl_union_map *isl_union_map_coalesce(
2084 __isl_take isl_union_map *umap);
2086 One of the methods for combining pairs of basic sets or relations
2087 can result in coefficients that are much larger than those that appear
2088 in the constraints of the input. By default, the coefficients are
2089 not allowed to grow larger, but this can be changed by unsetting
2090 the following option.
2092 int isl_options_set_coalesce_bounded_wrapping(
2093 isl_ctx *ctx, int val);
2094 int isl_options_get_coalesce_bounded_wrapping(
2097 =item * Detecting equalities
2099 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2100 __isl_take isl_basic_set *bset);
2101 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2102 __isl_take isl_basic_map *bmap);
2103 __isl_give isl_set *isl_set_detect_equalities(
2104 __isl_take isl_set *set);
2105 __isl_give isl_map *isl_map_detect_equalities(
2106 __isl_take isl_map *map);
2107 __isl_give isl_union_set *isl_union_set_detect_equalities(
2108 __isl_take isl_union_set *uset);
2109 __isl_give isl_union_map *isl_union_map_detect_equalities(
2110 __isl_take isl_union_map *umap);
2112 Simplify the representation of a set or relation by detecting implicit
2115 =item * Removing redundant constraints
2117 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2118 __isl_take isl_basic_set *bset);
2119 __isl_give isl_set *isl_set_remove_redundancies(
2120 __isl_take isl_set *set);
2121 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2122 __isl_take isl_basic_map *bmap);
2123 __isl_give isl_map *isl_map_remove_redundancies(
2124 __isl_take isl_map *map);
2128 __isl_give isl_basic_set *isl_set_convex_hull(
2129 __isl_take isl_set *set);
2130 __isl_give isl_basic_map *isl_map_convex_hull(
2131 __isl_take isl_map *map);
2133 If the input set or relation has any existentially quantified
2134 variables, then the result of these operations is currently undefined.
2138 __isl_give isl_basic_set *isl_set_simple_hull(
2139 __isl_take isl_set *set);
2140 __isl_give isl_basic_map *isl_map_simple_hull(
2141 __isl_take isl_map *map);
2142 __isl_give isl_union_map *isl_union_map_simple_hull(
2143 __isl_take isl_union_map *umap);
2145 These functions compute a single basic set or relation
2146 that contains the whole input set or relation.
2147 In particular, the output is described by translates
2148 of the constraints describing the basic sets or relations in the input.
2152 (See \autoref{s:simple hull}.)
2158 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2159 __isl_take isl_basic_set *bset);
2160 __isl_give isl_basic_set *isl_set_affine_hull(
2161 __isl_take isl_set *set);
2162 __isl_give isl_union_set *isl_union_set_affine_hull(
2163 __isl_take isl_union_set *uset);
2164 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2165 __isl_take isl_basic_map *bmap);
2166 __isl_give isl_basic_map *isl_map_affine_hull(
2167 __isl_take isl_map *map);
2168 __isl_give isl_union_map *isl_union_map_affine_hull(
2169 __isl_take isl_union_map *umap);
2171 In case of union sets and relations, the affine hull is computed
2174 =item * Polyhedral hull
2176 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2177 __isl_take isl_set *set);
2178 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2179 __isl_take isl_map *map);
2180 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2181 __isl_take isl_union_set *uset);
2182 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2183 __isl_take isl_union_map *umap);
2185 These functions compute a single basic set or relation
2186 not involving any existentially quantified variables
2187 that contains the whole input set or relation.
2188 In case of union sets and relations, the polyhedral hull is computed
2193 __isl_give isl_basic_set *isl_basic_set_sample(
2194 __isl_take isl_basic_set *bset);
2195 __isl_give isl_basic_set *isl_set_sample(
2196 __isl_take isl_set *set);
2197 __isl_give isl_basic_map *isl_basic_map_sample(
2198 __isl_take isl_basic_map *bmap);
2199 __isl_give isl_basic_map *isl_map_sample(
2200 __isl_take isl_map *map);
2202 If the input (basic) set or relation is non-empty, then return
2203 a singleton subset of the input. Otherwise, return an empty set.
2205 =item * Optimization
2207 #include <isl/ilp.h>
2208 enum isl_lp_result isl_basic_set_max(
2209 __isl_keep isl_basic_set *bset,
2210 __isl_keep isl_aff *obj, isl_int *opt)
2211 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2212 __isl_keep isl_aff *obj, isl_int *opt);
2213 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2214 __isl_keep isl_aff *obj, isl_int *opt);
2216 Compute the minimum or maximum of the integer affine expression C<obj>
2217 over the points in C<set>, returning the result in C<opt>.
2218 The return value may be one of C<isl_lp_error>,
2219 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2221 =item * Parametric optimization
2223 __isl_give isl_pw_aff *isl_set_dim_min(
2224 __isl_take isl_set *set, int pos);
2225 __isl_give isl_pw_aff *isl_set_dim_max(
2226 __isl_take isl_set *set, int pos);
2227 __isl_give isl_pw_aff *isl_map_dim_max(
2228 __isl_take isl_map *map, int pos);
2230 Compute the minimum or maximum of the given set or output dimension
2231 as a function of the parameters (and input dimensions), but independently
2232 of the other set or output dimensions.
2233 For lexicographic optimization, see L<"Lexicographic Optimization">.
2237 The following functions compute either the set of (rational) coefficient
2238 values of valid constraints for the given set or the set of (rational)
2239 values satisfying the constraints with coefficients from the given set.
2240 Internally, these two sets of functions perform essentially the
2241 same operations, except that the set of coefficients is assumed to
2242 be a cone, while the set of values may be any polyhedron.
2243 The current implementation is based on the Farkas lemma and
2244 Fourier-Motzkin elimination, but this may change or be made optional
2245 in future. In particular, future implementations may use different
2246 dualization algorithms or skip the elimination step.
2248 __isl_give isl_basic_set *isl_basic_set_coefficients(
2249 __isl_take isl_basic_set *bset);
2250 __isl_give isl_basic_set *isl_set_coefficients(
2251 __isl_take isl_set *set);
2252 __isl_give isl_union_set *isl_union_set_coefficients(
2253 __isl_take isl_union_set *bset);
2254 __isl_give isl_basic_set *isl_basic_set_solutions(
2255 __isl_take isl_basic_set *bset);
2256 __isl_give isl_basic_set *isl_set_solutions(
2257 __isl_take isl_set *set);
2258 __isl_give isl_union_set *isl_union_set_solutions(
2259 __isl_take isl_union_set *bset);
2263 __isl_give isl_map *isl_map_fixed_power(
2264 __isl_take isl_map *map, isl_int exp);
2265 __isl_give isl_union_map *isl_union_map_fixed_power(
2266 __isl_take isl_union_map *umap, isl_int exp);
2268 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2269 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2270 of C<map> is computed.
2272 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2274 __isl_give isl_union_map *isl_union_map_power(
2275 __isl_take isl_union_map *umap, int *exact);
2277 Compute a parametric representation for all positive powers I<k> of C<map>.
2278 The result maps I<k> to a nested relation corresponding to the
2279 I<k>th power of C<map>.
2280 The result may be an overapproximation. If the result is known to be exact,
2281 then C<*exact> is set to C<1>.
2283 =item * Transitive closure
2285 __isl_give isl_map *isl_map_transitive_closure(
2286 __isl_take isl_map *map, int *exact);
2287 __isl_give isl_union_map *isl_union_map_transitive_closure(
2288 __isl_take isl_union_map *umap, int *exact);
2290 Compute the transitive closure of C<map>.
2291 The result may be an overapproximation. If the result is known to be exact,
2292 then C<*exact> is set to C<1>.
2294 =item * Reaching path lengths
2296 __isl_give isl_map *isl_map_reaching_path_lengths(
2297 __isl_take isl_map *map, int *exact);
2299 Compute a relation that maps each element in the range of C<map>
2300 to the lengths of all paths composed of edges in C<map> that
2301 end up in the given element.
2302 The result may be an overapproximation. If the result is known to be exact,
2303 then C<*exact> is set to C<1>.
2304 To compute the I<maximal> path length, the resulting relation
2305 should be postprocessed by C<isl_map_lexmax>.
2306 In particular, if the input relation is a dependence relation
2307 (mapping sources to sinks), then the maximal path length corresponds
2308 to the free schedule.
2309 Note, however, that C<isl_map_lexmax> expects the maximum to be
2310 finite, so if the path lengths are unbounded (possibly due to
2311 the overapproximation), then you will get an error message.
2315 __isl_give isl_basic_set *isl_basic_map_wrap(
2316 __isl_take isl_basic_map *bmap);
2317 __isl_give isl_set *isl_map_wrap(
2318 __isl_take isl_map *map);
2319 __isl_give isl_union_set *isl_union_map_wrap(
2320 __isl_take isl_union_map *umap);
2321 __isl_give isl_basic_map *isl_basic_set_unwrap(
2322 __isl_take isl_basic_set *bset);
2323 __isl_give isl_map *isl_set_unwrap(
2324 __isl_take isl_set *set);
2325 __isl_give isl_union_map *isl_union_set_unwrap(
2326 __isl_take isl_union_set *uset);
2330 Remove any internal structure of domain (and range) of the given
2331 set or relation. If there is any such internal structure in the input,
2332 then the name of the space is also removed.
2334 __isl_give isl_basic_set *isl_basic_set_flatten(
2335 __isl_take isl_basic_set *bset);
2336 __isl_give isl_set *isl_set_flatten(
2337 __isl_take isl_set *set);
2338 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2339 __isl_take isl_basic_map *bmap);
2340 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2341 __isl_take isl_basic_map *bmap);
2342 __isl_give isl_map *isl_map_flatten_range(
2343 __isl_take isl_map *map);
2344 __isl_give isl_map *isl_map_flatten_domain(
2345 __isl_take isl_map *map);
2346 __isl_give isl_basic_map *isl_basic_map_flatten(
2347 __isl_take isl_basic_map *bmap);
2348 __isl_give isl_map *isl_map_flatten(
2349 __isl_take isl_map *map);
2351 __isl_give isl_map *isl_set_flatten_map(
2352 __isl_take isl_set *set);
2354 The function above constructs a relation
2355 that maps the input set to a flattened version of the set.
2359 Lift the input set to a space with extra dimensions corresponding
2360 to the existentially quantified variables in the input.
2361 In particular, the result lives in a wrapped map where the domain
2362 is the original space and the range corresponds to the original
2363 existentially quantified variables.
2365 __isl_give isl_basic_set *isl_basic_set_lift(
2366 __isl_take isl_basic_set *bset);
2367 __isl_give isl_set *isl_set_lift(
2368 __isl_take isl_set *set);
2369 __isl_give isl_union_set *isl_union_set_lift(
2370 __isl_take isl_union_set *uset);
2372 Given a local space that contains the existentially quantified
2373 variables of a set, a basic relation that, when applied to
2374 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2375 can be constructed using the following function.
2377 #include <isl/local_space.h>
2378 __isl_give isl_basic_map *isl_local_space_lifting(
2379 __isl_take isl_local_space *ls);
2381 =item * Internal Product
2383 __isl_give isl_basic_map *isl_basic_map_zip(
2384 __isl_take isl_basic_map *bmap);
2385 __isl_give isl_map *isl_map_zip(
2386 __isl_take isl_map *map);
2387 __isl_give isl_union_map *isl_union_map_zip(
2388 __isl_take isl_union_map *umap);
2390 Given a relation with nested relations for domain and range,
2391 interchange the range of the domain with the domain of the range.
2395 __isl_give isl_basic_map *isl_basic_map_curry(
2396 __isl_take isl_basic_map *bmap);
2397 __isl_give isl_map *isl_map_curry(
2398 __isl_take isl_map *map);
2399 __isl_give isl_union_map *isl_union_map_curry(
2400 __isl_take isl_union_map *umap);
2402 Given a relation with a nested relation for domain,
2403 move the range of the nested relation out of the domain
2404 and use it as the domain of a nested relation in the range,
2405 with the original range as range of this nested relation.
2407 =item * Aligning parameters
2409 __isl_give isl_basic_set *isl_basic_set_align_params(
2410 __isl_take isl_basic_set *bset,
2411 __isl_take isl_space *model);
2412 __isl_give isl_set *isl_set_align_params(
2413 __isl_take isl_set *set,
2414 __isl_take isl_space *model);
2415 __isl_give isl_basic_map *isl_basic_map_align_params(
2416 __isl_take isl_basic_map *bmap,
2417 __isl_take isl_space *model);
2418 __isl_give isl_map *isl_map_align_params(
2419 __isl_take isl_map *map,
2420 __isl_take isl_space *model);
2422 Change the order of the parameters of the given set or relation
2423 such that the first parameters match those of C<model>.
