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);
2865 Lists are defined over several element types, including
2866 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2867 Here we take lists of C<isl_set>s as an example.
2868 Lists can be created, copied, modified and freed using the following functions.
2870 #include <isl/list.h>
2871 __isl_give isl_set_list *isl_set_list_from_set(
2872 __isl_take isl_set *el);
2873 __isl_give isl_set_list *isl_set_list_alloc(
2874 isl_ctx *ctx, int n);
2875 __isl_give isl_set_list *isl_set_list_copy(
2876 __isl_keep isl_set_list *list);
2877 __isl_give isl_set_list *isl_set_list_add(
2878 __isl_take isl_set_list *list,
2879 __isl_take isl_set *el);
2880 __isl_give isl_set_list *isl_set_list_set_set(
2881 __isl_take isl_set_list *list, int index,
2882 __isl_take isl_set *set);
2883 __isl_give isl_set_list *isl_set_list_concat(
2884 __isl_take isl_set_list *list1,
2885 __isl_take isl_set_list *list2);
2886 void *isl_set_list_free(__isl_take isl_set_list *list);
2888 C<isl_set_list_alloc> creates an empty list with a capacity for
2889 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2892 Lists can be inspected using the following functions.
2894 #include <isl/list.h>
2895 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2896 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2897 __isl_give isl_set *isl_set_list_get_set(
2898 __isl_keep isl_set_list *list, int index);
2899 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2900 int (*fn)(__isl_take isl_set *el, void *user),
2903 Lists can be printed using
2905 #include <isl/list.h>
2906 __isl_give isl_printer *isl_printer_print_set_list(
2907 __isl_take isl_printer *p,
2908 __isl_keep isl_set_list *list);
2912 Vectors can be created, copied and freed using the following functions.
2914 #include <isl/vec.h>
2915 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2917 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2918 void isl_vec_free(__isl_take isl_vec *vec);
2920 Note that the elements of a newly created vector may have arbitrary values.
2921 The elements can be changed and inspected using the following functions.
2923 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2924 int isl_vec_size(__isl_keep isl_vec *vec);
2925 int isl_vec_get_element(__isl_keep isl_vec *vec,
2926 int pos, isl_int *v);
2927 __isl_give isl_vec *isl_vec_set_element(
2928 __isl_take isl_vec *vec, int pos, isl_int v);
2929 __isl_give isl_vec *isl_vec_set_element_si(
2930 __isl_take isl_vec *vec, int pos, int v);
2931 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2933 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2936 C<isl_vec_get_element> will return a negative value if anything went wrong.
2937 In that case, the value of C<*v> is undefined.
2941 Matrices can be created, copied and freed using the following functions.
2943 #include <isl/mat.h>
2944 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2945 unsigned n_row, unsigned n_col);
2946 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2947 void isl_mat_free(__isl_take isl_mat *mat);
2949 Note that the elements of a newly created matrix may have arbitrary values.
2950 The elements can be changed and inspected using the following functions.
2952 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2953 int isl_mat_rows(__isl_keep isl_mat *mat);
2954 int isl_mat_cols(__isl_keep isl_mat *mat);
2955 int isl_mat_get_element(__isl_keep isl_mat *mat,
2956 int row, int col, isl_int *v);
2957 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2958 int row, int col, isl_int v);
2959 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2960 int row, int col, int v);
2962 C<isl_mat_get_element> will return a negative value if anything went wrong.
2963 In that case, the value of C<*v> is undefined.
2965 The following function can be used to compute the (right) inverse
2966 of a matrix, i.e., a matrix such that the product of the original
2967 and the inverse (in that order) is a multiple of the identity matrix.
2968 The input matrix is assumed to be of full row-rank.
2970 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2972 The following function can be used to compute the (right) kernel
2973 (or null space) of a matrix, i.e., a matrix such that the product of
2974 the original and the kernel (in that order) is the zero matrix.
2976 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2978 =head2 Piecewise Quasi Affine Expressions
2980 The zero quasi affine expression on a given domain can be created using
2982 __isl_give isl_aff *isl_aff_zero_on_domain(
2983 __isl_take isl_local_space *ls);
2985 Note that the space in which the resulting object lives is a map space
2986 with the given space as domain and a one-dimensional range.
2988 An empty piecewise quasi affine expression (one with no cells)
2989 or a piecewise quasi affine expression with a single cell can
2990 be created using the following functions.
2992 #include <isl/aff.h>
2993 __isl_give isl_pw_aff *isl_pw_aff_empty(
2994 __isl_take isl_space *space);
2995 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2996 __isl_take isl_set *set, __isl_take isl_aff *aff);
2997 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2998 __isl_take isl_aff *aff);
3000 A piecewise quasi affine expression that is equal to 1 on a set
3001 and 0 outside the set can be created using the following function.
3003 #include <isl/aff.h>
3004 __isl_give isl_pw_aff *isl_set_indicator_function(
3005 __isl_take isl_set *set);
3007 Quasi affine expressions can be copied and freed using
3009 #include <isl/aff.h>
3010 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3011 void *isl_aff_free(__isl_take isl_aff *aff);
3013 __isl_give isl_pw_aff *isl_pw_aff_copy(
3014 __isl_keep isl_pw_aff *pwaff);
3015 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3017 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3018 using the following function. The constraint is required to have
3019 a non-zero coefficient for the specified dimension.
3021 #include <isl/constraint.h>
3022 __isl_give isl_aff *isl_constraint_get_bound(
3023 __isl_keep isl_constraint *constraint,
3024 enum isl_dim_type type, int pos);
3026 The entire affine expression of the constraint can also be extracted
3027 using the following function.
3029 #include <isl/constraint.h>
3030 __isl_give isl_aff *isl_constraint_get_aff(
3031 __isl_keep isl_constraint *constraint);
3033 Conversely, an equality constraint equating
3034 the affine expression to zero or an inequality constraint enforcing
3035 the affine expression to be non-negative, can be constructed using
3037 __isl_give isl_constraint *isl_equality_from_aff(
3038 __isl_take isl_aff *aff);
3039 __isl_give isl_constraint *isl_inequality_from_aff(
3040 __isl_take isl_aff *aff);
3042 The expression can be inspected using
3044 #include <isl/aff.h>
3045 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3046 int isl_aff_dim(__isl_keep isl_aff *aff,
3047 enum isl_dim_type type);
3048 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3049 __isl_keep isl_aff *aff);
3050 __isl_give isl_local_space *isl_aff_get_local_space(
3051 __isl_keep isl_aff *aff);
3052 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3053 enum isl_dim_type type, unsigned pos);
3054 const char *isl_pw_aff_get_dim_name(
3055 __isl_keep isl_pw_aff *pa,
3056 enum isl_dim_type type, unsigned pos);
3057 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3058 enum isl_dim_type type, unsigned pos);
3059 __isl_give isl_id *isl_pw_aff_get_dim_id(
3060 __isl_keep isl_pw_aff *pa,
3061 enum isl_dim_type type, unsigned pos);
3062 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3063 __isl_keep isl_pw_aff *pa,
3064 enum isl_dim_type type);
3065 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3067 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3068 enum isl_dim_type type, int pos, isl_int *v);
3069 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3071 __isl_give isl_aff *isl_aff_get_div(
3072 __isl_keep isl_aff *aff, int pos);
3074 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3075 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3076 int (*fn)(__isl_take isl_set *set,
3077 __isl_take isl_aff *aff,
3078 void *user), void *user);
3080 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3081 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3083 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3084 enum isl_dim_type type, unsigned first, unsigned n);
3085 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3086 enum isl_dim_type type, unsigned first, unsigned n);
3088 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3089 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3090 enum isl_dim_type type);
3091 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3093 It can be modified using
3095 #include <isl/aff.h>
3096 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3097 __isl_take isl_pw_aff *pwaff,
3098 enum isl_dim_type type, __isl_take isl_id *id);
3099 __isl_give isl_aff *isl_aff_set_dim_name(
3100 __isl_take isl_aff *aff, enum isl_dim_type type,
3101 unsigned pos, const char *s);
3102 __isl_give isl_aff *isl_aff_set_dim_id(
3103 __isl_take isl_aff *aff, enum isl_dim_type type,
3104 unsigned pos, __isl_take isl_id *id);
3105 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3106 __isl_take isl_pw_aff *pma,
3107 enum isl_dim_type type, unsigned pos,
3108 __isl_take isl_id *id);
3109 __isl_give isl_aff *isl_aff_set_constant(
3110 __isl_take isl_aff *aff, isl_int v);
3111 __isl_give isl_aff *isl_aff_set_constant_si(
3112 __isl_take isl_aff *aff, int v);
3113 __isl_give isl_aff *isl_aff_set_coefficient(
3114 __isl_take isl_aff *aff,
3115 enum isl_dim_type type, int pos, isl_int v);
3116 __isl_give isl_aff *isl_aff_set_coefficient_si(
3117 __isl_take isl_aff *aff,
3118 enum isl_dim_type type, int pos, int v);
3119 __isl_give isl_aff *isl_aff_set_denominator(
3120 __isl_take isl_aff *aff, isl_int v);
3122 __isl_give isl_aff *isl_aff_add_constant(
3123 __isl_take isl_aff *aff, isl_int v);
3124 __isl_give isl_aff *isl_aff_add_constant_si(
3125 __isl_take isl_aff *aff, int v);
3126 __isl_give isl_aff *isl_aff_add_constant_num(
3127 __isl_take isl_aff *aff, isl_int v);
3128 __isl_give isl_aff *isl_aff_add_constant_num_si(
3129 __isl_take isl_aff *aff, int v);
3130 __isl_give isl_aff *isl_aff_add_coefficient(
3131 __isl_take isl_aff *aff,
3132 enum isl_dim_type type, int pos, isl_int v);
3133 __isl_give isl_aff *isl_aff_add_coefficient_si(
3134 __isl_take isl_aff *aff,
3135 enum isl_dim_type type, int pos, int v);
3137 __isl_give isl_aff *isl_aff_insert_dims(
3138 __isl_take isl_aff *aff,
3139 enum isl_dim_type type, unsigned first, unsigned n);
3140 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3141 __isl_take isl_pw_aff *pwaff,
3142 enum isl_dim_type type, unsigned first, unsigned n);
3143 __isl_give isl_aff *isl_aff_add_dims(
3144 __isl_take isl_aff *aff,
3145 enum isl_dim_type type, unsigned n);
3146 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3147 __isl_take isl_pw_aff *pwaff,
3148 enum isl_dim_type type, unsigned n);
3149 __isl_give isl_aff *isl_aff_drop_dims(
3150 __isl_take isl_aff *aff,
3151 enum isl_dim_type type, unsigned first, unsigned n);
3152 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3153 __isl_take isl_pw_aff *pwaff,
3154 enum isl_dim_type type, unsigned first, unsigned n);
3156 Note that the C<set_constant> and C<set_coefficient> functions
3157 set the I<numerator> of the constant or coefficient, while
3158 C<add_constant> and C<add_coefficient> add an integer value to
3159 the possibly rational constant or coefficient.
