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/set.h>
1039 __isl_give isl_printer *isl_printer_print_basic_set(
1040 __isl_take isl_printer *printer,
1041 __isl_keep isl_basic_set *bset);
1042 __isl_give isl_printer *isl_printer_print_set(
1043 __isl_take isl_printer *printer,
1044 __isl_keep isl_set *set);
1046 #include <isl/map.h>
1047 __isl_give isl_printer *isl_printer_print_basic_map(
1048 __isl_take isl_printer *printer,
1049 __isl_keep isl_basic_map *bmap);
1050 __isl_give isl_printer *isl_printer_print_map(
1051 __isl_take isl_printer *printer,
1052 __isl_keep isl_map *map);
1054 #include <isl/union_set.h>
1055 __isl_give isl_printer *isl_printer_print_union_set(
1056 __isl_take isl_printer *p,
1057 __isl_keep isl_union_set *uset);
1059 #include <isl/union_map.h>
1060 __isl_give isl_printer *isl_printer_print_union_map(
1061 __isl_take isl_printer *p,
1062 __isl_keep isl_union_map *umap);
1064 When called on a file printer, the following function flushes
1065 the file. When called on a string printer, the buffer is cleared.
1067 __isl_give isl_printer *isl_printer_flush(
1068 __isl_take isl_printer *p);
1070 =head2 Creating New Sets and Relations
1072 C<isl> has functions for creating some standard sets and relations.
1076 =item * Empty sets and relations
1078 __isl_give isl_basic_set *isl_basic_set_empty(
1079 __isl_take isl_space *space);
1080 __isl_give isl_basic_map *isl_basic_map_empty(
1081 __isl_take isl_space *space);
1082 __isl_give isl_set *isl_set_empty(
1083 __isl_take isl_space *space);
1084 __isl_give isl_map *isl_map_empty(
1085 __isl_take isl_space *space);
1086 __isl_give isl_union_set *isl_union_set_empty(
1087 __isl_take isl_space *space);
1088 __isl_give isl_union_map *isl_union_map_empty(
1089 __isl_take isl_space *space);
1091 For C<isl_union_set>s and C<isl_union_map>s, the space
1092 is only used to specify the parameters.
1094 =item * Universe sets and relations
1096 __isl_give isl_basic_set *isl_basic_set_universe(
1097 __isl_take isl_space *space);
1098 __isl_give isl_basic_map *isl_basic_map_universe(
1099 __isl_take isl_space *space);
1100 __isl_give isl_set *isl_set_universe(
1101 __isl_take isl_space *space);
1102 __isl_give isl_map *isl_map_universe(
1103 __isl_take isl_space *space);
1104 __isl_give isl_union_set *isl_union_set_universe(
1105 __isl_take isl_union_set *uset);
1106 __isl_give isl_union_map *isl_union_map_universe(
1107 __isl_take isl_union_map *umap);
1109 The sets and relations constructed by the functions above
1110 contain all integer values, while those constructed by the
1111 functions below only contain non-negative values.
1113 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1114 __isl_take isl_space *space);
1115 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1116 __isl_take isl_space *space);
1117 __isl_give isl_set *isl_set_nat_universe(
1118 __isl_take isl_space *space);
1119 __isl_give isl_map *isl_map_nat_universe(
1120 __isl_take isl_space *space);
1122 =item * Identity relations
1124 __isl_give isl_basic_map *isl_basic_map_identity(
1125 __isl_take isl_space *space);
1126 __isl_give isl_map *isl_map_identity(
1127 __isl_take isl_space *space);
1129 The number of input and output dimensions in C<space> needs
1132 =item * Lexicographic order
1134 __isl_give isl_map *isl_map_lex_lt(
1135 __isl_take isl_space *set_space);
1136 __isl_give isl_map *isl_map_lex_le(
1137 __isl_take isl_space *set_space);
1138 __isl_give isl_map *isl_map_lex_gt(
1139 __isl_take isl_space *set_space);
1140 __isl_give isl_map *isl_map_lex_ge(
1141 __isl_take isl_space *set_space);
1142 __isl_give isl_map *isl_map_lex_lt_first(
1143 __isl_take isl_space *space, unsigned n);
1144 __isl_give isl_map *isl_map_lex_le_first(
1145 __isl_take isl_space *space, unsigned n);
1146 __isl_give isl_map *isl_map_lex_gt_first(
1147 __isl_take isl_space *space, unsigned n);
1148 __isl_give isl_map *isl_map_lex_ge_first(
1149 __isl_take isl_space *space, unsigned n);
1151 The first four functions take a space for a B<set>
1152 and return relations that express that the elements in the domain
1153 are lexicographically less
1154 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1155 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1156 than the elements in the range.
1157 The last four functions take a space for a map
1158 and return relations that express that the first C<n> dimensions
1159 in the domain are lexicographically less
1160 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1161 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1162 than the first C<n> dimensions in the range.
1166 A basic set or relation can be converted to a set or relation
1167 using the following functions.
1169 __isl_give isl_set *isl_set_from_basic_set(
1170 __isl_take isl_basic_set *bset);
1171 __isl_give isl_map *isl_map_from_basic_map(
1172 __isl_take isl_basic_map *bmap);
1174 Sets and relations can be converted to union sets and relations
1175 using the following functions.
1177 __isl_give isl_union_map *isl_union_map_from_map(
1178 __isl_take isl_map *map);
1179 __isl_give isl_union_set *isl_union_set_from_set(
1180 __isl_take isl_set *set);
1182 The inverse conversions below can only be used if the input
1183 union set or relation is known to contain elements in exactly one
1186 __isl_give isl_set *isl_set_from_union_set(
1187 __isl_take isl_union_set *uset);
1188 __isl_give isl_map *isl_map_from_union_map(
1189 __isl_take isl_union_map *umap);
1191 A zero-dimensional set can be constructed on a given parameter domain
1192 using the following function.
1194 __isl_give isl_set *isl_set_from_params(
1195 __isl_take isl_set *set);
1197 Sets and relations can be copied and freed again using the following
1200 __isl_give isl_basic_set *isl_basic_set_copy(
1201 __isl_keep isl_basic_set *bset);
1202 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1203 __isl_give isl_union_set *isl_union_set_copy(
1204 __isl_keep isl_union_set *uset);
1205 __isl_give isl_basic_map *isl_basic_map_copy(
1206 __isl_keep isl_basic_map *bmap);
1207 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1208 __isl_give isl_union_map *isl_union_map_copy(
1209 __isl_keep isl_union_map *umap);
1210 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1211 void isl_set_free(__isl_take isl_set *set);
1212 void *isl_union_set_free(__isl_take isl_union_set *uset);
1213 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1214 void isl_map_free(__isl_take isl_map *map);
1215 void *isl_union_map_free(__isl_take isl_union_map *umap);
1217 Other sets and relations can be constructed by starting
1218 from a universe set or relation, adding equality and/or
1219 inequality constraints and then projecting out the
1220 existentially quantified variables, if any.
1221 Constraints can be constructed, manipulated and
1222 added to (or removed from) (basic) sets and relations
1223 using the following functions.
1225 #include <isl/constraint.h>
1226 __isl_give isl_constraint *isl_equality_alloc(
1227 __isl_take isl_local_space *ls);
1228 __isl_give isl_constraint *isl_inequality_alloc(
1229 __isl_take isl_local_space *ls);
1230 __isl_give isl_constraint *isl_constraint_set_constant(
1231 __isl_take isl_constraint *constraint, isl_int v);
1232 __isl_give isl_constraint *isl_constraint_set_constant_si(
1233 __isl_take isl_constraint *constraint, int v);
1234 __isl_give isl_constraint *isl_constraint_set_coefficient(
1235 __isl_take isl_constraint *constraint,
1236 enum isl_dim_type type, int pos, isl_int v);
1237 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1238 __isl_take isl_constraint *constraint,
1239 enum isl_dim_type type, int pos, int v);
1240 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1241 __isl_take isl_basic_map *bmap,
1242 __isl_take isl_constraint *constraint);
1243 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1244 __isl_take isl_basic_set *bset,
1245 __isl_take isl_constraint *constraint);
1246 __isl_give isl_map *isl_map_add_constraint(
1247 __isl_take isl_map *map,
1248 __isl_take isl_constraint *constraint);
1249 __isl_give isl_set *isl_set_add_constraint(
1250 __isl_take isl_set *set,
1251 __isl_take isl_constraint *constraint);
1252 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1253 __isl_take isl_basic_set *bset,
1254 __isl_take isl_constraint *constraint);
1256 For example, to create a set containing the even integers
1257 between 10 and 42, you would use the following code.
1260 isl_local_space *ls;
1262 isl_basic_set *bset;
1264 space = isl_space_set_alloc(ctx, 0, 2);
1265 bset = isl_basic_set_universe(isl_space_copy(space));
1266 ls = isl_local_space_from_space(space);
1268 c = isl_equality_alloc(isl_local_space_copy(ls));
1269 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1270 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1271 bset = isl_basic_set_add_constraint(bset, c);
1273 c = isl_inequality_alloc(isl_local_space_copy(ls));
1274 c = isl_constraint_set_constant_si(c, -10);
1275 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1276 bset = isl_basic_set_add_constraint(bset, c);
1278 c = isl_inequality_alloc(ls);
1279 c = isl_constraint_set_constant_si(c, 42);
1280 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1281 bset = isl_basic_set_add_constraint(bset, c);
1283 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1287 isl_basic_set *bset;
1288 bset = isl_basic_set_read_from_str(ctx,
1289 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1291 A basic set or relation can also be constructed from two matrices
1292 describing the equalities and the inequalities.
1294 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1295 __isl_take isl_space *space,
1296 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1297 enum isl_dim_type c1,
1298 enum isl_dim_type c2, enum isl_dim_type c3,
1299 enum isl_dim_type c4);
1300 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1301 __isl_take isl_space *space,
1302 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1303 enum isl_dim_type c1,
1304 enum isl_dim_type c2, enum isl_dim_type c3,
1305 enum isl_dim_type c4, enum isl_dim_type c5);
1307 The C<isl_dim_type> arguments indicate the order in which
1308 different kinds of variables appear in the input matrices
1309 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1310 C<isl_dim_set> and C<isl_dim_div> for sets and
1311 of C<isl_dim_cst>, C<isl_dim_param>,
1312 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1314 A (basic or union) set or relation can also be constructed from a
1315 (union) (piecewise) (multiple) affine expression
1316 or a list of affine expressions
1317 (See L<"Piecewise Quasi Affine Expressions"> and
1318 L<"Piecewise Multiple Quasi Affine Expressions">).
1320 __isl_give isl_basic_map *isl_basic_map_from_aff(
1321 __isl_take isl_aff *aff);
1322 __isl_give isl_map *isl_map_from_aff(
1323 __isl_take isl_aff *aff);
1324 __isl_give isl_set *isl_set_from_pw_aff(
1325 __isl_take isl_pw_aff *pwaff);
1326 __isl_give isl_map *isl_map_from_pw_aff(
1327 __isl_take isl_pw_aff *pwaff);
1328 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1329 __isl_take isl_space *domain_space,
1330 __isl_take isl_aff_list *list);
1331 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1332 __isl_take isl_multi_aff *maff)
1333 __isl_give isl_map *isl_map_from_multi_aff(
1334 __isl_take isl_multi_aff *maff)
1335 __isl_give isl_set *isl_set_from_pw_multi_aff(
1336 __isl_take isl_pw_multi_aff *pma);
1337 __isl_give isl_map *isl_map_from_pw_multi_aff(
1338 __isl_take isl_pw_multi_aff *pma);
1339 __isl_give isl_union_map *
1340 isl_union_map_from_union_pw_multi_aff(
1341 __isl_take isl_union_pw_multi_aff *upma);
1343 The C<domain_dim> argument describes the domain of the resulting
1344 basic relation. It is required because the C<list> may consist
1345 of zero affine expressions.
1347 =head2 Inspecting Sets and Relations
1349 Usually, the user should not have to care about the actual constraints
1350 of the sets and maps, but should instead apply the abstract operations
1351 explained in the following sections.
1352 Occasionally, however, it may be required to inspect the individual
1353 coefficients of the constraints. This section explains how to do so.
1354 In these cases, it may also be useful to have C<isl> compute
1355 an explicit representation of the existentially quantified variables.
1357 __isl_give isl_set *isl_set_compute_divs(
1358 __isl_take isl_set *set);
1359 __isl_give isl_map *isl_map_compute_divs(
1360 __isl_take isl_map *map);
1361 __isl_give isl_union_set *isl_union_set_compute_divs(
1362 __isl_take isl_union_set *uset);
1363 __isl_give isl_union_map *isl_union_map_compute_divs(
1364 __isl_take isl_union_map *umap);
1366 This explicit representation defines the existentially quantified
1367 variables as integer divisions of the other variables, possibly
1368 including earlier existentially quantified variables.
1369 An explicitly represented existentially quantified variable therefore
1370 has a unique value when the values of the other variables are known.
1371 If, furthermore, the same existentials, i.e., existentials
1372 with the same explicit representations, should appear in the
1373 same order in each of the disjuncts of a set or map, then the user should call
1374 either of the following functions.
1376 __isl_give isl_set *isl_set_align_divs(
1377 __isl_take isl_set *set);
1378 __isl_give isl_map *isl_map_align_divs(
1379 __isl_take isl_map *map);
1381 Alternatively, the existentially quantified variables can be removed
1382 using the following functions, which compute an overapproximation.
1384 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1385 __isl_take isl_basic_set *bset);
1386 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1387 __isl_take isl_basic_map *bmap);
1388 __isl_give isl_set *isl_set_remove_divs(
1389 __isl_take isl_set *set);
1390 __isl_give isl_map *isl_map_remove_divs(
1391 __isl_take isl_map *map);
1393 To iterate over all the sets or maps in a union set or map, use
1395 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1396 int (*fn)(__isl_take isl_set *set, void *user),
1398 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1399 int (*fn)(__isl_take isl_map *map, void *user),
1402 The number of sets or maps in a union set or map can be obtained
1405 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1406 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1408 To extract the set or map in a given space from a union, use
1410 __isl_give isl_set *isl_union_set_extract_set(
1411 __isl_keep isl_union_set *uset,
1412 __isl_take isl_space *space);
1413 __isl_give isl_map *isl_union_map_extract_map(
1414 __isl_keep isl_union_map *umap,
1415 __isl_take isl_space *space);
1417 To iterate over all the basic sets or maps in a set or map, use
1419 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1420 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1422 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1423 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1426 The callback function C<fn> should return 0 if successful and
1427 -1 if an error occurs. In the latter case, or if any other error
1428 occurs, the above functions will return -1.
1430 It should be noted that C<isl> does not guarantee that
1431 the basic sets or maps passed to C<fn> are disjoint.
1432 If this is required, then the user should call one of
1433 the following functions first.
1435 __isl_give isl_set *isl_set_make_disjoint(
1436 __isl_take isl_set *set);
1437 __isl_give isl_map *isl_map_make_disjoint(
1438 __isl_take isl_map *map);
1440 The number of basic sets in a set can be obtained
1443 int isl_set_n_basic_set(__isl_keep isl_set *set);
1445 To iterate over the constraints of a basic set or map, use
1447 #include <isl/constraint.h>
1449 int isl_basic_set_n_constraint(
1450 __isl_keep isl_basic_set *bset);
1451 int isl_basic_set_foreach_constraint(
1452 __isl_keep isl_basic_set *bset,
1453 int (*fn)(__isl_take isl_constraint *c, void *user),
1455 int isl_basic_map_foreach_constraint(
1456 __isl_keep isl_basic_map *bmap,
1457 int (*fn)(__isl_take isl_constraint *c, void *user),
1459 void *isl_constraint_free(__isl_take isl_constraint *c);
1461 Again, the callback function C<fn> should return 0 if successful and
1462 -1 if an error occurs. In the latter case, or if any other error
1463 occurs, the above functions will return -1.
1464 The constraint C<c> represents either an equality or an inequality.
1465 Use the following function to find out whether a constraint
1466 represents an equality. If not, it represents an inequality.
1468 int isl_constraint_is_equality(
1469 __isl_keep isl_constraint *constraint);
1471 The coefficients of the constraints can be inspected using
1472 the following functions.
1474 int isl_constraint_is_lower_bound(
1475 __isl_keep isl_constraint *constraint,
1476 enum isl_dim_type type, unsigned pos);
1477 int isl_constraint_is_upper_bound(
1478 __isl_keep isl_constraint *constraint,
1479 enum isl_dim_type type, unsigned pos);
1480 void isl_constraint_get_constant(
1481 __isl_keep isl_constraint *constraint, isl_int *v);
1482 void isl_constraint_get_coefficient(
1483 __isl_keep isl_constraint *constraint,
1484 enum isl_dim_type type, int pos, isl_int *v);
1485 int isl_constraint_involves_dims(
1486 __isl_keep isl_constraint *constraint,
1487 enum isl_dim_type type, unsigned first, unsigned n);
1489 The explicit representations of the existentially quantified
1490 variables can be inspected using the following function.
1491 Note that the user is only allowed to use this function
1492 if the inspected set or map is the result of a call
1493 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1494 The existentially quantified variable is equal to the floor
1495 of the returned affine expression. The affine expression
1496 itself can be inspected using the functions in
1497 L<"Piecewise Quasi Affine Expressions">.
1499 __isl_give isl_aff *isl_constraint_get_div(
1500 __isl_keep isl_constraint *constraint, int pos);
1502 To obtain the constraints of a basic set or map in matrix
1503 form, use the following functions.
