3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
173 The source of C<isl> can be obtained either as a tarball
174 or from the git repository. Both are available from
175 L<http://freshmeat.net/projects/isl/>.
176 The installation process depends on how you obtained
179 =head2 Installation from the git repository
183 =item 1 Clone or update the repository
185 The first time the source is obtained, you need to clone
188 git clone git://repo.or.cz/isl.git
190 To obtain updates, you need to pull in the latest changes
194 =item 2 Generate C<configure>
200 After performing the above steps, continue
201 with the L<Common installation instructions>.
203 =head2 Common installation instructions
207 =item 1 Obtain C<GMP>
209 Building C<isl> requires C<GMP>, including its headers files.
210 Your distribution may not provide these header files by default
211 and you may need to install a package called C<gmp-devel> or something
212 similar. Alternatively, C<GMP> can be built from
213 source, available from L<http://gmplib.org/>.
217 C<isl> uses the standard C<autoconf> C<configure> script.
222 optionally followed by some configure options.
223 A complete list of options can be obtained by running
227 Below we discuss some of the more common options.
229 C<isl> can optionally use C<piplib>, but no
230 C<piplib> functionality is currently used by default.
231 The C<--with-piplib> option can
232 be used to specify which C<piplib>
233 library to use, either an installed version (C<system>),
234 an externally built version (C<build>)
235 or no version (C<no>). The option C<build> is mostly useful
236 in C<configure> scripts of larger projects that bundle both C<isl>
243 Installation prefix for C<isl>
245 =item C<--with-gmp-prefix>
247 Installation prefix for C<GMP> (architecture-independent files).
249 =item C<--with-gmp-exec-prefix>
251 Installation prefix for C<GMP> (architecture-dependent files).
253 =item C<--with-piplib>
255 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
257 =item C<--with-piplib-prefix>
259 Installation prefix for C<system> C<piplib> (architecture-independent files).
261 =item C<--with-piplib-exec-prefix>
263 Installation prefix for C<system> C<piplib> (architecture-dependent files).
265 =item C<--with-piplib-builddir>
267 Location where C<build> C<piplib> was built.
275 =item 4 Install (optional)
283 =head2 Initialization
285 All manipulations of integer sets and relations occur within
286 the context of an C<isl_ctx>.
287 A given C<isl_ctx> can only be used within a single thread.
288 All arguments of a function are required to have been allocated
289 within the same context.
290 There are currently no functions available for moving an object
291 from one C<isl_ctx> to another C<isl_ctx>. This means that
292 there is currently no way of safely moving an object from one
293 thread to another, unless the whole C<isl_ctx> is moved.
295 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
296 freed using C<isl_ctx_free>.
297 All objects allocated within an C<isl_ctx> should be freed
298 before the C<isl_ctx> itself is freed.
300 isl_ctx *isl_ctx_alloc();
301 void isl_ctx_free(isl_ctx *ctx);
305 All operations on integers, mainly the coefficients
306 of the constraints describing the sets and relations,
307 are performed in exact integer arithmetic using C<GMP>.
308 However, to allow future versions of C<isl> to optionally
309 support fixed integer arithmetic, all calls to C<GMP>
310 are wrapped inside C<isl> specific macros.
311 The basic type is C<isl_int> and the operations below
312 are available on this type.
313 The meanings of these operations are essentially the same
314 as their C<GMP> C<mpz_> counterparts.
315 As always with C<GMP> types, C<isl_int>s need to be
316 initialized with C<isl_int_init> before they can be used
317 and they need to be released with C<isl_int_clear>
319 The user should not assume that an C<isl_int> is represented
320 as a C<mpz_t>, but should instead explicitly convert between
321 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
322 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
326 =item isl_int_init(i)
328 =item isl_int_clear(i)
330 =item isl_int_set(r,i)
332 =item isl_int_set_si(r,i)
334 =item isl_int_set_gmp(r,g)
336 =item isl_int_get_gmp(i,g)
338 =item isl_int_abs(r,i)
340 =item isl_int_neg(r,i)
342 =item isl_int_swap(i,j)
344 =item isl_int_swap_or_set(i,j)
346 =item isl_int_add_ui(r,i,j)
348 =item isl_int_sub_ui(r,i,j)
350 =item isl_int_add(r,i,j)
352 =item isl_int_sub(r,i,j)
354 =item isl_int_mul(r,i,j)
356 =item isl_int_mul_ui(r,i,j)
358 =item isl_int_addmul(r,i,j)
360 =item isl_int_submul(r,i,j)
362 =item isl_int_gcd(r,i,j)
364 =item isl_int_lcm(r,i,j)
366 =item isl_int_divexact(r,i,j)
368 =item isl_int_cdiv_q(r,i,j)
370 =item isl_int_fdiv_q(r,i,j)
372 =item isl_int_fdiv_r(r,i,j)
374 =item isl_int_fdiv_q_ui(r,i,j)
376 =item isl_int_read(r,s)
378 =item isl_int_print(out,i,width)
382 =item isl_int_cmp(i,j)
384 =item isl_int_cmp_si(i,si)
386 =item isl_int_eq(i,j)
388 =item isl_int_ne(i,j)
390 =item isl_int_lt(i,j)
392 =item isl_int_le(i,j)
394 =item isl_int_gt(i,j)
396 =item isl_int_ge(i,j)
398 =item isl_int_abs_eq(i,j)
400 =item isl_int_abs_ne(i,j)
402 =item isl_int_abs_lt(i,j)
404 =item isl_int_abs_gt(i,j)
406 =item isl_int_abs_ge(i,j)
408 =item isl_int_is_zero(i)
410 =item isl_int_is_one(i)
412 =item isl_int_is_negone(i)
414 =item isl_int_is_pos(i)
416 =item isl_int_is_neg(i)
418 =item isl_int_is_nonpos(i)
420 =item isl_int_is_nonneg(i)
422 =item isl_int_is_divisible_by(i,j)
426 =head2 Sets and Relations
428 C<isl> uses six types of objects for representing sets and relations,
429 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
430 C<isl_union_set> and C<isl_union_map>.
431 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
432 can be described as a conjunction of affine constraints, while
433 C<isl_set> and C<isl_map> represent unions of
434 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
435 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
436 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
437 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
438 where spaces are considered different if they have a different number
439 of dimensions and/or different names (see L<"Spaces">).
440 The difference between sets and relations (maps) is that sets have
441 one set of variables, while relations have two sets of variables,
442 input variables and output variables.
444 =head2 Memory Management
446 Since a high-level operation on sets and/or relations usually involves
447 several substeps and since the user is usually not interested in
448 the intermediate results, most functions that return a new object
449 will also release all the objects passed as arguments.
450 If the user still wants to use one or more of these arguments
451 after the function call, she should pass along a copy of the
452 object rather than the object itself.
453 The user is then responsible for making sure that the original
454 object gets used somewhere else or is explicitly freed.
456 The arguments and return values of all documented functions are
457 annotated to make clear which arguments are released and which
458 arguments are preserved. In particular, the following annotations
465 C<__isl_give> means that a new object is returned.
466 The user should make sure that the returned pointer is
467 used exactly once as a value for an C<__isl_take> argument.
468 In between, it can be used as a value for as many
469 C<__isl_keep> arguments as the user likes.
470 There is one exception, and that is the case where the
471 pointer returned is C<NULL>. Is this case, the user
472 is free to use it as an C<__isl_take> argument or not.
476 C<__isl_take> means that the object the argument points to
477 is taken over by the function and may no longer be used
478 by the user as an argument to any other function.
479 The pointer value must be one returned by a function
480 returning an C<__isl_give> pointer.
481 If the user passes in a C<NULL> value, then this will
482 be treated as an error in the sense that the function will
483 not perform its usual operation. However, it will still
484 make sure that all the other C<__isl_take> arguments
489 C<__isl_keep> means that the function will only use the object
490 temporarily. After the function has finished, the user
491 can still use it as an argument to other functions.
492 A C<NULL> value will be treated in the same way as
493 a C<NULL> value for an C<__isl_take> argument.
497 =head2 Error Handling
499 C<isl> supports different ways to react in case a runtime error is triggered.
500 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
501 with two maps that have incompatible spaces. There are three possible ways
502 to react on error: to warn, to continue or to abort.
504 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
505 the last error in the corresponding C<isl_ctx> and the function in which the
506 error was triggered returns C<NULL>. An error does not corrupt internal state,
507 such that isl can continue to be used. C<isl> also provides functions to
508 read the last error and to reset the memory that stores the last error. The
509 last error is only stored for information purposes. Its presence does not
510 change the behavior of C<isl>. Hence, resetting an error is not required to
511 continue to use isl, but only to observe new errors.
514 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
515 void isl_ctx_reset_error(isl_ctx *ctx);
517 Another option is to continue on error. This is similar to warn on error mode,
518 except that C<isl> does not print any warning. This allows a program to
519 implement its own error reporting.
521 The last option is to directly abort the execution of the program from within
522 the isl library. This makes it obviously impossible to recover from an error,
523 but it allows to directly spot the error location. By aborting on error,
524 debuggers break at the location the error occurred and can provide a stack
525 trace. Other tools that automatically provide stack traces on abort or that do
526 not want to continue execution after an error was triggered may also prefer to
529 The on error behavior of isl can be specified by calling
530 C<isl_options_set_on_error> or by setting the command line option
531 C<--isl-on-error>. Valid arguments for the function call are
532 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
533 choices for the command line option are C<warn>, C<continue> and C<abort>.
534 It is also possible to query the current error mode.
536 #include <isl/options.h>
537 int isl_options_set_on_error(isl_ctx *ctx, int val);
538 int isl_options_get_on_error(isl_ctx *ctx);
542 Identifiers are used to identify both individual dimensions
543 and tuples of dimensions. They consist of a name and an optional
544 pointer. Identifiers with the same name but different pointer values
545 are considered to be distinct.
546 Identifiers can be constructed, copied, freed, inspected and printed
547 using the following functions.
550 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
551 __isl_keep const char *name, void *user);
552 __isl_give isl_id *isl_id_copy(isl_id *id);
553 void *isl_id_free(__isl_take isl_id *id);
555 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
556 void *isl_id_get_user(__isl_keep isl_id *id);
557 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
559 __isl_give isl_printer *isl_printer_print_id(
560 __isl_take isl_printer *p, __isl_keep isl_id *id);
562 Note that C<isl_id_get_name> returns a pointer to some internal
563 data structure, so the result can only be used while the
564 corresponding C<isl_id> is alive.
568 Whenever a new set, relation or similiar object is created from scratch,
569 the space in which it lives needs to be specified using an C<isl_space>.
570 Each space involves zero or more parameters and zero, one or two
571 tuples of set or input/output dimensions. The parameters and dimensions
572 are identified by an C<isl_dim_type> and a position.
573 The type C<isl_dim_param> refers to parameters,
574 the type C<isl_dim_set> refers to set dimensions (for spaces
575 with a single tuple of dimensions) and the types C<isl_dim_in>
576 and C<isl_dim_out> refer to input and output dimensions
577 (for spaces with two tuples of dimensions).
578 Local spaces (see L</"Local Spaces">) also contain dimensions
579 of type C<isl_dim_div>.
580 Note that parameters are only identified by their position within
581 a given object. Across different objects, parameters are (usually)
582 identified by their names or identifiers. Only unnamed parameters
583 are identified by their positions across objects. The use of unnamed
584 parameters is discouraged.
586 #include <isl/space.h>
587 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
588 unsigned nparam, unsigned n_in, unsigned n_out);
589 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
591 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
592 unsigned nparam, unsigned dim);
593 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
594 void isl_space_free(__isl_take isl_space *space);
595 unsigned isl_space_dim(__isl_keep isl_space *space,
596 enum isl_dim_type type);
598 The space used for creating a parameter domain
599 needs to be created using C<isl_space_params_alloc>.
600 For other sets, the space
601 needs to be created using C<isl_space_set_alloc>, while
602 for a relation, the space
603 needs to be created using C<isl_space_alloc>.
604 C<isl_space_dim> can be used
605 to find out the number of dimensions of each type in
606 a space, where type may be
607 C<isl_dim_param>, C<isl_dim_in> (only for relations),
608 C<isl_dim_out> (only for relations), C<isl_dim_set>
609 (only for sets) or C<isl_dim_all>.
611 To check whether a given space is that of a set or a map
612 or whether it is a parameter space, use these functions:
614 #include <isl/space.h>
615 int isl_space_is_params(__isl_keep isl_space *space);
616 int isl_space_is_set(__isl_keep isl_space *space);
618 It is often useful to create objects that live in the
619 same space as some other object. This can be accomplished
620 by creating the new objects
621 (see L<Creating New Sets and Relations> or
622 L<Creating New (Piecewise) Quasipolynomials>) based on the space
623 of the original object.
626 __isl_give isl_space *isl_basic_set_get_space(
627 __isl_keep isl_basic_set *bset);
628 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
630 #include <isl/union_set.h>
631 __isl_give isl_space *isl_union_set_get_space(
632 __isl_keep isl_union_set *uset);
635 __isl_give isl_space *isl_basic_map_get_space(
636 __isl_keep isl_basic_map *bmap);
637 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
639 #include <isl/union_map.h>
640 __isl_give isl_space *isl_union_map_get_space(
641 __isl_keep isl_union_map *umap);
643 #include <isl/constraint.h>
644 __isl_give isl_space *isl_constraint_get_space(
645 __isl_keep isl_constraint *constraint);
647 #include <isl/polynomial.h>
648 __isl_give isl_space *isl_qpolynomial_get_domain_space(
649 __isl_keep isl_qpolynomial *qp);
650 __isl_give isl_space *isl_qpolynomial_get_space(
651 __isl_keep isl_qpolynomial *qp);
652 __isl_give isl_space *isl_qpolynomial_fold_get_space(
653 __isl_keep isl_qpolynomial_fold *fold);
654 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
655 __isl_keep isl_pw_qpolynomial *pwqp);
656 __isl_give isl_space *isl_pw_qpolynomial_get_space(
657 __isl_keep isl_pw_qpolynomial *pwqp);
658 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
659 __isl_keep isl_pw_qpolynomial_fold *pwf);
660 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
661 __isl_keep isl_pw_qpolynomial_fold *pwf);
662 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
663 __isl_keep isl_union_pw_qpolynomial *upwqp);
664 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
665 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
668 __isl_give isl_space *isl_aff_get_domain_space(
669 __isl_keep isl_aff *aff);
670 __isl_give isl_space *isl_aff_get_space(
671 __isl_keep isl_aff *aff);
672 __isl_give isl_space *isl_pw_aff_get_domain_space(
673 __isl_keep isl_pw_aff *pwaff);
674 __isl_give isl_space *isl_pw_aff_get_space(
675 __isl_keep isl_pw_aff *pwaff);
676 __isl_give isl_space *isl_multi_aff_get_domain_space(
677 __isl_keep isl_multi_aff *maff);
678 __isl_give isl_space *isl_multi_aff_get_space(
679 __isl_keep isl_multi_aff *maff);
680 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
681 __isl_keep isl_pw_multi_aff *pma);
682 __isl_give isl_space *isl_pw_multi_aff_get_space(
683 __isl_keep isl_pw_multi_aff *pma);
684 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
685 __isl_keep isl_union_pw_multi_aff *upma);
687 #include <isl/point.h>
688 __isl_give isl_space *isl_point_get_space(
689 __isl_keep isl_point *pnt);
691 The identifiers or names of the individual dimensions may be set or read off
692 using the following functions.
694 #include <isl/space.h>
695 __isl_give isl_space *isl_space_set_dim_id(
696 __isl_take isl_space *space,
697 enum isl_dim_type type, unsigned pos,
698 __isl_take isl_id *id);
699 int isl_space_has_dim_id(__isl_keep isl_space *space,
700 enum isl_dim_type type, unsigned pos);
701 __isl_give isl_id *isl_space_get_dim_id(
702 __isl_keep isl_space *space,
703 enum isl_dim_type type, unsigned pos);
704 __isl_give isl_space *isl_space_set_dim_name(
705 __isl_take isl_space *space,
706 enum isl_dim_type type, unsigned pos,
707 __isl_keep const char *name);
708 int isl_space_has_dim_name(__isl_keep isl_space *space,
709 enum isl_dim_type type, unsigned pos);
710 __isl_keep const char *isl_space_get_dim_name(
711 __isl_keep isl_space *space,
712 enum isl_dim_type type, unsigned pos);
714 Note that C<isl_space_get_name> returns a pointer to some internal
715 data structure, so the result can only be used while the
716 corresponding C<isl_space> is alive.
717 Also note that every function that operates on two sets or relations
718 requires that both arguments have the same parameters. This also
719 means that if one of the arguments has named parameters, then the
720 other needs to have named parameters too and the names need to match.
721 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
722 arguments may have different parameters (as long as they are named),
723 in which case the result will have as parameters the union of the parameters of
726 Given the identifier or name of a dimension (typically a parameter),
727 its position can be obtained from the following function.
729 #include <isl/space.h>
730 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
731 enum isl_dim_type type, __isl_keep isl_id *id);
732 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
733 enum isl_dim_type type, const char *name);
735 The identifiers or names of entire spaces may be set or read off
736 using the following functions.
738 #include <isl/space.h>
739 __isl_give isl_space *isl_space_set_tuple_id(
740 __isl_take isl_space *space,
741 enum isl_dim_type type, __isl_take isl_id *id);
742 __isl_give isl_space *isl_space_reset_tuple_id(
743 __isl_take isl_space *space, enum isl_dim_type type);
744 int isl_space_has_tuple_id(__isl_keep isl_space *space,
745 enum isl_dim_type type);
746 __isl_give isl_id *isl_space_get_tuple_id(
747 __isl_keep isl_space *space, enum isl_dim_type type);
748 __isl_give isl_space *isl_space_set_tuple_name(
749 __isl_take isl_space *space,
750 enum isl_dim_type type, const char *s);
751 int isl_space_has_tuple_name(__isl_keep isl_space *space,
752 enum isl_dim_type type);
753 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
754 enum isl_dim_type type);
756 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
757 or C<isl_dim_set>. As with C<isl_space_get_name>,
758 the C<isl_space_get_tuple_name> function returns a pointer to some internal
760 Binary operations require the corresponding spaces of their arguments
761 to have the same name.
763 Spaces can be nested. In particular, the domain of a set or
764 the domain or range of a relation can be a nested relation.
765 The following functions can be used to construct and deconstruct
768 #include <isl/space.h>
769 int isl_space_is_wrapping(__isl_keep isl_space *space);
770 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
771 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
773 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
774 be the space of a set, while that of
775 C<isl_space_wrap> should be the space of a relation.
776 Conversely, the output of C<isl_space_unwrap> is the space
777 of a relation, while that of C<isl_space_wrap> is the space of a set.
779 Spaces can be created from other spaces
780 using the following functions.
782 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
783 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
784 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
785 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
786 __isl_give isl_space *isl_space_params(
787 __isl_take isl_space *space);
788 __isl_give isl_space *isl_space_set_from_params(
789 __isl_take isl_space *space);
790 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
791 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
792 __isl_take isl_space *right);
793 __isl_give isl_space *isl_space_align_params(
794 __isl_take isl_space *space1, __isl_take isl_space *space2)
795 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
796 enum isl_dim_type type, unsigned pos, unsigned n);
797 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
798 enum isl_dim_type type, unsigned n);
799 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
800 enum isl_dim_type type, unsigned first, unsigned n);
801 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
802 enum isl_dim_type dst_type, unsigned dst_pos,
803 enum isl_dim_type src_type, unsigned src_pos,
805 __isl_give isl_space *isl_space_map_from_set(
806 __isl_take isl_space *space);
807 __isl_give isl_space *isl_space_map_from_domain_and_range(
808 __isl_take isl_space *domain,
809 __isl_take isl_space *range);
810 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
811 __isl_give isl_space *isl_space_curry(
812 __isl_take isl_space *space);
814 Note that if dimensions are added or removed from a space, then
815 the name and the internal structure are lost.
819 A local space is essentially a space with
820 zero or more existentially quantified variables.
821 The local space of a (constraint of a) basic set or relation can be obtained
822 using the following functions.
