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);
1428 To iterate over all the sets or maps in a union set or map, use
1430 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1431 int (*fn)(__isl_take isl_set *set, void *user),
1433 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1434 int (*fn)(__isl_take isl_map *map, void *user),
1437 The number of sets or maps in a union set or map can be obtained
1440 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1441 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1443 To extract the set or map in a given space from a union, use
1445 __isl_give isl_set *isl_union_set_extract_set(
1446 __isl_keep isl_union_set *uset,
1447 __isl_take isl_space *space);
1448 __isl_give isl_map *isl_union_map_extract_map(
1449 __isl_keep isl_union_map *umap,
1450 __isl_take isl_space *space);
1452 To iterate over all the basic sets or maps in a set or map, use
1454 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1455 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1457 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1458 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1461 The callback function C<fn> should return 0 if successful and
1462 -1 if an error occurs. In the latter case, or if any other error
1463 occurs, the above functions will return -1.
1465 It should be noted that C<isl> does not guarantee that
1466 the basic sets or maps passed to C<fn> are disjoint.
1467 If this is required, then the user should call one of
1468 the following functions first.
1470 __isl_give isl_set *isl_set_make_disjoint(
1471 __isl_take isl_set *set);
1472 __isl_give isl_map *isl_map_make_disjoint(
1473 __isl_take isl_map *map);
1475 The number of basic sets in a set can be obtained
1478 int isl_set_n_basic_set(__isl_keep isl_set *set);
1480 To iterate over the constraints of a basic set or map, use
1482 #include <isl/constraint.h>
1484 int isl_basic_set_n_constraint(
1485 __isl_keep isl_basic_set *bset);
1486 int isl_basic_set_foreach_constraint(
1487 __isl_keep isl_basic_set *bset,
1488 int (*fn)(__isl_take isl_constraint *c, void *user),
1490 int isl_basic_map_foreach_constraint(
1491 __isl_keep isl_basic_map *bmap,
1492 int (*fn)(__isl_take isl_constraint *c, void *user),
1494 void *isl_constraint_free(__isl_take isl_constraint *c);
1496 Again, the callback function C<fn> should return 0 if successful and
1497 -1 if an error occurs. In the latter case, or if any other error
1498 occurs, the above functions will return -1.
1499 The constraint C<c> represents either an equality or an inequality.
1500 Use the following function to find out whether a constraint
1501 represents an equality. If not, it represents an inequality.
1503 int isl_constraint_is_equality(
1504 __isl_keep isl_constraint *constraint);
1506 The coefficients of the constraints can be inspected using
1507 the following functions.
1509 int isl_constraint_is_lower_bound(
1510 __isl_keep isl_constraint *constraint,
1511 enum isl_dim_type type, unsigned pos);
1512 int isl_constraint_is_upper_bound(
1513 __isl_keep isl_constraint *constraint,
1514 enum isl_dim_type type, unsigned pos);
1515 void isl_constraint_get_constant(
1516 __isl_keep isl_constraint *constraint, isl_int *v);
1517 void isl_constraint_get_coefficient(
1518 __isl_keep isl_constraint *constraint,
1519 enum isl_dim_type type, int pos, isl_int *v);
1520 int isl_constraint_involves_dims(
1521 __isl_keep isl_constraint *constraint,
1522 enum isl_dim_type type, unsigned first, unsigned n);
1524 The explicit representations of the existentially quantified
1525 variables can be inspected using the following function.
1526 Note that the user is only allowed to use this function
1527 if the inspected set or map is the result of a call
1528 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1529 The existentially quantified variable is equal to the floor
1530 of the returned affine expression. The affine expression
1531 itself can be inspected using the functions in
1532 L<"Piecewise Quasi Affine Expressions">.
1534 __isl_give isl_aff *isl_constraint_get_div(
1535 __isl_keep isl_constraint *constraint, int pos);
1537 To obtain the constraints of a basic set or map in matrix
1538 form, use the following functions.
1540 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1541 __isl_keep isl_basic_set *bset,
1542 enum isl_dim_type c1, enum isl_dim_type c2,
1543 enum isl_dim_type c3, enum isl_dim_type c4);
1544 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1545 __isl_keep isl_basic_set *bset,
1546 enum isl_dim_type c1, enum isl_dim_type c2,
1547 enum isl_dim_type c3, enum isl_dim_type c4);
1548 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1549 __isl_keep isl_basic_map *bmap,
1550 enum isl_dim_type c1,
1551 enum isl_dim_type c2, enum isl_dim_type c3,
1552 enum isl_dim_type c4, enum isl_dim_type c5);
1553 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1554 __isl_keep isl_basic_map *bmap,
1555 enum isl_dim_type c1,
1556 enum isl_dim_type c2, enum isl_dim_type c3,
1557 enum isl_dim_type c4, enum isl_dim_type c5);
1559 The C<isl_dim_type> arguments dictate the order in which
1560 different kinds of variables appear in the resulting matrix
1561 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1562 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1564 The number of parameters, input, output or set dimensions can
1565 be obtained using the following functions.
1567 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1568 enum isl_dim_type type);
1569 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1570 enum isl_dim_type type);
1571 unsigned isl_set_dim(__isl_keep isl_set *set,
1572 enum isl_dim_type type);
1573 unsigned isl_map_dim(__isl_keep isl_map *map,
1574 enum isl_dim_type type);
1576 To check whether the description of a set or relation depends
1577 on one or more given dimensions, it is not necessary to iterate over all
1578 constraints. Instead the following functions can be used.
1580 int isl_basic_set_involves_dims(
1581 __isl_keep isl_basic_set *bset,
1582 enum isl_dim_type type, unsigned first, unsigned n);
1583 int isl_set_involves_dims(__isl_keep isl_set *set,
1584 enum isl_dim_type type, unsigned first, unsigned n);
1585 int isl_basic_map_involves_dims(
1586 __isl_keep isl_basic_map *bmap,
1587 enum isl_dim_type type, unsigned first, unsigned n);
1588 int isl_map_involves_dims(__isl_keep isl_map *map,
1589 enum isl_dim_type type, unsigned first, unsigned n);
1591 Similarly, the following functions can be used to check whether
1592 a given dimension is involved in any lower or upper bound.
1594 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1595 enum isl_dim_type type, unsigned pos);
1596 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1597 enum isl_dim_type type, unsigned pos);
1599 The identifiers or names of the domain and range spaces of a set
1600 or relation can be read off or set using the following functions.
1602 __isl_give isl_set *isl_set_set_tuple_id(
1603 __isl_take isl_set *set, __isl_take isl_id *id);
1604 __isl_give isl_set *isl_set_reset_tuple_id(
1605 __isl_take isl_set *set);
1606 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1607 __isl_give isl_id *isl_set_get_tuple_id(
1608 __isl_keep isl_set *set);
1609 __isl_give isl_map *isl_map_set_tuple_id(
1610 __isl_take isl_map *map, enum isl_dim_type type,
1611 __isl_take isl_id *id);
1612 __isl_give isl_map *isl_map_reset_tuple_id(
1613 __isl_take isl_map *map, enum isl_dim_type type);
1614 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1615 enum isl_dim_type type);
1616 __isl_give isl_id *isl_map_get_tuple_id(
1617 __isl_keep isl_map *map, enum isl_dim_type type);
1619 const char *isl_basic_set_get_tuple_name(
1620 __isl_keep isl_basic_set *bset);
1621 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1622 __isl_take isl_basic_set *set, const char *s);
1623 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1624 const char *isl_set_get_tuple_name(
1625 __isl_keep isl_set *set);
1626 const char *isl_basic_map_get_tuple_name(
1627 __isl_keep isl_basic_map *bmap,
1628 enum isl_dim_type type);
1629 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1630 __isl_take isl_basic_map *bmap,
1631 enum isl_dim_type type, const char *s);
1632 const char *isl_map_get_tuple_name(
1633 __isl_keep isl_map *map,
1634 enum isl_dim_type type);
1636 As with C<isl_space_get_tuple_name>, the value returned points to
1637 an internal data structure.
1638 The identifiers, positions or names of individual dimensions can be
1639 read off using the following functions.
1641 __isl_give isl_id *isl_basic_set_get_dim_id(
1642 __isl_keep isl_basic_set *bset,
1643 enum isl_dim_type type, unsigned pos);
1644 __isl_give isl_set *isl_set_set_dim_id(
1645 __isl_take isl_set *set, enum isl_dim_type type,
1646 unsigned pos, __isl_take isl_id *id);
1647 int isl_set_has_dim_id(__isl_keep isl_set *set,
1648 enum isl_dim_type type, unsigned pos);
1649 __isl_give isl_id *isl_set_get_dim_id(
1650 __isl_keep isl_set *set, enum isl_dim_type type,
1652 int isl_basic_map_has_dim_id(
1653 __isl_keep isl_basic_map *bmap,
1654 enum isl_dim_type type, unsigned pos);
1655 __isl_give isl_map *isl_map_set_dim_id(
1656 __isl_take isl_map *map, enum isl_dim_type type,
1657 unsigned pos, __isl_take isl_id *id);
1658 int isl_map_has_dim_id(__isl_keep isl_map *map,
1659 enum isl_dim_type type, unsigned pos);
1660 __isl_give isl_id *isl_map_get_dim_id(
1661 __isl_keep isl_map *map, enum isl_dim_type type,
1664 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1665 enum isl_dim_type type, __isl_keep isl_id *id);
1666 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1667 enum isl_dim_type type, __isl_keep isl_id *id);
1668 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1669 enum isl_dim_type type, const char *name);
1670 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1671 enum isl_dim_type type, const char *name);
1673 const char *isl_constraint_get_dim_name(
1674 __isl_keep isl_constraint *constraint,
1675 enum isl_dim_type type, unsigned pos);
1676 const char *isl_basic_set_get_dim_name(
1677 __isl_keep isl_basic_set *bset,
1678 enum isl_dim_type type, unsigned pos);
1679 int isl_set_has_dim_name(__isl_keep isl_set *set,
1680 enum isl_dim_type type, unsigned pos);
1681 const char *isl_set_get_dim_name(
1682 __isl_keep isl_set *set,
1683 enum isl_dim_type type, unsigned pos);
1684 const char *isl_basic_map_get_dim_name(
1685 __isl_keep isl_basic_map *bmap,
1686 enum isl_dim_type type, unsigned pos);
1687 int isl_map_has_dim_name(__isl_keep isl_map *map,
1688 enum isl_dim_type type, unsigned pos);
1689 const char *isl_map_get_dim_name(
1690 __isl_keep isl_map *map,
1691 enum isl_dim_type type, unsigned pos);
1693 These functions are mostly useful to obtain the identifiers, positions
1694 or names of the parameters. Identifiers of individual dimensions are
1695 essentially only useful for printing. They are ignored by all other
1696 operations and may not be preserved across those operations.
1700 =head3 Unary Properties
1706 The following functions test whether the given set or relation
1707 contains any integer points. The ``plain'' variants do not perform
1708 any computations, but simply check if the given set or relation
1709 is already known to be empty.
1711 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1712 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1713 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1714 int isl_set_is_empty(__isl_keep isl_set *set);
1715 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1716 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1717 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1718 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1719 int isl_map_is_empty(__isl_keep isl_map *map);
1720 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1722 =item * Universality
1724 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1725 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1726 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1728 =item * Single-valuedness
1730 int isl_basic_map_is_single_valued(
1731 __isl_keep isl_basic_map *bmap);
1732 int isl_map_plain_is_single_valued(
1733 __isl_keep isl_map *map);
1734 int isl_map_is_single_valued(__isl_keep isl_map *map);
1735 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1739 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1740 int isl_map_is_injective(__isl_keep isl_map *map);
1741 int isl_union_map_plain_is_injective(
1742 __isl_keep isl_union_map *umap);
1743 int isl_union_map_is_injective(
1744 __isl_keep isl_union_map *umap);
1748 int isl_map_is_bijective(__isl_keep isl_map *map);
1749 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1753 int isl_basic_map_plain_is_fixed(
1754 __isl_keep isl_basic_map *bmap,
1755 enum isl_dim_type type, unsigned pos,
1757 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1758 enum isl_dim_type type, unsigned pos,
1760 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1761 enum isl_dim_type type, unsigned pos,
1764 Check if the relation obviously lies on a hyperplane where the given dimension
1765 has a fixed value and if so, return that value in C<*val>.
1769 To check whether a set is a parameter domain, use this function:
1771 int isl_set_is_params(__isl_keep isl_set *set);
1772 int isl_union_set_is_params(
1773 __isl_keep isl_union_set *uset);
1777 The following functions check whether the domain of the given
1778 (basic) set is a wrapped relation.
1780 int isl_basic_set_is_wrapping(
1781 __isl_keep isl_basic_set *bset);
1782 int isl_set_is_wrapping(__isl_keep isl_set *set);
1784 =item * Internal Product
1786 int isl_basic_map_can_zip(
1787 __isl_keep isl_basic_map *bmap);
1788 int isl_map_can_zip(__isl_keep isl_map *map);
1790 Check whether the product of domain and range of the given relation
1792 i.e., whether both domain and range are nested relations.
1796 int isl_basic_map_can_curry(
1797 __isl_keep isl_basic_map *bmap);
1798 int isl_map_can_curry(__isl_keep isl_map *map);
1800 Check whether the domain of the (basic) relation is a wrapped relation.
1804 =head3 Binary Properties
1810 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1811 __isl_keep isl_set *set2);
1812 int isl_set_is_equal(__isl_keep isl_set *set1,
1813 __isl_keep isl_set *set2);
1814 int isl_union_set_is_equal(
1815 __isl_keep isl_union_set *uset1,
1816 __isl_keep isl_union_set *uset2);
1817 int isl_basic_map_is_equal(
1818 __isl_keep isl_basic_map *bmap1,
1819 __isl_keep isl_basic_map *bmap2);
1820 int isl_map_is_equal(__isl_keep isl_map *map1,
1821 __isl_keep isl_map *map2);
1822 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1823 __isl_keep isl_map *map2);
1824 int isl_union_map_is_equal(
1825 __isl_keep isl_union_map *umap1,
1826 __isl_keep isl_union_map *umap2);
1828 =item * Disjointness
1830 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1831 __isl_keep isl_set *set2);
1835 int isl_basic_set_is_subset(
1836 __isl_keep isl_basic_set *bset1,
1837 __isl_keep isl_basic_set *bset2);
1838 int isl_set_is_subset(__isl_keep isl_set *set1,
1839 __isl_keep isl_set *set2);
1840 int isl_set_is_strict_subset(
1841 __isl_keep isl_set *set1,
1842 __isl_keep isl_set *set2);
1843 int isl_union_set_is_subset(
1844 __isl_keep isl_union_set *uset1,
1845 __isl_keep isl_union_set *uset2);
1846 int isl_union_set_is_strict_subset(
1847 __isl_keep isl_union_set *uset1,
1848 __isl_keep isl_union_set *uset2);
1849 int isl_basic_map_is_subset(
1850 __isl_keep isl_basic_map *bmap1,
1851 __isl_keep isl_basic_map *bmap2);
1852 int isl_basic_map_is_strict_subset(
1853 __isl_keep isl_basic_map *bmap1,
1854 __isl_keep isl_basic_map *bmap2);
1855 int isl_map_is_subset(
1856 __isl_keep isl_map *map1,
1857 __isl_keep isl_map *map2);
1858 int isl_map_is_strict_subset(
1859 __isl_keep isl_map *map1,
1860 __isl_keep isl_map *map2);
1861 int isl_union_map_is_subset(
1862 __isl_keep isl_union_map *umap1,
1863 __isl_keep isl_union_map *umap2);
1864 int isl_union_map_is_strict_subset(
1865 __isl_keep isl_union_map *umap1,
1866 __isl_keep isl_union_map *umap2);
1868 Check whether the first argument is a (strict) subset of the
1873 =head2 Unary Operations
1879 __isl_give isl_set *isl_set_complement(
1880 __isl_take isl_set *set);
1881 __isl_give isl_map *isl_map_complement(
1882 __isl_take isl_map *map);
1886 __isl_give isl_basic_map *isl_basic_map_reverse(
1887 __isl_take isl_basic_map *bmap);
1888 __isl_give isl_map *isl_map_reverse(
1889 __isl_take isl_map *map);
1890 __isl_give isl_union_map *isl_union_map_reverse(
1891 __isl_take isl_union_map *umap);
1895 __isl_give isl_basic_set *isl_basic_set_project_out(
1896 __isl_take isl_basic_set *bset,
1897 enum isl_dim_type type, unsigned first, unsigned n);
1898 __isl_give isl_basic_map *isl_basic_map_project_out(
1899 __isl_take isl_basic_map *bmap,
1900 enum isl_dim_type type, unsigned first, unsigned n);
1901 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1902 enum isl_dim_type type, unsigned first, unsigned n);
1903 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1904 enum isl_dim_type type, unsigned first, unsigned n);
1905 __isl_give isl_basic_set *isl_basic_set_params(
1906 __isl_take isl_basic_set *bset);
1907 __isl_give isl_basic_set *isl_basic_map_domain(
1908 __isl_take isl_basic_map *bmap);
1909 __isl_give isl_basic_set *isl_basic_map_range(
1910 __isl_take isl_basic_map *bmap);
1911 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1912 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1913 __isl_give isl_set *isl_map_domain(
1914 __isl_take isl_map *bmap);
1915 __isl_give isl_set *isl_map_range(
1916 __isl_take isl_map *map);
1917 __isl_give isl_set *isl_union_set_params(
1918 __isl_take isl_union_set *uset);
1919 __isl_give isl_set *isl_union_map_params(
1920 __isl_take isl_union_map *umap);
1921 __isl_give isl_union_set *isl_union_map_domain(
1922 __isl_take isl_union_map *umap);
1923 __isl_give isl_union_set *isl_union_map_range(
1924 __isl_take isl_union_map *umap);
1926 __isl_give isl_basic_map *isl_basic_map_domain_map(
1927 __isl_take isl_basic_map *bmap);
1928 __isl_give isl_basic_map *isl_basic_map_range_map(
1929 __isl_take isl_basic_map *bmap);
1930 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1931 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1932 __isl_give isl_union_map *isl_union_map_domain_map(
1933 __isl_take isl_union_map *umap);
1934 __isl_give isl_union_map *isl_union_map_range_map(
1935 __isl_take isl_union_map *umap);
1937 The functions above construct a (basic, regular or union) relation
1938 that maps (a wrapped version of) the input relation to its domain or range.