2424 This may involve the introduction of extra parameters.
2425 All parameters need to be named.
2427 =item * Dimension manipulation
2429 __isl_give isl_set *isl_set_add_dims(
2430 __isl_take isl_set *set,
2431 enum isl_dim_type type, unsigned n);
2432 __isl_give isl_map *isl_map_add_dims(
2433 __isl_take isl_map *map,
2434 enum isl_dim_type type, unsigned n);
2435 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2436 __isl_take isl_basic_set *bset,
2437 enum isl_dim_type type, unsigned pos,
2439 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2440 __isl_take isl_basic_map *bmap,
2441 enum isl_dim_type type, unsigned pos,
2443 __isl_give isl_set *isl_set_insert_dims(
2444 __isl_take isl_set *set,
2445 enum isl_dim_type type, unsigned pos, unsigned n);
2446 __isl_give isl_map *isl_map_insert_dims(
2447 __isl_take isl_map *map,
2448 enum isl_dim_type type, unsigned pos, unsigned n);
2449 __isl_give isl_basic_set *isl_basic_set_move_dims(
2450 __isl_take isl_basic_set *bset,
2451 enum isl_dim_type dst_type, unsigned dst_pos,
2452 enum isl_dim_type src_type, unsigned src_pos,
2454 __isl_give isl_basic_map *isl_basic_map_move_dims(
2455 __isl_take isl_basic_map *bmap,
2456 enum isl_dim_type dst_type, unsigned dst_pos,
2457 enum isl_dim_type src_type, unsigned src_pos,
2459 __isl_give isl_set *isl_set_move_dims(
2460 __isl_take isl_set *set,
2461 enum isl_dim_type dst_type, unsigned dst_pos,
2462 enum isl_dim_type src_type, unsigned src_pos,
2464 __isl_give isl_map *isl_map_move_dims(
2465 __isl_take isl_map *map,
2466 enum isl_dim_type dst_type, unsigned dst_pos,
2467 enum isl_dim_type src_type, unsigned src_pos,
2470 It is usually not advisable to directly change the (input or output)
2471 space of a set or a relation as this removes the name and the internal
2472 structure of the space. However, the above functions can be useful
2473 to add new parameters, assuming
2474 C<isl_set_align_params> and C<isl_map_align_params>
2479 =head2 Binary Operations
2481 The two arguments of a binary operation not only need to live
2482 in the same C<isl_ctx>, they currently also need to have
2483 the same (number of) parameters.
2485 =head3 Basic Operations
2489 =item * Intersection
2491 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2492 __isl_take isl_basic_set *bset1,
2493 __isl_take isl_basic_set *bset2);
2494 __isl_give isl_basic_set *isl_basic_set_intersect(
2495 __isl_take isl_basic_set *bset1,
2496 __isl_take isl_basic_set *bset2);
2497 __isl_give isl_set *isl_set_intersect_params(
2498 __isl_take isl_set *set,
2499 __isl_take isl_set *params);
2500 __isl_give isl_set *isl_set_intersect(
2501 __isl_take isl_set *set1,
2502 __isl_take isl_set *set2);
2503 __isl_give isl_union_set *isl_union_set_intersect_params(
2504 __isl_take isl_union_set *uset,
2505 __isl_take isl_set *set);
2506 __isl_give isl_union_map *isl_union_map_intersect_params(
2507 __isl_take isl_union_map *umap,
2508 __isl_take isl_set *set);
2509 __isl_give isl_union_set *isl_union_set_intersect(
2510 __isl_take isl_union_set *uset1,
2511 __isl_take isl_union_set *uset2);
2512 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2513 __isl_take isl_basic_map *bmap,
2514 __isl_take isl_basic_set *bset);
2515 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2516 __isl_take isl_basic_map *bmap,
2517 __isl_take isl_basic_set *bset);
2518 __isl_give isl_basic_map *isl_basic_map_intersect(
2519 __isl_take isl_basic_map *bmap1,
2520 __isl_take isl_basic_map *bmap2);
2521 __isl_give isl_map *isl_map_intersect_params(
2522 __isl_take isl_map *map,
2523 __isl_take isl_set *params);
2524 __isl_give isl_map *isl_map_intersect_domain(
2525 __isl_take isl_map *map,
2526 __isl_take isl_set *set);
2527 __isl_give isl_map *isl_map_intersect_range(
2528 __isl_take isl_map *map,
2529 __isl_take isl_set *set);
2530 __isl_give isl_map *isl_map_intersect(
2531 __isl_take isl_map *map1,
2532 __isl_take isl_map *map2);
2533 __isl_give isl_union_map *isl_union_map_intersect_domain(
2534 __isl_take isl_union_map *umap,
2535 __isl_take isl_union_set *uset);
2536 __isl_give isl_union_map *isl_union_map_intersect_range(
2537 __isl_take isl_union_map *umap,
2538 __isl_take isl_union_set *uset);
2539 __isl_give isl_union_map *isl_union_map_intersect(
2540 __isl_take isl_union_map *umap1,
2541 __isl_take isl_union_map *umap2);
2543 The second argument to the C<_params> functions needs to be
2544 a parametric (basic) set. For the other functions, a parametric set
2545 for either argument is only allowed if the other argument is
2546 a parametric set as well.
2550 __isl_give isl_set *isl_basic_set_union(
2551 __isl_take isl_basic_set *bset1,
2552 __isl_take isl_basic_set *bset2);
2553 __isl_give isl_map *isl_basic_map_union(
2554 __isl_take isl_basic_map *bmap1,
2555 __isl_take isl_basic_map *bmap2);
2556 __isl_give isl_set *isl_set_union(
2557 __isl_take isl_set *set1,
2558 __isl_take isl_set *set2);
2559 __isl_give isl_map *isl_map_union(
2560 __isl_take isl_map *map1,
2561 __isl_take isl_map *map2);
2562 __isl_give isl_union_set *isl_union_set_union(
2563 __isl_take isl_union_set *uset1,
2564 __isl_take isl_union_set *uset2);
2565 __isl_give isl_union_map *isl_union_map_union(
2566 __isl_take isl_union_map *umap1,
2567 __isl_take isl_union_map *umap2);
2569 =item * Set difference
2571 __isl_give isl_set *isl_set_subtract(
2572 __isl_take isl_set *set1,
2573 __isl_take isl_set *set2);
2574 __isl_give isl_map *isl_map_subtract(
2575 __isl_take isl_map *map1,
2576 __isl_take isl_map *map2);
2577 __isl_give isl_map *isl_map_subtract_domain(
2578 __isl_take isl_map *map,
2579 __isl_take isl_set *dom);
2580 __isl_give isl_map *isl_map_subtract_range(
2581 __isl_take isl_map *map,
2582 __isl_take isl_set *dom);
2583 __isl_give isl_union_set *isl_union_set_subtract(
2584 __isl_take isl_union_set *uset1,
2585 __isl_take isl_union_set *uset2);
2586 __isl_give isl_union_map *isl_union_map_subtract(
2587 __isl_take isl_union_map *umap1,
2588 __isl_take isl_union_map *umap2);
2592 __isl_give isl_basic_set *isl_basic_set_apply(
2593 __isl_take isl_basic_set *bset,
2594 __isl_take isl_basic_map *bmap);
2595 __isl_give isl_set *isl_set_apply(
2596 __isl_take isl_set *set,
2597 __isl_take isl_map *map);
2598 __isl_give isl_union_set *isl_union_set_apply(
2599 __isl_take isl_union_set *uset,
2600 __isl_take isl_union_map *umap);
2601 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2602 __isl_take isl_basic_map *bmap1,
2603 __isl_take isl_basic_map *bmap2);
2604 __isl_give isl_basic_map *isl_basic_map_apply_range(
2605 __isl_take isl_basic_map *bmap1,
2606 __isl_take isl_basic_map *bmap2);
2607 __isl_give isl_map *isl_map_apply_domain(
2608 __isl_take isl_map *map1,
2609 __isl_take isl_map *map2);
2610 __isl_give isl_union_map *isl_union_map_apply_domain(
2611 __isl_take isl_union_map *umap1,
2612 __isl_take isl_union_map *umap2);
2613 __isl_give isl_map *isl_map_apply_range(
2614 __isl_take isl_map *map1,
2615 __isl_take isl_map *map2);
2616 __isl_give isl_union_map *isl_union_map_apply_range(
2617 __isl_take isl_union_map *umap1,
2618 __isl_take isl_union_map *umap2);
2620 =item * Cartesian Product
2622 __isl_give isl_set *isl_set_product(
2623 __isl_take isl_set *set1,
2624 __isl_take isl_set *set2);
2625 __isl_give isl_union_set *isl_union_set_product(
2626 __isl_take isl_union_set *uset1,
2627 __isl_take isl_union_set *uset2);
2628 __isl_give isl_basic_map *isl_basic_map_domain_product(
2629 __isl_take isl_basic_map *bmap1,
2630 __isl_take isl_basic_map *bmap2);
2631 __isl_give isl_basic_map *isl_basic_map_range_product(
2632 __isl_take isl_basic_map *bmap1,
2633 __isl_take isl_basic_map *bmap2);
2634 __isl_give isl_basic_map *isl_basic_map_product(
2635 __isl_take isl_basic_map *bmap1,
2636 __isl_take isl_basic_map *bmap2);
2637 __isl_give isl_map *isl_map_domain_product(
2638 __isl_take isl_map *map1,
2639 __isl_take isl_map *map2);
2640 __isl_give isl_map *isl_map_range_product(
2641 __isl_take isl_map *map1,
2642 __isl_take isl_map *map2);
2643 __isl_give isl_union_map *isl_union_map_domain_product(
2644 __isl_take isl_union_map *umap1,
2645 __isl_take isl_union_map *umap2);
2646 __isl_give isl_union_map *isl_union_map_range_product(
2647 __isl_take isl_union_map *umap1,
2648 __isl_take isl_union_map *umap2);
2649 __isl_give isl_map *isl_map_product(
2650 __isl_take isl_map *map1,
2651 __isl_take isl_map *map2);
2652 __isl_give isl_union_map *isl_union_map_product(
2653 __isl_take isl_union_map *umap1,
2654 __isl_take isl_union_map *umap2);
2656 The above functions compute the cross product of the given
2657 sets or relations. The domains and ranges of the results
2658 are wrapped maps between domains and ranges of the inputs.
2659 To obtain a ``flat'' product, use the following functions
2662 __isl_give isl_basic_set *isl_basic_set_flat_product(
2663 __isl_take isl_basic_set *bset1,
2664 __isl_take isl_basic_set *bset2);
2665 __isl_give isl_set *isl_set_flat_product(
2666 __isl_take isl_set *set1,
2667 __isl_take isl_set *set2);
2668 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2669 __isl_take isl_basic_map *bmap1,
2670 __isl_take isl_basic_map *bmap2);
2671 __isl_give isl_map *isl_map_flat_domain_product(
2672 __isl_take isl_map *map1,
2673 __isl_take isl_map *map2);
2674 __isl_give isl_map *isl_map_flat_range_product(
2675 __isl_take isl_map *map1,
2676 __isl_take isl_map *map2);
2677 __isl_give isl_union_map *isl_union_map_flat_range_product(
2678 __isl_take isl_union_map *umap1,
2679 __isl_take isl_union_map *umap2);
2680 __isl_give isl_basic_map *isl_basic_map_flat_product(
2681 __isl_take isl_basic_map *bmap1,
2682 __isl_take isl_basic_map *bmap2);
2683 __isl_give isl_map *isl_map_flat_product(
2684 __isl_take isl_map *map1,
2685 __isl_take isl_map *map2);
2687 =item * Simplification
2689 __isl_give isl_basic_set *isl_basic_set_gist(
2690 __isl_take isl_basic_set *bset,
2691 __isl_take isl_basic_set *context);
2692 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2693 __isl_take isl_set *context);
2694 __isl_give isl_set *isl_set_gist_params(
2695 __isl_take isl_set *set,
2696 __isl_take isl_set *context);
2697 __isl_give isl_union_set *isl_union_set_gist(
2698 __isl_take isl_union_set *uset,
2699 __isl_take isl_union_set *context);
2700 __isl_give isl_union_set *isl_union_set_gist_params(
2701 __isl_take isl_union_set *uset,
2702 __isl_take isl_set *set);
2703 __isl_give isl_basic_map *isl_basic_map_gist(
2704 __isl_take isl_basic_map *bmap,
2705 __isl_take isl_basic_map *context);
2706 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2707 __isl_take isl_map *context);
2708 __isl_give isl_map *isl_map_gist_params(
2709 __isl_take isl_map *map,
2710 __isl_take isl_set *context);
2711 __isl_give isl_map *isl_map_gist_domain(
2712 __isl_take isl_map *map,
2713 __isl_take isl_set *context);
2714 __isl_give isl_map *isl_map_gist_range(
2715 __isl_take isl_map *map,
2716 __isl_take isl_set *context);
2717 __isl_give isl_union_map *isl_union_map_gist(
2718 __isl_take isl_union_map *umap,
2719 __isl_take isl_union_map *context);
2720 __isl_give isl_union_map *isl_union_map_gist_params(
2721 __isl_take isl_union_map *umap,
2722 __isl_take isl_set *set);
2723 __isl_give isl_union_map *isl_union_map_gist_domain(
2724 __isl_take isl_union_map *umap,
2725 __isl_take isl_union_set *uset);
2726 __isl_give isl_union_map *isl_union_map_gist_range(
2727 __isl_take isl_union_map *umap,
2728 __isl_take isl_union_set *uset);
2730 The gist operation returns a set or relation that has the
2731 same intersection with the context as the input set or relation.
