3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
173 C<isl> is released under the MIT license.
177 Permission is hereby granted, free of charge, to any person obtaining a copy of
178 this software and associated documentation files (the "Software"), to deal in
179 the Software without restriction, including without limitation the rights to
180 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
181 of the Software, and to permit persons to whom the Software is furnished to do
182 so, subject to the following conditions:
184 The above copyright notice and this permission notice shall be included in all
185 copies or substantial portions of the Software.
187 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
188 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
189 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
190 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
191 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
192 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
197 Note that C<isl> currently requires C<GMP>, which is released
198 under the GNU Lesser General Public License (LGPL). This means
199 that code linked against C<isl> is also linked against LGPL code.
203 The source of C<isl> can be obtained either as a tarball
204 or from the git repository. Both are available from
205 L<http://freshmeat.net/projects/isl/>.
206 The installation process depends on how you obtained
209 =head2 Installation from the git repository
213 =item 1 Clone or update the repository
215 The first time the source is obtained, you need to clone
218 git clone git://repo.or.cz/isl.git
220 To obtain updates, you need to pull in the latest changes
224 =item 2 Generate C<configure>
230 After performing the above steps, continue
231 with the L<Common installation instructions>.
233 =head2 Common installation instructions
237 =item 1 Obtain C<GMP>
239 Building C<isl> requires C<GMP>, including its headers files.
240 Your distribution may not provide these header files by default
241 and you may need to install a package called C<gmp-devel> or something
242 similar. Alternatively, C<GMP> can be built from
243 source, available from L<http://gmplib.org/>.
247 C<isl> uses the standard C<autoconf> C<configure> script.
252 optionally followed by some configure options.
253 A complete list of options can be obtained by running
257 Below we discuss some of the more common options.
259 C<isl> can optionally use C<piplib>, but no
260 C<piplib> functionality is currently used by default.
261 The C<--with-piplib> option can
262 be used to specify which C<piplib>
263 library to use, either an installed version (C<system>),
264 an externally built version (C<build>)
265 or no version (C<no>). The option C<build> is mostly useful
266 in C<configure> scripts of larger projects that bundle both C<isl>
273 Installation prefix for C<isl>
275 =item C<--with-gmp-prefix>
277 Installation prefix for C<GMP> (architecture-independent files).
279 =item C<--with-gmp-exec-prefix>
281 Installation prefix for C<GMP> (architecture-dependent files).
283 =item C<--with-piplib>
285 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
287 =item C<--with-piplib-prefix>
289 Installation prefix for C<system> C<piplib> (architecture-independent files).
291 =item C<--with-piplib-exec-prefix>
293 Installation prefix for C<system> C<piplib> (architecture-dependent files).
295 =item C<--with-piplib-builddir>
297 Location where C<build> C<piplib> was built.
305 =item 4 Install (optional)
313 =head2 Initialization
315 All manipulations of integer sets and relations occur within
316 the context of an C<isl_ctx>.
317 A given C<isl_ctx> can only be used within a single thread.
318 All arguments of a function are required to have been allocated
319 within the same context.
320 There are currently no functions available for moving an object
321 from one C<isl_ctx> to another C<isl_ctx>. This means that
322 there is currently no way of safely moving an object from one
323 thread to another, unless the whole C<isl_ctx> is moved.
325 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
326 freed using C<isl_ctx_free>.
327 All objects allocated within an C<isl_ctx> should be freed
328 before the C<isl_ctx> itself is freed.
330 isl_ctx *isl_ctx_alloc();
331 void isl_ctx_free(isl_ctx *ctx);
335 All operations on integers, mainly the coefficients
336 of the constraints describing the sets and relations,
337 are performed in exact integer arithmetic using C<GMP>.
338 However, to allow future versions of C<isl> to optionally
339 support fixed integer arithmetic, all calls to C<GMP>
340 are wrapped inside C<isl> specific macros.
341 The basic type is C<isl_int> and the operations below
342 are available on this type.
343 The meanings of these operations are essentially the same
344 as their C<GMP> C<mpz_> counterparts.
345 As always with C<GMP> types, C<isl_int>s need to be
346 initialized with C<isl_int_init> before they can be used
347 and they need to be released with C<isl_int_clear>
349 The user should not assume that an C<isl_int> is represented
350 as a C<mpz_t>, but should instead explicitly convert between
351 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
352 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
356 =item isl_int_init(i)
358 =item isl_int_clear(i)
360 =item isl_int_set(r,i)
362 =item isl_int_set_si(r,i)
364 =item isl_int_set_gmp(r,g)
366 =item isl_int_get_gmp(i,g)
368 =item isl_int_abs(r,i)
370 =item isl_int_neg(r,i)
372 =item isl_int_swap(i,j)
374 =item isl_int_swap_or_set(i,j)
376 =item isl_int_add_ui(r,i,j)
378 =item isl_int_sub_ui(r,i,j)
380 =item isl_int_add(r,i,j)
382 =item isl_int_sub(r,i,j)
384 =item isl_int_mul(r,i,j)
386 =item isl_int_mul_ui(r,i,j)
388 =item isl_int_addmul(r,i,j)
390 =item isl_int_submul(r,i,j)
392 =item isl_int_gcd(r,i,j)
394 =item isl_int_lcm(r,i,j)
396 =item isl_int_divexact(r,i,j)
398 =item isl_int_cdiv_q(r,i,j)
400 =item isl_int_fdiv_q(r,i,j)
402 =item isl_int_fdiv_r(r,i,j)
404 =item isl_int_fdiv_q_ui(r,i,j)
406 =item isl_int_read(r,s)
408 =item isl_int_print(out,i,width)
412 =item isl_int_cmp(i,j)
414 =item isl_int_cmp_si(i,si)
416 =item isl_int_eq(i,j)
418 =item isl_int_ne(i,j)
420 =item isl_int_lt(i,j)
422 =item isl_int_le(i,j)
424 =item isl_int_gt(i,j)
426 =item isl_int_ge(i,j)
428 =item isl_int_abs_eq(i,j)
430 =item isl_int_abs_ne(i,j)
432 =item isl_int_abs_lt(i,j)
434 =item isl_int_abs_gt(i,j)
436 =item isl_int_abs_ge(i,j)
438 =item isl_int_is_zero(i)
440 =item isl_int_is_one(i)
442 =item isl_int_is_negone(i)
444 =item isl_int_is_pos(i)
446 =item isl_int_is_neg(i)
448 =item isl_int_is_nonpos(i)
450 =item isl_int_is_nonneg(i)
452 =item isl_int_is_divisible_by(i,j)
456 =head2 Sets and Relations
458 C<isl> uses six types of objects for representing sets and relations,
459 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
460 C<isl_union_set> and C<isl_union_map>.
461 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
462 can be described as a conjunction of affine constraints, while
463 C<isl_set> and C<isl_map> represent unions of
464 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
465 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
466 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
467 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
468 where spaces are considered different if they have a different number
469 of dimensions and/or different names (see L<"Spaces">).
470 The difference between sets and relations (maps) is that sets have
471 one set of variables, while relations have two sets of variables,
472 input variables and output variables.
474 =head2 Memory Management
476 Since a high-level operation on sets and/or relations usually involves
477 several substeps and since the user is usually not interested in
478 the intermediate results, most functions that return a new object
479 will also release all the objects passed as arguments.
480 If the user still wants to use one or more of these arguments
481 after the function call, she should pass along a copy of the
482 object rather than the object itself.
483 The user is then responsible for making sure that the original
484 object gets used somewhere else or is explicitly freed.
486 The arguments and return values of all documented functions are
487 annotated to make clear which arguments are released and which
488 arguments are preserved. In particular, the following annotations
495 C<__isl_give> means that a new object is returned.
496 The user should make sure that the returned pointer is
497 used exactly once as a value for an C<__isl_take> argument.
498 In between, it can be used as a value for as many
499 C<__isl_keep> arguments as the user likes.
500 There is one exception, and that is the case where the
501 pointer returned is C<NULL>. Is this case, the user
502 is free to use it as an C<__isl_take> argument or not.
506 C<__isl_take> means that the object the argument points to
507 is taken over by the function and may no longer be used
508 by the user as an argument to any other function.
509 The pointer value must be one returned by a function
510 returning an C<__isl_give> pointer.
511 If the user passes in a C<NULL> value, then this will
512 be treated as an error in the sense that the function will
513 not perform its usual operation. However, it will still
514 make sure that all the other C<__isl_take> arguments
519 C<__isl_keep> means that the function will only use the object
520 temporarily. After the function has finished, the user
521 can still use it as an argument to other functions.
522 A C<NULL> value will be treated in the same way as
523 a C<NULL> value for an C<__isl_take> argument.
527 =head2 Error Handling
529 C<isl> supports different ways to react in case a runtime error is triggered.
530 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
531 with two maps that have incompatible spaces. There are three possible ways
532 to react on error: to warn, to continue or to abort.
534 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
535 the last error in the corresponding C<isl_ctx> and the function in which the
536 error was triggered returns C<NULL>. An error does not corrupt internal state,
537 such that isl can continue to be used. C<isl> also provides functions to
538 read the last error and to reset the memory that stores the last error. The
539 last error is only stored for information purposes. Its presence does not
540 change the behavior of C<isl>. Hence, resetting an error is not required to
541 continue to use isl, but only to observe new errors.
544 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
545 void isl_ctx_reset_error(isl_ctx *ctx);
547 Another option is to continue on error. This is similar to warn on error mode,
548 except that C<isl> does not print any warning. This allows a program to
549 implement its own error reporting.
551 The last option is to directly abort the execution of the program from within
552 the isl library. This makes it obviously impossible to recover from an error,
553 but it allows to directly spot the error location. By aborting on error,
554 debuggers break at the location the error occurred and can provide a stack
555 trace. Other tools that automatically provide stack traces on abort or that do
556 not want to continue execution after an error was triggered may also prefer to
559 The on error behavior of isl can be specified by calling
560 C<isl_options_set_on_error> or by setting the command line option
561 C<--isl-on-error>. Valid arguments for the function call are
562 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
563 choices for the command line option are C<warn>, C<continue> and C<abort>.
564 It is also possible to query the current error mode.
566 #include <isl/options.h>
567 int isl_options_set_on_error(isl_ctx *ctx, int val);
568 int isl_options_get_on_error(isl_ctx *ctx);
572 Identifiers are used to identify both individual dimensions
573 and tuples of dimensions. They consist of a name and an optional
574 pointer. Identifiers with the same name but different pointer values
575 are considered to be distinct.
576 Identifiers can be constructed, copied, freed, inspected and printed
577 using the following functions.
580 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
581 __isl_keep const char *name, void *user);
582 __isl_give isl_id *isl_id_copy(isl_id *id);
583 void *isl_id_free(__isl_take isl_id *id);
585 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
586 void *isl_id_get_user(__isl_keep isl_id *id);
587 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
589 __isl_give isl_printer *isl_printer_print_id(
590 __isl_take isl_printer *p, __isl_keep isl_id *id);
592 Note that C<isl_id_get_name> returns a pointer to some internal
593 data structure, so the result can only be used while the
594 corresponding C<isl_id> is alive.
598 Whenever a new set, relation or similiar object is created from scratch,
599 the space in which it lives needs to be specified using an C<isl_space>.
600 Each space involves zero or more parameters and zero, one or two
601 tuples of set or input/output dimensions. The parameters and dimensions
602 are identified by an C<isl_dim_type> and a position.
603 The type C<isl_dim_param> refers to parameters,
604 the type C<isl_dim_set> refers to set dimensions (for spaces
605 with a single tuple of dimensions) and the types C<isl_dim_in>
606 and C<isl_dim_out> refer to input and output dimensions
607 (for spaces with two tuples of dimensions).
608 Local spaces (see L</"Local Spaces">) also contain dimensions
609 of type C<isl_dim_div>.
610 Note that parameters are only identified by their position within
611 a given object. Across different objects, parameters are (usually)
612 identified by their names or identifiers. Only unnamed parameters
613 are identified by their positions across objects. The use of unnamed
614 parameters is discouraged.
616 #include <isl/space.h>
617 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
618 unsigned nparam, unsigned n_in, unsigned n_out);
619 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
621 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
622 unsigned nparam, unsigned dim);
623 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
624 void isl_space_free(__isl_take isl_space *space);
625 unsigned isl_space_dim(__isl_keep isl_space *space,
626 enum isl_dim_type type);
628 The space used for creating a parameter domain
629 needs to be created using C<isl_space_params_alloc>.
630 For other sets, the space
631 needs to be created using C<isl_space_set_alloc>, while
632 for a relation, the space
633 needs to be created using C<isl_space_alloc>.
634 C<isl_space_dim> can be used
635 to find out the number of dimensions of each type in
636 a space, where type may be
637 C<isl_dim_param>, C<isl_dim_in> (only for relations),
638 C<isl_dim_out> (only for relations), C<isl_dim_set>
639 (only for sets) or C<isl_dim_all>.
641 To check whether a given space is that of a set or a map
642 or whether it is a parameter space, use these functions:
644 #include <isl/space.h>
645 int isl_space_is_params(__isl_keep isl_space *space);
646 int isl_space_is_set(__isl_keep isl_space *space);
647 int isl_space_is_map(__isl_keep isl_space *space);
649 Spaces can be compared using the following functions:
651 #include <isl/space.h>
652 int isl_space_is_equal(__isl_keep isl_space *space1,
653 __isl_keep isl_space *space2);
654 int isl_space_is_domain(__isl_keep isl_space *space1,
655 __isl_keep isl_space *space2);
656 int isl_space_is_range(__isl_keep isl_space *space1,
657 __isl_keep isl_space *space2);
659 C<isl_space_is_domain> checks whether the first argument is equal
660 to the domain of the second argument. This requires in particular that
661 the first argument is a set space and that the second argument
664 It is often useful to create objects that live in the
665 same space as some other object. This can be accomplished
666 by creating the new objects
667 (see L<Creating New Sets and Relations> or
668 L<Creating New (Piecewise) Quasipolynomials>) based on the space
669 of the original object.
672 __isl_give isl_space *isl_basic_set_get_space(
673 __isl_keep isl_basic_set *bset);
674 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
676 #include <isl/union_set.h>
677 __isl_give isl_space *isl_union_set_get_space(
678 __isl_keep isl_union_set *uset);
681 __isl_give isl_space *isl_basic_map_get_space(
682 __isl_keep isl_basic_map *bmap);
683 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
685 #include <isl/union_map.h>
686 __isl_give isl_space *isl_union_map_get_space(
687 __isl_keep isl_union_map *umap);
689 #include <isl/constraint.h>
690 __isl_give isl_space *isl_constraint_get_space(
691 __isl_keep isl_constraint *constraint);
693 #include <isl/polynomial.h>
694 __isl_give isl_space *isl_qpolynomial_get_domain_space(
695 __isl_keep isl_qpolynomial *qp);
696 __isl_give isl_space *isl_qpolynomial_get_space(
697 __isl_keep isl_qpolynomial *qp);
698 __isl_give isl_space *isl_qpolynomial_fold_get_space(
699 __isl_keep isl_qpolynomial_fold *fold);
700 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
701 __isl_keep isl_pw_qpolynomial *pwqp);
702 __isl_give isl_space *isl_pw_qpolynomial_get_space(
703 __isl_keep isl_pw_qpolynomial *pwqp);
704 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
705 __isl_keep isl_pw_qpolynomial_fold *pwf);
706 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
707 __isl_keep isl_pw_qpolynomial_fold *pwf);
708 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
709 __isl_keep isl_union_pw_qpolynomial *upwqp);
710 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
711 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
714 __isl_give isl_space *isl_aff_get_domain_space(
715 __isl_keep isl_aff *aff);
716 __isl_give isl_space *isl_aff_get_space(
717 __isl_keep isl_aff *aff);
718 __isl_give isl_space *isl_pw_aff_get_domain_space(
719 __isl_keep isl_pw_aff *pwaff);
720 __isl_give isl_space *isl_pw_aff_get_space(
721 __isl_keep isl_pw_aff *pwaff);
722 __isl_give isl_space *isl_multi_aff_get_domain_space(
723 __isl_keep isl_multi_aff *maff);
724 __isl_give isl_space *isl_multi_aff_get_space(
725 __isl_keep isl_multi_aff *maff);
726 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
727 __isl_keep isl_pw_multi_aff *pma);
728 __isl_give isl_space *isl_pw_multi_aff_get_space(
729 __isl_keep isl_pw_multi_aff *pma);
730 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
731 __isl_keep isl_union_pw_multi_aff *upma);
733 #include <isl/point.h>
734 __isl_give isl_space *isl_point_get_space(
735 __isl_keep isl_point *pnt);
737 The identifiers or names of the individual dimensions may be set or read off
738 using the following functions.
740 #include <isl/space.h>
741 __isl_give isl_space *isl_space_set_dim_id(
742 __isl_take isl_space *space,
743 enum isl_dim_type type, unsigned pos,
744 __isl_take isl_id *id);
745 int isl_space_has_dim_id(__isl_keep isl_space *space,
746 enum isl_dim_type type, unsigned pos);
747 __isl_give isl_id *isl_space_get_dim_id(
748 __isl_keep isl_space *space,
749 enum isl_dim_type type, unsigned pos);
750 __isl_give isl_space *isl_space_set_dim_name(
751 __isl_take isl_space *space,
752 enum isl_dim_type type, unsigned pos,
753 __isl_keep const char *name);
754 int isl_space_has_dim_name(__isl_keep isl_space *space,
755 enum isl_dim_type type, unsigned pos);
756 __isl_keep const char *isl_space_get_dim_name(
757 __isl_keep isl_space *space,
758 enum isl_dim_type type, unsigned pos);
760 Note that C<isl_space_get_name> returns a pointer to some internal
761 data structure, so the result can only be used while the
762 corresponding C<isl_space> is alive.
763 Also note that every function that operates on two sets or relations
764 requires that both arguments have the same parameters. This also
765 means that if one of the arguments has named parameters, then the
766 other needs to have named parameters too and the names need to match.
767 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
768 arguments may have different parameters (as long as they are named),
769 in which case the result will have as parameters the union of the parameters of
772 Given the identifier or name of a dimension (typically a parameter),
773 its position can be obtained from the following function.
775 #include <isl/space.h>
776 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
777 enum isl_dim_type type, __isl_keep isl_id *id);
778 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
779 enum isl_dim_type type, const char *name);
781 The identifiers or names of entire spaces may be set or read off
782 using the following functions.
784 #include <isl/space.h>
785 __isl_give isl_space *isl_space_set_tuple_id(
786 __isl_take isl_space *space,
787 enum isl_dim_type type, __isl_take isl_id *id);
788 __isl_give isl_space *isl_space_reset_tuple_id(
789 __isl_take isl_space *space, enum isl_dim_type type);
790 int isl_space_has_tuple_id(__isl_keep isl_space *space,
791 enum isl_dim_type type);
792 __isl_give isl_id *isl_space_get_tuple_id(
793 __isl_keep isl_space *space, enum isl_dim_type type);
794 __isl_give isl_space *isl_space_set_tuple_name(
795 __isl_take isl_space *space,
796 enum isl_dim_type type, const char *s);
797 int isl_space_has_tuple_name(__isl_keep isl_space *space,
798 enum isl_dim_type type);
799 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
800 enum isl_dim_type type);
802 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
803 or C<isl_dim_set>. As with C<isl_space_get_name>,
804 the C<isl_space_get_tuple_name> function returns a pointer to some internal
806 Binary operations require the corresponding spaces of their arguments
807 to have the same name.
809 Spaces can be nested. In particular, the domain of a set or
810 the domain or range of a relation can be a nested relation.
811 The following functions can be used to construct and deconstruct
814 #include <isl/space.h>
815 int isl_space_is_wrapping(__isl_keep isl_space *space);
816 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
817 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
819 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
820 be the space of a set, while that of
821 C<isl_space_wrap> should be the space of a relation.
822 Conversely, the output of C<isl_space_unwrap> is the space
823 of a relation, while that of C<isl_space_wrap> is the space of a set.
825 Spaces can be created from other spaces
826 using the following functions.
828 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
829 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
830 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
831 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
832 __isl_give isl_space *isl_space_params(
833 __isl_take isl_space *space);
834 __isl_give isl_space *isl_space_set_from_params(
835 __isl_take isl_space *space);
836 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
837 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
838 __isl_take isl_space *right);
839 __isl_give isl_space *isl_space_align_params(
840 __isl_take isl_space *space1, __isl_take isl_space *space2)
841 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
842 enum isl_dim_type type, unsigned pos, unsigned n);
843 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
844 enum isl_dim_type type, unsigned n);
845 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
846 enum isl_dim_type type, unsigned first, unsigned n);
847 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
848 enum isl_dim_type dst_type, unsigned dst_pos,
849 enum isl_dim_type src_type, unsigned src_pos,
851 __isl_give isl_space *isl_space_map_from_set(
852 __isl_take isl_space *space);
853 __isl_give isl_space *isl_space_map_from_domain_and_range(
854 __isl_take isl_space *domain,
855 __isl_take isl_space *range);
856 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
857 __isl_give isl_space *isl_space_curry(
858 __isl_take isl_space *space);
860 Note that if dimensions are added or removed from a space, then
861 the name and the internal structure are lost.
865 A local space is essentially a space with
866 zero or more existentially quantified variables.
867 The local space of a (constraint of a) basic set or relation can be obtained
868 using the following functions.
