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_map *isl_union_map_from_map(
1190 __isl_take isl_map *map);
1191 __isl_give isl_union_set *isl_union_set_from_set(
1192 __isl_take isl_set *set);
1194 The inverse conversions below can only be used if the input
1195 union set or relation is known to contain elements in exactly one
1198 __isl_give isl_set *isl_set_from_union_set(
1199 __isl_take isl_union_set *uset);
1200 __isl_give isl_map *isl_map_from_union_map(
1201 __isl_take isl_union_map *umap);
1203 A zero-dimensional set can be constructed on a given parameter domain
1204 using the following function.
1206 __isl_give isl_set *isl_set_from_params(
1207 __isl_take isl_set *set);
1209 Sets and relations can be copied and freed again using the following
1212 __isl_give isl_basic_set *isl_basic_set_copy(
1213 __isl_keep isl_basic_set *bset);
1214 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1215 __isl_give isl_union_set *isl_union_set_copy(
1216 __isl_keep isl_union_set *uset);
1217 __isl_give isl_basic_map *isl_basic_map_copy(
1218 __isl_keep isl_basic_map *bmap);
1219 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1220 __isl_give isl_union_map *isl_union_map_copy(
1221 __isl_keep isl_union_map *umap);
1222 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1223 void *isl_set_free(__isl_take isl_set *set);
1224 void *isl_union_set_free(__isl_take isl_union_set *uset);
1225 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1226 void isl_map_free(__isl_take isl_map *map);
1227 void *isl_union_map_free(__isl_take isl_union_map *umap);
1229 Other sets and relations can be constructed by starting
1230 from a universe set or relation, adding equality and/or
1231 inequality constraints and then projecting out the
1232 existentially quantified variables, if any.
1233 Constraints can be constructed, manipulated and
1234 added to (or removed from) (basic) sets and relations
1235 using the following functions.
1237 #include <isl/constraint.h>
1238 __isl_give isl_constraint *isl_equality_alloc(
1239 __isl_take isl_local_space *ls);
1240 __isl_give isl_constraint *isl_inequality_alloc(
1241 __isl_take isl_local_space *ls);
1242 __isl_give isl_constraint *isl_constraint_set_constant(
1243 __isl_take isl_constraint *constraint, isl_int v);
1244 __isl_give isl_constraint *isl_constraint_set_constant_si(
1245 __isl_take isl_constraint *constraint, int v);
1246 __isl_give isl_constraint *isl_constraint_set_coefficient(
1247 __isl_take isl_constraint *constraint,
1248 enum isl_dim_type type, int pos, isl_int v);
1249 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1250 __isl_take isl_constraint *constraint,
1251 enum isl_dim_type type, int pos, int v);
1252 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1253 __isl_take isl_basic_map *bmap,
1254 __isl_take isl_constraint *constraint);
1255 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1256 __isl_take isl_basic_set *bset,
1257 __isl_take isl_constraint *constraint);
1258 __isl_give isl_map *isl_map_add_constraint(
1259 __isl_take isl_map *map,
1260 __isl_take isl_constraint *constraint);
1261 __isl_give isl_set *isl_set_add_constraint(
1262 __isl_take isl_set *set,
1263 __isl_take isl_constraint *constraint);
1264 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1265 __isl_take isl_basic_set *bset,
1266 __isl_take isl_constraint *constraint);
1268 For example, to create a set containing the even integers
1269 between 10 and 42, you would use the following code.
1272 isl_local_space *ls;
1274 isl_basic_set *bset;
1276 space = isl_space_set_alloc(ctx, 0, 2);
1277 bset = isl_basic_set_universe(isl_space_copy(space));
1278 ls = isl_local_space_from_space(space);
1280 c = isl_equality_alloc(isl_local_space_copy(ls));
1281 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1282 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1283 bset = isl_basic_set_add_constraint(bset, c);
1285 c = isl_inequality_alloc(isl_local_space_copy(ls));
1286 c = isl_constraint_set_constant_si(c, -10);
1287 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1288 bset = isl_basic_set_add_constraint(bset, c);
1290 c = isl_inequality_alloc(ls);
1291 c = isl_constraint_set_constant_si(c, 42);
1292 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1293 bset = isl_basic_set_add_constraint(bset, c);
1295 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1299 isl_basic_set *bset;
1300 bset = isl_basic_set_read_from_str(ctx,
1301 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1303 A basic set or relation can also be constructed from two matrices
1304 describing the equalities and the inequalities.
1306 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1307 __isl_take isl_space *space,
1308 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1309 enum isl_dim_type c1,
1310 enum isl_dim_type c2, enum isl_dim_type c3,
1311 enum isl_dim_type c4);
1312 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1313 __isl_take isl_space *space,
1314 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1315 enum isl_dim_type c1,
1316 enum isl_dim_type c2, enum isl_dim_type c3,
1317 enum isl_dim_type c4, enum isl_dim_type c5);
1319 The C<isl_dim_type> arguments indicate the order in which
1320 different kinds of variables appear in the input matrices
1321 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1322 C<isl_dim_set> and C<isl_dim_div> for sets and
1323 of C<isl_dim_cst>, C<isl_dim_param>,
1324 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1326 A (basic or union) set or relation can also be constructed from a
1327 (union) (piecewise) (multiple) affine expression
1328 or a list of affine expressions
1329 (See L<"Piecewise Quasi Affine Expressions"> and
1330 L<"Piecewise Multiple Quasi Affine Expressions">).
1332 __isl_give isl_basic_map *isl_basic_map_from_aff(
1333 __isl_take isl_aff *aff);
1334 __isl_give isl_map *isl_map_from_aff(
1335 __isl_take isl_aff *aff);
1336 __isl_give isl_set *isl_set_from_pw_aff(
1337 __isl_take isl_pw_aff *pwaff);
1338 __isl_give isl_map *isl_map_from_pw_aff(
1339 __isl_take isl_pw_aff *pwaff);
1340 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1341 __isl_take isl_space *domain_space,
1342 __isl_take isl_aff_list *list);
1343 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1344 __isl_take isl_multi_aff *maff)
1345 __isl_give isl_map *isl_map_from_multi_aff(
1346 __isl_take isl_multi_aff *maff)
1347 __isl_give isl_set *isl_set_from_pw_multi_aff(
1348 __isl_take isl_pw_multi_aff *pma);
1349 __isl_give isl_map *isl_map_from_pw_multi_aff(
1350 __isl_take isl_pw_multi_aff *pma);
1351 __isl_give isl_union_map *
1352 isl_union_map_from_union_pw_multi_aff(
1353 __isl_take isl_union_pw_multi_aff *upma);
1355 The C<domain_dim> argument describes the domain of the resulting
1356 basic relation. It is required because the C<list> may consist
1357 of zero affine expressions.
1359 =head2 Inspecting Sets and Relations
1361 Usually, the user should not have to care about the actual constraints
1362 of the sets and maps, but should instead apply the abstract operations
1363 explained in the following sections.
1364 Occasionally, however, it may be required to inspect the individual
1365 coefficients of the constraints. This section explains how to do so.
1366 In these cases, it may also be useful to have C<isl> compute
1367 an explicit representation of the existentially quantified variables.
1369 __isl_give isl_set *isl_set_compute_divs(
1370 __isl_take isl_set *set);
1371 __isl_give isl_map *isl_map_compute_divs(
1372 __isl_take isl_map *map);
1373 __isl_give isl_union_set *isl_union_set_compute_divs(
1374 __isl_take isl_union_set *uset);
1375 __isl_give isl_union_map *isl_union_map_compute_divs(
1376 __isl_take isl_union_map *umap);
1378 This explicit representation defines the existentially quantified
1379 variables as integer divisions of the other variables, possibly
1380 including earlier existentially quantified variables.
1381 An explicitly represented existentially quantified variable therefore
1382 has a unique value when the values of the other variables are known.
1383 If, furthermore, the same existentials, i.e., existentials
1384 with the same explicit representations, should appear in the
1385 same order in each of the disjuncts of a set or map, then the user should call
1386 either of the following functions.
1388 __isl_give isl_set *isl_set_align_divs(
1389 __isl_take isl_set *set);
1390 __isl_give isl_map *isl_map_align_divs(
1391 __isl_take isl_map *map);
1393 Alternatively, the existentially quantified variables can be removed
1394 using the following functions, which compute an overapproximation.
1396 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1397 __isl_take isl_basic_set *bset);
1398 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1399 __isl_take isl_basic_map *bmap);
1400 __isl_give isl_set *isl_set_remove_divs(
1401 __isl_take isl_set *set);
1402 __isl_give isl_map *isl_map_remove_divs(
1403 __isl_take isl_map *map);
1405 To iterate over all the sets or maps in a union set or map, use
1407 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1408 int (*fn)(__isl_take isl_set *set, void *user),
1410 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1411 int (*fn)(__isl_take isl_map *map, void *user),
1414 The number of sets or maps in a union set or map can be obtained
1417 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1418 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1420 To extract the set or map in a given space from a union, use
1422 __isl_give isl_set *isl_union_set_extract_set(
1423 __isl_keep isl_union_set *uset,
1424 __isl_take isl_space *space);
1425 __isl_give isl_map *isl_union_map_extract_map(
1426 __isl_keep isl_union_map *umap,
1427 __isl_take isl_space *space);
1429 To iterate over all the basic sets or maps in a set or map, use
1431 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1432 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1434 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1435 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1438 The callback function C<fn> should return 0 if successful and
1439 -1 if an error occurs. In the latter case, or if any other error
1440 occurs, the above functions will return -1.
1442 It should be noted that C<isl> does not guarantee that
1443 the basic sets or maps passed to C<fn> are disjoint.
1444 If this is required, then the user should call one of
1445 the following functions first.
1447 __isl_give isl_set *isl_set_make_disjoint(
1448 __isl_take isl_set *set);
1449 __isl_give isl_map *isl_map_make_disjoint(
1450 __isl_take isl_map *map);
1452 The number of basic sets in a set can be obtained
1455 int isl_set_n_basic_set(__isl_keep isl_set *set);
1457 To iterate over the constraints of a basic set or map, use
1459 #include <isl/constraint.h>
1461 int isl_basic_set_n_constraint(
1462 __isl_keep isl_basic_set *bset);
1463 int isl_basic_set_foreach_constraint(
1464 __isl_keep isl_basic_set *bset,
1465 int (*fn)(__isl_take isl_constraint *c, void *user),
1467 int isl_basic_map_foreach_constraint(
1468 __isl_keep isl_basic_map *bmap,
1469 int (*fn)(__isl_take isl_constraint *c, void *user),
1471 void *isl_constraint_free(__isl_take isl_constraint *c);
1473 Again, the callback function C<fn> should return 0 if successful and
1474 -1 if an error occurs. In the latter case, or if any other error
1475 occurs, the above functions will return -1.
1476 The constraint C<c> represents either an equality or an inequality.
1477 Use the following function to find out whether a constraint
1478 represents an equality. If not, it represents an inequality.
1480 int isl_constraint_is_equality(
1481 __isl_keep isl_constraint *constraint);
1483 The coefficients of the constraints can be inspected using
1484 the following functions.
1486 int isl_constraint_is_lower_bound(
1487 __isl_keep isl_constraint *constraint,
1488 enum isl_dim_type type, unsigned pos);
1489 int isl_constraint_is_upper_bound(
1490 __isl_keep isl_constraint *constraint,
1491 enum isl_dim_type type, unsigned pos);
1492 void isl_constraint_get_constant(
1493 __isl_keep isl_constraint *constraint, isl_int *v);
1494 void isl_constraint_get_coefficient(
1495 __isl_keep isl_constraint *constraint,
1496 enum isl_dim_type type, int pos, isl_int *v);
1497 int isl_constraint_involves_dims(
1498 __isl_keep isl_constraint *constraint,
1499 enum isl_dim_type type, unsigned first, unsigned n);
1501 The explicit representations of the existentially quantified
1502 variables can be inspected using the following function.
1503 Note that the user is only allowed to use this function
1504 if the inspected set or map is the result of a call
1505 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1506 The existentially quantified variable is equal to the floor
1507 of the returned affine expression. The affine expression
1508 itself can be inspected using the functions in
1509 L<"Piecewise Quasi Affine Expressions">.
1511 __isl_give isl_aff *isl_constraint_get_div(
1512 __isl_keep isl_constraint *constraint, int pos);
1514 To obtain the constraints of a basic set or map in matrix
1515 form, use the following functions.
1517 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1518 __isl_keep isl_basic_set *bset,
1519 enum isl_dim_type c1, enum isl_dim_type c2,
1520 enum isl_dim_type c3, enum isl_dim_type c4);
1521 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1522 __isl_keep isl_basic_set *bset,
1523 enum isl_dim_type c1, enum isl_dim_type c2,
1524 enum isl_dim_type c3, enum isl_dim_type c4);
1525 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1526 __isl_keep isl_basic_map *bmap,
1527 enum isl_dim_type c1,
1528 enum isl_dim_type c2, enum isl_dim_type c3,
1529 enum isl_dim_type c4, enum isl_dim_type c5);
1530 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1531 __isl_keep isl_basic_map *bmap,
1532 enum isl_dim_type c1,
1533 enum isl_dim_type c2, enum isl_dim_type c3,
1534 enum isl_dim_type c4, enum isl_dim_type c5);
1536 The C<isl_dim_type> arguments dictate the order in which
1537 different kinds of variables appear in the resulting matrix
1538 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1539 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1541 The number of parameters, input, output or set dimensions can
1542 be obtained using the following functions.
1544 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1545 enum isl_dim_type type);
1546 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1547 enum isl_dim_type type);
1548 unsigned isl_set_dim(__isl_keep isl_set *set,
1549 enum isl_dim_type type);
1550 unsigned isl_map_dim(__isl_keep isl_map *map,
1551 enum isl_dim_type type);
1553 To check whether the description of a set or relation depends
1554 on one or more given dimensions, it is not necessary to iterate over all
1555 constraints. Instead the following functions can be used.
1557 int isl_basic_set_involves_dims(
1558 __isl_keep isl_basic_set *bset,
1559 enum isl_dim_type type, unsigned first, unsigned n);
1560 int isl_set_involves_dims(__isl_keep isl_set *set,
1561 enum isl_dim_type type, unsigned first, unsigned n);
1562 int isl_basic_map_involves_dims(
1563 __isl_keep isl_basic_map *bmap,
1564 enum isl_dim_type type, unsigned first, unsigned n);
1565 int isl_map_involves_dims(__isl_keep isl_map *map,
1566 enum isl_dim_type type, unsigned first, unsigned n);
1568 Similarly, the following functions can be used to check whether
1569 a given dimension is involved in any lower or upper bound.
1571 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1572 enum isl_dim_type type, unsigned pos);
1573 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1574 enum isl_dim_type type, unsigned pos);
1576 The identifiers or names of the domain and range spaces of a set
1577 or relation can be read off or set using the following functions.
1579 __isl_give isl_set *isl_set_set_tuple_id(
1580 __isl_take isl_set *set, __isl_take isl_id *id);
1581 __isl_give isl_set *isl_set_reset_tuple_id(
1582 __isl_take isl_set *set);
1583 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1584 __isl_give isl_id *isl_set_get_tuple_id(
1585 __isl_keep isl_set *set);
1586 __isl_give isl_map *isl_map_set_tuple_id(
1587 __isl_take isl_map *map, enum isl_dim_type type,
1588 __isl_take isl_id *id);
1589 __isl_give isl_map *isl_map_reset_tuple_id(
1590 __isl_take isl_map *map, enum isl_dim_type type);
1591 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1592 enum isl_dim_type type);
1593 __isl_give isl_id *isl_map_get_tuple_id(
1594 __isl_keep isl_map *map, enum isl_dim_type type);
1596 const char *isl_basic_set_get_tuple_name(
1597 __isl_keep isl_basic_set *bset);
1598 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1599 __isl_take isl_basic_set *set, const char *s);
1600 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1601 const char *isl_set_get_tuple_name(
1602 __isl_keep isl_set *set);
1603 const char *isl_basic_map_get_tuple_name(
1604 __isl_keep isl_basic_map *bmap,
1605 enum isl_dim_type type);
1606 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1607 __isl_take isl_basic_map *bmap,
1608 enum isl_dim_type type, const char *s);
1609 const char *isl_map_get_tuple_name(
1610 __isl_keep isl_map *map,
1611 enum isl_dim_type type);
1613 As with C<isl_space_get_tuple_name>, the value returned points to
1614 an internal data structure.
1615 The identifiers, positions or names of individual dimensions can be
1616 read off using the following functions.