1505 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1506 __isl_keep isl_basic_set *bset,
1507 enum isl_dim_type c1, enum isl_dim_type c2,
1508 enum isl_dim_type c3, enum isl_dim_type c4);
1509 __isl_give isl_mat *isl_basic_set_inequalities_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_map_equalities_matrix(
1514 __isl_keep isl_basic_map *bmap,
1515 enum isl_dim_type c1,
1516 enum isl_dim_type c2, enum isl_dim_type c3,
1517 enum isl_dim_type c4, enum isl_dim_type c5);
1518 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1519 __isl_keep isl_basic_map *bmap,
1520 enum isl_dim_type c1,
1521 enum isl_dim_type c2, enum isl_dim_type c3,
1522 enum isl_dim_type c4, enum isl_dim_type c5);
1524 The C<isl_dim_type> arguments dictate the order in which
1525 different kinds of variables appear in the resulting matrix
1526 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1527 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1529 The number of parameters, input, output or set dimensions can
1530 be obtained using the following functions.
1532 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1533 enum isl_dim_type type);
1534 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1535 enum isl_dim_type type);
1536 unsigned isl_set_dim(__isl_keep isl_set *set,
1537 enum isl_dim_type type);
1538 unsigned isl_map_dim(__isl_keep isl_map *map,
1539 enum isl_dim_type type);
1541 To check whether the description of a set or relation depends
1542 on one or more given dimensions, it is not necessary to iterate over all
1543 constraints. Instead the following functions can be used.
1545 int isl_basic_set_involves_dims(
1546 __isl_keep isl_basic_set *bset,
1547 enum isl_dim_type type, unsigned first, unsigned n);
1548 int isl_set_involves_dims(__isl_keep isl_set *set,
1549 enum isl_dim_type type, unsigned first, unsigned n);
1550 int isl_basic_map_involves_dims(
1551 __isl_keep isl_basic_map *bmap,
1552 enum isl_dim_type type, unsigned first, unsigned n);
1553 int isl_map_involves_dims(__isl_keep isl_map *map,
1554 enum isl_dim_type type, unsigned first, unsigned n);
1556 Similarly, the following functions can be used to check whether
1557 a given dimension is involved in any lower or upper bound.
1559 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1560 enum isl_dim_type type, unsigned pos);
1561 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1562 enum isl_dim_type type, unsigned pos);
1564 The identifiers or names of the domain and range spaces of a set
1565 or relation can be read off or set using the following functions.
1567 __isl_give isl_set *isl_set_set_tuple_id(
1568 __isl_take isl_set *set, __isl_take isl_id *id);
1569 __isl_give isl_set *isl_set_reset_tuple_id(
1570 __isl_take isl_set *set);
1571 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1572 __isl_give isl_id *isl_set_get_tuple_id(
1573 __isl_keep isl_set *set);
1574 __isl_give isl_map *isl_map_set_tuple_id(
1575 __isl_take isl_map *map, enum isl_dim_type type,
1576 __isl_take isl_id *id);
1577 __isl_give isl_map *isl_map_reset_tuple_id(
1578 __isl_take isl_map *map, enum isl_dim_type type);
1579 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1580 enum isl_dim_type type);
1581 __isl_give isl_id *isl_map_get_tuple_id(
1582 __isl_keep isl_map *map, enum isl_dim_type type);
1584 const char *isl_basic_set_get_tuple_name(
1585 __isl_keep isl_basic_set *bset);
1586 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1587 __isl_take isl_basic_set *set, const char *s);
1588 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1589 const char *isl_set_get_tuple_name(
1590 __isl_keep isl_set *set);
1591 const char *isl_basic_map_get_tuple_name(
1592 __isl_keep isl_basic_map *bmap,
1593 enum isl_dim_type type);
1594 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1595 __isl_take isl_basic_map *bmap,
1596 enum isl_dim_type type, const char *s);
1597 const char *isl_map_get_tuple_name(
1598 __isl_keep isl_map *map,
1599 enum isl_dim_type type);
1601 As with C<isl_space_get_tuple_name>, the value returned points to
1602 an internal data structure.
1603 The identifiers, positions or names of individual dimensions can be
1604 read off using the following functions.
1606 __isl_give isl_id *isl_basic_set_get_dim_id(
1607 __isl_keep isl_basic_set *bset,
1608 enum isl_dim_type type, unsigned pos);
1609 __isl_give isl_set *isl_set_set_dim_id(
1610 __isl_take isl_set *set, enum isl_dim_type type,
1611 unsigned pos, __isl_take isl_id *id);
1612 int isl_set_has_dim_id(__isl_keep isl_set *set,
1613 enum isl_dim_type type, unsigned pos);
1614 __isl_give isl_id *isl_set_get_dim_id(
1615 __isl_keep isl_set *set, enum isl_dim_type type,
1617 int isl_basic_map_has_dim_id(
1618 __isl_keep isl_basic_map *bmap,
1619 enum isl_dim_type type, unsigned pos);
1620 __isl_give isl_map *isl_map_set_dim_id(
1621 __isl_take isl_map *map, enum isl_dim_type type,
1622 unsigned pos, __isl_take isl_id *id);
1623 int isl_map_has_dim_id(__isl_keep isl_map *map,
1624 enum isl_dim_type type, unsigned pos);
1625 __isl_give isl_id *isl_map_get_dim_id(
1626 __isl_keep isl_map *map, enum isl_dim_type type,
1629 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1630 enum isl_dim_type type, __isl_keep isl_id *id);
1631 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1632 enum isl_dim_type type, __isl_keep isl_id *id);
1633 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1634 enum isl_dim_type type, const char *name);
1635 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1636 enum isl_dim_type type, const char *name);
1638 const char *isl_constraint_get_dim_name(
1639 __isl_keep isl_constraint *constraint,
1640 enum isl_dim_type type, unsigned pos);
1641 const char *isl_basic_set_get_dim_name(
1642 __isl_keep isl_basic_set *bset,
1643 enum isl_dim_type type, unsigned pos);
1644 int isl_set_has_dim_name(__isl_keep isl_set *set,
1645 enum isl_dim_type type, unsigned pos);
1646 const char *isl_set_get_dim_name(
1647 __isl_keep isl_set *set,
1648 enum isl_dim_type type, unsigned pos);
1649 const char *isl_basic_map_get_dim_name(
1650 __isl_keep isl_basic_map *bmap,
1651 enum isl_dim_type type, unsigned pos);
1652 const char *isl_map_get_dim_name(
1653 __isl_keep isl_map *map,
1654 enum isl_dim_type type, unsigned pos);
1656 These functions are mostly useful to obtain the identifiers, positions
1657 or names of the parameters. Identifiers of individual dimensions are
1658 essentially only useful for printing. They are ignored by all other
1659 operations and may not be preserved across those operations.
1663 =head3 Unary Properties
1669 The following functions test whether the given set or relation
1670 contains any integer points. The ``plain'' variants do not perform
1671 any computations, but simply check if the given set or relation
1672 is already known to be empty.
1674 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1675 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1676 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1677 int isl_set_is_empty(__isl_keep isl_set *set);
1678 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1679 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1680 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1681 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1682 int isl_map_is_empty(__isl_keep isl_map *map);
1683 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1685 =item * Universality
1687 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1688 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1689 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1691 =item * Single-valuedness
1693 int isl_basic_map_is_single_valued(
1694 __isl_keep isl_basic_map *bmap);
1695 int isl_map_plain_is_single_valued(
1696 __isl_keep isl_map *map);
1697 int isl_map_is_single_valued(__isl_keep isl_map *map);
1698 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1702 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1703 int isl_map_is_injective(__isl_keep isl_map *map);
1704 int isl_union_map_plain_is_injective(
1705 __isl_keep isl_union_map *umap);
1706 int isl_union_map_is_injective(
1707 __isl_keep isl_union_map *umap);
1711 int isl_map_is_bijective(__isl_keep isl_map *map);
1712 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1716 int isl_basic_map_plain_is_fixed(
1717 __isl_keep isl_basic_map *bmap,
1718 enum isl_dim_type type, unsigned pos,
1720 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1721 enum isl_dim_type type, unsigned pos,
1723 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1724 enum isl_dim_type type, unsigned pos,
1727 Check if the relation obviously lies on a hyperplane where the given dimension
1728 has a fixed value and if so, return that value in C<*val>.
1732 To check whether a set is a parameter domain, use this function:
1734 int isl_set_is_params(__isl_keep isl_set *set);
1735 int isl_union_set_is_params(
1736 __isl_keep isl_union_set *uset);
1740 The following functions check whether the domain of the given
1741 (basic) set is a wrapped relation.
1743 int isl_basic_set_is_wrapping(
1744 __isl_keep isl_basic_set *bset);
1745 int isl_set_is_wrapping(__isl_keep isl_set *set);
1747 =item * Internal Product
1749 int isl_basic_map_can_zip(
1750 __isl_keep isl_basic_map *bmap);
1751 int isl_map_can_zip(__isl_keep isl_map *map);
1753 Check whether the product of domain and range of the given relation
1755 i.e., whether both domain and range are nested relations.
1759 int isl_basic_map_can_curry(
1760 __isl_keep isl_basic_map *bmap);
1761 int isl_map_can_curry(__isl_keep isl_map *map);
1763 Check whether the domain of the (basic) relation is a wrapped relation.
1767 =head3 Binary Properties
1773 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1774 __isl_keep isl_set *set2);
1775 int isl_set_is_equal(__isl_keep isl_set *set1,
1776 __isl_keep isl_set *set2);
1777 int isl_union_set_is_equal(
1778 __isl_keep isl_union_set *uset1,
1779 __isl_keep isl_union_set *uset2);
1780 int isl_basic_map_is_equal(
1781 __isl_keep isl_basic_map *bmap1,
1782 __isl_keep isl_basic_map *bmap2);
1783 int isl_map_is_equal(__isl_keep isl_map *map1,
1784 __isl_keep isl_map *map2);
1785 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1786 __isl_keep isl_map *map2);
1787 int isl_union_map_is_equal(
1788 __isl_keep isl_union_map *umap1,
1789 __isl_keep isl_union_map *umap2);
1791 =item * Disjointness
1793 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1794 __isl_keep isl_set *set2);
1798 int isl_basic_set_is_subset(
1799 __isl_keep isl_basic_set *bset1,
1800 __isl_keep isl_basic_set *bset2);
1801 int isl_set_is_subset(__isl_keep isl_set *set1,
1802 __isl_keep isl_set *set2);
1803 int isl_set_is_strict_subset(
1804 __isl_keep isl_set *set1,
1805 __isl_keep isl_set *set2);
1806 int isl_union_set_is_subset(
1807 __isl_keep isl_union_set *uset1,
1808 __isl_keep isl_union_set *uset2);
1809 int isl_union_set_is_strict_subset(
1810 __isl_keep isl_union_set *uset1,
1811 __isl_keep isl_union_set *uset2);
1812 int isl_basic_map_is_subset(
1813 __isl_keep isl_basic_map *bmap1,
1814 __isl_keep isl_basic_map *bmap2);
1815 int isl_basic_map_is_strict_subset(
1816 __isl_keep isl_basic_map *bmap1,
1817 __isl_keep isl_basic_map *bmap2);
1818 int isl_map_is_subset(
1819 __isl_keep isl_map *map1,
1820 __isl_keep isl_map *map2);
1821 int isl_map_is_strict_subset(
1822 __isl_keep isl_map *map1,
1823 __isl_keep isl_map *map2);
1824 int isl_union_map_is_subset(
1825 __isl_keep isl_union_map *umap1,
1826 __isl_keep isl_union_map *umap2);
1827 int isl_union_map_is_strict_subset(
1828 __isl_keep isl_union_map *umap1,
1829 __isl_keep isl_union_map *umap2);
1831 Check whether the first argument is a (strict) subset of the
1836 =head2 Unary Operations
1842 __isl_give isl_set *isl_set_complement(
1843 __isl_take isl_set *set);
1844 __isl_give isl_map *isl_map_complement(
1845 __isl_take isl_map *map);
1849 __isl_give isl_basic_map *isl_basic_map_reverse(
1850 __isl_take isl_basic_map *bmap);
1851 __isl_give isl_map *isl_map_reverse(
1852 __isl_take isl_map *map);
1853 __isl_give isl_union_map *isl_union_map_reverse(
1854 __isl_take isl_union_map *umap);
1858 __isl_give isl_basic_set *isl_basic_set_project_out(
1859 __isl_take isl_basic_set *bset,
1860 enum isl_dim_type type, unsigned first, unsigned n);
1861 __isl_give isl_basic_map *isl_basic_map_project_out(
1862 __isl_take isl_basic_map *bmap,
1863 enum isl_dim_type type, unsigned first, unsigned n);
1864 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1865 enum isl_dim_type type, unsigned first, unsigned n);
1866 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1867 enum isl_dim_type type, unsigned first, unsigned n);
1868 __isl_give isl_basic_set *isl_basic_set_params(
1869 __isl_take isl_basic_set *bset);
1870 __isl_give isl_basic_set *isl_basic_map_domain(
1871 __isl_take isl_basic_map *bmap);
1872 __isl_give isl_basic_set *isl_basic_map_range(
1873 __isl_take isl_basic_map *bmap);
1874 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1875 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1876 __isl_give isl_set *isl_map_domain(
1877 __isl_take isl_map *bmap);
1878 __isl_give isl_set *isl_map_range(
1879 __isl_take isl_map *map);
1880 __isl_give isl_set *isl_union_set_params(
1881 __isl_take isl_union_set *uset);
1882 __isl_give isl_set *isl_union_map_params(
1883 __isl_take isl_union_map *umap);
1884 __isl_give isl_union_set *isl_union_map_domain(
1885 __isl_take isl_union_map *umap);
1886 __isl_give isl_union_set *isl_union_map_range(
1887 __isl_take isl_union_map *umap);
1889 __isl_give isl_basic_map *isl_basic_map_domain_map(
1890 __isl_take isl_basic_map *bmap);
1891 __isl_give isl_basic_map *isl_basic_map_range_map(
1892 __isl_take isl_basic_map *bmap);
1893 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1894 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1895 __isl_give isl_union_map *isl_union_map_domain_map(
1896 __isl_take isl_union_map *umap);
1897 __isl_give isl_union_map *isl_union_map_range_map(
1898 __isl_take isl_union_map *umap);
1900 The functions above construct a (basic, regular or union) relation
1901 that maps (a wrapped version of) the input relation to its domain or range.
1905 __isl_give isl_set *isl_set_eliminate(
1906 __isl_take isl_set *set, enum isl_dim_type type,
1907 unsigned first, unsigned n);
1908 __isl_give isl_basic_map *isl_basic_map_eliminate(
1909 __isl_take isl_basic_map *bmap,
1910 enum isl_dim_type type,
1911 unsigned first, unsigned n);
1912 __isl_give isl_map *isl_map_eliminate(
1913 __isl_take isl_map *map, enum isl_dim_type type,
1914 unsigned first, unsigned n);
1916 Eliminate the coefficients for the given dimensions from the constraints,
1917 without removing the dimensions.
1921 __isl_give isl_basic_set *isl_basic_set_fix(
1922 __isl_take isl_basic_set *bset,
1923 enum isl_dim_type type, unsigned pos,
1925 __isl_give isl_basic_set *isl_basic_set_fix_si(
1926 __isl_take isl_basic_set *bset,
1927 enum isl_dim_type type, unsigned pos, int value);
1928 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1929 enum isl_dim_type type, unsigned pos,
1931 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1932 enum isl_dim_type type, unsigned pos, int value);
1933 __isl_give isl_basic_map *isl_basic_map_fix_si(
1934 __isl_take isl_basic_map *bmap,
1935 enum isl_dim_type type, unsigned pos, int value);
1936 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1937 enum isl_dim_type type, unsigned pos, int value);
1939 Intersect the set or relation with the hyperplane where the given
1940 dimension has the fixed given value.
1942 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1943 __isl_take isl_basic_map *bmap,
1944 enum isl_dim_type type, unsigned pos, int value);
1945 __isl_give isl_set *isl_set_lower_bound(
1946 __isl_take isl_set *set,
1947 enum isl_dim_type type, unsigned pos,
1949 __isl_give isl_set *isl_set_lower_bound_si(
1950 __isl_take isl_set *set,
1951 enum isl_dim_type type, unsigned pos, int value);
1952 __isl_give isl_map *isl_map_lower_bound_si(
1953 __isl_take isl_map *map,
1954 enum isl_dim_type type, unsigned pos, int value);
1955 __isl_give isl_set *isl_set_upper_bound(
1956 __isl_take isl_set *set,
1957 enum isl_dim_type type, unsigned pos,
1959 __isl_give isl_set *isl_set_upper_bound_si(
1960 __isl_take isl_set *set,
1961 enum isl_dim_type type, unsigned pos, int value);
1962 __isl_give isl_map *isl_map_upper_bound_si(
1963 __isl_take isl_map *map,
1964 enum isl_dim_type type, unsigned pos, int value);
1966 Intersect the set or relation with the half-space where the given
1967 dimension has a value bounded by the fixed given value.