3160 The C<add_constant_num> functions add an integer value to
3163 To check whether an affine expressions is obviously zero
3164 or obviously equal to some other affine expression, use
3166 #include <isl/aff.h>
3167 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3168 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3169 __isl_keep isl_aff *aff2);
3170 int isl_pw_aff_plain_is_equal(
3171 __isl_keep isl_pw_aff *pwaff1,
3172 __isl_keep isl_pw_aff *pwaff2);
3176 #include <isl/aff.h>
3177 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3178 __isl_take isl_aff *aff2);
3179 __isl_give isl_pw_aff *isl_pw_aff_add(
3180 __isl_take isl_pw_aff *pwaff1,
3181 __isl_take isl_pw_aff *pwaff2);
3182 __isl_give isl_pw_aff *isl_pw_aff_min(
3183 __isl_take isl_pw_aff *pwaff1,
3184 __isl_take isl_pw_aff *pwaff2);
3185 __isl_give isl_pw_aff *isl_pw_aff_max(
3186 __isl_take isl_pw_aff *pwaff1,
3187 __isl_take isl_pw_aff *pwaff2);
3188 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3189 __isl_take isl_aff *aff2);
3190 __isl_give isl_pw_aff *isl_pw_aff_sub(
3191 __isl_take isl_pw_aff *pwaff1,
3192 __isl_take isl_pw_aff *pwaff2);
3193 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3194 __isl_give isl_pw_aff *isl_pw_aff_neg(
3195 __isl_take isl_pw_aff *pwaff);
3196 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3197 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3198 __isl_take isl_pw_aff *pwaff);
3199 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3200 __isl_give isl_pw_aff *isl_pw_aff_floor(
3201 __isl_take isl_pw_aff *pwaff);
3202 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3204 __isl_give isl_pw_aff *isl_pw_aff_mod(
3205 __isl_take isl_pw_aff *pwaff, isl_int mod);
3206 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3208 __isl_give isl_pw_aff *isl_pw_aff_scale(
3209 __isl_take isl_pw_aff *pwaff, isl_int f);
3210 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3212 __isl_give isl_aff *isl_aff_scale_down_ui(
3213 __isl_take isl_aff *aff, unsigned f);
3214 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3215 __isl_take isl_pw_aff *pwaff, isl_int f);
3217 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3218 __isl_take isl_pw_aff_list *list);
3219 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3220 __isl_take isl_pw_aff_list *list);
3222 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3223 __isl_take isl_pw_aff *pwqp);
3225 __isl_give isl_aff *isl_aff_align_params(
3226 __isl_take isl_aff *aff,
3227 __isl_take isl_space *model);
3228 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3229 __isl_take isl_pw_aff *pwaff,
3230 __isl_take isl_space *model);
3232 __isl_give isl_aff *isl_aff_project_domain_on_params(
3233 __isl_take isl_aff *aff);
3235 __isl_give isl_aff *isl_aff_gist_params(
3236 __isl_take isl_aff *aff,
3237 __isl_take isl_set *context);
3238 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3239 __isl_take isl_set *context);
3240 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3241 __isl_take isl_pw_aff *pwaff,
3242 __isl_take isl_set *context);
3243 __isl_give isl_pw_aff *isl_pw_aff_gist(
3244 __isl_take isl_pw_aff *pwaff,
3245 __isl_take isl_set *context);
3247 __isl_give isl_set *isl_pw_aff_domain(
3248 __isl_take isl_pw_aff *pwaff);
3249 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3250 __isl_take isl_pw_aff *pa,
3251 __isl_take isl_set *set);
3252 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3253 __isl_take isl_pw_aff *pa,
3254 __isl_take isl_set *set);
3256 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3257 __isl_take isl_aff *aff2);
3258 __isl_give isl_pw_aff *isl_pw_aff_mul(
3259 __isl_take isl_pw_aff *pwaff1,
3260 __isl_take isl_pw_aff *pwaff2);
3262 When multiplying two affine expressions, at least one of the two needs
3265 #include <isl/aff.h>
3266 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3267 __isl_take isl_aff *aff);
3268 __isl_give isl_basic_set *isl_aff_le_basic_set(
3269 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3270 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3271 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3272 __isl_give isl_set *isl_pw_aff_eq_set(
3273 __isl_take isl_pw_aff *pwaff1,
3274 __isl_take isl_pw_aff *pwaff2);
3275 __isl_give isl_set *isl_pw_aff_ne_set(
3276 __isl_take isl_pw_aff *pwaff1,
3277 __isl_take isl_pw_aff *pwaff2);
3278 __isl_give isl_set *isl_pw_aff_le_set(
3279 __isl_take isl_pw_aff *pwaff1,
3280 __isl_take isl_pw_aff *pwaff2);
3281 __isl_give isl_set *isl_pw_aff_lt_set(
3282 __isl_take isl_pw_aff *pwaff1,
3283 __isl_take isl_pw_aff *pwaff2);
3284 __isl_give isl_set *isl_pw_aff_ge_set(
3285 __isl_take isl_pw_aff *pwaff1,
3286 __isl_take isl_pw_aff *pwaff2);
3287 __isl_give isl_set *isl_pw_aff_gt_set(
3288 __isl_take isl_pw_aff *pwaff1,
3289 __isl_take isl_pw_aff *pwaff2);
3291 __isl_give isl_set *isl_pw_aff_list_eq_set(
3292 __isl_take isl_pw_aff_list *list1,
3293 __isl_take isl_pw_aff_list *list2);
3294 __isl_give isl_set *isl_pw_aff_list_ne_set(
3295 __isl_take isl_pw_aff_list *list1,
3296 __isl_take isl_pw_aff_list *list2);
3297 __isl_give isl_set *isl_pw_aff_list_le_set(
3298 __isl_take isl_pw_aff_list *list1,
3299 __isl_take isl_pw_aff_list *list2);
3300 __isl_give isl_set *isl_pw_aff_list_lt_set(
3301 __isl_take isl_pw_aff_list *list1,
3302 __isl_take isl_pw_aff_list *list2);
3303 __isl_give isl_set *isl_pw_aff_list_ge_set(
3304 __isl_take isl_pw_aff_list *list1,
3305 __isl_take isl_pw_aff_list *list2);
3306 __isl_give isl_set *isl_pw_aff_list_gt_set(
3307 __isl_take isl_pw_aff_list *list1,
3308 __isl_take isl_pw_aff_list *list2);
3310 The function C<isl_aff_neg_basic_set> returns a basic set
3311 containing those elements in the domain space
3312 of C<aff> where C<aff> is negative.
3313 The function C<isl_aff_ge_basic_set> returns a basic set
3314 containing those elements in the shared space
3315 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3316 The function C<isl_pw_aff_ge_set> returns a set
3317 containing those elements in the shared domain
3318 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3319 The functions operating on C<isl_pw_aff_list> apply the corresponding
3320 C<isl_pw_aff> function to each pair of elements in the two lists.
3322 #include <isl/aff.h>
3323 __isl_give isl_set *isl_pw_aff_nonneg_set(
3324 __isl_take isl_pw_aff *pwaff);
3325 __isl_give isl_set *isl_pw_aff_zero_set(
3326 __isl_take isl_pw_aff *pwaff);
3327 __isl_give isl_set *isl_pw_aff_non_zero_set(
3328 __isl_take isl_pw_aff *pwaff);
3330 The function C<isl_pw_aff_nonneg_set> returns a set
3331 containing those elements in the domain
3332 of C<pwaff> where C<pwaff> is non-negative.
