3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
173 The source of C<isl> can be obtained either as a tarball
174 or from the git repository. Both are available from
175 L<http://freshmeat.net/projects/isl/>.
176 The installation process depends on how you obtained
179 =head2 Installation from the git repository
183 =item 1 Clone or update the repository
185 The first time the source is obtained, you need to clone
188 git clone git://repo.or.cz/isl.git
190 To obtain updates, you need to pull in the latest changes
194 =item 2 Generate C<configure>
200 After performing the above steps, continue
201 with the L<Common installation instructions>.
203 =head2 Common installation instructions
207 =item 1 Obtain C<GMP>
209 Building C<isl> requires C<GMP>, including its headers files.
210 Your distribution may not provide these header files by default
211 and you may need to install a package called C<gmp-devel> or something
212 similar. Alternatively, C<GMP> can be built from
213 source, available from L<http://gmplib.org/>.
217 C<isl> uses the standard C<autoconf> C<configure> script.
222 optionally followed by some configure options.
223 A complete list of options can be obtained by running
227 Below we discuss some of the more common options.
229 C<isl> can optionally use C<piplib>, but no
230 C<piplib> functionality is currently used by default.
231 The C<--with-piplib> option can
232 be used to specify which C<piplib>
233 library to use, either an installed version (C<system>),
234 an externally built version (C<build>)
235 or no version (C<no>). The option C<build> is mostly useful
236 in C<configure> scripts of larger projects that bundle both C<isl>
243 Installation prefix for C<isl>
245 =item C<--with-gmp-prefix>
247 Installation prefix for C<GMP> (architecture-independent files).
249 =item C<--with-gmp-exec-prefix>
251 Installation prefix for C<GMP> (architecture-dependent files).
253 =item C<--with-piplib>
255 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
257 =item C<--with-piplib-prefix>
259 Installation prefix for C<system> C<piplib> (architecture-independent files).
261 =item C<--with-piplib-exec-prefix>
263 Installation prefix for C<system> C<piplib> (architecture-dependent files).
265 =item C<--with-piplib-builddir>
267 Location where C<build> C<piplib> was built.
275 =item 4 Install (optional)
283 =head2 Initialization
285 All manipulations of integer sets and relations occur within
286 the context of an C<isl_ctx>.
287 A given C<isl_ctx> can only be used within a single thread.
288 All arguments of a function are required to have been allocated
289 within the same context.
290 There are currently no functions available for moving an object
291 from one C<isl_ctx> to another C<isl_ctx>. This means that
292 there is currently no way of safely moving an object from one
293 thread to another, unless the whole C<isl_ctx> is moved.
295 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
296 freed using C<isl_ctx_free>.
297 All objects allocated within an C<isl_ctx> should be freed
298 before the C<isl_ctx> itself is freed.
300 isl_ctx *isl_ctx_alloc();
301 void isl_ctx_free(isl_ctx *ctx);
305 All operations on integers, mainly the coefficients
306 of the constraints describing the sets and relations,
307 are performed in exact integer arithmetic using C<GMP>.
308 However, to allow future versions of C<isl> to optionally
309 support fixed integer arithmetic, all calls to C<GMP>
310 are wrapped inside C<isl> specific macros.
311 The basic type is C<isl_int> and the operations below
312 are available on this type.
313 The meanings of these operations are essentially the same
314 as their C<GMP> C<mpz_> counterparts.
315 As always with C<GMP> types, C<isl_int>s need to be
316 initialized with C<isl_int_init> before they can be used
317 and they need to be released with C<isl_int_clear>
319 The user should not assume that an C<isl_int> is represented
320 as a C<mpz_t>, but should instead explicitly convert between
321 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
322 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
326 =item isl_int_init(i)
328 =item isl_int_clear(i)
330 =item isl_int_set(r,i)
332 =item isl_int_set_si(r,i)
334 =item isl_int_set_gmp(r,g)
336 =item isl_int_get_gmp(i,g)
338 =item isl_int_abs(r,i)
340 =item isl_int_neg(r,i)
342 =item isl_int_swap(i,j)
344 =item isl_int_swap_or_set(i,j)
346 =item isl_int_add_ui(r,i,j)
348 =item isl_int_sub_ui(r,i,j)
350 =item isl_int_add(r,i,j)
352 =item isl_int_sub(r,i,j)
354 =item isl_int_mul(r,i,j)
356 =item isl_int_mul_ui(r,i,j)
358 =item isl_int_addmul(r,i,j)
360 =item isl_int_submul(r,i,j)
362 =item isl_int_gcd(r,i,j)
364 =item isl_int_lcm(r,i,j)
366 =item isl_int_divexact(r,i,j)
368 =item isl_int_cdiv_q(r,i,j)
370 =item isl_int_fdiv_q(r,i,j)
372 =item isl_int_fdiv_r(r,i,j)
374 =item isl_int_fdiv_q_ui(r,i,j)
376 =item isl_int_read(r,s)
378 =item isl_int_print(out,i,width)
382 =item isl_int_cmp(i,j)
384 =item isl_int_cmp_si(i,si)
386 =item isl_int_eq(i,j)
388 =item isl_int_ne(i,j)
390 =item isl_int_lt(i,j)
392 =item isl_int_le(i,j)
394 =item isl_int_gt(i,j)
396 =item isl_int_ge(i,j)
398 =item isl_int_abs_eq(i,j)
400 =item isl_int_abs_ne(i,j)
402 =item isl_int_abs_lt(i,j)
404 =item isl_int_abs_gt(i,j)
406 =item isl_int_abs_ge(i,j)
408 =item isl_int_is_zero(i)
410 =item isl_int_is_one(i)
412 =item isl_int_is_negone(i)
414 =item isl_int_is_pos(i)
416 =item isl_int_is_neg(i)
418 =item isl_int_is_nonpos(i)
420 =item isl_int_is_nonneg(i)
422 =item isl_int_is_divisible_by(i,j)
426 =head2 Sets and Relations
428 C<isl> uses six types of objects for representing sets and relations,
429 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
430 C<isl_union_set> and C<isl_union_map>.
431 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
432 can be described as a conjunction of affine constraints, while
433 C<isl_set> and C<isl_map> represent unions of
434 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
435 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
436 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
437 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
438 where spaces are considered different if they have a different number
439 of dimensions and/or different names (see L<"Spaces">).
440 The difference between sets and relations (maps) is that sets have
441 one set of variables, while relations have two sets of variables,
442 input variables and output variables.
444 =head2 Memory Management
446 Since a high-level operation on sets and/or relations usually involves
447 several substeps and since the user is usually not interested in
448 the intermediate results, most functions that return a new object
449 will also release all the objects passed as arguments.
450 If the user still wants to use one or more of these arguments
451 after the function call, she should pass along a copy of the
452 object rather than the object itself.
453 The user is then responsible for making sure that the original
454 object gets used somewhere else or is explicitly freed.
456 The arguments and return values of all documented functions are
457 annotated to make clear which arguments are released and which
458 arguments are preserved. In particular, the following annotations
465 C<__isl_give> means that a new object is returned.
466 The user should make sure that the returned pointer is
467 used exactly once as a value for an C<__isl_take> argument.
468 In between, it can be used as a value for as many
469 C<__isl_keep> arguments as the user likes.
470 There is one exception, and that is the case where the
471 pointer returned is C<NULL>. Is this case, the user
472 is free to use it as an C<__isl_take> argument or not.
476 C<__isl_take> means that the object the argument points to
477 is taken over by the function and may no longer be used
478 by the user as an argument to any other function.
479 The pointer value must be one returned by a function
480 returning an C<__isl_give> pointer.
481 If the user passes in a C<NULL> value, then this will
482 be treated as an error in the sense that the function will
483 not perform its usual operation. However, it will still
484 make sure that all the other C<__isl_take> arguments
489 C<__isl_keep> means that the function will only use the object
490 temporarily. After the function has finished, the user
491 can still use it as an argument to other functions.
492 A C<NULL> value will be treated in the same way as
493 a C<NULL> value for an C<__isl_take> argument.
497 =head2 Error Handling
499 C<isl> supports different ways to react in case a runtime error is triggered.
500 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
501 with two maps that have incompatible spaces. There are three possible ways
502 to react on error: to warn, to continue or to abort.
504 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
505 the last error in the corresponding C<isl_ctx> and the function in which the
506 error was triggered returns C<NULL>. An error does not corrupt internal state,
507 such that isl can continue to be used. C<isl> also provides functions to
508 read the last error and to reset the memory that stores the last error. The
509 last error is only stored for information purposes. Its presence does not
510 change the behavior of C<isl>. Hence, resetting an error is not required to
511 continue to use isl, but only to observe new errors.
514 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
515 void isl_ctx_reset_error(isl_ctx *ctx);
517 Another option is to continue on error. This is similar to warn on error mode,
518 except that C<isl> does not print any warning. This allows a program to
519 implement its own error reporting.
521 The last option is to directly abort the execution of the program from within
522 the isl library. This makes it obviously impossible to recover from an error,
523 but it allows to directly spot the error location. By aborting on error,
524 debuggers break at the location the error occurred and can provide a stack
525 trace. Other tools that automatically provide stack traces on abort or that do
526 not want to continue execution after an error was triggered may also prefer to
529 The on error behavior of isl can be specified by calling
530 C<isl_options_set_on_error> or by setting the command line option
531 C<--isl-on-error>. Valid arguments for the function call are
532 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
533 choices for the command line option are C<warn>, C<continue> and C<abort>.
534 It is also possible to query the current error mode.
536 #include <isl/options.h>
537 int isl_options_set_on_error(isl_ctx *ctx, int val);
538 int isl_options_get_on_error(isl_ctx *ctx);
542 Identifiers are used to identify both individual dimensions
543 and tuples of dimensions. They consist of a name and an optional
544 pointer. Identifiers with the same name but different pointer values
545 are considered to be distinct.
546 Identifiers can be constructed, copied, freed, inspected and printed
547 using the following functions.
550 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
551 __isl_keep const char *name, void *user);
552 __isl_give isl_id *isl_id_copy(isl_id *id);
553 void *isl_id_free(__isl_take isl_id *id);
555 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
556 void *isl_id_get_user(__isl_keep isl_id *id);
557 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
559 __isl_give isl_printer *isl_printer_print_id(
560 __isl_take isl_printer *p, __isl_keep isl_id *id);
562 Note that C<isl_id_get_name> returns a pointer to some internal
563 data structure, so the result can only be used while the
564 corresponding C<isl_id> is alive.
568 Whenever a new set, relation or similiar object is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
570 Each space involves zero or more parameters and zero, one or two
571 tuples of set or input/output dimensions. The parameters and dimensions
572 are identified by an C<isl_dim_type> and a position.
573 The type C<isl_dim_param> refers to parameters,
574 the type C<isl_dim_set> refers to set dimensions (for spaces
575 with a single tuple of dimensions) and the types C<isl_dim_in>
576 and C<isl_dim_out> refer to input and output dimensions
577 (for spaces with two tuples of dimensions).
578 Local spaces (see L</"Local Spaces">) also contain dimensions
579 of type C<isl_dim_div>.
580 Note that parameters are only identified by their position within
581 a given object. Across different objects, parameters are (usually)
582 identified by their names or identifiers. Only unnamed parameters
583 are identified by their positions across objects. The use of unnamed
584 parameters is discouraged.
586 #include <isl/space.h>
587 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
588 unsigned nparam, unsigned n_in, unsigned n_out);
589 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
591 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
592 unsigned nparam, unsigned dim);
593 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
594 void isl_space_free(__isl_take isl_space *space);
595 unsigned isl_space_dim(__isl_keep isl_space *space,
596 enum isl_dim_type type);
598 The space used for creating a parameter domain
599 needs to be created using C<isl_space_params_alloc>.
600 For other sets, the space
601 needs to be created using C<isl_space_set_alloc>, while
602 for a relation, the space
603 needs to be created using C<isl_space_alloc>.
604 C<isl_space_dim> can be used
605 to find out the number of dimensions of each type in
606 a space, where type may be
607 C<isl_dim_param>, C<isl_dim_in> (only for relations),
608 C<isl_dim_out> (only for relations), C<isl_dim_set>
609 (only for sets) or C<isl_dim_all>.
611 To check whether a given space is that of a set or a map
612 or whether it is a parameter space, use these functions:
614 #include <isl/space.h>
615 int isl_space_is_params(__isl_keep isl_space *space);
616 int isl_space_is_set(__isl_keep isl_space *space);
618 It is often useful to create objects that live in the
619 same space as some other object. This can be accomplished
620 by creating the new objects
621 (see L<Creating New Sets and Relations> or
622 L<Creating New (Piecewise) Quasipolynomials>) based on the space
623 of the original object.
626 __isl_give isl_space *isl_basic_set_get_space(
627 __isl_keep isl_basic_set *bset);
628 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
630 #include <isl/union_set.h>
631 __isl_give isl_space *isl_union_set_get_space(
632 __isl_keep isl_union_set *uset);
635 __isl_give isl_space *isl_basic_map_get_space(
636 __isl_keep isl_basic_map *bmap);
637 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
639 #include <isl/union_map.h>
640 __isl_give isl_space *isl_union_map_get_space(
641 __isl_keep isl_union_map *umap);
643 #include <isl/constraint.h>
644 __isl_give isl_space *isl_constraint_get_space(
645 __isl_keep isl_constraint *constraint);
647 #include <isl/polynomial.h>
648 __isl_give isl_space *isl_qpolynomial_get_domain_space(
649 __isl_keep isl_qpolynomial *qp);
650 __isl_give isl_space *isl_qpolynomial_get_space(
651 __isl_keep isl_qpolynomial *qp);
652 __isl_give isl_space *isl_qpolynomial_fold_get_space(
653 __isl_keep isl_qpolynomial_fold *fold);
654 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
655 __isl_keep isl_pw_qpolynomial *pwqp);
656 __isl_give isl_space *isl_pw_qpolynomial_get_space(
657 __isl_keep isl_pw_qpolynomial *pwqp);
658 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
659 __isl_keep isl_pw_qpolynomial_fold *pwf);
660 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
661 __isl_keep isl_pw_qpolynomial_fold *pwf);
662 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
663 __isl_keep isl_union_pw_qpolynomial *upwqp);
664 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
665 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
668 __isl_give isl_space *isl_aff_get_domain_space(
669 __isl_keep isl_aff *aff);
670 __isl_give isl_space *isl_aff_get_space(
671 __isl_keep isl_aff *aff);
672 __isl_give isl_space *isl_pw_aff_get_domain_space(
673 __isl_keep isl_pw_aff *pwaff);
674 __isl_give isl_space *isl_pw_aff_get_space(
675 __isl_keep isl_pw_aff *pwaff);
676 __isl_give isl_space *isl_multi_aff_get_domain_space(
677 __isl_keep isl_multi_aff *maff);
678 __isl_give isl_space *isl_multi_aff_get_space(
679 __isl_keep isl_multi_aff *maff);
680 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
681 __isl_keep isl_pw_multi_aff *pma);
682 __isl_give isl_space *isl_pw_multi_aff_get_space(
683 __isl_keep isl_pw_multi_aff *pma);
684 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
685 __isl_keep isl_union_pw_multi_aff *upma);
687 #include <isl/point.h>
688 __isl_give isl_space *isl_point_get_space(
689 __isl_keep isl_point *pnt);
691 The identifiers or names of the individual dimensions may be set or read off
692 using the following functions.
694 #include <isl/space.h>
695 __isl_give isl_space *isl_space_set_dim_id(
696 __isl_take isl_space *space,
697 enum isl_dim_type type, unsigned pos,
698 __isl_take isl_id *id);
699 int isl_space_has_dim_id(__isl_keep isl_space *space,
700 enum isl_dim_type type, unsigned pos);
701 __isl_give isl_id *isl_space_get_dim_id(
702 __isl_keep isl_space *space,
703 enum isl_dim_type type, unsigned pos);
704 __isl_give isl_space *isl_space_set_dim_name(
705 __isl_take isl_space *space,
706 enum isl_dim_type type, unsigned pos,
707 __isl_keep const char *name);
708 int isl_space_has_dim_name(__isl_keep isl_space *space,
709 enum isl_dim_type type, unsigned pos);
710 __isl_keep const char *isl_space_get_dim_name(
711 __isl_keep isl_space *space,
712 enum isl_dim_type type, unsigned pos);
714 Note that C<isl_space_get_name> returns a pointer to some internal
715 data structure, so the result can only be used while the
716 corresponding C<isl_space> is alive.
717 Also note that every function that operates on two sets or relations
718 requires that both arguments have the same parameters. This also
719 means that if one of the arguments has named parameters, then the
720 other needs to have named parameters too and the names need to match.
721 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
722 arguments may have different parameters (as long as they are named),
723 in which case the result will have as parameters the union of the parameters of
726 Given the identifier or name of a dimension (typically a parameter),
727 its position can be obtained from the following function.
729 #include <isl/space.h>
730 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
731 enum isl_dim_type type, __isl_keep isl_id *id);
732 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
733 enum isl_dim_type type, const char *name);
735 The identifiers or names of entire spaces may be set or read off
736 using the following functions.
738 #include <isl/space.h>
739 __isl_give isl_space *isl_space_set_tuple_id(
740 __isl_take isl_space *space,
741 enum isl_dim_type type, __isl_take isl_id *id);
742 __isl_give isl_space *isl_space_reset_tuple_id(
743 __isl_take isl_space *space, enum isl_dim_type type);
744 int isl_space_has_tuple_id(__isl_keep isl_space *space,
745 enum isl_dim_type type);
746 __isl_give isl_id *isl_space_get_tuple_id(
747 __isl_keep isl_space *space, enum isl_dim_type type);
748 __isl_give isl_space *isl_space_set_tuple_name(
749 __isl_take isl_space *space,
750 enum isl_dim_type type, const char *s);
751 int isl_space_has_tuple_name(__isl_keep isl_space *space,
752 enum isl_dim_type type);
753 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
754 enum isl_dim_type type);
756 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
757 or C<isl_dim_set>. As with C<isl_space_get_name>,
758 the C<isl_space_get_tuple_name> function returns a pointer to some internal
760 Binary operations require the corresponding spaces of their arguments
761 to have the same name.
763 Spaces can be nested. In particular, the domain of a set or
764 the domain or range of a relation can be a nested relation.
765 The following functions can be used to construct and deconstruct
768 #include <isl/space.h>
769 int isl_space_is_wrapping(__isl_keep isl_space *space);
770 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
771 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
773 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
774 be the space of a set, while that of
775 C<isl_space_wrap> should be the space of a relation.
776 Conversely, the output of C<isl_space_unwrap> is the space
777 of a relation, while that of C<isl_space_wrap> is the space of a set.
779 Spaces can be created from other spaces
780 using the following functions.
782 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
783 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
784 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
785 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
786 __isl_give isl_space *isl_space_params(
787 __isl_take isl_space *space);
788 __isl_give isl_space *isl_space_set_from_params(
789 __isl_take isl_space *space);
790 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
791 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
792 __isl_take isl_space *right);
793 __isl_give isl_space *isl_space_align_params(
794 __isl_take isl_space *space1, __isl_take isl_space *space2)
795 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
796 enum isl_dim_type type, unsigned pos, unsigned n);
797 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
798 enum isl_dim_type type, unsigned n);
799 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
800 enum isl_dim_type type, unsigned first, unsigned n);
801 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
802 enum isl_dim_type dst_type, unsigned dst_pos,
803 enum isl_dim_type src_type, unsigned src_pos,
805 __isl_give isl_space *isl_space_map_from_set(
806 __isl_take isl_space *space);
807 __isl_give isl_space *isl_space_map_from_domain_and_range(
808 __isl_take isl_space *domain,
809 __isl_take isl_space *range);
810 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
811 __isl_give isl_space *isl_space_curry(
812 __isl_take isl_space *space);
814 Note that if dimensions are added or removed from a space, then
815 the name and the internal structure are lost.
819 A local space is essentially a space with
820 zero or more existentially quantified variables.
821 The local space of a (constraint of a) basic set or relation can be obtained
822 using the following functions.
824 #include <isl/constraint.h>
825 __isl_give isl_local_space *isl_constraint_get_local_space(
826 __isl_keep isl_constraint *constraint);
829 __isl_give isl_local_space *isl_basic_set_get_local_space(
830 __isl_keep isl_basic_set *bset);
833 __isl_give isl_local_space *isl_basic_map_get_local_space(
834 __isl_keep isl_basic_map *bmap);
836 A new local space can be created from a space using
838 #include <isl/local_space.h>
839 __isl_give isl_local_space *isl_local_space_from_space(
840 __isl_take isl_space *space);
842 They can be inspected, modified, copied and freed using the following functions.
844 #include <isl/local_space.h>
845 isl_ctx *isl_local_space_get_ctx(
846 __isl_keep isl_local_space *ls);
847 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
848 int isl_local_space_dim(__isl_keep isl_local_space *ls,
849 enum isl_dim_type type);
850 int isl_local_space_has_dim_id(
851 __isl_keep isl_local_space *ls,
852 enum isl_dim_type type, unsigned pos);
853 __isl_give isl_id *isl_local_space_get_dim_id(
854 __isl_keep isl_local_space *ls,
855 enum isl_dim_type type, unsigned pos);
856 int isl_local_space_has_dim_name(
857 __isl_keep isl_local_space *ls,
858 enum isl_dim_type type, unsigned pos)
859 const char *isl_local_space_get_dim_name(
860 __isl_keep isl_local_space *ls,
861 enum isl_dim_type type, unsigned pos);
862 __isl_give isl_local_space *isl_local_space_set_dim_name(
863 __isl_take isl_local_space *ls,
864 enum isl_dim_type type, unsigned pos, const char *s);
865 __isl_give isl_local_space *isl_local_space_set_dim_id(
866 __isl_take isl_local_space *ls,
867 enum isl_dim_type type, unsigned pos,
868 __isl_take isl_id *id);
869 __isl_give isl_space *isl_local_space_get_space(
870 __isl_keep isl_local_space *ls);
871 __isl_give isl_aff *isl_local_space_get_div(
872 __isl_keep isl_local_space *ls, int pos);
873 __isl_give isl_local_space *isl_local_space_copy(
874 __isl_keep isl_local_space *ls);
875 void *isl_local_space_free(__isl_take isl_local_space *ls);
877 Two local spaces can be compared using
879 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
880 __isl_keep isl_local_space *ls2);
882 Local spaces can be created from other local spaces
883 using the following functions.