870 #include <isl/constraint.h>
871 __isl_give isl_local_space *isl_constraint_get_local_space(
872 __isl_keep isl_constraint *constraint);
875 __isl_give isl_local_space *isl_basic_set_get_local_space(
876 __isl_keep isl_basic_set *bset);
879 __isl_give isl_local_space *isl_basic_map_get_local_space(
880 __isl_keep isl_basic_map *bmap);
882 A new local space can be created from a space using
884 #include <isl/local_space.h>
885 __isl_give isl_local_space *isl_local_space_from_space(
886 __isl_take isl_space *space);
888 They can be inspected, modified, copied and freed using the following functions.
890 #include <isl/local_space.h>
891 isl_ctx *isl_local_space_get_ctx(
892 __isl_keep isl_local_space *ls);
893 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
894 int isl_local_space_dim(__isl_keep isl_local_space *ls,
895 enum isl_dim_type type);
896 int isl_local_space_has_dim_id(
897 __isl_keep isl_local_space *ls,
898 enum isl_dim_type type, unsigned pos);
899 __isl_give isl_id *isl_local_space_get_dim_id(
900 __isl_keep isl_local_space *ls,
901 enum isl_dim_type type, unsigned pos);
902 int isl_local_space_has_dim_name(
903 __isl_keep isl_local_space *ls,
904 enum isl_dim_type type, unsigned pos)
905 const char *isl_local_space_get_dim_name(
906 __isl_keep isl_local_space *ls,
907 enum isl_dim_type type, unsigned pos);
908 __isl_give isl_local_space *isl_local_space_set_dim_name(
909 __isl_take isl_local_space *ls,
910 enum isl_dim_type type, unsigned pos, const char *s);
911 __isl_give isl_local_space *isl_local_space_set_dim_id(
912 __isl_take isl_local_space *ls,
913 enum isl_dim_type type, unsigned pos,
914 __isl_take isl_id *id);
915 __isl_give isl_space *isl_local_space_get_space(
916 __isl_keep isl_local_space *ls);
917 __isl_give isl_aff *isl_local_space_get_div(
918 __isl_keep isl_local_space *ls, int pos);
919 __isl_give isl_local_space *isl_local_space_copy(
920 __isl_keep isl_local_space *ls);
921 void *isl_local_space_free(__isl_take isl_local_space *ls);
923 Two local spaces can be compared using
925 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
926 __isl_keep isl_local_space *ls2);
928 Local spaces can be created from other local spaces
929 using the following functions.
931 __isl_give isl_local_space *isl_local_space_domain(
932 __isl_take isl_local_space *ls);
933 __isl_give isl_local_space *isl_local_space_range(
934 __isl_take isl_local_space *ls);
935 __isl_give isl_local_space *isl_local_space_from_domain(
936 __isl_take isl_local_space *ls);
937 __isl_give isl_local_space *isl_local_space_intersect(
938 __isl_take isl_local_space *ls1,
939 __isl_take isl_local_space *ls2);
940 __isl_give isl_local_space *isl_local_space_add_dims(
941 __isl_take isl_local_space *ls,
942 enum isl_dim_type type, unsigned n);
943 __isl_give isl_local_space *isl_local_space_insert_dims(
944 __isl_take isl_local_space *ls,
945 enum isl_dim_type type, unsigned first, unsigned n);
946 __isl_give isl_local_space *isl_local_space_drop_dims(
947 __isl_take isl_local_space *ls,
948 enum isl_dim_type type, unsigned first, unsigned n);
950 =head2 Input and Output
952 C<isl> supports its own input/output format, which is similar
953 to the C<Omega> format, but also supports the C<PolyLib> format
958 The C<isl> format is similar to that of C<Omega>, but has a different
959 syntax for describing the parameters and allows for the definition
960 of an existentially quantified variable as the integer division
961 of an affine expression.
962 For example, the set of integers C<i> between C<0> and C<n>
963 such that C<i % 10 <= 6> can be described as
965 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
968 A set or relation can have several disjuncts, separated
969 by the keyword C<or>. Each disjunct is either a conjunction
970 of constraints or a projection (C<exists>) of a conjunction
971 of constraints. The constraints are separated by the keyword
974 =head3 C<PolyLib> format
976 If the represented set is a union, then the first line
977 contains a single number representing the number of disjuncts.
978 Otherwise, a line containing the number C<1> is optional.
980 Each disjunct is represented by a matrix of constraints.
981 The first line contains two numbers representing
982 the number of rows and columns,
983 where the number of rows is equal to the number of constraints
984 and the number of columns is equal to two plus the number of variables.
985 The following lines contain the actual rows of the constraint matrix.
986 In each row, the first column indicates whether the constraint
987 is an equality (C<0>) or inequality (C<1>). The final column
988 corresponds to the constant term.
990 If the set is parametric, then the coefficients of the parameters
991 appear in the last columns before the constant column.
992 The coefficients of any existentially quantified variables appear
993 between those of the set variables and those of the parameters.
995 =head3 Extended C<PolyLib> format
997 The extended C<PolyLib> format is nearly identical to the
998 C<PolyLib> format. The only difference is that the line
999 containing the number of rows and columns of a constraint matrix
1000 also contains four additional numbers:
1001 the number of output dimensions, the number of input dimensions,
1002 the number of local dimensions (i.e., the number of existentially
1003 quantified variables) and the number of parameters.
1004 For sets, the number of ``output'' dimensions is equal
1005 to the number of set dimensions, while the number of ``input''
1010 #include <isl/set.h>
1011 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1012 isl_ctx *ctx, FILE *input);
1013 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1014 isl_ctx *ctx, const char *str);
1015 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1017 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1020 #include <isl/map.h>
1021 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1022 isl_ctx *ctx, FILE *input);
1023 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1024 isl_ctx *ctx, const char *str);
1025 __isl_give isl_map *isl_map_read_from_file(
1026 isl_ctx *ctx, FILE *input);
1027 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1030 #include <isl/union_set.h>
1031 __isl_give isl_union_set *isl_union_set_read_from_file(
1032 isl_ctx *ctx, FILE *input);
1033 __isl_give isl_union_set *isl_union_set_read_from_str(
1034 isl_ctx *ctx, const char *str);
1036 #include <isl/union_map.h>
1037 __isl_give isl_union_map *isl_union_map_read_from_file(
1038 isl_ctx *ctx, FILE *input);
1039 __isl_give isl_union_map *isl_union_map_read_from_str(
1040 isl_ctx *ctx, const char *str);
1042 The input format is autodetected and may be either the C<PolyLib> format
1043 or the C<isl> format.
1047 Before anything can be printed, an C<isl_printer> needs to
1050 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1052 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1053 void *isl_printer_free(__isl_take isl_printer *printer);
1054 __isl_give char *isl_printer_get_str(
1055 __isl_keep isl_printer *printer);
1057 The printer can be inspected using the following functions.
1059 FILE *isl_printer_get_file(
1060 __isl_keep isl_printer *printer);
1061 int isl_printer_get_output_format(
1062 __isl_keep isl_printer *p);
1064 The behavior of the printer can be modified in various ways
1066 __isl_give isl_printer *isl_printer_set_output_format(
1067 __isl_take isl_printer *p, int output_format);
1068 __isl_give isl_printer *isl_printer_set_indent(
1069 __isl_take isl_printer *p, int indent);
1070 __isl_give isl_printer *isl_printer_indent(
1071 __isl_take isl_printer *p, int indent);
1072 __isl_give isl_printer *isl_printer_set_prefix(
1073 __isl_take isl_printer *p, const char *prefix);
1074 __isl_give isl_printer *isl_printer_set_suffix(
1075 __isl_take isl_printer *p, const char *suffix);
1077 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1078 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1079 and defaults to C<ISL_FORMAT_ISL>.
1080 Each line in the output is indented by C<indent> (set by
1081 C<isl_printer_set_indent>) spaces
1082 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1083 In the C<PolyLib> format output,
1084 the coefficients of the existentially quantified variables
1085 appear between those of the set variables and those
1087 The function C<isl_printer_indent> increases the indentation
1088 by the specified amount (which may be negative).
1090 To actually print something, use
1092 #include <isl/printer.h>
1093 __isl_give isl_printer *isl_printer_print_double(
1094 __isl_take isl_printer *p, double d);
1096 #include <isl/set.h>
1097 __isl_give isl_printer *isl_printer_print_basic_set(
1098 __isl_take isl_printer *printer,
1099 __isl_keep isl_basic_set *bset);
1100 __isl_give isl_printer *isl_printer_print_set(
1101 __isl_take isl_printer *printer,
1102 __isl_keep isl_set *set);
1104 #include <isl/map.h>
1105 __isl_give isl_printer *isl_printer_print_basic_map(
1106 __isl_take isl_printer *printer,
1107 __isl_keep isl_basic_map *bmap);
1108 __isl_give isl_printer *isl_printer_print_map(
1109 __isl_take isl_printer *printer,
1110 __isl_keep isl_map *map);
1112 #include <isl/union_set.h>
1113 __isl_give isl_printer *isl_printer_print_union_set(
1114 __isl_take isl_printer *p,
1115 __isl_keep isl_union_set *uset);
1117 #include <isl/union_map.h>
1118 __isl_give isl_printer *isl_printer_print_union_map(
1119 __isl_take isl_printer *p,
1120 __isl_keep isl_union_map *umap);
1122 When called on a file printer, the following function flushes
1123 the file. When called on a string printer, the buffer is cleared.
1125 __isl_give isl_printer *isl_printer_flush(
1126 __isl_take isl_printer *p);
1128 =head2 Creating New Sets and Relations
1130 C<isl> has functions for creating some standard sets and relations.
1134 =item * Empty sets and relations
1136 __isl_give isl_basic_set *isl_basic_set_empty(
1137 __isl_take isl_space *space);
1138 __isl_give isl_basic_map *isl_basic_map_empty(
1139 __isl_take isl_space *space);
1140 __isl_give isl_set *isl_set_empty(
1141 __isl_take isl_space *space);
1142 __isl_give isl_map *isl_map_empty(
1143 __isl_take isl_space *space);
1144 __isl_give isl_union_set *isl_union_set_empty(
1145 __isl_take isl_space *space);
1146 __isl_give isl_union_map *isl_union_map_empty(
1147 __isl_take isl_space *space);
1149 For C<isl_union_set>s and C<isl_union_map>s, the space
1150 is only used to specify the parameters.
1152 =item * Universe sets and relations
1154 __isl_give isl_basic_set *isl_basic_set_universe(
1155 __isl_take isl_space *space);
1156 __isl_give isl_basic_map *isl_basic_map_universe(
1157 __isl_take isl_space *space);
1158 __isl_give isl_set *isl_set_universe(
1159 __isl_take isl_space *space);
1160 __isl_give isl_map *isl_map_universe(
1161 __isl_take isl_space *space);
1162 __isl_give isl_union_set *isl_union_set_universe(
1163 __isl_take isl_union_set *uset);
1164 __isl_give isl_union_map *isl_union_map_universe(
1165 __isl_take isl_union_map *umap);
1167 The sets and relations constructed by the functions above
1168 contain all integer values, while those constructed by the
1169 functions below only contain non-negative values.
1171 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1172 __isl_take isl_space *space);
1173 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1174 __isl_take isl_space *space);
1175 __isl_give isl_set *isl_set_nat_universe(
1176 __isl_take isl_space *space);
1177 __isl_give isl_map *isl_map_nat_universe(
1178 __isl_take isl_space *space);
1180 =item * Identity relations
1182 __isl_give isl_basic_map *isl_basic_map_identity(
1183 __isl_take isl_space *space);
1184 __isl_give isl_map *isl_map_identity(
1185 __isl_take isl_space *space);
1187 The number of input and output dimensions in C<space> needs
1190 =item * Lexicographic order
1192 __isl_give isl_map *isl_map_lex_lt(
1193 __isl_take isl_space *set_space);
1194 __isl_give isl_map *isl_map_lex_le(
1195 __isl_take isl_space *set_space);
1196 __isl_give isl_map *isl_map_lex_gt(
1197 __isl_take isl_space *set_space);
1198 __isl_give isl_map *isl_map_lex_ge(
1199 __isl_take isl_space *set_space);
1200 __isl_give isl_map *isl_map_lex_lt_first(
1201 __isl_take isl_space *space, unsigned n);
1202 __isl_give isl_map *isl_map_lex_le_first(
1203 __isl_take isl_space *space, unsigned n);
1204 __isl_give isl_map *isl_map_lex_gt_first(
1205 __isl_take isl_space *space, unsigned n);
1206 __isl_give isl_map *isl_map_lex_ge_first(
1207 __isl_take isl_space *space, unsigned n);
1209 The first four functions take a space for a B<set>
1210 and return relations that express that the elements in the domain
1211 are lexicographically less
1212 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1213 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1214 than the elements in the range.
1215 The last four functions take a space for a map
1216 and return relations that express that the first C<n> dimensions
1217 in the domain are lexicographically less
1218 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1219 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1220 than the first C<n> dimensions in the range.
1224 A basic set or relation can be converted to a set or relation
1225 using the following functions.
1227 __isl_give isl_set *isl_set_from_basic_set(
1228 __isl_take isl_basic_set *bset);
1229 __isl_give isl_map *isl_map_from_basic_map(
1230 __isl_take isl_basic_map *bmap);
1232 Sets and relations can be converted to union sets and relations
1233 using the following functions.
1235 __isl_give isl_union_set *isl_union_set_from_basic_set(
1236 __isl_take isl_basic_set *bset);
1237 __isl_give isl_union_map *isl_union_map_from_basic_map(
1238 __isl_take isl_basic_map *bmap);
1239 __isl_give isl_union_set *isl_union_set_from_set(
1240 __isl_take isl_set *set);
1241 __isl_give isl_union_map *isl_union_map_from_map(
1242 __isl_take isl_map *map);
1244 The inverse conversions below can only be used if the input
1245 union set or relation is known to contain elements in exactly one
1248 __isl_give isl_set *isl_set_from_union_set(
1249 __isl_take isl_union_set *uset);
1250 __isl_give isl_map *isl_map_from_union_map(
1251 __isl_take isl_union_map *umap);
1253 A zero-dimensional set can be constructed on a given parameter domain
1254 using the following function.
1256 __isl_give isl_set *isl_set_from_params(
1257 __isl_take isl_set *set);
1259 Sets and relations can be copied and freed again using the following
1262 __isl_give isl_basic_set *isl_basic_set_copy(
1263 __isl_keep isl_basic_set *bset);
1264 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1265 __isl_give isl_union_set *isl_union_set_copy(
1266 __isl_keep isl_union_set *uset);
1267 __isl_give isl_basic_map *isl_basic_map_copy(
1268 __isl_keep isl_basic_map *bmap);
1269 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1270 __isl_give isl_union_map *isl_union_map_copy(
1271 __isl_keep isl_union_map *umap);
1272 void isl_basic_set_free(__isl_take isl_basic_set *bset);
1273 void *isl_set_free(__isl_take isl_set *set);
1274 void *isl_union_set_free(__isl_take isl_union_set *uset);
1275 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
1276 void isl_map_free(__isl_take isl_map *map);
1277 void *isl_union_map_free(__isl_take isl_union_map *umap);
1279 Other sets and relations can be constructed by starting
1280 from a universe set or relation, adding equality and/or
1281 inequality constraints and then projecting out the
1282 existentially quantified variables, if any.
1283 Constraints can be constructed, manipulated and
1284 added to (or removed from) (basic) sets and relations
1285 using the following functions.
1287 #include <isl/constraint.h>
1288 __isl_give isl_constraint *isl_equality_alloc(
1289 __isl_take isl_local_space *ls);
1290 __isl_give isl_constraint *isl_inequality_alloc(
1291 __isl_take isl_local_space *ls);
1292 __isl_give isl_constraint *isl_constraint_set_constant(
1293 __isl_take isl_constraint *constraint, isl_int v);
1294 __isl_give isl_constraint *isl_constraint_set_constant_si(
1295 __isl_take isl_constraint *constraint, int v);
1296 __isl_give isl_constraint *isl_constraint_set_coefficient(
1297 __isl_take isl_constraint *constraint,
1298 enum isl_dim_type type, int pos, isl_int v);
1299 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1300 __isl_take isl_constraint *constraint,
1301 enum isl_dim_type type, int pos, int v);
1302 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1303 __isl_take isl_basic_map *bmap,
1304 __isl_take isl_constraint *constraint);
1305 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1306 __isl_take isl_basic_set *bset,
1307 __isl_take isl_constraint *constraint);
1308 __isl_give isl_map *isl_map_add_constraint(
1309 __isl_take isl_map *map,
1310 __isl_take isl_constraint *constraint);
1311 __isl_give isl_set *isl_set_add_constraint(
1312 __isl_take isl_set *set,
1313 __isl_take isl_constraint *constraint);
1314 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1315 __isl_take isl_basic_set *bset,
1316 __isl_take isl_constraint *constraint);
1318 For example, to create a set containing the even integers
1319 between 10 and 42, you would use the following code.
1322 isl_local_space *ls;
1324 isl_basic_set *bset;
1326 space = isl_space_set_alloc(ctx, 0, 2);
1327 bset = isl_basic_set_universe(isl_space_copy(space));
1328 ls = isl_local_space_from_space(space);
1330 c = isl_equality_alloc(isl_local_space_copy(ls));
1331 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1332 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1333 bset = isl_basic_set_add_constraint(bset, c);
1335 c = isl_inequality_alloc(isl_local_space_copy(ls));
1336 c = isl_constraint_set_constant_si(c, -10);
1337 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1338 bset = isl_basic_set_add_constraint(bset, c);
1340 c = isl_inequality_alloc(ls);
1341 c = isl_constraint_set_constant_si(c, 42);
1342 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1343 bset = isl_basic_set_add_constraint(bset, c);
1345 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1349 isl_basic_set *bset;
1350 bset = isl_basic_set_read_from_str(ctx,
1351 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1353 A basic set or relation can also be constructed from two matrices
1354 describing the equalities and the inequalities.
1356 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1357 __isl_take isl_space *space,
1358 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1359 enum isl_dim_type c1,
1360 enum isl_dim_type c2, enum isl_dim_type c3,
1361 enum isl_dim_type c4);
1362 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1363 __isl_take isl_space *space,
1364 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1365 enum isl_dim_type c1,
1366 enum isl_dim_type c2, enum isl_dim_type c3,
1367 enum isl_dim_type c4, enum isl_dim_type c5);
1369 The C<isl_dim_type> arguments indicate the order in which
1370 different kinds of variables appear in the input matrices
1371 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1372 C<isl_dim_set> and C<isl_dim_div> for sets and
1373 of C<isl_dim_cst>, C<isl_dim_param>,
1374 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1376 A (basic or union) set or relation can also be constructed from a
1377 (union) (piecewise) (multiple) affine expression
1378 or a list of affine expressions
1379 (See L<"Piecewise Quasi Affine Expressions"> and
1380 L<"Piecewise Multiple Quasi Affine Expressions">).
1382 __isl_give isl_basic_map *isl_basic_map_from_aff(
1383 __isl_take isl_aff *aff);
1384 __isl_give isl_map *isl_map_from_aff(
1385 __isl_take isl_aff *aff);
1386 __isl_give isl_set *isl_set_from_pw_aff(
1387 __isl_take isl_pw_aff *pwaff);
1388 __isl_give isl_map *isl_map_from_pw_aff(
1389 __isl_take isl_pw_aff *pwaff);
1390 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1391 __isl_take isl_space *domain_space,
1392 __isl_take isl_aff_list *list);
1393 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1394 __isl_take isl_multi_aff *maff)
1395 __isl_give isl_map *isl_map_from_multi_aff(
1396 __isl_take isl_multi_aff *maff)
1397 __isl_give isl_set *isl_set_from_pw_multi_aff(
1398 __isl_take isl_pw_multi_aff *pma);
1399 __isl_give isl_map *isl_map_from_pw_multi_aff(
1400 __isl_take isl_pw_multi_aff *pma);
1401 __isl_give isl_union_map *
1402 isl_union_map_from_union_pw_multi_aff(
1403 __isl_take isl_union_pw_multi_aff *upma);
1405 The C<domain_dim> argument describes the domain of the resulting
1406 basic relation. It is required because the C<list> may consist
1407 of zero affine expressions.
1409 =head2 Inspecting Sets and Relations
1411 Usually, the user should not have to care about the actual constraints
1412 of the sets and maps, but should instead apply the abstract operations
1413 explained in the following sections.
1414 Occasionally, however, it may be required to inspect the individual
1415 coefficients of the constraints. This section explains how to do so.
1416 In these cases, it may also be useful to have C<isl> compute
1417 an explicit representation of the existentially quantified variables.
1419 __isl_give isl_set *isl_set_compute_divs(
1420 __isl_take isl_set *set);
1421 __isl_give isl_map *isl_map_compute_divs(
1422 __isl_take isl_map *map);
1423 __isl_give isl_union_set *isl_union_set_compute_divs(
1424 __isl_take isl_union_set *uset);
1425 __isl_give isl_union_map *isl_union_map_compute_divs(
1426 __isl_take isl_union_map *umap);
1428 This explicit representation defines the existentially quantified
1429 variables as integer divisions of the other variables, possibly
1430 including earlier existentially quantified variables.
1431 An explicitly represented existentially quantified variable therefore
1432 has a unique value when the values of the other variables are known.
1433 If, furthermore, the same existentials, i.e., existentials
1434 with the same explicit representations, should appear in the
1435 same order in each of the disjuncts of a set or map, then the user should call
1436 either of the following functions.
1438 __isl_give isl_set *isl_set_align_divs(
1439 __isl_take isl_set *set);
1440 __isl_give isl_map *isl_map_align_divs(
1441 __isl_take isl_map *map);
1443 Alternatively, the existentially quantified variables can be removed
1444 using the following functions, which compute an overapproximation.
1446 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1447 __isl_take isl_basic_set *bset);
1448 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1449 __isl_take isl_basic_map *bmap);
1450 __isl_give isl_set *isl_set_remove_divs(
1451 __isl_take isl_set *set);
1452 __isl_give isl_map *isl_map_remove_divs(
1453 __isl_take isl_map *map);
1455 It is also possible to only remove those divs that are defined
1456 in terms of a given range of dimensions or only those for which
1457 no explicit representation is known.