3334 #include <isl/aff.h>
3335 __isl_give isl_pw_aff *isl_pw_aff_cond(
3336 __isl_take isl_pw_aff *cond,
3337 __isl_take isl_pw_aff *pwaff_true,
3338 __isl_take isl_pw_aff *pwaff_false);
3340 The function C<isl_pw_aff_cond> performs a conditional operator
3341 and returns an expression that is equal to C<pwaff_true>
3342 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3343 where C<cond> is zero.
3345 #include <isl/aff.h>
3346 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3347 __isl_take isl_pw_aff *pwaff1,
3348 __isl_take isl_pw_aff *pwaff2);
3349 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3350 __isl_take isl_pw_aff *pwaff1,
3351 __isl_take isl_pw_aff *pwaff2);
3352 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3353 __isl_take isl_pw_aff *pwaff1,
3354 __isl_take isl_pw_aff *pwaff2);
3356 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3357 expression with a domain that is the union of those of C<pwaff1> and
3358 C<pwaff2> and such that on each cell, the quasi-affine expression is
3359 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3360 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3361 associated expression is the defined one.
3363 An expression can be read from input using
3365 #include <isl/aff.h>
3366 __isl_give isl_aff *isl_aff_read_from_str(
3367 isl_ctx *ctx, const char *str);
3368 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3369 isl_ctx *ctx, const char *str);
3371 An expression can be printed using
3373 #include <isl/aff.h>
3374 __isl_give isl_printer *isl_printer_print_aff(
3375 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3377 __isl_give isl_printer *isl_printer_print_pw_aff(
3378 __isl_take isl_printer *p,
3379 __isl_keep isl_pw_aff *pwaff);
3381 =head2 Piecewise Multiple Quasi Affine Expressions
3383 An C<isl_multi_aff> object represents a sequence of
3384 zero or more affine expressions, all defined on the same domain space.
3386 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3389 #include <isl/aff.h>
3390 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3391 __isl_take isl_space *space,
3392 __isl_take isl_aff_list *list);
3394 An empty piecewise multiple quasi affine expression (one with no cells),
3395 the zero piecewise multiple quasi affine expression (with value zero
3396 for each output dimension),
3397 a piecewise multiple quasi affine expression with a single cell (with
3398 either a universe or a specified domain) or
3399 a zero-dimensional piecewise multiple quasi affine expression
3401 can be created using the following functions.
3403 #include <isl/aff.h>
3404 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3405 __isl_take isl_space *space);
3406 __isl_give isl_multi_aff *isl_multi_aff_zero(
3407 __isl_take isl_space *space);
3408 __isl_give isl_multi_aff *isl_multi_aff_identity(
3409 __isl_take isl_space *space);
3410 __isl_give isl_pw_multi_aff *
3411 isl_pw_multi_aff_from_multi_aff(
3412 __isl_take isl_multi_aff *ma);
3413 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3414 __isl_take isl_set *set,
3415 __isl_take isl_multi_aff *maff);
3416 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3417 __isl_take isl_set *set);
3419 __isl_give isl_union_pw_multi_aff *
3420 isl_union_pw_multi_aff_empty(
3421 __isl_take isl_space *space);
3422 __isl_give isl_union_pw_multi_aff *
3423 isl_union_pw_multi_aff_add_pw_multi_aff(
3424 __isl_take isl_union_pw_multi_aff *upma,
3425 __isl_take isl_pw_multi_aff *pma);
3426 __isl_give isl_union_pw_multi_aff *
3427 isl_union_pw_multi_aff_from_domain(
3428 __isl_take isl_union_set *uset);
3430 A piecewise multiple quasi affine expression can also be initialized
3431 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3432 and the C<isl_map> is single-valued.
3434 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3435 __isl_take isl_set *set);
3436 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3437 __isl_take isl_map *map);
3439 Multiple quasi affine expressions can be copied and freed using
3441 #include <isl/aff.h>
3442 __isl_give isl_multi_aff *isl_multi_aff_copy(
3443 __isl_keep isl_multi_aff *maff);
3444 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3446 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3447 __isl_keep isl_pw_multi_aff *pma);
3448 void *isl_pw_multi_aff_free(
3449 __isl_take isl_pw_multi_aff *pma);
3451 __isl_give isl_union_pw_multi_aff *
3452 isl_union_pw_multi_aff_copy(
3453 __isl_keep isl_union_pw_multi_aff *upma);
3454 void *isl_union_pw_multi_aff_free(
3455 __isl_take isl_union_pw_multi_aff *upma);
3457 The expression can be inspected using
3459 #include <isl/aff.h>
3460 isl_ctx *isl_multi_aff_get_ctx(
3461 __isl_keep isl_multi_aff *maff);
3462 isl_ctx *isl_pw_multi_aff_get_ctx(
3463 __isl_keep isl_pw_multi_aff *pma);
3464 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3465 __isl_keep isl_union_pw_multi_aff *upma);
3466 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3467 enum isl_dim_type type);
3468 unsigned isl_pw_multi_aff_dim(
3469 __isl_keep isl_pw_multi_aff *pma,
3470 enum isl_dim_type type);
3471 __isl_give isl_aff *isl_multi_aff_get_aff(
3472 __isl_keep isl_multi_aff *multi, int pos);
3473 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3474 __isl_keep isl_pw_multi_aff *pma, int pos);
3475 const char *isl_pw_multi_aff_get_dim_name(
3476 __isl_keep isl_pw_multi_aff *pma,
3477 enum isl_dim_type type, unsigned pos);
3478 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3479 __isl_keep isl_pw_multi_aff *pma,
3480 enum isl_dim_type type, unsigned pos);
3481 const char *isl_multi_aff_get_tuple_name(
3482 __isl_keep isl_multi_aff *multi,
3483 enum isl_dim_type type);
3484 int isl_pw_multi_aff_has_tuple_name(
3485 __isl_keep isl_pw_multi_aff *pma,
3486 enum isl_dim_type type);
3487 const char *isl_pw_multi_aff_get_tuple_name(
3488 __isl_keep isl_pw_multi_aff *pma,
3489 enum isl_dim_type type);
3490 int isl_pw_multi_aff_has_tuple_id(
3491 __isl_keep isl_pw_multi_aff *pma,
3492 enum isl_dim_type type);
3493 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3494 __isl_keep isl_pw_multi_aff *pma,
3495 enum isl_dim_type type);
3497 int isl_pw_multi_aff_foreach_piece(
3498 __isl_keep isl_pw_multi_aff *pma,
3499 int (*fn)(__isl_take isl_set *set,
3500 __isl_take isl_multi_aff *maff,
3501 void *user), void *user);
3503 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3504 __isl_keep isl_union_pw_multi_aff *upma,
3505 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3506 void *user), void *user);
3508 It can be modified using
3510 #include <isl/aff.h>
3511 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3512 __isl_take isl_multi_aff *multi, int pos,
3513 __isl_take isl_aff *aff);
3514 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3515 __isl_take isl_multi_aff *maff,
3516 enum isl_dim_type type, unsigned pos, const char *s);
3517 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3518 __isl_take isl_multi_aff *maff,
3519 enum isl_dim_type type, __isl_take isl_id *id);
3520 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3521 __isl_take isl_pw_multi_aff *pma,
3522 enum isl_dim_type type, __isl_take isl_id *id);
3524 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3525 __isl_take isl_multi_aff *maff,
3526 enum isl_dim_type type, unsigned first, unsigned n);
3528 To check whether two multiple affine expressions are
3529 obviously equal to each other, use
3531 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3532 __isl_keep isl_multi_aff *maff2);
3533 int isl_pw_multi_aff_plain_is_equal(
3534 __isl_keep isl_pw_multi_aff *pma1,
3535 __isl_keep isl_pw_multi_aff *pma2);
3539 #include <isl/aff.h>
3540 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3541 __isl_take isl_pw_multi_aff *pma1,
3542 __isl_take isl_pw_multi_aff *pma2);
3543 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3544 __isl_take isl_pw_multi_aff *pma1,
3545 __isl_take isl_pw_multi_aff *pma2);
3546 __isl_give isl_multi_aff *isl_multi_aff_add(
3547 __isl_take isl_multi_aff *maff1,
3548 __isl_take isl_multi_aff *maff2);
3549 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3550 __isl_take isl_pw_multi_aff *pma1,
3551 __isl_take isl_pw_multi_aff *pma2);
3552 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3553 __isl_take isl_union_pw_multi_aff *upma1,
3554 __isl_take isl_union_pw_multi_aff *upma2);
3555 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3556 __isl_take isl_pw_multi_aff *pma1,
3557 __isl_take isl_pw_multi_aff *pma2);
3558 __isl_give isl_multi_aff *isl_multi_aff_scale(
3559 __isl_take isl_multi_aff *maff,
3561 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3562 __isl_take isl_pw_multi_aff *pma,
3563 __isl_take isl_set *set);
3564 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3565 __isl_take isl_pw_multi_aff *pma,
3566 __isl_take isl_set *set);
3567 __isl_give isl_multi_aff *isl_multi_aff_lift(
3568 __isl_take isl_multi_aff *maff,
3569 __isl_give isl_local_space **ls);
3570 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3571 __isl_take isl_pw_multi_aff *pma);
3572 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3573 __isl_take isl_multi_aff *maff,
3574 __isl_take isl_set *context);
3575 __isl_give isl_multi_aff *isl_multi_aff_gist(
3576 __isl_take isl_multi_aff *maff,
3577 __isl_take isl_set *context);
3578 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3579 __isl_take isl_pw_multi_aff *pma,
3580 __isl_take isl_set *set);
3581 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3582 __isl_take isl_pw_multi_aff *pma,
3583 __isl_take isl_set *set);
3584 __isl_give isl_set *isl_pw_multi_aff_domain(
3585 __isl_take isl_pw_multi_aff *pma);
3586 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3587 __isl_take isl_union_pw_multi_aff *upma);
3588 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3589 __isl_take isl_multi_aff *ma1,
3590 __isl_take isl_multi_aff *ma2);
3591 __isl_give isl_multi_aff *isl_multi_aff_product(
3592 __isl_take isl_multi_aff *ma1,
3593 __isl_take isl_multi_aff *ma2);
3594 __isl_give isl_pw_multi_aff *
3595 isl_pw_multi_aff_flat_range_product(
3596 __isl_take isl_pw_multi_aff *pma1,
3597 __isl_take isl_pw_multi_aff *pma2);
3598 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3599 __isl_take isl_pw_multi_aff *pma1,
3600 __isl_take isl_pw_multi_aff *pma2);
3601 __isl_give isl_union_pw_multi_aff *
3602 isl_union_pw_multi_aff_flat_range_product(
3603 __isl_take isl_union_pw_multi_aff *upma1,
3604 __isl_take isl_union_pw_multi_aff *upma2);
3606 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3607 then it is assigned the local space that lies at the basis of
3608 the lifting applied.