885 __isl_give isl_local_space *isl_local_space_domain(
886 __isl_take isl_local_space *ls);
887 __isl_give isl_local_space *isl_local_space_range(
888 __isl_take isl_local_space *ls);
889 __isl_give isl_local_space *isl_local_space_from_domain(
890 __isl_take isl_local_space *ls);
891 __isl_give isl_local_space *isl_local_space_intersect(
892 __isl_take isl_local_space *ls1,
893 __isl_take isl_local_space *ls2);
894 __isl_give isl_local_space *isl_local_space_add_dims(
895 __isl_take isl_local_space *ls,
896 enum isl_dim_type type, unsigned n);
897 __isl_give isl_local_space *isl_local_space_insert_dims(
898 __isl_take isl_local_space *ls,
899 enum isl_dim_type type, unsigned first, unsigned n);
900 __isl_give isl_local_space *isl_local_space_drop_dims(
901 __isl_take isl_local_space *ls,
902 enum isl_dim_type type, unsigned first, unsigned n);
904 =head2 Input and Output
906 C<isl> supports its own input/output format, which is similar
907 to the C<Omega> format, but also supports the C<PolyLib> format
912 The C<isl> format is similar to that of C<Omega>, but has a different
913 syntax for describing the parameters and allows for the definition
914 of an existentially quantified variable as the integer division
915 of an affine expression.
916 For example, the set of integers C<i> between C<0> and C<n>
917 such that C<i % 10 <= 6> can be described as
919 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
922 A set or relation can have several disjuncts, separated
923 by the keyword C<or>. Each disjunct is either a conjunction
924 of constraints or a projection (C<exists>) of a conjunction
925 of constraints. The constraints are separated by the keyword
928 =head3 C<PolyLib> format
930 If the represented set is a union, then the first line
931 contains a single number representing the number of disjuncts.
932 Otherwise, a line containing the number C<1> is optional.
934 Each disjunct is represented by a matrix of constraints.
935 The first line contains two numbers representing
936 the number of rows and columns,
937 where the number of rows is equal to the number of constraints
938 and the number of columns is equal to two plus the number of variables.
939 The following lines contain the actual rows of the constraint matrix.
940 In each row, the first column indicates whether the constraint
941 is an equality (C<0>) or inequality (C<1>). The final column
942 corresponds to the constant term.
944 If the set is parametric, then the coefficients of the parameters
945 appear in the last columns before the constant column.
946 The coefficients of any existentially quantified variables appear
947 between those of the set variables and those of the parameters.
949 =head3 Extended C<PolyLib> format
951 The extended C<PolyLib> format is nearly identical to the
952 C<PolyLib> format. The only difference is that the line
953 containing the number of rows and columns of a constraint matrix
954 also contains four additional numbers:
955 the number of output dimensions, the number of input dimensions,
956 the number of local dimensions (i.e., the number of existentially
957 quantified variables) and the number of parameters.
958 For sets, the number of ``output'' dimensions is equal
959 to the number of set dimensions, while the number of ``input''
965 __isl_give isl_basic_set *isl_basic_set_read_from_file(
966 isl_ctx *ctx, FILE *input);
967 __isl_give isl_basic_set *isl_basic_set_read_from_str(
968 isl_ctx *ctx, const char *str);
969 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
971 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
975 __isl_give isl_basic_map *isl_basic_map_read_from_file(
976 isl_ctx *ctx, FILE *input);
977 __isl_give isl_basic_map *isl_basic_map_read_from_str(
978 isl_ctx *ctx, const char *str);
979 __isl_give isl_map *isl_map_read_from_file(
980 isl_ctx *ctx, FILE *input);
981 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
984 #include <isl/union_set.h>
985 __isl_give isl_union_set *isl_union_set_read_from_file(
986 isl_ctx *ctx, FILE *input);
987 __isl_give isl_union_set *isl_union_set_read_from_str(
988 isl_ctx *ctx, const char *str);
990 #include <isl/union_map.h>
991 __isl_give isl_union_map *isl_union_map_read_from_file(
992 isl_ctx *ctx, FILE *input);
993 __isl_give isl_union_map *isl_union_map_read_from_str(
994 isl_ctx *ctx, const char *str);
996 The input format is autodetected and may be either the C<PolyLib> format
997 or the C<isl> format.
1001 Before anything can be printed, an C<isl_printer> needs to
1004 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1006 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1007 void isl_printer_free(__isl_take isl_printer *printer);
1008 __isl_give char *isl_printer_get_str(
1009 __isl_keep isl_printer *printer);
1011 The printer can be inspected using the following functions.
1013 FILE *isl_printer_get_file(
1014 __isl_keep isl_printer *printer);
1015 int isl_printer_get_output_format(
1016 __isl_keep isl_printer *p);
1018 The behavior of the printer can be modified in various ways
1020 __isl_give isl_printer *isl_printer_set_output_format(
1021 __isl_take isl_printer *p, int output_format);
1022 __isl_give isl_printer *isl_printer_set_indent(
1023 __isl_take isl_printer *p, int indent);
1024 __isl_give isl_printer *isl_printer_indent(
1025 __isl_take isl_printer *p, int indent);
1026 __isl_give isl_printer *isl_printer_set_prefix(
1027 __isl_take isl_printer *p, const char *prefix);
1028 __isl_give isl_printer *isl_printer_set_suffix(
1029 __isl_take isl_printer *p, const char *suffix);
1031 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1032 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1033 and defaults to C<ISL_FORMAT_ISL>.
1034 Each line in the output is indented by C<indent> (set by
1035 C<isl_printer_set_indent>) spaces
1036 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1037 In the C<PolyLib> format output,
1038 the coefficients of the existentially quantified variables
1039 appear between those of the set variables and those
1041 The function C<isl_printer_indent> increases the indentation
1042 by the specified amount (which may be negative).
1044 To actually print something, use
1046 #include <isl/printer.h>
1047 __isl_give isl_printer *isl_printer_print_double(
1048 __isl_take isl_printer *p, double d);
1050 #include <isl/set.h>
1051 __isl_give isl_printer *isl_printer_print_basic_set(
1052 __isl_take isl_printer *printer,
1053 __isl_keep isl_basic_set *bset);
1054 __isl_give isl_printer *isl_printer_print_set(
1055 __isl_take isl_printer *printer,
1056 __isl_keep isl_set *set);
1058 #include <isl/map.h>
1059 __isl_give isl_printer *isl_printer_print_basic_map(
1060 __isl_take isl_printer *printer,
1061 __isl_keep isl_basic_map *bmap);
1062 __isl_give isl_printer *isl_printer_print_map(
1063 __isl_take isl_printer *printer,
1064 __isl_keep isl_map *map);
1066 #include <isl/union_set.h>
1067 __isl_give isl_printer *isl_printer_print_union_set(
1068 __isl_take isl_printer *p,
1069 __isl_keep isl_union_set *uset);
1071 #include <isl/union_map.h>
1072 __isl_give isl_printer *isl_printer_print_union_map(
1073 __isl_take isl_printer *p,
1074 __isl_keep isl_union_map *umap);
1076 When called on a file printer, the following function flushes
1077 the file. When called on a string printer, the buffer is cleared.
1079 __isl_give isl_printer *isl_printer_flush(
1080 __isl_take isl_printer *p);
1082 =head2 Creating New Sets and Relations
1084 C<isl> has functions for creating some standard sets and relations.
1088 =item * Empty sets and relations
1090 __isl_give isl_basic_set *isl_basic_set_empty(
1091 __isl_take isl_space *space);
1092 __isl_give isl_basic_map *isl_basic_map_empty(
1093 __isl_take isl_space *space);
1094 __isl_give isl_set *isl_set_empty(
1095 __isl_take isl_space *space);
1096 __isl_give isl_map *isl_map_empty(
1097 __isl_take isl_space *space);
1098 __isl_give isl_union_set *isl_union_set_empty(
1099 __isl_take isl_space *space);
1100 __isl_give isl_union_map *isl_union_map_empty(
1101 __isl_take isl_space *space);
1103 For C<isl_union_set>s and C<isl_union_map>s, the space
1104 is only used to specify the parameters.
1106 =item * Universe sets and relations
1108 __isl_give isl_basic_set *isl_basic_set_universe(
1109 __isl_take isl_space *space);
1110 __isl_give isl_basic_map *isl_basic_map_universe(
1111 __isl_take isl_space *space);
1112 __isl_give isl_set *isl_set_universe(
1113 __isl_take isl_space *space);
1114 __isl_give isl_map *isl_map_universe(
1115 __isl_take isl_space *space);
1116 __isl_give isl_union_set *isl_union_set_universe(
1117 __isl_take isl_union_set *uset);
1118 __isl_give isl_union_map *isl_union_map_universe(
1119 __isl_take isl_union_map *umap);
1121 The sets and relations constructed by the functions above
1122 contain all integer values, while those constructed by the
1123 functions below only contain non-negative values.
1125 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1126 __isl_take isl_space *space);
1127 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1128 __isl_take isl_space *space);
1129 __isl_give isl_set *isl_set_nat_universe(
1130 __isl_take isl_space *space);
1131 __isl_give isl_map *isl_map_nat_universe(
1132 __isl_take isl_space *space);
1134 =item * Identity relations
1136 __isl_give isl_basic_map *isl_basic_map_identity(
1137 __isl_take isl_space *space);
1138 __isl_give isl_map *isl_map_identity(
1139 __isl_take isl_space *space);
1141 The number of input and output dimensions in C<space> needs
1144 =item * Lexicographic order
1146 __isl_give isl_map *isl_map_lex_lt(
1147 __isl_take isl_space *set_space);
1148 __isl_give isl_map *isl_map_lex_le(
1149 __isl_take isl_space *set_space);
1150 __isl_give isl_map *isl_map_lex_gt(
1151 __isl_take isl_space *set_space);
1152 __isl_give isl_map *isl_map_lex_ge(
1153 __isl_take isl_space *set_space);
1154 __isl_give isl_map *isl_map_lex_lt_first(
1155 __isl_take isl_space *space, unsigned n);
1156 __isl_give isl_map *isl_map_lex_le_first(
1157 __isl_take isl_space *space, unsigned n);
1158 __isl_give isl_map *isl_map_lex_gt_first(
1159 __isl_take isl_space *space, unsigned n);
1160 __isl_give isl_map *isl_map_lex_ge_first(
1161 __isl_take isl_space *space, unsigned n);
1163 The first four functions take a space for a B<set>
1164 and return relations that express that the elements in the domain
1165 are lexicographically less
1166 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1167 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1168 than the elements in the range.
1169 The last four functions take a space for a map
1170 and return relations that express that the first C<n> dimensions
1171 in the domain are lexicographically less
1172 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1173 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1174 than the first C<n> dimensions in the range.
1178 A basic set or relation can be converted to a set or relation
1179 using the following functions.
1181 __isl_give isl_set *isl_set_from_basic_set(
1182 __isl_take isl_basic_set *bset);
1183 __isl_give isl_map *isl_map_from_basic_map(
1184 __isl_take isl_basic_map *bmap);
1186 Sets and relations can be converted to union sets and relations
1187 using the following functions.
1189 __isl_give isl_union_set *isl_union_set_from_basic_set(
1190 __isl_take isl_basic_set *bset);
1191 __isl_give isl_union_map *isl_union_map_from_basic_map(
1192 __isl_take isl_basic_map *bmap);
1193 __isl_give isl_union_set *isl_union_set_from_set(
1194 __isl_take isl_set *set);
1195 __isl_give isl_union_map *isl_union_map_from_map(
1196 __isl_take isl_map *map);
1198 The inverse conversions below can only be used if the input
1199 union set or relation is known to contain elements in exactly one
1202 __isl_give isl_set *isl_set_from_union_set(
1203 __isl_take isl_union_set *uset);
1204 __isl_give isl_map *isl_map_from_union_map(
1205 __isl_take isl_union_map *umap);
1207 A zero-dimensional set can be constructed on a given parameter domain
1208 using the following function.
1210 __isl_give isl_set *isl_set_from_params(
1211 __isl_take isl_set *set);
1213 Sets and relations can be copied and freed again using the following
1216 __isl_give isl_basic_set *isl_basic_set_copy(
1217 __isl_keep isl_basic_set *bset);
1218 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1219 __isl_give isl_union_set *isl_union_set_copy(
1220 __isl_keep isl_union_set *uset);
1221 __isl_give isl_basic_map *isl_basic_map_copy(
1222 __isl_keep isl_basic_map *bmap);
1223 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1224 __isl_give isl_union_map *isl_union_map_copy(
1225 __isl_keep isl_union_map *umap);
1226 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1227 void *isl_set_free(__isl_take isl_set *set);
1228 void *isl_union_set_free(__isl_take isl_union_set *uset);
1229 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1230 void isl_map_free(__isl_take isl_map *map);
1231 void *isl_union_map_free(__isl_take isl_union_map *umap);
1233 Other sets and relations can be constructed by starting
1234 from a universe set or relation, adding equality and/or
1235 inequality constraints and then projecting out the
1236 existentially quantified variables, if any.
1237 Constraints can be constructed, manipulated and
1238 added to (or removed from) (basic) sets and relations
1239 using the following functions.
1241 #include <isl/constraint.h>
1242 __isl_give isl_constraint *isl_equality_alloc(
1243 __isl_take isl_local_space *ls);
1244 __isl_give isl_constraint *isl_inequality_alloc(
1245 __isl_take isl_local_space *ls);
1246 __isl_give isl_constraint *isl_constraint_set_constant(
1247 __isl_take isl_constraint *constraint, isl_int v);
1248 __isl_give isl_constraint *isl_constraint_set_constant_si(
1249 __isl_take isl_constraint *constraint, int v);
1250 __isl_give isl_constraint *isl_constraint_set_coefficient(
1251 __isl_take isl_constraint *constraint,
1252 enum isl_dim_type type, int pos, isl_int v);
1253 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1254 __isl_take isl_constraint *constraint,
1255 enum isl_dim_type type, int pos, int v);
1256 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1257 __isl_take isl_basic_map *bmap,
1258 __isl_take isl_constraint *constraint);
1259 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1260 __isl_take isl_basic_set *bset,
1261 __isl_take isl_constraint *constraint);
1262 __isl_give isl_map *isl_map_add_constraint(
1263 __isl_take isl_map *map,
1264 __isl_take isl_constraint *constraint);
1265 __isl_give isl_set *isl_set_add_constraint(
1266 __isl_take isl_set *set,
1267 __isl_take isl_constraint *constraint);
1268 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1269 __isl_take isl_basic_set *bset,
1270 __isl_take isl_constraint *constraint);
1272 For example, to create a set containing the even integers
1273 between 10 and 42, you would use the following code.
1276 isl_local_space *ls;
1278 isl_basic_set *bset;
1280 space = isl_space_set_alloc(ctx, 0, 2);
1281 bset = isl_basic_set_universe(isl_space_copy(space));
1282 ls = isl_local_space_from_space(space);
1284 c = isl_equality_alloc(isl_local_space_copy(ls));
1285 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1286 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1287 bset = isl_basic_set_add_constraint(bset, c);
1289 c = isl_inequality_alloc(isl_local_space_copy(ls));
1290 c = isl_constraint_set_constant_si(c, -10);
1291 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1292 bset = isl_basic_set_add_constraint(bset, c);
1294 c = isl_inequality_alloc(ls);
1295 c = isl_constraint_set_constant_si(c, 42);
1296 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1297 bset = isl_basic_set_add_constraint(bset, c);
1299 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1303 isl_basic_set *bset;
1304 bset = isl_basic_set_read_from_str(ctx,
1305 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1307 A basic set or relation can also be constructed from two matrices
1308 describing the equalities and the inequalities.
1310 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1311 __isl_take isl_space *space,
1312 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1313 enum isl_dim_type c1,
1314 enum isl_dim_type c2, enum isl_dim_type c3,
1315 enum isl_dim_type c4);
1316 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1317 __isl_take isl_space *space,
1318 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1319 enum isl_dim_type c1,
1320 enum isl_dim_type c2, enum isl_dim_type c3,
1321 enum isl_dim_type c4, enum isl_dim_type c5);
1323 The C<isl_dim_type> arguments indicate the order in which
1324 different kinds of variables appear in the input matrices
1325 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1326 C<isl_dim_set> and C<isl_dim_div> for sets and
1327 of C<isl_dim_cst>, C<isl_dim_param>,
1328 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1330 A (basic or union) set or relation can also be constructed from a
1331 (union) (piecewise) (multiple) affine expression
1332 or a list of affine expressions
1333 (See L<"Piecewise Quasi Affine Expressions"> and
1334 L<"Piecewise Multiple Quasi Affine Expressions">).
1336 __isl_give isl_basic_map *isl_basic_map_from_aff(
1337 __isl_take isl_aff *aff);
1338 __isl_give isl_map *isl_map_from_aff(
1339 __isl_take isl_aff *aff);
1340 __isl_give isl_set *isl_set_from_pw_aff(
1341 __isl_take isl_pw_aff *pwaff);
1342 __isl_give isl_map *isl_map_from_pw_aff(
1343 __isl_take isl_pw_aff *pwaff);
1344 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1345 __isl_take isl_space *domain_space,
1346 __isl_take isl_aff_list *list);
1347 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1348 __isl_take isl_multi_aff *maff)
1349 __isl_give isl_map *isl_map_from_multi_aff(
1350 __isl_take isl_multi_aff *maff)
1351 __isl_give isl_set *isl_set_from_pw_multi_aff(
1352 __isl_take isl_pw_multi_aff *pma);
1353 __isl_give isl_map *isl_map_from_pw_multi_aff(
1354 __isl_take isl_pw_multi_aff *pma);
1355 __isl_give isl_union_map *
1356 isl_union_map_from_union_pw_multi_aff(
1357 __isl_take isl_union_pw_multi_aff *upma);
1359 The C<domain_dim> argument describes the domain of the resulting
1360 basic relation. It is required because the C<list> may consist
1361 of zero affine expressions.
1363 =head2 Inspecting Sets and Relations
1365 Usually, the user should not have to care about the actual constraints
1366 of the sets and maps, but should instead apply the abstract operations
1367 explained in the following sections.
1368 Occasionally, however, it may be required to inspect the individual
1369 coefficients of the constraints. This section explains how to do so.
1370 In these cases, it may also be useful to have C<isl> compute
1371 an explicit representation of the existentially quantified variables.
1373 __isl_give isl_set *isl_set_compute_divs(
1374 __isl_take isl_set *set);
1375 __isl_give isl_map *isl_map_compute_divs(
1376 __isl_take isl_map *map);
1377 __isl_give isl_union_set *isl_union_set_compute_divs(
1378 __isl_take isl_union_set *uset);
1379 __isl_give isl_union_map *isl_union_map_compute_divs(
1380 __isl_take isl_union_map *umap);
1382 This explicit representation defines the existentially quantified
1383 variables as integer divisions of the other variables, possibly
1384 including earlier existentially quantified variables.
1385 An explicitly represented existentially quantified variable therefore
1386 has a unique value when the values of the other variables are known.
1387 If, furthermore, the same existentials, i.e., existentials
1388 with the same explicit representations, should appear in the
1389 same order in each of the disjuncts of a set or map, then the user should call
1390 either of the following functions.
1392 __isl_give isl_set *isl_set_align_divs(
1393 __isl_take isl_set *set);
1394 __isl_give isl_map *isl_map_align_divs(
1395 __isl_take isl_map *map);
1397 Alternatively, the existentially quantified variables can be removed
1398 using the following functions, which compute an overapproximation.
1400 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1401 __isl_take isl_basic_set *bset);
1402 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1403 __isl_take isl_basic_map *bmap);
1404 __isl_give isl_set *isl_set_remove_divs(
1405 __isl_take isl_set *set);
1406 __isl_give isl_map *isl_map_remove_divs(
1407 __isl_take isl_map *map);
1409 It is also possible to only remove those divs that are defined
1410 in terms of a given range of dimensions.
