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_set *isl_set_remove_divs_involving_dims(
1476 __isl_take isl_set *set, enum isl_dim_type type,
1477 unsigned first, unsigned n);
1478 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1479 __isl_take isl_map *map, enum isl_dim_type type,
1480 unsigned first, unsigned n);
1482 __isl_give isl_set *isl_set_remove_unknown_divs(
1483 __isl_take isl_set *set);
1484 __isl_give isl_map *isl_map_remove_unknown_divs(
1485 __isl_take isl_map *map);
1487 To iterate over all the sets or maps in a union set or map, use
1489 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1490 int (*fn)(__isl_take isl_set *set, void *user),
1492 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1493 int (*fn)(__isl_take isl_map *map, void *user),
1496 The number of sets or maps in a union set or map can be obtained
1499 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1500 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1502 To extract the set or map in a given space from a union, use
1504 __isl_give isl_set *isl_union_set_extract_set(
1505 __isl_keep isl_union_set *uset,
1506 __isl_take isl_space *space);
1507 __isl_give isl_map *isl_union_map_extract_map(
1508 __isl_keep isl_union_map *umap,
1509 __isl_take isl_space *space);
1511 To iterate over all the basic sets or maps in a set or map, use
1513 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1514 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1516 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1517 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1520 The callback function C<fn> should return 0 if successful and
1521 -1 if an error occurs. In the latter case, or if any other error
1522 occurs, the above functions will return -1.
1524 It should be noted that C<isl> does not guarantee that
1525 the basic sets or maps passed to C<fn> are disjoint.
1526 If this is required, then the user should call one of
1527 the following functions first.
1529 __isl_give isl_set *isl_set_make_disjoint(
1530 __isl_take isl_set *set);
1531 __isl_give isl_map *isl_map_make_disjoint(
1532 __isl_take isl_map *map);
1534 The number of basic sets in a set can be obtained
1537 int isl_set_n_basic_set(__isl_keep isl_set *set);
1539 To iterate over the constraints of a basic set or map, use
1541 #include <isl/constraint.h>
1543 int isl_basic_set_n_constraint(
1544 __isl_keep isl_basic_set *bset);
1545 int isl_basic_set_foreach_constraint(
1546 __isl_keep isl_basic_set *bset,
1547 int (*fn)(__isl_take isl_constraint *c, void *user),
1549 int isl_basic_map_foreach_constraint(
1550 __isl_keep isl_basic_map *bmap,
1551 int (*fn)(__isl_take isl_constraint *c, void *user),
1553 void *isl_constraint_free(__isl_take isl_constraint *c);
1555 Again, the callback function C<fn> should return 0 if successful and
1556 -1 if an error occurs. In the latter case, or if any other error
1557 occurs, the above functions will return -1.
1558 The constraint C<c> represents either an equality or an inequality.
1559 Use the following function to find out whether a constraint
1560 represents an equality. If not, it represents an inequality.
1562 int isl_constraint_is_equality(
1563 __isl_keep isl_constraint *constraint);
1565 The coefficients of the constraints can be inspected using
1566 the following functions.
1568 int isl_constraint_is_lower_bound(
1569 __isl_keep isl_constraint *constraint,
1570 enum isl_dim_type type, unsigned pos);
1571 int isl_constraint_is_upper_bound(
1572 __isl_keep isl_constraint *constraint,
1573 enum isl_dim_type type, unsigned pos);
1574 void isl_constraint_get_constant(
1575 __isl_keep isl_constraint *constraint, isl_int *v);
1576 void isl_constraint_get_coefficient(
1577 __isl_keep isl_constraint *constraint,
1578 enum isl_dim_type type, int pos, isl_int *v);
1579 int isl_constraint_involves_dims(
1580 __isl_keep isl_constraint *constraint,
1581 enum isl_dim_type type, unsigned first, unsigned n);
1583 The explicit representations of the existentially quantified
1584 variables can be inspected using the following function.
1585 Note that the user is only allowed to use this function
1586 if the inspected set or map is the result of a call
1587 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1588 The existentially quantified variable is equal to the floor
1589 of the returned affine expression. The affine expression
1590 itself can be inspected using the functions in
1591 L<"Piecewise Quasi Affine Expressions">.
1593 __isl_give isl_aff *isl_constraint_get_div(
1594 __isl_keep isl_constraint *constraint, int pos);
1596 To obtain the constraints of a basic set or map in matrix
1597 form, use the following functions.
1599 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1600 __isl_keep isl_basic_set *bset,
1601 enum isl_dim_type c1, enum isl_dim_type c2,
1602 enum isl_dim_type c3, enum isl_dim_type c4);
1603 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1604 __isl_keep isl_basic_set *bset,
1605 enum isl_dim_type c1, enum isl_dim_type c2,
1606 enum isl_dim_type c3, enum isl_dim_type c4);
1607 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1608 __isl_keep isl_basic_map *bmap,
1609 enum isl_dim_type c1,
1610 enum isl_dim_type c2, enum isl_dim_type c3,
1611 enum isl_dim_type c4, enum isl_dim_type c5);
1612 __isl_give isl_mat *isl_basic_map_inequalities_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);
1618 The C<isl_dim_type> arguments dictate the order in which
1619 different kinds of variables appear in the resulting matrix
1620 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1621 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1623 The number of parameters, input, output or set dimensions can
1624 be obtained using the following functions.
1626 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1627 enum isl_dim_type type);
1628 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1629 enum isl_dim_type type);
1630 unsigned isl_set_dim(__isl_keep isl_set *set,
1631 enum isl_dim_type type);
1632 unsigned isl_map_dim(__isl_keep isl_map *map,
1633 enum isl_dim_type type);
1635 To check whether the description of a set or relation depends
1636 on one or more given dimensions, it is not necessary to iterate over all
1637 constraints. Instead the following functions can be used.
1639 int isl_basic_set_involves_dims(
1640 __isl_keep isl_basic_set *bset,
1641 enum isl_dim_type type, unsigned first, unsigned n);
1642 int isl_set_involves_dims(__isl_keep isl_set *set,
1643 enum isl_dim_type type, unsigned first, unsigned n);
1644 int isl_basic_map_involves_dims(
1645 __isl_keep isl_basic_map *bmap,
1646 enum isl_dim_type type, unsigned first, unsigned n);
1647 int isl_map_involves_dims(__isl_keep isl_map *map,
1648 enum isl_dim_type type, unsigned first, unsigned n);
1650 Similarly, the following functions can be used to check whether
1651 a given dimension is involved in any lower or upper bound.
1653 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1654 enum isl_dim_type type, unsigned pos);
1655 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1656 enum isl_dim_type type, unsigned pos);
1658 The identifiers or names of the domain and range spaces of a set
1659 or relation can be read off or set using the following functions.
1661 __isl_give isl_set *isl_set_set_tuple_id(
1662 __isl_take isl_set *set, __isl_take isl_id *id);
1663 __isl_give isl_set *isl_set_reset_tuple_id(
1664 __isl_take isl_set *set);
1665 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1666 __isl_give isl_id *isl_set_get_tuple_id(
1667 __isl_keep isl_set *set);
1668 __isl_give isl_map *isl_map_set_tuple_id(
1669 __isl_take isl_map *map, enum isl_dim_type type,
1670 __isl_take isl_id *id);
1671 __isl_give isl_map *isl_map_reset_tuple_id(
1672 __isl_take isl_map *map, enum isl_dim_type type);
1673 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1674 enum isl_dim_type type);
1675 __isl_give isl_id *isl_map_get_tuple_id(
1676 __isl_keep isl_map *map, enum isl_dim_type type);
1678 const char *isl_basic_set_get_tuple_name(
1679 __isl_keep isl_basic_set *bset);
1680 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1681 __isl_take isl_basic_set *set, const char *s);
1682 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1683 const char *isl_set_get_tuple_name(
1684 __isl_keep isl_set *set);
1685 const char *isl_basic_map_get_tuple_name(
1686 __isl_keep isl_basic_map *bmap,
1687 enum isl_dim_type type);
1688 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1689 __isl_take isl_basic_map *bmap,
1690 enum isl_dim_type type, const char *s);
1691 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1692 enum isl_dim_type type);
1693 const char *isl_map_get_tuple_name(
1694 __isl_keep isl_map *map,
1695 enum isl_dim_type type);
1697 As with C<isl_space_get_tuple_name>, the value returned points to
1698 an internal data structure.
1699 The identifiers, positions or names of individual dimensions can be
1700 read off using the following functions.
1702 __isl_give isl_id *isl_basic_set_get_dim_id(
1703 __isl_keep isl_basic_set *bset,
1704 enum isl_dim_type type, unsigned pos);
1705 __isl_give isl_set *isl_set_set_dim_id(
1706 __isl_take isl_set *set, enum isl_dim_type type,
1707 unsigned pos, __isl_take isl_id *id);
1708 int isl_set_has_dim_id(__isl_keep isl_set *set,
1709 enum isl_dim_type type, unsigned pos);
1710 __isl_give isl_id *isl_set_get_dim_id(
1711 __isl_keep isl_set *set, enum isl_dim_type type,
1713 int isl_basic_map_has_dim_id(
1714 __isl_keep isl_basic_map *bmap,
1715 enum isl_dim_type type, unsigned pos);
1716 __isl_give isl_map *isl_map_set_dim_id(
1717 __isl_take isl_map *map, enum isl_dim_type type,
1718 unsigned pos, __isl_take isl_id *id);
1719 int isl_map_has_dim_id(__isl_keep isl_map *map,
1720 enum isl_dim_type type, unsigned pos);
1721 __isl_give isl_id *isl_map_get_dim_id(
1722 __isl_keep isl_map *map, enum isl_dim_type type,
1725 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1726 enum isl_dim_type type, __isl_keep isl_id *id);
1727 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1728 enum isl_dim_type type, __isl_keep isl_id *id);
1729 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1730 enum isl_dim_type type, const char *name);
1731 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1732 enum isl_dim_type type, const char *name);
1734 const char *isl_constraint_get_dim_name(
1735 __isl_keep isl_constraint *constraint,
1736 enum isl_dim_type type, unsigned pos);
1737 const char *isl_basic_set_get_dim_name(
1738 __isl_keep isl_basic_set *bset,
1739 enum isl_dim_type type, unsigned pos);
1740 int isl_set_has_dim_name(__isl_keep isl_set *set,
1741 enum isl_dim_type type, unsigned pos);
1742 const char *isl_set_get_dim_name(
1743 __isl_keep isl_set *set,
1744 enum isl_dim_type type, unsigned pos);
1745 const char *isl_basic_map_get_dim_name(
1746 __isl_keep isl_basic_map *bmap,
1747 enum isl_dim_type type, unsigned pos);
1748 int isl_map_has_dim_name(__isl_keep isl_map *map,
1749 enum isl_dim_type type, unsigned pos);
1750 const char *isl_map_get_dim_name(
1751 __isl_keep isl_map *map,
1752 enum isl_dim_type type, unsigned pos);
1754 These functions are mostly useful to obtain the identifiers, positions
1755 or names of the parameters. Identifiers of individual dimensions are
1756 essentially only useful for printing. They are ignored by all other
1757 operations and may not be preserved across those operations.
1761 =head3 Unary Properties
1767 The following functions test whether the given set or relation
1768 contains any integer points. The ``plain'' variants do not perform
1769 any computations, but simply check if the given set or relation
1770 is already known to be empty.
1772 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1773 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1774 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1775 int isl_set_is_empty(__isl_keep isl_set *set);
1776 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1777 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1778 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1779 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1780 int isl_map_is_empty(__isl_keep isl_map *map);
1781 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1783 =item * Universality
1785 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1786 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1787 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1789 =item * Single-valuedness
1791 int isl_basic_map_is_single_valued(
1792 __isl_keep isl_basic_map *bmap);
1793 int isl_map_plain_is_single_valued(
1794 __isl_keep isl_map *map);
1795 int isl_map_is_single_valued(__isl_keep isl_map *map);
1796 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1800 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1801 int isl_map_is_injective(__isl_keep isl_map *map);
1802 int isl_union_map_plain_is_injective(
1803 __isl_keep isl_union_map *umap);
1804 int isl_union_map_is_injective(
1805 __isl_keep isl_union_map *umap);
1809 int isl_map_is_bijective(__isl_keep isl_map *map);
1810 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1814 int isl_basic_map_plain_is_fixed(
1815 __isl_keep isl_basic_map *bmap,
1816 enum isl_dim_type type, unsigned pos,
1818 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1819 enum isl_dim_type type, unsigned pos,
1821 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1822 enum isl_dim_type type, unsigned pos,
1825 Check if the relation obviously lies on a hyperplane where the given dimension
1826 has a fixed value and if so, return that value in C<*val>.
1830 To check whether a set is a parameter domain, use this function:
1832 int isl_set_is_params(__isl_keep isl_set *set);
1833 int isl_union_set_is_params(
1834 __isl_keep isl_union_set *uset);
1838 The following functions check whether the domain of the given
1839 (basic) set is a wrapped relation.
1841 int isl_basic_set_is_wrapping(
1842 __isl_keep isl_basic_set *bset);
1843 int isl_set_is_wrapping(__isl_keep isl_set *set);
1845 =item * Internal Product
1847 int isl_basic_map_can_zip(
1848 __isl_keep isl_basic_map *bmap);
1849 int isl_map_can_zip(__isl_keep isl_map *map);
1851 Check whether the product of domain and range of the given relation
1853 i.e., whether both domain and range are nested relations.
1857 int isl_basic_map_can_curry(
1858 __isl_keep isl_basic_map *bmap);
1859 int isl_map_can_curry(__isl_keep isl_map *map);
