3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take a B<map> space as input. An old call
72 C<isl_map_identity(space)> can be rewritten to
73 C<isl_map_identity(isl_space_map_from_set(space))>.
75 =item * The function C<isl_map_power> no longer takes
76 a parameter position as input. Instead, the exponent
77 is now expressed as the domain of the resulting relation.
81 =head3 Changes since isl-0.06
85 =item * The format of C<isl_printer_print_qpolynomial>'s
86 C<ISL_FORMAT_ISL> output has changed.
87 Use C<ISL_FORMAT_C> to obtain the old output.
89 =item * The C<*_fast_*> functions have been renamed to C<*_plain_*>.
90 Some of the old names have been kept for backward compatibility,
91 but they will be removed in the future.
95 =head3 Changes since isl-0.07
99 =item * The function C<isl_pw_aff_max> has been renamed to
100 C<isl_pw_aff_union_max>.
101 Similarly, the function C<isl_pw_aff_add> has been renamed to
102 C<isl_pw_aff_union_add>.
104 =item * The C<isl_dim> type has been renamed to C<isl_space>
105 along with the associated functions.
106 Some of the old names have been kept for backward compatibility,
107 but they will be removed in the future.
109 =item * Spaces of maps, sets and parameter domains are now
110 treated differently. The distinction between map spaces and set spaces
111 has always been made on a conceptual level, but proper use of such spaces
112 was never checked. Furthermore, up until isl-0.07 there was no way
113 of explicitly creating a parameter space. These can now be created
114 directly using C<isl_space_params_alloc> or from other spaces using
117 =item * The space in which C<isl_aff>, C<isl_pw_aff>, C<isl_qpolynomial>,
118 C<isl_pw_qpolynomial>, C<isl_qpolynomial_fold> and C<isl_pw_qpolynomial_fold>
119 objects live is now a map space
120 instead of a set space. This means, for example, that the dimensions
121 of the domain of an C<isl_aff> are now considered to be of type
122 C<isl_dim_in> instead of C<isl_dim_set>. Extra functions have been
123 added to obtain the domain space. Some of the constructors still
124 take a domain space and have therefore been renamed.
126 =item * The functions C<isl_equality_alloc> and C<isl_inequality_alloc>
127 now take an C<isl_local_space> instead of an C<isl_space>.
128 An C<isl_local_space> can be created from an C<isl_space>
129 using C<isl_local_space_from_space>.
131 =item * The C<isl_div> type has been removed. Functions that used
132 to return an C<isl_div> now return an C<isl_aff>.
133 Note that the space of an C<isl_aff> is that of relation.
134 When replacing a call to C<isl_div_get_coefficient> by a call to
135 C<isl_aff_get_coefficient> any C<isl_dim_set> argument needs
136 to be replaced by C<isl_dim_in>.
137 A call to C<isl_aff_from_div> can be replaced by a call
139 A call to C<isl_qpolynomial_div(div)> call be replaced by
142 isl_qpolynomial_from_aff(isl_aff_floor(div))
144 The function C<isl_constraint_div> has also been renamed
145 to C<isl_constraint_get_div>.
147 =item * The C<nparam> argument has been removed from
148 C<isl_map_read_from_str> and similar functions.
149 When reading input in the original PolyLib format,
150 the result will have no parameters.
151 If parameters are expected, the caller may want to perform
152 dimension manipulation on the result.
156 =head3 Changes since isl-0.09
160 =item * The C<schedule_split_parallel> option has been replaced
161 by the C<schedule_split_scaled> option.
163 =item * The first argument of C<isl_pw_aff_cond> is now
164 an C<isl_pw_aff> instead of an C<isl_set>.
165 A call C<isl_pw_aff_cond(a, b, c)> can be replaced by
167 isl_pw_aff_cond(isl_set_indicator_function(a), b, c)
171 =head3 Changes since isl-0.10
175 =item * The functions C<isl_set_dim_has_lower_bound> and
176 C<isl_set_dim_has_upper_bound> have been renamed to
177 C<isl_set_dim_has_any_lower_bound> and
178 C<isl_set_dim_has_any_upper_bound>.
179 The new C<isl_set_dim_has_lower_bound> and
180 C<isl_set_dim_has_upper_bound> have slightly different meanings.
186 C<isl> is released under the MIT license.
190 Permission is hereby granted, free of charge, to any person obtaining a copy of
191 this software and associated documentation files (the "Software"), to deal in
192 the Software without restriction, including without limitation the rights to
193 use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies
194 of the Software, and to permit persons to whom the Software is furnished to do
195 so, subject to the following conditions:
197 The above copyright notice and this permission notice shall be included in all
198 copies or substantial portions of the Software.
200 THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
201 IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
202 FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
203 AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
204 LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
205 OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
210 Note that C<isl> currently requires C<GMP>, which is released
211 under the GNU Lesser General Public License (LGPL). This means
212 that code linked against C<isl> is also linked against LGPL code.
216 The source of C<isl> can be obtained either as a tarball
217 or from the git repository. Both are available from
218 L<http://freshmeat.net/projects/isl/>.
219 The installation process depends on how you obtained
222 =head2 Installation from the git repository
226 =item 1 Clone or update the repository
228 The first time the source is obtained, you need to clone
231 git clone git://repo.or.cz/isl.git
233 To obtain updates, you need to pull in the latest changes
237 =item 2 Generate C<configure>
243 After performing the above steps, continue
244 with the L<Common installation instructions>.
246 =head2 Common installation instructions
250 =item 1 Obtain C<GMP>
252 Building C<isl> requires C<GMP>, including its headers files.
253 Your distribution may not provide these header files by default
254 and you may need to install a package called C<gmp-devel> or something
255 similar. Alternatively, C<GMP> can be built from
256 source, available from L<http://gmplib.org/>.
260 C<isl> uses the standard C<autoconf> C<configure> script.
265 optionally followed by some configure options.
266 A complete list of options can be obtained by running
270 Below we discuss some of the more common options.
272 C<isl> can optionally use C<piplib>, but no
273 C<piplib> functionality is currently used by default.
274 The C<--with-piplib> option can
275 be used to specify which C<piplib>
276 library to use, either an installed version (C<system>),
277 an externally built version (C<build>)
278 or no version (C<no>). The option C<build> is mostly useful
279 in C<configure> scripts of larger projects that bundle both C<isl>
286 Installation prefix for C<isl>
288 =item C<--with-gmp-prefix>
290 Installation prefix for C<GMP> (architecture-independent files).
292 =item C<--with-gmp-exec-prefix>
294 Installation prefix for C<GMP> (architecture-dependent files).
296 =item C<--with-piplib>
298 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
300 =item C<--with-piplib-prefix>
302 Installation prefix for C<system> C<piplib> (architecture-independent files).
304 =item C<--with-piplib-exec-prefix>
306 Installation prefix for C<system> C<piplib> (architecture-dependent files).
308 =item C<--with-piplib-builddir>
310 Location where C<build> C<piplib> was built.
318 =item 4 Install (optional)
324 =head1 Integer Set Library
326 =head2 Initialization
328 All manipulations of integer sets and relations occur within
329 the context of an C<isl_ctx>.
330 A given C<isl_ctx> can only be used within a single thread.
331 All arguments of a function are required to have been allocated
332 within the same context.
333 There are currently no functions available for moving an object
334 from one C<isl_ctx> to another C<isl_ctx>. This means that
335 there is currently no way of safely moving an object from one
336 thread to another, unless the whole C<isl_ctx> is moved.
338 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
339 freed using C<isl_ctx_free>.