1969 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1970 enum isl_dim_type type1, int pos1,
1971 enum isl_dim_type type2, int pos2);
1972 __isl_give isl_basic_map *isl_basic_map_equate(
1973 __isl_take isl_basic_map *bmap,
1974 enum isl_dim_type type1, int pos1,
1975 enum isl_dim_type type2, int pos2);
1976 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1977 enum isl_dim_type type1, int pos1,
1978 enum isl_dim_type type2, int pos2);
1980 Intersect the set or relation with the hyperplane where the given
1981 dimensions are equal to each other.
1983 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1984 enum isl_dim_type type1, int pos1,
1985 enum isl_dim_type type2, int pos2);
1987 Intersect the relation with the hyperplane where the given
1988 dimensions have opposite values.
1990 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
1991 enum isl_dim_type type1, int pos1,
1992 enum isl_dim_type type2, int pos2);
1993 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
1994 enum isl_dim_type type1, int pos1,
1995 enum isl_dim_type type2, int pos2);
1997 Intersect the relation with the half-space where the given
1998 dimensions satisfy the given ordering.
2002 __isl_give isl_map *isl_set_identity(
2003 __isl_take isl_set *set);
2004 __isl_give isl_union_map *isl_union_set_identity(
2005 __isl_take isl_union_set *uset);
2007 Construct an identity relation on the given (union) set.
2011 __isl_give isl_basic_set *isl_basic_map_deltas(
2012 __isl_take isl_basic_map *bmap);
2013 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2014 __isl_give isl_union_set *isl_union_map_deltas(
2015 __isl_take isl_union_map *umap);
2017 These functions return a (basic) set containing the differences
2018 between image elements and corresponding domain elements in the input.
2020 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2021 __isl_take isl_basic_map *bmap);
2022 __isl_give isl_map *isl_map_deltas_map(
2023 __isl_take isl_map *map);
2024 __isl_give isl_union_map *isl_union_map_deltas_map(
2025 __isl_take isl_union_map *umap);
2027 The functions above construct a (basic, regular or union) relation
2028 that maps (a wrapped version of) the input relation to its delta set.
2032 Simplify the representation of a set or relation by trying
2033 to combine pairs of basic sets or relations into a single
2034 basic set or relation.
2036 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2037 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2038 __isl_give isl_union_set *isl_union_set_coalesce(
2039 __isl_take isl_union_set *uset);
2040 __isl_give isl_union_map *isl_union_map_coalesce(
2041 __isl_take isl_union_map *umap);
2043 One of the methods for combining pairs of basic sets or relations
2044 can result in coefficients that are much larger than those that appear
2045 in the constraints of the input. By default, the coefficients are
2046 not allowed to grow larger, but this can be changed by unsetting
2047 the following option.
2049 int isl_options_set_coalesce_bounded_wrapping(
2050 isl_ctx *ctx, int val);
2051 int isl_options_get_coalesce_bounded_wrapping(
2054 =item * Detecting equalities
2056 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2057 __isl_take isl_basic_set *bset);
2058 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2059 __isl_take isl_basic_map *bmap);
2060 __isl_give isl_set *isl_set_detect_equalities(
2061 __isl_take isl_set *set);
2062 __isl_give isl_map *isl_map_detect_equalities(
2063 __isl_take isl_map *map);
2064 __isl_give isl_union_set *isl_union_set_detect_equalities(
2065 __isl_take isl_union_set *uset);
2066 __isl_give isl_union_map *isl_union_map_detect_equalities(
2067 __isl_take isl_union_map *umap);
2069 Simplify the representation of a set or relation by detecting implicit
2072 =item * Removing redundant constraints
2074 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2075 __isl_take isl_basic_set *bset);
2076 __isl_give isl_set *isl_set_remove_redundancies(
2077 __isl_take isl_set *set);
2078 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2079 __isl_take isl_basic_map *bmap);
2080 __isl_give isl_map *isl_map_remove_redundancies(
2081 __isl_take isl_map *map);
2085 __isl_give isl_basic_set *isl_set_convex_hull(
2086 __isl_take isl_set *set);
2087 __isl_give isl_basic_map *isl_map_convex_hull(
2088 __isl_take isl_map *map);
2090 If the input set or relation has any existentially quantified
2091 variables, then the result of these operations is currently undefined.
2095 __isl_give isl_basic_set *isl_set_simple_hull(
2096 __isl_take isl_set *set);
2097 __isl_give isl_basic_map *isl_map_simple_hull(
2098 __isl_take isl_map *map);
2099 __isl_give isl_union_map *isl_union_map_simple_hull(
2100 __isl_take isl_union_map *umap);
2102 These functions compute a single basic set or relation
2103 that contains the whole input set or relation.
2104 In particular, the output is described by translates
2105 of the constraints describing the basic sets or relations in the input.
2109 (See \autoref{s:simple hull}.)
2115 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2116 __isl_take isl_basic_set *bset);
2117 __isl_give isl_basic_set *isl_set_affine_hull(
2118 __isl_take isl_set *set);
2119 __isl_give isl_union_set *isl_union_set_affine_hull(
2120 __isl_take isl_union_set *uset);
2121 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2122 __isl_take isl_basic_map *bmap);
2123 __isl_give isl_basic_map *isl_map_affine_hull(
2124 __isl_take isl_map *map);
2125 __isl_give isl_union_map *isl_union_map_affine_hull(
2126 __isl_take isl_union_map *umap);
2128 In case of union sets and relations, the affine hull is computed
2131 =item * Polyhedral hull
2133 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2134 __isl_take isl_set *set);
2135 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2136 __isl_take isl_map *map);
2137 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2138 __isl_take isl_union_set *uset);
2139 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2140 __isl_take isl_union_map *umap);
2142 These functions compute a single basic set or relation
2143 not involving any existentially quantified variables
2144 that contains the whole input set or relation.
2145 In case of union sets and relations, the polyhedral hull is computed
2150 __isl_give isl_basic_set *isl_basic_set_sample(
2151 __isl_take isl_basic_set *bset);
2152 __isl_give isl_basic_set *isl_set_sample(
2153 __isl_take isl_set *set);
2154 __isl_give isl_basic_map *isl_basic_map_sample(
2155 __isl_take isl_basic_map *bmap);
2156 __isl_give isl_basic_map *isl_map_sample(
2157 __isl_take isl_map *map);
2159 If the input (basic) set or relation is non-empty, then return
2160 a singleton subset of the input. Otherwise, return an empty set.
2162 =item * Optimization
2164 #include <isl/ilp.h>
2165 enum isl_lp_result isl_basic_set_max(
2166 __isl_keep isl_basic_set *bset,
2167 __isl_keep isl_aff *obj, isl_int *opt)
2168 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2169 __isl_keep isl_aff *obj, isl_int *opt);
2170 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2171 __isl_keep isl_aff *obj, isl_int *opt);
2173 Compute the minimum or maximum of the integer affine expression C<obj>
2174 over the points in C<set>, returning the result in C<opt>.
2175 The return value may be one of C<isl_lp_error>,
2176 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2178 =item * Parametric optimization
2180 __isl_give isl_pw_aff *isl_set_dim_min(
2181 __isl_take isl_set *set, int pos);
2182 __isl_give isl_pw_aff *isl_set_dim_max(
2183 __isl_take isl_set *set, int pos);
2184 __isl_give isl_pw_aff *isl_map_dim_max(
2185 __isl_take isl_map *map, int pos);
2187 Compute the minimum or maximum of the given set or output dimension
2188 as a function of the parameters (and input dimensions), but independently
2189 of the other set or output dimensions.
2190 For lexicographic optimization, see L<"Lexicographic Optimization">.
2194 The following functions compute either the set of (rational) coefficient
2195 values of valid constraints for the given set or the set of (rational)
2196 values satisfying the constraints with coefficients from the given set.
2197 Internally, these two sets of functions perform essentially the
2198 same operations, except that the set of coefficients is assumed to
2199 be a cone, while the set of values may be any polyhedron.
2200 The current implementation is based on the Farkas lemma and
2201 Fourier-Motzkin elimination, but this may change or be made optional
2202 in future. In particular, future implementations may use different
2203 dualization algorithms or skip the elimination step.
2205 __isl_give isl_basic_set *isl_basic_set_coefficients(
2206 __isl_take isl_basic_set *bset);
2207 __isl_give isl_basic_set *isl_set_coefficients(
2208 __isl_take isl_set *set);
2209 __isl_give isl_union_set *isl_union_set_coefficients(
2210 __isl_take isl_union_set *bset);
2211 __isl_give isl_basic_set *isl_basic_set_solutions(
2212 __isl_take isl_basic_set *bset);
2213 __isl_give isl_basic_set *isl_set_solutions(
2214 __isl_take isl_set *set);
2215 __isl_give isl_union_set *isl_union_set_solutions(
2216 __isl_take isl_union_set *bset);
2220 __isl_give isl_map *isl_map_fixed_power(
2221 __isl_take isl_map *map, isl_int exp);
2222 __isl_give isl_union_map *isl_union_map_fixed_power(
2223 __isl_take isl_union_map *umap, isl_int exp);
2225 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2226 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2227 of C<map> is computed.
2229 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2231 __isl_give isl_union_map *isl_union_map_power(
2232 __isl_take isl_union_map *umap, int *exact);
2234 Compute a parametric representation for all positive powers I<k> of C<map>.
2235 The result maps I<k> to a nested relation corresponding to the
2236 I<k>th power of C<map>.
2237 The result may be an overapproximation. If the result is known to be exact,
2238 then C<*exact> is set to C<1>.
2240 =item * Transitive closure
2242 __isl_give isl_map *isl_map_transitive_closure(
2243 __isl_take isl_map *map, int *exact);
2244 __isl_give isl_union_map *isl_union_map_transitive_closure(
2245 __isl_take isl_union_map *umap, int *exact);
2247 Compute the transitive closure of C<map>.
2248 The result may be an overapproximation. If the result is known to be exact,
2249 then C<*exact> is set to C<1>.
2251 =item * Reaching path lengths
2253 __isl_give isl_map *isl_map_reaching_path_lengths(
2254 __isl_take isl_map *map, int *exact);
2256 Compute a relation that maps each element in the range of C<map>
2257 to the lengths of all paths composed of edges in C<map> that
2258 end up in the given element.
2259 The result may be an overapproximation. If the result is known to be exact,
2260 then C<*exact> is set to C<1>.
2261 To compute the I<maximal> path length, the resulting relation
2262 should be postprocessed by C<isl_map_lexmax>.
2263 In particular, if the input relation is a dependence relation
2264 (mapping sources to sinks), then the maximal path length corresponds
2265 to the free schedule.
2266 Note, however, that C<isl_map_lexmax> expects the maximum to be
2267 finite, so if the path lengths are unbounded (possibly due to
2268 the overapproximation), then you will get an error message.
2272 __isl_give isl_basic_set *isl_basic_map_wrap(
2273 __isl_take isl_basic_map *bmap);
2274 __isl_give isl_set *isl_map_wrap(
2275 __isl_take isl_map *map);
2276 __isl_give isl_union_set *isl_union_map_wrap(
2277 __isl_take isl_union_map *umap);
2278 __isl_give isl_basic_map *isl_basic_set_unwrap(
2279 __isl_take isl_basic_set *bset);
2280 __isl_give isl_map *isl_set_unwrap(
2281 __isl_take isl_set *set);
2282 __isl_give isl_union_map *isl_union_set_unwrap(
2283 __isl_take isl_union_set *uset);
2287 Remove any internal structure of domain (and range) of the given
2288 set or relation. If there is any such internal structure in the input,
2289 then the name of the space is also removed.
2291 __isl_give isl_basic_set *isl_basic_set_flatten(
2292 __isl_take isl_basic_set *bset);
2293 __isl_give isl_set *isl_set_flatten(
2294 __isl_take isl_set *set);
2295 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2296 __isl_take isl_basic_map *bmap);
2297 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2298 __isl_take isl_basic_map *bmap);
2299 __isl_give isl_map *isl_map_flatten_range(
2300 __isl_take isl_map *map);
2301 __isl_give isl_map *isl_map_flatten_domain(
2302 __isl_take isl_map *map);
2303 __isl_give isl_basic_map *isl_basic_map_flatten(
2304 __isl_take isl_basic_map *bmap);
2305 __isl_give isl_map *isl_map_flatten(
2306 __isl_take isl_map *map);
2308 __isl_give isl_map *isl_set_flatten_map(
2309 __isl_take isl_set *set);
2311 The function above constructs a relation
2312 that maps the input set to a flattened version of the set.
2316 Lift the input set to a space with extra dimensions corresponding
2317 to the existentially quantified variables in the input.
2318 In particular, the result lives in a wrapped map where the domain
2319 is the original space and the range corresponds to the original
2320 existentially quantified variables.
2322 __isl_give isl_basic_set *isl_basic_set_lift(
2323 __isl_take isl_basic_set *bset);
2324 __isl_give isl_set *isl_set_lift(
2325 __isl_take isl_set *set);
2326 __isl_give isl_union_set *isl_union_set_lift(
2327 __isl_take isl_union_set *uset);
2329 Given a local space that contains the existentially quantified
2330 variables of a set, a basic relation that, when applied to
2331 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2332 can be constructed using the following function.
2334 #include <isl/local_space.h>
2335 __isl_give isl_basic_map *isl_local_space_lifting(
2336 __isl_take isl_local_space *ls);
2338 =item * Internal Product
2340 __isl_give isl_basic_map *isl_basic_map_zip(
2341 __isl_take isl_basic_map *bmap);
2342 __isl_give isl_map *isl_map_zip(
2343 __isl_take isl_map *map);
2344 __isl_give isl_union_map *isl_union_map_zip(
2345 __isl_take isl_union_map *umap);
2347 Given a relation with nested relations for domain and range,
2348 interchange the range of the domain with the domain of the range.
2352 __isl_give isl_basic_map *isl_basic_map_curry(
2353 __isl_take isl_basic_map *bmap);
2354 __isl_give isl_map *isl_map_curry(
2355 __isl_take isl_map *map);
2356 __isl_give isl_union_map *isl_union_map_curry(
2357 __isl_take isl_union_map *umap);
2359 Given a relation with a nested relation for domain,
2360 move the range of the nested relation out of the domain
2361 and use it as the domain of a nested relation in the range,
2362 with the original range as range of this nested relation.
2364 =item * Aligning parameters
2366 __isl_give isl_set *isl_set_align_params(
2367 __isl_take isl_set *set,
2368 __isl_take isl_space *model);
2369 __isl_give isl_map *isl_map_align_params(
2370 __isl_take isl_map *map,
2371 __isl_take isl_space *model);
2373 Change the order of the parameters of the given set or relation
2374 such that the first parameters match those of C<model>.
2375 This may involve the introduction of extra parameters.
2376 All parameters need to be named.
2378 =item * Dimension manipulation
2380 __isl_give isl_set *isl_set_add_dims(
2381 __isl_take isl_set *set,
2382 enum isl_dim_type type, unsigned n);
2383 __isl_give isl_map *isl_map_add_dims(
2384 __isl_take isl_map *map,
2385 enum isl_dim_type type, unsigned n);
2386 __isl_give isl_set *isl_set_insert_dims(
2387 __isl_take isl_set *set,
2388 enum isl_dim_type type, unsigned pos, unsigned n);
2389 __isl_give isl_map *isl_map_insert_dims(
2390 __isl_take isl_map *map,
2391 enum isl_dim_type type, unsigned pos, unsigned n);
2392 __isl_give isl_basic_set *isl_basic_set_move_dims(
2393 __isl_take isl_basic_set *bset,
2394 enum isl_dim_type dst_type, unsigned dst_pos,
2395 enum isl_dim_type src_type, unsigned src_pos,
2397 __isl_give isl_basic_map *isl_basic_map_move_dims(
2398 __isl_take isl_basic_map *bmap,
2399 enum isl_dim_type dst_type, unsigned dst_pos,
2400 enum isl_dim_type src_type, unsigned src_pos,
2402 __isl_give isl_set *isl_set_move_dims(
2403 __isl_take isl_set *set,
2404 enum isl_dim_type dst_type, unsigned dst_pos,
2405 enum isl_dim_type src_type, unsigned src_pos,
2407 __isl_give isl_map *isl_map_move_dims(
2408 __isl_take isl_map *map,
2409 enum isl_dim_type dst_type, unsigned dst_pos,
2410 enum isl_dim_type src_type, unsigned src_pos,
2413 It is usually not advisable to directly change the (input or output)
2414 space of a set or a relation as this removes the name and the internal
2415 structure of the space. However, the above functions can be useful
2416 to add new parameters, assuming
2417 C<isl_set_align_params> and C<isl_map_align_params>
2422 =head2 Binary Operations
2424 The two arguments of a binary operation not only need to live
2425 in the same C<isl_ctx>, they currently also need to have
2426 the same (number of) parameters.