1861 Check whether the domain of the (basic) relation is a wrapped relation.
1865 =head3 Binary Properties
1871 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1872 __isl_keep isl_set *set2);
1873 int isl_set_is_equal(__isl_keep isl_set *set1,
1874 __isl_keep isl_set *set2);
1875 int isl_union_set_is_equal(
1876 __isl_keep isl_union_set *uset1,
1877 __isl_keep isl_union_set *uset2);
1878 int isl_basic_map_is_equal(
1879 __isl_keep isl_basic_map *bmap1,
1880 __isl_keep isl_basic_map *bmap2);
1881 int isl_map_is_equal(__isl_keep isl_map *map1,
1882 __isl_keep isl_map *map2);
1883 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1884 __isl_keep isl_map *map2);
1885 int isl_union_map_is_equal(
1886 __isl_keep isl_union_map *umap1,
1887 __isl_keep isl_union_map *umap2);
1889 =item * Disjointness
1891 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1892 __isl_keep isl_set *set2);
1896 int isl_basic_set_is_subset(
1897 __isl_keep isl_basic_set *bset1,
1898 __isl_keep isl_basic_set *bset2);
1899 int isl_set_is_subset(__isl_keep isl_set *set1,
1900 __isl_keep isl_set *set2);
1901 int isl_set_is_strict_subset(
1902 __isl_keep isl_set *set1,
1903 __isl_keep isl_set *set2);
1904 int isl_union_set_is_subset(
1905 __isl_keep isl_union_set *uset1,
1906 __isl_keep isl_union_set *uset2);
1907 int isl_union_set_is_strict_subset(
1908 __isl_keep isl_union_set *uset1,
1909 __isl_keep isl_union_set *uset2);
1910 int isl_basic_map_is_subset(
1911 __isl_keep isl_basic_map *bmap1,
1912 __isl_keep isl_basic_map *bmap2);
1913 int isl_basic_map_is_strict_subset(
1914 __isl_keep isl_basic_map *bmap1,
1915 __isl_keep isl_basic_map *bmap2);
1916 int isl_map_is_subset(
1917 __isl_keep isl_map *map1,
1918 __isl_keep isl_map *map2);
1919 int isl_map_is_strict_subset(
1920 __isl_keep isl_map *map1,
1921 __isl_keep isl_map *map2);
1922 int isl_union_map_is_subset(
1923 __isl_keep isl_union_map *umap1,
1924 __isl_keep isl_union_map *umap2);
1925 int isl_union_map_is_strict_subset(
1926 __isl_keep isl_union_map *umap1,
1927 __isl_keep isl_union_map *umap2);
1929 Check whether the first argument is a (strict) subset of the
1934 =head2 Unary Operations
1940 __isl_give isl_set *isl_set_complement(
1941 __isl_take isl_set *set);
1942 __isl_give isl_map *isl_map_complement(
1943 __isl_take isl_map *map);
1947 __isl_give isl_basic_map *isl_basic_map_reverse(
1948 __isl_take isl_basic_map *bmap);
1949 __isl_give isl_map *isl_map_reverse(
1950 __isl_take isl_map *map);
1951 __isl_give isl_union_map *isl_union_map_reverse(
1952 __isl_take isl_union_map *umap);
1956 __isl_give isl_basic_set *isl_basic_set_project_out(
1957 __isl_take isl_basic_set *bset,
1958 enum isl_dim_type type, unsigned first, unsigned n);
1959 __isl_give isl_basic_map *isl_basic_map_project_out(
1960 __isl_take isl_basic_map *bmap,
1961 enum isl_dim_type type, unsigned first, unsigned n);
1962 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1963 enum isl_dim_type type, unsigned first, unsigned n);
1964 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1965 enum isl_dim_type type, unsigned first, unsigned n);
1966 __isl_give isl_basic_set *isl_basic_set_params(
1967 __isl_take isl_basic_set *bset);
1968 __isl_give isl_basic_set *isl_basic_map_domain(
1969 __isl_take isl_basic_map *bmap);
1970 __isl_give isl_basic_set *isl_basic_map_range(
1971 __isl_take isl_basic_map *bmap);
1972 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1973 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1974 __isl_give isl_set *isl_map_domain(
1975 __isl_take isl_map *bmap);
1976 __isl_give isl_set *isl_map_range(
1977 __isl_take isl_map *map);
1978 __isl_give isl_set *isl_union_set_params(
1979 __isl_take isl_union_set *uset);
1980 __isl_give isl_set *isl_union_map_params(
1981 __isl_take isl_union_map *umap);
1982 __isl_give isl_union_set *isl_union_map_domain(
1983 __isl_take isl_union_map *umap);
1984 __isl_give isl_union_set *isl_union_map_range(
1985 __isl_take isl_union_map *umap);
1987 __isl_give isl_basic_map *isl_basic_map_domain_map(
1988 __isl_take isl_basic_map *bmap);
1989 __isl_give isl_basic_map *isl_basic_map_range_map(
1990 __isl_take isl_basic_map *bmap);
1991 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1992 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1993 __isl_give isl_union_map *isl_union_map_domain_map(
1994 __isl_take isl_union_map *umap);
1995 __isl_give isl_union_map *isl_union_map_range_map(
1996 __isl_take isl_union_map *umap);
1998 The functions above construct a (basic, regular or union) relation
1999 that maps (a wrapped version of) the input relation to its domain or range.
2003 __isl_give isl_basic_set *isl_basic_set_eliminate(
2004 __isl_take isl_basic_set *bset,
2005 enum isl_dim_type type,
2006 unsigned first, unsigned n);
2007 __isl_give isl_set *isl_set_eliminate(
2008 __isl_take isl_set *set, enum isl_dim_type type,
2009 unsigned first, unsigned n);
2010 __isl_give isl_basic_map *isl_basic_map_eliminate(
2011 __isl_take isl_basic_map *bmap,
2012 enum isl_dim_type type,
2013 unsigned first, unsigned n);
2014 __isl_give isl_map *isl_map_eliminate(
2015 __isl_take isl_map *map, enum isl_dim_type type,
2016 unsigned first, unsigned n);
2018 Eliminate the coefficients for the given dimensions from the constraints,
2019 without removing the dimensions.
2023 __isl_give isl_basic_set *isl_basic_set_fix(
2024 __isl_take isl_basic_set *bset,
2025 enum isl_dim_type type, unsigned pos,
2027 __isl_give isl_basic_set *isl_basic_set_fix_si(
2028 __isl_take isl_basic_set *bset,
2029 enum isl_dim_type type, unsigned pos, int value);
2030 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2031 enum isl_dim_type type, unsigned pos,
2033 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2034 enum isl_dim_type type, unsigned pos, int value);
2035 __isl_give isl_basic_map *isl_basic_map_fix_si(
2036 __isl_take isl_basic_map *bmap,
2037 enum isl_dim_type type, unsigned pos, int value);
2038 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2039 enum isl_dim_type type, unsigned pos, int value);
2041 Intersect the set or relation with the hyperplane where the given
2042 dimension has the fixed given value.
2044 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2045 __isl_take isl_basic_map *bmap,
2046 enum isl_dim_type type, unsigned pos, int value);
2047 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2048 __isl_take isl_basic_map *bmap,
2049 enum isl_dim_type type, unsigned pos, int value);
2050 __isl_give isl_set *isl_set_lower_bound(
2051 __isl_take isl_set *set,
2052 enum isl_dim_type type, unsigned pos,
2054 __isl_give isl_set *isl_set_lower_bound_si(
2055 __isl_take isl_set *set,
2056 enum isl_dim_type type, unsigned pos, int value);
2057 __isl_give isl_map *isl_map_lower_bound_si(
2058 __isl_take isl_map *map,
2059 enum isl_dim_type type, unsigned pos, int value);
2060 __isl_give isl_set *isl_set_upper_bound(
2061 __isl_take isl_set *set,
2062 enum isl_dim_type type, unsigned pos,
2064 __isl_give isl_set *isl_set_upper_bound_si(
2065 __isl_take isl_set *set,
2066 enum isl_dim_type type, unsigned pos, int value);
2067 __isl_give isl_map *isl_map_upper_bound_si(
2068 __isl_take isl_map *map,
2069 enum isl_dim_type type, unsigned pos, int value);
2071 Intersect the set or relation with the half-space where the given
2072 dimension has a value bounded by the fixed given value.
2074 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2075 enum isl_dim_type type1, int pos1,
2076 enum isl_dim_type type2, int pos2);
2077 __isl_give isl_basic_map *isl_basic_map_equate(
2078 __isl_take isl_basic_map *bmap,
2079 enum isl_dim_type type1, int pos1,
2080 enum isl_dim_type type2, int pos2);
2081 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2082 enum isl_dim_type type1, int pos1,
2083 enum isl_dim_type type2, int pos2);
2085 Intersect the set or relation with the hyperplane where the given
2086 dimensions are equal to each other.
2088 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2089 enum isl_dim_type type1, int pos1,
2090 enum isl_dim_type type2, int pos2);
2092 Intersect the relation with the hyperplane where the given
2093 dimensions have opposite values.
2095 __isl_give isl_basic_map *isl_basic_map_order_ge(
2096 __isl_take isl_basic_map *bmap,
2097 enum isl_dim_type type1, int pos1,
2098 enum isl_dim_type type2, int pos2);
2099 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2100 enum isl_dim_type type1, int pos1,
2101 enum isl_dim_type type2, int pos2);
2102 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2103 enum isl_dim_type type1, int pos1,
2104 enum isl_dim_type type2, int pos2);
2106 Intersect the relation with the half-space where the given
2107 dimensions satisfy the given ordering.
2111 __isl_give isl_map *isl_set_identity(
2112 __isl_take isl_set *set);
2113 __isl_give isl_union_map *isl_union_set_identity(
2114 __isl_take isl_union_set *uset);
2116 Construct an identity relation on the given (union) set.
2120 __isl_give isl_basic_set *isl_basic_map_deltas(
2121 __isl_take isl_basic_map *bmap);
2122 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2123 __isl_give isl_union_set *isl_union_map_deltas(
2124 __isl_take isl_union_map *umap);
2126 These functions return a (basic) set containing the differences
2127 between image elements and corresponding domain elements in the input.
2129 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2130 __isl_take isl_basic_map *bmap);
2131 __isl_give isl_map *isl_map_deltas_map(
2132 __isl_take isl_map *map);
2133 __isl_give isl_union_map *isl_union_map_deltas_map(
2134 __isl_take isl_union_map *umap);
2136 The functions above construct a (basic, regular or union) relation
2137 that maps (a wrapped version of) the input relation to its delta set.
2141 Simplify the representation of a set or relation by trying
2142 to combine pairs of basic sets or relations into a single
2143 basic set or relation.
2145 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2146 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2147 __isl_give isl_union_set *isl_union_set_coalesce(
2148 __isl_take isl_union_set *uset);
2149 __isl_give isl_union_map *isl_union_map_coalesce(
2150 __isl_take isl_union_map *umap);
2152 One of the methods for combining pairs of basic sets or relations
2153 can result in coefficients that are much larger than those that appear
2154 in the constraints of the input. By default, the coefficients are
2155 not allowed to grow larger, but this can be changed by unsetting
2156 the following option.
2158 int isl_options_set_coalesce_bounded_wrapping(
2159 isl_ctx *ctx, int val);
2160 int isl_options_get_coalesce_bounded_wrapping(
2163 =item * Detecting equalities
2165 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2166 __isl_take isl_basic_set *bset);
2167 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2168 __isl_take isl_basic_map *bmap);
2169 __isl_give isl_set *isl_set_detect_equalities(
2170 __isl_take isl_set *set);
2171 __isl_give isl_map *isl_map_detect_equalities(
2172 __isl_take isl_map *map);
2173 __isl_give isl_union_set *isl_union_set_detect_equalities(
2174 __isl_take isl_union_set *uset);
2175 __isl_give isl_union_map *isl_union_map_detect_equalities(
2176 __isl_take isl_union_map *umap);
2178 Simplify the representation of a set or relation by detecting implicit
2181 =item * Removing redundant constraints
2183 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2184 __isl_take isl_basic_set *bset);
2185 __isl_give isl_set *isl_set_remove_redundancies(
2186 __isl_take isl_set *set);
2187 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2188 __isl_take isl_basic_map *bmap);
2189 __isl_give isl_map *isl_map_remove_redundancies(
2190 __isl_take isl_map *map);
2194 __isl_give isl_basic_set *isl_set_convex_hull(
2195 __isl_take isl_set *set);
2196 __isl_give isl_basic_map *isl_map_convex_hull(
2197 __isl_take isl_map *map);
2199 If the input set or relation has any existentially quantified
2200 variables, then the result of these operations is currently undefined.
2204 __isl_give isl_basic_set *isl_set_simple_hull(
2205 __isl_take isl_set *set);
2206 __isl_give isl_basic_map *isl_map_simple_hull(
2207 __isl_take isl_map *map);
2208 __isl_give isl_union_map *isl_union_map_simple_hull(
2209 __isl_take isl_union_map *umap);
2211 These functions compute a single basic set or relation
2212 that contains the whole input set or relation.
2213 In particular, the output is described by translates
2214 of the constraints describing the basic sets or relations in the input.
2218 (See \autoref{s:simple hull}.)
2224 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2225 __isl_take isl_basic_set *bset);
2226 __isl_give isl_basic_set *isl_set_affine_hull(
2227 __isl_take isl_set *set);
2228 __isl_give isl_union_set *isl_union_set_affine_hull(
2229 __isl_take isl_union_set *uset);
2230 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2231 __isl_take isl_basic_map *bmap);
2232 __isl_give isl_basic_map *isl_map_affine_hull(
2233 __isl_take isl_map *map);
2234 __isl_give isl_union_map *isl_union_map_affine_hull(
2235 __isl_take isl_union_map *umap);
2237 In case of union sets and relations, the affine hull is computed
2240 =item * Polyhedral hull
2242 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2243 __isl_take isl_set *set);
2244 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2245 __isl_take isl_map *map);
2246 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2247 __isl_take isl_union_set *uset);
2248 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2249 __isl_take isl_union_map *umap);
2251 These functions compute a single basic set or relation
2252 not involving any existentially quantified variables
2253 that contains the whole input set or relation.
2254 In case of union sets and relations, the polyhedral hull is computed
2259 __isl_give isl_basic_set *isl_basic_set_sample(
2260 __isl_take isl_basic_set *bset);
2261 __isl_give isl_basic_set *isl_set_sample(
2262 __isl_take isl_set *set);
2263 __isl_give isl_basic_map *isl_basic_map_sample(
2264 __isl_take isl_basic_map *bmap);
2265 __isl_give isl_basic_map *isl_map_sample(
2266 __isl_take isl_map *map);
2268 If the input (basic) set or relation is non-empty, then return
2269 a singleton subset of the input. Otherwise, return an empty set.
2271 =item * Optimization
2273 #include <isl/ilp.h>
2274 enum isl_lp_result isl_basic_set_max(
2275 __isl_keep isl_basic_set *bset,
2276 __isl_keep isl_aff *obj, isl_int *opt)
2277 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2278 __isl_keep isl_aff *obj, isl_int *opt);
2279 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2280 __isl_keep isl_aff *obj, isl_int *opt);
2282 Compute the minimum or maximum of the integer affine expression C<obj>
2283 over the points in C<set>, returning the result in C<opt>.
2284 The return value may be one of C<isl_lp_error>,
2285 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2287 =item * Parametric optimization
2289 __isl_give isl_pw_aff *isl_set_dim_min(
2290 __isl_take isl_set *set, int pos);
2291 __isl_give isl_pw_aff *isl_set_dim_max(
2292 __isl_take isl_set *set, int pos);
2293 __isl_give isl_pw_aff *isl_map_dim_max(
2294 __isl_take isl_map *map, int pos);
2296 Compute the minimum or maximum of the given set or output dimension
2297 as a function of the parameters (and input dimensions), but independently
2298 of the other set or output dimensions.
2299 For lexicographic optimization, see L<"Lexicographic Optimization">.
2303 The following functions compute either the set of (rational) coefficient
2304 values of valid constraints for the given set or the set of (rational)
2305 values satisfying the constraints with coefficients from the given set.
2306 Internally, these two sets of functions perform essentially the
2307 same operations, except that the set of coefficients is assumed to
2308 be a cone, while the set of values may be any polyhedron.
2309 The current implementation is based on the Farkas lemma and
2310 Fourier-Motzkin elimination, but this may change or be made optional
2311 in future. In particular, future implementations may use different
2312 dualization algorithms or skip the elimination step.
2314 __isl_give isl_basic_set *isl_basic_set_coefficients(
2315 __isl_take isl_basic_set *bset);
2316 __isl_give isl_basic_set *isl_set_coefficients(
2317 __isl_take isl_set *set);
2318 __isl_give isl_union_set *isl_union_set_coefficients(
2319 __isl_take isl_union_set *bset);
2320 __isl_give isl_basic_set *isl_basic_set_solutions(
2321 __isl_take isl_basic_set *bset);
2322 __isl_give isl_basic_set *isl_set_solutions(
2323 __isl_take isl_set *set);
2324 __isl_give isl_union_set *isl_union_set_solutions(
2325 __isl_take isl_union_set *bset);
2329 __isl_give isl_map *isl_map_fixed_power(
2330 __isl_take isl_map *map, isl_int exp);
2331 __isl_give isl_union_map *isl_union_map_fixed_power(
2332 __isl_take isl_union_map *umap, isl_int exp);
2334 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2335 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2336 of C<map> is computed.
2338 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2340 __isl_give isl_union_map *isl_union_map_power(
2341 __isl_take isl_union_map *umap, int *exact);
2343 Compute a parametric representation for all positive powers I<k> of C<map>.
2344 The result maps I<k> to a nested relation corresponding to the
2345 I<k>th power of C<map>.
2346 The result may be an overapproximation. If the result is known to be exact,
2347 then C<*exact> is set to C<1>.
2349 =item * Transitive closure
2351 __isl_give isl_map *isl_map_transitive_closure(
2352 __isl_take isl_map *map, int *exact);
2353 __isl_give isl_union_map *isl_union_map_transitive_closure(
2354 __isl_take isl_union_map *umap, int *exact);
2356 Compute the transitive closure of C<map>.
2357 The result may be an overapproximation. If the result is known to be exact,
2358 then C<*exact> is set to C<1>.
2360 =item * Reaching path lengths
2362 __isl_give isl_map *isl_map_reaching_path_lengths(
2363 __isl_take isl_map *map, int *exact);
2365 Compute a relation that maps each element in the range of C<map>
2366 to the lengths of all paths composed of edges in C<map> that
2367 end up in the given element.
2368 The result may be an overapproximation. If the result is known to be exact,
2369 then C<*exact> is set to C<1>.
2370 To compute the I<maximal> path length, the resulting relation
2371 should be postprocessed by C<isl_map_lexmax>.
