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)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
184 C<isl> is released under the MIT license.
188 Permission is hereby granted, free of charge, to any person obtaining a copy of
189 this software and associated documentation files (the "Software"), to deal in
190 the Software without restriction, including without limitation the rights to
191 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
192 of the Software, and to permit persons to whom the Software is furnished to do
193 so, subject to the following conditions:
195 The above copyright notice and this permission notice shall be included in all
196 copies or substantial portions of the Software.
198 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
199 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
200 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
201 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
202 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
203 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
208 Note that C<isl> currently requires C<GMP>, which is released
209 under the GNU Lesser General Public License (LGPL). This means
210 that code linked against C<isl> is also linked against LGPL code.
214 The source of C<isl> can be obtained either as a tarball
215 or from the git repository. Both are available from
216 L<http://freshmeat.net/projects/isl/>.
217 The installation process depends on how you obtained
220 =head2 Installation from the git repository
224 =item 1 Clone or update the repository
226 The first time the source is obtained, you need to clone
229 git clone git://repo.or.cz/isl.git
231 To obtain updates, you need to pull in the latest changes
235 =item 2 Generate C<configure>
241 After performing the above steps, continue
242 with the L<Common installation instructions>.
244 =head2 Common installation instructions
248 =item 1 Obtain C<GMP>
250 Building C<isl> requires C<GMP>, including its headers files.
251 Your distribution may not provide these header files by default
252 and you may need to install a package called C<gmp-devel> or something
253 similar. Alternatively, C<GMP> can be built from
254 source, available from L<http://gmplib.org/>.
258 C<isl> uses the standard C<autoconf> C<configure> script.
263 optionally followed by some configure options.
264 A complete list of options can be obtained by running
268 Below we discuss some of the more common options.
270 C<isl> can optionally use C<piplib>, but no
271 C<piplib> functionality is currently used by default.
272 The C<--with-piplib> option can
273 be used to specify which C<piplib>
274 library to use, either an installed version (C<system>),
275 an externally built version (C<build>)
276 or no version (C<no>). The option C<build> is mostly useful
277 in C<configure> scripts of larger projects that bundle both C<isl>
284 Installation prefix for C<isl>
286 =item C<--with-gmp-prefix>
288 Installation prefix for C<GMP> (architecture-independent files).
290 =item C<--with-gmp-exec-prefix>
292 Installation prefix for C<GMP> (architecture-dependent files).
294 =item C<--with-piplib>
296 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
298 =item C<--with-piplib-prefix>
300 Installation prefix for C<system> C<piplib> (architecture-independent files).
302 =item C<--with-piplib-exec-prefix>
304 Installation prefix for C<system> C<piplib> (architecture-dependent files).
306 =item C<--with-piplib-builddir>
308 Location where C<build> C<piplib> was built.
316 =item 4 Install (optional)
324 =head2 Initialization
326 All manipulations of integer sets and relations occur within
327 the context of an C<isl_ctx>.
328 A given C<isl_ctx> can only be used within a single thread.
329 All arguments of a function are required to have been allocated
330 within the same context.
331 There are currently no functions available for moving an object
332 from one C<isl_ctx> to another C<isl_ctx>. This means that
333 there is currently no way of safely moving an object from one
334 thread to another, unless the whole C<isl_ctx> is moved.
336 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
337 freed using C<isl_ctx_free>.
338 All objects allocated within an C<isl_ctx> should be freed
339 before the C<isl_ctx> itself is freed.
341 isl_ctx *isl_ctx_alloc();
342 void isl_ctx_free(isl_ctx *ctx);
346 All operations on integers, mainly the coefficients
347 of the constraints describing the sets and relations,
348 are performed in exact integer arithmetic using C<GMP>.
349 However, to allow future versions of C<isl> to optionally
350 support fixed integer arithmetic, all calls to C<GMP>
351 are wrapped inside C<isl> specific macros.
352 The basic type is C<isl_int> and the operations below
353 are available on this type.
354 The meanings of these operations are essentially the same
355 as their C<GMP> C<mpz_> counterparts.
356 As always with C<GMP> types, C<isl_int>s need to be
357 initialized with C<isl_int_init> before they can be used
358 and they need to be released with C<isl_int_clear>
360 The user should not assume that an C<isl_int> is represented
361 as a C<mpz_t>, but should instead explicitly convert between
362 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
363 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
367 =item isl_int_init(i)
369 =item isl_int_clear(i)
371 =item isl_int_set(r,i)
373 =item isl_int_set_si(r,i)
375 =item isl_int_set_gmp(r,g)
377 =item isl_int_get_gmp(i,g)
379 =item isl_int_abs(r,i)
381 =item isl_int_neg(r,i)
383 =item isl_int_swap(i,j)
385 =item isl_int_swap_or_set(i,j)
387 =item isl_int_add_ui(r,i,j)
389 =item isl_int_sub_ui(r,i,j)
391 =item isl_int_add(r,i,j)
393 =item isl_int_sub(r,i,j)
395 =item isl_int_mul(r,i,j)
397 =item isl_int_mul_ui(r,i,j)
399 =item isl_int_addmul(r,i,j)
401 =item isl_int_submul(r,i,j)
403 =item isl_int_gcd(r,i,j)
405 =item isl_int_lcm(r,i,j)
407 =item isl_int_divexact(r,i,j)
409 =item isl_int_cdiv_q(r,i,j)
411 =item isl_int_fdiv_q(r,i,j)
413 =item isl_int_fdiv_r(r,i,j)
415 =item isl_int_fdiv_q_ui(r,i,j)
417 =item isl_int_read(r,s)
419 =item isl_int_print(out,i,width)
423 =item isl_int_cmp(i,j)
425 =item isl_int_cmp_si(i,si)
427 =item isl_int_eq(i,j)
429 =item isl_int_ne(i,j)
431 =item isl_int_lt(i,j)
433 =item isl_int_le(i,j)
435 =item isl_int_gt(i,j)
437 =item isl_int_ge(i,j)
439 =item isl_int_abs_eq(i,j)
441 =item isl_int_abs_ne(i,j)
443 =item isl_int_abs_lt(i,j)
445 =item isl_int_abs_gt(i,j)
447 =item isl_int_abs_ge(i,j)
449 =item isl_int_is_zero(i)
451 =item isl_int_is_one(i)
453 =item isl_int_is_negone(i)
455 =item isl_int_is_pos(i)
457 =item isl_int_is_neg(i)
459 =item isl_int_is_nonpos(i)
461 =item isl_int_is_nonneg(i)
463 =item isl_int_is_divisible_by(i,j)
467 =head2 Sets and Relations
469 C<isl> uses six types of objects for representing sets and relations,
470 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
471 C<isl_union_set> and C<isl_union_map>.
472 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
473 can be described as a conjunction of affine constraints, while
474 C<isl_set> and C<isl_map> represent unions of
475 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
476 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
477 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
478 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
479 where spaces are considered different if they have a different number
480 of dimensions and/or different names (see L<"Spaces">).
481 The difference between sets and relations (maps) is that sets have
482 one set of variables, while relations have two sets of variables,
483 input variables and output variables.
485 =head2 Memory Management
487 Since a high-level operation on sets and/or relations usually involves
488 several substeps and since the user is usually not interested in
489 the intermediate results, most functions that return a new object
490 will also release all the objects passed as arguments.
491 If the user still wants to use one or more of these arguments
492 after the function call, she should pass along a copy of the
493 object rather than the object itself.
494 The user is then responsible for making sure that the original
495 object gets used somewhere else or is explicitly freed.
497 The arguments and return values of all documented functions are
498 annotated to make clear which arguments are released and which
499 arguments are preserved. In particular, the following annotations
506 C<__isl_give> means that a new object is returned.
507 The user should make sure that the returned pointer is
508 used exactly once as a value for an C<__isl_take> argument.
509 In between, it can be used as a value for as many
510 C<__isl_keep> arguments as the user likes.
511 There is one exception, and that is the case where the
512 pointer returned is C<NULL>. Is this case, the user
513 is free to use it as an C<__isl_take> argument or not.
517 C<__isl_take> means that the object the argument points to
518 is taken over by the function and may no longer be used
519 by the user as an argument to any other function.
520 The pointer value must be one returned by a function
521 returning an C<__isl_give> pointer.
522 If the user passes in a C<NULL> value, then this will
523 be treated as an error in the sense that the function will
524 not perform its usual operation. However, it will still
525 make sure that all the other C<__isl_take> arguments
530 C<__isl_keep> means that the function will only use the object
531 temporarily. After the function has finished, the user
532 can still use it as an argument to other functions.
533 A C<NULL> value will be treated in the same way as
534 a C<NULL> value for an C<__isl_take> argument.
538 =head2 Error Handling
540 C<isl> supports different ways to react in case a runtime error is triggered.
541 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
542 with two maps that have incompatible spaces. There are three possible ways
543 to react on error: to warn, to continue or to abort.
545 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
546 the last error in the corresponding C<isl_ctx> and the function in which the
547 error was triggered returns C<NULL>. An error does not corrupt internal state,
548 such that isl can continue to be used. C<isl> also provides functions to
549 read the last error and to reset the memory that stores the last error. The
550 last error is only stored for information purposes. Its presence does not
551 change the behavior of C<isl>. Hence, resetting an error is not required to
552 continue to use isl, but only to observe new errors.
555 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
556 void isl_ctx_reset_error(isl_ctx *ctx);
558 Another option is to continue on error. This is similar to warn on error mode,
559 except that C<isl> does not print any warning. This allows a program to
560 implement its own error reporting.
562 The last option is to directly abort the execution of the program from within
563 the isl library. This makes it obviously impossible to recover from an error,
564 but it allows to directly spot the error location. By aborting on error,
565 debuggers break at the location the error occurred and can provide a stack
566 trace. Other tools that automatically provide stack traces on abort or that do
567 not want to continue execution after an error was triggered may also prefer to
570 The on error behavior of isl can be specified by calling
571 C<isl_options_set_on_error> or by setting the command line option
572 C<--isl-on-error>. Valid arguments for the function call are
573 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
574 choices for the command line option are C<warn>, C<continue> and C<abort>.
575 It is also possible to query the current error mode.
577 #include <isl/options.h>
578 int isl_options_set_on_error(isl_ctx *ctx, int val);
579 int isl_options_get_on_error(isl_ctx *ctx);
583 Identifiers are used to identify both individual dimensions
584 and tuples of dimensions. They consist of a name and an optional
585 pointer. Identifiers with the same name but different pointer values
586 are considered to be distinct.
587 Identifiers can be constructed, copied, freed, inspected and printed
588 using the following functions.
591 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
592 __isl_keep const char *name, void *user);
593 __isl_give isl_id *isl_id_copy(isl_id *id);
594 void *isl_id_free(__isl_take isl_id *id);
596 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
597 void *isl_id_get_user(__isl_keep isl_id *id);
598 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
600 __isl_give isl_printer *isl_printer_print_id(
601 __isl_take isl_printer *p, __isl_keep isl_id *id);
603 Note that C<isl_id_get_name> returns a pointer to some internal
604 data structure, so the result can only be used while the
605 corresponding C<isl_id> is alive.
609 Whenever a new set, relation or similiar object is created from scratch,
610 the space in which it lives needs to be specified using an C<isl_space>.
611 Each space involves zero or more parameters and zero, one or two
612 tuples of set or input/output dimensions. The parameters and dimensions
613 are identified by an C<isl_dim_type> and a position.
614 The type C<isl_dim_param> refers to parameters,
615 the type C<isl_dim_set> refers to set dimensions (for spaces
616 with a single tuple of dimensions) and the types C<isl_dim_in>
617 and C<isl_dim_out> refer to input and output dimensions
618 (for spaces with two tuples of dimensions).
619 Local spaces (see L</"Local Spaces">) also contain dimensions
620 of type C<isl_dim_div>.
621 Note that parameters are only identified by their position within
622 a given object. Across different objects, parameters are (usually)
623 identified by their names or identifiers. Only unnamed parameters
624 are identified by their positions across objects. The use of unnamed
625 parameters is discouraged.
627 #include <isl/space.h>
628 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
629 unsigned nparam, unsigned n_in, unsigned n_out);
630 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
632 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
633 unsigned nparam, unsigned dim);
634 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
635 void *isl_space_free(__isl_take isl_space *space);
636 unsigned isl_space_dim(__isl_keep isl_space *space,
637 enum isl_dim_type type);
639 The space used for creating a parameter domain
640 needs to be created using C<isl_space_params_alloc>.
641 For other sets, the space
642 needs to be created using C<isl_space_set_alloc>, while
643 for a relation, the space
644 needs to be created using C<isl_space_alloc>.
645 C<isl_space_dim> can be used
646 to find out the number of dimensions of each type in
647 a space, where type may be
648 C<isl_dim_param>, C<isl_dim_in> (only for relations),
649 C<isl_dim_out> (only for relations), C<isl_dim_set>
650 (only for sets) or C<isl_dim_all>.
652 To check whether a given space is that of a set or a map
653 or whether it is a parameter space, use these functions:
655 #include <isl/space.h>
656 int isl_space_is_params(__isl_keep isl_space *space);
657 int isl_space_is_set(__isl_keep isl_space *space);
658 int isl_space_is_map(__isl_keep isl_space *space);
660 Spaces can be compared using the following functions:
662 #include <isl/space.h>
663 int isl_space_is_equal(__isl_keep isl_space *space1,
664 __isl_keep isl_space *space2);
665 int isl_space_is_domain(__isl_keep isl_space *space1,
666 __isl_keep isl_space *space2);
667 int isl_space_is_range(__isl_keep isl_space *space1,
668 __isl_keep isl_space *space2);
670 C<isl_space_is_domain> checks whether the first argument is equal
671 to the domain of the second argument. This requires in particular that
672 the first argument is a set space and that the second argument
675 It is often useful to create objects that live in the
676 same space as some other object. This can be accomplished
677 by creating the new objects
678 (see L<Creating New Sets and Relations> or
679 L<Creating New (Piecewise) Quasipolynomials>) based on the space
680 of the original object.
683 __isl_give isl_space *isl_basic_set_get_space(
684 __isl_keep isl_basic_set *bset);
685 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
687 #include <isl/union_set.h>
688 __isl_give isl_space *isl_union_set_get_space(
689 __isl_keep isl_union_set *uset);
692 __isl_give isl_space *isl_basic_map_get_space(
693 __isl_keep isl_basic_map *bmap);
694 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
696 #include <isl/union_map.h>
697 __isl_give isl_space *isl_union_map_get_space(
698 __isl_keep isl_union_map *umap);
700 #include <isl/constraint.h>
701 __isl_give isl_space *isl_constraint_get_space(
702 __isl_keep isl_constraint *constraint);
704 #include <isl/polynomial.h>
705 __isl_give isl_space *isl_qpolynomial_get_domain_space(
706 __isl_keep isl_qpolynomial *qp);
707 __isl_give isl_space *isl_qpolynomial_get_space(
708 __isl_keep isl_qpolynomial *qp);
709 __isl_give isl_space *isl_qpolynomial_fold_get_space(
710 __isl_keep isl_qpolynomial_fold *fold);
711 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
712 __isl_keep isl_pw_qpolynomial *pwqp);
713 __isl_give isl_space *isl_pw_qpolynomial_get_space(
714 __isl_keep isl_pw_qpolynomial *pwqp);
715 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
716 __isl_keep isl_pw_qpolynomial_fold *pwf);
717 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
718 __isl_keep isl_pw_qpolynomial_fold *pwf);
719 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
720 __isl_keep isl_union_pw_qpolynomial *upwqp);
721 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
722 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
725 __isl_give isl_space *isl_aff_get_domain_space(
726 __isl_keep isl_aff *aff);
727 __isl_give isl_space *isl_aff_get_space(
728 __isl_keep isl_aff *aff);
729 __isl_give isl_space *isl_pw_aff_get_domain_space(
730 __isl_keep isl_pw_aff *pwaff);
731 __isl_give isl_space *isl_pw_aff_get_space(
732 __isl_keep isl_pw_aff *pwaff);
733 __isl_give isl_space *isl_multi_aff_get_domain_space(
734 __isl_keep isl_multi_aff *maff);
735 __isl_give isl_space *isl_multi_aff_get_space(
736 __isl_keep isl_multi_aff *maff);
737 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
738 __isl_keep isl_pw_multi_aff *pma);
739 __isl_give isl_space *isl_pw_multi_aff_get_space(
740 __isl_keep isl_pw_multi_aff *pma);
741 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
742 __isl_keep isl_union_pw_multi_aff *upma);
744 #include <isl/point.h>
745 __isl_give isl_space *isl_point_get_space(
746 __isl_keep isl_point *pnt);
748 The identifiers or names of the individual dimensions may be set or read off
749 using the following functions.
751 #include <isl/space.h>
752 __isl_give isl_space *isl_space_set_dim_id(
753 __isl_take isl_space *space,
754 enum isl_dim_type type, unsigned pos,
755 __isl_take isl_id *id);
756 int isl_space_has_dim_id(__isl_keep isl_space *space,
757 enum isl_dim_type type, unsigned pos);
758 __isl_give isl_id *isl_space_get_dim_id(
759 __isl_keep isl_space *space,
760 enum isl_dim_type type, unsigned pos);
761 __isl_give isl_space *isl_space_set_dim_name(
762 __isl_take isl_space *space,
763 enum isl_dim_type type, unsigned pos,
764 __isl_keep const char *name);
765 int isl_space_has_dim_name(__isl_keep isl_space *space,
766 enum isl_dim_type type, unsigned pos);
767 __isl_keep const char *isl_space_get_dim_name(
768 __isl_keep isl_space *space,
769 enum isl_dim_type type, unsigned pos);
771 Note that C<isl_space_get_name> returns a pointer to some internal
772 data structure, so the result can only be used while the
773 corresponding C<isl_space> is alive.
774 Also note that every function that operates on two sets or relations
775 requires that both arguments have the same parameters. This also
776 means that if one of the arguments has named parameters, then the
777 other needs to have named parameters too and the names need to match.
778 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
779 arguments may have different parameters (as long as they are named),
780 in which case the result will have as parameters the union of the parameters of
783 Given the identifier or name of a dimension (typically a parameter),
784 its position can be obtained from the following function.
786 #include <isl/space.h>
787 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
788 enum isl_dim_type type, __isl_keep isl_id *id);
789 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
790 enum isl_dim_type type, const char *name);
792 The identifiers or names of entire spaces may be set or read off
793 using the following functions.
795 #include <isl/space.h>
796 __isl_give isl_space *isl_space_set_tuple_id(
797 __isl_take isl_space *space,
798 enum isl_dim_type type, __isl_take isl_id *id);
799 __isl_give isl_space *isl_space_reset_tuple_id(
800 __isl_take isl_space *space, enum isl_dim_type type);
801 int isl_space_has_tuple_id(__isl_keep isl_space *space,
802 enum isl_dim_type type);
803 __isl_give isl_id *isl_space_get_tuple_id(
804 __isl_keep isl_space *space, enum isl_dim_type type);
805 __isl_give isl_space *isl_space_set_tuple_name(
806 __isl_take isl_space *space,
807 enum isl_dim_type type, const char *s);
808 int isl_space_has_tuple_name(__isl_keep isl_space *space,
809 enum isl_dim_type type);
810 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
811 enum isl_dim_type type);
813 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
814 or C<isl_dim_set>. As with C<isl_space_get_name>,
815 the C<isl_space_get_tuple_name> function returns a pointer to some internal
817 Binary operations require the corresponding spaces of their arguments
818 to have the same name.
820 Spaces can be nested. In particular, the domain of a set or
821 the domain or range of a relation can be a nested relation.
822 The following functions can be used to construct and deconstruct
825 #include <isl/space.h>
826 int isl_space_is_wrapping(__isl_keep isl_space *space);
827 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
828 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
830 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
831 be the space of a set, while that of
832 C<isl_space_wrap> should be the space of a relation.
833 Conversely, the output of C<isl_space_unwrap> is the space
834 of a relation, while that of C<isl_space_wrap> is the space of a set.
836 Spaces can be created from other spaces
837 using the following functions.
839 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
840 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
841 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
842 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
843 __isl_give isl_space *isl_space_params(
844 __isl_take isl_space *space);
845 __isl_give isl_space *isl_space_set_from_params(
846 __isl_take isl_space *space);
847 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
848 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
849 __isl_take isl_space *right);
850 __isl_give isl_space *isl_space_align_params(
851 __isl_take isl_space *space1, __isl_take isl_space *space2)
852 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
853 enum isl_dim_type type, unsigned pos, unsigned n);
854 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
855 enum isl_dim_type type, unsigned n);
856 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
857 enum isl_dim_type type, unsigned first, unsigned n);
858 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
859 enum isl_dim_type dst_type, unsigned dst_pos,
860 enum isl_dim_type src_type, unsigned src_pos,
862 __isl_give isl_space *isl_space_map_from_set(
863 __isl_take isl_space *space);
864 __isl_give isl_space *isl_space_map_from_domain_and_range(
865 __isl_take isl_space *domain,
866 __isl_take isl_space *range);
867 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
868 __isl_give isl_space *isl_space_curry(
869 __isl_take isl_space *space);
871 Note that if dimensions are added or removed from a space, then
872 the name and the internal structure are lost.
876 A local space is essentially a space with
877 zero or more existentially quantified variables.
878 The local space of a (constraint of a) basic set or relation can be obtained
879 using the following functions.