1618 __isl_give isl_id *isl_basic_set_get_dim_id(
1619 __isl_keep isl_basic_set *bset,
1620 enum isl_dim_type type, unsigned pos);
1621 __isl_give isl_set *isl_set_set_dim_id(
1622 __isl_take isl_set *set, enum isl_dim_type type,
1623 unsigned pos, __isl_take isl_id *id);
1624 int isl_set_has_dim_id(__isl_keep isl_set *set,
1625 enum isl_dim_type type, unsigned pos);
1626 __isl_give isl_id *isl_set_get_dim_id(
1627 __isl_keep isl_set *set, enum isl_dim_type type,
1629 int isl_basic_map_has_dim_id(
1630 __isl_keep isl_basic_map *bmap,
1631 enum isl_dim_type type, unsigned pos);
1632 __isl_give isl_map *isl_map_set_dim_id(
1633 __isl_take isl_map *map, enum isl_dim_type type,
1634 unsigned pos, __isl_take isl_id *id);
1635 int isl_map_has_dim_id(__isl_keep isl_map *map,
1636 enum isl_dim_type type, unsigned pos);
1637 __isl_give isl_id *isl_map_get_dim_id(
1638 __isl_keep isl_map *map, enum isl_dim_type type,
1641 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1642 enum isl_dim_type type, __isl_keep isl_id *id);
1643 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1644 enum isl_dim_type type, __isl_keep isl_id *id);
1645 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1646 enum isl_dim_type type, const char *name);
1647 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1648 enum isl_dim_type type, const char *name);
1650 const char *isl_constraint_get_dim_name(
1651 __isl_keep isl_constraint *constraint,
1652 enum isl_dim_type type, unsigned pos);
1653 const char *isl_basic_set_get_dim_name(
1654 __isl_keep isl_basic_set *bset,
1655 enum isl_dim_type type, unsigned pos);
1656 int isl_set_has_dim_name(__isl_keep isl_set *set,
1657 enum isl_dim_type type, unsigned pos);
1658 const char *isl_set_get_dim_name(
1659 __isl_keep isl_set *set,
1660 enum isl_dim_type type, unsigned pos);
1661 const char *isl_basic_map_get_dim_name(
1662 __isl_keep isl_basic_map *bmap,
1663 enum isl_dim_type type, unsigned pos);
1664 int isl_map_has_dim_name(__isl_keep isl_map *map,
1665 enum isl_dim_type type, unsigned pos);
1666 const char *isl_map_get_dim_name(
1667 __isl_keep isl_map *map,
1668 enum isl_dim_type type, unsigned pos);
1670 These functions are mostly useful to obtain the identifiers, positions
1671 or names of the parameters. Identifiers of individual dimensions are
1672 essentially only useful for printing. They are ignored by all other
1673 operations and may not be preserved across those operations.
1677 =head3 Unary Properties
1683 The following functions test whether the given set or relation
1684 contains any integer points. The ``plain'' variants do not perform
1685 any computations, but simply check if the given set or relation
1686 is already known to be empty.
1688 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1689 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1690 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1691 int isl_set_is_empty(__isl_keep isl_set *set);
1692 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1693 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1694 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1695 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1696 int isl_map_is_empty(__isl_keep isl_map *map);
1697 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1699 =item * Universality
1701 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1702 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1703 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1705 =item * Single-valuedness
1707 int isl_basic_map_is_single_valued(
1708 __isl_keep isl_basic_map *bmap);
1709 int isl_map_plain_is_single_valued(
1710 __isl_keep isl_map *map);
1711 int isl_map_is_single_valued(__isl_keep isl_map *map);
1712 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1716 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1717 int isl_map_is_injective(__isl_keep isl_map *map);
1718 int isl_union_map_plain_is_injective(
1719 __isl_keep isl_union_map *umap);
1720 int isl_union_map_is_injective(
1721 __isl_keep isl_union_map *umap);
1725 int isl_map_is_bijective(__isl_keep isl_map *map);
1726 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1730 int isl_basic_map_plain_is_fixed(
1731 __isl_keep isl_basic_map *bmap,
1732 enum isl_dim_type type, unsigned pos,
1734 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1735 enum isl_dim_type type, unsigned pos,
1737 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1738 enum isl_dim_type type, unsigned pos,
1741 Check if the relation obviously lies on a hyperplane where the given dimension
1742 has a fixed value and if so, return that value in C<*val>.
1746 To check whether a set is a parameter domain, use this function:
1748 int isl_set_is_params(__isl_keep isl_set *set);
1749 int isl_union_set_is_params(
1750 __isl_keep isl_union_set *uset);
1754 The following functions check whether the domain of the given
1755 (basic) set is a wrapped relation.
1757 int isl_basic_set_is_wrapping(
1758 __isl_keep isl_basic_set *bset);
1759 int isl_set_is_wrapping(__isl_keep isl_set *set);
1761 =item * Internal Product
1763 int isl_basic_map_can_zip(
1764 __isl_keep isl_basic_map *bmap);
1765 int isl_map_can_zip(__isl_keep isl_map *map);
1767 Check whether the product of domain and range of the given relation
1769 i.e., whether both domain and range are nested relations.
1773 int isl_basic_map_can_curry(
1774 __isl_keep isl_basic_map *bmap);
1775 int isl_map_can_curry(__isl_keep isl_map *map);
1777 Check whether the domain of the (basic) relation is a wrapped relation.
1781 =head3 Binary Properties
1787 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1788 __isl_keep isl_set *set2);
1789 int isl_set_is_equal(__isl_keep isl_set *set1,
1790 __isl_keep isl_set *set2);
1791 int isl_union_set_is_equal(
1792 __isl_keep isl_union_set *uset1,
1793 __isl_keep isl_union_set *uset2);
1794 int isl_basic_map_is_equal(
1795 __isl_keep isl_basic_map *bmap1,
1796 __isl_keep isl_basic_map *bmap2);
1797 int isl_map_is_equal(__isl_keep isl_map *map1,
1798 __isl_keep isl_map *map2);
1799 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1800 __isl_keep isl_map *map2);
1801 int isl_union_map_is_equal(
1802 __isl_keep isl_union_map *umap1,
1803 __isl_keep isl_union_map *umap2);
1805 =item * Disjointness
1807 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1808 __isl_keep isl_set *set2);
1812 int isl_basic_set_is_subset(
1813 __isl_keep isl_basic_set *bset1,
1814 __isl_keep isl_basic_set *bset2);
1815 int isl_set_is_subset(__isl_keep isl_set *set1,
1816 __isl_keep isl_set *set2);
1817 int isl_set_is_strict_subset(
1818 __isl_keep isl_set *set1,
1819 __isl_keep isl_set *set2);
1820 int isl_union_set_is_subset(
1821 __isl_keep isl_union_set *uset1,
1822 __isl_keep isl_union_set *uset2);
1823 int isl_union_set_is_strict_subset(
1824 __isl_keep isl_union_set *uset1,
1825 __isl_keep isl_union_set *uset2);
1826 int isl_basic_map_is_subset(
1827 __isl_keep isl_basic_map *bmap1,
1828 __isl_keep isl_basic_map *bmap2);
1829 int isl_basic_map_is_strict_subset(
1830 __isl_keep isl_basic_map *bmap1,
1831 __isl_keep isl_basic_map *bmap2);
1832 int isl_map_is_subset(
1833 __isl_keep isl_map *map1,
1834 __isl_keep isl_map *map2);
1835 int isl_map_is_strict_subset(
1836 __isl_keep isl_map *map1,
1837 __isl_keep isl_map *map2);
1838 int isl_union_map_is_subset(
1839 __isl_keep isl_union_map *umap1,
1840 __isl_keep isl_union_map *umap2);
1841 int isl_union_map_is_strict_subset(
1842 __isl_keep isl_union_map *umap1,
1843 __isl_keep isl_union_map *umap2);
1845 Check whether the first argument is a (strict) subset of the
1850 =head2 Unary Operations
1856 __isl_give isl_set *isl_set_complement(
1857 __isl_take isl_set *set);
1858 __isl_give isl_map *isl_map_complement(
1859 __isl_take isl_map *map);
1863 __isl_give isl_basic_map *isl_basic_map_reverse(
1864 __isl_take isl_basic_map *bmap);
1865 __isl_give isl_map *isl_map_reverse(
1866 __isl_take isl_map *map);
1867 __isl_give isl_union_map *isl_union_map_reverse(
1868 __isl_take isl_union_map *umap);
1872 __isl_give isl_basic_set *isl_basic_set_project_out(
1873 __isl_take isl_basic_set *bset,
1874 enum isl_dim_type type, unsigned first, unsigned n);
1875 __isl_give isl_basic_map *isl_basic_map_project_out(
1876 __isl_take isl_basic_map *bmap,
1877 enum isl_dim_type type, unsigned first, unsigned n);
1878 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1879 enum isl_dim_type type, unsigned first, unsigned n);
1880 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1881 enum isl_dim_type type, unsigned first, unsigned n);
1882 __isl_give isl_basic_set *isl_basic_set_params(
1883 __isl_take isl_basic_set *bset);
1884 __isl_give isl_basic_set *isl_basic_map_domain(
1885 __isl_take isl_basic_map *bmap);
1886 __isl_give isl_basic_set *isl_basic_map_range(
1887 __isl_take isl_basic_map *bmap);
1888 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1889 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1890 __isl_give isl_set *isl_map_domain(
1891 __isl_take isl_map *bmap);
1892 __isl_give isl_set *isl_map_range(
1893 __isl_take isl_map *map);
1894 __isl_give isl_set *isl_union_set_params(
1895 __isl_take isl_union_set *uset);
1896 __isl_give isl_set *isl_union_map_params(
1897 __isl_take isl_union_map *umap);
1898 __isl_give isl_union_set *isl_union_map_domain(
1899 __isl_take isl_union_map *umap);
1900 __isl_give isl_union_set *isl_union_map_range(
1901 __isl_take isl_union_map *umap);
1903 __isl_give isl_basic_map *isl_basic_map_domain_map(
1904 __isl_take isl_basic_map *bmap);
1905 __isl_give isl_basic_map *isl_basic_map_range_map(
1906 __isl_take isl_basic_map *bmap);
1907 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1908 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1909 __isl_give isl_union_map *isl_union_map_domain_map(
1910 __isl_take isl_union_map *umap);
1911 __isl_give isl_union_map *isl_union_map_range_map(
1912 __isl_take isl_union_map *umap);
1914 The functions above construct a (basic, regular or union) relation
1915 that maps (a wrapped version of) the input relation to its domain or range.
1919 __isl_give isl_set *isl_set_eliminate(
1920 __isl_take isl_set *set, enum isl_dim_type type,
1921 unsigned first, unsigned n);
1922 __isl_give isl_basic_map *isl_basic_map_eliminate(
1923 __isl_take isl_basic_map *bmap,
1924 enum isl_dim_type type,
1925 unsigned first, unsigned n);
1926 __isl_give isl_map *isl_map_eliminate(
1927 __isl_take isl_map *map, enum isl_dim_type type,
1928 unsigned first, unsigned n);
1930 Eliminate the coefficients for the given dimensions from the constraints,
1931 without removing the dimensions.
1935 __isl_give isl_basic_set *isl_basic_set_fix(
1936 __isl_take isl_basic_set *bset,
1937 enum isl_dim_type type, unsigned pos,
1939 __isl_give isl_basic_set *isl_basic_set_fix_si(
1940 __isl_take isl_basic_set *bset,
1941 enum isl_dim_type type, unsigned pos, int value);
1942 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1943 enum isl_dim_type type, unsigned pos,
1945 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1946 enum isl_dim_type type, unsigned pos, int value);
1947 __isl_give isl_basic_map *isl_basic_map_fix_si(
1948 __isl_take isl_basic_map *bmap,
1949 enum isl_dim_type type, unsigned pos, int value);
1950 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1951 enum isl_dim_type type, unsigned pos, int value);
1953 Intersect the set or relation with the hyperplane where the given
1954 dimension has the fixed given value.
1956 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1957 __isl_take isl_basic_map *bmap,
1958 enum isl_dim_type type, unsigned pos, int value);
1959 __isl_give isl_set *isl_set_lower_bound(
1960 __isl_take isl_set *set,
1961 enum isl_dim_type type, unsigned pos,
1963 __isl_give isl_set *isl_set_lower_bound_si(
1964 __isl_take isl_set *set,
1965 enum isl_dim_type type, unsigned pos, int value);
1966 __isl_give isl_map *isl_map_lower_bound_si(
1967 __isl_take isl_map *map,
1968 enum isl_dim_type type, unsigned pos, int value);
1969 __isl_give isl_set *isl_set_upper_bound(
1970 __isl_take isl_set *set,
1971 enum isl_dim_type type, unsigned pos,
1973 __isl_give isl_set *isl_set_upper_bound_si(
1974 __isl_take isl_set *set,
1975 enum isl_dim_type type, unsigned pos, int value);
1976 __isl_give isl_map *isl_map_upper_bound_si(
1977 __isl_take isl_map *map,
1978 enum isl_dim_type type, unsigned pos, int value);
1980 Intersect the set or relation with the half-space where the given
1981 dimension has a value bounded by the fixed given value.
1983 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1984 enum isl_dim_type type1, int pos1,
1985 enum isl_dim_type type2, int pos2);
1986 __isl_give isl_basic_map *isl_basic_map_equate(
1987 __isl_take isl_basic_map *bmap,
1988 enum isl_dim_type type1, int pos1,
1989 enum isl_dim_type type2, int pos2);
1990 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1991 enum isl_dim_type type1, int pos1,
1992 enum isl_dim_type type2, int pos2);
1994 Intersect the set or relation with the hyperplane where the given
1995 dimensions are equal to each other.
1997 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
1998 enum isl_dim_type type1, int pos1,
1999 enum isl_dim_type type2, int pos2);
2001 Intersect the relation with the hyperplane where the given
2002 dimensions have opposite values.
2004 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2005 enum isl_dim_type type1, int pos1,
2006 enum isl_dim_type type2, int pos2);
2007 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2008 enum isl_dim_type type1, int pos1,
2009 enum isl_dim_type type2, int pos2);
2011 Intersect the relation with the half-space where the given
2012 dimensions satisfy the given ordering.
2016 __isl_give isl_map *isl_set_identity(
2017 __isl_take isl_set *set);
2018 __isl_give isl_union_map *isl_union_set_identity(
2019 __isl_take isl_union_set *uset);
2021 Construct an identity relation on the given (union) set.
2025 __isl_give isl_basic_set *isl_basic_map_deltas(
2026 __isl_take isl_basic_map *bmap);
2027 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2028 __isl_give isl_union_set *isl_union_map_deltas(
2029 __isl_take isl_union_map *umap);
2031 These functions return a (basic) set containing the differences
2032 between image elements and corresponding domain elements in the input.
2034 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2035 __isl_take isl_basic_map *bmap);
2036 __isl_give isl_map *isl_map_deltas_map(
2037 __isl_take isl_map *map);
2038 __isl_give isl_union_map *isl_union_map_deltas_map(
2039 __isl_take isl_union_map *umap);
2041 The functions above construct a (basic, regular or union) relation
2042 that maps (a wrapped version of) the input relation to its delta set.
2046 Simplify the representation of a set or relation by trying
2047 to combine pairs of basic sets or relations into a single
2048 basic set or relation.
2050 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2051 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2052 __isl_give isl_union_set *isl_union_set_coalesce(
2053 __isl_take isl_union_set *uset);
2054 __isl_give isl_union_map *isl_union_map_coalesce(
2055 __isl_take isl_union_map *umap);
2057 One of the methods for combining pairs of basic sets or relations
2058 can result in coefficients that are much larger than those that appear
2059 in the constraints of the input. By default, the coefficients are
2060 not allowed to grow larger, but this can be changed by unsetting
2061 the following option.
2063 int isl_options_set_coalesce_bounded_wrapping(
2064 isl_ctx *ctx, int val);
2065 int isl_options_get_coalesce_bounded_wrapping(
2068 =item * Detecting equalities
2070 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2071 __isl_take isl_basic_set *bset);
2072 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2073 __isl_take isl_basic_map *bmap);
2074 __isl_give isl_set *isl_set_detect_equalities(
2075 __isl_take isl_set *set);
2076 __isl_give isl_map *isl_map_detect_equalities(
2077 __isl_take isl_map *map);
2078 __isl_give isl_union_set *isl_union_set_detect_equalities(
2079 __isl_take isl_union_set *uset);
2080 __isl_give isl_union_map *isl_union_map_detect_equalities(
2081 __isl_take isl_union_map *umap);
2083 Simplify the representation of a set or relation by detecting implicit
2086 =item * Removing redundant constraints
2088 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2089 __isl_take isl_basic_set *bset);
2090 __isl_give isl_set *isl_set_remove_redundancies(
2091 __isl_take isl_set *set);
2092 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2093 __isl_take isl_basic_map *bmap);
2094 __isl_give isl_map *isl_map_remove_redundancies(
2095 __isl_take isl_map *map);
2099 __isl_give isl_basic_set *isl_set_convex_hull(
2100 __isl_take isl_set *set);
2101 __isl_give isl_basic_map *isl_map_convex_hull(
2102 __isl_take isl_map *map);
2104 If the input set or relation has any existentially quantified
2105 variables, then the result of these operations is currently undefined.