2372 In particular, if the input relation is a dependence relation
2373 (mapping sources to sinks), then the maximal path length corresponds
2374 to the free schedule.
2375 Note, however, that C<isl_map_lexmax> expects the maximum to be
2376 finite, so if the path lengths are unbounded (possibly due to
2377 the overapproximation), then you will get an error message.
2381 __isl_give isl_basic_set *isl_basic_map_wrap(
2382 __isl_take isl_basic_map *bmap);
2383 __isl_give isl_set *isl_map_wrap(
2384 __isl_take isl_map *map);
2385 __isl_give isl_union_set *isl_union_map_wrap(
2386 __isl_take isl_union_map *umap);
2387 __isl_give isl_basic_map *isl_basic_set_unwrap(
2388 __isl_take isl_basic_set *bset);
2389 __isl_give isl_map *isl_set_unwrap(
2390 __isl_take isl_set *set);
2391 __isl_give isl_union_map *isl_union_set_unwrap(
2392 __isl_take isl_union_set *uset);
2396 Remove any internal structure of domain (and range) of the given
2397 set or relation. If there is any such internal structure in the input,
2398 then the name of the space is also removed.
2400 __isl_give isl_basic_set *isl_basic_set_flatten(
2401 __isl_take isl_basic_set *bset);
2402 __isl_give isl_set *isl_set_flatten(
2403 __isl_take isl_set *set);
2404 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2405 __isl_take isl_basic_map *bmap);
2406 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2407 __isl_take isl_basic_map *bmap);
2408 __isl_give isl_map *isl_map_flatten_range(
2409 __isl_take isl_map *map);
2410 __isl_give isl_map *isl_map_flatten_domain(
2411 __isl_take isl_map *map);
2412 __isl_give isl_basic_map *isl_basic_map_flatten(
2413 __isl_take isl_basic_map *bmap);
2414 __isl_give isl_map *isl_map_flatten(
2415 __isl_take isl_map *map);
2417 __isl_give isl_map *isl_set_flatten_map(
2418 __isl_take isl_set *set);
2420 The function above constructs a relation
2421 that maps the input set to a flattened version of the set.
2425 Lift the input set to a space with extra dimensions corresponding
2426 to the existentially quantified variables in the input.
2427 In particular, the result lives in a wrapped map where the domain
2428 is the original space and the range corresponds to the original
2429 existentially quantified variables.
2431 __isl_give isl_basic_set *isl_basic_set_lift(
2432 __isl_take isl_basic_set *bset);
2433 __isl_give isl_set *isl_set_lift(
2434 __isl_take isl_set *set);
2435 __isl_give isl_union_set *isl_union_set_lift(
2436 __isl_take isl_union_set *uset);
2438 Given a local space that contains the existentially quantified
2439 variables of a set, a basic relation that, when applied to
2440 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2441 can be constructed using the following function.
2443 #include <isl/local_space.h>
2444 __isl_give isl_basic_map *isl_local_space_lifting(
2445 __isl_take isl_local_space *ls);
2447 =item * Internal Product
2449 __isl_give isl_basic_map *isl_basic_map_zip(
2450 __isl_take isl_basic_map *bmap);
2451 __isl_give isl_map *isl_map_zip(
2452 __isl_take isl_map *map);
2453 __isl_give isl_union_map *isl_union_map_zip(
2454 __isl_take isl_union_map *umap);
2456 Given a relation with nested relations for domain and range,
2457 interchange the range of the domain with the domain of the range.
2461 __isl_give isl_basic_map *isl_basic_map_curry(
2462 __isl_take isl_basic_map *bmap);
2463 __isl_give isl_map *isl_map_curry(
2464 __isl_take isl_map *map);
2465 __isl_give isl_union_map *isl_union_map_curry(
2466 __isl_take isl_union_map *umap);
2468 Given a relation with a nested relation for domain,
2469 move the range of the nested relation out of the domain
2470 and use it as the domain of a nested relation in the range,
2471 with the original range as range of this nested relation.
2473 =item * Aligning parameters
2475 __isl_give isl_basic_set *isl_basic_set_align_params(
2476 __isl_take isl_basic_set *bset,
2477 __isl_take isl_space *model);
2478 __isl_give isl_set *isl_set_align_params(
2479 __isl_take isl_set *set,
2480 __isl_take isl_space *model);
2481 __isl_give isl_basic_map *isl_basic_map_align_params(
2482 __isl_take isl_basic_map *bmap,
2483 __isl_take isl_space *model);
2484 __isl_give isl_map *isl_map_align_params(
2485 __isl_take isl_map *map,
2486 __isl_take isl_space *model);
2488 Change the order of the parameters of the given set or relation
2489 such that the first parameters match those of C<model>.
2490 This may involve the introduction of extra parameters.
2491 All parameters need to be named.
2493 =item * Dimension manipulation
2495 __isl_give isl_set *isl_set_add_dims(
2496 __isl_take isl_set *set,
2497 enum isl_dim_type type, unsigned n);
2498 __isl_give isl_map *isl_map_add_dims(
2499 __isl_take isl_map *map,
2500 enum isl_dim_type type, unsigned n);
2501 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2502 __isl_take isl_basic_set *bset,
2503 enum isl_dim_type type, unsigned pos,
2505 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2506 __isl_take isl_basic_map *bmap,
2507 enum isl_dim_type type, unsigned pos,
2509 __isl_give isl_set *isl_set_insert_dims(
2510 __isl_take isl_set *set,
2511 enum isl_dim_type type, unsigned pos, unsigned n);
2512 __isl_give isl_map *isl_map_insert_dims(
2513 __isl_take isl_map *map,
2514 enum isl_dim_type type, unsigned pos, unsigned n);
2515 __isl_give isl_basic_set *isl_basic_set_move_dims(
2516 __isl_take isl_basic_set *bset,
2517 enum isl_dim_type dst_type, unsigned dst_pos,
2518 enum isl_dim_type src_type, unsigned src_pos,
2520 __isl_give isl_basic_map *isl_basic_map_move_dims(
2521 __isl_take isl_basic_map *bmap,
2522 enum isl_dim_type dst_type, unsigned dst_pos,
2523 enum isl_dim_type src_type, unsigned src_pos,
2525 __isl_give isl_set *isl_set_move_dims(
2526 __isl_take isl_set *set,
2527 enum isl_dim_type dst_type, unsigned dst_pos,
2528 enum isl_dim_type src_type, unsigned src_pos,
2530 __isl_give isl_map *isl_map_move_dims(
2531 __isl_take isl_map *map,
2532 enum isl_dim_type dst_type, unsigned dst_pos,
2533 enum isl_dim_type src_type, unsigned src_pos,
2536 It is usually not advisable to directly change the (input or output)
2537 space of a set or a relation as this removes the name and the internal
2538 structure of the space. However, the above functions can be useful
2539 to add new parameters, assuming
2540 C<isl_set_align_params> and C<isl_map_align_params>
2545 =head2 Binary Operations
2547 The two arguments of a binary operation not only need to live
2548 in the same C<isl_ctx>, they currently also need to have
2549 the same (number of) parameters.
2551 =head3 Basic Operations
2555 =item * Intersection
2557 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2558 __isl_take isl_basic_set *bset1,
2559 __isl_take isl_basic_set *bset2);
2560 __isl_give isl_basic_set *isl_basic_set_intersect(
2561 __isl_take isl_basic_set *bset1,
2562 __isl_take isl_basic_set *bset2);
2563 __isl_give isl_set *isl_set_intersect_params(
2564 __isl_take isl_set *set,
2565 __isl_take isl_set *params);
2566 __isl_give isl_set *isl_set_intersect(
2567 __isl_take isl_set *set1,
2568 __isl_take isl_set *set2);
2569 __isl_give isl_union_set *isl_union_set_intersect_params(
2570 __isl_take isl_union_set *uset,
2571 __isl_take isl_set *set);
2572 __isl_give isl_union_map *isl_union_map_intersect_params(
2573 __isl_take isl_union_map *umap,
2574 __isl_take isl_set *set);
2575 __isl_give isl_union_set *isl_union_set_intersect(
2576 __isl_take isl_union_set *uset1,
2577 __isl_take isl_union_set *uset2);
2578 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2579 __isl_take isl_basic_map *bmap,
2580 __isl_take isl_basic_set *bset);
2581 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2582 __isl_take isl_basic_map *bmap,
2583 __isl_take isl_basic_set *bset);
2584 __isl_give isl_basic_map *isl_basic_map_intersect(
2585 __isl_take isl_basic_map *bmap1,
2586 __isl_take isl_basic_map *bmap2);
2587 __isl_give isl_map *isl_map_intersect_params(
2588 __isl_take isl_map *map,
2589 __isl_take isl_set *params);
2590 __isl_give isl_map *isl_map_intersect_domain(
2591 __isl_take isl_map *map,
2592 __isl_take isl_set *set);
2593 __isl_give isl_map *isl_map_intersect_range(
2594 __isl_take isl_map *map,
2595 __isl_take isl_set *set);
2596 __isl_give isl_map *isl_map_intersect(
2597 __isl_take isl_map *map1,
2598 __isl_take isl_map *map2);
2599 __isl_give isl_union_map *isl_union_map_intersect_domain(
2600 __isl_take isl_union_map *umap,
2601 __isl_take isl_union_set *uset);
2602 __isl_give isl_union_map *isl_union_map_intersect_range(
2603 __isl_take isl_union_map *umap,
2604 __isl_take isl_union_set *uset);
2605 __isl_give isl_union_map *isl_union_map_intersect(
2606 __isl_take isl_union_map *umap1,
2607 __isl_take isl_union_map *umap2);
2609 The second argument to the C<_params> functions needs to be
2610 a parametric (basic) set. For the other functions, a parametric set
2611 for either argument is only allowed if the other argument is
2612 a parametric set as well.
2616 __isl_give isl_set *isl_basic_set_union(
2617 __isl_take isl_basic_set *bset1,
2618 __isl_take isl_basic_set *bset2);
2619 __isl_give isl_map *isl_basic_map_union(
2620 __isl_take isl_basic_map *bmap1,
2621 __isl_take isl_basic_map *bmap2);
2622 __isl_give isl_set *isl_set_union(
2623 __isl_take isl_set *set1,
2624 __isl_take isl_set *set2);
2625 __isl_give isl_map *isl_map_union(
2626 __isl_take isl_map *map1,
2627 __isl_take isl_map *map2);
2628 __isl_give isl_union_set *isl_union_set_union(
2629 __isl_take isl_union_set *uset1,
2630 __isl_take isl_union_set *uset2);
2631 __isl_give isl_union_map *isl_union_map_union(
2632 __isl_take isl_union_map *umap1,
2633 __isl_take isl_union_map *umap2);
2635 =item * Set difference
2637 __isl_give isl_set *isl_set_subtract(
2638 __isl_take isl_set *set1,
2639 __isl_take isl_set *set2);
2640 __isl_give isl_map *isl_map_subtract(
2641 __isl_take isl_map *map1,
2642 __isl_take isl_map *map2);
2643 __isl_give isl_map *isl_map_subtract_domain(
2644 __isl_take isl_map *map,
2645 __isl_take isl_set *dom);
2646 __isl_give isl_map *isl_map_subtract_range(
2647 __isl_take isl_map *map,
2648 __isl_take isl_set *dom);
2649 __isl_give isl_union_set *isl_union_set_subtract(
2650 __isl_take isl_union_set *uset1,
2651 __isl_take isl_union_set *uset2);
2652 __isl_give isl_union_map *isl_union_map_subtract(
2653 __isl_take isl_union_map *umap1,
2654 __isl_take isl_union_map *umap2);
2658 __isl_give isl_basic_set *isl_basic_set_apply(
2659 __isl_take isl_basic_set *bset,
2660 __isl_take isl_basic_map *bmap);
2661 __isl_give isl_set *isl_set_apply(
2662 __isl_take isl_set *set,
2663 __isl_take isl_map *map);
2664 __isl_give isl_union_set *isl_union_set_apply(
2665 __isl_take isl_union_set *uset,
2666 __isl_take isl_union_map *umap);
2667 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2668 __isl_take isl_basic_map *bmap1,
2669 __isl_take isl_basic_map *bmap2);
2670 __isl_give isl_basic_map *isl_basic_map_apply_range(
2671 __isl_take isl_basic_map *bmap1,
2672 __isl_take isl_basic_map *bmap2);
2673 __isl_give isl_map *isl_map_apply_domain(
2674 __isl_take isl_map *map1,
2675 __isl_take isl_map *map2);
2676 __isl_give isl_union_map *isl_union_map_apply_domain(
2677 __isl_take isl_union_map *umap1,
2678 __isl_take isl_union_map *umap2);
2679 __isl_give isl_map *isl_map_apply_range(
2680 __isl_take isl_map *map1,
2681 __isl_take isl_map *map2);
2682 __isl_give isl_union_map *isl_union_map_apply_range(
2683 __isl_take isl_union_map *umap1,
2684 __isl_take isl_union_map *umap2);
2686 =item * Cartesian Product
2688 __isl_give isl_set *isl_set_product(
2689 __isl_take isl_set *set1,
2690 __isl_take isl_set *set2);
2691 __isl_give isl_union_set *isl_union_set_product(
2692 __isl_take isl_union_set *uset1,
2693 __isl_take isl_union_set *uset2);
2694 __isl_give isl_basic_map *isl_basic_map_domain_product(
2695 __isl_take isl_basic_map *bmap1,
2696 __isl_take isl_basic_map *bmap2);
2697 __isl_give isl_basic_map *isl_basic_map_range_product(
2698 __isl_take isl_basic_map *bmap1,
2699 __isl_take isl_basic_map *bmap2);
2700 __isl_give isl_basic_map *isl_basic_map_product(
2701 __isl_take isl_basic_map *bmap1,
2702 __isl_take isl_basic_map *bmap2);
2703 __isl_give isl_map *isl_map_domain_product(
2704 __isl_take isl_map *map1,
2705 __isl_take isl_map *map2);
2706 __isl_give isl_map *isl_map_range_product(
2707 __isl_take isl_map *map1,
2708 __isl_take isl_map *map2);
2709 __isl_give isl_union_map *isl_union_map_domain_product(
2710 __isl_take isl_union_map *umap1,
2711 __isl_take isl_union_map *umap2);
2712 __isl_give isl_union_map *isl_union_map_range_product(
2713 __isl_take isl_union_map *umap1,
2714 __isl_take isl_union_map *umap2);
2715 __isl_give isl_map *isl_map_product(
2716 __isl_take isl_map *map1,
2717 __isl_take isl_map *map2);
2718 __isl_give isl_union_map *isl_union_map_product(
2719 __isl_take isl_union_map *umap1,
2720 __isl_take isl_union_map *umap2);
2722 The above functions compute the cross product of the given
2723 sets or relations. The domains and ranges of the results
2724 are wrapped maps between domains and ranges of the inputs.