881 #include <isl/constraint.h>
882 __isl_give isl_local_space *isl_constraint_get_local_space(
883 __isl_keep isl_constraint *constraint);
886 __isl_give isl_local_space *isl_basic_set_get_local_space(
887 __isl_keep isl_basic_set *bset);
890 __isl_give isl_local_space *isl_basic_map_get_local_space(
891 __isl_keep isl_basic_map *bmap);
893 A new local space can be created from a space using
895 #include <isl/local_space.h>
896 __isl_give isl_local_space *isl_local_space_from_space(
897 __isl_take isl_space *space);
899 They can be inspected, modified, copied and freed using the following functions.
901 #include <isl/local_space.h>
902 isl_ctx *isl_local_space_get_ctx(
903 __isl_keep isl_local_space *ls);
904 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
905 int isl_local_space_dim(__isl_keep isl_local_space *ls,
906 enum isl_dim_type type);
907 int isl_local_space_has_dim_id(
908 __isl_keep isl_local_space *ls,
909 enum isl_dim_type type, unsigned pos);
910 __isl_give isl_id *isl_local_space_get_dim_id(
911 __isl_keep isl_local_space *ls,
912 enum isl_dim_type type, unsigned pos);
913 int isl_local_space_has_dim_name(
914 __isl_keep isl_local_space *ls,
915 enum isl_dim_type type, unsigned pos)
916 const char *isl_local_space_get_dim_name(
917 __isl_keep isl_local_space *ls,
918 enum isl_dim_type type, unsigned pos);
919 __isl_give isl_local_space *isl_local_space_set_dim_name(
920 __isl_take isl_local_space *ls,
921 enum isl_dim_type type, unsigned pos, const char *s);
922 __isl_give isl_local_space *isl_local_space_set_dim_id(
923 __isl_take isl_local_space *ls,
924 enum isl_dim_type type, unsigned pos,
925 __isl_take isl_id *id);
926 __isl_give isl_space *isl_local_space_get_space(
927 __isl_keep isl_local_space *ls);
928 __isl_give isl_aff *isl_local_space_get_div(
929 __isl_keep isl_local_space *ls, int pos);
930 __isl_give isl_local_space *isl_local_space_copy(
931 __isl_keep isl_local_space *ls);
932 void *isl_local_space_free(__isl_take isl_local_space *ls);
934 Two local spaces can be compared using
936 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
937 __isl_keep isl_local_space *ls2);
939 Local spaces can be created from other local spaces
940 using the following functions.
942 __isl_give isl_local_space *isl_local_space_domain(
943 __isl_take isl_local_space *ls);
944 __isl_give isl_local_space *isl_local_space_range(
945 __isl_take isl_local_space *ls);
946 __isl_give isl_local_space *isl_local_space_from_domain(
947 __isl_take isl_local_space *ls);
948 __isl_give isl_local_space *isl_local_space_intersect(
949 __isl_take isl_local_space *ls1,
950 __isl_take isl_local_space *ls2);
951 __isl_give isl_local_space *isl_local_space_add_dims(
952 __isl_take isl_local_space *ls,
953 enum isl_dim_type type, unsigned n);
954 __isl_give isl_local_space *isl_local_space_insert_dims(
955 __isl_take isl_local_space *ls,
956 enum isl_dim_type type, unsigned first, unsigned n);
957 __isl_give isl_local_space *isl_local_space_drop_dims(
958 __isl_take isl_local_space *ls,
959 enum isl_dim_type type, unsigned first, unsigned n);
961 =head2 Input and Output
963 C<isl> supports its own input/output format, which is similar
964 to the C<Omega> format, but also supports the C<PolyLib> format
969 The C<isl> format is similar to that of C<Omega>, but has a different
970 syntax for describing the parameters and allows for the definition
971 of an existentially quantified variable as the integer division
972 of an affine expression.
973 For example, the set of integers C<i> between C<0> and C<n>
974 such that C<i % 10 <= 6> can be described as
976 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
979 A set or relation can have several disjuncts, separated
980 by the keyword C<or>. Each disjunct is either a conjunction
981 of constraints or a projection (C<exists>) of a conjunction
982 of constraints. The constraints are separated by the keyword
985 =head3 C<PolyLib> format
987 If the represented set is a union, then the first line
988 contains a single number representing the number of disjuncts.
989 Otherwise, a line containing the number C<1> is optional.
991 Each disjunct is represented by a matrix of constraints.
992 The first line contains two numbers representing
993 the number of rows and columns,
994 where the number of rows is equal to the number of constraints
995 and the number of columns is equal to two plus the number of variables.
996 The following lines contain the actual rows of the constraint matrix.
997 In each row, the first column indicates whether the constraint
998 is an equality (C<0>) or inequality (C<1>). The final column
999 corresponds to the constant term.
1001 If the set is parametric, then the coefficients of the parameters
1002 appear in the last columns before the constant column.
1003 The coefficients of any existentially quantified variables appear
1004 between those of the set variables and those of the parameters.
1006 =head3 Extended C<PolyLib> format
1008 The extended C<PolyLib> format is nearly identical to the
1009 C<PolyLib> format. The only difference is that the line
1010 containing the number of rows and columns of a constraint matrix
1011 also contains four additional numbers:
1012 the number of output dimensions, the number of input dimensions,
1013 the number of local dimensions (i.e., the number of existentially
1014 quantified variables) and the number of parameters.
1015 For sets, the number of ``output'' dimensions is equal
1016 to the number of set dimensions, while the number of ``input''
1021 #include <isl/set.h>
1022 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1023 isl_ctx *ctx, FILE *input);
1024 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1025 isl_ctx *ctx, const char *str);
1026 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1028 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1031 #include <isl/map.h>
1032 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1033 isl_ctx *ctx, FILE *input);
1034 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1035 isl_ctx *ctx, const char *str);
1036 __isl_give isl_map *isl_map_read_from_file(
1037 isl_ctx *ctx, FILE *input);
1038 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1041 #include <isl/union_set.h>
1042 __isl_give isl_union_set *isl_union_set_read_from_file(
1043 isl_ctx *ctx, FILE *input);
1044 __isl_give isl_union_set *isl_union_set_read_from_str(
1045 isl_ctx *ctx, const char *str);
1047 #include <isl/union_map.h>
1048 __isl_give isl_union_map *isl_union_map_read_from_file(
1049 isl_ctx *ctx, FILE *input);
1050 __isl_give isl_union_map *isl_union_map_read_from_str(
1051 isl_ctx *ctx, const char *str);
1053 The input format is autodetected and may be either the C<PolyLib> format
1054 or the C<isl> format.
1058 Before anything can be printed, an C<isl_printer> needs to
1061 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1063 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1064 void *isl_printer_free(__isl_take isl_printer *printer);
1065 __isl_give char *isl_printer_get_str(
1066 __isl_keep isl_printer *printer);
1068 The printer can be inspected using the following functions.
1070 FILE *isl_printer_get_file(
1071 __isl_keep isl_printer *printer);
1072 int isl_printer_get_output_format(
1073 __isl_keep isl_printer *p);
1075 The behavior of the printer can be modified in various ways
1077 __isl_give isl_printer *isl_printer_set_output_format(
1078 __isl_take isl_printer *p, int output_format);
1079 __isl_give isl_printer *isl_printer_set_indent(
1080 __isl_take isl_printer *p, int indent);
1081 __isl_give isl_printer *isl_printer_indent(
1082 __isl_take isl_printer *p, int indent);
1083 __isl_give isl_printer *isl_printer_set_prefix(
1084 __isl_take isl_printer *p, const char *prefix);
1085 __isl_give isl_printer *isl_printer_set_suffix(
1086 __isl_take isl_printer *p, const char *suffix);
1088 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1089 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1090 and defaults to C<ISL_FORMAT_ISL>.
1091 Each line in the output is indented by C<indent> (set by
1092 C<isl_printer_set_indent>) spaces
1093 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1094 In the C<PolyLib> format output,
1095 the coefficients of the existentially quantified variables
1096 appear between those of the set variables and those
1098 The function C<isl_printer_indent> increases the indentation
1099 by the specified amount (which may be negative).
1101 To actually print something, use
1103 #include <isl/printer.h>
1104 __isl_give isl_printer *isl_printer_print_double(
1105 __isl_take isl_printer *p, double d);
1107 #include <isl/set.h>
1108 __isl_give isl_printer *isl_printer_print_basic_set(
1109 __isl_take isl_printer *printer,
1110 __isl_keep isl_basic_set *bset);
1111 __isl_give isl_printer *isl_printer_print_set(
1112 __isl_take isl_printer *printer,
1113 __isl_keep isl_set *set);
1115 #include <isl/map.h>
1116 __isl_give isl_printer *isl_printer_print_basic_map(
1117 __isl_take isl_printer *printer,
1118 __isl_keep isl_basic_map *bmap);
1119 __isl_give isl_printer *isl_printer_print_map(
1120 __isl_take isl_printer *printer,
1121 __isl_keep isl_map *map);
1123 #include <isl/union_set.h>
1124 __isl_give isl_printer *isl_printer_print_union_set(
1125 __isl_take isl_printer *p,
1126 __isl_keep isl_union_set *uset);
1128 #include <isl/union_map.h>
1129 __isl_give isl_printer *isl_printer_print_union_map(
1130 __isl_take isl_printer *p,
1131 __isl_keep isl_union_map *umap);
1133 When called on a file printer, the following function flushes
1134 the file. When called on a string printer, the buffer is cleared.
1136 __isl_give isl_printer *isl_printer_flush(
1137 __isl_take isl_printer *p);
1139 =head2 Creating New Sets and Relations
1141 C<isl> has functions for creating some standard sets and relations.
1145 =item * Empty sets and relations
1147 __isl_give isl_basic_set *isl_basic_set_empty(
1148 __isl_take isl_space *space);
1149 __isl_give isl_basic_map *isl_basic_map_empty(
1150 __isl_take isl_space *space);
1151 __isl_give isl_set *isl_set_empty(
1152 __isl_take isl_space *space);
1153 __isl_give isl_map *isl_map_empty(
1154 __isl_take isl_space *space);
1155 __isl_give isl_union_set *isl_union_set_empty(
1156 __isl_take isl_space *space);
1157 __isl_give isl_union_map *isl_union_map_empty(
1158 __isl_take isl_space *space);
1160 For C<isl_union_set>s and C<isl_union_map>s, the space
1161 is only used to specify the parameters.
1163 =item * Universe sets and relations
1165 __isl_give isl_basic_set *isl_basic_set_universe(
1166 __isl_take isl_space *space);
1167 __isl_give isl_basic_map *isl_basic_map_universe(
1168 __isl_take isl_space *space);
1169 __isl_give isl_set *isl_set_universe(
1170 __isl_take isl_space *space);
1171 __isl_give isl_map *isl_map_universe(
1172 __isl_take isl_space *space);
1173 __isl_give isl_union_set *isl_union_set_universe(
1174 __isl_take isl_union_set *uset);
1175 __isl_give isl_union_map *isl_union_map_universe(
1176 __isl_take isl_union_map *umap);
1178 The sets and relations constructed by the functions above
1179 contain all integer values, while those constructed by the
1180 functions below only contain non-negative values.
1182 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1183 __isl_take isl_space *space);
1184 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1185 __isl_take isl_space *space);
1186 __isl_give isl_set *isl_set_nat_universe(
1187 __isl_take isl_space *space);
1188 __isl_give isl_map *isl_map_nat_universe(
1189 __isl_take isl_space *space);
1191 =item * Identity relations
1193 __isl_give isl_basic_map *isl_basic_map_identity(
1194 __isl_take isl_space *space);
1195 __isl_give isl_map *isl_map_identity(
1196 __isl_take isl_space *space);
1198 The number of input and output dimensions in C<space> needs
1201 =item * Lexicographic order
1203 __isl_give isl_map *isl_map_lex_lt(
1204 __isl_take isl_space *set_space);
1205 __isl_give isl_map *isl_map_lex_le(
1206 __isl_take isl_space *set_space);
1207 __isl_give isl_map *isl_map_lex_gt(
1208 __isl_take isl_space *set_space);
1209 __isl_give isl_map *isl_map_lex_ge(
1210 __isl_take isl_space *set_space);
1211 __isl_give isl_map *isl_map_lex_lt_first(
1212 __isl_take isl_space *space, unsigned n);
1213 __isl_give isl_map *isl_map_lex_le_first(
1214 __isl_take isl_space *space, unsigned n);
1215 __isl_give isl_map *isl_map_lex_gt_first(
1216 __isl_take isl_space *space, unsigned n);
1217 __isl_give isl_map *isl_map_lex_ge_first(
1218 __isl_take isl_space *space, unsigned n);
1220 The first four functions take a space for a B<set>
1221 and return relations that express that the elements in the domain
1222 are lexicographically less
1223 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1224 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1225 than the elements in the range.
1226 The last four functions take a space for a map
1227 and return relations that express that the first C<n> dimensions
1228 in the domain are lexicographically less
1229 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1230 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1231 than the first C<n> dimensions in the range.
1235 A basic set or relation can be converted to a set or relation
1236 using the following functions.
1238 __isl_give isl_set *isl_set_from_basic_set(
1239 __isl_take isl_basic_set *bset);
1240 __isl_give isl_map *isl_map_from_basic_map(
1241 __isl_take isl_basic_map *bmap);
1243 Sets and relations can be converted to union sets and relations
1244 using the following functions.
1246 __isl_give isl_union_set *isl_union_set_from_basic_set(
1247 __isl_take isl_basic_set *bset);
1248 __isl_give isl_union_map *isl_union_map_from_basic_map(
1249 __isl_take isl_basic_map *bmap);
1250 __isl_give isl_union_set *isl_union_set_from_set(
1251 __isl_take isl_set *set);
1252 __isl_give isl_union_map *isl_union_map_from_map(
1253 __isl_take isl_map *map);
1255 The inverse conversions below can only be used if the input
1256 union set or relation is known to contain elements in exactly one
1259 __isl_give isl_set *isl_set_from_union_set(
1260 __isl_take isl_union_set *uset);
1261 __isl_give isl_map *isl_map_from_union_map(
1262 __isl_take isl_union_map *umap);
1264 A zero-dimensional set can be constructed on a given parameter domain
1265 using the following function.
1267 __isl_give isl_set *isl_set_from_params(
1268 __isl_take isl_set *set);
1270 Sets and relations can be copied and freed again using the following
1273 __isl_give isl_basic_set *isl_basic_set_copy(
1274 __isl_keep isl_basic_set *bset);
1275 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1276 __isl_give isl_union_set *isl_union_set_copy(
1277 __isl_keep isl_union_set *uset);
1278 __isl_give isl_basic_map *isl_basic_map_copy(
1279 __isl_keep isl_basic_map *bmap);
1280 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1281 __isl_give isl_union_map *isl_union_map_copy(
1282 __isl_keep isl_union_map *umap);
1283 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1284 void *isl_set_free(__isl_take isl_set *set);
1285 void *isl_union_set_free(__isl_take isl_union_set *uset);
1286 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1287 void *isl_map_free(__isl_take isl_map *map);
1288 void *isl_union_map_free(__isl_take isl_union_map *umap);
1290 Other sets and relations can be constructed by starting
1291 from a universe set or relation, adding equality and/or
1292 inequality constraints and then projecting out the
1293 existentially quantified variables, if any.
1294 Constraints can be constructed, manipulated and
1295 added to (or removed from) (basic) sets and relations
1296 using the following functions.
1298 #include <isl/constraint.h>
1299 __isl_give isl_constraint *isl_equality_alloc(
1300 __isl_take isl_local_space *ls);
1301 __isl_give isl_constraint *isl_inequality_alloc(
1302 __isl_take isl_local_space *ls);
1303 __isl_give isl_constraint *isl_constraint_set_constant(
1304 __isl_take isl_constraint *constraint, isl_int v);
1305 __isl_give isl_constraint *isl_constraint_set_constant_si(
1306 __isl_take isl_constraint *constraint, int v);
1307 __isl_give isl_constraint *isl_constraint_set_coefficient(
1308 __isl_take isl_constraint *constraint,
1309 enum isl_dim_type type, int pos, isl_int v);
1310 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1311 __isl_take isl_constraint *constraint,
1312 enum isl_dim_type type, int pos, int v);
1313 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1314 __isl_take isl_basic_map *bmap,
1315 __isl_take isl_constraint *constraint);
1316 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1317 __isl_take isl_basic_set *bset,
1318 __isl_take isl_constraint *constraint);
1319 __isl_give isl_map *isl_map_add_constraint(
1320 __isl_take isl_map *map,
1321 __isl_take isl_constraint *constraint);
1322 __isl_give isl_set *isl_set_add_constraint(
1323 __isl_take isl_set *set,
1324 __isl_take isl_constraint *constraint);
1325 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1326 __isl_take isl_basic_set *bset,
1327 __isl_take isl_constraint *constraint);
1329 For example, to create a set containing the even integers
1330 between 10 and 42, you would use the following code.
1333 isl_local_space *ls;
1335 isl_basic_set *bset;
1337 space = isl_space_set_alloc(ctx, 0, 2);
1338 bset = isl_basic_set_universe(isl_space_copy(space));
1339 ls = isl_local_space_from_space(space);
1341 c = isl_equality_alloc(isl_local_space_copy(ls));
1342 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1343 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1344 bset = isl_basic_set_add_constraint(bset, c);
1346 c = isl_inequality_alloc(isl_local_space_copy(ls));
1347 c = isl_constraint_set_constant_si(c, -10);
1348 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1349 bset = isl_basic_set_add_constraint(bset, c);
1351 c = isl_inequality_alloc(ls);
1352 c = isl_constraint_set_constant_si(c, 42);
1353 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1354 bset = isl_basic_set_add_constraint(bset, c);
1356 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1360 isl_basic_set *bset;
1361 bset = isl_basic_set_read_from_str(ctx,
1362 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1364 A basic set or relation can also be constructed from two matrices
1365 describing the equalities and the inequalities.
1367 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1368 __isl_take isl_space *space,
1369 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1370 enum isl_dim_type c1,
1371 enum isl_dim_type c2, enum isl_dim_type c3,
1372 enum isl_dim_type c4);
1373 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1374 __isl_take isl_space *space,
1375 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1376 enum isl_dim_type c1,
1377 enum isl_dim_type c2, enum isl_dim_type c3,
1378 enum isl_dim_type c4, enum isl_dim_type c5);
1380 The C<isl_dim_type> arguments indicate the order in which
1381 different kinds of variables appear in the input matrices
1382 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1383 C<isl_dim_set> and C<isl_dim_div> for sets and
1384 of C<isl_dim_cst>, C<isl_dim_param>,
1385 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1387 A (basic or union) set or relation can also be constructed from a
1388 (union) (piecewise) (multiple) affine expression
1389 or a list of affine expressions
1390 (See L<"Piecewise Quasi Affine Expressions"> and
1391 L<"Piecewise Multiple Quasi Affine Expressions">).
1393 __isl_give isl_basic_map *isl_basic_map_from_aff(
1394 __isl_take isl_aff *aff);
1395 __isl_give isl_map *isl_map_from_aff(
1396 __isl_take isl_aff *aff);
1397 __isl_give isl_set *isl_set_from_pw_aff(
1398 __isl_take isl_pw_aff *pwaff);
1399 __isl_give isl_map *isl_map_from_pw_aff(
1400 __isl_take isl_pw_aff *pwaff);
1401 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1402 __isl_take isl_space *domain_space,
1403 __isl_take isl_aff_list *list);
1404 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1405 __isl_take isl_multi_aff *maff)
1406 __isl_give isl_map *isl_map_from_multi_aff(
1407 __isl_take isl_multi_aff *maff)
1408 __isl_give isl_set *isl_set_from_pw_multi_aff(
1409 __isl_take isl_pw_multi_aff *pma);
1410 __isl_give isl_map *isl_map_from_pw_multi_aff(
1411 __isl_take isl_pw_multi_aff *pma);
1412 __isl_give isl_union_map *
1413 isl_union_map_from_union_pw_multi_aff(
1414 __isl_take isl_union_pw_multi_aff *upma);
1416 The C<domain_dim> argument describes the domain of the resulting
1417 basic relation. It is required because the C<list> may consist
1418 of zero affine expressions.
1420 =head2 Inspecting Sets and Relations
1422 Usually, the user should not have to care about the actual constraints
1423 of the sets and maps, but should instead apply the abstract operations
1424 explained in the following sections.
1425 Occasionally, however, it may be required to inspect the individual
1426 coefficients of the constraints. This section explains how to do so.
1427 In these cases, it may also be useful to have C<isl> compute
1428 an explicit representation of the existentially quantified variables.
1430 __isl_give isl_set *isl_set_compute_divs(
1431 __isl_take isl_set *set);
1432 __isl_give isl_map *isl_map_compute_divs(
1433 __isl_take isl_map *map);
1434 __isl_give isl_union_set *isl_union_set_compute_divs(
1435 __isl_take isl_union_set *uset);
1436 __isl_give isl_union_map *isl_union_map_compute_divs(
1437 __isl_take isl_union_map *umap);
1439 This explicit representation defines the existentially quantified
1440 variables as integer divisions of the other variables, possibly
1441 including earlier existentially quantified variables.
1442 An explicitly represented existentially quantified variable therefore
1443 has a unique value when the values of the other variables are known.
1444 If, furthermore, the same existentials, i.e., existentials
1445 with the same explicit representations, should appear in the
1446 same order in each of the disjuncts of a set or map, then the user should call
1447 either of the following functions.
1449 __isl_give isl_set *isl_set_align_divs(
1450 __isl_take isl_set *set);
1451 __isl_give isl_map *isl_map_align_divs(
1452 __isl_take isl_map *map);
1454 Alternatively, the existentially quantified variables can be removed
1455 using the following functions, which compute an overapproximation.
1457 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1458 __isl_take isl_basic_set *bset);
1459 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1460 __isl_take isl_basic_map *bmap);
1461 __isl_give isl_set *isl_set_remove_divs(
1462 __isl_take isl_set *set);
1463 __isl_give isl_map *isl_map_remove_divs(
1464 __isl_take isl_map *map);
1466 It is also possible to only remove those divs that are defined
1467 in terms of a given range of dimensions or only those for which
1468 no explicit representation is known.