1412 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1413 __isl_take isl_set *set, enum isl_dim_type type,
1414 unsigned first, unsigned n);
1416 To iterate over all the sets or maps in a union set or map, use
1418 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1419 int (*fn)(__isl_take isl_set *set, void *user),
1421 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1422 int (*fn)(__isl_take isl_map *map, void *user),
1425 The number of sets or maps in a union set or map can be obtained
1428 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1429 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1431 To extract the set or map in a given space from a union, use
1433 __isl_give isl_set *isl_union_set_extract_set(
1434 __isl_keep isl_union_set *uset,
1435 __isl_take isl_space *space);
1436 __isl_give isl_map *isl_union_map_extract_map(
1437 __isl_keep isl_union_map *umap,
1438 __isl_take isl_space *space);
1440 To iterate over all the basic sets or maps in a set or map, use
1442 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1443 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1445 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1446 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1449 The callback function C<fn> should return 0 if successful and
1450 -1 if an error occurs. In the latter case, or if any other error
1451 occurs, the above functions will return -1.
1453 It should be noted that C<isl> does not guarantee that
1454 the basic sets or maps passed to C<fn> are disjoint.
1455 If this is required, then the user should call one of
1456 the following functions first.
1458 __isl_give isl_set *isl_set_make_disjoint(
1459 __isl_take isl_set *set);
1460 __isl_give isl_map *isl_map_make_disjoint(
1461 __isl_take isl_map *map);
1463 The number of basic sets in a set can be obtained
1466 int isl_set_n_basic_set(__isl_keep isl_set *set);
1468 To iterate over the constraints of a basic set or map, use
1470 #include <isl/constraint.h>
1472 int isl_basic_set_n_constraint(
1473 __isl_keep isl_basic_set *bset);
1474 int isl_basic_set_foreach_constraint(
1475 __isl_keep isl_basic_set *bset,
1476 int (*fn)(__isl_take isl_constraint *c, void *user),
1478 int isl_basic_map_foreach_constraint(
1479 __isl_keep isl_basic_map *bmap,
1480 int (*fn)(__isl_take isl_constraint *c, void *user),
1482 void *isl_constraint_free(__isl_take isl_constraint *c);
1484 Again, the callback function C<fn> should return 0 if successful and
1485 -1 if an error occurs. In the latter case, or if any other error
1486 occurs, the above functions will return -1.
1487 The constraint C<c> represents either an equality or an inequality.
1488 Use the following function to find out whether a constraint
1489 represents an equality. If not, it represents an inequality.
1491 int isl_constraint_is_equality(
1492 __isl_keep isl_constraint *constraint);
1494 The coefficients of the constraints can be inspected using
1495 the following functions.
1497 int isl_constraint_is_lower_bound(
1498 __isl_keep isl_constraint *constraint,
1499 enum isl_dim_type type, unsigned pos);
1500 int isl_constraint_is_upper_bound(
1501 __isl_keep isl_constraint *constraint,
1502 enum isl_dim_type type, unsigned pos);
1503 void isl_constraint_get_constant(
1504 __isl_keep isl_constraint *constraint, isl_int *v);
1505 void isl_constraint_get_coefficient(
1506 __isl_keep isl_constraint *constraint,
1507 enum isl_dim_type type, int pos, isl_int *v);
1508 int isl_constraint_involves_dims(
1509 __isl_keep isl_constraint *constraint,
1510 enum isl_dim_type type, unsigned first, unsigned n);
1512 The explicit representations of the existentially quantified
1513 variables can be inspected using the following function.
1514 Note that the user is only allowed to use this function
1515 if the inspected set or map is the result of a call
1516 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1517 The existentially quantified variable is equal to the floor
1518 of the returned affine expression. The affine expression
1519 itself can be inspected using the functions in
1520 L<"Piecewise Quasi Affine Expressions">.
1522 __isl_give isl_aff *isl_constraint_get_div(
1523 __isl_keep isl_constraint *constraint, int pos);
1525 To obtain the constraints of a basic set or map in matrix
1526 form, use the following functions.
1528 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1529 __isl_keep isl_basic_set *bset,
1530 enum isl_dim_type c1, enum isl_dim_type c2,
1531 enum isl_dim_type c3, enum isl_dim_type c4);
1532 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1533 __isl_keep isl_basic_set *bset,
1534 enum isl_dim_type c1, enum isl_dim_type c2,
1535 enum isl_dim_type c3, enum isl_dim_type c4);
1536 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1537 __isl_keep isl_basic_map *bmap,
1538 enum isl_dim_type c1,
1539 enum isl_dim_type c2, enum isl_dim_type c3,
1540 enum isl_dim_type c4, enum isl_dim_type c5);
1541 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1542 __isl_keep isl_basic_map *bmap,
1543 enum isl_dim_type c1,
1544 enum isl_dim_type c2, enum isl_dim_type c3,
1545 enum isl_dim_type c4, enum isl_dim_type c5);
1547 The C<isl_dim_type> arguments dictate the order in which
1548 different kinds of variables appear in the resulting matrix
1549 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1550 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1552 The number of parameters, input, output or set dimensions can
1553 be obtained using the following functions.
1555 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1556 enum isl_dim_type type);
1557 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1558 enum isl_dim_type type);
1559 unsigned isl_set_dim(__isl_keep isl_set *set,
1560 enum isl_dim_type type);
1561 unsigned isl_map_dim(__isl_keep isl_map *map,
1562 enum isl_dim_type type);
1564 To check whether the description of a set or relation depends
1565 on one or more given dimensions, it is not necessary to iterate over all
1566 constraints. Instead the following functions can be used.
1568 int isl_basic_set_involves_dims(
1569 __isl_keep isl_basic_set *bset,
1570 enum isl_dim_type type, unsigned first, unsigned n);
1571 int isl_set_involves_dims(__isl_keep isl_set *set,
1572 enum isl_dim_type type, unsigned first, unsigned n);
1573 int isl_basic_map_involves_dims(
1574 __isl_keep isl_basic_map *bmap,
1575 enum isl_dim_type type, unsigned first, unsigned n);
1576 int isl_map_involves_dims(__isl_keep isl_map *map,
1577 enum isl_dim_type type, unsigned first, unsigned n);
1579 Similarly, the following functions can be used to check whether
1580 a given dimension is involved in any lower or upper bound.
1582 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1583 enum isl_dim_type type, unsigned pos);
1584 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1585 enum isl_dim_type type, unsigned pos);
1587 The identifiers or names of the domain and range spaces of a set
1588 or relation can be read off or set using the following functions.
1590 __isl_give isl_set *isl_set_set_tuple_id(
1591 __isl_take isl_set *set, __isl_take isl_id *id);
1592 __isl_give isl_set *isl_set_reset_tuple_id(
1593 __isl_take isl_set *set);
1594 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1595 __isl_give isl_id *isl_set_get_tuple_id(
1596 __isl_keep isl_set *set);
1597 __isl_give isl_map *isl_map_set_tuple_id(
1598 __isl_take isl_map *map, enum isl_dim_type type,
1599 __isl_take isl_id *id);
1600 __isl_give isl_map *isl_map_reset_tuple_id(
1601 __isl_take isl_map *map, enum isl_dim_type type);
1602 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1603 enum isl_dim_type type);
1604 __isl_give isl_id *isl_map_get_tuple_id(
1605 __isl_keep isl_map *map, enum isl_dim_type type);
1607 const char *isl_basic_set_get_tuple_name(
1608 __isl_keep isl_basic_set *bset);
1609 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1610 __isl_take isl_basic_set *set, const char *s);
1611 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1612 const char *isl_set_get_tuple_name(
1613 __isl_keep isl_set *set);
1614 const char *isl_basic_map_get_tuple_name(
1615 __isl_keep isl_basic_map *bmap,
1616 enum isl_dim_type type);
1617 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1618 __isl_take isl_basic_map *bmap,
1619 enum isl_dim_type type, const char *s);
1620 const char *isl_map_get_tuple_name(
1621 __isl_keep isl_map *map,
1622 enum isl_dim_type type);
1624 As with C<isl_space_get_tuple_name>, the value returned points to
1625 an internal data structure.
1626 The identifiers, positions or names of individual dimensions can be
1627 read off using the following functions.
1629 __isl_give isl_id *isl_basic_set_get_dim_id(
1630 __isl_keep isl_basic_set *bset,
1631 enum isl_dim_type type, unsigned pos);
1632 __isl_give isl_set *isl_set_set_dim_id(
1633 __isl_take isl_set *set, enum isl_dim_type type,
1634 unsigned pos, __isl_take isl_id *id);
1635 int isl_set_has_dim_id(__isl_keep isl_set *set,
1636 enum isl_dim_type type, unsigned pos);
1637 __isl_give isl_id *isl_set_get_dim_id(
1638 __isl_keep isl_set *set, enum isl_dim_type type,
1640 int isl_basic_map_has_dim_id(
1641 __isl_keep isl_basic_map *bmap,
1642 enum isl_dim_type type, unsigned pos);
1643 __isl_give isl_map *isl_map_set_dim_id(
1644 __isl_take isl_map *map, enum isl_dim_type type,
1645 unsigned pos, __isl_take isl_id *id);
1646 int isl_map_has_dim_id(__isl_keep isl_map *map,
1647 enum isl_dim_type type, unsigned pos);
1648 __isl_give isl_id *isl_map_get_dim_id(
1649 __isl_keep isl_map *map, enum isl_dim_type type,
1652 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1653 enum isl_dim_type type, __isl_keep isl_id *id);
1654 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1655 enum isl_dim_type type, __isl_keep isl_id *id);
1656 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1657 enum isl_dim_type type, const char *name);
1658 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1659 enum isl_dim_type type, const char *name);
1661 const char *isl_constraint_get_dim_name(
1662 __isl_keep isl_constraint *constraint,
1663 enum isl_dim_type type, unsigned pos);
1664 const char *isl_basic_set_get_dim_name(
1665 __isl_keep isl_basic_set *bset,
1666 enum isl_dim_type type, unsigned pos);
1667 int isl_set_has_dim_name(__isl_keep isl_set *set,
1668 enum isl_dim_type type, unsigned pos);
1669 const char *isl_set_get_dim_name(
1670 __isl_keep isl_set *set,
1671 enum isl_dim_type type, unsigned pos);
1672 const char *isl_basic_map_get_dim_name(
1673 __isl_keep isl_basic_map *bmap,
1674 enum isl_dim_type type, unsigned pos);
1675 int isl_map_has_dim_name(__isl_keep isl_map *map,
1676 enum isl_dim_type type, unsigned pos);
1677 const char *isl_map_get_dim_name(
1678 __isl_keep isl_map *map,
1679 enum isl_dim_type type, unsigned pos);
1681 These functions are mostly useful to obtain the identifiers, positions
1682 or names of the parameters. Identifiers of individual dimensions are
1683 essentially only useful for printing. They are ignored by all other
1684 operations and may not be preserved across those operations.
1688 =head3 Unary Properties
1694 The following functions test whether the given set or relation
1695 contains any integer points. The ``plain'' variants do not perform
1696 any computations, but simply check if the given set or relation
1697 is already known to be empty.
1699 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1700 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1701 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1702 int isl_set_is_empty(__isl_keep isl_set *set);
1703 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1704 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1705 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1706 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1707 int isl_map_is_empty(__isl_keep isl_map *map);
1708 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1710 =item * Universality
1712 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1713 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1714 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1716 =item * Single-valuedness
1718 int isl_basic_map_is_single_valued(
1719 __isl_keep isl_basic_map *bmap);
1720 int isl_map_plain_is_single_valued(
1721 __isl_keep isl_map *map);
1722 int isl_map_is_single_valued(__isl_keep isl_map *map);
1723 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1727 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1728 int isl_map_is_injective(__isl_keep isl_map *map);
1729 int isl_union_map_plain_is_injective(
1730 __isl_keep isl_union_map *umap);
1731 int isl_union_map_is_injective(
1732 __isl_keep isl_union_map *umap);
1736 int isl_map_is_bijective(__isl_keep isl_map *map);
1737 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1741 int isl_basic_map_plain_is_fixed(
1742 __isl_keep isl_basic_map *bmap,
1743 enum isl_dim_type type, unsigned pos,
1745 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1746 enum isl_dim_type type, unsigned pos,
1748 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1749 enum isl_dim_type type, unsigned pos,
1752 Check if the relation obviously lies on a hyperplane where the given dimension
1753 has a fixed value and if so, return that value in C<*val>.
1757 To check whether a set is a parameter domain, use this function:
1759 int isl_set_is_params(__isl_keep isl_set *set);
1760 int isl_union_set_is_params(
1761 __isl_keep isl_union_set *uset);
1765 The following functions check whether the domain of the given
1766 (basic) set is a wrapped relation.
1768 int isl_basic_set_is_wrapping(
1769 __isl_keep isl_basic_set *bset);
1770 int isl_set_is_wrapping(__isl_keep isl_set *set);
1772 =item * Internal Product
1774 int isl_basic_map_can_zip(
1775 __isl_keep isl_basic_map *bmap);
1776 int isl_map_can_zip(__isl_keep isl_map *map);
1778 Check whether the product of domain and range of the given relation
1780 i.e., whether both domain and range are nested relations.
1784 int isl_basic_map_can_curry(
1785 __isl_keep isl_basic_map *bmap);
1786 int isl_map_can_curry(__isl_keep isl_map *map);
1788 Check whether the domain of the (basic) relation is a wrapped relation.
1792 =head3 Binary Properties
1798 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1799 __isl_keep isl_set *set2);
1800 int isl_set_is_equal(__isl_keep isl_set *set1,
1801 __isl_keep isl_set *set2);
1802 int isl_union_set_is_equal(
1803 __isl_keep isl_union_set *uset1,
1804 __isl_keep isl_union_set *uset2);
1805 int isl_basic_map_is_equal(
1806 __isl_keep isl_basic_map *bmap1,
1807 __isl_keep isl_basic_map *bmap2);
1808 int isl_map_is_equal(__isl_keep isl_map *map1,
1809 __isl_keep isl_map *map2);
1810 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1811 __isl_keep isl_map *map2);
1812 int isl_union_map_is_equal(
1813 __isl_keep isl_union_map *umap1,
1814 __isl_keep isl_union_map *umap2);
1816 =item * Disjointness
1818 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1819 __isl_keep isl_set *set2);
1823 int isl_basic_set_is_subset(
1824 __isl_keep isl_basic_set *bset1,
1825 __isl_keep isl_basic_set *bset2);
1826 int isl_set_is_subset(__isl_keep isl_set *set1,
1827 __isl_keep isl_set *set2);
1828 int isl_set_is_strict_subset(
1829 __isl_keep isl_set *set1,
1830 __isl_keep isl_set *set2);
1831 int isl_union_set_is_subset(
1832 __isl_keep isl_union_set *uset1,
1833 __isl_keep isl_union_set *uset2);
1834 int isl_union_set_is_strict_subset(
1835 __isl_keep isl_union_set *uset1,
1836 __isl_keep isl_union_set *uset2);
1837 int isl_basic_map_is_subset(
1838 __isl_keep isl_basic_map *bmap1,
1839 __isl_keep isl_basic_map *bmap2);
1840 int isl_basic_map_is_strict_subset(
1841 __isl_keep isl_basic_map *bmap1,
1842 __isl_keep isl_basic_map *bmap2);
1843 int isl_map_is_subset(
1844 __isl_keep isl_map *map1,
1845 __isl_keep isl_map *map2);
1846 int isl_map_is_strict_subset(
1847 __isl_keep isl_map *map1,
1848 __isl_keep isl_map *map2);
1849 int isl_union_map_is_subset(
1850 __isl_keep isl_union_map *umap1,
1851 __isl_keep isl_union_map *umap2);
1852 int isl_union_map_is_strict_subset(
1853 __isl_keep isl_union_map *umap1,
1854 __isl_keep isl_union_map *umap2);
1856 Check whether the first argument is a (strict) subset of the
1861 =head2 Unary Operations
1867 __isl_give isl_set *isl_set_complement(
1868 __isl_take isl_set *set);
1869 __isl_give isl_map *isl_map_complement(
1870 __isl_take isl_map *map);
1874 __isl_give isl_basic_map *isl_basic_map_reverse(
1875 __isl_take isl_basic_map *bmap);
1876 __isl_give isl_map *isl_map_reverse(
1877 __isl_take isl_map *map);
1878 __isl_give isl_union_map *isl_union_map_reverse(
1879 __isl_take isl_union_map *umap);
1883 __isl_give isl_basic_set *isl_basic_set_project_out(
1884 __isl_take isl_basic_set *bset,
1885 enum isl_dim_type type, unsigned first, unsigned n);
1886 __isl_give isl_basic_map *isl_basic_map_project_out(
1887 __isl_take isl_basic_map *bmap,
1888 enum isl_dim_type type, unsigned first, unsigned n);
1889 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1890 enum isl_dim_type type, unsigned first, unsigned n);
1891 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1892 enum isl_dim_type type, unsigned first, unsigned n);
1893 __isl_give isl_basic_set *isl_basic_set_params(
1894 __isl_take isl_basic_set *bset);
1895 __isl_give isl_basic_set *isl_basic_map_domain(
1896 __isl_take isl_basic_map *bmap);
1897 __isl_give isl_basic_set *isl_basic_map_range(
1898 __isl_take isl_basic_map *bmap);
1899 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1900 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1901 __isl_give isl_set *isl_map_domain(
1902 __isl_take isl_map *bmap);
1903 __isl_give isl_set *isl_map_range(
1904 __isl_take isl_map *map);
1905 __isl_give isl_set *isl_union_set_params(
1906 __isl_take isl_union_set *uset);
1907 __isl_give isl_set *isl_union_map_params(
1908 __isl_take isl_union_map *umap);
1909 __isl_give isl_union_set *isl_union_map_domain(
1910 __isl_take isl_union_map *umap);
1911 __isl_give isl_union_set *isl_union_map_range(
1912 __isl_take isl_union_map *umap);
1914 __isl_give isl_basic_map *isl_basic_map_domain_map(
1915 __isl_take isl_basic_map *bmap);
1916 __isl_give isl_basic_map *isl_basic_map_range_map(
1917 __isl_take isl_basic_map *bmap);
1918 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1919 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1920 __isl_give isl_union_map *isl_union_map_domain_map(
1921 __isl_take isl_union_map *umap);
1922 __isl_give isl_union_map *isl_union_map_range_map(
1923 __isl_take isl_union_map *umap);
1925 The functions above construct a (basic, regular or union) relation
1926 that maps (a wrapped version of) the input relation to its domain or range.
1930 __isl_give isl_basic_set *isl_basic_set_eliminate(
1931 __isl_take isl_basic_set *bset,
1932 enum isl_dim_type type,
1933 unsigned first, unsigned n);
1934 __isl_give isl_set *isl_set_eliminate(
1935 __isl_take isl_set *set, enum isl_dim_type type,
1936 unsigned first, unsigned n);
1937 __isl_give isl_basic_map *isl_basic_map_eliminate(
1938 __isl_take isl_basic_map *bmap,
1939 enum isl_dim_type type,
1940 unsigned first, unsigned n);
1941 __isl_give isl_map *isl_map_eliminate(
1942 __isl_take isl_map *map, enum isl_dim_type type,
1943 unsigned first, unsigned n);
1945 Eliminate the coefficients for the given dimensions from the constraints,
1946 without removing the dimensions.
1950 __isl_give isl_basic_set *isl_basic_set_fix(
1951 __isl_take isl_basic_set *bset,
1952 enum isl_dim_type type, unsigned pos,
1954 __isl_give isl_basic_set *isl_basic_set_fix_si(
1955 __isl_take isl_basic_set *bset,
1956 enum isl_dim_type type, unsigned pos, int value);
1957 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1958 enum isl_dim_type type, unsigned pos,
1960 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1961 enum isl_dim_type type, unsigned pos, int value);
1962 __isl_give isl_basic_map *isl_basic_map_fix_si(
1963 __isl_take isl_basic_map *bmap,
1964 enum isl_dim_type type, unsigned pos, int value);
1965 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1966 enum isl_dim_type type, unsigned pos, int value);
1968 Intersect the set or relation with the hyperplane where the given
1969 dimension has the fixed given value.
1971 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1972 __isl_take isl_basic_map *bmap,
1973 enum isl_dim_type type, unsigned pos, int value);
1974 __isl_give isl_set *isl_set_lower_bound(
1975 __isl_take isl_set *set,
1976 enum isl_dim_type type, unsigned pos,
1978 __isl_give isl_set *isl_set_lower_bound_si(
1979 __isl_take isl_set *set,
1980 enum isl_dim_type type, unsigned pos, int value);
1981 __isl_give isl_map *isl_map_lower_bound_si(
1982 __isl_take isl_map *map,
1983 enum isl_dim_type type, unsigned pos, int value);
1984 __isl_give isl_set *isl_set_upper_bound(
1985 __isl_take isl_set *set,
1986 enum isl_dim_type type, unsigned pos,
1988 __isl_give isl_set *isl_set_upper_bound_si(
1989 __isl_take isl_set *set,
1990 enum isl_dim_type type, unsigned pos, int value);
1991 __isl_give isl_map *isl_map_upper_bound_si(
1992 __isl_take isl_map *map,
1993 enum isl_dim_type type, unsigned pos, int value);
1995 Intersect the set or relation with the half-space where the given
1996 dimension has a value bounded by the fixed given value.