824 #include <isl/constraint.h>
825 __isl_give isl_local_space *isl_constraint_get_local_space(
826 __isl_keep isl_constraint *constraint);
829 __isl_give isl_local_space *isl_basic_set_get_local_space(
830 __isl_keep isl_basic_set *bset);
833 __isl_give isl_local_space *isl_basic_map_get_local_space(
834 __isl_keep isl_basic_map *bmap);
836 A new local space can be created from a space using
838 #include <isl/local_space.h>
839 __isl_give isl_local_space *isl_local_space_from_space(
840 __isl_take isl_space *space);
842 They can be inspected, modified, copied and freed using the following functions.
844 #include <isl/local_space.h>
845 isl_ctx *isl_local_space_get_ctx(
846 __isl_keep isl_local_space *ls);
847 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
848 int isl_local_space_dim(__isl_keep isl_local_space *ls,
849 enum isl_dim_type type);
850 int isl_local_space_has_dim_id(
851 __isl_keep isl_local_space *ls,
852 enum isl_dim_type type, unsigned pos);
853 __isl_give isl_id *isl_local_space_get_dim_id(
854 __isl_keep isl_local_space *ls,
855 enum isl_dim_type type, unsigned pos);
856 int isl_local_space_has_dim_name(
857 __isl_keep isl_local_space *ls,
858 enum isl_dim_type type, unsigned pos)
859 const char *isl_local_space_get_dim_name(
860 __isl_keep isl_local_space *ls,
861 enum isl_dim_type type, unsigned pos);
862 __isl_give isl_local_space *isl_local_space_set_dim_name(
863 __isl_take isl_local_space *ls,
864 enum isl_dim_type type, unsigned pos, const char *s);
865 __isl_give isl_local_space *isl_local_space_set_dim_id(
866 __isl_take isl_local_space *ls,
867 enum isl_dim_type type, unsigned pos,
868 __isl_take isl_id *id);
869 __isl_give isl_space *isl_local_space_get_space(
870 __isl_keep isl_local_space *ls);
871 __isl_give isl_aff *isl_local_space_get_div(
872 __isl_keep isl_local_space *ls, int pos);
873 __isl_give isl_local_space *isl_local_space_copy(
874 __isl_keep isl_local_space *ls);
875 void *isl_local_space_free(__isl_take isl_local_space *ls);
877 Two local spaces can be compared using
879 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
880 __isl_keep isl_local_space *ls2);
882 Local spaces can be created from other local spaces
883 using the following functions.
885 __isl_give isl_local_space *isl_local_space_domain(
886 __isl_take isl_local_space *ls);
887 __isl_give isl_local_space *isl_local_space_range(
888 __isl_take isl_local_space *ls);
889 __isl_give isl_local_space *isl_local_space_from_domain(
890 __isl_take isl_local_space *ls);
891 __isl_give isl_local_space *isl_local_space_intersect(
892 __isl_take isl_local_space *ls1,
893 __isl_take isl_local_space *ls2);
894 __isl_give isl_local_space *isl_local_space_add_dims(
895 __isl_take isl_local_space *ls,
896 enum isl_dim_type type, unsigned n);
897 __isl_give isl_local_space *isl_local_space_insert_dims(
898 __isl_take isl_local_space *ls,
899 enum isl_dim_type type, unsigned first, unsigned n);
900 __isl_give isl_local_space *isl_local_space_drop_dims(
901 __isl_take isl_local_space *ls,
902 enum isl_dim_type type, unsigned first, unsigned n);
904 =head2 Input and Output
906 C<isl> supports its own input/output format, which is similar
907 to the C<Omega> format, but also supports the C<PolyLib> format
912 The C<isl> format is similar to that of C<Omega>, but has a different
913 syntax for describing the parameters and allows for the definition
914 of an existentially quantified variable as the integer division
915 of an affine expression.
916 For example, the set of integers C<i> between C<0> and C<n>
917 such that C<i % 10 <= 6> can be described as
919 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
922 A set or relation can have several disjuncts, separated
923 by the keyword C<or>. Each disjunct is either a conjunction
924 of constraints or a projection (C<exists>) of a conjunction
925 of constraints. The constraints are separated by the keyword
928 =head3 C<PolyLib> format
930 If the represented set is a union, then the first line
931 contains a single number representing the number of disjuncts.
932 Otherwise, a line containing the number C<1> is optional.
934 Each disjunct is represented by a matrix of constraints.
935 The first line contains two numbers representing
936 the number of rows and columns,
937 where the number of rows is equal to the number of constraints
938 and the number of columns is equal to two plus the number of variables.
939 The following lines contain the actual rows of the constraint matrix.
940 In each row, the first column indicates whether the constraint
941 is an equality (C<0>) or inequality (C<1>). The final column
942 corresponds to the constant term.
944 If the set is parametric, then the coefficients of the parameters
945 appear in the last columns before the constant column.
946 The coefficients of any existentially quantified variables appear
947 between those of the set variables and those of the parameters.
949 =head3 Extended C<PolyLib> format
951 The extended C<PolyLib> format is nearly identical to the
952 C<PolyLib> format. The only difference is that the line
953 containing the number of rows and columns of a constraint matrix
954 also contains four additional numbers:
955 the number of output dimensions, the number of input dimensions,
956 the number of local dimensions (i.e., the number of existentially
957 quantified variables) and the number of parameters.
958 For sets, the number of ``output'' dimensions is equal
959 to the number of set dimensions, while the number of ``input''
965 __isl_give isl_basic_set *isl_basic_set_read_from_file(
966 isl_ctx *ctx, FILE *input);
967 __isl_give isl_basic_set *isl_basic_set_read_from_str(
968 isl_ctx *ctx, const char *str);
969 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
971 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
975 __isl_give isl_basic_map *isl_basic_map_read_from_file(
976 isl_ctx *ctx, FILE *input);
977 __isl_give isl_basic_map *isl_basic_map_read_from_str(
978 isl_ctx *ctx, const char *str);
979 __isl_give isl_map *isl_map_read_from_file(
980 isl_ctx *ctx, FILE *input);
981 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
984 #include <isl/union_set.h>
985 __isl_give isl_union_set *isl_union_set_read_from_file(
986 isl_ctx *ctx, FILE *input);
987 __isl_give isl_union_set *isl_union_set_read_from_str(
988 isl_ctx *ctx, const char *str);
990 #include <isl/union_map.h>
991 __isl_give isl_union_map *isl_union_map_read_from_file(
992 isl_ctx *ctx, FILE *input);
993 __isl_give isl_union_map *isl_union_map_read_from_str(
994 isl_ctx *ctx, const char *str);
996 The input format is autodetected and may be either the C<PolyLib> format
997 or the C<isl> format.
1001 Before anything can be printed, an C<isl_printer> needs to
1004 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1006 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1007 void isl_printer_free(__isl_take isl_printer *printer);
1008 __isl_give char *isl_printer_get_str(
1009 __isl_keep isl_printer *printer);
1011 The printer can be inspected using the following functions.
1013 FILE *isl_printer_get_file(
1014 __isl_keep isl_printer *printer);
1015 int isl_printer_get_output_format(
1016 __isl_keep isl_printer *p);
1018 The behavior of the printer can be modified in various ways
1020 __isl_give isl_printer *isl_printer_set_output_format(
1021 __isl_take isl_printer *p, int output_format);
1022 __isl_give isl_printer *isl_printer_set_indent(
1023 __isl_take isl_printer *p, int indent);
1024 __isl_give isl_printer *isl_printer_indent(
1025 __isl_take isl_printer *p, int indent);
1026 __isl_give isl_printer *isl_printer_set_prefix(
1027 __isl_take isl_printer *p, const char *prefix);
1028 __isl_give isl_printer *isl_printer_set_suffix(
1029 __isl_take isl_printer *p, const char *suffix);
1031 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1032 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1033 and defaults to C<ISL_FORMAT_ISL>.
1034 Each line in the output is indented by C<indent> (set by
1035 C<isl_printer_set_indent>) spaces
1036 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1037 In the C<PolyLib> format output,
1038 the coefficients of the existentially quantified variables
1039 appear between those of the set variables and those
1041 The function C<isl_printer_indent> increases the indentation
1042 by the specified amount (which may be negative).
1044 To actually print something, use
1046 #include <isl/printer.h>
1047 __isl_give isl_printer *isl_printer_print_double(
1048 __isl_take isl_printer *p, double d);
1050 #include <isl/set.h>
1051 __isl_give isl_printer *isl_printer_print_basic_set(
1052 __isl_take isl_printer *printer,
1053 __isl_keep isl_basic_set *bset);
1054 __isl_give isl_printer *isl_printer_print_set(
1055 __isl_take isl_printer *printer,
1056 __isl_keep isl_set *set);
1058 #include <isl/map.h>
1059 __isl_give isl_printer *isl_printer_print_basic_map(
1060 __isl_take isl_printer *printer,
1061 __isl_keep isl_basic_map *bmap);
1062 __isl_give isl_printer *isl_printer_print_map(
1063 __isl_take isl_printer *printer,
1064 __isl_keep isl_map *map);
1066 #include <isl/union_set.h>
1067 __isl_give isl_printer *isl_printer_print_union_set(
1068 __isl_take isl_printer *p,
1069 __isl_keep isl_union_set *uset);
1071 #include <isl/union_map.h>
1072 __isl_give isl_printer *isl_printer_print_union_map(
1073 __isl_take isl_printer *p,
1074 __isl_keep isl_union_map *umap);
1076 When called on a file printer, the following function flushes
1077 the file. When called on a string printer, the buffer is cleared.
1079 __isl_give isl_printer *isl_printer_flush(
1080 __isl_take isl_printer *p);
1082 =head2 Creating New Sets and Relations
1084 C<isl> has functions for creating some standard sets and relations.
1088 =item * Empty sets and relations
1090 __isl_give isl_basic_set *isl_basic_set_empty(
1091 __isl_take isl_space *space);
1092 __isl_give isl_basic_map *isl_basic_map_empty(
1093 __isl_take isl_space *space);
1094 __isl_give isl_set *isl_set_empty(
1095 __isl_take isl_space *space);
1096 __isl_give isl_map *isl_map_empty(
1097 __isl_take isl_space *space);
1098 __isl_give isl_union_set *isl_union_set_empty(
1099 __isl_take isl_space *space);
1100 __isl_give isl_union_map *isl_union_map_empty(
1101 __isl_take isl_space *space);
1103 For C<isl_union_set>s and C<isl_union_map>s, the space
1104 is only used to specify the parameters.
1106 =item * Universe sets and relations
1108 __isl_give isl_basic_set *isl_basic_set_universe(
1109 __isl_take isl_space *space);
1110 __isl_give isl_basic_map *isl_basic_map_universe(
1111 __isl_take isl_space *space);
1112 __isl_give isl_set *isl_set_universe(
1113 __isl_take isl_space *space);
1114 __isl_give isl_map *isl_map_universe(
1115 __isl_take isl_space *space);
1116 __isl_give isl_union_set *isl_union_set_universe(
1117 __isl_take isl_union_set *uset);
1118 __isl_give isl_union_map *isl_union_map_universe(
1119 __isl_take isl_union_map *umap);
1121 The sets and relations constructed by the functions above
1122 contain all integer values, while those constructed by the
1123 functions below only contain non-negative values.
1125 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1126 __isl_take isl_space *space);
1127 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1128 __isl_take isl_space *space);
1129 __isl_give isl_set *isl_set_nat_universe(
1130 __isl_take isl_space *space);
1131 __isl_give isl_map *isl_map_nat_universe(
1132 __isl_take isl_space *space);
1134 =item * Identity relations
1136 __isl_give isl_basic_map *isl_basic_map_identity(
1137 __isl_take isl_space *space);
1138 __isl_give isl_map *isl_map_identity(
1139 __isl_take isl_space *space);
1141 The number of input and output dimensions in C<space> needs
1144 =item * Lexicographic order
1146 __isl_give isl_map *isl_map_lex_lt(
1147 __isl_take isl_space *set_space);
1148 __isl_give isl_map *isl_map_lex_le(
1149 __isl_take isl_space *set_space);
1150 __isl_give isl_map *isl_map_lex_gt(
1151 __isl_take isl_space *set_space);
1152 __isl_give isl_map *isl_map_lex_ge(
1153 __isl_take isl_space *set_space);
1154 __isl_give isl_map *isl_map_lex_lt_first(
1155 __isl_take isl_space *space, unsigned n);
1156 __isl_give isl_map *isl_map_lex_le_first(
1157 __isl_take isl_space *space, unsigned n);
1158 __isl_give isl_map *isl_map_lex_gt_first(
1159 __isl_take isl_space *space, unsigned n);
1160 __isl_give isl_map *isl_map_lex_ge_first(
1161 __isl_take isl_space *space, unsigned n);
1163 The first four functions take a space for a B<set>
1164 and return relations that express that the elements in the domain
1165 are lexicographically less
1166 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1167 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1168 than the elements in the range.
1169 The last four functions take a space for a map
1170 and return relations that express that the first C<n> dimensions
1171 in the domain are lexicographically less
1172 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1173 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1174 than the first C<n> dimensions in the range.
1178 A basic set or relation can be converted to a set or relation
1179 using the following functions.
1181 __isl_give isl_set *isl_set_from_basic_set(
1182 __isl_take isl_basic_set *bset);
1183 __isl_give isl_map *isl_map_from_basic_map(
1184 __isl_take isl_basic_map *bmap);
1186 Sets and relations can be converted to union sets and relations
1187 using the following functions.
1189 __isl_give isl_union_set *isl_union_set_from_basic_set(
1190 __isl_take isl_basic_set *bset);
1191 __isl_give isl_union_map *isl_union_map_from_basic_map(
1192 __isl_take isl_basic_map *bmap);
1193 __isl_give isl_union_set *isl_union_set_from_set(
1194 __isl_take isl_set *set);
1195 __isl_give isl_union_map *isl_union_map_from_map(
1196 __isl_take isl_map *map);
1198 The inverse conversions below can only be used if the input
1199 union set or relation is known to contain elements in exactly one
1202 __isl_give isl_set *isl_set_from_union_set(
1203 __isl_take isl_union_set *uset);
1204 __isl_give isl_map *isl_map_from_union_map(
1205 __isl_take isl_union_map *umap);
1207 A zero-dimensional set can be constructed on a given parameter domain
1208 using the following function.
1210 __isl_give isl_set *isl_set_from_params(
1211 __isl_take isl_set *set);
1213 Sets and relations can be copied and freed again using the following
1216 __isl_give isl_basic_set *isl_basic_set_copy(
1217 __isl_keep isl_basic_set *bset);
1218 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1219 __isl_give isl_union_set *isl_union_set_copy(
1220 __isl_keep isl_union_set *uset);
1221 __isl_give isl_basic_map *isl_basic_map_copy(
1222 __isl_keep isl_basic_map *bmap);
1223 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1224 __isl_give isl_union_map *isl_union_map_copy(
1225 __isl_keep isl_union_map *umap);
1226 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1227 void *isl_set_free(__isl_take isl_set *set);
1228 void *isl_union_set_free(__isl_take isl_union_set *uset);
1229 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1230 void isl_map_free(__isl_take isl_map *map);
1231 void *isl_union_map_free(__isl_take isl_union_map *umap);
1233 Other sets and relations can be constructed by starting
1234 from a universe set or relation, adding equality and/or
1235 inequality constraints and then projecting out the
1236 existentially quantified variables, if any.
1237 Constraints can be constructed, manipulated and
1238 added to (or removed from) (basic) sets and relations
1239 using the following functions.
1241 #include <isl/constraint.h>
1242 __isl_give isl_constraint *isl_equality_alloc(
1243 __isl_take isl_local_space *ls);
1244 __isl_give isl_constraint *isl_inequality_alloc(
1245 __isl_take isl_local_space *ls);
1246 __isl_give isl_constraint *isl_constraint_set_constant(
1247 __isl_take isl_constraint *constraint, isl_int v);
1248 __isl_give isl_constraint *isl_constraint_set_constant_si(
1249 __isl_take isl_constraint *constraint, int v);
1250 __isl_give isl_constraint *isl_constraint_set_coefficient(
1251 __isl_take isl_constraint *constraint,
1252 enum isl_dim_type type, int pos, isl_int v);
1253 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1254 __isl_take isl_constraint *constraint,
1255 enum isl_dim_type type, int pos, int v);
1256 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1257 __isl_take isl_basic_map *bmap,
1258 __isl_take isl_constraint *constraint);
1259 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1260 __isl_take isl_basic_set *bset,
1261 __isl_take isl_constraint *constraint);
1262 __isl_give isl_map *isl_map_add_constraint(
1263 __isl_take isl_map *map,
1264 __isl_take isl_constraint *constraint);
1265 __isl_give isl_set *isl_set_add_constraint(
1266 __isl_take isl_set *set,
1267 __isl_take isl_constraint *constraint);
1268 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1269 __isl_take isl_basic_set *bset,
1270 __isl_take isl_constraint *constraint);
1272 For example, to create a set containing the even integers
1273 between 10 and 42, you would use the following code.
1276 isl_local_space *ls;
1278 isl_basic_set *bset;
1280 space = isl_space_set_alloc(ctx, 0, 2);
1281 bset = isl_basic_set_universe(isl_space_copy(space));
1282 ls = isl_local_space_from_space(space);
1284 c = isl_equality_alloc(isl_local_space_copy(ls));
1285 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1286 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1287 bset = isl_basic_set_add_constraint(bset, c);
1289 c = isl_inequality_alloc(isl_local_space_copy(ls));
1290 c = isl_constraint_set_constant_si(c, -10);
1291 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1292 bset = isl_basic_set_add_constraint(bset, c);
1294 c = isl_inequality_alloc(ls);
1295 c = isl_constraint_set_constant_si(c, 42);
1296 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1297 bset = isl_basic_set_add_constraint(bset, c);
1299 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1303 isl_basic_set *bset;
1304 bset = isl_basic_set_read_from_str(ctx,
1305 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1307 A basic set or relation can also be constructed from two matrices
1308 describing the equalities and the inequalities.
1310 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1311 __isl_take isl_space *space,
1312 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1313 enum isl_dim_type c1,
1314 enum isl_dim_type c2, enum isl_dim_type c3,
1315 enum isl_dim_type c4);
1316 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1317 __isl_take isl_space *space,
1318 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1319 enum isl_dim_type c1,
1320 enum isl_dim_type c2, enum isl_dim_type c3,
1321 enum isl_dim_type c4, enum isl_dim_type c5);
1323 The C<isl_dim_type> arguments indicate the order in which
1324 different kinds of variables appear in the input matrices
1325 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1326 C<isl_dim_set> and C<isl_dim_div> for sets and
1327 of C<isl_dim_cst>, C<isl_dim_param>,
1328 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1330 A (basic or union) set or relation can also be constructed from a
1331 (union) (piecewise) (multiple) affine expression
1332 or a list of affine expressions
1333 (See L<"Piecewise Quasi Affine Expressions"> and
1334 L<"Piecewise Multiple Quasi Affine Expressions">).
1336 __isl_give isl_basic_map *isl_basic_map_from_aff(
1337 __isl_take isl_aff *aff);
1338 __isl_give isl_map *isl_map_from_aff(
1339 __isl_take isl_aff *aff);
1340 __isl_give isl_set *isl_set_from_pw_aff(
1341 __isl_take isl_pw_aff *pwaff);
1342 __isl_give isl_map *isl_map_from_pw_aff(
1343 __isl_take isl_pw_aff *pwaff);
1344 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1345 __isl_take isl_space *domain_space,
1346 __isl_take isl_aff_list *list);
1347 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1348 __isl_take isl_multi_aff *maff)
1349 __isl_give isl_map *isl_map_from_multi_aff(
1350 __isl_take isl_multi_aff *maff)
1351 __isl_give isl_set *isl_set_from_pw_multi_aff(
1352 __isl_take isl_pw_multi_aff *pma);
1353 __isl_give isl_map *isl_map_from_pw_multi_aff(
1354 __isl_take isl_pw_multi_aff *pma);
1355 __isl_give isl_union_map *
1356 isl_union_map_from_union_pw_multi_aff(
1357 __isl_take isl_union_pw_multi_aff *upma);
1359 The C<domain_dim> argument describes the domain of the resulting
1360 basic relation. It is required because the C<list> may consist
1361 of zero affine expressions.
1363 =head2 Inspecting Sets and Relations
1365 Usually, the user should not have to care about the actual constraints
1366 of the sets and maps, but should instead apply the abstract operations
1367 explained in the following sections.
1368 Occasionally, however, it may be required to inspect the individual
1369 coefficients of the constraints. This section explains how to do so.
1370 In these cases, it may also be useful to have C<isl> compute
1371 an explicit representation of the existentially quantified variables.
1373 __isl_give isl_set *isl_set_compute_divs(
1374 __isl_take isl_set *set);
1375 __isl_give isl_map *isl_map_compute_divs(
1376 __isl_take isl_map *map);
1377 __isl_give isl_union_set *isl_union_set_compute_divs(
1378 __isl_take isl_union_set *uset);
1379 __isl_give isl_union_map *isl_union_map_compute_divs(
1380 __isl_take isl_union_map *umap);
1382 This explicit representation defines the existentially quantified
1383 variables as integer divisions of the other variables, possibly
1384 including earlier existentially quantified variables.
1385 An explicitly represented existentially quantified variable therefore
1386 has a unique value when the values of the other variables are known.
1387 If, furthermore, the same existentials, i.e., existentials
1388 with the same explicit representations, should appear in the
1389 same order in each of the disjuncts of a set or map, then the user should call
1390 either of the following functions.
1392 __isl_give isl_set *isl_set_align_divs(
1393 __isl_take isl_set *set);
1394 __isl_give isl_map *isl_map_align_divs(
1395 __isl_take isl_map *map);
1397 Alternatively, the existentially quantified variables can be removed
1398 using the following functions, which compute an overapproximation.