340 All objects allocated within an C<isl_ctx> should be freed
341 before the C<isl_ctx> itself is freed.
343 isl_ctx *isl_ctx_alloc();
344 void isl_ctx_free(isl_ctx *ctx);
348 All operations on integers, mainly the coefficients
349 of the constraints describing the sets and relations,
350 are performed in exact integer arithmetic using C<GMP>.
351 However, to allow future versions of C<isl> to optionally
352 support fixed integer arithmetic, all calls to C<GMP>
353 are wrapped inside C<isl> specific macros.
354 The basic type is C<isl_int> and the operations below
355 are available on this type.
356 The meanings of these operations are essentially the same
357 as their C<GMP> C<mpz_> counterparts.
358 As always with C<GMP> types, C<isl_int>s need to be
359 initialized with C<isl_int_init> before they can be used
360 and they need to be released with C<isl_int_clear>
362 The user should not assume that an C<isl_int> is represented
363 as a C<mpz_t>, but should instead explicitly convert between
364 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
365 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
369 =item isl_int_init(i)
371 =item isl_int_clear(i)
373 =item isl_int_set(r,i)
375 =item isl_int_set_si(r,i)
377 =item isl_int_set_gmp(r,g)
379 =item isl_int_get_gmp(i,g)
381 =item isl_int_abs(r,i)
383 =item isl_int_neg(r,i)
385 =item isl_int_swap(i,j)
387 =item isl_int_swap_or_set(i,j)
389 =item isl_int_add_ui(r,i,j)
391 =item isl_int_sub_ui(r,i,j)
393 =item isl_int_add(r,i,j)
395 =item isl_int_sub(r,i,j)
397 =item isl_int_mul(r,i,j)
399 =item isl_int_mul_ui(r,i,j)
401 =item isl_int_addmul(r,i,j)
403 =item isl_int_submul(r,i,j)
405 =item isl_int_gcd(r,i,j)
407 =item isl_int_lcm(r,i,j)
409 =item isl_int_divexact(r,i,j)
411 =item isl_int_cdiv_q(r,i,j)
413 =item isl_int_fdiv_q(r,i,j)
415 =item isl_int_fdiv_r(r,i,j)
417 =item isl_int_fdiv_q_ui(r,i,j)
419 =item isl_int_read(r,s)
421 =item isl_int_print(out,i,width)
425 =item isl_int_cmp(i,j)
427 =item isl_int_cmp_si(i,si)
429 =item isl_int_eq(i,j)
431 =item isl_int_ne(i,j)
433 =item isl_int_lt(i,j)
435 =item isl_int_le(i,j)
437 =item isl_int_gt(i,j)
439 =item isl_int_ge(i,j)
441 =item isl_int_abs_eq(i,j)
443 =item isl_int_abs_ne(i,j)
445 =item isl_int_abs_lt(i,j)
447 =item isl_int_abs_gt(i,j)
449 =item isl_int_abs_ge(i,j)
451 =item isl_int_is_zero(i)
453 =item isl_int_is_one(i)
455 =item isl_int_is_negone(i)
457 =item isl_int_is_pos(i)
459 =item isl_int_is_neg(i)
461 =item isl_int_is_nonpos(i)
463 =item isl_int_is_nonneg(i)
465 =item isl_int_is_divisible_by(i,j)
469 =head2 Sets and Relations
471 C<isl> uses six types of objects for representing sets and relations,
472 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
473 C<isl_union_set> and C<isl_union_map>.
474 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
475 can be described as a conjunction of affine constraints, while
476 C<isl_set> and C<isl_map> represent unions of
477 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
478 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
479 to live in the same space. C<isl_union_set>s and C<isl_union_map>s
480 represent unions of C<isl_set>s or C<isl_map>s in I<different> spaces,
481 where spaces are considered different if they have a different number
482 of dimensions and/or different names (see L<"Spaces">).
483 The difference between sets and relations (maps) is that sets have
484 one set of variables, while relations have two sets of variables,
485 input variables and output variables.
487 =head2 Memory Management
489 Since a high-level operation on sets and/or relations usually involves
490 several substeps and since the user is usually not interested in
491 the intermediate results, most functions that return a new object
492 will also release all the objects passed as arguments.
493 If the user still wants to use one or more of these arguments
494 after the function call, she should pass along a copy of the
495 object rather than the object itself.
496 The user is then responsible for making sure that the original
497 object gets used somewhere else or is explicitly freed.
499 The arguments and return values of all documented functions are
500 annotated to make clear which arguments are released and which
501 arguments are preserved. In particular, the following annotations
508 C<__isl_give> means that a new object is returned.
509 The user should make sure that the returned pointer is
510 used exactly once as a value for an C<__isl_take> argument.
511 In between, it can be used as a value for as many
512 C<__isl_keep> arguments as the user likes.
513 There is one exception, and that is the case where the
514 pointer returned is C<NULL>. Is this case, the user
515 is free to use it as an C<__isl_take> argument or not.
519 C<__isl_take> means that the object the argument points to
520 is taken over by the function and may no longer be used
521 by the user as an argument to any other function.
522 The pointer value must be one returned by a function
523 returning an C<__isl_give> pointer.
524 If the user passes in a C<NULL> value, then this will
525 be treated as an error in the sense that the function will
526 not perform its usual operation. However, it will still
527 make sure that all the other C<__isl_take> arguments
532 C<__isl_keep> means that the function will only use the object
533 temporarily. After the function has finished, the user
534 can still use it as an argument to other functions.
535 A C<NULL> value will be treated in the same way as
536 a C<NULL> value for an C<__isl_take> argument.
540 =head2 Error Handling
542 C<isl> supports different ways to react in case a runtime error is triggered.
543 Runtime errors arise, e.g., if a function such as C<isl_map_intersect> is called
544 with two maps that have incompatible spaces. There are three possible ways
545 to react on error: to warn, to continue or to abort.
547 The default behavior is to warn. In this mode, C<isl> prints a warning, stores
548 the last error in the corresponding C<isl_ctx> and the function in which the
549 error was triggered returns C<NULL>. An error does not corrupt internal state,
550 such that isl can continue to be used. C<isl> also provides functions to
551 read the last error and to reset the memory that stores the last error. The
552 last error is only stored for information purposes. Its presence does not
553 change the behavior of C<isl>. Hence, resetting an error is not required to
554 continue to use isl, but only to observe new errors.
557 enum isl_error isl_ctx_last_error(isl_ctx *ctx);
558 void isl_ctx_reset_error(isl_ctx *ctx);
560 Another option is to continue on error. This is similar to warn on error mode,
561 except that C<isl> does not print any warning. This allows a program to
562 implement its own error reporting.
564 The last option is to directly abort the execution of the program from within
565 the isl library. This makes it obviously impossible to recover from an error,
566 but it allows to directly spot the error location. By aborting on error,
567 debuggers break at the location the error occurred and can provide a stack
568 trace. Other tools that automatically provide stack traces on abort or that do
569 not want to continue execution after an error was triggered may also prefer to
572 The on error behavior of isl can be specified by calling
573 C<isl_options_set_on_error> or by setting the command line option
574 C<--isl-on-error>. Valid arguments for the function call are
575 C<ISL_ON_ERROR_WARN>, C<ISL_ON_ERROR_CONTINUE> and C<ISL_ON_ERROR_ABORT>. The
576 choices for the command line option are C<warn>, C<continue> and C<abort>.
577 It is also possible to query the current error mode.
579 #include <isl/options.h>
580 int isl_options_set_on_error(isl_ctx *ctx, int val);
581 int isl_options_get_on_error(isl_ctx *ctx);
585 Identifiers are used to identify both individual dimensions
586 and tuples of dimensions. They consist of an optional name and an optional
587 user pointer. The name and the user pointer cannot both be C<NULL>, however.