2428 =head3 Basic Operations
2432 =item * Intersection
2434 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2435 __isl_take isl_basic_set *bset1,
2436 __isl_take isl_basic_set *bset2);
2437 __isl_give isl_basic_set *isl_basic_set_intersect(
2438 __isl_take isl_basic_set *bset1,
2439 __isl_take isl_basic_set *bset2);
2440 __isl_give isl_set *isl_set_intersect_params(
2441 __isl_take isl_set *set,
2442 __isl_take isl_set *params);
2443 __isl_give isl_set *isl_set_intersect(
2444 __isl_take isl_set *set1,
2445 __isl_take isl_set *set2);
2446 __isl_give isl_union_set *isl_union_set_intersect_params(
2447 __isl_take isl_union_set *uset,
2448 __isl_take isl_set *set);
2449 __isl_give isl_union_map *isl_union_map_intersect_params(
2450 __isl_take isl_union_map *umap,
2451 __isl_take isl_set *set);
2452 __isl_give isl_union_set *isl_union_set_intersect(
2453 __isl_take isl_union_set *uset1,
2454 __isl_take isl_union_set *uset2);
2455 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2456 __isl_take isl_basic_map *bmap,
2457 __isl_take isl_basic_set *bset);
2458 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2459 __isl_take isl_basic_map *bmap,
2460 __isl_take isl_basic_set *bset);
2461 __isl_give isl_basic_map *isl_basic_map_intersect(
2462 __isl_take isl_basic_map *bmap1,
2463 __isl_take isl_basic_map *bmap2);
2464 __isl_give isl_map *isl_map_intersect_params(
2465 __isl_take isl_map *map,
2466 __isl_take isl_set *params);
2467 __isl_give isl_map *isl_map_intersect_domain(
2468 __isl_take isl_map *map,
2469 __isl_take isl_set *set);
2470 __isl_give isl_map *isl_map_intersect_range(
2471 __isl_take isl_map *map,
2472 __isl_take isl_set *set);
2473 __isl_give isl_map *isl_map_intersect(
2474 __isl_take isl_map *map1,
2475 __isl_take isl_map *map2);
2476 __isl_give isl_union_map *isl_union_map_intersect_domain(
2477 __isl_take isl_union_map *umap,
2478 __isl_take isl_union_set *uset);
2479 __isl_give isl_union_map *isl_union_map_intersect_range(
2480 __isl_take isl_union_map *umap,
2481 __isl_take isl_union_set *uset);
2482 __isl_give isl_union_map *isl_union_map_intersect(
2483 __isl_take isl_union_map *umap1,
2484 __isl_take isl_union_map *umap2);
2486 The second argument to the C<_params> functions needs to be
2487 a parametric (basic) set. For the other functions, a parametric set
2488 for either argument is only allowed if the other argument is
2489 a parametric set as well.
2493 __isl_give isl_set *isl_basic_set_union(
2494 __isl_take isl_basic_set *bset1,
2495 __isl_take isl_basic_set *bset2);
2496 __isl_give isl_map *isl_basic_map_union(
2497 __isl_take isl_basic_map *bmap1,
2498 __isl_take isl_basic_map *bmap2);
2499 __isl_give isl_set *isl_set_union(
2500 __isl_take isl_set *set1,
2501 __isl_take isl_set *set2);
2502 __isl_give isl_map *isl_map_union(
2503 __isl_take isl_map *map1,
2504 __isl_take isl_map *map2);
2505 __isl_give isl_union_set *isl_union_set_union(
2506 __isl_take isl_union_set *uset1,
2507 __isl_take isl_union_set *uset2);
2508 __isl_give isl_union_map *isl_union_map_union(
2509 __isl_take isl_union_map *umap1,
2510 __isl_take isl_union_map *umap2);
2512 =item * Set difference
2514 __isl_give isl_set *isl_set_subtract(
2515 __isl_take isl_set *set1,
2516 __isl_take isl_set *set2);
2517 __isl_give isl_map *isl_map_subtract(
2518 __isl_take isl_map *map1,
2519 __isl_take isl_map *map2);
2520 __isl_give isl_map *isl_map_subtract_domain(
2521 __isl_take isl_map *map,
2522 __isl_take isl_set *dom);
2523 __isl_give isl_map *isl_map_subtract_range(
2524 __isl_take isl_map *map,
2525 __isl_take isl_set *dom);
2526 __isl_give isl_union_set *isl_union_set_subtract(
2527 __isl_take isl_union_set *uset1,
2528 __isl_take isl_union_set *uset2);
2529 __isl_give isl_union_map *isl_union_map_subtract(
2530 __isl_take isl_union_map *umap1,
2531 __isl_take isl_union_map *umap2);
2535 __isl_give isl_basic_set *isl_basic_set_apply(
2536 __isl_take isl_basic_set *bset,
2537 __isl_take isl_basic_map *bmap);
2538 __isl_give isl_set *isl_set_apply(
2539 __isl_take isl_set *set,
2540 __isl_take isl_map *map);
2541 __isl_give isl_union_set *isl_union_set_apply(
2542 __isl_take isl_union_set *uset,
2543 __isl_take isl_union_map *umap);
2544 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2545 __isl_take isl_basic_map *bmap1,
2546 __isl_take isl_basic_map *bmap2);
2547 __isl_give isl_basic_map *isl_basic_map_apply_range(
2548 __isl_take isl_basic_map *bmap1,
2549 __isl_take isl_basic_map *bmap2);
2550 __isl_give isl_map *isl_map_apply_domain(
2551 __isl_take isl_map *map1,
2552 __isl_take isl_map *map2);
2553 __isl_give isl_union_map *isl_union_map_apply_domain(
2554 __isl_take isl_union_map *umap1,
2555 __isl_take isl_union_map *umap2);
2556 __isl_give isl_map *isl_map_apply_range(
2557 __isl_take isl_map *map1,
2558 __isl_take isl_map *map2);
2559 __isl_give isl_union_map *isl_union_map_apply_range(
2560 __isl_take isl_union_map *umap1,
2561 __isl_take isl_union_map *umap2);
2563 =item * Cartesian Product
2565 __isl_give isl_set *isl_set_product(
2566 __isl_take isl_set *set1,
2567 __isl_take isl_set *set2);
2568 __isl_give isl_union_set *isl_union_set_product(
2569 __isl_take isl_union_set *uset1,
2570 __isl_take isl_union_set *uset2);
2571 __isl_give isl_basic_map *isl_basic_map_domain_product(
2572 __isl_take isl_basic_map *bmap1,
2573 __isl_take isl_basic_map *bmap2);
2574 __isl_give isl_basic_map *isl_basic_map_range_product(
2575 __isl_take isl_basic_map *bmap1,
2576 __isl_take isl_basic_map *bmap2);
2577 __isl_give isl_map *isl_map_domain_product(
2578 __isl_take isl_map *map1,
2579 __isl_take isl_map *map2);
2580 __isl_give isl_map *isl_map_range_product(
2581 __isl_take isl_map *map1,
2582 __isl_take isl_map *map2);
2583 __isl_give isl_union_map *isl_union_map_range_product(
2584 __isl_take isl_union_map *umap1,
2585 __isl_take isl_union_map *umap2);
2586 __isl_give isl_map *isl_map_product(
2587 __isl_take isl_map *map1,
2588 __isl_take isl_map *map2);
2589 __isl_give isl_union_map *isl_union_map_product(
2590 __isl_take isl_union_map *umap1,
2591 __isl_take isl_union_map *umap2);
2593 The above functions compute the cross product of the given
2594 sets or relations. The domains and ranges of the results
2595 are wrapped maps between domains and ranges of the inputs.
2596 To obtain a ``flat'' product, use the following functions
2599 __isl_give isl_basic_set *isl_basic_set_flat_product(
2600 __isl_take isl_basic_set *bset1,
2601 __isl_take isl_basic_set *bset2);
2602 __isl_give isl_set *isl_set_flat_product(
2603 __isl_take isl_set *set1,
2604 __isl_take isl_set *set2);
2605 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2606 __isl_take isl_basic_map *bmap1,
2607 __isl_take isl_basic_map *bmap2);
2608 __isl_give isl_map *isl_map_flat_domain_product(
2609 __isl_take isl_map *map1,
2610 __isl_take isl_map *map2);
2611 __isl_give isl_map *isl_map_flat_range_product(
2612 __isl_take isl_map *map1,
2613 __isl_take isl_map *map2);
2614 __isl_give isl_union_map *isl_union_map_flat_range_product(
2615 __isl_take isl_union_map *umap1,
2616 __isl_take isl_union_map *umap2);
2617 __isl_give isl_basic_map *isl_basic_map_flat_product(
2618 __isl_take isl_basic_map *bmap1,
2619 __isl_take isl_basic_map *bmap2);
2620 __isl_give isl_map *isl_map_flat_product(
2621 __isl_take isl_map *map1,
2622 __isl_take isl_map *map2);
2624 =item * Simplification
2626 __isl_give isl_basic_set *isl_basic_set_gist(
2627 __isl_take isl_basic_set *bset,
2628 __isl_take isl_basic_set *context);
2629 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2630 __isl_take isl_set *context);
2631 __isl_give isl_set *isl_set_gist_params(
2632 __isl_take isl_set *set,
2633 __isl_take isl_set *context);
2634 __isl_give isl_union_set *isl_union_set_gist(
2635 __isl_take isl_union_set *uset,
2636 __isl_take isl_union_set *context);
2637 __isl_give isl_union_set *isl_union_set_gist_params(
2638 __isl_take isl_union_set *uset,
2639 __isl_take isl_set *set);
2640 __isl_give isl_basic_map *isl_basic_map_gist(
2641 __isl_take isl_basic_map *bmap,
2642 __isl_take isl_basic_map *context);
2643 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2644 __isl_take isl_map *context);
2645 __isl_give isl_map *isl_map_gist_params(
2646 __isl_take isl_map *map,
2647 __isl_take isl_set *context);
2648 __isl_give isl_map *isl_map_gist_domain(
2649 __isl_take isl_map *map,
2650 __isl_take isl_set *context);
2651 __isl_give isl_map *isl_map_gist_range(
2652 __isl_take isl_map *map,
2653 __isl_take isl_set *context);
2654 __isl_give isl_union_map *isl_union_map_gist(
2655 __isl_take isl_union_map *umap,
2656 __isl_take isl_union_map *context);
2657 __isl_give isl_union_map *isl_union_map_gist_params(
2658 __isl_take isl_union_map *umap,
2659 __isl_take isl_set *set);
2660 __isl_give isl_union_map *isl_union_map_gist_domain(
2661 __isl_take isl_union_map *umap,
2662 __isl_take isl_union_set *uset);
2663 __isl_give isl_union_map *isl_union_map_gist_range(
2664 __isl_take isl_union_map *umap,
2665 __isl_take isl_union_set *uset);
2667 The gist operation returns a set or relation that has the
2668 same intersection with the context as the input set or relation.
2669 Any implicit equality in the intersection is made explicit in the result,
2670 while all inequalities that are redundant with respect to the intersection
2672 In case of union sets and relations, the gist operation is performed
2677 =head3 Lexicographic Optimization
2679 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2680 the following functions
2681 compute a set that contains the lexicographic minimum or maximum
2682 of the elements in C<set> (or C<bset>) for those values of the parameters
2683 that satisfy C<dom>.
2684 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2685 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2687 In other words, the union of the parameter values
2688 for which the result is non-empty and of C<*empty>
2691 __isl_give isl_set *isl_basic_set_partial_lexmin(
2692 __isl_take isl_basic_set *bset,
2693 __isl_take isl_basic_set *dom,
2694 __isl_give isl_set **empty);
2695 __isl_give isl_set *isl_basic_set_partial_lexmax(
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_set_partial_lexmin(
2700 __isl_take isl_set *set, __isl_take isl_set *dom,
2701 __isl_give isl_set **empty);
2702 __isl_give isl_set *isl_set_partial_lexmax(
2703 __isl_take isl_set *set, __isl_take isl_set *dom,
2704 __isl_give isl_set **empty);
2706 Given a (basic) set C<set> (or C<bset>), the following functions simply
2707 return a set containing the lexicographic minimum or maximum
2708 of the elements in C<set> (or C<bset>).
2709 In case of union sets, the optimum is computed per space.
2711 __isl_give isl_set *isl_basic_set_lexmin(
2712 __isl_take isl_basic_set *bset);
2713 __isl_give isl_set *isl_basic_set_lexmax(
2714 __isl_take isl_basic_set *bset);
2715 __isl_give isl_set *isl_set_lexmin(
2716 __isl_take isl_set *set);
2717 __isl_give isl_set *isl_set_lexmax(
2718 __isl_take isl_set *set);
2719 __isl_give isl_union_set *isl_union_set_lexmin(
2720 __isl_take isl_union_set *uset);
2721 __isl_give isl_union_set *isl_union_set_lexmax(
2722 __isl_take isl_union_set *uset);
2724 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2725 the following functions
2726 compute a relation that maps each element of C<dom>
2727 to the single lexicographic minimum or maximum
2728 of the elements that are associated to that same
2729 element in C<map> (or C<bmap>).
2730 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2731 that contains the elements in C<dom> that do not map
2732 to any elements in C<map> (or C<bmap>).
2733 In other words, the union of the domain of the result and of C<*empty>
2736 __isl_give isl_map *isl_basic_map_partial_lexmax(
2737 __isl_take isl_basic_map *bmap,
2738 __isl_take isl_basic_set *dom,
2739 __isl_give isl_set **empty);
2740 __isl_give isl_map *isl_basic_map_partial_lexmin(
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_map_partial_lexmax(
2745 __isl_take isl_map *map, __isl_take isl_set *dom,
2746 __isl_give isl_set **empty);
2747 __isl_give isl_map *isl_map_partial_lexmin(
2748 __isl_take isl_map *map, __isl_take isl_set *dom,
2749 __isl_give isl_set **empty);
2751 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2752 return a map mapping each element in the domain of
2753 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2754 of all elements associated to that element.
2755 In case of union relations, the optimum is computed per space.
2757 __isl_give isl_map *isl_basic_map_lexmin(
2758 __isl_take isl_basic_map *bmap);
2759 __isl_give isl_map *isl_basic_map_lexmax(
2760 __isl_take isl_basic_map *bmap);
2761 __isl_give isl_map *isl_map_lexmin(
2762 __isl_take isl_map *map);
2763 __isl_give isl_map *isl_map_lexmax(
2764 __isl_take isl_map *map);
2765 __isl_give isl_union_map *isl_union_map_lexmin(
2766 __isl_take isl_union_map *umap);
2767 __isl_give isl_union_map *isl_union_map_lexmax(
2768 __isl_take isl_union_map *umap);
2770 The following functions return their result in the form of
2771 a piecewise multi-affine expression
2772 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2773 but are otherwise equivalent to the corresponding functions
2774 returning a basic set or relation.
2776 __isl_give isl_pw_multi_aff *
2777 isl_basic_map_lexmin_pw_multi_aff(
2778 __isl_take isl_basic_map *bmap);
2779 __isl_give isl_pw_multi_aff *
2780 isl_basic_set_partial_lexmin_pw_multi_aff(
2781 __isl_take isl_basic_set *bset,
2782 __isl_take isl_basic_set *dom,
2783 __isl_give isl_set **empty);
2784 __isl_give isl_pw_multi_aff *
2785 isl_basic_set_partial_lexmax_pw_multi_aff(
2786 __isl_take isl_basic_set *bset,
2787 __isl_take isl_basic_set *dom,
2788 __isl_give isl_set **empty);
2789 __isl_give isl_pw_multi_aff *
2790 isl_basic_map_partial_lexmin_pw_multi_aff(
2791 __isl_take isl_basic_map *bmap,
2792 __isl_take isl_basic_set *dom,
2793 __isl_give isl_set **empty);
2794 __isl_give isl_pw_multi_aff *
2795 isl_basic_map_partial_lexmax_pw_multi_aff(
2796 __isl_take isl_basic_map *bmap,
2797 __isl_take isl_basic_set *dom,
2798 __isl_give isl_set **empty);
2802 Lists are defined over several element types, including
2803 C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2804 Here we take lists of C<isl_set>s as an example.
2805 Lists can be created, copied and freed using the following functions.
2807 #include <isl/list.h>
2808 __isl_give isl_set_list *isl_set_list_from_set(
2809 __isl_take isl_set *el);
2810 __isl_give isl_set_list *isl_set_list_alloc(
2811 isl_ctx *ctx, int n);
2812 __isl_give isl_set_list *isl_set_list_copy(
2813 __isl_keep isl_set_list *list);
2814 __isl_give isl_set_list *isl_set_list_add(
2815 __isl_take isl_set_list *list,
2816 __isl_take isl_set *el);
2817 __isl_give isl_set_list *isl_set_list_concat(
2818 __isl_take isl_set_list *list1,
2819 __isl_take isl_set_list *list2);
2820 void *isl_set_list_free(__isl_take isl_set_list *list);
2822 C<isl_set_list_alloc> creates an empty list with a capacity for
2823 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2826 Lists can be inspected using the following functions.