3610 __isl_give isl_set *isl_multi_aff_lex_le_set(
3611 __isl_take isl_multi_aff *ma1,
3612 __isl_take isl_multi_aff *ma2);
3613 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3614 __isl_take isl_multi_aff *ma1,
3615 __isl_take isl_multi_aff *ma2);
3617 The function C<isl_multi_aff_lex_le_set> returns a set
3618 containing those elements in the shared domain space
3619 where C<ma1> is lexicographically smaller than or
3622 An expression can be read from input using
3624 #include <isl/aff.h>
3625 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3626 isl_ctx *ctx, const char *str);
3627 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3628 isl_ctx *ctx, const char *str);
3630 An expression can be printed using
3632 #include <isl/aff.h>
3633 __isl_give isl_printer *isl_printer_print_multi_aff(
3634 __isl_take isl_printer *p,
3635 __isl_keep isl_multi_aff *maff);
3636 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3637 __isl_take isl_printer *p,
3638 __isl_keep isl_pw_multi_aff *pma);
3639 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3640 __isl_take isl_printer *p,
3641 __isl_keep isl_union_pw_multi_aff *upma);
3645 Points are elements of a set. They can be used to construct
3646 simple sets (boxes) or they can be used to represent the
3647 individual elements of a set.
3648 The zero point (the origin) can be created using
3650 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3652 The coordinates of a point can be inspected, set and changed
3655 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3656 enum isl_dim_type type, int pos, isl_int *v);
3657 __isl_give isl_point *isl_point_set_coordinate(
3658 __isl_take isl_point *pnt,
3659 enum isl_dim_type type, int pos, isl_int v);
3661 __isl_give isl_point *isl_point_add_ui(
3662 __isl_take isl_point *pnt,
3663 enum isl_dim_type type, int pos, unsigned val);
3664 __isl_give isl_point *isl_point_sub_ui(
3665 __isl_take isl_point *pnt,
3666 enum isl_dim_type type, int pos, unsigned val);
3668 Other properties can be obtained using
3670 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3672 Points can be copied or freed using
3674 __isl_give isl_point *isl_point_copy(
3675 __isl_keep isl_point *pnt);
3676 void isl_point_free(__isl_take isl_point *pnt);
3678 A singleton set can be created from a point using
3680 __isl_give isl_basic_set *isl_basic_set_from_point(
3681 __isl_take isl_point *pnt);
3682 __isl_give isl_set *isl_set_from_point(
3683 __isl_take isl_point *pnt);
3685 and a box can be created from two opposite extremal points using
3687 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3688 __isl_take isl_point *pnt1,
3689 __isl_take isl_point *pnt2);
3690 __isl_give isl_set *isl_set_box_from_points(
3691 __isl_take isl_point *pnt1,
3692 __isl_take isl_point *pnt2);
3694 All elements of a B<bounded> (union) set can be enumerated using
3695 the following functions.
3697 int isl_set_foreach_point(__isl_keep isl_set *set,
3698 int (*fn)(__isl_take isl_point *pnt, void *user),
3700 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3701 int (*fn)(__isl_take isl_point *pnt, void *user),
3704 The function C<fn> is called for each integer point in
3705 C<set> with as second argument the last argument of
3706 the C<isl_set_foreach_point> call. The function C<fn>
3707 should return C<0> on success and C<-1> on failure.
3708 In the latter case, C<isl_set_foreach_point> will stop
3709 enumerating and return C<-1> as well.
3710 If the enumeration is performed successfully and to completion,
3711 then C<isl_set_foreach_point> returns C<0>.
3713 To obtain a single point of a (basic) set, use
3715 __isl_give isl_point *isl_basic_set_sample_point(
3716 __isl_take isl_basic_set *bset);
3717 __isl_give isl_point *isl_set_sample_point(
3718 __isl_take isl_set *set);
3720 If C<set> does not contain any (integer) points, then the
3721 resulting point will be ``void'', a property that can be
3724 int isl_point_is_void(__isl_keep isl_point *pnt);
3726 =head2 Piecewise Quasipolynomials
3728 A piecewise quasipolynomial is a particular kind of function that maps
3729 a parametric point to a rational value.
3730 More specifically, a quasipolynomial is a polynomial expression in greatest
3731 integer parts of affine expressions of parameters and variables.
3732 A piecewise quasipolynomial is a subdivision of a given parametric
3733 domain into disjoint cells with a quasipolynomial associated to
3734 each cell. The value of the piecewise quasipolynomial at a given
3735 point is the value of the quasipolynomial associated to the cell
3736 that contains the point. Outside of the union of cells,
3737 the value is assumed to be zero.
3738 For example, the piecewise quasipolynomial
3740 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3742 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3743 A given piecewise quasipolynomial has a fixed domain dimension.
3744 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3745 defined over different domains.
3746 Piecewise quasipolynomials are mainly used by the C<barvinok>
3747 library for representing the number of elements in a parametric set or map.
3748 For example, the piecewise quasipolynomial above represents
3749 the number of points in the map
3751 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3753 =head3 Input and Output
3755 Piecewise quasipolynomials can be read from input using
3757 __isl_give isl_union_pw_qpolynomial *
3758 isl_union_pw_qpolynomial_read_from_str(
3759 isl_ctx *ctx, const char *str);
3761 Quasipolynomials and piecewise quasipolynomials can be printed
3762 using the following functions.
3764 __isl_give isl_printer *isl_printer_print_qpolynomial(
3765 __isl_take isl_printer *p,
3766 __isl_keep isl_qpolynomial *qp);
3768 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3769 __isl_take isl_printer *p,
3770 __isl_keep isl_pw_qpolynomial *pwqp);
3772 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3773 __isl_take isl_printer *p,
3774 __isl_keep isl_union_pw_qpolynomial *upwqp);
3776 The output format of the printer
3777 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3778 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3780 In case of printing in C<ISL_FORMAT_C>, the user may want
3781 to set the names of all dimensions
3783 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3784 __isl_take isl_qpolynomial *qp,
3785 enum isl_dim_type type, unsigned pos,
3787 __isl_give isl_pw_qpolynomial *
3788 isl_pw_qpolynomial_set_dim_name(
3789 __isl_take isl_pw_qpolynomial *pwqp,
3790 enum isl_dim_type type, unsigned pos,
3793 =head3 Creating New (Piecewise) Quasipolynomials
3795 Some simple quasipolynomials can be created using the following functions.
3796 More complicated quasipolynomials can be created by applying
3797 operations such as addition and multiplication
3798 on the resulting quasipolynomials
3800 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3801 __isl_take isl_space *domain);
3802 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3803 __isl_take isl_space *domain);
3804 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3805 __isl_take isl_space *domain);
3806 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3807 __isl_take isl_space *domain);
3808 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3809 __isl_take isl_space *domain);
3810 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3811 __isl_take isl_space *domain,
3812 const isl_int n, const isl_int d);
3813 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3814 __isl_take isl_space *domain,
3815 enum isl_dim_type type, unsigned pos);
3816 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3817 __isl_take isl_aff *aff);
3819 Note that the space in which a quasipolynomial lives is a map space
3820 with a one-dimensional range. The C<domain> argument in some of
3821 the functions above corresponds to the domain of this map space.
3823 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3824 with a single cell can be created using the following functions.