1459 __isl_give isl_basic_set *
1460 isl_basic_set_remove_divs_involving_dims(
1461 __isl_take isl_basic_set *bset,
1462 enum isl_dim_type type,
1463 unsigned first, unsigned n);
1464 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1465 __isl_take isl_set *set, enum isl_dim_type type,
1466 unsigned first, unsigned n);
1467 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1468 __isl_take isl_map *map, enum isl_dim_type type,
1469 unsigned first, unsigned n);
1471 __isl_give isl_set *isl_set_remove_unknown_divs(
1472 __isl_take isl_set *set);
1473 __isl_give isl_map *isl_map_remove_unknown_divs(
1474 __isl_take isl_map *map);
1476 To iterate over all the sets or maps in a union set or map, use
1478 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1479 int (*fn)(__isl_take isl_set *set, void *user),
1481 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1482 int (*fn)(__isl_take isl_map *map, void *user),
1485 The number of sets or maps in a union set or map can be obtained
1488 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1489 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1491 To extract the set or map in a given space from a union, use
1493 __isl_give isl_set *isl_union_set_extract_set(
1494 __isl_keep isl_union_set *uset,
1495 __isl_take isl_space *space);
1496 __isl_give isl_map *isl_union_map_extract_map(
1497 __isl_keep isl_union_map *umap,
1498 __isl_take isl_space *space);
1500 To iterate over all the basic sets or maps in a set or map, use
1502 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1503 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1505 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1506 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1509 The callback function C<fn> should return 0 if successful and
1510 -1 if an error occurs. In the latter case, or if any other error
1511 occurs, the above functions will return -1.
1513 It should be noted that C<isl> does not guarantee that
1514 the basic sets or maps passed to C<fn> are disjoint.
1515 If this is required, then the user should call one of
1516 the following functions first.
1518 __isl_give isl_set *isl_set_make_disjoint(
1519 __isl_take isl_set *set);
1520 __isl_give isl_map *isl_map_make_disjoint(
1521 __isl_take isl_map *map);
1523 The number of basic sets in a set can be obtained
1526 int isl_set_n_basic_set(__isl_keep isl_set *set);
1528 To iterate over the constraints of a basic set or map, use
1530 #include <isl/constraint.h>
1532 int isl_basic_set_n_constraint(
1533 __isl_keep isl_basic_set *bset);
1534 int isl_basic_set_foreach_constraint(
1535 __isl_keep isl_basic_set *bset,
1536 int (*fn)(__isl_take isl_constraint *c, void *user),
1538 int isl_basic_map_foreach_constraint(
1539 __isl_keep isl_basic_map *bmap,
1540 int (*fn)(__isl_take isl_constraint *c, void *user),
1542 void *isl_constraint_free(__isl_take isl_constraint *c);
1544 Again, the callback function C<fn> should return 0 if successful and
1545 -1 if an error occurs. In the latter case, or if any other error
1546 occurs, the above functions will return -1.
1547 The constraint C<c> represents either an equality or an inequality.
1548 Use the following function to find out whether a constraint
1549 represents an equality. If not, it represents an inequality.
1551 int isl_constraint_is_equality(
1552 __isl_keep isl_constraint *constraint);
1554 The coefficients of the constraints can be inspected using
1555 the following functions.
1557 int isl_constraint_is_lower_bound(
1558 __isl_keep isl_constraint *constraint,
1559 enum isl_dim_type type, unsigned pos);
1560 int isl_constraint_is_upper_bound(
1561 __isl_keep isl_constraint *constraint,
1562 enum isl_dim_type type, unsigned pos);
1563 void isl_constraint_get_constant(
1564 __isl_keep isl_constraint *constraint, isl_int *v);
1565 void isl_constraint_get_coefficient(
1566 __isl_keep isl_constraint *constraint,
1567 enum isl_dim_type type, int pos, isl_int *v);
1568 int isl_constraint_involves_dims(
1569 __isl_keep isl_constraint *constraint,
1570 enum isl_dim_type type, unsigned first, unsigned n);
1572 The explicit representations of the existentially quantified
1573 variables can be inspected using the following function.
1574 Note that the user is only allowed to use this function
1575 if the inspected set or map is the result of a call
1576 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1577 The existentially quantified variable is equal to the floor
1578 of the returned affine expression. The affine expression
1579 itself can be inspected using the functions in
1580 L<"Piecewise Quasi Affine Expressions">.
1582 __isl_give isl_aff *isl_constraint_get_div(
1583 __isl_keep isl_constraint *constraint, int pos);
1585 To obtain the constraints of a basic set or map in matrix
1586 form, use the following functions.
1588 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1589 __isl_keep isl_basic_set *bset,
1590 enum isl_dim_type c1, enum isl_dim_type c2,
1591 enum isl_dim_type c3, enum isl_dim_type c4);
1592 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1593 __isl_keep isl_basic_set *bset,
1594 enum isl_dim_type c1, enum isl_dim_type c2,
1595 enum isl_dim_type c3, enum isl_dim_type c4);
1596 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1597 __isl_keep isl_basic_map *bmap,
1598 enum isl_dim_type c1,
1599 enum isl_dim_type c2, enum isl_dim_type c3,
1600 enum isl_dim_type c4, enum isl_dim_type c5);
1601 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1602 __isl_keep isl_basic_map *bmap,
1603 enum isl_dim_type c1,
1604 enum isl_dim_type c2, enum isl_dim_type c3,
1605 enum isl_dim_type c4, enum isl_dim_type c5);
1607 The C<isl_dim_type> arguments dictate the order in which
1608 different kinds of variables appear in the resulting matrix
1609 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1610 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1612 The number of parameters, input, output or set dimensions can
1613 be obtained using the following functions.
1615 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1616 enum isl_dim_type type);
1617 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1618 enum isl_dim_type type);
1619 unsigned isl_set_dim(__isl_keep isl_set *set,
1620 enum isl_dim_type type);
1621 unsigned isl_map_dim(__isl_keep isl_map *map,
1622 enum isl_dim_type type);
1624 To check whether the description of a set or relation depends
1625 on one or more given dimensions, it is not necessary to iterate over all
1626 constraints. Instead the following functions can be used.
1628 int isl_basic_set_involves_dims(
1629 __isl_keep isl_basic_set *bset,
1630 enum isl_dim_type type, unsigned first, unsigned n);
1631 int isl_set_involves_dims(__isl_keep isl_set *set,
1632 enum isl_dim_type type, unsigned first, unsigned n);
1633 int isl_basic_map_involves_dims(
1634 __isl_keep isl_basic_map *bmap,
1635 enum isl_dim_type type, unsigned first, unsigned n);
1636 int isl_map_involves_dims(__isl_keep isl_map *map,
1637 enum isl_dim_type type, unsigned first, unsigned n);
1639 Similarly, the following functions can be used to check whether
1640 a given dimension is involved in any lower or upper bound.
1642 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1643 enum isl_dim_type type, unsigned pos);
1644 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1645 enum isl_dim_type type, unsigned pos);
1647 The identifiers or names of the domain and range spaces of a set
1648 or relation can be read off or set using the following functions.
1650 __isl_give isl_set *isl_set_set_tuple_id(
1651 __isl_take isl_set *set, __isl_take isl_id *id);
1652 __isl_give isl_set *isl_set_reset_tuple_id(
1653 __isl_take isl_set *set);
1654 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1655 __isl_give isl_id *isl_set_get_tuple_id(
1656 __isl_keep isl_set *set);
1657 __isl_give isl_map *isl_map_set_tuple_id(
1658 __isl_take isl_map *map, enum isl_dim_type type,
1659 __isl_take isl_id *id);
1660 __isl_give isl_map *isl_map_reset_tuple_id(
1661 __isl_take isl_map *map, enum isl_dim_type type);
1662 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1663 enum isl_dim_type type);
1664 __isl_give isl_id *isl_map_get_tuple_id(
1665 __isl_keep isl_map *map, enum isl_dim_type type);
1667 const char *isl_basic_set_get_tuple_name(
1668 __isl_keep isl_basic_set *bset);
1669 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1670 __isl_take isl_basic_set *set, const char *s);
1671 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1672 const char *isl_set_get_tuple_name(
1673 __isl_keep isl_set *set);
1674 const char *isl_basic_map_get_tuple_name(
1675 __isl_keep isl_basic_map *bmap,
1676 enum isl_dim_type type);
1677 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1678 __isl_take isl_basic_map *bmap,
1679 enum isl_dim_type type, const char *s);
1680 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1681 enum isl_dim_type type);
1682 const char *isl_map_get_tuple_name(
1683 __isl_keep isl_map *map,
1684 enum isl_dim_type type);
1686 As with C<isl_space_get_tuple_name>, the value returned points to
1687 an internal data structure.
1688 The identifiers, positions or names of individual dimensions can be
1689 read off using the following functions.
1691 __isl_give isl_id *isl_basic_set_get_dim_id(
1692 __isl_keep isl_basic_set *bset,
1693 enum isl_dim_type type, unsigned pos);
1694 __isl_give isl_set *isl_set_set_dim_id(
1695 __isl_take isl_set *set, enum isl_dim_type type,
1696 unsigned pos, __isl_take isl_id *id);
1697 int isl_set_has_dim_id(__isl_keep isl_set *set,
1698 enum isl_dim_type type, unsigned pos);
1699 __isl_give isl_id *isl_set_get_dim_id(
1700 __isl_keep isl_set *set, enum isl_dim_type type,
1702 int isl_basic_map_has_dim_id(
1703 __isl_keep isl_basic_map *bmap,
1704 enum isl_dim_type type, unsigned pos);
1705 __isl_give isl_map *isl_map_set_dim_id(
1706 __isl_take isl_map *map, enum isl_dim_type type,
1707 unsigned pos, __isl_take isl_id *id);
1708 int isl_map_has_dim_id(__isl_keep isl_map *map,
1709 enum isl_dim_type type, unsigned pos);
1710 __isl_give isl_id *isl_map_get_dim_id(
1711 __isl_keep isl_map *map, enum isl_dim_type type,
1714 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1715 enum isl_dim_type type, __isl_keep isl_id *id);
1716 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1717 enum isl_dim_type type, __isl_keep isl_id *id);
1718 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1719 enum isl_dim_type type, const char *name);
1720 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1721 enum isl_dim_type type, const char *name);
1723 const char *isl_constraint_get_dim_name(
1724 __isl_keep isl_constraint *constraint,
1725 enum isl_dim_type type, unsigned pos);
1726 const char *isl_basic_set_get_dim_name(
1727 __isl_keep isl_basic_set *bset,
1728 enum isl_dim_type type, unsigned pos);
1729 int isl_set_has_dim_name(__isl_keep isl_set *set,
1730 enum isl_dim_type type, unsigned pos);
1731 const char *isl_set_get_dim_name(
1732 __isl_keep isl_set *set,
1733 enum isl_dim_type type, unsigned pos);
1734 const char *isl_basic_map_get_dim_name(
1735 __isl_keep isl_basic_map *bmap,
1736 enum isl_dim_type type, unsigned pos);
1737 int isl_map_has_dim_name(__isl_keep isl_map *map,
1738 enum isl_dim_type type, unsigned pos);
1739 const char *isl_map_get_dim_name(
1740 __isl_keep isl_map *map,
1741 enum isl_dim_type type, unsigned pos);
1743 These functions are mostly useful to obtain the identifiers, positions
1744 or names of the parameters. Identifiers of individual dimensions are
1745 essentially only useful for printing. They are ignored by all other
1746 operations and may not be preserved across those operations.
1750 =head3 Unary Properties
1756 The following functions test whether the given set or relation
1757 contains any integer points. The ``plain'' variants do not perform
1758 any computations, but simply check if the given set or relation
1759 is already known to be empty.
1761 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1762 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1763 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1764 int isl_set_is_empty(__isl_keep isl_set *set);
1765 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1766 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1767 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1768 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1769 int isl_map_is_empty(__isl_keep isl_map *map);
1770 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1772 =item * Universality
1774 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1775 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1776 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1778 =item * Single-valuedness
1780 int isl_basic_map_is_single_valued(
1781 __isl_keep isl_basic_map *bmap);
1782 int isl_map_plain_is_single_valued(
1783 __isl_keep isl_map *map);
1784 int isl_map_is_single_valued(__isl_keep isl_map *map);
1785 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1789 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1790 int isl_map_is_injective(__isl_keep isl_map *map);
1791 int isl_union_map_plain_is_injective(
1792 __isl_keep isl_union_map *umap);
1793 int isl_union_map_is_injective(
1794 __isl_keep isl_union_map *umap);
1798 int isl_map_is_bijective(__isl_keep isl_map *map);
1799 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1803 int isl_basic_map_plain_is_fixed(
1804 __isl_keep isl_basic_map *bmap,
1805 enum isl_dim_type type, unsigned pos,
1807 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1808 enum isl_dim_type type, unsigned pos,
1810 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1811 enum isl_dim_type type, unsigned pos,
1814 Check if the relation obviously lies on a hyperplane where the given dimension
1815 has a fixed value and if so, return that value in C<*val>.
1819 To check whether a set is a parameter domain, use this function:
1821 int isl_set_is_params(__isl_keep isl_set *set);
1822 int isl_union_set_is_params(
1823 __isl_keep isl_union_set *uset);
1827 The following functions check whether the domain of the given
1828 (basic) set is a wrapped relation.
1830 int isl_basic_set_is_wrapping(
1831 __isl_keep isl_basic_set *bset);
1832 int isl_set_is_wrapping(__isl_keep isl_set *set);
1834 =item * Internal Product
1836 int isl_basic_map_can_zip(
1837 __isl_keep isl_basic_map *bmap);
1838 int isl_map_can_zip(__isl_keep isl_map *map);
1840 Check whether the product of domain and range of the given relation
1842 i.e., whether both domain and range are nested relations.
1846 int isl_basic_map_can_curry(
1847 __isl_keep isl_basic_map *bmap);
1848 int isl_map_can_curry(__isl_keep isl_map *map);
1850 Check whether the domain of the (basic) relation is a wrapped relation.
1854 =head3 Binary Properties
1860 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1861 __isl_keep isl_set *set2);
1862 int isl_set_is_equal(__isl_keep isl_set *set1,
1863 __isl_keep isl_set *set2);
1864 int isl_union_set_is_equal(
1865 __isl_keep isl_union_set *uset1,
1866 __isl_keep isl_union_set *uset2);
1867 int isl_basic_map_is_equal(
1868 __isl_keep isl_basic_map *bmap1,
1869 __isl_keep isl_basic_map *bmap2);
1870 int isl_map_is_equal(__isl_keep isl_map *map1,
1871 __isl_keep isl_map *map2);
1872 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1873 __isl_keep isl_map *map2);
1874 int isl_union_map_is_equal(
1875 __isl_keep isl_union_map *umap1,
1876 __isl_keep isl_union_map *umap2);
1878 =item * Disjointness
1880 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1881 __isl_keep isl_set *set2);
1885 int isl_basic_set_is_subset(
1886 __isl_keep isl_basic_set *bset1,
1887 __isl_keep isl_basic_set *bset2);
1888 int isl_set_is_subset(__isl_keep isl_set *set1,
1889 __isl_keep isl_set *set2);
1890 int isl_set_is_strict_subset(
1891 __isl_keep isl_set *set1,
1892 __isl_keep isl_set *set2);
1893 int isl_union_set_is_subset(
1894 __isl_keep isl_union_set *uset1,
1895 __isl_keep isl_union_set *uset2);
1896 int isl_union_set_is_strict_subset(
1897 __isl_keep isl_union_set *uset1,
1898 __isl_keep isl_union_set *uset2);
1899 int isl_basic_map_is_subset(
1900 __isl_keep isl_basic_map *bmap1,
1901 __isl_keep isl_basic_map *bmap2);
1902 int isl_basic_map_is_strict_subset(
1903 __isl_keep isl_basic_map *bmap1,
1904 __isl_keep isl_basic_map *bmap2);
1905 int isl_map_is_subset(
1906 __isl_keep isl_map *map1,
1907 __isl_keep isl_map *map2);
1908 int isl_map_is_strict_subset(
1909 __isl_keep isl_map *map1,
1910 __isl_keep isl_map *map2);
1911 int isl_union_map_is_subset(
1912 __isl_keep isl_union_map *umap1,
1913 __isl_keep isl_union_map *umap2);
1914 int isl_union_map_is_strict_subset(
1915 __isl_keep isl_union_map *umap1,
1916 __isl_keep isl_union_map *umap2);
1918 Check whether the first argument is a (strict) subset of the
1923 =head2 Unary Operations
1929 __isl_give isl_set *isl_set_complement(
1930 __isl_take isl_set *set);
1931 __isl_give isl_map *isl_map_complement(
1932 __isl_take isl_map *map);
1936 __isl_give isl_basic_map *isl_basic_map_reverse(
1937 __isl_take isl_basic_map *bmap);
1938 __isl_give isl_map *isl_map_reverse(
1939 __isl_take isl_map *map);
1940 __isl_give isl_union_map *isl_union_map_reverse(
1941 __isl_take isl_union_map *umap);
1945 __isl_give isl_basic_set *isl_basic_set_project_out(
1946 __isl_take isl_basic_set *bset,
1947 enum isl_dim_type type, unsigned first, unsigned n);
1948 __isl_give isl_basic_map *isl_basic_map_project_out(
1949 __isl_take isl_basic_map *bmap,
1950 enum isl_dim_type type, unsigned first, unsigned n);
1951 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1952 enum isl_dim_type type, unsigned first, unsigned n);
1953 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1954 enum isl_dim_type type, unsigned first, unsigned n);
1955 __isl_give isl_basic_set *isl_basic_set_params(
1956 __isl_take isl_basic_set *bset);
1957 __isl_give isl_basic_set *isl_basic_map_domain(
1958 __isl_take isl_basic_map *bmap);
1959 __isl_give isl_basic_set *isl_basic_map_range(
1960 __isl_take isl_basic_map *bmap);
1961 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
1962 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
1963 __isl_give isl_set *isl_map_domain(
1964 __isl_take isl_map *bmap);
1965 __isl_give isl_set *isl_map_range(
1966 __isl_take isl_map *map);
1967 __isl_give isl_set *isl_union_set_params(
1968 __isl_take isl_union_set *uset);
1969 __isl_give isl_set *isl_union_map_params(
1970 __isl_take isl_union_map *umap);
1971 __isl_give isl_union_set *isl_union_map_domain(
1972 __isl_take isl_union_map *umap);
1973 __isl_give isl_union_set *isl_union_map_range(
1974 __isl_take isl_union_map *umap);
1976 __isl_give isl_basic_map *isl_basic_map_domain_map(
1977 __isl_take isl_basic_map *bmap);
1978 __isl_give isl_basic_map *isl_basic_map_range_map(
1979 __isl_take isl_basic_map *bmap);
1980 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1981 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1982 __isl_give isl_union_map *isl_union_map_domain_map(
1983 __isl_take isl_union_map *umap);
1984 __isl_give isl_union_map *isl_union_map_range_map(
1985 __isl_take isl_union_map *umap);
1987 The functions above construct a (basic, regular or union) relation
1988 that maps (a wrapped version of) the input relation to its domain or range.
1992 __isl_give isl_basic_set *isl_basic_set_eliminate(
1993 __isl_take isl_basic_set *bset,
1994 enum isl_dim_type type,
1995 unsigned first, unsigned n);
1996 __isl_give isl_set *isl_set_eliminate(
1997 __isl_take isl_set *set, enum isl_dim_type type,
1998 unsigned first, unsigned n);
1999 __isl_give isl_basic_map *isl_basic_map_eliminate(
2000 __isl_take isl_basic_map *bmap,
2001 enum isl_dim_type type,
2002 unsigned first, unsigned n);
2003 __isl_give isl_map *isl_map_eliminate(
2004 __isl_take isl_map *map, enum isl_dim_type type,
2005 unsigned first, unsigned n);
2007 Eliminate the coefficients for the given dimensions from the constraints,
2008 without removing the dimensions.
2012 __isl_give isl_basic_set *isl_basic_set_fix(
2013 __isl_take isl_basic_set *bset,
2014 enum isl_dim_type type, unsigned pos,
2016 __isl_give isl_basic_set *isl_basic_set_fix_si(
2017 __isl_take isl_basic_set *bset,
2018 enum isl_dim_type type, unsigned pos, int value);
2019 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2020 enum isl_dim_type type, unsigned pos,
2022 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2023 enum isl_dim_type type, unsigned pos, int value);
2024 __isl_give isl_basic_map *isl_basic_map_fix_si(
2025 __isl_take isl_basic_map *bmap,
2026 enum isl_dim_type type, unsigned pos, int value);
2027 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2028 enum isl_dim_type type, unsigned pos, int value);
2030 Intersect the set or relation with the hyperplane where the given
2031 dimension has the fixed given value.
2033 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2034 __isl_take isl_basic_map *bmap,
2035 enum isl_dim_type type, unsigned pos, int value);
2036 __isl_give isl_set *isl_set_lower_bound(
2037 __isl_take isl_set *set,
2038 enum isl_dim_type type, unsigned pos,
2040 __isl_give isl_set *isl_set_lower_bound_si(
2041 __isl_take isl_set *set,
2042 enum isl_dim_type type, unsigned pos, int value);
2043 __isl_give isl_map *isl_map_lower_bound_si(
2044 __isl_take isl_map *map,
2045 enum isl_dim_type type, unsigned pos, int value);
2046 __isl_give isl_set *isl_set_upper_bound(
2047 __isl_take isl_set *set,
2048 enum isl_dim_type type, unsigned pos,
2050 __isl_give isl_set *isl_set_upper_bound_si(
2051 __isl_take isl_set *set,
2052 enum isl_dim_type type, unsigned pos, int value);
2053 __isl_give isl_map *isl_map_upper_bound_si(
2054 __isl_take isl_map *map,
2055 enum isl_dim_type type, unsigned pos, int value);
2057 Intersect the set or relation with the half-space where the given
2058 dimension has a value bounded by the fixed given value.