2732 Any implicit equality in the intersection is made explicit in the result,
2733 while all inequalities that are redundant with respect to the intersection
2735 In case of union sets and relations, the gist operation is performed
2740 =head3 Lexicographic Optimization
2742 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2743 the following functions
2744 compute a set that contains the lexicographic minimum or maximum
2745 of the elements in C<set> (or C<bset>) for those values of the parameters
2746 that satisfy C<dom>.
2747 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2748 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2750 In other words, the union of the parameter values
2751 for which the result is non-empty and of C<*empty>
2754 __isl_give isl_set *isl_basic_set_partial_lexmin(
2755 __isl_take isl_basic_set *bset,
2756 __isl_take isl_basic_set *dom,
2757 __isl_give isl_set **empty);
2758 __isl_give isl_set *isl_basic_set_partial_lexmax(
2759 __isl_take isl_basic_set *bset,
2760 __isl_take isl_basic_set *dom,
2761 __isl_give isl_set **empty);
2762 __isl_give isl_set *isl_set_partial_lexmin(
2763 __isl_take isl_set *set, __isl_take isl_set *dom,
2764 __isl_give isl_set **empty);
2765 __isl_give isl_set *isl_set_partial_lexmax(
2766 __isl_take isl_set *set, __isl_take isl_set *dom,
2767 __isl_give isl_set **empty);
2769 Given a (basic) set C<set> (or C<bset>), the following functions simply
2770 return a set containing the lexicographic minimum or maximum
2771 of the elements in C<set> (or C<bset>).
2772 In case of union sets, the optimum is computed per space.
2774 __isl_give isl_set *isl_basic_set_lexmin(
2775 __isl_take isl_basic_set *bset);
2776 __isl_give isl_set *isl_basic_set_lexmax(
2777 __isl_take isl_basic_set *bset);
2778 __isl_give isl_set *isl_set_lexmin(
2779 __isl_take isl_set *set);
2780 __isl_give isl_set *isl_set_lexmax(
2781 __isl_take isl_set *set);
2782 __isl_give isl_union_set *isl_union_set_lexmin(
2783 __isl_take isl_union_set *uset);
2784 __isl_give isl_union_set *isl_union_set_lexmax(
2785 __isl_take isl_union_set *uset);
2787 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2788 the following functions
2789 compute a relation that maps each element of C<dom>
2790 to the single lexicographic minimum or maximum
2791 of the elements that are associated to that same
2792 element in C<map> (or C<bmap>).
2793 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2794 that contains the elements in C<dom> that do not map
2795 to any elements in C<map> (or C<bmap>).
2796 In other words, the union of the domain of the result and of C<*empty>
2799 __isl_give isl_map *isl_basic_map_partial_lexmax(
2800 __isl_take isl_basic_map *bmap,
2801 __isl_take isl_basic_set *dom,
2802 __isl_give isl_set **empty);
2803 __isl_give isl_map *isl_basic_map_partial_lexmin(
2804 __isl_take isl_basic_map *bmap,
2805 __isl_take isl_basic_set *dom,
2806 __isl_give isl_set **empty);
2807 __isl_give isl_map *isl_map_partial_lexmax(
2808 __isl_take isl_map *map, __isl_take isl_set *dom,
2809 __isl_give isl_set **empty);
2810 __isl_give isl_map *isl_map_partial_lexmin(
2811 __isl_take isl_map *map, __isl_take isl_set *dom,
2812 __isl_give isl_set **empty);
2814 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2815 return a map mapping each element in the domain of
2816 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2817 of all elements associated to that element.
2818 In case of union relations, the optimum is computed per space.
2820 __isl_give isl_map *isl_basic_map_lexmin(
2821 __isl_take isl_basic_map *bmap);
2822 __isl_give isl_map *isl_basic_map_lexmax(
2823 __isl_take isl_basic_map *bmap);
2824 __isl_give isl_map *isl_map_lexmin(
2825 __isl_take isl_map *map);
2826 __isl_give isl_map *isl_map_lexmax(
2827 __isl_take isl_map *map);
2828 __isl_give isl_union_map *isl_union_map_lexmin(
2829 __isl_take isl_union_map *umap);
2830 __isl_give isl_union_map *isl_union_map_lexmax(
2831 __isl_take isl_union_map *umap);
2833 The following functions return their result in the form of
2834 a piecewise multi-affine expression
2835 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2836 but are otherwise equivalent to the corresponding functions
2837 returning a basic set or relation.
2839 __isl_give isl_pw_multi_aff *
2840 isl_basic_map_lexmin_pw_multi_aff(
2841 __isl_take isl_basic_map *bmap);
2842 __isl_give isl_pw_multi_aff *
2843 isl_basic_set_partial_lexmin_pw_multi_aff(
2844 __isl_take isl_basic_set *bset,
2845 __isl_take isl_basic_set *dom,
2846 __isl_give isl_set **empty);
2847 __isl_give isl_pw_multi_aff *
2848 isl_basic_set_partial_lexmax_pw_multi_aff(
2849 __isl_take isl_basic_set *bset,
2850 __isl_take isl_basic_set *dom,
2851 __isl_give isl_set **empty);
2852 __isl_give isl_pw_multi_aff *
2853 isl_basic_map_partial_lexmin_pw_multi_aff(
2854 __isl_take isl_basic_map *bmap,
2855 __isl_take isl_basic_set *dom,
2856 __isl_give isl_set **empty);
2857 __isl_give isl_pw_multi_aff *
2858 isl_basic_map_partial_lexmax_pw_multi_aff(
2859 __isl_take isl_basic_map *bmap,
2860 __isl_take isl_basic_set *dom,
2861 __isl_give isl_set **empty);
2862 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2863 __isl_take isl_map *map);
2864 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2865 __isl_take isl_map *map);
2869 Lists are defined over several element types, including
2870 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2871 Here we take lists of C<isl_set>s as an example.
2872 Lists can be created, copied, modified and freed using the following functions.
2874 #include <isl/list.h>
2875 __isl_give isl_set_list *isl_set_list_from_set(
2876 __isl_take isl_set *el);
2877 __isl_give isl_set_list *isl_set_list_alloc(
2878 isl_ctx *ctx, int n);
2879 __isl_give isl_set_list *isl_set_list_copy(
2880 __isl_keep isl_set_list *list);
2881 __isl_give isl_set_list *isl_set_list_add(
2882 __isl_take isl_set_list *list,
2883 __isl_take isl_set *el);
2884 __isl_give isl_set_list *isl_set_list_set_set(
2885 __isl_take isl_set_list *list, int index,
2886 __isl_take isl_set *set);
2887 __isl_give isl_set_list *isl_set_list_concat(
2888 __isl_take isl_set_list *list1,
2889 __isl_take isl_set_list *list2);
2890 void *isl_set_list_free(__isl_take isl_set_list *list);
2892 C<isl_set_list_alloc> creates an empty list with a capacity for
2893 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2896 Lists can be inspected using the following functions.
2898 #include <isl/list.h>
2899 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2900 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2901 __isl_give isl_set *isl_set_list_get_set(
2902 __isl_keep isl_set_list *list, int index);
2903 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2904 int (*fn)(__isl_take isl_set *el, void *user),
2907 Lists can be printed using
2909 #include <isl/list.h>
2910 __isl_give isl_printer *isl_printer_print_set_list(
2911 __isl_take isl_printer *p,
2912 __isl_keep isl_set_list *list);
2916 Vectors can be created, copied and freed using the following functions.
2918 #include <isl/vec.h>
2919 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2921 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2922 void isl_vec_free(__isl_take isl_vec *vec);
2924 Note that the elements of a newly created vector may have arbitrary values.
2925 The elements can be changed and inspected using the following functions.
2927 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2928 int isl_vec_size(__isl_keep isl_vec *vec);
2929 int isl_vec_get_element(__isl_keep isl_vec *vec,
2930 int pos, isl_int *v);
2931 __isl_give isl_vec *isl_vec_set_element(
2932 __isl_take isl_vec *vec, int pos, isl_int v);
2933 __isl_give isl_vec *isl_vec_set_element_si(
2934 __isl_take isl_vec *vec, int pos, int v);
2935 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2937 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2940 C<isl_vec_get_element> will return a negative value if anything went wrong.
2941 In that case, the value of C<*v> is undefined.
2945 Matrices can be created, copied and freed using the following functions.
2947 #include <isl/mat.h>
2948 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2949 unsigned n_row, unsigned n_col);
2950 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2951 void isl_mat_free(__isl_take isl_mat *mat);
2953 Note that the elements of a newly created matrix may have arbitrary values.
2954 The elements can be changed and inspected using the following functions.
2956 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2957 int isl_mat_rows(__isl_keep isl_mat *mat);
2958 int isl_mat_cols(__isl_keep isl_mat *mat);
2959 int isl_mat_get_element(__isl_keep isl_mat *mat,
2960 int row, int col, isl_int *v);
2961 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2962 int row, int col, isl_int v);
2963 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2964 int row, int col, int v);
2966 C<isl_mat_get_element> will return a negative value if anything went wrong.
2967 In that case, the value of C<*v> is undefined.
2969 The following function can be used to compute the (right) inverse
2970 of a matrix, i.e., a matrix such that the product of the original
2971 and the inverse (in that order) is a multiple of the identity matrix.
2972 The input matrix is assumed to be of full row-rank.
2974 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2976 The following function can be used to compute the (right) kernel
2977 (or null space) of a matrix, i.e., a matrix such that the product of
2978 the original and the kernel (in that order) is the zero matrix.
2980 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2982 =head2 Piecewise Quasi Affine Expressions
2984 The zero quasi affine expression on a given domain can be created using
2986 __isl_give isl_aff *isl_aff_zero_on_domain(
2987 __isl_take isl_local_space *ls);
2989 Note that the space in which the resulting object lives is a map space
2990 with the given space as domain and a one-dimensional range.
2992 An empty piecewise quasi affine expression (one with no cells)
2993 or a piecewise quasi affine expression with a single cell can
2994 be created using the following functions.
2996 #include <isl/aff.h>
2997 __isl_give isl_pw_aff *isl_pw_aff_empty(
2998 __isl_take isl_space *space);
2999 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3000 __isl_take isl_set *set, __isl_take isl_aff *aff);
3001 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3002 __isl_take isl_aff *aff);
3004 A piecewise quasi affine expression that is equal to 1 on a set
3005 and 0 outside the set can be created using the following function.
3007 #include <isl/aff.h>
3008 __isl_give isl_pw_aff *isl_set_indicator_function(
3009 __isl_take isl_set *set);
3011 Quasi affine expressions can be copied and freed using
3013 #include <isl/aff.h>
3014 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3015 void *isl_aff_free(__isl_take isl_aff *aff);
3017 __isl_give isl_pw_aff *isl_pw_aff_copy(
3018 __isl_keep isl_pw_aff *pwaff);
3019 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3021 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3022 using the following function. The constraint is required to have
3023 a non-zero coefficient for the specified dimension.
3025 #include <isl/constraint.h>
3026 __isl_give isl_aff *isl_constraint_get_bound(
3027 __isl_keep isl_constraint *constraint,
3028 enum isl_dim_type type, int pos);
3030 The entire affine expression of the constraint can also be extracted
3031 using the following function.