1470 __isl_give isl_basic_set *
1471 isl_basic_set_remove_divs_involving_dims(
1472 __isl_take isl_basic_set *bset,
1473 enum isl_dim_type type,
1474 unsigned first, unsigned n);
1475 __isl_give isl_basic_map *
1476 isl_basic_map_remove_divs_involving_dims(
1477 __isl_take isl_basic_map *bmap,
1478 enum isl_dim_type type,
1479 unsigned first, unsigned n);
1480 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1481 __isl_take isl_set *set, enum isl_dim_type type,
1482 unsigned first, unsigned n);
1483 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1484 __isl_take isl_map *map, enum isl_dim_type type,
1485 unsigned first, unsigned n);
1487 __isl_give isl_set *isl_set_remove_unknown_divs(
1488 __isl_take isl_set *set);
1489 __isl_give isl_map *isl_map_remove_unknown_divs(
1490 __isl_take isl_map *map);
1492 To iterate over all the sets or maps in a union set or map, use
1494 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1495 int (*fn)(__isl_take isl_set *set, void *user),
1497 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1498 int (*fn)(__isl_take isl_map *map, void *user),
1501 The number of sets or maps in a union set or map can be obtained
1504 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1505 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1507 To extract the set or map in a given space from a union, use
1509 __isl_give isl_set *isl_union_set_extract_set(
1510 __isl_keep isl_union_set *uset,
1511 __isl_take isl_space *space);
1512 __isl_give isl_map *isl_union_map_extract_map(
1513 __isl_keep isl_union_map *umap,
1514 __isl_take isl_space *space);
1516 To iterate over all the basic sets or maps in a set or map, use
1518 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1519 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1521 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1522 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1525 The callback function C<fn> should return 0 if successful and
1526 -1 if an error occurs. In the latter case, or if any other error
1527 occurs, the above functions will return -1.
1529 It should be noted that C<isl> does not guarantee that
1530 the basic sets or maps passed to C<fn> are disjoint.
1531 If this is required, then the user should call one of
1532 the following functions first.
1534 __isl_give isl_set *isl_set_make_disjoint(
1535 __isl_take isl_set *set);
1536 __isl_give isl_map *isl_map_make_disjoint(
1537 __isl_take isl_map *map);
1539 The number of basic sets in a set can be obtained
1542 int isl_set_n_basic_set(__isl_keep isl_set *set);
1544 To iterate over the constraints of a basic set or map, use
1546 #include <isl/constraint.h>
1548 int isl_basic_set_n_constraint(
1549 __isl_keep isl_basic_set *bset);
1550 int isl_basic_set_foreach_constraint(
1551 __isl_keep isl_basic_set *bset,
1552 int (*fn)(__isl_take isl_constraint *c, void *user),
1554 int isl_basic_map_foreach_constraint(
1555 __isl_keep isl_basic_map *bmap,
1556 int (*fn)(__isl_take isl_constraint *c, void *user),
1558 void *isl_constraint_free(__isl_take isl_constraint *c);
1560 Again, the callback function C<fn> should return 0 if successful and
1561 -1 if an error occurs. In the latter case, or if any other error
1562 occurs, the above functions will return -1.
1563 The constraint C<c> represents either an equality or an inequality.
1564 Use the following function to find out whether a constraint
1565 represents an equality. If not, it represents an inequality.
1567 int isl_constraint_is_equality(
1568 __isl_keep isl_constraint *constraint);
1570 The coefficients of the constraints can be inspected using
1571 the following functions.
1573 int isl_constraint_is_lower_bound(
1574 __isl_keep isl_constraint *constraint,
1575 enum isl_dim_type type, unsigned pos);
1576 int isl_constraint_is_upper_bound(
1577 __isl_keep isl_constraint *constraint,
1578 enum isl_dim_type type, unsigned pos);
1579 void isl_constraint_get_constant(
1580 __isl_keep isl_constraint *constraint, isl_int *v);
1581 void isl_constraint_get_coefficient(
1582 __isl_keep isl_constraint *constraint,
1583 enum isl_dim_type type, int pos, isl_int *v);
1584 int isl_constraint_involves_dims(
1585 __isl_keep isl_constraint *constraint,
1586 enum isl_dim_type type, unsigned first, unsigned n);
1588 The explicit representations of the existentially quantified
1589 variables can be inspected using the following function.
1590 Note that the user is only allowed to use this function
1591 if the inspected set or map is the result of a call
1592 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1593 The existentially quantified variable is equal to the floor
1594 of the returned affine expression. The affine expression
1595 itself can be inspected using the functions in
1596 L<"Piecewise Quasi Affine Expressions">.
1598 __isl_give isl_aff *isl_constraint_get_div(
1599 __isl_keep isl_constraint *constraint, int pos);
1601 To obtain the constraints of a basic set or map in matrix
1602 form, use the following functions.
1604 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1605 __isl_keep isl_basic_set *bset,
1606 enum isl_dim_type c1, enum isl_dim_type c2,
1607 enum isl_dim_type c3, enum isl_dim_type c4);
1608 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1609 __isl_keep isl_basic_set *bset,
1610 enum isl_dim_type c1, enum isl_dim_type c2,
1611 enum isl_dim_type c3, enum isl_dim_type c4);
1612 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1613 __isl_keep isl_basic_map *bmap,
1614 enum isl_dim_type c1,
1615 enum isl_dim_type c2, enum isl_dim_type c3,
1616 enum isl_dim_type c4, enum isl_dim_type c5);
1617 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1618 __isl_keep isl_basic_map *bmap,
1619 enum isl_dim_type c1,
1620 enum isl_dim_type c2, enum isl_dim_type c3,
1621 enum isl_dim_type c4, enum isl_dim_type c5);
1623 The C<isl_dim_type> arguments dictate the order in which
1624 different kinds of variables appear in the resulting matrix
1625 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1626 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1628 The number of parameters, input, output or set dimensions can
1629 be obtained using the following functions.
1631 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1632 enum isl_dim_type type);
1633 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1634 enum isl_dim_type type);
1635 unsigned isl_set_dim(__isl_keep isl_set *set,
1636 enum isl_dim_type type);
1637 unsigned isl_map_dim(__isl_keep isl_map *map,
1638 enum isl_dim_type type);
1640 To check whether the description of a set or relation depends
1641 on one or more given dimensions, it is not necessary to iterate over all
1642 constraints. Instead the following functions can be used.
1644 int isl_basic_set_involves_dims(
1645 __isl_keep isl_basic_set *bset,
1646 enum isl_dim_type type, unsigned first, unsigned n);
1647 int isl_set_involves_dims(__isl_keep isl_set *set,
1648 enum isl_dim_type type, unsigned first, unsigned n);
1649 int isl_basic_map_involves_dims(
1650 __isl_keep isl_basic_map *bmap,
1651 enum isl_dim_type type, unsigned first, unsigned n);
1652 int isl_map_involves_dims(__isl_keep isl_map *map,
1653 enum isl_dim_type type, unsigned first, unsigned n);
1655 Similarly, the following functions can be used to check whether
1656 a given dimension is involved in any lower or upper bound.
1658 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1659 enum isl_dim_type type, unsigned pos);
1660 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1661 enum isl_dim_type type, unsigned pos);
1663 The identifiers or names of the domain and range spaces of a set
1664 or relation can be read off or set using the following functions.
1666 __isl_give isl_set *isl_set_set_tuple_id(
1667 __isl_take isl_set *set, __isl_take isl_id *id);
1668 __isl_give isl_set *isl_set_reset_tuple_id(
1669 __isl_take isl_set *set);
1670 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1671 __isl_give isl_id *isl_set_get_tuple_id(
1672 __isl_keep isl_set *set);
1673 __isl_give isl_map *isl_map_set_tuple_id(
1674 __isl_take isl_map *map, enum isl_dim_type type,
1675 __isl_take isl_id *id);
1676 __isl_give isl_map *isl_map_reset_tuple_id(
1677 __isl_take isl_map *map, enum isl_dim_type type);
1678 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1679 enum isl_dim_type type);
1680 __isl_give isl_id *isl_map_get_tuple_id(
1681 __isl_keep isl_map *map, enum isl_dim_type type);
1683 const char *isl_basic_set_get_tuple_name(
1684 __isl_keep isl_basic_set *bset);
1685 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1686 __isl_take isl_basic_set *set, const char *s);
1687 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1688 const char *isl_set_get_tuple_name(
1689 __isl_keep isl_set *set);
1690 const char *isl_basic_map_get_tuple_name(
1691 __isl_keep isl_basic_map *bmap,
1692 enum isl_dim_type type);
1693 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1694 __isl_take isl_basic_map *bmap,
1695 enum isl_dim_type type, const char *s);
1696 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1697 enum isl_dim_type type);
1698 const char *isl_map_get_tuple_name(
1699 __isl_keep isl_map *map,
1700 enum isl_dim_type type);
1702 As with C<isl_space_get_tuple_name>, the value returned points to
1703 an internal data structure.
1704 The identifiers, positions or names of individual dimensions can be
1705 read off using the following functions.
1707 __isl_give isl_id *isl_basic_set_get_dim_id(
1708 __isl_keep isl_basic_set *bset,
1709 enum isl_dim_type type, unsigned pos);
1710 __isl_give isl_set *isl_set_set_dim_id(
1711 __isl_take isl_set *set, enum isl_dim_type type,
1712 unsigned pos, __isl_take isl_id *id);
1713 int isl_set_has_dim_id(__isl_keep isl_set *set,
1714 enum isl_dim_type type, unsigned pos);
1715 __isl_give isl_id *isl_set_get_dim_id(
1716 __isl_keep isl_set *set, enum isl_dim_type type,
1718 int isl_basic_map_has_dim_id(
1719 __isl_keep isl_basic_map *bmap,
1720 enum isl_dim_type type, unsigned pos);
1721 __isl_give isl_map *isl_map_set_dim_id(
1722 __isl_take isl_map *map, enum isl_dim_type type,
1723 unsigned pos, __isl_take isl_id *id);
1724 int isl_map_has_dim_id(__isl_keep isl_map *map,
1725 enum isl_dim_type type, unsigned pos);
1726 __isl_give isl_id *isl_map_get_dim_id(
1727 __isl_keep isl_map *map, enum isl_dim_type type,
1730 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1731 enum isl_dim_type type, __isl_keep isl_id *id);
1732 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1733 enum isl_dim_type type, __isl_keep isl_id *id);
1734 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1735 enum isl_dim_type type, const char *name);
1736 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1737 enum isl_dim_type type, const char *name);
1739 const char *isl_constraint_get_dim_name(
1740 __isl_keep isl_constraint *constraint,
1741 enum isl_dim_type type, unsigned pos);
1742 const char *isl_basic_set_get_dim_name(
1743 __isl_keep isl_basic_set *bset,
1744 enum isl_dim_type type, unsigned pos);
1745 int isl_set_has_dim_name(__isl_keep isl_set *set,
1746 enum isl_dim_type type, unsigned pos);
1747 const char *isl_set_get_dim_name(
1748 __isl_keep isl_set *set,
1749 enum isl_dim_type type, unsigned pos);
1750 const char *isl_basic_map_get_dim_name(
1751 __isl_keep isl_basic_map *bmap,
1752 enum isl_dim_type type, unsigned pos);
1753 int isl_map_has_dim_name(__isl_keep isl_map *map,
1754 enum isl_dim_type type, unsigned pos);
1755 const char *isl_map_get_dim_name(
1756 __isl_keep isl_map *map,
1757 enum isl_dim_type type, unsigned pos);
1759 These functions are mostly useful to obtain the identifiers, positions
1760 or names of the parameters. Identifiers of individual dimensions are
1761 essentially only useful for printing. They are ignored by all other
1762 operations and may not be preserved across those operations.
1766 =head3 Unary Properties
1772 The following functions test whether the given set or relation
1773 contains any integer points. The ``plain'' variants do not perform
1774 any computations, but simply check if the given set or relation
1775 is already known to be empty.
1777 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1778 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1779 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1780 int isl_set_is_empty(__isl_keep isl_set *set);
1781 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1782 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1783 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1784 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1785 int isl_map_is_empty(__isl_keep isl_map *map);
1786 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1788 =item * Universality
1790 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1791 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1792 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1794 =item * Single-valuedness
1796 int isl_basic_map_is_single_valued(
1797 __isl_keep isl_basic_map *bmap);
1798 int isl_map_plain_is_single_valued(
1799 __isl_keep isl_map *map);
1800 int isl_map_is_single_valued(__isl_keep isl_map *map);
1801 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1805 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1806 int isl_map_is_injective(__isl_keep isl_map *map);
1807 int isl_union_map_plain_is_injective(
1808 __isl_keep isl_union_map *umap);
1809 int isl_union_map_is_injective(
1810 __isl_keep isl_union_map *umap);
1814 int isl_map_is_bijective(__isl_keep isl_map *map);
1815 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1819 int isl_basic_map_plain_is_fixed(
1820 __isl_keep isl_basic_map *bmap,
1821 enum isl_dim_type type, unsigned pos,
1823 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1824 enum isl_dim_type type, unsigned pos,
1826 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1827 enum isl_dim_type type, unsigned pos,
1830 Check if the relation obviously lies on a hyperplane where the given dimension
1831 has a fixed value and if so, return that value in C<*val>.
1835 To check whether a set is a parameter domain, use this function:
1837 int isl_set_is_params(__isl_keep isl_set *set);
1838 int isl_union_set_is_params(
1839 __isl_keep isl_union_set *uset);
1843 The following functions check whether the domain of the given
1844 (basic) set is a wrapped relation.
1846 int isl_basic_set_is_wrapping(
1847 __isl_keep isl_basic_set *bset);
1848 int isl_set_is_wrapping(__isl_keep isl_set *set);
1850 =item * Internal Product
1852 int isl_basic_map_can_zip(
1853 __isl_keep isl_basic_map *bmap);
1854 int isl_map_can_zip(__isl_keep isl_map *map);
1856 Check whether the product of domain and range of the given relation
1858 i.e., whether both domain and range are nested relations.
1862 int isl_basic_map_can_curry(
1863 __isl_keep isl_basic_map *bmap);
1864 int isl_map_can_curry(__isl_keep isl_map *map);
1866 Check whether the domain of the (basic) relation is a wrapped relation.
1870 =head3 Binary Properties
1876 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1877 __isl_keep isl_set *set2);
1878 int isl_set_is_equal(__isl_keep isl_set *set1,
1879 __isl_keep isl_set *set2);
1880 int isl_union_set_is_equal(
1881 __isl_keep isl_union_set *uset1,
1882 __isl_keep isl_union_set *uset2);
1883 int isl_basic_map_is_equal(
1884 __isl_keep isl_basic_map *bmap1,
1885 __isl_keep isl_basic_map *bmap2);
1886 int isl_map_is_equal(__isl_keep isl_map *map1,
1887 __isl_keep isl_map *map2);
1888 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1889 __isl_keep isl_map *map2);
1890 int isl_union_map_is_equal(
1891 __isl_keep isl_union_map *umap1,
1892 __isl_keep isl_union_map *umap2);
1894 =item * Disjointness
1896 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1897 __isl_keep isl_set *set2);
1901 int isl_basic_set_is_subset(
1902 __isl_keep isl_basic_set *bset1,
1903 __isl_keep isl_basic_set *bset2);
1904 int isl_set_is_subset(__isl_keep isl_set *set1,
1905 __isl_keep isl_set *set2);
1906 int isl_set_is_strict_subset(
1907 __isl_keep isl_set *set1,
1908 __isl_keep isl_set *set2);
1909 int isl_union_set_is_subset(
1910 __isl_keep isl_union_set *uset1,
1911 __isl_keep isl_union_set *uset2);
1912 int isl_union_set_is_strict_subset(
1913 __isl_keep isl_union_set *uset1,
1914 __isl_keep isl_union_set *uset2);
1915 int isl_basic_map_is_subset(
1916 __isl_keep isl_basic_map *bmap1,
1917 __isl_keep isl_basic_map *bmap2);
1918 int isl_basic_map_is_strict_subset(
1919 __isl_keep isl_basic_map *bmap1,
1920 __isl_keep isl_basic_map *bmap2);
1921 int isl_map_is_subset(
1922 __isl_keep isl_map *map1,
1923 __isl_keep isl_map *map2);
1924 int isl_map_is_strict_subset(
1925 __isl_keep isl_map *map1,
1926 __isl_keep isl_map *map2);
1927 int isl_union_map_is_subset(
1928 __isl_keep isl_union_map *umap1,
1929 __isl_keep isl_union_map *umap2);
1930 int isl_union_map_is_strict_subset(
1931 __isl_keep isl_union_map *umap1,
1932 __isl_keep isl_union_map *umap2);
1934 Check whether the first argument is a (strict) subset of the
1939 =head2 Unary Operations
1945 __isl_give isl_set *isl_set_complement(
1946 __isl_take isl_set *set);
1947 __isl_give isl_map *isl_map_complement(
1948 __isl_take isl_map *map);
1952 __isl_give isl_basic_map *isl_basic_map_reverse(
1953 __isl_take isl_basic_map *bmap);
1954 __isl_give isl_map *isl_map_reverse(
1955 __isl_take isl_map *map);
1956 __isl_give isl_union_map *isl_union_map_reverse(
1957 __isl_take isl_union_map *umap);
1961 __isl_give isl_basic_set *isl_basic_set_project_out(
1962 __isl_take isl_basic_set *bset,
1963 enum isl_dim_type type, unsigned first, unsigned n);
1964 __isl_give isl_basic_map *isl_basic_map_project_out(
1965 __isl_take isl_basic_map *bmap,
1966 enum isl_dim_type type, unsigned first, unsigned n);
1967 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1968 enum isl_dim_type type, unsigned first, unsigned n);
1969 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1970 enum isl_dim_type type, unsigned first, unsigned n);
1971 __isl_give isl_basic_set *isl_basic_set_params(
1972 __isl_take isl_basic_set *bset);
1973 __isl_give isl_basic_set *isl_basic_map_domain(
1974 __isl_take isl_basic_map *bmap);
1975 __isl_give isl_basic_set *isl_basic_map_range(
1976 __isl_take isl_basic_map *bmap);
1977 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1978 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1979 __isl_give isl_set *isl_map_domain(
1980 __isl_take isl_map *bmap);
1981 __isl_give isl_set *isl_map_range(
1982 __isl_take isl_map *map);
1983 __isl_give isl_set *isl_union_set_params(
1984 __isl_take isl_union_set *uset);
1985 __isl_give isl_set *isl_union_map_params(
1986 __isl_take isl_union_map *umap);
1987 __isl_give isl_union_set *isl_union_map_domain(
1988 __isl_take isl_union_map *umap);
1989 __isl_give isl_union_set *isl_union_map_range(
1990 __isl_take isl_union_map *umap);
1992 __isl_give isl_basic_map *isl_basic_map_domain_map(
1993 __isl_take isl_basic_map *bmap);
1994 __isl_give isl_basic_map *isl_basic_map_range_map(
1995 __isl_take isl_basic_map *bmap);
1996 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1997 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1998 __isl_give isl_union_map *isl_union_map_domain_map(
1999 __isl_take isl_union_map *umap);
2000 __isl_give isl_union_map *isl_union_map_range_map(
2001 __isl_take isl_union_map *umap);
2003 The functions above construct a (basic, regular or union) relation
2004 that maps (a wrapped version of) the input relation to its domain or range.
2008 __isl_give isl_basic_set *isl_basic_set_eliminate(
2009 __isl_take isl_basic_set *bset,
2010 enum isl_dim_type type,
2011 unsigned first, unsigned n);
2012 __isl_give isl_set *isl_set_eliminate(
2013 __isl_take isl_set *set, enum isl_dim_type type,
2014 unsigned first, unsigned n);
2015 __isl_give isl_basic_map *isl_basic_map_eliminate(
2016 __isl_take isl_basic_map *bmap,
2017 enum isl_dim_type type,
2018 unsigned first, unsigned n);
2019 __isl_give isl_map *isl_map_eliminate(
2020 __isl_take isl_map *map, enum isl_dim_type type,
2021 unsigned first, unsigned n);
2023 Eliminate the coefficients for the given dimensions from the constraints,
2024 without removing the dimensions.
2028 __isl_give isl_basic_set *isl_basic_set_fix(
2029 __isl_take isl_basic_set *bset,
2030 enum isl_dim_type type, unsigned pos,
2032 __isl_give isl_basic_set *isl_basic_set_fix_si(
2033 __isl_take isl_basic_set *bset,
2034 enum isl_dim_type type, unsigned pos, int value);
2035 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2036 enum isl_dim_type type, unsigned pos,
2038 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2039 enum isl_dim_type type, unsigned pos, int value);
2040 __isl_give isl_basic_map *isl_basic_map_fix_si(
2041 __isl_take isl_basic_map *bmap,
2042 enum isl_dim_type type, unsigned pos, int value);
2043 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2044 enum isl_dim_type type, unsigned pos,
2046 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2047 enum isl_dim_type type, unsigned pos, int value);
2049 Intersect the set or relation with the hyperplane where the given
2050 dimension has the fixed given value.