2060 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2061 enum isl_dim_type type1, int pos1,
2062 enum isl_dim_type type2, int pos2);
2063 __isl_give isl_basic_map *isl_basic_map_equate(
2064 __isl_take isl_basic_map *bmap,
2065 enum isl_dim_type type1, int pos1,
2066 enum isl_dim_type type2, int pos2);
2067 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2068 enum isl_dim_type type1, int pos1,
2069 enum isl_dim_type type2, int pos2);
2071 Intersect the set or relation with the hyperplane where the given
2072 dimensions are equal to each other.
2074 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2075 enum isl_dim_type type1, int pos1,
2076 enum isl_dim_type type2, int pos2);
2078 Intersect the relation with the hyperplane where the given
2079 dimensions have opposite values.
2081 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2082 enum isl_dim_type type1, int pos1,
2083 enum isl_dim_type type2, int pos2);
2084 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2085 enum isl_dim_type type1, int pos1,
2086 enum isl_dim_type type2, int pos2);
2088 Intersect the relation with the half-space where the given
2089 dimensions satisfy the given ordering.
2093 __isl_give isl_map *isl_set_identity(
2094 __isl_take isl_set *set);
2095 __isl_give isl_union_map *isl_union_set_identity(
2096 __isl_take isl_union_set *uset);
2098 Construct an identity relation on the given (union) set.
2102 __isl_give isl_basic_set *isl_basic_map_deltas(
2103 __isl_take isl_basic_map *bmap);
2104 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2105 __isl_give isl_union_set *isl_union_map_deltas(
2106 __isl_take isl_union_map *umap);
2108 These functions return a (basic) set containing the differences
2109 between image elements and corresponding domain elements in the input.
2111 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2112 __isl_take isl_basic_map *bmap);
2113 __isl_give isl_map *isl_map_deltas_map(
2114 __isl_take isl_map *map);
2115 __isl_give isl_union_map *isl_union_map_deltas_map(
2116 __isl_take isl_union_map *umap);
2118 The functions above construct a (basic, regular or union) relation
2119 that maps (a wrapped version of) the input relation to its delta set.
2123 Simplify the representation of a set or relation by trying
2124 to combine pairs of basic sets or relations into a single
2125 basic set or relation.
2127 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2128 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2129 __isl_give isl_union_set *isl_union_set_coalesce(
2130 __isl_take isl_union_set *uset);
2131 __isl_give isl_union_map *isl_union_map_coalesce(
2132 __isl_take isl_union_map *umap);
2134 One of the methods for combining pairs of basic sets or relations
2135 can result in coefficients that are much larger than those that appear
2136 in the constraints of the input. By default, the coefficients are
2137 not allowed to grow larger, but this can be changed by unsetting
2138 the following option.
2140 int isl_options_set_coalesce_bounded_wrapping(
2141 isl_ctx *ctx, int val);
2142 int isl_options_get_coalesce_bounded_wrapping(
2145 =item * Detecting equalities
2147 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2148 __isl_take isl_basic_set *bset);
2149 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2150 __isl_take isl_basic_map *bmap);
2151 __isl_give isl_set *isl_set_detect_equalities(
2152 __isl_take isl_set *set);
2153 __isl_give isl_map *isl_map_detect_equalities(
2154 __isl_take isl_map *map);
2155 __isl_give isl_union_set *isl_union_set_detect_equalities(
2156 __isl_take isl_union_set *uset);
2157 __isl_give isl_union_map *isl_union_map_detect_equalities(
2158 __isl_take isl_union_map *umap);
2160 Simplify the representation of a set or relation by detecting implicit
2163 =item * Removing redundant constraints
2165 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2166 __isl_take isl_basic_set *bset);
2167 __isl_give isl_set *isl_set_remove_redundancies(
2168 __isl_take isl_set *set);
2169 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2170 __isl_take isl_basic_map *bmap);
2171 __isl_give isl_map *isl_map_remove_redundancies(
2172 __isl_take isl_map *map);
2176 __isl_give isl_basic_set *isl_set_convex_hull(
2177 __isl_take isl_set *set);
2178 __isl_give isl_basic_map *isl_map_convex_hull(
2179 __isl_take isl_map *map);
2181 If the input set or relation has any existentially quantified
2182 variables, then the result of these operations is currently undefined.
2186 __isl_give isl_basic_set *isl_set_simple_hull(
2187 __isl_take isl_set *set);
2188 __isl_give isl_basic_map *isl_map_simple_hull(
2189 __isl_take isl_map *map);
2190 __isl_give isl_union_map *isl_union_map_simple_hull(
2191 __isl_take isl_union_map *umap);
2193 These functions compute a single basic set or relation
2194 that contains the whole input set or relation.
2195 In particular, the output is described by translates
2196 of the constraints describing the basic sets or relations in the input.
2200 (See \autoref{s:simple hull}.)
2206 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2207 __isl_take isl_basic_set *bset);
2208 __isl_give isl_basic_set *isl_set_affine_hull(
2209 __isl_take isl_set *set);
2210 __isl_give isl_union_set *isl_union_set_affine_hull(
2211 __isl_take isl_union_set *uset);
2212 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2213 __isl_take isl_basic_map *bmap);
2214 __isl_give isl_basic_map *isl_map_affine_hull(
2215 __isl_take isl_map *map);
2216 __isl_give isl_union_map *isl_union_map_affine_hull(
2217 __isl_take isl_union_map *umap);
2219 In case of union sets and relations, the affine hull is computed
2222 =item * Polyhedral hull
2224 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2225 __isl_take isl_set *set);
2226 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2227 __isl_take isl_map *map);
2228 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2229 __isl_take isl_union_set *uset);
2230 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2231 __isl_take isl_union_map *umap);
2233 These functions compute a single basic set or relation
2234 not involving any existentially quantified variables
2235 that contains the whole input set or relation.
2236 In case of union sets and relations, the polyhedral hull is computed
2241 __isl_give isl_basic_set *isl_basic_set_sample(
2242 __isl_take isl_basic_set *bset);
2243 __isl_give isl_basic_set *isl_set_sample(
2244 __isl_take isl_set *set);
2245 __isl_give isl_basic_map *isl_basic_map_sample(
2246 __isl_take isl_basic_map *bmap);
2247 __isl_give isl_basic_map *isl_map_sample(
2248 __isl_take isl_map *map);
2250 If the input (basic) set or relation is non-empty, then return
2251 a singleton subset of the input. Otherwise, return an empty set.
2253 =item * Optimization
2255 #include <isl/ilp.h>
2256 enum isl_lp_result isl_basic_set_max(
2257 __isl_keep isl_basic_set *bset,
2258 __isl_keep isl_aff *obj, isl_int *opt)
2259 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2260 __isl_keep isl_aff *obj, isl_int *opt);
2261 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2262 __isl_keep isl_aff *obj, isl_int *opt);
2264 Compute the minimum or maximum of the integer affine expression C<obj>
2265 over the points in C<set>, returning the result in C<opt>.
2266 The return value may be one of C<isl_lp_error>,
2267 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2269 =item * Parametric optimization
2271 __isl_give isl_pw_aff *isl_set_dim_min(
2272 __isl_take isl_set *set, int pos);
2273 __isl_give isl_pw_aff *isl_set_dim_max(
2274 __isl_take isl_set *set, int pos);
2275 __isl_give isl_pw_aff *isl_map_dim_max(
2276 __isl_take isl_map *map, int pos);
2278 Compute the minimum or maximum of the given set or output dimension
2279 as a function of the parameters (and input dimensions), but independently
2280 of the other set or output dimensions.
2281 For lexicographic optimization, see L<"Lexicographic Optimization">.
2285 The following functions compute either the set of (rational) coefficient
2286 values of valid constraints for the given set or the set of (rational)
2287 values satisfying the constraints with coefficients from the given set.
2288 Internally, these two sets of functions perform essentially the
2289 same operations, except that the set of coefficients is assumed to
2290 be a cone, while the set of values may be any polyhedron.
2291 The current implementation is based on the Farkas lemma and
2292 Fourier-Motzkin elimination, but this may change or be made optional
2293 in future. In particular, future implementations may use different
2294 dualization algorithms or skip the elimination step.
2296 __isl_give isl_basic_set *isl_basic_set_coefficients(
2297 __isl_take isl_basic_set *bset);
2298 __isl_give isl_basic_set *isl_set_coefficients(
2299 __isl_take isl_set *set);
2300 __isl_give isl_union_set *isl_union_set_coefficients(
2301 __isl_take isl_union_set *bset);
2302 __isl_give isl_basic_set *isl_basic_set_solutions(
2303 __isl_take isl_basic_set *bset);
2304 __isl_give isl_basic_set *isl_set_solutions(
2305 __isl_take isl_set *set);
2306 __isl_give isl_union_set *isl_union_set_solutions(
2307 __isl_take isl_union_set *bset);
2311 __isl_give isl_map *isl_map_fixed_power(
2312 __isl_take isl_map *map, isl_int exp);
2313 __isl_give isl_union_map *isl_union_map_fixed_power(
2314 __isl_take isl_union_map *umap, isl_int exp);
2316 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2317 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2318 of C<map> is computed.
2320 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2322 __isl_give isl_union_map *isl_union_map_power(
2323 __isl_take isl_union_map *umap, int *exact);
2325 Compute a parametric representation for all positive powers I<k> of C<map>.
2326 The result maps I<k> to a nested relation corresponding to the
2327 I<k>th power of C<map>.
2328 The result may be an overapproximation. If the result is known to be exact,
2329 then C<*exact> is set to C<1>.
2331 =item * Transitive closure
2333 __isl_give isl_map *isl_map_transitive_closure(
2334 __isl_take isl_map *map, int *exact);
2335 __isl_give isl_union_map *isl_union_map_transitive_closure(
2336 __isl_take isl_union_map *umap, int *exact);
2338 Compute the transitive closure of C<map>.
2339 The result may be an overapproximation. If the result is known to be exact,
2340 then C<*exact> is set to C<1>.
2342 =item * Reaching path lengths
2344 __isl_give isl_map *isl_map_reaching_path_lengths(
2345 __isl_take isl_map *map, int *exact);
2347 Compute a relation that maps each element in the range of C<map>
2348 to the lengths of all paths composed of edges in C<map> that
2349 end up in the given element.
2350 The result may be an overapproximation. If the result is known to be exact,
2351 then C<*exact> is set to C<1>.
2352 To compute the I<maximal> path length, the resulting relation
2353 should be postprocessed by C<isl_map_lexmax>.
2354 In particular, if the input relation is a dependence relation
2355 (mapping sources to sinks), then the maximal path length corresponds
2356 to the free schedule.
2357 Note, however, that C<isl_map_lexmax> expects the maximum to be
2358 finite, so if the path lengths are unbounded (possibly due to
2359 the overapproximation), then you will get an error message.
2363 __isl_give isl_basic_set *isl_basic_map_wrap(
2364 __isl_take isl_basic_map *bmap);
2365 __isl_give isl_set *isl_map_wrap(
2366 __isl_take isl_map *map);
2367 __isl_give isl_union_set *isl_union_map_wrap(
2368 __isl_take isl_union_map *umap);
2369 __isl_give isl_basic_map *isl_basic_set_unwrap(
2370 __isl_take isl_basic_set *bset);
2371 __isl_give isl_map *isl_set_unwrap(
2372 __isl_take isl_set *set);
2373 __isl_give isl_union_map *isl_union_set_unwrap(
2374 __isl_take isl_union_set *uset);
2378 Remove any internal structure of domain (and range) of the given
2379 set or relation. If there is any such internal structure in the input,
2380 then the name of the space is also removed.
2382 __isl_give isl_basic_set *isl_basic_set_flatten(
2383 __isl_take isl_basic_set *bset);
2384 __isl_give isl_set *isl_set_flatten(
2385 __isl_take isl_set *set);
2386 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2387 __isl_take isl_basic_map *bmap);
2388 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2389 __isl_take isl_basic_map *bmap);
2390 __isl_give isl_map *isl_map_flatten_range(
2391 __isl_take isl_map *map);
2392 __isl_give isl_map *isl_map_flatten_domain(
2393 __isl_take isl_map *map);
2394 __isl_give isl_basic_map *isl_basic_map_flatten(
2395 __isl_take isl_basic_map *bmap);
2396 __isl_give isl_map *isl_map_flatten(
2397 __isl_take isl_map *map);
2399 __isl_give isl_map *isl_set_flatten_map(
2400 __isl_take isl_set *set);
2402 The function above constructs a relation
2403 that maps the input set to a flattened version of the set.
2407 Lift the input set to a space with extra dimensions corresponding
2408 to the existentially quantified variables in the input.
2409 In particular, the result lives in a wrapped map where the domain
2410 is the original space and the range corresponds to the original
2411 existentially quantified variables.
2413 __isl_give isl_basic_set *isl_basic_set_lift(
2414 __isl_take isl_basic_set *bset);
2415 __isl_give isl_set *isl_set_lift(
2416 __isl_take isl_set *set);
2417 __isl_give isl_union_set *isl_union_set_lift(
2418 __isl_take isl_union_set *uset);
2420 Given a local space that contains the existentially quantified
2421 variables of a set, a basic relation that, when applied to
2422 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2423 can be constructed using the following function.
2425 #include <isl/local_space.h>
2426 __isl_give isl_basic_map *isl_local_space_lifting(
2427 __isl_take isl_local_space *ls);
2429 =item * Internal Product
2431 __isl_give isl_basic_map *isl_basic_map_zip(
2432 __isl_take isl_basic_map *bmap);
2433 __isl_give isl_map *isl_map_zip(
2434 __isl_take isl_map *map);
2435 __isl_give isl_union_map *isl_union_map_zip(
2436 __isl_take isl_union_map *umap);
2438 Given a relation with nested relations for domain and range,
2439 interchange the range of the domain with the domain of the range.
2443 __isl_give isl_basic_map *isl_basic_map_curry(
2444 __isl_take isl_basic_map *bmap);
2445 __isl_give isl_map *isl_map_curry(
2446 __isl_take isl_map *map);
2447 __isl_give isl_union_map *isl_union_map_curry(
2448 __isl_take isl_union_map *umap);
2450 Given a relation with a nested relation for domain,
2451 move the range of the nested relation out of the domain
2452 and use it as the domain of a nested relation in the range,
2453 with the original range as range of this nested relation.
2455 =item * Aligning parameters
2457 __isl_give isl_basic_set *isl_basic_set_align_params(
2458 __isl_take isl_basic_set *bset,
2459 __isl_take isl_space *model);
2460 __isl_give isl_set *isl_set_align_params(
2461 __isl_take isl_set *set,
2462 __isl_take isl_space *model);
2463 __isl_give isl_basic_map *isl_basic_map_align_params(
2464 __isl_take isl_basic_map *bmap,
2465 __isl_take isl_space *model);
2466 __isl_give isl_map *isl_map_align_params(
2467 __isl_take isl_map *map,
2468 __isl_take isl_space *model);
2470 Change the order of the parameters of the given set or relation
2471 such that the first parameters match those of C<model>.
2472 This may involve the introduction of extra parameters.
2473 All parameters need to be named.
2475 =item * Dimension manipulation
2477 __isl_give isl_set *isl_set_add_dims(
2478 __isl_take isl_set *set,
2479 enum isl_dim_type type, unsigned n);
2480 __isl_give isl_map *isl_map_add_dims(
2481 __isl_take isl_map *map,
2482 enum isl_dim_type type, unsigned n);
2483 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2484 __isl_take isl_basic_set *bset,
2485 enum isl_dim_type type, unsigned pos,
2487 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2488 __isl_take isl_basic_map *bmap,
2489 enum isl_dim_type type, unsigned pos,
2491 __isl_give isl_set *isl_set_insert_dims(
2492 __isl_take isl_set *set,
2493 enum isl_dim_type type, unsigned pos, unsigned n);
2494 __isl_give isl_map *isl_map_insert_dims(
2495 __isl_take isl_map *map,
2496 enum isl_dim_type type, unsigned pos, unsigned n);
2497 __isl_give isl_basic_set *isl_basic_set_move_dims(
2498 __isl_take isl_basic_set *bset,
2499 enum isl_dim_type dst_type, unsigned dst_pos,
2500 enum isl_dim_type src_type, unsigned src_pos,
2502 __isl_give isl_basic_map *isl_basic_map_move_dims(
2503 __isl_take isl_basic_map *bmap,
2504 enum isl_dim_type dst_type, unsigned dst_pos,
2505 enum isl_dim_type src_type, unsigned src_pos,
2507 __isl_give isl_set *isl_set_move_dims(
2508 __isl_take isl_set *set,
2509 enum isl_dim_type dst_type, unsigned dst_pos,
2510 enum isl_dim_type src_type, unsigned src_pos,
2512 __isl_give isl_map *isl_map_move_dims(
2513 __isl_take isl_map *map,
2514 enum isl_dim_type dst_type, unsigned dst_pos,
2515 enum isl_dim_type src_type, unsigned src_pos,
2518 It is usually not advisable to directly change the (input or output)
2519 space of a set or a relation as this removes the name and the internal
2520 structure of the space. However, the above functions can be useful
2521 to add new parameters, assuming
2522 C<isl_set_align_params> and C<isl_map_align_params>
2527 =head2 Binary Operations
2529 The two arguments of a binary operation not only need to live
2530 in the same C<isl_ctx>, they currently also need to have
2531 the same (number of) parameters.
2533 =head3 Basic Operations
2537 =item * Intersection
2539 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2540 __isl_take isl_basic_set *bset1,
2541 __isl_take isl_basic_set *bset2);
2542 __isl_give isl_basic_set *isl_basic_set_intersect(
2543 __isl_take isl_basic_set *bset1,
2544 __isl_take isl_basic_set *bset2);
2545 __isl_give isl_set *isl_set_intersect_params(
2546 __isl_take isl_set *set,
2547 __isl_take isl_set *params);
2548 __isl_give isl_set *isl_set_intersect(
2549 __isl_take isl_set *set1,
2550 __isl_take isl_set *set2);
2551 __isl_give isl_union_set *isl_union_set_intersect_params(
2552 __isl_take isl_union_set *uset,
2553 __isl_take isl_set *set);
2554 __isl_give isl_union_map *isl_union_map_intersect_params(
2555 __isl_take isl_union_map *umap,
2556 __isl_take isl_set *set);
2557 __isl_give isl_union_set *isl_union_set_intersect(
2558 __isl_take isl_union_set *uset1,
2559 __isl_take isl_union_set *uset2);
2560 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2561 __isl_take isl_basic_map *bmap,
2562 __isl_take isl_basic_set *bset);
2563 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2564 __isl_take isl_basic_map *bmap,
2565 __isl_take isl_basic_set *bset);
2566 __isl_give isl_basic_map *isl_basic_map_intersect(
2567 __isl_take isl_basic_map *bmap1,
2568 __isl_take isl_basic_map *bmap2);
2569 __isl_give isl_map *isl_map_intersect_params(
2570 __isl_take isl_map *map,
2571 __isl_take isl_set *params);
2572 __isl_give isl_map *isl_map_intersect_domain(
2573 __isl_take isl_map *map,
2574 __isl_take isl_set *set);
2575 __isl_give isl_map *isl_map_intersect_range(
2576 __isl_take isl_map *map,
2577 __isl_take isl_set *set);
2578 __isl_give isl_map *isl_map_intersect(
2579 __isl_take isl_map *map1,
2580 __isl_take isl_map *map2);
2581 __isl_give isl_union_map *isl_union_map_intersect_domain(
2582 __isl_take isl_union_map *umap,
2583 __isl_take isl_union_set *uset);
2584 __isl_give isl_union_map *isl_union_map_intersect_range(
2585 __isl_take isl_union_map *umap,
2586 __isl_take isl_union_set *uset);
2587 __isl_give isl_union_map *isl_union_map_intersect(
2588 __isl_take isl_union_map *umap1,
2589 __isl_take isl_union_map *umap2);
2591 The second argument to the C<_params> functions needs to be
2592 a parametric (basic) set. For the other functions, a parametric set
2593 for either argument is only allowed if the other argument is
2594 a parametric set as well.