588 Identifiers with the same name but different pointer values
589 are considered to be distinct.
590 Similarly, identifiers with different names but the same pointer value
591 are also considered to be distinct.
592 Equal identifiers are represented using the same object.
593 Pairs of identifiers can therefore be tested for equality using the
595 Identifiers can be constructed, copied, freed, inspected and printed
596 using the following functions.
599 __isl_give isl_id *isl_id_alloc(isl_ctx *ctx,
600 __isl_keep const char *name, void *user);
601 __isl_give isl_id *isl_id_set_free_user(
602 __isl_take isl_id *id,
603 __isl_give void (*free_user)(void *user));
604 __isl_give isl_id *isl_id_copy(isl_id *id);
605 void *isl_id_free(__isl_take isl_id *id);
607 isl_ctx *isl_id_get_ctx(__isl_keep isl_id *id);
608 void *isl_id_get_user(__isl_keep isl_id *id);
609 __isl_keep const char *isl_id_get_name(__isl_keep isl_id *id);
611 __isl_give isl_printer *isl_printer_print_id(
612 __isl_take isl_printer *p, __isl_keep isl_id *id);
614 The callback set by C<isl_id_set_free_user> is called on the user
615 pointer when the last reference to the C<isl_id> is freed.
616 Note that C<isl_id_get_name> returns a pointer to some internal
617 data structure, so the result can only be used while the
618 corresponding C<isl_id> is alive.
622 Whenever a new set, relation or similiar object is created from scratch,
623 the space in which it lives needs to be specified using an C<isl_space>.
624 Each space involves zero or more parameters and zero, one or two
625 tuples of set or input/output dimensions. The parameters and dimensions
626 are identified by an C<isl_dim_type> and a position.
627 The type C<isl_dim_param> refers to parameters,
628 the type C<isl_dim_set> refers to set dimensions (for spaces
629 with a single tuple of dimensions) and the types C<isl_dim_in>
630 and C<isl_dim_out> refer to input and output dimensions
631 (for spaces with two tuples of dimensions).
632 Local spaces (see L</"Local Spaces">) also contain dimensions
633 of type C<isl_dim_div>.
634 Note that parameters are only identified by their position within
635 a given object. Across different objects, parameters are (usually)
636 identified by their names or identifiers. Only unnamed parameters
637 are identified by their positions across objects. The use of unnamed
638 parameters is discouraged.
640 #include <isl/space.h>
641 __isl_give isl_space *isl_space_alloc(isl_ctx *ctx,
642 unsigned nparam, unsigned n_in, unsigned n_out);
643 __isl_give isl_space *isl_space_params_alloc(isl_ctx *ctx,
645 __isl_give isl_space *isl_space_set_alloc(isl_ctx *ctx,
646 unsigned nparam, unsigned dim);
647 __isl_give isl_space *isl_space_copy(__isl_keep isl_space *space);
648 void *isl_space_free(__isl_take isl_space *space);
649 unsigned isl_space_dim(__isl_keep isl_space *space,
650 enum isl_dim_type type);
652 The space used for creating a parameter domain
653 needs to be created using C<isl_space_params_alloc>.
654 For other sets, the space
655 needs to be created using C<isl_space_set_alloc>, while
656 for a relation, the space
657 needs to be created using C<isl_space_alloc>.
658 C<isl_space_dim> can be used
659 to find out the number of dimensions of each type in
660 a space, where type may be
661 C<isl_dim_param>, C<isl_dim_in> (only for relations),
662 C<isl_dim_out> (only for relations), C<isl_dim_set>
663 (only for sets) or C<isl_dim_all>.
665 To check whether a given space is that of a set or a map
666 or whether it is a parameter space, use these functions:
668 #include <isl/space.h>
669 int isl_space_is_params(__isl_keep isl_space *space);
670 int isl_space_is_set(__isl_keep isl_space *space);
671 int isl_space_is_map(__isl_keep isl_space *space);
673 Spaces can be compared using the following functions:
675 #include <isl/space.h>
676 int isl_space_is_equal(__isl_keep isl_space *space1,
677 __isl_keep isl_space *space2);
678 int isl_space_is_domain(__isl_keep isl_space *space1,
679 __isl_keep isl_space *space2);
680 int isl_space_is_range(__isl_keep isl_space *space1,
681 __isl_keep isl_space *space2);
683 C<isl_space_is_domain> checks whether the first argument is equal
684 to the domain of the second argument. This requires in particular that
685 the first argument is a set space and that the second argument
688 It is often useful to create objects that live in the
689 same space as some other object. This can be accomplished
690 by creating the new objects
691 (see L<Creating New Sets and Relations> or
692 L<Creating New (Piecewise) Quasipolynomials>) based on the space
693 of the original object.
696 __isl_give isl_space *isl_basic_set_get_space(
697 __isl_keep isl_basic_set *bset);
698 __isl_give isl_space *isl_set_get_space(__isl_keep isl_set *set);
700 #include <isl/union_set.h>
701 __isl_give isl_space *isl_union_set_get_space(
702 __isl_keep isl_union_set *uset);
705 __isl_give isl_space *isl_basic_map_get_space(
706 __isl_keep isl_basic_map *bmap);
707 __isl_give isl_space *isl_map_get_space(__isl_keep isl_map *map);
709 #include <isl/union_map.h>
710 __isl_give isl_space *isl_union_map_get_space(
711 __isl_keep isl_union_map *umap);
713 #include <isl/constraint.h>
714 __isl_give isl_space *isl_constraint_get_space(
715 __isl_keep isl_constraint *constraint);
717 #include <isl/polynomial.h>
718 __isl_give isl_space *isl_qpolynomial_get_domain_space(
719 __isl_keep isl_qpolynomial *qp);
720 __isl_give isl_space *isl_qpolynomial_get_space(
721 __isl_keep isl_qpolynomial *qp);
722 __isl_give isl_space *isl_qpolynomial_fold_get_space(
723 __isl_keep isl_qpolynomial_fold *fold);
724 __isl_give isl_space *isl_pw_qpolynomial_get_domain_space(
725 __isl_keep isl_pw_qpolynomial *pwqp);
726 __isl_give isl_space *isl_pw_qpolynomial_get_space(
727 __isl_keep isl_pw_qpolynomial *pwqp);
728 __isl_give isl_space *isl_pw_qpolynomial_fold_get_domain_space(
729 __isl_keep isl_pw_qpolynomial_fold *pwf);
730 __isl_give isl_space *isl_pw_qpolynomial_fold_get_space(
731 __isl_keep isl_pw_qpolynomial_fold *pwf);
732 __isl_give isl_space *isl_union_pw_qpolynomial_get_space(
733 __isl_keep isl_union_pw_qpolynomial *upwqp);
734 __isl_give isl_space *isl_union_pw_qpolynomial_fold_get_space(
735 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
738 __isl_give isl_space *isl_aff_get_domain_space(
739 __isl_keep isl_aff *aff);
740 __isl_give isl_space *isl_aff_get_space(
741 __isl_keep isl_aff *aff);
742 __isl_give isl_space *isl_pw_aff_get_domain_space(
743 __isl_keep isl_pw_aff *pwaff);
744 __isl_give isl_space *isl_pw_aff_get_space(
745 __isl_keep isl_pw_aff *pwaff);
746 __isl_give isl_space *isl_multi_aff_get_domain_space(
747 __isl_keep isl_multi_aff *maff);
748 __isl_give isl_space *isl_multi_aff_get_space(
749 __isl_keep isl_multi_aff *maff);
750 __isl_give isl_space *isl_pw_multi_aff_get_domain_space(
751 __isl_keep isl_pw_multi_aff *pma);
752 __isl_give isl_space *isl_pw_multi_aff_get_space(
753 __isl_keep isl_pw_multi_aff *pma);
754 __isl_give isl_space *isl_union_pw_multi_aff_get_space(
755 __isl_keep isl_union_pw_multi_aff *upma);
756 __isl_give isl_space *isl_multi_pw_aff_get_domain_space(
757 __isl_keep isl_multi_pw_aff *mpa);
758 __isl_give isl_space *isl_multi_pw_aff_get_space(
759 __isl_keep isl_multi_pw_aff *mpa);
761 #include <isl/point.h>
762 __isl_give isl_space *isl_point_get_space(
763 __isl_keep isl_point *pnt);
765 The identifiers or names of the individual dimensions may be set or read off
766 using the following functions.