2109 __isl_give isl_basic_set *isl_set_simple_hull(
2110 __isl_take isl_set *set);
2111 __isl_give isl_basic_map *isl_map_simple_hull(
2112 __isl_take isl_map *map);
2113 __isl_give isl_union_map *isl_union_map_simple_hull(
2114 __isl_take isl_union_map *umap);
2116 These functions compute a single basic set or relation
2117 that contains the whole input set or relation.
2118 In particular, the output is described by translates
2119 of the constraints describing the basic sets or relations in the input.
2123 (See \autoref{s:simple hull}.)
2129 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2130 __isl_take isl_basic_set *bset);
2131 __isl_give isl_basic_set *isl_set_affine_hull(
2132 __isl_take isl_set *set);
2133 __isl_give isl_union_set *isl_union_set_affine_hull(
2134 __isl_take isl_union_set *uset);
2135 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2136 __isl_take isl_basic_map *bmap);
2137 __isl_give isl_basic_map *isl_map_affine_hull(
2138 __isl_take isl_map *map);
2139 __isl_give isl_union_map *isl_union_map_affine_hull(
2140 __isl_take isl_union_map *umap);
2142 In case of union sets and relations, the affine hull is computed
2145 =item * Polyhedral hull
2147 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2148 __isl_take isl_set *set);
2149 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2150 __isl_take isl_map *map);
2151 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2152 __isl_take isl_union_set *uset);
2153 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2154 __isl_take isl_union_map *umap);
2156 These functions compute a single basic set or relation
2157 not involving any existentially quantified variables
2158 that contains the whole input set or relation.
2159 In case of union sets and relations, the polyhedral hull is computed
2164 __isl_give isl_basic_set *isl_basic_set_sample(
2165 __isl_take isl_basic_set *bset);
2166 __isl_give isl_basic_set *isl_set_sample(
2167 __isl_take isl_set *set);
2168 __isl_give isl_basic_map *isl_basic_map_sample(
2169 __isl_take isl_basic_map *bmap);
2170 __isl_give isl_basic_map *isl_map_sample(
2171 __isl_take isl_map *map);
2173 If the input (basic) set or relation is non-empty, then return
2174 a singleton subset of the input. Otherwise, return an empty set.
2176 =item * Optimization
2178 #include <isl/ilp.h>
2179 enum isl_lp_result isl_basic_set_max(
2180 __isl_keep isl_basic_set *bset,
2181 __isl_keep isl_aff *obj, isl_int *opt)
2182 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2183 __isl_keep isl_aff *obj, isl_int *opt);
2184 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2185 __isl_keep isl_aff *obj, isl_int *opt);
2187 Compute the minimum or maximum of the integer affine expression C<obj>
2188 over the points in C<set>, returning the result in C<opt>.
2189 The return value may be one of C<isl_lp_error>,
2190 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2192 =item * Parametric optimization
2194 __isl_give isl_pw_aff *isl_set_dim_min(
2195 __isl_take isl_set *set, int pos);
2196 __isl_give isl_pw_aff *isl_set_dim_max(
2197 __isl_take isl_set *set, int pos);
2198 __isl_give isl_pw_aff *isl_map_dim_max(
2199 __isl_take isl_map *map, int pos);
2201 Compute the minimum or maximum of the given set or output dimension
2202 as a function of the parameters (and input dimensions), but independently
2203 of the other set or output dimensions.
2204 For lexicographic optimization, see L<"Lexicographic Optimization">.
2208 The following functions compute either the set of (rational) coefficient
2209 values of valid constraints for the given set or the set of (rational)
2210 values satisfying the constraints with coefficients from the given set.
2211 Internally, these two sets of functions perform essentially the
2212 same operations, except that the set of coefficients is assumed to
2213 be a cone, while the set of values may be any polyhedron.
2214 The current implementation is based on the Farkas lemma and
2215 Fourier-Motzkin elimination, but this may change or be made optional
2216 in future. In particular, future implementations may use different
2217 dualization algorithms or skip the elimination step.
2219 __isl_give isl_basic_set *isl_basic_set_coefficients(
2220 __isl_take isl_basic_set *bset);
2221 __isl_give isl_basic_set *isl_set_coefficients(
2222 __isl_take isl_set *set);
2223 __isl_give isl_union_set *isl_union_set_coefficients(
2224 __isl_take isl_union_set *bset);
2225 __isl_give isl_basic_set *isl_basic_set_solutions(
2226 __isl_take isl_basic_set *bset);
2227 __isl_give isl_basic_set *isl_set_solutions(
2228 __isl_take isl_set *set);
2229 __isl_give isl_union_set *isl_union_set_solutions(
2230 __isl_take isl_union_set *bset);
2234 __isl_give isl_map *isl_map_fixed_power(
2235 __isl_take isl_map *map, isl_int exp);
2236 __isl_give isl_union_map *isl_union_map_fixed_power(
2237 __isl_take isl_union_map *umap, isl_int exp);
2239 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2240 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2241 of C<map> is computed.
2243 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2245 __isl_give isl_union_map *isl_union_map_power(
2246 __isl_take isl_union_map *umap, int *exact);
2248 Compute a parametric representation for all positive powers I<k> of C<map>.
2249 The result maps I<k> to a nested relation corresponding to the
2250 I<k>th power of C<map>.
2251 The result may be an overapproximation. If the result is known to be exact,
2252 then C<*exact> is set to C<1>.
2254 =item * Transitive closure
2256 __isl_give isl_map *isl_map_transitive_closure(
2257 __isl_take isl_map *map, int *exact);
2258 __isl_give isl_union_map *isl_union_map_transitive_closure(
2259 __isl_take isl_union_map *umap, int *exact);
2261 Compute the transitive closure of C<map>.
2262 The result may be an overapproximation. If the result is known to be exact,
2263 then C<*exact> is set to C<1>.
2265 =item * Reaching path lengths
2267 __isl_give isl_map *isl_map_reaching_path_lengths(
2268 __isl_take isl_map *map, int *exact);
2270 Compute a relation that maps each element in the range of C<map>
2271 to the lengths of all paths composed of edges in C<map> that
2272 end up in the given element.
2273 The result may be an overapproximation. If the result is known to be exact,
2274 then C<*exact> is set to C<1>.
2275 To compute the I<maximal> path length, the resulting relation
2276 should be postprocessed by C<isl_map_lexmax>.
2277 In particular, if the input relation is a dependence relation
2278 (mapping sources to sinks), then the maximal path length corresponds
2279 to the free schedule.
2280 Note, however, that C<isl_map_lexmax> expects the maximum to be
2281 finite, so if the path lengths are unbounded (possibly due to
2282 the overapproximation), then you will get an error message.
2286 __isl_give isl_basic_set *isl_basic_map_wrap(
2287 __isl_take isl_basic_map *bmap);
2288 __isl_give isl_set *isl_map_wrap(
2289 __isl_take isl_map *map);
2290 __isl_give isl_union_set *isl_union_map_wrap(
2291 __isl_take isl_union_map *umap);
2292 __isl_give isl_basic_map *isl_basic_set_unwrap(
2293 __isl_take isl_basic_set *bset);
2294 __isl_give isl_map *isl_set_unwrap(
2295 __isl_take isl_set *set);
2296 __isl_give isl_union_map *isl_union_set_unwrap(
2297 __isl_take isl_union_set *uset);
2301 Remove any internal structure of domain (and range) of the given
2302 set or relation. If there is any such internal structure in the input,
2303 then the name of the space is also removed.
2305 __isl_give isl_basic_set *isl_basic_set_flatten(
2306 __isl_take isl_basic_set *bset);
2307 __isl_give isl_set *isl_set_flatten(
2308 __isl_take isl_set *set);
2309 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2310 __isl_take isl_basic_map *bmap);
2311 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2312 __isl_take isl_basic_map *bmap);
2313 __isl_give isl_map *isl_map_flatten_range(
2314 __isl_take isl_map *map);
2315 __isl_give isl_map *isl_map_flatten_domain(
2316 __isl_take isl_map *map);
2317 __isl_give isl_basic_map *isl_basic_map_flatten(
2318 __isl_take isl_basic_map *bmap);
2319 __isl_give isl_map *isl_map_flatten(
2320 __isl_take isl_map *map);
2322 __isl_give isl_map *isl_set_flatten_map(
2323 __isl_take isl_set *set);
2325 The function above constructs a relation
2326 that maps the input set to a flattened version of the set.
2330 Lift the input set to a space with extra dimensions corresponding
2331 to the existentially quantified variables in the input.
2332 In particular, the result lives in a wrapped map where the domain
2333 is the original space and the range corresponds to the original
2334 existentially quantified variables.
2336 __isl_give isl_basic_set *isl_basic_set_lift(
2337 __isl_take isl_basic_set *bset);
2338 __isl_give isl_set *isl_set_lift(
2339 __isl_take isl_set *set);
2340 __isl_give isl_union_set *isl_union_set_lift(
2341 __isl_take isl_union_set *uset);
2343 Given a local space that contains the existentially quantified
2344 variables of a set, a basic relation that, when applied to
2345 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2346 can be constructed using the following function.
2348 #include <isl/local_space.h>
2349 __isl_give isl_basic_map *isl_local_space_lifting(
2350 __isl_take isl_local_space *ls);
2352 =item * Internal Product
2354 __isl_give isl_basic_map *isl_basic_map_zip(
2355 __isl_take isl_basic_map *bmap);
2356 __isl_give isl_map *isl_map_zip(
2357 __isl_take isl_map *map);
2358 __isl_give isl_union_map *isl_union_map_zip(
2359 __isl_take isl_union_map *umap);
2361 Given a relation with nested relations for domain and range,
2362 interchange the range of the domain with the domain of the range.
2366 __isl_give isl_basic_map *isl_basic_map_curry(
2367 __isl_take isl_basic_map *bmap);
2368 __isl_give isl_map *isl_map_curry(
2369 __isl_take isl_map *map);
2370 __isl_give isl_union_map *isl_union_map_curry(
2371 __isl_take isl_union_map *umap);
2373 Given a relation with a nested relation for domain,
2374 move the range of the nested relation out of the domain
2375 and use it as the domain of a nested relation in the range,
2376 with the original range as range of this nested relation.
2378 =item * Aligning parameters
2380 __isl_give isl_set *isl_set_align_params(
2381 __isl_take isl_set *set,
2382 __isl_take isl_space *model);
2383 __isl_give isl_map *isl_map_align_params(
2384 __isl_take isl_map *map,
2385 __isl_take isl_space *model);
2387 Change the order of the parameters of the given set or relation
2388 such that the first parameters match those of C<model>.
2389 This may involve the introduction of extra parameters.
2390 All parameters need to be named.
2392 =item * Dimension manipulation
2394 __isl_give isl_set *isl_set_add_dims(
2395 __isl_take isl_set *set,
2396 enum isl_dim_type type, unsigned n);
2397 __isl_give isl_map *isl_map_add_dims(
2398 __isl_take isl_map *map,
2399 enum isl_dim_type type, unsigned n);
2400 __isl_give isl_set *isl_set_insert_dims(
2401 __isl_take isl_set *set,
2402 enum isl_dim_type type, unsigned pos, unsigned n);
2403 __isl_give isl_map *isl_map_insert_dims(
2404 __isl_take isl_map *map,
2405 enum isl_dim_type type, unsigned pos, unsigned n);
2406 __isl_give isl_basic_set *isl_basic_set_move_dims(
2407 __isl_take isl_basic_set *bset,
2408 enum isl_dim_type dst_type, unsigned dst_pos,
2409 enum isl_dim_type src_type, unsigned src_pos,
2411 __isl_give isl_basic_map *isl_basic_map_move_dims(
2412 __isl_take isl_basic_map *bmap,
2413 enum isl_dim_type dst_type, unsigned dst_pos,
2414 enum isl_dim_type src_type, unsigned src_pos,
2416 __isl_give isl_set *isl_set_move_dims(
2417 __isl_take isl_set *set,
2418 enum isl_dim_type dst_type, unsigned dst_pos,
2419 enum isl_dim_type src_type, unsigned src_pos,
2421 __isl_give isl_map *isl_map_move_dims(
2422 __isl_take isl_map *map,
2423 enum isl_dim_type dst_type, unsigned dst_pos,
2424 enum isl_dim_type src_type, unsigned src_pos,
2427 It is usually not advisable to directly change the (input or output)
2428 space of a set or a relation as this removes the name and the internal
2429 structure of the space. However, the above functions can be useful
2430 to add new parameters, assuming
2431 C<isl_set_align_params> and C<isl_map_align_params>
2436 =head2 Binary Operations
2438 The two arguments of a binary operation not only need to live
2439 in the same C<isl_ctx>, they currently also need to have
2440 the same (number of) parameters.
2442 =head3 Basic Operations
2446 =item * Intersection
2448 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2449 __isl_take isl_basic_set *bset1,
2450 __isl_take isl_basic_set *bset2);
2451 __isl_give isl_basic_set *isl_basic_set_intersect(
2452 __isl_take isl_basic_set *bset1,
2453 __isl_take isl_basic_set *bset2);
2454 __isl_give isl_set *isl_set_intersect_params(
2455 __isl_take isl_set *set,
2456 __isl_take isl_set *params);
2457 __isl_give isl_set *isl_set_intersect(
2458 __isl_take isl_set *set1,
2459 __isl_take isl_set *set2);
2460 __isl_give isl_union_set *isl_union_set_intersect_params(
2461 __isl_take isl_union_set *uset,
2462 __isl_take isl_set *set);
2463 __isl_give isl_union_map *isl_union_map_intersect_params(
2464 __isl_take isl_union_map *umap,
2465 __isl_take isl_set *set);
2466 __isl_give isl_union_set *isl_union_set_intersect(
2467 __isl_take isl_union_set *uset1,
2468 __isl_take isl_union_set *uset2);
2469 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2470 __isl_take isl_basic_map *bmap,
2471 __isl_take isl_basic_set *bset);
2472 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2473 __isl_take isl_basic_map *bmap,
2474 __isl_take isl_basic_set *bset);
2475 __isl_give isl_basic_map *isl_basic_map_intersect(
2476 __isl_take isl_basic_map *bmap1,
2477 __isl_take isl_basic_map *bmap2);
2478 __isl_give isl_map *isl_map_intersect_params(
2479 __isl_take isl_map *map,
2480 __isl_take isl_set *params);
2481 __isl_give isl_map *isl_map_intersect_domain(
2482 __isl_take isl_map *map,
2483 __isl_take isl_set *set);
2484 __isl_give isl_map *isl_map_intersect_range(
2485 __isl_take isl_map *map,
2486 __isl_take isl_set *set);
2487 __isl_give isl_map *isl_map_intersect(
2488 __isl_take isl_map *map1,
2489 __isl_take isl_map *map2);
2490 __isl_give isl_union_map *isl_union_map_intersect_domain(
2491 __isl_take isl_union_map *umap,
2492 __isl_take isl_union_set *uset);
2493 __isl_give isl_union_map *isl_union_map_intersect_range(
2494 __isl_take isl_union_map *umap,
2495 __isl_take isl_union_set *uset);
2496 __isl_give isl_union_map *isl_union_map_intersect(
2497 __isl_take isl_union_map *umap1,
2498 __isl_take isl_union_map *umap2);
2500 The second argument to the C<_params> functions needs to be
2501 a parametric (basic) set. For the other functions, a parametric set
2502 for either argument is only allowed if the other argument is
2503 a parametric set as well.