2598 __isl_give isl_set *isl_basic_set_union(
2599 __isl_take isl_basic_set *bset1,
2600 __isl_take isl_basic_set *bset2);
2601 __isl_give isl_map *isl_basic_map_union(
2602 __isl_take isl_basic_map *bmap1,
2603 __isl_take isl_basic_map *bmap2);
2604 __isl_give isl_set *isl_set_union(
2605 __isl_take isl_set *set1,
2606 __isl_take isl_set *set2);
2607 __isl_give isl_map *isl_map_union(
2608 __isl_take isl_map *map1,
2609 __isl_take isl_map *map2);
2610 __isl_give isl_union_set *isl_union_set_union(
2611 __isl_take isl_union_set *uset1,
2612 __isl_take isl_union_set *uset2);
2613 __isl_give isl_union_map *isl_union_map_union(
2614 __isl_take isl_union_map *umap1,
2615 __isl_take isl_union_map *umap2);
2617 =item * Set difference
2619 __isl_give isl_set *isl_set_subtract(
2620 __isl_take isl_set *set1,
2621 __isl_take isl_set *set2);
2622 __isl_give isl_map *isl_map_subtract(
2623 __isl_take isl_map *map1,
2624 __isl_take isl_map *map2);
2625 __isl_give isl_map *isl_map_subtract_domain(
2626 __isl_take isl_map *map,
2627 __isl_take isl_set *dom);
2628 __isl_give isl_map *isl_map_subtract_range(
2629 __isl_take isl_map *map,
2630 __isl_take isl_set *dom);
2631 __isl_give isl_union_set *isl_union_set_subtract(
2632 __isl_take isl_union_set *uset1,
2633 __isl_take isl_union_set *uset2);
2634 __isl_give isl_union_map *isl_union_map_subtract(
2635 __isl_take isl_union_map *umap1,
2636 __isl_take isl_union_map *umap2);
2640 __isl_give isl_basic_set *isl_basic_set_apply(
2641 __isl_take isl_basic_set *bset,
2642 __isl_take isl_basic_map *bmap);
2643 __isl_give isl_set *isl_set_apply(
2644 __isl_take isl_set *set,
2645 __isl_take isl_map *map);
2646 __isl_give isl_union_set *isl_union_set_apply(
2647 __isl_take isl_union_set *uset,
2648 __isl_take isl_union_map *umap);
2649 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2650 __isl_take isl_basic_map *bmap1,
2651 __isl_take isl_basic_map *bmap2);
2652 __isl_give isl_basic_map *isl_basic_map_apply_range(
2653 __isl_take isl_basic_map *bmap1,
2654 __isl_take isl_basic_map *bmap2);
2655 __isl_give isl_map *isl_map_apply_domain(
2656 __isl_take isl_map *map1,
2657 __isl_take isl_map *map2);
2658 __isl_give isl_union_map *isl_union_map_apply_domain(
2659 __isl_take isl_union_map *umap1,
2660 __isl_take isl_union_map *umap2);
2661 __isl_give isl_map *isl_map_apply_range(
2662 __isl_take isl_map *map1,
2663 __isl_take isl_map *map2);
2664 __isl_give isl_union_map *isl_union_map_apply_range(
2665 __isl_take isl_union_map *umap1,
2666 __isl_take isl_union_map *umap2);
2668 =item * Cartesian Product
2670 __isl_give isl_set *isl_set_product(
2671 __isl_take isl_set *set1,
2672 __isl_take isl_set *set2);
2673 __isl_give isl_union_set *isl_union_set_product(
2674 __isl_take isl_union_set *uset1,
2675 __isl_take isl_union_set *uset2);
2676 __isl_give isl_basic_map *isl_basic_map_domain_product(
2677 __isl_take isl_basic_map *bmap1,
2678 __isl_take isl_basic_map *bmap2);
2679 __isl_give isl_basic_map *isl_basic_map_range_product(
2680 __isl_take isl_basic_map *bmap1,
2681 __isl_take isl_basic_map *bmap2);
2682 __isl_give isl_basic_map *isl_basic_map_product(
2683 __isl_take isl_basic_map *bmap1,
2684 __isl_take isl_basic_map *bmap2);
2685 __isl_give isl_map *isl_map_domain_product(
2686 __isl_take isl_map *map1,
2687 __isl_take isl_map *map2);
2688 __isl_give isl_map *isl_map_range_product(
2689 __isl_take isl_map *map1,
2690 __isl_take isl_map *map2);
2691 __isl_give isl_union_map *isl_union_map_domain_product(
2692 __isl_take isl_union_map *umap1,
2693 __isl_take isl_union_map *umap2);
2694 __isl_give isl_union_map *isl_union_map_range_product(
2695 __isl_take isl_union_map *umap1,
2696 __isl_take isl_union_map *umap2);
2697 __isl_give isl_map *isl_map_product(
2698 __isl_take isl_map *map1,
2699 __isl_take isl_map *map2);
2700 __isl_give isl_union_map *isl_union_map_product(
2701 __isl_take isl_union_map *umap1,
2702 __isl_take isl_union_map *umap2);
2704 The above functions compute the cross product of the given
2705 sets or relations. The domains and ranges of the results
2706 are wrapped maps between domains and ranges of the inputs.
2707 To obtain a ``flat'' product, use the following functions
2710 __isl_give isl_basic_set *isl_basic_set_flat_product(
2711 __isl_take isl_basic_set *bset1,
2712 __isl_take isl_basic_set *bset2);
2713 __isl_give isl_set *isl_set_flat_product(
2714 __isl_take isl_set *set1,
2715 __isl_take isl_set *set2);
2716 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2717 __isl_take isl_basic_map *bmap1,
2718 __isl_take isl_basic_map *bmap2);
2719 __isl_give isl_map *isl_map_flat_domain_product(
2720 __isl_take isl_map *map1,
2721 __isl_take isl_map *map2);
2722 __isl_give isl_map *isl_map_flat_range_product(
2723 __isl_take isl_map *map1,
2724 __isl_take isl_map *map2);
2725 __isl_give isl_union_map *isl_union_map_flat_range_product(
2726 __isl_take isl_union_map *umap1,
2727 __isl_take isl_union_map *umap2);
2728 __isl_give isl_basic_map *isl_basic_map_flat_product(
2729 __isl_take isl_basic_map *bmap1,
2730 __isl_take isl_basic_map *bmap2);
2731 __isl_give isl_map *isl_map_flat_product(
2732 __isl_take isl_map *map1,
2733 __isl_take isl_map *map2);
2735 =item * Simplification
2737 __isl_give isl_basic_set *isl_basic_set_gist(
2738 __isl_take isl_basic_set *bset,
2739 __isl_take isl_basic_set *context);
2740 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2741 __isl_take isl_set *context);
2742 __isl_give isl_set *isl_set_gist_params(
2743 __isl_take isl_set *set,
2744 __isl_take isl_set *context);
2745 __isl_give isl_union_set *isl_union_set_gist(
2746 __isl_take isl_union_set *uset,
2747 __isl_take isl_union_set *context);
2748 __isl_give isl_union_set *isl_union_set_gist_params(
2749 __isl_take isl_union_set *uset,
2750 __isl_take isl_set *set);
2751 __isl_give isl_basic_map *isl_basic_map_gist(
2752 __isl_take isl_basic_map *bmap,
2753 __isl_take isl_basic_map *context);
2754 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2755 __isl_take isl_map *context);
2756 __isl_give isl_map *isl_map_gist_params(
2757 __isl_take isl_map *map,
2758 __isl_take isl_set *context);
2759 __isl_give isl_map *isl_map_gist_domain(
2760 __isl_take isl_map *map,
2761 __isl_take isl_set *context);
2762 __isl_give isl_map *isl_map_gist_range(
2763 __isl_take isl_map *map,
2764 __isl_take isl_set *context);
2765 __isl_give isl_union_map *isl_union_map_gist(
2766 __isl_take isl_union_map *umap,
2767 __isl_take isl_union_map *context);
2768 __isl_give isl_union_map *isl_union_map_gist_params(
2769 __isl_take isl_union_map *umap,
2770 __isl_take isl_set *set);
2771 __isl_give isl_union_map *isl_union_map_gist_domain(
2772 __isl_take isl_union_map *umap,
2773 __isl_take isl_union_set *uset);
2774 __isl_give isl_union_map *isl_union_map_gist_range(
2775 __isl_take isl_union_map *umap,
2776 __isl_take isl_union_set *uset);
2778 The gist operation returns a set or relation that has the
2779 same intersection with the context as the input set or relation.
2780 Any implicit equality in the intersection is made explicit in the result,
2781 while all inequalities that are redundant with respect to the intersection
2783 In case of union sets and relations, the gist operation is performed
2788 =head3 Lexicographic Optimization
2790 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2791 the following functions
2792 compute a set that contains the lexicographic minimum or maximum
2793 of the elements in C<set> (or C<bset>) for those values of the parameters
2794 that satisfy C<dom>.
2795 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2796 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2798 In other words, the union of the parameter values
2799 for which the result is non-empty and of C<*empty>
2802 __isl_give isl_set *isl_basic_set_partial_lexmin(
2803 __isl_take isl_basic_set *bset,
2804 __isl_take isl_basic_set *dom,
2805 __isl_give isl_set **empty);
2806 __isl_give isl_set *isl_basic_set_partial_lexmax(
2807 __isl_take isl_basic_set *bset,
2808 __isl_take isl_basic_set *dom,
2809 __isl_give isl_set **empty);
2810 __isl_give isl_set *isl_set_partial_lexmin(
2811 __isl_take isl_set *set, __isl_take isl_set *dom,
2812 __isl_give isl_set **empty);
2813 __isl_give isl_set *isl_set_partial_lexmax(
2814 __isl_take isl_set *set, __isl_take isl_set *dom,
2815 __isl_give isl_set **empty);
2817 Given a (basic) set C<set> (or C<bset>), the following functions simply
2818 return a set containing the lexicographic minimum or maximum
2819 of the elements in C<set> (or C<bset>).
2820 In case of union sets, the optimum is computed per space.
2822 __isl_give isl_set *isl_basic_set_lexmin(
2823 __isl_take isl_basic_set *bset);
2824 __isl_give isl_set *isl_basic_set_lexmax(
2825 __isl_take isl_basic_set *bset);
2826 __isl_give isl_set *isl_set_lexmin(
2827 __isl_take isl_set *set);
2828 __isl_give isl_set *isl_set_lexmax(
2829 __isl_take isl_set *set);
2830 __isl_give isl_union_set *isl_union_set_lexmin(
2831 __isl_take isl_union_set *uset);
2832 __isl_give isl_union_set *isl_union_set_lexmax(
2833 __isl_take isl_union_set *uset);
2835 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2836 the following functions
2837 compute a relation that maps each element of C<dom>
2838 to the single lexicographic minimum or maximum
2839 of the elements that are associated to that same
2840 element in C<map> (or C<bmap>).
2841 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2842 that contains the elements in C<dom> that do not map
2843 to any elements in C<map> (or C<bmap>).
2844 In other words, the union of the domain of the result and of C<*empty>
2847 __isl_give isl_map *isl_basic_map_partial_lexmax(
2848 __isl_take isl_basic_map *bmap,
2849 __isl_take isl_basic_set *dom,
2850 __isl_give isl_set **empty);
2851 __isl_give isl_map *isl_basic_map_partial_lexmin(
2852 __isl_take isl_basic_map *bmap,
2853 __isl_take isl_basic_set *dom,
2854 __isl_give isl_set **empty);
2855 __isl_give isl_map *isl_map_partial_lexmax(
2856 __isl_take isl_map *map, __isl_take isl_set *dom,
2857 __isl_give isl_set **empty);
2858 __isl_give isl_map *isl_map_partial_lexmin(
2859 __isl_take isl_map *map, __isl_take isl_set *dom,
2860 __isl_give isl_set **empty);
2862 Given a (basic) map C<map> (or C<bmap>), the following functions simply
2863 return a map mapping each element in the domain of
2864 C<map> (or C<bmap>) to the lexicographic minimum or maximum
2865 of all elements associated to that element.
2866 In case of union relations, the optimum is computed per space.
2868 __isl_give isl_map *isl_basic_map_lexmin(
2869 __isl_take isl_basic_map *bmap);
2870 __isl_give isl_map *isl_basic_map_lexmax(
2871 __isl_take isl_basic_map *bmap);
2872 __isl_give isl_map *isl_map_lexmin(
2873 __isl_take isl_map *map);
2874 __isl_give isl_map *isl_map_lexmax(
2875 __isl_take isl_map *map);
2876 __isl_give isl_union_map *isl_union_map_lexmin(
2877 __isl_take isl_union_map *umap);
2878 __isl_give isl_union_map *isl_union_map_lexmax(
2879 __isl_take isl_union_map *umap);
2881 The following functions return their result in the form of
2882 a piecewise multi-affine expression
2883 (See L<"Piecewise Multiple Quasi Affine Expressions">),
2884 but are otherwise equivalent to the corresponding functions
2885 returning a basic set or relation.
2887 __isl_give isl_pw_multi_aff *
2888 isl_basic_map_lexmin_pw_multi_aff(
2889 __isl_take isl_basic_map *bmap);
2890 __isl_give isl_pw_multi_aff *
2891 isl_basic_set_partial_lexmin_pw_multi_aff(
2892 __isl_take isl_basic_set *bset,
2893 __isl_take isl_basic_set *dom,
2894 __isl_give isl_set **empty);
2895 __isl_give isl_pw_multi_aff *
2896 isl_basic_set_partial_lexmax_pw_multi_aff(
2897 __isl_take isl_basic_set *bset,
2898 __isl_take isl_basic_set *dom,
2899 __isl_give isl_set **empty);
2900 __isl_give isl_pw_multi_aff *
2901 isl_basic_map_partial_lexmin_pw_multi_aff(
2902 __isl_take isl_basic_map *bmap,
2903 __isl_take isl_basic_set *dom,
2904 __isl_give isl_set **empty);
2905 __isl_give isl_pw_multi_aff *
2906 isl_basic_map_partial_lexmax_pw_multi_aff(
2907 __isl_take isl_basic_map *bmap,
2908 __isl_take isl_basic_set *dom,
2909 __isl_give isl_set **empty);
2910 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
2911 __isl_take isl_map *map);
2912 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
2913 __isl_take isl_map *map);
2917 Lists are defined over several element types, including
2918 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_basic_set> and C<isl_set>.
2919 Here we take lists of C<isl_set>s as an example.
2920 Lists can be created, copied, modified and freed using the following functions.
2922 #include <isl/list.h>
2923 __isl_give isl_set_list *isl_set_list_from_set(
2924 __isl_take isl_set *el);
2925 __isl_give isl_set_list *isl_set_list_alloc(
2926 isl_ctx *ctx, int n);
2927 __isl_give isl_set_list *isl_set_list_copy(
2928 __isl_keep isl_set_list *list);
2929 __isl_give isl_set_list *isl_set_list_add(
2930 __isl_take isl_set_list *list,
2931 __isl_take isl_set *el);
2932 __isl_give isl_set_list *isl_set_list_drop(
2933 __isl_take isl_set_list *list,
2934 unsigned first, unsigned n);
2935 __isl_give isl_set_list *isl_set_list_set_set(
2936 __isl_take isl_set_list *list, int index,
2937 __isl_take isl_set *set);
2938 __isl_give isl_set_list *isl_set_list_concat(
2939 __isl_take isl_set_list *list1,
2940 __isl_take isl_set_list *list2);
2941 void *isl_set_list_free(__isl_take isl_set_list *list);
2943 C<isl_set_list_alloc> creates an empty list with a capacity for
2944 C<n> elements. C<isl_set_list_from_set> creates a list with a single
2947 Lists can be inspected using the following functions.
2949 #include <isl/list.h>
2950 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
2951 int isl_set_list_n_set(__isl_keep isl_set_list *list);
2952 __isl_give isl_set *isl_set_list_get_set(
2953 __isl_keep isl_set_list *list, int index);
2954 int isl_set_list_foreach(__isl_keep isl_set_list *list,
2955 int (*fn)(__isl_take isl_set *el, void *user),
2958 Lists can be printed using
2960 #include <isl/list.h>
2961 __isl_give isl_printer *isl_printer_print_set_list(
2962 __isl_take isl_printer *p,
2963 __isl_keep isl_set_list *list);
2967 Vectors can be created, copied and freed using the following functions.
2969 #include <isl/vec.h>
2970 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
2972 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
2973 void isl_vec_free(__isl_take isl_vec *vec);
2975 Note that the elements of a newly created vector may have arbitrary values.
2976 The elements can be changed and inspected using the following functions.
2978 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
2979 int isl_vec_size(__isl_keep isl_vec *vec);
2980 int isl_vec_get_element(__isl_keep isl_vec *vec,
2981 int pos, isl_int *v);
2982 __isl_give isl_vec *isl_vec_set_element(
2983 __isl_take isl_vec *vec, int pos, isl_int v);
2984 __isl_give isl_vec *isl_vec_set_element_si(
2985 __isl_take isl_vec *vec, int pos, int v);
2986 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
2988 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
2991 C<isl_vec_get_element> will return a negative value if anything went wrong.
2992 In that case, the value of C<*v> is undefined.
2996 Matrices can be created, copied and freed using the following functions.
2998 #include <isl/mat.h>
2999 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3000 unsigned n_row, unsigned n_col);
3001 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3002 void isl_mat_free(__isl_take isl_mat *mat);
3004 Note that the elements of a newly created matrix may have arbitrary values.
3005 The elements can be changed and inspected using the following functions.
3007 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3008 int isl_mat_rows(__isl_keep isl_mat *mat);
3009 int isl_mat_cols(__isl_keep isl_mat *mat);
3010 int isl_mat_get_element(__isl_keep isl_mat *mat,
3011 int row, int col, isl_int *v);
3012 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3013 int row, int col, isl_int v);
3014 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3015 int row, int col, int v);
3017 C<isl_mat_get_element> will return a negative value if anything went wrong.
3018 In that case, the value of C<*v> is undefined.
3020 The following function can be used to compute the (right) inverse
3021 of a matrix, i.e., a matrix such that the product of the original
3022 and the inverse (in that order) is a multiple of the identity matrix.
3023 The input matrix is assumed to be of full row-rank.
3025 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3027 The following function can be used to compute the (right) kernel
3028 (or null space) of a matrix, i.e., a matrix such that the product of
3029 the original and the kernel (in that order) is the zero matrix.
3031 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3033 =head2 Piecewise Quasi Affine Expressions
3035 The zero quasi affine expression on a given domain can be created using
3037 __isl_give isl_aff *isl_aff_zero_on_domain(
3038 __isl_take isl_local_space *ls);
3040 Note that the space in which the resulting object lives is a map space
3041 with the given space as domain and a one-dimensional range.
3043 An empty piecewise quasi affine expression (one with no cells)
3044 or a piecewise quasi affine expression with a single cell can
3045 be created using the following functions.
3047 #include <isl/aff.h>
3048 __isl_give isl_pw_aff *isl_pw_aff_empty(
3049 __isl_take isl_space *space);
3050 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3051 __isl_take isl_set *set, __isl_take isl_aff *aff);
3052 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3053 __isl_take isl_aff *aff);
3055 A piecewise quasi affine expression that is equal to 1 on a set
3056 and 0 outside the set can be created using the following function.
3058 #include <isl/aff.h>
3059 __isl_give isl_pw_aff *isl_set_indicator_function(
3060 __isl_take isl_set *set);
3062 Quasi affine expressions can be copied and freed using
3064 #include <isl/aff.h>
3065 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3066 void *isl_aff_free(__isl_take isl_aff *aff);
3068 __isl_give isl_pw_aff *isl_pw_aff_copy(
3069 __isl_keep isl_pw_aff *pwaff);
3070 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3072 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3073 using the following function. The constraint is required to have
3074 a non-zero coefficient for the specified dimension.
3076 #include <isl/constraint.h>
3077 __isl_give isl_aff *isl_constraint_get_bound(
3078 __isl_keep isl_constraint *constraint,
3079 enum isl_dim_type type, int pos);
3081 The entire affine expression of the constraint can also be extracted
3082 using the following function.
3084 #include <isl/constraint.h>
3085 __isl_give isl_aff *isl_constraint_get_aff(
3086 __isl_keep isl_constraint *constraint);
3088 Conversely, an equality constraint equating
3089 the affine expression to zero or an inequality constraint enforcing
3090 the affine expression to be non-negative, can be constructed using
3092 __isl_give isl_constraint *isl_equality_from_aff(
3093 __isl_take isl_aff *aff);
3094 __isl_give isl_constraint *isl_inequality_from_aff(
3095 __isl_take isl_aff *aff);
3097 The expression can be inspected using
3099 #include <isl/aff.h>
3100 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3101 int isl_aff_dim(__isl_keep isl_aff *aff,
3102 enum isl_dim_type type);
3103 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3104 __isl_keep isl_aff *aff);
3105 __isl_give isl_local_space *isl_aff_get_local_space(
3106 __isl_keep isl_aff *aff);
3107 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3108 enum isl_dim_type type, unsigned pos);
3109 const char *isl_pw_aff_get_dim_name(
3110 __isl_keep isl_pw_aff *pa,
3111 enum isl_dim_type type, unsigned pos);
3112 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3113 enum isl_dim_type type, unsigned pos);
3114 __isl_give isl_id *isl_pw_aff_get_dim_id(
3115 __isl_keep isl_pw_aff *pa,
3116 enum isl_dim_type type, unsigned pos);
3117 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3118 __isl_keep isl_pw_aff *pa,
3119 enum isl_dim_type type);
3120 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3122 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3123 enum isl_dim_type type, int pos, isl_int *v);
3124 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3126 __isl_give isl_aff *isl_aff_get_div(
3127 __isl_keep isl_aff *aff, int pos);
3129 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3130 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3131 int (*fn)(__isl_take isl_set *set,
3132 __isl_take isl_aff *aff,
3133 void *user), void *user);
3135 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3136 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3138 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3139 enum isl_dim_type type, unsigned first, unsigned n);
3140 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3141 enum isl_dim_type type, unsigned first, unsigned n);
3143 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3144 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3145 enum isl_dim_type type);
3146 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3148 It can be modified using
3150 #include <isl/aff.h>
3151 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3152 __isl_take isl_pw_aff *pwaff,
3153 enum isl_dim_type type, __isl_take isl_id *id);
3154 __isl_give isl_aff *isl_aff_set_dim_name(
3155 __isl_take isl_aff *aff, enum isl_dim_type type,
3156 unsigned pos, const char *s);
3157 __isl_give isl_aff *isl_aff_set_dim_id(
3158 __isl_take isl_aff *aff, enum isl_dim_type type,
3159 unsigned pos, __isl_take isl_id *id);
3160 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3161 __isl_take isl_pw_aff *pma,
3162 enum isl_dim_type type, unsigned pos,
3163 __isl_take isl_id *id);
3164 __isl_give isl_aff *isl_aff_set_constant(
3165 __isl_take isl_aff *aff, isl_int v);
3166 __isl_give isl_aff *isl_aff_set_constant_si(
3167 __isl_take isl_aff *aff, int v);
3168 __isl_give isl_aff *isl_aff_set_coefficient(
3169 __isl_take isl_aff *aff,
3170 enum isl_dim_type type, int pos, isl_int v);
3171 __isl_give isl_aff *isl_aff_set_coefficient_si(
3172 __isl_take isl_aff *aff,
3173 enum isl_dim_type type, int pos, int v);
3174 __isl_give isl_aff *isl_aff_set_denominator(
3175 __isl_take isl_aff *aff, isl_int v);
3177 __isl_give isl_aff *isl_aff_add_constant(
3178 __isl_take isl_aff *aff, isl_int v);
3179 __isl_give isl_aff *isl_aff_add_constant_si(
3180 __isl_take isl_aff *aff, int v);
3181 __isl_give isl_aff *isl_aff_add_constant_num(
3182 __isl_take isl_aff *aff, isl_int v);
3183 __isl_give isl_aff *isl_aff_add_constant_num_si(
3184 __isl_take isl_aff *aff, int v);
3185 __isl_give isl_aff *isl_aff_add_coefficient(
3186 __isl_take isl_aff *aff,
3187 enum isl_dim_type type, int pos, isl_int v);
3188 __isl_give isl_aff *isl_aff_add_coefficient_si(
3189 __isl_take isl_aff *aff,
3190 enum isl_dim_type type, int pos, int v);
3192 __isl_give isl_aff *isl_aff_insert_dims(
3193 __isl_take isl_aff *aff,
3194 enum isl_dim_type type, unsigned first, unsigned n);
3195 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3196 __isl_take isl_pw_aff *pwaff,
3197 enum isl_dim_type type, unsigned first, unsigned n);
3198 __isl_give isl_aff *isl_aff_add_dims(
3199 __isl_take isl_aff *aff,
3200 enum isl_dim_type type, unsigned n);
3201 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3202 __isl_take isl_pw_aff *pwaff,
3203 enum isl_dim_type type, unsigned n);
3204 __isl_give isl_aff *isl_aff_drop_dims(
3205 __isl_take isl_aff *aff,
3206 enum isl_dim_type type, unsigned first, unsigned n);
3207 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3208 __isl_take isl_pw_aff *pwaff,
3209 enum isl_dim_type type, unsigned first, unsigned n);
3211 Note that the C<set_constant> and C<set_coefficient> functions
3212 set the I<numerator> of the constant or coefficient, while
3213 C<add_constant> and C<add_coefficient> add an integer value to
3214 the possibly rational constant or coefficient.