3033 #include <isl/constraint.h>
3034 __isl_give isl_aff *isl_constraint_get_aff(
3035 __isl_keep isl_constraint *constraint);
3037 Conversely, an equality constraint equating
3038 the affine expression to zero or an inequality constraint enforcing
3039 the affine expression to be non-negative, can be constructed using
3041 __isl_give isl_constraint *isl_equality_from_aff(
3042 __isl_take isl_aff *aff);
3043 __isl_give isl_constraint *isl_inequality_from_aff(
3044 __isl_take isl_aff *aff);
3046 The expression can be inspected using
3048 #include <isl/aff.h>
3049 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3050 int isl_aff_dim(__isl_keep isl_aff *aff,
3051 enum isl_dim_type type);
3052 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3053 __isl_keep isl_aff *aff);
3054 __isl_give isl_local_space *isl_aff_get_local_space(
3055 __isl_keep isl_aff *aff);
3056 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3057 enum isl_dim_type type, unsigned pos);
3058 const char *isl_pw_aff_get_dim_name(
3059 __isl_keep isl_pw_aff *pa,
3060 enum isl_dim_type type, unsigned pos);
3061 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3062 enum isl_dim_type type, unsigned pos);
3063 __isl_give isl_id *isl_pw_aff_get_dim_id(
3064 __isl_keep isl_pw_aff *pa,
3065 enum isl_dim_type type, unsigned pos);
3066 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3067 __isl_keep isl_pw_aff *pa,
3068 enum isl_dim_type type);
3069 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3071 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3072 enum isl_dim_type type, int pos, isl_int *v);
3073 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3075 __isl_give isl_aff *isl_aff_get_div(
3076 __isl_keep isl_aff *aff, int pos);
3078 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3079 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3080 int (*fn)(__isl_take isl_set *set,
3081 __isl_take isl_aff *aff,
3082 void *user), void *user);
3084 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3085 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3087 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3088 enum isl_dim_type type, unsigned first, unsigned n);
3089 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3090 enum isl_dim_type type, unsigned first, unsigned n);
3092 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3093 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3094 enum isl_dim_type type);
3095 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3097 It can be modified using
3099 #include <isl/aff.h>
3100 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3101 __isl_take isl_pw_aff *pwaff,
3102 enum isl_dim_type type, __isl_take isl_id *id);
3103 __isl_give isl_aff *isl_aff_set_dim_name(
3104 __isl_take isl_aff *aff, enum isl_dim_type type,
3105 unsigned pos, const char *s);
3106 __isl_give isl_aff *isl_aff_set_dim_id(
3107 __isl_take isl_aff *aff, enum isl_dim_type type,
3108 unsigned pos, __isl_take isl_id *id);
3109 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3110 __isl_take isl_pw_aff *pma,
3111 enum isl_dim_type type, unsigned pos,
3112 __isl_take isl_id *id);
3113 __isl_give isl_aff *isl_aff_set_constant(
3114 __isl_take isl_aff *aff, isl_int v);
3115 __isl_give isl_aff *isl_aff_set_constant_si(
3116 __isl_take isl_aff *aff, int v);
3117 __isl_give isl_aff *isl_aff_set_coefficient(
3118 __isl_take isl_aff *aff,
3119 enum isl_dim_type type, int pos, isl_int v);
3120 __isl_give isl_aff *isl_aff_set_coefficient_si(
3121 __isl_take isl_aff *aff,
3122 enum isl_dim_type type, int pos, int v);
3123 __isl_give isl_aff *isl_aff_set_denominator(
3124 __isl_take isl_aff *aff, isl_int v);
3126 __isl_give isl_aff *isl_aff_add_constant(
3127 __isl_take isl_aff *aff, isl_int v);
3128 __isl_give isl_aff *isl_aff_add_constant_si(
3129 __isl_take isl_aff *aff, int v);
3130 __isl_give isl_aff *isl_aff_add_constant_num(
3131 __isl_take isl_aff *aff, isl_int v);
3132 __isl_give isl_aff *isl_aff_add_constant_num_si(
3133 __isl_take isl_aff *aff, int v);
3134 __isl_give isl_aff *isl_aff_add_coefficient(
3135 __isl_take isl_aff *aff,
3136 enum isl_dim_type type, int pos, isl_int v);
3137 __isl_give isl_aff *isl_aff_add_coefficient_si(
3138 __isl_take isl_aff *aff,
3139 enum isl_dim_type type, int pos, int v);
3141 __isl_give isl_aff *isl_aff_insert_dims(
3142 __isl_take isl_aff *aff,
3143 enum isl_dim_type type, unsigned first, unsigned n);
3144 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3145 __isl_take isl_pw_aff *pwaff,
3146 enum isl_dim_type type, unsigned first, unsigned n);
3147 __isl_give isl_aff *isl_aff_add_dims(
3148 __isl_take isl_aff *aff,
3149 enum isl_dim_type type, unsigned n);
3150 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3151 __isl_take isl_pw_aff *pwaff,
3152 enum isl_dim_type type, unsigned n);
3153 __isl_give isl_aff *isl_aff_drop_dims(
3154 __isl_take isl_aff *aff,
3155 enum isl_dim_type type, unsigned first, unsigned n);
3156 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3157 __isl_take isl_pw_aff *pwaff,
3158 enum isl_dim_type type, unsigned first, unsigned n);
3160 Note that the C<set_constant> and C<set_coefficient> functions
3161 set the I<numerator> of the constant or coefficient, while
3162 C<add_constant> and C<add_coefficient> add an integer value to
3163 the possibly rational constant or coefficient.
3164 The C<add_constant_num> functions add an integer value to
3167 To check whether an affine expressions is obviously zero
3168 or obviously equal to some other affine expression, use
3170 #include <isl/aff.h>
3171 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3172 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3173 __isl_keep isl_aff *aff2);
3174 int isl_pw_aff_plain_is_equal(
3175 __isl_keep isl_pw_aff *pwaff1,
3176 __isl_keep isl_pw_aff *pwaff2);
3180 #include <isl/aff.h>
3181 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3182 __isl_take isl_aff *aff2);
3183 __isl_give isl_pw_aff *isl_pw_aff_add(
3184 __isl_take isl_pw_aff *pwaff1,
3185 __isl_take isl_pw_aff *pwaff2);
3186 __isl_give isl_pw_aff *isl_pw_aff_min(
3187 __isl_take isl_pw_aff *pwaff1,
3188 __isl_take isl_pw_aff *pwaff2);
3189 __isl_give isl_pw_aff *isl_pw_aff_max(
3190 __isl_take isl_pw_aff *pwaff1,
3191 __isl_take isl_pw_aff *pwaff2);
3192 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3193 __isl_take isl_aff *aff2);
3194 __isl_give isl_pw_aff *isl_pw_aff_sub(
3195 __isl_take isl_pw_aff *pwaff1,
3196 __isl_take isl_pw_aff *pwaff2);
3197 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3198 __isl_give isl_pw_aff *isl_pw_aff_neg(
3199 __isl_take isl_pw_aff *pwaff);
3200 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3201 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3202 __isl_take isl_pw_aff *pwaff);
3203 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3204 __isl_give isl_pw_aff *isl_pw_aff_floor(
3205 __isl_take isl_pw_aff *pwaff);
3206 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3208 __isl_give isl_pw_aff *isl_pw_aff_mod(
3209 __isl_take isl_pw_aff *pwaff, isl_int mod);
3210 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3212 __isl_give isl_pw_aff *isl_pw_aff_scale(
3213 __isl_take isl_pw_aff *pwaff, isl_int f);
3214 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3216 __isl_give isl_aff *isl_aff_scale_down_ui(
3217 __isl_take isl_aff *aff, unsigned f);
3218 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3219 __isl_take isl_pw_aff *pwaff, isl_int f);
3221 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3222 __isl_take isl_pw_aff_list *list);
3223 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3224 __isl_take isl_pw_aff_list *list);
3226 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3227 __isl_take isl_pw_aff *pwqp);
3229 __isl_give isl_aff *isl_aff_align_params(
3230 __isl_take isl_aff *aff,
3231 __isl_take isl_space *model);
3232 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3233 __isl_take isl_pw_aff *pwaff,
3234 __isl_take isl_space *model);
3236 __isl_give isl_aff *isl_aff_project_domain_on_params(
3237 __isl_take isl_aff *aff);
3239 __isl_give isl_aff *isl_aff_gist_params(
3240 __isl_take isl_aff *aff,
3241 __isl_take isl_set *context);
3242 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3243 __isl_take isl_set *context);
3244 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3245 __isl_take isl_pw_aff *pwaff,
3246 __isl_take isl_set *context);
3247 __isl_give isl_pw_aff *isl_pw_aff_gist(
3248 __isl_take isl_pw_aff *pwaff,
3249 __isl_take isl_set *context);
3251 __isl_give isl_set *isl_pw_aff_domain(
3252 __isl_take isl_pw_aff *pwaff);
3253 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3254 __isl_take isl_pw_aff *pa,
3255 __isl_take isl_set *set);
3256 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3257 __isl_take isl_pw_aff *pa,
3258 __isl_take isl_set *set);
3260 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3261 __isl_take isl_aff *aff2);
3262 __isl_give isl_pw_aff *isl_pw_aff_mul(
3263 __isl_take isl_pw_aff *pwaff1,
3264 __isl_take isl_pw_aff *pwaff2);
3266 When multiplying two affine expressions, at least one of the two needs
3269 #include <isl/aff.h>
3270 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3271 __isl_take isl_aff *aff);
3272 __isl_give isl_basic_set *isl_aff_le_basic_set(
3273 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3274 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3275 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3276 __isl_give isl_set *isl_pw_aff_eq_set(
3277 __isl_take isl_pw_aff *pwaff1,
3278 __isl_take isl_pw_aff *pwaff2);
3279 __isl_give isl_set *isl_pw_aff_ne_set(
3280 __isl_take isl_pw_aff *pwaff1,
3281 __isl_take isl_pw_aff *pwaff2);
3282 __isl_give isl_set *isl_pw_aff_le_set(
3283 __isl_take isl_pw_aff *pwaff1,
3284 __isl_take isl_pw_aff *pwaff2);
3285 __isl_give isl_set *isl_pw_aff_lt_set(
3286 __isl_take isl_pw_aff *pwaff1,
3287 __isl_take isl_pw_aff *pwaff2);
3288 __isl_give isl_set *isl_pw_aff_ge_set(
3289 __isl_take isl_pw_aff *pwaff1,
3290 __isl_take isl_pw_aff *pwaff2);
3291 __isl_give isl_set *isl_pw_aff_gt_set(
3292 __isl_take isl_pw_aff *pwaff1,
3293 __isl_take isl_pw_aff *pwaff2);
3295 __isl_give isl_set *isl_pw_aff_list_eq_set(
3296 __isl_take isl_pw_aff_list *list1,
3297 __isl_take isl_pw_aff_list *list2);
3298 __isl_give isl_set *isl_pw_aff_list_ne_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_le_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_lt_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_ge_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_gt_set(
3311 __isl_take isl_pw_aff_list *list1,
3312 __isl_take isl_pw_aff_list *list2);
3314 The function C<isl_aff_neg_basic_set> returns a basic set
3315 containing those elements in the domain space
3316 of C<aff> where C<aff> is negative.
3317 The function C<isl_aff_ge_basic_set> returns a basic set
3318 containing those elements in the shared space
3319 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3320 The function C<isl_pw_aff_ge_set> returns a set
3321 containing those elements in the shared domain
3322 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3323 The functions operating on C<isl_pw_aff_list> apply the corresponding
3324 C<isl_pw_aff> function to each pair of elements in the two lists.
3326 #include <isl/aff.h>
3327 __isl_give isl_set *isl_pw_aff_nonneg_set(
3328 __isl_take isl_pw_aff *pwaff);
3329 __isl_give isl_set *isl_pw_aff_zero_set(
3330 __isl_take isl_pw_aff *pwaff);
3331 __isl_give isl_set *isl_pw_aff_non_zero_set(
3332 __isl_take isl_pw_aff *pwaff);
3334 The function C<isl_pw_aff_nonneg_set> returns a set
3335 containing those elements in the domain
3336 of C<pwaff> where C<pwaff> is non-negative.
3338 #include <isl/aff.h>
3339 __isl_give isl_pw_aff *isl_pw_aff_cond(
3340 __isl_take isl_pw_aff *cond,
3341 __isl_take isl_pw_aff *pwaff_true,
3342 __isl_take isl_pw_aff *pwaff_false);
3344 The function C<isl_pw_aff_cond> performs a conditional operator
3345 and returns an expression that is equal to C<pwaff_true>
3346 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3347 where C<cond> is zero.
3349 #include <isl/aff.h>
3350 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3351 __isl_take isl_pw_aff *pwaff1,
3352 __isl_take isl_pw_aff *pwaff2);
3353 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3354 __isl_take isl_pw_aff *pwaff1,
3355 __isl_take isl_pw_aff *pwaff2);
3356 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3357 __isl_take isl_pw_aff *pwaff1,
3358 __isl_take isl_pw_aff *pwaff2);
3360 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3361 expression with a domain that is the union of those of C<pwaff1> and
3362 C<pwaff2> and such that on each cell, the quasi-affine expression is
3363 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3364 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3365 associated expression is the defined one.
3367 An expression can be read from input using
3369 #include <isl/aff.h>
3370 __isl_give isl_aff *isl_aff_read_from_str(
3371 isl_ctx *ctx, const char *str);
3372 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3373 isl_ctx *ctx, const char *str);
3375 An expression can be printed using
3377 #include <isl/aff.h>
3378 __isl_give isl_printer *isl_printer_print_aff(
3379 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3381 __isl_give isl_printer *isl_printer_print_pw_aff(
3382 __isl_take isl_printer *p,
3383 __isl_keep isl_pw_aff *pwaff);
3385 =head2 Piecewise Multiple Quasi Affine Expressions
3387 An C<isl_multi_aff> object represents a sequence of
3388 zero or more affine expressions, all defined on the same domain space.
3390 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3393 #include <isl/aff.h>
3394 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3395 __isl_take isl_space *space,
3396 __isl_take isl_aff_list *list);
3398 An empty piecewise multiple quasi affine expression (one with no cells),
3399 the zero piecewise multiple quasi affine expression (with value zero
3400 for each output dimension),
3401 a piecewise multiple quasi affine expression with a single cell (with
3402 either a universe or a specified domain) or
3403 a zero-dimensional piecewise multiple quasi affine expression
3405 can be created using the following functions.