2507 __isl_give isl_set *isl_basic_set_union(
2508 __isl_take isl_basic_set *bset1,
2509 __isl_take isl_basic_set *bset2);
2510 __isl_give isl_map *isl_basic_map_union(
2511 __isl_take isl_basic_map *bmap1,
2512 __isl_take isl_basic_map *bmap2);
2513 __isl_give isl_set *isl_set_union(
2514 __isl_take isl_set *set1,
2515 __isl_take isl_set *set2);
2516 __isl_give isl_map *isl_map_union(
2517 __isl_take isl_map *map1,
2518 __isl_take isl_map *map2);
2519 __isl_give isl_union_set *isl_union_set_union(
2520 __isl_take isl_union_set *uset1,
2521 __isl_take isl_union_set *uset2);
2522 __isl_give isl_union_map *isl_union_map_union(
2523 __isl_take isl_union_map *umap1,
2524 __isl_take isl_union_map *umap2);
2526 =item * Set difference
2528 __isl_give isl_set *isl_set_subtract(
2529 __isl_take isl_set *set1,
2530 __isl_take isl_set *set2);
2531 __isl_give isl_map *isl_map_subtract(
2532 __isl_take isl_map *map1,
2533 __isl_take isl_map *map2);
2534 __isl_give isl_map *isl_map_subtract_domain(
2535 __isl_take isl_map *map,
2536 __isl_take isl_set *dom);
2537 __isl_give isl_map *isl_map_subtract_range(
2538 __isl_take isl_map *map,
2539 __isl_take isl_set *dom);
2540 __isl_give isl_union_set *isl_union_set_subtract(
2541 __isl_take isl_union_set *uset1,
2542 __isl_take isl_union_set *uset2);
2543 __isl_give isl_union_map *isl_union_map_subtract(
2544 __isl_take isl_union_map *umap1,
2545 __isl_take isl_union_map *umap2);
2549 __isl_give isl_basic_set *isl_basic_set_apply(
2550 __isl_take isl_basic_set *bset,
2551 __isl_take isl_basic_map *bmap);
2552 __isl_give isl_set *isl_set_apply(
2553 __isl_take isl_set *set,
2554 __isl_take isl_map *map);
2555 __isl_give isl_union_set *isl_union_set_apply(
2556 __isl_take isl_union_set *uset,
2557 __isl_take isl_union_map *umap);
2558 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2559 __isl_take isl_basic_map *bmap1,
2560 __isl_take isl_basic_map *bmap2);
2561 __isl_give isl_basic_map *isl_basic_map_apply_range(
2562 __isl_take isl_basic_map *bmap1,
2563 __isl_take isl_basic_map *bmap2);
2564 __isl_give isl_map *isl_map_apply_domain(
2565 __isl_take isl_map *map1,
2566 __isl_take isl_map *map2);
2567 __isl_give isl_union_map *isl_union_map_apply_domain(
2568 __isl_take isl_union_map *umap1,
2569 __isl_take isl_union_map *umap2);
2570 __isl_give isl_map *isl_map_apply_range(
2571 __isl_take isl_map *map1,
2572 __isl_take isl_map *map2);
2573 __isl_give isl_union_map *isl_union_map_apply_range(
2574 __isl_take isl_union_map *umap1,
2575 __isl_take isl_union_map *umap2);
2577 =item * Cartesian Product
2579 __isl_give isl_set *isl_set_product(
2580 __isl_take isl_set *set1,
2581 __isl_take isl_set *set2);
2582 __isl_give isl_union_set *isl_union_set_product(
2583 __isl_take isl_union_set *uset1,
2584 __isl_take isl_union_set *uset2);
2585 __isl_give isl_basic_map *isl_basic_map_domain_product(
2586 __isl_take isl_basic_map *bmap1,
2587 __isl_take isl_basic_map *bmap2);
2588 __isl_give isl_basic_map *isl_basic_map_range_product(
2589 __isl_take isl_basic_map *bmap1,
2590 __isl_take isl_basic_map *bmap2);
2591 __isl_give isl_basic_map *isl_basic_map_product(
2592 __isl_take isl_basic_map *bmap1,
2593 __isl_take isl_basic_map *bmap2);
2594 __isl_give isl_map *isl_map_domain_product(
2595 __isl_take isl_map *map1,
2596 __isl_take isl_map *map2);
2597 __isl_give isl_map *isl_map_range_product(
2598 __isl_take isl_map *map1,
2599 __isl_take isl_map *map2);
2600 __isl_give isl_union_map *isl_union_map_domain_product(
2601 __isl_take isl_union_map *umap1,
2602 __isl_take isl_union_map *umap2);
2603 __isl_give isl_union_map *isl_union_map_range_product(
2604 __isl_take isl_union_map *umap1,
2605 __isl_take isl_union_map *umap2);
2606 __isl_give isl_map *isl_map_product(
2607 __isl_take isl_map *map1,
2608 __isl_take isl_map *map2);
2609 __isl_give isl_union_map *isl_union_map_product(
2610 __isl_take isl_union_map *umap1,
2611 __isl_take isl_union_map *umap2);
2613 The above functions compute the cross product of the given
2614 sets or relations. The domains and ranges of the results
2615 are wrapped maps between domains and ranges of the inputs.
2616 To obtain a ``flat'' product, use the following functions
2619 __isl_give isl_basic_set *isl_basic_set_flat_product(
2620 __isl_take isl_basic_set *bset1,
2621 __isl_take isl_basic_set *bset2);
2622 __isl_give isl_set *isl_set_flat_product(
2623 __isl_take isl_set *set1,
2624 __isl_take isl_set *set2);
2625 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2626 __isl_take isl_basic_map *bmap1,
2627 __isl_take isl_basic_map *bmap2);
2628 __isl_give isl_map *isl_map_flat_domain_product(
2629 __isl_take isl_map *map1,
2630 __isl_take isl_map *map2);
2631 __isl_give isl_map *isl_map_flat_range_product(
2632 __isl_take isl_map *map1,
2633 __isl_take isl_map *map2);
2634 __isl_give isl_union_map *isl_union_map_flat_range_product(
2635 __isl_take isl_union_map *umap1,
2636 __isl_take isl_union_map *umap2);
2637 __isl_give isl_basic_map *isl_basic_map_flat_product(
2638 __isl_take isl_basic_map *bmap1,
2639 __isl_take isl_basic_map *bmap2);
2640 __isl_give isl_map *isl_map_flat_product(
2641 __isl_take isl_map *map1,
2642 __isl_take isl_map *map2);
2644 =item * Simplification
2646 __isl_give isl_basic_set *isl_basic_set_gist(
2647 __isl_take isl_basic_set *bset,
2648 __isl_take isl_basic_set *context);
2649 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2650 __isl_take isl_set *context);
2651 __isl_give isl_set *isl_set_gist_params(
2652 __isl_take isl_set *set,
2653 __isl_take isl_set *context);
2654 __isl_give isl_union_set *isl_union_set_gist(
2655 __isl_take isl_union_set *uset,
2656 __isl_take isl_union_set *context);
2657 __isl_give isl_union_set *isl_union_set_gist_params(
2658 __isl_take isl_union_set *uset,
2659 __isl_take isl_set *set);
2660 __isl_give isl_basic_map *isl_basic_map_gist(
2661 __isl_take isl_basic_map *bmap,
2662 __isl_take isl_basic_map *context);
2663 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2664 __isl_take isl_map *context);
2665 __isl_give isl_map *isl_map_gist_params(
2666 __isl_take isl_map *map,
2667 __isl_take isl_set *context);
2668 __isl_give isl_map *isl_map_gist_domain(
2669 __isl_take isl_map *map,
2670 __isl_take isl_set *context);
2671 __isl_give isl_map *isl_map_gist_range(
2672 __isl_take isl_map *map,
2673 __isl_take isl_set *context);
2674 __isl_give isl_union_map *isl_union_map_gist(
2675 __isl_take isl_union_map *umap,
2676 __isl_take isl_union_map *context);
2677 __isl_give isl_union_map *isl_union_map_gist_params(
2678 __isl_take isl_union_map *umap,
2679 __isl_take isl_set *set);
2680 __isl_give isl_union_map *isl_union_map_gist_domain(
2681 __isl_take isl_union_map *umap,
2682 __isl_take isl_union_set *uset);
2683 __isl_give isl_union_map *isl_union_map_gist_range(
2684 __isl_take isl_union_map *umap,
2685 __isl_take isl_union_set *uset);
2687 The gist operation returns a set or relation that has the
2688 same intersection with the context as the input set or relation.
2689 Any implicit equality in the intersection is made explicit in the result,
2690 while all inequalities that are redundant with respect to the intersection
2692 In case of union sets and relations, the gist operation is performed
2697 =head3 Lexicographic Optimization
2699 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2700 the following functions
2701 compute a set that contains the lexicographic minimum or maximum
2702 of the elements in C<set> (or C<bset>) for those values of the parameters
2703 that satisfy C<dom>.
2704 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2705 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2707 In other words, the union of the parameter values
2708 for which the result is non-empty and of C<*empty>
2711 __isl_give isl_set *isl_basic_set_partial_lexmin(
2712 __isl_take isl_basic_set *bset,
2713 __isl_take isl_basic_set *dom,
2714 __isl_give isl_set **empty);
2715 __isl_give isl_set *isl_basic_set_partial_lexmax(
2716 __isl_take isl_basic_set *bset,
2717 __isl_take isl_basic_set *dom,
2718 __isl_give isl_set **empty);
2719 __isl_give isl_set *isl_set_partial_lexmin(
2720 __isl_take isl_set *set, __isl_take isl_set *dom,
2721 __isl_give isl_set **empty);
2722 __isl_give isl_set *isl_set_partial_lexmax(
2723 __isl_take isl_set *set, __isl_take isl_set *dom,
2724 __isl_give isl_set **empty);
2726 Given a (basic) set C<set> (or C<bset>), the following functions simply
2727 return a set containing the lexicographic minimum or maximum
2728 of the elements in C<set> (or C<bset>).
2729 In case of union sets, the optimum is computed per space.
2731 __isl_give isl_set *isl_basic_set_lexmin(
2732 __isl_take isl_basic_set *bset);
2733 __isl_give isl_set *isl_basic_set_lexmax(
2734 __isl_take isl_basic_set *bset);
2735 __isl_give isl_set *isl_set_lexmin(
2736 __isl_take isl_set *set);
2737 __isl_give isl_set *isl_set_lexmax(
2738 __isl_take isl_set *set);
2739 __isl_give isl_union_set *isl_union_set_lexmin(
2740 __isl_take isl_union_set *uset);
2741 __isl_give isl_union_set *isl_union_set_lexmax(
2742 __isl_take isl_union_set *uset);
2744 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2745 the following functions
2746 compute a relation that maps each element of C<dom>
2747 to the single lexicographic minimum or maximum
2748 of the elements that are associated to that same
2749 element in C<map> (or C<bmap>).
2750 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2751 that contains the elements in C<dom> that do not map
2752 to any elements in C<map> (or C<bmap>).
2753 In other words, the union of the domain of the result and of C<*empty>
2756 __isl_give isl_map *isl_basic_map_partial_lexmax(
2757 __isl_take isl_basic_map *bmap,
2758 __isl_take isl_basic_set *dom,
2759 __isl_give isl_set **empty);
2760 __isl_give isl_map *isl_basic_map_partial_lexmin(
2761 __isl_take isl_basic_map *bmap,
2762 __isl_take isl_basic_set *dom,
2763 __isl_give isl_set **empty);
2764 __isl_give isl_map *isl_map_partial_lexmax(
2765 __isl_take isl_map *map, __isl_take isl_set *dom,
2766 __isl_give isl_set **empty);
2767 __isl_give isl_map *isl_map_partial_lexmin(
2768 __isl_take isl_map *map, __isl_take isl_set *dom,
2769 __isl_give isl_set **empty);
2771 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2772 return a map mapping each element in the domain of
2773 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2774 of all elements associated to that element.
2775 In case of union relations, the optimum is computed per space.
2777 __isl_give isl_map *isl_basic_map_lexmin(
2778 __isl_take isl_basic_map *bmap);
2779 __isl_give isl_map *isl_basic_map_lexmax(
2780 __isl_take isl_basic_map *bmap);
2781 __isl_give isl_map *isl_map_lexmin(
2782 __isl_take isl_map *map);
2783 __isl_give isl_map *isl_map_lexmax(
2784 __isl_take isl_map *map);
2785 __isl_give isl_union_map *isl_union_map_lexmin(
2786 __isl_take isl_union_map *umap);
2787 __isl_give isl_union_map *isl_union_map_lexmax(
2788 __isl_take isl_union_map *umap);
2790 The following functions return their result in the form of
2791 a piecewise multi-affine expression
2792 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2793 but are otherwise equivalent to the corresponding functions
2794 returning a basic set or relation.
2796 __isl_give isl_pw_multi_aff *
2797 isl_basic_map_lexmin_pw_multi_aff(
2798 __isl_take isl_basic_map *bmap);
2799 __isl_give isl_pw_multi_aff *
2800 isl_basic_set_partial_lexmin_pw_multi_aff(
2801 __isl_take isl_basic_set *bset,
2802 __isl_take isl_basic_set *dom,
2803 __isl_give isl_set **empty);
2804 __isl_give isl_pw_multi_aff *
2805 isl_basic_set_partial_lexmax_pw_multi_aff(
2806 __isl_take isl_basic_set *bset,
2807 __isl_take isl_basic_set *dom,
2808 __isl_give isl_set **empty);
2809 __isl_give isl_pw_multi_aff *
2810 isl_basic_map_partial_lexmin_pw_multi_aff(
2811 __isl_take isl_basic_map *bmap,
2812 __isl_take isl_basic_set *dom,
2813 __isl_give isl_set **empty);
2814 __isl_give isl_pw_multi_aff *
2815 isl_basic_map_partial_lexmax_pw_multi_aff(
2816 __isl_take isl_basic_map *bmap,
2817 __isl_take isl_basic_set *dom,
2818 __isl_give isl_set **empty);
2822 Lists are defined over several element types, including
2823 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2824 Here we take lists of C<isl_set>s as an example.
2825 Lists can be created, copied, modified and freed using the following functions.
2827 #include <isl/list.h>
2828 __isl_give isl_set_list *isl_set_list_from_set(
2829 __isl_take isl_set *el);
2830 __isl_give isl_set_list *isl_set_list_alloc(
2831 isl_ctx *ctx, int n);
2832 __isl_give isl_set_list *isl_set_list_copy(
2833 __isl_keep isl_set_list *list);
2834 __isl_give isl_set_list *isl_set_list_add(
2835 __isl_take isl_set_list *list,
2836 __isl_take isl_set *el);
2837 __isl_give isl_set_list *isl_set_list_set_set(
2838 __isl_take isl_set_list *list, int index,
2839 __isl_take isl_set *set);
2840 __isl_give isl_set_list *isl_set_list_concat(
2841 __isl_take isl_set_list *list1,
2842 __isl_take isl_set_list *list2);
2843 void *isl_set_list_free(__isl_take isl_set_list *list);
2845 C<isl_set_list_alloc> creates an empty list with a capacity for
2846 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2849 Lists can be inspected using the following functions.
2851 #include <isl/list.h>
2852 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2853 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2854 __isl_give isl_set *isl_set_list_get_set(
2855 __isl_keep isl_set_list *list, int index);
2856 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2857 int (*fn)(__isl_take isl_set *el, void *user),
2860 Lists can be printed using
2862 #include <isl/list.h>
2863 __isl_give isl_printer *isl_printer_print_set_list(
2864 __isl_take isl_printer *p,
2865 __isl_keep isl_set_list *list);
2869 Vectors can be created, copied and freed using the following functions.
2871 #include <isl/vec.h>
2872 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2874 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2875 void isl_vec_free(__isl_take isl_vec *vec);
2877 Note that the elements of a newly created vector may have arbitrary values.
2878 The elements can be changed and inspected using the following functions.
2880 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2881 int isl_vec_size(__isl_keep isl_vec *vec);
2882 int isl_vec_get_element(__isl_keep isl_vec *vec,
2883 int pos, isl_int *v);
2884 __isl_give isl_vec *isl_vec_set_element(
2885 __isl_take isl_vec *vec, int pos, isl_int v);
2886 __isl_give isl_vec *isl_vec_set_element_si(
2887 __isl_take isl_vec *vec, int pos, int v);
2888 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2890 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2893 C<isl_vec_get_element> will return a negative value if anything went wrong.
2894 In that case, the value of C<*v> is undefined.
2898 Matrices can be created, copied and freed using the following functions.
2900 #include <isl/mat.h>
2901 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2902 unsigned n_row, unsigned n_col);
2903 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2904 void isl_mat_free(__isl_take isl_mat *mat);
2906 Note that the elements of a newly created matrix may have arbitrary values.
2907 The elements can be changed and inspected using the following functions.
2909 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2910 int isl_mat_rows(__isl_keep isl_mat *mat);
2911 int isl_mat_cols(__isl_keep isl_mat *mat);
2912 int isl_mat_get_element(__isl_keep isl_mat *mat,
2913 int row, int col, isl_int *v);
2914 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2915 int row, int col, isl_int v);
2916 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2917 int row, int col, int v);
2919 C<isl_mat_get_element> will return a negative value if anything went wrong.
2920 In that case, the value of C<*v> is undefined.
2922 The following function can be used to compute the (right) inverse
2923 of a matrix, i.e., a matrix such that the product of the original
2924 and the inverse (in that order) is a multiple of the identity matrix.
2925 The input matrix is assumed to be of full row-rank.
2927 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2929 The following function can be used to compute the (right) kernel
2930 (or null space) of a matrix, i.e., a matrix such that the product of
2931 the original and the kernel (in that order) is the zero matrix.
2933 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2935 =head2 Piecewise Quasi Affine Expressions
2937 The zero quasi affine expression on a given domain can be created using
2939 __isl_give isl_aff *isl_aff_zero_on_domain(
2940 __isl_take isl_local_space *ls);
2942 Note that the space in which the resulting object lives is a map space
2943 with the given space as domain and a one-dimensional range.
2945 An empty piecewise quasi affine expression (one with no cells)
2946 or a piecewise quasi affine expression with a single cell can
2947 be created using the following functions.
2949 #include <isl/aff.h>
2950 __isl_give isl_pw_aff *isl_pw_aff_empty(
2951 __isl_take isl_space *space);
2952 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2953 __isl_take isl_set *set, __isl_take isl_aff *aff);
2954 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2955 __isl_take isl_aff *aff);
2957 A piecewise quasi affine expression that is equal to 1 on a set
2958 and 0 outside the set can be created using the following function.