3215 The C<add_constant_num> functions add an integer value to
3218 To check whether an affine expressions is obviously zero
3219 or obviously equal to some other affine expression, use
3221 #include <isl/aff.h>
3222 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3223 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3224 __isl_keep isl_aff *aff2);
3225 int isl_pw_aff_plain_is_equal(
3226 __isl_keep isl_pw_aff *pwaff1,
3227 __isl_keep isl_pw_aff *pwaff2);
3231 #include <isl/aff.h>
3232 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3233 __isl_take isl_aff *aff2);
3234 __isl_give isl_pw_aff *isl_pw_aff_add(
3235 __isl_take isl_pw_aff *pwaff1,
3236 __isl_take isl_pw_aff *pwaff2);
3237 __isl_give isl_pw_aff *isl_pw_aff_min(
3238 __isl_take isl_pw_aff *pwaff1,
3239 __isl_take isl_pw_aff *pwaff2);
3240 __isl_give isl_pw_aff *isl_pw_aff_max(
3241 __isl_take isl_pw_aff *pwaff1,
3242 __isl_take isl_pw_aff *pwaff2);
3243 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3244 __isl_take isl_aff *aff2);
3245 __isl_give isl_pw_aff *isl_pw_aff_sub(
3246 __isl_take isl_pw_aff *pwaff1,
3247 __isl_take isl_pw_aff *pwaff2);
3248 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3249 __isl_give isl_pw_aff *isl_pw_aff_neg(
3250 __isl_take isl_pw_aff *pwaff);
3251 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3252 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3253 __isl_take isl_pw_aff *pwaff);
3254 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3255 __isl_give isl_pw_aff *isl_pw_aff_floor(
3256 __isl_take isl_pw_aff *pwaff);
3257 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3259 __isl_give isl_pw_aff *isl_pw_aff_mod(
3260 __isl_take isl_pw_aff *pwaff, isl_int mod);
3261 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3263 __isl_give isl_pw_aff *isl_pw_aff_scale(
3264 __isl_take isl_pw_aff *pwaff, isl_int f);
3265 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3267 __isl_give isl_aff *isl_aff_scale_down_ui(
3268 __isl_take isl_aff *aff, unsigned f);
3269 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3270 __isl_take isl_pw_aff *pwaff, isl_int f);
3272 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3273 __isl_take isl_pw_aff_list *list);
3274 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3275 __isl_take isl_pw_aff_list *list);
3277 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3278 __isl_take isl_pw_aff *pwqp);
3280 __isl_give isl_aff *isl_aff_align_params(
3281 __isl_take isl_aff *aff,
3282 __isl_take isl_space *model);
3283 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3284 __isl_take isl_pw_aff *pwaff,
3285 __isl_take isl_space *model);
3287 __isl_give isl_aff *isl_aff_project_domain_on_params(
3288 __isl_take isl_aff *aff);
3290 __isl_give isl_aff *isl_aff_gist_params(
3291 __isl_take isl_aff *aff,
3292 __isl_take isl_set *context);
3293 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3294 __isl_take isl_set *context);
3295 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3296 __isl_take isl_pw_aff *pwaff,
3297 __isl_take isl_set *context);
3298 __isl_give isl_pw_aff *isl_pw_aff_gist(
3299 __isl_take isl_pw_aff *pwaff,
3300 __isl_take isl_set *context);
3302 __isl_give isl_set *isl_pw_aff_domain(
3303 __isl_take isl_pw_aff *pwaff);
3304 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3305 __isl_take isl_pw_aff *pa,
3306 __isl_take isl_set *set);
3307 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3308 __isl_take isl_pw_aff *pa,
3309 __isl_take isl_set *set);
3311 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3312 __isl_take isl_aff *aff2);
3313 __isl_give isl_pw_aff *isl_pw_aff_mul(
3314 __isl_take isl_pw_aff *pwaff1,
3315 __isl_take isl_pw_aff *pwaff2);
3317 When multiplying two affine expressions, at least one of the two needs
3320 #include <isl/aff.h>
3321 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3322 __isl_take isl_aff *aff);
3323 __isl_give isl_basic_set *isl_aff_le_basic_set(
3324 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3325 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3326 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3327 __isl_give isl_set *isl_pw_aff_eq_set(
3328 __isl_take isl_pw_aff *pwaff1,
3329 __isl_take isl_pw_aff *pwaff2);
3330 __isl_give isl_set *isl_pw_aff_ne_set(
3331 __isl_take isl_pw_aff *pwaff1,
3332 __isl_take isl_pw_aff *pwaff2);
3333 __isl_give isl_set *isl_pw_aff_le_set(
3334 __isl_take isl_pw_aff *pwaff1,
3335 __isl_take isl_pw_aff *pwaff2);
3336 __isl_give isl_set *isl_pw_aff_lt_set(
3337 __isl_take isl_pw_aff *pwaff1,
3338 __isl_take isl_pw_aff *pwaff2);
3339 __isl_give isl_set *isl_pw_aff_ge_set(
3340 __isl_take isl_pw_aff *pwaff1,
3341 __isl_take isl_pw_aff *pwaff2);
3342 __isl_give isl_set *isl_pw_aff_gt_set(
3343 __isl_take isl_pw_aff *pwaff1,
3344 __isl_take isl_pw_aff *pwaff2);
3346 __isl_give isl_set *isl_pw_aff_list_eq_set(
3347 __isl_take isl_pw_aff_list *list1,
3348 __isl_take isl_pw_aff_list *list2);
3349 __isl_give isl_set *isl_pw_aff_list_ne_set(
3350 __isl_take isl_pw_aff_list *list1,
3351 __isl_take isl_pw_aff_list *list2);
3352 __isl_give isl_set *isl_pw_aff_list_le_set(
3353 __isl_take isl_pw_aff_list *list1,
3354 __isl_take isl_pw_aff_list *list2);
3355 __isl_give isl_set *isl_pw_aff_list_lt_set(
3356 __isl_take isl_pw_aff_list *list1,
3357 __isl_take isl_pw_aff_list *list2);
3358 __isl_give isl_set *isl_pw_aff_list_ge_set(
3359 __isl_take isl_pw_aff_list *list1,
3360 __isl_take isl_pw_aff_list *list2);
3361 __isl_give isl_set *isl_pw_aff_list_gt_set(
3362 __isl_take isl_pw_aff_list *list1,
3363 __isl_take isl_pw_aff_list *list2);
3365 The function C<isl_aff_neg_basic_set> returns a basic set
3366 containing those elements in the domain space
3367 of C<aff> where C<aff> is negative.
3368 The function C<isl_aff_ge_basic_set> returns a basic set
3369 containing those elements in the shared space
3370 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3371 The function C<isl_pw_aff_ge_set> returns a set
3372 containing those elements in the shared domain
3373 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3374 The functions operating on C<isl_pw_aff_list> apply the corresponding
3375 C<isl_pw_aff> function to each pair of elements in the two lists.
3377 #include <isl/aff.h>
3378 __isl_give isl_set *isl_pw_aff_nonneg_set(
3379 __isl_take isl_pw_aff *pwaff);
3380 __isl_give isl_set *isl_pw_aff_zero_set(
3381 __isl_take isl_pw_aff *pwaff);
3382 __isl_give isl_set *isl_pw_aff_non_zero_set(
3383 __isl_take isl_pw_aff *pwaff);
3385 The function C<isl_pw_aff_nonneg_set> returns a set
3386 containing those elements in the domain
3387 of C<pwaff> where C<pwaff> is non-negative.
3389 #include <isl/aff.h>
3390 __isl_give isl_pw_aff *isl_pw_aff_cond(
3391 __isl_take isl_pw_aff *cond,
3392 __isl_take isl_pw_aff *pwaff_true,
3393 __isl_take isl_pw_aff *pwaff_false);
3395 The function C<isl_pw_aff_cond> performs a conditional operator
3396 and returns an expression that is equal to C<pwaff_true>
3397 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3398 where C<cond> is zero.
3400 #include <isl/aff.h>
3401 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3402 __isl_take isl_pw_aff *pwaff1,
3403 __isl_take isl_pw_aff *pwaff2);
3404 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3405 __isl_take isl_pw_aff *pwaff1,
3406 __isl_take isl_pw_aff *pwaff2);
3407 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3408 __isl_take isl_pw_aff *pwaff1,
3409 __isl_take isl_pw_aff *pwaff2);
3411 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3412 expression with a domain that is the union of those of C<pwaff1> and
3413 C<pwaff2> and such that on each cell, the quasi-affine expression is
3414 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3415 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3416 associated expression is the defined one.
3418 An expression can be read from input using
3420 #include <isl/aff.h>
3421 __isl_give isl_aff *isl_aff_read_from_str(
3422 isl_ctx *ctx, const char *str);
3423 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3424 isl_ctx *ctx, const char *str);
3426 An expression can be printed using
3428 #include <isl/aff.h>
3429 __isl_give isl_printer *isl_printer_print_aff(
3430 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3432 __isl_give isl_printer *isl_printer_print_pw_aff(
3433 __isl_take isl_printer *p,
3434 __isl_keep isl_pw_aff *pwaff);
3436 =head2 Piecewise Multiple Quasi Affine Expressions
3438 An C<isl_multi_aff> object represents a sequence of
3439 zero or more affine expressions, all defined on the same domain space.
3441 An C<isl_multi_aff> can be constructed from a C<isl_aff_list> using the
3444 #include <isl/aff.h>
3445 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3446 __isl_take isl_space *space,
3447 __isl_take isl_aff_list *list);
3449 An empty piecewise multiple quasi affine expression (one with no cells),
3450 the zero piecewise multiple quasi affine expression (with value zero
3451 for each output dimension),
3452 a piecewise multiple quasi affine expression with a single cell (with
3453 either a universe or a specified domain) or
3454 a zero-dimensional piecewise multiple quasi affine expression
3456 can be created using the following functions.
3458 #include <isl/aff.h>
3459 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3460 __isl_take isl_space *space);
3461 __isl_give isl_multi_aff *isl_multi_aff_zero(
3462 __isl_take isl_space *space);
3463 __isl_give isl_multi_aff *isl_multi_aff_identity(
3464 __isl_take isl_space *space);
3465 __isl_give isl_pw_multi_aff *
3466 isl_pw_multi_aff_from_multi_aff(
3467 __isl_take isl_multi_aff *ma);
3468 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3469 __isl_take isl_set *set,
3470 __isl_take isl_multi_aff *maff);
3471 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3472 __isl_take isl_set *set);
3474 __isl_give isl_union_pw_multi_aff *
3475 isl_union_pw_multi_aff_empty(
3476 __isl_take isl_space *space);
3477 __isl_give isl_union_pw_multi_aff *
3478 isl_union_pw_multi_aff_add_pw_multi_aff(
3479 __isl_take isl_union_pw_multi_aff *upma,
3480 __isl_take isl_pw_multi_aff *pma);
3481 __isl_give isl_union_pw_multi_aff *
3482 isl_union_pw_multi_aff_from_domain(
3483 __isl_take isl_union_set *uset);
3485 A piecewise multiple quasi affine expression can also be initialized
3486 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3487 and the C<isl_map> is single-valued.
3489 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3490 __isl_take isl_set *set);
3491 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3492 __isl_take isl_map *map);
3494 Multiple quasi affine expressions can be copied and freed using
3496 #include <isl/aff.h>
3497 __isl_give isl_multi_aff *isl_multi_aff_copy(
3498 __isl_keep isl_multi_aff *maff);
3499 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3501 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3502 __isl_keep isl_pw_multi_aff *pma);
3503 void *isl_pw_multi_aff_free(
3504 __isl_take isl_pw_multi_aff *pma);
3506 __isl_give isl_union_pw_multi_aff *
3507 isl_union_pw_multi_aff_copy(
3508 __isl_keep isl_union_pw_multi_aff *upma);
3509 void *isl_union_pw_multi_aff_free(
3510 __isl_take isl_union_pw_multi_aff *upma);
3512 The expression can be inspected using
3514 #include <isl/aff.h>
3515 isl_ctx *isl_multi_aff_get_ctx(
3516 __isl_keep isl_multi_aff *maff);
3517 isl_ctx *isl_pw_multi_aff_get_ctx(
3518 __isl_keep isl_pw_multi_aff *pma);
3519 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3520 __isl_keep isl_union_pw_multi_aff *upma);
3521 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3522 enum isl_dim_type type);
3523 unsigned isl_pw_multi_aff_dim(
3524 __isl_keep isl_pw_multi_aff *pma,
3525 enum isl_dim_type type);
3526 __isl_give isl_aff *isl_multi_aff_get_aff(
3527 __isl_keep isl_multi_aff *multi, int pos);
3528 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3529 __isl_keep isl_pw_multi_aff *pma, int pos);
3530 const char *isl_pw_multi_aff_get_dim_name(
3531 __isl_keep isl_pw_multi_aff *pma,
3532 enum isl_dim_type type, unsigned pos);
3533 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3534 __isl_keep isl_pw_multi_aff *pma,
3535 enum isl_dim_type type, unsigned pos);
3536 const char *isl_multi_aff_get_tuple_name(
3537 __isl_keep isl_multi_aff *multi,
3538 enum isl_dim_type type);
3539 int isl_pw_multi_aff_has_tuple_name(
3540 __isl_keep isl_pw_multi_aff *pma,
3541 enum isl_dim_type type);
3542 const char *isl_pw_multi_aff_get_tuple_name(
3543 __isl_keep isl_pw_multi_aff *pma,
3544 enum isl_dim_type type);
3545 int isl_pw_multi_aff_has_tuple_id(
3546 __isl_keep isl_pw_multi_aff *pma,
3547 enum isl_dim_type type);
3548 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3549 __isl_keep isl_pw_multi_aff *pma,
3550 enum isl_dim_type type);
3552 int isl_pw_multi_aff_foreach_piece(
3553 __isl_keep isl_pw_multi_aff *pma,
3554 int (*fn)(__isl_take isl_set *set,
3555 __isl_take isl_multi_aff *maff,
3556 void *user), void *user);
3558 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3559 __isl_keep isl_union_pw_multi_aff *upma,
3560 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3561 void *user), void *user);
3563 It can be modified using
3565 #include <isl/aff.h>
3566 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3567 __isl_take isl_multi_aff *multi, int pos,
3568 __isl_take isl_aff *aff);
3569 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3570 __isl_take isl_multi_aff *maff,
3571 enum isl_dim_type type, unsigned pos, const char *s);
3572 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3573 __isl_take isl_multi_aff *maff,
3574 enum isl_dim_type type, __isl_take isl_id *id);
3575 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3576 __isl_take isl_pw_multi_aff *pma,
3577 enum isl_dim_type type, __isl_take isl_id *id);
3579 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3580 __isl_take isl_multi_aff *maff,
3581 enum isl_dim_type type, unsigned first, unsigned n);
3582 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3583 __isl_take isl_pw_multi_aff *pma,
3584 enum isl_dim_type type, unsigned first, unsigned n);
3586 To check whether two multiple affine expressions are
3587 obviously equal to each other, use
3589 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3590 __isl_keep isl_multi_aff *maff2);
3591 int isl_pw_multi_aff_plain_is_equal(
3592 __isl_keep isl_pw_multi_aff *pma1,
3593 __isl_keep isl_pw_multi_aff *pma2);
3597 #include <isl/aff.h>
3598 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3599 __isl_take isl_pw_multi_aff *pma1,
3600 __isl_take isl_pw_multi_aff *pma2);
3601 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3602 __isl_take isl_pw_multi_aff *pma1,
3603 __isl_take isl_pw_multi_aff *pma2);
3604 __isl_give isl_multi_aff *isl_multi_aff_add(
3605 __isl_take isl_multi_aff *maff1,
3606 __isl_take isl_multi_aff *maff2);
3607 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3608 __isl_take isl_pw_multi_aff *pma1,
3609 __isl_take isl_pw_multi_aff *pma2);
3610 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3611 __isl_take isl_union_pw_multi_aff *upma1,
3612 __isl_take isl_union_pw_multi_aff *upma2);
3613 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3614 __isl_take isl_pw_multi_aff *pma1,
3615 __isl_take isl_pw_multi_aff *pma2);
3616 __isl_give isl_multi_aff *isl_multi_aff_scale(
3617 __isl_take isl_multi_aff *maff,
3619 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3620 __isl_take isl_pw_multi_aff *pma,
3621 __isl_take isl_set *set);
3622 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3623 __isl_take isl_pw_multi_aff *pma,
3624 __isl_take isl_set *set);
3625 __isl_give isl_multi_aff *isl_multi_aff_lift(
3626 __isl_take isl_multi_aff *maff,
3627 __isl_give isl_local_space **ls);
3628 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3629 __isl_take isl_pw_multi_aff *pma);
3630 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3631 __isl_take isl_multi_aff *multi,
3632 __isl_take isl_space *model);
3633 __isl_give isl_pw_multi_aff *
3634 isl_pw_multi_aff_project_domain_on_params(
3635 __isl_take isl_pw_multi_aff *pma);
3636 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3637 __isl_take isl_multi_aff *maff,
3638 __isl_take isl_set *context);
3639 __isl_give isl_multi_aff *isl_multi_aff_gist(
3640 __isl_take isl_multi_aff *maff,
3641 __isl_take isl_set *context);
3642 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3643 __isl_take isl_pw_multi_aff *pma,
3644 __isl_take isl_set *set);
3645 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3646 __isl_take isl_pw_multi_aff *pma,
3647 __isl_take isl_set *set);
3648 __isl_give isl_set *isl_pw_multi_aff_domain(
3649 __isl_take isl_pw_multi_aff *pma);
3650 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3651 __isl_take isl_union_pw_multi_aff *upma);
3652 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3653 __isl_take isl_multi_aff *ma1,
3654 __isl_take isl_multi_aff *ma2);
3655 __isl_give isl_multi_aff *isl_multi_aff_product(
3656 __isl_take isl_multi_aff *ma1,
3657 __isl_take isl_multi_aff *ma2);
3658 __isl_give isl_pw_multi_aff *
3659 isl_pw_multi_aff_flat_range_product(
3660 __isl_take isl_pw_multi_aff *pma1,
3661 __isl_take isl_pw_multi_aff *pma2);
3662 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3663 __isl_take isl_pw_multi_aff *pma1,
3664 __isl_take isl_pw_multi_aff *pma2);
3665 __isl_give isl_union_pw_multi_aff *
3666 isl_union_pw_multi_aff_flat_range_product(
3667 __isl_take isl_union_pw_multi_aff *upma1,
3668 __isl_take isl_union_pw_multi_aff *upma2);
3670 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3671 then it is assigned the local space that lies at the basis of
3672 the lifting applied.
