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_space(
677 __isl_keep isl_multi_aff *maff);
678 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
679 __isl_keep isl_pw_multi_aff *pma);
680 __isl_give isl_space *isl_pw_multi_aff_get_space(
681 __isl_keep isl_pw_multi_aff *pma);
682 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
683 __isl_keep isl_union_pw_multi_aff *upma);
685 #include <isl/point.h>
686 __isl_give isl_space *isl_point_get_space(
687 __isl_keep isl_point *pnt);
689 The identifiers or names of the individual dimensions may be set or read off
690 using the following functions.
692 #include <isl/space.h>
693 __isl_give isl_space *isl_space_set_dim_id(
694 __isl_take isl_space *space,
695 enum isl_dim_type type, unsigned pos,
696 __isl_take isl_id *id);
697 int isl_space_has_dim_id(__isl_keep isl_space *space,
698 enum isl_dim_type type, unsigned pos);
699 __isl_give isl_id *isl_space_get_dim_id(
700 __isl_keep isl_space *space,
701 enum isl_dim_type type, unsigned pos);
702 __isl_give isl_space *isl_space_set_dim_name(
703 __isl_take isl_space *space,
704 enum isl_dim_type type, unsigned pos,
705 __isl_keep const char *name);
706 int isl_space_has_dim_name(__isl_keep isl_space *space,
707 enum isl_dim_type type, unsigned pos);
708 __isl_keep const char *isl_space_get_dim_name(
709 __isl_keep isl_space *space,
710 enum isl_dim_type type, unsigned pos);
712 Note that C<isl_space_get_name> returns a pointer to some internal
713 data structure, so the result can only be used while the
714 corresponding C<isl_space> is alive.
715 Also note that every function that operates on two sets or relations
716 requires that both arguments have the same parameters. This also
717 means that if one of the arguments has named parameters, then the
718 other needs to have named parameters too and the names need to match.
719 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
720 arguments may have different parameters (as long as they are named),
721 in which case the result will have as parameters the union of the parameters of
724 Given the identifier or name of a dimension (typically a parameter),
725 its position can be obtained from the following function.
727 #include <isl/space.h>
728 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
729 enum isl_dim_type type, __isl_keep isl_id *id);
730 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
731 enum isl_dim_type type, const char *name);
733 The identifiers or names of entire spaces may be set or read off
734 using the following functions.
736 #include <isl/space.h>
737 __isl_give isl_space *isl_space_set_tuple_id(
738 __isl_take isl_space *space,
739 enum isl_dim_type type, __isl_take isl_id *id);
740 __isl_give isl_space *isl_space_reset_tuple_id(
741 __isl_take isl_space *space, enum isl_dim_type type);
742 int isl_space_has_tuple_id(__isl_keep isl_space *space,
743 enum isl_dim_type type);
744 __isl_give isl_id *isl_space_get_tuple_id(
745 __isl_keep isl_space *space, enum isl_dim_type type);
746 __isl_give isl_space *isl_space_set_tuple_name(
747 __isl_take isl_space *space,
748 enum isl_dim_type type, const char *s);
749 int isl_space_has_tuple_name(__isl_keep isl_space *space,
750 enum isl_dim_type type);
751 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
752 enum isl_dim_type type);
754 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
755 or C<isl_dim_set>. As with C<isl_space_get_name>,
756 the C<isl_space_get_tuple_name> function returns a pointer to some internal
758 Binary operations require the corresponding spaces of their arguments
759 to have the same name.
761 Spaces can be nested. In particular, the domain of a set or
762 the domain or range of a relation can be a nested relation.
763 The following functions can be used to construct and deconstruct
766 #include <isl/space.h>
767 int isl_space_is_wrapping(__isl_keep isl_space *space);
768 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
769 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
771 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
772 be the space of a set, while that of
773 C<isl_space_wrap> should be the space of a relation.
774 Conversely, the output of C<isl_space_unwrap> is the space
775 of a relation, while that of C<isl_space_wrap> is the space of a set.
777 Spaces can be created from other spaces
778 using the following functions.
780 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
781 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
782 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
783 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
784 __isl_give isl_space *isl_space_params(
785 __isl_take isl_space *space);
786 __isl_give isl_space *isl_space_set_from_params(
787 __isl_take isl_space *space);
788 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
789 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
790 __isl_take isl_space *right);
791 __isl_give isl_space *isl_space_align_params(
792 __isl_take isl_space *space1, __isl_take isl_space *space2)
793 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
794 enum isl_dim_type type, unsigned pos, unsigned n);
795 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
796 enum isl_dim_type type, unsigned n);
797 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
798 enum isl_dim_type type, unsigned first, unsigned n);
799 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
800 enum isl_dim_type dst_type, unsigned dst_pos,
801 enum isl_dim_type src_type, unsigned src_pos,
803 __isl_give isl_space *isl_space_map_from_set(
804 __isl_take isl_space *space);
805 __isl_give isl_space *isl_space_map_from_domain_and_range(
806 __isl_take isl_space *domain,
807 __isl_take isl_space *range);
808 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
809 __isl_give isl_space *isl_space_curry(
810 __isl_take isl_space *space);
812 Note that if dimensions are added or removed from a space, then
813 the name and the internal structure are lost.
817 A local space is essentially a space with
818 zero or more existentially quantified variables.
819 The local space of a (constraint of a) basic set or relation can be obtained
820 using the following functions.
822 #include <isl/constraint.h>
823 __isl_give isl_local_space *isl_constraint_get_local_space(
824 __isl_keep isl_constraint *constraint);
827 __isl_give isl_local_space *isl_basic_set_get_local_space(
828 __isl_keep isl_basic_set *bset);
831 __isl_give isl_local_space *isl_basic_map_get_local_space(
832 __isl_keep isl_basic_map *bmap);
834 A new local space can be created from a space using
836 #include <isl/local_space.h>
837 __isl_give isl_local_space *isl_local_space_from_space(
838 __isl_take isl_space *space);
840 They can be inspected, modified, copied and freed using the following functions.
842 #include <isl/local_space.h>
843 isl_ctx *isl_local_space_get_ctx(
844 __isl_keep isl_local_space *ls);
845 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
846 int isl_local_space_dim(__isl_keep isl_local_space *ls,
847 enum isl_dim_type type);
848 int isl_local_space_has_dim_name(
849 __isl_keep isl_local_space *ls,
850 enum isl_dim_type type, unsigned pos)
851 const char *isl_local_space_get_dim_name(
852 __isl_keep isl_local_space *ls,
853 enum isl_dim_type type, unsigned pos);
854 __isl_give isl_local_space *isl_local_space_set_dim_name(
855 __isl_take isl_local_space *ls,
856 enum isl_dim_type type, unsigned pos, const char *s);
857 __isl_give isl_local_space *isl_local_space_set_dim_id(
858 __isl_take isl_local_space *ls,
859 enum isl_dim_type type, unsigned pos,
860 __isl_take isl_id *id);
861 __isl_give isl_space *isl_local_space_get_space(
862 __isl_keep isl_local_space *ls);
863 __isl_give isl_aff *isl_local_space_get_div(
864 __isl_keep isl_local_space *ls, int pos);
865 __isl_give isl_local_space *isl_local_space_copy(
866 __isl_keep isl_local_space *ls);
867 void *isl_local_space_free(__isl_take isl_local_space *ls);
869 Two local spaces can be compared using
871 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
872 __isl_keep isl_local_space *ls2);
874 Local spaces can be created from other local spaces
875 using the following functions.
877 __isl_give isl_local_space *isl_local_space_domain(
878 __isl_take isl_local_space *ls);
879 __isl_give isl_local_space *isl_local_space_range(
880 __isl_take isl_local_space *ls);
881 __isl_give isl_local_space *isl_local_space_from_domain(
882 __isl_take isl_local_space *ls);
883 __isl_give isl_local_space *isl_local_space_intersect(
884 __isl_take isl_local_space *ls1,
885 __isl_take isl_local_space *ls2);
886 __isl_give isl_local_space *isl_local_space_add_dims(
887 __isl_take isl_local_space *ls,
888 enum isl_dim_type type, unsigned n);
889 __isl_give isl_local_space *isl_local_space_insert_dims(
890 __isl_take isl_local_space *ls,
891 enum isl_dim_type type, unsigned first, unsigned n);
892 __isl_give isl_local_space *isl_local_space_drop_dims(
893 __isl_take isl_local_space *ls,
894 enum isl_dim_type type, unsigned first, unsigned n);
896 =head2 Input and Output
898 C<isl> supports its own input/output format, which is similar
899 to the C<Omega> format, but also supports the C<PolyLib> format
904 The C<isl> format is similar to that of C<Omega>, but has a different
905 syntax for describing the parameters and allows for the definition
906 of an existentially quantified variable as the integer division
907 of an affine expression.
908 For example, the set of integers C<i> between C<0> and C<n>
909 such that C<i % 10 <= 6> can be described as
911 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
914 A set or relation can have several disjuncts, separated
915 by the keyword C<or>. Each disjunct is either a conjunction
916 of constraints or a projection (C<exists>) of a conjunction
917 of constraints. The constraints are separated by the keyword
920 =head3 C<PolyLib> format
922 If the represented set is a union, then the first line
923 contains a single number representing the number of disjuncts.
924 Otherwise, a line containing the number C<1> is optional.
926 Each disjunct is represented by a matrix of constraints.
927 The first line contains two numbers representing
928 the number of rows and columns,
929 where the number of rows is equal to the number of constraints
930 and the number of columns is equal to two plus the number of variables.
931 The following lines contain the actual rows of the constraint matrix.
932 In each row, the first column indicates whether the constraint
933 is an equality (C<0>) or inequality (C<1>). The final column
934 corresponds to the constant term.
936 If the set is parametric, then the coefficients of the parameters
937 appear in the last columns before the constant column.
938 The coefficients of any existentially quantified variables appear
939 between those of the set variables and those of the parameters.
941 =head3 Extended C<PolyLib> format
943 The extended C<PolyLib> format is nearly identical to the
944 C<PolyLib> format. The only difference is that the line
945 containing the number of rows and columns of a constraint matrix
946 also contains four additional numbers:
947 the number of output dimensions, the number of input dimensions,
948 the number of local dimensions (i.e., the number of existentially
949 quantified variables) and the number of parameters.
950 For sets, the number of ``output'' dimensions is equal
951 to the number of set dimensions, while the number of ``input''
957 __isl_give isl_basic_set *isl_basic_set_read_from_file(
958 isl_ctx *ctx, FILE *input);
959 __isl_give isl_basic_set *isl_basic_set_read_from_str(
960 isl_ctx *ctx, const char *str);
961 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
963 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
967 __isl_give isl_basic_map *isl_basic_map_read_from_file(
968 isl_ctx *ctx, FILE *input);
969 __isl_give isl_basic_map *isl_basic_map_read_from_str(
970 isl_ctx *ctx, const char *str);
971 __isl_give isl_map *isl_map_read_from_file(
972 isl_ctx *ctx, FILE *input);
973 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
976 #include <isl/union_set.h>
977 __isl_give isl_union_set *isl_union_set_read_from_file(
978 isl_ctx *ctx, FILE *input);
979 __isl_give isl_union_set *isl_union_set_read_from_str(
980 isl_ctx *ctx, const char *str);
982 #include <isl/union_map.h>
983 __isl_give isl_union_map *isl_union_map_read_from_file(
984 isl_ctx *ctx, FILE *input);
985 __isl_give isl_union_map *isl_union_map_read_from_str(
986 isl_ctx *ctx, const char *str);
988 The input format is autodetected and may be either the C<PolyLib> format
989 or the C<isl> format.
993 Before anything can be printed, an C<isl_printer> needs to
996 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
998 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
999 void isl_printer_free(__isl_take isl_printer *printer);
1000 __isl_give char *isl_printer_get_str(
1001 __isl_keep isl_printer *printer);
1003 The printer can be inspected using the following functions.
1005 FILE *isl_printer_get_file(
1006 __isl_keep isl_printer *printer);
1007 int isl_printer_get_output_format(
1008 __isl_keep isl_printer *p);
1010 The behavior of the printer can be modified in various ways
1012 __isl_give isl_printer *isl_printer_set_output_format(
1013 __isl_take isl_printer *p, int output_format);
1014 __isl_give isl_printer *isl_printer_set_indent(
1015 __isl_take isl_printer *p, int indent);
1016 __isl_give isl_printer *isl_printer_indent(
1017 __isl_take isl_printer *p, int indent);
1018 __isl_give isl_printer *isl_printer_set_prefix(
1019 __isl_take isl_printer *p, const char *prefix);
1020 __isl_give isl_printer *isl_printer_set_suffix(
1021 __isl_take isl_printer *p, const char *suffix);
1023 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1024 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1025 and defaults to C<ISL_FORMAT_ISL>.
1026 Each line in the output is indented by C<indent> (set by
1027 C<isl_printer_set_indent>) spaces
1028 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1029 In the C<PolyLib> format output,
1030 the coefficients of the existentially quantified variables
1031 appear between those of the set variables and those
1033 The function C<isl_printer_indent> increases the indentation
1034 by the specified amount (which may be negative).
1036 To actually print something, use
1038 #include <isl/printer.h>
1039 __isl_give isl_printer *isl_printer_print_double(
1040 __isl_take isl_printer *p, double d);
1042 #include <isl/set.h>
1043 __isl_give isl_printer *isl_printer_print_basic_set(
1044 __isl_take isl_printer *printer,
1045 __isl_keep isl_basic_set *bset);
1046 __isl_give isl_printer *isl_printer_print_set(
1047 __isl_take isl_printer *printer,
1048 __isl_keep isl_set *set);
1050 #include <isl/map.h>
1051 __isl_give isl_printer *isl_printer_print_basic_map(
1052 __isl_take isl_printer *printer,
1053 __isl_keep isl_basic_map *bmap);
1054 __isl_give isl_printer *isl_printer_print_map(
1055 __isl_take isl_printer *printer,
1056 __isl_keep isl_map *map);
1058 #include <isl/union_set.h>
1059 __isl_give isl_printer *isl_printer_print_union_set(
1060 __isl_take isl_printer *p,
1061 __isl_keep isl_union_set *uset);
1063 #include <isl/union_map.h>
1064 __isl_give isl_printer *isl_printer_print_union_map(
1065 __isl_take isl_printer *p,
1066 __isl_keep isl_union_map *umap);
1068 When called on a file printer, the following function flushes
1069 the file. When called on a string printer, the buffer is cleared.
1071 __isl_give isl_printer *isl_printer_flush(
1072 __isl_take isl_printer *p);
1074 =head2 Creating New Sets and Relations
1076 C<isl> has functions for creating some standard sets and relations.
1080 =item * Empty sets and relations
1082 __isl_give isl_basic_set *isl_basic_set_empty(
1083 __isl_take isl_space *space);
1084 __isl_give isl_basic_map *isl_basic_map_empty(
1085 __isl_take isl_space *space);
1086 __isl_give isl_set *isl_set_empty(
1087 __isl_take isl_space *space);
1088 __isl_give isl_map *isl_map_empty(
1089 __isl_take isl_space *space);
1090 __isl_give isl_union_set *isl_union_set_empty(
1091 __isl_take isl_space *space);
1092 __isl_give isl_union_map *isl_union_map_empty(
1093 __isl_take isl_space *space);
1095 For C<isl_union_set>s and C<isl_union_map>s, the space
1096 is only used to specify the parameters.
1098 =item * Universe sets and relations
1100 __isl_give isl_basic_set *isl_basic_set_universe(
1101 __isl_take isl_space *space);
1102 __isl_give isl_basic_map *isl_basic_map_universe(
1103 __isl_take isl_space *space);
1104 __isl_give isl_set *isl_set_universe(
1105 __isl_take isl_space *space);
1106 __isl_give isl_map *isl_map_universe(
1107 __isl_take isl_space *space);
1108 __isl_give isl_union_set *isl_union_set_universe(
1109 __isl_take isl_union_set *uset);
1110 __isl_give isl_union_map *isl_union_map_universe(
1111 __isl_take isl_union_map *umap);
1113 The sets and relations constructed by the functions above
1114 contain all integer values, while those constructed by the
1115 functions below only contain non-negative values.
1117 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1118 __isl_take isl_space *space);
1119 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1120 __isl_take isl_space *space);
1121 __isl_give isl_set *isl_set_nat_universe(
1122 __isl_take isl_space *space);
1123 __isl_give isl_map *isl_map_nat_universe(
1124 __isl_take isl_space *space);
1126 =item * Identity relations
1128 __isl_give isl_basic_map *isl_basic_map_identity(
1129 __isl_take isl_space *space);
1130 __isl_give isl_map *isl_map_identity(
1131 __isl_take isl_space *space);
1133 The number of input and output dimensions in C<space> needs
1136 =item * Lexicographic order
1138 __isl_give isl_map *isl_map_lex_lt(
1139 __isl_take isl_space *set_space);
1140 __isl_give isl_map *isl_map_lex_le(
1141 __isl_take isl_space *set_space);
1142 __isl_give isl_map *isl_map_lex_gt(
1143 __isl_take isl_space *set_space);
1144 __isl_give isl_map *isl_map_lex_ge(
1145 __isl_take isl_space *set_space);
1146 __isl_give isl_map *isl_map_lex_lt_first(
1147 __isl_take isl_space *space, unsigned n);
1148 __isl_give isl_map *isl_map_lex_le_first(
1149 __isl_take isl_space *space, unsigned n);
1150 __isl_give isl_map *isl_map_lex_gt_first(
1151 __isl_take isl_space *space, unsigned n);
1152 __isl_give isl_map *isl_map_lex_ge_first(
1153 __isl_take isl_space *space, unsigned n);
1155 The first four functions take a space for a B<set>
1156 and return relations that express that the elements in the domain
1157 are lexicographically less
1158 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1159 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1160 than the elements in the range.
1161 The last four functions take a space for a map
1162 and return relations that express that the first C<n> dimensions
1163 in the domain are lexicographically less
1164 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1165 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1166 than the first C<n> dimensions in the range.
1170 A basic set or relation can be converted to a set or relation
1171 using the following functions.
1173 __isl_give isl_set *isl_set_from_basic_set(
1174 __isl_take isl_basic_set *bset);
1175 __isl_give isl_map *isl_map_from_basic_map(
1176 __isl_take isl_basic_map *bmap);
1178 Sets and relations can be converted to union sets and relations
1179 using the following functions.
1181 __isl_give isl_union_map *isl_union_map_from_map(
1182 __isl_take isl_map *map);
1183 __isl_give isl_union_set *isl_union_set_from_set(
1184 __isl_take isl_set *set);
1186 The inverse conversions below can only be used if the input
1187 union set or relation is known to contain elements in exactly one
1190 __isl_give isl_set *isl_set_from_union_set(
1191 __isl_take isl_union_set *uset);
1192 __isl_give isl_map *isl_map_from_union_map(
1193 __isl_take isl_union_map *umap);
1195 A zero-dimensional set can be constructed on a given parameter domain
1196 using the following function.