1942 __isl_give isl_basic_set *isl_basic_set_eliminate(
1943 __isl_take isl_basic_set *bset,
1944 enum isl_dim_type type,
1945 unsigned first, unsigned n);
1946 __isl_give isl_set *isl_set_eliminate(
1947 __isl_take isl_set *set, enum isl_dim_type type,
1948 unsigned first, unsigned n);
1949 __isl_give isl_basic_map *isl_basic_map_eliminate(
1950 __isl_take isl_basic_map *bmap,
1951 enum isl_dim_type type,
1952 unsigned first, unsigned n);
1953 __isl_give isl_map *isl_map_eliminate(
1954 __isl_take isl_map *map, enum isl_dim_type type,
1955 unsigned first, unsigned n);
1957 Eliminate the coefficients for the given dimensions from the constraints,
1958 without removing the dimensions.
1962 __isl_give isl_basic_set *isl_basic_set_fix(
1963 __isl_take isl_basic_set *bset,
1964 enum isl_dim_type type, unsigned pos,
1966 __isl_give isl_basic_set *isl_basic_set_fix_si(
1967 __isl_take isl_basic_set *bset,
1968 enum isl_dim_type type, unsigned pos, int value);
1969 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1970 enum isl_dim_type type, unsigned pos,
1972 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1973 enum isl_dim_type type, unsigned pos, int value);
1974 __isl_give isl_basic_map *isl_basic_map_fix_si(
1975 __isl_take isl_basic_map *bmap,
1976 enum isl_dim_type type, unsigned pos, int value);
1977 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1978 enum isl_dim_type type, unsigned pos, int value);
1980 Intersect the set or relation with the hyperplane where the given
1981 dimension has the fixed given value.
1983 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1984 __isl_take isl_basic_map *bmap,
1985 enum isl_dim_type type, unsigned pos, int value);
1986 __isl_give isl_set *isl_set_lower_bound(
1987 __isl_take isl_set *set,
1988 enum isl_dim_type type, unsigned pos,
1990 __isl_give isl_set *isl_set_lower_bound_si(
1991 __isl_take isl_set *set,
1992 enum isl_dim_type type, unsigned pos, int value);
1993 __isl_give isl_map *isl_map_lower_bound_si(
1994 __isl_take isl_map *map,
1995 enum isl_dim_type type, unsigned pos, int value);
1996 __isl_give isl_set *isl_set_upper_bound(
1997 __isl_take isl_set *set,
1998 enum isl_dim_type type, unsigned pos,
2000 __isl_give isl_set *isl_set_upper_bound_si(
2001 __isl_take isl_set *set,
2002 enum isl_dim_type type, unsigned pos, int value);
2003 __isl_give isl_map *isl_map_upper_bound_si(
2004 __isl_take isl_map *map,
2005 enum isl_dim_type type, unsigned pos, int value);
2007 Intersect the set or relation with the half-space where the given
2008 dimension has a value bounded by the fixed given value.
2010 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2011 enum isl_dim_type type1, int pos1,
2012 enum isl_dim_type type2, int pos2);
2013 __isl_give isl_basic_map *isl_basic_map_equate(
2014 __isl_take isl_basic_map *bmap,
2015 enum isl_dim_type type1, int pos1,
2016 enum isl_dim_type type2, int pos2);
2017 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2018 enum isl_dim_type type1, int pos1,
2019 enum isl_dim_type type2, int pos2);
2021 Intersect the set or relation with the hyperplane where the given
2022 dimensions are equal to each other.
2024 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2025 enum isl_dim_type type1, int pos1,
2026 enum isl_dim_type type2, int pos2);
2028 Intersect the relation with the hyperplane where the given
2029 dimensions have opposite values.
2031 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2032 enum isl_dim_type type1, int pos1,
2033 enum isl_dim_type type2, int pos2);
2034 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2035 enum isl_dim_type type1, int pos1,
2036 enum isl_dim_type type2, int pos2);
2038 Intersect the relation with the half-space where the given
2039 dimensions satisfy the given ordering.
2043 __isl_give isl_map *isl_set_identity(
2044 __isl_take isl_set *set);
2045 __isl_give isl_union_map *isl_union_set_identity(
2046 __isl_take isl_union_set *uset);
2048 Construct an identity relation on the given (union) set.
2052 __isl_give isl_basic_set *isl_basic_map_deltas(
2053 __isl_take isl_basic_map *bmap);
2054 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2055 __isl_give isl_union_set *isl_union_map_deltas(
2056 __isl_take isl_union_map *umap);
2058 These functions return a (basic) set containing the differences
2059 between image elements and corresponding domain elements in the input.
2061 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2062 __isl_take isl_basic_map *bmap);
2063 __isl_give isl_map *isl_map_deltas_map(
2064 __isl_take isl_map *map);
2065 __isl_give isl_union_map *isl_union_map_deltas_map(
2066 __isl_take isl_union_map *umap);
2068 The functions above construct a (basic, regular or union) relation
2069 that maps (a wrapped version of) the input relation to its delta set.
2073 Simplify the representation of a set or relation by trying
2074 to combine pairs of basic sets or relations into a single
2075 basic set or relation.
2077 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2078 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2079 __isl_give isl_union_set *isl_union_set_coalesce(
2080 __isl_take isl_union_set *uset);
2081 __isl_give isl_union_map *isl_union_map_coalesce(
2082 __isl_take isl_union_map *umap);
2084 One of the methods for combining pairs of basic sets or relations
2085 can result in coefficients that are much larger than those that appear
2086 in the constraints of the input. By default, the coefficients are
2087 not allowed to grow larger, but this can be changed by unsetting
2088 the following option.
2090 int isl_options_set_coalesce_bounded_wrapping(
2091 isl_ctx *ctx, int val);
2092 int isl_options_get_coalesce_bounded_wrapping(
2095 =item * Detecting equalities
2097 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2098 __isl_take isl_basic_set *bset);
2099 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2100 __isl_take isl_basic_map *bmap);
2101 __isl_give isl_set *isl_set_detect_equalities(
2102 __isl_take isl_set *set);
2103 __isl_give isl_map *isl_map_detect_equalities(
2104 __isl_take isl_map *map);
2105 __isl_give isl_union_set *isl_union_set_detect_equalities(
2106 __isl_take isl_union_set *uset);
2107 __isl_give isl_union_map *isl_union_map_detect_equalities(
2108 __isl_take isl_union_map *umap);
2110 Simplify the representation of a set or relation by detecting implicit
2113 =item * Removing redundant constraints
2115 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2116 __isl_take isl_basic_set *bset);
2117 __isl_give isl_set *isl_set_remove_redundancies(
2118 __isl_take isl_set *set);
2119 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2120 __isl_take isl_basic_map *bmap);
2121 __isl_give isl_map *isl_map_remove_redundancies(
2122 __isl_take isl_map *map);
2126 __isl_give isl_basic_set *isl_set_convex_hull(
2127 __isl_take isl_set *set);
2128 __isl_give isl_basic_map *isl_map_convex_hull(
2129 __isl_take isl_map *map);
2131 If the input set or relation has any existentially quantified
2132 variables, then the result of these operations is currently undefined.
2136 __isl_give isl_basic_set *isl_set_simple_hull(
2137 __isl_take isl_set *set);
2138 __isl_give isl_basic_map *isl_map_simple_hull(
2139 __isl_take isl_map *map);
2140 __isl_give isl_union_map *isl_union_map_simple_hull(
2141 __isl_take isl_union_map *umap);
2143 These functions compute a single basic set or relation
2144 that contains the whole input set or relation.
2145 In particular, the output is described by translates
2146 of the constraints describing the basic sets or relations in the input.
2150 (See \autoref{s:simple hull}.)
2156 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2157 __isl_take isl_basic_set *bset);
2158 __isl_give isl_basic_set *isl_set_affine_hull(
2159 __isl_take isl_set *set);
2160 __isl_give isl_union_set *isl_union_set_affine_hull(
2161 __isl_take isl_union_set *uset);
2162 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2163 __isl_take isl_basic_map *bmap);
2164 __isl_give isl_basic_map *isl_map_affine_hull(
2165 __isl_take isl_map *map);
2166 __isl_give isl_union_map *isl_union_map_affine_hull(
2167 __isl_take isl_union_map *umap);
2169 In case of union sets and relations, the affine hull is computed
2172 =item * Polyhedral hull
2174 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2175 __isl_take isl_set *set);
2176 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2177 __isl_take isl_map *map);
2178 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2179 __isl_take isl_union_set *uset);
2180 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2181 __isl_take isl_union_map *umap);
2183 These functions compute a single basic set or relation
2184 not involving any existentially quantified variables
2185 that contains the whole input set or relation.
2186 In case of union sets and relations, the polyhedral hull is computed
2191 __isl_give isl_basic_set *isl_basic_set_sample(
2192 __isl_take isl_basic_set *bset);
2193 __isl_give isl_basic_set *isl_set_sample(
2194 __isl_take isl_set *set);
2195 __isl_give isl_basic_map *isl_basic_map_sample(
2196 __isl_take isl_basic_map *bmap);
2197 __isl_give isl_basic_map *isl_map_sample(
2198 __isl_take isl_map *map);
2200 If the input (basic) set or relation is non-empty, then return
2201 a singleton subset of the input. Otherwise, return an empty set.
2203 =item * Optimization
2205 #include <isl/ilp.h>
2206 enum isl_lp_result isl_basic_set_max(
2207 __isl_keep isl_basic_set *bset,
2208 __isl_keep isl_aff *obj, isl_int *opt)
2209 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2210 __isl_keep isl_aff *obj, isl_int *opt);
2211 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2212 __isl_keep isl_aff *obj, isl_int *opt);
2214 Compute the minimum or maximum of the integer affine expression C<obj>
2215 over the points in C<set>, returning the result in C<opt>.
2216 The return value may be one of C<isl_lp_error>,
2217 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2219 =item * Parametric optimization
2221 __isl_give isl_pw_aff *isl_set_dim_min(
2222 __isl_take isl_set *set, int pos);
2223 __isl_give isl_pw_aff *isl_set_dim_max(
2224 __isl_take isl_set *set, int pos);
2225 __isl_give isl_pw_aff *isl_map_dim_max(
2226 __isl_take isl_map *map, int pos);
2228 Compute the minimum or maximum of the given set or output dimension
2229 as a function of the parameters (and input dimensions), but independently
2230 of the other set or output dimensions.
2231 For lexicographic optimization, see L<"Lexicographic Optimization">.
2235 The following functions compute either the set of (rational) coefficient
2236 values of valid constraints for the given set or the set of (rational)
2237 values satisfying the constraints with coefficients from the given set.
2238 Internally, these two sets of functions perform essentially the
2239 same operations, except that the set of coefficients is assumed to
2240 be a cone, while the set of values may be any polyhedron.
2241 The current implementation is based on the Farkas lemma and
2242 Fourier-Motzkin elimination, but this may change or be made optional
2243 in future. In particular, future implementations may use different
2244 dualization algorithms or skip the elimination step.
2246 __isl_give isl_basic_set *isl_basic_set_coefficients(
2247 __isl_take isl_basic_set *bset);
2248 __isl_give isl_basic_set *isl_set_coefficients(
2249 __isl_take isl_set *set);
2250 __isl_give isl_union_set *isl_union_set_coefficients(
2251 __isl_take isl_union_set *bset);
2252 __isl_give isl_basic_set *isl_basic_set_solutions(
2253 __isl_take isl_basic_set *bset);
2254 __isl_give isl_basic_set *isl_set_solutions(
2255 __isl_take isl_set *set);
2256 __isl_give isl_union_set *isl_union_set_solutions(
2257 __isl_take isl_union_set *bset);
2261 __isl_give isl_map *isl_map_fixed_power(
2262 __isl_take isl_map *map, isl_int exp);
2263 __isl_give isl_union_map *isl_union_map_fixed_power(
2264 __isl_take isl_union_map *umap, isl_int exp);
2266 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2267 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2268 of C<map> is computed.
2270 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2272 __isl_give isl_union_map *isl_union_map_power(
2273 __isl_take isl_union_map *umap, int *exact);
2275 Compute a parametric representation for all positive powers I<k> of C<map>.
2276 The result maps I<k> to a nested relation corresponding to the
2277 I<k>th power of C<map>.
2278 The result may be an overapproximation. If the result is known to be exact,
2279 then C<*exact> is set to C<1>.
2281 =item * Transitive closure
2283 __isl_give isl_map *isl_map_transitive_closure(
2284 __isl_take isl_map *map, int *exact);
2285 __isl_give isl_union_map *isl_union_map_transitive_closure(
2286 __isl_take isl_union_map *umap, int *exact);
2288 Compute the transitive closure of C<map>.
2289 The result may be an overapproximation. If the result is known to be exact,
2290 then C<*exact> is set to C<1>.
2292 =item * Reaching path lengths
2294 __isl_give isl_map *isl_map_reaching_path_lengths(
2295 __isl_take isl_map *map, int *exact);
2297 Compute a relation that maps each element in the range of C<map>
2298 to the lengths of all paths composed of edges in C<map> that
2299 end up in the given element.
2300 The result may be an overapproximation. If the result is known to be exact,
2301 then C<*exact> is set to C<1>.
2302 To compute the I<maximal> path length, the resulting relation
2303 should be postprocessed by C<isl_map_lexmax>.
2304 In particular, if the input relation is a dependence relation
2305 (mapping sources to sinks), then the maximal path length corresponds
2306 to the free schedule.
2307 Note, however, that C<isl_map_lexmax> expects the maximum to be
2308 finite, so if the path lengths are unbounded (possibly due to
2309 the overapproximation), then you will get an error message.