768 #include <isl/space.h>
769 __isl_give isl_space *isl_space_set_dim_id(
770 __isl_take isl_space *space,
771 enum isl_dim_type type, unsigned pos,
772 __isl_take isl_id *id);
773 int isl_space_has_dim_id(__isl_keep isl_space *space,
774 enum isl_dim_type type, unsigned pos);
775 __isl_give isl_id *isl_space_get_dim_id(
776 __isl_keep isl_space *space,
777 enum isl_dim_type type, unsigned pos);
778 __isl_give isl_space *isl_space_set_dim_name(
779 __isl_take isl_space *space,
780 enum isl_dim_type type, unsigned pos,
781 __isl_keep const char *name);
782 int isl_space_has_dim_name(__isl_keep isl_space *space,
783 enum isl_dim_type type, unsigned pos);
784 __isl_keep const char *isl_space_get_dim_name(
785 __isl_keep isl_space *space,
786 enum isl_dim_type type, unsigned pos);
788 Note that C<isl_space_get_name> returns a pointer to some internal
789 data structure, so the result can only be used while the
790 corresponding C<isl_space> is alive.
791 Also note that every function that operates on two sets or relations
792 requires that both arguments have the same parameters. This also
793 means that if one of the arguments has named parameters, then the
794 other needs to have named parameters too and the names need to match.
795 Pairs of C<isl_set>, C<isl_map>, C<isl_union_set> and/or C<isl_union_map>
796 arguments may have different parameters (as long as they are named),
797 in which case the result will have as parameters the union of the parameters of
800 Given the identifier or name of a dimension (typically a parameter),
801 its position can be obtained from the following function.
803 #include <isl/space.h>
804 int isl_space_find_dim_by_id(__isl_keep isl_space *space,
805 enum isl_dim_type type, __isl_keep isl_id *id);
806 int isl_space_find_dim_by_name(__isl_keep isl_space *space,
807 enum isl_dim_type type, const char *name);
809 The identifiers or names of entire spaces may be set or read off
810 using the following functions.
812 #include <isl/space.h>
813 __isl_give isl_space *isl_space_set_tuple_id(
814 __isl_take isl_space *space,
815 enum isl_dim_type type, __isl_take isl_id *id);
816 __isl_give isl_space *isl_space_reset_tuple_id(
817 __isl_take isl_space *space, enum isl_dim_type type);
818 int isl_space_has_tuple_id(__isl_keep isl_space *space,
819 enum isl_dim_type type);
820 __isl_give isl_id *isl_space_get_tuple_id(
821 __isl_keep isl_space *space, enum isl_dim_type type);
822 __isl_give isl_space *isl_space_set_tuple_name(
823 __isl_take isl_space *space,
824 enum isl_dim_type type, const char *s);
825 int isl_space_has_tuple_name(__isl_keep isl_space *space,
826 enum isl_dim_type type);
827 const char *isl_space_get_tuple_name(__isl_keep isl_space *space,
828 enum isl_dim_type type);
830 The C<type> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
831 or C<isl_dim_set>. As with C<isl_space_get_name>,
832 the C<isl_space_get_tuple_name> function returns a pointer to some internal
834 Binary operations require the corresponding spaces of their arguments
835 to have the same name.
837 Spaces can be nested. In particular, the domain of a set or
838 the domain or range of a relation can be a nested relation.
839 The following functions can be used to construct and deconstruct
842 #include <isl/space.h>
843 int isl_space_is_wrapping(__isl_keep isl_space *space);
844 __isl_give isl_space *isl_space_wrap(__isl_take isl_space *space);
845 __isl_give isl_space *isl_space_unwrap(__isl_take isl_space *space);
847 The input to C<isl_space_is_wrapping> and C<isl_space_unwrap> should
848 be the space of a set, while that of
849 C<isl_space_wrap> should be the space of a relation.
850 Conversely, the output of C<isl_space_unwrap> is the space
851 of a relation, while that of C<isl_space_wrap> is the space of a set.
853 Spaces can be created from other spaces
854 using the following functions.
856 __isl_give isl_space *isl_space_domain(__isl_take isl_space *space);
857 __isl_give isl_space *isl_space_from_domain(__isl_take isl_space *space);
858 __isl_give isl_space *isl_space_range(__isl_take isl_space *space);
859 __isl_give isl_space *isl_space_from_range(__isl_take isl_space *space);
860 __isl_give isl_space *isl_space_params(
861 __isl_take isl_space *space);
862 __isl_give isl_space *isl_space_set_from_params(
863 __isl_take isl_space *space);
864 __isl_give isl_space *isl_space_reverse(__isl_take isl_space *space);
865 __isl_give isl_space *isl_space_join(__isl_take isl_space *left,
866 __isl_take isl_space *right);
867 __isl_give isl_space *isl_space_align_params(
868 __isl_take isl_space *space1, __isl_take isl_space *space2)
869 __isl_give isl_space *isl_space_insert_dims(__isl_take isl_space *space,
870 enum isl_dim_type type, unsigned pos, unsigned n);
871 __isl_give isl_space *isl_space_add_dims(__isl_take isl_space *space,
872 enum isl_dim_type type, unsigned n);
873 __isl_give isl_space *isl_space_drop_dims(__isl_take isl_space *space,
874 enum isl_dim_type type, unsigned first, unsigned n);
875 __isl_give isl_space *isl_space_move_dims(__isl_take isl_space *space,
876 enum isl_dim_type dst_type, unsigned dst_pos,
877 enum isl_dim_type src_type, unsigned src_pos,
879 __isl_give isl_space *isl_space_map_from_set(
880 __isl_take isl_space *space);
881 __isl_give isl_space *isl_space_map_from_domain_and_range(
882 __isl_take isl_space *domain,
883 __isl_take isl_space *range);
884 __isl_give isl_space *isl_space_zip(__isl_take isl_space *space);
885 __isl_give isl_space *isl_space_curry(
886 __isl_take isl_space *space);
887 __isl_give isl_space *isl_space_uncurry(
888 __isl_take isl_space *space);
890 Note that if dimensions are added or removed from a space, then
891 the name and the internal structure are lost.
895 A local space is essentially a space with
896 zero or more existentially quantified variables.
897 The local space of a (constraint of a) basic set or relation can be obtained
898 using the following functions.