1198 __isl_give isl_set *isl_set_from_params(
1199 __isl_take isl_set *set);
1201 Sets and relations can be copied and freed again using the following
1204 __isl_give isl_basic_set *isl_basic_set_copy(
1205 __isl_keep isl_basic_set *bset);
1206 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1207 __isl_give isl_union_set *isl_union_set_copy(
1208 __isl_keep isl_union_set *uset);
1209 __isl_give isl_basic_map *isl_basic_map_copy(
1210 __isl_keep isl_basic_map *bmap);
1211 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1212 __isl_give isl_union_map *isl_union_map_copy(
1213 __isl_keep isl_union_map *umap);
1214 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1215 void isl_set_free(__isl_take isl_set *set);
1216 void *isl_union_set_free(__isl_take isl_union_set *uset);
1217 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1218 void isl_map_free(__isl_take isl_map *map);
1219 void *isl_union_map_free(__isl_take isl_union_map *umap);
1221 Other sets and relations can be constructed by starting
1222 from a universe set or relation, adding equality and/or
1223 inequality constraints and then projecting out the
1224 existentially quantified variables, if any.
1225 Constraints can be constructed, manipulated and
1226 added to (or removed from) (basic) sets and relations
1227 using the following functions.
1229 #include <isl/constraint.h>
1230 __isl_give isl_constraint *isl_equality_alloc(
1231 __isl_take isl_local_space *ls);
1232 __isl_give isl_constraint *isl_inequality_alloc(
1233 __isl_take isl_local_space *ls);
1234 __isl_give isl_constraint *isl_constraint_set_constant(
1235 __isl_take isl_constraint *constraint, isl_int v);
1236 __isl_give isl_constraint *isl_constraint_set_constant_si(
1237 __isl_take isl_constraint *constraint, int v);
1238 __isl_give isl_constraint *isl_constraint_set_coefficient(
1239 __isl_take isl_constraint *constraint,
1240 enum isl_dim_type type, int pos, isl_int v);
1241 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1242 __isl_take isl_constraint *constraint,
1243 enum isl_dim_type type, int pos, int v);
1244 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1245 __isl_take isl_basic_map *bmap,
1246 __isl_take isl_constraint *constraint);
1247 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1248 __isl_take isl_basic_set *bset,
1249 __isl_take isl_constraint *constraint);
1250 __isl_give isl_map *isl_map_add_constraint(
1251 __isl_take isl_map *map,
1252 __isl_take isl_constraint *constraint);
1253 __isl_give isl_set *isl_set_add_constraint(
1254 __isl_take isl_set *set,
1255 __isl_take isl_constraint *constraint);
1256 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1257 __isl_take isl_basic_set *bset,
1258 __isl_take isl_constraint *constraint);
1260 For example, to create a set containing the even integers
1261 between 10 and 42, you would use the following code.
1264 isl_local_space *ls;
1266 isl_basic_set *bset;
1268 space = isl_space_set_alloc(ctx, 0, 2);
1269 bset = isl_basic_set_universe(isl_space_copy(space));
1270 ls = isl_local_space_from_space(space);
1272 c = isl_equality_alloc(isl_local_space_copy(ls));
1273 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1274 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1275 bset = isl_basic_set_add_constraint(bset, c);
1277 c = isl_inequality_alloc(isl_local_space_copy(ls));
1278 c = isl_constraint_set_constant_si(c, -10);
1279 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1280 bset = isl_basic_set_add_constraint(bset, c);
1282 c = isl_inequality_alloc(ls);
1283 c = isl_constraint_set_constant_si(c, 42);
1284 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1285 bset = isl_basic_set_add_constraint(bset, c);
1287 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1291 isl_basic_set *bset;
1292 bset = isl_basic_set_read_from_str(ctx,
1293 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1295 A basic set or relation can also be constructed from two matrices
1296 describing the equalities and the inequalities.
1298 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1299 __isl_take isl_space *space,
1300 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1301 enum isl_dim_type c1,
1302 enum isl_dim_type c2, enum isl_dim_type c3,
1303 enum isl_dim_type c4);
1304 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1305 __isl_take isl_space *space,
1306 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1307 enum isl_dim_type c1,
1308 enum isl_dim_type c2, enum isl_dim_type c3,
1309 enum isl_dim_type c4, enum isl_dim_type c5);
1311 The C<isl_dim_type> arguments indicate the order in which
1312 different kinds of variables appear in the input matrices
1313 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1314 C<isl_dim_set> and C<isl_dim_div> for sets and
1315 of C<isl_dim_cst>, C<isl_dim_param>,
1316 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1318 A (basic or union) set or relation can also be constructed from a
1319 (union) (piecewise) (multiple) affine expression
1320 or a list of affine expressions
1321 (See L<"Piecewise Quasi Affine Expressions"> and
1322 L<"Piecewise Multiple Quasi Affine Expressions">).
1324 __isl_give isl_basic_map *isl_basic_map_from_aff(
1325 __isl_take isl_aff *aff);
1326 __isl_give isl_map *isl_map_from_aff(
1327 __isl_take isl_aff *aff);
1328 __isl_give isl_set *isl_set_from_pw_aff(
1329 __isl_take isl_pw_aff *pwaff);
1330 __isl_give isl_map *isl_map_from_pw_aff(
1331 __isl_take isl_pw_aff *pwaff);
1332 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1333 __isl_take isl_space *domain_space,
1334 __isl_take isl_aff_list *list);
1335 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1336 __isl_take isl_multi_aff *maff)
1337 __isl_give isl_map *isl_map_from_multi_aff(
1338 __isl_take isl_multi_aff *maff)
1339 __isl_give isl_set *isl_set_from_pw_multi_aff(
1340 __isl_take isl_pw_multi_aff *pma);
1341 __isl_give isl_map *isl_map_from_pw_multi_aff(
1342 __isl_take isl_pw_multi_aff *pma);
1343 __isl_give isl_union_map *
1344 isl_union_map_from_union_pw_multi_aff(
1345 __isl_take isl_union_pw_multi_aff *upma);
1347 The C<domain_dim> argument describes the domain of the resulting
1348 basic relation. It is required because the C<list> may consist
1349 of zero affine expressions.
1351 =head2 Inspecting Sets and Relations
1353 Usually, the user should not have to care about the actual constraints
1354 of the sets and maps, but should instead apply the abstract operations
1355 explained in the following sections.
1356 Occasionally, however, it may be required to inspect the individual
1357 coefficients of the constraints. This section explains how to do so.
1358 In these cases, it may also be useful to have C<isl> compute
1359 an explicit representation of the existentially quantified variables.
1361 __isl_give isl_set *isl_set_compute_divs(
1362 __isl_take isl_set *set);
1363 __isl_give isl_map *isl_map_compute_divs(
1364 __isl_take isl_map *map);
1365 __isl_give isl_union_set *isl_union_set_compute_divs(
1366 __isl_take isl_union_set *uset);
1367 __isl_give isl_union_map *isl_union_map_compute_divs(
1368 __isl_take isl_union_map *umap);
1370 This explicit representation defines the existentially quantified
1371 variables as integer divisions of the other variables, possibly
1372 including earlier existentially quantified variables.
1373 An explicitly represented existentially quantified variable therefore
1374 has a unique value when the values of the other variables are known.
1375 If, furthermore, the same existentials, i.e., existentials
1376 with the same explicit representations, should appear in the
1377 same order in each of the disjuncts of a set or map, then the user should call
1378 either of the following functions.
1380 __isl_give isl_set *isl_set_align_divs(
1381 __isl_take isl_set *set);
1382 __isl_give isl_map *isl_map_align_divs(
1383 __isl_take isl_map *map);
1385 Alternatively, the existentially quantified variables can be removed
1386 using the following functions, which compute an overapproximation.
1388 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1389 __isl_take isl_basic_set *bset);
1390 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1391 __isl_take isl_basic_map *bmap);
1392 __isl_give isl_set *isl_set_remove_divs(
1393 __isl_take isl_set *set);
1394 __isl_give isl_map *isl_map_remove_divs(
1395 __isl_take isl_map *map);
1397 To iterate over all the sets or maps in a union set or map, use
1399 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1400 int (*fn)(__isl_take isl_set *set, void *user),
1402 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1403 int (*fn)(__isl_take isl_map *map, void *user),
1406 The number of sets or maps in a union set or map can be obtained
1409 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1410 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1412 To extract the set or map in a given space from a union, use
1414 __isl_give isl_set *isl_union_set_extract_set(
1415 __isl_keep isl_union_set *uset,
1416 __isl_take isl_space *space);
1417 __isl_give isl_map *isl_union_map_extract_map(
1418 __isl_keep isl_union_map *umap,
1419 __isl_take isl_space *space);
1421 To iterate over all the basic sets or maps in a set or map, use
1423 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1424 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1426 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1427 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1430 The callback function C<fn> should return 0 if successful and
1431 -1 if an error occurs. In the latter case, or if any other error
1432 occurs, the above functions will return -1.
1434 It should be noted that C<isl> does not guarantee that
1435 the basic sets or maps passed to C<fn> are disjoint.
1436 If this is required, then the user should call one of
1437 the following functions first.
1439 __isl_give isl_set *isl_set_make_disjoint(
1440 __isl_take isl_set *set);
1441 __isl_give isl_map *isl_map_make_disjoint(
1442 __isl_take isl_map *map);
1444 The number of basic sets in a set can be obtained
1447 int isl_set_n_basic_set(__isl_keep isl_set *set);
1449 To iterate over the constraints of a basic set or map, use
1451 #include <isl/constraint.h>
1453 int isl_basic_set_n_constraint(
1454 __isl_keep isl_basic_set *bset);
1455 int isl_basic_set_foreach_constraint(
1456 __isl_keep isl_basic_set *bset,
1457 int (*fn)(__isl_take isl_constraint *c, void *user),
1459 int isl_basic_map_foreach_constraint(
1460 __isl_keep isl_basic_map *bmap,
1461 int (*fn)(__isl_take isl_constraint *c, void *user),
1463 void *isl_constraint_free(__isl_take isl_constraint *c);
1465 Again, the callback function C<fn> should return 0 if successful and
1466 -1 if an error occurs. In the latter case, or if any other error
1467 occurs, the above functions will return -1.
1468 The constraint C<c> represents either an equality or an inequality.
1469 Use the following function to find out whether a constraint
1470 represents an equality. If not, it represents an inequality.
1472 int isl_constraint_is_equality(
1473 __isl_keep isl_constraint *constraint);
1475 The coefficients of the constraints can be inspected using
1476 the following functions.
1478 int isl_constraint_is_lower_bound(
1479 __isl_keep isl_constraint *constraint,
1480 enum isl_dim_type type, unsigned pos);
1481 int isl_constraint_is_upper_bound(
1482 __isl_keep isl_constraint *constraint,
1483 enum isl_dim_type type, unsigned pos);
1484 void isl_constraint_get_constant(
1485 __isl_keep isl_constraint *constraint, isl_int *v);
1486 void isl_constraint_get_coefficient(
1487 __isl_keep isl_constraint *constraint,
1488 enum isl_dim_type type, int pos, isl_int *v);
1489 int isl_constraint_involves_dims(
1490 __isl_keep isl_constraint *constraint,
1491 enum isl_dim_type type, unsigned first, unsigned n);
1493 The explicit representations of the existentially quantified
1494 variables can be inspected using the following function.
1495 Note that the user is only allowed to use this function
1496 if the inspected set or map is the result of a call
1497 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1498 The existentially quantified variable is equal to the floor
1499 of the returned affine expression. The affine expression
1500 itself can be inspected using the functions in
1501 L<"Piecewise Quasi Affine Expressions">.
1503 __isl_give isl_aff *isl_constraint_get_div(
1504 __isl_keep isl_constraint *constraint, int pos);
1506 To obtain the constraints of a basic set or map in matrix
1507 form, use the following functions.
1509 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1510 __isl_keep isl_basic_set *bset,
1511 enum isl_dim_type c1, enum isl_dim_type c2,
1512 enum isl_dim_type c3, enum isl_dim_type c4);
1513 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1514 __isl_keep isl_basic_set *bset,
1515 enum isl_dim_type c1, enum isl_dim_type c2,
1516 enum isl_dim_type c3, enum isl_dim_type c4);
1517 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1518 __isl_keep isl_basic_map *bmap,
1519 enum isl_dim_type c1,
1520 enum isl_dim_type c2, enum isl_dim_type c3,
1521 enum isl_dim_type c4, enum isl_dim_type c5);
1522 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1523 __isl_keep isl_basic_map *bmap,
1524 enum isl_dim_type c1,
1525 enum isl_dim_type c2, enum isl_dim_type c3,
1526 enum isl_dim_type c4, enum isl_dim_type c5);
1528 The C<isl_dim_type> arguments dictate the order in which
1529 different kinds of variables appear in the resulting matrix
1530 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1531 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1533 The number of parameters, input, output or set dimensions can
1534 be obtained using the following functions.
1536 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1537 enum isl_dim_type type);
1538 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1539 enum isl_dim_type type);
1540 unsigned isl_set_dim(__isl_keep isl_set *set,
1541 enum isl_dim_type type);
1542 unsigned isl_map_dim(__isl_keep isl_map *map,
1543 enum isl_dim_type type);
1545 To check whether the description of a set or relation depends
1546 on one or more given dimensions, it is not necessary to iterate over all
1547 constraints. Instead the following functions can be used.
1549 int isl_basic_set_involves_dims(
1550 __isl_keep isl_basic_set *bset,
1551 enum isl_dim_type type, unsigned first, unsigned n);
1552 int isl_set_involves_dims(__isl_keep isl_set *set,
1553 enum isl_dim_type type, unsigned first, unsigned n);
1554 int isl_basic_map_involves_dims(
1555 __isl_keep isl_basic_map *bmap,
1556 enum isl_dim_type type, unsigned first, unsigned n);
1557 int isl_map_involves_dims(__isl_keep isl_map *map,
1558 enum isl_dim_type type, unsigned first, unsigned n);
1560 Similarly, the following functions can be used to check whether
1561 a given dimension is involved in any lower or upper bound.
1563 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1564 enum isl_dim_type type, unsigned pos);
1565 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1566 enum isl_dim_type type, unsigned pos);
1568 The identifiers or names of the domain and range spaces of a set
1569 or relation can be read off or set using the following functions.
1571 __isl_give isl_set *isl_set_set_tuple_id(
1572 __isl_take isl_set *set, __isl_take isl_id *id);
1573 __isl_give isl_set *isl_set_reset_tuple_id(
1574 __isl_take isl_set *set);
1575 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1576 __isl_give isl_id *isl_set_get_tuple_id(
1577 __isl_keep isl_set *set);
1578 __isl_give isl_map *isl_map_set_tuple_id(
1579 __isl_take isl_map *map, enum isl_dim_type type,
1580 __isl_take isl_id *id);
1581 __isl_give isl_map *isl_map_reset_tuple_id(
1582 __isl_take isl_map *map, enum isl_dim_type type);
1583 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1584 enum isl_dim_type type);
1585 __isl_give isl_id *isl_map_get_tuple_id(
1586 __isl_keep isl_map *map, enum isl_dim_type type);
1588 const char *isl_basic_set_get_tuple_name(
1589 __isl_keep isl_basic_set *bset);
1590 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1591 __isl_take isl_basic_set *set, const char *s);
1592 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1593 const char *isl_set_get_tuple_name(
1594 __isl_keep isl_set *set);
1595 const char *isl_basic_map_get_tuple_name(
1596 __isl_keep isl_basic_map *bmap,
1597 enum isl_dim_type type);
1598 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1599 __isl_take isl_basic_map *bmap,
1600 enum isl_dim_type type, const char *s);
1601 const char *isl_map_get_tuple_name(
1602 __isl_keep isl_map *map,
1603 enum isl_dim_type type);
1605 As with C<isl_space_get_tuple_name>, the value returned points to
1606 an internal data structure.
1607 The identifiers, positions or names of individual dimensions can be
1608 read off using the following functions.
1610 __isl_give isl_id *isl_basic_set_get_dim_id(
1611 __isl_keep isl_basic_set *bset,
1612 enum isl_dim_type type, unsigned pos);
1613 __isl_give isl_set *isl_set_set_dim_id(
1614 __isl_take isl_set *set, enum isl_dim_type type,
1615 unsigned pos, __isl_take isl_id *id);
1616 int isl_set_has_dim_id(__isl_keep isl_set *set,
1617 enum isl_dim_type type, unsigned pos);
1618 __isl_give isl_id *isl_set_get_dim_id(
1619 __isl_keep isl_set *set, enum isl_dim_type type,
1621 int isl_basic_map_has_dim_id(
1622 __isl_keep isl_basic_map *bmap,
1623 enum isl_dim_type type, unsigned pos);
1624 __isl_give isl_map *isl_map_set_dim_id(
1625 __isl_take isl_map *map, enum isl_dim_type type,
1626 unsigned pos, __isl_take isl_id *id);
1627 int isl_map_has_dim_id(__isl_keep isl_map *map,
1628 enum isl_dim_type type, unsigned pos);
1629 __isl_give isl_id *isl_map_get_dim_id(
1630 __isl_keep isl_map *map, enum isl_dim_type type,
1633 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1634 enum isl_dim_type type, __isl_keep isl_id *id);
1635 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1636 enum isl_dim_type type, __isl_keep isl_id *id);
1637 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1638 enum isl_dim_type type, const char *name);
1639 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1640 enum isl_dim_type type, const char *name);
1642 const char *isl_constraint_get_dim_name(
1643 __isl_keep isl_constraint *constraint,
1644 enum isl_dim_type type, unsigned pos);
1645 const char *isl_basic_set_get_dim_name(
1646 __isl_keep isl_basic_set *bset,
1647 enum isl_dim_type type, unsigned pos);
1648 int isl_set_has_dim_name(__isl_keep isl_set *set,
1649 enum isl_dim_type type, unsigned pos);
1650 const char *isl_set_get_dim_name(
1651 __isl_keep isl_set *set,
1652 enum isl_dim_type type, unsigned pos);
1653 const char *isl_basic_map_get_dim_name(
1654 __isl_keep isl_basic_map *bmap,
1655 enum isl_dim_type type, unsigned pos);
1656 const char *isl_map_get_dim_name(
1657 __isl_keep isl_map *map,
1658 enum isl_dim_type type, unsigned pos);
1660 These functions are mostly useful to obtain the identifiers, positions
1661 or names of the parameters. Identifiers of individual dimensions are
1662 essentially only useful for printing. They are ignored by all other
1663 operations and may not be preserved across those operations.
1667 =head3 Unary Properties
1673 The following functions test whether the given set or relation
1674 contains any integer points. The ``plain'' variants do not perform
1675 any computations, but simply check if the given set or relation
1676 is already known to be empty.