2960 #include <isl/aff.h>
2961 __isl_give isl_pw_aff *isl_set_indicator_function(
2962 __isl_take isl_set *set);
2964 Quasi affine expressions can be copied and freed using
2966 #include <isl/aff.h>
2967 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2968 void *isl_aff_free(__isl_take isl_aff *aff);
2970 __isl_give isl_pw_aff *isl_pw_aff_copy(
2971 __isl_keep isl_pw_aff *pwaff);
2972 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2974 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2975 using the following function. The constraint is required to have
2976 a non-zero coefficient for the specified dimension.
2978 #include <isl/constraint.h>
2979 __isl_give isl_aff *isl_constraint_get_bound(
2980 __isl_keep isl_constraint *constraint,
2981 enum isl_dim_type type, int pos);
2983 The entire affine expression of the constraint can also be extracted
2984 using the following function.
2986 #include <isl/constraint.h>
2987 __isl_give isl_aff *isl_constraint_get_aff(
2988 __isl_keep isl_constraint *constraint);
2990 Conversely, an equality constraint equating
2991 the affine expression to zero or an inequality constraint enforcing
2992 the affine expression to be non-negative, can be constructed using
2994 __isl_give isl_constraint *isl_equality_from_aff(
2995 __isl_take isl_aff *aff);
2996 __isl_give isl_constraint *isl_inequality_from_aff(
2997 __isl_take isl_aff *aff);
2999 The expression can be inspected using
3001 #include <isl/aff.h>
3002 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3003 int isl_aff_dim(__isl_keep isl_aff *aff,
3004 enum isl_dim_type type);
3005 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3006 __isl_keep isl_aff *aff);
3007 __isl_give isl_local_space *isl_aff_get_local_space(
3008 __isl_keep isl_aff *aff);
3009 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3010 enum isl_dim_type type, unsigned pos);
3011 const char *isl_pw_aff_get_dim_name(
3012 __isl_keep isl_pw_aff *pa,
3013 enum isl_dim_type type, unsigned pos);
3014 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3015 enum isl_dim_type type, unsigned pos);
3016 __isl_give isl_id *isl_pw_aff_get_dim_id(
3017 __isl_keep isl_pw_aff *pa,
3018 enum isl_dim_type type, unsigned pos);
3019 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3020 __isl_keep isl_pw_aff *pa,
3021 enum isl_dim_type type);
3022 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3024 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3025 enum isl_dim_type type, int pos, isl_int *v);
3026 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3028 __isl_give isl_aff *isl_aff_get_div(
3029 __isl_keep isl_aff *aff, int pos);
3031 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3032 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3033 int (*fn)(__isl_take isl_set *set,
3034 __isl_take isl_aff *aff,
3035 void *user), void *user);
3037 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3038 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3040 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3041 enum isl_dim_type type, unsigned first, unsigned n);
3042 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3043 enum isl_dim_type type, unsigned first, unsigned n);
3045 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3046 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3047 enum isl_dim_type type);
3048 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3050 It can be modified using
3052 #include <isl/aff.h>
3053 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3054 __isl_take isl_pw_aff *pwaff,
3055 enum isl_dim_type type, __isl_take isl_id *id);
3056 __isl_give isl_aff *isl_aff_set_dim_name(
3057 __isl_take isl_aff *aff, enum isl_dim_type type,
3058 unsigned pos, const char *s);
3059 __isl_give isl_aff *isl_aff_set_dim_id(
3060 __isl_take isl_aff *aff, enum isl_dim_type type,
3061 unsigned pos, __isl_take isl_id *id);
3062 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3063 __isl_take isl_pw_aff *pma,
3064 enum isl_dim_type type, unsigned pos,
3065 __isl_take isl_id *id);
3066 __isl_give isl_aff *isl_aff_set_constant(
3067 __isl_take isl_aff *aff, isl_int v);
3068 __isl_give isl_aff *isl_aff_set_constant_si(
3069 __isl_take isl_aff *aff, int v);
3070 __isl_give isl_aff *isl_aff_set_coefficient(
3071 __isl_take isl_aff *aff,
3072 enum isl_dim_type type, int pos, isl_int v);
3073 __isl_give isl_aff *isl_aff_set_coefficient_si(
3074 __isl_take isl_aff *aff,
3075 enum isl_dim_type type, int pos, int v);
3076 __isl_give isl_aff *isl_aff_set_denominator(
3077 __isl_take isl_aff *aff, isl_int v);
3079 __isl_give isl_aff *isl_aff_add_constant(
3080 __isl_take isl_aff *aff, isl_int v);
3081 __isl_give isl_aff *isl_aff_add_constant_si(
3082 __isl_take isl_aff *aff, int v);
3083 __isl_give isl_aff *isl_aff_add_constant_num(
3084 __isl_take isl_aff *aff, isl_int v);
3085 __isl_give isl_aff *isl_aff_add_constant_num_si(
3086 __isl_take isl_aff *aff, int v);
3087 __isl_give isl_aff *isl_aff_add_coefficient(
3088 __isl_take isl_aff *aff,
3089 enum isl_dim_type type, int pos, isl_int v);
3090 __isl_give isl_aff *isl_aff_add_coefficient_si(
3091 __isl_take isl_aff *aff,
3092 enum isl_dim_type type, int pos, int v);
3094 __isl_give isl_aff *isl_aff_insert_dims(
3095 __isl_take isl_aff *aff,
3096 enum isl_dim_type type, unsigned first, unsigned n);
3097 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3098 __isl_take isl_pw_aff *pwaff,
3099 enum isl_dim_type type, unsigned first, unsigned n);
3100 __isl_give isl_aff *isl_aff_add_dims(
3101 __isl_take isl_aff *aff,
3102 enum isl_dim_type type, unsigned n);
3103 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3104 __isl_take isl_pw_aff *pwaff,
3105 enum isl_dim_type type, unsigned n);
3106 __isl_give isl_aff *isl_aff_drop_dims(
3107 __isl_take isl_aff *aff,
3108 enum isl_dim_type type, unsigned first, unsigned n);
3109 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3110 __isl_take isl_pw_aff *pwaff,
3111 enum isl_dim_type type, unsigned first, unsigned n);
3113 Note that the C<set_constant> and C<set_coefficient> functions
3114 set the I<numerator> of the constant or coefficient, while
3115 C<add_constant> and C<add_coefficient> add an integer value to
3116 the possibly rational constant or coefficient.
3117 The C<add_constant_num> functions add an integer value to
3120 To check whether an affine expressions is obviously zero
3121 or obviously equal to some other affine expression, use
3123 #include <isl/aff.h>
3124 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3125 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3126 __isl_keep isl_aff *aff2);
3127 int isl_pw_aff_plain_is_equal(
3128 __isl_keep isl_pw_aff *pwaff1,
3129 __isl_keep isl_pw_aff *pwaff2);
3133 #include <isl/aff.h>
3134 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3135 __isl_take isl_aff *aff2);
3136 __isl_give isl_pw_aff *isl_pw_aff_add(
3137 __isl_take isl_pw_aff *pwaff1,
3138 __isl_take isl_pw_aff *pwaff2);
3139 __isl_give isl_pw_aff *isl_pw_aff_min(
3140 __isl_take isl_pw_aff *pwaff1,
3141 __isl_take isl_pw_aff *pwaff2);
3142 __isl_give isl_pw_aff *isl_pw_aff_max(
3143 __isl_take isl_pw_aff *pwaff1,
3144 __isl_take isl_pw_aff *pwaff2);
3145 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3146 __isl_take isl_aff *aff2);
3147 __isl_give isl_pw_aff *isl_pw_aff_sub(
3148 __isl_take isl_pw_aff *pwaff1,
3149 __isl_take isl_pw_aff *pwaff2);
3150 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3151 __isl_give isl_pw_aff *isl_pw_aff_neg(
3152 __isl_take isl_pw_aff *pwaff);
3153 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3154 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3155 __isl_take isl_pw_aff *pwaff);
3156 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3157 __isl_give isl_pw_aff *isl_pw_aff_floor(
3158 __isl_take isl_pw_aff *pwaff);
3159 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3161 __isl_give isl_pw_aff *isl_pw_aff_mod(
3162 __isl_take isl_pw_aff *pwaff, isl_int mod);
3163 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3165 __isl_give isl_pw_aff *isl_pw_aff_scale(
3166 __isl_take isl_pw_aff *pwaff, isl_int f);
3167 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3169 __isl_give isl_aff *isl_aff_scale_down_ui(
3170 __isl_take isl_aff *aff, unsigned f);
3171 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3172 __isl_take isl_pw_aff *pwaff, isl_int f);
3174 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3175 __isl_take isl_pw_aff_list *list);
3176 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3177 __isl_take isl_pw_aff_list *list);
3179 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3180 __isl_take isl_pw_aff *pwqp);
3182 __isl_give isl_aff *isl_aff_align_params(
3183 __isl_take isl_aff *aff,
3184 __isl_take isl_space *model);
3185 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3186 __isl_take isl_pw_aff *pwaff,
3187 __isl_take isl_space *model);
3189 __isl_give isl_aff *isl_aff_project_domain_on_params(
3190 __isl_take isl_aff *aff);
3192 __isl_give isl_aff *isl_aff_gist_params(
3193 __isl_take isl_aff *aff,
3194 __isl_take isl_set *context);
3195 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3196 __isl_take isl_set *context);
3197 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3198 __isl_take isl_pw_aff *pwaff,
3199 __isl_take isl_set *context);
3200 __isl_give isl_pw_aff *isl_pw_aff_gist(
3201 __isl_take isl_pw_aff *pwaff,
3202 __isl_take isl_set *context);
3204 __isl_give isl_set *isl_pw_aff_domain(
3205 __isl_take isl_pw_aff *pwaff);
3206 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3207 __isl_take isl_pw_aff *pa,
3208 __isl_take isl_set *set);
3209 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3210 __isl_take isl_pw_aff *pa,
3211 __isl_take isl_set *set);
3213 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3214 __isl_take isl_aff *aff2);
3215 __isl_give isl_pw_aff *isl_pw_aff_mul(
3216 __isl_take isl_pw_aff *pwaff1,
3217 __isl_take isl_pw_aff *pwaff2);
3219 When multiplying two affine expressions, at least one of the two needs
3222 #include <isl/aff.h>
3223 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3224 __isl_take isl_aff *aff);
3225 __isl_give isl_basic_set *isl_aff_le_basic_set(
3226 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3227 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3228 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3229 __isl_give isl_set *isl_pw_aff_eq_set(
3230 __isl_take isl_pw_aff *pwaff1,
3231 __isl_take isl_pw_aff *pwaff2);
3232 __isl_give isl_set *isl_pw_aff_ne_set(
3233 __isl_take isl_pw_aff *pwaff1,
3234 __isl_take isl_pw_aff *pwaff2);
3235 __isl_give isl_set *isl_pw_aff_le_set(
3236 __isl_take isl_pw_aff *pwaff1,
3237 __isl_take isl_pw_aff *pwaff2);
3238 __isl_give isl_set *isl_pw_aff_lt_set(
3239 __isl_take isl_pw_aff *pwaff1,
3240 __isl_take isl_pw_aff *pwaff2);
3241 __isl_give isl_set *isl_pw_aff_ge_set(
3242 __isl_take isl_pw_aff *pwaff1,
3243 __isl_take isl_pw_aff *pwaff2);
3244 __isl_give isl_set *isl_pw_aff_gt_set(
3245 __isl_take isl_pw_aff *pwaff1,
3246 __isl_take isl_pw_aff *pwaff2);
3248 __isl_give isl_set *isl_pw_aff_list_eq_set(
3249 __isl_take isl_pw_aff_list *list1,
3250 __isl_take isl_pw_aff_list *list2);
3251 __isl_give isl_set *isl_pw_aff_list_ne_set(
3252 __isl_take isl_pw_aff_list *list1,
3253 __isl_take isl_pw_aff_list *list2);
3254 __isl_give isl_set *isl_pw_aff_list_le_set(
3255 __isl_take isl_pw_aff_list *list1,
3256 __isl_take isl_pw_aff_list *list2);
3257 __isl_give isl_set *isl_pw_aff_list_lt_set(
3258 __isl_take isl_pw_aff_list *list1,
3259 __isl_take isl_pw_aff_list *list2);
3260 __isl_give isl_set *isl_pw_aff_list_ge_set(
3261 __isl_take isl_pw_aff_list *list1,
3262 __isl_take isl_pw_aff_list *list2);
3263 __isl_give isl_set *isl_pw_aff_list_gt_set(
3264 __isl_take isl_pw_aff_list *list1,
3265 __isl_take isl_pw_aff_list *list2);
3267 The function C<isl_aff_neg_basic_set> returns a basic set
3268 containing those elements in the domain space
3269 of C<aff> where C<aff> is negative.
3270 The function C<isl_aff_ge_basic_set> returns a basic set
3271 containing those elements in the shared space
3272 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3273 The function C<isl_pw_aff_ge_set> returns a set
3274 containing those elements in the shared domain
3275 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3276 The functions operating on C<isl_pw_aff_list> apply the corresponding
3277 C<isl_pw_aff> function to each pair of elements in the two lists.
3279 #include <isl/aff.h>
3280 __isl_give isl_set *isl_pw_aff_nonneg_set(
3281 __isl_take isl_pw_aff *pwaff);
3282 __isl_give isl_set *isl_pw_aff_zero_set(
3283 __isl_take isl_pw_aff *pwaff);
3284 __isl_give isl_set *isl_pw_aff_non_zero_set(
3285 __isl_take isl_pw_aff *pwaff);
3287 The function C<isl_pw_aff_nonneg_set> returns a set
3288 containing those elements in the domain
3289 of C<pwaff> where C<pwaff> is non-negative.
3291 #include <isl/aff.h>
3292 __isl_give isl_pw_aff *isl_pw_aff_cond(
3293 __isl_take isl_pw_aff *cond,
3294 __isl_take isl_pw_aff *pwaff_true,
3295 __isl_take isl_pw_aff *pwaff_false);
3297 The function C<isl_pw_aff_cond> performs a conditional operator
3298 and returns an expression that is equal to C<pwaff_true>
3299 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3300 where C<cond> is zero.
3302 #include <isl/aff.h>
3303 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3304 __isl_take isl_pw_aff *pwaff1,
3305 __isl_take isl_pw_aff *pwaff2);
3306 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3307 __isl_take isl_pw_aff *pwaff1,
3308 __isl_take isl_pw_aff *pwaff2);
3309 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3310 __isl_take isl_pw_aff *pwaff1,
3311 __isl_take isl_pw_aff *pwaff2);
3313 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3314 expression with a domain that is the union of those of C<pwaff1> and
3315 C<pwaff2> and such that on each cell, the quasi-affine expression is
3316 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3317 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3318 associated expression is the defined one.
3320 An expression can be read from input using
3322 #include <isl/aff.h>
3323 __isl_give isl_aff *isl_aff_read_from_str(
3324 isl_ctx *ctx, const char *str);
3325 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3326 isl_ctx *ctx, const char *str);
3328 An expression can be printed using
3330 #include <isl/aff.h>
3331 __isl_give isl_printer *isl_printer_print_aff(
3332 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3334 __isl_give isl_printer *isl_printer_print_pw_aff(
3335 __isl_take isl_printer *p,
3336 __isl_keep isl_pw_aff *pwaff);
3338 =head2 Piecewise Multiple Quasi Affine Expressions
3340 An C<isl_multi_aff> object represents a sequence of
3341 zero or more affine expressions, all defined on the same domain space.
3343 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3346 #include <isl/aff.h>
3347 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3348 __isl_take isl_space *space,
3349 __isl_take isl_aff_list *list);
3351 An empty piecewise multiple quasi affine expression (one with no cells),
3352 the zero piecewise multiple quasi affine expression (with value zero
3353 for each output dimension),
3354 a piecewise multiple quasi affine expression with a single cell (with
3355 either a universe or a specified domain) or
3356 a zero-dimensional piecewise multiple quasi affine expression
3358 can be created using the following functions.
3360 #include <isl/aff.h>
3361 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3362 __isl_take isl_space *space);
3363 __isl_give isl_multi_aff *isl_multi_aff_zero(
3364 __isl_take isl_space *space);
3365 __isl_give isl_multi_aff *isl_multi_aff_identity(
3366 __isl_take isl_space *space);
3367 __isl_give isl_pw_multi_aff *
3368 isl_pw_multi_aff_from_multi_aff(
3369 __isl_take isl_multi_aff *ma);
3370 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3371 __isl_take isl_set *set,
3372 __isl_take isl_multi_aff *maff);
3373 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3374 __isl_take isl_set *set);
3376 __isl_give isl_union_pw_multi_aff *
3377 isl_union_pw_multi_aff_empty(
3378 __isl_take isl_space *space);
3379 __isl_give isl_union_pw_multi_aff *
3380 isl_union_pw_multi_aff_add_pw_multi_aff(
3381 __isl_take isl_union_pw_multi_aff *upma,
3382 __isl_take isl_pw_multi_aff *pma);
3383 __isl_give isl_union_pw_multi_aff *
3384 isl_union_pw_multi_aff_from_domain(
3385 __isl_take isl_union_set *uset);
3387 A piecewise multiple quasi affine expression can also be initialized
3388 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3389 and the C<isl_map> is single-valued.