2052 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2053 __isl_take isl_basic_map *bmap,
2054 enum isl_dim_type type, unsigned pos, int value);
2055 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2056 __isl_take isl_basic_map *bmap,
2057 enum isl_dim_type type, unsigned pos, int value);
2058 __isl_give isl_set *isl_set_lower_bound(
2059 __isl_take isl_set *set,
2060 enum isl_dim_type type, unsigned pos,
2062 __isl_give isl_set *isl_set_lower_bound_si(
2063 __isl_take isl_set *set,
2064 enum isl_dim_type type, unsigned pos, int value);
2065 __isl_give isl_map *isl_map_lower_bound_si(
2066 __isl_take isl_map *map,
2067 enum isl_dim_type type, unsigned pos, int value);
2068 __isl_give isl_set *isl_set_upper_bound(
2069 __isl_take isl_set *set,
2070 enum isl_dim_type type, unsigned pos,
2072 __isl_give isl_set *isl_set_upper_bound_si(
2073 __isl_take isl_set *set,
2074 enum isl_dim_type type, unsigned pos, int value);
2075 __isl_give isl_map *isl_map_upper_bound_si(
2076 __isl_take isl_map *map,
2077 enum isl_dim_type type, unsigned pos, int value);
2079 Intersect the set or relation with the half-space where the given
2080 dimension has a value bounded by the fixed given value.
2082 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2083 enum isl_dim_type type1, int pos1,
2084 enum isl_dim_type type2, int pos2);
2085 __isl_give isl_basic_map *isl_basic_map_equate(
2086 __isl_take isl_basic_map *bmap,
2087 enum isl_dim_type type1, int pos1,
2088 enum isl_dim_type type2, int pos2);
2089 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2090 enum isl_dim_type type1, int pos1,
2091 enum isl_dim_type type2, int pos2);
2093 Intersect the set or relation with the hyperplane where the given
2094 dimensions are equal to each other.
2096 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2097 enum isl_dim_type type1, int pos1,
2098 enum isl_dim_type type2, int pos2);
2100 Intersect the relation with the hyperplane where the given
2101 dimensions have opposite values.
2103 __isl_give isl_basic_map *isl_basic_map_order_ge(
2104 __isl_take isl_basic_map *bmap,
2105 enum isl_dim_type type1, int pos1,
2106 enum isl_dim_type type2, int pos2);
2107 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2108 enum isl_dim_type type1, int pos1,
2109 enum isl_dim_type type2, int pos2);
2110 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2111 enum isl_dim_type type1, int pos1,
2112 enum isl_dim_type type2, int pos2);
2114 Intersect the relation with the half-space where the given
2115 dimensions satisfy the given ordering.
2119 __isl_give isl_map *isl_set_identity(
2120 __isl_take isl_set *set);
2121 __isl_give isl_union_map *isl_union_set_identity(
2122 __isl_take isl_union_set *uset);
2124 Construct an identity relation on the given (union) set.
2128 __isl_give isl_basic_set *isl_basic_map_deltas(
2129 __isl_take isl_basic_map *bmap);
2130 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2131 __isl_give isl_union_set *isl_union_map_deltas(
2132 __isl_take isl_union_map *umap);
2134 These functions return a (basic) set containing the differences
2135 between image elements and corresponding domain elements in the input.
2137 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2138 __isl_take isl_basic_map *bmap);
2139 __isl_give isl_map *isl_map_deltas_map(
2140 __isl_take isl_map *map);
2141 __isl_give isl_union_map *isl_union_map_deltas_map(
2142 __isl_take isl_union_map *umap);
2144 The functions above construct a (basic, regular or union) relation
2145 that maps (a wrapped version of) the input relation to its delta set.
2149 Simplify the representation of a set or relation by trying
2150 to combine pairs of basic sets or relations into a single
2151 basic set or relation.
2153 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2154 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2155 __isl_give isl_union_set *isl_union_set_coalesce(
2156 __isl_take isl_union_set *uset);
2157 __isl_give isl_union_map *isl_union_map_coalesce(
2158 __isl_take isl_union_map *umap);
2160 One of the methods for combining pairs of basic sets or relations
2161 can result in coefficients that are much larger than those that appear
2162 in the constraints of the input. By default, the coefficients are
2163 not allowed to grow larger, but this can be changed by unsetting
2164 the following option.
2166 int isl_options_set_coalesce_bounded_wrapping(
2167 isl_ctx *ctx, int val);
2168 int isl_options_get_coalesce_bounded_wrapping(
2171 =item * Detecting equalities
2173 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2174 __isl_take isl_basic_set *bset);
2175 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2176 __isl_take isl_basic_map *bmap);
2177 __isl_give isl_set *isl_set_detect_equalities(
2178 __isl_take isl_set *set);
2179 __isl_give isl_map *isl_map_detect_equalities(
2180 __isl_take isl_map *map);
2181 __isl_give isl_union_set *isl_union_set_detect_equalities(
2182 __isl_take isl_union_set *uset);
2183 __isl_give isl_union_map *isl_union_map_detect_equalities(
2184 __isl_take isl_union_map *umap);
2186 Simplify the representation of a set or relation by detecting implicit
2189 =item * Removing redundant constraints
2191 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2192 __isl_take isl_basic_set *bset);
2193 __isl_give isl_set *isl_set_remove_redundancies(
2194 __isl_take isl_set *set);
2195 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2196 __isl_take isl_basic_map *bmap);
2197 __isl_give isl_map *isl_map_remove_redundancies(
2198 __isl_take isl_map *map);
2202 __isl_give isl_basic_set *isl_set_convex_hull(
2203 __isl_take isl_set *set);
2204 __isl_give isl_basic_map *isl_map_convex_hull(
2205 __isl_take isl_map *map);
2207 If the input set or relation has any existentially quantified
2208 variables, then the result of these operations is currently undefined.
2212 __isl_give isl_basic_set *isl_set_simple_hull(
2213 __isl_take isl_set *set);
2214 __isl_give isl_basic_map *isl_map_simple_hull(
2215 __isl_take isl_map *map);
2216 __isl_give isl_union_map *isl_union_map_simple_hull(
2217 __isl_take isl_union_map *umap);
2219 These functions compute a single basic set or relation
2220 that contains the whole input set or relation.
2221 In particular, the output is described by translates
2222 of the constraints describing the basic sets or relations in the input.
2226 (See \autoref{s:simple hull}.)
2232 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2233 __isl_take isl_basic_set *bset);
2234 __isl_give isl_basic_set *isl_set_affine_hull(
2235 __isl_take isl_set *set);
2236 __isl_give isl_union_set *isl_union_set_affine_hull(
2237 __isl_take isl_union_set *uset);
2238 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2239 __isl_take isl_basic_map *bmap);
2240 __isl_give isl_basic_map *isl_map_affine_hull(
2241 __isl_take isl_map *map);
2242 __isl_give isl_union_map *isl_union_map_affine_hull(
2243 __isl_take isl_union_map *umap);
2245 In case of union sets and relations, the affine hull is computed
2248 =item * Polyhedral hull
2250 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2251 __isl_take isl_set *set);
2252 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2253 __isl_take isl_map *map);
2254 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2255 __isl_take isl_union_set *uset);
2256 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2257 __isl_take isl_union_map *umap);
2259 These functions compute a single basic set or relation
2260 not involving any existentially quantified variables
2261 that contains the whole input set or relation.
2262 In case of union sets and relations, the polyhedral hull is computed
2267 __isl_give isl_basic_set *isl_basic_set_sample(
2268 __isl_take isl_basic_set *bset);
2269 __isl_give isl_basic_set *isl_set_sample(
2270 __isl_take isl_set *set);
2271 __isl_give isl_basic_map *isl_basic_map_sample(
2272 __isl_take isl_basic_map *bmap);
2273 __isl_give isl_basic_map *isl_map_sample(
2274 __isl_take isl_map *map);
2276 If the input (basic) set or relation is non-empty, then return
2277 a singleton subset of the input. Otherwise, return an empty set.
2279 =item * Optimization
2281 #include <isl/ilp.h>
2282 enum isl_lp_result isl_basic_set_max(
2283 __isl_keep isl_basic_set *bset,
2284 __isl_keep isl_aff *obj, isl_int *opt)
2285 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2286 __isl_keep isl_aff *obj, isl_int *opt);
2287 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2288 __isl_keep isl_aff *obj, isl_int *opt);
2290 Compute the minimum or maximum of the integer affine expression C<obj>
2291 over the points in C<set>, returning the result in C<opt>.
2292 The return value may be one of C<isl_lp_error>,
2293 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2295 =item * Parametric optimization
2297 __isl_give isl_pw_aff *isl_set_dim_min(
2298 __isl_take isl_set *set, int pos);
2299 __isl_give isl_pw_aff *isl_set_dim_max(
2300 __isl_take isl_set *set, int pos);
2301 __isl_give isl_pw_aff *isl_map_dim_max(
2302 __isl_take isl_map *map, int pos);
2304 Compute the minimum or maximum of the given set or output dimension
2305 as a function of the parameters (and input dimensions), but independently
2306 of the other set or output dimensions.
2307 For lexicographic optimization, see L<"Lexicographic Optimization">.
2311 The following functions compute either the set of (rational) coefficient
2312 values of valid constraints for the given set or the set of (rational)
2313 values satisfying the constraints with coefficients from the given set.
2314 Internally, these two sets of functions perform essentially the
2315 same operations, except that the set of coefficients is assumed to
2316 be a cone, while the set of values may be any polyhedron.
2317 The current implementation is based on the Farkas lemma and
2318 Fourier-Motzkin elimination, but this may change or be made optional
2319 in future. In particular, future implementations may use different
2320 dualization algorithms or skip the elimination step.
2322 __isl_give isl_basic_set *isl_basic_set_coefficients(
2323 __isl_take isl_basic_set *bset);
2324 __isl_give isl_basic_set *isl_set_coefficients(
2325 __isl_take isl_set *set);
2326 __isl_give isl_union_set *isl_union_set_coefficients(
2327 __isl_take isl_union_set *bset);
2328 __isl_give isl_basic_set *isl_basic_set_solutions(
2329 __isl_take isl_basic_set *bset);
2330 __isl_give isl_basic_set *isl_set_solutions(
2331 __isl_take isl_set *set);
2332 __isl_give isl_union_set *isl_union_set_solutions(
2333 __isl_take isl_union_set *bset);
2337 __isl_give isl_map *isl_map_fixed_power(
2338 __isl_take isl_map *map, isl_int exp);
2339 __isl_give isl_union_map *isl_union_map_fixed_power(
2340 __isl_take isl_union_map *umap, isl_int exp);
2342 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2343 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2344 of C<map> is computed.
2346 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2348 __isl_give isl_union_map *isl_union_map_power(
2349 __isl_take isl_union_map *umap, int *exact);
2351 Compute a parametric representation for all positive powers I<k> of C<map>.
2352 The result maps I<k> to a nested relation corresponding to the
2353 I<k>th power of C<map>.
2354 The result may be an overapproximation. If the result is known to be exact,
2355 then C<*exact> is set to C<1>.
2357 =item * Transitive closure
2359 __isl_give isl_map *isl_map_transitive_closure(
2360 __isl_take isl_map *map, int *exact);
2361 __isl_give isl_union_map *isl_union_map_transitive_closure(
2362 __isl_take isl_union_map *umap, int *exact);
2364 Compute the transitive closure of C<map>.
2365 The result may be an overapproximation. If the result is known to be exact,
2366 then C<*exact> is set to C<1>.
2368 =item * Reaching path lengths
2370 __isl_give isl_map *isl_map_reaching_path_lengths(
2371 __isl_take isl_map *map, int *exact);
2373 Compute a relation that maps each element in the range of C<map>
2374 to the lengths of all paths composed of edges in C<map> that
2375 end up in the given element.
2376 The result may be an overapproximation. If the result is known to be exact,
2377 then C<*exact> is set to C<1>.
2378 To compute the I<maximal> path length, the resulting relation
2379 should be postprocessed by C<isl_map_lexmax>.
2380 In particular, if the input relation is a dependence relation
2381 (mapping sources to sinks), then the maximal path length corresponds
2382 to the free schedule.
2383 Note, however, that C<isl_map_lexmax> expects the maximum to be
2384 finite, so if the path lengths are unbounded (possibly due to
2385 the overapproximation), then you will get an error message.
2389 __isl_give isl_basic_set *isl_basic_map_wrap(
2390 __isl_take isl_basic_map *bmap);
2391 __isl_give isl_set *isl_map_wrap(
2392 __isl_take isl_map *map);
2393 __isl_give isl_union_set *isl_union_map_wrap(
2394 __isl_take isl_union_map *umap);
2395 __isl_give isl_basic_map *isl_basic_set_unwrap(
2396 __isl_take isl_basic_set *bset);
2397 __isl_give isl_map *isl_set_unwrap(
2398 __isl_take isl_set *set);
2399 __isl_give isl_union_map *isl_union_set_unwrap(
2400 __isl_take isl_union_set *uset);
2404 Remove any internal structure of domain (and range) of the given
2405 set or relation. If there is any such internal structure in the input,
2406 then the name of the space is also removed.
2408 __isl_give isl_basic_set *isl_basic_set_flatten(
2409 __isl_take isl_basic_set *bset);
2410 __isl_give isl_set *isl_set_flatten(
2411 __isl_take isl_set *set);
2412 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2413 __isl_take isl_basic_map *bmap);
2414 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2415 __isl_take isl_basic_map *bmap);
2416 __isl_give isl_map *isl_map_flatten_range(
2417 __isl_take isl_map *map);
2418 __isl_give isl_map *isl_map_flatten_domain(
2419 __isl_take isl_map *map);
2420 __isl_give isl_basic_map *isl_basic_map_flatten(
2421 __isl_take isl_basic_map *bmap);
2422 __isl_give isl_map *isl_map_flatten(
2423 __isl_take isl_map *map);
2425 __isl_give isl_map *isl_set_flatten_map(
2426 __isl_take isl_set *set);
2428 The function above constructs a relation
2429 that maps the input set to a flattened version of the set.
2433 Lift the input set to a space with extra dimensions corresponding
2434 to the existentially quantified variables in the input.
2435 In particular, the result lives in a wrapped map where the domain
2436 is the original space and the range corresponds to the original
2437 existentially quantified variables.
2439 __isl_give isl_basic_set *isl_basic_set_lift(
2440 __isl_take isl_basic_set *bset);
2441 __isl_give isl_set *isl_set_lift(
2442 __isl_take isl_set *set);
2443 __isl_give isl_union_set *isl_union_set_lift(
2444 __isl_take isl_union_set *uset);
2446 Given a local space that contains the existentially quantified
2447 variables of a set, a basic relation that, when applied to
2448 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2449 can be constructed using the following function.
2451 #include <isl/local_space.h>
2452 __isl_give isl_basic_map *isl_local_space_lifting(
2453 __isl_take isl_local_space *ls);
2455 =item * Internal Product
2457 __isl_give isl_basic_map *isl_basic_map_zip(
2458 __isl_take isl_basic_map *bmap);
2459 __isl_give isl_map *isl_map_zip(
2460 __isl_take isl_map *map);
2461 __isl_give isl_union_map *isl_union_map_zip(
2462 __isl_take isl_union_map *umap);
2464 Given a relation with nested relations for domain and range,
2465 interchange the range of the domain with the domain of the range.
2469 __isl_give isl_basic_map *isl_basic_map_curry(
2470 __isl_take isl_basic_map *bmap);
2471 __isl_give isl_map *isl_map_curry(
2472 __isl_take isl_map *map);
2473 __isl_give isl_union_map *isl_union_map_curry(
2474 __isl_take isl_union_map *umap);
2476 Given a relation with a nested relation for domain,
2477 move the range of the nested relation out of the domain
2478 and use it as the domain of a nested relation in the range,
2479 with the original range as range of this nested relation.
2481 =item * Aligning parameters
2483 __isl_give isl_basic_set *isl_basic_set_align_params(
2484 __isl_take isl_basic_set *bset,
2485 __isl_take isl_space *model);
2486 __isl_give isl_set *isl_set_align_params(
2487 __isl_take isl_set *set,
2488 __isl_take isl_space *model);
2489 __isl_give isl_basic_map *isl_basic_map_align_params(
2490 __isl_take isl_basic_map *bmap,
2491 __isl_take isl_space *model);
2492 __isl_give isl_map *isl_map_align_params(
2493 __isl_take isl_map *map,
2494 __isl_take isl_space *model);
2496 Change the order of the parameters of the given set or relation
2497 such that the first parameters match those of C<model>.
2498 This may involve the introduction of extra parameters.
2499 All parameters need to be named.
2501 =item * Dimension manipulation
2503 __isl_give isl_set *isl_set_add_dims(
2504 __isl_take isl_set *set,
2505 enum isl_dim_type type, unsigned n);
2506 __isl_give isl_map *isl_map_add_dims(
2507 __isl_take isl_map *map,
2508 enum isl_dim_type type, unsigned n);
2509 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2510 __isl_take isl_basic_set *bset,
2511 enum isl_dim_type type, unsigned pos,
2513 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2514 __isl_take isl_basic_map *bmap,
2515 enum isl_dim_type type, unsigned pos,
2517 __isl_give isl_set *isl_set_insert_dims(
2518 __isl_take isl_set *set,
2519 enum isl_dim_type type, unsigned pos, unsigned n);
2520 __isl_give isl_map *isl_map_insert_dims(
2521 __isl_take isl_map *map,
2522 enum isl_dim_type type, unsigned pos, unsigned n);
2523 __isl_give isl_basic_set *isl_basic_set_move_dims(
2524 __isl_take isl_basic_set *bset,
2525 enum isl_dim_type dst_type, unsigned dst_pos,
2526 enum isl_dim_type src_type, unsigned src_pos,
2528 __isl_give isl_basic_map *isl_basic_map_move_dims(
2529 __isl_take isl_basic_map *bmap,
2530 enum isl_dim_type dst_type, unsigned dst_pos,
2531 enum isl_dim_type src_type, unsigned src_pos,
2533 __isl_give isl_set *isl_set_move_dims(
2534 __isl_take isl_set *set,
2535 enum isl_dim_type dst_type, unsigned dst_pos,
2536 enum isl_dim_type src_type, unsigned src_pos,
2538 __isl_give isl_map *isl_map_move_dims(
2539 __isl_take isl_map *map,
2540 enum isl_dim_type dst_type, unsigned dst_pos,
2541 enum isl_dim_type src_type, unsigned src_pos,
2544 It is usually not advisable to directly change the (input or output)
2545 space of a set or a relation as this removes the name and the internal
2546 structure of the space. However, the above functions can be useful
2547 to add new parameters, assuming
2548 C<isl_set_align_params> and C<isl_map_align_params>
2553 =head2 Binary Operations
2555 The two arguments of a binary operation not only need to live
2556 in the same C<isl_ctx>, they currently also need to have
2557 the same (number of) parameters.
2559 =head3 Basic Operations
2563 =item * Intersection
2565 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2566 __isl_take isl_basic_set *bset1,
2567 __isl_take isl_basic_set *bset2);
2568 __isl_give isl_basic_set *isl_basic_set_intersect(
2569 __isl_take isl_basic_set *bset1,
2570 __isl_take isl_basic_set *bset2);
2571 __isl_give isl_set *isl_set_intersect_params(
2572 __isl_take isl_set *set,
2573 __isl_take isl_set *params);
2574 __isl_give isl_set *isl_set_intersect(
2575 __isl_take isl_set *set1,
2576 __isl_take isl_set *set2);
2577 __isl_give isl_union_set *isl_union_set_intersect_params(
2578 __isl_take isl_union_set *uset,
2579 __isl_take isl_set *set);
2580 __isl_give isl_union_map *isl_union_map_intersect_params(
2581 __isl_take isl_union_map *umap,
2582 __isl_take isl_set *set);
2583 __isl_give isl_union_set *isl_union_set_intersect(
2584 __isl_take isl_union_set *uset1,
2585 __isl_take isl_union_set *uset2);
2586 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2587 __isl_take isl_basic_map *bmap,
2588 __isl_take isl_basic_set *bset);
2589 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2590 __isl_take isl_basic_map *bmap,
2591 __isl_take isl_basic_set *bset);
2592 __isl_give isl_basic_map *isl_basic_map_intersect(
2593 __isl_take isl_basic_map *bmap1,
2594 __isl_take isl_basic_map *bmap2);
2595 __isl_give isl_map *isl_map_intersect_params(
2596 __isl_take isl_map *map,
2597 __isl_take isl_set *params);
2598 __isl_give isl_map *isl_map_intersect_domain(
2599 __isl_take isl_map *map,
2600 __isl_take isl_set *set);
2601 __isl_give isl_map *isl_map_intersect_range(
2602 __isl_take isl_map *map,
2603 __isl_take isl_set *set);
2604 __isl_give isl_map *isl_map_intersect(
2605 __isl_take isl_map *map1,
2606 __isl_take isl_map *map2);
2607 __isl_give isl_union_map *isl_union_map_intersect_domain(
2608 __isl_take isl_union_map *umap,
2609 __isl_take isl_union_set *uset);
2610 __isl_give isl_union_map *isl_union_map_intersect_range(
2611 __isl_take isl_union_map *umap,
2612 __isl_take isl_union_set *uset);
2613 __isl_give isl_union_map *isl_union_map_intersect(
2614 __isl_take isl_union_map *umap1,
2615 __isl_take isl_union_map *umap2);
2617 The second argument to the C<_params> functions needs to be
2618 a parametric (basic) set. For the other functions, a parametric set
2619 for either argument is only allowed if the other argument is
2620 a parametric set as well.