1678 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1679 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1680 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1681 int isl_set_is_empty(__isl_keep isl_set *set);
1682 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1683 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1684 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1685 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1686 int isl_map_is_empty(__isl_keep isl_map *map);
1687 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1689 =item * Universality
1691 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1692 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1693 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1695 =item * Single-valuedness
1697 int isl_basic_map_is_single_valued(
1698 __isl_keep isl_basic_map *bmap);
1699 int isl_map_plain_is_single_valued(
1700 __isl_keep isl_map *map);
1701 int isl_map_is_single_valued(__isl_keep isl_map *map);
1702 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1706 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1707 int isl_map_is_injective(__isl_keep isl_map *map);
1708 int isl_union_map_plain_is_injective(
1709 __isl_keep isl_union_map *umap);
1710 int isl_union_map_is_injective(
1711 __isl_keep isl_union_map *umap);
1715 int isl_map_is_bijective(__isl_keep isl_map *map);
1716 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1720 int isl_basic_map_plain_is_fixed(
1721 __isl_keep isl_basic_map *bmap,
1722 enum isl_dim_type type, unsigned pos,
1724 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1725 enum isl_dim_type type, unsigned pos,
1727 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1728 enum isl_dim_type type, unsigned pos,
1731 Check if the relation obviously lies on a hyperplane where the given dimension
1732 has a fixed value and if so, return that value in C<*val>.
1736 To check whether a set is a parameter domain, use this function:
1738 int isl_set_is_params(__isl_keep isl_set *set);
1739 int isl_union_set_is_params(
1740 __isl_keep isl_union_set *uset);
1744 The following functions check whether the domain of the given
1745 (basic) set is a wrapped relation.
1747 int isl_basic_set_is_wrapping(
1748 __isl_keep isl_basic_set *bset);
1749 int isl_set_is_wrapping(__isl_keep isl_set *set);
1751 =item * Internal Product
1753 int isl_basic_map_can_zip(
1754 __isl_keep isl_basic_map *bmap);
1755 int isl_map_can_zip(__isl_keep isl_map *map);
1757 Check whether the product of domain and range of the given relation
1759 i.e., whether both domain and range are nested relations.
1763 int isl_basic_map_can_curry(
1764 __isl_keep isl_basic_map *bmap);
1765 int isl_map_can_curry(__isl_keep isl_map *map);
1767 Check whether the domain of the (basic) relation is a wrapped relation.
1771 =head3 Binary Properties
1777 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1778 __isl_keep isl_set *set2);
1779 int isl_set_is_equal(__isl_keep isl_set *set1,
1780 __isl_keep isl_set *set2);
1781 int isl_union_set_is_equal(
1782 __isl_keep isl_union_set *uset1,
1783 __isl_keep isl_union_set *uset2);
1784 int isl_basic_map_is_equal(
1785 __isl_keep isl_basic_map *bmap1,
1786 __isl_keep isl_basic_map *bmap2);
1787 int isl_map_is_equal(__isl_keep isl_map *map1,
1788 __isl_keep isl_map *map2);
1789 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1790 __isl_keep isl_map *map2);
1791 int isl_union_map_is_equal(
1792 __isl_keep isl_union_map *umap1,
1793 __isl_keep isl_union_map *umap2);
1795 =item * Disjointness
1797 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1798 __isl_keep isl_set *set2);
1802 int isl_basic_set_is_subset(
1803 __isl_keep isl_basic_set *bset1,
1804 __isl_keep isl_basic_set *bset2);
1805 int isl_set_is_subset(__isl_keep isl_set *set1,
1806 __isl_keep isl_set *set2);
1807 int isl_set_is_strict_subset(
1808 __isl_keep isl_set *set1,
1809 __isl_keep isl_set *set2);
1810 int isl_union_set_is_subset(
1811 __isl_keep isl_union_set *uset1,
1812 __isl_keep isl_union_set *uset2);
1813 int isl_union_set_is_strict_subset(
1814 __isl_keep isl_union_set *uset1,
1815 __isl_keep isl_union_set *uset2);
1816 int isl_basic_map_is_subset(
1817 __isl_keep isl_basic_map *bmap1,
1818 __isl_keep isl_basic_map *bmap2);
1819 int isl_basic_map_is_strict_subset(
1820 __isl_keep isl_basic_map *bmap1,
1821 __isl_keep isl_basic_map *bmap2);
1822 int isl_map_is_subset(
1823 __isl_keep isl_map *map1,
1824 __isl_keep isl_map *map2);
1825 int isl_map_is_strict_subset(
1826 __isl_keep isl_map *map1,
1827 __isl_keep isl_map *map2);
1828 int isl_union_map_is_subset(
1829 __isl_keep isl_union_map *umap1,
1830 __isl_keep isl_union_map *umap2);
1831 int isl_union_map_is_strict_subset(
1832 __isl_keep isl_union_map *umap1,
1833 __isl_keep isl_union_map *umap2);
1835 Check whether the first argument is a (strict) subset of the
1840 =head2 Unary Operations
1846 __isl_give isl_set *isl_set_complement(
1847 __isl_take isl_set *set);
1848 __isl_give isl_map *isl_map_complement(
1849 __isl_take isl_map *map);
1853 __isl_give isl_basic_map *isl_basic_map_reverse(
1854 __isl_take isl_basic_map *bmap);
1855 __isl_give isl_map *isl_map_reverse(
1856 __isl_take isl_map *map);
1857 __isl_give isl_union_map *isl_union_map_reverse(
1858 __isl_take isl_union_map *umap);
1862 __isl_give isl_basic_set *isl_basic_set_project_out(
1863 __isl_take isl_basic_set *bset,
1864 enum isl_dim_type type, unsigned first, unsigned n);
1865 __isl_give isl_basic_map *isl_basic_map_project_out(
1866 __isl_take isl_basic_map *bmap,
1867 enum isl_dim_type type, unsigned first, unsigned n);
1868 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1869 enum isl_dim_type type, unsigned first, unsigned n);
1870 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1871 enum isl_dim_type type, unsigned first, unsigned n);
1872 __isl_give isl_basic_set *isl_basic_set_params(
1873 __isl_take isl_basic_set *bset);
1874 __isl_give isl_basic_set *isl_basic_map_domain(
1875 __isl_take isl_basic_map *bmap);
1876 __isl_give isl_basic_set *isl_basic_map_range(
1877 __isl_take isl_basic_map *bmap);
1878 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1879 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1880 __isl_give isl_set *isl_map_domain(
1881 __isl_take isl_map *bmap);
1882 __isl_give isl_set *isl_map_range(
1883 __isl_take isl_map *map);
1884 __isl_give isl_set *isl_union_set_params(
1885 __isl_take isl_union_set *uset);
1886 __isl_give isl_set *isl_union_map_params(
1887 __isl_take isl_union_map *umap);
1888 __isl_give isl_union_set *isl_union_map_domain(
1889 __isl_take isl_union_map *umap);
1890 __isl_give isl_union_set *isl_union_map_range(
1891 __isl_take isl_union_map *umap);
1893 __isl_give isl_basic_map *isl_basic_map_domain_map(
1894 __isl_take isl_basic_map *bmap);
1895 __isl_give isl_basic_map *isl_basic_map_range_map(
1896 __isl_take isl_basic_map *bmap);
1897 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1898 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1899 __isl_give isl_union_map *isl_union_map_domain_map(
1900 __isl_take isl_union_map *umap);
1901 __isl_give isl_union_map *isl_union_map_range_map(
1902 __isl_take isl_union_map *umap);
1904 The functions above construct a (basic, regular or union) relation
1905 that maps (a wrapped version of) the input relation to its domain or range.
1909 __isl_give isl_set *isl_set_eliminate(
1910 __isl_take isl_set *set, enum isl_dim_type type,
1911 unsigned first, unsigned n);
1912 __isl_give isl_basic_map *isl_basic_map_eliminate(
1913 __isl_take isl_basic_map *bmap,
1914 enum isl_dim_type type,
1915 unsigned first, unsigned n);
1916 __isl_give isl_map *isl_map_eliminate(
1917 __isl_take isl_map *map, enum isl_dim_type type,
1918 unsigned first, unsigned n);
1920 Eliminate the coefficients for the given dimensions from the constraints,
1921 without removing the dimensions.
1925 __isl_give isl_basic_set *isl_basic_set_fix(
1926 __isl_take isl_basic_set *bset,
1927 enum isl_dim_type type, unsigned pos,
1929 __isl_give isl_basic_set *isl_basic_set_fix_si(
1930 __isl_take isl_basic_set *bset,
1931 enum isl_dim_type type, unsigned pos, int value);
1932 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1933 enum isl_dim_type type, unsigned pos,
1935 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1936 enum isl_dim_type type, unsigned pos, int value);
1937 __isl_give isl_basic_map *isl_basic_map_fix_si(
1938 __isl_take isl_basic_map *bmap,
1939 enum isl_dim_type type, unsigned pos, int value);
1940 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1941 enum isl_dim_type type, unsigned pos, int value);
1943 Intersect the set or relation with the hyperplane where the given
1944 dimension has the fixed given value.
1946 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1947 __isl_take isl_basic_map *bmap,
1948 enum isl_dim_type type, unsigned pos, int value);
1949 __isl_give isl_set *isl_set_lower_bound(
1950 __isl_take isl_set *set,
1951 enum isl_dim_type type, unsigned pos,
1953 __isl_give isl_set *isl_set_lower_bound_si(
1954 __isl_take isl_set *set,
1955 enum isl_dim_type type, unsigned pos, int value);
1956 __isl_give isl_map *isl_map_lower_bound_si(
1957 __isl_take isl_map *map,
1958 enum isl_dim_type type, unsigned pos, int value);
1959 __isl_give isl_set *isl_set_upper_bound(
1960 __isl_take isl_set *set,
1961 enum isl_dim_type type, unsigned pos,
1963 __isl_give isl_set *isl_set_upper_bound_si(
1964 __isl_take isl_set *set,
1965 enum isl_dim_type type, unsigned pos, int value);
1966 __isl_give isl_map *isl_map_upper_bound_si(
1967 __isl_take isl_map *map,
1968 enum isl_dim_type type, unsigned pos, int value);
1970 Intersect the set or relation with the half-space where the given
1971 dimension has a value bounded by the fixed given value.
1973 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1974 enum isl_dim_type type1, int pos1,
1975 enum isl_dim_type type2, int pos2);
1976 __isl_give isl_basic_map *isl_basic_map_equate(
1977 __isl_take isl_basic_map *bmap,
1978 enum isl_dim_type type1, int pos1,
1979 enum isl_dim_type type2, int pos2);
1980 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1981 enum isl_dim_type type1, int pos1,
1982 enum isl_dim_type type2, int pos2);
1984 Intersect the set or relation with the hyperplane where the given
1985 dimensions are equal to each other.
1987 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1988 enum isl_dim_type type1, int pos1,
1989 enum isl_dim_type type2, int pos2);
1991 Intersect the relation with the hyperplane where the given
1992 dimensions have opposite values.
1994 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
1995 enum isl_dim_type type1, int pos1,
1996 enum isl_dim_type type2, int pos2);
1997 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1998 enum isl_dim_type type1, int pos1,
1999 enum isl_dim_type type2, int pos2);
2001 Intersect the relation with the half-space where the given
2002 dimensions satisfy the given ordering.
2006 __isl_give isl_map *isl_set_identity(
2007 __isl_take isl_set *set);
2008 __isl_give isl_union_map *isl_union_set_identity(
2009 __isl_take isl_union_set *uset);
2011 Construct an identity relation on the given (union) set.
2015 __isl_give isl_basic_set *isl_basic_map_deltas(
2016 __isl_take isl_basic_map *bmap);
2017 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2018 __isl_give isl_union_set *isl_union_map_deltas(
2019 __isl_take isl_union_map *umap);
2021 These functions return a (basic) set containing the differences
2022 between image elements and corresponding domain elements in the input.
2024 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2025 __isl_take isl_basic_map *bmap);
2026 __isl_give isl_map *isl_map_deltas_map(
2027 __isl_take isl_map *map);
2028 __isl_give isl_union_map *isl_union_map_deltas_map(
2029 __isl_take isl_union_map *umap);
2031 The functions above construct a (basic, regular or union) relation
2032 that maps (a wrapped version of) the input relation to its delta set.
2036 Simplify the representation of a set or relation by trying
2037 to combine pairs of basic sets or relations into a single
2038 basic set or relation.
2040 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2041 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2042 __isl_give isl_union_set *isl_union_set_coalesce(
2043 __isl_take isl_union_set *uset);
2044 __isl_give isl_union_map *isl_union_map_coalesce(
2045 __isl_take isl_union_map *umap);
2047 One of the methods for combining pairs of basic sets or relations
2048 can result in coefficients that are much larger than those that appear
2049 in the constraints of the input. By default, the coefficients are
2050 not allowed to grow larger, but this can be changed by unsetting
2051 the following option.
2053 int isl_options_set_coalesce_bounded_wrapping(
2054 isl_ctx *ctx, int val);
2055 int isl_options_get_coalesce_bounded_wrapping(
2058 =item * Detecting equalities
2060 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2061 __isl_take isl_basic_set *bset);
2062 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2063 __isl_take isl_basic_map *bmap);
2064 __isl_give isl_set *isl_set_detect_equalities(
2065 __isl_take isl_set *set);
2066 __isl_give isl_map *isl_map_detect_equalities(
2067 __isl_take isl_map *map);
2068 __isl_give isl_union_set *isl_union_set_detect_equalities(
2069 __isl_take isl_union_set *uset);
2070 __isl_give isl_union_map *isl_union_map_detect_equalities(
2071 __isl_take isl_union_map *umap);
2073 Simplify the representation of a set or relation by detecting implicit
2076 =item * Removing redundant constraints
2078 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2079 __isl_take isl_basic_set *bset);
2080 __isl_give isl_set *isl_set_remove_redundancies(
2081 __isl_take isl_set *set);
2082 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2083 __isl_take isl_basic_map *bmap);
2084 __isl_give isl_map *isl_map_remove_redundancies(
2085 __isl_take isl_map *map);
2089 __isl_give isl_basic_set *isl_set_convex_hull(
2090 __isl_take isl_set *set);
2091 __isl_give isl_basic_map *isl_map_convex_hull(
2092 __isl_take isl_map *map);
2094 If the input set or relation has any existentially quantified
2095 variables, then the result of these operations is currently undefined.
2099 __isl_give isl_basic_set *isl_set_simple_hull(
2100 __isl_take isl_set *set);
2101 __isl_give isl_basic_map *isl_map_simple_hull(
2102 __isl_take isl_map *map);
2103 __isl_give isl_union_map *isl_union_map_simple_hull(
2104 __isl_take isl_union_map *umap);
2106 These functions compute a single basic set or relation
2107 that contains the whole input set or relation.
2108 In particular, the output is described by translates
2109 of the constraints describing the basic sets or relations in the input.
2113 (See \autoref{s:simple hull}.)
2119 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2120 __isl_take isl_basic_set *bset);
2121 __isl_give isl_basic_set *isl_set_affine_hull(
2122 __isl_take isl_set *set);
2123 __isl_give isl_union_set *isl_union_set_affine_hull(
2124 __isl_take isl_union_set *uset);
2125 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2126 __isl_take isl_basic_map *bmap);
2127 __isl_give isl_basic_map *isl_map_affine_hull(
2128 __isl_take isl_map *map);
2129 __isl_give isl_union_map *isl_union_map_affine_hull(
2130 __isl_take isl_union_map *umap);
2132 In case of union sets and relations, the affine hull is computed
2135 =item * Polyhedral hull
2137 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2138 __isl_take isl_set *set);
2139 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2140 __isl_take isl_map *map);
2141 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2142 __isl_take isl_union_set *uset);
2143 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2144 __isl_take isl_union_map *umap);
2146 These functions compute a single basic set or relation
2147 not involving any existentially quantified variables
2148 that contains the whole input set or relation.
2149 In case of union sets and relations, the polyhedral hull is computed
2154 __isl_give isl_basic_set *isl_basic_set_sample(
2155 __isl_take isl_basic_set *bset);
2156 __isl_give isl_basic_set *isl_set_sample(
2157 __isl_take isl_set *set);
2158 __isl_give isl_basic_map *isl_basic_map_sample(
2159 __isl_take isl_basic_map *bmap);
2160 __isl_give isl_basic_map *isl_map_sample(
2161 __isl_take isl_map *map);
2163 If the input (basic) set or relation is non-empty, then return
2164 a singleton subset of the input. Otherwise, return an empty set.
2166 =item * Optimization
2168 #include <isl/ilp.h>
2169 enum isl_lp_result isl_basic_set_max(
2170 __isl_keep isl_basic_set *bset,
2171 __isl_keep isl_aff *obj, isl_int *opt)
2172 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2173 __isl_keep isl_aff *obj, isl_int *opt);
2174 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2175 __isl_keep isl_aff *obj, isl_int *opt);
2177 Compute the minimum or maximum of the integer affine expression C<obj>
2178 over the points in C<set>, returning the result in C<opt>.
2179 The return value may be one of C<isl_lp_error>,
2180 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2182 =item * Parametric optimization
2184 __isl_give isl_pw_aff *isl_set_dim_min(
2185 __isl_take isl_set *set, int pos);
2186 __isl_give isl_pw_aff *isl_set_dim_max(
2187 __isl_take isl_set *set, int pos);
2188 __isl_give isl_pw_aff *isl_map_dim_max(
2189 __isl_take isl_map *map, int pos);
2191 Compute the minimum or maximum of the given set or output dimension
2192 as a function of the parameters (and input dimensions), but independently
2193 of the other set or output dimensions.
2194 For lexicographic optimization, see L<"Lexicographic Optimization">.
2198 The following functions compute either the set of (rational) coefficient
2199 values of valid constraints for the given set or the set of (rational)
2200 values satisfying the constraints with coefficients from the given set.
2201 Internally, these two sets of functions perform essentially the
2202 same operations, except that the set of coefficients is assumed to
2203 be a cone, while the set of values may be any polyhedron.
2204 The current implementation is based on the Farkas lemma and
2205 Fourier-Motzkin elimination, but this may change or be made optional
2206 in future. In particular, future implementations may use different
2207 dualization algorithms or skip the elimination step.
2209 __isl_give isl_basic_set *isl_basic_set_coefficients(
2210 __isl_take isl_basic_set *bset);
2211 __isl_give isl_basic_set *isl_set_coefficients(
2212 __isl_take isl_set *set);
2213 __isl_give isl_union_set *isl_union_set_coefficients(
2214 __isl_take isl_union_set *bset);
2215 __isl_give isl_basic_set *isl_basic_set_solutions(
2216 __isl_take isl_basic_set *bset);
2217 __isl_give isl_basic_set *isl_set_solutions(
2218 __isl_take isl_set *set);
2219 __isl_give isl_union_set *isl_union_set_solutions(
2220 __isl_take isl_union_set *bset);
2224 __isl_give isl_map *isl_map_fixed_power(
2225 __isl_take isl_map *map, isl_int exp);
2226 __isl_give isl_union_map *isl_union_map_fixed_power(
2227 __isl_take isl_union_map *umap, isl_int exp);
2229 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2230 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2231 of C<map> is computed.