900 #include <isl/constraint.h>
901 __isl_give isl_local_space *isl_constraint_get_local_space(
902 __isl_keep isl_constraint *constraint);
905 __isl_give isl_local_space *isl_basic_set_get_local_space(
906 __isl_keep isl_basic_set *bset);
909 __isl_give isl_local_space *isl_basic_map_get_local_space(
910 __isl_keep isl_basic_map *bmap);
912 A new local space can be created from a space using
914 #include <isl/local_space.h>
915 __isl_give isl_local_space *isl_local_space_from_space(
916 __isl_take isl_space *space);
918 They can be inspected, modified, copied and freed using the following functions.
920 #include <isl/local_space.h>
921 isl_ctx *isl_local_space_get_ctx(
922 __isl_keep isl_local_space *ls);
923 int isl_local_space_is_set(__isl_keep isl_local_space *ls);
924 int isl_local_space_dim(__isl_keep isl_local_space *ls,
925 enum isl_dim_type type);
926 int isl_local_space_has_dim_id(
927 __isl_keep isl_local_space *ls,
928 enum isl_dim_type type, unsigned pos);
929 __isl_give isl_id *isl_local_space_get_dim_id(
930 __isl_keep isl_local_space *ls,
931 enum isl_dim_type type, unsigned pos);
932 int isl_local_space_has_dim_name(
933 __isl_keep isl_local_space *ls,
934 enum isl_dim_type type, unsigned pos)
935 const char *isl_local_space_get_dim_name(
936 __isl_keep isl_local_space *ls,
937 enum isl_dim_type type, unsigned pos);
938 __isl_give isl_local_space *isl_local_space_set_dim_name(
939 __isl_take isl_local_space *ls,
940 enum isl_dim_type type, unsigned pos, const char *s);
941 __isl_give isl_local_space *isl_local_space_set_dim_id(
942 __isl_take isl_local_space *ls,
943 enum isl_dim_type type, unsigned pos,
944 __isl_take isl_id *id);
945 __isl_give isl_space *isl_local_space_get_space(
946 __isl_keep isl_local_space *ls);
947 __isl_give isl_aff *isl_local_space_get_div(
948 __isl_keep isl_local_space *ls, int pos);
949 __isl_give isl_local_space *isl_local_space_copy(
950 __isl_keep isl_local_space *ls);
951 void *isl_local_space_free(__isl_take isl_local_space *ls);
953 Note that C<isl_local_space_get_div> can only be used on local spaces
956 Two local spaces can be compared using
958 int isl_local_space_is_equal(__isl_keep isl_local_space *ls1,
959 __isl_keep isl_local_space *ls2);
961 Local spaces can be created from other local spaces
962 using the following functions.
964 __isl_give isl_local_space *isl_local_space_domain(
965 __isl_take isl_local_space *ls);
966 __isl_give isl_local_space *isl_local_space_range(
967 __isl_take isl_local_space *ls);
968 __isl_give isl_local_space *isl_local_space_from_domain(
969 __isl_take isl_local_space *ls);
970 __isl_give isl_local_space *isl_local_space_intersect(
971 __isl_take isl_local_space *ls1,
972 __isl_take isl_local_space *ls2);
973 __isl_give isl_local_space *isl_local_space_add_dims(
974 __isl_take isl_local_space *ls,
975 enum isl_dim_type type, unsigned n);
976 __isl_give isl_local_space *isl_local_space_insert_dims(
977 __isl_take isl_local_space *ls,
978 enum isl_dim_type type, unsigned first, unsigned n);
979 __isl_give isl_local_space *isl_local_space_drop_dims(
980 __isl_take isl_local_space *ls,
981 enum isl_dim_type type, unsigned first, unsigned n);
983 =head2 Input and Output
985 C<isl> supports its own input/output format, which is similar
986 to the C<Omega> format, but also supports the C<PolyLib> format
991 The C<isl> format is similar to that of C<Omega>, but has a different
992 syntax for describing the parameters and allows for the definition
993 of an existentially quantified variable as the integer division
994 of an affine expression.
995 For example, the set of integers C<i> between C<0> and C<n>
996 such that C<i % 10 <= 6> can be described as
998 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
1001 A set or relation can have several disjuncts, separated
1002 by the keyword C<or>. Each disjunct is either a conjunction
1003 of constraints or a projection (C<exists>) of a conjunction
1004 of constraints. The constraints are separated by the keyword
1007 =head3 C<PolyLib> format
1009 If the represented set is a union, then the first line
1010 contains a single number representing the number of disjuncts.
1011 Otherwise, a line containing the number C<1> is optional.
1013 Each disjunct is represented by a matrix of constraints.
1014 The first line contains two numbers representing
1015 the number of rows and columns,
1016 where the number of rows is equal to the number of constraints
1017 and the number of columns is equal to two plus the number of variables.
1018 The following lines contain the actual rows of the constraint matrix.
1019 In each row, the first column indicates whether the constraint
1020 is an equality (C<0>) or inequality (C<1>). The final column
1021 corresponds to the constant term.
1023 If the set is parametric, then the coefficients of the parameters
1024 appear in the last columns before the constant column.
1025 The coefficients of any existentially quantified variables appear
1026 between those of the set variables and those of the parameters.
1028 =head3 Extended C<PolyLib> format
1030 The extended C<PolyLib> format is nearly identical to the
1031 C<PolyLib> format. The only difference is that the line
1032 containing the number of rows and columns of a constraint matrix
1033 also contains four additional numbers:
1034 the number of output dimensions, the number of input dimensions,
1035 the number of local dimensions (i.e., the number of existentially
1036 quantified variables) and the number of parameters.
1037 For sets, the number of ``output'' dimensions is equal
1038 to the number of set dimensions, while the number of ``input''
1043 #include <isl/set.h>
1044 __isl_give isl_basic_set *isl_basic_set_read_from_file(
1045 isl_ctx *ctx, FILE *input);
1046 __isl_give isl_basic_set *isl_basic_set_read_from_str(
1047 isl_ctx *ctx, const char *str);
1048 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
1050 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
1053 #include <isl/map.h>
1054 __isl_give isl_basic_map *isl_basic_map_read_from_file(
1055 isl_ctx *ctx, FILE *input);
1056 __isl_give isl_basic_map *isl_basic_map_read_from_str(
1057 isl_ctx *ctx, const char *str);
1058 __isl_give isl_map *isl_map_read_from_file(
1059 isl_ctx *ctx, FILE *input);
1060 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
1063 #include <isl/union_set.h>
1064 __isl_give isl_union_set *isl_union_set_read_from_file(
1065 isl_ctx *ctx, FILE *input);
1066 __isl_give isl_union_set *isl_union_set_read_from_str(
1067 isl_ctx *ctx, const char *str);
1069 #include <isl/union_map.h>
1070 __isl_give isl_union_map *isl_union_map_read_from_file(
1071 isl_ctx *ctx, FILE *input);
1072 __isl_give isl_union_map *isl_union_map_read_from_str(
1073 isl_ctx *ctx, const char *str);
1075 The input format is autodetected and may be either the C<PolyLib> format
1076 or the C<isl> format.
1080 Before anything can be printed, an C<isl_printer> needs to
1083 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
1085 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
1086 void *isl_printer_free(__isl_take isl_printer *printer);
1087 __isl_give char *isl_printer_get_str(
1088 __isl_keep isl_printer *printer);
1090 The printer can be inspected using the following functions.
1092 FILE *isl_printer_get_file(
1093 __isl_keep isl_printer *printer);
1094 int isl_printer_get_output_format(
1095 __isl_keep isl_printer *p);
1097 The behavior of the printer can be modified in various ways
1099 __isl_give isl_printer *isl_printer_set_output_format(
1100 __isl_take isl_printer *p, int output_format);
1101 __isl_give isl_printer *isl_printer_set_indent(
1102 __isl_take isl_printer *p, int indent);
1103 __isl_give isl_printer *isl_printer_indent(
1104 __isl_take isl_printer *p, int indent);
1105 __isl_give isl_printer *isl_printer_set_prefix(
1106 __isl_take isl_printer *p, const char *prefix);
1107 __isl_give isl_printer *isl_printer_set_suffix(
1108 __isl_take isl_printer *p, const char *suffix);
1110 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
1111 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
1112 and defaults to C<ISL_FORMAT_ISL>.