1400 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1401 __isl_take isl_basic_set *bset);
1402 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1403 __isl_take isl_basic_map *bmap);
1404 __isl_give isl_set *isl_set_remove_divs(
1405 __isl_take isl_set *set);
1406 __isl_give isl_map *isl_map_remove_divs(
1407 __isl_take isl_map *map);
1409 To iterate over all the sets or maps in a union set or map, use
1411 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1412 int (*fn)(__isl_take isl_set *set, void *user),
1414 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1415 int (*fn)(__isl_take isl_map *map, void *user),
1418 The number of sets or maps in a union set or map can be obtained
1421 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1422 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1424 To extract the set or map in a given space from a union, use
1426 __isl_give isl_set *isl_union_set_extract_set(
1427 __isl_keep isl_union_set *uset,
1428 __isl_take isl_space *space);
1429 __isl_give isl_map *isl_union_map_extract_map(
1430 __isl_keep isl_union_map *umap,
1431 __isl_take isl_space *space);
1433 To iterate over all the basic sets or maps in a set or map, use
1435 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1436 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1438 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1439 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1442 The callback function C<fn> should return 0 if successful and
1443 -1 if an error occurs. In the latter case, or if any other error
1444 occurs, the above functions will return -1.
1446 It should be noted that C<isl> does not guarantee that
1447 the basic sets or maps passed to C<fn> are disjoint.
1448 If this is required, then the user should call one of
1449 the following functions first.
1451 __isl_give isl_set *isl_set_make_disjoint(
1452 __isl_take isl_set *set);
1453 __isl_give isl_map *isl_map_make_disjoint(
1454 __isl_take isl_map *map);
1456 The number of basic sets in a set can be obtained
1459 int isl_set_n_basic_set(__isl_keep isl_set *set);
1461 To iterate over the constraints of a basic set or map, use
1463 #include <isl/constraint.h>
1465 int isl_basic_set_n_constraint(
1466 __isl_keep isl_basic_set *bset);
1467 int isl_basic_set_foreach_constraint(
1468 __isl_keep isl_basic_set *bset,
1469 int (*fn)(__isl_take isl_constraint *c, void *user),
1471 int isl_basic_map_foreach_constraint(
1472 __isl_keep isl_basic_map *bmap,
1473 int (*fn)(__isl_take isl_constraint *c, void *user),
1475 void *isl_constraint_free(__isl_take isl_constraint *c);
1477 Again, the callback function C<fn> should return 0 if successful and
1478 -1 if an error occurs. In the latter case, or if any other error
1479 occurs, the above functions will return -1.
1480 The constraint C<c> represents either an equality or an inequality.
1481 Use the following function to find out whether a constraint
1482 represents an equality. If not, it represents an inequality.
1484 int isl_constraint_is_equality(
1485 __isl_keep isl_constraint *constraint);
1487 The coefficients of the constraints can be inspected using
1488 the following functions.
1490 int isl_constraint_is_lower_bound(
1491 __isl_keep isl_constraint *constraint,
1492 enum isl_dim_type type, unsigned pos);
1493 int isl_constraint_is_upper_bound(
1494 __isl_keep isl_constraint *constraint,
1495 enum isl_dim_type type, unsigned pos);
1496 void isl_constraint_get_constant(
1497 __isl_keep isl_constraint *constraint, isl_int *v);
1498 void isl_constraint_get_coefficient(
1499 __isl_keep isl_constraint *constraint,
1500 enum isl_dim_type type, int pos, isl_int *v);
1501 int isl_constraint_involves_dims(
1502 __isl_keep isl_constraint *constraint,
1503 enum isl_dim_type type, unsigned first, unsigned n);
1505 The explicit representations of the existentially quantified
1506 variables can be inspected using the following function.
1507 Note that the user is only allowed to use this function
1508 if the inspected set or map is the result of a call
1509 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1510 The existentially quantified variable is equal to the floor
1511 of the returned affine expression. The affine expression
1512 itself can be inspected using the functions in
1513 L<"Piecewise Quasi Affine Expressions">.
1515 __isl_give isl_aff *isl_constraint_get_div(
1516 __isl_keep isl_constraint *constraint, int pos);
1518 To obtain the constraints of a basic set or map in matrix
1519 form, use the following functions.
1521 __isl_give isl_mat *isl_basic_set_equalities_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_set_inequalities_matrix(
1526 __isl_keep isl_basic_set *bset,
1527 enum isl_dim_type c1, enum isl_dim_type c2,
1528 enum isl_dim_type c3, enum isl_dim_type c4);
1529 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1530 __isl_keep isl_basic_map *bmap,
1531 enum isl_dim_type c1,
1532 enum isl_dim_type c2, enum isl_dim_type c3,
1533 enum isl_dim_type c4, enum isl_dim_type c5);
1534 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1535 __isl_keep isl_basic_map *bmap,
1536 enum isl_dim_type c1,
1537 enum isl_dim_type c2, enum isl_dim_type c3,
1538 enum isl_dim_type c4, enum isl_dim_type c5);
1540 The C<isl_dim_type> arguments dictate the order in which
1541 different kinds of variables appear in the resulting matrix
1542 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1543 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1545 The number of parameters, input, output or set dimensions can
1546 be obtained using the following functions.
1548 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1549 enum isl_dim_type type);
1550 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1551 enum isl_dim_type type);
1552 unsigned isl_set_dim(__isl_keep isl_set *set,
1553 enum isl_dim_type type);
1554 unsigned isl_map_dim(__isl_keep isl_map *map,
1555 enum isl_dim_type type);
1557 To check whether the description of a set or relation depends
1558 on one or more given dimensions, it is not necessary to iterate over all
1559 constraints. Instead the following functions can be used.
1561 int isl_basic_set_involves_dims(
1562 __isl_keep isl_basic_set *bset,
1563 enum isl_dim_type type, unsigned first, unsigned n);
1564 int isl_set_involves_dims(__isl_keep isl_set *set,
1565 enum isl_dim_type type, unsigned first, unsigned n);
1566 int isl_basic_map_involves_dims(
1567 __isl_keep isl_basic_map *bmap,
1568 enum isl_dim_type type, unsigned first, unsigned n);
1569 int isl_map_involves_dims(__isl_keep isl_map *map,
1570 enum isl_dim_type type, unsigned first, unsigned n);
1572 Similarly, the following functions can be used to check whether
1573 a given dimension is involved in any lower or upper bound.
1575 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1576 enum isl_dim_type type, unsigned pos);
1577 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1578 enum isl_dim_type type, unsigned pos);
1580 The identifiers or names of the domain and range spaces of a set
1581 or relation can be read off or set using the following functions.
1583 __isl_give isl_set *isl_set_set_tuple_id(
1584 __isl_take isl_set *set, __isl_take isl_id *id);
1585 __isl_give isl_set *isl_set_reset_tuple_id(
1586 __isl_take isl_set *set);
1587 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1588 __isl_give isl_id *isl_set_get_tuple_id(
1589 __isl_keep isl_set *set);
1590 __isl_give isl_map *isl_map_set_tuple_id(
1591 __isl_take isl_map *map, enum isl_dim_type type,
1592 __isl_take isl_id *id);
1593 __isl_give isl_map *isl_map_reset_tuple_id(
1594 __isl_take isl_map *map, enum isl_dim_type type);
1595 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1596 enum isl_dim_type type);
1597 __isl_give isl_id *isl_map_get_tuple_id(
1598 __isl_keep isl_map *map, enum isl_dim_type type);
1600 const char *isl_basic_set_get_tuple_name(
1601 __isl_keep isl_basic_set *bset);
1602 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1603 __isl_take isl_basic_set *set, const char *s);
1604 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1605 const char *isl_set_get_tuple_name(
1606 __isl_keep isl_set *set);
1607 const char *isl_basic_map_get_tuple_name(
1608 __isl_keep isl_basic_map *bmap,
1609 enum isl_dim_type type);
1610 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1611 __isl_take isl_basic_map *bmap,
1612 enum isl_dim_type type, const char *s);
1613 const char *isl_map_get_tuple_name(
1614 __isl_keep isl_map *map,
1615 enum isl_dim_type type);
1617 As with C<isl_space_get_tuple_name>, the value returned points to
1618 an internal data structure.
1619 The identifiers, positions or names of individual dimensions can be
1620 read off using the following functions.
1622 __isl_give isl_id *isl_basic_set_get_dim_id(
1623 __isl_keep isl_basic_set *bset,
1624 enum isl_dim_type type, unsigned pos);
1625 __isl_give isl_set *isl_set_set_dim_id(
1626 __isl_take isl_set *set, enum isl_dim_type type,
1627 unsigned pos, __isl_take isl_id *id);
1628 int isl_set_has_dim_id(__isl_keep isl_set *set,
1629 enum isl_dim_type type, unsigned pos);
1630 __isl_give isl_id *isl_set_get_dim_id(
1631 __isl_keep isl_set *set, enum isl_dim_type type,
1633 int isl_basic_map_has_dim_id(
1634 __isl_keep isl_basic_map *bmap,
1635 enum isl_dim_type type, unsigned pos);
1636 __isl_give isl_map *isl_map_set_dim_id(
1637 __isl_take isl_map *map, enum isl_dim_type type,
1638 unsigned pos, __isl_take isl_id *id);
1639 int isl_map_has_dim_id(__isl_keep isl_map *map,
1640 enum isl_dim_type type, unsigned pos);
1641 __isl_give isl_id *isl_map_get_dim_id(
1642 __isl_keep isl_map *map, enum isl_dim_type type,
1645 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1646 enum isl_dim_type type, __isl_keep isl_id *id);
1647 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1648 enum isl_dim_type type, __isl_keep isl_id *id);
1649 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1650 enum isl_dim_type type, const char *name);
1651 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1652 enum isl_dim_type type, const char *name);
1654 const char *isl_constraint_get_dim_name(
1655 __isl_keep isl_constraint *constraint,
1656 enum isl_dim_type type, unsigned pos);
1657 const char *isl_basic_set_get_dim_name(
1658 __isl_keep isl_basic_set *bset,
1659 enum isl_dim_type type, unsigned pos);
1660 int isl_set_has_dim_name(__isl_keep isl_set *set,
1661 enum isl_dim_type type, unsigned pos);
1662 const char *isl_set_get_dim_name(
1663 __isl_keep isl_set *set,
1664 enum isl_dim_type type, unsigned pos);
1665 const char *isl_basic_map_get_dim_name(
1666 __isl_keep isl_basic_map *bmap,
1667 enum isl_dim_type type, unsigned pos);
1668 int isl_map_has_dim_name(__isl_keep isl_map *map,
1669 enum isl_dim_type type, unsigned pos);
1670 const char *isl_map_get_dim_name(
1671 __isl_keep isl_map *map,
1672 enum isl_dim_type type, unsigned pos);
1674 These functions are mostly useful to obtain the identifiers, positions
1675 or names of the parameters. Identifiers of individual dimensions are
1676 essentially only useful for printing. They are ignored by all other
1677 operations and may not be preserved across those operations.
1681 =head3 Unary Properties
1687 The following functions test whether the given set or relation
1688 contains any integer points. The ``plain'' variants do not perform
1689 any computations, but simply check if the given set or relation
1690 is already known to be empty.
1692 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1693 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1694 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1695 int isl_set_is_empty(__isl_keep isl_set *set);
1696 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1697 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1698 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1699 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1700 int isl_map_is_empty(__isl_keep isl_map *map);
1701 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1703 =item * Universality
1705 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1706 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1707 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1709 =item * Single-valuedness
1711 int isl_basic_map_is_single_valued(
1712 __isl_keep isl_basic_map *bmap);
1713 int isl_map_plain_is_single_valued(
1714 __isl_keep isl_map *map);
1715 int isl_map_is_single_valued(__isl_keep isl_map *map);
1716 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1720 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1721 int isl_map_is_injective(__isl_keep isl_map *map);
1722 int isl_union_map_plain_is_injective(
1723 __isl_keep isl_union_map *umap);
1724 int isl_union_map_is_injective(
1725 __isl_keep isl_union_map *umap);
1729 int isl_map_is_bijective(__isl_keep isl_map *map);
1730 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1734 int isl_basic_map_plain_is_fixed(
1735 __isl_keep isl_basic_map *bmap,
1736 enum isl_dim_type type, unsigned pos,
1738 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1739 enum isl_dim_type type, unsigned pos,
1741 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1742 enum isl_dim_type type, unsigned pos,
1745 Check if the relation obviously lies on a hyperplane where the given dimension
1746 has a fixed value and if so, return that value in C<*val>.
1750 To check whether a set is a parameter domain, use this function:
1752 int isl_set_is_params(__isl_keep isl_set *set);
1753 int isl_union_set_is_params(
1754 __isl_keep isl_union_set *uset);
1758 The following functions check whether the domain of the given
1759 (basic) set is a wrapped relation.
1761 int isl_basic_set_is_wrapping(
1762 __isl_keep isl_basic_set *bset);
1763 int isl_set_is_wrapping(__isl_keep isl_set *set);
1765 =item * Internal Product
1767 int isl_basic_map_can_zip(
1768 __isl_keep isl_basic_map *bmap);
1769 int isl_map_can_zip(__isl_keep isl_map *map);
1771 Check whether the product of domain and range of the given relation
1773 i.e., whether both domain and range are nested relations.
1777 int isl_basic_map_can_curry(
1778 __isl_keep isl_basic_map *bmap);
1779 int isl_map_can_curry(__isl_keep isl_map *map);
1781 Check whether the domain of the (basic) relation is a wrapped relation.
1785 =head3 Binary Properties
1791 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1792 __isl_keep isl_set *set2);
1793 int isl_set_is_equal(__isl_keep isl_set *set1,
1794 __isl_keep isl_set *set2);
1795 int isl_union_set_is_equal(
1796 __isl_keep isl_union_set *uset1,
1797 __isl_keep isl_union_set *uset2);
1798 int isl_basic_map_is_equal(
1799 __isl_keep isl_basic_map *bmap1,
1800 __isl_keep isl_basic_map *bmap2);
1801 int isl_map_is_equal(__isl_keep isl_map *map1,
1802 __isl_keep isl_map *map2);
1803 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1804 __isl_keep isl_map *map2);
1805 int isl_union_map_is_equal(
1806 __isl_keep isl_union_map *umap1,
1807 __isl_keep isl_union_map *umap2);
1809 =item * Disjointness
1811 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1812 __isl_keep isl_set *set2);
1816 int isl_basic_set_is_subset(
1817 __isl_keep isl_basic_set *bset1,
1818 __isl_keep isl_basic_set *bset2);
1819 int isl_set_is_subset(__isl_keep isl_set *set1,
1820 __isl_keep isl_set *set2);
1821 int isl_set_is_strict_subset(
1822 __isl_keep isl_set *set1,
1823 __isl_keep isl_set *set2);
1824 int isl_union_set_is_subset(
1825 __isl_keep isl_union_set *uset1,
1826 __isl_keep isl_union_set *uset2);
1827 int isl_union_set_is_strict_subset(
1828 __isl_keep isl_union_set *uset1,
1829 __isl_keep isl_union_set *uset2);
1830 int isl_basic_map_is_subset(
1831 __isl_keep isl_basic_map *bmap1,
1832 __isl_keep isl_basic_map *bmap2);
1833 int isl_basic_map_is_strict_subset(
1834 __isl_keep isl_basic_map *bmap1,
1835 __isl_keep isl_basic_map *bmap2);
1836 int isl_map_is_subset(
1837 __isl_keep isl_map *map1,
1838 __isl_keep isl_map *map2);
1839 int isl_map_is_strict_subset(
1840 __isl_keep isl_map *map1,
1841 __isl_keep isl_map *map2);
1842 int isl_union_map_is_subset(
1843 __isl_keep isl_union_map *umap1,
1844 __isl_keep isl_union_map *umap2);
1845 int isl_union_map_is_strict_subset(
1846 __isl_keep isl_union_map *umap1,
1847 __isl_keep isl_union_map *umap2);
1849 Check whether the first argument is a (strict) subset of the
1854 =head2 Unary Operations
1860 __isl_give isl_set *isl_set_complement(
1861 __isl_take isl_set *set);
1862 __isl_give isl_map *isl_map_complement(
1863 __isl_take isl_map *map);
1867 __isl_give isl_basic_map *isl_basic_map_reverse(
1868 __isl_take isl_basic_map *bmap);
1869 __isl_give isl_map *isl_map_reverse(
1870 __isl_take isl_map *map);
1871 __isl_give isl_union_map *isl_union_map_reverse(
1872 __isl_take isl_union_map *umap);
1876 __isl_give isl_basic_set *isl_basic_set_project_out(
1877 __isl_take isl_basic_set *bset,
1878 enum isl_dim_type type, unsigned first, unsigned n);
1879 __isl_give isl_basic_map *isl_basic_map_project_out(
1880 __isl_take isl_basic_map *bmap,
1881 enum isl_dim_type type, unsigned first, unsigned n);
1882 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1883 enum isl_dim_type type, unsigned first, unsigned n);
1884 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1885 enum isl_dim_type type, unsigned first, unsigned n);
1886 __isl_give isl_basic_set *isl_basic_set_params(
1887 __isl_take isl_basic_set *bset);
1888 __isl_give isl_basic_set *isl_basic_map_domain(
1889 __isl_take isl_basic_map *bmap);
1890 __isl_give isl_basic_set *isl_basic_map_range(
1891 __isl_take isl_basic_map *bmap);
1892 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1893 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1894 __isl_give isl_set *isl_map_domain(
1895 __isl_take isl_map *bmap);
1896 __isl_give isl_set *isl_map_range(
1897 __isl_take isl_map *map);
1898 __isl_give isl_set *isl_union_set_params(
1899 __isl_take isl_union_set *uset);
1900 __isl_give isl_set *isl_union_map_params(
1901 __isl_take isl_union_map *umap);
1902 __isl_give isl_union_set *isl_union_map_domain(
1903 __isl_take isl_union_map *umap);
1904 __isl_give isl_union_set *isl_union_map_range(
1905 __isl_take isl_union_map *umap);
1907 __isl_give isl_basic_map *isl_basic_map_domain_map(
1908 __isl_take isl_basic_map *bmap);
1909 __isl_give isl_basic_map *isl_basic_map_range_map(
1910 __isl_take isl_basic_map *bmap);
1911 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1912 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1913 __isl_give isl_union_map *isl_union_map_domain_map(
1914 __isl_take isl_union_map *umap);
1915 __isl_give isl_union_map *isl_union_map_range_map(
1916 __isl_take isl_union_map *umap);
1918 The functions above construct a (basic, regular or union) relation
1919 that maps (a wrapped version of) the input relation to its domain or range.
1923 __isl_give isl_set *isl_set_eliminate(
1924 __isl_take isl_set *set, enum isl_dim_type type,
1925 unsigned first, unsigned n);
1926 __isl_give isl_basic_map *isl_basic_map_eliminate(
1927 __isl_take isl_basic_map *bmap,
1928 enum isl_dim_type type,
1929 unsigned first, unsigned n);
1930 __isl_give isl_map *isl_map_eliminate(
1931 __isl_take isl_map *map, enum isl_dim_type type,
1932 unsigned first, unsigned n);
1934 Eliminate the coefficients for the given dimensions from the constraints,
1935 without removing the dimensions.
1939 __isl_give isl_basic_set *isl_basic_set_fix(
1940 __isl_take isl_basic_set *bset,
1941 enum isl_dim_type type, unsigned pos,
1943 __isl_give isl_basic_set *isl_basic_set_fix_si(
1944 __isl_take isl_basic_set *bset,
1945 enum isl_dim_type type, unsigned pos, int value);
1946 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
1947 enum isl_dim_type type, unsigned pos,
1949 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
1950 enum isl_dim_type type, unsigned pos, int value);
1951 __isl_give isl_basic_map *isl_basic_map_fix_si(
1952 __isl_take isl_basic_map *bmap,
1953 enum isl_dim_type type, unsigned pos, int value);
1954 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
1955 enum isl_dim_type type, unsigned pos, int value);
1957 Intersect the set or relation with the hyperplane where the given
1958 dimension has the fixed given value.
1960 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
1961 __isl_take isl_basic_map *bmap,
1962 enum isl_dim_type type, unsigned pos, int value);
1963 __isl_give isl_set *isl_set_lower_bound(
1964 __isl_take isl_set *set,
1965 enum isl_dim_type type, unsigned pos,
1967 __isl_give isl_set *isl_set_lower_bound_si(
1968 __isl_take isl_set *set,
1969 enum isl_dim_type type, unsigned pos, int value);
1970 __isl_give isl_map *isl_map_lower_bound_si(
1971 __isl_take isl_map *map,
1972 enum isl_dim_type type, unsigned pos, int value);
1973 __isl_give isl_set *isl_set_upper_bound(
1974 __isl_take isl_set *set,
1975 enum isl_dim_type type, unsigned pos,
1977 __isl_give isl_set *isl_set_upper_bound_si(
1978 __isl_take isl_set *set,
1979 enum isl_dim_type type, unsigned pos, int value);
1980 __isl_give isl_map *isl_map_upper_bound_si(
1981 __isl_take isl_map *map,
1982 enum isl_dim_type type, unsigned pos, int value);
1984 Intersect the set or relation with the half-space where the given
1985 dimension has a value bounded by the fixed given value.
1987 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
1988 enum isl_dim_type type1, int pos1,
1989 enum isl_dim_type type2, int pos2);
1990 __isl_give isl_basic_map *isl_basic_map_equate(
1991 __isl_take isl_basic_map *bmap,
1992 enum isl_dim_type type1, int pos1,
1993 enum isl_dim_type type2, int pos2);
1994 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
1995 enum isl_dim_type type1, int pos1,
1996 enum isl_dim_type type2, int pos2);
1998 Intersect the set or relation with the hyperplane where the given
1999 dimensions are equal to each other.