2828 #include <isl/list.h>
2829 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2830 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2831 __isl_give isl_set *isl_set_list_get_set(
2832 __isl_keep isl_set_list *list, int index);
2833 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2834 int (*fn)(__isl_take isl_set *el, void *user),
2837 Lists can be printed using
2839 #include <isl/list.h>
2840 __isl_give isl_printer *isl_printer_print_set_list(
2841 __isl_take isl_printer *p,
2842 __isl_keep isl_set_list *list);
2846 Vectors can be created, copied and freed using the following functions.
2848 #include <isl/vec.h>
2849 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2851 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2852 void isl_vec_free(__isl_take isl_vec *vec);
2854 Note that the elements of a newly created vector may have arbitrary values.
2855 The elements can be changed and inspected using the following functions.
2857 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2858 int isl_vec_size(__isl_keep isl_vec *vec);
2859 int isl_vec_get_element(__isl_keep isl_vec *vec,
2860 int pos, isl_int *v);
2861 __isl_give isl_vec *isl_vec_set_element(
2862 __isl_take isl_vec *vec, int pos, isl_int v);
2863 __isl_give isl_vec *isl_vec_set_element_si(
2864 __isl_take isl_vec *vec, int pos, int v);
2865 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2867 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2870 C<isl_vec_get_element> will return a negative value if anything went wrong.
2871 In that case, the value of C<*v> is undefined.
2875 Matrices can be created, copied and freed using the following functions.
2877 #include <isl/mat.h>
2878 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2879 unsigned n_row, unsigned n_col);
2880 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2881 void isl_mat_free(__isl_take isl_mat *mat);
2883 Note that the elements of a newly created matrix may have arbitrary values.
2884 The elements can be changed and inspected using the following functions.
2886 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2887 int isl_mat_rows(__isl_keep isl_mat *mat);
2888 int isl_mat_cols(__isl_keep isl_mat *mat);
2889 int isl_mat_get_element(__isl_keep isl_mat *mat,
2890 int row, int col, isl_int *v);
2891 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2892 int row, int col, isl_int v);
2893 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2894 int row, int col, int v);
2896 C<isl_mat_get_element> will return a negative value if anything went wrong.
2897 In that case, the value of C<*v> is undefined.
2899 The following function can be used to compute the (right) inverse
2900 of a matrix, i.e., a matrix such that the product of the original
2901 and the inverse (in that order) is a multiple of the identity matrix.
2902 The input matrix is assumed to be of full row-rank.
2904 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2906 The following function can be used to compute the (right) kernel
2907 (or null space) of a matrix, i.e., a matrix such that the product of
2908 the original and the kernel (in that order) is the zero matrix.
2910 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2912 =head2 Piecewise Quasi Affine Expressions
2914 The zero quasi affine expression on a given domain can be created using
2916 __isl_give isl_aff *isl_aff_zero_on_domain(
2917 __isl_take isl_local_space *ls);
2919 Note that the space in which the resulting object lives is a map space
2920 with the given space as domain and a one-dimensional range.
2922 An empty piecewise quasi affine expression (one with no cells)
2923 or a piecewise quasi affine expression with a single cell can
2924 be created using the following functions.
2926 #include <isl/aff.h>
2927 __isl_give isl_pw_aff *isl_pw_aff_empty(
2928 __isl_take isl_space *space);
2929 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2930 __isl_take isl_set *set, __isl_take isl_aff *aff);
2931 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2932 __isl_take isl_aff *aff);
2934 A piecewise quasi affine expression that is equal to 1 on a set
2935 and 0 outside the set can be created using the following function.
2937 #include <isl/aff.h>
2938 __isl_give isl_pw_aff *isl_set_indicator_function(
2939 __isl_take isl_set *set);
2941 Quasi affine expressions can be copied and freed using
2943 #include <isl/aff.h>
2944 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2945 void *isl_aff_free(__isl_take isl_aff *aff);
2947 __isl_give isl_pw_aff *isl_pw_aff_copy(
2948 __isl_keep isl_pw_aff *pwaff);
2949 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2951 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2952 using the following function. The constraint is required to have
2953 a non-zero coefficient for the specified dimension.
2955 #include <isl/constraint.h>
2956 __isl_give isl_aff *isl_constraint_get_bound(
2957 __isl_keep isl_constraint *constraint,
2958 enum isl_dim_type type, int pos);
2960 The entire affine expression of the constraint can also be extracted
2961 using the following function.
2963 #include <isl/constraint.h>
2964 __isl_give isl_aff *isl_constraint_get_aff(
2965 __isl_keep isl_constraint *constraint);
2967 Conversely, an equality constraint equating
2968 the affine expression to zero or an inequality constraint enforcing
2969 the affine expression to be non-negative, can be constructed using
2971 __isl_give isl_constraint *isl_equality_from_aff(
2972 __isl_take isl_aff *aff);
2973 __isl_give isl_constraint *isl_inequality_from_aff(
2974 __isl_take isl_aff *aff);
2976 The expression can be inspected using
2978 #include <isl/aff.h>
2979 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
2980 int isl_aff_dim(__isl_keep isl_aff *aff,
2981 enum isl_dim_type type);
2982 __isl_give isl_local_space *isl_aff_get_domain_local_space(
2983 __isl_keep isl_aff *aff);
2984 __isl_give isl_local_space *isl_aff_get_local_space(
2985 __isl_keep isl_aff *aff);
2986 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
2987 enum isl_dim_type type, unsigned pos);
2988 const char *isl_pw_aff_get_dim_name(
2989 __isl_keep isl_pw_aff *pa,
2990 enum isl_dim_type type, unsigned pos);
2991 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
2992 enum isl_dim_type type, unsigned pos);
2993 __isl_give isl_id *isl_pw_aff_get_dim_id(
2994 __isl_keep isl_pw_aff *pa,
2995 enum isl_dim_type type, unsigned pos);
2996 int isl_aff_get_constant(__isl_keep isl_aff *aff,
2998 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
2999 enum isl_dim_type type, int pos, isl_int *v);
3000 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3002 __isl_give isl_aff *isl_aff_get_div(
3003 __isl_keep isl_aff *aff, int pos);
3005 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3006 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3007 int (*fn)(__isl_take isl_set *set,
3008 __isl_take isl_aff *aff,
3009 void *user), void *user);
3011 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3012 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3014 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3015 enum isl_dim_type type, unsigned first, unsigned n);
3016 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3017 enum isl_dim_type type, unsigned first, unsigned n);
3019 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3020 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3021 enum isl_dim_type type);
3022 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3024 It can be modified using
3026 #include <isl/aff.h>
3027 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3028 __isl_take isl_pw_aff *pwaff,
3029 enum isl_dim_type type, __isl_take isl_id *id);
3030 __isl_give isl_aff *isl_aff_set_dim_name(
3031 __isl_take isl_aff *aff, enum isl_dim_type type,
3032 unsigned pos, const char *s);
3033 __isl_give isl_aff *isl_aff_set_dim_id(
3034 __isl_take isl_aff *aff, enum isl_dim_type type,
3035 unsigned pos, __isl_take isl_id *id);
3036 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3037 __isl_take isl_pw_aff *pma,
3038 enum isl_dim_type type, unsigned pos,
3039 __isl_take isl_id *id);
3040 __isl_give isl_aff *isl_aff_set_constant(
3041 __isl_take isl_aff *aff, isl_int v);
3042 __isl_give isl_aff *isl_aff_set_constant_si(
3043 __isl_take isl_aff *aff, int v);
3044 __isl_give isl_aff *isl_aff_set_coefficient(
3045 __isl_take isl_aff *aff,
3046 enum isl_dim_type type, int pos, isl_int v);
3047 __isl_give isl_aff *isl_aff_set_coefficient_si(
3048 __isl_take isl_aff *aff,
3049 enum isl_dim_type type, int pos, int v);
3050 __isl_give isl_aff *isl_aff_set_denominator(
3051 __isl_take isl_aff *aff, isl_int v);
3053 __isl_give isl_aff *isl_aff_add_constant(
3054 __isl_take isl_aff *aff, isl_int v);
3055 __isl_give isl_aff *isl_aff_add_constant_si(
3056 __isl_take isl_aff *aff, int v);
3057 __isl_give isl_aff *isl_aff_add_coefficient(
3058 __isl_take isl_aff *aff,
3059 enum isl_dim_type type, int pos, isl_int v);
3060 __isl_give isl_aff *isl_aff_add_coefficient_si(
3061 __isl_take isl_aff *aff,
3062 enum isl_dim_type type, int pos, int v);
3064 __isl_give isl_aff *isl_aff_insert_dims(
3065 __isl_take isl_aff *aff,
3066 enum isl_dim_type type, unsigned first, unsigned n);
3067 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3068 __isl_take isl_pw_aff *pwaff,
3069 enum isl_dim_type type, unsigned first, unsigned n);
3070 __isl_give isl_aff *isl_aff_add_dims(
3071 __isl_take isl_aff *aff,
3072 enum isl_dim_type type, unsigned n);
3073 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3074 __isl_take isl_pw_aff *pwaff,
3075 enum isl_dim_type type, unsigned n);
3076 __isl_give isl_aff *isl_aff_drop_dims(
3077 __isl_take isl_aff *aff,
3078 enum isl_dim_type type, unsigned first, unsigned n);
3079 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3080 __isl_take isl_pw_aff *pwaff,
3081 enum isl_dim_type type, unsigned first, unsigned n);
3083 Note that the C<set_constant> and C<set_coefficient> functions
3084 set the I<numerator> of the constant or coefficient, while
3085 C<add_constant> and C<add_coefficient> add an integer value to
3086 the possibly rational constant or coefficient.
3088 To check whether an affine expressions is obviously zero
3089 or obviously equal to some other affine expression, use
3091 #include <isl/aff.h>
3092 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3093 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3094 __isl_keep isl_aff *aff2);
3095 int isl_pw_aff_plain_is_equal(
3096 __isl_keep isl_pw_aff *pwaff1,
3097 __isl_keep isl_pw_aff *pwaff2);
3101 #include <isl/aff.h>
3102 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3103 __isl_take isl_aff *aff2);
3104 __isl_give isl_pw_aff *isl_pw_aff_add(
3105 __isl_take isl_pw_aff *pwaff1,
3106 __isl_take isl_pw_aff *pwaff2);
3107 __isl_give isl_pw_aff *isl_pw_aff_min(
3108 __isl_take isl_pw_aff *pwaff1,
3109 __isl_take isl_pw_aff *pwaff2);
3110 __isl_give isl_pw_aff *isl_pw_aff_max(
3111 __isl_take isl_pw_aff *pwaff1,
3112 __isl_take isl_pw_aff *pwaff2);
3113 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3114 __isl_take isl_aff *aff2);
3115 __isl_give isl_pw_aff *isl_pw_aff_sub(
3116 __isl_take isl_pw_aff *pwaff1,
3117 __isl_take isl_pw_aff *pwaff2);
3118 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3119 __isl_give isl_pw_aff *isl_pw_aff_neg(
3120 __isl_take isl_pw_aff *pwaff);
3121 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3122 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3123 __isl_take isl_pw_aff *pwaff);
3124 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3125 __isl_give isl_pw_aff *isl_pw_aff_floor(
3126 __isl_take isl_pw_aff *pwaff);
3127 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3129 __isl_give isl_pw_aff *isl_pw_aff_mod(
3130 __isl_take isl_pw_aff *pwaff, isl_int mod);
3131 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3133 __isl_give isl_pw_aff *isl_pw_aff_scale(
3134 __isl_take isl_pw_aff *pwaff, isl_int f);
3135 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3137 __isl_give isl_aff *isl_aff_scale_down_ui(
3138 __isl_take isl_aff *aff, unsigned f);
3139 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3140 __isl_take isl_pw_aff *pwaff, isl_int f);
3142 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3143 __isl_take isl_pw_aff_list *list);
3144 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3145 __isl_take isl_pw_aff_list *list);
3147 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3148 __isl_take isl_pw_aff *pwqp);
3150 __isl_give isl_aff *isl_aff_align_params(
3151 __isl_take isl_aff *aff,
3152 __isl_take isl_space *model);
3153 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3154 __isl_take isl_pw_aff *pwaff,
3155 __isl_take isl_space *model);
3157 __isl_give isl_aff *isl_aff_project_domain_on_params(
3158 __isl_take isl_aff *aff);
3160 __isl_give isl_aff *isl_aff_gist_params(
3161 __isl_take isl_aff *aff,
3162 __isl_take isl_set *context);
3163 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3164 __isl_take isl_set *context);
3165 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3166 __isl_take isl_pw_aff *pwaff,
3167 __isl_take isl_set *context);
3168 __isl_give isl_pw_aff *isl_pw_aff_gist(
3169 __isl_take isl_pw_aff *pwaff,
3170 __isl_take isl_set *context);
3172 __isl_give isl_set *isl_pw_aff_domain(
3173 __isl_take isl_pw_aff *pwaff);
3174 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3175 __isl_take isl_pw_aff *pa,
3176 __isl_take isl_set *set);
3177 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3178 __isl_take isl_pw_aff *pa,
3179 __isl_take isl_set *set);
3181 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3182 __isl_take isl_aff *aff2);
3183 __isl_give isl_pw_aff *isl_pw_aff_mul(
3184 __isl_take isl_pw_aff *pwaff1,
3185 __isl_take isl_pw_aff *pwaff2);
3187 When multiplying two affine expressions, at least one of the two needs
3190 #include <isl/aff.h>
3191 __isl_give isl_basic_set *isl_aff_le_basic_set(
3192 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3193 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3194 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3195 __isl_give isl_set *isl_pw_aff_eq_set(
3196 __isl_take isl_pw_aff *pwaff1,
3197 __isl_take isl_pw_aff *pwaff2);
3198 __isl_give isl_set *isl_pw_aff_ne_set(
3199 __isl_take isl_pw_aff *pwaff1,
3200 __isl_take isl_pw_aff *pwaff2);
3201 __isl_give isl_set *isl_pw_aff_le_set(
3202 __isl_take isl_pw_aff *pwaff1,
3203 __isl_take isl_pw_aff *pwaff2);
3204 __isl_give isl_set *isl_pw_aff_lt_set(
3205 __isl_take isl_pw_aff *pwaff1,
3206 __isl_take isl_pw_aff *pwaff2);
3207 __isl_give isl_set *isl_pw_aff_ge_set(
3208 __isl_take isl_pw_aff *pwaff1,
3209 __isl_take isl_pw_aff *pwaff2);
3210 __isl_give isl_set *isl_pw_aff_gt_set(
3211 __isl_take isl_pw_aff *pwaff1,
3212 __isl_take isl_pw_aff *pwaff2);
3214 __isl_give isl_set *isl_pw_aff_list_eq_set(
3215 __isl_take isl_pw_aff_list *list1,
3216 __isl_take isl_pw_aff_list *list2);
3217 __isl_give isl_set *isl_pw_aff_list_ne_set(
3218 __isl_take isl_pw_aff_list *list1,
3219 __isl_take isl_pw_aff_list *list2);
3220 __isl_give isl_set *isl_pw_aff_list_le_set(
3221 __isl_take isl_pw_aff_list *list1,
3222 __isl_take isl_pw_aff_list *list2);
3223 __isl_give isl_set *isl_pw_aff_list_lt_set(
3224 __isl_take isl_pw_aff_list *list1,
3225 __isl_take isl_pw_aff_list *list2);
3226 __isl_give isl_set *isl_pw_aff_list_ge_set(
3227 __isl_take isl_pw_aff_list *list1,
3228 __isl_take isl_pw_aff_list *list2);
3229 __isl_give isl_set *isl_pw_aff_list_gt_set(
3230 __isl_take isl_pw_aff_list *list1,
3231 __isl_take isl_pw_aff_list *list2);
3233 The function C<isl_aff_ge_basic_set> returns a basic set
3234 containing those elements in the shared space
3235 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3236 The function C<isl_pw_aff_ge_set> returns a set
3237 containing those elements in the shared domain
3238 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3239 The functions operating on C<isl_pw_aff_list> apply the corresponding
3240 C<isl_pw_aff> function to each pair of elements in the two lists.
3242 #include <isl/aff.h>
3243 __isl_give isl_set *isl_pw_aff_nonneg_set(
3244 __isl_take isl_pw_aff *pwaff);
3245 __isl_give isl_set *isl_pw_aff_zero_set(
3246 __isl_take isl_pw_aff *pwaff);
3247 __isl_give isl_set *isl_pw_aff_non_zero_set(
3248 __isl_take isl_pw_aff *pwaff);
3250 The function C<isl_pw_aff_nonneg_set> returns a set
3251 containing those elements in the domain
3252 of C<pwaff> where C<pwaff> is non-negative.
3254 #include <isl/aff.h>
3255 __isl_give isl_pw_aff *isl_pw_aff_cond(
3256 __isl_take isl_pw_aff *cond,
3257 __isl_take isl_pw_aff *pwaff_true,
3258 __isl_take isl_pw_aff *pwaff_false);
3260 The function C<isl_pw_aff_cond> performs a conditional operator
3261 and returns an expression that is equal to C<pwaff_true>
3262 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3263 where C<cond> is zero.
3265 #include <isl/aff.h>
3266 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3267 __isl_take isl_pw_aff *pwaff1,
3268 __isl_take isl_pw_aff *pwaff2);
3269 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3270 __isl_take isl_pw_aff *pwaff1,
3271 __isl_take isl_pw_aff *pwaff2);
3272 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3273 __isl_take isl_pw_aff *pwaff1,
3274 __isl_take isl_pw_aff *pwaff2);
3276 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3277 expression with a domain that is the union of those of C<pwaff1> and
3278 C<pwaff2> and such that on each cell, the quasi-affine expression is
3279 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3280 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3281 associated expression is the defined one.