3391 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3392 __isl_take isl_set *set);
3393 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3394 __isl_take isl_map *map);
3396 Multiple quasi affine expressions can be copied and freed using
3398 #include <isl/aff.h>
3399 __isl_give isl_multi_aff *isl_multi_aff_copy(
3400 __isl_keep isl_multi_aff *maff);
3401 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3403 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3404 __isl_keep isl_pw_multi_aff *pma);
3405 void *isl_pw_multi_aff_free(
3406 __isl_take isl_pw_multi_aff *pma);
3408 __isl_give isl_union_pw_multi_aff *
3409 isl_union_pw_multi_aff_copy(
3410 __isl_keep isl_union_pw_multi_aff *upma);
3411 void *isl_union_pw_multi_aff_free(
3412 __isl_take isl_union_pw_multi_aff *upma);
3414 The expression can be inspected using
3416 #include <isl/aff.h>
3417 isl_ctx *isl_multi_aff_get_ctx(
3418 __isl_keep isl_multi_aff *maff);
3419 isl_ctx *isl_pw_multi_aff_get_ctx(
3420 __isl_keep isl_pw_multi_aff *pma);
3421 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3422 __isl_keep isl_union_pw_multi_aff *upma);
3423 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3424 enum isl_dim_type type);
3425 unsigned isl_pw_multi_aff_dim(
3426 __isl_keep isl_pw_multi_aff *pma,
3427 enum isl_dim_type type);
3428 __isl_give isl_aff *isl_multi_aff_get_aff(
3429 __isl_keep isl_multi_aff *multi, int pos);
3430 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3431 __isl_keep isl_pw_multi_aff *pma, int pos);
3432 const char *isl_pw_multi_aff_get_dim_name(
3433 __isl_keep isl_pw_multi_aff *pma,
3434 enum isl_dim_type type, unsigned pos);
3435 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3436 __isl_keep isl_pw_multi_aff *pma,
3437 enum isl_dim_type type, unsigned pos);
3438 const char *isl_multi_aff_get_tuple_name(
3439 __isl_keep isl_multi_aff *multi,
3440 enum isl_dim_type type);
3441 int isl_pw_multi_aff_has_tuple_name(
3442 __isl_keep isl_pw_multi_aff *pma,
3443 enum isl_dim_type type);
3444 const char *isl_pw_multi_aff_get_tuple_name(
3445 __isl_keep isl_pw_multi_aff *pma,
3446 enum isl_dim_type type);
3447 int isl_pw_multi_aff_has_tuple_id(
3448 __isl_keep isl_pw_multi_aff *pma,
3449 enum isl_dim_type type);
3450 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3451 __isl_keep isl_pw_multi_aff *pma,
3452 enum isl_dim_type type);
3454 int isl_pw_multi_aff_foreach_piece(
3455 __isl_keep isl_pw_multi_aff *pma,
3456 int (*fn)(__isl_take isl_set *set,
3457 __isl_take isl_multi_aff *maff,
3458 void *user), void *user);
3460 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3461 __isl_keep isl_union_pw_multi_aff *upma,
3462 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3463 void *user), void *user);
3465 It can be modified using
3467 #include <isl/aff.h>
3468 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3469 __isl_take isl_multi_aff *multi, int pos,
3470 __isl_take isl_aff *aff);
3471 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3472 __isl_take isl_multi_aff *maff,
3473 enum isl_dim_type type, unsigned pos, const char *s);
3474 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3475 __isl_take isl_multi_aff *maff,
3476 enum isl_dim_type type, __isl_take isl_id *id);
3477 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3478 __isl_take isl_pw_multi_aff *pma,
3479 enum isl_dim_type type, __isl_take isl_id *id);
3481 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3482 __isl_take isl_multi_aff *maff,
3483 enum isl_dim_type type, unsigned first, unsigned n);
3485 To check whether two multiple affine expressions are
3486 obviously equal to each other, use
3488 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3489 __isl_keep isl_multi_aff *maff2);
3490 int isl_pw_multi_aff_plain_is_equal(
3491 __isl_keep isl_pw_multi_aff *pma1,
3492 __isl_keep isl_pw_multi_aff *pma2);
3496 #include <isl/aff.h>
3497 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3498 __isl_take isl_pw_multi_aff *pma1,
3499 __isl_take isl_pw_multi_aff *pma2);
3500 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3501 __isl_take isl_pw_multi_aff *pma1,
3502 __isl_take isl_pw_multi_aff *pma2);
3503 __isl_give isl_multi_aff *isl_multi_aff_add(
3504 __isl_take isl_multi_aff *maff1,
3505 __isl_take isl_multi_aff *maff2);
3506 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3507 __isl_take isl_pw_multi_aff *pma1,
3508 __isl_take isl_pw_multi_aff *pma2);
3509 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3510 __isl_take isl_union_pw_multi_aff *upma1,
3511 __isl_take isl_union_pw_multi_aff *upma2);
3512 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3513 __isl_take isl_pw_multi_aff *pma1,
3514 __isl_take isl_pw_multi_aff *pma2);
3515 __isl_give isl_multi_aff *isl_multi_aff_scale(
3516 __isl_take isl_multi_aff *maff,
3518 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3519 __isl_take isl_pw_multi_aff *pma,
3520 __isl_take isl_set *set);
3521 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3522 __isl_take isl_pw_multi_aff *pma,
3523 __isl_take isl_set *set);
3524 __isl_give isl_multi_aff *isl_multi_aff_lift(
3525 __isl_take isl_multi_aff *maff,
3526 __isl_give isl_local_space **ls);
3527 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3528 __isl_take isl_pw_multi_aff *pma);
3529 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3530 __isl_take isl_multi_aff *maff,
3531 __isl_take isl_set *context);
3532 __isl_give isl_multi_aff *isl_multi_aff_gist(
3533 __isl_take isl_multi_aff *maff,
3534 __isl_take isl_set *context);
3535 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3536 __isl_take isl_pw_multi_aff *pma,
3537 __isl_take isl_set *set);
3538 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3539 __isl_take isl_pw_multi_aff *pma,
3540 __isl_take isl_set *set);
3541 __isl_give isl_set *isl_pw_multi_aff_domain(
3542 __isl_take isl_pw_multi_aff *pma);
3543 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3544 __isl_take isl_union_pw_multi_aff *upma);
3545 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3546 __isl_take isl_multi_aff *ma1,
3547 __isl_take isl_multi_aff *ma2);
3548 __isl_give isl_multi_aff *isl_multi_aff_product(
3549 __isl_take isl_multi_aff *ma1,
3550 __isl_take isl_multi_aff *ma2);
3551 __isl_give isl_pw_multi_aff *
3552 isl_pw_multi_aff_flat_range_product(
3553 __isl_take isl_pw_multi_aff *pma1,
3554 __isl_take isl_pw_multi_aff *pma2);
3555 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3556 __isl_take isl_pw_multi_aff *pma1,
3557 __isl_take isl_pw_multi_aff *pma2);
3558 __isl_give isl_union_pw_multi_aff *
3559 isl_union_pw_multi_aff_flat_range_product(
3560 __isl_take isl_union_pw_multi_aff *upma1,
3561 __isl_take isl_union_pw_multi_aff *upma2);
3563 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3564 then it is assigned the local space that lies at the basis of
3565 the lifting applied.
3567 __isl_give isl_set *isl_multi_aff_lex_le_set(
3568 __isl_take isl_multi_aff *ma1,
3569 __isl_take isl_multi_aff *ma2);
3570 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3571 __isl_take isl_multi_aff *ma1,
3572 __isl_take isl_multi_aff *ma2);
3574 The function C<isl_multi_aff_lex_le_set> returns a set
3575 containing those elements in the shared domain space
3576 where C<ma1> is lexicographically smaller than or
3579 An expression can be read from input using
3581 #include <isl/aff.h>
3582 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3583 isl_ctx *ctx, const char *str);
3584 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3585 isl_ctx *ctx, const char *str);
3587 An expression can be printed using
3589 #include <isl/aff.h>
3590 __isl_give isl_printer *isl_printer_print_multi_aff(
3591 __isl_take isl_printer *p,
3592 __isl_keep isl_multi_aff *maff);
3593 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3594 __isl_take isl_printer *p,
3595 __isl_keep isl_pw_multi_aff *pma);
3596 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3597 __isl_take isl_printer *p,
3598 __isl_keep isl_union_pw_multi_aff *upma);
3602 Points are elements of a set. They can be used to construct
3603 simple sets (boxes) or they can be used to represent the
3604 individual elements of a set.
3605 The zero point (the origin) can be created using
3607 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3609 The coordinates of a point can be inspected, set and changed
3612 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3613 enum isl_dim_type type, int pos, isl_int *v);
3614 __isl_give isl_point *isl_point_set_coordinate(
3615 __isl_take isl_point *pnt,
3616 enum isl_dim_type type, int pos, isl_int v);
3618 __isl_give isl_point *isl_point_add_ui(
3619 __isl_take isl_point *pnt,
3620 enum isl_dim_type type, int pos, unsigned val);
3621 __isl_give isl_point *isl_point_sub_ui(
3622 __isl_take isl_point *pnt,
3623 enum isl_dim_type type, int pos, unsigned val);
3625 Other properties can be obtained using
3627 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3629 Points can be copied or freed using
3631 __isl_give isl_point *isl_point_copy(
3632 __isl_keep isl_point *pnt);
3633 void isl_point_free(__isl_take isl_point *pnt);
3635 A singleton set can be created from a point using
3637 __isl_give isl_basic_set *isl_basic_set_from_point(
3638 __isl_take isl_point *pnt);
3639 __isl_give isl_set *isl_set_from_point(
3640 __isl_take isl_point *pnt);
3642 and a box can be created from two opposite extremal points using
3644 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3645 __isl_take isl_point *pnt1,
3646 __isl_take isl_point *pnt2);
3647 __isl_give isl_set *isl_set_box_from_points(
3648 __isl_take isl_point *pnt1,
3649 __isl_take isl_point *pnt2);
3651 All elements of a B<bounded> (union) set can be enumerated using
3652 the following functions.
3654 int isl_set_foreach_point(__isl_keep isl_set *set,
3655 int (*fn)(__isl_take isl_point *pnt, void *user),
3657 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3658 int (*fn)(__isl_take isl_point *pnt, void *user),
3661 The function C<fn> is called for each integer point in
3662 C<set> with as second argument the last argument of
3663 the C<isl_set_foreach_point> call. The function C<fn>
3664 should return C<0> on success and C<-1> on failure.
3665 In the latter case, C<isl_set_foreach_point> will stop
3666 enumerating and return C<-1> as well.
3667 If the enumeration is performed successfully and to completion,
3668 then C<isl_set_foreach_point> returns C<0>.
3670 To obtain a single point of a (basic) set, use
3672 __isl_give isl_point *isl_basic_set_sample_point(
3673 __isl_take isl_basic_set *bset);
3674 __isl_give isl_point *isl_set_sample_point(
3675 __isl_take isl_set *set);
3677 If C<set> does not contain any (integer) points, then the
3678 resulting point will be ``void'', a property that can be
3681 int isl_point_is_void(__isl_keep isl_point *pnt);
3683 =head2 Piecewise Quasipolynomials
3685 A piecewise quasipolynomial is a particular kind of function that maps
3686 a parametric point to a rational value.
3687 More specifically, a quasipolynomial is a polynomial expression in greatest
3688 integer parts of affine expressions of parameters and variables.
3689 A piecewise quasipolynomial is a subdivision of a given parametric
3690 domain into disjoint cells with a quasipolynomial associated to
3691 each cell. The value of the piecewise quasipolynomial at a given
3692 point is the value of the quasipolynomial associated to the cell
3693 that contains the point. Outside of the union of cells,
3694 the value is assumed to be zero.
3695 For example, the piecewise quasipolynomial
3697 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3699 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3700 A given piecewise quasipolynomial has a fixed domain dimension.
3701 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3702 defined over different domains.
3703 Piecewise quasipolynomials are mainly used by the C<barvinok>
3704 library for representing the number of elements in a parametric set or map.
3705 For example, the piecewise quasipolynomial above represents
3706 the number of points in the map
3708 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3710 =head3 Input and Output
3712 Piecewise quasipolynomials can be read from input using
3714 __isl_give isl_union_pw_qpolynomial *
3715 isl_union_pw_qpolynomial_read_from_str(
3716 isl_ctx *ctx, const char *str);
3718 Quasipolynomials and piecewise quasipolynomials can be printed
3719 using the following functions.
3721 __isl_give isl_printer *isl_printer_print_qpolynomial(
3722 __isl_take isl_printer *p,
3723 __isl_keep isl_qpolynomial *qp);
3725 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3726 __isl_take isl_printer *p,
3727 __isl_keep isl_pw_qpolynomial *pwqp);
3729 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3730 __isl_take isl_printer *p,
3731 __isl_keep isl_union_pw_qpolynomial *upwqp);
3733 The output format of the printer
3734 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3735 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3737 In case of printing in C<ISL_FORMAT_C>, the user may want
3738 to set the names of all dimensions
3740 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3741 __isl_take isl_qpolynomial *qp,
3742 enum isl_dim_type type, unsigned pos,
3744 __isl_give isl_pw_qpolynomial *
3745 isl_pw_qpolynomial_set_dim_name(
3746 __isl_take isl_pw_qpolynomial *pwqp,
3747 enum isl_dim_type type, unsigned pos,
3750 =head3 Creating New (Piecewise) Quasipolynomials
3752 Some simple quasipolynomials can be created using the following functions.
3753 More complicated quasipolynomials can be created by applying
3754 operations such as addition and multiplication
3755 on the resulting quasipolynomials
3757 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3758 __isl_take isl_space *domain);
3759 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3760 __isl_take isl_space *domain);
3761 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3762 __isl_take isl_space *domain);
3763 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3764 __isl_take isl_space *domain);
3765 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3766 __isl_take isl_space *domain);
3767 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3768 __isl_take isl_space *domain,
3769 const isl_int n, const isl_int d);
3770 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3771 __isl_take isl_space *domain,
3772 enum isl_dim_type type, unsigned pos);
3773 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3774 __isl_take isl_aff *aff);
3776 Note that the space in which a quasipolynomial lives is a map space
3777 with a one-dimensional range. The C<domain> argument in some of
3778 the functions above corresponds to the domain of this map space.
3780 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3781 with a single cell can be created using the following functions.
3782 Multiple of these single cell piecewise quasipolynomials can
3783 be combined to create more complicated piecewise quasipolynomials.
3785 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3786 __isl_take isl_space *space);
3787 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3788 __isl_take isl_set *set,
3789 __isl_take isl_qpolynomial *qp);
3790 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3791 __isl_take isl_qpolynomial *qp);
3792 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3793 __isl_take isl_pw_aff *pwaff);
3795 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3796 __isl_take isl_space *space);
3797 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3798 __isl_take isl_pw_qpolynomial *pwqp);
3799 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3800 __isl_take isl_union_pw_qpolynomial *upwqp,
3801 __isl_take isl_pw_qpolynomial *pwqp);
3803 Quasipolynomials can be copied and freed again using the following
3806 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3807 __isl_keep isl_qpolynomial *qp);
3808 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3810 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3811 __isl_keep isl_pw_qpolynomial *pwqp);
3812 void *isl_pw_qpolynomial_free(
3813 __isl_take isl_pw_qpolynomial *pwqp);
3815 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3816 __isl_keep isl_union_pw_qpolynomial *upwqp);
3817 void *isl_union_pw_qpolynomial_free(
3818 __isl_take isl_union_pw_qpolynomial *upwqp);
3820 =head3 Inspecting (Piecewise) Quasipolynomials
3822 To iterate over all piecewise quasipolynomials in a union
3823 piecewise quasipolynomial, use the following function
3825 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3826 __isl_keep isl_union_pw_qpolynomial *upwqp,
3827 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3830 To extract the piecewise quasipolynomial in a given space from a union, use
3832 __isl_give isl_pw_qpolynomial *
3833 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3834 __isl_keep isl_union_pw_qpolynomial *upwqp,
3835 __isl_take isl_space *space);
3837 To iterate over the cells in a piecewise quasipolynomial,
3838 use either of the following two functions
3840 int isl_pw_qpolynomial_foreach_piece(
3841 __isl_keep isl_pw_qpolynomial *pwqp,
3842 int (*fn)(__isl_take isl_set *set,
3843 __isl_take isl_qpolynomial *qp,
3844 void *user), void *user);
3845 int isl_pw_qpolynomial_foreach_lifted_piece(
3846 __isl_keep isl_pw_qpolynomial *pwqp,
3847 int (*fn)(__isl_take isl_set *set,
3848 __isl_take isl_qpolynomial *qp,
3849 void *user), void *user);
3851 As usual, the function C<fn> should return C<0> on success
3852 and C<-1> on failure. The difference between
3853 C<isl_pw_qpolynomial_foreach_piece> and
3854 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3855 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3856 compute unique representations for all existentially quantified
3857 variables and then turn these existentially quantified variables
3858 into extra set variables, adapting the associated quasipolynomial
3859 accordingly. This means that the C<set> passed to C<fn>
3860 will not have any existentially quantified variables, but that
3861 the dimensions of the sets may be different for different
3862 invocations of C<fn>.