1998 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1999 enum isl_dim_type type1, int pos1,
2000 enum isl_dim_type type2, int pos2);
2001 __isl_give isl_basic_map *isl_basic_map_equate(
2002 __isl_take isl_basic_map *bmap,
2003 enum isl_dim_type type1, int pos1,
2004 enum isl_dim_type type2, int pos2);
2005 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2006 enum isl_dim_type type1, int pos1,
2007 enum isl_dim_type type2, int pos2);
2009 Intersect the set or relation with the hyperplane where the given
2010 dimensions are equal to each other.
2012 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2013 enum isl_dim_type type1, int pos1,
2014 enum isl_dim_type type2, int pos2);
2016 Intersect the relation with the hyperplane where the given
2017 dimensions have opposite values.
2019 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2020 enum isl_dim_type type1, int pos1,
2021 enum isl_dim_type type2, int pos2);
2022 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2023 enum isl_dim_type type1, int pos1,
2024 enum isl_dim_type type2, int pos2);
2026 Intersect the relation with the half-space where the given
2027 dimensions satisfy the given ordering.
2031 __isl_give isl_map *isl_set_identity(
2032 __isl_take isl_set *set);
2033 __isl_give isl_union_map *isl_union_set_identity(
2034 __isl_take isl_union_set *uset);
2036 Construct an identity relation on the given (union) set.
2040 __isl_give isl_basic_set *isl_basic_map_deltas(
2041 __isl_take isl_basic_map *bmap);
2042 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2043 __isl_give isl_union_set *isl_union_map_deltas(
2044 __isl_take isl_union_map *umap);
2046 These functions return a (basic) set containing the differences
2047 between image elements and corresponding domain elements in the input.
2049 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2050 __isl_take isl_basic_map *bmap);
2051 __isl_give isl_map *isl_map_deltas_map(
2052 __isl_take isl_map *map);
2053 __isl_give isl_union_map *isl_union_map_deltas_map(
2054 __isl_take isl_union_map *umap);
2056 The functions above construct a (basic, regular or union) relation
2057 that maps (a wrapped version of) the input relation to its delta set.
2061 Simplify the representation of a set or relation by trying
2062 to combine pairs of basic sets or relations into a single
2063 basic set or relation.
2065 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2066 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2067 __isl_give isl_union_set *isl_union_set_coalesce(
2068 __isl_take isl_union_set *uset);
2069 __isl_give isl_union_map *isl_union_map_coalesce(
2070 __isl_take isl_union_map *umap);
2072 One of the methods for combining pairs of basic sets or relations
2073 can result in coefficients that are much larger than those that appear
2074 in the constraints of the input. By default, the coefficients are
2075 not allowed to grow larger, but this can be changed by unsetting
2076 the following option.
2078 int isl_options_set_coalesce_bounded_wrapping(
2079 isl_ctx *ctx, int val);
2080 int isl_options_get_coalesce_bounded_wrapping(
2083 =item * Detecting equalities
2085 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2086 __isl_take isl_basic_set *bset);
2087 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2088 __isl_take isl_basic_map *bmap);
2089 __isl_give isl_set *isl_set_detect_equalities(
2090 __isl_take isl_set *set);
2091 __isl_give isl_map *isl_map_detect_equalities(
2092 __isl_take isl_map *map);
2093 __isl_give isl_union_set *isl_union_set_detect_equalities(
2094 __isl_take isl_union_set *uset);
2095 __isl_give isl_union_map *isl_union_map_detect_equalities(
2096 __isl_take isl_union_map *umap);
2098 Simplify the representation of a set or relation by detecting implicit
2101 =item * Removing redundant constraints
2103 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2104 __isl_take isl_basic_set *bset);
2105 __isl_give isl_set *isl_set_remove_redundancies(
2106 __isl_take isl_set *set);
2107 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2108 __isl_take isl_basic_map *bmap);
2109 __isl_give isl_map *isl_map_remove_redundancies(
2110 __isl_take isl_map *map);
2114 __isl_give isl_basic_set *isl_set_convex_hull(
2115 __isl_take isl_set *set);
2116 __isl_give isl_basic_map *isl_map_convex_hull(
2117 __isl_take isl_map *map);
2119 If the input set or relation has any existentially quantified
2120 variables, then the result of these operations is currently undefined.
2124 __isl_give isl_basic_set *isl_set_simple_hull(
2125 __isl_take isl_set *set);
2126 __isl_give isl_basic_map *isl_map_simple_hull(
2127 __isl_take isl_map *map);
2128 __isl_give isl_union_map *isl_union_map_simple_hull(
2129 __isl_take isl_union_map *umap);
2131 These functions compute a single basic set or relation
2132 that contains the whole input set or relation.
2133 In particular, the output is described by translates
2134 of the constraints describing the basic sets or relations in the input.
2138 (See \autoref{s:simple hull}.)
2144 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2145 __isl_take isl_basic_set *bset);
2146 __isl_give isl_basic_set *isl_set_affine_hull(
2147 __isl_take isl_set *set);
2148 __isl_give isl_union_set *isl_union_set_affine_hull(
2149 __isl_take isl_union_set *uset);
2150 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2151 __isl_take isl_basic_map *bmap);
2152 __isl_give isl_basic_map *isl_map_affine_hull(
2153 __isl_take isl_map *map);
2154 __isl_give isl_union_map *isl_union_map_affine_hull(
2155 __isl_take isl_union_map *umap);
2157 In case of union sets and relations, the affine hull is computed
2160 =item * Polyhedral hull
2162 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2163 __isl_take isl_set *set);
2164 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2165 __isl_take isl_map *map);
2166 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2167 __isl_take isl_union_set *uset);
2168 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2169 __isl_take isl_union_map *umap);
2171 These functions compute a single basic set or relation
2172 not involving any existentially quantified variables
2173 that contains the whole input set or relation.
2174 In case of union sets and relations, the polyhedral hull is computed
2179 __isl_give isl_basic_set *isl_basic_set_sample(
2180 __isl_take isl_basic_set *bset);
2181 __isl_give isl_basic_set *isl_set_sample(
2182 __isl_take isl_set *set);
2183 __isl_give isl_basic_map *isl_basic_map_sample(
2184 __isl_take isl_basic_map *bmap);
2185 __isl_give isl_basic_map *isl_map_sample(
2186 __isl_take isl_map *map);
2188 If the input (basic) set or relation is non-empty, then return
2189 a singleton subset of the input. Otherwise, return an empty set.
2191 =item * Optimization
2193 #include <isl/ilp.h>
2194 enum isl_lp_result isl_basic_set_max(
2195 __isl_keep isl_basic_set *bset,
2196 __isl_keep isl_aff *obj, isl_int *opt)
2197 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2198 __isl_keep isl_aff *obj, isl_int *opt);
2199 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2200 __isl_keep isl_aff *obj, isl_int *opt);
2202 Compute the minimum or maximum of the integer affine expression C<obj>
2203 over the points in C<set>, returning the result in C<opt>.
2204 The return value may be one of C<isl_lp_error>,
2205 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2207 =item * Parametric optimization
2209 __isl_give isl_pw_aff *isl_set_dim_min(
2210 __isl_take isl_set *set, int pos);
2211 __isl_give isl_pw_aff *isl_set_dim_max(
2212 __isl_take isl_set *set, int pos);
2213 __isl_give isl_pw_aff *isl_map_dim_max(
2214 __isl_take isl_map *map, int pos);
2216 Compute the minimum or maximum of the given set or output dimension
2217 as a function of the parameters (and input dimensions), but independently
2218 of the other set or output dimensions.
2219 For lexicographic optimization, see L<"Lexicographic Optimization">.
2223 The following functions compute either the set of (rational) coefficient
2224 values of valid constraints for the given set or the set of (rational)
2225 values satisfying the constraints with coefficients from the given set.
2226 Internally, these two sets of functions perform essentially the
2227 same operations, except that the set of coefficients is assumed to
2228 be a cone, while the set of values may be any polyhedron.
2229 The current implementation is based on the Farkas lemma and
2230 Fourier-Motzkin elimination, but this may change or be made optional
2231 in future. In particular, future implementations may use different
2232 dualization algorithms or skip the elimination step.
2234 __isl_give isl_basic_set *isl_basic_set_coefficients(
2235 __isl_take isl_basic_set *bset);
2236 __isl_give isl_basic_set *isl_set_coefficients(
2237 __isl_take isl_set *set);
2238 __isl_give isl_union_set *isl_union_set_coefficients(
2239 __isl_take isl_union_set *bset);
2240 __isl_give isl_basic_set *isl_basic_set_solutions(
2241 __isl_take isl_basic_set *bset);
2242 __isl_give isl_basic_set *isl_set_solutions(
2243 __isl_take isl_set *set);
2244 __isl_give isl_union_set *isl_union_set_solutions(
2245 __isl_take isl_union_set *bset);
2249 __isl_give isl_map *isl_map_fixed_power(
2250 __isl_take isl_map *map, isl_int exp);
2251 __isl_give isl_union_map *isl_union_map_fixed_power(
2252 __isl_take isl_union_map *umap, isl_int exp);
2254 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2255 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2256 of C<map> is computed.
2258 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2260 __isl_give isl_union_map *isl_union_map_power(
2261 __isl_take isl_union_map *umap, int *exact);
2263 Compute a parametric representation for all positive powers I<k> of C<map>.
2264 The result maps I<k> to a nested relation corresponding to the
2265 I<k>th power of C<map>.
2266 The result may be an overapproximation. If the result is known to be exact,
2267 then C<*exact> is set to C<1>.
2269 =item * Transitive closure
2271 __isl_give isl_map *isl_map_transitive_closure(
2272 __isl_take isl_map *map, int *exact);
2273 __isl_give isl_union_map *isl_union_map_transitive_closure(
2274 __isl_take isl_union_map *umap, int *exact);
2276 Compute the transitive closure of C<map>.
2277 The result may be an overapproximation. If the result is known to be exact,
2278 then C<*exact> is set to C<1>.
2280 =item * Reaching path lengths
2282 __isl_give isl_map *isl_map_reaching_path_lengths(
2283 __isl_take isl_map *map, int *exact);
2285 Compute a relation that maps each element in the range of C<map>
2286 to the lengths of all paths composed of edges in C<map> that
2287 end up in the given element.
2288 The result may be an overapproximation. If the result is known to be exact,
2289 then C<*exact> is set to C<1>.
2290 To compute the I<maximal> path length, the resulting relation
2291 should be postprocessed by C<isl_map_lexmax>.
2292 In particular, if the input relation is a dependence relation
2293 (mapping sources to sinks), then the maximal path length corresponds
2294 to the free schedule.
2295 Note, however, that C<isl_map_lexmax> expects the maximum to be
2296 finite, so if the path lengths are unbounded (possibly due to
2297 the overapproximation), then you will get an error message.
2301 __isl_give isl_basic_set *isl_basic_map_wrap(
2302 __isl_take isl_basic_map *bmap);
2303 __isl_give isl_set *isl_map_wrap(
2304 __isl_take isl_map *map);
2305 __isl_give isl_union_set *isl_union_map_wrap(
2306 __isl_take isl_union_map *umap);
2307 __isl_give isl_basic_map *isl_basic_set_unwrap(
2308 __isl_take isl_basic_set *bset);
2309 __isl_give isl_map *isl_set_unwrap(
2310 __isl_take isl_set *set);
2311 __isl_give isl_union_map *isl_union_set_unwrap(
2312 __isl_take isl_union_set *uset);
2316 Remove any internal structure of domain (and range) of the given
2317 set or relation. If there is any such internal structure in the input,
2318 then the name of the space is also removed.
2320 __isl_give isl_basic_set *isl_basic_set_flatten(
2321 __isl_take isl_basic_set *bset);
2322 __isl_give isl_set *isl_set_flatten(
2323 __isl_take isl_set *set);
2324 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2325 __isl_take isl_basic_map *bmap);
2326 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2327 __isl_take isl_basic_map *bmap);
2328 __isl_give isl_map *isl_map_flatten_range(
2329 __isl_take isl_map *map);
2330 __isl_give isl_map *isl_map_flatten_domain(
2331 __isl_take isl_map *map);
2332 __isl_give isl_basic_map *isl_basic_map_flatten(
2333 __isl_take isl_basic_map *bmap);
2334 __isl_give isl_map *isl_map_flatten(
2335 __isl_take isl_map *map);
2337 __isl_give isl_map *isl_set_flatten_map(
2338 __isl_take isl_set *set);
2340 The function above constructs a relation
2341 that maps the input set to a flattened version of the set.
2345 Lift the input set to a space with extra dimensions corresponding
2346 to the existentially quantified variables in the input.
2347 In particular, the result lives in a wrapped map where the domain
2348 is the original space and the range corresponds to the original
2349 existentially quantified variables.
2351 __isl_give isl_basic_set *isl_basic_set_lift(
2352 __isl_take isl_basic_set *bset);
2353 __isl_give isl_set *isl_set_lift(
2354 __isl_take isl_set *set);
2355 __isl_give isl_union_set *isl_union_set_lift(
2356 __isl_take isl_union_set *uset);
2358 Given a local space that contains the existentially quantified
2359 variables of a set, a basic relation that, when applied to
2360 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2361 can be constructed using the following function.
2363 #include <isl/local_space.h>
2364 __isl_give isl_basic_map *isl_local_space_lifting(
2365 __isl_take isl_local_space *ls);
2367 =item * Internal Product
2369 __isl_give isl_basic_map *isl_basic_map_zip(
2370 __isl_take isl_basic_map *bmap);
2371 __isl_give isl_map *isl_map_zip(
2372 __isl_take isl_map *map);
2373 __isl_give isl_union_map *isl_union_map_zip(
2374 __isl_take isl_union_map *umap);
2376 Given a relation with nested relations for domain and range,
2377 interchange the range of the domain with the domain of the range.
2381 __isl_give isl_basic_map *isl_basic_map_curry(
2382 __isl_take isl_basic_map *bmap);
2383 __isl_give isl_map *isl_map_curry(
2384 __isl_take isl_map *map);
2385 __isl_give isl_union_map *isl_union_map_curry(
2386 __isl_take isl_union_map *umap);
2388 Given a relation with a nested relation for domain,
2389 move the range of the nested relation out of the domain
2390 and use it as the domain of a nested relation in the range,
2391 with the original range as range of this nested relation.
2393 =item * Aligning parameters
2395 __isl_give isl_basic_set *isl_basic_set_align_params(
2396 __isl_take isl_basic_set *bset,
2397 __isl_take isl_space *model);
2398 __isl_give isl_set *isl_set_align_params(
2399 __isl_take isl_set *set,
2400 __isl_take isl_space *model);
2401 __isl_give isl_basic_map *isl_basic_map_align_params(
2402 __isl_take isl_basic_map *bmap,
2403 __isl_take isl_space *model);
2404 __isl_give isl_map *isl_map_align_params(
2405 __isl_take isl_map *map,
2406 __isl_take isl_space *model);
2408 Change the order of the parameters of the given set or relation
2409 such that the first parameters match those of C<model>.
2410 This may involve the introduction of extra parameters.
2411 All parameters need to be named.
2413 =item * Dimension manipulation
2415 __isl_give isl_set *isl_set_add_dims(
2416 __isl_take isl_set *set,
2417 enum isl_dim_type type, unsigned n);
2418 __isl_give isl_map *isl_map_add_dims(
2419 __isl_take isl_map *map,
2420 enum isl_dim_type type, unsigned n);
2421 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2422 __isl_take isl_basic_set *bset,
2423 enum isl_dim_type type, unsigned pos,
2425 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2426 __isl_take isl_basic_map *bmap,
2427 enum isl_dim_type type, unsigned pos,
2429 __isl_give isl_set *isl_set_insert_dims(
2430 __isl_take isl_set *set,
2431 enum isl_dim_type type, unsigned pos, unsigned n);
2432 __isl_give isl_map *isl_map_insert_dims(
2433 __isl_take isl_map *map,
2434 enum isl_dim_type type, unsigned pos, unsigned n);
2435 __isl_give isl_basic_set *isl_basic_set_move_dims(
2436 __isl_take isl_basic_set *bset,
2437 enum isl_dim_type dst_type, unsigned dst_pos,
2438 enum isl_dim_type src_type, unsigned src_pos,
2440 __isl_give isl_basic_map *isl_basic_map_move_dims(
2441 __isl_take isl_basic_map *bmap,
2442 enum isl_dim_type dst_type, unsigned dst_pos,
2443 enum isl_dim_type src_type, unsigned src_pos,
2445 __isl_give isl_set *isl_set_move_dims(
2446 __isl_take isl_set *set,
2447 enum isl_dim_type dst_type, unsigned dst_pos,
2448 enum isl_dim_type src_type, unsigned src_pos,
2450 __isl_give isl_map *isl_map_move_dims(
2451 __isl_take isl_map *map,
2452 enum isl_dim_type dst_type, unsigned dst_pos,
2453 enum isl_dim_type src_type, unsigned src_pos,
2456 It is usually not advisable to directly change the (input or output)
2457 space of a set or a relation as this removes the name and the internal
2458 structure of the space. However, the above functions can be useful
2459 to add new parameters, assuming
2460 C<isl_set_align_params> and C<isl_map_align_params>
2465 =head2 Binary Operations
2467 The two arguments of a binary operation not only need to live
2468 in the same C<isl_ctx>, they currently also need to have
2469 the same (number of) parameters.
2471 =head3 Basic Operations
2475 =item * Intersection
2477 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2478 __isl_take isl_basic_set *bset1,
2479 __isl_take isl_basic_set *bset2);
2480 __isl_give isl_basic_set *isl_basic_set_intersect(
2481 __isl_take isl_basic_set *bset1,
2482 __isl_take isl_basic_set *bset2);
2483 __isl_give isl_set *isl_set_intersect_params(
2484 __isl_take isl_set *set,
2485 __isl_take isl_set *params);
2486 __isl_give isl_set *isl_set_intersect(
2487 __isl_take isl_set *set1,
2488 __isl_take isl_set *set2);
2489 __isl_give isl_union_set *isl_union_set_intersect_params(
2490 __isl_take isl_union_set *uset,
2491 __isl_take isl_set *set);
2492 __isl_give isl_union_map *isl_union_map_intersect_params(
2493 __isl_take isl_union_map *umap,
2494 __isl_take isl_set *set);
2495 __isl_give isl_union_set *isl_union_set_intersect(
2496 __isl_take isl_union_set *uset1,
2497 __isl_take isl_union_set *uset2);
2498 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2499 __isl_take isl_basic_map *bmap,
2500 __isl_take isl_basic_set *bset);
2501 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2502 __isl_take isl_basic_map *bmap,
2503 __isl_take isl_basic_set *bset);
2504 __isl_give isl_basic_map *isl_basic_map_intersect(
2505 __isl_take isl_basic_map *bmap1,
2506 __isl_take isl_basic_map *bmap2);
2507 __isl_give isl_map *isl_map_intersect_params(
2508 __isl_take isl_map *map,
2509 __isl_take isl_set *params);
2510 __isl_give isl_map *isl_map_intersect_domain(
2511 __isl_take isl_map *map,
2512 __isl_take isl_set *set);
2513 __isl_give isl_map *isl_map_intersect_range(
2514 __isl_take isl_map *map,
2515 __isl_take isl_set *set);
2516 __isl_give isl_map *isl_map_intersect(
2517 __isl_take isl_map *map1,
2518 __isl_take isl_map *map2);
2519 __isl_give isl_union_map *isl_union_map_intersect_domain(
2520 __isl_take isl_union_map *umap,
2521 __isl_take isl_union_set *uset);
2522 __isl_give isl_union_map *isl_union_map_intersect_range(
2523 __isl_take isl_union_map *umap,
2524 __isl_take isl_union_set *uset);
2525 __isl_give isl_union_map *isl_union_map_intersect(
2526 __isl_take isl_union_map *umap1,
2527 __isl_take isl_union_map *umap2);
2529 The second argument to the C<_params> functions needs to be
2530 a parametric (basic) set. For the other functions, a parametric set
2531 for either argument is only allowed if the other argument is
2532 a parametric set as well.