2001 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2002 enum isl_dim_type type1, int pos1,
2003 enum isl_dim_type type2, int pos2);
2005 Intersect the relation with the hyperplane where the given
2006 dimensions have opposite values.
2008 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2009 enum isl_dim_type type1, int pos1,
2010 enum isl_dim_type type2, int pos2);
2011 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2012 enum isl_dim_type type1, int pos1,
2013 enum isl_dim_type type2, int pos2);
2015 Intersect the relation with the half-space where the given
2016 dimensions satisfy the given ordering.
2020 __isl_give isl_map *isl_set_identity(
2021 __isl_take isl_set *set);
2022 __isl_give isl_union_map *isl_union_set_identity(
2023 __isl_take isl_union_set *uset);
2025 Construct an identity relation on the given (union) set.
2029 __isl_give isl_basic_set *isl_basic_map_deltas(
2030 __isl_take isl_basic_map *bmap);
2031 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2032 __isl_give isl_union_set *isl_union_map_deltas(
2033 __isl_take isl_union_map *umap);
2035 These functions return a (basic) set containing the differences
2036 between image elements and corresponding domain elements in the input.
2038 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2039 __isl_take isl_basic_map *bmap);
2040 __isl_give isl_map *isl_map_deltas_map(
2041 __isl_take isl_map *map);
2042 __isl_give isl_union_map *isl_union_map_deltas_map(
2043 __isl_take isl_union_map *umap);
2045 The functions above construct a (basic, regular or union) relation
2046 that maps (a wrapped version of) the input relation to its delta set.
2050 Simplify the representation of a set or relation by trying
2051 to combine pairs of basic sets or relations into a single
2052 basic set or relation.
2054 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2055 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2056 __isl_give isl_union_set *isl_union_set_coalesce(
2057 __isl_take isl_union_set *uset);
2058 __isl_give isl_union_map *isl_union_map_coalesce(
2059 __isl_take isl_union_map *umap);
2061 One of the methods for combining pairs of basic sets or relations
2062 can result in coefficients that are much larger than those that appear
2063 in the constraints of the input. By default, the coefficients are
2064 not allowed to grow larger, but this can be changed by unsetting
2065 the following option.
2067 int isl_options_set_coalesce_bounded_wrapping(
2068 isl_ctx *ctx, int val);
2069 int isl_options_get_coalesce_bounded_wrapping(
2072 =item * Detecting equalities
2074 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2075 __isl_take isl_basic_set *bset);
2076 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2077 __isl_take isl_basic_map *bmap);
2078 __isl_give isl_set *isl_set_detect_equalities(
2079 __isl_take isl_set *set);
2080 __isl_give isl_map *isl_map_detect_equalities(
2081 __isl_take isl_map *map);
2082 __isl_give isl_union_set *isl_union_set_detect_equalities(
2083 __isl_take isl_union_set *uset);
2084 __isl_give isl_union_map *isl_union_map_detect_equalities(
2085 __isl_take isl_union_map *umap);
2087 Simplify the representation of a set or relation by detecting implicit
2090 =item * Removing redundant constraints
2092 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2093 __isl_take isl_basic_set *bset);
2094 __isl_give isl_set *isl_set_remove_redundancies(
2095 __isl_take isl_set *set);
2096 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2097 __isl_take isl_basic_map *bmap);
2098 __isl_give isl_map *isl_map_remove_redundancies(
2099 __isl_take isl_map *map);
2103 __isl_give isl_basic_set *isl_set_convex_hull(
2104 __isl_take isl_set *set);
2105 __isl_give isl_basic_map *isl_map_convex_hull(
2106 __isl_take isl_map *map);
2108 If the input set or relation has any existentially quantified
2109 variables, then the result of these operations is currently undefined.
2113 __isl_give isl_basic_set *isl_set_simple_hull(
2114 __isl_take isl_set *set);
2115 __isl_give isl_basic_map *isl_map_simple_hull(
2116 __isl_take isl_map *map);
2117 __isl_give isl_union_map *isl_union_map_simple_hull(
2118 __isl_take isl_union_map *umap);
2120 These functions compute a single basic set or relation
2121 that contains the whole input set or relation.
2122 In particular, the output is described by translates
2123 of the constraints describing the basic sets or relations in the input.
2127 (See \autoref{s:simple hull}.)
2133 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2134 __isl_take isl_basic_set *bset);
2135 __isl_give isl_basic_set *isl_set_affine_hull(
2136 __isl_take isl_set *set);
2137 __isl_give isl_union_set *isl_union_set_affine_hull(
2138 __isl_take isl_union_set *uset);
2139 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2140 __isl_take isl_basic_map *bmap);
2141 __isl_give isl_basic_map *isl_map_affine_hull(
2142 __isl_take isl_map *map);
2143 __isl_give isl_union_map *isl_union_map_affine_hull(
2144 __isl_take isl_union_map *umap);
2146 In case of union sets and relations, the affine hull is computed
2149 =item * Polyhedral hull
2151 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2152 __isl_take isl_set *set);
2153 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2154 __isl_take isl_map *map);
2155 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2156 __isl_take isl_union_set *uset);
2157 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2158 __isl_take isl_union_map *umap);
2160 These functions compute a single basic set or relation
2161 not involving any existentially quantified variables
2162 that contains the whole input set or relation.
2163 In case of union sets and relations, the polyhedral hull is computed
2168 __isl_give isl_basic_set *isl_basic_set_sample(
2169 __isl_take isl_basic_set *bset);
2170 __isl_give isl_basic_set *isl_set_sample(
2171 __isl_take isl_set *set);
2172 __isl_give isl_basic_map *isl_basic_map_sample(
2173 __isl_take isl_basic_map *bmap);
2174 __isl_give isl_basic_map *isl_map_sample(
2175 __isl_take isl_map *map);
2177 If the input (basic) set or relation is non-empty, then return
2178 a singleton subset of the input. Otherwise, return an empty set.
2180 =item * Optimization
2182 #include <isl/ilp.h>
2183 enum isl_lp_result isl_basic_set_max(
2184 __isl_keep isl_basic_set *bset,
2185 __isl_keep isl_aff *obj, isl_int *opt)
2186 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2187 __isl_keep isl_aff *obj, isl_int *opt);
2188 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2189 __isl_keep isl_aff *obj, isl_int *opt);
2191 Compute the minimum or maximum of the integer affine expression C<obj>
2192 over the points in C<set>, returning the result in C<opt>.
2193 The return value may be one of C<isl_lp_error>,
2194 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2196 =item * Parametric optimization
2198 __isl_give isl_pw_aff *isl_set_dim_min(
2199 __isl_take isl_set *set, int pos);
2200 __isl_give isl_pw_aff *isl_set_dim_max(
2201 __isl_take isl_set *set, int pos);
2202 __isl_give isl_pw_aff *isl_map_dim_max(
2203 __isl_take isl_map *map, int pos);
2205 Compute the minimum or maximum of the given set or output dimension
2206 as a function of the parameters (and input dimensions), but independently
2207 of the other set or output dimensions.
2208 For lexicographic optimization, see L<"Lexicographic Optimization">.
2212 The following functions compute either the set of (rational) coefficient
2213 values of valid constraints for the given set or the set of (rational)
2214 values satisfying the constraints with coefficients from the given set.
2215 Internally, these two sets of functions perform essentially the
2216 same operations, except that the set of coefficients is assumed to
2217 be a cone, while the set of values may be any polyhedron.
2218 The current implementation is based on the Farkas lemma and
2219 Fourier-Motzkin elimination, but this may change or be made optional
2220 in future. In particular, future implementations may use different
2221 dualization algorithms or skip the elimination step.
2223 __isl_give isl_basic_set *isl_basic_set_coefficients(
2224 __isl_take isl_basic_set *bset);
2225 __isl_give isl_basic_set *isl_set_coefficients(
2226 __isl_take isl_set *set);
2227 __isl_give isl_union_set *isl_union_set_coefficients(
2228 __isl_take isl_union_set *bset);
2229 __isl_give isl_basic_set *isl_basic_set_solutions(
2230 __isl_take isl_basic_set *bset);
2231 __isl_give isl_basic_set *isl_set_solutions(
2232 __isl_take isl_set *set);
2233 __isl_give isl_union_set *isl_union_set_solutions(
2234 __isl_take isl_union_set *bset);
2238 __isl_give isl_map *isl_map_fixed_power(
2239 __isl_take isl_map *map, isl_int exp);
2240 __isl_give isl_union_map *isl_union_map_fixed_power(
2241 __isl_take isl_union_map *umap, isl_int exp);
2243 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2244 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2245 of C<map> is computed.
2247 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2249 __isl_give isl_union_map *isl_union_map_power(
2250 __isl_take isl_union_map *umap, int *exact);
2252 Compute a parametric representation for all positive powers I<k> of C<map>.
2253 The result maps I<k> to a nested relation corresponding to the
2254 I<k>th power of C<map>.
2255 The result may be an overapproximation. If the result is known to be exact,
2256 then C<*exact> is set to C<1>.
2258 =item * Transitive closure
2260 __isl_give isl_map *isl_map_transitive_closure(
2261 __isl_take isl_map *map, int *exact);
2262 __isl_give isl_union_map *isl_union_map_transitive_closure(
2263 __isl_take isl_union_map *umap, int *exact);
2265 Compute the transitive closure of C<map>.
2266 The result may be an overapproximation. If the result is known to be exact,
2267 then C<*exact> is set to C<1>.
2269 =item * Reaching path lengths
2271 __isl_give isl_map *isl_map_reaching_path_lengths(
2272 __isl_take isl_map *map, int *exact);
2274 Compute a relation that maps each element in the range of C<map>
2275 to the lengths of all paths composed of edges in C<map> that
2276 end up in the given element.
2277 The result may be an overapproximation. If the result is known to be exact,
2278 then C<*exact> is set to C<1>.
2279 To compute the I<maximal> path length, the resulting relation
2280 should be postprocessed by C<isl_map_lexmax>.
2281 In particular, if the input relation is a dependence relation
2282 (mapping sources to sinks), then the maximal path length corresponds
2283 to the free schedule.
2284 Note, however, that C<isl_map_lexmax> expects the maximum to be
2285 finite, so if the path lengths are unbounded (possibly due to
2286 the overapproximation), then you will get an error message.
2290 __isl_give isl_basic_set *isl_basic_map_wrap(
2291 __isl_take isl_basic_map *bmap);
2292 __isl_give isl_set *isl_map_wrap(
2293 __isl_take isl_map *map);
2294 __isl_give isl_union_set *isl_union_map_wrap(
2295 __isl_take isl_union_map *umap);
2296 __isl_give isl_basic_map *isl_basic_set_unwrap(
2297 __isl_take isl_basic_set *bset);
2298 __isl_give isl_map *isl_set_unwrap(
2299 __isl_take isl_set *set);
2300 __isl_give isl_union_map *isl_union_set_unwrap(
2301 __isl_take isl_union_set *uset);
2305 Remove any internal structure of domain (and range) of the given
2306 set or relation. If there is any such internal structure in the input,
2307 then the name of the space is also removed.
2309 __isl_give isl_basic_set *isl_basic_set_flatten(
2310 __isl_take isl_basic_set *bset);
2311 __isl_give isl_set *isl_set_flatten(
2312 __isl_take isl_set *set);
2313 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2314 __isl_take isl_basic_map *bmap);
2315 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2316 __isl_take isl_basic_map *bmap);
2317 __isl_give isl_map *isl_map_flatten_range(
2318 __isl_take isl_map *map);
2319 __isl_give isl_map *isl_map_flatten_domain(
2320 __isl_take isl_map *map);
2321 __isl_give isl_basic_map *isl_basic_map_flatten(
2322 __isl_take isl_basic_map *bmap);
2323 __isl_give isl_map *isl_map_flatten(
2324 __isl_take isl_map *map);
2326 __isl_give isl_map *isl_set_flatten_map(
2327 __isl_take isl_set *set);
2329 The function above constructs a relation
2330 that maps the input set to a flattened version of the set.
2334 Lift the input set to a space with extra dimensions corresponding
2335 to the existentially quantified variables in the input.
2336 In particular, the result lives in a wrapped map where the domain
2337 is the original space and the range corresponds to the original
2338 existentially quantified variables.
2340 __isl_give isl_basic_set *isl_basic_set_lift(
2341 __isl_take isl_basic_set *bset);
2342 __isl_give isl_set *isl_set_lift(
2343 __isl_take isl_set *set);
2344 __isl_give isl_union_set *isl_union_set_lift(
2345 __isl_take isl_union_set *uset);
2347 Given a local space that contains the existentially quantified
2348 variables of a set, a basic relation that, when applied to
2349 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2350 can be constructed using the following function.
2352 #include <isl/local_space.h>
2353 __isl_give isl_basic_map *isl_local_space_lifting(
2354 __isl_take isl_local_space *ls);
2356 =item * Internal Product
2358 __isl_give isl_basic_map *isl_basic_map_zip(
2359 __isl_take isl_basic_map *bmap);
2360 __isl_give isl_map *isl_map_zip(
2361 __isl_take isl_map *map);
2362 __isl_give isl_union_map *isl_union_map_zip(
2363 __isl_take isl_union_map *umap);
2365 Given a relation with nested relations for domain and range,
2366 interchange the range of the domain with the domain of the range.
2370 __isl_give isl_basic_map *isl_basic_map_curry(
2371 __isl_take isl_basic_map *bmap);
2372 __isl_give isl_map *isl_map_curry(
2373 __isl_take isl_map *map);
2374 __isl_give isl_union_map *isl_union_map_curry(
2375 __isl_take isl_union_map *umap);
2377 Given a relation with a nested relation for domain,
2378 move the range of the nested relation out of the domain
2379 and use it as the domain of a nested relation in the range,
2380 with the original range as range of this nested relation.
2382 =item * Aligning parameters
2384 __isl_give isl_basic_set *isl_basic_set_align_params(
2385 __isl_take isl_basic_set *bset,
2386 __isl_take isl_space *model);
2387 __isl_give isl_set *isl_set_align_params(
2388 __isl_take isl_set *set,
2389 __isl_take isl_space *model);
2390 __isl_give isl_basic_map *isl_basic_map_align_params(
2391 __isl_take isl_basic_map *bmap,
2392 __isl_take isl_space *model);
2393 __isl_give isl_map *isl_map_align_params(
2394 __isl_take isl_map *map,
2395 __isl_take isl_space *model);
2397 Change the order of the parameters of the given set or relation
2398 such that the first parameters match those of C<model>.
2399 This may involve the introduction of extra parameters.
2400 All parameters need to be named.
2402 =item * Dimension manipulation
2404 __isl_give isl_set *isl_set_add_dims(
2405 __isl_take isl_set *set,
2406 enum isl_dim_type type, unsigned n);
2407 __isl_give isl_map *isl_map_add_dims(
2408 __isl_take isl_map *map,
2409 enum isl_dim_type type, unsigned n);
2410 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2411 __isl_take isl_basic_set *bset,
2412 enum isl_dim_type type, unsigned pos,
2414 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2415 __isl_take isl_basic_map *bmap,
2416 enum isl_dim_type type, unsigned pos,
2418 __isl_give isl_set *isl_set_insert_dims(
2419 __isl_take isl_set *set,
2420 enum isl_dim_type type, unsigned pos, unsigned n);
2421 __isl_give isl_map *isl_map_insert_dims(
2422 __isl_take isl_map *map,
2423 enum isl_dim_type type, unsigned pos, unsigned n);
2424 __isl_give isl_basic_set *isl_basic_set_move_dims(
2425 __isl_take isl_basic_set *bset,
2426 enum isl_dim_type dst_type, unsigned dst_pos,
2427 enum isl_dim_type src_type, unsigned src_pos,
2429 __isl_give isl_basic_map *isl_basic_map_move_dims(
2430 __isl_take isl_basic_map *bmap,
2431 enum isl_dim_type dst_type, unsigned dst_pos,
2432 enum isl_dim_type src_type, unsigned src_pos,
2434 __isl_give isl_set *isl_set_move_dims(
2435 __isl_take isl_set *set,
2436 enum isl_dim_type dst_type, unsigned dst_pos,
2437 enum isl_dim_type src_type, unsigned src_pos,
2439 __isl_give isl_map *isl_map_move_dims(
2440 __isl_take isl_map *map,
2441 enum isl_dim_type dst_type, unsigned dst_pos,
2442 enum isl_dim_type src_type, unsigned src_pos,
2445 It is usually not advisable to directly change the (input or output)
2446 space of a set or a relation as this removes the name and the internal
2447 structure of the space. However, the above functions can be useful
2448 to add new parameters, assuming
2449 C<isl_set_align_params> and C<isl_map_align_params>
2454 =head2 Binary Operations
2456 The two arguments of a binary operation not only need to live
2457 in the same C<isl_ctx>, they currently also need to have
2458 the same (number of) parameters.
2460 =head3 Basic Operations
2464 =item * Intersection
2466 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2467 __isl_take isl_basic_set *bset1,
2468 __isl_take isl_basic_set *bset2);
2469 __isl_give isl_basic_set *isl_basic_set_intersect(
2470 __isl_take isl_basic_set *bset1,
2471 __isl_take isl_basic_set *bset2);
2472 __isl_give isl_set *isl_set_intersect_params(
2473 __isl_take isl_set *set,
2474 __isl_take isl_set *params);
2475 __isl_give isl_set *isl_set_intersect(
2476 __isl_take isl_set *set1,
2477 __isl_take isl_set *set2);
2478 __isl_give isl_union_set *isl_union_set_intersect_params(
2479 __isl_take isl_union_set *uset,
2480 __isl_take isl_set *set);
2481 __isl_give isl_union_map *isl_union_map_intersect_params(
2482 __isl_take isl_union_map *umap,
2483 __isl_take isl_set *set);
2484 __isl_give isl_union_set *isl_union_set_intersect(
2485 __isl_take isl_union_set *uset1,
2486 __isl_take isl_union_set *uset2);
2487 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2488 __isl_take isl_basic_map *bmap,
2489 __isl_take isl_basic_set *bset);
2490 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2491 __isl_take isl_basic_map *bmap,
2492 __isl_take isl_basic_set *bset);
2493 __isl_give isl_basic_map *isl_basic_map_intersect(
2494 __isl_take isl_basic_map *bmap1,
2495 __isl_take isl_basic_map *bmap2);
2496 __isl_give isl_map *isl_map_intersect_params(
2497 __isl_take isl_map *map,
2498 __isl_take isl_set *params);
2499 __isl_give isl_map *isl_map_intersect_domain(
2500 __isl_take isl_map *map,
2501 __isl_take isl_set *set);
2502 __isl_give isl_map *isl_map_intersect_range(
2503 __isl_take isl_map *map,
2504 __isl_take isl_set *set);
2505 __isl_give isl_map *isl_map_intersect(
2506 __isl_take isl_map *map1,
2507 __isl_take isl_map *map2);
2508 __isl_give isl_union_map *isl_union_map_intersect_domain(
2509 __isl_take isl_union_map *umap,
2510 __isl_take isl_union_set *uset);
2511 __isl_give isl_union_map *isl_union_map_intersect_range(
2512 __isl_take isl_union_map *umap,
2513 __isl_take isl_union_set *uset);
2514 __isl_give isl_union_map *isl_union_map_intersect(
2515 __isl_take isl_union_map *umap1,
2516 __isl_take isl_union_map *umap2);
2518 The second argument to the C<_params> functions needs to be
2519 a parametric (basic) set. For the other functions, a parametric set
2520 for either argument is only allowed if the other argument is
2521 a parametric set as well.