2725 To obtain a ``flat'' product, use the following functions
2728 __isl_give isl_basic_set *isl_basic_set_flat_product(
2729 __isl_take isl_basic_set *bset1,
2730 __isl_take isl_basic_set *bset2);
2731 __isl_give isl_set *isl_set_flat_product(
2732 __isl_take isl_set *set1,
2733 __isl_take isl_set *set2);
2734 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2735 __isl_take isl_basic_map *bmap1,
2736 __isl_take isl_basic_map *bmap2);
2737 __isl_give isl_map *isl_map_flat_domain_product(
2738 __isl_take isl_map *map1,
2739 __isl_take isl_map *map2);
2740 __isl_give isl_map *isl_map_flat_range_product(
2741 __isl_take isl_map *map1,
2742 __isl_take isl_map *map2);
2743 __isl_give isl_union_map *isl_union_map_flat_range_product(
2744 __isl_take isl_union_map *umap1,
2745 __isl_take isl_union_map *umap2);
2746 __isl_give isl_basic_map *isl_basic_map_flat_product(
2747 __isl_take isl_basic_map *bmap1,
2748 __isl_take isl_basic_map *bmap2);
2749 __isl_give isl_map *isl_map_flat_product(
2750 __isl_take isl_map *map1,
2751 __isl_take isl_map *map2);
2753 =item * Simplification
2755 __isl_give isl_basic_set *isl_basic_set_gist(
2756 __isl_take isl_basic_set *bset,
2757 __isl_take isl_basic_set *context);
2758 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2759 __isl_take isl_set *context);
2760 __isl_give isl_set *isl_set_gist_params(
2761 __isl_take isl_set *set,
2762 __isl_take isl_set *context);
2763 __isl_give isl_union_set *isl_union_set_gist(
2764 __isl_take isl_union_set *uset,
2765 __isl_take isl_union_set *context);
2766 __isl_give isl_union_set *isl_union_set_gist_params(
2767 __isl_take isl_union_set *uset,
2768 __isl_take isl_set *set);
2769 __isl_give isl_basic_map *isl_basic_map_gist(
2770 __isl_take isl_basic_map *bmap,
2771 __isl_take isl_basic_map *context);
2772 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2773 __isl_take isl_map *context);
2774 __isl_give isl_map *isl_map_gist_params(
2775 __isl_take isl_map *map,
2776 __isl_take isl_set *context);
2777 __isl_give isl_map *isl_map_gist_domain(
2778 __isl_take isl_map *map,
2779 __isl_take isl_set *context);
2780 __isl_give isl_map *isl_map_gist_range(
2781 __isl_take isl_map *map,
2782 __isl_take isl_set *context);
2783 __isl_give isl_union_map *isl_union_map_gist(
2784 __isl_take isl_union_map *umap,
2785 __isl_take isl_union_map *context);
2786 __isl_give isl_union_map *isl_union_map_gist_params(
2787 __isl_take isl_union_map *umap,
2788 __isl_take isl_set *set);
2789 __isl_give isl_union_map *isl_union_map_gist_domain(
2790 __isl_take isl_union_map *umap,
2791 __isl_take isl_union_set *uset);
2792 __isl_give isl_union_map *isl_union_map_gist_range(
2793 __isl_take isl_union_map *umap,
2794 __isl_take isl_union_set *uset);
2796 The gist operation returns a set or relation that has the
2797 same intersection with the context as the input set or relation.
2798 Any implicit equality in the intersection is made explicit in the result,
2799 while all inequalities that are redundant with respect to the intersection
2801 In case of union sets and relations, the gist operation is performed
2806 =head3 Lexicographic Optimization
2808 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2809 the following functions
2810 compute a set that contains the lexicographic minimum or maximum
2811 of the elements in C<set> (or C<bset>) for those values of the parameters
2812 that satisfy C<dom>.
2813 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2814 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2816 In other words, the union of the parameter values
2817 for which the result is non-empty and of C<*empty>
2820 __isl_give isl_set *isl_basic_set_partial_lexmin(
2821 __isl_take isl_basic_set *bset,
2822 __isl_take isl_basic_set *dom,
2823 __isl_give isl_set **empty);
2824 __isl_give isl_set *isl_basic_set_partial_lexmax(
2825 __isl_take isl_basic_set *bset,
2826 __isl_take isl_basic_set *dom,
2827 __isl_give isl_set **empty);
2828 __isl_give isl_set *isl_set_partial_lexmin(
2829 __isl_take isl_set *set, __isl_take isl_set *dom,
2830 __isl_give isl_set **empty);
2831 __isl_give isl_set *isl_set_partial_lexmax(
2832 __isl_take isl_set *set, __isl_take isl_set *dom,
2833 __isl_give isl_set **empty);
2835 Given a (basic) set C<set> (or C<bset>), the following functions simply
2836 return a set containing the lexicographic minimum or maximum
2837 of the elements in C<set> (or C<bset>).
2838 In case of union sets, the optimum is computed per space.
2840 __isl_give isl_set *isl_basic_set_lexmin(
2841 __isl_take isl_basic_set *bset);
2842 __isl_give isl_set *isl_basic_set_lexmax(
2843 __isl_take isl_basic_set *bset);
2844 __isl_give isl_set *isl_set_lexmin(
2845 __isl_take isl_set *set);
2846 __isl_give isl_set *isl_set_lexmax(
2847 __isl_take isl_set *set);
2848 __isl_give isl_union_set *isl_union_set_lexmin(
2849 __isl_take isl_union_set *uset);
2850 __isl_give isl_union_set *isl_union_set_lexmax(
2851 __isl_take isl_union_set *uset);
2853 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2854 the following functions
2855 compute a relation that maps each element of C<dom>
2856 to the single lexicographic minimum or maximum
2857 of the elements that are associated to that same
2858 element in C<map> (or C<bmap>).
2859 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2860 that contains the elements in C<dom> that do not map
2861 to any elements in C<map> (or C<bmap>).
2862 In other words, the union of the domain of the result and of C<*empty>
2865 __isl_give isl_map *isl_basic_map_partial_lexmax(
2866 __isl_take isl_basic_map *bmap,
2867 __isl_take isl_basic_set *dom,
2868 __isl_give isl_set **empty);
2869 __isl_give isl_map *isl_basic_map_partial_lexmin(
2870 __isl_take isl_basic_map *bmap,
2871 __isl_take isl_basic_set *dom,
2872 __isl_give isl_set **empty);
2873 __isl_give isl_map *isl_map_partial_lexmax(
2874 __isl_take isl_map *map, __isl_take isl_set *dom,
2875 __isl_give isl_set **empty);
2876 __isl_give isl_map *isl_map_partial_lexmin(
2877 __isl_take isl_map *map, __isl_take isl_set *dom,
2878 __isl_give isl_set **empty);
2880 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2881 return a map mapping each element in the domain of
2882 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2883 of all elements associated to that element.
2884 In case of union relations, the optimum is computed per space.
2886 __isl_give isl_map *isl_basic_map_lexmin(
2887 __isl_take isl_basic_map *bmap);
2888 __isl_give isl_map *isl_basic_map_lexmax(
2889 __isl_take isl_basic_map *bmap);
2890 __isl_give isl_map *isl_map_lexmin(
2891 __isl_take isl_map *map);
2892 __isl_give isl_map *isl_map_lexmax(
2893 __isl_take isl_map *map);
2894 __isl_give isl_union_map *isl_union_map_lexmin(
2895 __isl_take isl_union_map *umap);
2896 __isl_give isl_union_map *isl_union_map_lexmax(
2897 __isl_take isl_union_map *umap);
2899 The following functions return their result in the form of
2900 a piecewise multi-affine expression
2901 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2902 but are otherwise equivalent to the corresponding functions
2903 returning a basic set or relation.
2905 __isl_give isl_pw_multi_aff *
2906 isl_basic_map_lexmin_pw_multi_aff(
2907 __isl_take isl_basic_map *bmap);
2908 __isl_give isl_pw_multi_aff *
2909 isl_basic_set_partial_lexmin_pw_multi_aff(
2910 __isl_take isl_basic_set *bset,
2911 __isl_take isl_basic_set *dom,
2912 __isl_give isl_set **empty);
2913 __isl_give isl_pw_multi_aff *
2914 isl_basic_set_partial_lexmax_pw_multi_aff(
2915 __isl_take isl_basic_set *bset,
2916 __isl_take isl_basic_set *dom,
2917 __isl_give isl_set **empty);
2918 __isl_give isl_pw_multi_aff *
2919 isl_basic_map_partial_lexmin_pw_multi_aff(
2920 __isl_take isl_basic_map *bmap,
2921 __isl_take isl_basic_set *dom,
2922 __isl_give isl_set **empty);
2923 __isl_give isl_pw_multi_aff *
2924 isl_basic_map_partial_lexmax_pw_multi_aff(
2925 __isl_take isl_basic_map *bmap,
2926 __isl_take isl_basic_set *dom,
2927 __isl_give isl_set **empty);
2928 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2929 __isl_take isl_map *map);
2930 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2931 __isl_take isl_map *map);
2935 Lists are defined over several element types, including
2936 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2937 Here we take lists of C<isl_set>s as an example.
2938 Lists can be created, copied, modified and freed using the following functions.
2940 #include <isl/list.h>
2941 __isl_give isl_set_list *isl_set_list_from_set(
2942 __isl_take isl_set *el);
2943 __isl_give isl_set_list *isl_set_list_alloc(
2944 isl_ctx *ctx, int n);
2945 __isl_give isl_set_list *isl_set_list_copy(
2946 __isl_keep isl_set_list *list);
2947 __isl_give isl_set_list *isl_set_list_add(
2948 __isl_take isl_set_list *list,
2949 __isl_take isl_set *el);
2950 __isl_give isl_set_list *isl_set_list_drop(
2951 __isl_take isl_set_list *list,
2952 unsigned first, unsigned n);
2953 __isl_give isl_set_list *isl_set_list_set_set(
2954 __isl_take isl_set_list *list, int index,
2955 __isl_take isl_set *set);
2956 __isl_give isl_set_list *isl_set_list_concat(
2957 __isl_take isl_set_list *list1,
2958 __isl_take isl_set_list *list2);
2959 void *isl_set_list_free(__isl_take isl_set_list *list);
2961 C<isl_set_list_alloc> creates an empty list with a capacity for
2962 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2965 Lists can be inspected using the following functions.
2967 #include <isl/list.h>
2968 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2969 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2970 __isl_give isl_set *isl_set_list_get_set(
2971 __isl_keep isl_set_list *list, int index);
2972 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2973 int (*fn)(__isl_take isl_set *el, void *user),
2976 Lists can be printed using
2978 #include <isl/list.h>
2979 __isl_give isl_printer *isl_printer_print_set_list(
2980 __isl_take isl_printer *p,
2981 __isl_keep isl_set_list *list);
2985 Vectors can be created, copied and freed using the following functions.
2987 #include <isl/vec.h>
2988 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2990 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2991 void *isl_vec_free(__isl_take isl_vec *vec);
2993 Note that the elements of a newly created vector may have arbitrary values.
2994 The elements can be changed and inspected using the following functions.
2996 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2997 int isl_vec_size(__isl_keep isl_vec *vec);
2998 int isl_vec_get_element(__isl_keep isl_vec *vec,
2999 int pos, isl_int *v);
3000 __isl_give isl_vec *isl_vec_set_element(
3001 __isl_take isl_vec *vec, int pos, isl_int v);
3002 __isl_give isl_vec *isl_vec_set_element_si(
3003 __isl_take isl_vec *vec, int pos, int v);
3004 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3006 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3009 C<isl_vec_get_element> will return a negative value if anything went wrong.
3010 In that case, the value of C<*v> is undefined.
3012 The following function can be used to concatenate two vectors.
3014 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3015 __isl_take isl_vec *vec2);
3019 Matrices can be created, copied and freed using the following functions.
3021 #include <isl/mat.h>
3022 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3023 unsigned n_row, unsigned n_col);
3024 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3025 void isl_mat_free(__isl_take isl_mat *mat);
3027 Note that the elements of a newly created matrix may have arbitrary values.
3028 The elements can be changed and inspected using the following functions.
3030 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3031 int isl_mat_rows(__isl_keep isl_mat *mat);
3032 int isl_mat_cols(__isl_keep isl_mat *mat);
3033 int isl_mat_get_element(__isl_keep isl_mat *mat,
3034 int row, int col, isl_int *v);
3035 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3036 int row, int col, isl_int v);
3037 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3038 int row, int col, int v);
3040 C<isl_mat_get_element> will return a negative value if anything went wrong.
3041 In that case, the value of C<*v> is undefined.
3043 The following function can be used to compute the (right) inverse
3044 of a matrix, i.e., a matrix such that the product of the original
3045 and the inverse (in that order) is a multiple of the identity matrix.
3046 The input matrix is assumed to be of full row-rank.
3048 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3050 The following function can be used to compute the (right) kernel
3051 (or null space) of a matrix, i.e., a matrix such that the product of
3052 the original and the kernel (in that order) is the zero matrix.
3054 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3056 =head2 Piecewise Quasi Affine Expressions
3058 The zero quasi affine expression on a given domain can be created using
3060 __isl_give isl_aff *isl_aff_zero_on_domain(
3061 __isl_take isl_local_space *ls);
3063 Note that the space in which the resulting object lives is a map space
3064 with the given space as domain and a one-dimensional range.
3066 An empty piecewise quasi affine expression (one with no cells)
3067 or a piecewise quasi affine expression with a single cell can
3068 be created using the following functions.
3070 #include <isl/aff.h>
3071 __isl_give isl_pw_aff *isl_pw_aff_empty(
3072 __isl_take isl_space *space);
3073 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3074 __isl_take isl_set *set, __isl_take isl_aff *aff);
3075 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3076 __isl_take isl_aff *aff);
3078 A piecewise quasi affine expression that is equal to 1 on a set
3079 and 0 outside the set can be created using the following function.
3081 #include <isl/aff.h>
3082 __isl_give isl_pw_aff *isl_set_indicator_function(
3083 __isl_take isl_set *set);
3085 Quasi affine expressions can be copied and freed using
3087 #include <isl/aff.h>
3088 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3089 void *isl_aff_free(__isl_take isl_aff *aff);
3091 __isl_give isl_pw_aff *isl_pw_aff_copy(
3092 __isl_keep isl_pw_aff *pwaff);
3093 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3095 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3096 using the following function. The constraint is required to have
3097 a non-zero coefficient for the specified dimension.
3099 #include <isl/constraint.h>
3100 __isl_give isl_aff *isl_constraint_get_bound(
3101 __isl_keep isl_constraint *constraint,
3102 enum isl_dim_type type, int pos);
3104 The entire affine expression of the constraint can also be extracted
3105 using the following function.
3107 #include <isl/constraint.h>
3108 __isl_give isl_aff *isl_constraint_get_aff(
3109 __isl_keep isl_constraint *constraint);
3111 Conversely, an equality constraint equating
3112 the affine expression to zero or an inequality constraint enforcing
3113 the affine expression to be non-negative, can be constructed using
3115 __isl_give isl_constraint *isl_equality_from_aff(
3116 __isl_take isl_aff *aff);
3117 __isl_give isl_constraint *isl_inequality_from_aff(
3118 __isl_take isl_aff *aff);
3120 The expression can be inspected using
3122 #include <isl/aff.h>
3123 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3124 int isl_aff_dim(__isl_keep isl_aff *aff,
3125 enum isl_dim_type type);
3126 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3127 __isl_keep isl_aff *aff);
3128 __isl_give isl_local_space *isl_aff_get_local_space(
3129 __isl_keep isl_aff *aff);
3130 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3131 enum isl_dim_type type, unsigned pos);
3132 const char *isl_pw_aff_get_dim_name(
3133 __isl_keep isl_pw_aff *pa,
3134 enum isl_dim_type type, unsigned pos);
3135 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3136 enum isl_dim_type type, unsigned pos);
3137 __isl_give isl_id *isl_pw_aff_get_dim_id(
3138 __isl_keep isl_pw_aff *pa,
3139 enum isl_dim_type type, unsigned pos);
3140 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3141 __isl_keep isl_pw_aff *pa,
3142 enum isl_dim_type type);
3143 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3145 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3146 enum isl_dim_type type, int pos, isl_int *v);
3147 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3149 __isl_give isl_aff *isl_aff_get_div(
3150 __isl_keep isl_aff *aff, int pos);
3152 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3153 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3154 int (*fn)(__isl_take isl_set *set,
3155 __isl_take isl_aff *aff,
3156 void *user), void *user);
3158 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3159 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3161 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3162 enum isl_dim_type type, unsigned first, unsigned n);
3163 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3164 enum isl_dim_type type, unsigned first, unsigned n);
3166 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3167 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3168 enum isl_dim_type type);
3169 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3171 It can be modified using
3173 #include <isl/aff.h>
3174 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3175 __isl_take isl_pw_aff *pwaff,
3176 enum isl_dim_type type, __isl_take isl_id *id);
3177 __isl_give isl_aff *isl_aff_set_dim_name(
3178 __isl_take isl_aff *aff, enum isl_dim_type type,
3179 unsigned pos, const char *s);
3180 __isl_give isl_aff *isl_aff_set_dim_id(
3181 __isl_take isl_aff *aff, enum isl_dim_type type,
3182 unsigned pos, __isl_take isl_id *id);
3183 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3184 __isl_take isl_pw_aff *pma,
3185 enum isl_dim_type type, unsigned pos,
3186 __isl_take isl_id *id);
3187 __isl_give isl_aff *isl_aff_set_constant(
3188 __isl_take isl_aff *aff, isl_int v);
3189 __isl_give isl_aff *isl_aff_set_constant_si(
3190 __isl_take isl_aff *aff, int v);
3191 __isl_give isl_aff *isl_aff_set_coefficient(
3192 __isl_take isl_aff *aff,
3193 enum isl_dim_type type, int pos, isl_int v);
3194 __isl_give isl_aff *isl_aff_set_coefficient_si(
3195 __isl_take isl_aff *aff,
3196 enum isl_dim_type type, int pos, int v);
3197 __isl_give isl_aff *isl_aff_set_denominator(
3198 __isl_take isl_aff *aff, isl_int v);
3200 __isl_give isl_aff *isl_aff_add_constant(
3201 __isl_take isl_aff *aff, isl_int v);
3202 __isl_give isl_aff *isl_aff_add_constant_si(
3203 __isl_take isl_aff *aff, int v);
3204 __isl_give isl_aff *isl_aff_add_constant_num(
3205 __isl_take isl_aff *aff, isl_int v);
3206 __isl_give isl_aff *isl_aff_add_constant_num_si(
3207 __isl_take isl_aff *aff, int v);
3208 __isl_give isl_aff *isl_aff_add_coefficient(
3209 __isl_take isl_aff *aff,
3210 enum isl_dim_type type, int pos, isl_int v);
3211 __isl_give isl_aff *isl_aff_add_coefficient_si(
3212 __isl_take isl_aff *aff,
3213 enum isl_dim_type type, int pos, int v);
3215 __isl_give isl_aff *isl_aff_insert_dims(
3216 __isl_take isl_aff *aff,
3217 enum isl_dim_type type, unsigned first, unsigned n);
3218 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3219 __isl_take isl_pw_aff *pwaff,
3220 enum isl_dim_type type, unsigned first, unsigned n);
3221 __isl_give isl_aff *isl_aff_add_dims(
3222 __isl_take isl_aff *aff,
3223 enum isl_dim_type type, unsigned n);
3224 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3225 __isl_take isl_pw_aff *pwaff,
3226 enum isl_dim_type type, unsigned n);
3227 __isl_give isl_aff *isl_aff_drop_dims(
3228 __isl_take isl_aff *aff,
3229 enum isl_dim_type type, unsigned first, unsigned n);
3230 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3231 __isl_take isl_pw_aff *pwaff,
3232 enum isl_dim_type type, unsigned first, unsigned n);
3234 Note that the C<set_constant> and C<set_coefficient> functions
3235 set the I<numerator> of the constant or coefficient, while
3236 C<add_constant> and C<add_coefficient> add an integer value to
3237 the possibly rational constant or coefficient.