2313 __isl_give isl_basic_set *isl_basic_map_wrap(
2314 __isl_take isl_basic_map *bmap);
2315 __isl_give isl_set *isl_map_wrap(
2316 __isl_take isl_map *map);
2317 __isl_give isl_union_set *isl_union_map_wrap(
2318 __isl_take isl_union_map *umap);
2319 __isl_give isl_basic_map *isl_basic_set_unwrap(
2320 __isl_take isl_basic_set *bset);
2321 __isl_give isl_map *isl_set_unwrap(
2322 __isl_take isl_set *set);
2323 __isl_give isl_union_map *isl_union_set_unwrap(
2324 __isl_take isl_union_set *uset);
2328 Remove any internal structure of domain (and range) of the given
2329 set or relation. If there is any such internal structure in the input,
2330 then the name of the space is also removed.
2332 __isl_give isl_basic_set *isl_basic_set_flatten(
2333 __isl_take isl_basic_set *bset);
2334 __isl_give isl_set *isl_set_flatten(
2335 __isl_take isl_set *set);
2336 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2337 __isl_take isl_basic_map *bmap);
2338 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2339 __isl_take isl_basic_map *bmap);
2340 __isl_give isl_map *isl_map_flatten_range(
2341 __isl_take isl_map *map);
2342 __isl_give isl_map *isl_map_flatten_domain(
2343 __isl_take isl_map *map);
2344 __isl_give isl_basic_map *isl_basic_map_flatten(
2345 __isl_take isl_basic_map *bmap);
2346 __isl_give isl_map *isl_map_flatten(
2347 __isl_take isl_map *map);
2349 __isl_give isl_map *isl_set_flatten_map(
2350 __isl_take isl_set *set);
2352 The function above constructs a relation
2353 that maps the input set to a flattened version of the set.
2357 Lift the input set to a space with extra dimensions corresponding
2358 to the existentially quantified variables in the input.
2359 In particular, the result lives in a wrapped map where the domain
2360 is the original space and the range corresponds to the original
2361 existentially quantified variables.
2363 __isl_give isl_basic_set *isl_basic_set_lift(
2364 __isl_take isl_basic_set *bset);
2365 __isl_give isl_set *isl_set_lift(
2366 __isl_take isl_set *set);
2367 __isl_give isl_union_set *isl_union_set_lift(
2368 __isl_take isl_union_set *uset);
2370 Given a local space that contains the existentially quantified
2371 variables of a set, a basic relation that, when applied to
2372 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2373 can be constructed using the following function.
2375 #include <isl/local_space.h>
2376 __isl_give isl_basic_map *isl_local_space_lifting(
2377 __isl_take isl_local_space *ls);
2379 =item * Internal Product
2381 __isl_give isl_basic_map *isl_basic_map_zip(
2382 __isl_take isl_basic_map *bmap);
2383 __isl_give isl_map *isl_map_zip(
2384 __isl_take isl_map *map);
2385 __isl_give isl_union_map *isl_union_map_zip(
2386 __isl_take isl_union_map *umap);
2388 Given a relation with nested relations for domain and range,
2389 interchange the range of the domain with the domain of the range.
2393 __isl_give isl_basic_map *isl_basic_map_curry(
2394 __isl_take isl_basic_map *bmap);
2395 __isl_give isl_map *isl_map_curry(
2396 __isl_take isl_map *map);
2397 __isl_give isl_union_map *isl_union_map_curry(
2398 __isl_take isl_union_map *umap);
2400 Given a relation with a nested relation for domain,
2401 move the range of the nested relation out of the domain
2402 and use it as the domain of a nested relation in the range,
2403 with the original range as range of this nested relation.
2405 =item * Aligning parameters
2407 __isl_give isl_basic_set *isl_basic_set_align_params(
2408 __isl_take isl_basic_set *bset,
2409 __isl_take isl_space *model);
2410 __isl_give isl_set *isl_set_align_params(
2411 __isl_take isl_set *set,
2412 __isl_take isl_space *model);
2413 __isl_give isl_basic_map *isl_basic_map_align_params(
2414 __isl_take isl_basic_map *bmap,
2415 __isl_take isl_space *model);
2416 __isl_give isl_map *isl_map_align_params(
2417 __isl_take isl_map *map,
2418 __isl_take isl_space *model);
2420 Change the order of the parameters of the given set or relation
2421 such that the first parameters match those of C<model>.
2422 This may involve the introduction of extra parameters.
2423 All parameters need to be named.
2425 =item * Dimension manipulation
2427 __isl_give isl_set *isl_set_add_dims(
2428 __isl_take isl_set *set,
2429 enum isl_dim_type type, unsigned n);
2430 __isl_give isl_map *isl_map_add_dims(
2431 __isl_take isl_map *map,
2432 enum isl_dim_type type, unsigned n);
2433 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2434 __isl_take isl_basic_set *bset,
2435 enum isl_dim_type type, unsigned pos,
2437 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2438 __isl_take isl_basic_map *bmap,
2439 enum isl_dim_type type, unsigned pos,
2441 __isl_give isl_set *isl_set_insert_dims(
2442 __isl_take isl_set *set,
2443 enum isl_dim_type type, unsigned pos, unsigned n);
2444 __isl_give isl_map *isl_map_insert_dims(
2445 __isl_take isl_map *map,
2446 enum isl_dim_type type, unsigned pos, unsigned n);
2447 __isl_give isl_basic_set *isl_basic_set_move_dims(
2448 __isl_take isl_basic_set *bset,
2449 enum isl_dim_type dst_type, unsigned dst_pos,
2450 enum isl_dim_type src_type, unsigned src_pos,
2452 __isl_give isl_basic_map *isl_basic_map_move_dims(
2453 __isl_take isl_basic_map *bmap,
2454 enum isl_dim_type dst_type, unsigned dst_pos,
2455 enum isl_dim_type src_type, unsigned src_pos,
2457 __isl_give isl_set *isl_set_move_dims(
2458 __isl_take isl_set *set,
2459 enum isl_dim_type dst_type, unsigned dst_pos,
2460 enum isl_dim_type src_type, unsigned src_pos,
2462 __isl_give isl_map *isl_map_move_dims(
2463 __isl_take isl_map *map,
2464 enum isl_dim_type dst_type, unsigned dst_pos,
2465 enum isl_dim_type src_type, unsigned src_pos,
2468 It is usually not advisable to directly change the (input or output)
2469 space of a set or a relation as this removes the name and the internal
2470 structure of the space. However, the above functions can be useful
2471 to add new parameters, assuming
2472 C<isl_set_align_params> and C<isl_map_align_params>
2477 =head2 Binary Operations
2479 The two arguments of a binary operation not only need to live
2480 in the same C<isl_ctx>, they currently also need to have
2481 the same (number of) parameters.
2483 =head3 Basic Operations
2487 =item * Intersection
2489 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2490 __isl_take isl_basic_set *bset1,
2491 __isl_take isl_basic_set *bset2);
2492 __isl_give isl_basic_set *isl_basic_set_intersect(
2493 __isl_take isl_basic_set *bset1,
2494 __isl_take isl_basic_set *bset2);
2495 __isl_give isl_set *isl_set_intersect_params(
2496 __isl_take isl_set *set,
2497 __isl_take isl_set *params);
2498 __isl_give isl_set *isl_set_intersect(
2499 __isl_take isl_set *set1,
2500 __isl_take isl_set *set2);
2501 __isl_give isl_union_set *isl_union_set_intersect_params(
2502 __isl_take isl_union_set *uset,
2503 __isl_take isl_set *set);
2504 __isl_give isl_union_map *isl_union_map_intersect_params(
2505 __isl_take isl_union_map *umap,
2506 __isl_take isl_set *set);
2507 __isl_give isl_union_set *isl_union_set_intersect(
2508 __isl_take isl_union_set *uset1,
2509 __isl_take isl_union_set *uset2);
2510 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2511 __isl_take isl_basic_map *bmap,
2512 __isl_take isl_basic_set *bset);
2513 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2514 __isl_take isl_basic_map *bmap,
2515 __isl_take isl_basic_set *bset);
2516 __isl_give isl_basic_map *isl_basic_map_intersect(
2517 __isl_take isl_basic_map *bmap1,
2518 __isl_take isl_basic_map *bmap2);
2519 __isl_give isl_map *isl_map_intersect_params(
2520 __isl_take isl_map *map,
2521 __isl_take isl_set *params);
2522 __isl_give isl_map *isl_map_intersect_domain(
2523 __isl_take isl_map *map,
2524 __isl_take isl_set *set);
2525 __isl_give isl_map *isl_map_intersect_range(
2526 __isl_take isl_map *map,
2527 __isl_take isl_set *set);
2528 __isl_give isl_map *isl_map_intersect(
2529 __isl_take isl_map *map1,
2530 __isl_take isl_map *map2);
2531 __isl_give isl_union_map *isl_union_map_intersect_domain(
2532 __isl_take isl_union_map *umap,
2533 __isl_take isl_union_set *uset);
2534 __isl_give isl_union_map *isl_union_map_intersect_range(
2535 __isl_take isl_union_map *umap,
2536 __isl_take isl_union_set *uset);
2537 __isl_give isl_union_map *isl_union_map_intersect(
2538 __isl_take isl_union_map *umap1,
2539 __isl_take isl_union_map *umap2);
2541 The second argument to the C<_params> functions needs to be
2542 a parametric (basic) set. For the other functions, a parametric set
2543 for either argument is only allowed if the other argument is
2544 a parametric set as well.
2548 __isl_give isl_set *isl_basic_set_union(
2549 __isl_take isl_basic_set *bset1,
2550 __isl_take isl_basic_set *bset2);
2551 __isl_give isl_map *isl_basic_map_union(
2552 __isl_take isl_basic_map *bmap1,
2553 __isl_take isl_basic_map *bmap2);
2554 __isl_give isl_set *isl_set_union(
2555 __isl_take isl_set *set1,
2556 __isl_take isl_set *set2);
2557 __isl_give isl_map *isl_map_union(
2558 __isl_take isl_map *map1,
2559 __isl_take isl_map *map2);
2560 __isl_give isl_union_set *isl_union_set_union(
2561 __isl_take isl_union_set *uset1,
2562 __isl_take isl_union_set *uset2);
2563 __isl_give isl_union_map *isl_union_map_union(
2564 __isl_take isl_union_map *umap1,
2565 __isl_take isl_union_map *umap2);
2567 =item * Set difference
2569 __isl_give isl_set *isl_set_subtract(
2570 __isl_take isl_set *set1,
2571 __isl_take isl_set *set2);
2572 __isl_give isl_map *isl_map_subtract(
2573 __isl_take isl_map *map1,
2574 __isl_take isl_map *map2);
2575 __isl_give isl_map *isl_map_subtract_domain(
2576 __isl_take isl_map *map,
2577 __isl_take isl_set *dom);
2578 __isl_give isl_map *isl_map_subtract_range(
2579 __isl_take isl_map *map,
2580 __isl_take isl_set *dom);
2581 __isl_give isl_union_set *isl_union_set_subtract(
2582 __isl_take isl_union_set *uset1,
2583 __isl_take isl_union_set *uset2);
2584 __isl_give isl_union_map *isl_union_map_subtract(
2585 __isl_take isl_union_map *umap1,
2586 __isl_take isl_union_map *umap2);
2590 __isl_give isl_basic_set *isl_basic_set_apply(
2591 __isl_take isl_basic_set *bset,
2592 __isl_take isl_basic_map *bmap);
2593 __isl_give isl_set *isl_set_apply(
2594 __isl_take isl_set *set,
2595 __isl_take isl_map *map);
2596 __isl_give isl_union_set *isl_union_set_apply(
2597 __isl_take isl_union_set *uset,
2598 __isl_take isl_union_map *umap);
2599 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2600 __isl_take isl_basic_map *bmap1,
2601 __isl_take isl_basic_map *bmap2);
2602 __isl_give isl_basic_map *isl_basic_map_apply_range(
2603 __isl_take isl_basic_map *bmap1,
2604 __isl_take isl_basic_map *bmap2);
2605 __isl_give isl_map *isl_map_apply_domain(
2606 __isl_take isl_map *map1,
2607 __isl_take isl_map *map2);
2608 __isl_give isl_union_map *isl_union_map_apply_domain(
2609 __isl_take isl_union_map *umap1,
2610 __isl_take isl_union_map *umap2);
2611 __isl_give isl_map *isl_map_apply_range(
2612 __isl_take isl_map *map1,
2613 __isl_take isl_map *map2);
2614 __isl_give isl_union_map *isl_union_map_apply_range(
2615 __isl_take isl_union_map *umap1,
2616 __isl_take isl_union_map *umap2);
2618 =item * Cartesian Product
2620 __isl_give isl_set *isl_set_product(
2621 __isl_take isl_set *set1,
2622 __isl_take isl_set *set2);
2623 __isl_give isl_union_set *isl_union_set_product(
2624 __isl_take isl_union_set *uset1,
2625 __isl_take isl_union_set *uset2);
2626 __isl_give isl_basic_map *isl_basic_map_domain_product(
2627 __isl_take isl_basic_map *bmap1,
2628 __isl_take isl_basic_map *bmap2);
2629 __isl_give isl_basic_map *isl_basic_map_range_product(
2630 __isl_take isl_basic_map *bmap1,
2631 __isl_take isl_basic_map *bmap2);
2632 __isl_give isl_basic_map *isl_basic_map_product(
2633 __isl_take isl_basic_map *bmap1,
2634 __isl_take isl_basic_map *bmap2);
2635 __isl_give isl_map *isl_map_domain_product(
2636 __isl_take isl_map *map1,
2637 __isl_take isl_map *map2);
2638 __isl_give isl_map *isl_map_range_product(
2639 __isl_take isl_map *map1,
2640 __isl_take isl_map *map2);
2641 __isl_give isl_union_map *isl_union_map_domain_product(
2642 __isl_take isl_union_map *umap1,
2643 __isl_take isl_union_map *umap2);
2644 __isl_give isl_union_map *isl_union_map_range_product(
2645 __isl_take isl_union_map *umap1,
2646 __isl_take isl_union_map *umap2);
2647 __isl_give isl_map *isl_map_product(
2648 __isl_take isl_map *map1,
2649 __isl_take isl_map *map2);
2650 __isl_give isl_union_map *isl_union_map_product(
2651 __isl_take isl_union_map *umap1,
2652 __isl_take isl_union_map *umap2);
2654 The above functions compute the cross product of the given
2655 sets or relations. The domains and ranges of the results
2656 are wrapped maps between domains and ranges of the inputs.