3825 Multiple of these single cell piecewise quasipolynomials can
3826 be combined to create more complicated piecewise quasipolynomials.
3828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3829 __isl_take isl_space *space);
3830 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3831 __isl_take isl_set *set,
3832 __isl_take isl_qpolynomial *qp);
3833 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3834 __isl_take isl_qpolynomial *qp);
3835 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3836 __isl_take isl_pw_aff *pwaff);
3838 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3839 __isl_take isl_space *space);
3840 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3841 __isl_take isl_pw_qpolynomial *pwqp);
3842 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3843 __isl_take isl_union_pw_qpolynomial *upwqp,
3844 __isl_take isl_pw_qpolynomial *pwqp);
3846 Quasipolynomials can be copied and freed again using the following
3849 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3850 __isl_keep isl_qpolynomial *qp);
3851 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3853 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3854 __isl_keep isl_pw_qpolynomial *pwqp);
3855 void *isl_pw_qpolynomial_free(
3856 __isl_take isl_pw_qpolynomial *pwqp);
3858 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3859 __isl_keep isl_union_pw_qpolynomial *upwqp);
3860 void *isl_union_pw_qpolynomial_free(
3861 __isl_take isl_union_pw_qpolynomial *upwqp);
3863 =head3 Inspecting (Piecewise) Quasipolynomials
3865 To iterate over all piecewise quasipolynomials in a union
3866 piecewise quasipolynomial, use the following function
3868 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3869 __isl_keep isl_union_pw_qpolynomial *upwqp,
3870 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3873 To extract the piecewise quasipolynomial in a given space from a union, use
3875 __isl_give isl_pw_qpolynomial *
3876 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3877 __isl_keep isl_union_pw_qpolynomial *upwqp,
3878 __isl_take isl_space *space);
3880 To iterate over the cells in a piecewise quasipolynomial,
3881 use either of the following two functions
3883 int isl_pw_qpolynomial_foreach_piece(
3884 __isl_keep isl_pw_qpolynomial *pwqp,
3885 int (*fn)(__isl_take isl_set *set,
3886 __isl_take isl_qpolynomial *qp,
3887 void *user), void *user);
3888 int isl_pw_qpolynomial_foreach_lifted_piece(
3889 __isl_keep isl_pw_qpolynomial *pwqp,
3890 int (*fn)(__isl_take isl_set *set,
3891 __isl_take isl_qpolynomial *qp,
3892 void *user), void *user);
3894 As usual, the function C<fn> should return C<0> on success
3895 and C<-1> on failure. The difference between
3896 C<isl_pw_qpolynomial_foreach_piece> and
3897 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3898 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3899 compute unique representations for all existentially quantified
3900 variables and then turn these existentially quantified variables
3901 into extra set variables, adapting the associated quasipolynomial
3902 accordingly. This means that the C<set> passed to C<fn>
3903 will not have any existentially quantified variables, but that
3904 the dimensions of the sets may be different for different
3905 invocations of C<fn>.
3907 To iterate over all terms in a quasipolynomial,
3910 int isl_qpolynomial_foreach_term(
3911 __isl_keep isl_qpolynomial *qp,
3912 int (*fn)(__isl_take isl_term *term,
3913 void *user), void *user);
3915 The terms themselves can be inspected and freed using
3918 unsigned isl_term_dim(__isl_keep isl_term *term,
3919 enum isl_dim_type type);
3920 void isl_term_get_num(__isl_keep isl_term *term,
3922 void isl_term_get_den(__isl_keep isl_term *term,
3924 int isl_term_get_exp(__isl_keep isl_term *term,
3925 enum isl_dim_type type, unsigned pos);
3926 __isl_give isl_aff *isl_term_get_div(
3927 __isl_keep isl_term *term, unsigned pos);
3928 void isl_term_free(__isl_take isl_term *term);
3930 Each term is a product of parameters, set variables and
3931 integer divisions. The function C<isl_term_get_exp>
3932 returns the exponent of a given dimensions in the given term.
3933 The C<isl_int>s in the arguments of C<isl_term_get_num>
3934 and C<isl_term_get_den> need to have been initialized
3935 using C<isl_int_init> before calling these functions.
3937 =head3 Properties of (Piecewise) Quasipolynomials
3939 To check whether a quasipolynomial is actually a constant,
3940 use the following function.
3942 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3943 isl_int *n, isl_int *d);
3945 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3946 then the numerator and denominator of the constant
3947 are returned in C<*n> and C<*d>, respectively.
3949 To check whether two union piecewise quasipolynomials are
3950 obviously equal, use
3952 int isl_union_pw_qpolynomial_plain_is_equal(
3953 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3954 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3956 =head3 Operations on (Piecewise) Quasipolynomials
3958 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3959 __isl_take isl_qpolynomial *qp, isl_int v);
3960 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3961 __isl_take isl_qpolynomial *qp);
3962 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3963 __isl_take isl_qpolynomial *qp1,
3964 __isl_take isl_qpolynomial *qp2);
3965 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3966 __isl_take isl_qpolynomial *qp1,
3967 __isl_take isl_qpolynomial *qp2);
3968 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3969 __isl_take isl_qpolynomial *qp1,
3970 __isl_take isl_qpolynomial *qp2);
3971 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3972 __isl_take isl_qpolynomial *qp, unsigned exponent);
3974 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3975 __isl_take isl_pw_qpolynomial *pwqp1,
3976 __isl_take isl_pw_qpolynomial *pwqp2);
3977 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3978 __isl_take isl_pw_qpolynomial *pwqp1,
3979 __isl_take isl_pw_qpolynomial *pwqp2);
3980 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3981 __isl_take isl_pw_qpolynomial *pwqp1,
3982 __isl_take isl_pw_qpolynomial *pwqp2);
3983 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3984 __isl_take isl_pw_qpolynomial *pwqp);
3985 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3986 __isl_take isl_pw_qpolynomial *pwqp1,
3987 __isl_take isl_pw_qpolynomial *pwqp2);
3988 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3989 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3991 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3992 __isl_take isl_union_pw_qpolynomial *upwqp1,
3993 __isl_take isl_union_pw_qpolynomial *upwqp2);
3994 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3995 __isl_take isl_union_pw_qpolynomial *upwqp1,
3996 __isl_take isl_union_pw_qpolynomial *upwqp2);
3997 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3998 __isl_take isl_union_pw_qpolynomial *upwqp1,
3999 __isl_take isl_union_pw_qpolynomial *upwqp2);
4001 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4002 __isl_take isl_pw_qpolynomial *pwqp,
4003 __isl_take isl_point *pnt);
4005 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4006 __isl_take isl_union_pw_qpolynomial *upwqp,
4007 __isl_take isl_point *pnt);
4009 __isl_give isl_set *isl_pw_qpolynomial_domain(
4010 __isl_take isl_pw_qpolynomial *pwqp);
4011 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4012 __isl_take isl_pw_qpolynomial *pwpq,
4013 __isl_take isl_set *set);
4014 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4015 __isl_take isl_pw_qpolynomial *pwpq,
4016 __isl_take isl_set *set);
4018 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4019 __isl_take isl_union_pw_qpolynomial *upwqp);
4020 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4021 __isl_take isl_union_pw_qpolynomial *upwpq,
4022 __isl_take isl_union_set *uset);
4023 __isl_give isl_union_pw_qpolynomial *
4024 isl_union_pw_qpolynomial_intersect_params(
4025 __isl_take isl_union_pw_qpolynomial *upwpq,
4026 __isl_take isl_set *set);
4028 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4029 __isl_take isl_qpolynomial *qp,
4030 __isl_take isl_space *model);
4032 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4033 __isl_take isl_qpolynomial *qp);
4034 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4035 __isl_take isl_pw_qpolynomial *pwqp);
4037 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4038 __isl_take isl_union_pw_qpolynomial *upwqp);
4040 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4041 __isl_take isl_qpolynomial *qp,
4042 __isl_take isl_set *context);
4043 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4044 __isl_take isl_qpolynomial *qp,
4045 __isl_take isl_set *context);
4047 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4048 __isl_take isl_pw_qpolynomial *pwqp,
4049 __isl_take isl_set *context);
4050 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4051 __isl_take isl_pw_qpolynomial *pwqp,
4052 __isl_take isl_set *context);
4054 __isl_give isl_union_pw_qpolynomial *
4055 isl_union_pw_qpolynomial_gist_params(
4056 __isl_take isl_union_pw_qpolynomial *upwqp,
4057 __isl_take isl_set *context);
4058 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4059 __isl_take isl_union_pw_qpolynomial *upwqp,
4060 __isl_take isl_union_set *context);
4062 The gist operation applies the gist operation to each of
4063 the cells in the domain of the input piecewise quasipolynomial.
4064 The context is also exploited
4065 to simplify the quasipolynomials associated to each cell.
4067 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4068 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4069 __isl_give isl_union_pw_qpolynomial *
4070 isl_union_pw_qpolynomial_to_polynomial(
4071 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4073 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4074 the polynomial will be an overapproximation. If C<sign> is negative,
4075 it will be an underapproximation. If C<sign> is zero, the approximation
4076 will lie somewhere in between.
4078 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4080 A piecewise quasipolynomial reduction is a piecewise
4081 reduction (or fold) of quasipolynomials.