3674 __isl_give isl_set *isl_multi_aff_lex_le_set(
3675 __isl_take isl_multi_aff *ma1,
3676 __isl_take isl_multi_aff *ma2);
3677 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3678 __isl_take isl_multi_aff *ma1,
3679 __isl_take isl_multi_aff *ma2);
3681 The function C<isl_multi_aff_lex_le_set> returns a set
3682 containing those elements in the shared domain space
3683 where C<ma1> is lexicographically smaller than or
3686 An expression can be read from input using
3688 #include <isl/aff.h>
3689 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
3690 isl_ctx *ctx, const char *str);
3691 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
3692 isl_ctx *ctx, const char *str);
3694 An expression can be printed using
3696 #include <isl/aff.h>
3697 __isl_give isl_printer *isl_printer_print_multi_aff(
3698 __isl_take isl_printer *p,
3699 __isl_keep isl_multi_aff *maff);
3700 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
3701 __isl_take isl_printer *p,
3702 __isl_keep isl_pw_multi_aff *pma);
3703 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
3704 __isl_take isl_printer *p,
3705 __isl_keep isl_union_pw_multi_aff *upma);
3709 Points are elements of a set. They can be used to construct
3710 simple sets (boxes) or they can be used to represent the
3711 individual elements of a set.
3712 The zero point (the origin) can be created using
3714 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
3716 The coordinates of a point can be inspected, set and changed
3719 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
3720 enum isl_dim_type type, int pos, isl_int *v);
3721 __isl_give isl_point *isl_point_set_coordinate(
3722 __isl_take isl_point *pnt,
3723 enum isl_dim_type type, int pos, isl_int v);
3725 __isl_give isl_point *isl_point_add_ui(
3726 __isl_take isl_point *pnt,
3727 enum isl_dim_type type, int pos, unsigned val);
3728 __isl_give isl_point *isl_point_sub_ui(
3729 __isl_take isl_point *pnt,
3730 enum isl_dim_type type, int pos, unsigned val);
3732 Other properties can be obtained using
3734 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
3736 Points can be copied or freed using
3738 __isl_give isl_point *isl_point_copy(
3739 __isl_keep isl_point *pnt);
3740 void isl_point_free(__isl_take isl_point *pnt);
3742 A singleton set can be created from a point using
3744 __isl_give isl_basic_set *isl_basic_set_from_point(
3745 __isl_take isl_point *pnt);
3746 __isl_give isl_set *isl_set_from_point(
3747 __isl_take isl_point *pnt);
3749 and a box can be created from two opposite extremal points using
3751 __isl_give isl_basic_set *isl_basic_set_box_from_points(
3752 __isl_take isl_point *pnt1,
3753 __isl_take isl_point *pnt2);
3754 __isl_give isl_set *isl_set_box_from_points(
3755 __isl_take isl_point *pnt1,
3756 __isl_take isl_point *pnt2);
3758 All elements of a B<bounded> (union) set can be enumerated using
3759 the following functions.
3761 int isl_set_foreach_point(__isl_keep isl_set *set,
3762 int (*fn)(__isl_take isl_point *pnt, void *user),
3764 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
3765 int (*fn)(__isl_take isl_point *pnt, void *user),
3768 The function C<fn> is called for each integer point in
3769 C<set> with as second argument the last argument of
3770 the C<isl_set_foreach_point> call. The function C<fn>
3771 should return C<0> on success and C<-1> on failure.
3772 In the latter case, C<isl_set_foreach_point> will stop
3773 enumerating and return C<-1> as well.
3774 If the enumeration is performed successfully and to completion,
3775 then C<isl_set_foreach_point> returns C<0>.
3777 To obtain a single point of a (basic) set, use
3779 __isl_give isl_point *isl_basic_set_sample_point(
3780 __isl_take isl_basic_set *bset);
3781 __isl_give isl_point *isl_set_sample_point(
3782 __isl_take isl_set *set);
3784 If C<set> does not contain any (integer) points, then the
3785 resulting point will be ``void'', a property that can be
3788 int isl_point_is_void(__isl_keep isl_point *pnt);
3790 =head2 Piecewise Quasipolynomials
3792 A piecewise quasipolynomial is a particular kind of function that maps
3793 a parametric point to a rational value.
3794 More specifically, a quasipolynomial is a polynomial expression in greatest
3795 integer parts of affine expressions of parameters and variables.
3796 A piecewise quasipolynomial is a subdivision of a given parametric
3797 domain into disjoint cells with a quasipolynomial associated to
3798 each cell. The value of the piecewise quasipolynomial at a given
3799 point is the value of the quasipolynomial associated to the cell
3800 that contains the point. Outside of the union of cells,
3801 the value is assumed to be zero.
3802 For example, the piecewise quasipolynomial
3804 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
3806 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
3807 A given piecewise quasipolynomial has a fixed domain dimension.
3808 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
3809 defined over different domains.
3810 Piecewise quasipolynomials are mainly used by the C<barvinok>
3811 library for representing the number of elements in a parametric set or map.
3812 For example, the piecewise quasipolynomial above represents
3813 the number of points in the map
3815 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
3817 =head3 Input and Output
3819 Piecewise quasipolynomials can be read from input using
3821 __isl_give isl_union_pw_qpolynomial *
3822 isl_union_pw_qpolynomial_read_from_str(
3823 isl_ctx *ctx, const char *str);
3825 Quasipolynomials and piecewise quasipolynomials can be printed
3826 using the following functions.
3828 __isl_give isl_printer *isl_printer_print_qpolynomial(
3829 __isl_take isl_printer *p,
3830 __isl_keep isl_qpolynomial *qp);
3832 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
3833 __isl_take isl_printer *p,
3834 __isl_keep isl_pw_qpolynomial *pwqp);
3836 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
3837 __isl_take isl_printer *p,
3838 __isl_keep isl_union_pw_qpolynomial *upwqp);
3840 The output format of the printer
3841 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
3842 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
3844 In case of printing in C<ISL_FORMAT_C>, the user may want
3845 to set the names of all dimensions
3847 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
3848 __isl_take isl_qpolynomial *qp,
3849 enum isl_dim_type type, unsigned pos,
3851 __isl_give isl_pw_qpolynomial *
3852 isl_pw_qpolynomial_set_dim_name(
3853 __isl_take isl_pw_qpolynomial *pwqp,
3854 enum isl_dim_type type, unsigned pos,
3857 =head3 Creating New (Piecewise) Quasipolynomials
3859 Some simple quasipolynomials can be created using the following functions.
3860 More complicated quasipolynomials can be created by applying
3861 operations such as addition and multiplication
3862 on the resulting quasipolynomials
3864 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
3865 __isl_take isl_space *domain);
3866 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
3867 __isl_take isl_space *domain);
3868 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
3869 __isl_take isl_space *domain);
3870 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
3871 __isl_take isl_space *domain);
3872 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
3873 __isl_take isl_space *domain);
3874 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
3875 __isl_take isl_space *domain,
3876 const isl_int n, const isl_int d);
3877 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
3878 __isl_take isl_space *domain,
3879 enum isl_dim_type type, unsigned pos);
3880 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
3881 __isl_take isl_aff *aff);
3883 Note that the space in which a quasipolynomial lives is a map space
3884 with a one-dimensional range. The C<domain> argument in some of
3885 the functions above corresponds to the domain of this map space.
3887 The zero piecewise quasipolynomial or a piecewise quasipolynomial
3888 with a single cell can be created using the following functions.
3889 Multiple of these single cell piecewise quasipolynomials can
3890 be combined to create more complicated piecewise quasipolynomials.
3892 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
3893 __isl_take isl_space *space);
3894 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
3895 __isl_take isl_set *set,
3896 __isl_take isl_qpolynomial *qp);
3897 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
3898 __isl_take isl_qpolynomial *qp);
3899 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
3900 __isl_take isl_pw_aff *pwaff);
3902 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
3903 __isl_take isl_space *space);
3904 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
3905 __isl_take isl_pw_qpolynomial *pwqp);
3906 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
3907 __isl_take isl_union_pw_qpolynomial *upwqp,
3908 __isl_take isl_pw_qpolynomial *pwqp);
3910 Quasipolynomials can be copied and freed again using the following
3913 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
3914 __isl_keep isl_qpolynomial *qp);
3915 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
3917 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
3918 __isl_keep isl_pw_qpolynomial *pwqp);
3919 void *isl_pw_qpolynomial_free(
3920 __isl_take isl_pw_qpolynomial *pwqp);
3922 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
3923 __isl_keep isl_union_pw_qpolynomial *upwqp);
3924 void *isl_union_pw_qpolynomial_free(
3925 __isl_take isl_union_pw_qpolynomial *upwqp);
3927 =head3 Inspecting (Piecewise) Quasipolynomials
3929 To iterate over all piecewise quasipolynomials in a union
3930 piecewise quasipolynomial, use the following function
3932 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
3933 __isl_keep isl_union_pw_qpolynomial *upwqp,
3934 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
3937 To extract the piecewise quasipolynomial in a given space from a union, use
3939 __isl_give isl_pw_qpolynomial *
3940 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
3941 __isl_keep isl_union_pw_qpolynomial *upwqp,
3942 __isl_take isl_space *space);
3944 To iterate over the cells in a piecewise quasipolynomial,
3945 use either of the following two functions
3947 int isl_pw_qpolynomial_foreach_piece(
3948 __isl_keep isl_pw_qpolynomial *pwqp,
3949 int (*fn)(__isl_take isl_set *set,
3950 __isl_take isl_qpolynomial *qp,
3951 void *user), void *user);
3952 int isl_pw_qpolynomial_foreach_lifted_piece(
3953 __isl_keep isl_pw_qpolynomial *pwqp,
3954 int (*fn)(__isl_take isl_set *set,
3955 __isl_take isl_qpolynomial *qp,
3956 void *user), void *user);
3958 As usual, the function C<fn> should return C<0> on success
3959 and C<-1> on failure. The difference between
3960 C<isl_pw_qpolynomial_foreach_piece> and
3961 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
3962 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
3963 compute unique representations for all existentially quantified
3964 variables and then turn these existentially quantified variables
3965 into extra set variables, adapting the associated quasipolynomial
3966 accordingly. This means that the C<set> passed to C<fn>
3967 will not have any existentially quantified variables, but that
3968 the dimensions of the sets may be different for different
3969 invocations of C<fn>.
3971 To iterate over all terms in a quasipolynomial,
3974 int isl_qpolynomial_foreach_term(
3975 __isl_keep isl_qpolynomial *qp,
3976 int (*fn)(__isl_take isl_term *term,
3977 void *user), void *user);
3979 The terms themselves can be inspected and freed using
3982 unsigned isl_term_dim(__isl_keep isl_term *term,
3983 enum isl_dim_type type);
3984 void isl_term_get_num(__isl_keep isl_term *term,
3986 void isl_term_get_den(__isl_keep isl_term *term,
3988 int isl_term_get_exp(__isl_keep isl_term *term,
3989 enum isl_dim_type type, unsigned pos);
3990 __isl_give isl_aff *isl_term_get_div(
3991 __isl_keep isl_term *term, unsigned pos);
3992 void isl_term_free(__isl_take isl_term *term);
3994 Each term is a product of parameters, set variables and
3995 integer divisions. The function C<isl_term_get_exp>
3996 returns the exponent of a given dimensions in the given term.
3997 The C<isl_int>s in the arguments of C<isl_term_get_num>
3998 and C<isl_term_get_den> need to have been initialized
3999 using C<isl_int_init> before calling these functions.
4001 =head3 Properties of (Piecewise) Quasipolynomials
4003 To check whether a quasipolynomial is actually a constant,
4004 use the following function.
4006 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4007 isl_int *n, isl_int *d);
4009 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4010 then the numerator and denominator of the constant
4011 are returned in C<*n> and C<*d>, respectively.
4013 To check whether two union piecewise quasipolynomials are
4014 obviously equal, use
4016 int isl_union_pw_qpolynomial_plain_is_equal(
4017 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4018 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4020 =head3 Operations on (Piecewise) Quasipolynomials
4022 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4023 __isl_take isl_qpolynomial *qp, isl_int v);
4024 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4025 __isl_take isl_qpolynomial *qp);
4026 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4027 __isl_take isl_qpolynomial *qp1,
4028 __isl_take isl_qpolynomial *qp2);
4029 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4030 __isl_take isl_qpolynomial *qp1,
4031 __isl_take isl_qpolynomial *qp2);
4032 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4033 __isl_take isl_qpolynomial *qp1,
4034 __isl_take isl_qpolynomial *qp2);
4035 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4036 __isl_take isl_qpolynomial *qp, unsigned exponent);
4038 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4039 __isl_take isl_pw_qpolynomial *pwqp1,
4040 __isl_take isl_pw_qpolynomial *pwqp2);
4041 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4042 __isl_take isl_pw_qpolynomial *pwqp1,
4043 __isl_take isl_pw_qpolynomial *pwqp2);
4044 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4045 __isl_take isl_pw_qpolynomial *pwqp1,
4046 __isl_take isl_pw_qpolynomial *pwqp2);
4047 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4048 __isl_take isl_pw_qpolynomial *pwqp);
4049 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4050 __isl_take isl_pw_qpolynomial *pwqp1,
4051 __isl_take isl_pw_qpolynomial *pwqp2);
4052 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4053 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4055 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4056 __isl_take isl_union_pw_qpolynomial *upwqp1,
4057 __isl_take isl_union_pw_qpolynomial *upwqp2);
4058 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4059 __isl_take isl_union_pw_qpolynomial *upwqp1,
4060 __isl_take isl_union_pw_qpolynomial *upwqp2);
4061 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4062 __isl_take isl_union_pw_qpolynomial *upwqp1,
4063 __isl_take isl_union_pw_qpolynomial *upwqp2);
4065 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4066 __isl_take isl_pw_qpolynomial *pwqp,
4067 __isl_take isl_point *pnt);
4069 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4070 __isl_take isl_union_pw_qpolynomial *upwqp,
4071 __isl_take isl_point *pnt);
4073 __isl_give isl_set *isl_pw_qpolynomial_domain(
4074 __isl_take isl_pw_qpolynomial *pwqp);
4075 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4076 __isl_take isl_pw_qpolynomial *pwpq,
4077 __isl_take isl_set *set);
4078 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4079 __isl_take isl_pw_qpolynomial *pwpq,
4080 __isl_take isl_set *set);
4082 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4083 __isl_take isl_union_pw_qpolynomial *upwqp);
4084 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4085 __isl_take isl_union_pw_qpolynomial *upwpq,
4086 __isl_take isl_union_set *uset);
4087 __isl_give isl_union_pw_qpolynomial *
4088 isl_union_pw_qpolynomial_intersect_params(
4089 __isl_take isl_union_pw_qpolynomial *upwpq,
4090 __isl_take isl_set *set);
4092 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4093 __isl_take isl_qpolynomial *qp,
4094 __isl_take isl_space *model);
4096 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4097 __isl_take isl_qpolynomial *qp);
4098 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4099 __isl_take isl_pw_qpolynomial *pwqp);
4101 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4102 __isl_take isl_union_pw_qpolynomial *upwqp);
4104 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4105 __isl_take isl_qpolynomial *qp,
4106 __isl_take isl_set *context);
4107 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4108 __isl_take isl_qpolynomial *qp,
4109 __isl_take isl_set *context);
4111 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4112 __isl_take isl_pw_qpolynomial *pwqp,
4113 __isl_take isl_set *context);
4114 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4115 __isl_take isl_pw_qpolynomial *pwqp,
4116 __isl_take isl_set *context);
4118 __isl_give isl_union_pw_qpolynomial *
4119 isl_union_pw_qpolynomial_gist_params(
4120 __isl_take isl_union_pw_qpolynomial *upwqp,
4121 __isl_take isl_set *context);
4122 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4123 __isl_take isl_union_pw_qpolynomial *upwqp,
4124 __isl_take isl_union_set *context);
4126 The gist operation applies the gist operation to each of
4127 the cells in the domain of the input piecewise quasipolynomial.
4128 The context is also exploited
4129 to simplify the quasipolynomials associated to each cell.
4131 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4132 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4133 __isl_give isl_union_pw_qpolynomial *
4134 isl_union_pw_qpolynomial_to_polynomial(
4135 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4137 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4138 the polynomial will be an overapproximation. If C<sign> is negative,
4139 it will be an underapproximation. If C<sign> is zero, the approximation
4140 will lie somewhere in between.
4142 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4144 A piecewise quasipolynomial reduction is a piecewise
4145 reduction (or fold) of quasipolynomials.
4146 In particular, the reduction can be maximum or a minimum.
4147 The objects are mainly used to represent the result of
4148 an upper or lower bound on a quasipolynomial over its domain,
4149 i.e., as the result of the following function.
4151 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4152 __isl_take isl_pw_qpolynomial *pwqp,
4153 enum isl_fold type, int *tight);
4155 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4156 __isl_take isl_union_pw_qpolynomial *upwqp,
4157 enum isl_fold type, int *tight);
4159 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4160 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4161 is the returned bound is known be tight, i.e., for each value
4162 of the parameters there is at least
4163 one element in the domain that reaches the bound.
4164 If the domain of C<pwqp> is not wrapping, then the bound is computed
4165 over all elements in that domain and the result has a purely parametric
4166 domain. If the domain of C<pwqp> is wrapping, then the bound is
4167 computed over the range of the wrapped relation. The domain of the
4168 wrapped relation becomes the domain of the result.
4170 A (piecewise) quasipolynomial reduction can be copied or freed using the
4171 following functions.
4173 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4174 __isl_keep isl_qpolynomial_fold *fold);
4175 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4176 __isl_keep isl_pw_qpolynomial_fold *pwf);
4177 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4178 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4179 void isl_qpolynomial_fold_free(
4180 __isl_take isl_qpolynomial_fold *fold);
4181 void *isl_pw_qpolynomial_fold_free(
4182 __isl_take isl_pw_qpolynomial_fold *pwf);
4183 void *isl_union_pw_qpolynomial_fold_free(
4184 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4186 =head3 Printing Piecewise Quasipolynomial Reductions
4188 Piecewise quasipolynomial reductions can be printed
4189 using the following function.
4191 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4192 __isl_take isl_printer *p,
4193 __isl_keep isl_pw_qpolynomial_fold *pwf);
4194 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4195 __isl_take isl_printer *p,
4196 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4198 For C<isl_printer_print_pw_qpolynomial_fold>,
4199 output format of the printer
4200 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4201 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4202 output format of the printer
4203 needs to be set to C<ISL_FORMAT_ISL>.
4204 In case of printing in C<ISL_FORMAT_C>, the user may want
4205 to set the names of all dimensions
4207 __isl_give isl_pw_qpolynomial_fold *
4208 isl_pw_qpolynomial_fold_set_dim_name(
4209 __isl_take isl_pw_qpolynomial_fold *pwf,
4210 enum isl_dim_type type, unsigned pos,
4213 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4215 To iterate over all piecewise quasipolynomial reductions in a union
4216 piecewise quasipolynomial reduction, use the following function
4218 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4219 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4220 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4221 void *user), void *user);
4223 To iterate over the cells in a piecewise quasipolynomial reduction,
4224 use either of the following two functions
4226 int isl_pw_qpolynomial_fold_foreach_piece(
4227 __isl_keep isl_pw_qpolynomial_fold *pwf,
4228 int (*fn)(__isl_take isl_set *set,
4229 __isl_take isl_qpolynomial_fold *fold,
4230 void *user), void *user);
4231 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4232 __isl_keep isl_pw_qpolynomial_fold *pwf,
4233 int (*fn)(__isl_take isl_set *set,
4234 __isl_take isl_qpolynomial_fold *fold,
4235 void *user), void *user);
4237 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4238 of the difference between these two functions.
4240 To iterate over all quasipolynomials in a reduction, use
4242 int isl_qpolynomial_fold_foreach_qpolynomial(
4243 __isl_keep isl_qpolynomial_fold *fold,
4244 int (*fn)(__isl_take isl_qpolynomial *qp,
4245 void *user), void *user);
4247 =head3 Properties of Piecewise Quasipolynomial Reductions
4249 To check whether two union piecewise quasipolynomial reductions are
4250 obviously equal, use
4252 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4253 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4254 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4256 =head3 Operations on Piecewise Quasipolynomial Reductions
4258 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4259 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4261 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4262 __isl_take isl_pw_qpolynomial_fold *pwf1,
4263 __isl_take isl_pw_qpolynomial_fold *pwf2);
4265 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4266 __isl_take isl_pw_qpolynomial_fold *pwf1,
4267 __isl_take isl_pw_qpolynomial_fold *pwf2);
4269 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4270 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4271 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4273 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4274 __isl_take isl_pw_qpolynomial_fold *pwf,
4275 __isl_take isl_point *pnt);
4277 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4278 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4279 __isl_take isl_point *pnt);
4281 __isl_give isl_pw_qpolynomial_fold *
4282 isl_pw_qpolynomial_fold_intersect_params(
4283 __isl_take isl_pw_qpolynomial_fold *pwf,
4284 __isl_take isl_set *set);
4286 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4287 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4288 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4289 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4290 __isl_take isl_union_set *uset);
4291 __isl_give isl_union_pw_qpolynomial_fold *
4292 isl_union_pw_qpolynomial_fold_intersect_params(
4293 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4294 __isl_take isl_set *set);
4296 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4297 __isl_take isl_pw_qpolynomial_fold *pwf);
4299 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4300 __isl_take isl_pw_qpolynomial_fold *pwf);
4302 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4303 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4305 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4306 __isl_take isl_qpolynomial_fold *fold,
4307 __isl_take isl_set *context);
4308 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4309 __isl_take isl_qpolynomial_fold *fold,
4310 __isl_take isl_set *context);
4312 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4313 __isl_take isl_pw_qpolynomial_fold *pwf,
4314 __isl_take isl_set *context);
4315 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4316 __isl_take isl_pw_qpolynomial_fold *pwf,
4317 __isl_take isl_set *context);
4319 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4320 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4321 __isl_take isl_union_set *context);
4322 __isl_give isl_union_pw_qpolynomial_fold *
4323 isl_union_pw_qpolynomial_fold_gist_params(
4324 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4325 __isl_take isl_set *context);
4327 The gist operation applies the gist operation to each of
4328 the cells in the domain of the input piecewise quasipolynomial reduction.