2657 To obtain a ``flat'' product, use the following functions
2660 __isl_give isl_basic_set *isl_basic_set_flat_product(
2661 __isl_take isl_basic_set *bset1,
2662 __isl_take isl_basic_set *bset2);
2663 __isl_give isl_set *isl_set_flat_product(
2664 __isl_take isl_set *set1,
2665 __isl_take isl_set *set2);
2666 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2667 __isl_take isl_basic_map *bmap1,
2668 __isl_take isl_basic_map *bmap2);
2669 __isl_give isl_map *isl_map_flat_domain_product(
2670 __isl_take isl_map *map1,
2671 __isl_take isl_map *map2);
2672 __isl_give isl_map *isl_map_flat_range_product(
2673 __isl_take isl_map *map1,
2674 __isl_take isl_map *map2);
2675 __isl_give isl_union_map *isl_union_map_flat_range_product(
2676 __isl_take isl_union_map *umap1,
2677 __isl_take isl_union_map *umap2);
2678 __isl_give isl_basic_map *isl_basic_map_flat_product(
2679 __isl_take isl_basic_map *bmap1,
2680 __isl_take isl_basic_map *bmap2);
2681 __isl_give isl_map *isl_map_flat_product(
2682 __isl_take isl_map *map1,
2683 __isl_take isl_map *map2);
2685 =item * Simplification
2687 __isl_give isl_basic_set *isl_basic_set_gist(
2688 __isl_take isl_basic_set *bset,
2689 __isl_take isl_basic_set *context);
2690 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2691 __isl_take isl_set *context);
2692 __isl_give isl_set *isl_set_gist_params(
2693 __isl_take isl_set *set,
2694 __isl_take isl_set *context);
2695 __isl_give isl_union_set *isl_union_set_gist(
2696 __isl_take isl_union_set *uset,
2697 __isl_take isl_union_set *context);
2698 __isl_give isl_union_set *isl_union_set_gist_params(
2699 __isl_take isl_union_set *uset,
2700 __isl_take isl_set *set);
2701 __isl_give isl_basic_map *isl_basic_map_gist(
2702 __isl_take isl_basic_map *bmap,
2703 __isl_take isl_basic_map *context);
2704 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2705 __isl_take isl_map *context);
2706 __isl_give isl_map *isl_map_gist_params(
2707 __isl_take isl_map *map,
2708 __isl_take isl_set *context);
2709 __isl_give isl_map *isl_map_gist_domain(
2710 __isl_take isl_map *map,
2711 __isl_take isl_set *context);
2712 __isl_give isl_map *isl_map_gist_range(
2713 __isl_take isl_map *map,
2714 __isl_take isl_set *context);
2715 __isl_give isl_union_map *isl_union_map_gist(
2716 __isl_take isl_union_map *umap,
2717 __isl_take isl_union_map *context);
2718 __isl_give isl_union_map *isl_union_map_gist_params(
2719 __isl_take isl_union_map *umap,
2720 __isl_take isl_set *set);
2721 __isl_give isl_union_map *isl_union_map_gist_domain(
2722 __isl_take isl_union_map *umap,
2723 __isl_take isl_union_set *uset);
2724 __isl_give isl_union_map *isl_union_map_gist_range(
2725 __isl_take isl_union_map *umap,
2726 __isl_take isl_union_set *uset);
2728 The gist operation returns a set or relation that has the
2729 same intersection with the context as the input set or relation.
2730 Any implicit equality in the intersection is made explicit in the result,
2731 while all inequalities that are redundant with respect to the intersection
2733 In case of union sets and relations, the gist operation is performed
2738 =head3 Lexicographic Optimization
2740 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2741 the following functions
2742 compute a set that contains the lexicographic minimum or maximum
2743 of the elements in C<set> (or C<bset>) for those values of the parameters
2744 that satisfy C<dom>.
2745 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2746 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2748 In other words, the union of the parameter values
2749 for which the result is non-empty and of C<*empty>
2752 __isl_give isl_set *isl_basic_set_partial_lexmin(
2753 __isl_take isl_basic_set *bset,
2754 __isl_take isl_basic_set *dom,
2755 __isl_give isl_set **empty);
2756 __isl_give isl_set *isl_basic_set_partial_lexmax(
2757 __isl_take isl_basic_set *bset,
2758 __isl_take isl_basic_set *dom,
2759 __isl_give isl_set **empty);
2760 __isl_give isl_set *isl_set_partial_lexmin(
2761 __isl_take isl_set *set, __isl_take isl_set *dom,
2762 __isl_give isl_set **empty);
2763 __isl_give isl_set *isl_set_partial_lexmax(
2764 __isl_take isl_set *set, __isl_take isl_set *dom,
2765 __isl_give isl_set **empty);
2767 Given a (basic) set C<set> (or C<bset>), the following functions simply
2768 return a set containing the lexicographic minimum or maximum
2769 of the elements in C<set> (or C<bset>).
2770 In case of union sets, the optimum is computed per space.
2772 __isl_give isl_set *isl_basic_set_lexmin(
2773 __isl_take isl_basic_set *bset);
2774 __isl_give isl_set *isl_basic_set_lexmax(
2775 __isl_take isl_basic_set *bset);
2776 __isl_give isl_set *isl_set_lexmin(
2777 __isl_take isl_set *set);
2778 __isl_give isl_set *isl_set_lexmax(
2779 __isl_take isl_set *set);
2780 __isl_give isl_union_set *isl_union_set_lexmin(
2781 __isl_take isl_union_set *uset);
2782 __isl_give isl_union_set *isl_union_set_lexmax(
2783 __isl_take isl_union_set *uset);
2785 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2786 the following functions
2787 compute a relation that maps each element of C<dom>
2788 to the single lexicographic minimum or maximum
2789 of the elements that are associated to that same
2790 element in C<map> (or C<bmap>).
2791 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2792 that contains the elements in C<dom> that do not map
2793 to any elements in C<map> (or C<bmap>).
2794 In other words, the union of the domain of the result and of C<*empty>
2797 __isl_give isl_map *isl_basic_map_partial_lexmax(
2798 __isl_take isl_basic_map *bmap,
2799 __isl_take isl_basic_set *dom,
2800 __isl_give isl_set **empty);
2801 __isl_give isl_map *isl_basic_map_partial_lexmin(
2802 __isl_take isl_basic_map *bmap,
2803 __isl_take isl_basic_set *dom,
2804 __isl_give isl_set **empty);
2805 __isl_give isl_map *isl_map_partial_lexmax(
2806 __isl_take isl_map *map, __isl_take isl_set *dom,
2807 __isl_give isl_set **empty);
2808 __isl_give isl_map *isl_map_partial_lexmin(
2809 __isl_take isl_map *map, __isl_take isl_set *dom,
2810 __isl_give isl_set **empty);
2812 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2813 return a map mapping each element in the domain of
2814 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2815 of all elements associated to that element.
2816 In case of union relations, the optimum is computed per space.
2818 __isl_give isl_map *isl_basic_map_lexmin(
2819 __isl_take isl_basic_map *bmap);
2820 __isl_give isl_map *isl_basic_map_lexmax(
2821 __isl_take isl_basic_map *bmap);
2822 __isl_give isl_map *isl_map_lexmin(
2823 __isl_take isl_map *map);
2824 __isl_give isl_map *isl_map_lexmax(
2825 __isl_take isl_map *map);
2826 __isl_give isl_union_map *isl_union_map_lexmin(
2827 __isl_take isl_union_map *umap);
2828 __isl_give isl_union_map *isl_union_map_lexmax(
2829 __isl_take isl_union_map *umap);
2831 The following functions return their result in the form of
2832 a piecewise multi-affine expression
2833 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2834 but are otherwise equivalent to the corresponding functions
2835 returning a basic set or relation.
2837 __isl_give isl_pw_multi_aff *
2838 isl_basic_map_lexmin_pw_multi_aff(
2839 __isl_take isl_basic_map *bmap);
2840 __isl_give isl_pw_multi_aff *
2841 isl_basic_set_partial_lexmin_pw_multi_aff(
2842 __isl_take isl_basic_set *bset,
2843 __isl_take isl_basic_set *dom,
2844 __isl_give isl_set **empty);
2845 __isl_give isl_pw_multi_aff *
2846 isl_basic_set_partial_lexmax_pw_multi_aff(
2847 __isl_take isl_basic_set *bset,
2848 __isl_take isl_basic_set *dom,
2849 __isl_give isl_set **empty);
2850 __isl_give isl_pw_multi_aff *
2851 isl_basic_map_partial_lexmin_pw_multi_aff(
2852 __isl_take isl_basic_map *bmap,
2853 __isl_take isl_basic_set *dom,
2854 __isl_give isl_set **empty);
2855 __isl_give isl_pw_multi_aff *
2856 isl_basic_map_partial_lexmax_pw_multi_aff(
2857 __isl_take isl_basic_map *bmap,
2858 __isl_take isl_basic_set *dom,
2859 __isl_give isl_set **empty);
2863 Lists are defined over several element types, including
2864 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2865 Here we take lists of C<isl_set>s as an example.
2866 Lists can be created, copied, modified and freed using the following functions.
2868 #include <isl/list.h>
2869 __isl_give isl_set_list *isl_set_list_from_set(
2870 __isl_take isl_set *el);
2871 __isl_give isl_set_list *isl_set_list_alloc(
2872 isl_ctx *ctx, int n);
2873 __isl_give isl_set_list *isl_set_list_copy(
2874 __isl_keep isl_set_list *list);
2875 __isl_give isl_set_list *isl_set_list_add(
2876 __isl_take isl_set_list *list,
2877 __isl_take isl_set *el);
2878 __isl_give isl_set_list *isl_set_list_set_set(
2879 __isl_take isl_set_list *list, int index,
2880 __isl_take isl_set *set);
2881 __isl_give isl_set_list *isl_set_list_concat(
2882 __isl_take isl_set_list *list1,
2883 __isl_take isl_set_list *list2);
2884 void *isl_set_list_free(__isl_take isl_set_list *list);
2886 C<isl_set_list_alloc> creates an empty list with a capacity for
2887 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2890 Lists can be inspected using the following functions.
2892 #include <isl/list.h>
2893 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2894 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2895 __isl_give isl_set *isl_set_list_get_set(
2896 __isl_keep isl_set_list *list, int index);
2897 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2898 int (*fn)(__isl_take isl_set *el, void *user),
2901 Lists can be printed using
2903 #include <isl/list.h>
2904 __isl_give isl_printer *isl_printer_print_set_list(
2905 __isl_take isl_printer *p,
2906 __isl_keep isl_set_list *list);
2910 Vectors can be created, copied and freed using the following functions.
2912 #include <isl/vec.h>
2913 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2915 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2916 void isl_vec_free(__isl_take isl_vec *vec);
2918 Note that the elements of a newly created vector may have arbitrary values.
2919 The elements can be changed and inspected using the following functions.
2921 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2922 int isl_vec_size(__isl_keep isl_vec *vec);
2923 int isl_vec_get_element(__isl_keep isl_vec *vec,
2924 int pos, isl_int *v);
2925 __isl_give isl_vec *isl_vec_set_element(
2926 __isl_take isl_vec *vec, int pos, isl_int v);
2927 __isl_give isl_vec *isl_vec_set_element_si(
2928 __isl_take isl_vec *vec, int pos, int v);
2929 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2931 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2934 C<isl_vec_get_element> will return a negative value if anything went wrong.
2935 In that case, the value of C<*v> is undefined.
2939 Matrices can be created, copied and freed using the following functions.
2941 #include <isl/mat.h>
2942 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2943 unsigned n_row, unsigned n_col);
2944 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2945 void isl_mat_free(__isl_take isl_mat *mat);
2947 Note that the elements of a newly created matrix may have arbitrary values.
2948 The elements can be changed and inspected using the following functions.
2950 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2951 int isl_mat_rows(__isl_keep isl_mat *mat);
2952 int isl_mat_cols(__isl_keep isl_mat *mat);
2953 int isl_mat_get_element(__isl_keep isl_mat *mat,
2954 int row, int col, isl_int *v);
2955 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2956 int row, int col, isl_int v);
2957 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2958 int row, int col, int v);
2960 C<isl_mat_get_element> will return a negative value if anything went wrong.
2961 In that case, the value of C<*v> is undefined.
2963 The following function can be used to compute the (right) inverse
2964 of a matrix, i.e., a matrix such that the product of the original
2965 and the inverse (in that order) is a multiple of the identity matrix.
2966 The input matrix is assumed to be of full row-rank.
2968 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2970 The following function can be used to compute the (right) kernel
2971 (or null space) of a matrix, i.e., a matrix such that the product of
2972 the original and the kernel (in that order) is the zero matrix.
2974 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2976 =head2 Piecewise Quasi Affine Expressions
2978 The zero quasi affine expression on a given domain can be created using
2980 __isl_give isl_aff *isl_aff_zero_on_domain(
2981 __isl_take isl_local_space *ls);
2983 Note that the space in which the resulting object lives is a map space
2984 with the given space as domain and a one-dimensional range.
2986 An empty piecewise quasi affine expression (one with no cells)
2987 or a piecewise quasi affine expression with a single cell can
2988 be created using the following functions.
2990 #include <isl/aff.h>
2991 __isl_give isl_pw_aff *isl_pw_aff_empty(
2992 __isl_take isl_space *space);
2993 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2994 __isl_take isl_set *set, __isl_take isl_aff *aff);
2995 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2996 __isl_take isl_aff *aff);
2998 A piecewise quasi affine expression that is equal to 1 on a set
2999 and 0 outside the set can be created using the following function.
3001 #include <isl/aff.h>
3002 __isl_give isl_pw_aff *isl_set_indicator_function(
3003 __isl_take isl_set *set);
3005 Quasi affine expressions can be copied and freed using
3007 #include <isl/aff.h>
3008 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3009 void *isl_aff_free(__isl_take isl_aff *aff);
3011 __isl_give isl_pw_aff *isl_pw_aff_copy(
3012 __isl_keep isl_pw_aff *pwaff);
3013 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3015 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3016 using the following function. The constraint is required to have
3017 a non-zero coefficient for the specified dimension.
3019 #include <isl/constraint.h>
3020 __isl_give isl_aff *isl_constraint_get_bound(
3021 __isl_keep isl_constraint *constraint,
3022 enum isl_dim_type type, int pos);
3024 The entire affine expression of the constraint can also be extracted
3025 using the following function.
3027 #include <isl/constraint.h>
3028 __isl_give isl_aff *isl_constraint_get_aff(
3029 __isl_keep isl_constraint *constraint);
3031 Conversely, an equality constraint equating
3032 the affine expression to zero or an inequality constraint enforcing
3033 the affine expression to be non-negative, can be constructed using
3035 __isl_give isl_constraint *isl_equality_from_aff(
3036 __isl_take isl_aff *aff);
3037 __isl_give isl_constraint *isl_inequality_from_aff(
3038 __isl_take isl_aff *aff);
3040 The expression can be inspected using
3042 #include <isl/aff.h>
3043 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3044 int isl_aff_dim(__isl_keep isl_aff *aff,
3045 enum isl_dim_type type);
3046 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3047 __isl_keep isl_aff *aff);
3048 __isl_give isl_local_space *isl_aff_get_local_space(
3049 __isl_keep isl_aff *aff);
3050 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3051 enum isl_dim_type type, unsigned pos);
3052 const char *isl_pw_aff_get_dim_name(
3053 __isl_keep isl_pw_aff *pa,
3054 enum isl_dim_type type, unsigned pos);
3055 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3056 enum isl_dim_type type, unsigned pos);
3057 __isl_give isl_id *isl_pw_aff_get_dim_id(
3058 __isl_keep isl_pw_aff *pa,
3059 enum isl_dim_type type, unsigned pos);
3060 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3061 __isl_keep isl_pw_aff *pa,
3062 enum isl_dim_type type);
3063 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3065 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3066 enum isl_dim_type type, int pos, isl_int *v);
3067 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3069 __isl_give isl_aff *isl_aff_get_div(
3070 __isl_keep isl_aff *aff, int pos);
3072 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3073 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3074 int (*fn)(__isl_take isl_set *set,
3075 __isl_take isl_aff *aff,
3076 void *user), void *user);
3078 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3079 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3081 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3082 enum isl_dim_type type, unsigned first, unsigned n);
3083 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3084 enum isl_dim_type type, unsigned first, unsigned n);
3086 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3087 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3088 enum isl_dim_type type);
3089 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3091 It can be modified using
3093 #include <isl/aff.h>
3094 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3095 __isl_take isl_pw_aff *pwaff,
3096 enum isl_dim_type type, __isl_take isl_id *id);
3097 __isl_give isl_aff *isl_aff_set_dim_name(
3098 __isl_take isl_aff *aff, enum isl_dim_type type,
3099 unsigned pos, const char *s);
3100 __isl_give isl_aff *isl_aff_set_dim_id(
3101 __isl_take isl_aff *aff, enum isl_dim_type type,
3102 unsigned pos, __isl_take isl_id *id);
3103 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3104 __isl_take isl_pw_aff *pma,
3105 enum isl_dim_type type, unsigned pos,
3106 __isl_take isl_id *id);
3107 __isl_give isl_aff *isl_aff_set_constant(
3108 __isl_take isl_aff *aff, isl_int v);
3109 __isl_give isl_aff *isl_aff_set_constant_si(
3110 __isl_take isl_aff *aff, int v);
3111 __isl_give isl_aff *isl_aff_set_coefficient(
3112 __isl_take isl_aff *aff,
3113 enum isl_dim_type type, int pos, isl_int v);
3114 __isl_give isl_aff *isl_aff_set_coefficient_si(
3115 __isl_take isl_aff *aff,
3116 enum isl_dim_type type, int pos, int v);
3117 __isl_give isl_aff *isl_aff_set_denominator(
3118 __isl_take isl_aff *aff, isl_int v);
3120 __isl_give isl_aff *isl_aff_add_constant(
3121 __isl_take isl_aff *aff, isl_int v);
3122 __isl_give isl_aff *isl_aff_add_constant_si(
3123 __isl_take isl_aff *aff, int v);
3124 __isl_give isl_aff *isl_aff_add_constant_num(
3125 __isl_take isl_aff *aff, isl_int v);
3126 __isl_give isl_aff *isl_aff_add_constant_num_si(
3127 __isl_take isl_aff *aff, int v);
3128 __isl_give isl_aff *isl_aff_add_coefficient(
3129 __isl_take isl_aff *aff,
3130 enum isl_dim_type type, int pos, isl_int v);
3131 __isl_give isl_aff *isl_aff_add_coefficient_si(
3132 __isl_take isl_aff *aff,
3133 enum isl_dim_type type, int pos, int v);
3135 __isl_give isl_aff *isl_aff_insert_dims(
3136 __isl_take isl_aff *aff,
3137 enum isl_dim_type type, unsigned first, unsigned n);
3138 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3139 __isl_take isl_pw_aff *pwaff,
3140 enum isl_dim_type type, unsigned first, unsigned n);
3141 __isl_give isl_aff *isl_aff_add_dims(
3142 __isl_take isl_aff *aff,
3143 enum isl_dim_type type, unsigned n);
3144 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3145 __isl_take isl_pw_aff *pwaff,
3146 enum isl_dim_type type, unsigned n);
3147 __isl_give isl_aff *isl_aff_drop_dims(
3148 __isl_take isl_aff *aff,
3149 enum isl_dim_type type, unsigned first, unsigned n);
3150 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3151 __isl_take isl_pw_aff *pwaff,
3152 enum isl_dim_type type, unsigned first, unsigned n);
3154 Note that the C<set_constant> and C<set_coefficient> functions
3155 set the I<numerator> of the constant or coefficient, while
3156 C<add_constant> and C<add_coefficient> add an integer value to
3157 the possibly rational constant or coefficient.