3238 The C<add_constant_num> functions add an integer value to
3241 To check whether an affine expressions is obviously zero
3242 or obviously equal to some other affine expression, use
3244 #include <isl/aff.h>
3245 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3246 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3247 __isl_keep isl_aff *aff2);
3248 int isl_pw_aff_plain_is_equal(
3249 __isl_keep isl_pw_aff *pwaff1,
3250 __isl_keep isl_pw_aff *pwaff2);
3254 #include <isl/aff.h>
3255 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3256 __isl_take isl_aff *aff2);
3257 __isl_give isl_pw_aff *isl_pw_aff_add(
3258 __isl_take isl_pw_aff *pwaff1,
3259 __isl_take isl_pw_aff *pwaff2);
3260 __isl_give isl_pw_aff *isl_pw_aff_min(
3261 __isl_take isl_pw_aff *pwaff1,
3262 __isl_take isl_pw_aff *pwaff2);
3263 __isl_give isl_pw_aff *isl_pw_aff_max(
3264 __isl_take isl_pw_aff *pwaff1,
3265 __isl_take isl_pw_aff *pwaff2);
3266 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3267 __isl_take isl_aff *aff2);
3268 __isl_give isl_pw_aff *isl_pw_aff_sub(
3269 __isl_take isl_pw_aff *pwaff1,
3270 __isl_take isl_pw_aff *pwaff2);
3271 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3272 __isl_give isl_pw_aff *isl_pw_aff_neg(
3273 __isl_take isl_pw_aff *pwaff);
3274 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3275 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3276 __isl_take isl_pw_aff *pwaff);
3277 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3278 __isl_give isl_pw_aff *isl_pw_aff_floor(
3279 __isl_take isl_pw_aff *pwaff);
3280 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3282 __isl_give isl_pw_aff *isl_pw_aff_mod(
3283 __isl_take isl_pw_aff *pwaff, isl_int mod);
3284 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3286 __isl_give isl_pw_aff *isl_pw_aff_scale(
3287 __isl_take isl_pw_aff *pwaff, isl_int f);
3288 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3290 __isl_give isl_aff *isl_aff_scale_down_ui(
3291 __isl_take isl_aff *aff, unsigned f);
3292 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3293 __isl_take isl_pw_aff *pwaff, isl_int f);
3295 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3296 __isl_take isl_pw_aff_list *list);
3297 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3298 __isl_take isl_pw_aff_list *list);
3300 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3301 __isl_take isl_pw_aff *pwqp);
3303 __isl_give isl_aff *isl_aff_align_params(
3304 __isl_take isl_aff *aff,
3305 __isl_take isl_space *model);
3306 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3307 __isl_take isl_pw_aff *pwaff,
3308 __isl_take isl_space *model);
3310 __isl_give isl_aff *isl_aff_project_domain_on_params(
3311 __isl_take isl_aff *aff);
3313 __isl_give isl_aff *isl_aff_gist_params(
3314 __isl_take isl_aff *aff,
3315 __isl_take isl_set *context);
3316 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3317 __isl_take isl_set *context);
3318 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3319 __isl_take isl_pw_aff *pwaff,
3320 __isl_take isl_set *context);
3321 __isl_give isl_pw_aff *isl_pw_aff_gist(
3322 __isl_take isl_pw_aff *pwaff,
3323 __isl_take isl_set *context);
3325 __isl_give isl_set *isl_pw_aff_domain(
3326 __isl_take isl_pw_aff *pwaff);
3327 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3328 __isl_take isl_pw_aff *pa,
3329 __isl_take isl_set *set);
3330 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3331 __isl_take isl_pw_aff *pa,
3332 __isl_take isl_set *set);
3334 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3335 __isl_take isl_aff *aff2);
3336 __isl_give isl_pw_aff *isl_pw_aff_mul(
3337 __isl_take isl_pw_aff *pwaff1,
3338 __isl_take isl_pw_aff *pwaff2);
3340 When multiplying two affine expressions, at least one of the two needs
3343 #include <isl/aff.h>
3344 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3345 __isl_take isl_aff *aff);
3346 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3347 __isl_take isl_aff *aff);
3348 __isl_give isl_basic_set *isl_aff_le_basic_set(
3349 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3350 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3351 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3352 __isl_give isl_set *isl_pw_aff_eq_set(
3353 __isl_take isl_pw_aff *pwaff1,
3354 __isl_take isl_pw_aff *pwaff2);
3355 __isl_give isl_set *isl_pw_aff_ne_set(
3356 __isl_take isl_pw_aff *pwaff1,
3357 __isl_take isl_pw_aff *pwaff2);
3358 __isl_give isl_set *isl_pw_aff_le_set(
3359 __isl_take isl_pw_aff *pwaff1,
3360 __isl_take isl_pw_aff *pwaff2);
3361 __isl_give isl_set *isl_pw_aff_lt_set(
3362 __isl_take isl_pw_aff *pwaff1,
3363 __isl_take isl_pw_aff *pwaff2);
3364 __isl_give isl_set *isl_pw_aff_ge_set(
3365 __isl_take isl_pw_aff *pwaff1,
3366 __isl_take isl_pw_aff *pwaff2);
3367 __isl_give isl_set *isl_pw_aff_gt_set(
3368 __isl_take isl_pw_aff *pwaff1,
3369 __isl_take isl_pw_aff *pwaff2);
3371 __isl_give isl_set *isl_pw_aff_list_eq_set(
3372 __isl_take isl_pw_aff_list *list1,
3373 __isl_take isl_pw_aff_list *list2);
3374 __isl_give isl_set *isl_pw_aff_list_ne_set(
3375 __isl_take isl_pw_aff_list *list1,
3376 __isl_take isl_pw_aff_list *list2);
3377 __isl_give isl_set *isl_pw_aff_list_le_set(
3378 __isl_take isl_pw_aff_list *list1,
3379 __isl_take isl_pw_aff_list *list2);
3380 __isl_give isl_set *isl_pw_aff_list_lt_set(
3381 __isl_take isl_pw_aff_list *list1,
3382 __isl_take isl_pw_aff_list *list2);
3383 __isl_give isl_set *isl_pw_aff_list_ge_set(
3384 __isl_take isl_pw_aff_list *list1,
3385 __isl_take isl_pw_aff_list *list2);
3386 __isl_give isl_set *isl_pw_aff_list_gt_set(
3387 __isl_take isl_pw_aff_list *list1,
3388 __isl_take isl_pw_aff_list *list2);
3390 The function C<isl_aff_neg_basic_set> returns a basic set
3391 containing those elements in the domain space
3392 of C<aff> where C<aff> is negative.
3393 The function C<isl_aff_ge_basic_set> returns a basic set
3394 containing those elements in the shared space
3395 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3396 The function C<isl_pw_aff_ge_set> returns a set
3397 containing those elements in the shared domain
3398 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3399 The functions operating on C<isl_pw_aff_list> apply the corresponding
3400 C<isl_pw_aff> function to each pair of elements in the two lists.
3402 #include <isl/aff.h>
3403 __isl_give isl_set *isl_pw_aff_nonneg_set(
3404 __isl_take isl_pw_aff *pwaff);
3405 __isl_give isl_set *isl_pw_aff_zero_set(
3406 __isl_take isl_pw_aff *pwaff);
3407 __isl_give isl_set *isl_pw_aff_non_zero_set(
3408 __isl_take isl_pw_aff *pwaff);
3410 The function C<isl_pw_aff_nonneg_set> returns a set
3411 containing those elements in the domain
3412 of C<pwaff> where C<pwaff> is non-negative.
3414 #include <isl/aff.h>
3415 __isl_give isl_pw_aff *isl_pw_aff_cond(
3416 __isl_take isl_pw_aff *cond,
3417 __isl_take isl_pw_aff *pwaff_true,
3418 __isl_take isl_pw_aff *pwaff_false);
3420 The function C<isl_pw_aff_cond> performs a conditional operator
3421 and returns an expression that is equal to C<pwaff_true>
3422 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3423 where C<cond> is zero.
3425 #include <isl/aff.h>
3426 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3427 __isl_take isl_pw_aff *pwaff1,
3428 __isl_take isl_pw_aff *pwaff2);
3429 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3430 __isl_take isl_pw_aff *pwaff1,
3431 __isl_take isl_pw_aff *pwaff2);
3432 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3433 __isl_take isl_pw_aff *pwaff1,
3434 __isl_take isl_pw_aff *pwaff2);
3436 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3437 expression with a domain that is the union of those of C<pwaff1> and
3438 C<pwaff2> and such that on each cell, the quasi-affine expression is
3439 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3440 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3441 associated expression is the defined one.
3443 An expression can be read from input using
3445 #include <isl/aff.h>
3446 __isl_give isl_aff *isl_aff_read_from_str(
3447 isl_ctx *ctx, const char *str);
3448 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3449 isl_ctx *ctx, const char *str);
3451 An expression can be printed using
3453 #include <isl/aff.h>
3454 __isl_give isl_printer *isl_printer_print_aff(
3455 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3457 __isl_give isl_printer *isl_printer_print_pw_aff(
3458 __isl_take isl_printer *p,
3459 __isl_keep isl_pw_aff *pwaff);
3461 =head2 Piecewise Multiple Quasi Affine Expressions
3463 An C<isl_multi_aff> object represents a sequence of
3464 zero or more affine expressions, all defined on the same domain space.
3466 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3469 #include <isl/aff.h>
3470 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3471 __isl_take isl_space *space,
3472 __isl_take isl_aff_list *list);
3474 An empty piecewise multiple quasi affine expression (one with no cells),
3475 the zero piecewise multiple quasi affine expression (with value zero
3476 for each output dimension),
3477 a piecewise multiple quasi affine expression with a single cell (with
3478 either a universe or a specified domain) or
3479 a zero-dimensional piecewise multiple quasi affine expression
3481 can be created using the following functions.
3483 #include <isl/aff.h>
3484 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3485 __isl_take isl_space *space);
3486 __isl_give isl_multi_aff *isl_multi_aff_zero(
3487 __isl_take isl_space *space);
3488 __isl_give isl_multi_aff *isl_multi_aff_identity(
3489 __isl_take isl_space *space);
3490 __isl_give isl_pw_multi_aff *
3491 isl_pw_multi_aff_from_multi_aff(
3492 __isl_take isl_multi_aff *ma);
3493 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3494 __isl_take isl_set *set,
3495 __isl_take isl_multi_aff *maff);
3496 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3497 __isl_take isl_set *set);
3499 __isl_give isl_union_pw_multi_aff *
3500 isl_union_pw_multi_aff_empty(
3501 __isl_take isl_space *space);
3502 __isl_give isl_union_pw_multi_aff *
3503 isl_union_pw_multi_aff_add_pw_multi_aff(
3504 __isl_take isl_union_pw_multi_aff *upma,
3505 __isl_take isl_pw_multi_aff *pma);
3506 __isl_give isl_union_pw_multi_aff *
3507 isl_union_pw_multi_aff_from_domain(
3508 __isl_take isl_union_set *uset);
3510 A piecewise multiple quasi affine expression can also be initialized
3511 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3512 and the C<isl_map> is single-valued.