2536 __isl_give isl_set *isl_basic_set_union(
2537 __isl_take isl_basic_set *bset1,
2538 __isl_take isl_basic_set *bset2);
2539 __isl_give isl_map *isl_basic_map_union(
2540 __isl_take isl_basic_map *bmap1,
2541 __isl_take isl_basic_map *bmap2);
2542 __isl_give isl_set *isl_set_union(
2543 __isl_take isl_set *set1,
2544 __isl_take isl_set *set2);
2545 __isl_give isl_map *isl_map_union(
2546 __isl_take isl_map *map1,
2547 __isl_take isl_map *map2);
2548 __isl_give isl_union_set *isl_union_set_union(
2549 __isl_take isl_union_set *uset1,
2550 __isl_take isl_union_set *uset2);
2551 __isl_give isl_union_map *isl_union_map_union(
2552 __isl_take isl_union_map *umap1,
2553 __isl_take isl_union_map *umap2);
2555 =item * Set difference
2557 __isl_give isl_set *isl_set_subtract(
2558 __isl_take isl_set *set1,
2559 __isl_take isl_set *set2);
2560 __isl_give isl_map *isl_map_subtract(
2561 __isl_take isl_map *map1,
2562 __isl_take isl_map *map2);
2563 __isl_give isl_map *isl_map_subtract_domain(
2564 __isl_take isl_map *map,
2565 __isl_take isl_set *dom);
2566 __isl_give isl_map *isl_map_subtract_range(
2567 __isl_take isl_map *map,
2568 __isl_take isl_set *dom);
2569 __isl_give isl_union_set *isl_union_set_subtract(
2570 __isl_take isl_union_set *uset1,
2571 __isl_take isl_union_set *uset2);
2572 __isl_give isl_union_map *isl_union_map_subtract(
2573 __isl_take isl_union_map *umap1,
2574 __isl_take isl_union_map *umap2);
2578 __isl_give isl_basic_set *isl_basic_set_apply(
2579 __isl_take isl_basic_set *bset,
2580 __isl_take isl_basic_map *bmap);
2581 __isl_give isl_set *isl_set_apply(
2582 __isl_take isl_set *set,
2583 __isl_take isl_map *map);
2584 __isl_give isl_union_set *isl_union_set_apply(
2585 __isl_take isl_union_set *uset,
2586 __isl_take isl_union_map *umap);
2587 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2588 __isl_take isl_basic_map *bmap1,
2589 __isl_take isl_basic_map *bmap2);
2590 __isl_give isl_basic_map *isl_basic_map_apply_range(
2591 __isl_take isl_basic_map *bmap1,
2592 __isl_take isl_basic_map *bmap2);
2593 __isl_give isl_map *isl_map_apply_domain(
2594 __isl_take isl_map *map1,
2595 __isl_take isl_map *map2);
2596 __isl_give isl_union_map *isl_union_map_apply_domain(
2597 __isl_take isl_union_map *umap1,
2598 __isl_take isl_union_map *umap2);
2599 __isl_give isl_map *isl_map_apply_range(
2600 __isl_take isl_map *map1,
2601 __isl_take isl_map *map2);
2602 __isl_give isl_union_map *isl_union_map_apply_range(
2603 __isl_take isl_union_map *umap1,
2604 __isl_take isl_union_map *umap2);
2606 =item * Cartesian Product
2608 __isl_give isl_set *isl_set_product(
2609 __isl_take isl_set *set1,
2610 __isl_take isl_set *set2);
2611 __isl_give isl_union_set *isl_union_set_product(
2612 __isl_take isl_union_set *uset1,
2613 __isl_take isl_union_set *uset2);
2614 __isl_give isl_basic_map *isl_basic_map_domain_product(
2615 __isl_take isl_basic_map *bmap1,
2616 __isl_take isl_basic_map *bmap2);
2617 __isl_give isl_basic_map *isl_basic_map_range_product(
2618 __isl_take isl_basic_map *bmap1,
2619 __isl_take isl_basic_map *bmap2);
2620 __isl_give isl_basic_map *isl_basic_map_product(
2621 __isl_take isl_basic_map *bmap1,
2622 __isl_take isl_basic_map *bmap2);
2623 __isl_give isl_map *isl_map_domain_product(
2624 __isl_take isl_map *map1,
2625 __isl_take isl_map *map2);
2626 __isl_give isl_map *isl_map_range_product(
2627 __isl_take isl_map *map1,
2628 __isl_take isl_map *map2);
2629 __isl_give isl_union_map *isl_union_map_domain_product(
2630 __isl_take isl_union_map *umap1,
2631 __isl_take isl_union_map *umap2);
2632 __isl_give isl_union_map *isl_union_map_range_product(
2633 __isl_take isl_union_map *umap1,
2634 __isl_take isl_union_map *umap2);
2635 __isl_give isl_map *isl_map_product(
2636 __isl_take isl_map *map1,
2637 __isl_take isl_map *map2);
2638 __isl_give isl_union_map *isl_union_map_product(
2639 __isl_take isl_union_map *umap1,
2640 __isl_take isl_union_map *umap2);
2642 The above functions compute the cross product of the given
2643 sets or relations. The domains and ranges of the results
2644 are wrapped maps between domains and ranges of the inputs.
2645 To obtain a ``flat'' product, use the following functions
2648 __isl_give isl_basic_set *isl_basic_set_flat_product(
2649 __isl_take isl_basic_set *bset1,
2650 __isl_take isl_basic_set *bset2);
2651 __isl_give isl_set *isl_set_flat_product(
2652 __isl_take isl_set *set1,
2653 __isl_take isl_set *set2);
2654 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2655 __isl_take isl_basic_map *bmap1,
2656 __isl_take isl_basic_map *bmap2);
2657 __isl_give isl_map *isl_map_flat_domain_product(
2658 __isl_take isl_map *map1,
2659 __isl_take isl_map *map2);
2660 __isl_give isl_map *isl_map_flat_range_product(
2661 __isl_take isl_map *map1,
2662 __isl_take isl_map *map2);
2663 __isl_give isl_union_map *isl_union_map_flat_range_product(
2664 __isl_take isl_union_map *umap1,
2665 __isl_take isl_union_map *umap2);
2666 __isl_give isl_basic_map *isl_basic_map_flat_product(
2667 __isl_take isl_basic_map *bmap1,
2668 __isl_take isl_basic_map *bmap2);
2669 __isl_give isl_map *isl_map_flat_product(
2670 __isl_take isl_map *map1,
2671 __isl_take isl_map *map2);
2673 =item * Simplification
2675 __isl_give isl_basic_set *isl_basic_set_gist(
2676 __isl_take isl_basic_set *bset,
2677 __isl_take isl_basic_set *context);
2678 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2679 __isl_take isl_set *context);
2680 __isl_give isl_set *isl_set_gist_params(
2681 __isl_take isl_set *set,
2682 __isl_take isl_set *context);
2683 __isl_give isl_union_set *isl_union_set_gist(
2684 __isl_take isl_union_set *uset,
2685 __isl_take isl_union_set *context);
2686 __isl_give isl_union_set *isl_union_set_gist_params(
2687 __isl_take isl_union_set *uset,
2688 __isl_take isl_set *set);
2689 __isl_give isl_basic_map *isl_basic_map_gist(
2690 __isl_take isl_basic_map *bmap,
2691 __isl_take isl_basic_map *context);
2692 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2693 __isl_take isl_map *context);
2694 __isl_give isl_map *isl_map_gist_params(
2695 __isl_take isl_map *map,
2696 __isl_take isl_set *context);
2697 __isl_give isl_map *isl_map_gist_domain(
2698 __isl_take isl_map *map,
2699 __isl_take isl_set *context);
2700 __isl_give isl_map *isl_map_gist_range(
2701 __isl_take isl_map *map,
2702 __isl_take isl_set *context);
2703 __isl_give isl_union_map *isl_union_map_gist(
2704 __isl_take isl_union_map *umap,
2705 __isl_take isl_union_map *context);
2706 __isl_give isl_union_map *isl_union_map_gist_params(
2707 __isl_take isl_union_map *umap,
2708 __isl_take isl_set *set);
2709 __isl_give isl_union_map *isl_union_map_gist_domain(
2710 __isl_take isl_union_map *umap,
2711 __isl_take isl_union_set *uset);
2712 __isl_give isl_union_map *isl_union_map_gist_range(
2713 __isl_take isl_union_map *umap,
2714 __isl_take isl_union_set *uset);
2716 The gist operation returns a set or relation that has the
2717 same intersection with the context as the input set or relation.
2718 Any implicit equality in the intersection is made explicit in the result,
2719 while all inequalities that are redundant with respect to the intersection
2721 In case of union sets and relations, the gist operation is performed
2726 =head3 Lexicographic Optimization
2728 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2729 the following functions
2730 compute a set that contains the lexicographic minimum or maximum
2731 of the elements in C<set> (or C<bset>) for those values of the parameters
2732 that satisfy C<dom>.
2733 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2734 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2736 In other words, the union of the parameter values
2737 for which the result is non-empty and of C<*empty>
2740 __isl_give isl_set *isl_basic_set_partial_lexmin(
2741 __isl_take isl_basic_set *bset,
2742 __isl_take isl_basic_set *dom,
2743 __isl_give isl_set **empty);
2744 __isl_give isl_set *isl_basic_set_partial_lexmax(
2745 __isl_take isl_basic_set *bset,
2746 __isl_take isl_basic_set *dom,
2747 __isl_give isl_set **empty);
2748 __isl_give isl_set *isl_set_partial_lexmin(
2749 __isl_take isl_set *set, __isl_take isl_set *dom,
2750 __isl_give isl_set **empty);
2751 __isl_give isl_set *isl_set_partial_lexmax(
2752 __isl_take isl_set *set, __isl_take isl_set *dom,
2753 __isl_give isl_set **empty);
2755 Given a (basic) set C<set> (or C<bset>), the following functions simply
2756 return a set containing the lexicographic minimum or maximum
2757 of the elements in C<set> (or C<bset>).
2758 In case of union sets, the optimum is computed per space.
2760 __isl_give isl_set *isl_basic_set_lexmin(
2761 __isl_take isl_basic_set *bset);
2762 __isl_give isl_set *isl_basic_set_lexmax(
2763 __isl_take isl_basic_set *bset);
2764 __isl_give isl_set *isl_set_lexmin(
2765 __isl_take isl_set *set);
2766 __isl_give isl_set *isl_set_lexmax(
2767 __isl_take isl_set *set);
2768 __isl_give isl_union_set *isl_union_set_lexmin(
2769 __isl_take isl_union_set *uset);
2770 __isl_give isl_union_set *isl_union_set_lexmax(
2771 __isl_take isl_union_set *uset);
2773 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2774 the following functions
2775 compute a relation that maps each element of C<dom>
2776 to the single lexicographic minimum or maximum
2777 of the elements that are associated to that same
2778 element in C<map> (or C<bmap>).
2779 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2780 that contains the elements in C<dom> that do not map
2781 to any elements in C<map> (or C<bmap>).
2782 In other words, the union of the domain of the result and of C<*empty>
2785 __isl_give isl_map *isl_basic_map_partial_lexmax(
2786 __isl_take isl_basic_map *bmap,
2787 __isl_take isl_basic_set *dom,
2788 __isl_give isl_set **empty);
2789 __isl_give isl_map *isl_basic_map_partial_lexmin(
2790 __isl_take isl_basic_map *bmap,
2791 __isl_take isl_basic_set *dom,
2792 __isl_give isl_set **empty);
2793 __isl_give isl_map *isl_map_partial_lexmax(
2794 __isl_take isl_map *map, __isl_take isl_set *dom,
2795 __isl_give isl_set **empty);
2796 __isl_give isl_map *isl_map_partial_lexmin(
2797 __isl_take isl_map *map, __isl_take isl_set *dom,
2798 __isl_give isl_set **empty);
2800 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2801 return a map mapping each element in the domain of
2802 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2803 of all elements associated to that element.
2804 In case of union relations, the optimum is computed per space.
2806 __isl_give isl_map *isl_basic_map_lexmin(
2807 __isl_take isl_basic_map *bmap);
2808 __isl_give isl_map *isl_basic_map_lexmax(
2809 __isl_take isl_basic_map *bmap);
2810 __isl_give isl_map *isl_map_lexmin(
2811 __isl_take isl_map *map);
2812 __isl_give isl_map *isl_map_lexmax(
2813 __isl_take isl_map *map);
2814 __isl_give isl_union_map *isl_union_map_lexmin(
2815 __isl_take isl_union_map *umap);
2816 __isl_give isl_union_map *isl_union_map_lexmax(
2817 __isl_take isl_union_map *umap);
2819 The following functions return their result in the form of
2820 a piecewise multi-affine expression
2821 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2822 but are otherwise equivalent to the corresponding functions
2823 returning a basic set or relation.
2825 __isl_give isl_pw_multi_aff *
2826 isl_basic_map_lexmin_pw_multi_aff(
2827 __isl_take isl_basic_map *bmap);
2828 __isl_give isl_pw_multi_aff *
2829 isl_basic_set_partial_lexmin_pw_multi_aff(
2830 __isl_take isl_basic_set *bset,
2831 __isl_take isl_basic_set *dom,
2832 __isl_give isl_set **empty);
2833 __isl_give isl_pw_multi_aff *
2834 isl_basic_set_partial_lexmax_pw_multi_aff(
2835 __isl_take isl_basic_set *bset,
2836 __isl_take isl_basic_set *dom,
2837 __isl_give isl_set **empty);
2838 __isl_give isl_pw_multi_aff *
2839 isl_basic_map_partial_lexmin_pw_multi_aff(
2840 __isl_take isl_basic_map *bmap,
2841 __isl_take isl_basic_set *dom,
2842 __isl_give isl_set **empty);
2843 __isl_give isl_pw_multi_aff *
2844 isl_basic_map_partial_lexmax_pw_multi_aff(
2845 __isl_take isl_basic_map *bmap,
2846 __isl_take isl_basic_set *dom,
2847 __isl_give isl_set **empty);
2851 Lists are defined over several element types, including
2852 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2853 Here we take lists of C<isl_set>s as an example.
2854 Lists can be created, copied, modified and freed using the following functions.
2856 #include <isl/list.h>
2857 __isl_give isl_set_list *isl_set_list_from_set(
2858 __isl_take isl_set *el);
2859 __isl_give isl_set_list *isl_set_list_alloc(
2860 isl_ctx *ctx, int n);
2861 __isl_give isl_set_list *isl_set_list_copy(
2862 __isl_keep isl_set_list *list);
2863 __isl_give isl_set_list *isl_set_list_add(
2864 __isl_take isl_set_list *list,
2865 __isl_take isl_set *el);
2866 __isl_give isl_set_list *isl_set_list_set_set(
2867 __isl_take isl_set_list *list, int index,
2868 __isl_take isl_set *set);
2869 __isl_give isl_set_list *isl_set_list_concat(
2870 __isl_take isl_set_list *list1,
2871 __isl_take isl_set_list *list2);
2872 void *isl_set_list_free(__isl_take isl_set_list *list);
2874 C<isl_set_list_alloc> creates an empty list with a capacity for
2875 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2878 Lists can be inspected using the following functions.
2880 #include <isl/list.h>
2881 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2882 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2883 __isl_give isl_set *isl_set_list_get_set(
2884 __isl_keep isl_set_list *list, int index);
2885 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2886 int (*fn)(__isl_take isl_set *el, void *user),
2889 Lists can be printed using
2891 #include <isl/list.h>
2892 __isl_give isl_printer *isl_printer_print_set_list(
2893 __isl_take isl_printer *p,
2894 __isl_keep isl_set_list *list);
2898 Vectors can be created, copied and freed using the following functions.
2900 #include <isl/vec.h>
2901 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2903 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2904 void isl_vec_free(__isl_take isl_vec *vec);
2906 Note that the elements of a newly created vector may have arbitrary values.
2907 The elements can be changed and inspected using the following functions.
2909 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2910 int isl_vec_size(__isl_keep isl_vec *vec);
2911 int isl_vec_get_element(__isl_keep isl_vec *vec,
2912 int pos, isl_int *v);
2913 __isl_give isl_vec *isl_vec_set_element(
2914 __isl_take isl_vec *vec, int pos, isl_int v);
2915 __isl_give isl_vec *isl_vec_set_element_si(
2916 __isl_take isl_vec *vec, int pos, int v);
2917 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2919 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2922 C<isl_vec_get_element> will return a negative value if anything went wrong.
2923 In that case, the value of C<*v> is undefined.
2927 Matrices can be created, copied and freed using the following functions.
2929 #include <isl/mat.h>
2930 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2931 unsigned n_row, unsigned n_col);
2932 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2933 void isl_mat_free(__isl_take isl_mat *mat);
2935 Note that the elements of a newly created matrix may have arbitrary values.
2936 The elements can be changed and inspected using the following functions.
2938 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2939 int isl_mat_rows(__isl_keep isl_mat *mat);
2940 int isl_mat_cols(__isl_keep isl_mat *mat);
2941 int isl_mat_get_element(__isl_keep isl_mat *mat,
2942 int row, int col, isl_int *v);
2943 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2944 int row, int col, isl_int v);
2945 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2946 int row, int col, int v);
2948 C<isl_mat_get_element> will return a negative value if anything went wrong.
2949 In that case, the value of C<*v> is undefined.
2951 The following function can be used to compute the (right) inverse
2952 of a matrix, i.e., a matrix such that the product of the original
2953 and the inverse (in that order) is a multiple of the identity matrix.
2954 The input matrix is assumed to be of full row-rank.
2956 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2958 The following function can be used to compute the (right) kernel
2959 (or null space) of a matrix, i.e., a matrix such that the product of
2960 the original and the kernel (in that order) is the zero matrix.
2962 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2964 =head2 Piecewise Quasi Affine Expressions
2966 The zero quasi affine expression on a given domain can be created using
2968 __isl_give isl_aff *isl_aff_zero_on_domain(
2969 __isl_take isl_local_space *ls);
2971 Note that the space in which the resulting object lives is a map space
2972 with the given space as domain and a one-dimensional range.
2974 An empty piecewise quasi affine expression (one with no cells)
2975 or a piecewise quasi affine expression with a single cell can
2976 be created using the following functions.
2978 #include <isl/aff.h>
2979 __isl_give isl_pw_aff *isl_pw_aff_empty(
2980 __isl_take isl_space *space);
2981 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2982 __isl_take isl_set *set, __isl_take isl_aff *aff);
2983 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2984 __isl_take isl_aff *aff);
2986 A piecewise quasi affine expression that is equal to 1 on a set
2987 and 0 outside the set can be created using the following function.
2989 #include <isl/aff.h>
2990 __isl_give isl_pw_aff *isl_set_indicator_function(
2991 __isl_take isl_set *set);
2993 Quasi affine expressions can be copied and freed using
2995 #include <isl/aff.h>
2996 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2997 void *isl_aff_free(__isl_take isl_aff *aff);
2999 __isl_give isl_pw_aff *isl_pw_aff_copy(
3000 __isl_keep isl_pw_aff *pwaff);
3001 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3003 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3004 using the following function. The constraint is required to have
3005 a non-zero coefficient for the specified dimension.
3007 #include <isl/constraint.h>
3008 __isl_give isl_aff *isl_constraint_get_bound(
3009 __isl_keep isl_constraint *constraint,
3010 enum isl_dim_type type, int pos);
3012 The entire affine expression of the constraint can also be extracted
3013 using the following function.
3015 #include <isl/constraint.h>
3016 __isl_give isl_aff *isl_constraint_get_aff(
3017 __isl_keep isl_constraint *constraint);
3019 Conversely, an equality constraint equating
3020 the affine expression to zero or an inequality constraint enforcing
3021 the affine expression to be non-negative, can be constructed using
3023 __isl_give isl_constraint *isl_equality_from_aff(
3024 __isl_take isl_aff *aff);
3025 __isl_give isl_constraint *isl_inequality_from_aff(
3026 __isl_take isl_aff *aff);
3028 The expression can be inspected using
3030 #include <isl/aff.h>
3031 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3032 int isl_aff_dim(__isl_keep isl_aff *aff,
3033 enum isl_dim_type type);
3034 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3035 __isl_keep isl_aff *aff);
3036 __isl_give isl_local_space *isl_aff_get_local_space(
3037 __isl_keep isl_aff *aff);
3038 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3039 enum isl_dim_type type, unsigned pos);
3040 const char *isl_pw_aff_get_dim_name(
3041 __isl_keep isl_pw_aff *pa,
3042 enum isl_dim_type type, unsigned pos);
3043 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3044 enum isl_dim_type type, unsigned pos);
3045 __isl_give isl_id *isl_pw_aff_get_dim_id(
3046 __isl_keep isl_pw_aff *pa,
3047 enum isl_dim_type type, unsigned pos);
3048 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3049 __isl_keep isl_pw_aff *pa,
3050 enum isl_dim_type type);
3051 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3053 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3054 enum isl_dim_type type, int pos, isl_int *v);
3055 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3057 __isl_give isl_aff *isl_aff_get_div(
3058 __isl_keep isl_aff *aff, int pos);
3060 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3061 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3062 int (*fn)(__isl_take isl_set *set,
3063 __isl_take isl_aff *aff,
3064 void *user), void *user);
3066 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3067 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3069 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3070 enum isl_dim_type type, unsigned first, unsigned n);
3071 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3072 enum isl_dim_type type, unsigned first, unsigned n);
3074 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3075 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3076 enum isl_dim_type type);
3077 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3079 It can be modified using
3081 #include <isl/aff.h>
3082 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3083 __isl_take isl_pw_aff *pwaff,
3084 enum isl_dim_type type, __isl_take isl_id *id);
3085 __isl_give isl_aff *isl_aff_set_dim_name(
3086 __isl_take isl_aff *aff, enum isl_dim_type type,
3087 unsigned pos, const char *s);
3088 __isl_give isl_aff *isl_aff_set_dim_id(
3089 __isl_take isl_aff *aff, enum isl_dim_type type,
3090 unsigned pos, __isl_take isl_id *id);
3091 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3092 __isl_take isl_pw_aff *pma,
3093 enum isl_dim_type type, unsigned pos,
3094 __isl_take isl_id *id);
3095 __isl_give isl_aff *isl_aff_set_constant(
3096 __isl_take isl_aff *aff, isl_int v);
3097 __isl_give isl_aff *isl_aff_set_constant_si(
3098 __isl_take isl_aff *aff, int v);
3099 __isl_give isl_aff *isl_aff_set_coefficient(
3100 __isl_take isl_aff *aff,
3101 enum isl_dim_type type, int pos, isl_int v);
3102 __isl_give isl_aff *isl_aff_set_coefficient_si(
3103 __isl_take isl_aff *aff,
3104 enum isl_dim_type type, int pos, int v);
3105 __isl_give isl_aff *isl_aff_set_denominator(
3106 __isl_take isl_aff *aff, isl_int v);
3108 __isl_give isl_aff *isl_aff_add_constant(
3109 __isl_take isl_aff *aff, isl_int v);
3110 __isl_give isl_aff *isl_aff_add_constant_si(
3111 __isl_take isl_aff *aff, int v);
3112 __isl_give isl_aff *isl_aff_add_constant_num(
3113 __isl_take isl_aff *aff, isl_int v);
3114 __isl_give isl_aff *isl_aff_add_constant_num_si(
3115 __isl_take isl_aff *aff, int v);
3116 __isl_give isl_aff *isl_aff_add_coefficient(
3117 __isl_take isl_aff *aff,
3118 enum isl_dim_type type, int pos, isl_int v);
3119 __isl_give isl_aff *isl_aff_add_coefficient_si(
3120 __isl_take isl_aff *aff,
3121 enum isl_dim_type type, int pos, int v);
3123 __isl_give isl_aff *isl_aff_insert_dims(
3124 __isl_take isl_aff *aff,
3125 enum isl_dim_type type, unsigned first, unsigned n);
3126 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3127 __isl_take isl_pw_aff *pwaff,
3128 enum isl_dim_type type, unsigned first, unsigned n);
3129 __isl_give isl_aff *isl_aff_add_dims(
3130 __isl_take isl_aff *aff,
3131 enum isl_dim_type type, unsigned n);
3132 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3133 __isl_take isl_pw_aff *pwaff,
3134 enum isl_dim_type type, unsigned n);
3135 __isl_give isl_aff *isl_aff_drop_dims(
3136 __isl_take isl_aff *aff,
3137 enum isl_dim_type type, unsigned first, unsigned n);
3138 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3139 __isl_take isl_pw_aff *pwaff,
3140 enum isl_dim_type type, unsigned first, unsigned n);
3142 Note that the C<set_constant> and C<set_coefficient> functions
3143 set the I<numerator> of the constant or coefficient, while
3144 C<add_constant> and C<add_coefficient> add an integer value to
3145 the possibly rational constant or coefficient.