4082 In particular, the reduction can be maximum or a minimum.
4083 The objects are mainly used to represent the result of
4084 an upper or lower bound on a quasipolynomial over its domain,
4085 i.e., as the result of the following function.
4087 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4088 __isl_take isl_pw_qpolynomial *pwqp,
4089 enum isl_fold type, int *tight);
4091 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4092 __isl_take isl_union_pw_qpolynomial *upwqp,
4093 enum isl_fold type, int *tight);
4095 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4096 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4097 is the returned bound is known be tight, i.e., for each value
4098 of the parameters there is at least
4099 one element in the domain that reaches the bound.
4100 If the domain of C<pwqp> is not wrapping, then the bound is computed
4101 over all elements in that domain and the result has a purely parametric
4102 domain. If the domain of C<pwqp> is wrapping, then the bound is
4103 computed over the range of the wrapped relation. The domain of the
4104 wrapped relation becomes the domain of the result.
4106 A (piecewise) quasipolynomial reduction can be copied or freed using the
4107 following functions.
4109 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4110 __isl_keep isl_qpolynomial_fold *fold);
4111 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4112 __isl_keep isl_pw_qpolynomial_fold *pwf);
4113 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4114 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4115 void isl_qpolynomial_fold_free(
4116 __isl_take isl_qpolynomial_fold *fold);
4117 void *isl_pw_qpolynomial_fold_free(
4118 __isl_take isl_pw_qpolynomial_fold *pwf);
4119 void *isl_union_pw_qpolynomial_fold_free(
4120 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4122 =head3 Printing Piecewise Quasipolynomial Reductions
4124 Piecewise quasipolynomial reductions can be printed
4125 using the following function.
4127 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4128 __isl_take isl_printer *p,
4129 __isl_keep isl_pw_qpolynomial_fold *pwf);
4130 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4131 __isl_take isl_printer *p,
4132 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4134 For C<isl_printer_print_pw_qpolynomial_fold>,
4135 output format of the printer
4136 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4137 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4138 output format of the printer
4139 needs to be set to C<ISL_FORMAT_ISL>.
4140 In case of printing in C<ISL_FORMAT_C>, the user may want
4141 to set the names of all dimensions
4143 __isl_give isl_pw_qpolynomial_fold *
4144 isl_pw_qpolynomial_fold_set_dim_name(
4145 __isl_take isl_pw_qpolynomial_fold *pwf,
4146 enum isl_dim_type type, unsigned pos,
4149 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4151 To iterate over all piecewise quasipolynomial reductions in a union
4152 piecewise quasipolynomial reduction, use the following function
4154 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4155 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4156 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4157 void *user), void *user);
4159 To iterate over the cells in a piecewise quasipolynomial reduction,
4160 use either of the following two functions
4162 int isl_pw_qpolynomial_fold_foreach_piece(
4163 __isl_keep isl_pw_qpolynomial_fold *pwf,
4164 int (*fn)(__isl_take isl_set *set,
4165 __isl_take isl_qpolynomial_fold *fold,
4166 void *user), void *user);
4167 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4168 __isl_keep isl_pw_qpolynomial_fold *pwf,
4169 int (*fn)(__isl_take isl_set *set,
4170 __isl_take isl_qpolynomial_fold *fold,
4171 void *user), void *user);
4173 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4174 of the difference between these two functions.
4176 To iterate over all quasipolynomials in a reduction, use
4178 int isl_qpolynomial_fold_foreach_qpolynomial(
4179 __isl_keep isl_qpolynomial_fold *fold,
4180 int (*fn)(__isl_take isl_qpolynomial *qp,
4181 void *user), void *user);
4183 =head3 Properties of Piecewise Quasipolynomial Reductions
4185 To check whether two union piecewise quasipolynomial reductions are
4186 obviously equal, use
4188 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4189 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4190 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4192 =head3 Operations on Piecewise Quasipolynomial Reductions
4194 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4195 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4197 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4198 __isl_take isl_pw_qpolynomial_fold *pwf1,
4199 __isl_take isl_pw_qpolynomial_fold *pwf2);
4201 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4202 __isl_take isl_pw_qpolynomial_fold *pwf1,
4203 __isl_take isl_pw_qpolynomial_fold *pwf2);
4205 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4206 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4207 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4209 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4210 __isl_take isl_pw_qpolynomial_fold *pwf,
4211 __isl_take isl_point *pnt);
4213 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4214 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4215 __isl_take isl_point *pnt);
4217 __isl_give isl_pw_qpolynomial_fold *
4218 isl_pw_qpolynomial_fold_intersect_params(
4219 __isl_take isl_pw_qpolynomial_fold *pwf,
4220 __isl_take isl_set *set);
4222 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4223 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4224 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4225 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4226 __isl_take isl_union_set *uset);
4227 __isl_give isl_union_pw_qpolynomial_fold *
4228 isl_union_pw_qpolynomial_fold_intersect_params(
4229 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4230 __isl_take isl_set *set);
4232 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4233 __isl_take isl_pw_qpolynomial_fold *pwf);
4235 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4236 __isl_take isl_pw_qpolynomial_fold *pwf);
4238 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4239 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4241 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4242 __isl_take isl_qpolynomial_fold *fold,
4243 __isl_take isl_set *context);
4244 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4245 __isl_take isl_qpolynomial_fold *fold,
4246 __isl_take isl_set *context);
4248 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4249 __isl_take isl_pw_qpolynomial_fold *pwf,
4250 __isl_take isl_set *context);
4251 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4252 __isl_take isl_pw_qpolynomial_fold *pwf,
4253 __isl_take isl_set *context);
4255 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4256 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4257 __isl_take isl_union_set *context);
4258 __isl_give isl_union_pw_qpolynomial_fold *
4259 isl_union_pw_qpolynomial_fold_gist_params(
4260 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4261 __isl_take isl_set *context);
4263 The gist operation applies the gist operation to each of
4264 the cells in the domain of the input piecewise quasipolynomial reduction.
4265 In future, the operation will also exploit the context
4266 to simplify the quasipolynomial reductions associated to each cell.
4268 __isl_give isl_pw_qpolynomial_fold *
4269 isl_set_apply_pw_qpolynomial_fold(
4270 __isl_take isl_set *set,
4271 __isl_take isl_pw_qpolynomial_fold *pwf,
4273 __isl_give isl_pw_qpolynomial_fold *
4274 isl_map_apply_pw_qpolynomial_fold(
4275 __isl_take isl_map *map,
4276 __isl_take isl_pw_qpolynomial_fold *pwf,
4278 __isl_give isl_union_pw_qpolynomial_fold *
4279 isl_union_set_apply_union_pw_qpolynomial_fold(
4280 __isl_take isl_union_set *uset,
4281 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4283 __isl_give isl_union_pw_qpolynomial_fold *
4284 isl_union_map_apply_union_pw_qpolynomial_fold(
4285 __isl_take isl_union_map *umap,
4286 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4289 The functions taking a map
4290 compose the given map with the given piecewise quasipolynomial reduction.
4291 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4292 over all elements in the intersection of the range of the map
4293 and the domain of the piecewise quasipolynomial reduction
4294 as a function of an element in the domain of the map.
4295 The functions taking a set compute a bound over all elements in the
4296 intersection of the set and the domain of the
4297 piecewise quasipolynomial reduction.
4299 =head2 Dependence Analysis
4301 C<isl> contains specialized functionality for performing
4302 array dataflow analysis. That is, given a I<sink> access relation
4303 and a collection of possible I<source> access relations,
4304 C<isl> can compute relations that describe
4305 for each iteration of the sink access, which iteration
4306 of which of the source access relations was the last
4307 to access the same data element before the given iteration
4309 The resulting dependence relations map source iterations
4310 to the corresponding sink iterations.
4311 To compute standard flow dependences, the sink should be
4312 a read, while the sources should be writes.
4313 If any of the source accesses are marked as being I<may>
4314 accesses, then there will be a dependence from the last
4315 I<must> access B<and> from any I<may> access that follows
4316 this last I<must> access.
4317 In particular, if I<all> sources are I<may> accesses,
4318 then memory based dependence analysis is performed.
4319 If, on the other hand, all sources are I<must> accesses,
4320 then value based dependence analysis is performed.
4322 #include <isl/flow.h>
4324 typedef int (*isl_access_level_before)(void *first, void *second);
4326 __isl_give isl_access_info *isl_access_info_alloc(
4327 __isl_take isl_map *sink,
4328 void *sink_user, isl_access_level_before fn,
4330 __isl_give isl_access_info *isl_access_info_add_source(
4331 __isl_take isl_access_info *acc,
4332 __isl_take isl_map *source, int must,
4334 void *isl_access_info_free(__isl_take isl_access_info *acc);
4336 __isl_give isl_flow *isl_access_info_compute_flow(
4337 __isl_take isl_access_info *acc);
4339 int isl_flow_foreach(__isl_keep isl_flow *deps,
4340 int (*fn)(__isl_take isl_map *dep, int must,
4341 void *dep_user, void *user),
4343 __isl_give isl_map *isl_flow_get_no_source(
4344 __isl_keep isl_flow *deps, int must);
4345 void isl_flow_free(__isl_take isl_flow *deps);
4347 The function C<isl_access_info_compute_flow> performs the actual
4348 dependence analysis. The other functions are used to construct
4349 the input for this function or to read off the output.