2233 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2235 __isl_give isl_union_map *isl_union_map_power(
2236 __isl_take isl_union_map *umap, int *exact);
2238 Compute a parametric representation for all positive powers I<k> of C<map>.
2239 The result maps I<k> to a nested relation corresponding to the
2240 I<k>th power of C<map>.
2241 The result may be an overapproximation. If the result is known to be exact,
2242 then C<*exact> is set to C<1>.
2244 =item * Transitive closure
2246 __isl_give isl_map *isl_map_transitive_closure(
2247 __isl_take isl_map *map, int *exact);
2248 __isl_give isl_union_map *isl_union_map_transitive_closure(
2249 __isl_take isl_union_map *umap, int *exact);
2251 Compute the transitive closure of C<map>.
2252 The result may be an overapproximation. If the result is known to be exact,
2253 then C<*exact> is set to C<1>.
2255 =item * Reaching path lengths
2257 __isl_give isl_map *isl_map_reaching_path_lengths(
2258 __isl_take isl_map *map, int *exact);
2260 Compute a relation that maps each element in the range of C<map>
2261 to the lengths of all paths composed of edges in C<map> that
2262 end up in the given element.
2263 The result may be an overapproximation. If the result is known to be exact,
2264 then C<*exact> is set to C<1>.
2265 To compute the I<maximal> path length, the resulting relation
2266 should be postprocessed by C<isl_map_lexmax>.
2267 In particular, if the input relation is a dependence relation
2268 (mapping sources to sinks), then the maximal path length corresponds
2269 to the free schedule.
2270 Note, however, that C<isl_map_lexmax> expects the maximum to be
2271 finite, so if the path lengths are unbounded (possibly due to
2272 the overapproximation), then you will get an error message.
2276 __isl_give isl_basic_set *isl_basic_map_wrap(
2277 __isl_take isl_basic_map *bmap);
2278 __isl_give isl_set *isl_map_wrap(
2279 __isl_take isl_map *map);
2280 __isl_give isl_union_set *isl_union_map_wrap(
2281 __isl_take isl_union_map *umap);
2282 __isl_give isl_basic_map *isl_basic_set_unwrap(
2283 __isl_take isl_basic_set *bset);
2284 __isl_give isl_map *isl_set_unwrap(
2285 __isl_take isl_set *set);
2286 __isl_give isl_union_map *isl_union_set_unwrap(
2287 __isl_take isl_union_set *uset);
2291 Remove any internal structure of domain (and range) of the given
2292 set or relation. If there is any such internal structure in the input,
2293 then the name of the space is also removed.
2295 __isl_give isl_basic_set *isl_basic_set_flatten(
2296 __isl_take isl_basic_set *bset);
2297 __isl_give isl_set *isl_set_flatten(
2298 __isl_take isl_set *set);
2299 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2300 __isl_take isl_basic_map *bmap);
2301 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2302 __isl_take isl_basic_map *bmap);
2303 __isl_give isl_map *isl_map_flatten_range(
2304 __isl_take isl_map *map);
2305 __isl_give isl_map *isl_map_flatten_domain(
2306 __isl_take isl_map *map);
2307 __isl_give isl_basic_map *isl_basic_map_flatten(
2308 __isl_take isl_basic_map *bmap);
2309 __isl_give isl_map *isl_map_flatten(
2310 __isl_take isl_map *map);
2312 __isl_give isl_map *isl_set_flatten_map(
2313 __isl_take isl_set *set);
2315 The function above constructs a relation
2316 that maps the input set to a flattened version of the set.
2320 Lift the input set to a space with extra dimensions corresponding
2321 to the existentially quantified variables in the input.
2322 In particular, the result lives in a wrapped map where the domain
2323 is the original space and the range corresponds to the original
2324 existentially quantified variables.
2326 __isl_give isl_basic_set *isl_basic_set_lift(
2327 __isl_take isl_basic_set *bset);
2328 __isl_give isl_set *isl_set_lift(
2329 __isl_take isl_set *set);
2330 __isl_give isl_union_set *isl_union_set_lift(
2331 __isl_take isl_union_set *uset);
2333 Given a local space that contains the existentially quantified
2334 variables of a set, a basic relation that, when applied to
2335 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2336 can be constructed using the following function.
2338 #include <isl/local_space.h>
2339 __isl_give isl_basic_map *isl_local_space_lifting(
2340 __isl_take isl_local_space *ls);
2342 =item * Internal Product
2344 __isl_give isl_basic_map *isl_basic_map_zip(
2345 __isl_take isl_basic_map *bmap);
2346 __isl_give isl_map *isl_map_zip(
2347 __isl_take isl_map *map);
2348 __isl_give isl_union_map *isl_union_map_zip(
2349 __isl_take isl_union_map *umap);
2351 Given a relation with nested relations for domain and range,
2352 interchange the range of the domain with the domain of the range.
2356 __isl_give isl_basic_map *isl_basic_map_curry(
2357 __isl_take isl_basic_map *bmap);
2358 __isl_give isl_map *isl_map_curry(
2359 __isl_take isl_map *map);
2360 __isl_give isl_union_map *isl_union_map_curry(
2361 __isl_take isl_union_map *umap);
2363 Given a relation with a nested relation for domain,
2364 move the range of the nested relation out of the domain
2365 and use it as the domain of a nested relation in the range,
2366 with the original range as range of this nested relation.
2368 =item * Aligning parameters
2370 __isl_give isl_set *isl_set_align_params(
2371 __isl_take isl_set *set,
2372 __isl_take isl_space *model);
2373 __isl_give isl_map *isl_map_align_params(
2374 __isl_take isl_map *map,
2375 __isl_take isl_space *model);
2377 Change the order of the parameters of the given set or relation
2378 such that the first parameters match those of C<model>.
2379 This may involve the introduction of extra parameters.
2380 All parameters need to be named.
2382 =item * Dimension manipulation
2384 __isl_give isl_set *isl_set_add_dims(
2385 __isl_take isl_set *set,
2386 enum isl_dim_type type, unsigned n);
2387 __isl_give isl_map *isl_map_add_dims(
2388 __isl_take isl_map *map,
2389 enum isl_dim_type type, unsigned n);
2390 __isl_give isl_set *isl_set_insert_dims(
2391 __isl_take isl_set *set,
2392 enum isl_dim_type type, unsigned pos, unsigned n);
2393 __isl_give isl_map *isl_map_insert_dims(
2394 __isl_take isl_map *map,
2395 enum isl_dim_type type, unsigned pos, unsigned n);
2396 __isl_give isl_basic_set *isl_basic_set_move_dims(
2397 __isl_take isl_basic_set *bset,
2398 enum isl_dim_type dst_type, unsigned dst_pos,
2399 enum isl_dim_type src_type, unsigned src_pos,
2401 __isl_give isl_basic_map *isl_basic_map_move_dims(
2402 __isl_take isl_basic_map *bmap,
2403 enum isl_dim_type dst_type, unsigned dst_pos,
2404 enum isl_dim_type src_type, unsigned src_pos,
2406 __isl_give isl_set *isl_set_move_dims(
2407 __isl_take isl_set *set,
2408 enum isl_dim_type dst_type, unsigned dst_pos,
2409 enum isl_dim_type src_type, unsigned src_pos,
2411 __isl_give isl_map *isl_map_move_dims(
2412 __isl_take isl_map *map,
2413 enum isl_dim_type dst_type, unsigned dst_pos,
2414 enum isl_dim_type src_type, unsigned src_pos,
2417 It is usually not advisable to directly change the (input or output)
2418 space of a set or a relation as this removes the name and the internal
2419 structure of the space. However, the above functions can be useful
2420 to add new parameters, assuming
2421 C<isl_set_align_params> and C<isl_map_align_params>
2426 =head2 Binary Operations
2428 The two arguments of a binary operation not only need to live
2429 in the same C<isl_ctx>, they currently also need to have
2430 the same (number of) parameters.
2432 =head3 Basic Operations
2436 =item * Intersection
2438 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2439 __isl_take isl_basic_set *bset1,
2440 __isl_take isl_basic_set *bset2);
2441 __isl_give isl_basic_set *isl_basic_set_intersect(
2442 __isl_take isl_basic_set *bset1,
2443 __isl_take isl_basic_set *bset2);
2444 __isl_give isl_set *isl_set_intersect_params(
2445 __isl_take isl_set *set,
2446 __isl_take isl_set *params);
2447 __isl_give isl_set *isl_set_intersect(
2448 __isl_take isl_set *set1,
2449 __isl_take isl_set *set2);
2450 __isl_give isl_union_set *isl_union_set_intersect_params(
2451 __isl_take isl_union_set *uset,
2452 __isl_take isl_set *set);
2453 __isl_give isl_union_map *isl_union_map_intersect_params(
2454 __isl_take isl_union_map *umap,
2455 __isl_take isl_set *set);
2456 __isl_give isl_union_set *isl_union_set_intersect(
2457 __isl_take isl_union_set *uset1,
2458 __isl_take isl_union_set *uset2);
2459 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2460 __isl_take isl_basic_map *bmap,
2461 __isl_take isl_basic_set *bset);
2462 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2463 __isl_take isl_basic_map *bmap,
2464 __isl_take isl_basic_set *bset);
2465 __isl_give isl_basic_map *isl_basic_map_intersect(
2466 __isl_take isl_basic_map *bmap1,
2467 __isl_take isl_basic_map *bmap2);
2468 __isl_give isl_map *isl_map_intersect_params(
2469 __isl_take isl_map *map,
2470 __isl_take isl_set *params);
2471 __isl_give isl_map *isl_map_intersect_domain(
2472 __isl_take isl_map *map,
2473 __isl_take isl_set *set);
2474 __isl_give isl_map *isl_map_intersect_range(
2475 __isl_take isl_map *map,
2476 __isl_take isl_set *set);
2477 __isl_give isl_map *isl_map_intersect(
2478 __isl_take isl_map *map1,
2479 __isl_take isl_map *map2);
2480 __isl_give isl_union_map *isl_union_map_intersect_domain(
2481 __isl_take isl_union_map *umap,
2482 __isl_take isl_union_set *uset);
2483 __isl_give isl_union_map *isl_union_map_intersect_range(
2484 __isl_take isl_union_map *umap,
2485 __isl_take isl_union_set *uset);
2486 __isl_give isl_union_map *isl_union_map_intersect(
2487 __isl_take isl_union_map *umap1,
2488 __isl_take isl_union_map *umap2);
2490 The second argument to the C<_params> functions needs to be
2491 a parametric (basic) set. For the other functions, a parametric set
2492 for either argument is only allowed if the other argument is
2493 a parametric set as well.
2497 __isl_give isl_set *isl_basic_set_union(
2498 __isl_take isl_basic_set *bset1,
2499 __isl_take isl_basic_set *bset2);
2500 __isl_give isl_map *isl_basic_map_union(
2501 __isl_take isl_basic_map *bmap1,
2502 __isl_take isl_basic_map *bmap2);
2503 __isl_give isl_set *isl_set_union(
2504 __isl_take isl_set *set1,
2505 __isl_take isl_set *set2);
2506 __isl_give isl_map *isl_map_union(
2507 __isl_take isl_map *map1,
2508 __isl_take isl_map *map2);
2509 __isl_give isl_union_set *isl_union_set_union(
2510 __isl_take isl_union_set *uset1,
2511 __isl_take isl_union_set *uset2);
2512 __isl_give isl_union_map *isl_union_map_union(
2513 __isl_take isl_union_map *umap1,
2514 __isl_take isl_union_map *umap2);
2516 =item * Set difference
2518 __isl_give isl_set *isl_set_subtract(
2519 __isl_take isl_set *set1,
2520 __isl_take isl_set *set2);
2521 __isl_give isl_map *isl_map_subtract(
2522 __isl_take isl_map *map1,
2523 __isl_take isl_map *map2);
2524 __isl_give isl_map *isl_map_subtract_domain(
2525 __isl_take isl_map *map,
2526 __isl_take isl_set *dom);
2527 __isl_give isl_map *isl_map_subtract_range(
2528 __isl_take isl_map *map,
2529 __isl_take isl_set *dom);
2530 __isl_give isl_union_set *isl_union_set_subtract(
2531 __isl_take isl_union_set *uset1,
2532 __isl_take isl_union_set *uset2);
2533 __isl_give isl_union_map *isl_union_map_subtract(
2534 __isl_take isl_union_map *umap1,
2535 __isl_take isl_union_map *umap2);
2539 __isl_give isl_basic_set *isl_basic_set_apply(
2540 __isl_take isl_basic_set *bset,
2541 __isl_take isl_basic_map *bmap);
2542 __isl_give isl_set *isl_set_apply(
2543 __isl_take isl_set *set,
2544 __isl_take isl_map *map);
2545 __isl_give isl_union_set *isl_union_set_apply(
2546 __isl_take isl_union_set *uset,
2547 __isl_take isl_union_map *umap);
2548 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2549 __isl_take isl_basic_map *bmap1,
2550 __isl_take isl_basic_map *bmap2);
2551 __isl_give isl_basic_map *isl_basic_map_apply_range(
2552 __isl_take isl_basic_map *bmap1,
2553 __isl_take isl_basic_map *bmap2);
2554 __isl_give isl_map *isl_map_apply_domain(
2555 __isl_take isl_map *map1,
2556 __isl_take isl_map *map2);
2557 __isl_give isl_union_map *isl_union_map_apply_domain(
2558 __isl_take isl_union_map *umap1,
2559 __isl_take isl_union_map *umap2);
2560 __isl_give isl_map *isl_map_apply_range(
2561 __isl_take isl_map *map1,
2562 __isl_take isl_map *map2);
2563 __isl_give isl_union_map *isl_union_map_apply_range(
2564 __isl_take isl_union_map *umap1,
2565 __isl_take isl_union_map *umap2);
2567 =item * Cartesian Product
2569 __isl_give isl_set *isl_set_product(
2570 __isl_take isl_set *set1,
2571 __isl_take isl_set *set2);
2572 __isl_give isl_union_set *isl_union_set_product(
2573 __isl_take isl_union_set *uset1,
2574 __isl_take isl_union_set *uset2);
2575 __isl_give isl_basic_map *isl_basic_map_domain_product(
2576 __isl_take isl_basic_map *bmap1,
2577 __isl_take isl_basic_map *bmap2);
2578 __isl_give isl_basic_map *isl_basic_map_range_product(
2579 __isl_take isl_basic_map *bmap1,
2580 __isl_take isl_basic_map *bmap2);
2581 __isl_give isl_map *isl_map_domain_product(
2582 __isl_take isl_map *map1,
2583 __isl_take isl_map *map2);
2584 __isl_give isl_map *isl_map_range_product(
2585 __isl_take isl_map *map1,
2586 __isl_take isl_map *map2);
2587 __isl_give isl_union_map *isl_union_map_range_product(
2588 __isl_take isl_union_map *umap1,
2589 __isl_take isl_union_map *umap2);
2590 __isl_give isl_map *isl_map_product(
2591 __isl_take isl_map *map1,
2592 __isl_take isl_map *map2);
2593 __isl_give isl_union_map *isl_union_map_product(
2594 __isl_take isl_union_map *umap1,
2595 __isl_take isl_union_map *umap2);
2597 The above functions compute the cross product of the given
2598 sets or relations. The domains and ranges of the results
2599 are wrapped maps between domains and ranges of the inputs.
2600 To obtain a ``flat'' product, use the following functions
2603 __isl_give isl_basic_set *isl_basic_set_flat_product(
2604 __isl_take isl_basic_set *bset1,
2605 __isl_take isl_basic_set *bset2);
2606 __isl_give isl_set *isl_set_flat_product(
2607 __isl_take isl_set *set1,
2608 __isl_take isl_set *set2);
2609 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2610 __isl_take isl_basic_map *bmap1,
2611 __isl_take isl_basic_map *bmap2);
2612 __isl_give isl_map *isl_map_flat_domain_product(
2613 __isl_take isl_map *map1,
2614 __isl_take isl_map *map2);
2615 __isl_give isl_map *isl_map_flat_range_product(
2616 __isl_take isl_map *map1,
2617 __isl_take isl_map *map2);
2618 __isl_give isl_union_map *isl_union_map_flat_range_product(
2619 __isl_take isl_union_map *umap1,
2620 __isl_take isl_union_map *umap2);
2621 __isl_give isl_basic_map *isl_basic_map_flat_product(
2622 __isl_take isl_basic_map *bmap1,
2623 __isl_take isl_basic_map *bmap2);
2624 __isl_give isl_map *isl_map_flat_product(
2625 __isl_take isl_map *map1,
2626 __isl_take isl_map *map2);
2628 =item * Simplification
2630 __isl_give isl_basic_set *isl_basic_set_gist(
2631 __isl_take isl_basic_set *bset,
2632 __isl_take isl_basic_set *context);
2633 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2634 __isl_take isl_set *context);
2635 __isl_give isl_set *isl_set_gist_params(
2636 __isl_take isl_set *set,
2637 __isl_take isl_set *context);
2638 __isl_give isl_union_set *isl_union_set_gist(
2639 __isl_take isl_union_set *uset,
2640 __isl_take isl_union_set *context);
2641 __isl_give isl_union_set *isl_union_set_gist_params(
2642 __isl_take isl_union_set *uset,
2643 __isl_take isl_set *set);
2644 __isl_give isl_basic_map *isl_basic_map_gist(
2645 __isl_take isl_basic_map *bmap,
2646 __isl_take isl_basic_map *context);
2647 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2648 __isl_take isl_map *context);
2649 __isl_give isl_map *isl_map_gist_params(
2650 __isl_take isl_map *map,
2651 __isl_take isl_set *context);
2652 __isl_give isl_map *isl_map_gist_domain(
2653 __isl_take isl_map *map,
2654 __isl_take isl_set *context);
2655 __isl_give isl_map *isl_map_gist_range(
2656 __isl_take isl_map *map,
2657 __isl_take isl_set *context);
2658 __isl_give isl_union_map *isl_union_map_gist(
2659 __isl_take isl_union_map *umap,
2660 __isl_take isl_union_map *context);
2661 __isl_give isl_union_map *isl_union_map_gist_params(
2662 __isl_take isl_union_map *umap,
2663 __isl_take isl_set *set);
2664 __isl_give isl_union_map *isl_union_map_gist_domain(
2665 __isl_take isl_union_map *umap,
2666 __isl_take isl_union_set *uset);
2667 __isl_give isl_union_map *isl_union_map_gist_range(
2668 __isl_take isl_union_map *umap,
2669 __isl_take isl_union_set *uset);
2671 The gist operation returns a set or relation that has the
2672 same intersection with the context as the input set or relation.
2673 Any implicit equality in the intersection is made explicit in the result,
2674 while all inequalities that are redundant with respect to the intersection
2676 In case of union sets and relations, the gist operation is performed
2681 =head3 Lexicographic Optimization
2683 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2684 the following functions
2685 compute a set that contains the lexicographic minimum or maximum
2686 of the elements in C<set> (or C<bset>) for those values of the parameters
2687 that satisfy C<dom>.