3146 The C<add_constant_num> functions add an integer value to
3149 To check whether an affine expressions is obviously zero
3150 or obviously equal to some other affine expression, use
3152 #include <isl/aff.h>
3153 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3154 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3155 __isl_keep isl_aff *aff2);
3156 int isl_pw_aff_plain_is_equal(
3157 __isl_keep isl_pw_aff *pwaff1,
3158 __isl_keep isl_pw_aff *pwaff2);
3162 #include <isl/aff.h>
3163 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3164 __isl_take isl_aff *aff2);
3165 __isl_give isl_pw_aff *isl_pw_aff_add(
3166 __isl_take isl_pw_aff *pwaff1,
3167 __isl_take isl_pw_aff *pwaff2);
3168 __isl_give isl_pw_aff *isl_pw_aff_min(
3169 __isl_take isl_pw_aff *pwaff1,
3170 __isl_take isl_pw_aff *pwaff2);
3171 __isl_give isl_pw_aff *isl_pw_aff_max(
3172 __isl_take isl_pw_aff *pwaff1,
3173 __isl_take isl_pw_aff *pwaff2);
3174 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3175 __isl_take isl_aff *aff2);
3176 __isl_give isl_pw_aff *isl_pw_aff_sub(
3177 __isl_take isl_pw_aff *pwaff1,
3178 __isl_take isl_pw_aff *pwaff2);
3179 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3180 __isl_give isl_pw_aff *isl_pw_aff_neg(
3181 __isl_take isl_pw_aff *pwaff);
3182 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3183 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3184 __isl_take isl_pw_aff *pwaff);
3185 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3186 __isl_give isl_pw_aff *isl_pw_aff_floor(
3187 __isl_take isl_pw_aff *pwaff);
3188 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3190 __isl_give isl_pw_aff *isl_pw_aff_mod(
3191 __isl_take isl_pw_aff *pwaff, isl_int mod);
3192 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3194 __isl_give isl_pw_aff *isl_pw_aff_scale(
3195 __isl_take isl_pw_aff *pwaff, isl_int f);
3196 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3198 __isl_give isl_aff *isl_aff_scale_down_ui(
3199 __isl_take isl_aff *aff, unsigned f);
3200 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3201 __isl_take isl_pw_aff *pwaff, isl_int f);
3203 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3204 __isl_take isl_pw_aff_list *list);
3205 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3206 __isl_take isl_pw_aff_list *list);
3208 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3209 __isl_take isl_pw_aff *pwqp);
3211 __isl_give isl_aff *isl_aff_align_params(
3212 __isl_take isl_aff *aff,
3213 __isl_take isl_space *model);
3214 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3215 __isl_take isl_pw_aff *pwaff,
3216 __isl_take isl_space *model);
3218 __isl_give isl_aff *isl_aff_project_domain_on_params(
3219 __isl_take isl_aff *aff);
3221 __isl_give isl_aff *isl_aff_gist_params(
3222 __isl_take isl_aff *aff,
3223 __isl_take isl_set *context);
3224 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3225 __isl_take isl_set *context);
3226 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3227 __isl_take isl_pw_aff *pwaff,
3228 __isl_take isl_set *context);
3229 __isl_give isl_pw_aff *isl_pw_aff_gist(
3230 __isl_take isl_pw_aff *pwaff,
3231 __isl_take isl_set *context);
3233 __isl_give isl_set *isl_pw_aff_domain(
3234 __isl_take isl_pw_aff *pwaff);
3235 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3236 __isl_take isl_pw_aff *pa,
3237 __isl_take isl_set *set);
3238 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3239 __isl_take isl_pw_aff *pa,
3240 __isl_take isl_set *set);
3242 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3243 __isl_take isl_aff *aff2);
3244 __isl_give isl_pw_aff *isl_pw_aff_mul(
3245 __isl_take isl_pw_aff *pwaff1,
3246 __isl_take isl_pw_aff *pwaff2);
3248 When multiplying two affine expressions, at least one of the two needs
3251 #include <isl/aff.h>
3252 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3253 __isl_take isl_aff *aff);
3254 __isl_give isl_basic_set *isl_aff_le_basic_set(
3255 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3256 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3257 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3258 __isl_give isl_set *isl_pw_aff_eq_set(
3259 __isl_take isl_pw_aff *pwaff1,
3260 __isl_take isl_pw_aff *pwaff2);
3261 __isl_give isl_set *isl_pw_aff_ne_set(
3262 __isl_take isl_pw_aff *pwaff1,
3263 __isl_take isl_pw_aff *pwaff2);
3264 __isl_give isl_set *isl_pw_aff_le_set(
3265 __isl_take isl_pw_aff *pwaff1,
3266 __isl_take isl_pw_aff *pwaff2);
3267 __isl_give isl_set *isl_pw_aff_lt_set(
3268 __isl_take isl_pw_aff *pwaff1,
3269 __isl_take isl_pw_aff *pwaff2);
3270 __isl_give isl_set *isl_pw_aff_ge_set(
3271 __isl_take isl_pw_aff *pwaff1,
3272 __isl_take isl_pw_aff *pwaff2);
3273 __isl_give isl_set *isl_pw_aff_gt_set(
3274 __isl_take isl_pw_aff *pwaff1,
3275 __isl_take isl_pw_aff *pwaff2);
3277 __isl_give isl_set *isl_pw_aff_list_eq_set(
3278 __isl_take isl_pw_aff_list *list1,
3279 __isl_take isl_pw_aff_list *list2);
3280 __isl_give isl_set *isl_pw_aff_list_ne_set(
3281 __isl_take isl_pw_aff_list *list1,
3282 __isl_take isl_pw_aff_list *list2);
3283 __isl_give isl_set *isl_pw_aff_list_le_set(
3284 __isl_take isl_pw_aff_list *list1,
3285 __isl_take isl_pw_aff_list *list2);
3286 __isl_give isl_set *isl_pw_aff_list_lt_set(
3287 __isl_take isl_pw_aff_list *list1,
3288 __isl_take isl_pw_aff_list *list2);
3289 __isl_give isl_set *isl_pw_aff_list_ge_set(
3290 __isl_take isl_pw_aff_list *list1,
3291 __isl_take isl_pw_aff_list *list2);
3292 __isl_give isl_set *isl_pw_aff_list_gt_set(
3293 __isl_take isl_pw_aff_list *list1,
3294 __isl_take isl_pw_aff_list *list2);
3296 The function C<isl_aff_neg_basic_set> returns a basic set
3297 containing those elements in the domain space
3298 of C<aff> where C<aff> is negative.
3299 The function C<isl_aff_ge_basic_set> returns a basic set
3300 containing those elements in the shared space
3301 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3302 The function C<isl_pw_aff_ge_set> returns a set
3303 containing those elements in the shared domain
3304 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3305 The functions operating on C<isl_pw_aff_list> apply the corresponding
3306 C<isl_pw_aff> function to each pair of elements in the two lists.
3308 #include <isl/aff.h>
3309 __isl_give isl_set *isl_pw_aff_nonneg_set(
3310 __isl_take isl_pw_aff *pwaff);
3311 __isl_give isl_set *isl_pw_aff_zero_set(
3312 __isl_take isl_pw_aff *pwaff);
3313 __isl_give isl_set *isl_pw_aff_non_zero_set(
3314 __isl_take isl_pw_aff *pwaff);
3316 The function C<isl_pw_aff_nonneg_set> returns a set
3317 containing those elements in the domain
3318 of C<pwaff> where C<pwaff> is non-negative.
3320 #include <isl/aff.h>
3321 __isl_give isl_pw_aff *isl_pw_aff_cond(
3322 __isl_take isl_pw_aff *cond,
3323 __isl_take isl_pw_aff *pwaff_true,
3324 __isl_take isl_pw_aff *pwaff_false);
3326 The function C<isl_pw_aff_cond> performs a conditional operator
3327 and returns an expression that is equal to C<pwaff_true>
3328 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3329 where C<cond> is zero.
3331 #include <isl/aff.h>
3332 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3333 __isl_take isl_pw_aff *pwaff1,
3334 __isl_take isl_pw_aff *pwaff2);
3335 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3336 __isl_take isl_pw_aff *pwaff1,
3337 __isl_take isl_pw_aff *pwaff2);
3338 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3339 __isl_take isl_pw_aff *pwaff1,
3340 __isl_take isl_pw_aff *pwaff2);
3342 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3343 expression with a domain that is the union of those of C<pwaff1> and
3344 C<pwaff2> and such that on each cell, the quasi-affine expression is
3345 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3346 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3347 associated expression is the defined one.
3349 An expression can be read from input using
3351 #include <isl/aff.h>
3352 __isl_give isl_aff *isl_aff_read_from_str(
3353 isl_ctx *ctx, const char *str);
3354 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3355 isl_ctx *ctx, const char *str);
3357 An expression can be printed using
3359 #include <isl/aff.h>
3360 __isl_give isl_printer *isl_printer_print_aff(
3361 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3363 __isl_give isl_printer *isl_printer_print_pw_aff(
3364 __isl_take isl_printer *p,
3365 __isl_keep isl_pw_aff *pwaff);
3367 =head2 Piecewise Multiple Quasi Affine Expressions
3369 An C<isl_multi_aff> object represents a sequence of
3370 zero or more affine expressions, all defined on the same domain space.
3372 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3375 #include <isl/aff.h>
3376 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3377 __isl_take isl_space *space,
3378 __isl_take isl_aff_list *list);
3380 An empty piecewise multiple quasi affine expression (one with no cells),
3381 the zero piecewise multiple quasi affine expression (with value zero
3382 for each output dimension),
3383 a piecewise multiple quasi affine expression with a single cell (with
3384 either a universe or a specified domain) or
3385 a zero-dimensional piecewise multiple quasi affine expression
3387 can be created using the following functions.
3389 #include <isl/aff.h>
3390 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3391 __isl_take isl_space *space);
3392 __isl_give isl_multi_aff *isl_multi_aff_zero(
3393 __isl_take isl_space *space);
3394 __isl_give isl_multi_aff *isl_multi_aff_identity(
3395 __isl_take isl_space *space);
3396 __isl_give isl_pw_multi_aff *
3397 isl_pw_multi_aff_from_multi_aff(
3398 __isl_take isl_multi_aff *ma);
3399 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3400 __isl_take isl_set *set,
3401 __isl_take isl_multi_aff *maff);
3402 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3403 __isl_take isl_set *set);
3405 __isl_give isl_union_pw_multi_aff *
3406 isl_union_pw_multi_aff_empty(
3407 __isl_take isl_space *space);
3408 __isl_give isl_union_pw_multi_aff *
3409 isl_union_pw_multi_aff_add_pw_multi_aff(
3410 __isl_take isl_union_pw_multi_aff *upma,
3411 __isl_take isl_pw_multi_aff *pma);
3412 __isl_give isl_union_pw_multi_aff *
3413 isl_union_pw_multi_aff_from_domain(
3414 __isl_take isl_union_set *uset);
3416 A piecewise multiple quasi affine expression can also be initialized
3417 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3418 and the C<isl_map> is single-valued.
3420 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3421 __isl_take isl_set *set);
3422 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3423 __isl_take isl_map *map);
3425 Multiple quasi affine expressions can be copied and freed using
3427 #include <isl/aff.h>
3428 __isl_give isl_multi_aff *isl_multi_aff_copy(
3429 __isl_keep isl_multi_aff *maff);
3430 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3432 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3433 __isl_keep isl_pw_multi_aff *pma);
3434 void *isl_pw_multi_aff_free(
3435 __isl_take isl_pw_multi_aff *pma);
3437 __isl_give isl_union_pw_multi_aff *
3438 isl_union_pw_multi_aff_copy(
3439 __isl_keep isl_union_pw_multi_aff *upma);
3440 void *isl_union_pw_multi_aff_free(
3441 __isl_take isl_union_pw_multi_aff *upma);
3443 The expression can be inspected using
3445 #include <isl/aff.h>
3446 isl_ctx *isl_multi_aff_get_ctx(
3447 __isl_keep isl_multi_aff *maff);
3448 isl_ctx *isl_pw_multi_aff_get_ctx(
3449 __isl_keep isl_pw_multi_aff *pma);
3450 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3451 __isl_keep isl_union_pw_multi_aff *upma);
3452 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3453 enum isl_dim_type type);
3454 unsigned isl_pw_multi_aff_dim(
3455 __isl_keep isl_pw_multi_aff *pma,
3456 enum isl_dim_type type);
3457 __isl_give isl_aff *isl_multi_aff_get_aff(
3458 __isl_keep isl_multi_aff *multi, int pos);
3459 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3460 __isl_keep isl_pw_multi_aff *pma, int pos);
3461 const char *isl_pw_multi_aff_get_dim_name(
3462 __isl_keep isl_pw_multi_aff *pma,
3463 enum isl_dim_type type, unsigned pos);
3464 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3465 __isl_keep isl_pw_multi_aff *pma,
3466 enum isl_dim_type type, unsigned pos);
3467 const char *isl_multi_aff_get_tuple_name(
3468 __isl_keep isl_multi_aff *multi,
3469 enum isl_dim_type type);
3470 int isl_pw_multi_aff_has_tuple_name(
3471 __isl_keep isl_pw_multi_aff *pma,
3472 enum isl_dim_type type);
3473 const char *isl_pw_multi_aff_get_tuple_name(
3474 __isl_keep isl_pw_multi_aff *pma,
3475 enum isl_dim_type type);
3476 int isl_pw_multi_aff_has_tuple_id(
3477 __isl_keep isl_pw_multi_aff *pma,
3478 enum isl_dim_type type);
3479 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3480 __isl_keep isl_pw_multi_aff *pma,
3481 enum isl_dim_type type);
3483 int isl_pw_multi_aff_foreach_piece(
3484 __isl_keep isl_pw_multi_aff *pma,
3485 int (*fn)(__isl_take isl_set *set,
3486 __isl_take isl_multi_aff *maff,
3487 void *user), void *user);
3489 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3490 __isl_keep isl_union_pw_multi_aff *upma,
3491 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3492 void *user), void *user);
3494 It can be modified using
3496 #include <isl/aff.h>
3497 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3498 __isl_take isl_multi_aff *multi, int pos,
3499 __isl_take isl_aff *aff);
3500 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3501 __isl_take isl_multi_aff *maff,
3502 enum isl_dim_type type, unsigned pos, const char *s);
3503 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3504 __isl_take isl_multi_aff *maff,
3505 enum isl_dim_type type, __isl_take isl_id *id);
3506 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3507 __isl_take isl_pw_multi_aff *pma,
3508 enum isl_dim_type type, __isl_take isl_id *id);
3510 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3511 __isl_take isl_multi_aff *maff,
3512 enum isl_dim_type type, unsigned first, unsigned n);
3514 To check whether two multiple affine expressions are
3515 obviously equal to each other, use
3517 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3518 __isl_keep isl_multi_aff *maff2);
3519 int isl_pw_multi_aff_plain_is_equal(
3520 __isl_keep isl_pw_multi_aff *pma1,
3521 __isl_keep isl_pw_multi_aff *pma2);
3525 #include <isl/aff.h>
3526 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3527 __isl_take isl_pw_multi_aff *pma1,
3528 __isl_take isl_pw_multi_aff *pma2);
3529 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3530 __isl_take isl_pw_multi_aff *pma1,
3531 __isl_take isl_pw_multi_aff *pma2);
3532 __isl_give isl_multi_aff *isl_multi_aff_add(
3533 __isl_take isl_multi_aff *maff1,
3534 __isl_take isl_multi_aff *maff2);
3535 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3536 __isl_take isl_pw_multi_aff *pma1,
3537 __isl_take isl_pw_multi_aff *pma2);
3538 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3539 __isl_take isl_union_pw_multi_aff *upma1,
3540 __isl_take isl_union_pw_multi_aff *upma2);
3541 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3542 __isl_take isl_pw_multi_aff *pma1,
3543 __isl_take isl_pw_multi_aff *pma2);
3544 __isl_give isl_multi_aff *isl_multi_aff_scale(
3545 __isl_take isl_multi_aff *maff,
3547 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3548 __isl_take isl_pw_multi_aff *pma,
3549 __isl_take isl_set *set);
3550 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3551 __isl_take isl_pw_multi_aff *pma,
3552 __isl_take isl_set *set);
3553 __isl_give isl_multi_aff *isl_multi_aff_lift(
3554 __isl_take isl_multi_aff *maff,
3555 __isl_give isl_local_space **ls);
3556 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3557 __isl_take isl_pw_multi_aff *pma);
3558 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3559 __isl_take isl_multi_aff *maff,
3560 __isl_take isl_set *context);
3561 __isl_give isl_multi_aff *isl_multi_aff_gist(
3562 __isl_take isl_multi_aff *maff,
3563 __isl_take isl_set *context);
3564 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3565 __isl_take isl_pw_multi_aff *pma,
3566 __isl_take isl_set *set);
3567 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3568 __isl_take isl_pw_multi_aff *pma,
3569 __isl_take isl_set *set);
3570 __isl_give isl_set *isl_pw_multi_aff_domain(
3571 __isl_take isl_pw_multi_aff *pma);
3572 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3573 __isl_take isl_union_pw_multi_aff *upma);
3574 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3575 __isl_take isl_multi_aff *ma1,
3576 __isl_take isl_multi_aff *ma2);
3577 __isl_give isl_multi_aff *isl_multi_aff_product(
3578 __isl_take isl_multi_aff *ma1,
3579 __isl_take isl_multi_aff *ma2);
3580 __isl_give isl_pw_multi_aff *
3581 isl_pw_multi_aff_flat_range_product(
3582 __isl_take isl_pw_multi_aff *pma1,
3583 __isl_take isl_pw_multi_aff *pma2);
3584 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3585 __isl_take isl_pw_multi_aff *pma1,
3586 __isl_take isl_pw_multi_aff *pma2);
3587 __isl_give isl_union_pw_multi_aff *
3588 isl_union_pw_multi_aff_flat_range_product(
3589 __isl_take isl_union_pw_multi_aff *upma1,
3590 __isl_take isl_union_pw_multi_aff *upma2);
3592 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3593 then it is assigned the local space that lies at the basis of
3594 the lifting applied.
3596 __isl_give isl_set *isl_multi_aff_lex_le_set(
3597 __isl_take isl_multi_aff *ma1,
3598 __isl_take isl_multi_aff *ma2);
3599 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3600 __isl_take isl_multi_aff *ma1,
3601 __isl_take isl_multi_aff *ma2);
3603 The function C<isl_multi_aff_lex_le_set> returns a set
3604 containing those elements in the shared domain space
3605 where C<ma1> is lexicographically smaller than or
3608 An expression can be read from input using
3610 #include <isl/aff.h>
3611 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3612 isl_ctx *ctx, const char *str);
3613 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3614 isl_ctx *ctx, const char *str);
3616 An expression can be printed using
3618 #include <isl/aff.h>
3619 __isl_give isl_printer *isl_printer_print_multi_aff(
3620 __isl_take isl_printer *p,
3621 __isl_keep isl_multi_aff *maff);
3622 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3623 __isl_take isl_printer *p,
3624 __isl_keep isl_pw_multi_aff *pma);
3625 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3626 __isl_take isl_printer *p,
3627 __isl_keep isl_union_pw_multi_aff *upma);
3631 Points are elements of a set. They can be used to construct
3632 simple sets (boxes) or they can be used to represent the
3633 individual elements of a set.