4351 The input is collected in an C<isl_access_info>, which can
4352 be created through a call to C<isl_access_info_alloc>.
4353 The arguments to this functions are the sink access relation
4354 C<sink>, a token C<sink_user> used to identify the sink
4355 access to the user, a callback function for specifying the
4356 relative order of source and sink accesses, and the number
4357 of source access relations that will be added.
4358 The callback function has type C<int (*)(void *first, void *second)>.
4359 The function is called with two user supplied tokens identifying
4360 either a source or the sink and it should return the shared nesting
4361 level and the relative order of the two accesses.
4362 In particular, let I<n> be the number of loops shared by
4363 the two accesses. If C<first> precedes C<second> textually,
4364 then the function should return I<2 * n + 1>; otherwise,
4365 it should return I<2 * n>.
4366 The sources can be added to the C<isl_access_info> by performing
4367 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4368 C<must> indicates whether the source is a I<must> access
4369 or a I<may> access. Note that a multi-valued access relation
4370 should only be marked I<must> if every iteration in the domain
4371 of the relation accesses I<all> elements in its image.
4372 The C<source_user> token is again used to identify
4373 the source access. The range of the source access relation
4374 C<source> should have the same dimension as the range
4375 of the sink access relation.
4376 The C<isl_access_info_free> function should usually not be
4377 called explicitly, because it is called implicitly by
4378 C<isl_access_info_compute_flow>.
4380 The result of the dependence analysis is collected in an
4381 C<isl_flow>. There may be elements of
4382 the sink access for which no preceding source access could be
4383 found or for which all preceding sources are I<may> accesses.
4384 The relations containing these elements can be obtained through
4385 calls to C<isl_flow_get_no_source>, the first with C<must> set
4386 and the second with C<must> unset.
4387 In the case of standard flow dependence analysis,
4388 with the sink a read and the sources I<must> writes,
4389 the first relation corresponds to the reads from uninitialized
4390 array elements and the second relation is empty.
4391 The actual flow dependences can be extracted using
4392 C<isl_flow_foreach>. This function will call the user-specified
4393 callback function C<fn> for each B<non-empty> dependence between
4394 a source and the sink. The callback function is called
4395 with four arguments, the actual flow dependence relation
4396 mapping source iterations to sink iterations, a boolean that
4397 indicates whether it is a I<must> or I<may> dependence, a token
4398 identifying the source and an additional C<void *> with value
4399 equal to the third argument of the C<isl_flow_foreach> call.
4400 A dependence is marked I<must> if it originates from a I<must>
4401 source and if it is not followed by any I<may> sources.
4403 After finishing with an C<isl_flow>, the user should call
4404 C<isl_flow_free> to free all associated memory.
4406 A higher-level interface to dependence analysis is provided
4407 by the following function.
4409 #include <isl/flow.h>
4411 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4412 __isl_take isl_union_map *must_source,
4413 __isl_take isl_union_map *may_source,
4414 __isl_take isl_union_map *schedule,
4415 __isl_give isl_union_map **must_dep,
4416 __isl_give isl_union_map **may_dep,
4417 __isl_give isl_union_map **must_no_source,
4418 __isl_give isl_union_map **may_no_source);
4420 The arrays are identified by the tuple names of the ranges
4421 of the accesses. The iteration domains by the tuple names
4422 of the domains of the accesses and of the schedule.
4423 The relative order of the iteration domains is given by the
4424 schedule. The relations returned through C<must_no_source>
4425 and C<may_no_source> are subsets of C<sink>.
4426 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4427 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4428 any of the other arguments is treated as an error.
4430 =head3 Interaction with Dependence Analysis
4432 During the dependence analysis, we frequently need to perform
4433 the following operation. Given a relation between sink iterations
4434 and potential source iterations from a particular source domain,
4435 what is the last potential source iteration corresponding to each
4436 sink iteration. It can sometimes be convenient to adjust
4437 the set of potential source iterations before or after each such operation.
4438 The prototypical example is fuzzy array dataflow analysis,
4439 where we need to analyze if, based on data-dependent constraints,
4440 the sink iteration can ever be executed without one or more of
4441 the corresponding potential source iterations being executed.
4442 If so, we can introduce extra parameters and select an unknown
4443 but fixed source iteration from the potential source iterations.
4444 To be able to perform such manipulations, C<isl> provides the following
4447 #include <isl/flow.h>
4449 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4450 __isl_keep isl_map *source_map,
4451 __isl_keep isl_set *sink, void *source_user,
4453 __isl_give isl_access_info *isl_access_info_set_restrict(
4454 __isl_take isl_access_info *acc,
4455 isl_access_restrict fn, void *user);
4457 The function C<isl_access_info_set_restrict> should be called
4458 before calling C<isl_access_info_compute_flow> and registers a callback function
4459 that will be called any time C<isl> is about to compute the last
4460 potential source. The first argument is the (reverse) proto-dependence,
4461 mapping sink iterations to potential source iterations.
4462 The second argument represents the sink iterations for which
4463 we want to compute the last source iteration.
4464 The third argument is the token corresponding to the source
4465 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4466 The callback is expected to return a restriction on either the input or
4467 the output of the operation computing the last potential source.
4468 If the input needs to be restricted then restrictions are needed
4469 for both the source and the sink iterations. The sink iterations
4470 and the potential source iterations will be intersected with these sets.
4471 If the output needs to be restricted then only a restriction on the source
4472 iterations is required.
4473 If any error occurs, the callback should return C<NULL>.
4474 An C<isl_restriction> object can be created, freed and inspected
4475 using the following functions.
4477 #include <isl/flow.h>
4479 __isl_give isl_restriction *isl_restriction_input(
4480 __isl_take isl_set *source_restr,
4481 __isl_take isl_set *sink_restr);
4482 __isl_give isl_restriction *isl_restriction_output(
4483 __isl_take isl_set *source_restr);
4484 __isl_give isl_restriction *isl_restriction_none(
4485 __isl_take isl_map *source_map);
4486 __isl_give isl_restriction *isl_restriction_empty(
4487 __isl_take isl_map *source_map);
4488 void *isl_restriction_free(
4489 __isl_take isl_restriction *restr);
4490 isl_ctx *isl_restriction_get_ctx(
4491 __isl_keep isl_restriction *restr);
4493 C<isl_restriction_none> and C<isl_restriction_empty> are special
4494 cases of C<isl_restriction_input>. C<isl_restriction_none>
4495 is essentially equivalent to
4497 isl_restriction_input(isl_set_universe(
4498 isl_space_range(isl_map_get_space(source_map))),
4500 isl_space_domain(isl_map_get_space(source_map))));
4502 whereas C<isl_restriction_empty> is essentially equivalent to
4504 isl_restriction_input(isl_set_empty(
4505 isl_space_range(isl_map_get_space(source_map))),
4507 isl_space_domain(isl_map_get_space(source_map))));
4511 B<The functionality described in this section is fairly new
4512 and may be subject to change.>
4514 The following function can be used to compute a schedule
4515 for a union of domains.
4516 By default, the algorithm used to construct the schedule is similar
4517 to that of C<Pluto>.
4518 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4520 The generated schedule respects all C<validity> dependences.
4521 That is, all dependence distances over these dependences in the
4522 scheduled space are lexicographically positive.
4523 The default algorithm tries to minimize the dependence distances over
4524 C<proximity> dependences.
4525 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4526 for groups of domains where the dependence distances have only
4527 non-negative values.
4528 When using Feautrier's algorithm, the C<proximity> dependence
4529 distances are only minimized during the extension to a
4530 full-dimensional schedule.
4532 #include <isl/schedule.h>
4533 __isl_give isl_schedule *isl_union_set_compute_schedule(
4534 __isl_take isl_union_set *domain,
4535 __isl_take isl_union_map *validity,
4536 __isl_take isl_union_map *proximity);
4537 void *isl_schedule_free(__isl_take isl_schedule *sched);
4539 A mapping from the domains to the scheduled space can be obtained
4540 from an C<isl_schedule> using the following function.
4542 __isl_give isl_union_map *isl_schedule_get_map(
4543 __isl_keep isl_schedule *sched);
4545 A representation of the schedule can be printed using
4547 __isl_give isl_printer *isl_printer_print_schedule(
4548 __isl_take isl_printer *p,
4549 __isl_keep isl_schedule *schedule);
4551 A representation of the schedule as a forest of bands can be obtained
4552 using the following function.
4554 __isl_give isl_band_list *isl_schedule_get_band_forest(
4555 __isl_keep isl_schedule *schedule);
4557 The individual bands can be visited in depth-first post-order
4558 using the following function.
4560 #include <isl/schedule.h>
4561 int isl_schedule_foreach_band(
4562 __isl_keep isl_schedule *sched,
4563 int (*fn)(__isl_keep isl_band *band, void *user),
4566 The list can be manipulated as explained in L<"Lists">.
4567 The bands inside the list can be copied and freed using the following
4570 #include <isl/band.h>
4571 __isl_give isl_band *isl_band_copy(
4572 __isl_keep isl_band *band);
4573 void *isl_band_free(__isl_take isl_band *band);
4575 Each band contains zero or more scheduling dimensions.
4576 These are referred to as the members of the band.
4577 The section of the schedule that corresponds to the band is
4578 referred to as the partial schedule of the band.