3158 The C<add_constant_num> functions add an integer value to
3161 To check whether an affine expressions is obviously zero
3162 or obviously equal to some other affine expression, use
3164 #include <isl/aff.h>
3165 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3166 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3167 __isl_keep isl_aff *aff2);
3168 int isl_pw_aff_plain_is_equal(
3169 __isl_keep isl_pw_aff *pwaff1,
3170 __isl_keep isl_pw_aff *pwaff2);
3174 #include <isl/aff.h>
3175 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3176 __isl_take isl_aff *aff2);
3177 __isl_give isl_pw_aff *isl_pw_aff_add(
3178 __isl_take isl_pw_aff *pwaff1,
3179 __isl_take isl_pw_aff *pwaff2);
3180 __isl_give isl_pw_aff *isl_pw_aff_min(
3181 __isl_take isl_pw_aff *pwaff1,
3182 __isl_take isl_pw_aff *pwaff2);
3183 __isl_give isl_pw_aff *isl_pw_aff_max(
3184 __isl_take isl_pw_aff *pwaff1,
3185 __isl_take isl_pw_aff *pwaff2);
3186 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3187 __isl_take isl_aff *aff2);
3188 __isl_give isl_pw_aff *isl_pw_aff_sub(
3189 __isl_take isl_pw_aff *pwaff1,
3190 __isl_take isl_pw_aff *pwaff2);
3191 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3192 __isl_give isl_pw_aff *isl_pw_aff_neg(
3193 __isl_take isl_pw_aff *pwaff);
3194 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3195 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3196 __isl_take isl_pw_aff *pwaff);
3197 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3198 __isl_give isl_pw_aff *isl_pw_aff_floor(
3199 __isl_take isl_pw_aff *pwaff);
3200 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3202 __isl_give isl_pw_aff *isl_pw_aff_mod(
3203 __isl_take isl_pw_aff *pwaff, isl_int mod);
3204 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3206 __isl_give isl_pw_aff *isl_pw_aff_scale(
3207 __isl_take isl_pw_aff *pwaff, isl_int f);
3208 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3210 __isl_give isl_aff *isl_aff_scale_down_ui(
3211 __isl_take isl_aff *aff, unsigned f);
3212 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3213 __isl_take isl_pw_aff *pwaff, isl_int f);
3215 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3216 __isl_take isl_pw_aff_list *list);
3217 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3218 __isl_take isl_pw_aff_list *list);
3220 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3221 __isl_take isl_pw_aff *pwqp);
3223 __isl_give isl_aff *isl_aff_align_params(
3224 __isl_take isl_aff *aff,
3225 __isl_take isl_space *model);
3226 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3227 __isl_take isl_pw_aff *pwaff,
3228 __isl_take isl_space *model);
3230 __isl_give isl_aff *isl_aff_project_domain_on_params(
3231 __isl_take isl_aff *aff);
3233 __isl_give isl_aff *isl_aff_gist_params(
3234 __isl_take isl_aff *aff,
3235 __isl_take isl_set *context);
3236 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3237 __isl_take isl_set *context);
3238 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3239 __isl_take isl_pw_aff *pwaff,
3240 __isl_take isl_set *context);
3241 __isl_give isl_pw_aff *isl_pw_aff_gist(
3242 __isl_take isl_pw_aff *pwaff,
3243 __isl_take isl_set *context);
3245 __isl_give isl_set *isl_pw_aff_domain(
3246 __isl_take isl_pw_aff *pwaff);
3247 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3248 __isl_take isl_pw_aff *pa,
3249 __isl_take isl_set *set);
3250 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3251 __isl_take isl_pw_aff *pa,
3252 __isl_take isl_set *set);
3254 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3255 __isl_take isl_aff *aff2);
3256 __isl_give isl_pw_aff *isl_pw_aff_mul(
3257 __isl_take isl_pw_aff *pwaff1,
3258 __isl_take isl_pw_aff *pwaff2);
3260 When multiplying two affine expressions, at least one of the two needs
3263 #include <isl/aff.h>
3264 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3265 __isl_take isl_aff *aff);
3266 __isl_give isl_basic_set *isl_aff_le_basic_set(
3267 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3268 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3269 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3270 __isl_give isl_set *isl_pw_aff_eq_set(
3271 __isl_take isl_pw_aff *pwaff1,
3272 __isl_take isl_pw_aff *pwaff2);
3273 __isl_give isl_set *isl_pw_aff_ne_set(
3274 __isl_take isl_pw_aff *pwaff1,
3275 __isl_take isl_pw_aff *pwaff2);
3276 __isl_give isl_set *isl_pw_aff_le_set(
3277 __isl_take isl_pw_aff *pwaff1,
3278 __isl_take isl_pw_aff *pwaff2);
3279 __isl_give isl_set *isl_pw_aff_lt_set(
3280 __isl_take isl_pw_aff *pwaff1,
3281 __isl_take isl_pw_aff *pwaff2);
3282 __isl_give isl_set *isl_pw_aff_ge_set(
3283 __isl_take isl_pw_aff *pwaff1,
3284 __isl_take isl_pw_aff *pwaff2);
3285 __isl_give isl_set *isl_pw_aff_gt_set(
3286 __isl_take isl_pw_aff *pwaff1,
3287 __isl_take isl_pw_aff *pwaff2);
3289 __isl_give isl_set *isl_pw_aff_list_eq_set(
3290 __isl_take isl_pw_aff_list *list1,
3291 __isl_take isl_pw_aff_list *list2);
3292 __isl_give isl_set *isl_pw_aff_list_ne_set(
3293 __isl_take isl_pw_aff_list *list1,
3294 __isl_take isl_pw_aff_list *list2);
3295 __isl_give isl_set *isl_pw_aff_list_le_set(
3296 __isl_take isl_pw_aff_list *list1,
3297 __isl_take isl_pw_aff_list *list2);
3298 __isl_give isl_set *isl_pw_aff_list_lt_set(
3299 __isl_take isl_pw_aff_list *list1,
3300 __isl_take isl_pw_aff_list *list2);
3301 __isl_give isl_set *isl_pw_aff_list_ge_set(
3302 __isl_take isl_pw_aff_list *list1,
3303 __isl_take isl_pw_aff_list *list2);
3304 __isl_give isl_set *isl_pw_aff_list_gt_set(
3305 __isl_take isl_pw_aff_list *list1,
3306 __isl_take isl_pw_aff_list *list2);
3308 The function C<isl_aff_neg_basic_set> returns a basic set
3309 containing those elements in the domain space
3310 of C<aff> where C<aff> is negative.
3311 The function C<isl_aff_ge_basic_set> returns a basic set
3312 containing those elements in the shared space
3313 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3314 The function C<isl_pw_aff_ge_set> returns a set
3315 containing those elements in the shared domain
3316 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3317 The functions operating on C<isl_pw_aff_list> apply the corresponding
3318 C<isl_pw_aff> function to each pair of elements in the two lists.
3320 #include <isl/aff.h>
3321 __isl_give isl_set *isl_pw_aff_nonneg_set(
3322 __isl_take isl_pw_aff *pwaff);
3323 __isl_give isl_set *isl_pw_aff_zero_set(
3324 __isl_take isl_pw_aff *pwaff);
3325 __isl_give isl_set *isl_pw_aff_non_zero_set(
3326 __isl_take isl_pw_aff *pwaff);
3328 The function C<isl_pw_aff_nonneg_set> returns a set
3329 containing those elements in the domain
3330 of C<pwaff> where C<pwaff> is non-negative.
3332 #include <isl/aff.h>
3333 __isl_give isl_pw_aff *isl_pw_aff_cond(
3334 __isl_take isl_pw_aff *cond,
3335 __isl_take isl_pw_aff *pwaff_true,
3336 __isl_take isl_pw_aff *pwaff_false);
3338 The function C<isl_pw_aff_cond> performs a conditional operator
3339 and returns an expression that is equal to C<pwaff_true>
3340 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3341 where C<cond> is zero.
3343 #include <isl/aff.h>
3344 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3345 __isl_take isl_pw_aff *pwaff1,
3346 __isl_take isl_pw_aff *pwaff2);
3347 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3348 __isl_take isl_pw_aff *pwaff1,
3349 __isl_take isl_pw_aff *pwaff2);
3350 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3351 __isl_take isl_pw_aff *pwaff1,
3352 __isl_take isl_pw_aff *pwaff2);
3354 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3355 expression with a domain that is the union of those of C<pwaff1> and
3356 C<pwaff2> and such that on each cell, the quasi-affine expression is
3357 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3358 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3359 associated expression is the defined one.
3361 An expression can be read from input using
3363 #include <isl/aff.h>
3364 __isl_give isl_aff *isl_aff_read_from_str(
3365 isl_ctx *ctx, const char *str);
3366 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3367 isl_ctx *ctx, const char *str);
3369 An expression can be printed using
3371 #include <isl/aff.h>
3372 __isl_give isl_printer *isl_printer_print_aff(
3373 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3375 __isl_give isl_printer *isl_printer_print_pw_aff(
3376 __isl_take isl_printer *p,
3377 __isl_keep isl_pw_aff *pwaff);
3379 =head2 Piecewise Multiple Quasi Affine Expressions
3381 An C<isl_multi_aff> object represents a sequence of
3382 zero or more affine expressions, all defined on the same domain space.
3384 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3387 #include <isl/aff.h>
3388 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3389 __isl_take isl_space *space,
3390 __isl_take isl_aff_list *list);
3392 An empty piecewise multiple quasi affine expression (one with no cells),
3393 the zero piecewise multiple quasi affine expression (with value zero
3394 for each output dimension),
3395 a piecewise multiple quasi affine expression with a single cell (with
3396 either a universe or a specified domain) or
3397 a zero-dimensional piecewise multiple quasi affine expression
3399 can be created using the following functions.
3401 #include <isl/aff.h>
3402 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3403 __isl_take isl_space *space);
3404 __isl_give isl_multi_aff *isl_multi_aff_zero(
3405 __isl_take isl_space *space);
3406 __isl_give isl_multi_aff *isl_multi_aff_identity(
3407 __isl_take isl_space *space);
3408 __isl_give isl_pw_multi_aff *
3409 isl_pw_multi_aff_from_multi_aff(
3410 __isl_take isl_multi_aff *ma);
3411 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3412 __isl_take isl_set *set,
3413 __isl_take isl_multi_aff *maff);
3414 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3415 __isl_take isl_set *set);
3417 __isl_give isl_union_pw_multi_aff *
3418 isl_union_pw_multi_aff_empty(
3419 __isl_take isl_space *space);
3420 __isl_give isl_union_pw_multi_aff *
3421 isl_union_pw_multi_aff_add_pw_multi_aff(
3422 __isl_take isl_union_pw_multi_aff *upma,
3423 __isl_take isl_pw_multi_aff *pma);
3424 __isl_give isl_union_pw_multi_aff *
3425 isl_union_pw_multi_aff_from_domain(
3426 __isl_take isl_union_set *uset);
3428 A piecewise multiple quasi affine expression can also be initialized
3429 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3430 and the C<isl_map> is single-valued.