3864 To iterate over all terms in a quasipolynomial,
3867 int isl_qpolynomial_foreach_term(
3868 __isl_keep isl_qpolynomial *qp,
3869 int (*fn)(__isl_take isl_term *term,
3870 void *user), void *user);
3872 The terms themselves can be inspected and freed using
3875 unsigned isl_term_dim(__isl_keep isl_term *term,
3876 enum isl_dim_type type);
3877 void isl_term_get_num(__isl_keep isl_term *term,
3879 void isl_term_get_den(__isl_keep isl_term *term,
3881 int isl_term_get_exp(__isl_keep isl_term *term,
3882 enum isl_dim_type type, unsigned pos);
3883 __isl_give isl_aff *isl_term_get_div(
3884 __isl_keep isl_term *term, unsigned pos);
3885 void isl_term_free(__isl_take isl_term *term);
3887 Each term is a product of parameters, set variables and
3888 integer divisions. The function C<isl_term_get_exp>
3889 returns the exponent of a given dimensions in the given term.
3890 The C<isl_int>s in the arguments of C<isl_term_get_num>
3891 and C<isl_term_get_den> need to have been initialized
3892 using C<isl_int_init> before calling these functions.
3894 =head3 Properties of (Piecewise) Quasipolynomials
3896 To check whether a quasipolynomial is actually a constant,
3897 use the following function.
3899 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3900 isl_int *n, isl_int *d);
3902 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3903 then the numerator and denominator of the constant
3904 are returned in C<*n> and C<*d>, respectively.
3906 To check whether two union piecewise quasipolynomials are
3907 obviously equal, use
3909 int isl_union_pw_qpolynomial_plain_is_equal(
3910 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3911 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3913 =head3 Operations on (Piecewise) Quasipolynomials
3915 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3916 __isl_take isl_qpolynomial *qp, isl_int v);
3917 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3918 __isl_take isl_qpolynomial *qp);
3919 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3920 __isl_take isl_qpolynomial *qp1,
3921 __isl_take isl_qpolynomial *qp2);
3922 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3923 __isl_take isl_qpolynomial *qp1,
3924 __isl_take isl_qpolynomial *qp2);
3925 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3926 __isl_take isl_qpolynomial *qp1,
3927 __isl_take isl_qpolynomial *qp2);
3928 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3929 __isl_take isl_qpolynomial *qp, unsigned exponent);
3931 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3932 __isl_take isl_pw_qpolynomial *pwqp1,
3933 __isl_take isl_pw_qpolynomial *pwqp2);
3934 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3935 __isl_take isl_pw_qpolynomial *pwqp1,
3936 __isl_take isl_pw_qpolynomial *pwqp2);
3937 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3938 __isl_take isl_pw_qpolynomial *pwqp1,
3939 __isl_take isl_pw_qpolynomial *pwqp2);
3940 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3941 __isl_take isl_pw_qpolynomial *pwqp);
3942 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3943 __isl_take isl_pw_qpolynomial *pwqp1,
3944 __isl_take isl_pw_qpolynomial *pwqp2);
3945 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3946 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3948 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3949 __isl_take isl_union_pw_qpolynomial *upwqp1,
3950 __isl_take isl_union_pw_qpolynomial *upwqp2);
3951 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3952 __isl_take isl_union_pw_qpolynomial *upwqp1,
3953 __isl_take isl_union_pw_qpolynomial *upwqp2);
3954 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3955 __isl_take isl_union_pw_qpolynomial *upwqp1,
3956 __isl_take isl_union_pw_qpolynomial *upwqp2);
3958 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3959 __isl_take isl_pw_qpolynomial *pwqp,
3960 __isl_take isl_point *pnt);
3962 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3963 __isl_take isl_union_pw_qpolynomial *upwqp,
3964 __isl_take isl_point *pnt);
3966 __isl_give isl_set *isl_pw_qpolynomial_domain(
3967 __isl_take isl_pw_qpolynomial *pwqp);
3968 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3969 __isl_take isl_pw_qpolynomial *pwpq,
3970 __isl_take isl_set *set);
3971 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3972 __isl_take isl_pw_qpolynomial *pwpq,
3973 __isl_take isl_set *set);
3975 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3976 __isl_take isl_union_pw_qpolynomial *upwqp);
3977 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3978 __isl_take isl_union_pw_qpolynomial *upwpq,
3979 __isl_take isl_union_set *uset);
3980 __isl_give isl_union_pw_qpolynomial *
3981 isl_union_pw_qpolynomial_intersect_params(
3982 __isl_take isl_union_pw_qpolynomial *upwpq,
3983 __isl_take isl_set *set);
3985 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
3986 __isl_take isl_qpolynomial *qp,
3987 __isl_take isl_space *model);
3989 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
3990 __isl_take isl_qpolynomial *qp);
3991 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
3992 __isl_take isl_pw_qpolynomial *pwqp);
3994 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
3995 __isl_take isl_union_pw_qpolynomial *upwqp);
3997 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
3998 __isl_take isl_qpolynomial *qp,
3999 __isl_take isl_set *context);
4000 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4001 __isl_take isl_qpolynomial *qp,
4002 __isl_take isl_set *context);
4004 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4005 __isl_take isl_pw_qpolynomial *pwqp,
4006 __isl_take isl_set *context);
4007 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4008 __isl_take isl_pw_qpolynomial *pwqp,
4009 __isl_take isl_set *context);
4011 __isl_give isl_union_pw_qpolynomial *
4012 isl_union_pw_qpolynomial_gist_params(
4013 __isl_take isl_union_pw_qpolynomial *upwqp,
4014 __isl_take isl_set *context);
4015 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4016 __isl_take isl_union_pw_qpolynomial *upwqp,
4017 __isl_take isl_union_set *context);
4019 The gist operation applies the gist operation to each of
4020 the cells in the domain of the input piecewise quasipolynomial.
4021 The context is also exploited
4022 to simplify the quasipolynomials associated to each cell.
4024 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4025 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4026 __isl_give isl_union_pw_qpolynomial *
4027 isl_union_pw_qpolynomial_to_polynomial(
4028 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4030 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4031 the polynomial will be an overapproximation. If C<sign> is negative,
4032 it will be an underapproximation. If C<sign> is zero, the approximation
4033 will lie somewhere in between.
4035 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4037 A piecewise quasipolynomial reduction is a piecewise
4038 reduction (or fold) of quasipolynomials.
4039 In particular, the reduction can be maximum or a minimum.
4040 The objects are mainly used to represent the result of
4041 an upper or lower bound on a quasipolynomial over its domain,
4042 i.e., as the result of the following function.
4044 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4045 __isl_take isl_pw_qpolynomial *pwqp,
4046 enum isl_fold type, int *tight);
4048 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4049 __isl_take isl_union_pw_qpolynomial *upwqp,
4050 enum isl_fold type, int *tight);
4052 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4053 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4054 is the returned bound is known be tight, i.e., for each value
4055 of the parameters there is at least
4056 one element in the domain that reaches the bound.
4057 If the domain of C<pwqp> is not wrapping, then the bound is computed
4058 over all elements in that domain and the result has a purely parametric
4059 domain. If the domain of C<pwqp> is wrapping, then the bound is
4060 computed over the range of the wrapped relation. The domain of the
4061 wrapped relation becomes the domain of the result.
4063 A (piecewise) quasipolynomial reduction can be copied or freed using the
4064 following functions.
4066 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4067 __isl_keep isl_qpolynomial_fold *fold);
4068 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4069 __isl_keep isl_pw_qpolynomial_fold *pwf);
4070 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4071 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4072 void isl_qpolynomial_fold_free(
4073 __isl_take isl_qpolynomial_fold *fold);
4074 void *isl_pw_qpolynomial_fold_free(
4075 __isl_take isl_pw_qpolynomial_fold *pwf);
4076 void *isl_union_pw_qpolynomial_fold_free(
4077 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4079 =head3 Printing Piecewise Quasipolynomial Reductions
4081 Piecewise quasipolynomial reductions can be printed
4082 using the following function.
4084 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4085 __isl_take isl_printer *p,
4086 __isl_keep isl_pw_qpolynomial_fold *pwf);
4087 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4088 __isl_take isl_printer *p,
4089 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4091 For C<isl_printer_print_pw_qpolynomial_fold>,
4092 output format of the printer
4093 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4094 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4095 output format of the printer
4096 needs to be set to C<ISL_FORMAT_ISL>.
4097 In case of printing in C<ISL_FORMAT_C>, the user may want
4098 to set the names of all dimensions
4100 __isl_give isl_pw_qpolynomial_fold *
4101 isl_pw_qpolynomial_fold_set_dim_name(
4102 __isl_take isl_pw_qpolynomial_fold *pwf,
4103 enum isl_dim_type type, unsigned pos,
4106 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4108 To iterate over all piecewise quasipolynomial reductions in a union
4109 piecewise quasipolynomial reduction, use the following function
4111 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4112 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4113 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4114 void *user), void *user);
4116 To iterate over the cells in a piecewise quasipolynomial reduction,
4117 use either of the following two functions
4119 int isl_pw_qpolynomial_fold_foreach_piece(
4120 __isl_keep isl_pw_qpolynomial_fold *pwf,
4121 int (*fn)(__isl_take isl_set *set,
4122 __isl_take isl_qpolynomial_fold *fold,
4123 void *user), void *user);
4124 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4125 __isl_keep isl_pw_qpolynomial_fold *pwf,
4126 int (*fn)(__isl_take isl_set *set,
4127 __isl_take isl_qpolynomial_fold *fold,
4128 void *user), void *user);
4130 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4131 of the difference between these two functions.
4133 To iterate over all quasipolynomials in a reduction, use
4135 int isl_qpolynomial_fold_foreach_qpolynomial(
4136 __isl_keep isl_qpolynomial_fold *fold,
4137 int (*fn)(__isl_take isl_qpolynomial *qp,
4138 void *user), void *user);
4140 =head3 Properties of Piecewise Quasipolynomial Reductions
4142 To check whether two union piecewise quasipolynomial reductions are
4143 obviously equal, use
4145 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4146 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4147 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4149 =head3 Operations on Piecewise Quasipolynomial Reductions
4151 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4152 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4154 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4155 __isl_take isl_pw_qpolynomial_fold *pwf1,
4156 __isl_take isl_pw_qpolynomial_fold *pwf2);
4158 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4159 __isl_take isl_pw_qpolynomial_fold *pwf1,
4160 __isl_take isl_pw_qpolynomial_fold *pwf2);
4162 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4163 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4164 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4166 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4167 __isl_take isl_pw_qpolynomial_fold *pwf,
4168 __isl_take isl_point *pnt);
4170 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4171 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4172 __isl_take isl_point *pnt);
4174 __isl_give isl_pw_qpolynomial_fold *
4175 isl_pw_qpolynomial_fold_intersect_params(
4176 __isl_take isl_pw_qpolynomial_fold *pwf,
4177 __isl_take isl_set *set);
4179 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4180 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4181 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4182 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4183 __isl_take isl_union_set *uset);
4184 __isl_give isl_union_pw_qpolynomial_fold *
4185 isl_union_pw_qpolynomial_fold_intersect_params(
4186 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4187 __isl_take isl_set *set);
4189 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4190 __isl_take isl_pw_qpolynomial_fold *pwf);
4192 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4193 __isl_take isl_pw_qpolynomial_fold *pwf);
4195 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4196 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4198 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4199 __isl_take isl_qpolynomial_fold *fold,
4200 __isl_take isl_set *context);
4201 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4202 __isl_take isl_qpolynomial_fold *fold,
4203 __isl_take isl_set *context);
4205 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4206 __isl_take isl_pw_qpolynomial_fold *pwf,
4207 __isl_take isl_set *context);
4208 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4209 __isl_take isl_pw_qpolynomial_fold *pwf,
4210 __isl_take isl_set *context);
4212 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4213 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4214 __isl_take isl_union_set *context);
4215 __isl_give isl_union_pw_qpolynomial_fold *
4216 isl_union_pw_qpolynomial_fold_gist_params(
4217 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4218 __isl_take isl_set *context);
4220 The gist operation applies the gist operation to each of
4221 the cells in the domain of the input piecewise quasipolynomial reduction.
4222 In future, the operation will also exploit the context
4223 to simplify the quasipolynomial reductions associated to each cell.
4225 __isl_give isl_pw_qpolynomial_fold *
4226 isl_set_apply_pw_qpolynomial_fold(
4227 __isl_take isl_set *set,
4228 __isl_take isl_pw_qpolynomial_fold *pwf,
4230 __isl_give isl_pw_qpolynomial_fold *
4231 isl_map_apply_pw_qpolynomial_fold(
4232 __isl_take isl_map *map,
4233 __isl_take isl_pw_qpolynomial_fold *pwf,
4235 __isl_give isl_union_pw_qpolynomial_fold *
4236 isl_union_set_apply_union_pw_qpolynomial_fold(
4237 __isl_take isl_union_set *uset,
4238 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4240 __isl_give isl_union_pw_qpolynomial_fold *
4241 isl_union_map_apply_union_pw_qpolynomial_fold(
4242 __isl_take isl_union_map *umap,
4243 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4246 The functions taking a map
4247 compose the given map with the given piecewise quasipolynomial reduction.
4248 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4249 over all elements in the intersection of the range of the map
4250 and the domain of the piecewise quasipolynomial reduction
4251 as a function of an element in the domain of the map.
4252 The functions taking a set compute a bound over all elements in the
4253 intersection of the set and the domain of the
4254 piecewise quasipolynomial reduction.
4256 =head2 Dependence Analysis
4258 C<isl> contains specialized functionality for performing
4259 array dataflow analysis. That is, given a I<sink> access relation
4260 and a collection of possible I<source> access relations,
4261 C<isl> can compute relations that describe
4262 for each iteration of the sink access, which iteration
4263 of which of the source access relations was the last
4264 to access the same data element before the given iteration
4266 The resulting dependence relations map source iterations
4267 to the corresponding sink iterations.
4268 To compute standard flow dependences, the sink should be
4269 a read, while the sources should be writes.
4270 If any of the source accesses are marked as being I<may>
4271 accesses, then there will be a dependence from the last
4272 I<must> access B<and> from any I<may> access that follows
4273 this last I<must> access.
4274 In particular, if I<all> sources are I<may> accesses,
4275 then memory based dependence analysis is performed.
4276 If, on the other hand, all sources are I<must> accesses,
4277 then value based dependence analysis is performed.
4279 #include <isl/flow.h>
4281 typedef int (*isl_access_level_before)(void *first, void *second);
4283 __isl_give isl_access_info *isl_access_info_alloc(
4284 __isl_take isl_map *sink,
4285 void *sink_user, isl_access_level_before fn,
4287 __isl_give isl_access_info *isl_access_info_add_source(
4288 __isl_take isl_access_info *acc,
4289 __isl_take isl_map *source, int must,
4291 void *isl_access_info_free(__isl_take isl_access_info *acc);
4293 __isl_give isl_flow *isl_access_info_compute_flow(
4294 __isl_take isl_access_info *acc);
4296 int isl_flow_foreach(__isl_keep isl_flow *deps,
4297 int (*fn)(__isl_take isl_map *dep, int must,
4298 void *dep_user, void *user),
4300 __isl_give isl_map *isl_flow_get_no_source(
4301 __isl_keep isl_flow *deps, int must);
4302 void isl_flow_free(__isl_take isl_flow *deps);
4304 The function C<isl_access_info_compute_flow> performs the actual
4305 dependence analysis. The other functions are used to construct
4306 the input for this function or to read off the output.
4308 The input is collected in an C<isl_access_info>, which can
4309 be created through a call to C<isl_access_info_alloc>.
4310 The arguments to this functions are the sink access relation
4311 C<sink>, a token C<sink_user> used to identify the sink
4312 access to the user, a callback function for specifying the
4313 relative order of source and sink accesses, and the number
4314 of source access relations that will be added.
4315 The callback function has type C<int (*)(void *first, void *second)>.
4316 The function is called with two user supplied tokens identifying
4317 either a source or the sink and it should return the shared nesting
4318 level and the relative order of the two accesses.
4319 In particular, let I<n> be the number of loops shared by
4320 the two accesses. If C<first> precedes C<second> textually,
4321 then the function should return I<2 * n + 1>; otherwise,
4322 it should return I<2 * n>.
4323 The sources can be added to the C<isl_access_info> by performing
4324 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4325 C<must> indicates whether the source is a I<must> access
4326 or a I<may> access. Note that a multi-valued access relation
4327 should only be marked I<must> if every iteration in the domain
4328 of the relation accesses I<all> elements in its image.