3407 #include <isl/aff.h>
3408 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3409 __isl_take isl_space *space);
3410 __isl_give isl_multi_aff *isl_multi_aff_zero(
3411 __isl_take isl_space *space);
3412 __isl_give isl_multi_aff *isl_multi_aff_identity(
3413 __isl_take isl_space *space);
3414 __isl_give isl_pw_multi_aff *
3415 isl_pw_multi_aff_from_multi_aff(
3416 __isl_take isl_multi_aff *ma);
3417 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3418 __isl_take isl_set *set,
3419 __isl_take isl_multi_aff *maff);
3420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3421 __isl_take isl_set *set);
3423 __isl_give isl_union_pw_multi_aff *
3424 isl_union_pw_multi_aff_empty(
3425 __isl_take isl_space *space);
3426 __isl_give isl_union_pw_multi_aff *
3427 isl_union_pw_multi_aff_add_pw_multi_aff(
3428 __isl_take isl_union_pw_multi_aff *upma,
3429 __isl_take isl_pw_multi_aff *pma);
3430 __isl_give isl_union_pw_multi_aff *
3431 isl_union_pw_multi_aff_from_domain(
3432 __isl_take isl_union_set *uset);
3434 A piecewise multiple quasi affine expression can also be initialized
3435 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3436 and the C<isl_map> is single-valued.
3438 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3439 __isl_take isl_set *set);
3440 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3441 __isl_take isl_map *map);
3443 Multiple quasi affine expressions can be copied and freed using
3445 #include <isl/aff.h>
3446 __isl_give isl_multi_aff *isl_multi_aff_copy(
3447 __isl_keep isl_multi_aff *maff);
3448 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3450 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3451 __isl_keep isl_pw_multi_aff *pma);
3452 void *isl_pw_multi_aff_free(
3453 __isl_take isl_pw_multi_aff *pma);
3455 __isl_give isl_union_pw_multi_aff *
3456 isl_union_pw_multi_aff_copy(
3457 __isl_keep isl_union_pw_multi_aff *upma);
3458 void *isl_union_pw_multi_aff_free(
3459 __isl_take isl_union_pw_multi_aff *upma);
3461 The expression can be inspected using
3463 #include <isl/aff.h>
3464 isl_ctx *isl_multi_aff_get_ctx(
3465 __isl_keep isl_multi_aff *maff);
3466 isl_ctx *isl_pw_multi_aff_get_ctx(
3467 __isl_keep isl_pw_multi_aff *pma);
3468 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3469 __isl_keep isl_union_pw_multi_aff *upma);
3470 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3471 enum isl_dim_type type);
3472 unsigned isl_pw_multi_aff_dim(
3473 __isl_keep isl_pw_multi_aff *pma,
3474 enum isl_dim_type type);
3475 __isl_give isl_aff *isl_multi_aff_get_aff(
3476 __isl_keep isl_multi_aff *multi, int pos);
3477 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3478 __isl_keep isl_pw_multi_aff *pma, int pos);
3479 const char *isl_pw_multi_aff_get_dim_name(
3480 __isl_keep isl_pw_multi_aff *pma,
3481 enum isl_dim_type type, unsigned pos);
3482 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3483 __isl_keep isl_pw_multi_aff *pma,
3484 enum isl_dim_type type, unsigned pos);
3485 const char *isl_multi_aff_get_tuple_name(
3486 __isl_keep isl_multi_aff *multi,
3487 enum isl_dim_type type);
3488 int isl_pw_multi_aff_has_tuple_name(
3489 __isl_keep isl_pw_multi_aff *pma,
3490 enum isl_dim_type type);
3491 const char *isl_pw_multi_aff_get_tuple_name(
3492 __isl_keep isl_pw_multi_aff *pma,
3493 enum isl_dim_type type);
3494 int isl_pw_multi_aff_has_tuple_id(
3495 __isl_keep isl_pw_multi_aff *pma,
3496 enum isl_dim_type type);
3497 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3498 __isl_keep isl_pw_multi_aff *pma,
3499 enum isl_dim_type type);
3501 int isl_pw_multi_aff_foreach_piece(
3502 __isl_keep isl_pw_multi_aff *pma,
3503 int (*fn)(__isl_take isl_set *set,
3504 __isl_take isl_multi_aff *maff,
3505 void *user), void *user);
3507 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3508 __isl_keep isl_union_pw_multi_aff *upma,
3509 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3510 void *user), void *user);
3512 It can be modified using
3514 #include <isl/aff.h>
3515 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3516 __isl_take isl_multi_aff *multi, int pos,
3517 __isl_take isl_aff *aff);
3518 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3519 __isl_take isl_multi_aff *maff,
3520 enum isl_dim_type type, unsigned pos, const char *s);
3521 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3522 __isl_take isl_multi_aff *maff,
3523 enum isl_dim_type type, __isl_take isl_id *id);
3524 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3525 __isl_take isl_pw_multi_aff *pma,
3526 enum isl_dim_type type, __isl_take isl_id *id);
3528 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3529 __isl_take isl_multi_aff *maff,
3530 enum isl_dim_type type, unsigned first, unsigned n);
3531 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3532 __isl_take isl_pw_multi_aff *pma,
3533 enum isl_dim_type type, unsigned first, unsigned n);
3535 To check whether two multiple affine expressions are
3536 obviously equal to each other, use
3538 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3539 __isl_keep isl_multi_aff *maff2);
3540 int isl_pw_multi_aff_plain_is_equal(
3541 __isl_keep isl_pw_multi_aff *pma1,
3542 __isl_keep isl_pw_multi_aff *pma2);
3546 #include <isl/aff.h>
3547 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3548 __isl_take isl_pw_multi_aff *pma1,
3549 __isl_take isl_pw_multi_aff *pma2);
3550 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3551 __isl_take isl_pw_multi_aff *pma1,
3552 __isl_take isl_pw_multi_aff *pma2);
3553 __isl_give isl_multi_aff *isl_multi_aff_add(
3554 __isl_take isl_multi_aff *maff1,
3555 __isl_take isl_multi_aff *maff2);
3556 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3557 __isl_take isl_pw_multi_aff *pma1,
3558 __isl_take isl_pw_multi_aff *pma2);
3559 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3560 __isl_take isl_union_pw_multi_aff *upma1,
3561 __isl_take isl_union_pw_multi_aff *upma2);
3562 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3563 __isl_take isl_pw_multi_aff *pma1,
3564 __isl_take isl_pw_multi_aff *pma2);
3565 __isl_give isl_multi_aff *isl_multi_aff_scale(
3566 __isl_take isl_multi_aff *maff,
3568 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3569 __isl_take isl_pw_multi_aff *pma,
3570 __isl_take isl_set *set);
3571 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3572 __isl_take isl_pw_multi_aff *pma,
3573 __isl_take isl_set *set);
3574 __isl_give isl_multi_aff *isl_multi_aff_lift(
3575 __isl_take isl_multi_aff *maff,
3576 __isl_give isl_local_space **ls);
3577 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3578 __isl_take isl_pw_multi_aff *pma);
3579 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3580 __isl_take isl_multi_aff *multi,
3581 __isl_take isl_space *model);
3582 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3583 __isl_take isl_multi_aff *maff,
3584 __isl_take isl_set *context);
3585 __isl_give isl_multi_aff *isl_multi_aff_gist(
3586 __isl_take isl_multi_aff *maff,
3587 __isl_take isl_set *context);
3588 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3589 __isl_take isl_pw_multi_aff *pma,
3590 __isl_take isl_set *set);
3591 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3592 __isl_take isl_pw_multi_aff *pma,
3593 __isl_take isl_set *set);
3594 __isl_give isl_set *isl_pw_multi_aff_domain(
3595 __isl_take isl_pw_multi_aff *pma);
3596 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3597 __isl_take isl_union_pw_multi_aff *upma);
3598 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3599 __isl_take isl_multi_aff *ma1,
3600 __isl_take isl_multi_aff *ma2);
3601 __isl_give isl_multi_aff *isl_multi_aff_product(
3602 __isl_take isl_multi_aff *ma1,
3603 __isl_take isl_multi_aff *ma2);
3604 __isl_give isl_pw_multi_aff *
3605 isl_pw_multi_aff_flat_range_product(
3606 __isl_take isl_pw_multi_aff *pma1,
3607 __isl_take isl_pw_multi_aff *pma2);
3608 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3609 __isl_take isl_pw_multi_aff *pma1,
3610 __isl_take isl_pw_multi_aff *pma2);
3611 __isl_give isl_union_pw_multi_aff *
3612 isl_union_pw_multi_aff_flat_range_product(
3613 __isl_take isl_union_pw_multi_aff *upma1,
3614 __isl_take isl_union_pw_multi_aff *upma2);
3616 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3617 then it is assigned the local space that lies at the basis of
3618 the lifting applied.
3620 __isl_give isl_set *isl_multi_aff_lex_le_set(
3621 __isl_take isl_multi_aff *ma1,
3622 __isl_take isl_multi_aff *ma2);
3623 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3624 __isl_take isl_multi_aff *ma1,
3625 __isl_take isl_multi_aff *ma2);
3627 The function C<isl_multi_aff_lex_le_set> returns a set
3628 containing those elements in the shared domain space
3629 where C<ma1> is lexicographically smaller than or
3632 An expression can be read from input using
3634 #include <isl/aff.h>
3635 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3636 isl_ctx *ctx, const char *str);
3637 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3638 isl_ctx *ctx, const char *str);
3640 An expression can be printed using
3642 #include <isl/aff.h>
3643 __isl_give isl_printer *isl_printer_print_multi_aff(
3644 __isl_take isl_printer *p,
3645 __isl_keep isl_multi_aff *maff);
3646 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3647 __isl_take isl_printer *p,
3648 __isl_keep isl_pw_multi_aff *pma);
3649 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3650 __isl_take isl_printer *p,
3651 __isl_keep isl_union_pw_multi_aff *upma);
3655 Points are elements of a set. They can be used to construct
3656 simple sets (boxes) or they can be used to represent the
3657 individual elements of a set.
3658 The zero point (the origin) can be created using
3660 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3662 The coordinates of a point can be inspected, set and changed
3665 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3666 enum isl_dim_type type, int pos, isl_int *v);
3667 __isl_give isl_point *isl_point_set_coordinate(
3668 __isl_take isl_point *pnt,
3669 enum isl_dim_type type, int pos, isl_int v);
3671 __isl_give isl_point *isl_point_add_ui(
3672 __isl_take isl_point *pnt,
3673 enum isl_dim_type type, int pos, unsigned val);
3674 __isl_give isl_point *isl_point_sub_ui(
3675 __isl_take isl_point *pnt,
3676 enum isl_dim_type type, int pos, unsigned val);
3678 Other properties can be obtained using
3680 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3682 Points can be copied or freed using
3684 __isl_give isl_point *isl_point_copy(
3685 __isl_keep isl_point *pnt);
3686 void isl_point_free(__isl_take isl_point *pnt);
3688 A singleton set can be created from a point using
3690 __isl_give isl_basic_set *isl_basic_set_from_point(
3691 __isl_take isl_point *pnt);
3692 __isl_give isl_set *isl_set_from_point(
3693 __isl_take isl_point *pnt);
3695 and a box can be created from two opposite extremal points using
3697 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3698 __isl_take isl_point *pnt1,
3699 __isl_take isl_point *pnt2);
3700 __isl_give isl_set *isl_set_box_from_points(
3701 __isl_take isl_point *pnt1,
3702 __isl_take isl_point *pnt2);
3704 All elements of a B<bounded> (union) set can be enumerated using
3705 the following functions.
3707 int isl_set_foreach_point(__isl_keep isl_set *set,
3708 int (*fn)(__isl_take isl_point *pnt, void *user),
3710 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3711 int (*fn)(__isl_take isl_point *pnt, void *user),
3714 The function C<fn> is called for each integer point in
3715 C<set> with as second argument the last argument of
3716 the C<isl_set_foreach_point> call. The function C<fn>
3717 should return C<0> on success and C<-1> on failure.
3718 In the latter case, C<isl_set_foreach_point> will stop
3719 enumerating and return C<-1> as well.
3720 If the enumeration is performed successfully and to completion,
3721 then C<isl_set_foreach_point> returns C<0>.
3723 To obtain a single point of a (basic) set, use
3725 __isl_give isl_point *isl_basic_set_sample_point(
3726 __isl_take isl_basic_set *bset);
3727 __isl_give isl_point *isl_set_sample_point(
3728 __isl_take isl_set *set);
3730 If C<set> does not contain any (integer) points, then the
3731 resulting point will be ``void'', a property that can be
3734 int isl_point_is_void(__isl_keep isl_point *pnt);
3736 =head2 Piecewise Quasipolynomials
3738 A piecewise quasipolynomial is a particular kind of function that maps
3739 a parametric point to a rational value.
3740 More specifically, a quasipolynomial is a polynomial expression in greatest
3741 integer parts of affine expressions of parameters and variables.
3742 A piecewise quasipolynomial is a subdivision of a given parametric
3743 domain into disjoint cells with a quasipolynomial associated to
3744 each cell. The value of the piecewise quasipolynomial at a given
3745 point is the value of the quasipolynomial associated to the cell
3746 that contains the point. Outside of the union of cells,
3747 the value is assumed to be zero.