3514 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3515 __isl_take isl_set *set);
3516 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3517 __isl_take isl_map *map);
3519 Multiple quasi affine expressions can be copied and freed using
3521 #include <isl/aff.h>
3522 __isl_give isl_multi_aff *isl_multi_aff_copy(
3523 __isl_keep isl_multi_aff *maff);
3524 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3526 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3527 __isl_keep isl_pw_multi_aff *pma);
3528 void *isl_pw_multi_aff_free(
3529 __isl_take isl_pw_multi_aff *pma);
3531 __isl_give isl_union_pw_multi_aff *
3532 isl_union_pw_multi_aff_copy(
3533 __isl_keep isl_union_pw_multi_aff *upma);
3534 void *isl_union_pw_multi_aff_free(
3535 __isl_take isl_union_pw_multi_aff *upma);
3537 The expression can be inspected using
3539 #include <isl/aff.h>
3540 isl_ctx *isl_multi_aff_get_ctx(
3541 __isl_keep isl_multi_aff *maff);
3542 isl_ctx *isl_pw_multi_aff_get_ctx(
3543 __isl_keep isl_pw_multi_aff *pma);
3544 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3545 __isl_keep isl_union_pw_multi_aff *upma);
3546 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3547 enum isl_dim_type type);
3548 unsigned isl_pw_multi_aff_dim(
3549 __isl_keep isl_pw_multi_aff *pma,
3550 enum isl_dim_type type);
3551 __isl_give isl_aff *isl_multi_aff_get_aff(
3552 __isl_keep isl_multi_aff *multi, int pos);
3553 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3554 __isl_keep isl_pw_multi_aff *pma, int pos);
3555 const char *isl_pw_multi_aff_get_dim_name(
3556 __isl_keep isl_pw_multi_aff *pma,
3557 enum isl_dim_type type, unsigned pos);
3558 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3559 __isl_keep isl_pw_multi_aff *pma,
3560 enum isl_dim_type type, unsigned pos);
3561 const char *isl_multi_aff_get_tuple_name(
3562 __isl_keep isl_multi_aff *multi,
3563 enum isl_dim_type type);
3564 int isl_pw_multi_aff_has_tuple_name(
3565 __isl_keep isl_pw_multi_aff *pma,
3566 enum isl_dim_type type);
3567 const char *isl_pw_multi_aff_get_tuple_name(
3568 __isl_keep isl_pw_multi_aff *pma,
3569 enum isl_dim_type type);
3570 int isl_pw_multi_aff_has_tuple_id(
3571 __isl_keep isl_pw_multi_aff *pma,
3572 enum isl_dim_type type);
3573 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3574 __isl_keep isl_pw_multi_aff *pma,
3575 enum isl_dim_type type);
3577 int isl_pw_multi_aff_foreach_piece(
3578 __isl_keep isl_pw_multi_aff *pma,
3579 int (*fn)(__isl_take isl_set *set,
3580 __isl_take isl_multi_aff *maff,
3581 void *user), void *user);
3583 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3584 __isl_keep isl_union_pw_multi_aff *upma,
3585 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3586 void *user), void *user);
3588 It can be modified using
3590 #include <isl/aff.h>
3591 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3592 __isl_take isl_multi_aff *multi, int pos,
3593 __isl_take isl_aff *aff);
3594 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3595 __isl_take isl_multi_aff *maff,
3596 enum isl_dim_type type, unsigned pos, const char *s);
3597 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3598 __isl_take isl_multi_aff *maff,
3599 enum isl_dim_type type, __isl_take isl_id *id);
3600 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3601 __isl_take isl_pw_multi_aff *pma,
3602 enum isl_dim_type type, __isl_take isl_id *id);
3604 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3605 __isl_take isl_multi_aff *maff,
3606 enum isl_dim_type type, unsigned first, unsigned n);
3607 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3608 __isl_take isl_pw_multi_aff *pma,
3609 enum isl_dim_type type, unsigned first, unsigned n);
3611 To check whether two multiple affine expressions are
3612 obviously equal to each other, use
3614 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3615 __isl_keep isl_multi_aff *maff2);
3616 int isl_pw_multi_aff_plain_is_equal(
3617 __isl_keep isl_pw_multi_aff *pma1,
3618 __isl_keep isl_pw_multi_aff *pma2);
3622 #include <isl/aff.h>
3623 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3624 __isl_take isl_pw_multi_aff *pma1,
3625 __isl_take isl_pw_multi_aff *pma2);
3626 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3627 __isl_take isl_pw_multi_aff *pma1,
3628 __isl_take isl_pw_multi_aff *pma2);
3629 __isl_give isl_multi_aff *isl_multi_aff_add(
3630 __isl_take isl_multi_aff *maff1,
3631 __isl_take isl_multi_aff *maff2);
3632 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3633 __isl_take isl_pw_multi_aff *pma1,
3634 __isl_take isl_pw_multi_aff *pma2);
3635 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3636 __isl_take isl_union_pw_multi_aff *upma1,
3637 __isl_take isl_union_pw_multi_aff *upma2);
3638 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3639 __isl_take isl_pw_multi_aff *pma1,
3640 __isl_take isl_pw_multi_aff *pma2);
3641 __isl_give isl_multi_aff *isl_multi_aff_scale(
3642 __isl_take isl_multi_aff *maff,
3644 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3645 __isl_take isl_pw_multi_aff *pma,
3646 __isl_take isl_set *set);
3647 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3648 __isl_take isl_pw_multi_aff *pma,
3649 __isl_take isl_set *set);
3650 __isl_give isl_multi_aff *isl_multi_aff_lift(
3651 __isl_take isl_multi_aff *maff,
3652 __isl_give isl_local_space **ls);
3653 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3654 __isl_take isl_pw_multi_aff *pma);
3655 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3656 __isl_take isl_multi_aff *multi,
3657 __isl_take isl_space *model);
3658 __isl_give isl_pw_multi_aff *
3659 isl_pw_multi_aff_project_domain_on_params(
3660 __isl_take isl_pw_multi_aff *pma);
3661 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3662 __isl_take isl_multi_aff *maff,
3663 __isl_take isl_set *context);
3664 __isl_give isl_multi_aff *isl_multi_aff_gist(
3665 __isl_take isl_multi_aff *maff,
3666 __isl_take isl_set *context);
3667 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3668 __isl_take isl_pw_multi_aff *pma,
3669 __isl_take isl_set *set);
3670 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3671 __isl_take isl_pw_multi_aff *pma,
3672 __isl_take isl_set *set);
3673 __isl_give isl_set *isl_pw_multi_aff_domain(
3674 __isl_take isl_pw_multi_aff *pma);
3675 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3676 __isl_take isl_union_pw_multi_aff *upma);
3677 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3678 __isl_take isl_multi_aff *ma1,
3679 __isl_take isl_multi_aff *ma2);
3680 __isl_give isl_multi_aff *isl_multi_aff_product(
3681 __isl_take isl_multi_aff *ma1,
3682 __isl_take isl_multi_aff *ma2);
3683 __isl_give isl_pw_multi_aff *
3684 isl_pw_multi_aff_flat_range_product(
3685 __isl_take isl_pw_multi_aff *pma1,
3686 __isl_take isl_pw_multi_aff *pma2);
3687 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3688 __isl_take isl_pw_multi_aff *pma1,
3689 __isl_take isl_pw_multi_aff *pma2);
3690 __isl_give isl_union_pw_multi_aff *
3691 isl_union_pw_multi_aff_flat_range_product(
3692 __isl_take isl_union_pw_multi_aff *upma1,
3693 __isl_take isl_union_pw_multi_aff *upma2);
3695 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3696 then it is assigned the local space that lies at the basis of
3697 the lifting applied.
3699 __isl_give isl_set *isl_multi_aff_lex_le_set(
3700 __isl_take isl_multi_aff *ma1,
3701 __isl_take isl_multi_aff *ma2);
3702 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3703 __isl_take isl_multi_aff *ma1,
3704 __isl_take isl_multi_aff *ma2);
3706 The function C<isl_multi_aff_lex_le_set> returns a set
3707 containing those elements in the shared domain space
3708 where C<ma1> is lexicographically smaller than or
3711 An expression can be read from input using
3713 #include <isl/aff.h>
3714 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3715 isl_ctx *ctx, const char *str);
3716 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3717 isl_ctx *ctx, const char *str);
3719 An expression can be printed using
3721 #include <isl/aff.h>
3722 __isl_give isl_printer *isl_printer_print_multi_aff(
3723 __isl_take isl_printer *p,
3724 __isl_keep isl_multi_aff *maff);
3725 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3726 __isl_take isl_printer *p,
3727 __isl_keep isl_pw_multi_aff *pma);
3728 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3729 __isl_take isl_printer *p,
3730 __isl_keep isl_union_pw_multi_aff *upma);
3734 Points are elements of a set. They can be used to construct
3735 simple sets (boxes) or they can be used to represent the
3736 individual elements of a set.
3737 The zero point (the origin) can be created using
3739 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3741 The coordinates of a point can be inspected, set and changed
3744 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3745 enum isl_dim_type type, int pos, isl_int *v);
3746 __isl_give isl_point *isl_point_set_coordinate(
3747 __isl_take isl_point *pnt,
3748 enum isl_dim_type type, int pos, isl_int v);
3750 __isl_give isl_point *isl_point_add_ui(
3751 __isl_take isl_point *pnt,
3752 enum isl_dim_type type, int pos, unsigned val);
3753 __isl_give isl_point *isl_point_sub_ui(
3754 __isl_take isl_point *pnt,
3755 enum isl_dim_type type, int pos, unsigned val);
3757 Other properties can be obtained using
3759 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3761 Points can be copied or freed using
3763 __isl_give isl_point *isl_point_copy(
3764 __isl_keep isl_point *pnt);
3765 void isl_point_free(__isl_take isl_point *pnt);
3767 A singleton set can be created from a point using
3769 __isl_give isl_basic_set *isl_basic_set_from_point(
3770 __isl_take isl_point *pnt);
3771 __isl_give isl_set *isl_set_from_point(
3772 __isl_take isl_point *pnt);
3774 and a box can be created from two opposite extremal points using
3776 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3777 __isl_take isl_point *pnt1,
3778 __isl_take isl_point *pnt2);
3779 __isl_give isl_set *isl_set_box_from_points(
3780 __isl_take isl_point *pnt1,
3781 __isl_take isl_point *pnt2);
3783 All elements of a B<bounded> (union) set can be enumerated using
3784 the following functions.
3786 int isl_set_foreach_point(__isl_keep isl_set *set,
3787 int (*fn)(__isl_take isl_point *pnt, void *user),
3789 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3790 int (*fn)(__isl_take isl_point *pnt, void *user),
3793 The function C<fn> is called for each integer point in
3794 C<set> with as second argument the last argument of
3795 the C<isl_set_foreach_point> call. The function C<fn>
3796 should return C<0> on success and C<-1> on failure.
3797 In the latter case, C<isl_set_foreach_point> will stop
3798 enumerating and return C<-1> as well.
3799 If the enumeration is performed successfully and to completion,
3800 then C<isl_set_foreach_point> returns C<0>.
3802 To obtain a single point of a (basic) set, use
3804 __isl_give isl_point *isl_basic_set_sample_point(
3805 __isl_take isl_basic_set *bset);
3806 __isl_give isl_point *isl_set_sample_point(
3807 __isl_take isl_set *set);
3809 If C<set> does not contain any (integer) points, then the
3810 resulting point will be ``void'', a property that can be
3813 int isl_point_is_void(__isl_keep isl_point *pnt);
3815 =head2 Piecewise Quasipolynomials
3817 A piecewise quasipolynomial is a particular kind of function that maps
3818 a parametric point to a rational value.
3819 More specifically, a quasipolynomial is a polynomial expression in greatest
3820 integer parts of affine expressions of parameters and variables.
3821 A piecewise quasipolynomial is a subdivision of a given parametric
3822 domain into disjoint cells with a quasipolynomial associated to
3823 each cell. The value of the piecewise quasipolynomial at a given
3824 point is the value of the quasipolynomial associated to the cell
3825 that contains the point. Outside of the union of cells,
3826 the value is assumed to be zero.
3827 For example, the piecewise quasipolynomial
3829 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3831 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3832 A given piecewise quasipolynomial has a fixed domain dimension.
3833 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3834 defined over different domains.
3835 Piecewise quasipolynomials are mainly used by the C<barvinok>
3836 library for representing the number of elements in a parametric set or map.
3837 For example, the piecewise quasipolynomial above represents
3838 the number of points in the map
3840 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3842 =head3 Input and Output
3844 Piecewise quasipolynomials can be read from input using
3846 __isl_give isl_union_pw_qpolynomial *
3847 isl_union_pw_qpolynomial_read_from_str(
3848 isl_ctx *ctx, const char *str);
3850 Quasipolynomials and piecewise quasipolynomials can be printed
3851 using the following functions.
3853 __isl_give isl_printer *isl_printer_print_qpolynomial(
3854 __isl_take isl_printer *p,
3855 __isl_keep isl_qpolynomial *qp);
3857 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3858 __isl_take isl_printer *p,
3859 __isl_keep isl_pw_qpolynomial *pwqp);
3861 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3862 __isl_take isl_printer *p,
3863 __isl_keep isl_union_pw_qpolynomial *upwqp);
3865 The output format of the printer
3866 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3867 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3869 In case of printing in C<ISL_FORMAT_C>, the user may want
3870 to set the names of all dimensions
3872 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3873 __isl_take isl_qpolynomial *qp,
3874 enum isl_dim_type type, unsigned pos,
3876 __isl_give isl_pw_qpolynomial *
3877 isl_pw_qpolynomial_set_dim_name(
3878 __isl_take isl_pw_qpolynomial *pwqp,
3879 enum isl_dim_type type, unsigned pos,
3882 =head3 Creating New (Piecewise) Quasipolynomials
3884 Some simple quasipolynomials can be created using the following functions.
3885 More complicated quasipolynomials can be created by applying
3886 operations such as addition and multiplication
3887 on the resulting quasipolynomials
3889 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3890 __isl_take isl_space *domain);
3891 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3892 __isl_take isl_space *domain);
3893 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3894 __isl_take isl_space *domain);
3895 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3896 __isl_take isl_space *domain);
3897 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3898 __isl_take isl_space *domain);
3899 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3900 __isl_take isl_space *domain,
3901 const isl_int n, const isl_int d);
3902 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3903 __isl_take isl_space *domain,
3904 enum isl_dim_type type, unsigned pos);
3905 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3906 __isl_take isl_aff *aff);
3908 Note that the space in which a quasipolynomial lives is a map space
3909 with a one-dimensional range. The C<domain> argument in some of
3910 the functions above corresponds to the domain of this map space.
3912 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3913 with a single cell can be created using the following functions.
3914 Multiple of these single cell piecewise quasipolynomials can
3915 be combined to create more complicated piecewise quasipolynomials.
3917 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3918 __isl_take isl_space *space);
3919 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3920 __isl_take isl_set *set,
3921 __isl_take isl_qpolynomial *qp);
3922 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3923 __isl_take isl_qpolynomial *qp);
3924 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3925 __isl_take isl_pw_aff *pwaff);
3927 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3928 __isl_take isl_space *space);
3929 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3930 __isl_take isl_pw_qpolynomial *pwqp);
3931 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3932 __isl_take isl_union_pw_qpolynomial *upwqp,
3933 __isl_take isl_pw_qpolynomial *pwqp);
3935 Quasipolynomials can be copied and freed again using the following
3938 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3939 __isl_keep isl_qpolynomial *qp);
3940 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3942 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3943 __isl_keep isl_pw_qpolynomial *pwqp);
3944 void *isl_pw_qpolynomial_free(
3945 __isl_take isl_pw_qpolynomial *pwqp);
3947 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3948 __isl_keep isl_union_pw_qpolynomial *upwqp);
3949 void *isl_union_pw_qpolynomial_free(
3950 __isl_take isl_union_pw_qpolynomial *upwqp);
3952 =head3 Inspecting (Piecewise) Quasipolynomials
3954 To iterate over all piecewise quasipolynomials in a union
3955 piecewise quasipolynomial, use the following function
3957 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3958 __isl_keep isl_union_pw_qpolynomial *upwqp,
3959 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3962 To extract the piecewise quasipolynomial in a given space from a union, use
3964 __isl_give isl_pw_qpolynomial *
3965 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3966 __isl_keep isl_union_pw_qpolynomial *upwqp,
3967 __isl_take isl_space *space);
3969 To iterate over the cells in a piecewise quasipolynomial,
3970 use either of the following two functions
3972 int isl_pw_qpolynomial_foreach_piece(
3973 __isl_keep isl_pw_qpolynomial *pwqp,
3974 int (*fn)(__isl_take isl_set *set,
3975 __isl_take isl_qpolynomial *qp,
3976 void *user), void *user);
3977 int isl_pw_qpolynomial_foreach_lifted_piece(
3978 __isl_keep isl_pw_qpolynomial *pwqp,
3979 int (*fn)(__isl_take isl_set *set,
3980 __isl_take isl_qpolynomial *qp,
3981 void *user), void *user);
3983 As usual, the function C<fn> should return C<0> on success
3984 and C<-1> on failure. The difference between
3985 C<isl_pw_qpolynomial_foreach_piece> and
3986 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3987 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3988 compute unique representations for all existentially quantified
3989 variables and then turn these existentially quantified variables
3990 into extra set variables, adapting the associated quasipolynomial
3991 accordingly. This means that the C<set> passed to C<fn>
3992 will not have any existentially quantified variables, but that
3993 the dimensions of the sets may be different for different
3994 invocations of C<fn>.
3996 To iterate over all terms in a quasipolynomial,
3999 int isl_qpolynomial_foreach_term(
4000 __isl_keep isl_qpolynomial *qp,
4001 int (*fn)(__isl_take isl_term *term,
4002 void *user), void *user);
4004 The terms themselves can be inspected and freed using
4007 unsigned isl_term_dim(__isl_keep isl_term *term,
4008 enum isl_dim_type type);
4009 void isl_term_get_num(__isl_keep isl_term *term,
4011 void isl_term_get_den(__isl_keep isl_term *term,
4013 int isl_term_get_exp(__isl_keep isl_term *term,
4014 enum isl_dim_type type, unsigned pos);
4015 __isl_give isl_aff *isl_term_get_div(
4016 __isl_keep isl_term *term, unsigned pos);
4017 void isl_term_free(__isl_take isl_term *term);
4019 Each term is a product of parameters, set variables and
4020 integer divisions. The function C<isl_term_get_exp>
4021 returns the exponent of a given dimensions in the given term.
4022 The C<isl_int>s in the arguments of C<isl_term_get_num>
4023 and C<isl_term_get_den> need to have been initialized
4024 using C<isl_int_init> before calling these functions.