4329 The C<source_user> token is again used to identify
4330 the source access. The range of the source access relation
4331 C<source> should have the same dimension as the range
4332 of the sink access relation.
4333 The C<isl_access_info_free> function should usually not be
4334 called explicitly, because it is called implicitly by
4335 C<isl_access_info_compute_flow>.
4337 The result of the dependence analysis is collected in an
4338 C<isl_flow>. There may be elements of
4339 the sink access for which no preceding source access could be
4340 found or for which all preceding sources are I<may> accesses.
4341 The relations containing these elements can be obtained through
4342 calls to C<isl_flow_get_no_source>, the first with C<must> set
4343 and the second with C<must> unset.
4344 In the case of standard flow dependence analysis,
4345 with the sink a read and the sources I<must> writes,
4346 the first relation corresponds to the reads from uninitialized
4347 array elements and the second relation is empty.
4348 The actual flow dependences can be extracted using
4349 C<isl_flow_foreach>. This function will call the user-specified
4350 callback function C<fn> for each B<non-empty> dependence between
4351 a source and the sink. The callback function is called
4352 with four arguments, the actual flow dependence relation
4353 mapping source iterations to sink iterations, a boolean that
4354 indicates whether it is a I<must> or I<may> dependence, a token
4355 identifying the source and an additional C<void *> with value
4356 equal to the third argument of the C<isl_flow_foreach> call.
4357 A dependence is marked I<must> if it originates from a I<must>
4358 source and if it is not followed by any I<may> sources.
4360 After finishing with an C<isl_flow>, the user should call
4361 C<isl_flow_free> to free all associated memory.
4363 A higher-level interface to dependence analysis is provided
4364 by the following function.
4366 #include <isl/flow.h>
4368 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4369 __isl_take isl_union_map *must_source,
4370 __isl_take isl_union_map *may_source,
4371 __isl_take isl_union_map *schedule,
4372 __isl_give isl_union_map **must_dep,
4373 __isl_give isl_union_map **may_dep,
4374 __isl_give isl_union_map **must_no_source,
4375 __isl_give isl_union_map **may_no_source);
4377 The arrays are identified by the tuple names of the ranges
4378 of the accesses. The iteration domains by the tuple names
4379 of the domains of the accesses and of the schedule.
4380 The relative order of the iteration domains is given by the
4381 schedule. The relations returned through C<must_no_source>
4382 and C<may_no_source> are subsets of C<sink>.
4383 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4384 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4385 any of the other arguments is treated as an error.
4387 =head3 Interaction with Dependence Analysis
4389 During the dependence analysis, we frequently need to perform
4390 the following operation. Given a relation between sink iterations
4391 and potential source iterations from a particular source domain,
4392 what is the last potential source iteration corresponding to each
4393 sink iteration. It can sometimes be convenient to adjust
4394 the set of potential source iterations before or after each such operation.
4395 The prototypical example is fuzzy array dataflow analysis,
4396 where we need to analyze if, based on data-dependent constraints,
4397 the sink iteration can ever be executed without one or more of
4398 the corresponding potential source iterations being executed.
4399 If so, we can introduce extra parameters and select an unknown
4400 but fixed source iteration from the potential source iterations.
4401 To be able to perform such manipulations, C<isl> provides the following
4404 #include <isl/flow.h>
4406 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4407 __isl_keep isl_map *source_map,
4408 __isl_keep isl_set *sink, void *source_user,
4410 __isl_give isl_access_info *isl_access_info_set_restrict(
4411 __isl_take isl_access_info *acc,
4412 isl_access_restrict fn, void *user);
4414 The function C<isl_access_info_set_restrict> should be called
4415 before calling C<isl_access_info_compute_flow> and registers a callback function
4416 that will be called any time C<isl> is about to compute the last
4417 potential source. The first argument is the (reverse) proto-dependence,
4418 mapping sink iterations to potential source iterations.
4419 The second argument represents the sink iterations for which
4420 we want to compute the last source iteration.
4421 The third argument is the token corresponding to the source
4422 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4423 The callback is expected to return a restriction on either the input or
4424 the output of the operation computing the last potential source.
4425 If the input needs to be restricted then restrictions are needed
4426 for both the source and the sink iterations. The sink iterations
4427 and the potential source iterations will be intersected with these sets.
4428 If the output needs to be restricted then only a restriction on the source
4429 iterations is required.
4430 If any error occurs, the callback should return C<NULL>.
4431 An C<isl_restriction> object can be created, freed and inspected
4432 using the following functions.
4434 #include <isl/flow.h>
4436 __isl_give isl_restriction *isl_restriction_input(
4437 __isl_take isl_set *source_restr,
4438 __isl_take isl_set *sink_restr);
4439 __isl_give isl_restriction *isl_restriction_output(
4440 __isl_take isl_set *source_restr);
4441 __isl_give isl_restriction *isl_restriction_none(
4442 __isl_take isl_map *source_map);
4443 __isl_give isl_restriction *isl_restriction_empty(
4444 __isl_take isl_map *source_map);
4445 void *isl_restriction_free(
4446 __isl_take isl_restriction *restr);
4447 isl_ctx *isl_restriction_get_ctx(
4448 __isl_keep isl_restriction *restr);
4450 C<isl_restriction_none> and C<isl_restriction_empty> are special
4451 cases of C<isl_restriction_input>. C<isl_restriction_none>
4452 is essentially equivalent to
4454 isl_restriction_input(isl_set_universe(
4455 isl_space_range(isl_map_get_space(source_map))),
4457 isl_space_domain(isl_map_get_space(source_map))));
4459 whereas C<isl_restriction_empty> is essentially equivalent to
4461 isl_restriction_input(isl_set_empty(
4462 isl_space_range(isl_map_get_space(source_map))),
4464 isl_space_domain(isl_map_get_space(source_map))));
4468 B<The functionality described in this section is fairly new
4469 and may be subject to change.>
4471 The following function can be used to compute a schedule
4472 for a union of domains.
4473 By default, the algorithm used to construct the schedule is similar
4474 to that of C<Pluto>.
4475 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4477 The generated schedule respects all C<validity> dependences.
4478 That is, all dependence distances over these dependences in the
4479 scheduled space are lexicographically positive.
4480 The default algorithm tries to minimize the dependence distances over
4481 C<proximity> dependences.
4482 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4483 for groups of domains where the dependence distances have only
4484 non-negative values.
4485 When using Feautrier's algorithm, the C<proximity> dependence
4486 distances are only minimized during the extension to a
4487 full-dimensional schedule.
4489 #include <isl/schedule.h>
4490 __isl_give isl_schedule *isl_union_set_compute_schedule(
4491 __isl_take isl_union_set *domain,
4492 __isl_take isl_union_map *validity,
4493 __isl_take isl_union_map *proximity);
4494 void *isl_schedule_free(__isl_take isl_schedule *sched);
4496 A mapping from the domains to the scheduled space can be obtained
4497 from an C<isl_schedule> using the following function.
4499 __isl_give isl_union_map *isl_schedule_get_map(
4500 __isl_keep isl_schedule *sched);
4502 A representation of the schedule can be printed using
4504 __isl_give isl_printer *isl_printer_print_schedule(
4505 __isl_take isl_printer *p,
4506 __isl_keep isl_schedule *schedule);
4508 A representation of the schedule as a forest of bands can be obtained
4509 using the following function.
4511 __isl_give isl_band_list *isl_schedule_get_band_forest(
4512 __isl_keep isl_schedule *schedule);
4514 The individual bands can be visited in depth-first post-order
4515 using the following function.
4517 #include <isl/schedule.h>
4518 int isl_schedule_foreach_band(
4519 __isl_keep isl_schedule *sched,
4520 int (*fn)(__isl_keep isl_band *band, void *user),
4523 The list can be manipulated as explained in L<"Lists">.
4524 The bands inside the list can be copied and freed using the following
4527 #include <isl/band.h>
4528 __isl_give isl_band *isl_band_copy(
4529 __isl_keep isl_band *band);
4530 void *isl_band_free(__isl_take isl_band *band);
4532 Each band contains zero or more scheduling dimensions.
4533 These are referred to as the members of the band.
4534 The section of the schedule that corresponds to the band is
4535 referred to as the partial schedule of the band.
4536 For those nodes that participate in a band, the outer scheduling
4537 dimensions form the prefix schedule, while the inner scheduling
4538 dimensions form the suffix schedule.
4539 That is, if we take a cut of the band forest, then the union of
4540 the concatenations of the prefix, partial and suffix schedules of
4541 each band in the cut is equal to the entire schedule (modulo
4542 some possible padding at the end with zero scheduling dimensions).
4543 The properties of a band can be inspected using the following functions.
4545 #include <isl/band.h>
4546 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4548 int isl_band_has_children(__isl_keep isl_band *band);
4549 __isl_give isl_band_list *isl_band_get_children(
4550 __isl_keep isl_band *band);
4552 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4553 __isl_keep isl_band *band);
4554 __isl_give isl_union_map *isl_band_get_partial_schedule(
4555 __isl_keep isl_band *band);
4556 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4557 __isl_keep isl_band *band);
4559 int isl_band_n_member(__isl_keep isl_band *band);
4560 int isl_band_member_is_zero_distance(
4561 __isl_keep isl_band *band, int pos);
4563 int isl_band_list_foreach_band(
4564 __isl_keep isl_band_list *list,
4565 int (*fn)(__isl_keep isl_band *band, void *user),
4568 Note that a scheduling dimension is considered to be ``zero
4569 distance'' if it does not carry any proximity dependences
4571 That is, if the dependence distances of the proximity
4572 dependences are all zero in that direction (for fixed
4573 iterations of outer bands).
4574 Like C<isl_schedule_foreach_band>,
4575 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4576 in depth-first post-order.
4578 A band can be tiled using the following function.
4580 #include <isl/band.h>
4581 int isl_band_tile(__isl_keep isl_band *band,
4582 __isl_take isl_vec *sizes);
4584 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4586 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4588 The C<isl_band_tile> function tiles the band using the given tile sizes
4589 inside its schedule.
4590 A new child band is created to represent the point loops and it is
4591 inserted between the modified band and its children.
4592 The C<tile_scale_tile_loops> option specifies whether the tile
4593 loops iterators should be scaled by the tile sizes.
4595 A representation of the band can be printed using
4597 #include <isl/band.h>
4598 __isl_give isl_printer *isl_printer_print_band(
4599 __isl_take isl_printer *p,
4600 __isl_keep isl_band *band);
4604 #include <isl/schedule.h>
4605 int isl_options_set_schedule_max_coefficient(
4606 isl_ctx *ctx, int val);
4607 int isl_options_get_schedule_max_coefficient(
4609 int isl_options_set_schedule_max_constant_term(
4610 isl_ctx *ctx, int val);
4611 int isl_options_get_schedule_max_constant_term(
4613 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4614 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4615 int isl_options_set_schedule_maximize_band_depth(
4616 isl_ctx *ctx, int val);
4617 int isl_options_get_schedule_maximize_band_depth(
4619 int isl_options_set_schedule_outer_zero_distance(
4620 isl_ctx *ctx, int val);
4621 int isl_options_get_schedule_outer_zero_distance(
4623 int isl_options_set_schedule_split_scaled(
4624 isl_ctx *ctx, int val);
4625 int isl_options_get_schedule_split_scaled(
4627 int isl_options_set_schedule_algorithm(
4628 isl_ctx *ctx, int val);
4629 int isl_options_get_schedule_algorithm(
4631 int isl_options_set_schedule_separate_components(
4632 isl_ctx *ctx, int val);
4633 int isl_options_get_schedule_separate_components(
4638 =item * schedule_max_coefficient
4640 This option enforces that the coefficients for variable and parameter
4641 dimensions in the calculated schedule are not larger than the specified value.
4642 This option can significantly increase the speed of the scheduling calculation
4643 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4644 this option does not introduce bounds on the variable or parameter
4647 =item * schedule_max_constant_term
4649 This option enforces that the constant coefficients in the calculated schedule
4650 are not larger than the maximal constant term. This option can significantly
4651 increase the speed of the scheduling calculation and may also prevent fusing of
4652 unrelated dimensions. A value of -1 means that this option does not introduce
4653 bounds on the constant coefficients.
4655 =item * schedule_fuse
4657 This option controls the level of fusion.
4658 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4659 resulting schedule will be distributed as much as possible.
4660 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4661 try to fuse loops in the resulting schedule.
4663 =item * schedule_maximize_band_depth
4665 If this option is set, we do not split bands at the point
4666 where we detect splitting is necessary. Instead, we
4667 backtrack and split bands as early as possible. This
4668 reduces the number of splits and maximizes the width of
4669 the bands. Wider bands give more possibilities for tiling.
4670 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4671 then bands will be split as early as possible, even if there is no need.
4672 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4674 =item * schedule_outer_zero_distance
4676 If this option is set, then we try to construct schedules
4677 where the outermost scheduling dimension in each band
4678 results in a zero dependence distance over the proximity
4681 =item * schedule_split_scaled
4683 If this option is set, then we try to construct schedules in which the
4684 constant term is split off from the linear part if the linear parts of
4685 the scheduling rows for all nodes in the graphs have a common non-trivial
4687 The constant term is then placed in a separate band and the linear
4690 =item * schedule_algorithm
4692 Selects the scheduling algorithm to be used.
4693 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4694 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4696 =item * schedule_separate_components
4698 If at any point the dependence graph contains any (weakly connected) components,
4699 then these components are scheduled separately.
4700 If this option is not set, then some iterations of the domains
4701 in these components may be scheduled together.
4702 If this option is set, then the components are given consecutive
4707 =head2 Parametric Vertex Enumeration
4709 The parametric vertex enumeration described in this section
4710 is mainly intended to be used internally and by the C<barvinok>
4713 #include <isl/vertices.h>
4714 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4715 __isl_keep isl_basic_set *bset);
4717 The function C<isl_basic_set_compute_vertices> performs the
4718 actual computation of the parametric vertices and the chamber
4719 decomposition and store the result in an C<isl_vertices> object.
4720 This information can be queried by either iterating over all
4721 the vertices or iterating over all the chambers or cells
4722 and then iterating over all vertices that are active on the chamber.
4724 int isl_vertices_foreach_vertex(
4725 __isl_keep isl_vertices *vertices,
4726 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4729 int isl_vertices_foreach_cell(
4730 __isl_keep isl_vertices *vertices,
4731 int (*fn)(__isl_take isl_cell *cell, void *user),
4733 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4734 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4737 Other operations that can be performed on an C<isl_vertices> object are
4740 isl_ctx *isl_vertices_get_ctx(
4741 __isl_keep isl_vertices *vertices);
4742 int isl_vertices_get_n_vertices(
4743 __isl_keep isl_vertices *vertices);
4744 void isl_vertices_free(__isl_take isl_vertices *vertices);
4746 Vertices can be inspected and destroyed using the following functions.
4748 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4749 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4750 __isl_give isl_basic_set *isl_vertex_get_domain(
4751 __isl_keep isl_vertex *vertex);
4752 __isl_give isl_basic_set *isl_vertex_get_expr(
4753 __isl_keep isl_vertex *vertex);
4754 void isl_vertex_free(__isl_take isl_vertex *vertex);
4756 C<isl_vertex_get_expr> returns a singleton parametric set describing
4757 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4759 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4760 B<rational> basic sets, so they should mainly be used for inspection
4761 and should not be mixed with integer sets.
4763 Chambers can be inspected and destroyed using the following functions.
4765 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4766 __isl_give isl_basic_set *isl_cell_get_domain(
4767 __isl_keep isl_cell *cell);
4768 void isl_cell_free(__isl_take isl_cell *cell);
4772 Although C<isl> is mainly meant to be used as a library,
4773 it also contains some basic applications that use some
4774 of the functionality of C<isl>.
4775 The input may be specified in either the L<isl format>
4776 or the L<PolyLib format>.
4778 =head2 C<isl_polyhedron_sample>
4780 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4781 an integer element of the polyhedron, if there is any.
4782 The first column in the output is the denominator and is always
4783 equal to 1. If the polyhedron contains no integer points,
4784 then a vector of length zero is printed.
4788 C<isl_pip> takes the same input as the C<example> program
4789 from the C<piplib> distribution, i.e., a set of constraints
4790 on the parameters, a line containing only -1 and finally a set
4791 of constraints on a parametric polyhedron.
4792 The coefficients of the parameters appear in the last columns
4793 (but before the final constant column).
4794 The output is the lexicographic minimum of the parametric polyhedron.
4795 As C<isl> currently does not have its own output format, the output
4796 is just a dump of the internal state.
4798 =head2 C<isl_polyhedron_minimize>
4800 C<isl_polyhedron_minimize> computes the minimum of some linear
4801 or affine objective function over the integer points in a polyhedron.
4802 If an affine objective function
4803 is given, then the constant should appear in the last column.
4805 =head2 C<isl_polytope_scan>
4807 Given a polytope, C<isl_polytope_scan> prints
4808 all integer points in the polytope.