2688 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2689 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2691 In other words, the union of the parameter values
2692 for which the result is non-empty and of C<*empty>
2695 __isl_give isl_set *isl_basic_set_partial_lexmin(
2696 __isl_take isl_basic_set *bset,
2697 __isl_take isl_basic_set *dom,
2698 __isl_give isl_set **empty);
2699 __isl_give isl_set *isl_basic_set_partial_lexmax(
2700 __isl_take isl_basic_set *bset,
2701 __isl_take isl_basic_set *dom,
2702 __isl_give isl_set **empty);
2703 __isl_give isl_set *isl_set_partial_lexmin(
2704 __isl_take isl_set *set, __isl_take isl_set *dom,
2705 __isl_give isl_set **empty);
2706 __isl_give isl_set *isl_set_partial_lexmax(
2707 __isl_take isl_set *set, __isl_take isl_set *dom,
2708 __isl_give isl_set **empty);
2710 Given a (basic) set C<set> (or C<bset>), the following functions simply
2711 return a set containing the lexicographic minimum or maximum
2712 of the elements in C<set> (or C<bset>).
2713 In case of union sets, the optimum is computed per space.
2715 __isl_give isl_set *isl_basic_set_lexmin(
2716 __isl_take isl_basic_set *bset);
2717 __isl_give isl_set *isl_basic_set_lexmax(
2718 __isl_take isl_basic_set *bset);
2719 __isl_give isl_set *isl_set_lexmin(
2720 __isl_take isl_set *set);
2721 __isl_give isl_set *isl_set_lexmax(
2722 __isl_take isl_set *set);
2723 __isl_give isl_union_set *isl_union_set_lexmin(
2724 __isl_take isl_union_set *uset);
2725 __isl_give isl_union_set *isl_union_set_lexmax(
2726 __isl_take isl_union_set *uset);
2728 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2729 the following functions
2730 compute a relation that maps each element of C<dom>
2731 to the single lexicographic minimum or maximum
2732 of the elements that are associated to that same
2733 element in C<map> (or C<bmap>).
2734 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2735 that contains the elements in C<dom> that do not map
2736 to any elements in C<map> (or C<bmap>).
2737 In other words, the union of the domain of the result and of C<*empty>
2740 __isl_give isl_map *isl_basic_map_partial_lexmax(
2741 __isl_take isl_basic_map *bmap,
2742 __isl_take isl_basic_set *dom,
2743 __isl_give isl_set **empty);
2744 __isl_give isl_map *isl_basic_map_partial_lexmin(
2745 __isl_take isl_basic_map *bmap,
2746 __isl_take isl_basic_set *dom,
2747 __isl_give isl_set **empty);
2748 __isl_give isl_map *isl_map_partial_lexmax(
2749 __isl_take isl_map *map, __isl_take isl_set *dom,
2750 __isl_give isl_set **empty);
2751 __isl_give isl_map *isl_map_partial_lexmin(
2752 __isl_take isl_map *map, __isl_take isl_set *dom,
2753 __isl_give isl_set **empty);
2755 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2756 return a map mapping each element in the domain of
2757 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2758 of all elements associated to that element.
2759 In case of union relations, the optimum is computed per space.
2761 __isl_give isl_map *isl_basic_map_lexmin(
2762 __isl_take isl_basic_map *bmap);
2763 __isl_give isl_map *isl_basic_map_lexmax(
2764 __isl_take isl_basic_map *bmap);
2765 __isl_give isl_map *isl_map_lexmin(
2766 __isl_take isl_map *map);
2767 __isl_give isl_map *isl_map_lexmax(
2768 __isl_take isl_map *map);
2769 __isl_give isl_union_map *isl_union_map_lexmin(
2770 __isl_take isl_union_map *umap);
2771 __isl_give isl_union_map *isl_union_map_lexmax(
2772 __isl_take isl_union_map *umap);
2774 The following functions return their result in the form of
2775 a piecewise multi-affine expression
2776 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2777 but are otherwise equivalent to the corresponding functions
2778 returning a basic set or relation.
2780 __isl_give isl_pw_multi_aff *
2781 isl_basic_map_lexmin_pw_multi_aff(
2782 __isl_take isl_basic_map *bmap);
2783 __isl_give isl_pw_multi_aff *
2784 isl_basic_set_partial_lexmin_pw_multi_aff(
2785 __isl_take isl_basic_set *bset,
2786 __isl_take isl_basic_set *dom,
2787 __isl_give isl_set **empty);
2788 __isl_give isl_pw_multi_aff *
2789 isl_basic_set_partial_lexmax_pw_multi_aff(
2790 __isl_take isl_basic_set *bset,
2791 __isl_take isl_basic_set *dom,
2792 __isl_give isl_set **empty);
2793 __isl_give isl_pw_multi_aff *
2794 isl_basic_map_partial_lexmin_pw_multi_aff(
2795 __isl_take isl_basic_map *bmap,
2796 __isl_take isl_basic_set *dom,
2797 __isl_give isl_set **empty);
2798 __isl_give isl_pw_multi_aff *
2799 isl_basic_map_partial_lexmax_pw_multi_aff(
2800 __isl_take isl_basic_map *bmap,
2801 __isl_take isl_basic_set *dom,
2802 __isl_give isl_set **empty);
2806 Lists are defined over several element types, including
2807 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2808 Here we take lists of C<isl_set>s as an example.
2809 Lists can be created, copied and freed using the following functions.
2811 #include <isl/list.h>
2812 __isl_give isl_set_list *isl_set_list_from_set(
2813 __isl_take isl_set *el);
2814 __isl_give isl_set_list *isl_set_list_alloc(
2815 isl_ctx *ctx, int n);
2816 __isl_give isl_set_list *isl_set_list_copy(
2817 __isl_keep isl_set_list *list);
2818 __isl_give isl_set_list *isl_set_list_add(
2819 __isl_take isl_set_list *list,
2820 __isl_take isl_set *el);
2821 __isl_give isl_set_list *isl_set_list_concat(
2822 __isl_take isl_set_list *list1,
2823 __isl_take isl_set_list *list2);
2824 void *isl_set_list_free(__isl_take isl_set_list *list);
2826 C<isl_set_list_alloc> creates an empty list with a capacity for
2827 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2830 Lists can be inspected using the following functions.
2832 #include <isl/list.h>
2833 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2834 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2835 __isl_give isl_set *isl_set_list_get_set(
2836 __isl_keep isl_set_list *list, int index);
2837 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2838 int (*fn)(__isl_take isl_set *el, void *user),
2841 Lists can be printed using
2843 #include <isl/list.h>
2844 __isl_give isl_printer *isl_printer_print_set_list(
2845 __isl_take isl_printer *p,
2846 __isl_keep isl_set_list *list);
2850 Vectors can be created, copied and freed using the following functions.
2852 #include <isl/vec.h>
2853 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2855 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2856 void isl_vec_free(__isl_take isl_vec *vec);
2858 Note that the elements of a newly created vector may have arbitrary values.
2859 The elements can be changed and inspected using the following functions.
2861 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2862 int isl_vec_size(__isl_keep isl_vec *vec);
2863 int isl_vec_get_element(__isl_keep isl_vec *vec,
2864 int pos, isl_int *v);
2865 __isl_give isl_vec *isl_vec_set_element(
2866 __isl_take isl_vec *vec, int pos, isl_int v);
2867 __isl_give isl_vec *isl_vec_set_element_si(
2868 __isl_take isl_vec *vec, int pos, int v);
2869 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2871 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2874 C<isl_vec_get_element> will return a negative value if anything went wrong.
2875 In that case, the value of C<*v> is undefined.
2879 Matrices can be created, copied and freed using the following functions.
2881 #include <isl/mat.h>
2882 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2883 unsigned n_row, unsigned n_col);
2884 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2885 void isl_mat_free(__isl_take isl_mat *mat);
2887 Note that the elements of a newly created matrix may have arbitrary values.
2888 The elements can be changed and inspected using the following functions.
2890 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2891 int isl_mat_rows(__isl_keep isl_mat *mat);
2892 int isl_mat_cols(__isl_keep isl_mat *mat);
2893 int isl_mat_get_element(__isl_keep isl_mat *mat,
2894 int row, int col, isl_int *v);
2895 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2896 int row, int col, isl_int v);
2897 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2898 int row, int col, int v);
2900 C<isl_mat_get_element> will return a negative value if anything went wrong.
2901 In that case, the value of C<*v> is undefined.
2903 The following function can be used to compute the (right) inverse
2904 of a matrix, i.e., a matrix such that the product of the original
2905 and the inverse (in that order) is a multiple of the identity matrix.
2906 The input matrix is assumed to be of full row-rank.
2908 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2910 The following function can be used to compute the (right) kernel
2911 (or null space) of a matrix, i.e., a matrix such that the product of
2912 the original and the kernel (in that order) is the zero matrix.
2914 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2916 =head2 Piecewise Quasi Affine Expressions
2918 The zero quasi affine expression on a given domain can be created using
2920 __isl_give isl_aff *isl_aff_zero_on_domain(
2921 __isl_take isl_local_space *ls);
2923 Note that the space in which the resulting object lives is a map space
2924 with the given space as domain and a one-dimensional range.
2926 An empty piecewise quasi affine expression (one with no cells)
2927 or a piecewise quasi affine expression with a single cell can
2928 be created using the following functions.
2930 #include <isl/aff.h>
2931 __isl_give isl_pw_aff *isl_pw_aff_empty(
2932 __isl_take isl_space *space);
2933 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2934 __isl_take isl_set *set, __isl_take isl_aff *aff);
2935 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2936 __isl_take isl_aff *aff);
2938 A piecewise quasi affine expression that is equal to 1 on a set
2939 and 0 outside the set can be created using the following function.
2941 #include <isl/aff.h>
2942 __isl_give isl_pw_aff *isl_set_indicator_function(
2943 __isl_take isl_set *set);
2945 Quasi affine expressions can be copied and freed using
2947 #include <isl/aff.h>
2948 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2949 void *isl_aff_free(__isl_take isl_aff *aff);
2951 __isl_give isl_pw_aff *isl_pw_aff_copy(
2952 __isl_keep isl_pw_aff *pwaff);
2953 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2955 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2956 using the following function. The constraint is required to have
2957 a non-zero coefficient for the specified dimension.
2959 #include <isl/constraint.h>
2960 __isl_give isl_aff *isl_constraint_get_bound(
2961 __isl_keep isl_constraint *constraint,
2962 enum isl_dim_type type, int pos);
2964 The entire affine expression of the constraint can also be extracted
2965 using the following function.
2967 #include <isl/constraint.h>
2968 __isl_give isl_aff *isl_constraint_get_aff(
2969 __isl_keep isl_constraint *constraint);
2971 Conversely, an equality constraint equating
2972 the affine expression to zero or an inequality constraint enforcing
2973 the affine expression to be non-negative, can be constructed using
2975 __isl_give isl_constraint *isl_equality_from_aff(
2976 __isl_take isl_aff *aff);
2977 __isl_give isl_constraint *isl_inequality_from_aff(
2978 __isl_take isl_aff *aff);
2980 The expression can be inspected using
2982 #include <isl/aff.h>
2983 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2984 int isl_aff_dim(__isl_keep isl_aff *aff,
2985 enum isl_dim_type type);
2986 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2987 __isl_keep isl_aff *aff);
2988 __isl_give isl_local_space *isl_aff_get_local_space(
2989 __isl_keep isl_aff *aff);
2990 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2991 enum isl_dim_type type, unsigned pos);
2992 const char *isl_pw_aff_get_dim_name(
2993 __isl_keep isl_pw_aff *pa,
2994 enum isl_dim_type type, unsigned pos);
2995 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2996 enum isl_dim_type type, unsigned pos);
2997 __isl_give isl_id *isl_pw_aff_get_dim_id(
2998 __isl_keep isl_pw_aff *pa,
2999 enum isl_dim_type type, unsigned pos);
3000 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3002 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3003 enum isl_dim_type type, int pos, isl_int *v);
3004 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3006 __isl_give isl_aff *isl_aff_get_div(
3007 __isl_keep isl_aff *aff, int pos);
3009 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3010 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3011 int (*fn)(__isl_take isl_set *set,
3012 __isl_take isl_aff *aff,
3013 void *user), void *user);
3015 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3016 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3018 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3019 enum isl_dim_type type, unsigned first, unsigned n);
3020 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3021 enum isl_dim_type type, unsigned first, unsigned n);
3023 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3024 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3025 enum isl_dim_type type);
3026 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3028 It can be modified using
3030 #include <isl/aff.h>
3031 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3032 __isl_take isl_pw_aff *pwaff,
3033 enum isl_dim_type type, __isl_take isl_id *id);
3034 __isl_give isl_aff *isl_aff_set_dim_name(
3035 __isl_take isl_aff *aff, enum isl_dim_type type,
3036 unsigned pos, const char *s);
3037 __isl_give isl_aff *isl_aff_set_dim_id(
3038 __isl_take isl_aff *aff, enum isl_dim_type type,
3039 unsigned pos, __isl_take isl_id *id);
3040 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3041 __isl_take isl_pw_aff *pma,
3042 enum isl_dim_type type, unsigned pos,
3043 __isl_take isl_id *id);
3044 __isl_give isl_aff *isl_aff_set_constant(
3045 __isl_take isl_aff *aff, isl_int v);
3046 __isl_give isl_aff *isl_aff_set_constant_si(
3047 __isl_take isl_aff *aff, int v);
3048 __isl_give isl_aff *isl_aff_set_coefficient(
3049 __isl_take isl_aff *aff,
3050 enum isl_dim_type type, int pos, isl_int v);
3051 __isl_give isl_aff *isl_aff_set_coefficient_si(
3052 __isl_take isl_aff *aff,
3053 enum isl_dim_type type, int pos, int v);
3054 __isl_give isl_aff *isl_aff_set_denominator(
3055 __isl_take isl_aff *aff, isl_int v);
3057 __isl_give isl_aff *isl_aff_add_constant(
3058 __isl_take isl_aff *aff, isl_int v);
3059 __isl_give isl_aff *isl_aff_add_constant_si(
3060 __isl_take isl_aff *aff, int v);
3061 __isl_give isl_aff *isl_aff_add_coefficient(
3062 __isl_take isl_aff *aff,
3063 enum isl_dim_type type, int pos, isl_int v);
3064 __isl_give isl_aff *isl_aff_add_coefficient_si(
3065 __isl_take isl_aff *aff,
3066 enum isl_dim_type type, int pos, int v);
3068 __isl_give isl_aff *isl_aff_insert_dims(
3069 __isl_take isl_aff *aff,
3070 enum isl_dim_type type, unsigned first, unsigned n);
3071 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3072 __isl_take isl_pw_aff *pwaff,
3073 enum isl_dim_type type, unsigned first, unsigned n);
3074 __isl_give isl_aff *isl_aff_add_dims(
3075 __isl_take isl_aff *aff,
3076 enum isl_dim_type type, unsigned n);
3077 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3078 __isl_take isl_pw_aff *pwaff,
3079 enum isl_dim_type type, unsigned n);
3080 __isl_give isl_aff *isl_aff_drop_dims(
3081 __isl_take isl_aff *aff,
3082 enum isl_dim_type type, unsigned first, unsigned n);
3083 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3084 __isl_take isl_pw_aff *pwaff,
3085 enum isl_dim_type type, unsigned first, unsigned n);
3087 Note that the C<set_constant> and C<set_coefficient> functions
3088 set the I<numerator> of the constant or coefficient, while
3089 C<add_constant> and C<add_coefficient> add an integer value to
3090 the possibly rational constant or coefficient.