3634 The zero point (the origin) can be created using
3636 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3638 The coordinates of a point can be inspected, set and changed
3641 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3642 enum isl_dim_type type, int pos, isl_int *v);
3643 __isl_give isl_point *isl_point_set_coordinate(
3644 __isl_take isl_point *pnt,
3645 enum isl_dim_type type, int pos, isl_int v);
3647 __isl_give isl_point *isl_point_add_ui(
3648 __isl_take isl_point *pnt,
3649 enum isl_dim_type type, int pos, unsigned val);
3650 __isl_give isl_point *isl_point_sub_ui(
3651 __isl_take isl_point *pnt,
3652 enum isl_dim_type type, int pos, unsigned val);
3654 Other properties can be obtained using
3656 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3658 Points can be copied or freed using
3660 __isl_give isl_point *isl_point_copy(
3661 __isl_keep isl_point *pnt);
3662 void isl_point_free(__isl_take isl_point *pnt);
3664 A singleton set can be created from a point using
3666 __isl_give isl_basic_set *isl_basic_set_from_point(
3667 __isl_take isl_point *pnt);
3668 __isl_give isl_set *isl_set_from_point(
3669 __isl_take isl_point *pnt);
3671 and a box can be created from two opposite extremal points using
3673 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3674 __isl_take isl_point *pnt1,
3675 __isl_take isl_point *pnt2);
3676 __isl_give isl_set *isl_set_box_from_points(
3677 __isl_take isl_point *pnt1,
3678 __isl_take isl_point *pnt2);
3680 All elements of a B<bounded> (union) set can be enumerated using
3681 the following functions.
3683 int isl_set_foreach_point(__isl_keep isl_set *set,
3684 int (*fn)(__isl_take isl_point *pnt, void *user),
3686 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3687 int (*fn)(__isl_take isl_point *pnt, void *user),
3690 The function C<fn> is called for each integer point in
3691 C<set> with as second argument the last argument of
3692 the C<isl_set_foreach_point> call. The function C<fn>
3693 should return C<0> on success and C<-1> on failure.
3694 In the latter case, C<isl_set_foreach_point> will stop
3695 enumerating and return C<-1> as well.
3696 If the enumeration is performed successfully and to completion,
3697 then C<isl_set_foreach_point> returns C<0>.
3699 To obtain a single point of a (basic) set, use
3701 __isl_give isl_point *isl_basic_set_sample_point(
3702 __isl_take isl_basic_set *bset);
3703 __isl_give isl_point *isl_set_sample_point(
3704 __isl_take isl_set *set);
3706 If C<set> does not contain any (integer) points, then the
3707 resulting point will be ``void'', a property that can be
3710 int isl_point_is_void(__isl_keep isl_point *pnt);
3712 =head2 Piecewise Quasipolynomials
3714 A piecewise quasipolynomial is a particular kind of function that maps
3715 a parametric point to a rational value.
3716 More specifically, a quasipolynomial is a polynomial expression in greatest
3717 integer parts of affine expressions of parameters and variables.
3718 A piecewise quasipolynomial is a subdivision of a given parametric
3719 domain into disjoint cells with a quasipolynomial associated to
3720 each cell. The value of the piecewise quasipolynomial at a given
3721 point is the value of the quasipolynomial associated to the cell
3722 that contains the point. Outside of the union of cells,
3723 the value is assumed to be zero.
3724 For example, the piecewise quasipolynomial
3726 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3728 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3729 A given piecewise quasipolynomial has a fixed domain dimension.
3730 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3731 defined over different domains.
3732 Piecewise quasipolynomials are mainly used by the C<barvinok>
3733 library for representing the number of elements in a parametric set or map.
3734 For example, the piecewise quasipolynomial above represents
3735 the number of points in the map
3737 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3739 =head3 Input and Output
3741 Piecewise quasipolynomials can be read from input using
3743 __isl_give isl_union_pw_qpolynomial *
3744 isl_union_pw_qpolynomial_read_from_str(
3745 isl_ctx *ctx, const char *str);
3747 Quasipolynomials and piecewise quasipolynomials can be printed
3748 using the following functions.
3750 __isl_give isl_printer *isl_printer_print_qpolynomial(
3751 __isl_take isl_printer *p,
3752 __isl_keep isl_qpolynomial *qp);
3754 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3755 __isl_take isl_printer *p,
3756 __isl_keep isl_pw_qpolynomial *pwqp);
3758 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3759 __isl_take isl_printer *p,
3760 __isl_keep isl_union_pw_qpolynomial *upwqp);
3762 The output format of the printer
3763 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3764 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3766 In case of printing in C<ISL_FORMAT_C>, the user may want
3767 to set the names of all dimensions
3769 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3770 __isl_take isl_qpolynomial *qp,
3771 enum isl_dim_type type, unsigned pos,
3773 __isl_give isl_pw_qpolynomial *
3774 isl_pw_qpolynomial_set_dim_name(
3775 __isl_take isl_pw_qpolynomial *pwqp,
3776 enum isl_dim_type type, unsigned pos,
3779 =head3 Creating New (Piecewise) Quasipolynomials
3781 Some simple quasipolynomials can be created using the following functions.
3782 More complicated quasipolynomials can be created by applying
3783 operations such as addition and multiplication
3784 on the resulting quasipolynomials
3786 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3787 __isl_take isl_space *domain);
3788 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3789 __isl_take isl_space *domain);
3790 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3791 __isl_take isl_space *domain);
3792 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3793 __isl_take isl_space *domain);
3794 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3795 __isl_take isl_space *domain);
3796 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3797 __isl_take isl_space *domain,
3798 const isl_int n, const isl_int d);
3799 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3800 __isl_take isl_space *domain,
3801 enum isl_dim_type type, unsigned pos);
3802 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3803 __isl_take isl_aff *aff);
3805 Note that the space in which a quasipolynomial lives is a map space
3806 with a one-dimensional range. The C<domain> argument in some of
3807 the functions above corresponds to the domain of this map space.
3809 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3810 with a single cell can be created using the following functions.
3811 Multiple of these single cell piecewise quasipolynomials can
3812 be combined to create more complicated piecewise quasipolynomials.
3814 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3815 __isl_take isl_space *space);
3816 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3817 __isl_take isl_set *set,
3818 __isl_take isl_qpolynomial *qp);
3819 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3820 __isl_take isl_qpolynomial *qp);
3821 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3822 __isl_take isl_pw_aff *pwaff);
3824 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3825 __isl_take isl_space *space);
3826 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3827 __isl_take isl_pw_qpolynomial *pwqp);
3828 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3829 __isl_take isl_union_pw_qpolynomial *upwqp,
3830 __isl_take isl_pw_qpolynomial *pwqp);
3832 Quasipolynomials can be copied and freed again using the following
3835 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3836 __isl_keep isl_qpolynomial *qp);
3837 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3839 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3840 __isl_keep isl_pw_qpolynomial *pwqp);
3841 void *isl_pw_qpolynomial_free(
3842 __isl_take isl_pw_qpolynomial *pwqp);
3844 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3845 __isl_keep isl_union_pw_qpolynomial *upwqp);
3846 void *isl_union_pw_qpolynomial_free(
3847 __isl_take isl_union_pw_qpolynomial *upwqp);
3849 =head3 Inspecting (Piecewise) Quasipolynomials
3851 To iterate over all piecewise quasipolynomials in a union
3852 piecewise quasipolynomial, use the following function
3854 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3855 __isl_keep isl_union_pw_qpolynomial *upwqp,
3856 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3859 To extract the piecewise quasipolynomial in a given space from a union, use
3861 __isl_give isl_pw_qpolynomial *
3862 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3863 __isl_keep isl_union_pw_qpolynomial *upwqp,
3864 __isl_take isl_space *space);
3866 To iterate over the cells in a piecewise quasipolynomial,
3867 use either of the following two functions
3869 int isl_pw_qpolynomial_foreach_piece(
3870 __isl_keep isl_pw_qpolynomial *pwqp,
3871 int (*fn)(__isl_take isl_set *set,
3872 __isl_take isl_qpolynomial *qp,
3873 void *user), void *user);
3874 int isl_pw_qpolynomial_foreach_lifted_piece(
3875 __isl_keep isl_pw_qpolynomial *pwqp,
3876 int (*fn)(__isl_take isl_set *set,
3877 __isl_take isl_qpolynomial *qp,
3878 void *user), void *user);
3880 As usual, the function C<fn> should return C<0> on success
3881 and C<-1> on failure. The difference between
3882 C<isl_pw_qpolynomial_foreach_piece> and
3883 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3884 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3885 compute unique representations for all existentially quantified
3886 variables and then turn these existentially quantified variables
3887 into extra set variables, adapting the associated quasipolynomial
3888 accordingly. This means that the C<set> passed to C<fn>
3889 will not have any existentially quantified variables, but that
3890 the dimensions of the sets may be different for different
3891 invocations of C<fn>.
3893 To iterate over all terms in a quasipolynomial,
3896 int isl_qpolynomial_foreach_term(
3897 __isl_keep isl_qpolynomial *qp,
3898 int (*fn)(__isl_take isl_term *term,
3899 void *user), void *user);
3901 The terms themselves can be inspected and freed using
3904 unsigned isl_term_dim(__isl_keep isl_term *term,
3905 enum isl_dim_type type);
3906 void isl_term_get_num(__isl_keep isl_term *term,
3908 void isl_term_get_den(__isl_keep isl_term *term,
3910 int isl_term_get_exp(__isl_keep isl_term *term,
3911 enum isl_dim_type type, unsigned pos);
3912 __isl_give isl_aff *isl_term_get_div(
3913 __isl_keep isl_term *term, unsigned pos);
3914 void isl_term_free(__isl_take isl_term *term);
3916 Each term is a product of parameters, set variables and
3917 integer divisions. The function C<isl_term_get_exp>
3918 returns the exponent of a given dimensions in the given term.
3919 The C<isl_int>s in the arguments of C<isl_term_get_num>
3920 and C<isl_term_get_den> need to have been initialized
3921 using C<isl_int_init> before calling these functions.
3923 =head3 Properties of (Piecewise) Quasipolynomials
3925 To check whether a quasipolynomial is actually a constant,
3926 use the following function.
3928 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3929 isl_int *n, isl_int *d);
3931 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3932 then the numerator and denominator of the constant
3933 are returned in C<*n> and C<*d>, respectively.
3935 To check whether two union piecewise quasipolynomials are
3936 obviously equal, use
3938 int isl_union_pw_qpolynomial_plain_is_equal(
3939 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3940 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3942 =head3 Operations on (Piecewise) Quasipolynomials
3944 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3945 __isl_take isl_qpolynomial *qp, isl_int v);
3946 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3947 __isl_take isl_qpolynomial *qp);
3948 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3949 __isl_take isl_qpolynomial *qp1,
3950 __isl_take isl_qpolynomial *qp2);
3951 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3952 __isl_take isl_qpolynomial *qp1,
3953 __isl_take isl_qpolynomial *qp2);
3954 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3955 __isl_take isl_qpolynomial *qp1,
3956 __isl_take isl_qpolynomial *qp2);
3957 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3958 __isl_take isl_qpolynomial *qp, unsigned exponent);
3960 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3961 __isl_take isl_pw_qpolynomial *pwqp1,
3962 __isl_take isl_pw_qpolynomial *pwqp2);
3963 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3964 __isl_take isl_pw_qpolynomial *pwqp1,
3965 __isl_take isl_pw_qpolynomial *pwqp2);
3966 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3967 __isl_take isl_pw_qpolynomial *pwqp1,
3968 __isl_take isl_pw_qpolynomial *pwqp2);
3969 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3970 __isl_take isl_pw_qpolynomial *pwqp);
3971 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3972 __isl_take isl_pw_qpolynomial *pwqp1,
3973 __isl_take isl_pw_qpolynomial *pwqp2);
3974 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3975 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3977 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3978 __isl_take isl_union_pw_qpolynomial *upwqp1,
3979 __isl_take isl_union_pw_qpolynomial *upwqp2);
3980 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3981 __isl_take isl_union_pw_qpolynomial *upwqp1,
3982 __isl_take isl_union_pw_qpolynomial *upwqp2);
3983 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3984 __isl_take isl_union_pw_qpolynomial *upwqp1,
3985 __isl_take isl_union_pw_qpolynomial *upwqp2);
3987 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3988 __isl_take isl_pw_qpolynomial *pwqp,
3989 __isl_take isl_point *pnt);
3991 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3992 __isl_take isl_union_pw_qpolynomial *upwqp,
3993 __isl_take isl_point *pnt);
3995 __isl_give isl_set *isl_pw_qpolynomial_domain(
3996 __isl_take isl_pw_qpolynomial *pwqp);
3997 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3998 __isl_take isl_pw_qpolynomial *pwpq,
3999 __isl_take isl_set *set);
4000 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4001 __isl_take isl_pw_qpolynomial *pwpq,
4002 __isl_take isl_set *set);
4004 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4005 __isl_take isl_union_pw_qpolynomial *upwqp);
4006 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4007 __isl_take isl_union_pw_qpolynomial *upwpq,
4008 __isl_take isl_union_set *uset);
4009 __isl_give isl_union_pw_qpolynomial *
4010 isl_union_pw_qpolynomial_intersect_params(
4011 __isl_take isl_union_pw_qpolynomial *upwpq,
4012 __isl_take isl_set *set);
4014 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4015 __isl_take isl_qpolynomial *qp,
4016 __isl_take isl_space *model);
4018 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4019 __isl_take isl_qpolynomial *qp);
4020 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4021 __isl_take isl_pw_qpolynomial *pwqp);
4023 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4024 __isl_take isl_union_pw_qpolynomial *upwqp);
4026 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4027 __isl_take isl_qpolynomial *qp,
4028 __isl_take isl_set *context);
4029 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4030 __isl_take isl_qpolynomial *qp,
4031 __isl_take isl_set *context);
4033 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4034 __isl_take isl_pw_qpolynomial *pwqp,
4035 __isl_take isl_set *context);
4036 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4037 __isl_take isl_pw_qpolynomial *pwqp,
4038 __isl_take isl_set *context);
4040 __isl_give isl_union_pw_qpolynomial *
4041 isl_union_pw_qpolynomial_gist_params(
4042 __isl_take isl_union_pw_qpolynomial *upwqp,
4043 __isl_take isl_set *context);
4044 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4045 __isl_take isl_union_pw_qpolynomial *upwqp,
4046 __isl_take isl_union_set *context);
4048 The gist operation applies the gist operation to each of
4049 the cells in the domain of the input piecewise quasipolynomial.
4050 The context is also exploited
4051 to simplify the quasipolynomials associated to each cell.
4053 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4054 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4055 __isl_give isl_union_pw_qpolynomial *
4056 isl_union_pw_qpolynomial_to_polynomial(
4057 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4059 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4060 the polynomial will be an overapproximation. If C<sign> is negative,
4061 it will be an underapproximation. If C<sign> is zero, the approximation
4062 will lie somewhere in between.
4064 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4066 A piecewise quasipolynomial reduction is a piecewise
4067 reduction (or fold) of quasipolynomials.
4068 In particular, the reduction can be maximum or a minimum.
4069 The objects are mainly used to represent the result of
4070 an upper or lower bound on a quasipolynomial over its domain,
4071 i.e., as the result of the following function.
4073 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4074 __isl_take isl_pw_qpolynomial *pwqp,
4075 enum isl_fold type, int *tight);
4077 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4078 __isl_take isl_union_pw_qpolynomial *upwqp,
4079 enum isl_fold type, int *tight);
4081 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4082 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4083 is the returned bound is known be tight, i.e., for each value
4084 of the parameters there is at least
4085 one element in the domain that reaches the bound.
4086 If the domain of C<pwqp> is not wrapping, then the bound is computed
4087 over all elements in that domain and the result has a purely parametric
4088 domain. If the domain of C<pwqp> is wrapping, then the bound is
4089 computed over the range of the wrapped relation. The domain of the
4090 wrapped relation becomes the domain of the result.
4092 A (piecewise) quasipolynomial reduction can be copied or freed using the
4093 following functions.
4095 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4096 __isl_keep isl_qpolynomial_fold *fold);
4097 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4098 __isl_keep isl_pw_qpolynomial_fold *pwf);
4099 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4100 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4101 void isl_qpolynomial_fold_free(
4102 __isl_take isl_qpolynomial_fold *fold);
4103 void *isl_pw_qpolynomial_fold_free(
4104 __isl_take isl_pw_qpolynomial_fold *pwf);
4105 void *isl_union_pw_qpolynomial_fold_free(
4106 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4108 =head3 Printing Piecewise Quasipolynomial Reductions
4110 Piecewise quasipolynomial reductions can be printed
4111 using the following function.
4113 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4114 __isl_take isl_printer *p,
4115 __isl_keep isl_pw_qpolynomial_fold *pwf);
4116 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4117 __isl_take isl_printer *p,
4118 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4120 For C<isl_printer_print_pw_qpolynomial_fold>,
4121 output format of the printer
4122 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4123 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4124 output format of the printer
4125 needs to be set to C<ISL_FORMAT_ISL>.
4126 In case of printing in C<ISL_FORMAT_C>, the user may want
4127 to set the names of all dimensions
4129 __isl_give isl_pw_qpolynomial_fold *
4130 isl_pw_qpolynomial_fold_set_dim_name(
4131 __isl_take isl_pw_qpolynomial_fold *pwf,
4132 enum isl_dim_type type, unsigned pos,
4135 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4137 To iterate over all piecewise quasipolynomial reductions in a union
4138 piecewise quasipolynomial reduction, use the following function
4140 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4141 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4142 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4143 void *user), void *user);
4145 To iterate over the cells in a piecewise quasipolynomial reduction,
4146 use either of the following two functions
4148 int isl_pw_qpolynomial_fold_foreach_piece(
4149 __isl_keep isl_pw_qpolynomial_fold *pwf,
4150 int (*fn)(__isl_take isl_set *set,
4151 __isl_take isl_qpolynomial_fold *fold,
4152 void *user), void *user);
4153 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4154 __isl_keep isl_pw_qpolynomial_fold *pwf,
4155 int (*fn)(__isl_take isl_set *set,
4156 __isl_take isl_qpolynomial_fold *fold,
4157 void *user), void *user);
4159 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4160 of the difference between these two functions.
4162 To iterate over all quasipolynomials in a reduction, use
4164 int isl_qpolynomial_fold_foreach_qpolynomial(
4165 __isl_keep isl_qpolynomial_fold *fold,
4166 int (*fn)(__isl_take isl_qpolynomial *qp,
4167 void *user), void *user);
4169 =head3 Properties of Piecewise Quasipolynomial Reductions
4171 To check whether two union piecewise quasipolynomial reductions are
4172 obviously equal, use
4174 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4175 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4176 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4178 =head3 Operations on Piecewise Quasipolynomial Reductions
4180 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4181 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4183 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4184 __isl_take isl_pw_qpolynomial_fold *pwf1,
4185 __isl_take isl_pw_qpolynomial_fold *pwf2);
4187 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4188 __isl_take isl_pw_qpolynomial_fold *pwf1,
4189 __isl_take isl_pw_qpolynomial_fold *pwf2);
4191 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4192 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4193 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4195 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4196 __isl_take isl_pw_qpolynomial_fold *pwf,
4197 __isl_take isl_point *pnt);
4199 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4200 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4201 __isl_take isl_point *pnt);
4203 __isl_give isl_pw_qpolynomial_fold *
4204 isl_pw_qpolynomial_fold_intersect_params(
4205 __isl_take isl_pw_qpolynomial_fold *pwf,
4206 __isl_take isl_set *set);
4208 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4209 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4210 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4211 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4212 __isl_take isl_union_set *uset);
4213 __isl_give isl_union_pw_qpolynomial_fold *
4214 isl_union_pw_qpolynomial_fold_intersect_params(
4215 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4216 __isl_take isl_set *set);
4218 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4219 __isl_take isl_pw_qpolynomial_fold *pwf);
4221 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4222 __isl_take isl_pw_qpolynomial_fold *pwf);
4224 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4225 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4227 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4228 __isl_take isl_qpolynomial_fold *fold,
4229 __isl_take isl_set *context);
4230 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4231 __isl_take isl_qpolynomial_fold *fold,
4232 __isl_take isl_set *context);
4234 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4235 __isl_take isl_pw_qpolynomial_fold *pwf,
4236 __isl_take isl_set *context);
4237 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4238 __isl_take isl_pw_qpolynomial_fold *pwf,
4239 __isl_take isl_set *context);
4241 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4242 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4243 __isl_take isl_union_set *context);
4244 __isl_give isl_union_pw_qpolynomial_fold *
4245 isl_union_pw_qpolynomial_fold_gist_params(
4246 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4247 __isl_take isl_set *context);
4249 The gist operation applies the gist operation to each of
4250 the cells in the domain of the input piecewise quasipolynomial reduction.
4251 In future, the operation will also exploit the context
4252 to simplify the quasipolynomial reductions associated to each cell.