3748 For example, the piecewise quasipolynomial
3750 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3752 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3753 A given piecewise quasipolynomial has a fixed domain dimension.
3754 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3755 defined over different domains.
3756 Piecewise quasipolynomials are mainly used by the C<barvinok>
3757 library for representing the number of elements in a parametric set or map.
3758 For example, the piecewise quasipolynomial above represents
3759 the number of points in the map
3761 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3763 =head3 Input and Output
3765 Piecewise quasipolynomials can be read from input using
3767 __isl_give isl_union_pw_qpolynomial *
3768 isl_union_pw_qpolynomial_read_from_str(
3769 isl_ctx *ctx, const char *str);
3771 Quasipolynomials and piecewise quasipolynomials can be printed
3772 using the following functions.
3774 __isl_give isl_printer *isl_printer_print_qpolynomial(
3775 __isl_take isl_printer *p,
3776 __isl_keep isl_qpolynomial *qp);
3778 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3779 __isl_take isl_printer *p,
3780 __isl_keep isl_pw_qpolynomial *pwqp);
3782 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3783 __isl_take isl_printer *p,
3784 __isl_keep isl_union_pw_qpolynomial *upwqp);
3786 The output format of the printer
3787 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3788 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3790 In case of printing in C<ISL_FORMAT_C>, the user may want
3791 to set the names of all dimensions
3793 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3794 __isl_take isl_qpolynomial *qp,
3795 enum isl_dim_type type, unsigned pos,
3797 __isl_give isl_pw_qpolynomial *
3798 isl_pw_qpolynomial_set_dim_name(
3799 __isl_take isl_pw_qpolynomial *pwqp,
3800 enum isl_dim_type type, unsigned pos,
3803 =head3 Creating New (Piecewise) Quasipolynomials
3805 Some simple quasipolynomials can be created using the following functions.
3806 More complicated quasipolynomials can be created by applying
3807 operations such as addition and multiplication
3808 on the resulting quasipolynomials
3810 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3811 __isl_take isl_space *domain);
3812 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3813 __isl_take isl_space *domain);
3814 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3815 __isl_take isl_space *domain);
3816 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3817 __isl_take isl_space *domain);
3818 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3819 __isl_take isl_space *domain);
3820 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3821 __isl_take isl_space *domain,
3822 const isl_int n, const isl_int d);
3823 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3824 __isl_take isl_space *domain,
3825 enum isl_dim_type type, unsigned pos);
3826 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3827 __isl_take isl_aff *aff);
3829 Note that the space in which a quasipolynomial lives is a map space
3830 with a one-dimensional range. The C<domain> argument in some of
3831 the functions above corresponds to the domain of this map space.
3833 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3834 with a single cell can be created using the following functions.
3835 Multiple of these single cell piecewise quasipolynomials can
3836 be combined to create more complicated piecewise quasipolynomials.
3838 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3839 __isl_take isl_space *space);
3840 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3841 __isl_take isl_set *set,
3842 __isl_take isl_qpolynomial *qp);
3843 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3844 __isl_take isl_qpolynomial *qp);
3845 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3846 __isl_take isl_pw_aff *pwaff);
3848 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3849 __isl_take isl_space *space);
3850 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3851 __isl_take isl_pw_qpolynomial *pwqp);
3852 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3853 __isl_take isl_union_pw_qpolynomial *upwqp,
3854 __isl_take isl_pw_qpolynomial *pwqp);
3856 Quasipolynomials can be copied and freed again using the following
3859 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3860 __isl_keep isl_qpolynomial *qp);
3861 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3863 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3864 __isl_keep isl_pw_qpolynomial *pwqp);
3865 void *isl_pw_qpolynomial_free(
3866 __isl_take isl_pw_qpolynomial *pwqp);
3868 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3869 __isl_keep isl_union_pw_qpolynomial *upwqp);
3870 void *isl_union_pw_qpolynomial_free(
3871 __isl_take isl_union_pw_qpolynomial *upwqp);
3873 =head3 Inspecting (Piecewise) Quasipolynomials
3875 To iterate over all piecewise quasipolynomials in a union
3876 piecewise quasipolynomial, use the following function
3878 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3879 __isl_keep isl_union_pw_qpolynomial *upwqp,
3880 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3883 To extract the piecewise quasipolynomial in a given space from a union, use
3885 __isl_give isl_pw_qpolynomial *
3886 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3887 __isl_keep isl_union_pw_qpolynomial *upwqp,
3888 __isl_take isl_space *space);
3890 To iterate over the cells in a piecewise quasipolynomial,
3891 use either of the following two functions
3893 int isl_pw_qpolynomial_foreach_piece(
3894 __isl_keep isl_pw_qpolynomial *pwqp,
3895 int (*fn)(__isl_take isl_set *set,
3896 __isl_take isl_qpolynomial *qp,
3897 void *user), void *user);
3898 int isl_pw_qpolynomial_foreach_lifted_piece(
3899 __isl_keep isl_pw_qpolynomial *pwqp,
3900 int (*fn)(__isl_take isl_set *set,
3901 __isl_take isl_qpolynomial *qp,
3902 void *user), void *user);
3904 As usual, the function C<fn> should return C<0> on success
3905 and C<-1> on failure. The difference between
3906 C<isl_pw_qpolynomial_foreach_piece> and
3907 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3908 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3909 compute unique representations for all existentially quantified
3910 variables and then turn these existentially quantified variables
3911 into extra set variables, adapting the associated quasipolynomial
3912 accordingly. This means that the C<set> passed to C<fn>
3913 will not have any existentially quantified variables, but that
3914 the dimensions of the sets may be different for different
3915 invocations of C<fn>.
3917 To iterate over all terms in a quasipolynomial,
3920 int isl_qpolynomial_foreach_term(
3921 __isl_keep isl_qpolynomial *qp,
3922 int (*fn)(__isl_take isl_term *term,
3923 void *user), void *user);
3925 The terms themselves can be inspected and freed using
3928 unsigned isl_term_dim(__isl_keep isl_term *term,
3929 enum isl_dim_type type);
3930 void isl_term_get_num(__isl_keep isl_term *term,
3932 void isl_term_get_den(__isl_keep isl_term *term,
3934 int isl_term_get_exp(__isl_keep isl_term *term,
3935 enum isl_dim_type type, unsigned pos);
3936 __isl_give isl_aff *isl_term_get_div(
3937 __isl_keep isl_term *term, unsigned pos);
3938 void isl_term_free(__isl_take isl_term *term);
3940 Each term is a product of parameters, set variables and
3941 integer divisions. The function C<isl_term_get_exp>
3942 returns the exponent of a given dimensions in the given term.
3943 The C<isl_int>s in the arguments of C<isl_term_get_num>
3944 and C<isl_term_get_den> need to have been initialized
3945 using C<isl_int_init> before calling these functions.
3947 =head3 Properties of (Piecewise) Quasipolynomials
3949 To check whether a quasipolynomial is actually a constant,
3950 use the following function.
3952 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3953 isl_int *n, isl_int *d);
3955 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3956 then the numerator and denominator of the constant
3957 are returned in C<*n> and C<*d>, respectively.
3959 To check whether two union piecewise quasipolynomials are
3960 obviously equal, use
3962 int isl_union_pw_qpolynomial_plain_is_equal(
3963 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3964 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3966 =head3 Operations on (Piecewise) Quasipolynomials
3968 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3969 __isl_take isl_qpolynomial *qp, isl_int v);
3970 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3971 __isl_take isl_qpolynomial *qp);
3972 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3973 __isl_take isl_qpolynomial *qp1,
3974 __isl_take isl_qpolynomial *qp2);
3975 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3976 __isl_take isl_qpolynomial *qp1,
3977 __isl_take isl_qpolynomial *qp2);
3978 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3979 __isl_take isl_qpolynomial *qp1,
3980 __isl_take isl_qpolynomial *qp2);
3981 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3982 __isl_take isl_qpolynomial *qp, unsigned exponent);
3984 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3985 __isl_take isl_pw_qpolynomial *pwqp1,
3986 __isl_take isl_pw_qpolynomial *pwqp2);
3987 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3988 __isl_take isl_pw_qpolynomial *pwqp1,
3989 __isl_take isl_pw_qpolynomial *pwqp2);
3990 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3991 __isl_take isl_pw_qpolynomial *pwqp1,
3992 __isl_take isl_pw_qpolynomial *pwqp2);
3993 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3994 __isl_take isl_pw_qpolynomial *pwqp);
3995 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3996 __isl_take isl_pw_qpolynomial *pwqp1,
3997 __isl_take isl_pw_qpolynomial *pwqp2);
3998 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3999 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4001 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4002 __isl_take isl_union_pw_qpolynomial *upwqp1,
4003 __isl_take isl_union_pw_qpolynomial *upwqp2);
4004 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4005 __isl_take isl_union_pw_qpolynomial *upwqp1,
4006 __isl_take isl_union_pw_qpolynomial *upwqp2);
4007 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4008 __isl_take isl_union_pw_qpolynomial *upwqp1,
4009 __isl_take isl_union_pw_qpolynomial *upwqp2);
4011 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4012 __isl_take isl_pw_qpolynomial *pwqp,
4013 __isl_take isl_point *pnt);
4015 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4016 __isl_take isl_union_pw_qpolynomial *upwqp,
4017 __isl_take isl_point *pnt);
4019 __isl_give isl_set *isl_pw_qpolynomial_domain(
4020 __isl_take isl_pw_qpolynomial *pwqp);
4021 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4022 __isl_take isl_pw_qpolynomial *pwpq,
4023 __isl_take isl_set *set);
4024 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4025 __isl_take isl_pw_qpolynomial *pwpq,
4026 __isl_take isl_set *set);
4028 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4029 __isl_take isl_union_pw_qpolynomial *upwqp);
4030 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4031 __isl_take isl_union_pw_qpolynomial *upwpq,
4032 __isl_take isl_union_set *uset);
4033 __isl_give isl_union_pw_qpolynomial *
4034 isl_union_pw_qpolynomial_intersect_params(
4035 __isl_take isl_union_pw_qpolynomial *upwpq,
4036 __isl_take isl_set *set);
4038 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4039 __isl_take isl_qpolynomial *qp,
4040 __isl_take isl_space *model);
4042 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4043 __isl_take isl_qpolynomial *qp);
4044 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4045 __isl_take isl_pw_qpolynomial *pwqp);
4047 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4048 __isl_take isl_union_pw_qpolynomial *upwqp);
4050 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4051 __isl_take isl_qpolynomial *qp,
4052 __isl_take isl_set *context);
4053 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4054 __isl_take isl_qpolynomial *qp,
4055 __isl_take isl_set *context);
4057 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4058 __isl_take isl_pw_qpolynomial *pwqp,
4059 __isl_take isl_set *context);
4060 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4061 __isl_take isl_pw_qpolynomial *pwqp,
4062 __isl_take isl_set *context);
4064 __isl_give isl_union_pw_qpolynomial *
4065 isl_union_pw_qpolynomial_gist_params(
4066 __isl_take isl_union_pw_qpolynomial *upwqp,
4067 __isl_take isl_set *context);
4068 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4069 __isl_take isl_union_pw_qpolynomial *upwqp,
4070 __isl_take isl_union_set *context);
4072 The gist operation applies the gist operation to each of
4073 the cells in the domain of the input piecewise quasipolynomial.
4074 The context is also exploited
4075 to simplify the quasipolynomials associated to each cell.
4077 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4078 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4079 __isl_give isl_union_pw_qpolynomial *
4080 isl_union_pw_qpolynomial_to_polynomial(
4081 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4083 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4084 the polynomial will be an overapproximation. If C<sign> is negative,
4085 it will be an underapproximation. If C<sign> is zero, the approximation
4086 will lie somewhere in between.
4088 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4090 A piecewise quasipolynomial reduction is a piecewise
4091 reduction (or fold) of quasipolynomials.
4092 In particular, the reduction can be maximum or a minimum.
4093 The objects are mainly used to represent the result of
4094 an upper or lower bound on a quasipolynomial over its domain,
4095 i.e., as the result of the following function.
4097 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4098 __isl_take isl_pw_qpolynomial *pwqp,
4099 enum isl_fold type, int *tight);
4101 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4102 __isl_take isl_union_pw_qpolynomial *upwqp,
4103 enum isl_fold type, int *tight);
4105 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4106 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4107 is the returned bound is known be tight, i.e., for each value
4108 of the parameters there is at least
4109 one element in the domain that reaches the bound.
4110 If the domain of C<pwqp> is not wrapping, then the bound is computed
4111 over all elements in that domain and the result has a purely parametric
4112 domain. If the domain of C<pwqp> is wrapping, then the bound is
4113 computed over the range of the wrapped relation. The domain of the
4114 wrapped relation becomes the domain of the result.
4116 A (piecewise) quasipolynomial reduction can be copied or freed using the
4117 following functions.