3092 To check whether an affine expressions is obviously zero
3093 or obviously equal to some other affine expression, use
3095 #include <isl/aff.h>
3096 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3097 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3098 __isl_keep isl_aff *aff2);
3099 int isl_pw_aff_plain_is_equal(
3100 __isl_keep isl_pw_aff *pwaff1,
3101 __isl_keep isl_pw_aff *pwaff2);
3105 #include <isl/aff.h>
3106 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3107 __isl_take isl_aff *aff2);
3108 __isl_give isl_pw_aff *isl_pw_aff_add(
3109 __isl_take isl_pw_aff *pwaff1,
3110 __isl_take isl_pw_aff *pwaff2);
3111 __isl_give isl_pw_aff *isl_pw_aff_min(
3112 __isl_take isl_pw_aff *pwaff1,
3113 __isl_take isl_pw_aff *pwaff2);
3114 __isl_give isl_pw_aff *isl_pw_aff_max(
3115 __isl_take isl_pw_aff *pwaff1,
3116 __isl_take isl_pw_aff *pwaff2);
3117 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3118 __isl_take isl_aff *aff2);
3119 __isl_give isl_pw_aff *isl_pw_aff_sub(
3120 __isl_take isl_pw_aff *pwaff1,
3121 __isl_take isl_pw_aff *pwaff2);
3122 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3123 __isl_give isl_pw_aff *isl_pw_aff_neg(
3124 __isl_take isl_pw_aff *pwaff);
3125 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3126 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3127 __isl_take isl_pw_aff *pwaff);
3128 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3129 __isl_give isl_pw_aff *isl_pw_aff_floor(
3130 __isl_take isl_pw_aff *pwaff);
3131 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3133 __isl_give isl_pw_aff *isl_pw_aff_mod(
3134 __isl_take isl_pw_aff *pwaff, isl_int mod);
3135 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3137 __isl_give isl_pw_aff *isl_pw_aff_scale(
3138 __isl_take isl_pw_aff *pwaff, isl_int f);
3139 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3141 __isl_give isl_aff *isl_aff_scale_down_ui(
3142 __isl_take isl_aff *aff, unsigned f);
3143 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3144 __isl_take isl_pw_aff *pwaff, isl_int f);
3146 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3147 __isl_take isl_pw_aff_list *list);
3148 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3149 __isl_take isl_pw_aff_list *list);
3151 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3152 __isl_take isl_pw_aff *pwqp);
3154 __isl_give isl_aff *isl_aff_align_params(
3155 __isl_take isl_aff *aff,
3156 __isl_take isl_space *model);
3157 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3158 __isl_take isl_pw_aff *pwaff,
3159 __isl_take isl_space *model);
3161 __isl_give isl_aff *isl_aff_project_domain_on_params(
3162 __isl_take isl_aff *aff);
3164 __isl_give isl_aff *isl_aff_gist_params(
3165 __isl_take isl_aff *aff,
3166 __isl_take isl_set *context);
3167 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3168 __isl_take isl_set *context);
3169 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3170 __isl_take isl_pw_aff *pwaff,
3171 __isl_take isl_set *context);
3172 __isl_give isl_pw_aff *isl_pw_aff_gist(
3173 __isl_take isl_pw_aff *pwaff,
3174 __isl_take isl_set *context);
3176 __isl_give isl_set *isl_pw_aff_domain(
3177 __isl_take isl_pw_aff *pwaff);
3178 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3179 __isl_take isl_pw_aff *pa,
3180 __isl_take isl_set *set);
3181 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3182 __isl_take isl_pw_aff *pa,
3183 __isl_take isl_set *set);
3185 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3186 __isl_take isl_aff *aff2);
3187 __isl_give isl_pw_aff *isl_pw_aff_mul(
3188 __isl_take isl_pw_aff *pwaff1,
3189 __isl_take isl_pw_aff *pwaff2);
3191 When multiplying two affine expressions, at least one of the two needs
3194 #include <isl/aff.h>
3195 __isl_give isl_basic_set *isl_aff_le_basic_set(
3196 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3197 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3198 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3199 __isl_give isl_set *isl_pw_aff_eq_set(
3200 __isl_take isl_pw_aff *pwaff1,
3201 __isl_take isl_pw_aff *pwaff2);
3202 __isl_give isl_set *isl_pw_aff_ne_set(
3203 __isl_take isl_pw_aff *pwaff1,
3204 __isl_take isl_pw_aff *pwaff2);
3205 __isl_give isl_set *isl_pw_aff_le_set(
3206 __isl_take isl_pw_aff *pwaff1,
3207 __isl_take isl_pw_aff *pwaff2);
3208 __isl_give isl_set *isl_pw_aff_lt_set(
3209 __isl_take isl_pw_aff *pwaff1,
3210 __isl_take isl_pw_aff *pwaff2);
3211 __isl_give isl_set *isl_pw_aff_ge_set(
3212 __isl_take isl_pw_aff *pwaff1,
3213 __isl_take isl_pw_aff *pwaff2);
3214 __isl_give isl_set *isl_pw_aff_gt_set(
3215 __isl_take isl_pw_aff *pwaff1,
3216 __isl_take isl_pw_aff *pwaff2);
3218 __isl_give isl_set *isl_pw_aff_list_eq_set(
3219 __isl_take isl_pw_aff_list *list1,
3220 __isl_take isl_pw_aff_list *list2);
3221 __isl_give isl_set *isl_pw_aff_list_ne_set(
3222 __isl_take isl_pw_aff_list *list1,
3223 __isl_take isl_pw_aff_list *list2);
3224 __isl_give isl_set *isl_pw_aff_list_le_set(
3225 __isl_take isl_pw_aff_list *list1,
3226 __isl_take isl_pw_aff_list *list2);
3227 __isl_give isl_set *isl_pw_aff_list_lt_set(
3228 __isl_take isl_pw_aff_list *list1,
3229 __isl_take isl_pw_aff_list *list2);
3230 __isl_give isl_set *isl_pw_aff_list_ge_set(
3231 __isl_take isl_pw_aff_list *list1,
3232 __isl_take isl_pw_aff_list *list2);
3233 __isl_give isl_set *isl_pw_aff_list_gt_set(
3234 __isl_take isl_pw_aff_list *list1,
3235 __isl_take isl_pw_aff_list *list2);
3237 The function C<isl_aff_ge_basic_set> returns a basic set
3238 containing those elements in the shared space
3239 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3240 The function C<isl_pw_aff_ge_set> returns a set
3241 containing those elements in the shared domain
3242 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3243 The functions operating on C<isl_pw_aff_list> apply the corresponding
3244 C<isl_pw_aff> function to each pair of elements in the two lists.
3246 #include <isl/aff.h>
3247 __isl_give isl_set *isl_pw_aff_nonneg_set(
3248 __isl_take isl_pw_aff *pwaff);
3249 __isl_give isl_set *isl_pw_aff_zero_set(
3250 __isl_take isl_pw_aff *pwaff);
3251 __isl_give isl_set *isl_pw_aff_non_zero_set(
3252 __isl_take isl_pw_aff *pwaff);
3254 The function C<isl_pw_aff_nonneg_set> returns a set
3255 containing those elements in the domain
3256 of C<pwaff> where C<pwaff> is non-negative.
3258 #include <isl/aff.h>
3259 __isl_give isl_pw_aff *isl_pw_aff_cond(
3260 __isl_take isl_pw_aff *cond,
3261 __isl_take isl_pw_aff *pwaff_true,
3262 __isl_take isl_pw_aff *pwaff_false);
3264 The function C<isl_pw_aff_cond> performs a conditional operator
3265 and returns an expression that is equal to C<pwaff_true>
3266 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3267 where C<cond> is zero.
3269 #include <isl/aff.h>
3270 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3271 __isl_take isl_pw_aff *pwaff1,
3272 __isl_take isl_pw_aff *pwaff2);
3273 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3274 __isl_take isl_pw_aff *pwaff1,
3275 __isl_take isl_pw_aff *pwaff2);
3276 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3277 __isl_take isl_pw_aff *pwaff1,
3278 __isl_take isl_pw_aff *pwaff2);
3280 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3281 expression with a domain that is the union of those of C<pwaff1> and
3282 C<pwaff2> and such that on each cell, the quasi-affine expression is
3283 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3284 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3285 associated expression is the defined one.
3287 An expression can be read from input using
3289 #include <isl/aff.h>
3290 __isl_give isl_aff *isl_aff_read_from_str(
3291 isl_ctx *ctx, const char *str);
3292 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3293 isl_ctx *ctx, const char *str);
3295 An expression can be printed using
3297 #include <isl/aff.h>
3298 __isl_give isl_printer *isl_printer_print_aff(
3299 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3301 __isl_give isl_printer *isl_printer_print_pw_aff(
3302 __isl_take isl_printer *p,
3303 __isl_keep isl_pw_aff *pwaff);
3305 =head2 Piecewise Multiple Quasi Affine Expressions
3307 An C<isl_multi_aff> object represents a sequence of
3308 zero or more affine expressions, all defined on the same domain space.
3310 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3313 #include <isl/aff.h>
3314 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3315 __isl_take isl_space *space,
3316 __isl_take isl_aff_list *list);
3318 An empty piecewise multiple quasi affine expression (one with no cells),
3319 the zero piecewise multiple quasi affine expression (with value zero
3320 for each output dimension),
3321 a piecewise multiple quasi affine expression with a single cell (with
3322 either a universe or a specified domain) or
3323 a zero-dimensional piecewise multiple quasi affine expression
3325 can be created using the following functions.
3327 #include <isl/aff.h>
3328 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3329 __isl_take isl_space *space);
3330 __isl_give isl_multi_aff *isl_multi_aff_zero(
3331 __isl_take isl_space *space);
3332 __isl_give isl_pw_multi_aff *
3333 isl_pw_multi_aff_from_multi_aff(
3334 __isl_take isl_multi_aff *ma);
3335 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3336 __isl_take isl_set *set,
3337 __isl_take isl_multi_aff *maff);
3338 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3339 __isl_take isl_set *set);
3341 __isl_give isl_union_pw_multi_aff *
3342 isl_union_pw_multi_aff_empty(
3343 __isl_take isl_space *space);
3344 __isl_give isl_union_pw_multi_aff *
3345 isl_union_pw_multi_aff_add_pw_multi_aff(
3346 __isl_take isl_union_pw_multi_aff *upma,
3347 __isl_take isl_pw_multi_aff *pma);
3348 __isl_give isl_union_pw_multi_aff *
3349 isl_union_pw_multi_aff_from_domain(
3350 __isl_take isl_union_set *uset);
3352 A piecewise multiple quasi affine expression can also be initialized
3353 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3354 and the C<isl_map> is single-valued.
3356 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3357 __isl_take isl_set *set);
3358 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3359 __isl_take isl_map *map);
3361 Multiple quasi affine expressions can be copied and freed using
3363 #include <isl/aff.h>
3364 __isl_give isl_multi_aff *isl_multi_aff_copy(
3365 __isl_keep isl_multi_aff *maff);
3366 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3368 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3369 __isl_keep isl_pw_multi_aff *pma);
3370 void *isl_pw_multi_aff_free(
3371 __isl_take isl_pw_multi_aff *pma);
3373 __isl_give isl_union_pw_multi_aff *
3374 isl_union_pw_multi_aff_copy(
3375 __isl_keep isl_union_pw_multi_aff *upma);
3376 void *isl_union_pw_multi_aff_free(
3377 __isl_take isl_union_pw_multi_aff *upma);
3379 The expression can be inspected using
3381 #include <isl/aff.h>
3382 isl_ctx *isl_multi_aff_get_ctx(
3383 __isl_keep isl_multi_aff *maff);
3384 isl_ctx *isl_pw_multi_aff_get_ctx(
3385 __isl_keep isl_pw_multi_aff *pma);
3386 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3387 __isl_keep isl_union_pw_multi_aff *upma);
3388 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3389 enum isl_dim_type type);
3390 unsigned isl_pw_multi_aff_dim(
3391 __isl_keep isl_pw_multi_aff *pma,
3392 enum isl_dim_type type);
3393 __isl_give isl_aff *isl_multi_aff_get_aff(
3394 __isl_keep isl_multi_aff *multi, int pos);
3395 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3396 __isl_keep isl_pw_multi_aff *pma, int pos);
3397 const char *isl_pw_multi_aff_get_dim_name(
3398 __isl_keep isl_pw_multi_aff *pma,
3399 enum isl_dim_type type, unsigned pos);
3400 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3401 __isl_keep isl_pw_multi_aff *pma,
3402 enum isl_dim_type type, unsigned pos);
3403 const char *isl_multi_aff_get_tuple_name(
3404 __isl_keep isl_multi_aff *multi,
3405 enum isl_dim_type type);
3406 const char *isl_pw_multi_aff_get_tuple_name(
3407 __isl_keep isl_pw_multi_aff *pma,
3408 enum isl_dim_type type);
3409 int isl_pw_multi_aff_has_tuple_id(
3410 __isl_keep isl_pw_multi_aff *pma,
3411 enum isl_dim_type type);
3412 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3413 __isl_keep isl_pw_multi_aff *pma,
3414 enum isl_dim_type type);
3416 int isl_pw_multi_aff_foreach_piece(
3417 __isl_keep isl_pw_multi_aff *pma,
3418 int (*fn)(__isl_take isl_set *set,
3419 __isl_take isl_multi_aff *maff,
3420 void *user), void *user);
3422 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3423 __isl_keep isl_union_pw_multi_aff *upma,
3424 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3425 void *user), void *user);
3427 It can be modified using
3429 #include <isl/aff.h>
3430 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3431 __isl_take isl_multi_aff *multi, int pos,
3432 __isl_take isl_aff *aff);
3433 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3434 __isl_take isl_multi_aff *maff,
3435 enum isl_dim_type type, unsigned pos, const char *s);
3436 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3437 __isl_take isl_multi_aff *maff,
3438 enum isl_dim_type type, __isl_take isl_id *id);
3439 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3440 __isl_take isl_pw_multi_aff *pma,
3441 enum isl_dim_type type, __isl_take isl_id *id);
3443 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3444 __isl_take isl_multi_aff *maff,
3445 enum isl_dim_type type, unsigned first, unsigned n);
3447 To check whether two multiple affine expressions are
3448 obviously equal to each other, use
3450 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3451 __isl_keep isl_multi_aff *maff2);
3452 int isl_pw_multi_aff_plain_is_equal(
3453 __isl_keep isl_pw_multi_aff *pma1,
3454 __isl_keep isl_pw_multi_aff *pma2);
3458 #include <isl/aff.h>
3459 __isl_give isl_multi_aff *isl_multi_aff_add(
3460 __isl_take isl_multi_aff *maff1,
3461 __isl_take isl_multi_aff *maff2);
3462 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3463 __isl_take isl_pw_multi_aff *pma1,
3464 __isl_take isl_pw_multi_aff *pma2);
3465 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3466 __isl_take isl_union_pw_multi_aff *upma1,
3467 __isl_take isl_union_pw_multi_aff *upma2);
3468 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3469 __isl_take isl_pw_multi_aff *pma1,
3470 __isl_take isl_pw_multi_aff *pma2);
3471 __isl_give isl_multi_aff *isl_multi_aff_scale(
3472 __isl_take isl_multi_aff *maff,
3474 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3475 __isl_take isl_pw_multi_aff *pma,
3476 __isl_take isl_set *set);
3477 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3478 __isl_take isl_pw_multi_aff *pma,
3479 __isl_take isl_set *set);
3480 __isl_give isl_multi_aff *isl_multi_aff_lift(
3481 __isl_take isl_multi_aff *maff,
3482 __isl_give isl_local_space **ls);
3483 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3484 __isl_take isl_pw_multi_aff *pma);
3485 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3486 __isl_take isl_multi_aff *maff,
3487 __isl_take isl_set *context);
3488 __isl_give isl_multi_aff *isl_multi_aff_gist(
3489 __isl_take isl_multi_aff *maff,
3490 __isl_take isl_set *context);
3491 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3492 __isl_take isl_pw_multi_aff *pma,
3493 __isl_take isl_set *set);
3494 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3495 __isl_take isl_pw_multi_aff *pma,
3496 __isl_take isl_set *set);
3497 __isl_give isl_set *isl_pw_multi_aff_domain(
3498 __isl_take isl_pw_multi_aff *pma);
3499 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3500 __isl_take isl_union_pw_multi_aff *upma);
3501 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3502 __isl_take isl_multi_aff *ma1,
3503 __isl_take isl_multi_aff *ma2);
3504 __isl_give isl_pw_multi_aff *
3505 isl_pw_multi_aff_flat_range_product(
3506 __isl_take isl_pw_multi_aff *pma1,
3507 __isl_take isl_pw_multi_aff *pma2);
3508 __isl_give isl_union_pw_multi_aff *
3509 isl_union_pw_multi_aff_flat_range_product(
3510 __isl_take isl_union_pw_multi_aff *upma1,
3511 __isl_take isl_union_pw_multi_aff *upma2);
3513 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3514 then it is assigned the local space that lies at the basis of
3515 the lifting applied.
3517 An expression can be read from input using
3519 #include <isl/aff.h>
3520 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3521 isl_ctx *ctx, const char *str);
3522 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3523 isl_ctx *ctx, const char *str);
3525 An expression can be printed using
3527 #include <isl/aff.h>
3528 __isl_give isl_printer *isl_printer_print_multi_aff(
3529 __isl_take isl_printer *p,
3530 __isl_keep isl_multi_aff *maff);
3531 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3532 __isl_take isl_printer *p,
3533 __isl_keep isl_pw_multi_aff *pma);
3534 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3535 __isl_take isl_printer *p,
3536 __isl_keep isl_union_pw_multi_aff *upma);
3540 Points are elements of a set. They can be used to construct
3541 simple sets (boxes) or they can be used to represent the
3542 individual elements of a set.
3543 The zero point (the origin) can be created using
3545 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3547 The coordinates of a point can be inspected, set and changed
3550 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3551 enum isl_dim_type type, int pos, isl_int *v);
3552 __isl_give isl_point *isl_point_set_coordinate(
3553 __isl_take isl_point *pnt,
3554 enum isl_dim_type type, int pos, isl_int v);
3556 __isl_give isl_point *isl_point_add_ui(
3557 __isl_take isl_point *pnt,
3558 enum isl_dim_type type, int pos, unsigned val);
3559 __isl_give isl_point *isl_point_sub_ui(
3560 __isl_take isl_point *pnt,
3561 enum isl_dim_type type, int pos, unsigned val);
3563 Other properties can be obtained using
3565 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3567 Points can be copied or freed using
3569 __isl_give isl_point *isl_point_copy(
3570 __isl_keep isl_point *pnt);
3571 void isl_point_free(__isl_take isl_point *pnt);
3573 A singleton set can be created from a point using
3575 __isl_give isl_basic_set *isl_basic_set_from_point(
3576 __isl_take isl_point *pnt);
3577 __isl_give isl_set *isl_set_from_point(
3578 __isl_take isl_point *pnt);
3580 and a box can be created from two opposite extremal points using
3582 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3583 __isl_take isl_point *pnt1,
3584 __isl_take isl_point *pnt2);
3585 __isl_give isl_set *isl_set_box_from_points(
3586 __isl_take isl_point *pnt1,
3587 __isl_take isl_point *pnt2);
3589 All elements of a B<bounded> (union) set can be enumerated using
3590 the following functions.
3592 int isl_set_foreach_point(__isl_keep isl_set *set,
3593 int (*fn)(__isl_take isl_point *pnt, void *user),
3595 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3596 int (*fn)(__isl_take isl_point *pnt, void *user),
3599 The function C<fn> is called for each integer point in
3600 C<set> with as second argument the last argument of
3601 the C<isl_set_foreach_point> call. The function C<fn>
3602 should return C<0> on success and C<-1> on failure.
3603 In the latter case, C<isl_set_foreach_point> will stop
3604 enumerating and return C<-1> as well.
3605 If the enumeration is performed successfully and to completion,
3606 then C<isl_set_foreach_point> returns C<0>.
3608 To obtain a single point of a (basic) set, use
3610 __isl_give isl_point *isl_basic_set_sample_point(
3611 __isl_take isl_basic_set *bset);
3612 __isl_give isl_point *isl_set_sample_point(
3613 __isl_take isl_set *set);
3615 If C<set> does not contain any (integer) points, then the
3616 resulting point will be ``void'', a property that can be
3619 int isl_point_is_void(__isl_keep isl_point *pnt);
3621 =head2 Piecewise Quasipolynomials
3623 A piecewise quasipolynomial is a particular kind of function that maps
3624 a parametric point to a rational value.
3625 More specifically, a quasipolynomial is a polynomial expression in greatest
3626 integer parts of affine expressions of parameters and variables.
3627 A piecewise quasipolynomial is a subdivision of a given parametric
3628 domain into disjoint cells with a quasipolynomial associated to
3629 each cell. The value of the piecewise quasipolynomial at a given
3630 point is the value of the quasipolynomial associated to the cell
3631 that contains the point. Outside of the union of cells,
3632 the value is assumed to be zero.
3633 For example, the piecewise quasipolynomial
3635 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3637 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3638 A given piecewise quasipolynomial has a fixed domain dimension.
3639 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3640 defined over different domains.
3641 Piecewise quasipolynomials are mainly used by the C<barvinok>
3642 library for representing the number of elements in a parametric set or map.
3643 For example, the piecewise quasipolynomial above represents
3644 the number of points in the map
3646 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3648 =head3 Input and Output
3650 Piecewise quasipolynomials can be read from input using
3652 __isl_give isl_union_pw_qpolynomial *
3653 isl_union_pw_qpolynomial_read_from_str(
3654 isl_ctx *ctx, const char *str);
3656 Quasipolynomials and piecewise quasipolynomials can be printed
3657 using the following functions.