2525 __isl_give isl_set *isl_basic_set_union(
2526 __isl_take isl_basic_set *bset1,
2527 __isl_take isl_basic_set *bset2);
2528 __isl_give isl_map *isl_basic_map_union(
2529 __isl_take isl_basic_map *bmap1,
2530 __isl_take isl_basic_map *bmap2);
2531 __isl_give isl_set *isl_set_union(
2532 __isl_take isl_set *set1,
2533 __isl_take isl_set *set2);
2534 __isl_give isl_map *isl_map_union(
2535 __isl_take isl_map *map1,
2536 __isl_take isl_map *map2);
2537 __isl_give isl_union_set *isl_union_set_union(
2538 __isl_take isl_union_set *uset1,
2539 __isl_take isl_union_set *uset2);
2540 __isl_give isl_union_map *isl_union_map_union(
2541 __isl_take isl_union_map *umap1,
2542 __isl_take isl_union_map *umap2);
2544 =item * Set difference
2546 __isl_give isl_set *isl_set_subtract(
2547 __isl_take isl_set *set1,
2548 __isl_take isl_set *set2);
2549 __isl_give isl_map *isl_map_subtract(
2550 __isl_take isl_map *map1,
2551 __isl_take isl_map *map2);
2552 __isl_give isl_map *isl_map_subtract_domain(
2553 __isl_take isl_map *map,
2554 __isl_take isl_set *dom);
2555 __isl_give isl_map *isl_map_subtract_range(
2556 __isl_take isl_map *map,
2557 __isl_take isl_set *dom);
2558 __isl_give isl_union_set *isl_union_set_subtract(
2559 __isl_take isl_union_set *uset1,
2560 __isl_take isl_union_set *uset2);
2561 __isl_give isl_union_map *isl_union_map_subtract(
2562 __isl_take isl_union_map *umap1,
2563 __isl_take isl_union_map *umap2);
2567 __isl_give isl_basic_set *isl_basic_set_apply(
2568 __isl_take isl_basic_set *bset,
2569 __isl_take isl_basic_map *bmap);
2570 __isl_give isl_set *isl_set_apply(
2571 __isl_take isl_set *set,
2572 __isl_take isl_map *map);
2573 __isl_give isl_union_set *isl_union_set_apply(
2574 __isl_take isl_union_set *uset,
2575 __isl_take isl_union_map *umap);
2576 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2577 __isl_take isl_basic_map *bmap1,
2578 __isl_take isl_basic_map *bmap2);
2579 __isl_give isl_basic_map *isl_basic_map_apply_range(
2580 __isl_take isl_basic_map *bmap1,
2581 __isl_take isl_basic_map *bmap2);
2582 __isl_give isl_map *isl_map_apply_domain(
2583 __isl_take isl_map *map1,
2584 __isl_take isl_map *map2);
2585 __isl_give isl_union_map *isl_union_map_apply_domain(
2586 __isl_take isl_union_map *umap1,
2587 __isl_take isl_union_map *umap2);
2588 __isl_give isl_map *isl_map_apply_range(
2589 __isl_take isl_map *map1,
2590 __isl_take isl_map *map2);
2591 __isl_give isl_union_map *isl_union_map_apply_range(
2592 __isl_take isl_union_map *umap1,
2593 __isl_take isl_union_map *umap2);
2595 =item * Cartesian Product
2597 __isl_give isl_set *isl_set_product(
2598 __isl_take isl_set *set1,
2599 __isl_take isl_set *set2);
2600 __isl_give isl_union_set *isl_union_set_product(
2601 __isl_take isl_union_set *uset1,
2602 __isl_take isl_union_set *uset2);
2603 __isl_give isl_basic_map *isl_basic_map_domain_product(
2604 __isl_take isl_basic_map *bmap1,
2605 __isl_take isl_basic_map *bmap2);
2606 __isl_give isl_basic_map *isl_basic_map_range_product(
2607 __isl_take isl_basic_map *bmap1,
2608 __isl_take isl_basic_map *bmap2);
2609 __isl_give isl_basic_map *isl_basic_map_product(
2610 __isl_take isl_basic_map *bmap1,
2611 __isl_take isl_basic_map *bmap2);
2612 __isl_give isl_map *isl_map_domain_product(
2613 __isl_take isl_map *map1,
2614 __isl_take isl_map *map2);
2615 __isl_give isl_map *isl_map_range_product(
2616 __isl_take isl_map *map1,
2617 __isl_take isl_map *map2);
2618 __isl_give isl_union_map *isl_union_map_domain_product(
2619 __isl_take isl_union_map *umap1,
2620 __isl_take isl_union_map *umap2);
2621 __isl_give isl_union_map *isl_union_map_range_product(
2622 __isl_take isl_union_map *umap1,
2623 __isl_take isl_union_map *umap2);
2624 __isl_give isl_map *isl_map_product(
2625 __isl_take isl_map *map1,
2626 __isl_take isl_map *map2);
2627 __isl_give isl_union_map *isl_union_map_product(
2628 __isl_take isl_union_map *umap1,
2629 __isl_take isl_union_map *umap2);
2631 The above functions compute the cross product of the given
2632 sets or relations. The domains and ranges of the results
2633 are wrapped maps between domains and ranges of the inputs.
2634 To obtain a ``flat'' product, use the following functions
2637 __isl_give isl_basic_set *isl_basic_set_flat_product(
2638 __isl_take isl_basic_set *bset1,
2639 __isl_take isl_basic_set *bset2);
2640 __isl_give isl_set *isl_set_flat_product(
2641 __isl_take isl_set *set1,
2642 __isl_take isl_set *set2);
2643 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2644 __isl_take isl_basic_map *bmap1,
2645 __isl_take isl_basic_map *bmap2);
2646 __isl_give isl_map *isl_map_flat_domain_product(
2647 __isl_take isl_map *map1,
2648 __isl_take isl_map *map2);
2649 __isl_give isl_map *isl_map_flat_range_product(
2650 __isl_take isl_map *map1,
2651 __isl_take isl_map *map2);
2652 __isl_give isl_union_map *isl_union_map_flat_range_product(
2653 __isl_take isl_union_map *umap1,
2654 __isl_take isl_union_map *umap2);
2655 __isl_give isl_basic_map *isl_basic_map_flat_product(
2656 __isl_take isl_basic_map *bmap1,
2657 __isl_take isl_basic_map *bmap2);
2658 __isl_give isl_map *isl_map_flat_product(
2659 __isl_take isl_map *map1,
2660 __isl_take isl_map *map2);
2662 =item * Simplification
2664 __isl_give isl_basic_set *isl_basic_set_gist(
2665 __isl_take isl_basic_set *bset,
2666 __isl_take isl_basic_set *context);
2667 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2668 __isl_take isl_set *context);
2669 __isl_give isl_set *isl_set_gist_params(
2670 __isl_take isl_set *set,
2671 __isl_take isl_set *context);
2672 __isl_give isl_union_set *isl_union_set_gist(
2673 __isl_take isl_union_set *uset,
2674 __isl_take isl_union_set *context);
2675 __isl_give isl_union_set *isl_union_set_gist_params(
2676 __isl_take isl_union_set *uset,
2677 __isl_take isl_set *set);
2678 __isl_give isl_basic_map *isl_basic_map_gist(
2679 __isl_take isl_basic_map *bmap,
2680 __isl_take isl_basic_map *context);
2681 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2682 __isl_take isl_map *context);
2683 __isl_give isl_map *isl_map_gist_params(
2684 __isl_take isl_map *map,
2685 __isl_take isl_set *context);
2686 __isl_give isl_map *isl_map_gist_domain(
2687 __isl_take isl_map *map,
2688 __isl_take isl_set *context);
2689 __isl_give isl_map *isl_map_gist_range(
2690 __isl_take isl_map *map,
2691 __isl_take isl_set *context);
2692 __isl_give isl_union_map *isl_union_map_gist(
2693 __isl_take isl_union_map *umap,
2694 __isl_take isl_union_map *context);
2695 __isl_give isl_union_map *isl_union_map_gist_params(
2696 __isl_take isl_union_map *umap,
2697 __isl_take isl_set *set);
2698 __isl_give isl_union_map *isl_union_map_gist_domain(
2699 __isl_take isl_union_map *umap,
2700 __isl_take isl_union_set *uset);
2701 __isl_give isl_union_map *isl_union_map_gist_range(
2702 __isl_take isl_union_map *umap,
2703 __isl_take isl_union_set *uset);
2705 The gist operation returns a set or relation that has the
2706 same intersection with the context as the input set or relation.
2707 Any implicit equality in the intersection is made explicit in the result,
2708 while all inequalities that are redundant with respect to the intersection
2710 In case of union sets and relations, the gist operation is performed
2715 =head3 Lexicographic Optimization
2717 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2718 the following functions
2719 compute a set that contains the lexicographic minimum or maximum
2720 of the elements in C<set> (or C<bset>) for those values of the parameters
2721 that satisfy C<dom>.
2722 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2723 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2725 In other words, the union of the parameter values
2726 for which the result is non-empty and of C<*empty>
2729 __isl_give isl_set *isl_basic_set_partial_lexmin(
2730 __isl_take isl_basic_set *bset,
2731 __isl_take isl_basic_set *dom,
2732 __isl_give isl_set **empty);
2733 __isl_give isl_set *isl_basic_set_partial_lexmax(
2734 __isl_take isl_basic_set *bset,
2735 __isl_take isl_basic_set *dom,
2736 __isl_give isl_set **empty);
2737 __isl_give isl_set *isl_set_partial_lexmin(
2738 __isl_take isl_set *set, __isl_take isl_set *dom,
2739 __isl_give isl_set **empty);
2740 __isl_give isl_set *isl_set_partial_lexmax(
2741 __isl_take isl_set *set, __isl_take isl_set *dom,
2742 __isl_give isl_set **empty);
2744 Given a (basic) set C<set> (or C<bset>), the following functions simply
2745 return a set containing the lexicographic minimum or maximum
2746 of the elements in C<set> (or C<bset>).
2747 In case of union sets, the optimum is computed per space.
2749 __isl_give isl_set *isl_basic_set_lexmin(
2750 __isl_take isl_basic_set *bset);
2751 __isl_give isl_set *isl_basic_set_lexmax(
2752 __isl_take isl_basic_set *bset);
2753 __isl_give isl_set *isl_set_lexmin(
2754 __isl_take isl_set *set);
2755 __isl_give isl_set *isl_set_lexmax(
2756 __isl_take isl_set *set);
2757 __isl_give isl_union_set *isl_union_set_lexmin(
2758 __isl_take isl_union_set *uset);
2759 __isl_give isl_union_set *isl_union_set_lexmax(
2760 __isl_take isl_union_set *uset);
2762 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2763 the following functions
2764 compute a relation that maps each element of C<dom>
2765 to the single lexicographic minimum or maximum
2766 of the elements that are associated to that same
2767 element in C<map> (or C<bmap>).
2768 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2769 that contains the elements in C<dom> that do not map
2770 to any elements in C<map> (or C<bmap>).
2771 In other words, the union of the domain of the result and of C<*empty>
2774 __isl_give isl_map *isl_basic_map_partial_lexmax(
2775 __isl_take isl_basic_map *bmap,
2776 __isl_take isl_basic_set *dom,
2777 __isl_give isl_set **empty);
2778 __isl_give isl_map *isl_basic_map_partial_lexmin(
2779 __isl_take isl_basic_map *bmap,
2780 __isl_take isl_basic_set *dom,
2781 __isl_give isl_set **empty);
2782 __isl_give isl_map *isl_map_partial_lexmax(
2783 __isl_take isl_map *map, __isl_take isl_set *dom,
2784 __isl_give isl_set **empty);
2785 __isl_give isl_map *isl_map_partial_lexmin(
2786 __isl_take isl_map *map, __isl_take isl_set *dom,
2787 __isl_give isl_set **empty);
2789 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2790 return a map mapping each element in the domain of
2791 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2792 of all elements associated to that element.
2793 In case of union relations, the optimum is computed per space.
2795 __isl_give isl_map *isl_basic_map_lexmin(
2796 __isl_take isl_basic_map *bmap);
2797 __isl_give isl_map *isl_basic_map_lexmax(
2798 __isl_take isl_basic_map *bmap);
2799 __isl_give isl_map *isl_map_lexmin(
2800 __isl_take isl_map *map);
2801 __isl_give isl_map *isl_map_lexmax(
2802 __isl_take isl_map *map);
2803 __isl_give isl_union_map *isl_union_map_lexmin(
2804 __isl_take isl_union_map *umap);
2805 __isl_give isl_union_map *isl_union_map_lexmax(
2806 __isl_take isl_union_map *umap);
2808 The following functions return their result in the form of
2809 a piecewise multi-affine expression
2810 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2811 but are otherwise equivalent to the corresponding functions
2812 returning a basic set or relation.
2814 __isl_give isl_pw_multi_aff *
2815 isl_basic_map_lexmin_pw_multi_aff(
2816 __isl_take isl_basic_map *bmap);
2817 __isl_give isl_pw_multi_aff *
2818 isl_basic_set_partial_lexmin_pw_multi_aff(
2819 __isl_take isl_basic_set *bset,
2820 __isl_take isl_basic_set *dom,
2821 __isl_give isl_set **empty);
2822 __isl_give isl_pw_multi_aff *
2823 isl_basic_set_partial_lexmax_pw_multi_aff(
2824 __isl_take isl_basic_set *bset,
2825 __isl_take isl_basic_set *dom,
2826 __isl_give isl_set **empty);
2827 __isl_give isl_pw_multi_aff *
2828 isl_basic_map_partial_lexmin_pw_multi_aff(
2829 __isl_take isl_basic_map *bmap,
2830 __isl_take isl_basic_set *dom,
2831 __isl_give isl_set **empty);
2832 __isl_give isl_pw_multi_aff *
2833 isl_basic_map_partial_lexmax_pw_multi_aff(
2834 __isl_take isl_basic_map *bmap,
2835 __isl_take isl_basic_set *dom,
2836 __isl_give isl_set **empty);
2840 Lists are defined over several element types, including
2841 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2842 Here we take lists of C<isl_set>s as an example.
2843 Lists can be created, copied, modified and freed using the following functions.
2845 #include <isl/list.h>
2846 __isl_give isl_set_list *isl_set_list_from_set(
2847 __isl_take isl_set *el);
2848 __isl_give isl_set_list *isl_set_list_alloc(
2849 isl_ctx *ctx, int n);
2850 __isl_give isl_set_list *isl_set_list_copy(
2851 __isl_keep isl_set_list *list);
2852 __isl_give isl_set_list *isl_set_list_add(
2853 __isl_take isl_set_list *list,
2854 __isl_take isl_set *el);
2855 __isl_give isl_set_list *isl_set_list_set_set(
2856 __isl_take isl_set_list *list, int index,
2857 __isl_take isl_set *set);
2858 __isl_give isl_set_list *isl_set_list_concat(
2859 __isl_take isl_set_list *list1,
2860 __isl_take isl_set_list *list2);
2861 void *isl_set_list_free(__isl_take isl_set_list *list);
2863 C<isl_set_list_alloc> creates an empty list with a capacity for
2864 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2867 Lists can be inspected using the following functions.
2869 #include <isl/list.h>
2870 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2871 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2872 __isl_give isl_set *isl_set_list_get_set(
2873 __isl_keep isl_set_list *list, int index);
2874 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2875 int (*fn)(__isl_take isl_set *el, void *user),
2878 Lists can be printed using
2880 #include <isl/list.h>
2881 __isl_give isl_printer *isl_printer_print_set_list(
2882 __isl_take isl_printer *p,
2883 __isl_keep isl_set_list *list);
2887 Vectors can be created, copied and freed using the following functions.
2889 #include <isl/vec.h>
2890 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2892 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2893 void isl_vec_free(__isl_take isl_vec *vec);
2895 Note that the elements of a newly created vector may have arbitrary values.
2896 The elements can be changed and inspected using the following functions.
2898 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2899 int isl_vec_size(__isl_keep isl_vec *vec);
2900 int isl_vec_get_element(__isl_keep isl_vec *vec,
2901 int pos, isl_int *v);
2902 __isl_give isl_vec *isl_vec_set_element(
2903 __isl_take isl_vec *vec, int pos, isl_int v);
2904 __isl_give isl_vec *isl_vec_set_element_si(
2905 __isl_take isl_vec *vec, int pos, int v);
2906 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2908 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2911 C<isl_vec_get_element> will return a negative value if anything went wrong.
2912 In that case, the value of C<*v> is undefined.
2916 Matrices can be created, copied and freed using the following functions.
2918 #include <isl/mat.h>
2919 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
2920 unsigned n_row, unsigned n_col);
2921 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
2922 void isl_mat_free(__isl_take isl_mat *mat);
2924 Note that the elements of a newly created matrix may have arbitrary values.
2925 The elements can be changed and inspected using the following functions.
2927 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
2928 int isl_mat_rows(__isl_keep isl_mat *mat);
2929 int isl_mat_cols(__isl_keep isl_mat *mat);
2930 int isl_mat_get_element(__isl_keep isl_mat *mat,
2931 int row, int col, isl_int *v);
2932 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
2933 int row, int col, isl_int v);
2934 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
2935 int row, int col, int v);
2937 C<isl_mat_get_element> will return a negative value if anything went wrong.
2938 In that case, the value of C<*v> is undefined.
2940 The following function can be used to compute the (right) inverse
2941 of a matrix, i.e., a matrix such that the product of the original
2942 and the inverse (in that order) is a multiple of the identity matrix.
2943 The input matrix is assumed to be of full row-rank.
2945 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
2947 The following function can be used to compute the (right) kernel
2948 (or null space) of a matrix, i.e., a matrix such that the product of
2949 the original and the kernel (in that order) is the zero matrix.
2951 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
2953 =head2 Piecewise Quasi Affine Expressions
2955 The zero quasi affine expression on a given domain can be created using
2957 __isl_give isl_aff *isl_aff_zero_on_domain(
2958 __isl_take isl_local_space *ls);
2960 Note that the space in which the resulting object lives is a map space
2961 with the given space as domain and a one-dimensional range.
2963 An empty piecewise quasi affine expression (one with no cells)
2964 or a piecewise quasi affine expression with a single cell can
2965 be created using the following functions.
2967 #include <isl/aff.h>
2968 __isl_give isl_pw_aff *isl_pw_aff_empty(
2969 __isl_take isl_space *space);
2970 __isl_give isl_pw_aff *isl_pw_aff_alloc(
2971 __isl_take isl_set *set, __isl_take isl_aff *aff);
2972 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
2973 __isl_take isl_aff *aff);
2975 A piecewise quasi affine expression that is equal to 1 on a set
2976 and 0 outside the set can be created using the following function.
2978 #include <isl/aff.h>
2979 __isl_give isl_pw_aff *isl_set_indicator_function(
2980 __isl_take isl_set *set);
2982 Quasi affine expressions can be copied and freed using
2984 #include <isl/aff.h>
2985 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
2986 void *isl_aff_free(__isl_take isl_aff *aff);
2988 __isl_give isl_pw_aff *isl_pw_aff_copy(
2989 __isl_keep isl_pw_aff *pwaff);
2990 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
2992 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
2993 using the following function. The constraint is required to have
2994 a non-zero coefficient for the specified dimension.
2996 #include <isl/constraint.h>
2997 __isl_give isl_aff *isl_constraint_get_bound(
2998 __isl_keep isl_constraint *constraint,
2999 enum isl_dim_type type, int pos);
3001 The entire affine expression of the constraint can also be extracted
3002 using the following function.
3004 #include <isl/constraint.h>
3005 __isl_give isl_aff *isl_constraint_get_aff(
3006 __isl_keep isl_constraint *constraint);
3008 Conversely, an equality constraint equating
3009 the affine expression to zero or an inequality constraint enforcing
3010 the affine expression to be non-negative, can be constructed using
3012 __isl_give isl_constraint *isl_equality_from_aff(
3013 __isl_take isl_aff *aff);
3014 __isl_give isl_constraint *isl_inequality_from_aff(
3015 __isl_take isl_aff *aff);
3017 The expression can be inspected using
3019 #include <isl/aff.h>
3020 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3021 int isl_aff_dim(__isl_keep isl_aff *aff,
3022 enum isl_dim_type type);
3023 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3024 __isl_keep isl_aff *aff);
3025 __isl_give isl_local_space *isl_aff_get_local_space(
3026 __isl_keep isl_aff *aff);
3027 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3028 enum isl_dim_type type, unsigned pos);
3029 const char *isl_pw_aff_get_dim_name(
3030 __isl_keep isl_pw_aff *pa,
3031 enum isl_dim_type type, unsigned pos);
3032 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3033 enum isl_dim_type type, unsigned pos);
3034 __isl_give isl_id *isl_pw_aff_get_dim_id(
3035 __isl_keep isl_pw_aff *pa,
3036 enum isl_dim_type type, unsigned pos);
3037 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3038 __isl_keep isl_pw_aff *pa,
3039 enum isl_dim_type type);
3040 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3042 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3043 enum isl_dim_type type, int pos, isl_int *v);
3044 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3046 __isl_give isl_aff *isl_aff_get_div(
3047 __isl_keep isl_aff *aff, int pos);
3049 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3050 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3051 int (*fn)(__isl_take isl_set *set,
3052 __isl_take isl_aff *aff,
3053 void *user), void *user);
3055 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3056 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3058 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3059 enum isl_dim_type type, unsigned first, unsigned n);
3060 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3061 enum isl_dim_type type, unsigned first, unsigned n);
3063 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3064 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3065 enum isl_dim_type type);
3066 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3068 It can be modified using
3070 #include <isl/aff.h>
3071 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3072 __isl_take isl_pw_aff *pwaff,
3073 enum isl_dim_type type, __isl_take isl_id *id);
3074 __isl_give isl_aff *isl_aff_set_dim_name(
3075 __isl_take isl_aff *aff, enum isl_dim_type type,
3076 unsigned pos, const char *s);
3077 __isl_give isl_aff *isl_aff_set_dim_id(
3078 __isl_take isl_aff *aff, enum isl_dim_type type,
3079 unsigned pos, __isl_take isl_id *id);
3080 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3081 __isl_take isl_pw_aff *pma,
3082 enum isl_dim_type type, unsigned pos,
3083 __isl_take isl_id *id);
3084 __isl_give isl_aff *isl_aff_set_constant(
3085 __isl_take isl_aff *aff, isl_int v);
3086 __isl_give isl_aff *isl_aff_set_constant_si(
3087 __isl_take isl_aff *aff, int v);
3088 __isl_give isl_aff *isl_aff_set_coefficient(
3089 __isl_take isl_aff *aff,
3090 enum isl_dim_type type, int pos, isl_int v);
3091 __isl_give isl_aff *isl_aff_set_coefficient_si(
3092 __isl_take isl_aff *aff,
3093 enum isl_dim_type type, int pos, int v);
3094 __isl_give isl_aff *isl_aff_set_denominator(
3095 __isl_take isl_aff *aff, isl_int v);
3097 __isl_give isl_aff *isl_aff_add_constant(
3098 __isl_take isl_aff *aff, isl_int v);
3099 __isl_give isl_aff *isl_aff_add_constant_si(
3100 __isl_take isl_aff *aff, int v);
3101 __isl_give isl_aff *isl_aff_add_constant_num(
3102 __isl_take isl_aff *aff, isl_int v);
3103 __isl_give isl_aff *isl_aff_add_constant_num_si(
3104 __isl_take isl_aff *aff, int v);
3105 __isl_give isl_aff *isl_aff_add_coefficient(
3106 __isl_take isl_aff *aff,
3107 enum isl_dim_type type, int pos, isl_int v);
3108 __isl_give isl_aff *isl_aff_add_coefficient_si(
3109 __isl_take isl_aff *aff,
3110 enum isl_dim_type type, int pos, int v);
3112 __isl_give isl_aff *isl_aff_insert_dims(
3113 __isl_take isl_aff *aff,
3114 enum isl_dim_type type, unsigned first, unsigned n);
3115 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3116 __isl_take isl_pw_aff *pwaff,
3117 enum isl_dim_type type, unsigned first, unsigned n);
3118 __isl_give isl_aff *isl_aff_add_dims(
3119 __isl_take isl_aff *aff,
3120 enum isl_dim_type type, unsigned n);
3121 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3122 __isl_take isl_pw_aff *pwaff,
3123 enum isl_dim_type type, unsigned n);
3124 __isl_give isl_aff *isl_aff_drop_dims(
3125 __isl_take isl_aff *aff,
3126 enum isl_dim_type type, unsigned first, unsigned n);
3127 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3128 __isl_take isl_pw_aff *pwaff,
3129 enum isl_dim_type type, unsigned first, unsigned n);
3131 Note that the C<set_constant> and C<set_coefficient> functions
3132 set the I<numerator> of the constant or coefficient, while
3133 C<add_constant> and C<add_coefficient> add an integer value to
3134 the possibly rational constant or coefficient.