3283 An expression can be read from input using
3285 #include <isl/aff.h>
3286 __isl_give isl_aff *isl_aff_read_from_str(
3287 isl_ctx *ctx, const char *str);
3288 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3289 isl_ctx *ctx, const char *str);
3291 An expression can be printed using
3293 #include <isl/aff.h>
3294 __isl_give isl_printer *isl_printer_print_aff(
3295 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3297 __isl_give isl_printer *isl_printer_print_pw_aff(
3298 __isl_take isl_printer *p,
3299 __isl_keep isl_pw_aff *pwaff);
3301 =head2 Piecewise Multiple Quasi Affine Expressions
3303 An C<isl_multi_aff> object represents a sequence of
3304 zero or more affine expressions, all defined on the same domain space.
3306 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3309 #include <isl/aff.h>
3310 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3311 __isl_take isl_space *space,
3312 __isl_take isl_aff_list *list);
3314 An empty piecewise multiple quasi affine expression (one with no cells),
3315 the zero piecewise multiple quasi affine expression (with value zero
3316 for each output dimension),
3317 a piecewise multiple quasi affine expression with a single cell (with
3318 either a universe or a specified domain) or
3319 a zero-dimensional piecewise multiple quasi affine expression
3321 can be created using the following functions.
3323 #include <isl/aff.h>
3324 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3325 __isl_take isl_space *space);
3326 __isl_give isl_multi_aff *isl_multi_aff_zero(
3327 __isl_take isl_space *space);
3328 __isl_give isl_pw_multi_aff *
3329 isl_pw_multi_aff_from_multi_aff(
3330 __isl_take isl_multi_aff *ma);
3331 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3332 __isl_take isl_set *set,
3333 __isl_take isl_multi_aff *maff);
3334 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3335 __isl_take isl_set *set);
3337 __isl_give isl_union_pw_multi_aff *
3338 isl_union_pw_multi_aff_empty(
3339 __isl_take isl_space *space);
3340 __isl_give isl_union_pw_multi_aff *
3341 isl_union_pw_multi_aff_add_pw_multi_aff(
3342 __isl_take isl_union_pw_multi_aff *upma,
3343 __isl_take isl_pw_multi_aff *pma);
3344 __isl_give isl_union_pw_multi_aff *
3345 isl_union_pw_multi_aff_from_domain(
3346 __isl_take isl_union_set *uset);
3348 A piecewise multiple quasi affine expression can also be initialized
3349 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3350 and the C<isl_map> is single-valued.
3352 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3353 __isl_take isl_set *set);
3354 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3355 __isl_take isl_map *map);
3357 Multiple quasi affine expressions can be copied and freed using
3359 #include <isl/aff.h>
3360 __isl_give isl_multi_aff *isl_multi_aff_copy(
3361 __isl_keep isl_multi_aff *maff);
3362 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3364 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3365 __isl_keep isl_pw_multi_aff *pma);
3366 void *isl_pw_multi_aff_free(
3367 __isl_take isl_pw_multi_aff *pma);
3369 __isl_give isl_union_pw_multi_aff *
3370 isl_union_pw_multi_aff_copy(
3371 __isl_keep isl_union_pw_multi_aff *upma);
3372 void *isl_union_pw_multi_aff_free(
3373 __isl_take isl_union_pw_multi_aff *upma);
3375 The expression can be inspected using
3377 #include <isl/aff.h>
3378 isl_ctx *isl_multi_aff_get_ctx(
3379 __isl_keep isl_multi_aff *maff);
3380 isl_ctx *isl_pw_multi_aff_get_ctx(
3381 __isl_keep isl_pw_multi_aff *pma);
3382 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3383 __isl_keep isl_union_pw_multi_aff *upma);
3384 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3385 enum isl_dim_type type);
3386 unsigned isl_pw_multi_aff_dim(
3387 __isl_keep isl_pw_multi_aff *pma,
3388 enum isl_dim_type type);
3389 __isl_give isl_aff *isl_multi_aff_get_aff(
3390 __isl_keep isl_multi_aff *multi, int pos);
3391 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3392 __isl_keep isl_pw_multi_aff *pma, int pos);
3393 const char *isl_pw_multi_aff_get_dim_name(
3394 __isl_keep isl_pw_multi_aff *pma,
3395 enum isl_dim_type type, unsigned pos);
3396 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3397 __isl_keep isl_pw_multi_aff *pma,
3398 enum isl_dim_type type, unsigned pos);
3399 const char *isl_multi_aff_get_tuple_name(
3400 __isl_keep isl_multi_aff *multi,
3401 enum isl_dim_type type);
3402 const char *isl_pw_multi_aff_get_tuple_name(
3403 __isl_keep isl_pw_multi_aff *pma,
3404 enum isl_dim_type type);
3405 int isl_pw_multi_aff_has_tuple_id(
3406 __isl_keep isl_pw_multi_aff *pma,
3407 enum isl_dim_type type);
3408 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3409 __isl_keep isl_pw_multi_aff *pma,
3410 enum isl_dim_type type);
3412 int isl_pw_multi_aff_foreach_piece(
3413 __isl_keep isl_pw_multi_aff *pma,
3414 int (*fn)(__isl_take isl_set *set,
3415 __isl_take isl_multi_aff *maff,
3416 void *user), void *user);
3418 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3419 __isl_keep isl_union_pw_multi_aff *upma,
3420 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3421 void *user), void *user);
3423 It can be modified using
3425 #include <isl/aff.h>
3426 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3427 __isl_take isl_multi_aff *multi, int pos,
3428 __isl_take isl_aff *aff);
3429 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3430 __isl_take isl_multi_aff *maff,
3431 enum isl_dim_type type, unsigned pos, const char *s);
3432 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3433 __isl_take isl_multi_aff *maff,
3434 enum isl_dim_type type, __isl_take isl_id *id);
3435 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3436 __isl_take isl_pw_multi_aff *pma,
3437 enum isl_dim_type type, __isl_take isl_id *id);
3439 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3440 __isl_take isl_multi_aff *maff,
3441 enum isl_dim_type type, unsigned first, unsigned n);
3443 To check whether two multiple affine expressions are
3444 obviously equal to each other, use
3446 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3447 __isl_keep isl_multi_aff *maff2);
3448 int isl_pw_multi_aff_plain_is_equal(
3449 __isl_keep isl_pw_multi_aff *pma1,
3450 __isl_keep isl_pw_multi_aff *pma2);
3454 #include <isl/aff.h>
3455 __isl_give isl_multi_aff *isl_multi_aff_add(
3456 __isl_take isl_multi_aff *maff1,
3457 __isl_take isl_multi_aff *maff2);
3458 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3459 __isl_take isl_pw_multi_aff *pma1,
3460 __isl_take isl_pw_multi_aff *pma2);
3461 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3462 __isl_take isl_union_pw_multi_aff *upma1,
3463 __isl_take isl_union_pw_multi_aff *upma2);
3464 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3465 __isl_take isl_pw_multi_aff *pma1,
3466 __isl_take isl_pw_multi_aff *pma2);
3467 __isl_give isl_multi_aff *isl_multi_aff_scale(
3468 __isl_take isl_multi_aff *maff,
3470 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3471 __isl_take isl_pw_multi_aff *pma,
3472 __isl_take isl_set *set);
3473 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3474 __isl_take isl_pw_multi_aff *pma,
3475 __isl_take isl_set *set);
3476 __isl_give isl_multi_aff *isl_multi_aff_lift(
3477 __isl_take isl_multi_aff *maff,
3478 __isl_give isl_local_space **ls);
3479 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3480 __isl_take isl_pw_multi_aff *pma);
3481 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3482 __isl_take isl_multi_aff *maff,
3483 __isl_take isl_set *context);
3484 __isl_give isl_multi_aff *isl_multi_aff_gist(
3485 __isl_take isl_multi_aff *maff,
3486 __isl_take isl_set *context);
3487 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3488 __isl_take isl_pw_multi_aff *pma,
3489 __isl_take isl_set *set);
3490 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3491 __isl_take isl_pw_multi_aff *pma,
3492 __isl_take isl_set *set);
3493 __isl_give isl_set *isl_pw_multi_aff_domain(
3494 __isl_take isl_pw_multi_aff *pma);
3495 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3496 __isl_take isl_union_pw_multi_aff *upma);
3497 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3498 __isl_take isl_multi_aff *ma1,
3499 __isl_take isl_multi_aff *ma2);
3500 __isl_give isl_pw_multi_aff *
3501 isl_pw_multi_aff_flat_range_product(
3502 __isl_take isl_pw_multi_aff *pma1,
3503 __isl_take isl_pw_multi_aff *pma2);
3504 __isl_give isl_union_pw_multi_aff *
3505 isl_union_pw_multi_aff_flat_range_product(
3506 __isl_take isl_union_pw_multi_aff *upma1,
3507 __isl_take isl_union_pw_multi_aff *upma2);
3509 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3510 then it is assigned the local space that lies at the basis of
3511 the lifting applied.
3513 An expression can be read from input using
3515 #include <isl/aff.h>
3516 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3517 isl_ctx *ctx, const char *str);
3518 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3519 isl_ctx *ctx, const char *str);
3521 An expression can be printed using
3523 #include <isl/aff.h>
3524 __isl_give isl_printer *isl_printer_print_multi_aff(
3525 __isl_take isl_printer *p,
3526 __isl_keep isl_multi_aff *maff);
3527 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3528 __isl_take isl_printer *p,
3529 __isl_keep isl_pw_multi_aff *pma);
3530 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3531 __isl_take isl_printer *p,
3532 __isl_keep isl_union_pw_multi_aff *upma);
3536 Points are elements of a set. They can be used to construct
3537 simple sets (boxes) or they can be used to represent the
3538 individual elements of a set.
3539 The zero point (the origin) can be created using
3541 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3543 The coordinates of a point can be inspected, set and changed
3546 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3547 enum isl_dim_type type, int pos, isl_int *v);
3548 __isl_give isl_point *isl_point_set_coordinate(
3549 __isl_take isl_point *pnt,
3550 enum isl_dim_type type, int pos, isl_int v);
3552 __isl_give isl_point *isl_point_add_ui(
3553 __isl_take isl_point *pnt,
3554 enum isl_dim_type type, int pos, unsigned val);
3555 __isl_give isl_point *isl_point_sub_ui(
3556 __isl_take isl_point *pnt,
3557 enum isl_dim_type type, int pos, unsigned val);
3559 Other properties can be obtained using
3561 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3563 Points can be copied or freed using
3565 __isl_give isl_point *isl_point_copy(
3566 __isl_keep isl_point *pnt);
3567 void isl_point_free(__isl_take isl_point *pnt);
3569 A singleton set can be created from a point using
3571 __isl_give isl_basic_set *isl_basic_set_from_point(
3572 __isl_take isl_point *pnt);
3573 __isl_give isl_set *isl_set_from_point(
3574 __isl_take isl_point *pnt);
3576 and a box can be created from two opposite extremal points using
3578 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3579 __isl_take isl_point *pnt1,
3580 __isl_take isl_point *pnt2);
3581 __isl_give isl_set *isl_set_box_from_points(
3582 __isl_take isl_point *pnt1,
3583 __isl_take isl_point *pnt2);
3585 All elements of a B<bounded> (union) set can be enumerated using
3586 the following functions.
3588 int isl_set_foreach_point(__isl_keep isl_set *set,
3589 int (*fn)(__isl_take isl_point *pnt, void *user),
3591 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3592 int (*fn)(__isl_take isl_point *pnt, void *user),
3595 The function C<fn> is called for each integer point in
3596 C<set> with as second argument the last argument of
3597 the C<isl_set_foreach_point> call. The function C<fn>
3598 should return C<0> on success and C<-1> on failure.
3599 In the latter case, C<isl_set_foreach_point> will stop
3600 enumerating and return C<-1> as well.
3601 If the enumeration is performed successfully and to completion,
3602 then C<isl_set_foreach_point> returns C<0>.
3604 To obtain a single point of a (basic) set, use
3606 __isl_give isl_point *isl_basic_set_sample_point(
3607 __isl_take isl_basic_set *bset);
3608 __isl_give isl_point *isl_set_sample_point(
3609 __isl_take isl_set *set);
3611 If C<set> does not contain any (integer) points, then the
3612 resulting point will be ``void'', a property that can be
3615 int isl_point_is_void(__isl_keep isl_point *pnt);
3617 =head2 Piecewise Quasipolynomials
3619 A piecewise quasipolynomial is a particular kind of function that maps
3620 a parametric point to a rational value.
3621 More specifically, a quasipolynomial is a polynomial expression in greatest
3622 integer parts of affine expressions of parameters and variables.
3623 A piecewise quasipolynomial is a subdivision of a given parametric
3624 domain into disjoint cells with a quasipolynomial associated to
3625 each cell. The value of the piecewise quasipolynomial at a given
3626 point is the value of the quasipolynomial associated to the cell
3627 that contains the point. Outside of the union of cells,
3628 the value is assumed to be zero.
3629 For example, the piecewise quasipolynomial
3631 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3633 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3634 A given piecewise quasipolynomial has a fixed domain dimension.
3635 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3636 defined over different domains.
3637 Piecewise quasipolynomials are mainly used by the C<barvinok>
3638 library for representing the number of elements in a parametric set or map.
3639 For example, the piecewise quasipolynomial above represents
3640 the number of points in the map
3642 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3644 =head3 Input and Output
3646 Piecewise quasipolynomials can be read from input using
3648 __isl_give isl_union_pw_qpolynomial *
3649 isl_union_pw_qpolynomial_read_from_str(
3650 isl_ctx *ctx, const char *str);
3652 Quasipolynomials and piecewise quasipolynomials can be printed
3653 using the following functions.
3655 __isl_give isl_printer *isl_printer_print_qpolynomial(
3656 __isl_take isl_printer *p,
3657 __isl_keep isl_qpolynomial *qp);
3659 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3660 __isl_take isl_printer *p,
3661 __isl_keep isl_pw_qpolynomial *pwqp);
3663 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3664 __isl_take isl_printer *p,
3665 __isl_keep isl_union_pw_qpolynomial *upwqp);
3667 The output format of the printer
3668 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3669 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3671 In case of printing in C<ISL_FORMAT_C>, the user may want
3672 to set the names of all dimensions
3674 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3675 __isl_take isl_qpolynomial *qp,
3676 enum isl_dim_type type, unsigned pos,
3678 __isl_give isl_pw_qpolynomial *
3679 isl_pw_qpolynomial_set_dim_name(
3680 __isl_take isl_pw_qpolynomial *pwqp,
3681 enum isl_dim_type type, unsigned pos,
3684 =head3 Creating New (Piecewise) Quasipolynomials
3686 Some simple quasipolynomials can be created using the following functions.
3687 More complicated quasipolynomials can be created by applying
3688 operations such as addition and multiplication
3689 on the resulting quasipolynomials
3691 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3692 __isl_take isl_space *domain);
3693 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3694 __isl_take isl_space *domain);
3695 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3696 __isl_take isl_space *domain);
3697 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3698 __isl_take isl_space *domain);
3699 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3700 __isl_take isl_space *domain);
3701 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3702 __isl_take isl_space *domain,
3703 const isl_int n, const isl_int d);
3704 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3705 __isl_take isl_space *domain,
3706 enum isl_dim_type type, unsigned pos);
3707 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3708 __isl_take isl_aff *aff);
3710 Note that the space in which a quasipolynomial lives is a map space
3711 with a one-dimensional range. The C<domain> argument in some of
3712 the functions above corresponds to the domain of this map space.
3714 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3715 with a single cell can be created using the following functions.
3716 Multiple of these single cell piecewise quasipolynomials can
3717 be combined to create more complicated piecewise quasipolynomials.
3719 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3720 __isl_take isl_space *space);
3721 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3722 __isl_take isl_set *set,
3723 __isl_take isl_qpolynomial *qp);
3724 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3725 __isl_take isl_qpolynomial *qp);
3726 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3727 __isl_take isl_pw_aff *pwaff);
3729 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3730 __isl_take isl_space *space);
3731 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3732 __isl_take isl_pw_qpolynomial *pwqp);
3733 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3734 __isl_take isl_union_pw_qpolynomial *upwqp,
3735 __isl_take isl_pw_qpolynomial *pwqp);
3737 Quasipolynomials can be copied and freed again using the following
3740 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3741 __isl_keep isl_qpolynomial *qp);
3742 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3744 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3745 __isl_keep isl_pw_qpolynomial *pwqp);
3746 void *isl_pw_qpolynomial_free(
3747 __isl_take isl_pw_qpolynomial *pwqp);
3749 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3750 __isl_keep isl_union_pw_qpolynomial *upwqp);
3751 void *isl_union_pw_qpolynomial_free(
3752 __isl_take isl_union_pw_qpolynomial *upwqp);
3754 =head3 Inspecting (Piecewise) Quasipolynomials
3756 To iterate over all piecewise quasipolynomials in a union
3757 piecewise quasipolynomial, use the following function
3759 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3760 __isl_keep isl_union_pw_qpolynomial *upwqp,
3761 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3764 To extract the piecewise quasipolynomial in a given space from a union, use
3766 __isl_give isl_pw_qpolynomial *
3767 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3768 __isl_keep isl_union_pw_qpolynomial *upwqp,
3769 __isl_take isl_space *space);
3771 To iterate over the cells in a piecewise quasipolynomial,
3772 use either of the following two functions
3774 int isl_pw_qpolynomial_foreach_piece(
3775 __isl_keep isl_pw_qpolynomial *pwqp,
3776 int (*fn)(__isl_take isl_set *set,
3777 __isl_take isl_qpolynomial *qp,
3778 void *user), void *user);
3779 int isl_pw_qpolynomial_foreach_lifted_piece(
3780 __isl_keep isl_pw_qpolynomial *pwqp,
3781 int (*fn)(__isl_take isl_set *set,
3782 __isl_take isl_qpolynomial *qp,
3783 void *user), void *user);
3785 As usual, the function C<fn> should return C<0> on success
3786 and C<-1> on failure. The difference between
3787 C<isl_pw_qpolynomial_foreach_piece> and
3788 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3789 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3790 compute unique representations for all existentially quantified
3791 variables and then turn these existentially quantified variables
3792 into extra set variables, adapting the associated quasipolynomial
3793 accordingly. This means that the C<set> passed to C<fn>
3794 will not have any existentially quantified variables, but that
3795 the dimensions of the sets may be different for different
3796 invocations of C<fn>.