4026 =head3 Properties of (Piecewise) Quasipolynomials
4028 To check whether a quasipolynomial is actually a constant,
4029 use the following function.
4031 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4032 isl_int *n, isl_int *d);
4034 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4035 then the numerator and denominator of the constant
4036 are returned in C<*n> and C<*d>, respectively.
4038 To check whether two union piecewise quasipolynomials are
4039 obviously equal, use
4041 int isl_union_pw_qpolynomial_plain_is_equal(
4042 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4043 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4045 =head3 Operations on (Piecewise) Quasipolynomials
4047 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4048 __isl_take isl_qpolynomial *qp, isl_int v);
4049 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4050 __isl_take isl_qpolynomial *qp);
4051 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4052 __isl_take isl_qpolynomial *qp1,
4053 __isl_take isl_qpolynomial *qp2);
4054 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4055 __isl_take isl_qpolynomial *qp1,
4056 __isl_take isl_qpolynomial *qp2);
4057 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4058 __isl_take isl_qpolynomial *qp1,
4059 __isl_take isl_qpolynomial *qp2);
4060 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4061 __isl_take isl_qpolynomial *qp, unsigned exponent);
4063 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4064 __isl_take isl_pw_qpolynomial *pwqp1,
4065 __isl_take isl_pw_qpolynomial *pwqp2);
4066 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4067 __isl_take isl_pw_qpolynomial *pwqp1,
4068 __isl_take isl_pw_qpolynomial *pwqp2);
4069 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4070 __isl_take isl_pw_qpolynomial *pwqp1,
4071 __isl_take isl_pw_qpolynomial *pwqp2);
4072 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4073 __isl_take isl_pw_qpolynomial *pwqp);
4074 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4075 __isl_take isl_pw_qpolynomial *pwqp1,
4076 __isl_take isl_pw_qpolynomial *pwqp2);
4077 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4078 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4080 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4081 __isl_take isl_union_pw_qpolynomial *upwqp1,
4082 __isl_take isl_union_pw_qpolynomial *upwqp2);
4083 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4084 __isl_take isl_union_pw_qpolynomial *upwqp1,
4085 __isl_take isl_union_pw_qpolynomial *upwqp2);
4086 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4087 __isl_take isl_union_pw_qpolynomial *upwqp1,
4088 __isl_take isl_union_pw_qpolynomial *upwqp2);
4090 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4091 __isl_take isl_pw_qpolynomial *pwqp,
4092 __isl_take isl_point *pnt);
4094 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4095 __isl_take isl_union_pw_qpolynomial *upwqp,
4096 __isl_take isl_point *pnt);
4098 __isl_give isl_set *isl_pw_qpolynomial_domain(
4099 __isl_take isl_pw_qpolynomial *pwqp);
4100 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4101 __isl_take isl_pw_qpolynomial *pwpq,
4102 __isl_take isl_set *set);
4103 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4104 __isl_take isl_pw_qpolynomial *pwpq,
4105 __isl_take isl_set *set);
4107 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4108 __isl_take isl_union_pw_qpolynomial *upwqp);
4109 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4110 __isl_take isl_union_pw_qpolynomial *upwpq,
4111 __isl_take isl_union_set *uset);
4112 __isl_give isl_union_pw_qpolynomial *
4113 isl_union_pw_qpolynomial_intersect_params(
4114 __isl_take isl_union_pw_qpolynomial *upwpq,
4115 __isl_take isl_set *set);
4117 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4118 __isl_take isl_qpolynomial *qp,
4119 __isl_take isl_space *model);
4121 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4122 __isl_take isl_qpolynomial *qp);
4123 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4124 __isl_take isl_pw_qpolynomial *pwqp);
4126 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4127 __isl_take isl_union_pw_qpolynomial *upwqp);
4129 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4130 __isl_take isl_qpolynomial *qp,
4131 __isl_take isl_set *context);
4132 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4133 __isl_take isl_qpolynomial *qp,
4134 __isl_take isl_set *context);
4136 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4137 __isl_take isl_pw_qpolynomial *pwqp,
4138 __isl_take isl_set *context);
4139 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4140 __isl_take isl_pw_qpolynomial *pwqp,
4141 __isl_take isl_set *context);
4143 __isl_give isl_union_pw_qpolynomial *
4144 isl_union_pw_qpolynomial_gist_params(
4145 __isl_take isl_union_pw_qpolynomial *upwqp,
4146 __isl_take isl_set *context);
4147 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4148 __isl_take isl_union_pw_qpolynomial *upwqp,
4149 __isl_take isl_union_set *context);
4151 The gist operation applies the gist operation to each of
4152 the cells in the domain of the input piecewise quasipolynomial.
4153 The context is also exploited
4154 to simplify the quasipolynomials associated to each cell.
4156 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4157 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4158 __isl_give isl_union_pw_qpolynomial *
4159 isl_union_pw_qpolynomial_to_polynomial(
4160 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4162 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4163 the polynomial will be an overapproximation. If C<sign> is negative,
4164 it will be an underapproximation. If C<sign> is zero, the approximation
4165 will lie somewhere in between.
4167 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4169 A piecewise quasipolynomial reduction is a piecewise
4170 reduction (or fold) of quasipolynomials.
4171 In particular, the reduction can be maximum or a minimum.
4172 The objects are mainly used to represent the result of
4173 an upper or lower bound on a quasipolynomial over its domain,
4174 i.e., as the result of the following function.
4176 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4177 __isl_take isl_pw_qpolynomial *pwqp,
4178 enum isl_fold type, int *tight);
4180 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4181 __isl_take isl_union_pw_qpolynomial *upwqp,
4182 enum isl_fold type, int *tight);
4184 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4185 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4186 is the returned bound is known be tight, i.e., for each value
4187 of the parameters there is at least
4188 one element in the domain that reaches the bound.
4189 If the domain of C<pwqp> is not wrapping, then the bound is computed
4190 over all elements in that domain and the result has a purely parametric
4191 domain. If the domain of C<pwqp> is wrapping, then the bound is
4192 computed over the range of the wrapped relation. The domain of the
4193 wrapped relation becomes the domain of the result.
4195 A (piecewise) quasipolynomial reduction can be copied or freed using the
4196 following functions.
4198 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4199 __isl_keep isl_qpolynomial_fold *fold);
4200 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4201 __isl_keep isl_pw_qpolynomial_fold *pwf);
4202 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4203 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4204 void isl_qpolynomial_fold_free(
4205 __isl_take isl_qpolynomial_fold *fold);
4206 void *isl_pw_qpolynomial_fold_free(
4207 __isl_take isl_pw_qpolynomial_fold *pwf);
4208 void *isl_union_pw_qpolynomial_fold_free(
4209 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4211 =head3 Printing Piecewise Quasipolynomial Reductions
4213 Piecewise quasipolynomial reductions can be printed
4214 using the following function.
4216 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4217 __isl_take isl_printer *p,
4218 __isl_keep isl_pw_qpolynomial_fold *pwf);
4219 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4220 __isl_take isl_printer *p,
4221 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4223 For C<isl_printer_print_pw_qpolynomial_fold>,
4224 output format of the printer
4225 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4226 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4227 output format of the printer
4228 needs to be set to C<ISL_FORMAT_ISL>.
4229 In case of printing in C<ISL_FORMAT_C>, the user may want
4230 to set the names of all dimensions
4232 __isl_give isl_pw_qpolynomial_fold *
4233 isl_pw_qpolynomial_fold_set_dim_name(
4234 __isl_take isl_pw_qpolynomial_fold *pwf,
4235 enum isl_dim_type type, unsigned pos,
4238 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4240 To iterate over all piecewise quasipolynomial reductions in a union
4241 piecewise quasipolynomial reduction, use the following function
4243 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4244 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4245 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4246 void *user), void *user);
4248 To iterate over the cells in a piecewise quasipolynomial reduction,
4249 use either of the following two functions
4251 int isl_pw_qpolynomial_fold_foreach_piece(
4252 __isl_keep isl_pw_qpolynomial_fold *pwf,
4253 int (*fn)(__isl_take isl_set *set,
4254 __isl_take isl_qpolynomial_fold *fold,
4255 void *user), void *user);
4256 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4257 __isl_keep isl_pw_qpolynomial_fold *pwf,
4258 int (*fn)(__isl_take isl_set *set,
4259 __isl_take isl_qpolynomial_fold *fold,
4260 void *user), void *user);
4262 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4263 of the difference between these two functions.
4265 To iterate over all quasipolynomials in a reduction, use
4267 int isl_qpolynomial_fold_foreach_qpolynomial(
4268 __isl_keep isl_qpolynomial_fold *fold,
4269 int (*fn)(__isl_take isl_qpolynomial *qp,
4270 void *user), void *user);
4272 =head3 Properties of Piecewise Quasipolynomial Reductions
4274 To check whether two union piecewise quasipolynomial reductions are
4275 obviously equal, use
4277 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4278 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4279 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4281 =head3 Operations on Piecewise Quasipolynomial Reductions
4283 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4284 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4286 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4287 __isl_take isl_pw_qpolynomial_fold *pwf1,
4288 __isl_take isl_pw_qpolynomial_fold *pwf2);
4290 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4291 __isl_take isl_pw_qpolynomial_fold *pwf1,
4292 __isl_take isl_pw_qpolynomial_fold *pwf2);
4294 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4295 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4296 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4298 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4299 __isl_take isl_pw_qpolynomial_fold *pwf,
4300 __isl_take isl_point *pnt);
4302 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4303 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4304 __isl_take isl_point *pnt);
4306 __isl_give isl_pw_qpolynomial_fold *
4307 isl_pw_qpolynomial_fold_intersect_params(
4308 __isl_take isl_pw_qpolynomial_fold *pwf,
4309 __isl_take isl_set *set);
4311 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4312 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4313 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4314 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4315 __isl_take isl_union_set *uset);
4316 __isl_give isl_union_pw_qpolynomial_fold *
4317 isl_union_pw_qpolynomial_fold_intersect_params(
4318 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4319 __isl_take isl_set *set);
4321 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4322 __isl_take isl_pw_qpolynomial_fold *pwf);
4324 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4325 __isl_take isl_pw_qpolynomial_fold *pwf);
4327 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4328 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4330 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4331 __isl_take isl_qpolynomial_fold *fold,
4332 __isl_take isl_set *context);
4333 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4334 __isl_take isl_qpolynomial_fold *fold,
4335 __isl_take isl_set *context);
4337 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4338 __isl_take isl_pw_qpolynomial_fold *pwf,
4339 __isl_take isl_set *context);
4340 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4341 __isl_take isl_pw_qpolynomial_fold *pwf,
4342 __isl_take isl_set *context);
4344 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4345 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4346 __isl_take isl_union_set *context);
4347 __isl_give isl_union_pw_qpolynomial_fold *
4348 isl_union_pw_qpolynomial_fold_gist_params(
4349 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4350 __isl_take isl_set *context);
4352 The gist operation applies the gist operation to each of
4353 the cells in the domain of the input piecewise quasipolynomial reduction.
4354 In future, the operation will also exploit the context
4355 to simplify the quasipolynomial reductions associated to each cell.
4357 __isl_give isl_pw_qpolynomial_fold *
4358 isl_set_apply_pw_qpolynomial_fold(
4359 __isl_take isl_set *set,
4360 __isl_take isl_pw_qpolynomial_fold *pwf,
4362 __isl_give isl_pw_qpolynomial_fold *
4363 isl_map_apply_pw_qpolynomial_fold(
4364 __isl_take isl_map *map,
4365 __isl_take isl_pw_qpolynomial_fold *pwf,
4367 __isl_give isl_union_pw_qpolynomial_fold *
4368 isl_union_set_apply_union_pw_qpolynomial_fold(
4369 __isl_take isl_union_set *uset,
4370 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4372 __isl_give isl_union_pw_qpolynomial_fold *
4373 isl_union_map_apply_union_pw_qpolynomial_fold(
4374 __isl_take isl_union_map *umap,
4375 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4378 The functions taking a map
4379 compose the given map with the given piecewise quasipolynomial reduction.
4380 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4381 over all elements in the intersection of the range of the map
4382 and the domain of the piecewise quasipolynomial reduction
4383 as a function of an element in the domain of the map.
4384 The functions taking a set compute a bound over all elements in the
4385 intersection of the set and the domain of the
4386 piecewise quasipolynomial reduction.
4388 =head2 Dependence Analysis
4390 C<isl> contains specialized functionality for performing
4391 array dataflow analysis. That is, given a I<sink> access relation
4392 and a collection of possible I<source> access relations,
4393 C<isl> can compute relations that describe
4394 for each iteration of the sink access, which iteration
4395 of which of the source access relations was the last
4396 to access the same data element before the given iteration
4398 The resulting dependence relations map source iterations
4399 to the corresponding sink iterations.
4400 To compute standard flow dependences, the sink should be
4401 a read, while the sources should be writes.
4402 If any of the source accesses are marked as being I<may>
4403 accesses, then there will be a dependence from the last
4404 I<must> access B<and> from any I<may> access that follows
4405 this last I<must> access.
4406 In particular, if I<all> sources are I<may> accesses,
4407 then memory based dependence analysis is performed.
4408 If, on the other hand, all sources are I<must> accesses,
4409 then value based dependence analysis is performed.
4411 #include <isl/flow.h>
4413 typedef int (*isl_access_level_before)(void *first, void *second);
4415 __isl_give isl_access_info *isl_access_info_alloc(
4416 __isl_take isl_map *sink,
4417 void *sink_user, isl_access_level_before fn,
4419 __isl_give isl_access_info *isl_access_info_add_source(
4420 __isl_take isl_access_info *acc,
4421 __isl_take isl_map *source, int must,
4423 void *isl_access_info_free(__isl_take isl_access_info *acc);
4425 __isl_give isl_flow *isl_access_info_compute_flow(
4426 __isl_take isl_access_info *acc);
4428 int isl_flow_foreach(__isl_keep isl_flow *deps,
4429 int (*fn)(__isl_take isl_map *dep, int must,
4430 void *dep_user, void *user),
4432 __isl_give isl_map *isl_flow_get_no_source(
4433 __isl_keep isl_flow *deps, int must);
4434 void isl_flow_free(__isl_take isl_flow *deps);
4436 The function C<isl_access_info_compute_flow> performs the actual
4437 dependence analysis. The other functions are used to construct
4438 the input for this function or to read off the output.
4440 The input is collected in an C<isl_access_info>, which can
4441 be created through a call to C<isl_access_info_alloc>.
4442 The arguments to this functions are the sink access relation
4443 C<sink>, a token C<sink_user> used to identify the sink
4444 access to the user, a callback function for specifying the
4445 relative order of source and sink accesses, and the number
4446 of source access relations that will be added.
4447 The callback function has type C<int (*)(void *first, void *second)>.
4448 The function is called with two user supplied tokens identifying
4449 either a source or the sink and it should return the shared nesting
4450 level and the relative order of the two accesses.
4451 In particular, let I<n> be the number of loops shared by
4452 the two accesses. If C<first> precedes C<second> textually,
4453 then the function should return I<2 * n + 1>; otherwise,
4454 it should return I<2 * n>.
4455 The sources can be added to the C<isl_access_info> by performing
4456 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4457 C<must> indicates whether the source is a I<must> access
4458 or a I<may> access. Note that a multi-valued access relation
4459 should only be marked I<must> if every iteration in the domain
4460 of the relation accesses I<all> elements in its image.
4461 The C<source_user> token is again used to identify
4462 the source access. The range of the source access relation
4463 C<source> should have the same dimension as the range
4464 of the sink access relation.
4465 The C<isl_access_info_free> function should usually not be
4466 called explicitly, because it is called implicitly by
4467 C<isl_access_info_compute_flow>.
4469 The result of the dependence analysis is collected in an
4470 C<isl_flow>. There may be elements of
4471 the sink access for which no preceding source access could be
4472 found or for which all preceding sources are I<may> accesses.
4473 The relations containing these elements can be obtained through
4474 calls to C<isl_flow_get_no_source>, the first with C<must> set
4475 and the second with C<must> unset.