3135 The C<add_constant_num> functions add an integer value to
3138 To check whether an affine expressions is obviously zero
3139 or obviously equal to some other affine expression, use
3141 #include <isl/aff.h>
3142 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3143 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3144 __isl_keep isl_aff *aff2);
3145 int isl_pw_aff_plain_is_equal(
3146 __isl_keep isl_pw_aff *pwaff1,
3147 __isl_keep isl_pw_aff *pwaff2);
3151 #include <isl/aff.h>
3152 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3153 __isl_take isl_aff *aff2);
3154 __isl_give isl_pw_aff *isl_pw_aff_add(
3155 __isl_take isl_pw_aff *pwaff1,
3156 __isl_take isl_pw_aff *pwaff2);
3157 __isl_give isl_pw_aff *isl_pw_aff_min(
3158 __isl_take isl_pw_aff *pwaff1,
3159 __isl_take isl_pw_aff *pwaff2);
3160 __isl_give isl_pw_aff *isl_pw_aff_max(
3161 __isl_take isl_pw_aff *pwaff1,
3162 __isl_take isl_pw_aff *pwaff2);
3163 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3164 __isl_take isl_aff *aff2);
3165 __isl_give isl_pw_aff *isl_pw_aff_sub(
3166 __isl_take isl_pw_aff *pwaff1,
3167 __isl_take isl_pw_aff *pwaff2);
3168 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3169 __isl_give isl_pw_aff *isl_pw_aff_neg(
3170 __isl_take isl_pw_aff *pwaff);
3171 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3172 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3173 __isl_take isl_pw_aff *pwaff);
3174 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3175 __isl_give isl_pw_aff *isl_pw_aff_floor(
3176 __isl_take isl_pw_aff *pwaff);
3177 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3179 __isl_give isl_pw_aff *isl_pw_aff_mod(
3180 __isl_take isl_pw_aff *pwaff, isl_int mod);
3181 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3183 __isl_give isl_pw_aff *isl_pw_aff_scale(
3184 __isl_take isl_pw_aff *pwaff, isl_int f);
3185 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3187 __isl_give isl_aff *isl_aff_scale_down_ui(
3188 __isl_take isl_aff *aff, unsigned f);
3189 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3190 __isl_take isl_pw_aff *pwaff, isl_int f);
3192 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3193 __isl_take isl_pw_aff_list *list);
3194 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3195 __isl_take isl_pw_aff_list *list);
3197 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3198 __isl_take isl_pw_aff *pwqp);
3200 __isl_give isl_aff *isl_aff_align_params(
3201 __isl_take isl_aff *aff,
3202 __isl_take isl_space *model);
3203 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3204 __isl_take isl_pw_aff *pwaff,
3205 __isl_take isl_space *model);
3207 __isl_give isl_aff *isl_aff_project_domain_on_params(
3208 __isl_take isl_aff *aff);
3210 __isl_give isl_aff *isl_aff_gist_params(
3211 __isl_take isl_aff *aff,
3212 __isl_take isl_set *context);
3213 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3214 __isl_take isl_set *context);
3215 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3216 __isl_take isl_pw_aff *pwaff,
3217 __isl_take isl_set *context);
3218 __isl_give isl_pw_aff *isl_pw_aff_gist(
3219 __isl_take isl_pw_aff *pwaff,
3220 __isl_take isl_set *context);
3222 __isl_give isl_set *isl_pw_aff_domain(
3223 __isl_take isl_pw_aff *pwaff);
3224 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3225 __isl_take isl_pw_aff *pa,
3226 __isl_take isl_set *set);
3227 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3228 __isl_take isl_pw_aff *pa,
3229 __isl_take isl_set *set);
3231 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3232 __isl_take isl_aff *aff2);
3233 __isl_give isl_pw_aff *isl_pw_aff_mul(
3234 __isl_take isl_pw_aff *pwaff1,
3235 __isl_take isl_pw_aff *pwaff2);
3237 When multiplying two affine expressions, at least one of the two needs
3240 #include <isl/aff.h>
3241 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3242 __isl_take isl_aff *aff);
3243 __isl_give isl_basic_set *isl_aff_le_basic_set(
3244 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3245 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3246 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3247 __isl_give isl_set *isl_pw_aff_eq_set(
3248 __isl_take isl_pw_aff *pwaff1,
3249 __isl_take isl_pw_aff *pwaff2);
3250 __isl_give isl_set *isl_pw_aff_ne_set(
3251 __isl_take isl_pw_aff *pwaff1,
3252 __isl_take isl_pw_aff *pwaff2);
3253 __isl_give isl_set *isl_pw_aff_le_set(
3254 __isl_take isl_pw_aff *pwaff1,
3255 __isl_take isl_pw_aff *pwaff2);
3256 __isl_give isl_set *isl_pw_aff_lt_set(
3257 __isl_take isl_pw_aff *pwaff1,
3258 __isl_take isl_pw_aff *pwaff2);
3259 __isl_give isl_set *isl_pw_aff_ge_set(
3260 __isl_take isl_pw_aff *pwaff1,
3261 __isl_take isl_pw_aff *pwaff2);
3262 __isl_give isl_set *isl_pw_aff_gt_set(
3263 __isl_take isl_pw_aff *pwaff1,
3264 __isl_take isl_pw_aff *pwaff2);
3266 __isl_give isl_set *isl_pw_aff_list_eq_set(
3267 __isl_take isl_pw_aff_list *list1,
3268 __isl_take isl_pw_aff_list *list2);
3269 __isl_give isl_set *isl_pw_aff_list_ne_set(
3270 __isl_take isl_pw_aff_list *list1,
3271 __isl_take isl_pw_aff_list *list2);
3272 __isl_give isl_set *isl_pw_aff_list_le_set(
3273 __isl_take isl_pw_aff_list *list1,
3274 __isl_take isl_pw_aff_list *list2);
3275 __isl_give isl_set *isl_pw_aff_list_lt_set(
3276 __isl_take isl_pw_aff_list *list1,
3277 __isl_take isl_pw_aff_list *list2);
3278 __isl_give isl_set *isl_pw_aff_list_ge_set(
3279 __isl_take isl_pw_aff_list *list1,
3280 __isl_take isl_pw_aff_list *list2);
3281 __isl_give isl_set *isl_pw_aff_list_gt_set(
3282 __isl_take isl_pw_aff_list *list1,
3283 __isl_take isl_pw_aff_list *list2);
3285 The function C<isl_aff_neg_basic_set> returns a basic set
3286 containing those elements in the domain space
3287 of C<aff> where C<aff> is negative.
3288 The function C<isl_aff_ge_basic_set> returns a basic set
3289 containing those elements in the shared space
3290 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3291 The function C<isl_pw_aff_ge_set> returns a set
3292 containing those elements in the shared domain
3293 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3294 The functions operating on C<isl_pw_aff_list> apply the corresponding
3295 C<isl_pw_aff> function to each pair of elements in the two lists.
3297 #include <isl/aff.h>
3298 __isl_give isl_set *isl_pw_aff_nonneg_set(
3299 __isl_take isl_pw_aff *pwaff);
3300 __isl_give isl_set *isl_pw_aff_zero_set(
3301 __isl_take isl_pw_aff *pwaff);
3302 __isl_give isl_set *isl_pw_aff_non_zero_set(
3303 __isl_take isl_pw_aff *pwaff);
3305 The function C<isl_pw_aff_nonneg_set> returns a set
3306 containing those elements in the domain
3307 of C<pwaff> where C<pwaff> is non-negative.
3309 #include <isl/aff.h>
3310 __isl_give isl_pw_aff *isl_pw_aff_cond(
3311 __isl_take isl_pw_aff *cond,
3312 __isl_take isl_pw_aff *pwaff_true,
3313 __isl_take isl_pw_aff *pwaff_false);
3315 The function C<isl_pw_aff_cond> performs a conditional operator
3316 and returns an expression that is equal to C<pwaff_true>
3317 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3318 where C<cond> is zero.
3320 #include <isl/aff.h>
3321 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3322 __isl_take isl_pw_aff *pwaff1,
3323 __isl_take isl_pw_aff *pwaff2);
3324 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3325 __isl_take isl_pw_aff *pwaff1,
3326 __isl_take isl_pw_aff *pwaff2);
3327 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3328 __isl_take isl_pw_aff *pwaff1,
3329 __isl_take isl_pw_aff *pwaff2);
3331 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3332 expression with a domain that is the union of those of C<pwaff1> and
3333 C<pwaff2> and such that on each cell, the quasi-affine expression is
3334 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3335 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3336 associated expression is the defined one.
3338 An expression can be read from input using
3340 #include <isl/aff.h>
3341 __isl_give isl_aff *isl_aff_read_from_str(
3342 isl_ctx *ctx, const char *str);
3343 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3344 isl_ctx *ctx, const char *str);
3346 An expression can be printed using
3348 #include <isl/aff.h>
3349 __isl_give isl_printer *isl_printer_print_aff(
3350 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3352 __isl_give isl_printer *isl_printer_print_pw_aff(
3353 __isl_take isl_printer *p,
3354 __isl_keep isl_pw_aff *pwaff);
3356 =head2 Piecewise Multiple Quasi Affine Expressions
3358 An C<isl_multi_aff> object represents a sequence of
3359 zero or more affine expressions, all defined on the same domain space.
3361 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3364 #include <isl/aff.h>
3365 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3366 __isl_take isl_space *space,
3367 __isl_take isl_aff_list *list);
3369 An empty piecewise multiple quasi affine expression (one with no cells),
3370 the zero piecewise multiple quasi affine expression (with value zero
3371 for each output dimension),
3372 a piecewise multiple quasi affine expression with a single cell (with
3373 either a universe or a specified domain) or
3374 a zero-dimensional piecewise multiple quasi affine expression
3376 can be created using the following functions.
3378 #include <isl/aff.h>
3379 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3380 __isl_take isl_space *space);
3381 __isl_give isl_multi_aff *isl_multi_aff_zero(
3382 __isl_take isl_space *space);
3383 __isl_give isl_multi_aff *isl_multi_aff_identity(
3384 __isl_take isl_space *space);
3385 __isl_give isl_pw_multi_aff *
3386 isl_pw_multi_aff_from_multi_aff(
3387 __isl_take isl_multi_aff *ma);
3388 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3389 __isl_take isl_set *set,
3390 __isl_take isl_multi_aff *maff);
3391 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3392 __isl_take isl_set *set);
3394 __isl_give isl_union_pw_multi_aff *
3395 isl_union_pw_multi_aff_empty(
3396 __isl_take isl_space *space);
3397 __isl_give isl_union_pw_multi_aff *
3398 isl_union_pw_multi_aff_add_pw_multi_aff(
3399 __isl_take isl_union_pw_multi_aff *upma,
3400 __isl_take isl_pw_multi_aff *pma);
3401 __isl_give isl_union_pw_multi_aff *
3402 isl_union_pw_multi_aff_from_domain(
3403 __isl_take isl_union_set *uset);
3405 A piecewise multiple quasi affine expression can also be initialized
3406 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3407 and the C<isl_map> is single-valued.
3409 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3410 __isl_take isl_set *set);
3411 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3412 __isl_take isl_map *map);
3414 Multiple quasi affine expressions can be copied and freed using
3416 #include <isl/aff.h>
3417 __isl_give isl_multi_aff *isl_multi_aff_copy(
3418 __isl_keep isl_multi_aff *maff);
3419 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3421 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3422 __isl_keep isl_pw_multi_aff *pma);
3423 void *isl_pw_multi_aff_free(
3424 __isl_take isl_pw_multi_aff *pma);
3426 __isl_give isl_union_pw_multi_aff *
3427 isl_union_pw_multi_aff_copy(
3428 __isl_keep isl_union_pw_multi_aff *upma);
3429 void *isl_union_pw_multi_aff_free(
3430 __isl_take isl_union_pw_multi_aff *upma);
3432 The expression can be inspected using
3434 #include <isl/aff.h>
3435 isl_ctx *isl_multi_aff_get_ctx(
3436 __isl_keep isl_multi_aff *maff);
3437 isl_ctx *isl_pw_multi_aff_get_ctx(
3438 __isl_keep isl_pw_multi_aff *pma);
3439 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3440 __isl_keep isl_union_pw_multi_aff *upma);
3441 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3442 enum isl_dim_type type);
3443 unsigned isl_pw_multi_aff_dim(
3444 __isl_keep isl_pw_multi_aff *pma,
3445 enum isl_dim_type type);
3446 __isl_give isl_aff *isl_multi_aff_get_aff(
3447 __isl_keep isl_multi_aff *multi, int pos);
3448 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3449 __isl_keep isl_pw_multi_aff *pma, int pos);
3450 const char *isl_pw_multi_aff_get_dim_name(
3451 __isl_keep isl_pw_multi_aff *pma,
3452 enum isl_dim_type type, unsigned pos);
3453 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3454 __isl_keep isl_pw_multi_aff *pma,
3455 enum isl_dim_type type, unsigned pos);
3456 const char *isl_multi_aff_get_tuple_name(
3457 __isl_keep isl_multi_aff *multi,
3458 enum isl_dim_type type);
3459 int isl_pw_multi_aff_has_tuple_name(
3460 __isl_keep isl_pw_multi_aff *pma,
3461 enum isl_dim_type type);
3462 const char *isl_pw_multi_aff_get_tuple_name(
3463 __isl_keep isl_pw_multi_aff *pma,
3464 enum isl_dim_type type);
3465 int isl_pw_multi_aff_has_tuple_id(
3466 __isl_keep isl_pw_multi_aff *pma,
3467 enum isl_dim_type type);
3468 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3469 __isl_keep isl_pw_multi_aff *pma,
3470 enum isl_dim_type type);
3472 int isl_pw_multi_aff_foreach_piece(
3473 __isl_keep isl_pw_multi_aff *pma,
3474 int (*fn)(__isl_take isl_set *set,
3475 __isl_take isl_multi_aff *maff,
3476 void *user), void *user);
3478 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3479 __isl_keep isl_union_pw_multi_aff *upma,
3480 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3481 void *user), void *user);
3483 It can be modified using
3485 #include <isl/aff.h>
3486 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3487 __isl_take isl_multi_aff *multi, int pos,
3488 __isl_take isl_aff *aff);
3489 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3490 __isl_take isl_multi_aff *maff,
3491 enum isl_dim_type type, unsigned pos, const char *s);
3492 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3493 __isl_take isl_multi_aff *maff,
3494 enum isl_dim_type type, __isl_take isl_id *id);
3495 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3496 __isl_take isl_pw_multi_aff *pma,
3497 enum isl_dim_type type, __isl_take isl_id *id);
3499 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3500 __isl_take isl_multi_aff *maff,
3501 enum isl_dim_type type, unsigned first, unsigned n);
3503 To check whether two multiple affine expressions are
3504 obviously equal to each other, use
3506 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3507 __isl_keep isl_multi_aff *maff2);
3508 int isl_pw_multi_aff_plain_is_equal(
3509 __isl_keep isl_pw_multi_aff *pma1,
3510 __isl_keep isl_pw_multi_aff *pma2);
3514 #include <isl/aff.h>
3515 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3516 __isl_take isl_pw_multi_aff *pma1,
3517 __isl_take isl_pw_multi_aff *pma2);
3518 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3519 __isl_take isl_pw_multi_aff *pma1,
3520 __isl_take isl_pw_multi_aff *pma2);
3521 __isl_give isl_multi_aff *isl_multi_aff_add(
3522 __isl_take isl_multi_aff *maff1,
3523 __isl_take isl_multi_aff *maff2);
3524 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3525 __isl_take isl_pw_multi_aff *pma1,
3526 __isl_take isl_pw_multi_aff *pma2);
3527 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3528 __isl_take isl_union_pw_multi_aff *upma1,
3529 __isl_take isl_union_pw_multi_aff *upma2);
3530 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3531 __isl_take isl_pw_multi_aff *pma1,
3532 __isl_take isl_pw_multi_aff *pma2);
3533 __isl_give isl_multi_aff *isl_multi_aff_scale(
3534 __isl_take isl_multi_aff *maff,
3536 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3537 __isl_take isl_pw_multi_aff *pma,
3538 __isl_take isl_set *set);
3539 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3540 __isl_take isl_pw_multi_aff *pma,
3541 __isl_take isl_set *set);
3542 __isl_give isl_multi_aff *isl_multi_aff_lift(
3543 __isl_take isl_multi_aff *maff,
3544 __isl_give isl_local_space **ls);
3545 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3546 __isl_take isl_pw_multi_aff *pma);
3547 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3548 __isl_take isl_multi_aff *maff,
3549 __isl_take isl_set *context);
3550 __isl_give isl_multi_aff *isl_multi_aff_gist(
3551 __isl_take isl_multi_aff *maff,
3552 __isl_take isl_set *context);
3553 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3554 __isl_take isl_pw_multi_aff *pma,
3555 __isl_take isl_set *set);
3556 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3557 __isl_take isl_pw_multi_aff *pma,
3558 __isl_take isl_set *set);
3559 __isl_give isl_set *isl_pw_multi_aff_domain(
3560 __isl_take isl_pw_multi_aff *pma);
3561 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3562 __isl_take isl_union_pw_multi_aff *upma);
3563 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3564 __isl_take isl_multi_aff *ma1,
3565 __isl_take isl_multi_aff *ma2);
3566 __isl_give isl_multi_aff *isl_multi_aff_product(
3567 __isl_take isl_multi_aff *ma1,
3568 __isl_take isl_multi_aff *ma2);
3569 __isl_give isl_pw_multi_aff *
3570 isl_pw_multi_aff_flat_range_product(
3571 __isl_take isl_pw_multi_aff *pma1,
3572 __isl_take isl_pw_multi_aff *pma2);
3573 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3574 __isl_take isl_pw_multi_aff *pma1,
3575 __isl_take isl_pw_multi_aff *pma2);
3576 __isl_give isl_union_pw_multi_aff *
3577 isl_union_pw_multi_aff_flat_range_product(
3578 __isl_take isl_union_pw_multi_aff *upma1,
3579 __isl_take isl_union_pw_multi_aff *upma2);
3581 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3582 then it is assigned the local space that lies at the basis of
3583 the lifting applied.
3585 __isl_give isl_set *isl_multi_aff_lex_le_set(
3586 __isl_take isl_multi_aff *ma1,
3587 __isl_take isl_multi_aff *ma2);
3588 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3589 __isl_take isl_multi_aff *ma1,
3590 __isl_take isl_multi_aff *ma2);
3592 The function C<isl_multi_aff_lex_le_set> returns a set
3593 containing those elements in the shared domain space
3594 where C<ma1> is lexicographically smaller than or
3597 An expression can be read from input using
3599 #include <isl/aff.h>
3600 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3601 isl_ctx *ctx, const char *str);
3602 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3603 isl_ctx *ctx, const char *str);
3605 An expression can be printed using
3607 #include <isl/aff.h>
3608 __isl_give isl_printer *isl_printer_print_multi_aff(
3609 __isl_take isl_printer *p,
3610 __isl_keep isl_multi_aff *maff);
3611 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3612 __isl_take isl_printer *p,
3613 __isl_keep isl_pw_multi_aff *pma);
3614 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3615 __isl_take isl_printer *p,
3616 __isl_keep isl_union_pw_multi_aff *upma);
3620 Points are elements of a set. They can be used to construct
3621 simple sets (boxes) or they can be used to represent the
3622 individual elements of a set.