3798 To iterate over all terms in a quasipolynomial,
3801 int isl_qpolynomial_foreach_term(
3802 __isl_keep isl_qpolynomial *qp,
3803 int (*fn)(__isl_take isl_term *term,
3804 void *user), void *user);
3806 The terms themselves can be inspected and freed using
3809 unsigned isl_term_dim(__isl_keep isl_term *term,
3810 enum isl_dim_type type);
3811 void isl_term_get_num(__isl_keep isl_term *term,
3813 void isl_term_get_den(__isl_keep isl_term *term,
3815 int isl_term_get_exp(__isl_keep isl_term *term,
3816 enum isl_dim_type type, unsigned pos);
3817 __isl_give isl_aff *isl_term_get_div(
3818 __isl_keep isl_term *term, unsigned pos);
3819 void isl_term_free(__isl_take isl_term *term);
3821 Each term is a product of parameters, set variables and
3822 integer divisions. The function C<isl_term_get_exp>
3823 returns the exponent of a given dimensions in the given term.
3824 The C<isl_int>s in the arguments of C<isl_term_get_num>
3825 and C<isl_term_get_den> need to have been initialized
3826 using C<isl_int_init> before calling these functions.
3828 =head3 Properties of (Piecewise) Quasipolynomials
3830 To check whether a quasipolynomial is actually a constant,
3831 use the following function.
3833 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3834 isl_int *n, isl_int *d);
3836 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3837 then the numerator and denominator of the constant
3838 are returned in C<*n> and C<*d>, respectively.
3840 To check whether two union piecewise quasipolynomials are
3841 obviously equal, use
3843 int isl_union_pw_qpolynomial_plain_is_equal(
3844 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3845 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3847 =head3 Operations on (Piecewise) Quasipolynomials
3849 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3850 __isl_take isl_qpolynomial *qp, isl_int v);
3851 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3852 __isl_take isl_qpolynomial *qp);
3853 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3854 __isl_take isl_qpolynomial *qp1,
3855 __isl_take isl_qpolynomial *qp2);
3856 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3857 __isl_take isl_qpolynomial *qp1,
3858 __isl_take isl_qpolynomial *qp2);
3859 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3860 __isl_take isl_qpolynomial *qp1,
3861 __isl_take isl_qpolynomial *qp2);
3862 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3863 __isl_take isl_qpolynomial *qp, unsigned exponent);
3865 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3866 __isl_take isl_pw_qpolynomial *pwqp1,
3867 __isl_take isl_pw_qpolynomial *pwqp2);
3868 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3869 __isl_take isl_pw_qpolynomial *pwqp1,
3870 __isl_take isl_pw_qpolynomial *pwqp2);
3871 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3872 __isl_take isl_pw_qpolynomial *pwqp1,
3873 __isl_take isl_pw_qpolynomial *pwqp2);
3874 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3875 __isl_take isl_pw_qpolynomial *pwqp);
3876 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3877 __isl_take isl_pw_qpolynomial *pwqp1,
3878 __isl_take isl_pw_qpolynomial *pwqp2);
3879 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3880 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3882 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3883 __isl_take isl_union_pw_qpolynomial *upwqp1,
3884 __isl_take isl_union_pw_qpolynomial *upwqp2);
3885 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3886 __isl_take isl_union_pw_qpolynomial *upwqp1,
3887 __isl_take isl_union_pw_qpolynomial *upwqp2);
3888 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3889 __isl_take isl_union_pw_qpolynomial *upwqp1,
3890 __isl_take isl_union_pw_qpolynomial *upwqp2);
3892 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3893 __isl_take isl_pw_qpolynomial *pwqp,
3894 __isl_take isl_point *pnt);
3896 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3897 __isl_take isl_union_pw_qpolynomial *upwqp,
3898 __isl_take isl_point *pnt);
3900 __isl_give isl_set *isl_pw_qpolynomial_domain(
3901 __isl_take isl_pw_qpolynomial *pwqp);
3902 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3903 __isl_take isl_pw_qpolynomial *pwpq,
3904 __isl_take isl_set *set);
3905 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3906 __isl_take isl_pw_qpolynomial *pwpq,
3907 __isl_take isl_set *set);
3909 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3910 __isl_take isl_union_pw_qpolynomial *upwqp);
3911 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3912 __isl_take isl_union_pw_qpolynomial *upwpq,
3913 __isl_take isl_union_set *uset);
3914 __isl_give isl_union_pw_qpolynomial *
3915 isl_union_pw_qpolynomial_intersect_params(
3916 __isl_take isl_union_pw_qpolynomial *upwpq,
3917 __isl_take isl_set *set);
3919 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3920 __isl_take isl_qpolynomial *qp,
3921 __isl_take isl_space *model);
3923 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3924 __isl_take isl_qpolynomial *qp);
3925 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3926 __isl_take isl_pw_qpolynomial *pwqp);
3928 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3929 __isl_take isl_union_pw_qpolynomial *upwqp);
3931 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3932 __isl_take isl_qpolynomial *qp,
3933 __isl_take isl_set *context);
3934 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
3935 __isl_take isl_qpolynomial *qp,
3936 __isl_take isl_set *context);
3938 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
3939 __isl_take isl_pw_qpolynomial *pwqp,
3940 __isl_take isl_set *context);
3941 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
3942 __isl_take isl_pw_qpolynomial *pwqp,
3943 __isl_take isl_set *context);
3945 __isl_give isl_union_pw_qpolynomial *
3946 isl_union_pw_qpolynomial_gist_params(
3947 __isl_take isl_union_pw_qpolynomial *upwqp,
3948 __isl_take isl_set *context);
3949 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
3950 __isl_take isl_union_pw_qpolynomial *upwqp,
3951 __isl_take isl_union_set *context);
3953 The gist operation applies the gist operation to each of
3954 the cells in the domain of the input piecewise quasipolynomial.
3955 The context is also exploited
3956 to simplify the quasipolynomials associated to each cell.
3958 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
3959 __isl_take isl_pw_qpolynomial *pwqp, int sign);
3960 __isl_give isl_union_pw_qpolynomial *
3961 isl_union_pw_qpolynomial_to_polynomial(
3962 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
3964 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
3965 the polynomial will be an overapproximation. If C<sign> is negative,
3966 it will be an underapproximation. If C<sign> is zero, the approximation
3967 will lie somewhere in between.
3969 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
3971 A piecewise quasipolynomial reduction is a piecewise
3972 reduction (or fold) of quasipolynomials.
3973 In particular, the reduction can be maximum or a minimum.
3974 The objects are mainly used to represent the result of
3975 an upper or lower bound on a quasipolynomial over its domain,
3976 i.e., as the result of the following function.
3978 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
3979 __isl_take isl_pw_qpolynomial *pwqp,
3980 enum isl_fold type, int *tight);
3982 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
3983 __isl_take isl_union_pw_qpolynomial *upwqp,
3984 enum isl_fold type, int *tight);
3986 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
3987 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
3988 is the returned bound is known be tight, i.e., for each value
3989 of the parameters there is at least
3990 one element in the domain that reaches the bound.
3991 If the domain of C<pwqp> is not wrapping, then the bound is computed
3992 over all elements in that domain and the result has a purely parametric
3993 domain. If the domain of C<pwqp> is wrapping, then the bound is
3994 computed over the range of the wrapped relation. The domain of the
3995 wrapped relation becomes the domain of the result.
3997 A (piecewise) quasipolynomial reduction can be copied or freed using the
3998 following functions.
4000 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4001 __isl_keep isl_qpolynomial_fold *fold);
4002 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4003 __isl_keep isl_pw_qpolynomial_fold *pwf);
4004 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4005 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4006 void isl_qpolynomial_fold_free(
4007 __isl_take isl_qpolynomial_fold *fold);
4008 void *isl_pw_qpolynomial_fold_free(
4009 __isl_take isl_pw_qpolynomial_fold *pwf);
4010 void *isl_union_pw_qpolynomial_fold_free(
4011 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4013 =head3 Printing Piecewise Quasipolynomial Reductions
4015 Piecewise quasipolynomial reductions can be printed
4016 using the following function.
4018 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4019 __isl_take isl_printer *p,
4020 __isl_keep isl_pw_qpolynomial_fold *pwf);
4021 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4022 __isl_take isl_printer *p,
4023 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4025 For C<isl_printer_print_pw_qpolynomial_fold>,
4026 output format of the printer
4027 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4028 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4029 output format of the printer
4030 needs to be set to C<ISL_FORMAT_ISL>.
4031 In case of printing in C<ISL_FORMAT_C>, the user may want
4032 to set the names of all dimensions
4034 __isl_give isl_pw_qpolynomial_fold *
4035 isl_pw_qpolynomial_fold_set_dim_name(
4036 __isl_take isl_pw_qpolynomial_fold *pwf,
4037 enum isl_dim_type type, unsigned pos,
4040 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4042 To iterate over all piecewise quasipolynomial reductions in a union
4043 piecewise quasipolynomial reduction, use the following function
4045 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4046 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4047 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4048 void *user), void *user);
4050 To iterate over the cells in a piecewise quasipolynomial reduction,
4051 use either of the following two functions
4053 int isl_pw_qpolynomial_fold_foreach_piece(
4054 __isl_keep isl_pw_qpolynomial_fold *pwf,
4055 int (*fn)(__isl_take isl_set *set,
4056 __isl_take isl_qpolynomial_fold *fold,
4057 void *user), void *user);
4058 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4059 __isl_keep isl_pw_qpolynomial_fold *pwf,
4060 int (*fn)(__isl_take isl_set *set,
4061 __isl_take isl_qpolynomial_fold *fold,
4062 void *user), void *user);
4064 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4065 of the difference between these two functions.
4067 To iterate over all quasipolynomials in a reduction, use
4069 int isl_qpolynomial_fold_foreach_qpolynomial(
4070 __isl_keep isl_qpolynomial_fold *fold,
4071 int (*fn)(__isl_take isl_qpolynomial *qp,
4072 void *user), void *user);
4074 =head3 Properties of Piecewise Quasipolynomial Reductions
4076 To check whether two union piecewise quasipolynomial reductions are
4077 obviously equal, use
4079 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4080 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4081 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4083 =head3 Operations on Piecewise Quasipolynomial Reductions
4085 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4086 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4088 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4089 __isl_take isl_pw_qpolynomial_fold *pwf1,
4090 __isl_take isl_pw_qpolynomial_fold *pwf2);
4092 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4093 __isl_take isl_pw_qpolynomial_fold *pwf1,
4094 __isl_take isl_pw_qpolynomial_fold *pwf2);
4096 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4097 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4098 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4100 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4101 __isl_take isl_pw_qpolynomial_fold *pwf,
4102 __isl_take isl_point *pnt);
4104 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4105 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4106 __isl_take isl_point *pnt);
4108 __isl_give isl_pw_qpolynomial_fold *
4109 isl_pw_qpolynomial_fold_intersect_params(
4110 __isl_take isl_pw_qpolynomial_fold *pwf,
4111 __isl_take isl_set *set);
4113 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4114 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4115 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4116 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4117 __isl_take isl_union_set *uset);
4118 __isl_give isl_union_pw_qpolynomial_fold *
4119 isl_union_pw_qpolynomial_fold_intersect_params(
4120 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4121 __isl_take isl_set *set);
4123 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4124 __isl_take isl_pw_qpolynomial_fold *pwf);
4126 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4127 __isl_take isl_pw_qpolynomial_fold *pwf);
4129 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4130 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4132 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4133 __isl_take isl_qpolynomial_fold *fold,
4134 __isl_take isl_set *context);
4135 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4136 __isl_take isl_qpolynomial_fold *fold,
4137 __isl_take isl_set *context);
4139 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4140 __isl_take isl_pw_qpolynomial_fold *pwf,
4141 __isl_take isl_set *context);
4142 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4143 __isl_take isl_pw_qpolynomial_fold *pwf,
4144 __isl_take isl_set *context);
4146 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4147 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4148 __isl_take isl_union_set *context);
4149 __isl_give isl_union_pw_qpolynomial_fold *
4150 isl_union_pw_qpolynomial_fold_gist_params(
4151 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4152 __isl_take isl_set *context);
4154 The gist operation applies the gist operation to each of
4155 the cells in the domain of the input piecewise quasipolynomial reduction.
4156 In future, the operation will also exploit the context
4157 to simplify the quasipolynomial reductions associated to each cell.
4159 __isl_give isl_pw_qpolynomial_fold *
4160 isl_set_apply_pw_qpolynomial_fold(
4161 __isl_take isl_set *set,
4162 __isl_take isl_pw_qpolynomial_fold *pwf,
4164 __isl_give isl_pw_qpolynomial_fold *
4165 isl_map_apply_pw_qpolynomial_fold(
4166 __isl_take isl_map *map,
4167 __isl_take isl_pw_qpolynomial_fold *pwf,
4169 __isl_give isl_union_pw_qpolynomial_fold *
4170 isl_union_set_apply_union_pw_qpolynomial_fold(
4171 __isl_take isl_union_set *uset,
4172 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4174 __isl_give isl_union_pw_qpolynomial_fold *
4175 isl_union_map_apply_union_pw_qpolynomial_fold(
4176 __isl_take isl_union_map *umap,
4177 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4180 The functions taking a map
4181 compose the given map with the given piecewise quasipolynomial reduction.
4182 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4183 over all elements in the intersection of the range of the map
4184 and the domain of the piecewise quasipolynomial reduction
4185 as a function of an element in the domain of the map.
4186 The functions taking a set compute a bound over all elements in the
4187 intersection of the set and the domain of the
4188 piecewise quasipolynomial reduction.
4190 =head2 Dependence Analysis
4192 C<isl> contains specialized functionality for performing
4193 array dataflow analysis. That is, given a I<sink> access relation
4194 and a collection of possible I<source> access relations,
4195 C<isl> can compute relations that describe
4196 for each iteration of the sink access, which iteration
4197 of which of the source access relations was the last
4198 to access the same data element before the given iteration
4200 The resulting dependence relations map source iterations
4201 to the corresponding sink iterations.
4202 To compute standard flow dependences, the sink should be
4203 a read, while the sources should be writes.
4204 If any of the source accesses are marked as being I<may>
4205 accesses, then there will be a dependence from the last
4206 I<must> access B<and> from any I<may> access that follows
4207 this last I<must> access.
4208 In particular, if I<all> sources are I<may> accesses,
4209 then memory based dependence analysis is performed.
4210 If, on the other hand, all sources are I<must> accesses,
4211 then value based dependence analysis is performed.
4213 #include <isl/flow.h>
4215 typedef int (*isl_access_level_before)(void *first, void *second);
4217 __isl_give isl_access_info *isl_access_info_alloc(
4218 __isl_take isl_map *sink,
4219 void *sink_user, isl_access_level_before fn,
4221 __isl_give isl_access_info *isl_access_info_add_source(
4222 __isl_take isl_access_info *acc,
4223 __isl_take isl_map *source, int must,
4225 void isl_access_info_free(__isl_take isl_access_info *acc);
4227 __isl_give isl_flow *isl_access_info_compute_flow(
4228 __isl_take isl_access_info *acc);
4230 int isl_flow_foreach(__isl_keep isl_flow *deps,
4231 int (*fn)(__isl_take isl_map *dep, int must,
4232 void *dep_user, void *user),
4234 __isl_give isl_map *isl_flow_get_no_source(
4235 __isl_keep isl_flow *deps, int must);
4236 void isl_flow_free(__isl_take isl_flow *deps);
4238 The function C<isl_access_info_compute_flow> performs the actual
4239 dependence analysis. The other functions are used to construct
4240 the input for this function or to read off the output.
4242 The input is collected in an C<isl_access_info>, which can
4243 be created through a call to C<isl_access_info_alloc>.
4244 The arguments to this functions are the sink access relation
4245 C<sink>, a token C<sink_user> used to identify the sink
4246 access to the user, a callback function for specifying the
4247 relative order of source and sink accesses, and the number
4248 of source access relations that will be added.
4249 The callback function has type C<int (*)(void *first, void *second)>.
4250 The function is called with two user supplied tokens identifying
4251 either a source or the sink and it should return the shared nesting
4252 level and the relative order of the two accesses.
4253 In particular, let I<n> be the number of loops shared by
4254 the two accesses. If C<first> precedes C<second> textually,
4255 then the function should return I<2 * n + 1>; otherwise,
4256 it should return I<2 * n>.