4579 For those nodes that participate in a band, the outer scheduling
4580 dimensions form the prefix schedule, while the inner scheduling
4581 dimensions form the suffix schedule.
4582 That is, if we take a cut of the band forest, then the union of
4583 the concatenations of the prefix, partial and suffix schedules of
4584 each band in the cut is equal to the entire schedule (modulo
4585 some possible padding at the end with zero scheduling dimensions).
4586 The properties of a band can be inspected using the following functions.
4588 #include <isl/band.h>
4589 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4591 int isl_band_has_children(__isl_keep isl_band *band);
4592 __isl_give isl_band_list *isl_band_get_children(
4593 __isl_keep isl_band *band);
4595 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4596 __isl_keep isl_band *band);
4597 __isl_give isl_union_map *isl_band_get_partial_schedule(
4598 __isl_keep isl_band *band);
4599 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4600 __isl_keep isl_band *band);
4602 int isl_band_n_member(__isl_keep isl_band *band);
4603 int isl_band_member_is_zero_distance(
4604 __isl_keep isl_band *band, int pos);
4606 int isl_band_list_foreach_band(
4607 __isl_keep isl_band_list *list,
4608 int (*fn)(__isl_keep isl_band *band, void *user),
4611 Note that a scheduling dimension is considered to be ``zero
4612 distance'' if it does not carry any proximity dependences
4614 That is, if the dependence distances of the proximity
4615 dependences are all zero in that direction (for fixed
4616 iterations of outer bands).
4617 Like C<isl_schedule_foreach_band>,
4618 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4619 in depth-first post-order.
4621 A band can be tiled using the following function.
4623 #include <isl/band.h>
4624 int isl_band_tile(__isl_keep isl_band *band,
4625 __isl_take isl_vec *sizes);
4627 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4629 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4631 The C<isl_band_tile> function tiles the band using the given tile sizes
4632 inside its schedule.
4633 A new child band is created to represent the point loops and it is
4634 inserted between the modified band and its children.
4635 The C<tile_scale_tile_loops> option specifies whether the tile
4636 loops iterators should be scaled by the tile sizes.
4638 A representation of the band can be printed using
4640 #include <isl/band.h>
4641 __isl_give isl_printer *isl_printer_print_band(
4642 __isl_take isl_printer *p,
4643 __isl_keep isl_band *band);
4647 #include <isl/schedule.h>
4648 int isl_options_set_schedule_max_coefficient(
4649 isl_ctx *ctx, int val);
4650 int isl_options_get_schedule_max_coefficient(
4652 int isl_options_set_schedule_max_constant_term(
4653 isl_ctx *ctx, int val);
4654 int isl_options_get_schedule_max_constant_term(
4656 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4657 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4658 int isl_options_set_schedule_maximize_band_depth(
4659 isl_ctx *ctx, int val);
4660 int isl_options_get_schedule_maximize_band_depth(
4662 int isl_options_set_schedule_outer_zero_distance(
4663 isl_ctx *ctx, int val);
4664 int isl_options_get_schedule_outer_zero_distance(
4666 int isl_options_set_schedule_split_scaled(
4667 isl_ctx *ctx, int val);
4668 int isl_options_get_schedule_split_scaled(
4670 int isl_options_set_schedule_algorithm(
4671 isl_ctx *ctx, int val);
4672 int isl_options_get_schedule_algorithm(
4674 int isl_options_set_schedule_separate_components(
4675 isl_ctx *ctx, int val);
4676 int isl_options_get_schedule_separate_components(
4681 =item * schedule_max_coefficient
4683 This option enforces that the coefficients for variable and parameter
4684 dimensions in the calculated schedule are not larger than the specified value.
4685 This option can significantly increase the speed of the scheduling calculation
4686 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4687 this option does not introduce bounds on the variable or parameter
4690 =item * schedule_max_constant_term
4692 This option enforces that the constant coefficients in the calculated schedule
4693 are not larger than the maximal constant term. This option can significantly
4694 increase the speed of the scheduling calculation and may also prevent fusing of
4695 unrelated dimensions. A value of -1 means that this option does not introduce
4696 bounds on the constant coefficients.
4698 =item * schedule_fuse
4700 This option controls the level of fusion.
4701 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4702 resulting schedule will be distributed as much as possible.
4703 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4704 try to fuse loops in the resulting schedule.
4706 =item * schedule_maximize_band_depth
4708 If this option is set, we do not split bands at the point
4709 where we detect splitting is necessary. Instead, we
4710 backtrack and split bands as early as possible. This
4711 reduces the number of splits and maximizes the width of
4712 the bands. Wider bands give more possibilities for tiling.
4713 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4714 then bands will be split as early as possible, even if there is no need.
4715 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4717 =item * schedule_outer_zero_distance
4719 If this option is set, then we try to construct schedules
4720 where the outermost scheduling dimension in each band
4721 results in a zero dependence distance over the proximity
4724 =item * schedule_split_scaled
4726 If this option is set, then we try to construct schedules in which the
4727 constant term is split off from the linear part if the linear parts of
4728 the scheduling rows for all nodes in the graphs have a common non-trivial
4730 The constant term is then placed in a separate band and the linear
4733 =item * schedule_algorithm
4735 Selects the scheduling algorithm to be used.
4736 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4737 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4739 =item * schedule_separate_components
4741 If at any point the dependence graph contains any (weakly connected) components,
4742 then these components are scheduled separately.
4743 If this option is not set, then some iterations of the domains
4744 in these components may be scheduled together.
4745 If this option is set, then the components are given consecutive
4750 =head2 Parametric Vertex Enumeration
4752 The parametric vertex enumeration described in this section
4753 is mainly intended to be used internally and by the C<barvinok>
4756 #include <isl/vertices.h>
4757 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4758 __isl_keep isl_basic_set *bset);
4760 The function C<isl_basic_set_compute_vertices> performs the
4761 actual computation of the parametric vertices and the chamber
4762 decomposition and store the result in an C<isl_vertices> object.
4763 This information can be queried by either iterating over all
4764 the vertices or iterating over all the chambers or cells
4765 and then iterating over all vertices that are active on the chamber.
4767 int isl_vertices_foreach_vertex(
4768 __isl_keep isl_vertices *vertices,
4769 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4772 int isl_vertices_foreach_cell(
4773 __isl_keep isl_vertices *vertices,
4774 int (*fn)(__isl_take isl_cell *cell, void *user),
4776 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4777 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4780 Other operations that can be performed on an C<isl_vertices> object are
4783 isl_ctx *isl_vertices_get_ctx(
4784 __isl_keep isl_vertices *vertices);
4785 int isl_vertices_get_n_vertices(
4786 __isl_keep isl_vertices *vertices);
4787 void isl_vertices_free(__isl_take isl_vertices *vertices);
4789 Vertices can be inspected and destroyed using the following functions.
4791 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4792 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4793 __isl_give isl_basic_set *isl_vertex_get_domain(
4794 __isl_keep isl_vertex *vertex);
4795 __isl_give isl_basic_set *isl_vertex_get_expr(
4796 __isl_keep isl_vertex *vertex);
4797 void isl_vertex_free(__isl_take isl_vertex *vertex);
4799 C<isl_vertex_get_expr> returns a singleton parametric set describing
4800 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4802 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4803 B<rational> basic sets, so they should mainly be used for inspection
4804 and should not be mixed with integer sets.
4806 Chambers can be inspected and destroyed using the following functions.
4808 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4809 __isl_give isl_basic_set *isl_cell_get_domain(
4810 __isl_keep isl_cell *cell);
4811 void isl_cell_free(__isl_take isl_cell *cell);
4815 Although C<isl> is mainly meant to be used as a library,
4816 it also contains some basic applications that use some
4817 of the functionality of C<isl>.
4818 The input may be specified in either the L<isl format>
4819 or the L<PolyLib format>.
4821 =head2 C<isl_polyhedron_sample>
4823 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4824 an integer element of the polyhedron, if there is any.
4825 The first column in the output is the denominator and is always
4826 equal to 1. If the polyhedron contains no integer points,
4827 then a vector of length zero is printed.
4831 C<isl_pip> takes the same input as the C<example> program
4832 from the C<piplib> distribution, i.e., a set of constraints
4833 on the parameters, a line containing only -1 and finally a set
4834 of constraints on a parametric polyhedron.
4835 The coefficients of the parameters appear in the last columns
4836 (but before the final constant column).
4837 The output is the lexicographic minimum of the parametric polyhedron.
4838 As C<isl> currently does not have its own output format, the output
4839 is just a dump of the internal state.
4841 =head2 C<isl_polyhedron_minimize>
4843 C<isl_polyhedron_minimize> computes the minimum of some linear
4844 or affine objective function over the integer points in a polyhedron.
4845 If an affine objective function
4846 is given, then the constant should appear in the last column.
4848 =head2 C<isl_polytope_scan>
4850 Given a polytope, C<isl_polytope_scan> prints
4851 all integer points in the polytope.