3623 The zero point (the origin) can be created using
3625 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3627 The coordinates of a point can be inspected, set and changed
3630 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3631 enum isl_dim_type type, int pos, isl_int *v);
3632 __isl_give isl_point *isl_point_set_coordinate(
3633 __isl_take isl_point *pnt,
3634 enum isl_dim_type type, int pos, isl_int v);
3636 __isl_give isl_point *isl_point_add_ui(
3637 __isl_take isl_point *pnt,
3638 enum isl_dim_type type, int pos, unsigned val);
3639 __isl_give isl_point *isl_point_sub_ui(
3640 __isl_take isl_point *pnt,
3641 enum isl_dim_type type, int pos, unsigned val);
3643 Other properties can be obtained using
3645 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3647 Points can be copied or freed using
3649 __isl_give isl_point *isl_point_copy(
3650 __isl_keep isl_point *pnt);
3651 void isl_point_free(__isl_take isl_point *pnt);
3653 A singleton set can be created from a point using
3655 __isl_give isl_basic_set *isl_basic_set_from_point(
3656 __isl_take isl_point *pnt);
3657 __isl_give isl_set *isl_set_from_point(
3658 __isl_take isl_point *pnt);
3660 and a box can be created from two opposite extremal points using
3662 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3663 __isl_take isl_point *pnt1,
3664 __isl_take isl_point *pnt2);
3665 __isl_give isl_set *isl_set_box_from_points(
3666 __isl_take isl_point *pnt1,
3667 __isl_take isl_point *pnt2);
3669 All elements of a B<bounded> (union) set can be enumerated using
3670 the following functions.
3672 int isl_set_foreach_point(__isl_keep isl_set *set,
3673 int (*fn)(__isl_take isl_point *pnt, void *user),
3675 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3676 int (*fn)(__isl_take isl_point *pnt, void *user),
3679 The function C<fn> is called for each integer point in
3680 C<set> with as second argument the last argument of
3681 the C<isl_set_foreach_point> call. The function C<fn>
3682 should return C<0> on success and C<-1> on failure.
3683 In the latter case, C<isl_set_foreach_point> will stop
3684 enumerating and return C<-1> as well.
3685 If the enumeration is performed successfully and to completion,
3686 then C<isl_set_foreach_point> returns C<0>.
3688 To obtain a single point of a (basic) set, use
3690 __isl_give isl_point *isl_basic_set_sample_point(
3691 __isl_take isl_basic_set *bset);
3692 __isl_give isl_point *isl_set_sample_point(
3693 __isl_take isl_set *set);
3695 If C<set> does not contain any (integer) points, then the
3696 resulting point will be ``void'', a property that can be
3699 int isl_point_is_void(__isl_keep isl_point *pnt);
3701 =head2 Piecewise Quasipolynomials
3703 A piecewise quasipolynomial is a particular kind of function that maps
3704 a parametric point to a rational value.
3705 More specifically, a quasipolynomial is a polynomial expression in greatest
3706 integer parts of affine expressions of parameters and variables.
3707 A piecewise quasipolynomial is a subdivision of a given parametric
3708 domain into disjoint cells with a quasipolynomial associated to
3709 each cell. The value of the piecewise quasipolynomial at a given
3710 point is the value of the quasipolynomial associated to the cell
3711 that contains the point. Outside of the union of cells,
3712 the value is assumed to be zero.
3713 For example, the piecewise quasipolynomial
3715 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3717 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3718 A given piecewise quasipolynomial has a fixed domain dimension.
3719 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3720 defined over different domains.
3721 Piecewise quasipolynomials are mainly used by the C<barvinok>
3722 library for representing the number of elements in a parametric set or map.
3723 For example, the piecewise quasipolynomial above represents
3724 the number of points in the map
3726 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3728 =head3 Input and Output
3730 Piecewise quasipolynomials can be read from input using
3732 __isl_give isl_union_pw_qpolynomial *
3733 isl_union_pw_qpolynomial_read_from_str(
3734 isl_ctx *ctx, const char *str);
3736 Quasipolynomials and piecewise quasipolynomials can be printed
3737 using the following functions.
3739 __isl_give isl_printer *isl_printer_print_qpolynomial(
3740 __isl_take isl_printer *p,
3741 __isl_keep isl_qpolynomial *qp);
3743 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3744 __isl_take isl_printer *p,
3745 __isl_keep isl_pw_qpolynomial *pwqp);
3747 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3748 __isl_take isl_printer *p,
3749 __isl_keep isl_union_pw_qpolynomial *upwqp);
3751 The output format of the printer
3752 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3753 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3755 In case of printing in C<ISL_FORMAT_C>, the user may want
3756 to set the names of all dimensions
3758 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3759 __isl_take isl_qpolynomial *qp,
3760 enum isl_dim_type type, unsigned pos,
3762 __isl_give isl_pw_qpolynomial *
3763 isl_pw_qpolynomial_set_dim_name(
3764 __isl_take isl_pw_qpolynomial *pwqp,
3765 enum isl_dim_type type, unsigned pos,
3768 =head3 Creating New (Piecewise) Quasipolynomials
3770 Some simple quasipolynomials can be created using the following functions.
3771 More complicated quasipolynomials can be created by applying
3772 operations such as addition and multiplication
3773 on the resulting quasipolynomials
3775 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3776 __isl_take isl_space *domain);
3777 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3778 __isl_take isl_space *domain);
3779 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3780 __isl_take isl_space *domain);
3781 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3782 __isl_take isl_space *domain);
3783 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3784 __isl_take isl_space *domain);
3785 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3786 __isl_take isl_space *domain,
3787 const isl_int n, const isl_int d);
3788 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3789 __isl_take isl_space *domain,
3790 enum isl_dim_type type, unsigned pos);
3791 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3792 __isl_take isl_aff *aff);
3794 Note that the space in which a quasipolynomial lives is a map space
3795 with a one-dimensional range. The C<domain> argument in some of
3796 the functions above corresponds to the domain of this map space.
3798 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3799 with a single cell can be created using the following functions.
3800 Multiple of these single cell piecewise quasipolynomials can
3801 be combined to create more complicated piecewise quasipolynomials.
3803 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3804 __isl_take isl_space *space);
3805 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3806 __isl_take isl_set *set,
3807 __isl_take isl_qpolynomial *qp);
3808 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3809 __isl_take isl_qpolynomial *qp);
3810 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3811 __isl_take isl_pw_aff *pwaff);
3813 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3814 __isl_take isl_space *space);
3815 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3816 __isl_take isl_pw_qpolynomial *pwqp);
3817 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3818 __isl_take isl_union_pw_qpolynomial *upwqp,
3819 __isl_take isl_pw_qpolynomial *pwqp);
3821 Quasipolynomials can be copied and freed again using the following
3824 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3825 __isl_keep isl_qpolynomial *qp);
3826 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3828 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3829 __isl_keep isl_pw_qpolynomial *pwqp);
3830 void *isl_pw_qpolynomial_free(
3831 __isl_take isl_pw_qpolynomial *pwqp);
3833 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3834 __isl_keep isl_union_pw_qpolynomial *upwqp);
3835 void *isl_union_pw_qpolynomial_free(
3836 __isl_take isl_union_pw_qpolynomial *upwqp);
3838 =head3 Inspecting (Piecewise) Quasipolynomials
3840 To iterate over all piecewise quasipolynomials in a union
3841 piecewise quasipolynomial, use the following function
3843 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3844 __isl_keep isl_union_pw_qpolynomial *upwqp,
3845 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3848 To extract the piecewise quasipolynomial in a given space from a union, use
3850 __isl_give isl_pw_qpolynomial *
3851 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3852 __isl_keep isl_union_pw_qpolynomial *upwqp,
3853 __isl_take isl_space *space);
3855 To iterate over the cells in a piecewise quasipolynomial,
3856 use either of the following two functions
3858 int isl_pw_qpolynomial_foreach_piece(
3859 __isl_keep isl_pw_qpolynomial *pwqp,
3860 int (*fn)(__isl_take isl_set *set,
3861 __isl_take isl_qpolynomial *qp,
3862 void *user), void *user);
3863 int isl_pw_qpolynomial_foreach_lifted_piece(
3864 __isl_keep isl_pw_qpolynomial *pwqp,
3865 int (*fn)(__isl_take isl_set *set,
3866 __isl_take isl_qpolynomial *qp,
3867 void *user), void *user);
3869 As usual, the function C<fn> should return C<0> on success
3870 and C<-1> on failure. The difference between
3871 C<isl_pw_qpolynomial_foreach_piece> and
3872 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3873 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3874 compute unique representations for all existentially quantified
3875 variables and then turn these existentially quantified variables
3876 into extra set variables, adapting the associated quasipolynomial
3877 accordingly. This means that the C<set> passed to C<fn>
3878 will not have any existentially quantified variables, but that
3879 the dimensions of the sets may be different for different
3880 invocations of C<fn>.
3882 To iterate over all terms in a quasipolynomial,
3885 int isl_qpolynomial_foreach_term(
3886 __isl_keep isl_qpolynomial *qp,
3887 int (*fn)(__isl_take isl_term *term,
3888 void *user), void *user);
3890 The terms themselves can be inspected and freed using
3893 unsigned isl_term_dim(__isl_keep isl_term *term,
3894 enum isl_dim_type type);
3895 void isl_term_get_num(__isl_keep isl_term *term,
3897 void isl_term_get_den(__isl_keep isl_term *term,
3899 int isl_term_get_exp(__isl_keep isl_term *term,
3900 enum isl_dim_type type, unsigned pos);
3901 __isl_give isl_aff *isl_term_get_div(
3902 __isl_keep isl_term *term, unsigned pos);
3903 void isl_term_free(__isl_take isl_term *term);
3905 Each term is a product of parameters, set variables and
3906 integer divisions. The function C<isl_term_get_exp>
3907 returns the exponent of a given dimensions in the given term.
3908 The C<isl_int>s in the arguments of C<isl_term_get_num>
3909 and C<isl_term_get_den> need to have been initialized
3910 using C<isl_int_init> before calling these functions.
3912 =head3 Properties of (Piecewise) Quasipolynomials
3914 To check whether a quasipolynomial is actually a constant,
3915 use the following function.
3917 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
3918 isl_int *n, isl_int *d);
3920 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
3921 then the numerator and denominator of the constant
3922 are returned in C<*n> and C<*d>, respectively.
3924 To check whether two union piecewise quasipolynomials are
3925 obviously equal, use
3927 int isl_union_pw_qpolynomial_plain_is_equal(
3928 __isl_keep isl_union_pw_qpolynomial *upwqp1,
3929 __isl_keep isl_union_pw_qpolynomial *upwqp2);
3931 =head3 Operations on (Piecewise) Quasipolynomials
3933 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
3934 __isl_take isl_qpolynomial *qp, isl_int v);
3935 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
3936 __isl_take isl_qpolynomial *qp);
3937 __isl_give isl_qpolynomial *isl_qpolynomial_add(
3938 __isl_take isl_qpolynomial *qp1,
3939 __isl_take isl_qpolynomial *qp2);
3940 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
3941 __isl_take isl_qpolynomial *qp1,
3942 __isl_take isl_qpolynomial *qp2);
3943 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
3944 __isl_take isl_qpolynomial *qp1,
3945 __isl_take isl_qpolynomial *qp2);
3946 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
3947 __isl_take isl_qpolynomial *qp, unsigned exponent);
3949 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
3950 __isl_take isl_pw_qpolynomial *pwqp1,
3951 __isl_take isl_pw_qpolynomial *pwqp2);
3952 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
3953 __isl_take isl_pw_qpolynomial *pwqp1,
3954 __isl_take isl_pw_qpolynomial *pwqp2);
3955 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
3956 __isl_take isl_pw_qpolynomial *pwqp1,
3957 __isl_take isl_pw_qpolynomial *pwqp2);
3958 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
3959 __isl_take isl_pw_qpolynomial *pwqp);
3960 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
3961 __isl_take isl_pw_qpolynomial *pwqp1,
3962 __isl_take isl_pw_qpolynomial *pwqp2);
3963 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
3964 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
3966 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
3967 __isl_take isl_union_pw_qpolynomial *upwqp1,
3968 __isl_take isl_union_pw_qpolynomial *upwqp2);
3969 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
3970 __isl_take isl_union_pw_qpolynomial *upwqp1,
3971 __isl_take isl_union_pw_qpolynomial *upwqp2);
3972 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
3973 __isl_take isl_union_pw_qpolynomial *upwqp1,
3974 __isl_take isl_union_pw_qpolynomial *upwqp2);
3976 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
3977 __isl_take isl_pw_qpolynomial *pwqp,
3978 __isl_take isl_point *pnt);
3980 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
3981 __isl_take isl_union_pw_qpolynomial *upwqp,
3982 __isl_take isl_point *pnt);
3984 __isl_give isl_set *isl_pw_qpolynomial_domain(
3985 __isl_take isl_pw_qpolynomial *pwqp);
3986 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
3987 __isl_take isl_pw_qpolynomial *pwpq,
3988 __isl_take isl_set *set);
3989 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
3990 __isl_take isl_pw_qpolynomial *pwpq,
3991 __isl_take isl_set *set);
3993 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
3994 __isl_take isl_union_pw_qpolynomial *upwqp);
3995 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
3996 __isl_take isl_union_pw_qpolynomial *upwpq,
3997 __isl_take isl_union_set *uset);
3998 __isl_give isl_union_pw_qpolynomial *
3999 isl_union_pw_qpolynomial_intersect_params(
4000 __isl_take isl_union_pw_qpolynomial *upwpq,
4001 __isl_take isl_set *set);
4003 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4004 __isl_take isl_qpolynomial *qp,
4005 __isl_take isl_space *model);
4007 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4008 __isl_take isl_qpolynomial *qp);
4009 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4010 __isl_take isl_pw_qpolynomial *pwqp);
4012 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4013 __isl_take isl_union_pw_qpolynomial *upwqp);
4015 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4016 __isl_take isl_qpolynomial *qp,
4017 __isl_take isl_set *context);
4018 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4019 __isl_take isl_qpolynomial *qp,
4020 __isl_take isl_set *context);
4022 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4023 __isl_take isl_pw_qpolynomial *pwqp,
4024 __isl_take isl_set *context);
4025 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4026 __isl_take isl_pw_qpolynomial *pwqp,
4027 __isl_take isl_set *context);
4029 __isl_give isl_union_pw_qpolynomial *
4030 isl_union_pw_qpolynomial_gist_params(
4031 __isl_take isl_union_pw_qpolynomial *upwqp,
4032 __isl_take isl_set *context);
4033 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4034 __isl_take isl_union_pw_qpolynomial *upwqp,
4035 __isl_take isl_union_set *context);
4037 The gist operation applies the gist operation to each of
4038 the cells in the domain of the input piecewise quasipolynomial.
4039 The context is also exploited
4040 to simplify the quasipolynomials associated to each cell.
4042 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4043 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4044 __isl_give isl_union_pw_qpolynomial *
4045 isl_union_pw_qpolynomial_to_polynomial(
4046 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4048 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4049 the polynomial will be an overapproximation. If C<sign> is negative,
4050 it will be an underapproximation. If C<sign> is zero, the approximation
4051 will lie somewhere in between.
4053 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4055 A piecewise quasipolynomial reduction is a piecewise
4056 reduction (or fold) of quasipolynomials.
4057 In particular, the reduction can be maximum or a minimum.
4058 The objects are mainly used to represent the result of
4059 an upper or lower bound on a quasipolynomial over its domain,
4060 i.e., as the result of the following function.
4062 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4063 __isl_take isl_pw_qpolynomial *pwqp,
4064 enum isl_fold type, int *tight);
4066 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4067 __isl_take isl_union_pw_qpolynomial *upwqp,
4068 enum isl_fold type, int *tight);
4070 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4071 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4072 is the returned bound is known be tight, i.e., for each value
4073 of the parameters there is at least
4074 one element in the domain that reaches the bound.
4075 If the domain of C<pwqp> is not wrapping, then the bound is computed
4076 over all elements in that domain and the result has a purely parametric
4077 domain. If the domain of C<pwqp> is wrapping, then the bound is
4078 computed over the range of the wrapped relation. The domain of the
4079 wrapped relation becomes the domain of the result.
4081 A (piecewise) quasipolynomial reduction can be copied or freed using the
4082 following functions.
4084 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4085 __isl_keep isl_qpolynomial_fold *fold);
4086 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4087 __isl_keep isl_pw_qpolynomial_fold *pwf);
4088 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4089 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4090 void isl_qpolynomial_fold_free(
4091 __isl_take isl_qpolynomial_fold *fold);
4092 void *isl_pw_qpolynomial_fold_free(
4093 __isl_take isl_pw_qpolynomial_fold *pwf);
4094 void *isl_union_pw_qpolynomial_fold_free(
4095 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4097 =head3 Printing Piecewise Quasipolynomial Reductions
4099 Piecewise quasipolynomial reductions can be printed
4100 using the following function.
4102 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4103 __isl_take isl_printer *p,
4104 __isl_keep isl_pw_qpolynomial_fold *pwf);
4105 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4106 __isl_take isl_printer *p,
4107 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4109 For C<isl_printer_print_pw_qpolynomial_fold>,
4110 output format of the printer
4111 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4112 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4113 output format of the printer
4114 needs to be set to C<ISL_FORMAT_ISL>.
4115 In case of printing in C<ISL_FORMAT_C>, the user may want
4116 to set the names of all dimensions
4118 __isl_give isl_pw_qpolynomial_fold *
4119 isl_pw_qpolynomial_fold_set_dim_name(
4120 __isl_take isl_pw_qpolynomial_fold *pwf,
4121 enum isl_dim_type type, unsigned pos,
4124 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4126 To iterate over all piecewise quasipolynomial reductions in a union
4127 piecewise quasipolynomial reduction, use the following function
4129 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4130 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4131 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4132 void *user), void *user);
4134 To iterate over the cells in a piecewise quasipolynomial reduction,
4135 use either of the following two functions
4137 int isl_pw_qpolynomial_fold_foreach_piece(
4138 __isl_keep isl_pw_qpolynomial_fold *pwf,
4139 int (*fn)(__isl_take isl_set *set,
4140 __isl_take isl_qpolynomial_fold *fold,
4141 void *user), void *user);
4142 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4143 __isl_keep isl_pw_qpolynomial_fold *pwf,
4144 int (*fn)(__isl_take isl_set *set,
4145 __isl_take isl_qpolynomial_fold *fold,
4146 void *user), void *user);
4148 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4149 of the difference between these two functions.
4151 To iterate over all quasipolynomials in a reduction, use
4153 int isl_qpolynomial_fold_foreach_qpolynomial(
4154 __isl_keep isl_qpolynomial_fold *fold,
4155 int (*fn)(__isl_take isl_qpolynomial *qp,
4156 void *user), void *user);
4158 =head3 Properties of Piecewise Quasipolynomial Reductions
4160 To check whether two union piecewise quasipolynomial reductions are
4161 obviously equal, use
4163 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4164 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4165 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4167 =head3 Operations on Piecewise Quasipolynomial Reductions
4169 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4170 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4172 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4173 __isl_take isl_pw_qpolynomial_fold *pwf1,
4174 __isl_take isl_pw_qpolynomial_fold *pwf2);
4176 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4177 __isl_take isl_pw_qpolynomial_fold *pwf1,
4178 __isl_take isl_pw_qpolynomial_fold *pwf2);
4180 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4181 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4182 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4184 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4185 __isl_take isl_pw_qpolynomial_fold *pwf,
4186 __isl_take isl_point *pnt);
4188 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4189 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4190 __isl_take isl_point *pnt);
4192 __isl_give isl_pw_qpolynomial_fold *
4193 isl_pw_qpolynomial_fold_intersect_params(
4194 __isl_take isl_pw_qpolynomial_fold *pwf,
4195 __isl_take isl_set *set);
4197 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4198 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4199 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4200 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4201 __isl_take isl_union_set *uset);
4202 __isl_give isl_union_pw_qpolynomial_fold *
4203 isl_union_pw_qpolynomial_fold_intersect_params(
4204 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4205 __isl_take isl_set *set);
4207 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4208 __isl_take isl_pw_qpolynomial_fold *pwf);
4210 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4211 __isl_take isl_pw_qpolynomial_fold *pwf);
4213 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4214 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4216 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4217 __isl_take isl_qpolynomial_fold *fold,
4218 __isl_take isl_set *context);
4219 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4220 __isl_take isl_qpolynomial_fold *fold,
4221 __isl_take isl_set *context);
4223 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4224 __isl_take isl_pw_qpolynomial_fold *pwf,
4225 __isl_take isl_set *context);
4226 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4227 __isl_take isl_pw_qpolynomial_fold *pwf,
4228 __isl_take isl_set *context);
4230 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4231 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4232 __isl_take isl_union_set *context);
4233 __isl_give isl_union_pw_qpolynomial_fold *
4234 isl_union_pw_qpolynomial_fold_gist_params(
4235 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4236 __isl_take isl_set *context);
4238 The gist operation applies the gist operation to each of
4239 the cells in the domain of the input piecewise quasipolynomial reduction.
4240 In future, the operation will also exploit the context
4241 to simplify the quasipolynomial reductions associated to each cell.