1113 Each line in the output is indented by C<indent> (set by
1114 C<isl_printer_set_indent>) spaces
1115 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
1116 In the C<PolyLib> format output,
1117 the coefficients of the existentially quantified variables
1118 appear between those of the set variables and those
1120 The function C<isl_printer_indent> increases the indentation
1121 by the specified amount (which may be negative).
1123 To actually print something, use
1125 #include <isl/printer.h>
1126 __isl_give isl_printer *isl_printer_print_double(
1127 __isl_take isl_printer *p, double d);
1129 #include <isl/set.h>
1130 __isl_give isl_printer *isl_printer_print_basic_set(
1131 __isl_take isl_printer *printer,
1132 __isl_keep isl_basic_set *bset);
1133 __isl_give isl_printer *isl_printer_print_set(
1134 __isl_take isl_printer *printer,
1135 __isl_keep isl_set *set);
1137 #include <isl/map.h>
1138 __isl_give isl_printer *isl_printer_print_basic_map(
1139 __isl_take isl_printer *printer,
1140 __isl_keep isl_basic_map *bmap);
1141 __isl_give isl_printer *isl_printer_print_map(
1142 __isl_take isl_printer *printer,
1143 __isl_keep isl_map *map);
1145 #include <isl/union_set.h>
1146 __isl_give isl_printer *isl_printer_print_union_set(
1147 __isl_take isl_printer *p,
1148 __isl_keep isl_union_set *uset);
1150 #include <isl/union_map.h>
1151 __isl_give isl_printer *isl_printer_print_union_map(
1152 __isl_take isl_printer *p,
1153 __isl_keep isl_union_map *umap);
1155 When called on a file printer, the following function flushes
1156 the file. When called on a string printer, the buffer is cleared.
1158 __isl_give isl_printer *isl_printer_flush(
1159 __isl_take isl_printer *p);
1161 =head2 Creating New Sets and Relations
1163 C<isl> has functions for creating some standard sets and relations.
1167 =item * Empty sets and relations
1169 __isl_give isl_basic_set *isl_basic_set_empty(
1170 __isl_take isl_space *space);
1171 __isl_give isl_basic_map *isl_basic_map_empty(
1172 __isl_take isl_space *space);
1173 __isl_give isl_set *isl_set_empty(
1174 __isl_take isl_space *space);
1175 __isl_give isl_map *isl_map_empty(
1176 __isl_take isl_space *space);
1177 __isl_give isl_union_set *isl_union_set_empty(
1178 __isl_take isl_space *space);
1179 __isl_give isl_union_map *isl_union_map_empty(
1180 __isl_take isl_space *space);
1182 For C<isl_union_set>s and C<isl_union_map>s, the space
1183 is only used to specify the parameters.
1185 =item * Universe sets and relations
1187 __isl_give isl_basic_set *isl_basic_set_universe(
1188 __isl_take isl_space *space);
1189 __isl_give isl_basic_map *isl_basic_map_universe(
1190 __isl_take isl_space *space);
1191 __isl_give isl_set *isl_set_universe(
1192 __isl_take isl_space *space);
1193 __isl_give isl_map *isl_map_universe(
1194 __isl_take isl_space *space);
1195 __isl_give isl_union_set *isl_union_set_universe(
1196 __isl_take isl_union_set *uset);
1197 __isl_give isl_union_map *isl_union_map_universe(
1198 __isl_take isl_union_map *umap);
1200 The sets and relations constructed by the functions above
1201 contain all integer values, while those constructed by the
1202 functions below only contain non-negative values.
1204 __isl_give isl_basic_set *isl_basic_set_nat_universe(
1205 __isl_take isl_space *space);
1206 __isl_give isl_basic_map *isl_basic_map_nat_universe(
1207 __isl_take isl_space *space);
1208 __isl_give isl_set *isl_set_nat_universe(
1209 __isl_take isl_space *space);
1210 __isl_give isl_map *isl_map_nat_universe(
1211 __isl_take isl_space *space);
1213 =item * Identity relations
1215 __isl_give isl_basic_map *isl_basic_map_identity(
1216 __isl_take isl_space *space);
1217 __isl_give isl_map *isl_map_identity(
1218 __isl_take isl_space *space);
1220 The number of input and output dimensions in C<space> needs
1223 =item * Lexicographic order
1225 __isl_give isl_map *isl_map_lex_lt(
1226 __isl_take isl_space *set_space);
1227 __isl_give isl_map *isl_map_lex_le(
1228 __isl_take isl_space *set_space);
1229 __isl_give isl_map *isl_map_lex_gt(
1230 __isl_take isl_space *set_space);
1231 __isl_give isl_map *isl_map_lex_ge(
1232 __isl_take isl_space *set_space);
1233 __isl_give isl_map *isl_map_lex_lt_first(
1234 __isl_take isl_space *space, unsigned n);
1235 __isl_give isl_map *isl_map_lex_le_first(
1236 __isl_take isl_space *space, unsigned n);
1237 __isl_give isl_map *isl_map_lex_gt_first(
1238 __isl_take isl_space *space, unsigned n);
1239 __isl_give isl_map *isl_map_lex_ge_first(
1240 __isl_take isl_space *space, unsigned n);
1242 The first four functions take a space for a B<set>
1243 and return relations that express that the elements in the domain
1244 are lexicographically less
1245 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
1246 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
1247 than the elements in the range.
1248 The last four functions take a space for a map
1249 and return relations that express that the first C<n> dimensions
1250 in the domain are lexicographically less
1251 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
1252 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
1253 than the first C<n> dimensions in the range.
1257 A basic set or relation can be converted to a set or relation
1258 using the following functions.
1260 __isl_give isl_set *isl_set_from_basic_set(
1261 __isl_take isl_basic_set *bset);
1262 __isl_give isl_map *isl_map_from_basic_map(
1263 __isl_take isl_basic_map *bmap);
1265 Sets and relations can be converted to union sets and relations
1266 using the following functions.
1268 __isl_give isl_union_set *isl_union_set_from_basic_set(
1269 __isl_take isl_basic_set *bset);
1270 __isl_give isl_union_map *isl_union_map_from_basic_map(
1271 __isl_take isl_basic_map *bmap);
1272 __isl_give isl_union_set *isl_union_set_from_set(
1273 __isl_take isl_set *set);
1274 __isl_give isl_union_map *isl_union_map_from_map(
1275 __isl_take isl_map *map);
1277 The inverse conversions below can only be used if the input
1278 union set or relation is known to contain elements in exactly one
1281 __isl_give isl_set *isl_set_from_union_set(
1282 __isl_take isl_union_set *uset);
1283 __isl_give isl_map *isl_map_from_union_map(
1284 __isl_take isl_union_map *umap);
1286 A zero-dimensional (basic) set can be constructed on a given parameter domain
1287 using the following function.