3432 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3433 __isl_take isl_set *set);
3434 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3435 __isl_take isl_map *map);
3437 Multiple quasi affine expressions can be copied and freed using
3439 #include <isl/aff.h>
3440 __isl_give isl_multi_aff *isl_multi_aff_copy(
3441 __isl_keep isl_multi_aff *maff);
3442 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3444 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3445 __isl_keep isl_pw_multi_aff *pma);
3446 void *isl_pw_multi_aff_free(
3447 __isl_take isl_pw_multi_aff *pma);
3449 __isl_give isl_union_pw_multi_aff *
3450 isl_union_pw_multi_aff_copy(
3451 __isl_keep isl_union_pw_multi_aff *upma);
3452 void *isl_union_pw_multi_aff_free(
3453 __isl_take isl_union_pw_multi_aff *upma);
3455 The expression can be inspected using
3457 #include <isl/aff.h>
3458 isl_ctx *isl_multi_aff_get_ctx(
3459 __isl_keep isl_multi_aff *maff);
3460 isl_ctx *isl_pw_multi_aff_get_ctx(
3461 __isl_keep isl_pw_multi_aff *pma);
3462 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3463 __isl_keep isl_union_pw_multi_aff *upma);
3464 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3465 enum isl_dim_type type);
3466 unsigned isl_pw_multi_aff_dim(
3467 __isl_keep isl_pw_multi_aff *pma,
3468 enum isl_dim_type type);
3469 __isl_give isl_aff *isl_multi_aff_get_aff(
3470 __isl_keep isl_multi_aff *multi, int pos);
3471 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3472 __isl_keep isl_pw_multi_aff *pma, int pos);
3473 const char *isl_pw_multi_aff_get_dim_name(
3474 __isl_keep isl_pw_multi_aff *pma,
3475 enum isl_dim_type type, unsigned pos);
3476 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3477 __isl_keep isl_pw_multi_aff *pma,
3478 enum isl_dim_type type, unsigned pos);
3479 const char *isl_multi_aff_get_tuple_name(
3480 __isl_keep isl_multi_aff *multi,
3481 enum isl_dim_type type);
3482 int isl_pw_multi_aff_has_tuple_name(
3483 __isl_keep isl_pw_multi_aff *pma,
3484 enum isl_dim_type type);
3485 const char *isl_pw_multi_aff_get_tuple_name(
3486 __isl_keep isl_pw_multi_aff *pma,
3487 enum isl_dim_type type);
3488 int isl_pw_multi_aff_has_tuple_id(
3489 __isl_keep isl_pw_multi_aff *pma,
3490 enum isl_dim_type type);
3491 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3492 __isl_keep isl_pw_multi_aff *pma,
3493 enum isl_dim_type type);
3495 int isl_pw_multi_aff_foreach_piece(
3496 __isl_keep isl_pw_multi_aff *pma,
3497 int (*fn)(__isl_take isl_set *set,
3498 __isl_take isl_multi_aff *maff,
3499 void *user), void *user);
3501 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3502 __isl_keep isl_union_pw_multi_aff *upma,
3503 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3504 void *user), void *user);
3506 It can be modified using
3508 #include <isl/aff.h>
3509 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3510 __isl_take isl_multi_aff *multi, int pos,
3511 __isl_take isl_aff *aff);
3512 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3513 __isl_take isl_multi_aff *maff,
3514 enum isl_dim_type type, unsigned pos, const char *s);
3515 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3516 __isl_take isl_multi_aff *maff,
3517 enum isl_dim_type type, __isl_take isl_id *id);
3518 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3519 __isl_take isl_pw_multi_aff *pma,
3520 enum isl_dim_type type, __isl_take isl_id *id);
3522 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3523 __isl_take isl_multi_aff *maff,
3524 enum isl_dim_type type, unsigned first, unsigned n);
3526 To check whether two multiple affine expressions are
3527 obviously equal to each other, use
3529 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3530 __isl_keep isl_multi_aff *maff2);
3531 int isl_pw_multi_aff_plain_is_equal(
3532 __isl_keep isl_pw_multi_aff *pma1,
3533 __isl_keep isl_pw_multi_aff *pma2);
3537 #include <isl/aff.h>
3538 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3539 __isl_take isl_pw_multi_aff *pma1,
3540 __isl_take isl_pw_multi_aff *pma2);
3541 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3542 __isl_take isl_pw_multi_aff *pma1,
3543 __isl_take isl_pw_multi_aff *pma2);
3544 __isl_give isl_multi_aff *isl_multi_aff_add(
3545 __isl_take isl_multi_aff *maff1,
3546 __isl_take isl_multi_aff *maff2);
3547 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3548 __isl_take isl_pw_multi_aff *pma1,
3549 __isl_take isl_pw_multi_aff *pma2);
3550 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3551 __isl_take isl_union_pw_multi_aff *upma1,
3552 __isl_take isl_union_pw_multi_aff *upma2);
3553 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3554 __isl_take isl_pw_multi_aff *pma1,
3555 __isl_take isl_pw_multi_aff *pma2);
3556 __isl_give isl_multi_aff *isl_multi_aff_scale(
3557 __isl_take isl_multi_aff *maff,
3559 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3560 __isl_take isl_pw_multi_aff *pma,
3561 __isl_take isl_set *set);
3562 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3563 __isl_take isl_pw_multi_aff *pma,
3564 __isl_take isl_set *set);
3565 __isl_give isl_multi_aff *isl_multi_aff_lift(
3566 __isl_take isl_multi_aff *maff,
3567 __isl_give isl_local_space **ls);
3568 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3569 __isl_take isl_pw_multi_aff *pma);
3570 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3571 __isl_take isl_multi_aff *maff,
3572 __isl_take isl_set *context);
3573 __isl_give isl_multi_aff *isl_multi_aff_gist(
3574 __isl_take isl_multi_aff *maff,
3575 __isl_take isl_set *context);
3576 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3577 __isl_take isl_pw_multi_aff *pma,
3578 __isl_take isl_set *set);
3579 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3580 __isl_take isl_pw_multi_aff *pma,
3581 __isl_take isl_set *set);
3582 __isl_give isl_set *isl_pw_multi_aff_domain(
3583 __isl_take isl_pw_multi_aff *pma);
3584 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3585 __isl_take isl_union_pw_multi_aff *upma);
3586 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3587 __isl_take isl_multi_aff *ma1,
3588 __isl_take isl_multi_aff *ma2);
3589 __isl_give isl_multi_aff *isl_multi_aff_product(
3590 __isl_take isl_multi_aff *ma1,
3591 __isl_take isl_multi_aff *ma2);
3592 __isl_give isl_pw_multi_aff *
3593 isl_pw_multi_aff_flat_range_product(
3594 __isl_take isl_pw_multi_aff *pma1,
3595 __isl_take isl_pw_multi_aff *pma2);
3596 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3597 __isl_take isl_pw_multi_aff *pma1,
3598 __isl_take isl_pw_multi_aff *pma2);
3599 __isl_give isl_union_pw_multi_aff *
3600 isl_union_pw_multi_aff_flat_range_product(
3601 __isl_take isl_union_pw_multi_aff *upma1,
3602 __isl_take isl_union_pw_multi_aff *upma2);
3604 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3605 then it is assigned the local space that lies at the basis of
3606 the lifting applied.
3608 __isl_give isl_set *isl_multi_aff_lex_le_set(
3609 __isl_take isl_multi_aff *ma1,
3610 __isl_take isl_multi_aff *ma2);
3611 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3612 __isl_take isl_multi_aff *ma1,
3613 __isl_take isl_multi_aff *ma2);
3615 The function C<isl_multi_aff_lex_le_set> returns a set
3616 containing those elements in the shared domain space
3617 where C<ma1> is lexicographically smaller than or
3620 An expression can be read from input using
3622 #include <isl/aff.h>
3623 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3624 isl_ctx *ctx, const char *str);
3625 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3626 isl_ctx *ctx, const char *str);
3628 An expression can be printed using
3630 #include <isl/aff.h>
3631 __isl_give isl_printer *isl_printer_print_multi_aff(
3632 __isl_take isl_printer *p,
3633 __isl_keep isl_multi_aff *maff);
3634 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3635 __isl_take isl_printer *p,
3636 __isl_keep isl_pw_multi_aff *pma);
3637 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3638 __isl_take isl_printer *p,
3639 __isl_keep isl_union_pw_multi_aff *upma);
3643 Points are elements of a set. They can be used to construct
3644 simple sets (boxes) or they can be used to represent the
3645 individual elements of a set.
3646 The zero point (the origin) can be created using
3648 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3650 The coordinates of a point can be inspected, set and changed
3653 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3654 enum isl_dim_type type, int pos, isl_int *v);
3655 __isl_give isl_point *isl_point_set_coordinate(
3656 __isl_take isl_point *pnt,
3657 enum isl_dim_type type, int pos, isl_int v);
3659 __isl_give isl_point *isl_point_add_ui(
3660 __isl_take isl_point *pnt,
3661 enum isl_dim_type type, int pos, unsigned val);
3662 __isl_give isl_point *isl_point_sub_ui(
3663 __isl_take isl_point *pnt,
3664 enum isl_dim_type type, int pos, unsigned val);
3666 Other properties can be obtained using
3668 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3670 Points can be copied or freed using
3672 __isl_give isl_point *isl_point_copy(
3673 __isl_keep isl_point *pnt);
3674 void isl_point_free(__isl_take isl_point *pnt);
3676 A singleton set can be created from a point using
3678 __isl_give isl_basic_set *isl_basic_set_from_point(
3679 __isl_take isl_point *pnt);
3680 __isl_give isl_set *isl_set_from_point(
3681 __isl_take isl_point *pnt);
3683 and a box can be created from two opposite extremal points using
3685 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3686 __isl_take isl_point *pnt1,
3687 __isl_take isl_point *pnt2);
3688 __isl_give isl_set *isl_set_box_from_points(
3689 __isl_take isl_point *pnt1,
3690 __isl_take isl_point *pnt2);
3692 All elements of a B<bounded> (union) set can be enumerated using
3693 the following functions.
3695 int isl_set_foreach_point(__isl_keep isl_set *set,
3696 int (*fn)(__isl_take isl_point *pnt, void *user),
3698 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3699 int (*fn)(__isl_take isl_point *pnt, void *user),
3702 The function C<fn> is called for each integer point in
3703 C<set> with as second argument the last argument of
3704 the C<isl_set_foreach_point> call. The function C<fn>
3705 should return C<0> on success and C<-1> on failure.
3706 In the latter case, C<isl_set_foreach_point> will stop
3707 enumerating and return C<-1> as well.
3708 If the enumeration is performed successfully and to completion,
3709 then C<isl_set_foreach_point> returns C<0>.
3711 To obtain a single point of a (basic) set, use
3713 __isl_give isl_point *isl_basic_set_sample_point(
3714 __isl_take isl_basic_set *bset);
3715 __isl_give isl_point *isl_set_sample_point(
3716 __isl_take isl_set *set);
3718 If C<set> does not contain any (integer) points, then the
3719 resulting point will be ``void'', a property that can be
3722 int isl_point_is_void(__isl_keep isl_point *pnt);
3724 =head2 Piecewise Quasipolynomials
3726 A piecewise quasipolynomial is a particular kind of function that maps
3727 a parametric point to a rational value.
3728 More specifically, a quasipolynomial is a polynomial expression in greatest
3729 integer parts of affine expressions of parameters and variables.
3730 A piecewise quasipolynomial is a subdivision of a given parametric
3731 domain into disjoint cells with a quasipolynomial associated to
3732 each cell. The value of the piecewise quasipolynomial at a given
3733 point is the value of the quasipolynomial associated to the cell
3734 that contains the point. Outside of the union of cells,
3735 the value is assumed to be zero.
3736 For example, the piecewise quasipolynomial
3738 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3740 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3741 A given piecewise quasipolynomial has a fixed domain dimension.
3742 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3743 defined over different domains.
3744 Piecewise quasipolynomials are mainly used by the C<barvinok>
3745 library for representing the number of elements in a parametric set or map.
3746 For example, the piecewise quasipolynomial above represents
3747 the number of points in the map
3749 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3751 =head3 Input and Output
3753 Piecewise quasipolynomials can be read from input using
3755 __isl_give isl_union_pw_qpolynomial *
3756 isl_union_pw_qpolynomial_read_from_str(
3757 isl_ctx *ctx, const char *str);
3759 Quasipolynomials and piecewise quasipolynomials can be printed
3760 using the following functions.
3762 __isl_give isl_printer *isl_printer_print_qpolynomial(
3763 __isl_take isl_printer *p,
3764 __isl_keep isl_qpolynomial *qp);
3766 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3767 __isl_take isl_printer *p,
3768 __isl_keep isl_pw_qpolynomial *pwqp);
3770 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3771 __isl_take isl_printer *p,
3772 __isl_keep isl_union_pw_qpolynomial *upwqp);
3774 The output format of the printer
3775 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3776 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3778 In case of printing in C<ISL_FORMAT_C>, the user may want
3779 to set the names of all dimensions
3781 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3782 __isl_take isl_qpolynomial *qp,
3783 enum isl_dim_type type, unsigned pos,
3785 __isl_give isl_pw_qpolynomial *
3786 isl_pw_qpolynomial_set_dim_name(
3787 __isl_take isl_pw_qpolynomial *pwqp,
3788 enum isl_dim_type type, unsigned pos,
3791 =head3 Creating New (Piecewise) Quasipolynomials
3793 Some simple quasipolynomials can be created using the following functions.
3794 More complicated quasipolynomials can be created by applying
3795 operations such as addition and multiplication
3796 on the resulting quasipolynomials
3798 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3799 __isl_take isl_space *domain);
3800 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3801 __isl_take isl_space *domain);
3802 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3803 __isl_take isl_space *domain);
3804 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3805 __isl_take isl_space *domain);
3806 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3807 __isl_take isl_space *domain);
3808 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3809 __isl_take isl_space *domain,
3810 const isl_int n, const isl_int d);
3811 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3812 __isl_take isl_space *domain,
3813 enum isl_dim_type type, unsigned pos);
3814 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3815 __isl_take isl_aff *aff);
3817 Note that the space in which a quasipolynomial lives is a map space
3818 with a one-dimensional range. The C<domain> argument in some of
3819 the functions above corresponds to the domain of this map space.
3821 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3822 with a single cell can be created using the following functions.
3823 Multiple of these single cell piecewise quasipolynomials can
3824 be combined to create more complicated piecewise quasipolynomials.
3826 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3827 __isl_take isl_space *space);
3828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3829 __isl_take isl_set *set,
3830 __isl_take isl_qpolynomial *qp);
3831 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3832 __isl_take isl_qpolynomial *qp);
3833 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3834 __isl_take isl_pw_aff *pwaff);
3836 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3837 __isl_take isl_space *space);
3838 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3839 __isl_take isl_pw_qpolynomial *pwqp);
3840 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3841 __isl_take isl_union_pw_qpolynomial *upwqp,
3842 __isl_take isl_pw_qpolynomial *pwqp);
3844 Quasipolynomials can be copied and freed again using the following
3847 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3848 __isl_keep isl_qpolynomial *qp);
3849 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3851 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3852 __isl_keep isl_pw_qpolynomial *pwqp);
3853 void *isl_pw_qpolynomial_free(
3854 __isl_take isl_pw_qpolynomial *pwqp);
3856 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3857 __isl_keep isl_union_pw_qpolynomial *upwqp);
3858 void *isl_union_pw_qpolynomial_free(
3859 __isl_take isl_union_pw_qpolynomial *upwqp);
3861 =head3 Inspecting (Piecewise) Quasipolynomials
3863 To iterate over all piecewise quasipolynomials in a union
3864 piecewise quasipolynomial, use the following function
3866 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3867 __isl_keep isl_union_pw_qpolynomial *upwqp,
3868 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3871 To extract the piecewise quasipolynomial in a given space from a union, use
3873 __isl_give isl_pw_qpolynomial *
3874 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3875 __isl_keep isl_union_pw_qpolynomial *upwqp,
3876 __isl_take isl_space *space);
3878 To iterate over the cells in a piecewise quasipolynomial,
3879 use either of the following two functions
3881 int isl_pw_qpolynomial_foreach_piece(
3882 __isl_keep isl_pw_qpolynomial *pwqp,
3883 int (*fn)(__isl_take isl_set *set,
3884 __isl_take isl_qpolynomial *qp,
3885 void *user), void *user);
3886 int isl_pw_qpolynomial_foreach_lifted_piece(
3887 __isl_keep isl_pw_qpolynomial *pwqp,
3888 int (*fn)(__isl_take isl_set *set,
3889 __isl_take isl_qpolynomial *qp,
3890 void *user), void *user);
3892 As usual, the function C<fn> should return C<0> on success
3893 and C<-1> on failure. The difference between
3894 C<isl_pw_qpolynomial_foreach_piece> and
3895 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3896 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3897 compute unique representations for all existentially quantified
3898 variables and then turn these existentially quantified variables
3899 into extra set variables, adapting the associated quasipolynomial
3900 accordingly. This means that the C<set> passed to C<fn>
3901 will not have any existentially quantified variables, but that
3902 the dimensions of the sets may be different for different
3903 invocations of C<fn>.
3905 To iterate over all terms in a quasipolynomial,
3908 int isl_qpolynomial_foreach_term(
3909 __isl_keep isl_qpolynomial *qp,
3910 int (*fn)(__isl_take isl_term *term,
3911 void *user), void *user);
3913 The terms themselves can be inspected and freed using
3916 unsigned isl_term_dim(__isl_keep isl_term *term,
3917 enum isl_dim_type type);
3918 void isl_term_get_num(__isl_keep isl_term *term,
3920 void isl_term_get_den(__isl_keep isl_term *term,
3922 int isl_term_get_exp(__isl_keep isl_term *term,
3923 enum isl_dim_type type, unsigned pos);
3924 __isl_give isl_aff *isl_term_get_div(
3925 __isl_keep isl_term *term, unsigned pos);
3926 void isl_term_free(__isl_take isl_term *term);
3928 Each term is a product of parameters, set variables and
3929 integer divisions. The function C<isl_term_get_exp>
3930 returns the exponent of a given dimensions in the given term.
3931 The C<isl_int>s in the arguments of C<isl_term_get_num>
3932 and C<isl_term_get_den> need to have been initialized
3933 using C<isl_int_init> before calling these functions.
3935 =head3 Properties of (Piecewise) Quasipolynomials
3937 To check whether a quasipolynomial is actually a constant,
3938 use the following function.
3940 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3941 isl_int *n, isl_int *d);
3943 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3944 then the numerator and denominator of the constant
3945 are returned in C<*n> and C<*d>, respectively.