4476 In the case of standard flow dependence analysis,
4477 with the sink a read and the sources I<must> writes,
4478 the first relation corresponds to the reads from uninitialized
4479 array elements and the second relation is empty.
4480 The actual flow dependences can be extracted using
4481 C<isl_flow_foreach>. This function will call the user-specified
4482 callback function C<fn> for each B<non-empty> dependence between
4483 a source and the sink. The callback function is called
4484 with four arguments, the actual flow dependence relation
4485 mapping source iterations to sink iterations, a boolean that
4486 indicates whether it is a I<must> or I<may> dependence, a token
4487 identifying the source and an additional C<void *> with value
4488 equal to the third argument of the C<isl_flow_foreach> call.
4489 A dependence is marked I<must> if it originates from a I<must>
4490 source and if it is not followed by any I<may> sources.
4492 After finishing with an C<isl_flow>, the user should call
4493 C<isl_flow_free> to free all associated memory.
4495 A higher-level interface to dependence analysis is provided
4496 by the following function.
4498 #include <isl/flow.h>
4500 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4501 __isl_take isl_union_map *must_source,
4502 __isl_take isl_union_map *may_source,
4503 __isl_take isl_union_map *schedule,
4504 __isl_give isl_union_map **must_dep,
4505 __isl_give isl_union_map **may_dep,
4506 __isl_give isl_union_map **must_no_source,
4507 __isl_give isl_union_map **may_no_source);
4509 The arrays are identified by the tuple names of the ranges
4510 of the accesses. The iteration domains by the tuple names
4511 of the domains of the accesses and of the schedule.
4512 The relative order of the iteration domains is given by the
4513 schedule. The relations returned through C<must_no_source>
4514 and C<may_no_source> are subsets of C<sink>.
4515 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4516 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4517 any of the other arguments is treated as an error.
4519 =head3 Interaction with Dependence Analysis
4521 During the dependence analysis, we frequently need to perform
4522 the following operation. Given a relation between sink iterations
4523 and potential source iterations from a particular source domain,
4524 what is the last potential source iteration corresponding to each
4525 sink iteration. It can sometimes be convenient to adjust
4526 the set of potential source iterations before or after each such operation.
4527 The prototypical example is fuzzy array dataflow analysis,
4528 where we need to analyze if, based on data-dependent constraints,
4529 the sink iteration can ever be executed without one or more of
4530 the corresponding potential source iterations being executed.
4531 If so, we can introduce extra parameters and select an unknown
4532 but fixed source iteration from the potential source iterations.
4533 To be able to perform such manipulations, C<isl> provides the following
4536 #include <isl/flow.h>
4538 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4539 __isl_keep isl_map *source_map,
4540 __isl_keep isl_set *sink, void *source_user,
4542 __isl_give isl_access_info *isl_access_info_set_restrict(
4543 __isl_take isl_access_info *acc,
4544 isl_access_restrict fn, void *user);
4546 The function C<isl_access_info_set_restrict> should be called
4547 before calling C<isl_access_info_compute_flow> and registers a callback function
4548 that will be called any time C<isl> is about to compute the last
4549 potential source. The first argument is the (reverse) proto-dependence,
4550 mapping sink iterations to potential source iterations.
4551 The second argument represents the sink iterations for which
4552 we want to compute the last source iteration.
4553 The third argument is the token corresponding to the source
4554 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4555 The callback is expected to return a restriction on either the input or
4556 the output of the operation computing the last potential source.
4557 If the input needs to be restricted then restrictions are needed
4558 for both the source and the sink iterations. The sink iterations
4559 and the potential source iterations will be intersected with these sets.
4560 If the output needs to be restricted then only a restriction on the source
4561 iterations is required.
4562 If any error occurs, the callback should return C<NULL>.
4563 An C<isl_restriction> object can be created, freed and inspected
4564 using the following functions.
4566 #include <isl/flow.h>
4568 __isl_give isl_restriction *isl_restriction_input(
4569 __isl_take isl_set *source_restr,
4570 __isl_take isl_set *sink_restr);
4571 __isl_give isl_restriction *isl_restriction_output(
4572 __isl_take isl_set *source_restr);
4573 __isl_give isl_restriction *isl_restriction_none(
4574 __isl_take isl_map *source_map);
4575 __isl_give isl_restriction *isl_restriction_empty(
4576 __isl_take isl_map *source_map);
4577 void *isl_restriction_free(
4578 __isl_take isl_restriction *restr);
4579 isl_ctx *isl_restriction_get_ctx(
4580 __isl_keep isl_restriction *restr);
4582 C<isl_restriction_none> and C<isl_restriction_empty> are special
4583 cases of C<isl_restriction_input>. C<isl_restriction_none>
4584 is essentially equivalent to
4586 isl_restriction_input(isl_set_universe(
4587 isl_space_range(isl_map_get_space(source_map))),
4589 isl_space_domain(isl_map_get_space(source_map))));
4591 whereas C<isl_restriction_empty> is essentially equivalent to
4593 isl_restriction_input(isl_set_empty(
4594 isl_space_range(isl_map_get_space(source_map))),
4596 isl_space_domain(isl_map_get_space(source_map))));
4600 B<The functionality described in this section is fairly new
4601 and may be subject to change.>
4603 The following function can be used to compute a schedule
4604 for a union of domains.
4605 By default, the algorithm used to construct the schedule is similar
4606 to that of C<Pluto>.
4607 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4609 The generated schedule respects all C<validity> dependences.
4610 That is, all dependence distances over these dependences in the
4611 scheduled space are lexicographically positive.
4612 The default algorithm tries to minimize the dependence distances over
4613 C<proximity> dependences.
4614 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4615 for groups of domains where the dependence distances have only
4616 non-negative values.
4617 When using Feautrier's algorithm, the C<proximity> dependence
4618 distances are only minimized during the extension to a
4619 full-dimensional schedule.
4621 #include <isl/schedule.h>
4622 __isl_give isl_schedule *isl_union_set_compute_schedule(
4623 __isl_take isl_union_set *domain,
4624 __isl_take isl_union_map *validity,
4625 __isl_take isl_union_map *proximity);
4626 void *isl_schedule_free(__isl_take isl_schedule *sched);
4628 A mapping from the domains to the scheduled space can be obtained
4629 from an C<isl_schedule> using the following function.
4631 __isl_give isl_union_map *isl_schedule_get_map(
4632 __isl_keep isl_schedule *sched);
4634 A representation of the schedule can be printed using
4636 __isl_give isl_printer *isl_printer_print_schedule(
4637 __isl_take isl_printer *p,
4638 __isl_keep isl_schedule *schedule);
4640 A representation of the schedule as a forest of bands can be obtained
4641 using the following function.
4643 __isl_give isl_band_list *isl_schedule_get_band_forest(
4644 __isl_keep isl_schedule *schedule);
4646 The individual bands can be visited in depth-first post-order
4647 using the following function.
4649 #include <isl/schedule.h>
4650 int isl_schedule_foreach_band(
4651 __isl_keep isl_schedule *sched,
4652 int (*fn)(__isl_keep isl_band *band, void *user),
4655 The list can be manipulated as explained in L<"Lists">.
4656 The bands inside the list can be copied and freed using the following
4659 #include <isl/band.h>
4660 __isl_give isl_band *isl_band_copy(
4661 __isl_keep isl_band *band);
4662 void *isl_band_free(__isl_take isl_band *band);
4664 Each band contains zero or more scheduling dimensions.
4665 These are referred to as the members of the band.
4666 The section of the schedule that corresponds to the band is
4667 referred to as the partial schedule of the band.
4668 For those nodes that participate in a band, the outer scheduling
4669 dimensions form the prefix schedule, while the inner scheduling
4670 dimensions form the suffix schedule.
4671 That is, if we take a cut of the band forest, then the union of
4672 the concatenations of the prefix, partial and suffix schedules of
4673 each band in the cut is equal to the entire schedule (modulo
4674 some possible padding at the end with zero scheduling dimensions).
4675 The properties of a band can be inspected using the following functions.
4677 #include <isl/band.h>
4678 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4680 int isl_band_has_children(__isl_keep isl_band *band);
4681 __isl_give isl_band_list *isl_band_get_children(
4682 __isl_keep isl_band *band);
4684 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4685 __isl_keep isl_band *band);
4686 __isl_give isl_union_map *isl_band_get_partial_schedule(
4687 __isl_keep isl_band *band);
4688 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4689 __isl_keep isl_band *band);
4691 int isl_band_n_member(__isl_keep isl_band *band);
4692 int isl_band_member_is_zero_distance(
4693 __isl_keep isl_band *band, int pos);
4695 int isl_band_list_foreach_band(
4696 __isl_keep isl_band_list *list,
4697 int (*fn)(__isl_keep isl_band *band, void *user),
4700 Note that a scheduling dimension is considered to be ``zero
4701 distance'' if it does not carry any proximity dependences
4703 That is, if the dependence distances of the proximity
4704 dependences are all zero in that direction (for fixed
4705 iterations of outer bands).
4706 Like C<isl_schedule_foreach_band>,
4707 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4708 in depth-first post-order.
4710 A band can be tiled using the following function.
4712 #include <isl/band.h>
4713 int isl_band_tile(__isl_keep isl_band *band,
4714 __isl_take isl_vec *sizes);
4716 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4718 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4720 The C<isl_band_tile> function tiles the band using the given tile sizes
4721 inside its schedule.
4722 A new child band is created to represent the point loops and it is
4723 inserted between the modified band and its children.
4724 The C<tile_scale_tile_loops> option specifies whether the tile
4725 loops iterators should be scaled by the tile sizes.
4727 A representation of the band can be printed using
4729 #include <isl/band.h>
4730 __isl_give isl_printer *isl_printer_print_band(
4731 __isl_take isl_printer *p,
4732 __isl_keep isl_band *band);
4736 #include <isl/schedule.h>
4737 int isl_options_set_schedule_max_coefficient(
4738 isl_ctx *ctx, int val);
4739 int isl_options_get_schedule_max_coefficient(
4741 int isl_options_set_schedule_max_constant_term(
4742 isl_ctx *ctx, int val);
4743 int isl_options_get_schedule_max_constant_term(
4745 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4746 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4747 int isl_options_set_schedule_maximize_band_depth(
4748 isl_ctx *ctx, int val);
4749 int isl_options_get_schedule_maximize_band_depth(
4751 int isl_options_set_schedule_outer_zero_distance(
4752 isl_ctx *ctx, int val);
4753 int isl_options_get_schedule_outer_zero_distance(
4755 int isl_options_set_schedule_split_scaled(
4756 isl_ctx *ctx, int val);
4757 int isl_options_get_schedule_split_scaled(
4759 int isl_options_set_schedule_algorithm(
4760 isl_ctx *ctx, int val);
4761 int isl_options_get_schedule_algorithm(
4763 int isl_options_set_schedule_separate_components(
4764 isl_ctx *ctx, int val);
4765 int isl_options_get_schedule_separate_components(
4770 =item * schedule_max_coefficient
4772 This option enforces that the coefficients for variable and parameter
4773 dimensions in the calculated schedule are not larger than the specified value.
4774 This option can significantly increase the speed of the scheduling calculation
4775 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4776 this option does not introduce bounds on the variable or parameter
4779 =item * schedule_max_constant_term
4781 This option enforces that the constant coefficients in the calculated schedule
4782 are not larger than the maximal constant term. This option can significantly
4783 increase the speed of the scheduling calculation and may also prevent fusing of
4784 unrelated dimensions. A value of -1 means that this option does not introduce
4785 bounds on the constant coefficients.
4787 =item * schedule_fuse
4789 This option controls the level of fusion.
4790 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4791 resulting schedule will be distributed as much as possible.
4792 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4793 try to fuse loops in the resulting schedule.
4795 =item * schedule_maximize_band_depth
4797 If this option is set, we do not split bands at the point
4798 where we detect splitting is necessary. Instead, we
4799 backtrack and split bands as early as possible. This
4800 reduces the number of splits and maximizes the width of
4801 the bands. Wider bands give more possibilities for tiling.
4802 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4803 then bands will be split as early as possible, even if there is no need.
4804 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4806 =item * schedule_outer_zero_distance
4808 If this option is set, then we try to construct schedules
4809 where the outermost scheduling dimension in each band
4810 results in a zero dependence distance over the proximity
4813 =item * schedule_split_scaled
4815 If this option is set, then we try to construct schedules in which the
4816 constant term is split off from the linear part if the linear parts of
4817 the scheduling rows for all nodes in the graphs have a common non-trivial
4819 The constant term is then placed in a separate band and the linear
4822 =item * schedule_algorithm
4824 Selects the scheduling algorithm to be used.
4825 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4826 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4828 =item * schedule_separate_components
4830 If at any point the dependence graph contains any (weakly connected) components,
4831 then these components are scheduled separately.
4832 If this option is not set, then some iterations of the domains
4833 in these components may be scheduled together.
4834 If this option is set, then the components are given consecutive
4839 =head2 Parametric Vertex Enumeration
4841 The parametric vertex enumeration described in this section
4842 is mainly intended to be used internally and by the C<barvinok>
4845 #include <isl/vertices.h>
4846 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4847 __isl_keep isl_basic_set *bset);
4849 The function C<isl_basic_set_compute_vertices> performs the
4850 actual computation of the parametric vertices and the chamber
4851 decomposition and store the result in an C<isl_vertices> object.
4852 This information can be queried by either iterating over all
4853 the vertices or iterating over all the chambers or cells
4854 and then iterating over all vertices that are active on the chamber.
4856 int isl_vertices_foreach_vertex(
4857 __isl_keep isl_vertices *vertices,
4858 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4861 int isl_vertices_foreach_cell(
4862 __isl_keep isl_vertices *vertices,
4863 int (*fn)(__isl_take isl_cell *cell, void *user),
4865 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4866 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4869 Other operations that can be performed on an C<isl_vertices> object are
4872 isl_ctx *isl_vertices_get_ctx(
4873 __isl_keep isl_vertices *vertices);
4874 int isl_vertices_get_n_vertices(
4875 __isl_keep isl_vertices *vertices);
4876 void isl_vertices_free(__isl_take isl_vertices *vertices);
4878 Vertices can be inspected and destroyed using the following functions.
4880 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4881 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4882 __isl_give isl_basic_set *isl_vertex_get_domain(
4883 __isl_keep isl_vertex *vertex);
4884 __isl_give isl_basic_set *isl_vertex_get_expr(
4885 __isl_keep isl_vertex *vertex);
4886 void isl_vertex_free(__isl_take isl_vertex *vertex);
4888 C<isl_vertex_get_expr> returns a singleton parametric set describing
4889 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4891 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4892 B<rational> basic sets, so they should mainly be used for inspection
4893 and should not be mixed with integer sets.
4895 Chambers can be inspected and destroyed using the following functions.
4897 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4898 __isl_give isl_basic_set *isl_cell_get_domain(
4899 __isl_keep isl_cell *cell);
4900 void isl_cell_free(__isl_take isl_cell *cell);
4904 Although C<isl> is mainly meant to be used as a library,
4905 it also contains some basic applications that use some
4906 of the functionality of C<isl>.
4907 The input may be specified in either the L<isl format>
4908 or the L<PolyLib format>.
4910 =head2 C<isl_polyhedron_sample>
4912 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4913 an integer element of the polyhedron, if there is any.
4914 The first column in the output is the denominator and is always
4915 equal to 1. If the polyhedron contains no integer points,
4916 then a vector of length zero is printed.
4920 C<isl_pip> takes the same input as the C<example> program
4921 from the C<piplib> distribution, i.e., a set of constraints
4922 on the parameters, a line containing only -1 and finally a set
4923 of constraints on a parametric polyhedron.
4924 The coefficients of the parameters appear in the last columns
4925 (but before the final constant column).
4926 The output is the lexicographic minimum of the parametric polyhedron.
4927 As C<isl> currently does not have its own output format, the output
4928 is just a dump of the internal state.
4930 =head2 C<isl_polyhedron_minimize>
4932 C<isl_polyhedron_minimize> computes the minimum of some linear
4933 or affine objective function over the integer points in a polyhedron.
4934 If an affine objective function
4935 is given, then the constant should appear in the last column.
4937 =head2 C<isl_polytope_scan>
4939 Given a polytope, C<isl_polytope_scan> prints
4940 all integer points in the polytope.