1289 __isl_give isl_basic_set *isl_basic_set_from_params(
1290 __isl_take isl_basic_set *bset);
1291 __isl_give isl_set *isl_set_from_params(
1292 __isl_take isl_set *set);
1294 Sets and relations can be copied and freed again using the following
1297 __isl_give isl_basic_set *isl_basic_set_copy(
1298 __isl_keep isl_basic_set *bset);
1299 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
1300 __isl_give isl_union_set *isl_union_set_copy(
1301 __isl_keep isl_union_set *uset);
1302 __isl_give isl_basic_map *isl_basic_map_copy(
1303 __isl_keep isl_basic_map *bmap);
1304 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
1305 __isl_give isl_union_map *isl_union_map_copy(
1306 __isl_keep isl_union_map *umap);
1307 void *isl_basic_set_free(__isl_take isl_basic_set *bset);
1308 void *isl_set_free(__isl_take isl_set *set);
1309 void *isl_union_set_free(__isl_take isl_union_set *uset);
1310 void *isl_basic_map_free(__isl_take isl_basic_map *bmap);
1311 void *isl_map_free(__isl_take isl_map *map);
1312 void *isl_union_map_free(__isl_take isl_union_map *umap);
1314 Other sets and relations can be constructed by starting
1315 from a universe set or relation, adding equality and/or
1316 inequality constraints and then projecting out the
1317 existentially quantified variables, if any.
1318 Constraints can be constructed, manipulated and
1319 added to (or removed from) (basic) sets and relations
1320 using the following functions.
1322 #include <isl/constraint.h>
1323 __isl_give isl_constraint *isl_equality_alloc(
1324 __isl_take isl_local_space *ls);
1325 __isl_give isl_constraint *isl_inequality_alloc(
1326 __isl_take isl_local_space *ls);
1327 __isl_give isl_constraint *isl_constraint_set_constant(
1328 __isl_take isl_constraint *constraint, isl_int v);
1329 __isl_give isl_constraint *isl_constraint_set_constant_si(
1330 __isl_take isl_constraint *constraint, int v);
1331 __isl_give isl_constraint *isl_constraint_set_coefficient(
1332 __isl_take isl_constraint *constraint,
1333 enum isl_dim_type type, int pos, isl_int v);
1334 __isl_give isl_constraint *isl_constraint_set_coefficient_si(
1335 __isl_take isl_constraint *constraint,
1336 enum isl_dim_type type, int pos, int v);
1337 __isl_give isl_basic_map *isl_basic_map_add_constraint(
1338 __isl_take isl_basic_map *bmap,
1339 __isl_take isl_constraint *constraint);
1340 __isl_give isl_basic_set *isl_basic_set_add_constraint(
1341 __isl_take isl_basic_set *bset,
1342 __isl_take isl_constraint *constraint);
1343 __isl_give isl_map *isl_map_add_constraint(
1344 __isl_take isl_map *map,
1345 __isl_take isl_constraint *constraint);
1346 __isl_give isl_set *isl_set_add_constraint(
1347 __isl_take isl_set *set,
1348 __isl_take isl_constraint *constraint);
1349 __isl_give isl_basic_set *isl_basic_set_drop_constraint(
1350 __isl_take isl_basic_set *bset,
1351 __isl_take isl_constraint *constraint);
1353 For example, to create a set containing the even integers
1354 between 10 and 42, you would use the following code.
1357 isl_local_space *ls;
1359 isl_basic_set *bset;
1361 space = isl_space_set_alloc(ctx, 0, 2);
1362 bset = isl_basic_set_universe(isl_space_copy(space));
1363 ls = isl_local_space_from_space(space);
1365 c = isl_equality_alloc(isl_local_space_copy(ls));
1366 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1367 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 1, 2);
1368 bset = isl_basic_set_add_constraint(bset, c);
1370 c = isl_inequality_alloc(isl_local_space_copy(ls));
1371 c = isl_constraint_set_constant_si(c, -10);
1372 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, 1);
1373 bset = isl_basic_set_add_constraint(bset, c);
1375 c = isl_inequality_alloc(ls);
1376 c = isl_constraint_set_constant_si(c, 42);
1377 c = isl_constraint_set_coefficient_si(c, isl_dim_set, 0, -1);
1378 bset = isl_basic_set_add_constraint(bset, c);
1380 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
1384 isl_basic_set *bset;
1385 bset = isl_basic_set_read_from_str(ctx,
1386 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}");
1388 A basic set or relation can also be constructed from two matrices
1389 describing the equalities and the inequalities.
1391 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
1392 __isl_take isl_space *space,
1393 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1394 enum isl_dim_type c1,
1395 enum isl_dim_type c2, enum isl_dim_type c3,
1396 enum isl_dim_type c4);
1397 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
1398 __isl_take isl_space *space,
1399 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
1400 enum isl_dim_type c1,
1401 enum isl_dim_type c2, enum isl_dim_type c3,
1402 enum isl_dim_type c4, enum isl_dim_type c5);
1404 The C<isl_dim_type> arguments indicate the order in which
1405 different kinds of variables appear in the input matrices
1406 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1407 C<isl_dim_set> and C<isl_dim_div> for sets and
1408 of C<isl_dim_cst>, C<isl_dim_param>,
1409 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
1411 A (basic or union) set or relation can also be constructed from a
1412 (union) (piecewise) (multiple) affine expression
1413 or a list of affine expressions
1414 (See L<"Piecewise Quasi Affine Expressions"> and
1415 L<"Piecewise Multiple Quasi Affine Expressions">).
1417 __isl_give isl_basic_map *isl_basic_map_from_aff(
1418 __isl_take isl_aff *aff);
1419 __isl_give isl_map *isl_map_from_aff(
1420 __isl_take isl_aff *aff);
1421 __isl_give isl_set *isl_set_from_pw_aff(
1422 __isl_take isl_pw_aff *pwaff);
1423 __isl_give isl_map *isl_map_from_pw_aff(
1424 __isl_take isl_pw_aff *pwaff);
1425 __isl_give isl_basic_map *isl_basic_map_from_aff_list(
1426 __isl_take isl_space *domain_space,
1427 __isl_take isl_aff_list *list);
1428 __isl_give isl_basic_map *isl_basic_map_from_multi_aff(
1429 __isl_take isl_multi_aff *maff)
1430 __isl_give isl_map *isl_map_from_multi_aff(
1431 __isl_take isl_multi_aff *maff)
1432 __isl_give isl_set *isl_set_from_pw_multi_aff(
1433 __isl_take isl_pw_multi_aff *pma);
1434 __isl_give isl_map *isl_map_from_pw_multi_aff(
1435 __isl_take isl_pw_multi_aff *pma);
1436 __isl_give isl_union_map *
1437 isl_union_map_from_union_pw_multi_aff(
1438 __isl_take isl_union_pw_multi_aff *upma);
1440 The C<domain_dim> argument describes the domain of the resulting
1441 basic relation. It is required because the C<list> may consist
1442 of zero affine expressions.
1444 =head2 Inspecting Sets and Relations
1446 Usually, the user should not have to care about the actual constraints
1447 of the sets and maps, but should instead apply the abstract operations
1448 explained in the following sections.
1449 Occasionally, however, it may be required to inspect the individual
1450 coefficients of the constraints. This section explains how to do so.
1451 In these cases, it may also be useful to have C<isl> compute
1452 an explicit representation of the existentially quantified variables.
1454 __isl_give isl_set *isl_set_compute_divs(
1455 __isl_take isl_set *set);
1456 __isl_give isl_map *isl_map_compute_divs(
1457 __isl_take isl_map *map);
1458 __isl_give isl_union_set *isl_union_set_compute_divs(
1459 __isl_take isl_union_set *uset);
1460 __isl_give isl_union_map *isl_union_map_compute_divs(
1461 __isl_take isl_union_map *umap);
1463 This explicit representation defines the existentially quantified
1464 variables as integer divisions of the other variables, possibly
1465 including earlier existentially quantified variables.