2624 __isl_give isl_set *isl_basic_set_union(
2625 __isl_take isl_basic_set *bset1,
2626 __isl_take isl_basic_set *bset2);
2627 __isl_give isl_map *isl_basic_map_union(
2628 __isl_take isl_basic_map *bmap1,
2629 __isl_take isl_basic_map *bmap2);
2630 __isl_give isl_set *isl_set_union(
2631 __isl_take isl_set *set1,
2632 __isl_take isl_set *set2);
2633 __isl_give isl_map *isl_map_union(
2634 __isl_take isl_map *map1,
2635 __isl_take isl_map *map2);
2636 __isl_give isl_union_set *isl_union_set_union(
2637 __isl_take isl_union_set *uset1,
2638 __isl_take isl_union_set *uset2);
2639 __isl_give isl_union_map *isl_union_map_union(
2640 __isl_take isl_union_map *umap1,
2641 __isl_take isl_union_map *umap2);
2643 =item * Set difference
2645 __isl_give isl_set *isl_set_subtract(
2646 __isl_take isl_set *set1,
2647 __isl_take isl_set *set2);
2648 __isl_give isl_map *isl_map_subtract(
2649 __isl_take isl_map *map1,
2650 __isl_take isl_map *map2);
2651 __isl_give isl_map *isl_map_subtract_domain(
2652 __isl_take isl_map *map,
2653 __isl_take isl_set *dom);
2654 __isl_give isl_map *isl_map_subtract_range(
2655 __isl_take isl_map *map,
2656 __isl_take isl_set *dom);
2657 __isl_give isl_union_set *isl_union_set_subtract(
2658 __isl_take isl_union_set *uset1,
2659 __isl_take isl_union_set *uset2);
2660 __isl_give isl_union_map *isl_union_map_subtract(
2661 __isl_take isl_union_map *umap1,
2662 __isl_take isl_union_map *umap2);
2666 __isl_give isl_basic_set *isl_basic_set_apply(
2667 __isl_take isl_basic_set *bset,
2668 __isl_take isl_basic_map *bmap);
2669 __isl_give isl_set *isl_set_apply(
2670 __isl_take isl_set *set,
2671 __isl_take isl_map *map);
2672 __isl_give isl_union_set *isl_union_set_apply(
2673 __isl_take isl_union_set *uset,
2674 __isl_take isl_union_map *umap);
2675 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2676 __isl_take isl_basic_map *bmap1,
2677 __isl_take isl_basic_map *bmap2);
2678 __isl_give isl_basic_map *isl_basic_map_apply_range(
2679 __isl_take isl_basic_map *bmap1,
2680 __isl_take isl_basic_map *bmap2);
2681 __isl_give isl_map *isl_map_apply_domain(
2682 __isl_take isl_map *map1,
2683 __isl_take isl_map *map2);
2684 __isl_give isl_union_map *isl_union_map_apply_domain(
2685 __isl_take isl_union_map *umap1,
2686 __isl_take isl_union_map *umap2);
2687 __isl_give isl_map *isl_map_apply_range(
2688 __isl_take isl_map *map1,
2689 __isl_take isl_map *map2);
2690 __isl_give isl_union_map *isl_union_map_apply_range(
2691 __isl_take isl_union_map *umap1,
2692 __isl_take isl_union_map *umap2);
2694 =item * Cartesian Product
2696 __isl_give isl_set *isl_set_product(
2697 __isl_take isl_set *set1,
2698 __isl_take isl_set *set2);
2699 __isl_give isl_union_set *isl_union_set_product(
2700 __isl_take isl_union_set *uset1,
2701 __isl_take isl_union_set *uset2);
2702 __isl_give isl_basic_map *isl_basic_map_domain_product(
2703 __isl_take isl_basic_map *bmap1,
2704 __isl_take isl_basic_map *bmap2);
2705 __isl_give isl_basic_map *isl_basic_map_range_product(
2706 __isl_take isl_basic_map *bmap1,
2707 __isl_take isl_basic_map *bmap2);
2708 __isl_give isl_basic_map *isl_basic_map_product(
2709 __isl_take isl_basic_map *bmap1,
2710 __isl_take isl_basic_map *bmap2);
2711 __isl_give isl_map *isl_map_domain_product(
2712 __isl_take isl_map *map1,
2713 __isl_take isl_map *map2);
2714 __isl_give isl_map *isl_map_range_product(
2715 __isl_take isl_map *map1,
2716 __isl_take isl_map *map2);
2717 __isl_give isl_union_map *isl_union_map_domain_product(
2718 __isl_take isl_union_map *umap1,
2719 __isl_take isl_union_map *umap2);
2720 __isl_give isl_union_map *isl_union_map_range_product(
2721 __isl_take isl_union_map *umap1,
2722 __isl_take isl_union_map *umap2);
2723 __isl_give isl_map *isl_map_product(
2724 __isl_take isl_map *map1,
2725 __isl_take isl_map *map2);
2726 __isl_give isl_union_map *isl_union_map_product(
2727 __isl_take isl_union_map *umap1,
2728 __isl_take isl_union_map *umap2);
2730 The above functions compute the cross product of the given
2731 sets or relations. The domains and ranges of the results
2732 are wrapped maps between domains and ranges of the inputs.
2733 To obtain a ``flat'' product, use the following functions
2736 __isl_give isl_basic_set *isl_basic_set_flat_product(
2737 __isl_take isl_basic_set *bset1,
2738 __isl_take isl_basic_set *bset2);
2739 __isl_give isl_set *isl_set_flat_product(
2740 __isl_take isl_set *set1,
2741 __isl_take isl_set *set2);
2742 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2743 __isl_take isl_basic_map *bmap1,
2744 __isl_take isl_basic_map *bmap2);
2745 __isl_give isl_map *isl_map_flat_domain_product(
2746 __isl_take isl_map *map1,
2747 __isl_take isl_map *map2);
2748 __isl_give isl_map *isl_map_flat_range_product(
2749 __isl_take isl_map *map1,
2750 __isl_take isl_map *map2);
2751 __isl_give isl_union_map *isl_union_map_flat_range_product(
2752 __isl_take isl_union_map *umap1,
2753 __isl_take isl_union_map *umap2);
2754 __isl_give isl_basic_map *isl_basic_map_flat_product(
2755 __isl_take isl_basic_map *bmap1,
2756 __isl_take isl_basic_map *bmap2);
2757 __isl_give isl_map *isl_map_flat_product(
2758 __isl_take isl_map *map1,
2759 __isl_take isl_map *map2);
2761 =item * Simplification
2763 __isl_give isl_basic_set *isl_basic_set_gist(
2764 __isl_take isl_basic_set *bset,
2765 __isl_take isl_basic_set *context);
2766 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2767 __isl_take isl_set *context);
2768 __isl_give isl_set *isl_set_gist_params(
2769 __isl_take isl_set *set,
2770 __isl_take isl_set *context);
2771 __isl_give isl_union_set *isl_union_set_gist(
2772 __isl_take isl_union_set *uset,
2773 __isl_take isl_union_set *context);
2774 __isl_give isl_union_set *isl_union_set_gist_params(
2775 __isl_take isl_union_set *uset,
2776 __isl_take isl_set *set);
2777 __isl_give isl_basic_map *isl_basic_map_gist(
2778 __isl_take isl_basic_map *bmap,
2779 __isl_take isl_basic_map *context);
2780 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2781 __isl_take isl_map *context);
2782 __isl_give isl_map *isl_map_gist_params(
2783 __isl_take isl_map *map,
2784 __isl_take isl_set *context);
2785 __isl_give isl_map *isl_map_gist_domain(
2786 __isl_take isl_map *map,
2787 __isl_take isl_set *context);
2788 __isl_give isl_map *isl_map_gist_range(
2789 __isl_take isl_map *map,
2790 __isl_take isl_set *context);
2791 __isl_give isl_union_map *isl_union_map_gist(
2792 __isl_take isl_union_map *umap,
2793 __isl_take isl_union_map *context);
2794 __isl_give isl_union_map *isl_union_map_gist_params(
2795 __isl_take isl_union_map *umap,
2796 __isl_take isl_set *set);
2797 __isl_give isl_union_map *isl_union_map_gist_domain(
2798 __isl_take isl_union_map *umap,
2799 __isl_take isl_union_set *uset);
2800 __isl_give isl_union_map *isl_union_map_gist_range(
2801 __isl_take isl_union_map *umap,
2802 __isl_take isl_union_set *uset);
2804 The gist operation returns a set or relation that has the
2805 same intersection with the context as the input set or relation.
2806 Any implicit equality in the intersection is made explicit in the result,
2807 while all inequalities that are redundant with respect to the intersection
2809 In case of union sets and relations, the gist operation is performed
2814 =head3 Lexicographic Optimization
2816 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2817 the following functions
2818 compute a set that contains the lexicographic minimum or maximum
2819 of the elements in C<set> (or C<bset>) for those values of the parameters
2820 that satisfy C<dom>.
2821 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2822 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2824 In other words, the union of the parameter values
2825 for which the result is non-empty and of C<*empty>
2828 __isl_give isl_set *isl_basic_set_partial_lexmin(
2829 __isl_take isl_basic_set *bset,
2830 __isl_take isl_basic_set *dom,
2831 __isl_give isl_set **empty);
2832 __isl_give isl_set *isl_basic_set_partial_lexmax(
2833 __isl_take isl_basic_set *bset,
2834 __isl_take isl_basic_set *dom,
2835 __isl_give isl_set **empty);
2836 __isl_give isl_set *isl_set_partial_lexmin(
2837 __isl_take isl_set *set, __isl_take isl_set *dom,
2838 __isl_give isl_set **empty);
2839 __isl_give isl_set *isl_set_partial_lexmax(
2840 __isl_take isl_set *set, __isl_take isl_set *dom,
2841 __isl_give isl_set **empty);
2843 Given a (basic) set C<set> (or C<bset>), the following functions simply
2844 return a set containing the lexicographic minimum or maximum
2845 of the elements in C<set> (or C<bset>).
2846 In case of union sets, the optimum is computed per space.
2848 __isl_give isl_set *isl_basic_set_lexmin(
2849 __isl_take isl_basic_set *bset);
2850 __isl_give isl_set *isl_basic_set_lexmax(
2851 __isl_take isl_basic_set *bset);
2852 __isl_give isl_set *isl_set_lexmin(
2853 __isl_take isl_set *set);
2854 __isl_give isl_set *isl_set_lexmax(
2855 __isl_take isl_set *set);
2856 __isl_give isl_union_set *isl_union_set_lexmin(
2857 __isl_take isl_union_set *uset);
2858 __isl_give isl_union_set *isl_union_set_lexmax(
2859 __isl_take isl_union_set *uset);
2861 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2862 the following functions
2863 compute a relation that maps each element of C<dom>
2864 to the single lexicographic minimum or maximum
2865 of the elements that are associated to that same
2866 element in C<map> (or C<bmap>).
2867 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2868 that contains the elements in C<dom> that do not map
2869 to any elements in C<map> (or C<bmap>).
2870 In other words, the union of the domain of the result and of C<*empty>
2873 __isl_give isl_map *isl_basic_map_partial_lexmax(
2874 __isl_take isl_basic_map *bmap,
2875 __isl_take isl_basic_set *dom,
2876 __isl_give isl_set **empty);
2877 __isl_give isl_map *isl_basic_map_partial_lexmin(
2878 __isl_take isl_basic_map *bmap,
2879 __isl_take isl_basic_set *dom,
2880 __isl_give isl_set **empty);
2881 __isl_give isl_map *isl_map_partial_lexmax(
2882 __isl_take isl_map *map, __isl_take isl_set *dom,
2883 __isl_give isl_set **empty);
2884 __isl_give isl_map *isl_map_partial_lexmin(
2885 __isl_take isl_map *map, __isl_take isl_set *dom,
2886 __isl_give isl_set **empty);
2888 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2889 return a map mapping each element in the domain of
2890 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2891 of all elements associated to that element.
2892 In case of union relations, the optimum is computed per space.
2894 __isl_give isl_map *isl_basic_map_lexmin(
2895 __isl_take isl_basic_map *bmap);
2896 __isl_give isl_map *isl_basic_map_lexmax(
2897 __isl_take isl_basic_map *bmap);
2898 __isl_give isl_map *isl_map_lexmin(
2899 __isl_take isl_map *map);
2900 __isl_give isl_map *isl_map_lexmax(
2901 __isl_take isl_map *map);
2902 __isl_give isl_union_map *isl_union_map_lexmin(
2903 __isl_take isl_union_map *umap);
2904 __isl_give isl_union_map *isl_union_map_lexmax(
2905 __isl_take isl_union_map *umap);
2907 The following functions return their result in the form of
2908 a piecewise multi-affine expression
2909 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2910 but are otherwise equivalent to the corresponding functions
2911 returning a basic set or relation.
2913 __isl_give isl_pw_multi_aff *
2914 isl_basic_map_lexmin_pw_multi_aff(
2915 __isl_take isl_basic_map *bmap);
2916 __isl_give isl_pw_multi_aff *
2917 isl_basic_set_partial_lexmin_pw_multi_aff(
2918 __isl_take isl_basic_set *bset,
2919 __isl_take isl_basic_set *dom,
2920 __isl_give isl_set **empty);
2921 __isl_give isl_pw_multi_aff *
2922 isl_basic_set_partial_lexmax_pw_multi_aff(
2923 __isl_take isl_basic_set *bset,
2924 __isl_take isl_basic_set *dom,
2925 __isl_give isl_set **empty);
2926 __isl_give isl_pw_multi_aff *
2927 isl_basic_map_partial_lexmin_pw_multi_aff(
2928 __isl_take isl_basic_map *bmap,
2929 __isl_take isl_basic_set *dom,
2930 __isl_give isl_set **empty);
2931 __isl_give isl_pw_multi_aff *
2932 isl_basic_map_partial_lexmax_pw_multi_aff(
2933 __isl_take isl_basic_map *bmap,
2934 __isl_take isl_basic_set *dom,
2935 __isl_give isl_set **empty);
2936 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2937 __isl_take isl_map *map);
2938 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2939 __isl_take isl_map *map);
2943 Lists are defined over several element types, including
2944 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2945 Here we take lists of C<isl_set>s as an example.
2946 Lists can be created, copied, modified and freed using the following functions.
2948 #include <isl/list.h>
2949 __isl_give isl_set_list *isl_set_list_from_set(
2950 __isl_take isl_set *el);
2951 __isl_give isl_set_list *isl_set_list_alloc(
2952 isl_ctx *ctx, int n);
2953 __isl_give isl_set_list *isl_set_list_copy(
2954 __isl_keep isl_set_list *list);
2955 __isl_give isl_set_list *isl_set_list_insert(
2956 __isl_take isl_set_list *list, unsigned pos,
2957 __isl_take isl_set *el);
2958 __isl_give isl_set_list *isl_set_list_add(
2959 __isl_take isl_set_list *list,
2960 __isl_take isl_set *el);
2961 __isl_give isl_set_list *isl_set_list_drop(
2962 __isl_take isl_set_list *list,
2963 unsigned first, unsigned n);
2964 __isl_give isl_set_list *isl_set_list_set_set(
2965 __isl_take isl_set_list *list, int index,
2966 __isl_take isl_set *set);
2967 __isl_give isl_set_list *isl_set_list_concat(
2968 __isl_take isl_set_list *list1,
2969 __isl_take isl_set_list *list2);
2970 void *isl_set_list_free(__isl_take isl_set_list *list);
2972 C<isl_set_list_alloc> creates an empty list with a capacity for
2973 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2976 Lists can be inspected using the following functions.
2978 #include <isl/list.h>
2979 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2980 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2981 __isl_give isl_set *isl_set_list_get_set(
2982 __isl_keep isl_set_list *list, int index);
2983 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2984 int (*fn)(__isl_take isl_set *el, void *user),
2987 Lists can be printed using
2989 #include <isl/list.h>
2990 __isl_give isl_printer *isl_printer_print_set_list(
2991 __isl_take isl_printer *p,
2992 __isl_keep isl_set_list *list);
2996 Vectors can be created, copied and freed using the following functions.
2998 #include <isl/vec.h>
2999 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3001 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3002 void *isl_vec_free(__isl_take isl_vec *vec);
3004 Note that the elements of a newly created vector may have arbitrary values.
3005 The elements can be changed and inspected using the following functions.
3007 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3008 int isl_vec_size(__isl_keep isl_vec *vec);
3009 int isl_vec_get_element(__isl_keep isl_vec *vec,
3010 int pos, isl_int *v);
3011 __isl_give isl_vec *isl_vec_set_element(
3012 __isl_take isl_vec *vec, int pos, isl_int v);
3013 __isl_give isl_vec *isl_vec_set_element_si(
3014 __isl_take isl_vec *vec, int pos, int v);
3015 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3017 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3019 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3022 C<isl_vec_get_element> will return a negative value if anything went wrong.
3023 In that case, the value of C<*v> is undefined.
3025 The following function can be used to concatenate two vectors.
3027 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3028 __isl_take isl_vec *vec2);
3032 Matrices can be created, copied and freed using the following functions.
3034 #include <isl/mat.h>
3035 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3036 unsigned n_row, unsigned n_col);
3037 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3038 void isl_mat_free(__isl_take isl_mat *mat);
3040 Note that the elements of a newly created matrix may have arbitrary values.
3041 The elements can be changed and inspected using the following functions.
3043 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3044 int isl_mat_rows(__isl_keep isl_mat *mat);
3045 int isl_mat_cols(__isl_keep isl_mat *mat);
3046 int isl_mat_get_element(__isl_keep isl_mat *mat,
3047 int row, int col, isl_int *v);
3048 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3049 int row, int col, isl_int v);
3050 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3051 int row, int col, int v);
3053 C<isl_mat_get_element> will return a negative value if anything went wrong.
3054 In that case, the value of C<*v> is undefined.
3056 The following function can be used to compute the (right) inverse
3057 of a matrix, i.e., a matrix such that the product of the original
3058 and the inverse (in that order) is a multiple of the identity matrix.
3059 The input matrix is assumed to be of full row-rank.
3061 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3063 The following function can be used to compute the (right) kernel
3064 (or null space) of a matrix, i.e., a matrix such that the product of
3065 the original and the kernel (in that order) is the zero matrix.
3067 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3069 =head2 Piecewise Quasi Affine Expressions
3071 The zero quasi affine expression on a given domain can be created using
3073 __isl_give isl_aff *isl_aff_zero_on_domain(
3074 __isl_take isl_local_space *ls);
3076 Note that the space in which the resulting object lives is a map space
3077 with the given space as domain and a one-dimensional range.
3079 An empty piecewise quasi affine expression (one with no cells)
3080 or a piecewise quasi affine expression with a single cell can
3081 be created using the following functions.
3083 #include <isl/aff.h>
3084 __isl_give isl_pw_aff *isl_pw_aff_empty(
3085 __isl_take isl_space *space);
3086 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3087 __isl_take isl_set *set, __isl_take isl_aff *aff);
3088 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3089 __isl_take isl_aff *aff);
3091 A piecewise quasi affine expression that is equal to 1 on a set
3092 and 0 outside the set can be created using the following function.
3094 #include <isl/aff.h>
3095 __isl_give isl_pw_aff *isl_set_indicator_function(
3096 __isl_take isl_set *set);
3098 Quasi affine expressions can be copied and freed using
3100 #include <isl/aff.h>
3101 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3102 void *isl_aff_free(__isl_take isl_aff *aff);
3104 __isl_give isl_pw_aff *isl_pw_aff_copy(
3105 __isl_keep isl_pw_aff *pwaff);
3106 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3108 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3109 using the following function. The constraint is required to have
3110 a non-zero coefficient for the specified dimension.
3112 #include <isl/constraint.h>
3113 __isl_give isl_aff *isl_constraint_get_bound(
3114 __isl_keep isl_constraint *constraint,
3115 enum isl_dim_type type, int pos);
3117 The entire affine expression of the constraint can also be extracted
3118 using the following function.