4119 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4120 __isl_keep isl_qpolynomial_fold *fold);
4121 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4122 __isl_keep isl_pw_qpolynomial_fold *pwf);
4123 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4124 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4125 void isl_qpolynomial_fold_free(
4126 __isl_take isl_qpolynomial_fold *fold);
4127 void *isl_pw_qpolynomial_fold_free(
4128 __isl_take isl_pw_qpolynomial_fold *pwf);
4129 void *isl_union_pw_qpolynomial_fold_free(
4130 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4132 =head3 Printing Piecewise Quasipolynomial Reductions
4134 Piecewise quasipolynomial reductions can be printed
4135 using the following function.
4137 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4138 __isl_take isl_printer *p,
4139 __isl_keep isl_pw_qpolynomial_fold *pwf);
4140 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4141 __isl_take isl_printer *p,
4142 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4144 For C<isl_printer_print_pw_qpolynomial_fold>,
4145 output format of the printer
4146 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4147 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4148 output format of the printer
4149 needs to be set to C<ISL_FORMAT_ISL>.
4150 In case of printing in C<ISL_FORMAT_C>, the user may want
4151 to set the names of all dimensions
4153 __isl_give isl_pw_qpolynomial_fold *
4154 isl_pw_qpolynomial_fold_set_dim_name(
4155 __isl_take isl_pw_qpolynomial_fold *pwf,
4156 enum isl_dim_type type, unsigned pos,
4159 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4161 To iterate over all piecewise quasipolynomial reductions in a union
4162 piecewise quasipolynomial reduction, use the following function
4164 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4165 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4166 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4167 void *user), void *user);
4169 To iterate over the cells in a piecewise quasipolynomial reduction,
4170 use either of the following two functions
4172 int isl_pw_qpolynomial_fold_foreach_piece(
4173 __isl_keep isl_pw_qpolynomial_fold *pwf,
4174 int (*fn)(__isl_take isl_set *set,
4175 __isl_take isl_qpolynomial_fold *fold,
4176 void *user), void *user);
4177 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4178 __isl_keep isl_pw_qpolynomial_fold *pwf,
4179 int (*fn)(__isl_take isl_set *set,
4180 __isl_take isl_qpolynomial_fold *fold,
4181 void *user), void *user);
4183 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4184 of the difference between these two functions.
4186 To iterate over all quasipolynomials in a reduction, use
4188 int isl_qpolynomial_fold_foreach_qpolynomial(
4189 __isl_keep isl_qpolynomial_fold *fold,
4190 int (*fn)(__isl_take isl_qpolynomial *qp,
4191 void *user), void *user);
4193 =head3 Properties of Piecewise Quasipolynomial Reductions
4195 To check whether two union piecewise quasipolynomial reductions are
4196 obviously equal, use
4198 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4199 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4200 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4202 =head3 Operations on Piecewise Quasipolynomial Reductions
4204 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4205 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4207 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4208 __isl_take isl_pw_qpolynomial_fold *pwf1,
4209 __isl_take isl_pw_qpolynomial_fold *pwf2);
4211 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4212 __isl_take isl_pw_qpolynomial_fold *pwf1,
4213 __isl_take isl_pw_qpolynomial_fold *pwf2);
4215 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4216 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4217 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4219 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4220 __isl_take isl_pw_qpolynomial_fold *pwf,
4221 __isl_take isl_point *pnt);
4223 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4224 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4225 __isl_take isl_point *pnt);
4227 __isl_give isl_pw_qpolynomial_fold *
4228 isl_pw_qpolynomial_fold_intersect_params(
4229 __isl_take isl_pw_qpolynomial_fold *pwf,
4230 __isl_take isl_set *set);
4232 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4233 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4234 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4235 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4236 __isl_take isl_union_set *uset);
4237 __isl_give isl_union_pw_qpolynomial_fold *
4238 isl_union_pw_qpolynomial_fold_intersect_params(
4239 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4240 __isl_take isl_set *set);
4242 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4243 __isl_take isl_pw_qpolynomial_fold *pwf);
4245 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4246 __isl_take isl_pw_qpolynomial_fold *pwf);
4248 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4249 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4251 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4252 __isl_take isl_qpolynomial_fold *fold,
4253 __isl_take isl_set *context);
4254 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4255 __isl_take isl_qpolynomial_fold *fold,
4256 __isl_take isl_set *context);
4258 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4259 __isl_take isl_pw_qpolynomial_fold *pwf,
4260 __isl_take isl_set *context);
4261 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4262 __isl_take isl_pw_qpolynomial_fold *pwf,
4263 __isl_take isl_set *context);
4265 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4266 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4267 __isl_take isl_union_set *context);
4268 __isl_give isl_union_pw_qpolynomial_fold *
4269 isl_union_pw_qpolynomial_fold_gist_params(
4270 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4271 __isl_take isl_set *context);
4273 The gist operation applies the gist operation to each of
4274 the cells in the domain of the input piecewise quasipolynomial reduction.
4275 In future, the operation will also exploit the context
4276 to simplify the quasipolynomial reductions associated to each cell.
4278 __isl_give isl_pw_qpolynomial_fold *
4279 isl_set_apply_pw_qpolynomial_fold(
4280 __isl_take isl_set *set,
4281 __isl_take isl_pw_qpolynomial_fold *pwf,
4283 __isl_give isl_pw_qpolynomial_fold *
4284 isl_map_apply_pw_qpolynomial_fold(
4285 __isl_take isl_map *map,
4286 __isl_take isl_pw_qpolynomial_fold *pwf,
4288 __isl_give isl_union_pw_qpolynomial_fold *
4289 isl_union_set_apply_union_pw_qpolynomial_fold(
4290 __isl_take isl_union_set *uset,
4291 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4293 __isl_give isl_union_pw_qpolynomial_fold *
4294 isl_union_map_apply_union_pw_qpolynomial_fold(
4295 __isl_take isl_union_map *umap,
4296 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4299 The functions taking a map
4300 compose the given map with the given piecewise quasipolynomial reduction.
4301 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4302 over all elements in the intersection of the range of the map
4303 and the domain of the piecewise quasipolynomial reduction
4304 as a function of an element in the domain of the map.
4305 The functions taking a set compute a bound over all elements in the
4306 intersection of the set and the domain of the
4307 piecewise quasipolynomial reduction.
4309 =head2 Dependence Analysis
4311 C<isl> contains specialized functionality for performing
4312 array dataflow analysis. That is, given a I<sink> access relation
4313 and a collection of possible I<source> access relations,
4314 C<isl> can compute relations that describe
4315 for each iteration of the sink access, which iteration
4316 of which of the source access relations was the last
4317 to access the same data element before the given iteration
4319 The resulting dependence relations map source iterations
4320 to the corresponding sink iterations.
4321 To compute standard flow dependences, the sink should be
4322 a read, while the sources should be writes.
4323 If any of the source accesses are marked as being I<may>
4324 accesses, then there will be a dependence from the last
4325 I<must> access B<and> from any I<may> access that follows
4326 this last I<must> access.
4327 In particular, if I<all> sources are I<may> accesses,
4328 then memory based dependence analysis is performed.
4329 If, on the other hand, all sources are I<must> accesses,
4330 then value based dependence analysis is performed.
4332 #include <isl/flow.h>
4334 typedef int (*isl_access_level_before)(void *first, void *second);
4336 __isl_give isl_access_info *isl_access_info_alloc(
4337 __isl_take isl_map *sink,
4338 void *sink_user, isl_access_level_before fn,
4340 __isl_give isl_access_info *isl_access_info_add_source(
4341 __isl_take isl_access_info *acc,
4342 __isl_take isl_map *source, int must,
4344 void *isl_access_info_free(__isl_take isl_access_info *acc);
4346 __isl_give isl_flow *isl_access_info_compute_flow(
4347 __isl_take isl_access_info *acc);
4349 int isl_flow_foreach(__isl_keep isl_flow *deps,
4350 int (*fn)(__isl_take isl_map *dep, int must,
4351 void *dep_user, void *user),
4353 __isl_give isl_map *isl_flow_get_no_source(
4354 __isl_keep isl_flow *deps, int must);
4355 void isl_flow_free(__isl_take isl_flow *deps);
4357 The function C<isl_access_info_compute_flow> performs the actual
4358 dependence analysis. The other functions are used to construct
4359 the input for this function or to read off the output.
4361 The input is collected in an C<isl_access_info>, which can
4362 be created through a call to C<isl_access_info_alloc>.
4363 The arguments to this functions are the sink access relation
4364 C<sink>, a token C<sink_user> used to identify the sink
4365 access to the user, a callback function for specifying the
4366 relative order of source and sink accesses, and the number
4367 of source access relations that will be added.
4368 The callback function has type C<int (*)(void *first, void *second)>.
4369 The function is called with two user supplied tokens identifying
4370 either a source or the sink and it should return the shared nesting
4371 level and the relative order of the two accesses.
4372 In particular, let I<n> be the number of loops shared by
4373 the two accesses. If C<first> precedes C<second> textually,
4374 then the function should return I<2 * n + 1>; otherwise,
4375 it should return I<2 * n>.
4376 The sources can be added to the C<isl_access_info> by performing
4377 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4378 C<must> indicates whether the source is a I<must> access
4379 or a I<may> access. Note that a multi-valued access relation
4380 should only be marked I<must> if every iteration in the domain
4381 of the relation accesses I<all> elements in its image.
4382 The C<source_user> token is again used to identify
4383 the source access. The range of the source access relation
4384 C<source> should have the same dimension as the range
4385 of the sink access relation.
4386 The C<isl_access_info_free> function should usually not be
4387 called explicitly, because it is called implicitly by
4388 C<isl_access_info_compute_flow>.
4390 The result of the dependence analysis is collected in an
4391 C<isl_flow>. There may be elements of
4392 the sink access for which no preceding source access could be
4393 found or for which all preceding sources are I<may> accesses.
4394 The relations containing these elements can be obtained through
4395 calls to C<isl_flow_get_no_source>, the first with C<must> set
4396 and the second with C<must> unset.
4397 In the case of standard flow dependence analysis,
4398 with the sink a read and the sources I<must> writes,
4399 the first relation corresponds to the reads from uninitialized
4400 array elements and the second relation is empty.
4401 The actual flow dependences can be extracted using
4402 C<isl_flow_foreach>. This function will call the user-specified
4403 callback function C<fn> for each B<non-empty> dependence between
4404 a source and the sink. The callback function is called
4405 with four arguments, the actual flow dependence relation
4406 mapping source iterations to sink iterations, a boolean that
4407 indicates whether it is a I<must> or I<may> dependence, a token
4408 identifying the source and an additional C<void *> with value
4409 equal to the third argument of the C<isl_flow_foreach> call.
4410 A dependence is marked I<must> if it originates from a I<must>
4411 source and if it is not followed by any I<may> sources.
4413 After finishing with an C<isl_flow>, the user should call
4414 C<isl_flow_free> to free all associated memory.
4416 A higher-level interface to dependence analysis is provided
4417 by the following function.
4419 #include <isl/flow.h>
4421 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4422 __isl_take isl_union_map *must_source,
4423 __isl_take isl_union_map *may_source,
4424 __isl_take isl_union_map *schedule,
4425 __isl_give isl_union_map **must_dep,
4426 __isl_give isl_union_map **may_dep,
4427 __isl_give isl_union_map **must_no_source,
4428 __isl_give isl_union_map **may_no_source);
4430 The arrays are identified by the tuple names of the ranges
4431 of the accesses. The iteration domains by the tuple names
4432 of the domains of the accesses and of the schedule.
4433 The relative order of the iteration domains is given by the
4434 schedule. The relations returned through C<must_no_source>
4435 and C<may_no_source> are subsets of C<sink>.
4436 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4437 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4438 any of the other arguments is treated as an error.
4440 =head3 Interaction with Dependence Analysis
4442 During the dependence analysis, we frequently need to perform
4443 the following operation. Given a relation between sink iterations
4444 and potential source iterations from a particular source domain,
4445 what is the last potential source iteration corresponding to each
4446 sink iteration. It can sometimes be convenient to adjust
4447 the set of potential source iterations before or after each such operation.
4448 The prototypical example is fuzzy array dataflow analysis,
4449 where we need to analyze if, based on data-dependent constraints,
4450 the sink iteration can ever be executed without one or more of
4451 the corresponding potential source iterations being executed.
4452 If so, we can introduce extra parameters and select an unknown
4453 but fixed source iteration from the potential source iterations.
4454 To be able to perform such manipulations, C<isl> provides the following
4457 #include <isl/flow.h>
4459 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4460 __isl_keep isl_map *source_map,
4461 __isl_keep isl_set *sink, void *source_user,
4463 __isl_give isl_access_info *isl_access_info_set_restrict(
4464 __isl_take isl_access_info *acc,
4465 isl_access_restrict fn, void *user);
4467 The function C<isl_access_info_set_restrict> should be called
4468 before calling C<isl_access_info_compute_flow> and registers a callback function
4469 that will be called any time C<isl> is about to compute the last
4470 potential source. The first argument is the (reverse) proto-dependence,
4471 mapping sink iterations to potential source iterations.
4472 The second argument represents the sink iterations for which
4473 we want to compute the last source iteration.
4474 The third argument is the token corresponding to the source
4475 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4476 The callback is expected to return a restriction on either the input or
4477 the output of the operation computing the last potential source.