3947 To check whether two union piecewise quasipolynomials are
3948 obviously equal, use
3950 int isl_union_pw_qpolynomial_plain_is_equal(
3951 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3952 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3954 =head3 Operations on (Piecewise) Quasipolynomials
3956 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3957 __isl_take isl_qpolynomial *qp, isl_int v);
3958 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3959 __isl_take isl_qpolynomial *qp);
3960 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3961 __isl_take isl_qpolynomial *qp1,
3962 __isl_take isl_qpolynomial *qp2);
3963 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3964 __isl_take isl_qpolynomial *qp1,
3965 __isl_take isl_qpolynomial *qp2);
3966 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3967 __isl_take isl_qpolynomial *qp1,
3968 __isl_take isl_qpolynomial *qp2);
3969 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3970 __isl_take isl_qpolynomial *qp, unsigned exponent);
3972 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3973 __isl_take isl_pw_qpolynomial *pwqp1,
3974 __isl_take isl_pw_qpolynomial *pwqp2);
3975 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3976 __isl_take isl_pw_qpolynomial *pwqp1,
3977 __isl_take isl_pw_qpolynomial *pwqp2);
3978 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3979 __isl_take isl_pw_qpolynomial *pwqp1,
3980 __isl_take isl_pw_qpolynomial *pwqp2);
3981 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3982 __isl_take isl_pw_qpolynomial *pwqp);
3983 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3984 __isl_take isl_pw_qpolynomial *pwqp1,
3985 __isl_take isl_pw_qpolynomial *pwqp2);
3986 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3987 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3989 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3990 __isl_take isl_union_pw_qpolynomial *upwqp1,
3991 __isl_take isl_union_pw_qpolynomial *upwqp2);
3992 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3993 __isl_take isl_union_pw_qpolynomial *upwqp1,
3994 __isl_take isl_union_pw_qpolynomial *upwqp2);
3995 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3996 __isl_take isl_union_pw_qpolynomial *upwqp1,
3997 __isl_take isl_union_pw_qpolynomial *upwqp2);
3999 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4000 __isl_take isl_pw_qpolynomial *pwqp,
4001 __isl_take isl_point *pnt);
4003 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4004 __isl_take isl_union_pw_qpolynomial *upwqp,
4005 __isl_take isl_point *pnt);
4007 __isl_give isl_set *isl_pw_qpolynomial_domain(
4008 __isl_take isl_pw_qpolynomial *pwqp);
4009 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4010 __isl_take isl_pw_qpolynomial *pwpq,
4011 __isl_take isl_set *set);
4012 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4013 __isl_take isl_pw_qpolynomial *pwpq,
4014 __isl_take isl_set *set);
4016 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4017 __isl_take isl_union_pw_qpolynomial *upwqp);
4018 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4019 __isl_take isl_union_pw_qpolynomial *upwpq,
4020 __isl_take isl_union_set *uset);
4021 __isl_give isl_union_pw_qpolynomial *
4022 isl_union_pw_qpolynomial_intersect_params(
4023 __isl_take isl_union_pw_qpolynomial *upwpq,
4024 __isl_take isl_set *set);
4026 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4027 __isl_take isl_qpolynomial *qp,
4028 __isl_take isl_space *model);
4030 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4031 __isl_take isl_qpolynomial *qp);
4032 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4033 __isl_take isl_pw_qpolynomial *pwqp);
4035 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4036 __isl_take isl_union_pw_qpolynomial *upwqp);
4038 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4039 __isl_take isl_qpolynomial *qp,
4040 __isl_take isl_set *context);
4041 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4042 __isl_take isl_qpolynomial *qp,
4043 __isl_take isl_set *context);
4045 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4046 __isl_take isl_pw_qpolynomial *pwqp,
4047 __isl_take isl_set *context);
4048 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4049 __isl_take isl_pw_qpolynomial *pwqp,
4050 __isl_take isl_set *context);
4052 __isl_give isl_union_pw_qpolynomial *
4053 isl_union_pw_qpolynomial_gist_params(
4054 __isl_take isl_union_pw_qpolynomial *upwqp,
4055 __isl_take isl_set *context);
4056 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4057 __isl_take isl_union_pw_qpolynomial *upwqp,
4058 __isl_take isl_union_set *context);
4060 The gist operation applies the gist operation to each of
4061 the cells in the domain of the input piecewise quasipolynomial.
4062 The context is also exploited
4063 to simplify the quasipolynomials associated to each cell.
4065 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4066 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4067 __isl_give isl_union_pw_qpolynomial *
4068 isl_union_pw_qpolynomial_to_polynomial(
4069 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4071 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4072 the polynomial will be an overapproximation. If C<sign> is negative,
4073 it will be an underapproximation. If C<sign> is zero, the approximation
4074 will lie somewhere in between.
4076 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4078 A piecewise quasipolynomial reduction is a piecewise
4079 reduction (or fold) of quasipolynomials.
4080 In particular, the reduction can be maximum or a minimum.
4081 The objects are mainly used to represent the result of
4082 an upper or lower bound on a quasipolynomial over its domain,
4083 i.e., as the result of the following function.
4085 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4086 __isl_take isl_pw_qpolynomial *pwqp,
4087 enum isl_fold type, int *tight);
4089 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4090 __isl_take isl_union_pw_qpolynomial *upwqp,
4091 enum isl_fold type, int *tight);
4093 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4094 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4095 is the returned bound is known be tight, i.e., for each value
4096 of the parameters there is at least
4097 one element in the domain that reaches the bound.
4098 If the domain of C<pwqp> is not wrapping, then the bound is computed
4099 over all elements in that domain and the result has a purely parametric
4100 domain. If the domain of C<pwqp> is wrapping, then the bound is
4101 computed over the range of the wrapped relation. The domain of the
4102 wrapped relation becomes the domain of the result.
4104 A (piecewise) quasipolynomial reduction can be copied or freed using the
4105 following functions.
4107 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4108 __isl_keep isl_qpolynomial_fold *fold);
4109 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4110 __isl_keep isl_pw_qpolynomial_fold *pwf);
4111 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4112 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4113 void isl_qpolynomial_fold_free(
4114 __isl_take isl_qpolynomial_fold *fold);
4115 void *isl_pw_qpolynomial_fold_free(
4116 __isl_take isl_pw_qpolynomial_fold *pwf);
4117 void *isl_union_pw_qpolynomial_fold_free(
4118 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4120 =head3 Printing Piecewise Quasipolynomial Reductions
4122 Piecewise quasipolynomial reductions can be printed
4123 using the following function.
4125 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4126 __isl_take isl_printer *p,
4127 __isl_keep isl_pw_qpolynomial_fold *pwf);
4128 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4129 __isl_take isl_printer *p,
4130 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4132 For C<isl_printer_print_pw_qpolynomial_fold>,
4133 output format of the printer
4134 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4135 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4136 output format of the printer
4137 needs to be set to C<ISL_FORMAT_ISL>.
4138 In case of printing in C<ISL_FORMAT_C>, the user may want
4139 to set the names of all dimensions
4141 __isl_give isl_pw_qpolynomial_fold *
4142 isl_pw_qpolynomial_fold_set_dim_name(
4143 __isl_take isl_pw_qpolynomial_fold *pwf,
4144 enum isl_dim_type type, unsigned pos,
4147 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4149 To iterate over all piecewise quasipolynomial reductions in a union
4150 piecewise quasipolynomial reduction, use the following function
4152 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4153 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4154 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4155 void *user), void *user);
4157 To iterate over the cells in a piecewise quasipolynomial reduction,
4158 use either of the following two functions
4160 int isl_pw_qpolynomial_fold_foreach_piece(
4161 __isl_keep isl_pw_qpolynomial_fold *pwf,
4162 int (*fn)(__isl_take isl_set *set,
4163 __isl_take isl_qpolynomial_fold *fold,
4164 void *user), void *user);
4165 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4166 __isl_keep isl_pw_qpolynomial_fold *pwf,
4167 int (*fn)(__isl_take isl_set *set,
4168 __isl_take isl_qpolynomial_fold *fold,
4169 void *user), void *user);
4171 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4172 of the difference between these two functions.
4174 To iterate over all quasipolynomials in a reduction, use
4176 int isl_qpolynomial_fold_foreach_qpolynomial(
4177 __isl_keep isl_qpolynomial_fold *fold,
4178 int (*fn)(__isl_take isl_qpolynomial *qp,
4179 void *user), void *user);
4181 =head3 Properties of Piecewise Quasipolynomial Reductions
4183 To check whether two union piecewise quasipolynomial reductions are
4184 obviously equal, use
4186 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4187 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4188 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4190 =head3 Operations on Piecewise Quasipolynomial Reductions
4192 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4193 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4195 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4196 __isl_take isl_pw_qpolynomial_fold *pwf1,
4197 __isl_take isl_pw_qpolynomial_fold *pwf2);
4199 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4200 __isl_take isl_pw_qpolynomial_fold *pwf1,
4201 __isl_take isl_pw_qpolynomial_fold *pwf2);
4203 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4204 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4205 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4207 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4208 __isl_take isl_pw_qpolynomial_fold *pwf,
4209 __isl_take isl_point *pnt);
4211 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4212 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4213 __isl_take isl_point *pnt);
4215 __isl_give isl_pw_qpolynomial_fold *
4216 isl_pw_qpolynomial_fold_intersect_params(
4217 __isl_take isl_pw_qpolynomial_fold *pwf,
4218 __isl_take isl_set *set);
4220 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4221 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4222 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4223 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4224 __isl_take isl_union_set *uset);
4225 __isl_give isl_union_pw_qpolynomial_fold *
4226 isl_union_pw_qpolynomial_fold_intersect_params(
4227 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4228 __isl_take isl_set *set);
4230 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4231 __isl_take isl_pw_qpolynomial_fold *pwf);
4233 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4234 __isl_take isl_pw_qpolynomial_fold *pwf);
4236 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4237 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4239 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4240 __isl_take isl_qpolynomial_fold *fold,
4241 __isl_take isl_set *context);
4242 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4243 __isl_take isl_qpolynomial_fold *fold,
4244 __isl_take isl_set *context);
4246 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4247 __isl_take isl_pw_qpolynomial_fold *pwf,
4248 __isl_take isl_set *context);
4249 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4250 __isl_take isl_pw_qpolynomial_fold *pwf,
4251 __isl_take isl_set *context);
4253 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4254 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4255 __isl_take isl_union_set *context);
4256 __isl_give isl_union_pw_qpolynomial_fold *
4257 isl_union_pw_qpolynomial_fold_gist_params(
4258 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4259 __isl_take isl_set *context);
4261 The gist operation applies the gist operation to each of
4262 the cells in the domain of the input piecewise quasipolynomial reduction.
4263 In future, the operation will also exploit the context
4264 to simplify the quasipolynomial reductions associated to each cell.
4266 __isl_give isl_pw_qpolynomial_fold *
4267 isl_set_apply_pw_qpolynomial_fold(
4268 __isl_take isl_set *set,
4269 __isl_take isl_pw_qpolynomial_fold *pwf,
4271 __isl_give isl_pw_qpolynomial_fold *
4272 isl_map_apply_pw_qpolynomial_fold(
4273 __isl_take isl_map *map,
4274 __isl_take isl_pw_qpolynomial_fold *pwf,
4276 __isl_give isl_union_pw_qpolynomial_fold *
4277 isl_union_set_apply_union_pw_qpolynomial_fold(
4278 __isl_take isl_union_set *uset,
4279 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4281 __isl_give isl_union_pw_qpolynomial_fold *
4282 isl_union_map_apply_union_pw_qpolynomial_fold(
4283 __isl_take isl_union_map *umap,
4284 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4287 The functions taking a map
4288 compose the given map with the given piecewise quasipolynomial reduction.
4289 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4290 over all elements in the intersection of the range of the map
4291 and the domain of the piecewise quasipolynomial reduction
4292 as a function of an element in the domain of the map.
4293 The functions taking a set compute a bound over all elements in the
4294 intersection of the set and the domain of the
4295 piecewise quasipolynomial reduction.
4297 =head2 Dependence Analysis
4299 C<isl> contains specialized functionality for performing
4300 array dataflow analysis. That is, given a I<sink> access relation
4301 and a collection of possible I<source> access relations,
4302 C<isl> can compute relations that describe
4303 for each iteration of the sink access, which iteration
4304 of which of the source access relations was the last
4305 to access the same data element before the given iteration
4307 The resulting dependence relations map source iterations
4308 to the corresponding sink iterations.
4309 To compute standard flow dependences, the sink should be
4310 a read, while the sources should be writes.
4311 If any of the source accesses are marked as being I<may>
4312 accesses, then there will be a dependence from the last
4313 I<must> access B<and> from any I<may> access that follows
4314 this last I<must> access.
4315 In particular, if I<all> sources are I<may> accesses,
4316 then memory based dependence analysis is performed.
4317 If, on the other hand, all sources are I<must> accesses,
4318 then value based dependence analysis is performed.
4320 #include <isl/flow.h>
4322 typedef int (*isl_access_level_before)(void *first, void *second);
4324 __isl_give isl_access_info *isl_access_info_alloc(
4325 __isl_take isl_map *sink,
4326 void *sink_user, isl_access_level_before fn,
4328 __isl_give isl_access_info *isl_access_info_add_source(
4329 __isl_take isl_access_info *acc,
4330 __isl_take isl_map *source, int must,
4332 void *isl_access_info_free(__isl_take isl_access_info *acc);
4334 __isl_give isl_flow *isl_access_info_compute_flow(
4335 __isl_take isl_access_info *acc);
4337 int isl_flow_foreach(__isl_keep isl_flow *deps,
4338 int (*fn)(__isl_take isl_map *dep, int must,
4339 void *dep_user, void *user),
4341 __isl_give isl_map *isl_flow_get_no_source(
4342 __isl_keep isl_flow *deps, int must);
4343 void isl_flow_free(__isl_take isl_flow *deps);
4345 The function C<isl_access_info_compute_flow> performs the actual
4346 dependence analysis. The other functions are used to construct
4347 the input for this function or to read off the output.
4349 The input is collected in an C<isl_access_info>, which can
4350 be created through a call to C<isl_access_info_alloc>.
4351 The arguments to this functions are the sink access relation
4352 C<sink>, a token C<sink_user> used to identify the sink
4353 access to the user, a callback function for specifying the
4354 relative order of source and sink accesses, and the number
4355 of source access relations that will be added.
4356 The callback function has type C<int (*)(void *first, void *second)>.
4357 The function is called with two user supplied tokens identifying
4358 either a source or the sink and it should return the shared nesting
4359 level and the relative order of the two accesses.
4360 In particular, let I<n> be the number of loops shared by
4361 the two accesses. If C<first> precedes C<second> textually,
4362 then the function should return I<2 * n + 1>; otherwise,
4363 it should return I<2 * n>.
4364 The sources can be added to the C<isl_access_info> by performing
4365 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4366 C<must> indicates whether the source is a I<must> access
4367 or a I<may> access. Note that a multi-valued access relation
4368 should only be marked I<must> if every iteration in the domain
4369 of the relation accesses I<all> elements in its image.
4370 The C<source_user> token is again used to identify
4371 the source access. The range of the source access relation
4372 C<source> should have the same dimension as the range
4373 of the sink access relation.
4374 The C<isl_access_info_free> function should usually not be
4375 called explicitly, because it is called implicitly by
4376 C<isl_access_info_compute_flow>.
4378 The result of the dependence analysis is collected in an
4379 C<isl_flow>. There may be elements of
4380 the sink access for which no preceding source access could be
4381 found or for which all preceding sources are I<may> accesses.
4382 The relations containing these elements can be obtained through
4383 calls to C<isl_flow_get_no_source>, the first with C<must> set
4384 and the second with C<must> unset.
4385 In the case of standard flow dependence analysis,
4386 with the sink a read and the sources I<must> writes,
4387 the first relation corresponds to the reads from uninitialized
4388 array elements and the second relation is empty.