3120 #include <isl/constraint.h>
3121 __isl_give isl_aff *isl_constraint_get_aff(
3122 __isl_keep isl_constraint *constraint);
3124 Conversely, an equality constraint equating
3125 the affine expression to zero or an inequality constraint enforcing
3126 the affine expression to be non-negative, can be constructed using
3128 __isl_give isl_constraint *isl_equality_from_aff(
3129 __isl_take isl_aff *aff);
3130 __isl_give isl_constraint *isl_inequality_from_aff(
3131 __isl_take isl_aff *aff);
3133 The expression can be inspected using
3135 #include <isl/aff.h>
3136 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3137 int isl_aff_dim(__isl_keep isl_aff *aff,
3138 enum isl_dim_type type);
3139 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3140 __isl_keep isl_aff *aff);
3141 __isl_give isl_local_space *isl_aff_get_local_space(
3142 __isl_keep isl_aff *aff);
3143 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3144 enum isl_dim_type type, unsigned pos);
3145 const char *isl_pw_aff_get_dim_name(
3146 __isl_keep isl_pw_aff *pa,
3147 enum isl_dim_type type, unsigned pos);
3148 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3149 enum isl_dim_type type, unsigned pos);
3150 __isl_give isl_id *isl_pw_aff_get_dim_id(
3151 __isl_keep isl_pw_aff *pa,
3152 enum isl_dim_type type, unsigned pos);
3153 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3154 __isl_keep isl_pw_aff *pa,
3155 enum isl_dim_type type);
3156 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3158 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3159 enum isl_dim_type type, int pos, isl_int *v);
3160 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3162 __isl_give isl_aff *isl_aff_get_div(
3163 __isl_keep isl_aff *aff, int pos);
3165 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3166 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3167 int (*fn)(__isl_take isl_set *set,
3168 __isl_take isl_aff *aff,
3169 void *user), void *user);
3171 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3172 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3174 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3175 enum isl_dim_type type, unsigned first, unsigned n);
3176 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3177 enum isl_dim_type type, unsigned first, unsigned n);
3179 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3180 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3181 enum isl_dim_type type);
3182 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3184 It can be modified using
3186 #include <isl/aff.h>
3187 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3188 __isl_take isl_pw_aff *pwaff,
3189 enum isl_dim_type type, __isl_take isl_id *id);
3190 __isl_give isl_aff *isl_aff_set_dim_name(
3191 __isl_take isl_aff *aff, enum isl_dim_type type,
3192 unsigned pos, const char *s);
3193 __isl_give isl_aff *isl_aff_set_dim_id(
3194 __isl_take isl_aff *aff, enum isl_dim_type type,
3195 unsigned pos, __isl_take isl_id *id);
3196 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3197 __isl_take isl_pw_aff *pma,
3198 enum isl_dim_type type, unsigned pos,
3199 __isl_take isl_id *id);
3200 __isl_give isl_aff *isl_aff_set_constant(
3201 __isl_take isl_aff *aff, isl_int v);
3202 __isl_give isl_aff *isl_aff_set_constant_si(
3203 __isl_take isl_aff *aff, int v);
3204 __isl_give isl_aff *isl_aff_set_coefficient(
3205 __isl_take isl_aff *aff,
3206 enum isl_dim_type type, int pos, isl_int v);
3207 __isl_give isl_aff *isl_aff_set_coefficient_si(
3208 __isl_take isl_aff *aff,
3209 enum isl_dim_type type, int pos, int v);
3210 __isl_give isl_aff *isl_aff_set_denominator(
3211 __isl_take isl_aff *aff, isl_int v);
3213 __isl_give isl_aff *isl_aff_add_constant(
3214 __isl_take isl_aff *aff, isl_int v);
3215 __isl_give isl_aff *isl_aff_add_constant_si(
3216 __isl_take isl_aff *aff, int v);
3217 __isl_give isl_aff *isl_aff_add_constant_num(
3218 __isl_take isl_aff *aff, isl_int v);
3219 __isl_give isl_aff *isl_aff_add_constant_num_si(
3220 __isl_take isl_aff *aff, int v);
3221 __isl_give isl_aff *isl_aff_add_coefficient(
3222 __isl_take isl_aff *aff,
3223 enum isl_dim_type type, int pos, isl_int v);
3224 __isl_give isl_aff *isl_aff_add_coefficient_si(
3225 __isl_take isl_aff *aff,
3226 enum isl_dim_type type, int pos, int v);
3228 __isl_give isl_aff *isl_aff_insert_dims(
3229 __isl_take isl_aff *aff,
3230 enum isl_dim_type type, unsigned first, unsigned n);
3231 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3232 __isl_take isl_pw_aff *pwaff,
3233 enum isl_dim_type type, unsigned first, unsigned n);
3234 __isl_give isl_aff *isl_aff_add_dims(
3235 __isl_take isl_aff *aff,
3236 enum isl_dim_type type, unsigned n);
3237 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3238 __isl_take isl_pw_aff *pwaff,
3239 enum isl_dim_type type, unsigned n);
3240 __isl_give isl_aff *isl_aff_drop_dims(
3241 __isl_take isl_aff *aff,
3242 enum isl_dim_type type, unsigned first, unsigned n);
3243 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3244 __isl_take isl_pw_aff *pwaff,
3245 enum isl_dim_type type, unsigned first, unsigned n);
3247 Note that the C<set_constant> and C<set_coefficient> functions
3248 set the I<numerator> of the constant or coefficient, while
3249 C<add_constant> and C<add_coefficient> add an integer value to
3250 the possibly rational constant or coefficient.
3251 The C<add_constant_num> functions add an integer value to
3254 To check whether an affine expressions is obviously zero
3255 or obviously equal to some other affine expression, use
3257 #include <isl/aff.h>
3258 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3259 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3260 __isl_keep isl_aff *aff2);
3261 int isl_pw_aff_plain_is_equal(
3262 __isl_keep isl_pw_aff *pwaff1,
3263 __isl_keep isl_pw_aff *pwaff2);
3267 #include <isl/aff.h>
3268 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3269 __isl_take isl_aff *aff2);
3270 __isl_give isl_pw_aff *isl_pw_aff_add(
3271 __isl_take isl_pw_aff *pwaff1,
3272 __isl_take isl_pw_aff *pwaff2);
3273 __isl_give isl_pw_aff *isl_pw_aff_min(
3274 __isl_take isl_pw_aff *pwaff1,
3275 __isl_take isl_pw_aff *pwaff2);
3276 __isl_give isl_pw_aff *isl_pw_aff_max(
3277 __isl_take isl_pw_aff *pwaff1,
3278 __isl_take isl_pw_aff *pwaff2);
3279 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3280 __isl_take isl_aff *aff2);
3281 __isl_give isl_pw_aff *isl_pw_aff_sub(
3282 __isl_take isl_pw_aff *pwaff1,
3283 __isl_take isl_pw_aff *pwaff2);
3284 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3285 __isl_give isl_pw_aff *isl_pw_aff_neg(
3286 __isl_take isl_pw_aff *pwaff);
3287 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3288 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3289 __isl_take isl_pw_aff *pwaff);
3290 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3291 __isl_give isl_pw_aff *isl_pw_aff_floor(
3292 __isl_take isl_pw_aff *pwaff);
3293 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3295 __isl_give isl_pw_aff *isl_pw_aff_mod(
3296 __isl_take isl_pw_aff *pwaff, isl_int mod);
3297 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3299 __isl_give isl_pw_aff *isl_pw_aff_scale(
3300 __isl_take isl_pw_aff *pwaff, isl_int f);
3301 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3303 __isl_give isl_aff *isl_aff_scale_down_ui(
3304 __isl_take isl_aff *aff, unsigned f);
3305 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3306 __isl_take isl_pw_aff *pwaff, isl_int f);
3308 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3309 __isl_take isl_pw_aff_list *list);
3310 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3311 __isl_take isl_pw_aff_list *list);
3313 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3314 __isl_take isl_pw_aff *pwqp);
3316 __isl_give isl_aff *isl_aff_align_params(
3317 __isl_take isl_aff *aff,
3318 __isl_take isl_space *model);
3319 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3320 __isl_take isl_pw_aff *pwaff,
3321 __isl_take isl_space *model);
3323 __isl_give isl_aff *isl_aff_project_domain_on_params(
3324 __isl_take isl_aff *aff);
3326 __isl_give isl_aff *isl_aff_gist_params(
3327 __isl_take isl_aff *aff,
3328 __isl_take isl_set *context);
3329 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3330 __isl_take isl_set *context);
3331 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3332 __isl_take isl_pw_aff *pwaff,
3333 __isl_take isl_set *context);
3334 __isl_give isl_pw_aff *isl_pw_aff_gist(
3335 __isl_take isl_pw_aff *pwaff,
3336 __isl_take isl_set *context);
3338 __isl_give isl_set *isl_pw_aff_domain(
3339 __isl_take isl_pw_aff *pwaff);
3340 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3341 __isl_take isl_pw_aff *pa,
3342 __isl_take isl_set *set);
3343 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3344 __isl_take isl_pw_aff *pa,
3345 __isl_take isl_set *set);
3347 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3348 __isl_take isl_aff *aff2);
3349 __isl_give isl_pw_aff *isl_pw_aff_mul(
3350 __isl_take isl_pw_aff *pwaff1,
3351 __isl_take isl_pw_aff *pwaff2);
3353 When multiplying two affine expressions, at least one of the two needs
3356 #include <isl/aff.h>
3357 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3358 __isl_take isl_aff *aff);
3359 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3360 __isl_take isl_aff *aff);
3361 __isl_give isl_basic_set *isl_aff_le_basic_set(
3362 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3363 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3364 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3365 __isl_give isl_set *isl_pw_aff_eq_set(
3366 __isl_take isl_pw_aff *pwaff1,
3367 __isl_take isl_pw_aff *pwaff2);
3368 __isl_give isl_set *isl_pw_aff_ne_set(
3369 __isl_take isl_pw_aff *pwaff1,
3370 __isl_take isl_pw_aff *pwaff2);
3371 __isl_give isl_set *isl_pw_aff_le_set(
3372 __isl_take isl_pw_aff *pwaff1,
3373 __isl_take isl_pw_aff *pwaff2);
3374 __isl_give isl_set *isl_pw_aff_lt_set(
3375 __isl_take isl_pw_aff *pwaff1,
3376 __isl_take isl_pw_aff *pwaff2);
3377 __isl_give isl_set *isl_pw_aff_ge_set(
3378 __isl_take isl_pw_aff *pwaff1,
3379 __isl_take isl_pw_aff *pwaff2);
3380 __isl_give isl_set *isl_pw_aff_gt_set(
3381 __isl_take isl_pw_aff *pwaff1,
3382 __isl_take isl_pw_aff *pwaff2);
3384 __isl_give isl_set *isl_pw_aff_list_eq_set(
3385 __isl_take isl_pw_aff_list *list1,
3386 __isl_take isl_pw_aff_list *list2);
3387 __isl_give isl_set *isl_pw_aff_list_ne_set(
3388 __isl_take isl_pw_aff_list *list1,
3389 __isl_take isl_pw_aff_list *list2);
3390 __isl_give isl_set *isl_pw_aff_list_le_set(
3391 __isl_take isl_pw_aff_list *list1,
3392 __isl_take isl_pw_aff_list *list2);
3393 __isl_give isl_set *isl_pw_aff_list_lt_set(
3394 __isl_take isl_pw_aff_list *list1,
3395 __isl_take isl_pw_aff_list *list2);
3396 __isl_give isl_set *isl_pw_aff_list_ge_set(
3397 __isl_take isl_pw_aff_list *list1,
3398 __isl_take isl_pw_aff_list *list2);
3399 __isl_give isl_set *isl_pw_aff_list_gt_set(
3400 __isl_take isl_pw_aff_list *list1,
3401 __isl_take isl_pw_aff_list *list2);
3403 The function C<isl_aff_neg_basic_set> returns a basic set
3404 containing those elements in the domain space
3405 of C<aff> where C<aff> is negative.
3406 The function C<isl_aff_ge_basic_set> returns a basic set
3407 containing those elements in the shared space
3408 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3409 The function C<isl_pw_aff_ge_set> returns a set
3410 containing those elements in the shared domain
3411 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3412 The functions operating on C<isl_pw_aff_list> apply the corresponding
3413 C<isl_pw_aff> function to each pair of elements in the two lists.
3415 #include <isl/aff.h>
3416 __isl_give isl_set *isl_pw_aff_nonneg_set(
3417 __isl_take isl_pw_aff *pwaff);
3418 __isl_give isl_set *isl_pw_aff_zero_set(
3419 __isl_take isl_pw_aff *pwaff);
3420 __isl_give isl_set *isl_pw_aff_non_zero_set(
3421 __isl_take isl_pw_aff *pwaff);
3423 The function C<isl_pw_aff_nonneg_set> returns a set
3424 containing those elements in the domain
3425 of C<pwaff> where C<pwaff> is non-negative.
3427 #include <isl/aff.h>
3428 __isl_give isl_pw_aff *isl_pw_aff_cond(
3429 __isl_take isl_pw_aff *cond,
3430 __isl_take isl_pw_aff *pwaff_true,
3431 __isl_take isl_pw_aff *pwaff_false);
3433 The function C<isl_pw_aff_cond> performs a conditional operator
3434 and returns an expression that is equal to C<pwaff_true>
3435 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3436 where C<cond> is zero.
3438 #include <isl/aff.h>
3439 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3440 __isl_take isl_pw_aff *pwaff1,
3441 __isl_take isl_pw_aff *pwaff2);
3442 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3443 __isl_take isl_pw_aff *pwaff1,
3444 __isl_take isl_pw_aff *pwaff2);
3445 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3446 __isl_take isl_pw_aff *pwaff1,
3447 __isl_take isl_pw_aff *pwaff2);
3449 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3450 expression with a domain that is the union of those of C<pwaff1> and
3451 C<pwaff2> and such that on each cell, the quasi-affine expression is
3452 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3453 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3454 associated expression is the defined one.
3456 An expression can be read from input using
3458 #include <isl/aff.h>
3459 __isl_give isl_aff *isl_aff_read_from_str(
3460 isl_ctx *ctx, const char *str);
3461 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3462 isl_ctx *ctx, const char *str);
3464 An expression can be printed using
3466 #include <isl/aff.h>
3467 __isl_give isl_printer *isl_printer_print_aff(
3468 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3470 __isl_give isl_printer *isl_printer_print_pw_aff(
3471 __isl_take isl_printer *p,
3472 __isl_keep isl_pw_aff *pwaff);
3474 =head2 Piecewise Multiple Quasi Affine Expressions
3476 An C<isl_multi_aff> object represents a sequence of
3477 zero or more affine expressions, all defined on the same domain space.
3479 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3482 #include <isl/aff.h>
3483 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3484 __isl_take isl_space *space,
3485 __isl_take isl_aff_list *list);
3487 An empty piecewise multiple quasi affine expression (one with no cells),
3488 the zero piecewise multiple quasi affine expression (with value zero
3489 for each output dimension),
3490 a piecewise multiple quasi affine expression with a single cell (with
3491 either a universe or a specified domain) or
3492 a zero-dimensional piecewise multiple quasi affine expression
3494 can be created using the following functions.
3496 #include <isl/aff.h>
3497 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3498 __isl_take isl_space *space);
3499 __isl_give isl_multi_aff *isl_multi_aff_zero(
3500 __isl_take isl_space *space);
3501 __isl_give isl_multi_aff *isl_multi_aff_identity(
3502 __isl_take isl_space *space);
3503 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3504 __isl_take isl_space *space);
3505 __isl_give isl_pw_multi_aff *
3506 isl_pw_multi_aff_from_multi_aff(
3507 __isl_take isl_multi_aff *ma);
3508 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3509 __isl_take isl_set *set,
3510 __isl_take isl_multi_aff *maff);
3511 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3512 __isl_take isl_set *set);
3514 __isl_give isl_union_pw_multi_aff *
3515 isl_union_pw_multi_aff_empty(
3516 __isl_take isl_space *space);
3517 __isl_give isl_union_pw_multi_aff *
3518 isl_union_pw_multi_aff_add_pw_multi_aff(
3519 __isl_take isl_union_pw_multi_aff *upma,
3520 __isl_take isl_pw_multi_aff *pma);
3521 __isl_give isl_union_pw_multi_aff *
3522 isl_union_pw_multi_aff_from_domain(
3523 __isl_take isl_union_set *uset);
3525 A piecewise multiple quasi affine expression can also be initialized
3526 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3527 and the C<isl_map> is single-valued.
3529 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3530 __isl_take isl_set *set);
3531 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3532 __isl_take isl_map *map);
3534 Multiple quasi affine expressions can be copied and freed using
3536 #include <isl/aff.h>
3537 __isl_give isl_multi_aff *isl_multi_aff_copy(
3538 __isl_keep isl_multi_aff *maff);
3539 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3541 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3542 __isl_keep isl_pw_multi_aff *pma);
3543 void *isl_pw_multi_aff_free(
3544 __isl_take isl_pw_multi_aff *pma);
3546 __isl_give isl_union_pw_multi_aff *
3547 isl_union_pw_multi_aff_copy(
3548 __isl_keep isl_union_pw_multi_aff *upma);
3549 void *isl_union_pw_multi_aff_free(
3550 __isl_take isl_union_pw_multi_aff *upma);
3552 The expression can be inspected using
3554 #include <isl/aff.h>
3555 isl_ctx *isl_multi_aff_get_ctx(
3556 __isl_keep isl_multi_aff *maff);
3557 isl_ctx *isl_pw_multi_aff_get_ctx(
3558 __isl_keep isl_pw_multi_aff *pma);
3559 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3560 __isl_keep isl_union_pw_multi_aff *upma);
3561 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3562 enum isl_dim_type type);
3563 unsigned isl_pw_multi_aff_dim(
3564 __isl_keep isl_pw_multi_aff *pma,
3565 enum isl_dim_type type);
3566 __isl_give isl_aff *isl_multi_aff_get_aff(
3567 __isl_keep isl_multi_aff *multi, int pos);
3568 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3569 __isl_keep isl_pw_multi_aff *pma, int pos);
3570 const char *isl_pw_multi_aff_get_dim_name(
3571 __isl_keep isl_pw_multi_aff *pma,
3572 enum isl_dim_type type, unsigned pos);
3573 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3574 __isl_keep isl_pw_multi_aff *pma,
3575 enum isl_dim_type type, unsigned pos);
3576 const char *isl_multi_aff_get_tuple_name(
3577 __isl_keep isl_multi_aff *multi,
3578 enum isl_dim_type type);
3579 int isl_pw_multi_aff_has_tuple_name(
3580 __isl_keep isl_pw_multi_aff *pma,
3581 enum isl_dim_type type);
3582 const char *isl_pw_multi_aff_get_tuple_name(
3583 __isl_keep isl_pw_multi_aff *pma,
3584 enum isl_dim_type type);
3585 int isl_pw_multi_aff_has_tuple_id(
3586 __isl_keep isl_pw_multi_aff *pma,
3587 enum isl_dim_type type);
3588 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3589 __isl_keep isl_pw_multi_aff *pma,
3590 enum isl_dim_type type);
3592 int isl_pw_multi_aff_foreach_piece(
3593 __isl_keep isl_pw_multi_aff *pma,
3594 int (*fn)(__isl_take isl_set *set,
3595 __isl_take isl_multi_aff *maff,
3596 void *user), void *user);
3598 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3599 __isl_keep isl_union_pw_multi_aff *upma,
3600 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3601 void *user), void *user);
3603 It can be modified using
3605 #include <isl/aff.h>
3606 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3607 __isl_take isl_multi_aff *multi, int pos,
3608 __isl_take isl_aff *aff);
3609 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3610 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3611 __isl_take isl_pw_aff *pa);
3612 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3613 __isl_take isl_multi_aff *maff,
3614 enum isl_dim_type type, unsigned pos, const char *s);
3615 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3616 __isl_take isl_multi_aff *maff,
3617 enum isl_dim_type type, __isl_take isl_id *id);
3618 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3619 __isl_take isl_pw_multi_aff *pma,
3620 enum isl_dim_type type, __isl_take isl_id *id);
3622 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3623 __isl_take isl_multi_aff *maff,
3624 enum isl_dim_type type, unsigned first, unsigned n);
3625 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3626 __isl_take isl_pw_multi_aff *pma,
3627 enum isl_dim_type type, unsigned first, unsigned n);
3629 To check whether two multiple affine expressions are
3630 obviously equal to each other, use
3632 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3633 __isl_keep isl_multi_aff *maff2);
3634 int isl_pw_multi_aff_plain_is_equal(
3635 __isl_keep isl_pw_multi_aff *pma1,
3636 __isl_keep isl_pw_multi_aff *pma2);
3640 #include <isl/aff.h>
3641 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3642 __isl_take isl_pw_multi_aff *pma1,
3643 __isl_take isl_pw_multi_aff *pma2);
3644 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3645 __isl_take isl_pw_multi_aff *pma1,
3646 __isl_take isl_pw_multi_aff *pma2);
3647 __isl_give isl_multi_aff *isl_multi_aff_add(
3648 __isl_take isl_multi_aff *maff1,
3649 __isl_take isl_multi_aff *maff2);
3650 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3651 __isl_take isl_pw_multi_aff *pma1,
3652 __isl_take isl_pw_multi_aff *pma2);
3653 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3654 __isl_take isl_union_pw_multi_aff *upma1,
3655 __isl_take isl_union_pw_multi_aff *upma2);
3656 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3657 __isl_take isl_pw_multi_aff *pma1,
3658 __isl_take isl_pw_multi_aff *pma2);
3659 __isl_give isl_multi_aff *isl_multi_aff_scale(
3660 __isl_take isl_multi_aff *maff,
3662 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3663 __isl_take isl_pw_multi_aff *pma,
3664 __isl_take isl_set *set);
3665 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3666 __isl_take isl_pw_multi_aff *pma,
3667 __isl_take isl_set *set);
3668 __isl_give isl_multi_aff *isl_multi_aff_lift(
3669 __isl_take isl_multi_aff *maff,
3670 __isl_give isl_local_space **ls);
3671 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3672 __isl_take isl_pw_multi_aff *pma);
3673 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3674 __isl_take isl_multi_aff *multi,
3675 __isl_take isl_space *model);
3676 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3677 __isl_take isl_pw_multi_aff *pma,
3678 __isl_take isl_space *model);
3679 __isl_give isl_pw_multi_aff *
3680 isl_pw_multi_aff_project_domain_on_params(
3681 __isl_take isl_pw_multi_aff *pma);
3682 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3683 __isl_take isl_multi_aff *maff,
3684 __isl_take isl_set *context);
3685 __isl_give isl_multi_aff *isl_multi_aff_gist(
3686 __isl_take isl_multi_aff *maff,
3687 __isl_take isl_set *context);
3688 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3689 __isl_take isl_pw_multi_aff *pma,
3690 __isl_take isl_set *set);
3691 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3692 __isl_take isl_pw_multi_aff *pma,
3693 __isl_take isl_set *set);
3694 __isl_give isl_set *isl_pw_multi_aff_domain(
3695 __isl_take isl_pw_multi_aff *pma);
3696 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3697 __isl_take isl_union_pw_multi_aff *upma);
3698 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3699 __isl_take isl_multi_aff *ma1,
3700 __isl_take isl_multi_aff *ma2);
3701 __isl_give isl_multi_aff *isl_multi_aff_product(
3702 __isl_take isl_multi_aff *ma1,
3703 __isl_take isl_multi_aff *ma2);
3704 __isl_give isl_pw_multi_aff *
3705 isl_pw_multi_aff_flat_range_product(
3706 __isl_take isl_pw_multi_aff *pma1,
3707 __isl_take isl_pw_multi_aff *pma2);
3708 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3709 __isl_take isl_pw_multi_aff *pma1,
3710 __isl_take isl_pw_multi_aff *pma2);
3711 __isl_give isl_union_pw_multi_aff *
3712 isl_union_pw_multi_aff_flat_range_product(
3713 __isl_take isl_union_pw_multi_aff *upma1,
3714 __isl_take isl_union_pw_multi_aff *upma2);
3716 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3717 then it is assigned the local space that lies at the basis of
3718 the lifting applied.