4329 In future, the operation will also exploit the context
4330 to simplify the quasipolynomial reductions associated to each cell.
4332 __isl_give isl_pw_qpolynomial_fold *
4333 isl_set_apply_pw_qpolynomial_fold(
4334 __isl_take isl_set *set,
4335 __isl_take isl_pw_qpolynomial_fold *pwf,
4337 __isl_give isl_pw_qpolynomial_fold *
4338 isl_map_apply_pw_qpolynomial_fold(
4339 __isl_take isl_map *map,
4340 __isl_take isl_pw_qpolynomial_fold *pwf,
4342 __isl_give isl_union_pw_qpolynomial_fold *
4343 isl_union_set_apply_union_pw_qpolynomial_fold(
4344 __isl_take isl_union_set *uset,
4345 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4347 __isl_give isl_union_pw_qpolynomial_fold *
4348 isl_union_map_apply_union_pw_qpolynomial_fold(
4349 __isl_take isl_union_map *umap,
4350 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4353 The functions taking a map
4354 compose the given map with the given piecewise quasipolynomial reduction.
4355 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4356 over all elements in the intersection of the range of the map
4357 and the domain of the piecewise quasipolynomial reduction
4358 as a function of an element in the domain of the map.
4359 The functions taking a set compute a bound over all elements in the
4360 intersection of the set and the domain of the
4361 piecewise quasipolynomial reduction.
4363 =head2 Dependence Analysis
4365 C<isl> contains specialized functionality for performing
4366 array dataflow analysis. That is, given a I<sink> access relation
4367 and a collection of possible I<source> access relations,
4368 C<isl> can compute relations that describe
4369 for each iteration of the sink access, which iteration
4370 of which of the source access relations was the last
4371 to access the same data element before the given iteration
4373 The resulting dependence relations map source iterations
4374 to the corresponding sink iterations.
4375 To compute standard flow dependences, the sink should be
4376 a read, while the sources should be writes.
4377 If any of the source accesses are marked as being I<may>
4378 accesses, then there will be a dependence from the last
4379 I<must> access B<and> from any I<may> access that follows
4380 this last I<must> access.
4381 In particular, if I<all> sources are I<may> accesses,
4382 then memory based dependence analysis is performed.
4383 If, on the other hand, all sources are I<must> accesses,
4384 then value based dependence analysis is performed.
4386 #include <isl/flow.h>
4388 typedef int (*isl_access_level_before)(void *first, void *second);
4390 __isl_give isl_access_info *isl_access_info_alloc(
4391 __isl_take isl_map *sink,
4392 void *sink_user, isl_access_level_before fn,
4394 __isl_give isl_access_info *isl_access_info_add_source(
4395 __isl_take isl_access_info *acc,
4396 __isl_take isl_map *source, int must,
4398 void *isl_access_info_free(__isl_take isl_access_info *acc);
4400 __isl_give isl_flow *isl_access_info_compute_flow(
4401 __isl_take isl_access_info *acc);
4403 int isl_flow_foreach(__isl_keep isl_flow *deps,
4404 int (*fn)(__isl_take isl_map *dep, int must,
4405 void *dep_user, void *user),
4407 __isl_give isl_map *isl_flow_get_no_source(
4408 __isl_keep isl_flow *deps, int must);
4409 void isl_flow_free(__isl_take isl_flow *deps);
4411 The function C<isl_access_info_compute_flow> performs the actual
4412 dependence analysis. The other functions are used to construct
4413 the input for this function or to read off the output.
4415 The input is collected in an C<isl_access_info>, which can
4416 be created through a call to C<isl_access_info_alloc>.
4417 The arguments to this functions are the sink access relation
4418 C<sink>, a token C<sink_user> used to identify the sink
4419 access to the user, a callback function for specifying the
4420 relative order of source and sink accesses, and the number
4421 of source access relations that will be added.
4422 The callback function has type C<int (*)(void *first, void *second)>.
4423 The function is called with two user supplied tokens identifying
4424 either a source or the sink and it should return the shared nesting
4425 level and the relative order of the two accesses.
4426 In particular, let I<n> be the number of loops shared by
4427 the two accesses. If C<first> precedes C<second> textually,
4428 then the function should return I<2 * n + 1>; otherwise,
4429 it should return I<2 * n>.
4430 The sources can be added to the C<isl_access_info> by performing
4431 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4432 C<must> indicates whether the source is a I<must> access
4433 or a I<may> access. Note that a multi-valued access relation
4434 should only be marked I<must> if every iteration in the domain
4435 of the relation accesses I<all> elements in its image.
4436 The C<source_user> token is again used to identify
4437 the source access. The range of the source access relation
4438 C<source> should have the same dimension as the range
4439 of the sink access relation.
4440 The C<isl_access_info_free> function should usually not be
4441 called explicitly, because it is called implicitly by
4442 C<isl_access_info_compute_flow>.
4444 The result of the dependence analysis is collected in an
4445 C<isl_flow>. There may be elements of
4446 the sink access for which no preceding source access could be
4447 found or for which all preceding sources are I<may> accesses.
4448 The relations containing these elements can be obtained through
4449 calls to C<isl_flow_get_no_source>, the first with C<must> set
4450 and the second with C<must> unset.
4451 In the case of standard flow dependence analysis,
4452 with the sink a read and the sources I<must> writes,
4453 the first relation corresponds to the reads from uninitialized
4454 array elements and the second relation is empty.
4455 The actual flow dependences can be extracted using
4456 C<isl_flow_foreach>. This function will call the user-specified
4457 callback function C<fn> for each B<non-empty> dependence between
4458 a source and the sink. The callback function is called
4459 with four arguments, the actual flow dependence relation
4460 mapping source iterations to sink iterations, a boolean that
4461 indicates whether it is a I<must> or I<may> dependence, a token
4462 identifying the source and an additional C<void *> with value
4463 equal to the third argument of the C<isl_flow_foreach> call.
4464 A dependence is marked I<must> if it originates from a I<must>
4465 source and if it is not followed by any I<may> sources.
4467 After finishing with an C<isl_flow>, the user should call
4468 C<isl_flow_free> to free all associated memory.
4470 A higher-level interface to dependence analysis is provided
4471 by the following function.
4473 #include <isl/flow.h>
4475 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4476 __isl_take isl_union_map *must_source,
4477 __isl_take isl_union_map *may_source,
4478 __isl_take isl_union_map *schedule,
4479 __isl_give isl_union_map **must_dep,
4480 __isl_give isl_union_map **may_dep,
4481 __isl_give isl_union_map **must_no_source,
4482 __isl_give isl_union_map **may_no_source);
4484 The arrays are identified by the tuple names of the ranges
4485 of the accesses. The iteration domains by the tuple names
4486 of the domains of the accesses and of the schedule.
4487 The relative order of the iteration domains is given by the
4488 schedule. The relations returned through C<must_no_source>
4489 and C<may_no_source> are subsets of C<sink>.
4490 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4491 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4492 any of the other arguments is treated as an error.
4494 =head3 Interaction with Dependence Analysis
4496 During the dependence analysis, we frequently need to perform
4497 the following operation. Given a relation between sink iterations
4498 and potential source iterations from a particular source domain,
4499 what is the last potential source iteration corresponding to each
4500 sink iteration. It can sometimes be convenient to adjust
4501 the set of potential source iterations before or after each such operation.
4502 The prototypical example is fuzzy array dataflow analysis,
4503 where we need to analyze if, based on data-dependent constraints,
4504 the sink iteration can ever be executed without one or more of
4505 the corresponding potential source iterations being executed.
4506 If so, we can introduce extra parameters and select an unknown
4507 but fixed source iteration from the potential source iterations.
4508 To be able to perform such manipulations, C<isl> provides the following
4511 #include <isl/flow.h>
4513 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4514 __isl_keep isl_map *source_map,
4515 __isl_keep isl_set *sink, void *source_user,
4517 __isl_give isl_access_info *isl_access_info_set_restrict(
4518 __isl_take isl_access_info *acc,
4519 isl_access_restrict fn, void *user);
4521 The function C<isl_access_info_set_restrict> should be called
4522 before calling C<isl_access_info_compute_flow> and registers a callback function
4523 that will be called any time C<isl> is about to compute the last
4524 potential source. The first argument is the (reverse) proto-dependence,
4525 mapping sink iterations to potential source iterations.
4526 The second argument represents the sink iterations for which
4527 we want to compute the last source iteration.
4528 The third argument is the token corresponding to the source
4529 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4530 The callback is expected to return a restriction on either the input or
4531 the output of the operation computing the last potential source.
4532 If the input needs to be restricted then restrictions are needed
4533 for both the source and the sink iterations. The sink iterations
4534 and the potential source iterations will be intersected with these sets.
4535 If the output needs to be restricted then only a restriction on the source
4536 iterations is required.
4537 If any error occurs, the callback should return C<NULL>.
4538 An C<isl_restriction> object can be created, freed and inspected
4539 using the following functions.
4541 #include <isl/flow.h>
4543 __isl_give isl_restriction *isl_restriction_input(
4544 __isl_take isl_set *source_restr,
4545 __isl_take isl_set *sink_restr);
4546 __isl_give isl_restriction *isl_restriction_output(
4547 __isl_take isl_set *source_restr);
4548 __isl_give isl_restriction *isl_restriction_none(
4549 __isl_take isl_map *source_map);
4550 __isl_give isl_restriction *isl_restriction_empty(
4551 __isl_take isl_map *source_map);
4552 void *isl_restriction_free(
4553 __isl_take isl_restriction *restr);
4554 isl_ctx *isl_restriction_get_ctx(
4555 __isl_keep isl_restriction *restr);
4557 C<isl_restriction_none> and C<isl_restriction_empty> are special
4558 cases of C<isl_restriction_input>. C<isl_restriction_none>
4559 is essentially equivalent to
4561 isl_restriction_input(isl_set_universe(
4562 isl_space_range(isl_map_get_space(source_map))),
4564 isl_space_domain(isl_map_get_space(source_map))));
4566 whereas C<isl_restriction_empty> is essentially equivalent to
4568 isl_restriction_input(isl_set_empty(
4569 isl_space_range(isl_map_get_space(source_map))),
4571 isl_space_domain(isl_map_get_space(source_map))));
4575 B<The functionality described in this section is fairly new
4576 and may be subject to change.>
4578 The following function can be used to compute a schedule
4579 for a union of domains.
4580 By default, the algorithm used to construct the schedule is similar
4581 to that of C<Pluto>.
4582 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4584 The generated schedule respects all C<validity> dependences.
4585 That is, all dependence distances over these dependences in the
4586 scheduled space are lexicographically positive.
4587 The default algorithm tries to minimize the dependence distances over
4588 C<proximity> dependences.
4589 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4590 for groups of domains where the dependence distances have only
4591 non-negative values.
4592 When using Feautrier's algorithm, the C<proximity> dependence
4593 distances are only minimized during the extension to a
4594 full-dimensional schedule.
4596 #include <isl/schedule.h>
4597 __isl_give isl_schedule *isl_union_set_compute_schedule(
4598 __isl_take isl_union_set *domain,
4599 __isl_take isl_union_map *validity,
4600 __isl_take isl_union_map *proximity);
4601 void *isl_schedule_free(__isl_take isl_schedule *sched);
4603 A mapping from the domains to the scheduled space can be obtained
4604 from an C<isl_schedule> using the following function.
4606 __isl_give isl_union_map *isl_schedule_get_map(
4607 __isl_keep isl_schedule *sched);
4609 A representation of the schedule can be printed using
4611 __isl_give isl_printer *isl_printer_print_schedule(
4612 __isl_take isl_printer *p,
4613 __isl_keep isl_schedule *schedule);
4615 A representation of the schedule as a forest of bands can be obtained
4616 using the following function.
4618 __isl_give isl_band_list *isl_schedule_get_band_forest(
4619 __isl_keep isl_schedule *schedule);
4621 The individual bands can be visited in depth-first post-order
4622 using the following function.
4624 #include <isl/schedule.h>
4625 int isl_schedule_foreach_band(
4626 __isl_keep isl_schedule *sched,
4627 int (*fn)(__isl_keep isl_band *band, void *user),
4630 The list can be manipulated as explained in L<"Lists">.
4631 The bands inside the list can be copied and freed using the following
4634 #include <isl/band.h>
4635 __isl_give isl_band *isl_band_copy(
4636 __isl_keep isl_band *band);
4637 void *isl_band_free(__isl_take isl_band *band);
4639 Each band contains zero or more scheduling dimensions.
4640 These are referred to as the members of the band.
4641 The section of the schedule that corresponds to the band is
4642 referred to as the partial schedule of the band.
4643 For those nodes that participate in a band, the outer scheduling
4644 dimensions form the prefix schedule, while the inner scheduling
4645 dimensions form the suffix schedule.
4646 That is, if we take a cut of the band forest, then the union of
4647 the concatenations of the prefix, partial and suffix schedules of
4648 each band in the cut is equal to the entire schedule (modulo
4649 some possible padding at the end with zero scheduling dimensions).
4650 The properties of a band can be inspected using the following functions.
4652 #include <isl/band.h>
4653 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
4655 int isl_band_has_children(__isl_keep isl_band *band);
4656 __isl_give isl_band_list *isl_band_get_children(
4657 __isl_keep isl_band *band);
4659 __isl_give isl_union_map *isl_band_get_prefix_schedule(
4660 __isl_keep isl_band *band);
4661 __isl_give isl_union_map *isl_band_get_partial_schedule(
4662 __isl_keep isl_band *band);
4663 __isl_give isl_union_map *isl_band_get_suffix_schedule(
4664 __isl_keep isl_band *band);
4666 int isl_band_n_member(__isl_keep isl_band *band);
4667 int isl_band_member_is_zero_distance(
4668 __isl_keep isl_band *band, int pos);
4670 int isl_band_list_foreach_band(
4671 __isl_keep isl_band_list *list,
4672 int (*fn)(__isl_keep isl_band *band, void *user),
4675 Note that a scheduling dimension is considered to be ``zero
4676 distance'' if it does not carry any proximity dependences
4678 That is, if the dependence distances of the proximity
4679 dependences are all zero in that direction (for fixed
4680 iterations of outer bands).
4681 Like C<isl_schedule_foreach_band>,
4682 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
4683 in depth-first post-order.
4685 A band can be tiled using the following function.
4687 #include <isl/band.h>
4688 int isl_band_tile(__isl_keep isl_band *band,
4689 __isl_take isl_vec *sizes);
4691 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
4693 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
4695 The C<isl_band_tile> function tiles the band using the given tile sizes
4696 inside its schedule.
4697 A new child band is created to represent the point loops and it is
4698 inserted between the modified band and its children.
4699 The C<tile_scale_tile_loops> option specifies whether the tile
4700 loops iterators should be scaled by the tile sizes.
4702 A representation of the band can be printed using
4704 #include <isl/band.h>
4705 __isl_give isl_printer *isl_printer_print_band(
4706 __isl_take isl_printer *p,
4707 __isl_keep isl_band *band);
4711 #include <isl/schedule.h>
4712 int isl_options_set_schedule_max_coefficient(
4713 isl_ctx *ctx, int val);
4714 int isl_options_get_schedule_max_coefficient(
4716 int isl_options_set_schedule_max_constant_term(
4717 isl_ctx *ctx, int val);
4718 int isl_options_get_schedule_max_constant_term(
4720 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
4721 int isl_options_get_schedule_fuse(isl_ctx *ctx);
4722 int isl_options_set_schedule_maximize_band_depth(
4723 isl_ctx *ctx, int val);
4724 int isl_options_get_schedule_maximize_band_depth(
4726 int isl_options_set_schedule_outer_zero_distance(
4727 isl_ctx *ctx, int val);
4728 int isl_options_get_schedule_outer_zero_distance(
4730 int isl_options_set_schedule_split_scaled(
4731 isl_ctx *ctx, int val);
4732 int isl_options_get_schedule_split_scaled(
4734 int isl_options_set_schedule_algorithm(
4735 isl_ctx *ctx, int val);
4736 int isl_options_get_schedule_algorithm(
4738 int isl_options_set_schedule_separate_components(
4739 isl_ctx *ctx, int val);
4740 int isl_options_get_schedule_separate_components(
4745 =item * schedule_max_coefficient
4747 This option enforces that the coefficients for variable and parameter
4748 dimensions in the calculated schedule are not larger than the specified value.
4749 This option can significantly increase the speed of the scheduling calculation
4750 and may also prevent fusing of unrelated dimensions. A value of -1 means that
4751 this option does not introduce bounds on the variable or parameter
4754 =item * schedule_max_constant_term
4756 This option enforces that the constant coefficients in the calculated schedule
4757 are not larger than the maximal constant term. This option can significantly
4758 increase the speed of the scheduling calculation and may also prevent fusing of
4759 unrelated dimensions. A value of -1 means that this option does not introduce
4760 bounds on the constant coefficients.
4762 =item * schedule_fuse
4764 This option controls the level of fusion.
4765 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
4766 resulting schedule will be distributed as much as possible.
4767 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
4768 try to fuse loops in the resulting schedule.
4770 =item * schedule_maximize_band_depth
4772 If this option is set, we do not split bands at the point
4773 where we detect splitting is necessary. Instead, we
4774 backtrack and split bands as early as possible. This
4775 reduces the number of splits and maximizes the width of
4776 the bands. Wider bands give more possibilities for tiling.
4777 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
4778 then bands will be split as early as possible, even if there is no need.
4779 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
4781 =item * schedule_outer_zero_distance
4783 If this option is set, then we try to construct schedules
4784 where the outermost scheduling dimension in each band
4785 results in a zero dependence distance over the proximity
4788 =item * schedule_split_scaled
4790 If this option is set, then we try to construct schedules in which the
4791 constant term is split off from the linear part if the linear parts of
4792 the scheduling rows for all nodes in the graphs have a common non-trivial
4794 The constant term is then placed in a separate band and the linear
4797 =item * schedule_algorithm
4799 Selects the scheduling algorithm to be used.
4800 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
4801 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
4803 =item * schedule_separate_components
4805 If at any point the dependence graph contains any (weakly connected) components,
4806 then these components are scheduled separately.
4807 If this option is not set, then some iterations of the domains
4808 in these components may be scheduled together.
4809 If this option is set, then the components are given consecutive
4814 =head2 Parametric Vertex Enumeration
4816 The parametric vertex enumeration described in this section
4817 is mainly intended to be used internally and by the C<barvinok>
4820 #include <isl/vertices.h>
4821 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4822 __isl_keep isl_basic_set *bset);
4824 The function C<isl_basic_set_compute_vertices> performs the
4825 actual computation of the parametric vertices and the chamber
4826 decomposition and store the result in an C<isl_vertices> object.
4827 This information can be queried by either iterating over all
4828 the vertices or iterating over all the chambers or cells
4829 and then iterating over all vertices that are active on the chamber.
4831 int isl_vertices_foreach_vertex(
4832 __isl_keep isl_vertices *vertices,
4833 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4836 int isl_vertices_foreach_cell(
4837 __isl_keep isl_vertices *vertices,
4838 int (*fn)(__isl_take isl_cell *cell, void *user),
4840 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4841 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4844 Other operations that can be performed on an C<isl_vertices> object are
4847 isl_ctx *isl_vertices_get_ctx(
4848 __isl_keep isl_vertices *vertices);
4849 int isl_vertices_get_n_vertices(
4850 __isl_keep isl_vertices *vertices);
4851 void isl_vertices_free(__isl_take isl_vertices *vertices);
4853 Vertices can be inspected and destroyed using the following functions.
4855 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4856 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4857 __isl_give isl_basic_set *isl_vertex_get_domain(
4858 __isl_keep isl_vertex *vertex);
4859 __isl_give isl_basic_set *isl_vertex_get_expr(
4860 __isl_keep isl_vertex *vertex);
4861 void isl_vertex_free(__isl_take isl_vertex *vertex);
4863 C<isl_vertex_get_expr> returns a singleton parametric set describing
4864 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4866 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4867 B<rational> basic sets, so they should mainly be used for inspection
4868 and should not be mixed with integer sets.
4870 Chambers can be inspected and destroyed using the following functions.
4872 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4873 __isl_give isl_basic_set *isl_cell_get_domain(
4874 __isl_keep isl_cell *cell);
4875 void isl_cell_free(__isl_take isl_cell *cell);
4879 Although C<isl> is mainly meant to be used as a library,
4880 it also contains some basic applications that use some
4881 of the functionality of C<isl>.
4882 The input may be specified in either the L<isl format>
4883 or the L<PolyLib format>.
4885 =head2 C<isl_polyhedron_sample>
4887 C<isl_polyhedron_sample> takes a polyhedron as input and prints
4888 an integer element of the polyhedron, if there is any.
4889 The first column in the output is the denominator and is always
4890 equal to 1. If the polyhedron contains no integer points,
4891 then a vector of length zero is printed.
4895 C<isl_pip> takes the same input as the C<example> program
4896 from the C<piplib> distribution, i.e., a set of constraints
4897 on the parameters, a line containing only -1 and finally a set
4898 of constraints on a parametric polyhedron.
4899 The coefficients of the parameters appear in the last columns
4900 (but before the final constant column).
4901 The output is the lexicographic minimum of the parametric polyhedron.
4902 As C<isl> currently does not have its own output format, the output
4903 is just a dump of the internal state.
4905 =head2 C<isl_polyhedron_minimize>
4907 C<isl_polyhedron_minimize> computes the minimum of some linear
4908 or affine objective function over the integer points in a polyhedron.
4909 If an affine objective function
4910 is given, then the constant should appear in the last column.
4912 =head2 C<isl_polytope_scan>
4914 Given a polytope, C<isl_polytope_scan> prints
4915 all integer points in the polytope.