4254 __isl_give isl_pw_qpolynomial_fold *
4255 isl_set_apply_pw_qpolynomial_fold(
4256 __isl_take isl_set *set,
4257 __isl_take isl_pw_qpolynomial_fold *pwf,
4259 __isl_give isl_pw_qpolynomial_fold *
4260 isl_map_apply_pw_qpolynomial_fold(
4261 __isl_take isl_map *map,
4262 __isl_take isl_pw_qpolynomial_fold *pwf,
4264 __isl_give isl_union_pw_qpolynomial_fold *
4265 isl_union_set_apply_union_pw_qpolynomial_fold(
4266 __isl_take isl_union_set *uset,
4267 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4269 __isl_give isl_union_pw_qpolynomial_fold *
4270 isl_union_map_apply_union_pw_qpolynomial_fold(
4271 __isl_take isl_union_map *umap,
4272 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4275 The functions taking a map
4276 compose the given map with the given piecewise quasipolynomial reduction.
4277 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4278 over all elements in the intersection of the range of the map
4279 and the domain of the piecewise quasipolynomial reduction
4280 as a function of an element in the domain of the map.
4281 The functions taking a set compute a bound over all elements in the
4282 intersection of the set and the domain of the
4283 piecewise quasipolynomial reduction.
4285 =head2 Dependence Analysis
4287 C<isl> contains specialized functionality for performing
4288 array dataflow analysis. That is, given a I<sink> access relation
4289 and a collection of possible I<source> access relations,
4290 C<isl> can compute relations that describe
4291 for each iteration of the sink access, which iteration
4292 of which of the source access relations was the last
4293 to access the same data element before the given iteration
4295 The resulting dependence relations map source iterations
4296 to the corresponding sink iterations.
4297 To compute standard flow dependences, the sink should be
4298 a read, while the sources should be writes.
4299 If any of the source accesses are marked as being I<may>
4300 accesses, then there will be a dependence from the last
4301 I<must> access B<and> from any I<may> access that follows
4302 this last I<must> access.
4303 In particular, if I<all> sources are I<may> accesses,
4304 then memory based dependence analysis is performed.
4305 If, on the other hand, all sources are I<must> accesses,
4306 then value based dependence analysis is performed.
4308 #include <isl/flow.h>
4310 typedef int (*isl_access_level_before)(void *first, void *second);
4312 __isl_give isl_access_info *isl_access_info_alloc(
4313 __isl_take isl_map *sink,
4314 void *sink_user, isl_access_level_before fn,
4316 __isl_give isl_access_info *isl_access_info_add_source(
4317 __isl_take isl_access_info *acc,
4318 __isl_take isl_map *source, int must,
4320 void *isl_access_info_free(__isl_take isl_access_info *acc);
4322 __isl_give isl_flow *isl_access_info_compute_flow(
4323 __isl_take isl_access_info *acc);
4325 int isl_flow_foreach(__isl_keep isl_flow *deps,
4326 int (*fn)(__isl_take isl_map *dep, int must,
4327 void *dep_user, void *user),
4329 __isl_give isl_map *isl_flow_get_no_source(
4330 __isl_keep isl_flow *deps, int must);
4331 void isl_flow_free(__isl_take isl_flow *deps);
4333 The function C<isl_access_info_compute_flow> performs the actual
4334 dependence analysis. The other functions are used to construct
4335 the input for this function or to read off the output.
4337 The input is collected in an C<isl_access_info>, which can
4338 be created through a call to C<isl_access_info_alloc>.
4339 The arguments to this functions are the sink access relation
4340 C<sink>, a token C<sink_user> used to identify the sink
4341 access to the user, a callback function for specifying the
4342 relative order of source and sink accesses, and the number
4343 of source access relations that will be added.
4344 The callback function has type C<int (*)(void *first, void *second)>.
4345 The function is called with two user supplied tokens identifying
4346 either a source or the sink and it should return the shared nesting
4347 level and the relative order of the two accesses.
4348 In particular, let I<n> be the number of loops shared by
4349 the two accesses. If C<first> precedes C<second> textually,
4350 then the function should return I<2 * n + 1>; otherwise,
4351 it should return I<2 * n>.
4352 The sources can be added to the C<isl_access_info> by performing
4353 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4354 C<must> indicates whether the source is a I<must> access
4355 or a I<may> access. Note that a multi-valued access relation
4356 should only be marked I<must> if every iteration in the domain
4357 of the relation accesses I<all> elements in its image.
4358 The C<source_user> token is again used to identify
4359 the source access. The range of the source access relation
4360 C<source> should have the same dimension as the range
4361 of the sink access relation.
4362 The C<isl_access_info_free> function should usually not be
4363 called explicitly, because it is called implicitly by
4364 C<isl_access_info_compute_flow>.
4366 The result of the dependence analysis is collected in an
4367 C<isl_flow>. There may be elements of
4368 the sink access for which no preceding source access could be
4369 found or for which all preceding sources are I<may> accesses.
4370 The relations containing these elements can be obtained through
4371 calls to C<isl_flow_get_no_source>, the first with C<must> set
4372 and the second with C<must> unset.
4373 In the case of standard flow dependence analysis,
4374 with the sink a read and the sources I<must> writes,
4375 the first relation corresponds to the reads from uninitialized
4376 array elements and the second relation is empty.
4377 The actual flow dependences can be extracted using
4378 C<isl_flow_foreach>. This function will call the user-specified
4379 callback function C<fn> for each B<non-empty> dependence between
4380 a source and the sink. The callback function is called
4381 with four arguments, the actual flow dependence relation
4382 mapping source iterations to sink iterations, a boolean that
4383 indicates whether it is a I<must> or I<may> dependence, a token
4384 identifying the source and an additional C<void *> with value
4385 equal to the third argument of the C<isl_flow_foreach> call.
4386 A dependence is marked I<must> if it originates from a I<must>
4387 source and if it is not followed by any I<may> sources.
4389 After finishing with an C<isl_flow>, the user should call
4390 C<isl_flow_free> to free all associated memory.
4392 A higher-level interface to dependence analysis is provided
4393 by the following function.
4395 #include <isl/flow.h>
4397 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4398 __isl_take isl_union_map *must_source,
4399 __isl_take isl_union_map *may_source,
4400 __isl_take isl_union_map *schedule,
4401 __isl_give isl_union_map **must_dep,
4402 __isl_give isl_union_map **may_dep,
4403 __isl_give isl_union_map **must_no_source,
4404 __isl_give isl_union_map **may_no_source);
4406 The arrays are identified by the tuple names of the ranges
4407 of the accesses. The iteration domains by the tuple names
4408 of the domains of the accesses and of the schedule.
4409 The relative order of the iteration domains is given by the
4410 schedule. The relations returned through C<must_no_source>
4411 and C<may_no_source> are subsets of C<sink>.
4412 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4413 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4414 any of the other arguments is treated as an error.
4416 =head3 Interaction with Dependence Analysis
4418 During the dependence analysis, we frequently need to perform
4419 the following operation. Given a relation between sink iterations
4420 and potential source iterations from a particular source domain,
4421 what is the last potential source iteration corresponding to each
4422 sink iteration. It can sometimes be convenient to adjust
4423 the set of potential source iterations before or after each such operation.
4424 The prototypical example is fuzzy array dataflow analysis,
4425 where we need to analyze if, based on data-dependent constraints,
4426 the sink iteration can ever be executed without one or more of
4427 the corresponding potential source iterations being executed.
4428 If so, we can introduce extra parameters and select an unknown
4429 but fixed source iteration from the potential source iterations.
4430 To be able to perform such manipulations, C<isl> provides the following
4433 #include <isl/flow.h>
4435 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4436 __isl_keep isl_map *source_map,
4437 __isl_keep isl_set *sink, void *source_user,
4439 __isl_give isl_access_info *isl_access_info_set_restrict(
4440 __isl_take isl_access_info *acc,
4441 isl_access_restrict fn, void *user);
4443 The function C<isl_access_info_set_restrict> should be called
4444 before calling C<isl_access_info_compute_flow> and registers a callback function
4445 that will be called any time C<isl> is about to compute the last
4446 potential source. The first argument is the (reverse) proto-dependence,
4447 mapping sink iterations to potential source iterations.
4448 The second argument represents the sink iterations for which
4449 we want to compute the last source iteration.
4450 The third argument is the token corresponding to the source
4451 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4452 The callback is expected to return a restriction on either the input or
4453 the output of the operation computing the last potential source.
4454 If the input needs to be restricted then restrictions are needed
4455 for both the source and the sink iterations. The sink iterations
4456 and the potential source iterations will be intersected with these sets.
4457 If the output needs to be restricted then only a restriction on the source
4458 iterations is required.
4459 If any error occurs, the callback should return C<NULL>.
4460 An C<isl_restriction> object can be created, freed and inspected
4461 using the following functions.
4463 #include <isl/flow.h>
4465 __isl_give isl_restriction *isl_restriction_input(
4466 __isl_take isl_set *source_restr,
4467 __isl_take isl_set *sink_restr);
4468 __isl_give isl_restriction *isl_restriction_output(
4469 __isl_take isl_set *source_restr);
4470 __isl_give isl_restriction *isl_restriction_none(
4471 __isl_take isl_map *source_map);
4472 __isl_give isl_restriction *isl_restriction_empty(
4473 __isl_take isl_map *source_map);
4474 void *isl_restriction_free(
4475 __isl_take isl_restriction *restr);
4476 isl_ctx *isl_restriction_get_ctx(
4477 __isl_keep isl_restriction *restr);
4479 C<isl_restriction_none> and C<isl_restriction_empty> are special
4480 cases of C<isl_restriction_input>. C<isl_restriction_none>
4481 is essentially equivalent to
4483 isl_restriction_input(isl_set_universe(
4484 isl_space_range(isl_map_get_space(source_map))),
4486 isl_space_domain(isl_map_get_space(source_map))));
4488 whereas C<isl_restriction_empty> is essentially equivalent to
4490 isl_restriction_input(isl_set_empty(
4491 isl_space_range(isl_map_get_space(source_map))),
4493 isl_space_domain(isl_map_get_space(source_map))));
4497 B<The functionality described in this section is fairly new
4498 and may be subject to change.>
4500 The following function can be used to compute a schedule
4501 for a union of domains.
4502 By default, the algorithm used to construct the schedule is similar
4503 to that of C<Pluto>.
4504 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4506 The generated schedule respects all C<validity> dependences.
4507 That is, all dependence distances over these dependences in the
4508 scheduled space are lexicographically positive.
4509 The default algorithm tries to minimize the dependence distances over
4510 C<proximity> dependences.
4511 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4512 for groups of domains where the dependence distances have only
4513 non-negative values.
4514 When using Feautrier's algorithm, the C<proximity> dependence
4515 distances are only minimized during the extension to a
4516 full-dimensional schedule.
4518 #include <isl/schedule.h>
4519 __isl_give isl_schedule *isl_union_set_compute_schedule(
4520 __isl_take isl_union_set *domain,
4521 __isl_take isl_union_map *validity,
4522 __isl_take isl_union_map *proximity);
4523 void *isl_schedule_free(__isl_take isl_schedule *sched);
4525 A mapping from the domains to the scheduled space can be obtained
4526 from an C<isl_schedule> using the following function.
4528 __isl_give isl_union_map *isl_schedule_get_map(
4529 __isl_keep isl_schedule *sched);
4531 A representation of the schedule can be printed using
4533 __isl_give isl_printer *isl_printer_print_schedule(
4534 __isl_take isl_printer *p,
4535 __isl_keep isl_schedule *schedule);
4537 A representation of the schedule as a forest of bands can be obtained
4538 using the following function.
4540 __isl_give isl_band_list *isl_schedule_get_band_forest(
4541 __isl_keep isl_schedule *schedule);
4543 The individual bands can be visited in depth-first post-order
4544 using the following function.
4546 #include <isl/schedule.h>
4547 int isl_schedule_foreach_band(
4548 __isl_keep isl_schedule *sched,
4549 int (*fn)(__isl_keep isl_band *band, void *user),
4552 The list can be manipulated as explained in L<"Lists">.
4553 The bands inside the list can be copied and freed using the following
4556 #include <isl/band.h>
4557 __isl_give isl_band *isl_band_copy(
4558 __isl_keep isl_band *band);
4559 void *isl_band_free(__isl_take isl_band *band);
4561 Each band contains zero or more scheduling dimensions.
4562 These are referred to as the members of the band.
4563 The section of the schedule that corresponds to the band is
4564 referred to as the partial schedule of the band.
4565 For those nodes that participate in a band, the outer scheduling
4566 dimensions form the prefix schedule, while the inner scheduling
4567 dimensions form the suffix schedule.
4568 That is, if we take a cut of the band forest, then the union of
4569 the concatenations of the prefix, partial and suffix schedules of
4570 each band in the cut is equal to the entire schedule (modulo
4571 some possible padding at the end with zero scheduling dimensions).
4572 The properties of a band can be inspected using the following functions.
4574 #include <isl/band.h>
4575 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4577 int isl_band_has_children(__isl_keep isl_band *band);
4578 __isl_give isl_band_list *isl_band_get_children(
4579 __isl_keep isl_band *band);
4581 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4582 __isl_keep isl_band *band);
4583 __isl_give isl_union_map *isl_band_get_partial_schedule(
4584 __isl_keep isl_band *band);
4585 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4586 __isl_keep isl_band *band);
4588 int isl_band_n_member(__isl_keep isl_band *band);
4589 int isl_band_member_is_zero_distance(
4590 __isl_keep isl_band *band, int pos);
4592 int isl_band_list_foreach_band(
4593 __isl_keep isl_band_list *list,
4594 int (*fn)(__isl_keep isl_band *band, void *user),
4597 Note that a scheduling dimension is considered to be ``zero
4598 distance'' if it does not carry any proximity dependences
4600 That is, if the dependence distances of the proximity
4601 dependences are all zero in that direction (for fixed
4602 iterations of outer bands).
4603 Like C<isl_schedule_foreach_band>,
4604 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4605 in depth-first post-order.
4607 A band can be tiled using the following function.
4609 #include <isl/band.h>
4610 int isl_band_tile(__isl_keep isl_band *band,
4611 __isl_take isl_vec *sizes);
4613 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4615 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4617 The C<isl_band_tile> function tiles the band using the given tile sizes
4618 inside its schedule.
4619 A new child band is created to represent the point loops and it is
4620 inserted between the modified band and its children.
4621 The C<tile_scale_tile_loops> option specifies whether the tile
4622 loops iterators should be scaled by the tile sizes.
4624 A representation of the band can be printed using
4626 #include <isl/band.h>
4627 __isl_give isl_printer *isl_printer_print_band(
4628 __isl_take isl_printer *p,
4629 __isl_keep isl_band *band);
4633 #include <isl/schedule.h>
4634 int isl_options_set_schedule_max_coefficient(
4635 isl_ctx *ctx, int val);
4636 int isl_options_get_schedule_max_coefficient(
4638 int isl_options_set_schedule_max_constant_term(
4639 isl_ctx *ctx, int val);
4640 int isl_options_get_schedule_max_constant_term(
4642 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4643 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4644 int isl_options_set_schedule_maximize_band_depth(
4645 isl_ctx *ctx, int val);
4646 int isl_options_get_schedule_maximize_band_depth(
4648 int isl_options_set_schedule_outer_zero_distance(
4649 isl_ctx *ctx, int val);
4650 int isl_options_get_schedule_outer_zero_distance(
4652 int isl_options_set_schedule_split_scaled(
4653 isl_ctx *ctx, int val);
4654 int isl_options_get_schedule_split_scaled(
4656 int isl_options_set_schedule_algorithm(
4657 isl_ctx *ctx, int val);
4658 int isl_options_get_schedule_algorithm(
4660 int isl_options_set_schedule_separate_components(
4661 isl_ctx *ctx, int val);
4662 int isl_options_get_schedule_separate_components(
4667 =item * schedule_max_coefficient
4669 This option enforces that the coefficients for variable and parameter
4670 dimensions in the calculated schedule are not larger than the specified value.
4671 This option can significantly increase the speed of the scheduling calculation
4672 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4673 this option does not introduce bounds on the variable or parameter
4676 =item * schedule_max_constant_term
4678 This option enforces that the constant coefficients in the calculated schedule
4679 are not larger than the maximal constant term. This option can significantly
4680 increase the speed of the scheduling calculation and may also prevent fusing of
4681 unrelated dimensions. A value of -1 means that this option does not introduce
4682 bounds on the constant coefficients.
4684 =item * schedule_fuse
4686 This option controls the level of fusion.
4687 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4688 resulting schedule will be distributed as much as possible.
4689 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4690 try to fuse loops in the resulting schedule.
4692 =item * schedule_maximize_band_depth
4694 If this option is set, we do not split bands at the point
4695 where we detect splitting is necessary. Instead, we
4696 backtrack and split bands as early as possible. This
4697 reduces the number of splits and maximizes the width of
4698 the bands. Wider bands give more possibilities for tiling.
4699 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4700 then bands will be split as early as possible, even if there is no need.
4701 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4703 =item * schedule_outer_zero_distance
4705 If this option is set, then we try to construct schedules
4706 where the outermost scheduling dimension in each band
4707 results in a zero dependence distance over the proximity
4710 =item * schedule_split_scaled
4712 If this option is set, then we try to construct schedules in which the
4713 constant term is split off from the linear part if the linear parts of
4714 the scheduling rows for all nodes in the graphs have a common non-trivial
4716 The constant term is then placed in a separate band and the linear
4719 =item * schedule_algorithm
4721 Selects the scheduling algorithm to be used.
4722 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4723 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4725 =item * schedule_separate_components
4727 If at any point the dependence graph contains any (weakly connected) components,
4728 then these components are scheduled separately.
4729 If this option is not set, then some iterations of the domains
4730 in these components may be scheduled together.
4731 If this option is set, then the components are given consecutive
4736 =head2 Parametric Vertex Enumeration
4738 The parametric vertex enumeration described in this section
4739 is mainly intended to be used internally and by the C<barvinok>
4742 #include <isl/vertices.h>
4743 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4744 __isl_keep isl_basic_set *bset);
4746 The function C<isl_basic_set_compute_vertices> performs the
4747 actual computation of the parametric vertices and the chamber
4748 decomposition and store the result in an C<isl_vertices> object.
4749 This information can be queried by either iterating over all
4750 the vertices or iterating over all the chambers or cells
4751 and then iterating over all vertices that are active on the chamber.
4753 int isl_vertices_foreach_vertex(
4754 __isl_keep isl_vertices *vertices,
4755 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4758 int isl_vertices_foreach_cell(
4759 __isl_keep isl_vertices *vertices,
4760 int (*fn)(__isl_take isl_cell *cell, void *user),
4762 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4763 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4766 Other operations that can be performed on an C<isl_vertices> object are
4769 isl_ctx *isl_vertices_get_ctx(
4770 __isl_keep isl_vertices *vertices);
4771 int isl_vertices_get_n_vertices(
4772 __isl_keep isl_vertices *vertices);
4773 void isl_vertices_free(__isl_take isl_vertices *vertices);
4775 Vertices can be inspected and destroyed using the following functions.
4777 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4778 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4779 __isl_give isl_basic_set *isl_vertex_get_domain(
4780 __isl_keep isl_vertex *vertex);
4781 __isl_give isl_basic_set *isl_vertex_get_expr(
4782 __isl_keep isl_vertex *vertex);
4783 void isl_vertex_free(__isl_take isl_vertex *vertex);
4785 C<isl_vertex_get_expr> returns a singleton parametric set describing
4786 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4788 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4789 B<rational> basic sets, so they should mainly be used for inspection
4790 and should not be mixed with integer sets.
4792 Chambers can be inspected and destroyed using the following functions.
4794 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4795 __isl_give isl_basic_set *isl_cell_get_domain(
4796 __isl_keep isl_cell *cell);
4797 void isl_cell_free(__isl_take isl_cell *cell);
4801 Although C<isl> is mainly meant to be used as a library,
4802 it also contains some basic applications that use some
4803 of the functionality of C<isl>.
4804 The input may be specified in either the L<isl format>
4805 or the L<PolyLib format>.
4807 =head2 C<isl_polyhedron_sample>
4809 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4810 an integer element of the polyhedron, if there is any.
4811 The first column in the output is the denominator and is always
4812 equal to 1. If the polyhedron contains no integer points,
4813 then a vector of length zero is printed.
4817 C<isl_pip> takes the same input as the C<example> program
4818 from the C<piplib> distribution, i.e., a set of constraints
4819 on the parameters, a line containing only -1 and finally a set
4820 of constraints on a parametric polyhedron.
4821 The coefficients of the parameters appear in the last columns
4822 (but before the final constant column).
4823 The output is the lexicographic minimum of the parametric polyhedron.
4824 As C<isl> currently does not have its own output format, the output
4825 is just a dump of the internal state.
4827 =head2 C<isl_polyhedron_minimize>
4829 C<isl_polyhedron_minimize> computes the minimum of some linear
4830 or affine objective function over the integer points in a polyhedron.
4831 If an affine objective function
4832 is given, then the constant should appear in the last column.
4834 =head2 C<isl_polytope_scan>
4836 Given a polytope, C<isl_polytope_scan> prints
4837 all integer points in the polytope.