3720 __isl_give isl_set *isl_multi_aff_lex_le_set(
3721 __isl_take isl_multi_aff *ma1,
3722 __isl_take isl_multi_aff *ma2);
3723 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3724 __isl_take isl_multi_aff *ma1,
3725 __isl_take isl_multi_aff *ma2);
3727 The function C<isl_multi_aff_lex_le_set> returns a set
3728 containing those elements in the shared domain space
3729 where C<ma1> is lexicographically smaller than or
3732 An expression can be read from input using
3734 #include <isl/aff.h>
3735 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3736 isl_ctx *ctx, const char *str);
3737 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3738 isl_ctx *ctx, const char *str);
3740 An expression can be printed using
3742 #include <isl/aff.h>
3743 __isl_give isl_printer *isl_printer_print_multi_aff(
3744 __isl_take isl_printer *p,
3745 __isl_keep isl_multi_aff *maff);
3746 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3747 __isl_take isl_printer *p,
3748 __isl_keep isl_pw_multi_aff *pma);
3749 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3750 __isl_take isl_printer *p,
3751 __isl_keep isl_union_pw_multi_aff *upma);
3755 Points are elements of a set. They can be used to construct
3756 simple sets (boxes) or they can be used to represent the
3757 individual elements of a set.
3758 The zero point (the origin) can be created using
3760 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3762 The coordinates of a point can be inspected, set and changed
3765 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3766 enum isl_dim_type type, int pos, isl_int *v);
3767 __isl_give isl_point *isl_point_set_coordinate(
3768 __isl_take isl_point *pnt,
3769 enum isl_dim_type type, int pos, isl_int v);
3771 __isl_give isl_point *isl_point_add_ui(
3772 __isl_take isl_point *pnt,
3773 enum isl_dim_type type, int pos, unsigned val);
3774 __isl_give isl_point *isl_point_sub_ui(
3775 __isl_take isl_point *pnt,
3776 enum isl_dim_type type, int pos, unsigned val);
3778 Other properties can be obtained using
3780 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3782 Points can be copied or freed using
3784 __isl_give isl_point *isl_point_copy(
3785 __isl_keep isl_point *pnt);
3786 void isl_point_free(__isl_take isl_point *pnt);
3788 A singleton set can be created from a point using
3790 __isl_give isl_basic_set *isl_basic_set_from_point(
3791 __isl_take isl_point *pnt);
3792 __isl_give isl_set *isl_set_from_point(
3793 __isl_take isl_point *pnt);
3795 and a box can be created from two opposite extremal points using
3797 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3798 __isl_take isl_point *pnt1,
3799 __isl_take isl_point *pnt2);
3800 __isl_give isl_set *isl_set_box_from_points(
3801 __isl_take isl_point *pnt1,
3802 __isl_take isl_point *pnt2);
3804 All elements of a B<bounded> (union) set can be enumerated using
3805 the following functions.
3807 int isl_set_foreach_point(__isl_keep isl_set *set,
3808 int (*fn)(__isl_take isl_point *pnt, void *user),
3810 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3811 int (*fn)(__isl_take isl_point *pnt, void *user),
3814 The function C<fn> is called for each integer point in
3815 C<set> with as second argument the last argument of
3816 the C<isl_set_foreach_point> call. The function C<fn>
3817 should return C<0> on success and C<-1> on failure.
3818 In the latter case, C<isl_set_foreach_point> will stop
3819 enumerating and return C<-1> as well.
3820 If the enumeration is performed successfully and to completion,
3821 then C<isl_set_foreach_point> returns C<0>.
3823 To obtain a single point of a (basic) set, use
3825 __isl_give isl_point *isl_basic_set_sample_point(
3826 __isl_take isl_basic_set *bset);
3827 __isl_give isl_point *isl_set_sample_point(
3828 __isl_take isl_set *set);
3830 If C<set> does not contain any (integer) points, then the
3831 resulting point will be ``void'', a property that can be
3834 int isl_point_is_void(__isl_keep isl_point *pnt);
3836 =head2 Piecewise Quasipolynomials
3838 A piecewise quasipolynomial is a particular kind of function that maps
3839 a parametric point to a rational value.
3840 More specifically, a quasipolynomial is a polynomial expression in greatest
3841 integer parts of affine expressions of parameters and variables.
3842 A piecewise quasipolynomial is a subdivision of a given parametric
3843 domain into disjoint cells with a quasipolynomial associated to
3844 each cell. The value of the piecewise quasipolynomial at a given
3845 point is the value of the quasipolynomial associated to the cell
3846 that contains the point. Outside of the union of cells,
3847 the value is assumed to be zero.
3848 For example, the piecewise quasipolynomial
3850 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3852 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3853 A given piecewise quasipolynomial has a fixed domain dimension.
3854 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3855 defined over different domains.
3856 Piecewise quasipolynomials are mainly used by the C<barvinok>
3857 library for representing the number of elements in a parametric set or map.
3858 For example, the piecewise quasipolynomial above represents
3859 the number of points in the map
3861 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3863 =head3 Input and Output
3865 Piecewise quasipolynomials can be read from input using
3867 __isl_give isl_union_pw_qpolynomial *
3868 isl_union_pw_qpolynomial_read_from_str(
3869 isl_ctx *ctx, const char *str);
3871 Quasipolynomials and piecewise quasipolynomials can be printed
3872 using the following functions.
3874 __isl_give isl_printer *isl_printer_print_qpolynomial(
3875 __isl_take isl_printer *p,
3876 __isl_keep isl_qpolynomial *qp);
3878 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3879 __isl_take isl_printer *p,
3880 __isl_keep isl_pw_qpolynomial *pwqp);
3882 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3883 __isl_take isl_printer *p,
3884 __isl_keep isl_union_pw_qpolynomial *upwqp);
3886 The output format of the printer
3887 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3888 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3890 In case of printing in C<ISL_FORMAT_C>, the user may want
3891 to set the names of all dimensions
3893 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3894 __isl_take isl_qpolynomial *qp,
3895 enum isl_dim_type type, unsigned pos,
3897 __isl_give isl_pw_qpolynomial *
3898 isl_pw_qpolynomial_set_dim_name(
3899 __isl_take isl_pw_qpolynomial *pwqp,
3900 enum isl_dim_type type, unsigned pos,
3903 =head3 Creating New (Piecewise) Quasipolynomials
3905 Some simple quasipolynomials can be created using the following functions.
3906 More complicated quasipolynomials can be created by applying
3907 operations such as addition and multiplication
3908 on the resulting quasipolynomials
3910 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3911 __isl_take isl_space *domain);
3912 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3913 __isl_take isl_space *domain);
3914 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3915 __isl_take isl_space *domain);
3916 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3917 __isl_take isl_space *domain);
3918 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3919 __isl_take isl_space *domain);
3920 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3921 __isl_take isl_space *domain,
3922 const isl_int n, const isl_int d);
3923 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3924 __isl_take isl_space *domain,
3925 enum isl_dim_type type, unsigned pos);
3926 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3927 __isl_take isl_aff *aff);
3929 Note that the space in which a quasipolynomial lives is a map space
3930 with a one-dimensional range. The C<domain> argument in some of
3931 the functions above corresponds to the domain of this map space.
3933 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3934 with a single cell can be created using the following functions.
3935 Multiple of these single cell piecewise quasipolynomials can
3936 be combined to create more complicated piecewise quasipolynomials.
3938 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3939 __isl_take isl_space *space);
3940 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3941 __isl_take isl_set *set,
3942 __isl_take isl_qpolynomial *qp);
3943 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3944 __isl_take isl_qpolynomial *qp);
3945 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3946 __isl_take isl_pw_aff *pwaff);
3948 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3949 __isl_take isl_space *space);
3950 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3951 __isl_take isl_pw_qpolynomial *pwqp);
3952 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3953 __isl_take isl_union_pw_qpolynomial *upwqp,
3954 __isl_take isl_pw_qpolynomial *pwqp);
3956 Quasipolynomials can be copied and freed again using the following
3959 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3960 __isl_keep isl_qpolynomial *qp);
3961 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3963 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3964 __isl_keep isl_pw_qpolynomial *pwqp);
3965 void *isl_pw_qpolynomial_free(
3966 __isl_take isl_pw_qpolynomial *pwqp);
3968 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3969 __isl_keep isl_union_pw_qpolynomial *upwqp);
3970 void *isl_union_pw_qpolynomial_free(
3971 __isl_take isl_union_pw_qpolynomial *upwqp);
3973 =head3 Inspecting (Piecewise) Quasipolynomials
3975 To iterate over all piecewise quasipolynomials in a union
3976 piecewise quasipolynomial, use the following function
3978 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3979 __isl_keep isl_union_pw_qpolynomial *upwqp,
3980 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3983 To extract the piecewise quasipolynomial in a given space from a union, use
3985 __isl_give isl_pw_qpolynomial *
3986 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3987 __isl_keep isl_union_pw_qpolynomial *upwqp,
3988 __isl_take isl_space *space);
3990 To iterate over the cells in a piecewise quasipolynomial,
3991 use either of the following two functions
3993 int isl_pw_qpolynomial_foreach_piece(
3994 __isl_keep isl_pw_qpolynomial *pwqp,
3995 int (*fn)(__isl_take isl_set *set,
3996 __isl_take isl_qpolynomial *qp,
3997 void *user), void *user);
3998 int isl_pw_qpolynomial_foreach_lifted_piece(
3999 __isl_keep isl_pw_qpolynomial *pwqp,
4000 int (*fn)(__isl_take isl_set *set,
4001 __isl_take isl_qpolynomial *qp,
4002 void *user), void *user);
4004 As usual, the function C<fn> should return C<0> on success
4005 and C<-1> on failure. The difference between
4006 C<isl_pw_qpolynomial_foreach_piece> and
4007 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4008 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4009 compute unique representations for all existentially quantified
4010 variables and then turn these existentially quantified variables
4011 into extra set variables, adapting the associated quasipolynomial
4012 accordingly. This means that the C<set> passed to C<fn>
4013 will not have any existentially quantified variables, but that
4014 the dimensions of the sets may be different for different
4015 invocations of C<fn>.
4017 To iterate over all terms in a quasipolynomial,
4020 int isl_qpolynomial_foreach_term(
4021 __isl_keep isl_qpolynomial *qp,
4022 int (*fn)(__isl_take isl_term *term,
4023 void *user), void *user);
4025 The terms themselves can be inspected and freed using
4028 unsigned isl_term_dim(__isl_keep isl_term *term,
4029 enum isl_dim_type type);
4030 void isl_term_get_num(__isl_keep isl_term *term,
4032 void isl_term_get_den(__isl_keep isl_term *term,
4034 int isl_term_get_exp(__isl_keep isl_term *term,
4035 enum isl_dim_type type, unsigned pos);
4036 __isl_give isl_aff *isl_term_get_div(
4037 __isl_keep isl_term *term, unsigned pos);
4038 void isl_term_free(__isl_take isl_term *term);
4040 Each term is a product of parameters, set variables and
4041 integer divisions. The function C<isl_term_get_exp>
4042 returns the exponent of a given dimensions in the given term.
4043 The C<isl_int>s in the arguments of C<isl_term_get_num>
4044 and C<isl_term_get_den> need to have been initialized
4045 using C<isl_int_init> before calling these functions.
4047 =head3 Properties of (Piecewise) Quasipolynomials
4049 To check whether a quasipolynomial is actually a constant,
4050 use the following function.
4052 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4053 isl_int *n, isl_int *d);
4055 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4056 then the numerator and denominator of the constant
4057 are returned in C<*n> and C<*d>, respectively.
4059 To check whether two union piecewise quasipolynomials are
4060 obviously equal, use
4062 int isl_union_pw_qpolynomial_plain_is_equal(
4063 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4064 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4066 =head3 Operations on (Piecewise) Quasipolynomials
4068 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4069 __isl_take isl_qpolynomial *qp, isl_int v);
4070 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4071 __isl_take isl_qpolynomial *qp);
4072 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4073 __isl_take isl_qpolynomial *qp1,
4074 __isl_take isl_qpolynomial *qp2);
4075 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4076 __isl_take isl_qpolynomial *qp1,
4077 __isl_take isl_qpolynomial *qp2);
4078 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4079 __isl_take isl_qpolynomial *qp1,
4080 __isl_take isl_qpolynomial *qp2);
4081 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4082 __isl_take isl_qpolynomial *qp, unsigned exponent);
4084 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4085 __isl_take isl_pw_qpolynomial *pwqp1,
4086 __isl_take isl_pw_qpolynomial *pwqp2);
4087 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4088 __isl_take isl_pw_qpolynomial *pwqp1,
4089 __isl_take isl_pw_qpolynomial *pwqp2);
4090 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4091 __isl_take isl_pw_qpolynomial *pwqp1,
4092 __isl_take isl_pw_qpolynomial *pwqp2);
4093 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4094 __isl_take isl_pw_qpolynomial *pwqp);
4095 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4096 __isl_take isl_pw_qpolynomial *pwqp1,
4097 __isl_take isl_pw_qpolynomial *pwqp2);
4098 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4099 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4101 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4102 __isl_take isl_union_pw_qpolynomial *upwqp1,
4103 __isl_take isl_union_pw_qpolynomial *upwqp2);
4104 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4105 __isl_take isl_union_pw_qpolynomial *upwqp1,
4106 __isl_take isl_union_pw_qpolynomial *upwqp2);
4107 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4108 __isl_take isl_union_pw_qpolynomial *upwqp1,
4109 __isl_take isl_union_pw_qpolynomial *upwqp2);
4111 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4112 __isl_take isl_pw_qpolynomial *pwqp,
4113 __isl_take isl_point *pnt);
4115 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4116 __isl_take isl_union_pw_qpolynomial *upwqp,
4117 __isl_take isl_point *pnt);
4119 __isl_give isl_set *isl_pw_qpolynomial_domain(
4120 __isl_take isl_pw_qpolynomial *pwqp);
4121 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4122 __isl_take isl_pw_qpolynomial *pwpq,
4123 __isl_take isl_set *set);
4124 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4125 __isl_take isl_pw_qpolynomial *pwpq,
4126 __isl_take isl_set *set);
4128 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4129 __isl_take isl_union_pw_qpolynomial *upwqp);
4130 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4131 __isl_take isl_union_pw_qpolynomial *upwpq,
4132 __isl_take isl_union_set *uset);
4133 __isl_give isl_union_pw_qpolynomial *
4134 isl_union_pw_qpolynomial_intersect_params(
4135 __isl_take isl_union_pw_qpolynomial *upwpq,
4136 __isl_take isl_set *set);
4138 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4139 __isl_take isl_qpolynomial *qp,
4140 __isl_take isl_space *model);
4142 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4143 __isl_take isl_qpolynomial *qp);
4144 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4145 __isl_take isl_pw_qpolynomial *pwqp);
4147 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4148 __isl_take isl_union_pw_qpolynomial *upwqp);
4150 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4151 __isl_take isl_qpolynomial *qp,
4152 __isl_take isl_set *context);
4153 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4154 __isl_take isl_qpolynomial *qp,
4155 __isl_take isl_set *context);
4157 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4158 __isl_take isl_pw_qpolynomial *pwqp,
4159 __isl_take isl_set *context);
4160 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4161 __isl_take isl_pw_qpolynomial *pwqp,
4162 __isl_take isl_set *context);
4164 __isl_give isl_union_pw_qpolynomial *
4165 isl_union_pw_qpolynomial_gist_params(
4166 __isl_take isl_union_pw_qpolynomial *upwqp,
4167 __isl_take isl_set *context);
4168 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4169 __isl_take isl_union_pw_qpolynomial *upwqp,
4170 __isl_take isl_union_set *context);
4172 The gist operation applies the gist operation to each of
4173 the cells in the domain of the input piecewise quasipolynomial.
4174 The context is also exploited
4175 to simplify the quasipolynomials associated to each cell.
4177 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4178 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4179 __isl_give isl_union_pw_qpolynomial *
4180 isl_union_pw_qpolynomial_to_polynomial(
4181 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4183 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4184 the polynomial will be an overapproximation. If C<sign> is negative,
4185 it will be an underapproximation. If C<sign> is zero, the approximation
4186 will lie somewhere in between.
4188 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4190 A piecewise quasipolynomial reduction is a piecewise
4191 reduction (or fold) of quasipolynomials.
4192 In particular, the reduction can be maximum or a minimum.
4193 The objects are mainly used to represent the result of
4194 an upper or lower bound on a quasipolynomial over its domain,
4195 i.e., as the result of the following function.
4197 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4198 __isl_take isl_pw_qpolynomial *pwqp,
4199 enum isl_fold type, int *tight);
4201 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4202 __isl_take isl_union_pw_qpolynomial *upwqp,
4203 enum isl_fold type, int *tight);
4205 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4206 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4207 is the returned bound is known be tight, i.e., for each value
4208 of the parameters there is at least
4209 one element in the domain that reaches the bound.
4210 If the domain of C<pwqp> is not wrapping, then the bound is computed
4211 over all elements in that domain and the result has a purely parametric
4212 domain. If the domain of C<pwqp> is wrapping, then the bound is
4213 computed over the range of the wrapped relation. The domain of the
4214 wrapped relation becomes the domain of the result.
4216 A (piecewise) quasipolynomial reduction can be copied or freed using the
4217 following functions.
4219 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4220 __isl_keep isl_qpolynomial_fold *fold);
4221 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4222 __isl_keep isl_pw_qpolynomial_fold *pwf);
4223 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4224 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4225 void isl_qpolynomial_fold_free(
4226 __isl_take isl_qpolynomial_fold *fold);
4227 void *isl_pw_qpolynomial_fold_free(
4228 __isl_take isl_pw_qpolynomial_fold *pwf);
4229 void *isl_union_pw_qpolynomial_fold_free(
4230 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4232 =head3 Printing Piecewise Quasipolynomial Reductions
4234 Piecewise quasipolynomial reductions can be printed
4235 using the following function.
4237 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4238 __isl_take isl_printer *p,
4239 __isl_keep isl_pw_qpolynomial_fold *pwf);
4240 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4241 __isl_take isl_printer *p,
4242 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4244 For C<isl_printer_print_pw_qpolynomial_fold>,
4245 output format of the printer
4246 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4247 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4248 output format of the printer
4249 needs to be set to C<ISL_FORMAT_ISL>.
4250 In case of printing in C<ISL_FORMAT_C>, the user may want
4251 to set the names of all dimensions
4253 __isl_give isl_pw_qpolynomial_fold *
4254 isl_pw_qpolynomial_fold_set_dim_name(
4255 __isl_take isl_pw_qpolynomial_fold *pwf,
4256 enum isl_dim_type type, unsigned pos,
4259 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4261 To iterate over all piecewise quasipolynomial reductions in a union
4262 piecewise quasipolynomial reduction, use the following function
4264 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4265 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4266 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4267 void *user), void *user);
4269 To iterate over the cells in a piecewise quasipolynomial reduction,
4270 use either of the following two functions
4272 int isl_pw_qpolynomial_fold_foreach_piece(
4273 __isl_keep isl_pw_qpolynomial_fold *pwf,
4274 int (*fn)(__isl_take isl_set *set,
4275 __isl_take isl_qpolynomial_fold *fold,
4276 void *user), void *user);
4277 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4278 __isl_keep isl_pw_qpolynomial_fold *pwf,
4279 int (*fn)(__isl_take isl_set *set,
4280 __isl_take isl_qpolynomial_fold *fold,
4281 void *user), void *user);
4283 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4284 of the difference between these two functions.
4286 To iterate over all quasipolynomials in a reduction, use
4288 int isl_qpolynomial_fold_foreach_qpolynomial(
4289 __isl_keep isl_qpolynomial_fold *fold,
4290 int (*fn)(__isl_take isl_qpolynomial *qp,
4291 void *user), void *user);
4293 =head3 Properties of Piecewise Quasipolynomial Reductions
4295 To check whether two union piecewise quasipolynomial reductions are
4296 obviously equal, use
4298 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4299 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4300 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4302 =head3 Operations on Piecewise Quasipolynomial Reductions
4304 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4305 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4307 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4308 __isl_take isl_pw_qpolynomial_fold *pwf1,
4309 __isl_take isl_pw_qpolynomial_fold *pwf2);
4311 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4312 __isl_take isl_pw_qpolynomial_fold *pwf1,
4313 __isl_take isl_pw_qpolynomial_fold *pwf2);
4315 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4316 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4317 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4319 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4320 __isl_take isl_pw_qpolynomial_fold *pwf,
4321 __isl_take isl_point *pnt);
4323 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4324 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4325 __isl_take isl_point *pnt);
4327 __isl_give isl_pw_qpolynomial_fold *
4328 isl_pw_qpolynomial_fold_intersect_params(
4329 __isl_take isl_pw_qpolynomial_fold *pwf,
4330 __isl_take isl_set *set);
4332 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4333 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4334 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4335 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4336 __isl_take isl_union_set *uset);
4337 __isl_give isl_union_pw_qpolynomial_fold *
4338 isl_union_pw_qpolynomial_fold_intersect_params(
4339 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4340 __isl_take isl_set *set);
4342 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4343 __isl_take isl_pw_qpolynomial_fold *pwf);
4345 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4346 __isl_take isl_pw_qpolynomial_fold *pwf);
4348 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4349 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4351 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4352 __isl_take isl_qpolynomial_fold *fold,
4353 __isl_take isl_set *context);
4354 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4355 __isl_take isl_qpolynomial_fold *fold,
4356 __isl_take isl_set *context);
4358 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4359 __isl_take isl_pw_qpolynomial_fold *pwf,
4360 __isl_take isl_set *context);
4361 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4362 __isl_take isl_pw_qpolynomial_fold *pwf,
4363 __isl_take isl_set *context);
4365 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4366 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4367 __isl_take isl_union_set *context);
4368 __isl_give isl_union_pw_qpolynomial_fold *
4369 isl_union_pw_qpolynomial_fold_gist_params(
4370 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4371 __isl_take isl_set *context);
4373 The gist operation applies the gist operation to each of
4374 the cells in the domain of the input piecewise quasipolynomial reduction.