4257 The sources can be added to the C<isl_access_info> by performing
4258 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4259 C<must> indicates whether the source is a I<must> access
4260 or a I<may> access. Note that a multi-valued access relation
4261 should only be marked I<must> if every iteration in the domain
4262 of the relation accesses I<all> elements in its image.
4263 The C<source_user> token is again used to identify
4264 the source access. The range of the source access relation
4265 C<source> should have the same dimension as the range
4266 of the sink access relation.
4267 The C<isl_access_info_free> function should usually not be
4268 called explicitly, because it is called implicitly by
4269 C<isl_access_info_compute_flow>.
4271 The result of the dependence analysis is collected in an
4272 C<isl_flow>. There may be elements of
4273 the sink access for which no preceding source access could be
4274 found or for which all preceding sources are I<may> accesses.
4275 The relations containing these elements can be obtained through
4276 calls to C<isl_flow_get_no_source>, the first with C<must> set
4277 and the second with C<must> unset.
4278 In the case of standard flow dependence analysis,
4279 with the sink a read and the sources I<must> writes,
4280 the first relation corresponds to the reads from uninitialized
4281 array elements and the second relation is empty.
4282 The actual flow dependences can be extracted using
4283 C<isl_flow_foreach>. This function will call the user-specified
4284 callback function C<fn> for each B<non-empty> dependence between
4285 a source and the sink. The callback function is called
4286 with four arguments, the actual flow dependence relation
4287 mapping source iterations to sink iterations, a boolean that
4288 indicates whether it is a I<must> or I<may> dependence, a token
4289 identifying the source and an additional C<void *> with value
4290 equal to the third argument of the C<isl_flow_foreach> call.
4291 A dependence is marked I<must> if it originates from a I<must>
4292 source and if it is not followed by any I<may> sources.
4294 After finishing with an C<isl_flow>, the user should call
4295 C<isl_flow_free> to free all associated memory.
4297 A higher-level interface to dependence analysis is provided
4298 by the following function.
4300 #include <isl/flow.h>
4302 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4303 __isl_take isl_union_map *must_source,
4304 __isl_take isl_union_map *may_source,
4305 __isl_take isl_union_map *schedule,
4306 __isl_give isl_union_map **must_dep,
4307 __isl_give isl_union_map **may_dep,
4308 __isl_give isl_union_map **must_no_source,
4309 __isl_give isl_union_map **may_no_source);
4311 The arrays are identified by the tuple names of the ranges
4312 of the accesses. The iteration domains by the tuple names
4313 of the domains of the accesses and of the schedule.
4314 The relative order of the iteration domains is given by the
4315 schedule. The relations returned through C<must_no_source>
4316 and C<may_no_source> are subsets of C<sink>.
4317 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4318 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4319 any of the other arguments is treated as an error.
4321 =head3 Interaction with Dependence Analysis
4323 During the dependence analysis, we frequently need to perform
4324 the following operation. Given a relation between sink iterations
4325 and potential source iterations from a particular source domain,
4326 what is the last potential source iteration corresponding to each
4327 sink iteration. It can sometimes be convenient to adjust
4328 the set of potential source iterations before or after each such operation.
4329 The prototypical example is fuzzy array dataflow analysis,
4330 where we need to analyze if, based on data-dependent constraints,
4331 the sink iteration can ever be executed without one or more of
4332 the corresponding potential source iterations being executed.
4333 If so, we can introduce extra parameters and select an unknown
4334 but fixed source iteration from the potential source iterations.
4335 To be able to perform such manipulations, C<isl> provides the following
4338 #include <isl/flow.h>
4340 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4341 __isl_keep isl_map *source_map,
4342 __isl_keep isl_set *sink, void *source_user,
4344 __isl_give isl_access_info *isl_access_info_set_restrict(
4345 __isl_take isl_access_info *acc,
4346 isl_access_restrict fn, void *user);
4348 The function C<isl_access_info_set_restrict> should be called
4349 before calling C<isl_access_info_compute_flow> and registers a callback function
4350 that will be called any time C<isl> is about to compute the last
4351 potential source. The first argument is the (reverse) proto-dependence,
4352 mapping sink iterations to potential source iterations.
4353 The second argument represents the sink iterations for which
4354 we want to compute the last source iteration.
4355 The third argument is the token corresponding to the source
4356 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4357 The callback is expected to return a restriction on either the input or
4358 the output of the operation computing the last potential source.
4359 If the input needs to be restricted then restrictions are needed
4360 for both the source and the sink iterations. The sink iterations
4361 and the potential source iterations will be intersected with these sets.
4362 If the output needs to be restricted then only a restriction on the source
4363 iterations is required.
4364 If any error occurs, the callback should return C<NULL>.
4365 An C<isl_restriction> object can be created, freed and inspected
4366 using the following functions.
4368 #include <isl/flow.h>
4370 __isl_give isl_restriction *isl_restriction_input(
4371 __isl_take isl_set *source_restr,
4372 __isl_take isl_set *sink_restr);
4373 __isl_give isl_restriction *isl_restriction_output(
4374 __isl_take isl_set *source_restr);
4375 __isl_give isl_restriction *isl_restriction_none(
4376 __isl_take isl_map *source_map);
4377 __isl_give isl_restriction *isl_restriction_empty(
4378 __isl_take isl_map *source_map);
4379 void *isl_restriction_free(
4380 __isl_take isl_restriction *restr);
4381 isl_ctx *isl_restriction_get_ctx(
4382 __isl_keep isl_restriction *restr);
4384 C<isl_restriction_none> and C<isl_restriction_empty> are special
4385 cases of C<isl_restriction_input>. C<isl_restriction_none>
4386 is essentially equivalent to
4388 isl_restriction_input(isl_set_universe(
4389 isl_space_range(isl_map_get_space(source_map))),
4391 isl_space_domain(isl_map_get_space(source_map))));
4393 whereas C<isl_restriction_empty> is essentially equivalent to
4395 isl_restriction_input(isl_set_empty(
4396 isl_space_range(isl_map_get_space(source_map))),
4398 isl_space_domain(isl_map_get_space(source_map))));
4402 B<The functionality described in this section is fairly new
4403 and may be subject to change.>
4405 The following function can be used to compute a schedule
4406 for a union of domains.
4407 By default, the algorithm used to construct the schedule is similar
4408 to that of C<Pluto>.
4409 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4411 The generated schedule respects all C<validity> dependences.
4412 That is, all dependence distances over these dependences in the
4413 scheduled space are lexicographically positive.
4414 The default algorithm tries to minimize the dependence distances over
4415 C<proximity> dependences.
4416 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4417 for groups of domains where the dependence distances have only
4418 non-negative values.
4419 When using Feautrier's algorithm, the C<proximity> dependence
4420 distances are only minimized during the extension to a
4421 full-dimensional schedule.
4423 #include <isl/schedule.h>
4424 __isl_give isl_schedule *isl_union_set_compute_schedule(
4425 __isl_take isl_union_set *domain,
4426 __isl_take isl_union_map *validity,
4427 __isl_take isl_union_map *proximity);
4428 void *isl_schedule_free(__isl_take isl_schedule *sched);
4430 A mapping from the domains to the scheduled space can be obtained
4431 from an C<isl_schedule> using the following function.
4433 __isl_give isl_union_map *isl_schedule_get_map(
4434 __isl_keep isl_schedule *sched);
4436 A representation of the schedule can be printed using
4438 __isl_give isl_printer *isl_printer_print_schedule(
4439 __isl_take isl_printer *p,
4440 __isl_keep isl_schedule *schedule);
4442 A representation of the schedule as a forest of bands can be obtained
4443 using the following function.
4445 __isl_give isl_band_list *isl_schedule_get_band_forest(
4446 __isl_keep isl_schedule *schedule);
4448 The individual bands can be visited in depth-first post-order
4449 using the following function.
4451 #include <isl/schedule.h>
4452 int isl_schedule_foreach_band(
4453 __isl_keep isl_schedule *sched,
4454 int (*fn)(__isl_keep isl_band *band, void *user),
4457 The list can be manipulated as explained in L<"Lists">.
4458 The bands inside the list can be copied and freed using the following
4461 #include <isl/band.h>
4462 __isl_give isl_band *isl_band_copy(
4463 __isl_keep isl_band *band);
4464 void *isl_band_free(__isl_take isl_band *band);
4466 Each band contains zero or more scheduling dimensions.
4467 These are referred to as the members of the band.
4468 The section of the schedule that corresponds to the band is
4469 referred to as the partial schedule of the band.
4470 For those nodes that participate in a band, the outer scheduling
4471 dimensions form the prefix schedule, while the inner scheduling
4472 dimensions form the suffix schedule.
4473 That is, if we take a cut of the band forest, then the union of
4474 the concatenations of the prefix, partial and suffix schedules of
4475 each band in the cut is equal to the entire schedule (modulo
4476 some possible padding at the end with zero scheduling dimensions).
4477 The properties of a band can be inspected using the following functions.
4479 #include <isl/band.h>
4480 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4482 int isl_band_has_children(__isl_keep isl_band *band);
4483 __isl_give isl_band_list *isl_band_get_children(
4484 __isl_keep isl_band *band);
4486 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4487 __isl_keep isl_band *band);
4488 __isl_give isl_union_map *isl_band_get_partial_schedule(
4489 __isl_keep isl_band *band);
4490 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4491 __isl_keep isl_band *band);
4493 int isl_band_n_member(__isl_keep isl_band *band);
4494 int isl_band_member_is_zero_distance(
4495 __isl_keep isl_band *band, int pos);
4497 int isl_band_list_foreach_band(
4498 __isl_keep isl_band_list *list,
4499 int (*fn)(__isl_keep isl_band *band, void *user),
4502 Note that a scheduling dimension is considered to be ``zero
4503 distance'' if it does not carry any proximity dependences
4505 That is, if the dependence distances of the proximity
4506 dependences are all zero in that direction (for fixed
4507 iterations of outer bands).
4508 Like C<isl_schedule_foreach_band>,
4509 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4510 in depth-first post-order.
4512 A band can be tiled using the following function.
4514 #include <isl/band.h>
4515 int isl_band_tile(__isl_keep isl_band *band,
4516 __isl_take isl_vec *sizes);
4518 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4520 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4522 The C<isl_band_tile> function tiles the band using the given tile sizes
4523 inside its schedule.
4524 A new child band is created to represent the point loops and it is
4525 inserted between the modified band and its children.
4526 The C<tile_scale_tile_loops> option specifies whether the tile
4527 loops iterators should be scaled by the tile sizes.
4529 A representation of the band can be printed using
4531 #include <isl/band.h>
4532 __isl_give isl_printer *isl_printer_print_band(
4533 __isl_take isl_printer *p,
4534 __isl_keep isl_band *band);
4538 #include <isl/schedule.h>
4539 int isl_options_set_schedule_max_coefficient(
4540 isl_ctx *ctx, int val);
4541 int isl_options_get_schedule_max_coefficient(
4543 int isl_options_set_schedule_max_constant_term(
4544 isl_ctx *ctx, int val);
4545 int isl_options_get_schedule_max_constant_term(
4547 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4548 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4549 int isl_options_set_schedule_maximize_band_depth(
4550 isl_ctx *ctx, int val);
4551 int isl_options_get_schedule_maximize_band_depth(
4553 int isl_options_set_schedule_outer_zero_distance(
4554 isl_ctx *ctx, int val);
4555 int isl_options_get_schedule_outer_zero_distance(
4557 int isl_options_set_schedule_split_scaled(
4558 isl_ctx *ctx, int val);
4559 int isl_options_get_schedule_split_scaled(
4561 int isl_options_set_schedule_algorithm(
4562 isl_ctx *ctx, int val);
4563 int isl_options_get_schedule_algorithm(
4565 int isl_options_set_schedule_separate_components(
4566 isl_ctx *ctx, int val);
4567 int isl_options_get_schedule_separate_components(
4572 =item * schedule_max_coefficient
4574 This option enforces that the coefficients for variable and parameter
4575 dimensions in the calculated schedule are not larger than the specified value.
4576 This option can significantly increase the speed of the scheduling calculation
4577 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4578 this option does not introduce bounds on the variable or parameter
4581 =item * schedule_max_constant_term
4583 This option enforces that the constant coefficients in the calculated schedule
4584 are not larger than the maximal constant term. This option can significantly
4585 increase the speed of the scheduling calculation and may also prevent fusing of
4586 unrelated dimensions. A value of -1 means that this option does not introduce
4587 bounds on the constant coefficients.
4589 =item * schedule_fuse
4591 This option controls the level of fusion.
4592 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4593 resulting schedule will be distributed as much as possible.
4594 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4595 try to fuse loops in the resulting schedule.
4597 =item * schedule_maximize_band_depth
4599 If this option is set, we do not split bands at the point
4600 where we detect splitting is necessary. Instead, we
4601 backtrack and split bands as early as possible. This
4602 reduces the number of splits and maximizes the width of
4603 the bands. Wider bands give more possibilities for tiling.
4604 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4605 then bands will be split as early as possible, even if there is no need.
4606 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4608 =item * schedule_outer_zero_distance
4610 If this option is set, then we try to construct schedules
4611 where the outermost scheduling dimension in each band
4612 results in a zero dependence distance over the proximity
4615 =item * schedule_split_scaled
4617 If this option is set, then we try to construct schedules in which the
4618 constant term is split off from the linear part if the linear parts of
4619 the scheduling rows for all nodes in the graphs have a common non-trivial
4621 The constant term is then placed in a separate band and the linear
4624 =item * schedule_algorithm
4626 Selects the scheduling algorithm to be used.
4627 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4628 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4630 =item * schedule_separate_components
4632 If at any point the dependence graph contains any (weakly connected) components,
4633 then these components are scheduled separately.
4634 If this option is not set, then some iterations of the domains
4635 in these components may be scheduled together.
4636 If this option is set, then the components are given consecutive
4641 =head2 Parametric Vertex Enumeration
4643 The parametric vertex enumeration described in this section
4644 is mainly intended to be used internally and by the C<barvinok>
4647 #include <isl/vertices.h>
4648 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4649 __isl_keep isl_basic_set *bset);
4651 The function C<isl_basic_set_compute_vertices> performs the
4652 actual computation of the parametric vertices and the chamber
4653 decomposition and store the result in an C<isl_vertices> object.
4654 This information can be queried by either iterating over all
4655 the vertices or iterating over all the chambers or cells
4656 and then iterating over all vertices that are active on the chamber.
4658 int isl_vertices_foreach_vertex(
4659 __isl_keep isl_vertices *vertices,
4660 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4663 int isl_vertices_foreach_cell(
4664 __isl_keep isl_vertices *vertices,
4665 int (*fn)(__isl_take isl_cell *cell, void *user),
4667 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4668 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4671 Other operations that can be performed on an C<isl_vertices> object are
4674 isl_ctx *isl_vertices_get_ctx(
4675 __isl_keep isl_vertices *vertices);
4676 int isl_vertices_get_n_vertices(
4677 __isl_keep isl_vertices *vertices);
4678 void isl_vertices_free(__isl_take isl_vertices *vertices);
4680 Vertices can be inspected and destroyed using the following functions.
4682 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4683 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4684 __isl_give isl_basic_set *isl_vertex_get_domain(
4685 __isl_keep isl_vertex *vertex);
4686 __isl_give isl_basic_set *isl_vertex_get_expr(
4687 __isl_keep isl_vertex *vertex);
4688 void isl_vertex_free(__isl_take isl_vertex *vertex);
4690 C<isl_vertex_get_expr> returns a singleton parametric set describing
4691 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4693 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4694 B<rational> basic sets, so they should mainly be used for inspection
4695 and should not be mixed with integer sets.
4697 Chambers can be inspected and destroyed using the following functions.
4699 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4700 __isl_give isl_basic_set *isl_cell_get_domain(
4701 __isl_keep isl_cell *cell);
4702 void isl_cell_free(__isl_take isl_cell *cell);
4706 Although C<isl> is mainly meant to be used as a library,
4707 it also contains some basic applications that use some
4708 of the functionality of C<isl>.
4709 The input may be specified in either the L<isl format>
4710 or the L<PolyLib format>.
4712 =head2 C<isl_polyhedron_sample>
4714 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4715 an integer element of the polyhedron, if there is any.
4716 The first column in the output is the denominator and is always
4717 equal to 1. If the polyhedron contains no integer points,
4718 then a vector of length zero is printed.
4722 C<isl_pip> takes the same input as the C<example> program
4723 from the C<piplib> distribution, i.e., a set of constraints
4724 on the parameters, a line containing only -1 and finally a set
4725 of constraints on a parametric polyhedron.
4726 The coefficients of the parameters appear in the last columns
4727 (but before the final constant column).
4728 The output is the lexicographic minimum of the parametric polyhedron.
4729 As C<isl> currently does not have its own output format, the output
4730 is just a dump of the internal state.
4732 =head2 C<isl_polyhedron_minimize>
4734 C<isl_polyhedron_minimize> computes the minimum of some linear
4735 or affine objective function over the integer points in a polyhedron.
4736 If an affine objective function
4737 is given, then the constant should appear in the last column.
4739 =head2 C<isl_polytope_scan>
4741 Given a polytope, C<isl_polytope_scan> prints
4742 all integer points in the polytope.