3659 __isl_give isl_printer *isl_printer_print_qpolynomial(
3660 __isl_take isl_printer *p,
3661 __isl_keep isl_qpolynomial *qp);
3663 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3664 __isl_take isl_printer *p,
3665 __isl_keep isl_pw_qpolynomial *pwqp);
3667 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3668 __isl_take isl_printer *p,
3669 __isl_keep isl_union_pw_qpolynomial *upwqp);
3671 The output format of the printer
3672 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3673 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3675 In case of printing in C<ISL_FORMAT_C>, the user may want
3676 to set the names of all dimensions
3678 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3679 __isl_take isl_qpolynomial *qp,
3680 enum isl_dim_type type, unsigned pos,
3682 __isl_give isl_pw_qpolynomial *
3683 isl_pw_qpolynomial_set_dim_name(
3684 __isl_take isl_pw_qpolynomial *pwqp,
3685 enum isl_dim_type type, unsigned pos,
3688 =head3 Creating New (Piecewise) Quasipolynomials
3690 Some simple quasipolynomials can be created using the following functions.
3691 More complicated quasipolynomials can be created by applying
3692 operations such as addition and multiplication
3693 on the resulting quasipolynomials
3695 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3696 __isl_take isl_space *domain);
3697 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3698 __isl_take isl_space *domain);
3699 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3700 __isl_take isl_space *domain);
3701 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3702 __isl_take isl_space *domain);
3703 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3704 __isl_take isl_space *domain);
3705 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3706 __isl_take isl_space *domain,
3707 const isl_int n, const isl_int d);
3708 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3709 __isl_take isl_space *domain,
3710 enum isl_dim_type type, unsigned pos);
3711 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3712 __isl_take isl_aff *aff);
3714 Note that the space in which a quasipolynomial lives is a map space
3715 with a one-dimensional range. The C<domain> argument in some of
3716 the functions above corresponds to the domain of this map space.
3718 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3719 with a single cell can be created using the following functions.
3720 Multiple of these single cell piecewise quasipolynomials can
3721 be combined to create more complicated piecewise quasipolynomials.
3723 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3724 __isl_take isl_space *space);
3725 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3726 __isl_take isl_set *set,
3727 __isl_take isl_qpolynomial *qp);
3728 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3729 __isl_take isl_qpolynomial *qp);
3730 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3731 __isl_take isl_pw_aff *pwaff);
3733 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3734 __isl_take isl_space *space);
3735 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3736 __isl_take isl_pw_qpolynomial *pwqp);
3737 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3738 __isl_take isl_union_pw_qpolynomial *upwqp,
3739 __isl_take isl_pw_qpolynomial *pwqp);
3741 Quasipolynomials can be copied and freed again using the following
3744 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3745 __isl_keep isl_qpolynomial *qp);
3746 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3748 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3749 __isl_keep isl_pw_qpolynomial *pwqp);
3750 void *isl_pw_qpolynomial_free(
3751 __isl_take isl_pw_qpolynomial *pwqp);
3753 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3754 __isl_keep isl_union_pw_qpolynomial *upwqp);
3755 void *isl_union_pw_qpolynomial_free(
3756 __isl_take isl_union_pw_qpolynomial *upwqp);
3758 =head3 Inspecting (Piecewise) Quasipolynomials
3760 To iterate over all piecewise quasipolynomials in a union
3761 piecewise quasipolynomial, use the following function
3763 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3764 __isl_keep isl_union_pw_qpolynomial *upwqp,
3765 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3768 To extract the piecewise quasipolynomial in a given space from a union, use
3770 __isl_give isl_pw_qpolynomial *
3771 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3772 __isl_keep isl_union_pw_qpolynomial *upwqp,
3773 __isl_take isl_space *space);
3775 To iterate over the cells in a piecewise quasipolynomial,
3776 use either of the following two functions
3778 int isl_pw_qpolynomial_foreach_piece(
3779 __isl_keep isl_pw_qpolynomial *pwqp,
3780 int (*fn)(__isl_take isl_set *set,
3781 __isl_take isl_qpolynomial *qp,
3782 void *user), void *user);
3783 int isl_pw_qpolynomial_foreach_lifted_piece(
3784 __isl_keep isl_pw_qpolynomial *pwqp,
3785 int (*fn)(__isl_take isl_set *set,
3786 __isl_take isl_qpolynomial *qp,
3787 void *user), void *user);
3789 As usual, the function C<fn> should return C<0> on success
3790 and C<-1> on failure. The difference between
3791 C<isl_pw_qpolynomial_foreach_piece> and
3792 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3793 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3794 compute unique representations for all existentially quantified
3795 variables and then turn these existentially quantified variables
3796 into extra set variables, adapting the associated quasipolynomial
3797 accordingly. This means that the C<set> passed to C<fn>
3798 will not have any existentially quantified variables, but that
3799 the dimensions of the sets may be different for different
3800 invocations of C<fn>.
3802 To iterate over all terms in a quasipolynomial,
3805 int isl_qpolynomial_foreach_term(
3806 __isl_keep isl_qpolynomial *qp,
3807 int (*fn)(__isl_take isl_term *term,
3808 void *user), void *user);
3810 The terms themselves can be inspected and freed using
3813 unsigned isl_term_dim(__isl_keep isl_term *term,
3814 enum isl_dim_type type);
3815 void isl_term_get_num(__isl_keep isl_term *term,
3817 void isl_term_get_den(__isl_keep isl_term *term,
3819 int isl_term_get_exp(__isl_keep isl_term *term,
3820 enum isl_dim_type type, unsigned pos);
3821 __isl_give isl_aff *isl_term_get_div(
3822 __isl_keep isl_term *term, unsigned pos);
3823 void isl_term_free(__isl_take isl_term *term);
3825 Each term is a product of parameters, set variables and
3826 integer divisions. The function C<isl_term_get_exp>
3827 returns the exponent of a given dimensions in the given term.
3828 The C<isl_int>s in the arguments of C<isl_term_get_num>
3829 and C<isl_term_get_den> need to have been initialized
3830 using C<isl_int_init> before calling these functions.
3832 =head3 Properties of (Piecewise) Quasipolynomials
3834 To check whether a quasipolynomial is actually a constant,
3835 use the following function.
3837 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3838 isl_int *n, isl_int *d);
3840 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3841 then the numerator and denominator of the constant
3842 are returned in C<*n> and C<*d>, respectively.
3844 To check whether two union piecewise quasipolynomials are
3845 obviously equal, use
3847 int isl_union_pw_qpolynomial_plain_is_equal(
3848 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3849 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3851 =head3 Operations on (Piecewise) Quasipolynomials
3853 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3854 __isl_take isl_qpolynomial *qp, isl_int v);
3855 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3856 __isl_take isl_qpolynomial *qp);
3857 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3858 __isl_take isl_qpolynomial *qp1,
3859 __isl_take isl_qpolynomial *qp2);
3860 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3861 __isl_take isl_qpolynomial *qp1,
3862 __isl_take isl_qpolynomial *qp2);
3863 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3864 __isl_take isl_qpolynomial *qp1,
3865 __isl_take isl_qpolynomial *qp2);
3866 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3867 __isl_take isl_qpolynomial *qp, unsigned exponent);
3869 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3870 __isl_take isl_pw_qpolynomial *pwqp1,
3871 __isl_take isl_pw_qpolynomial *pwqp2);
3872 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3873 __isl_take isl_pw_qpolynomial *pwqp1,
3874 __isl_take isl_pw_qpolynomial *pwqp2);
3875 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3876 __isl_take isl_pw_qpolynomial *pwqp1,
3877 __isl_take isl_pw_qpolynomial *pwqp2);
3878 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3879 __isl_take isl_pw_qpolynomial *pwqp);
3880 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3881 __isl_take isl_pw_qpolynomial *pwqp1,
3882 __isl_take isl_pw_qpolynomial *pwqp2);
3883 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3884 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3886 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3887 __isl_take isl_union_pw_qpolynomial *upwqp1,
3888 __isl_take isl_union_pw_qpolynomial *upwqp2);
3889 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3890 __isl_take isl_union_pw_qpolynomial *upwqp1,
3891 __isl_take isl_union_pw_qpolynomial *upwqp2);
3892 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3893 __isl_take isl_union_pw_qpolynomial *upwqp1,
3894 __isl_take isl_union_pw_qpolynomial *upwqp2);
3896 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3897 __isl_take isl_pw_qpolynomial *pwqp,
3898 __isl_take isl_point *pnt);
3900 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3901 __isl_take isl_union_pw_qpolynomial *upwqp,
3902 __isl_take isl_point *pnt);
3904 __isl_give isl_set *isl_pw_qpolynomial_domain(
3905 __isl_take isl_pw_qpolynomial *pwqp);
3906 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3907 __isl_take isl_pw_qpolynomial *pwpq,
3908 __isl_take isl_set *set);
3909 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3910 __isl_take isl_pw_qpolynomial *pwpq,
3911 __isl_take isl_set *set);
3913 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3914 __isl_take isl_union_pw_qpolynomial *upwqp);
3915 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3916 __isl_take isl_union_pw_qpolynomial *upwpq,
3917 __isl_take isl_union_set *uset);
3918 __isl_give isl_union_pw_qpolynomial *
3919 isl_union_pw_qpolynomial_intersect_params(
3920 __isl_take isl_union_pw_qpolynomial *upwpq,
3921 __isl_take isl_set *set);
3923 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3924 __isl_take isl_qpolynomial *qp,
3925 __isl_take isl_space *model);
3927 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3928 __isl_take isl_qpolynomial *qp);
3929 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3930 __isl_take isl_pw_qpolynomial *pwqp);
3932 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3933 __isl_take isl_union_pw_qpolynomial *upwqp);
3935 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3936 __isl_take isl_qpolynomial *qp,
3937 __isl_take isl_set *context);
3938 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3939 __isl_take isl_qpolynomial *qp,
3940 __isl_take isl_set *context);
3942 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3943 __isl_take isl_pw_qpolynomial *pwqp,
3944 __isl_take isl_set *context);
3945 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3946 __isl_take isl_pw_qpolynomial *pwqp,
3947 __isl_take isl_set *context);
3949 __isl_give isl_union_pw_qpolynomial *
3950 isl_union_pw_qpolynomial_gist_params(
3951 __isl_take isl_union_pw_qpolynomial *upwqp,
3952 __isl_take isl_set *context);
3953 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3954 __isl_take isl_union_pw_qpolynomial *upwqp,
3955 __isl_take isl_union_set *context);
3957 The gist operation applies the gist operation to each of
3958 the cells in the domain of the input piecewise quasipolynomial.
3959 The context is also exploited
3960 to simplify the quasipolynomials associated to each cell.
3962 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3963 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3964 __isl_give isl_union_pw_qpolynomial *
3965 isl_union_pw_qpolynomial_to_polynomial(
3966 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3968 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3969 the polynomial will be an overapproximation. If C<sign> is negative,
3970 it will be an underapproximation. If C<sign> is zero, the approximation
3971 will lie somewhere in between.
3973 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3975 A piecewise quasipolynomial reduction is a piecewise
3976 reduction (or fold) of quasipolynomials.
3977 In particular, the reduction can be maximum or a minimum.
3978 The objects are mainly used to represent the result of
3979 an upper or lower bound on a quasipolynomial over its domain,
3980 i.e., as the result of the following function.
3982 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3983 __isl_take isl_pw_qpolynomial *pwqp,
3984 enum isl_fold type, int *tight);
3986 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3987 __isl_take isl_union_pw_qpolynomial *upwqp,
3988 enum isl_fold type, int *tight);
3990 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3991 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3992 is the returned bound is known be tight, i.e., for each value
3993 of the parameters there is at least
3994 one element in the domain that reaches the bound.
3995 If the domain of C<pwqp> is not wrapping, then the bound is computed
3996 over all elements in that domain and the result has a purely parametric
3997 domain. If the domain of C<pwqp> is wrapping, then the bound is
3998 computed over the range of the wrapped relation. The domain of the
3999 wrapped relation becomes the domain of the result.
4001 A (piecewise) quasipolynomial reduction can be copied or freed using the
4002 following functions.
4004 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4005 __isl_keep isl_qpolynomial_fold *fold);
4006 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4007 __isl_keep isl_pw_qpolynomial_fold *pwf);
4008 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4009 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4010 void isl_qpolynomial_fold_free(
4011 __isl_take isl_qpolynomial_fold *fold);
4012 void *isl_pw_qpolynomial_fold_free(
4013 __isl_take isl_pw_qpolynomial_fold *pwf);
4014 void *isl_union_pw_qpolynomial_fold_free(
4015 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4017 =head3 Printing Piecewise Quasipolynomial Reductions
4019 Piecewise quasipolynomial reductions can be printed
4020 using the following function.
4022 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4023 __isl_take isl_printer *p,
4024 __isl_keep isl_pw_qpolynomial_fold *pwf);
4025 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4026 __isl_take isl_printer *p,
4027 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4029 For C<isl_printer_print_pw_qpolynomial_fold>,
4030 output format of the printer
4031 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4032 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4033 output format of the printer
4034 needs to be set to C<ISL_FORMAT_ISL>.
4035 In case of printing in C<ISL_FORMAT_C>, the user may want
4036 to set the names of all dimensions
4038 __isl_give isl_pw_qpolynomial_fold *
4039 isl_pw_qpolynomial_fold_set_dim_name(
4040 __isl_take isl_pw_qpolynomial_fold *pwf,
4041 enum isl_dim_type type, unsigned pos,
4044 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4046 To iterate over all piecewise quasipolynomial reductions in a union
4047 piecewise quasipolynomial reduction, use the following function
4049 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4050 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4051 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4052 void *user), void *user);
4054 To iterate over the cells in a piecewise quasipolynomial reduction,
4055 use either of the following two functions
4057 int isl_pw_qpolynomial_fold_foreach_piece(
4058 __isl_keep isl_pw_qpolynomial_fold *pwf,
4059 int (*fn)(__isl_take isl_set *set,
4060 __isl_take isl_qpolynomial_fold *fold,
4061 void *user), void *user);
4062 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4063 __isl_keep isl_pw_qpolynomial_fold *pwf,
4064 int (*fn)(__isl_take isl_set *set,
4065 __isl_take isl_qpolynomial_fold *fold,
4066 void *user), void *user);
4068 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4069 of the difference between these two functions.
4071 To iterate over all quasipolynomials in a reduction, use
4073 int isl_qpolynomial_fold_foreach_qpolynomial(
4074 __isl_keep isl_qpolynomial_fold *fold,
4075 int (*fn)(__isl_take isl_qpolynomial *qp,
4076 void *user), void *user);
4078 =head3 Properties of Piecewise Quasipolynomial Reductions
4080 To check whether two union piecewise quasipolynomial reductions are
4081 obviously equal, use
4083 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4084 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4085 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4087 =head3 Operations on Piecewise Quasipolynomial Reductions
4089 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4090 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4092 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4093 __isl_take isl_pw_qpolynomial_fold *pwf1,
4094 __isl_take isl_pw_qpolynomial_fold *pwf2);
4096 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4097 __isl_take isl_pw_qpolynomial_fold *pwf1,
4098 __isl_take isl_pw_qpolynomial_fold *pwf2);
4100 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4101 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4102 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4104 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4105 __isl_take isl_pw_qpolynomial_fold *pwf,
4106 __isl_take isl_point *pnt);
4108 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4109 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4110 __isl_take isl_point *pnt);
4112 __isl_give isl_pw_qpolynomial_fold *
4113 isl_pw_qpolynomial_fold_intersect_params(
4114 __isl_take isl_pw_qpolynomial_fold *pwf,
4115 __isl_take isl_set *set);
4117 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4118 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4119 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4120 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4121 __isl_take isl_union_set *uset);
4122 __isl_give isl_union_pw_qpolynomial_fold *
4123 isl_union_pw_qpolynomial_fold_intersect_params(
4124 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4125 __isl_take isl_set *set);
4127 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4128 __isl_take isl_pw_qpolynomial_fold *pwf);
4130 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4131 __isl_take isl_pw_qpolynomial_fold *pwf);
4133 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4134 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4136 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4137 __isl_take isl_qpolynomial_fold *fold,
4138 __isl_take isl_set *context);
4139 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4140 __isl_take isl_qpolynomial_fold *fold,
4141 __isl_take isl_set *context);
4143 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4144 __isl_take isl_pw_qpolynomial_fold *pwf,
4145 __isl_take isl_set *context);
4146 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4147 __isl_take isl_pw_qpolynomial_fold *pwf,
4148 __isl_take isl_set *context);
4150 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4151 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4152 __isl_take isl_union_set *context);
4153 __isl_give isl_union_pw_qpolynomial_fold *
4154 isl_union_pw_qpolynomial_fold_gist_params(
4155 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4156 __isl_take isl_set *context);
4158 The gist operation applies the gist operation to each of
4159 the cells in the domain of the input piecewise quasipolynomial reduction.
4160 In future, the operation will also exploit the context
4161 to simplify the quasipolynomial reductions associated to each cell.
4163 __isl_give isl_pw_qpolynomial_fold *
4164 isl_set_apply_pw_qpolynomial_fold(
4165 __isl_take isl_set *set,
4166 __isl_take isl_pw_qpolynomial_fold *pwf,
4168 __isl_give isl_pw_qpolynomial_fold *
4169 isl_map_apply_pw_qpolynomial_fold(
4170 __isl_take isl_map *map,
4171 __isl_take isl_pw_qpolynomial_fold *pwf,
4173 __isl_give isl_union_pw_qpolynomial_fold *
4174 isl_union_set_apply_union_pw_qpolynomial_fold(
4175 __isl_take isl_union_set *uset,
4176 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4178 __isl_give isl_union_pw_qpolynomial_fold *
4179 isl_union_map_apply_union_pw_qpolynomial_fold(
4180 __isl_take isl_union_map *umap,
4181 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4184 The functions taking a map
4185 compose the given map with the given piecewise quasipolynomial reduction.
4186 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4187 over all elements in the intersection of the range of the map
4188 and the domain of the piecewise quasipolynomial reduction
4189 as a function of an element in the domain of the map.
4190 The functions taking a set compute a bound over all elements in the
4191 intersection of the set and the domain of the
4192 piecewise quasipolynomial reduction.
4194 =head2 Dependence Analysis
4196 C<isl> contains specialized functionality for performing
4197 array dataflow analysis. That is, given a I<sink> access relation
4198 and a collection of possible I<source> access relations,
4199 C<isl> can compute relations that describe
4200 for each iteration of the sink access, which iteration
4201 of which of the source access relations was the last
4202 to access the same data element before the given iteration
4204 The resulting dependence relations map source iterations
4205 to the corresponding sink iterations.
4206 To compute standard flow dependences, the sink should be
4207 a read, while the sources should be writes.
4208 If any of the source accesses are marked as being I<may>
4209 accesses, then there will be a dependence from the last
4210 I<must> access B<and> from any I<may> access that follows
4211 this last I<must> access.
4212 In particular, if I<all> sources are I<may> accesses,
4213 then memory based dependence analysis is performed.
4214 If, on the other hand, all sources are I<must> accesses,
4215 then value based dependence analysis is performed.