4478 If the input needs to be restricted then restrictions are needed
4479 for both the source and the sink iterations. The sink iterations
4480 and the potential source iterations will be intersected with these sets.
4481 If the output needs to be restricted then only a restriction on the source
4482 iterations is required.
4483 If any error occurs, the callback should return C<NULL>.
4484 An C<isl_restriction> object can be created, freed and inspected
4485 using the following functions.
4487 #include <isl/flow.h>
4489 __isl_give isl_restriction *isl_restriction_input(
4490 __isl_take isl_set *source_restr,
4491 __isl_take isl_set *sink_restr);
4492 __isl_give isl_restriction *isl_restriction_output(
4493 __isl_take isl_set *source_restr);
4494 __isl_give isl_restriction *isl_restriction_none(
4495 __isl_take isl_map *source_map);
4496 __isl_give isl_restriction *isl_restriction_empty(
4497 __isl_take isl_map *source_map);
4498 void *isl_restriction_free(
4499 __isl_take isl_restriction *restr);
4500 isl_ctx *isl_restriction_get_ctx(
4501 __isl_keep isl_restriction *restr);
4503 C<isl_restriction_none> and C<isl_restriction_empty> are special
4504 cases of C<isl_restriction_input>. C<isl_restriction_none>
4505 is essentially equivalent to
4507 isl_restriction_input(isl_set_universe(
4508 isl_space_range(isl_map_get_space(source_map))),
4510 isl_space_domain(isl_map_get_space(source_map))));
4512 whereas C<isl_restriction_empty> is essentially equivalent to
4514 isl_restriction_input(isl_set_empty(
4515 isl_space_range(isl_map_get_space(source_map))),
4517 isl_space_domain(isl_map_get_space(source_map))));
4521 B<The functionality described in this section is fairly new
4522 and may be subject to change.>
4524 The following function can be used to compute a schedule
4525 for a union of domains.
4526 By default, the algorithm used to construct the schedule is similar
4527 to that of C<Pluto>.
4528 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4530 The generated schedule respects all C<validity> dependences.
4531 That is, all dependence distances over these dependences in the
4532 scheduled space are lexicographically positive.
4533 The default algorithm tries to minimize the dependence distances over
4534 C<proximity> dependences.
4535 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4536 for groups of domains where the dependence distances have only
4537 non-negative values.
4538 When using Feautrier's algorithm, the C<proximity> dependence
4539 distances are only minimized during the extension to a
4540 full-dimensional schedule.
4542 #include <isl/schedule.h>
4543 __isl_give isl_schedule *isl_union_set_compute_schedule(
4544 __isl_take isl_union_set *domain,
4545 __isl_take isl_union_map *validity,
4546 __isl_take isl_union_map *proximity);
4547 void *isl_schedule_free(__isl_take isl_schedule *sched);
4549 A mapping from the domains to the scheduled space can be obtained
4550 from an C<isl_schedule> using the following function.
4552 __isl_give isl_union_map *isl_schedule_get_map(
4553 __isl_keep isl_schedule *sched);
4555 A representation of the schedule can be printed using
4557 __isl_give isl_printer *isl_printer_print_schedule(
4558 __isl_take isl_printer *p,
4559 __isl_keep isl_schedule *schedule);
4561 A representation of the schedule as a forest of bands can be obtained
4562 using the following function.
4564 __isl_give isl_band_list *isl_schedule_get_band_forest(
4565 __isl_keep isl_schedule *schedule);
4567 The individual bands can be visited in depth-first post-order
4568 using the following function.
4570 #include <isl/schedule.h>
4571 int isl_schedule_foreach_band(
4572 __isl_keep isl_schedule *sched,
4573 int (*fn)(__isl_keep isl_band *band, void *user),
4576 The list can be manipulated as explained in L<"Lists">.
4577 The bands inside the list can be copied and freed using the following
4580 #include <isl/band.h>
4581 __isl_give isl_band *isl_band_copy(
4582 __isl_keep isl_band *band);
4583 void *isl_band_free(__isl_take isl_band *band);
4585 Each band contains zero or more scheduling dimensions.
4586 These are referred to as the members of the band.
4587 The section of the schedule that corresponds to the band is
4588 referred to as the partial schedule of the band.
4589 For those nodes that participate in a band, the outer scheduling
4590 dimensions form the prefix schedule, while the inner scheduling
4591 dimensions form the suffix schedule.
4592 That is, if we take a cut of the band forest, then the union of
4593 the concatenations of the prefix, partial and suffix schedules of
4594 each band in the cut is equal to the entire schedule (modulo
4595 some possible padding at the end with zero scheduling dimensions).
4596 The properties of a band can be inspected using the following functions.
4598 #include <isl/band.h>
4599 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4601 int isl_band_has_children(__isl_keep isl_band *band);
4602 __isl_give isl_band_list *isl_band_get_children(
4603 __isl_keep isl_band *band);
4605 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4606 __isl_keep isl_band *band);
4607 __isl_give isl_union_map *isl_band_get_partial_schedule(
4608 __isl_keep isl_band *band);
4609 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4610 __isl_keep isl_band *band);
4612 int isl_band_n_member(__isl_keep isl_band *band);
4613 int isl_band_member_is_zero_distance(
4614 __isl_keep isl_band *band, int pos);
4616 int isl_band_list_foreach_band(
4617 __isl_keep isl_band_list *list,
4618 int (*fn)(__isl_keep isl_band *band, void *user),
4621 Note that a scheduling dimension is considered to be ``zero
4622 distance'' if it does not carry any proximity dependences
4624 That is, if the dependence distances of the proximity
4625 dependences are all zero in that direction (for fixed
4626 iterations of outer bands).
4627 Like C<isl_schedule_foreach_band>,
4628 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4629 in depth-first post-order.
4631 A band can be tiled using the following function.
4633 #include <isl/band.h>
4634 int isl_band_tile(__isl_keep isl_band *band,
4635 __isl_take isl_vec *sizes);
4637 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4639 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4641 The C<isl_band_tile> function tiles the band using the given tile sizes
4642 inside its schedule.
4643 A new child band is created to represent the point loops and it is
4644 inserted between the modified band and its children.
4645 The C<tile_scale_tile_loops> option specifies whether the tile
4646 loops iterators should be scaled by the tile sizes.
4648 A representation of the band can be printed using
4650 #include <isl/band.h>
4651 __isl_give isl_printer *isl_printer_print_band(
4652 __isl_take isl_printer *p,
4653 __isl_keep isl_band *band);
4657 #include <isl/schedule.h>
4658 int isl_options_set_schedule_max_coefficient(
4659 isl_ctx *ctx, int val);
4660 int isl_options_get_schedule_max_coefficient(
4662 int isl_options_set_schedule_max_constant_term(
4663 isl_ctx *ctx, int val);
4664 int isl_options_get_schedule_max_constant_term(
4666 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4667 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4668 int isl_options_set_schedule_maximize_band_depth(
4669 isl_ctx *ctx, int val);
4670 int isl_options_get_schedule_maximize_band_depth(
4672 int isl_options_set_schedule_outer_zero_distance(
4673 isl_ctx *ctx, int val);
4674 int isl_options_get_schedule_outer_zero_distance(
4676 int isl_options_set_schedule_split_scaled(
4677 isl_ctx *ctx, int val);
4678 int isl_options_get_schedule_split_scaled(
4680 int isl_options_set_schedule_algorithm(
4681 isl_ctx *ctx, int val);
4682 int isl_options_get_schedule_algorithm(
4684 int isl_options_set_schedule_separate_components(
4685 isl_ctx *ctx, int val);
4686 int isl_options_get_schedule_separate_components(
4691 =item * schedule_max_coefficient
4693 This option enforces that the coefficients for variable and parameter
4694 dimensions in the calculated schedule are not larger than the specified value.
4695 This option can significantly increase the speed of the scheduling calculation
4696 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4697 this option does not introduce bounds on the variable or parameter
4700 =item * schedule_max_constant_term
4702 This option enforces that the constant coefficients in the calculated schedule
4703 are not larger than the maximal constant term. This option can significantly
4704 increase the speed of the scheduling calculation and may also prevent fusing of
4705 unrelated dimensions. A value of -1 means that this option does not introduce
4706 bounds on the constant coefficients.
4708 =item * schedule_fuse
4710 This option controls the level of fusion.
4711 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4712 resulting schedule will be distributed as much as possible.
4713 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4714 try to fuse loops in the resulting schedule.
4716 =item * schedule_maximize_band_depth
4718 If this option is set, we do not split bands at the point
4719 where we detect splitting is necessary. Instead, we
4720 backtrack and split bands as early as possible. This
4721 reduces the number of splits and maximizes the width of
4722 the bands. Wider bands give more possibilities for tiling.
4723 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4724 then bands will be split as early as possible, even if there is no need.
4725 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4727 =item * schedule_outer_zero_distance
4729 If this option is set, then we try to construct schedules
4730 where the outermost scheduling dimension in each band
4731 results in a zero dependence distance over the proximity
4734 =item * schedule_split_scaled
4736 If this option is set, then we try to construct schedules in which the
4737 constant term is split off from the linear part if the linear parts of
4738 the scheduling rows for all nodes in the graphs have a common non-trivial
4740 The constant term is then placed in a separate band and the linear
4743 =item * schedule_algorithm
4745 Selects the scheduling algorithm to be used.
4746 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4747 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4749 =item * schedule_separate_components
4751 If at any point the dependence graph contains any (weakly connected) components,
4752 then these components are scheduled separately.
4753 If this option is not set, then some iterations of the domains
4754 in these components may be scheduled together.
4755 If this option is set, then the components are given consecutive
4760 =head2 Parametric Vertex Enumeration
4762 The parametric vertex enumeration described in this section
4763 is mainly intended to be used internally and by the C<barvinok>
4766 #include <isl/vertices.h>
4767 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4768 __isl_keep isl_basic_set *bset);
4770 The function C<isl_basic_set_compute_vertices> performs the
4771 actual computation of the parametric vertices and the chamber
4772 decomposition and store the result in an C<isl_vertices> object.
4773 This information can be queried by either iterating over all
4774 the vertices or iterating over all the chambers or cells
4775 and then iterating over all vertices that are active on the chamber.
4777 int isl_vertices_foreach_vertex(
4778 __isl_keep isl_vertices *vertices,
4779 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4782 int isl_vertices_foreach_cell(
4783 __isl_keep isl_vertices *vertices,
4784 int (*fn)(__isl_take isl_cell *cell, void *user),
4786 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4787 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4790 Other operations that can be performed on an C<isl_vertices> object are
4793 isl_ctx *isl_vertices_get_ctx(
4794 __isl_keep isl_vertices *vertices);
4795 int isl_vertices_get_n_vertices(
4796 __isl_keep isl_vertices *vertices);
4797 void isl_vertices_free(__isl_take isl_vertices *vertices);
4799 Vertices can be inspected and destroyed using the following functions.
4801 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4802 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4803 __isl_give isl_basic_set *isl_vertex_get_domain(
4804 __isl_keep isl_vertex *vertex);
4805 __isl_give isl_basic_set *isl_vertex_get_expr(
4806 __isl_keep isl_vertex *vertex);
4807 void isl_vertex_free(__isl_take isl_vertex *vertex);
4809 C<isl_vertex_get_expr> returns a singleton parametric set describing
4810 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4812 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4813 B<rational> basic sets, so they should mainly be used for inspection
4814 and should not be mixed with integer sets.
4816 Chambers can be inspected and destroyed using the following functions.
4818 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4819 __isl_give isl_basic_set *isl_cell_get_domain(
4820 __isl_keep isl_cell *cell);
4821 void isl_cell_free(__isl_take isl_cell *cell);
4825 Although C<isl> is mainly meant to be used as a library,
4826 it also contains some basic applications that use some
4827 of the functionality of C<isl>.
4828 The input may be specified in either the L<isl format>
4829 or the L<PolyLib format>.
4831 =head2 C<isl_polyhedron_sample>
4833 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4834 an integer element of the polyhedron, if there is any.
4835 The first column in the output is the denominator and is always
4836 equal to 1. If the polyhedron contains no integer points,
4837 then a vector of length zero is printed.
4841 C<isl_pip> takes the same input as the C<example> program
4842 from the C<piplib> distribution, i.e., a set of constraints
4843 on the parameters, a line containing only -1 and finally a set
4844 of constraints on a parametric polyhedron.
4845 The coefficients of the parameters appear in the last columns
4846 (but before the final constant column).
4847 The output is the lexicographic minimum of the parametric polyhedron.
4848 As C<isl> currently does not have its own output format, the output
4849 is just a dump of the internal state.
4851 =head2 C<isl_polyhedron_minimize>
4853 C<isl_polyhedron_minimize> computes the minimum of some linear
4854 or affine objective function over the integer points in a polyhedron.
4855 If an affine objective function
4856 is given, then the constant should appear in the last column.
4858 =head2 C<isl_polytope_scan>
4860 Given a polytope, C<isl_polytope_scan> prints
4861 all integer points in the polytope.