4375 In future, the operation will also exploit the context
4376 to simplify the quasipolynomial reductions associated to each cell.
4378 __isl_give isl_pw_qpolynomial_fold *
4379 isl_set_apply_pw_qpolynomial_fold(
4380 __isl_take isl_set *set,
4381 __isl_take isl_pw_qpolynomial_fold *pwf,
4383 __isl_give isl_pw_qpolynomial_fold *
4384 isl_map_apply_pw_qpolynomial_fold(
4385 __isl_take isl_map *map,
4386 __isl_take isl_pw_qpolynomial_fold *pwf,
4388 __isl_give isl_union_pw_qpolynomial_fold *
4389 isl_union_set_apply_union_pw_qpolynomial_fold(
4390 __isl_take isl_union_set *uset,
4391 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4393 __isl_give isl_union_pw_qpolynomial_fold *
4394 isl_union_map_apply_union_pw_qpolynomial_fold(
4395 __isl_take isl_union_map *umap,
4396 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4399 The functions taking a map
4400 compose the given map with the given piecewise quasipolynomial reduction.
4401 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4402 over all elements in the intersection of the range of the map
4403 and the domain of the piecewise quasipolynomial reduction
4404 as a function of an element in the domain of the map.
4405 The functions taking a set compute a bound over all elements in the
4406 intersection of the set and the domain of the
4407 piecewise quasipolynomial reduction.
4409 =head2 Dependence Analysis
4411 C<isl> contains specialized functionality for performing
4412 array dataflow analysis. That is, given a I<sink> access relation
4413 and a collection of possible I<source> access relations,
4414 C<isl> can compute relations that describe
4415 for each iteration of the sink access, which iteration
4416 of which of the source access relations was the last
4417 to access the same data element before the given iteration
4419 The resulting dependence relations map source iterations
4420 to the corresponding sink iterations.
4421 To compute standard flow dependences, the sink should be
4422 a read, while the sources should be writes.
4423 If any of the source accesses are marked as being I<may>
4424 accesses, then there will be a dependence from the last
4425 I<must> access B<and> from any I<may> access that follows
4426 this last I<must> access.
4427 In particular, if I<all> sources are I<may> accesses,
4428 then memory based dependence analysis is performed.
4429 If, on the other hand, all sources are I<must> accesses,
4430 then value based dependence analysis is performed.
4432 #include <isl/flow.h>
4434 typedef int (*isl_access_level_before)(void *first, void *second);
4436 __isl_give isl_access_info *isl_access_info_alloc(
4437 __isl_take isl_map *sink,
4438 void *sink_user, isl_access_level_before fn,
4440 __isl_give isl_access_info *isl_access_info_add_source(
4441 __isl_take isl_access_info *acc,
4442 __isl_take isl_map *source, int must,
4444 void *isl_access_info_free(__isl_take isl_access_info *acc);
4446 __isl_give isl_flow *isl_access_info_compute_flow(
4447 __isl_take isl_access_info *acc);
4449 int isl_flow_foreach(__isl_keep isl_flow *deps,
4450 int (*fn)(__isl_take isl_map *dep, int must,
4451 void *dep_user, void *user),
4453 __isl_give isl_map *isl_flow_get_no_source(
4454 __isl_keep isl_flow *deps, int must);
4455 void isl_flow_free(__isl_take isl_flow *deps);
4457 The function C<isl_access_info_compute_flow> performs the actual
4458 dependence analysis. The other functions are used to construct
4459 the input for this function or to read off the output.
4461 The input is collected in an C<isl_access_info>, which can
4462 be created through a call to C<isl_access_info_alloc>.
4463 The arguments to this functions are the sink access relation
4464 C<sink>, a token C<sink_user> used to identify the sink
4465 access to the user, a callback function for specifying the
4466 relative order of source and sink accesses, and the number
4467 of source access relations that will be added.
4468 The callback function has type C<int (*)(void *first, void *second)>.
4469 The function is called with two user supplied tokens identifying
4470 either a source or the sink and it should return the shared nesting
4471 level and the relative order of the two accesses.
4472 In particular, let I<n> be the number of loops shared by
4473 the two accesses. If C<first> precedes C<second> textually,
4474 then the function should return I<2 * n + 1>; otherwise,
4475 it should return I<2 * n>.
4476 The sources can be added to the C<isl_access_info> by performing
4477 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4478 C<must> indicates whether the source is a I<must> access
4479 or a I<may> access. Note that a multi-valued access relation
4480 should only be marked I<must> if every iteration in the domain
4481 of the relation accesses I<all> elements in its image.
4482 The C<source_user> token is again used to identify
4483 the source access. The range of the source access relation
4484 C<source> should have the same dimension as the range
4485 of the sink access relation.
4486 The C<isl_access_info_free> function should usually not be
4487 called explicitly, because it is called implicitly by
4488 C<isl_access_info_compute_flow>.
4490 The result of the dependence analysis is collected in an
4491 C<isl_flow>. There may be elements of
4492 the sink access for which no preceding source access could be
4493 found or for which all preceding sources are I<may> accesses.
4494 The relations containing these elements can be obtained through
4495 calls to C<isl_flow_get_no_source>, the first with C<must> set
4496 and the second with C<must> unset.
4497 In the case of standard flow dependence analysis,
4498 with the sink a read and the sources I<must> writes,
4499 the first relation corresponds to the reads from uninitialized
4500 array elements and the second relation is empty.
4501 The actual flow dependences can be extracted using
4502 C<isl_flow_foreach>. This function will call the user-specified
4503 callback function C<fn> for each B<non-empty> dependence between
4504 a source and the sink. The callback function is called
4505 with four arguments, the actual flow dependence relation
4506 mapping source iterations to sink iterations, a boolean that
4507 indicates whether it is a I<must> or I<may> dependence, a token
4508 identifying the source and an additional C<void *> with value
4509 equal to the third argument of the C<isl_flow_foreach> call.
4510 A dependence is marked I<must> if it originates from a I<must>
4511 source and if it is not followed by any I<may> sources.
4513 After finishing with an C<isl_flow>, the user should call
4514 C<isl_flow_free> to free all associated memory.
4516 A higher-level interface to dependence analysis is provided
4517 by the following function.
4519 #include <isl/flow.h>
4521 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4522 __isl_take isl_union_map *must_source,
4523 __isl_take isl_union_map *may_source,
4524 __isl_take isl_union_map *schedule,
4525 __isl_give isl_union_map **must_dep,
4526 __isl_give isl_union_map **may_dep,
4527 __isl_give isl_union_map **must_no_source,
4528 __isl_give isl_union_map **may_no_source);
4530 The arrays are identified by the tuple names of the ranges
4531 of the accesses. The iteration domains by the tuple names
4532 of the domains of the accesses and of the schedule.
4533 The relative order of the iteration domains is given by the
4534 schedule. The relations returned through C<must_no_source>
4535 and C<may_no_source> are subsets of C<sink>.
4536 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4537 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4538 any of the other arguments is treated as an error.
4540 =head3 Interaction with Dependence Analysis
4542 During the dependence analysis, we frequently need to perform
4543 the following operation. Given a relation between sink iterations
4544 and potential source iterations from a particular source domain,
4545 what is the last potential source iteration corresponding to each
4546 sink iteration. It can sometimes be convenient to adjust
4547 the set of potential source iterations before or after each such operation.
4548 The prototypical example is fuzzy array dataflow analysis,
4549 where we need to analyze if, based on data-dependent constraints,
4550 the sink iteration can ever be executed without one or more of
4551 the corresponding potential source iterations being executed.
4552 If so, we can introduce extra parameters and select an unknown
4553 but fixed source iteration from the potential source iterations.
4554 To be able to perform such manipulations, C<isl> provides the following
4557 #include <isl/flow.h>
4559 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4560 __isl_keep isl_map *source_map,
4561 __isl_keep isl_set *sink, void *source_user,
4563 __isl_give isl_access_info *isl_access_info_set_restrict(
4564 __isl_take isl_access_info *acc,
4565 isl_access_restrict fn, void *user);
4567 The function C<isl_access_info_set_restrict> should be called
4568 before calling C<isl_access_info_compute_flow> and registers a callback function
4569 that will be called any time C<isl> is about to compute the last
4570 potential source. The first argument is the (reverse) proto-dependence,
4571 mapping sink iterations to potential source iterations.
4572 The second argument represents the sink iterations for which
4573 we want to compute the last source iteration.
4574 The third argument is the token corresponding to the source
4575 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4576 The callback is expected to return a restriction on either the input or
4577 the output of the operation computing the last potential source.
4578 If the input needs to be restricted then restrictions are needed
4579 for both the source and the sink iterations. The sink iterations
4580 and the potential source iterations will be intersected with these sets.
4581 If the output needs to be restricted then only a restriction on the source
4582 iterations is required.
4583 If any error occurs, the callback should return C<NULL>.
4584 An C<isl_restriction> object can be created, freed and inspected
4585 using the following functions.
4587 #include <isl/flow.h>
4589 __isl_give isl_restriction *isl_restriction_input(
4590 __isl_take isl_set *source_restr,
4591 __isl_take isl_set *sink_restr);
4592 __isl_give isl_restriction *isl_restriction_output(
4593 __isl_take isl_set *source_restr);
4594 __isl_give isl_restriction *isl_restriction_none(
4595 __isl_take isl_map *source_map);
4596 __isl_give isl_restriction *isl_restriction_empty(
4597 __isl_take isl_map *source_map);
4598 void *isl_restriction_free(
4599 __isl_take isl_restriction *restr);
4600 isl_ctx *isl_restriction_get_ctx(
4601 __isl_keep isl_restriction *restr);
4603 C<isl_restriction_none> and C<isl_restriction_empty> are special
4604 cases of C<isl_restriction_input>. C<isl_restriction_none>
4605 is essentially equivalent to
4607 isl_restriction_input(isl_set_universe(
4608 isl_space_range(isl_map_get_space(source_map))),
4610 isl_space_domain(isl_map_get_space(source_map))));
4612 whereas C<isl_restriction_empty> is essentially equivalent to
4614 isl_restriction_input(isl_set_empty(
4615 isl_space_range(isl_map_get_space(source_map))),
4617 isl_space_domain(isl_map_get_space(source_map))));
4621 B<The functionality described in this section is fairly new
4622 and may be subject to change.>
4624 The following function can be used to compute a schedule
4625 for a union of domains.
4626 By default, the algorithm used to construct the schedule is similar
4627 to that of C<Pluto>.
4628 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4630 The generated schedule respects all C<validity> dependences.
4631 That is, all dependence distances over these dependences in the
4632 scheduled space are lexicographically positive.
4633 The default algorithm tries to minimize the dependence distances over
4634 C<proximity> dependences.
4635 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4636 for groups of domains where the dependence distances have only
4637 non-negative values.
4638 When using Feautrier's algorithm, the C<proximity> dependence
4639 distances are only minimized during the extension to a
4640 full-dimensional schedule.
4642 #include <isl/schedule.h>
4643 __isl_give isl_schedule *isl_union_set_compute_schedule(
4644 __isl_take isl_union_set *domain,
4645 __isl_take isl_union_map *validity,
4646 __isl_take isl_union_map *proximity);
4647 void *isl_schedule_free(__isl_take isl_schedule *sched);
4649 A mapping from the domains to the scheduled space can be obtained
4650 from an C<isl_schedule> using the following function.
4652 __isl_give isl_union_map *isl_schedule_get_map(
4653 __isl_keep isl_schedule *sched);
4655 A representation of the schedule can be printed using
4657 __isl_give isl_printer *isl_printer_print_schedule(
4658 __isl_take isl_printer *p,
4659 __isl_keep isl_schedule *schedule);
4661 A representation of the schedule as a forest of bands can be obtained
4662 using the following function.
4664 __isl_give isl_band_list *isl_schedule_get_band_forest(
4665 __isl_keep isl_schedule *schedule);
4667 The individual bands can be visited in depth-first post-order
4668 using the following function.
4670 #include <isl/schedule.h>
4671 int isl_schedule_foreach_band(
4672 __isl_keep isl_schedule *sched,
4673 int (*fn)(__isl_keep isl_band *band, void *user),
4676 The list can be manipulated as explained in L<"Lists">.
4677 The bands inside the list can be copied and freed using the following
4680 #include <isl/band.h>
4681 __isl_give isl_band *isl_band_copy(
4682 __isl_keep isl_band *band);
4683 void *isl_band_free(__isl_take isl_band *band);
4685 Each band contains zero or more scheduling dimensions.
4686 These are referred to as the members of the band.
4687 The section of the schedule that corresponds to the band is
4688 referred to as the partial schedule of the band.
4689 For those nodes that participate in a band, the outer scheduling
4690 dimensions form the prefix schedule, while the inner scheduling
4691 dimensions form the suffix schedule.
4692 That is, if we take a cut of the band forest, then the union of
4693 the concatenations of the prefix, partial and suffix schedules of
4694 each band in the cut is equal to the entire schedule (modulo
4695 some possible padding at the end with zero scheduling dimensions).
4696 The properties of a band can be inspected using the following functions.
4698 #include <isl/band.h>
4699 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4701 int isl_band_has_children(__isl_keep isl_band *band);
4702 __isl_give isl_band_list *isl_band_get_children(
4703 __isl_keep isl_band *band);
4705 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4706 __isl_keep isl_band *band);
4707 __isl_give isl_union_map *isl_band_get_partial_schedule(
4708 __isl_keep isl_band *band);
4709 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4710 __isl_keep isl_band *band);
4712 int isl_band_n_member(__isl_keep isl_band *band);
4713 int isl_band_member_is_zero_distance(
4714 __isl_keep isl_band *band, int pos);
4716 int isl_band_list_foreach_band(
4717 __isl_keep isl_band_list *list,
4718 int (*fn)(__isl_keep isl_band *band, void *user),
4721 Note that a scheduling dimension is considered to be ``zero
4722 distance'' if it does not carry any proximity dependences
4724 That is, if the dependence distances of the proximity
4725 dependences are all zero in that direction (for fixed
4726 iterations of outer bands).
4727 Like C<isl_schedule_foreach_band>,
4728 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4729 in depth-first post-order.
4731 A band can be tiled using the following function.
4733 #include <isl/band.h>
4734 int isl_band_tile(__isl_keep isl_band *band,
4735 __isl_take isl_vec *sizes);
4737 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4739 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4741 The C<isl_band_tile> function tiles the band using the given tile sizes
4742 inside its schedule.
4743 A new child band is created to represent the point loops and it is
4744 inserted between the modified band and its children.
4745 The C<tile_scale_tile_loops> option specifies whether the tile
4746 loops iterators should be scaled by the tile sizes.
4748 A representation of the band can be printed using
4750 #include <isl/band.h>
4751 __isl_give isl_printer *isl_printer_print_band(
4752 __isl_take isl_printer *p,
4753 __isl_keep isl_band *band);
4757 #include <isl/schedule.h>
4758 int isl_options_set_schedule_max_coefficient(
4759 isl_ctx *ctx, int val);
4760 int isl_options_get_schedule_max_coefficient(
4762 int isl_options_set_schedule_max_constant_term(
4763 isl_ctx *ctx, int val);
4764 int isl_options_get_schedule_max_constant_term(
4766 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4767 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4768 int isl_options_set_schedule_maximize_band_depth(
4769 isl_ctx *ctx, int val);
4770 int isl_options_get_schedule_maximize_band_depth(
4772 int isl_options_set_schedule_outer_zero_distance(
4773 isl_ctx *ctx, int val);
4774 int isl_options_get_schedule_outer_zero_distance(
4776 int isl_options_set_schedule_split_scaled(
4777 isl_ctx *ctx, int val);
4778 int isl_options_get_schedule_split_scaled(
4780 int isl_options_set_schedule_algorithm(
4781 isl_ctx *ctx, int val);
4782 int isl_options_get_schedule_algorithm(
4784 int isl_options_set_schedule_separate_components(
4785 isl_ctx *ctx, int val);
4786 int isl_options_get_schedule_separate_components(
4791 =item * schedule_max_coefficient
4793 This option enforces that the coefficients for variable and parameter
4794 dimensions in the calculated schedule are not larger than the specified value.
4795 This option can significantly increase the speed of the scheduling calculation
4796 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4797 this option does not introduce bounds on the variable or parameter
4800 =item * schedule_max_constant_term
4802 This option enforces that the constant coefficients in the calculated schedule
4803 are not larger than the maximal constant term. This option can significantly
4804 increase the speed of the scheduling calculation and may also prevent fusing of
4805 unrelated dimensions. A value of -1 means that this option does not introduce
4806 bounds on the constant coefficients.
4808 =item * schedule_fuse
4810 This option controls the level of fusion.
4811 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4812 resulting schedule will be distributed as much as possible.
4813 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4814 try to fuse loops in the resulting schedule.
4816 =item * schedule_maximize_band_depth
4818 If this option is set, we do not split bands at the point
4819 where we detect splitting is necessary. Instead, we
4820 backtrack and split bands as early as possible. This
4821 reduces the number of splits and maximizes the width of
4822 the bands. Wider bands give more possibilities for tiling.
4823 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4824 then bands will be split as early as possible, even if there is no need.
4825 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4827 =item * schedule_outer_zero_distance
4829 If this option is set, then we try to construct schedules
4830 where the outermost scheduling dimension in each band
4831 results in a zero dependence distance over the proximity
4834 =item * schedule_split_scaled
4836 If this option is set, then we try to construct schedules in which the
4837 constant term is split off from the linear part if the linear parts of
4838 the scheduling rows for all nodes in the graphs have a common non-trivial
4840 The constant term is then placed in a separate band and the linear
4843 =item * schedule_algorithm
4845 Selects the scheduling algorithm to be used.
4846 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4847 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4849 =item * schedule_separate_components
4851 If at any point the dependence graph contains any (weakly connected) components,
4852 then these components are scheduled separately.
4853 If this option is not set, then some iterations of the domains
4854 in these components may be scheduled together.
4855 If this option is set, then the components are given consecutive
4860 =head2 Parametric Vertex Enumeration
4862 The parametric vertex enumeration described in this section
4863 is mainly intended to be used internally and by the C<barvinok>
4866 #include <isl/vertices.h>
4867 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4868 __isl_keep isl_basic_set *bset);
4870 The function C<isl_basic_set_compute_vertices> performs the
4871 actual computation of the parametric vertices and the chamber
4872 decomposition and store the result in an C<isl_vertices> object.
4873 This information can be queried by either iterating over all
4874 the vertices or iterating over all the chambers or cells
4875 and then iterating over all vertices that are active on the chamber.
4877 int isl_vertices_foreach_vertex(
4878 __isl_keep isl_vertices *vertices,
4879 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4882 int isl_vertices_foreach_cell(
4883 __isl_keep isl_vertices *vertices,
4884 int (*fn)(__isl_take isl_cell *cell, void *user),
4886 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4887 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4890 Other operations that can be performed on an C<isl_vertices> object are
4893 isl_ctx *isl_vertices_get_ctx(
4894 __isl_keep isl_vertices *vertices);
4895 int isl_vertices_get_n_vertices(
4896 __isl_keep isl_vertices *vertices);
4897 void isl_vertices_free(__isl_take isl_vertices *vertices);
4899 Vertices can be inspected and destroyed using the following functions.
4901 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4902 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4903 __isl_give isl_basic_set *isl_vertex_get_domain(
4904 __isl_keep isl_vertex *vertex);
4905 __isl_give isl_basic_set *isl_vertex_get_expr(
4906 __isl_keep isl_vertex *vertex);
4907 void isl_vertex_free(__isl_take isl_vertex *vertex);
4909 C<isl_vertex_get_expr> returns a singleton parametric set describing
4910 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4912 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4913 B<rational> basic sets, so they should mainly be used for inspection
4914 and should not be mixed with integer sets.
4916 Chambers can be inspected and destroyed using the following functions.
4918 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4919 __isl_give isl_basic_set *isl_cell_get_domain(
4920 __isl_keep isl_cell *cell);
4921 void isl_cell_free(__isl_take isl_cell *cell);
4925 Although C<isl> is mainly meant to be used as a library,
4926 it also contains some basic applications that use some
4927 of the functionality of C<isl>.
4928 The input may be specified in either the L<isl format>
4929 or the L<PolyLib format>.
4931 =head2 C<isl_polyhedron_sample>
4933 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4934 an integer element of the polyhedron, if there is any.
4935 The first column in the output is the denominator and is always
4936 equal to 1. If the polyhedron contains no integer points,
4937 then a vector of length zero is printed.
4941 C<isl_pip> takes the same input as the C<example> program
4942 from the C<piplib> distribution, i.e., a set of constraints
4943 on the parameters, a line containing only -1 and finally a set
4944 of constraints on a parametric polyhedron.
4945 The coefficients of the parameters appear in the last columns
4946 (but before the final constant column).
4947 The output is the lexicographic minimum of the parametric polyhedron.
4948 As C<isl> currently does not have its own output format, the output
4949 is just a dump of the internal state.
4951 =head2 C<isl_polyhedron_minimize>
4953 C<isl_polyhedron_minimize> computes the minimum of some linear
4954 or affine objective function over the integer points in a polyhedron.
4955 If an affine objective function
4956 is given, then the constant should appear in the last column.
4958 =head2 C<isl_polytope_scan>
4960 Given a polytope, C<isl_polytope_scan> prints
4961 all integer points in the polytope.