4217 #include <isl/flow.h>
4219 typedef int (*isl_access_level_before)(void *first, void *second);
4221 __isl_give isl_access_info *isl_access_info_alloc(
4222 __isl_take isl_map *sink,
4223 void *sink_user, isl_access_level_before fn,
4225 __isl_give isl_access_info *isl_access_info_add_source(
4226 __isl_take isl_access_info *acc,
4227 __isl_take isl_map *source, int must,
4229 void *isl_access_info_free(__isl_take isl_access_info *acc);
4231 __isl_give isl_flow *isl_access_info_compute_flow(
4232 __isl_take isl_access_info *acc);
4234 int isl_flow_foreach(__isl_keep isl_flow *deps,
4235 int (*fn)(__isl_take isl_map *dep, int must,
4236 void *dep_user, void *user),
4238 __isl_give isl_map *isl_flow_get_no_source(
4239 __isl_keep isl_flow *deps, int must);
4240 void isl_flow_free(__isl_take isl_flow *deps);
4242 The function C<isl_access_info_compute_flow> performs the actual
4243 dependence analysis. The other functions are used to construct
4244 the input for this function or to read off the output.
4246 The input is collected in an C<isl_access_info>, which can
4247 be created through a call to C<isl_access_info_alloc>.
4248 The arguments to this functions are the sink access relation
4249 C<sink>, a token C<sink_user> used to identify the sink
4250 access to the user, a callback function for specifying the
4251 relative order of source and sink accesses, and the number
4252 of source access relations that will be added.
4253 The callback function has type C<int (*)(void *first, void *second)>.
4254 The function is called with two user supplied tokens identifying
4255 either a source or the sink and it should return the shared nesting
4256 level and the relative order of the two accesses.
4257 In particular, let I<n> be the number of loops shared by
4258 the two accesses. If C<first> precedes C<second> textually,
4259 then the function should return I<2 * n + 1>; otherwise,
4260 it should return I<2 * n>.
4261 The sources can be added to the C<isl_access_info> by performing
4262 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4263 C<must> indicates whether the source is a I<must> access
4264 or a I<may> access. Note that a multi-valued access relation
4265 should only be marked I<must> if every iteration in the domain
4266 of the relation accesses I<all> elements in its image.
4267 The C<source_user> token is again used to identify
4268 the source access. The range of the source access relation
4269 C<source> should have the same dimension as the range
4270 of the sink access relation.
4271 The C<isl_access_info_free> function should usually not be
4272 called explicitly, because it is called implicitly by
4273 C<isl_access_info_compute_flow>.
4275 The result of the dependence analysis is collected in an
4276 C<isl_flow>. There may be elements of
4277 the sink access for which no preceding source access could be
4278 found or for which all preceding sources are I<may> accesses.
4279 The relations containing these elements can be obtained through
4280 calls to C<isl_flow_get_no_source>, the first with C<must> set
4281 and the second with C<must> unset.
4282 In the case of standard flow dependence analysis,
4283 with the sink a read and the sources I<must> writes,
4284 the first relation corresponds to the reads from uninitialized
4285 array elements and the second relation is empty.
4286 The actual flow dependences can be extracted using
4287 C<isl_flow_foreach>. This function will call the user-specified
4288 callback function C<fn> for each B<non-empty> dependence between
4289 a source and the sink. The callback function is called
4290 with four arguments, the actual flow dependence relation
4291 mapping source iterations to sink iterations, a boolean that
4292 indicates whether it is a I<must> or I<may> dependence, a token
4293 identifying the source and an additional C<void *> with value
4294 equal to the third argument of the C<isl_flow_foreach> call.
4295 A dependence is marked I<must> if it originates from a I<must>
4296 source and if it is not followed by any I<may> sources.
4298 After finishing with an C<isl_flow>, the user should call
4299 C<isl_flow_free> to free all associated memory.
4301 A higher-level interface to dependence analysis is provided
4302 by the following function.
4304 #include <isl/flow.h>
4306 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4307 __isl_take isl_union_map *must_source,
4308 __isl_take isl_union_map *may_source,
4309 __isl_take isl_union_map *schedule,
4310 __isl_give isl_union_map **must_dep,
4311 __isl_give isl_union_map **may_dep,
4312 __isl_give isl_union_map **must_no_source,
4313 __isl_give isl_union_map **may_no_source);
4315 The arrays are identified by the tuple names of the ranges
4316 of the accesses. The iteration domains by the tuple names
4317 of the domains of the accesses and of the schedule.
4318 The relative order of the iteration domains is given by the
4319 schedule. The relations returned through C<must_no_source>
4320 and C<may_no_source> are subsets of C<sink>.
4321 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4322 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4323 any of the other arguments is treated as an error.
4325 =head3 Interaction with Dependence Analysis
4327 During the dependence analysis, we frequently need to perform
4328 the following operation. Given a relation between sink iterations
4329 and potential source iterations from a particular source domain,
4330 what is the last potential source iteration corresponding to each
4331 sink iteration. It can sometimes be convenient to adjust
4332 the set of potential source iterations before or after each such operation.
4333 The prototypical example is fuzzy array dataflow analysis,
4334 where we need to analyze if, based on data-dependent constraints,
4335 the sink iteration can ever be executed without one or more of
4336 the corresponding potential source iterations being executed.
4337 If so, we can introduce extra parameters and select an unknown
4338 but fixed source iteration from the potential source iterations.
4339 To be able to perform such manipulations, C<isl> provides the following
4342 #include <isl/flow.h>
4344 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4345 __isl_keep isl_map *source_map,
4346 __isl_keep isl_set *sink, void *source_user,
4348 __isl_give isl_access_info *isl_access_info_set_restrict(
4349 __isl_take isl_access_info *acc,
4350 isl_access_restrict fn, void *user);
4352 The function C<isl_access_info_set_restrict> should be called
4353 before calling C<isl_access_info_compute_flow> and registers a callback function
4354 that will be called any time C<isl> is about to compute the last
4355 potential source. The first argument is the (reverse) proto-dependence,
4356 mapping sink iterations to potential source iterations.
4357 The second argument represents the sink iterations for which
4358 we want to compute the last source iteration.
4359 The third argument is the token corresponding to the source
4360 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4361 The callback is expected to return a restriction on either the input or
4362 the output of the operation computing the last potential source.
4363 If the input needs to be restricted then restrictions are needed
4364 for both the source and the sink iterations. The sink iterations
4365 and the potential source iterations will be intersected with these sets.
4366 If the output needs to be restricted then only a restriction on the source
4367 iterations is required.
4368 If any error occurs, the callback should return C<NULL>.
4369 An C<isl_restriction> object can be created, freed and inspected
4370 using the following functions.
4372 #include <isl/flow.h>
4374 __isl_give isl_restriction *isl_restriction_input(
4375 __isl_take isl_set *source_restr,
4376 __isl_take isl_set *sink_restr);
4377 __isl_give isl_restriction *isl_restriction_output(
4378 __isl_take isl_set *source_restr);
4379 __isl_give isl_restriction *isl_restriction_none(
4380 __isl_take isl_map *source_map);
4381 __isl_give isl_restriction *isl_restriction_empty(
4382 __isl_take isl_map *source_map);
4383 void *isl_restriction_free(
4384 __isl_take isl_restriction *restr);
4385 isl_ctx *isl_restriction_get_ctx(
4386 __isl_keep isl_restriction *restr);
4388 C<isl_restriction_none> and C<isl_restriction_empty> are special
4389 cases of C<isl_restriction_input>. C<isl_restriction_none>
4390 is essentially equivalent to
4392 isl_restriction_input(isl_set_universe(
4393 isl_space_range(isl_map_get_space(source_map))),
4395 isl_space_domain(isl_map_get_space(source_map))));
4397 whereas C<isl_restriction_empty> is essentially equivalent to
4399 isl_restriction_input(isl_set_empty(
4400 isl_space_range(isl_map_get_space(source_map))),
4402 isl_space_domain(isl_map_get_space(source_map))));
4406 B<The functionality described in this section is fairly new
4407 and may be subject to change.>
4409 The following function can be used to compute a schedule
4410 for a union of domains.
4411 By default, the algorithm used to construct the schedule is similar
4412 to that of C<Pluto>.
4413 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4415 The generated schedule respects all C<validity> dependences.
4416 That is, all dependence distances over these dependences in the
4417 scheduled space are lexicographically positive.
4418 The default algorithm tries to minimize the dependence distances over
4419 C<proximity> dependences.
4420 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4421 for groups of domains where the dependence distances have only
4422 non-negative values.
4423 When using Feautrier's algorithm, the C<proximity> dependence
4424 distances are only minimized during the extension to a
4425 full-dimensional schedule.
4427 #include <isl/schedule.h>
4428 __isl_give isl_schedule *isl_union_set_compute_schedule(
4429 __isl_take isl_union_set *domain,
4430 __isl_take isl_union_map *validity,
4431 __isl_take isl_union_map *proximity);
4432 void *isl_schedule_free(__isl_take isl_schedule *sched);
4434 A mapping from the domains to the scheduled space can be obtained
4435 from an C<isl_schedule> using the following function.
4437 __isl_give isl_union_map *isl_schedule_get_map(
4438 __isl_keep isl_schedule *sched);
4440 A representation of the schedule can be printed using
4442 __isl_give isl_printer *isl_printer_print_schedule(
4443 __isl_take isl_printer *p,
4444 __isl_keep isl_schedule *schedule);
4446 A representation of the schedule as a forest of bands can be obtained
4447 using the following function.
4449 __isl_give isl_band_list *isl_schedule_get_band_forest(
4450 __isl_keep isl_schedule *schedule);
4452 The individual bands can be visited in depth-first post-order
4453 using the following function.
4455 #include <isl/schedule.h>
4456 int isl_schedule_foreach_band(
4457 __isl_keep isl_schedule *sched,
4458 int (*fn)(__isl_keep isl_band *band, void *user),
4461 The list can be manipulated as explained in L<"Lists">.
4462 The bands inside the list can be copied and freed using the following
4465 #include <isl/band.h>
4466 __isl_give isl_band *isl_band_copy(
4467 __isl_keep isl_band *band);
4468 void *isl_band_free(__isl_take isl_band *band);
4470 Each band contains zero or more scheduling dimensions.
4471 These are referred to as the members of the band.
4472 The section of the schedule that corresponds to the band is
4473 referred to as the partial schedule of the band.
4474 For those nodes that participate in a band, the outer scheduling
4475 dimensions form the prefix schedule, while the inner scheduling
4476 dimensions form the suffix schedule.
4477 That is, if we take a cut of the band forest, then the union of
4478 the concatenations of the prefix, partial and suffix schedules of
4479 each band in the cut is equal to the entire schedule (modulo
4480 some possible padding at the end with zero scheduling dimensions).
4481 The properties of a band can be inspected using the following functions.
4483 #include <isl/band.h>
4484 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4486 int isl_band_has_children(__isl_keep isl_band *band);
4487 __isl_give isl_band_list *isl_band_get_children(
4488 __isl_keep isl_band *band);
4490 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4491 __isl_keep isl_band *band);
4492 __isl_give isl_union_map *isl_band_get_partial_schedule(
4493 __isl_keep isl_band *band);
4494 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4495 __isl_keep isl_band *band);
4497 int isl_band_n_member(__isl_keep isl_band *band);
4498 int isl_band_member_is_zero_distance(
4499 __isl_keep isl_band *band, int pos);
4501 int isl_band_list_foreach_band(
4502 __isl_keep isl_band_list *list,
4503 int (*fn)(__isl_keep isl_band *band, void *user),
4506 Note that a scheduling dimension is considered to be ``zero
4507 distance'' if it does not carry any proximity dependences
4509 That is, if the dependence distances of the proximity
4510 dependences are all zero in that direction (for fixed
4511 iterations of outer bands).
4512 Like C<isl_schedule_foreach_band>,
4513 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4514 in depth-first post-order.
4516 A band can be tiled using the following function.
4518 #include <isl/band.h>
4519 int isl_band_tile(__isl_keep isl_band *band,
4520 __isl_take isl_vec *sizes);
4522 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4524 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4526 The C<isl_band_tile> function tiles the band using the given tile sizes
4527 inside its schedule.
4528 A new child band is created to represent the point loops and it is
4529 inserted between the modified band and its children.
4530 The C<tile_scale_tile_loops> option specifies whether the tile
4531 loops iterators should be scaled by the tile sizes.
4533 A representation of the band can be printed using
4535 #include <isl/band.h>
4536 __isl_give isl_printer *isl_printer_print_band(
4537 __isl_take isl_printer *p,
4538 __isl_keep isl_band *band);
4542 #include <isl/schedule.h>
4543 int isl_options_set_schedule_max_coefficient(
4544 isl_ctx *ctx, int val);
4545 int isl_options_get_schedule_max_coefficient(
4547 int isl_options_set_schedule_max_constant_term(
4548 isl_ctx *ctx, int val);
4549 int isl_options_get_schedule_max_constant_term(
4551 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4552 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4553 int isl_options_set_schedule_maximize_band_depth(
4554 isl_ctx *ctx, int val);
4555 int isl_options_get_schedule_maximize_band_depth(
4557 int isl_options_set_schedule_outer_zero_distance(
4558 isl_ctx *ctx, int val);
4559 int isl_options_get_schedule_outer_zero_distance(
4561 int isl_options_set_schedule_split_scaled(
4562 isl_ctx *ctx, int val);
4563 int isl_options_get_schedule_split_scaled(
4565 int isl_options_set_schedule_algorithm(
4566 isl_ctx *ctx, int val);
4567 int isl_options_get_schedule_algorithm(
4569 int isl_options_set_schedule_separate_components(
4570 isl_ctx *ctx, int val);
4571 int isl_options_get_schedule_separate_components(
4576 =item * schedule_max_coefficient
4578 This option enforces that the coefficients for variable and parameter
4579 dimensions in the calculated schedule are not larger than the specified value.
4580 This option can significantly increase the speed of the scheduling calculation
4581 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4582 this option does not introduce bounds on the variable or parameter
4585 =item * schedule_max_constant_term
4587 This option enforces that the constant coefficients in the calculated schedule
4588 are not larger than the maximal constant term. This option can significantly
4589 increase the speed of the scheduling calculation and may also prevent fusing of
4590 unrelated dimensions. A value of -1 means that this option does not introduce
4591 bounds on the constant coefficients.
4593 =item * schedule_fuse
4595 This option controls the level of fusion.
4596 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4597 resulting schedule will be distributed as much as possible.
4598 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4599 try to fuse loops in the resulting schedule.
4601 =item * schedule_maximize_band_depth
4603 If this option is set, we do not split bands at the point
4604 where we detect splitting is necessary. Instead, we
4605 backtrack and split bands as early as possible. This
4606 reduces the number of splits and maximizes the width of
4607 the bands. Wider bands give more possibilities for tiling.
4608 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4609 then bands will be split as early as possible, even if there is no need.
4610 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4612 =item * schedule_outer_zero_distance
4614 If this option is set, then we try to construct schedules
4615 where the outermost scheduling dimension in each band
4616 results in a zero dependence distance over the proximity
4619 =item * schedule_split_scaled
4621 If this option is set, then we try to construct schedules in which the
4622 constant term is split off from the linear part if the linear parts of
4623 the scheduling rows for all nodes in the graphs have a common non-trivial
4625 The constant term is then placed in a separate band and the linear
4628 =item * schedule_algorithm
4630 Selects the scheduling algorithm to be used.
4631 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4632 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4634 =item * schedule_separate_components
4636 If at any point the dependence graph contains any (weakly connected) components,
4637 then these components are scheduled separately.
4638 If this option is not set, then some iterations of the domains
4639 in these components may be scheduled together.
4640 If this option is set, then the components are given consecutive
4645 =head2 Parametric Vertex Enumeration
4647 The parametric vertex enumeration described in this section
4648 is mainly intended to be used internally and by the C<barvinok>
4651 #include <isl/vertices.h>
4652 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4653 __isl_keep isl_basic_set *bset);
4655 The function C<isl_basic_set_compute_vertices> performs the
4656 actual computation of the parametric vertices and the chamber
4657 decomposition and store the result in an C<isl_vertices> object.
4658 This information can be queried by either iterating over all
4659 the vertices or iterating over all the chambers or cells
4660 and then iterating over all vertices that are active on the chamber.
4662 int isl_vertices_foreach_vertex(
4663 __isl_keep isl_vertices *vertices,
4664 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4667 int isl_vertices_foreach_cell(
4668 __isl_keep isl_vertices *vertices,
4669 int (*fn)(__isl_take isl_cell *cell, void *user),
4671 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4672 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4675 Other operations that can be performed on an C<isl_vertices> object are
4678 isl_ctx *isl_vertices_get_ctx(
4679 __isl_keep isl_vertices *vertices);
4680 int isl_vertices_get_n_vertices(
4681 __isl_keep isl_vertices *vertices);
4682 void isl_vertices_free(__isl_take isl_vertices *vertices);
4684 Vertices can be inspected and destroyed using the following functions.
4686 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4687 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4688 __isl_give isl_basic_set *isl_vertex_get_domain(
4689 __isl_keep isl_vertex *vertex);
4690 __isl_give isl_basic_set *isl_vertex_get_expr(
4691 __isl_keep isl_vertex *vertex);
4692 void isl_vertex_free(__isl_take isl_vertex *vertex);
4694 C<isl_vertex_get_expr> returns a singleton parametric set describing
4695 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4697 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4698 B<rational> basic sets, so they should mainly be used for inspection
4699 and should not be mixed with integer sets.
4701 Chambers can be inspected and destroyed using the following functions.
4703 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4704 __isl_give isl_basic_set *isl_cell_get_domain(
4705 __isl_keep isl_cell *cell);
4706 void isl_cell_free(__isl_take isl_cell *cell);
4710 Although C<isl> is mainly meant to be used as a library,
4711 it also contains some basic applications that use some
4712 of the functionality of C<isl>.
4713 The input may be specified in either the L<isl format>
4714 or the L<PolyLib format>.
4716 =head2 C<isl_polyhedron_sample>
4718 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4719 an integer element of the polyhedron, if there is any.
4720 The first column in the output is the denominator and is always
4721 equal to 1. If the polyhedron contains no integer points,
4722 then a vector of length zero is printed.
4726 C<isl_pip> takes the same input as the C<example> program
4727 from the C<piplib> distribution, i.e., a set of constraints
4728 on the parameters, a line containing only -1 and finally a set
4729 of constraints on a parametric polyhedron.
4730 The coefficients of the parameters appear in the last columns
4731 (but before the final constant column).
4732 The output is the lexicographic minimum of the parametric polyhedron.
4733 As C<isl> currently does not have its own output format, the output
4734 is just a dump of the internal state.
4736 =head2 C<isl_polyhedron_minimize>
4738 C<isl_polyhedron_minimize> computes the minimum of some linear
4739 or affine objective function over the integer points in a polyhedron.
4740 If an affine objective function
4741 is given, then the constant should appear in the last column.
4743 =head2 C<isl_polytope_scan>
4745 Given a polytope, C<isl_polytope_scan> prints
4746 all integer points in the polytope.