4389 The actual flow dependences can be extracted using
4390 C<isl_flow_foreach>. This function will call the user-specified
4391 callback function C<fn> for each B<non-empty> dependence between
4392 a source and the sink. The callback function is called
4393 with four arguments, the actual flow dependence relation
4394 mapping source iterations to sink iterations, a boolean that
4395 indicates whether it is a I<must> or I<may> dependence, a token
4396 identifying the source and an additional C<void *> with value
4397 equal to the third argument of the C<isl_flow_foreach> call.
4398 A dependence is marked I<must> if it originates from a I<must>
4399 source and if it is not followed by any I<may> sources.
4401 After finishing with an C<isl_flow>, the user should call
4402 C<isl_flow_free> to free all associated memory.
4404 A higher-level interface to dependence analysis is provided
4405 by the following function.
4407 #include <isl/flow.h>
4409 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4410 __isl_take isl_union_map *must_source,
4411 __isl_take isl_union_map *may_source,
4412 __isl_take isl_union_map *schedule,
4413 __isl_give isl_union_map **must_dep,
4414 __isl_give isl_union_map **may_dep,
4415 __isl_give isl_union_map **must_no_source,
4416 __isl_give isl_union_map **may_no_source);
4418 The arrays are identified by the tuple names of the ranges
4419 of the accesses. The iteration domains by the tuple names
4420 of the domains of the accesses and of the schedule.
4421 The relative order of the iteration domains is given by the
4422 schedule. The relations returned through C<must_no_source>
4423 and C<may_no_source> are subsets of C<sink>.
4424 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4425 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4426 any of the other arguments is treated as an error.
4428 =head3 Interaction with Dependence Analysis
4430 During the dependence analysis, we frequently need to perform
4431 the following operation. Given a relation between sink iterations
4432 and potential source iterations from a particular source domain,
4433 what is the last potential source iteration corresponding to each
4434 sink iteration. It can sometimes be convenient to adjust
4435 the set of potential source iterations before or after each such operation.
4436 The prototypical example is fuzzy array dataflow analysis,
4437 where we need to analyze if, based on data-dependent constraints,
4438 the sink iteration can ever be executed without one or more of
4439 the corresponding potential source iterations being executed.
4440 If so, we can introduce extra parameters and select an unknown
4441 but fixed source iteration from the potential source iterations.
4442 To be able to perform such manipulations, C<isl> provides the following
4445 #include <isl/flow.h>
4447 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4448 __isl_keep isl_map *source_map,
4449 __isl_keep isl_set *sink, void *source_user,
4451 __isl_give isl_access_info *isl_access_info_set_restrict(
4452 __isl_take isl_access_info *acc,
4453 isl_access_restrict fn, void *user);
4455 The function C<isl_access_info_set_restrict> should be called
4456 before calling C<isl_access_info_compute_flow> and registers a callback function
4457 that will be called any time C<isl> is about to compute the last
4458 potential source. The first argument is the (reverse) proto-dependence,
4459 mapping sink iterations to potential source iterations.
4460 The second argument represents the sink iterations for which
4461 we want to compute the last source iteration.
4462 The third argument is the token corresponding to the source
4463 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4464 The callback is expected to return a restriction on either the input or
4465 the output of the operation computing the last potential source.
4466 If the input needs to be restricted then restrictions are needed
4467 for both the source and the sink iterations. The sink iterations
4468 and the potential source iterations will be intersected with these sets.
4469 If the output needs to be restricted then only a restriction on the source
4470 iterations is required.
4471 If any error occurs, the callback should return C<NULL>.
4472 An C<isl_restriction> object can be created, freed and inspected
4473 using the following functions.
4475 #include <isl/flow.h>
4477 __isl_give isl_restriction *isl_restriction_input(
4478 __isl_take isl_set *source_restr,
4479 __isl_take isl_set *sink_restr);
4480 __isl_give isl_restriction *isl_restriction_output(
4481 __isl_take isl_set *source_restr);
4482 __isl_give isl_restriction *isl_restriction_none(
4483 __isl_take isl_map *source_map);
4484 __isl_give isl_restriction *isl_restriction_empty(
4485 __isl_take isl_map *source_map);
4486 void *isl_restriction_free(
4487 __isl_take isl_restriction *restr);
4488 isl_ctx *isl_restriction_get_ctx(
4489 __isl_keep isl_restriction *restr);
4491 C<isl_restriction_none> and C<isl_restriction_empty> are special
4492 cases of C<isl_restriction_input>. C<isl_restriction_none>
4493 is essentially equivalent to
4495 isl_restriction_input(isl_set_universe(
4496 isl_space_range(isl_map_get_space(source_map))),
4498 isl_space_domain(isl_map_get_space(source_map))));
4500 whereas C<isl_restriction_empty> is essentially equivalent to
4502 isl_restriction_input(isl_set_empty(
4503 isl_space_range(isl_map_get_space(source_map))),
4505 isl_space_domain(isl_map_get_space(source_map))));
4509 B<The functionality described in this section is fairly new
4510 and may be subject to change.>
4512 The following function can be used to compute a schedule
4513 for a union of domains.
4514 By default, the algorithm used to construct the schedule is similar
4515 to that of C<Pluto>.
4516 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4518 The generated schedule respects all C<validity> dependences.
4519 That is, all dependence distances over these dependences in the
4520 scheduled space are lexicographically positive.
4521 The default algorithm tries to minimize the dependence distances over
4522 C<proximity> dependences.
4523 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4524 for groups of domains where the dependence distances have only
4525 non-negative values.
4526 When using Feautrier's algorithm, the C<proximity> dependence
4527 distances are only minimized during the extension to a
4528 full-dimensional schedule.
4530 #include <isl/schedule.h>
4531 __isl_give isl_schedule *isl_union_set_compute_schedule(
4532 __isl_take isl_union_set *domain,
4533 __isl_take isl_union_map *validity,
4534 __isl_take isl_union_map *proximity);
4535 void *isl_schedule_free(__isl_take isl_schedule *sched);
4537 A mapping from the domains to the scheduled space can be obtained
4538 from an C<isl_schedule> using the following function.
4540 __isl_give isl_union_map *isl_schedule_get_map(
4541 __isl_keep isl_schedule *sched);
4543 A representation of the schedule can be printed using
4545 __isl_give isl_printer *isl_printer_print_schedule(
4546 __isl_take isl_printer *p,
4547 __isl_keep isl_schedule *schedule);
4549 A representation of the schedule as a forest of bands can be obtained
4550 using the following function.
4552 __isl_give isl_band_list *isl_schedule_get_band_forest(
4553 __isl_keep isl_schedule *schedule);
4555 The individual bands can be visited in depth-first post-order
4556 using the following function.
4558 #include <isl/schedule.h>
4559 int isl_schedule_foreach_band(
4560 __isl_keep isl_schedule *sched,
4561 int (*fn)(__isl_keep isl_band *band, void *user),
4564 The list can be manipulated as explained in L<"Lists">.
4565 The bands inside the list can be copied and freed using the following
4568 #include <isl/band.h>
4569 __isl_give isl_band *isl_band_copy(
4570 __isl_keep isl_band *band);
4571 void *isl_band_free(__isl_take isl_band *band);
4573 Each band contains zero or more scheduling dimensions.
4574 These are referred to as the members of the band.
4575 The section of the schedule that corresponds to the band is
4576 referred to as the partial schedule of the band.
4577 For those nodes that participate in a band, the outer scheduling
4578 dimensions form the prefix schedule, while the inner scheduling
4579 dimensions form the suffix schedule.
4580 That is, if we take a cut of the band forest, then the union of
4581 the concatenations of the prefix, partial and suffix schedules of
4582 each band in the cut is equal to the entire schedule (modulo
4583 some possible padding at the end with zero scheduling dimensions).
4584 The properties of a band can be inspected using the following functions.
4586 #include <isl/band.h>
4587 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4589 int isl_band_has_children(__isl_keep isl_band *band);
4590 __isl_give isl_band_list *isl_band_get_children(
4591 __isl_keep isl_band *band);
4593 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4594 __isl_keep isl_band *band);
4595 __isl_give isl_union_map *isl_band_get_partial_schedule(
4596 __isl_keep isl_band *band);
4597 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4598 __isl_keep isl_band *band);
4600 int isl_band_n_member(__isl_keep isl_band *band);
4601 int isl_band_member_is_zero_distance(
4602 __isl_keep isl_band *band, int pos);
4604 int isl_band_list_foreach_band(
4605 __isl_keep isl_band_list *list,
4606 int (*fn)(__isl_keep isl_band *band, void *user),
4609 Note that a scheduling dimension is considered to be ``zero
4610 distance'' if it does not carry any proximity dependences
4612 That is, if the dependence distances of the proximity
4613 dependences are all zero in that direction (for fixed
4614 iterations of outer bands).
4615 Like C<isl_schedule_foreach_band>,
4616 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4617 in depth-first post-order.
4619 A band can be tiled using the following function.
4621 #include <isl/band.h>
4622 int isl_band_tile(__isl_keep isl_band *band,
4623 __isl_take isl_vec *sizes);
4625 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4627 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4629 The C<isl_band_tile> function tiles the band using the given tile sizes
4630 inside its schedule.
4631 A new child band is created to represent the point loops and it is
4632 inserted between the modified band and its children.
4633 The C<tile_scale_tile_loops> option specifies whether the tile
4634 loops iterators should be scaled by the tile sizes.
4636 A representation of the band can be printed using
4638 #include <isl/band.h>
4639 __isl_give isl_printer *isl_printer_print_band(
4640 __isl_take isl_printer *p,
4641 __isl_keep isl_band *band);
4645 #include <isl/schedule.h>
4646 int isl_options_set_schedule_max_coefficient(
4647 isl_ctx *ctx, int val);
4648 int isl_options_get_schedule_max_coefficient(
4650 int isl_options_set_schedule_max_constant_term(
4651 isl_ctx *ctx, int val);
4652 int isl_options_get_schedule_max_constant_term(
4654 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4655 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4656 int isl_options_set_schedule_maximize_band_depth(
4657 isl_ctx *ctx, int val);
4658 int isl_options_get_schedule_maximize_band_depth(
4660 int isl_options_set_schedule_outer_zero_distance(
4661 isl_ctx *ctx, int val);
4662 int isl_options_get_schedule_outer_zero_distance(
4664 int isl_options_set_schedule_split_scaled(
4665 isl_ctx *ctx, int val);
4666 int isl_options_get_schedule_split_scaled(
4668 int isl_options_set_schedule_algorithm(
4669 isl_ctx *ctx, int val);
4670 int isl_options_get_schedule_algorithm(
4672 int isl_options_set_schedule_separate_components(
4673 isl_ctx *ctx, int val);
4674 int isl_options_get_schedule_separate_components(
4679 =item * schedule_max_coefficient
4681 This option enforces that the coefficients for variable and parameter
4682 dimensions in the calculated schedule are not larger than the specified value.
4683 This option can significantly increase the speed of the scheduling calculation
4684 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4685 this option does not introduce bounds on the variable or parameter
4688 =item * schedule_max_constant_term
4690 This option enforces that the constant coefficients in the calculated schedule
4691 are not larger than the maximal constant term. This option can significantly
4692 increase the speed of the scheduling calculation and may also prevent fusing of
4693 unrelated dimensions. A value of -1 means that this option does not introduce
4694 bounds on the constant coefficients.
4696 =item * schedule_fuse
4698 This option controls the level of fusion.
4699 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4700 resulting schedule will be distributed as much as possible.
4701 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4702 try to fuse loops in the resulting schedule.
4704 =item * schedule_maximize_band_depth
4706 If this option is set, we do not split bands at the point
4707 where we detect splitting is necessary. Instead, we
4708 backtrack and split bands as early as possible. This
4709 reduces the number of splits and maximizes the width of
4710 the bands. Wider bands give more possibilities for tiling.
4711 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4712 then bands will be split as early as possible, even if there is no need.
4713 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4715 =item * schedule_outer_zero_distance
4717 If this option is set, then we try to construct schedules
4718 where the outermost scheduling dimension in each band
4719 results in a zero dependence distance over the proximity
4722 =item * schedule_split_scaled
4724 If this option is set, then we try to construct schedules in which the
4725 constant term is split off from the linear part if the linear parts of
4726 the scheduling rows for all nodes in the graphs have a common non-trivial
4728 The constant term is then placed in a separate band and the linear
4731 =item * schedule_algorithm
4733 Selects the scheduling algorithm to be used.
4734 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4735 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4737 =item * schedule_separate_components
4739 If at any point the dependence graph contains any (weakly connected) components,
4740 then these components are scheduled separately.
4741 If this option is not set, then some iterations of the domains
4742 in these components may be scheduled together.
4743 If this option is set, then the components are given consecutive
4748 =head2 Parametric Vertex Enumeration
4750 The parametric vertex enumeration described in this section
4751 is mainly intended to be used internally and by the C<barvinok>
4754 #include <isl/vertices.h>
4755 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4756 __isl_keep isl_basic_set *bset);
4758 The function C<isl_basic_set_compute_vertices> performs the
4759 actual computation of the parametric vertices and the chamber
4760 decomposition and store the result in an C<isl_vertices> object.
4761 This information can be queried by either iterating over all
4762 the vertices or iterating over all the chambers or cells
4763 and then iterating over all vertices that are active on the chamber.
4765 int isl_vertices_foreach_vertex(
4766 __isl_keep isl_vertices *vertices,
4767 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4770 int isl_vertices_foreach_cell(
4771 __isl_keep isl_vertices *vertices,
4772 int (*fn)(__isl_take isl_cell *cell, void *user),
4774 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4775 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4778 Other operations that can be performed on an C<isl_vertices> object are
4781 isl_ctx *isl_vertices_get_ctx(
4782 __isl_keep isl_vertices *vertices);
4783 int isl_vertices_get_n_vertices(
4784 __isl_keep isl_vertices *vertices);
4785 void isl_vertices_free(__isl_take isl_vertices *vertices);
4787 Vertices can be inspected and destroyed using the following functions.
4789 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4790 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4791 __isl_give isl_basic_set *isl_vertex_get_domain(
4792 __isl_keep isl_vertex *vertex);
4793 __isl_give isl_basic_set *isl_vertex_get_expr(
4794 __isl_keep isl_vertex *vertex);
4795 void isl_vertex_free(__isl_take isl_vertex *vertex);
4797 C<isl_vertex_get_expr> returns a singleton parametric set describing
4798 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4800 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4801 B<rational> basic sets, so they should mainly be used for inspection
4802 and should not be mixed with integer sets.
4804 Chambers can be inspected and destroyed using the following functions.
4806 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4807 __isl_give isl_basic_set *isl_cell_get_domain(
4808 __isl_keep isl_cell *cell);
4809 void isl_cell_free(__isl_take isl_cell *cell);
4813 Although C<isl> is mainly meant to be used as a library,
4814 it also contains some basic applications that use some
4815 of the functionality of C<isl>.
4816 The input may be specified in either the L<isl format>
4817 or the L<PolyLib format>.
4819 =head2 C<isl_polyhedron_sample>
4821 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4822 an integer element of the polyhedron, if there is any.
4823 The first column in the output is the denominator and is always
4824 equal to 1. If the polyhedron contains no integer points,
4825 then a vector of length zero is printed.
4829 C<isl_pip> takes the same input as the C<example> program
4830 from the C<piplib> distribution, i.e., a set of constraints
4831 on the parameters, a line containing only -1 and finally a set
4832 of constraints on a parametric polyhedron.
4833 The coefficients of the parameters appear in the last columns
4834 (but before the final constant column).
4835 The output is the lexicographic minimum of the parametric polyhedron.
4836 As C<isl> currently does not have its own output format, the output
4837 is just a dump of the internal state.
4839 =head2 C<isl_polyhedron_minimize>
4841 C<isl_polyhedron_minimize> computes the minimum of some linear
4842 or affine objective function over the integer points in a polyhedron.
4843 If an affine objective function
4844 is given, then the constant should appear in the last column.
4846 =head2 C<isl_polytope_scan>
4848 Given a polytope, C<isl_polytope_scan> prints
4849 all integer points in the polytope.