4243 __isl_give isl_pw_qpolynomial_fold *
4244 isl_set_apply_pw_qpolynomial_fold(
4245 __isl_take isl_set *set,
4246 __isl_take isl_pw_qpolynomial_fold *pwf,
4248 __isl_give isl_pw_qpolynomial_fold *
4249 isl_map_apply_pw_qpolynomial_fold(
4250 __isl_take isl_map *map,
4251 __isl_take isl_pw_qpolynomial_fold *pwf,
4253 __isl_give isl_union_pw_qpolynomial_fold *
4254 isl_union_set_apply_union_pw_qpolynomial_fold(
4255 __isl_take isl_union_set *uset,
4256 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4258 __isl_give isl_union_pw_qpolynomial_fold *
4259 isl_union_map_apply_union_pw_qpolynomial_fold(
4260 __isl_take isl_union_map *umap,
4261 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4264 The functions taking a map
4265 compose the given map with the given piecewise quasipolynomial reduction.
4266 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4267 over all elements in the intersection of the range of the map
4268 and the domain of the piecewise quasipolynomial reduction
4269 as a function of an element in the domain of the map.
4270 The functions taking a set compute a bound over all elements in the
4271 intersection of the set and the domain of the
4272 piecewise quasipolynomial reduction.
4274 =head2 Dependence Analysis
4276 C<isl> contains specialized functionality for performing
4277 array dataflow analysis. That is, given a I<sink> access relation
4278 and a collection of possible I<source> access relations,
4279 C<isl> can compute relations that describe
4280 for each iteration of the sink access, which iteration
4281 of which of the source access relations was the last
4282 to access the same data element before the given iteration
4284 The resulting dependence relations map source iterations
4285 to the corresponding sink iterations.
4286 To compute standard flow dependences, the sink should be
4287 a read, while the sources should be writes.
4288 If any of the source accesses are marked as being I<may>
4289 accesses, then there will be a dependence from the last
4290 I<must> access B<and> from any I<may> access that follows
4291 this last I<must> access.
4292 In particular, if I<all> sources are I<may> accesses,
4293 then memory based dependence analysis is performed.
4294 If, on the other hand, all sources are I<must> accesses,
4295 then value based dependence analysis is performed.
4297 #include <isl/flow.h>
4299 typedef int (*isl_access_level_before)(void *first, void *second);
4301 __isl_give isl_access_info *isl_access_info_alloc(
4302 __isl_take isl_map *sink,
4303 void *sink_user, isl_access_level_before fn,
4305 __isl_give isl_access_info *isl_access_info_add_source(
4306 __isl_take isl_access_info *acc,
4307 __isl_take isl_map *source, int must,
4309 void *isl_access_info_free(__isl_take isl_access_info *acc);
4311 __isl_give isl_flow *isl_access_info_compute_flow(
4312 __isl_take isl_access_info *acc);
4314 int isl_flow_foreach(__isl_keep isl_flow *deps,
4315 int (*fn)(__isl_take isl_map *dep, int must,
4316 void *dep_user, void *user),
4318 __isl_give isl_map *isl_flow_get_no_source(
4319 __isl_keep isl_flow *deps, int must);
4320 void isl_flow_free(__isl_take isl_flow *deps);
4322 The function C<isl_access_info_compute_flow> performs the actual
4323 dependence analysis. The other functions are used to construct
4324 the input for this function or to read off the output.
4326 The input is collected in an C<isl_access_info>, which can
4327 be created through a call to C<isl_access_info_alloc>.
4328 The arguments to this functions are the sink access relation
4329 C<sink>, a token C<sink_user> used to identify the sink
4330 access to the user, a callback function for specifying the
4331 relative order of source and sink accesses, and the number
4332 of source access relations that will be added.
4333 The callback function has type C<int (*)(void *first, void *second)>.
4334 The function is called with two user supplied tokens identifying
4335 either a source or the sink and it should return the shared nesting
4336 level and the relative order of the two accesses.
4337 In particular, let I<n> be the number of loops shared by
4338 the two accesses. If C<first> precedes C<second> textually,
4339 then the function should return I<2 * n + 1>; otherwise,
4340 it should return I<2 * n>.
4341 The sources can be added to the C<isl_access_info> by performing
4342 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4343 C<must> indicates whether the source is a I<must> access
4344 or a I<may> access. Note that a multi-valued access relation
4345 should only be marked I<must> if every iteration in the domain
4346 of the relation accesses I<all> elements in its image.
4347 The C<source_user> token is again used to identify
4348 the source access. The range of the source access relation
4349 C<source> should have the same dimension as the range
4350 of the sink access relation.
4351 The C<isl_access_info_free> function should usually not be
4352 called explicitly, because it is called implicitly by
4353 C<isl_access_info_compute_flow>.
4355 The result of the dependence analysis is collected in an
4356 C<isl_flow>. There may be elements of
4357 the sink access for which no preceding source access could be
4358 found or for which all preceding sources are I<may> accesses.
4359 The relations containing these elements can be obtained through
4360 calls to C<isl_flow_get_no_source>, the first with C<must> set
4361 and the second with C<must> unset.
4362 In the case of standard flow dependence analysis,
4363 with the sink a read and the sources I<must> writes,
4364 the first relation corresponds to the reads from uninitialized
4365 array elements and the second relation is empty.
4366 The actual flow dependences can be extracted using
4367 C<isl_flow_foreach>. This function will call the user-specified
4368 callback function C<fn> for each B<non-empty> dependence between
4369 a source and the sink. The callback function is called
4370 with four arguments, the actual flow dependence relation
4371 mapping source iterations to sink iterations, a boolean that
4372 indicates whether it is a I<must> or I<may> dependence, a token
4373 identifying the source and an additional C<void *> with value
4374 equal to the third argument of the C<isl_flow_foreach> call.
4375 A dependence is marked I<must> if it originates from a I<must>
4376 source and if it is not followed by any I<may> sources.
4378 After finishing with an C<isl_flow>, the user should call
4379 C<isl_flow_free> to free all associated memory.
4381 A higher-level interface to dependence analysis is provided
4382 by the following function.
4384 #include <isl/flow.h>
4386 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4387 __isl_take isl_union_map *must_source,
4388 __isl_take isl_union_map *may_source,
4389 __isl_take isl_union_map *schedule,
4390 __isl_give isl_union_map **must_dep,
4391 __isl_give isl_union_map **may_dep,
4392 __isl_give isl_union_map **must_no_source,
4393 __isl_give isl_union_map **may_no_source);
4395 The arrays are identified by the tuple names of the ranges
4396 of the accesses. The iteration domains by the tuple names
4397 of the domains of the accesses and of the schedule.
4398 The relative order of the iteration domains is given by the
4399 schedule. The relations returned through C<must_no_source>
4400 and C<may_no_source> are subsets of C<sink>.
4401 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4402 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4403 any of the other arguments is treated as an error.
4405 =head3 Interaction with Dependence Analysis
4407 During the dependence analysis, we frequently need to perform
4408 the following operation. Given a relation between sink iterations
4409 and potential source iterations from a particular source domain,
4410 what is the last potential source iteration corresponding to each
4411 sink iteration. It can sometimes be convenient to adjust
4412 the set of potential source iterations before or after each such operation.
4413 The prototypical example is fuzzy array dataflow analysis,
4414 where we need to analyze if, based on data-dependent constraints,
4415 the sink iteration can ever be executed without one or more of
4416 the corresponding potential source iterations being executed.
4417 If so, we can introduce extra parameters and select an unknown
4418 but fixed source iteration from the potential source iterations.
4419 To be able to perform such manipulations, C<isl> provides the following
4422 #include <isl/flow.h>
4424 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4425 __isl_keep isl_map *source_map,
4426 __isl_keep isl_set *sink, void *source_user,
4428 __isl_give isl_access_info *isl_access_info_set_restrict(
4429 __isl_take isl_access_info *acc,
4430 isl_access_restrict fn, void *user);
4432 The function C<isl_access_info_set_restrict> should be called
4433 before calling C<isl_access_info_compute_flow> and registers a callback function
4434 that will be called any time C<isl> is about to compute the last
4435 potential source. The first argument is the (reverse) proto-dependence,
4436 mapping sink iterations to potential source iterations.
4437 The second argument represents the sink iterations for which
4438 we want to compute the last source iteration.
4439 The third argument is the token corresponding to the source
4440 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4441 The callback is expected to return a restriction on either the input or
4442 the output of the operation computing the last potential source.
4443 If the input needs to be restricted then restrictions are needed
4444 for both the source and the sink iterations. The sink iterations
4445 and the potential source iterations will be intersected with these sets.
4446 If the output needs to be restricted then only a restriction on the source
4447 iterations is required.
4448 If any error occurs, the callback should return C<NULL>.
4449 An C<isl_restriction> object can be created, freed and inspected
4450 using the following functions.
4452 #include <isl/flow.h>
4454 __isl_give isl_restriction *isl_restriction_input(
4455 __isl_take isl_set *source_restr,
4456 __isl_take isl_set *sink_restr);
4457 __isl_give isl_restriction *isl_restriction_output(
4458 __isl_take isl_set *source_restr);
4459 __isl_give isl_restriction *isl_restriction_none(
4460 __isl_take isl_map *source_map);
4461 __isl_give isl_restriction *isl_restriction_empty(
4462 __isl_take isl_map *source_map);
4463 void *isl_restriction_free(
4464 __isl_take isl_restriction *restr);
4465 isl_ctx *isl_restriction_get_ctx(
4466 __isl_keep isl_restriction *restr);
4468 C<isl_restriction_none> and C<isl_restriction_empty> are special
4469 cases of C<isl_restriction_input>. C<isl_restriction_none>
4470 is essentially equivalent to
4472 isl_restriction_input(isl_set_universe(
4473 isl_space_range(isl_map_get_space(source_map))),
4475 isl_space_domain(isl_map_get_space(source_map))));
4477 whereas C<isl_restriction_empty> is essentially equivalent to
4479 isl_restriction_input(isl_set_empty(
4480 isl_space_range(isl_map_get_space(source_map))),
4482 isl_space_domain(isl_map_get_space(source_map))));
4486 B<The functionality described in this section is fairly new
4487 and may be subject to change.>
4489 The following function can be used to compute a schedule
4490 for a union of domains.
4491 By default, the algorithm used to construct the schedule is similar
4492 to that of C<Pluto>.
4493 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4495 The generated schedule respects all C<validity> dependences.
4496 That is, all dependence distances over these dependences in the
4497 scheduled space are lexicographically positive.
4498 The default algorithm tries to minimize the dependence distances over
4499 C<proximity> dependences.
4500 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4501 for groups of domains where the dependence distances have only
4502 non-negative values.
4503 When using Feautrier's algorithm, the C<proximity> dependence
4504 distances are only minimized during the extension to a
4505 full-dimensional schedule.
4507 #include <isl/schedule.h>
4508 __isl_give isl_schedule *isl_union_set_compute_schedule(
4509 __isl_take isl_union_set *domain,
4510 __isl_take isl_union_map *validity,
4511 __isl_take isl_union_map *proximity);
4512 void *isl_schedule_free(__isl_take isl_schedule *sched);
4514 A mapping from the domains to the scheduled space can be obtained
4515 from an C<isl_schedule> using the following function.
4517 __isl_give isl_union_map *isl_schedule_get_map(
4518 __isl_keep isl_schedule *sched);
4520 A representation of the schedule can be printed using
4522 __isl_give isl_printer *isl_printer_print_schedule(
4523 __isl_take isl_printer *p,
4524 __isl_keep isl_schedule *schedule);
4526 A representation of the schedule as a forest of bands can be obtained
4527 using the following function.
4529 __isl_give isl_band_list *isl_schedule_get_band_forest(
4530 __isl_keep isl_schedule *schedule);
4532 The individual bands can be visited in depth-first post-order
4533 using the following function.
4535 #include <isl/schedule.h>
4536 int isl_schedule_foreach_band(
4537 __isl_keep isl_schedule *sched,
4538 int (*fn)(__isl_keep isl_band *band, void *user),
4541 The list can be manipulated as explained in L<"Lists">.
4542 The bands inside the list can be copied and freed using the following
4545 #include <isl/band.h>
4546 __isl_give isl_band *isl_band_copy(
4547 __isl_keep isl_band *band);
4548 void *isl_band_free(__isl_take isl_band *band);
4550 Each band contains zero or more scheduling dimensions.
4551 These are referred to as the members of the band.
4552 The section of the schedule that corresponds to the band is
4553 referred to as the partial schedule of the band.
4554 For those nodes that participate in a band, the outer scheduling
4555 dimensions form the prefix schedule, while the inner scheduling
4556 dimensions form the suffix schedule.
4557 That is, if we take a cut of the band forest, then the union of
4558 the concatenations of the prefix, partial and suffix schedules of
4559 each band in the cut is equal to the entire schedule (modulo
4560 some possible padding at the end with zero scheduling dimensions).
4561 The properties of a band can be inspected using the following functions.
4563 #include <isl/band.h>
4564 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4566 int isl_band_has_children(__isl_keep isl_band *band);
4567 __isl_give isl_band_list *isl_band_get_children(
4568 __isl_keep isl_band *band);
4570 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4571 __isl_keep isl_band *band);
4572 __isl_give isl_union_map *isl_band_get_partial_schedule(
4573 __isl_keep isl_band *band);
4574 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4575 __isl_keep isl_band *band);
4577 int isl_band_n_member(__isl_keep isl_band *band);
4578 int isl_band_member_is_zero_distance(
4579 __isl_keep isl_band *band, int pos);
4581 int isl_band_list_foreach_band(
4582 __isl_keep isl_band_list *list,
4583 int (*fn)(__isl_keep isl_band *band, void *user),
4586 Note that a scheduling dimension is considered to be ``zero
4587 distance'' if it does not carry any proximity dependences
4589 That is, if the dependence distances of the proximity
4590 dependences are all zero in that direction (for fixed
4591 iterations of outer bands).
4592 Like C<isl_schedule_foreach_band>,
4593 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4594 in depth-first post-order.
4596 A band can be tiled using the following function.
4598 #include <isl/band.h>
4599 int isl_band_tile(__isl_keep isl_band *band,
4600 __isl_take isl_vec *sizes);
4602 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4604 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4606 The C<isl_band_tile> function tiles the band using the given tile sizes
4607 inside its schedule.
4608 A new child band is created to represent the point loops and it is
4609 inserted between the modified band and its children.
4610 The C<tile_scale_tile_loops> option specifies whether the tile
4611 loops iterators should be scaled by the tile sizes.
4613 A representation of the band can be printed using
4615 #include <isl/band.h>
4616 __isl_give isl_printer *isl_printer_print_band(
4617 __isl_take isl_printer *p,
4618 __isl_keep isl_band *band);
4622 #include <isl/schedule.h>
4623 int isl_options_set_schedule_max_coefficient(
4624 isl_ctx *ctx, int val);
4625 int isl_options_get_schedule_max_coefficient(
4627 int isl_options_set_schedule_max_constant_term(
4628 isl_ctx *ctx, int val);
4629 int isl_options_get_schedule_max_constant_term(
4631 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4632 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4633 int isl_options_set_schedule_maximize_band_depth(
4634 isl_ctx *ctx, int val);
4635 int isl_options_get_schedule_maximize_band_depth(
4637 int isl_options_set_schedule_outer_zero_distance(
4638 isl_ctx *ctx, int val);
4639 int isl_options_get_schedule_outer_zero_distance(
4641 int isl_options_set_schedule_split_scaled(
4642 isl_ctx *ctx, int val);
4643 int isl_options_get_schedule_split_scaled(
4645 int isl_options_set_schedule_algorithm(
4646 isl_ctx *ctx, int val);
4647 int isl_options_get_schedule_algorithm(
4649 int isl_options_set_schedule_separate_components(
4650 isl_ctx *ctx, int val);
4651 int isl_options_get_schedule_separate_components(
4656 =item * schedule_max_coefficient
4658 This option enforces that the coefficients for variable and parameter
4659 dimensions in the calculated schedule are not larger than the specified value.
4660 This option can significantly increase the speed of the scheduling calculation
4661 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4662 this option does not introduce bounds on the variable or parameter
4665 =item * schedule_max_constant_term
4667 This option enforces that the constant coefficients in the calculated schedule
4668 are not larger than the maximal constant term. This option can significantly
4669 increase the speed of the scheduling calculation and may also prevent fusing of
4670 unrelated dimensions. A value of -1 means that this option does not introduce
4671 bounds on the constant coefficients.
4673 =item * schedule_fuse
4675 This option controls the level of fusion.
4676 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4677 resulting schedule will be distributed as much as possible.
4678 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4679 try to fuse loops in the resulting schedule.
4681 =item * schedule_maximize_band_depth
4683 If this option is set, we do not split bands at the point
4684 where we detect splitting is necessary. Instead, we
4685 backtrack and split bands as early as possible. This
4686 reduces the number of splits and maximizes the width of
4687 the bands. Wider bands give more possibilities for tiling.
4688 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4689 then bands will be split as early as possible, even if there is no need.
4690 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4692 =item * schedule_outer_zero_distance
4694 If this option is set, then we try to construct schedules
4695 where the outermost scheduling dimension in each band
4696 results in a zero dependence distance over the proximity
4699 =item * schedule_split_scaled
4701 If this option is set, then we try to construct schedules in which the
4702 constant term is split off from the linear part if the linear parts of
4703 the scheduling rows for all nodes in the graphs have a common non-trivial
4705 The constant term is then placed in a separate band and the linear
4708 =item * schedule_algorithm
4710 Selects the scheduling algorithm to be used.
4711 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4712 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4714 =item * schedule_separate_components
4716 If at any point the dependence graph contains any (weakly connected) components,
4717 then these components are scheduled separately.
4718 If this option is not set, then some iterations of the domains
4719 in these components may be scheduled together.
4720 If this option is set, then the components are given consecutive
4725 =head2 Parametric Vertex Enumeration
4727 The parametric vertex enumeration described in this section
4728 is mainly intended to be used internally and by the C<barvinok>
4731 #include <isl/vertices.h>
4732 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4733 __isl_keep isl_basic_set *bset);
4735 The function C<isl_basic_set_compute_vertices> performs the
4736 actual computation of the parametric vertices and the chamber
4737 decomposition and store the result in an C<isl_vertices> object.
4738 This information can be queried by either iterating over all
4739 the vertices or iterating over all the chambers or cells
4740 and then iterating over all vertices that are active on the chamber.
4742 int isl_vertices_foreach_vertex(
4743 __isl_keep isl_vertices *vertices,
4744 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4747 int isl_vertices_foreach_cell(
4748 __isl_keep isl_vertices *vertices,
4749 int (*fn)(__isl_take isl_cell *cell, void *user),
4751 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4752 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4755 Other operations that can be performed on an C<isl_vertices> object are
4758 isl_ctx *isl_vertices_get_ctx(
4759 __isl_keep isl_vertices *vertices);
4760 int isl_vertices_get_n_vertices(
4761 __isl_keep isl_vertices *vertices);
4762 void isl_vertices_free(__isl_take isl_vertices *vertices);
4764 Vertices can be inspected and destroyed using the following functions.
4766 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4767 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4768 __isl_give isl_basic_set *isl_vertex_get_domain(
4769 __isl_keep isl_vertex *vertex);
4770 __isl_give isl_basic_set *isl_vertex_get_expr(
4771 __isl_keep isl_vertex *vertex);
4772 void isl_vertex_free(__isl_take isl_vertex *vertex);
4774 C<isl_vertex_get_expr> returns a singleton parametric set describing
4775 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4777 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4778 B<rational> basic sets, so they should mainly be used for inspection
4779 and should not be mixed with integer sets.
4781 Chambers can be inspected and destroyed using the following functions.
4783 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4784 __isl_give isl_basic_set *isl_cell_get_domain(
4785 __isl_keep isl_cell *cell);
4786 void isl_cell_free(__isl_take isl_cell *cell);
4790 Although C<isl> is mainly meant to be used as a library,
4791 it also contains some basic applications that use some
4792 of the functionality of C<isl>.
4793 The input may be specified in either the L<isl format>
4794 or the L<PolyLib format>.
4796 =head2 C<isl_polyhedron_sample>
4798 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4799 an integer element of the polyhedron, if there is any.
4800 The first column in the output is the denominator and is always
4801 equal to 1. If the polyhedron contains no integer points,
4802 then a vector of length zero is printed.
4806 C<isl_pip> takes the same input as the C<example> program
4807 from the C<piplib> distribution, i.e., a set of constraints
4808 on the parameters, a line containing only -1 and finally a set
4809 of constraints on a parametric polyhedron.
4810 The coefficients of the parameters appear in the last columns
4811 (but before the final constant column).
4812 The output is the lexicographic minimum of the parametric polyhedron.
4813 As C<isl> currently does not have its own output format, the output
4814 is just a dump of the internal state.
4816 =head2 C<isl_polyhedron_minimize>
4818 C<isl_polyhedron_minimize> computes the minimum of some linear
4819 or affine objective function over the integer points in a polyhedron.
4820 If an affine objective function
4821 is given, then the constant should appear in the last column.
4823 =head2 C<isl_polytope_scan>
4825 Given a polytope, C<isl_polytope_scan> prints
4826 all integer points in the polytope.