1466 An explicitly represented existentially quantified variable therefore
1467 has a unique value when the values of the other variables are known.
1468 If, furthermore, the same existentials, i.e., existentials
1469 with the same explicit representations, should appear in the
1470 same order in each of the disjuncts of a set or map, then the user should call
1471 either of the following functions.
1473 __isl_give isl_set *isl_set_align_divs(
1474 __isl_take isl_set *set);
1475 __isl_give isl_map *isl_map_align_divs(
1476 __isl_take isl_map *map);
1478 Alternatively, the existentially quantified variables can be removed
1479 using the following functions, which compute an overapproximation.
1481 __isl_give isl_basic_set *isl_basic_set_remove_divs(
1482 __isl_take isl_basic_set *bset);
1483 __isl_give isl_basic_map *isl_basic_map_remove_divs(
1484 __isl_take isl_basic_map *bmap);
1485 __isl_give isl_set *isl_set_remove_divs(
1486 __isl_take isl_set *set);
1487 __isl_give isl_map *isl_map_remove_divs(
1488 __isl_take isl_map *map);
1490 It is also possible to only remove those divs that are defined
1491 in terms of a given range of dimensions or only those for which
1492 no explicit representation is known.
1494 __isl_give isl_basic_set *
1495 isl_basic_set_remove_divs_involving_dims(
1496 __isl_take isl_basic_set *bset,
1497 enum isl_dim_type type,
1498 unsigned first, unsigned n);
1499 __isl_give isl_basic_map *
1500 isl_basic_map_remove_divs_involving_dims(
1501 __isl_take isl_basic_map *bmap,
1502 enum isl_dim_type type,
1503 unsigned first, unsigned n);
1504 __isl_give isl_set *isl_set_remove_divs_involving_dims(
1505 __isl_take isl_set *set, enum isl_dim_type type,
1506 unsigned first, unsigned n);
1507 __isl_give isl_map *isl_map_remove_divs_involving_dims(
1508 __isl_take isl_map *map, enum isl_dim_type type,
1509 unsigned first, unsigned n);
1511 __isl_give isl_basic_set *
1512 isl_basic_set_remove_unknown_divs(
1513 __isl_take isl_basic_set *bset);
1514 __isl_give isl_set *isl_set_remove_unknown_divs(
1515 __isl_take isl_set *set);
1516 __isl_give isl_map *isl_map_remove_unknown_divs(
1517 __isl_take isl_map *map);
1519 To iterate over all the sets or maps in a union set or map, use
1521 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1522 int (*fn)(__isl_take isl_set *set, void *user),
1524 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1525 int (*fn)(__isl_take isl_map *map, void *user),
1528 The number of sets or maps in a union set or map can be obtained
1531 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1532 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1534 To extract the set or map in a given space from a union, use
1536 __isl_give isl_set *isl_union_set_extract_set(
1537 __isl_keep isl_union_set *uset,
1538 __isl_take isl_space *space);
1539 __isl_give isl_map *isl_union_map_extract_map(
1540 __isl_keep isl_union_map *umap,
1541 __isl_take isl_space *space);
1543 To iterate over all the basic sets or maps in a set or map, use
1545 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1546 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1548 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1549 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1552 The callback function C<fn> should return 0 if successful and
1553 -1 if an error occurs. In the latter case, or if any other error
1554 occurs, the above functions will return -1.
1556 It should be noted that C<isl> does not guarantee that
1557 the basic sets or maps passed to C<fn> are disjoint.
1558 If this is required, then the user should call one of
1559 the following functions first.
1561 __isl_give isl_set *isl_set_make_disjoint(
1562 __isl_take isl_set *set);
1563 __isl_give isl_map *isl_map_make_disjoint(
1564 __isl_take isl_map *map);
1566 The number of basic sets in a set can be obtained
1569 int isl_set_n_basic_set(__isl_keep isl_set *set);
1571 To iterate over the constraints of a basic set or map, use
1573 #include <isl/constraint.h>
1575 int isl_basic_set_n_constraint(
1576 __isl_keep isl_basic_set *bset);
1577 int isl_basic_set_foreach_constraint(
1578 __isl_keep isl_basic_set *bset,
1579 int (*fn)(__isl_take isl_constraint *c, void *user),
1581 int isl_basic_map_foreach_constraint(
1582 __isl_keep isl_basic_map *bmap,
1583 int (*fn)(__isl_take isl_constraint *c, void *user),
1585 void *isl_constraint_free(__isl_take isl_constraint *c);
1587 Again, the callback function C<fn> should return 0 if successful and
1588 -1 if an error occurs. In the latter case, or if any other error
1589 occurs, the above functions will return -1.
1590 The constraint C<c> represents either an equality or an inequality.
1591 Use the following function to find out whether a constraint
1592 represents an equality. If not, it represents an inequality.
1594 int isl_constraint_is_equality(
1595 __isl_keep isl_constraint *constraint);
1597 The coefficients of the constraints can be inspected using
1598 the following functions.
1600 int isl_constraint_is_lower_bound(
1601 __isl_keep isl_constraint *constraint,
1602 enum isl_dim_type type, unsigned pos);
1603 int isl_constraint_is_upper_bound(
1604 __isl_keep isl_constraint *constraint,
1605 enum isl_dim_type type, unsigned pos);
1606 void isl_constraint_get_constant(
1607 __isl_keep isl_constraint *constraint, isl_int *v);
1608 void isl_constraint_get_coefficient(
1609 __isl_keep isl_constraint *constraint,
1610 enum isl_dim_type type, int pos, isl_int *v);
1611 int isl_constraint_involves_dims(
1612 __isl_keep isl_constraint *constraint,
1613 enum isl_dim_type type, unsigned first, unsigned n);
1615 The explicit representations of the existentially quantified
1616 variables can be inspected using the following function.
1617 Note that the user is only allowed to use this function
1618 if the inspected set or map is the result of a call
1619 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1620 The existentially quantified variable is equal to the floor
1621 of the returned affine expression. The affine expression
1622 itself can be inspected using the functions in
1623 L<"Piecewise Quasi Affine Expressions">.
1625 __isl_give isl_aff *isl_constraint_get_div(
1626 __isl_keep isl_constraint *constraint, int pos);
1628 To obtain the constraints of a basic set or map in matrix
1629 form, use the following functions.
1631 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1632 __isl_keep isl_basic_set *bset,
1633 enum isl_dim_type c1, enum isl_dim_type c2,
1634 enum isl_dim_type c3, enum isl_dim_type c4);
1635 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1636 __isl_keep isl_basic_set *bset,
1637 enum isl_dim_type c1, enum isl_dim_type c2,
1638 enum isl_dim_type c3, enum isl_dim_type c4);
1639 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1640 __isl_keep isl_basic_map *bmap,
1641 enum isl_dim_type c1,
1642 enum isl_dim_type c2, enum isl_dim_type c3,
1643 enum isl_dim_type c4, enum isl_dim_type c5);
1644 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1645 __isl_keep isl_basic_map *bmap,
1646 enum isl_dim_type c1,
1647 enum isl_dim_type c2, enum isl_dim_type c3,
1648 enum isl_dim_type c4, enum isl_dim_type c5);
1650 The C<isl_dim_type> arguments dictate the order in which
1651 different kinds of variables appear in the resulting matrix
1652 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1653 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1655 The number of parameters, input, output or set dimensions can
1656 be obtained using the following functions.
1658 unsigned isl_basic_set_dim(__isl_keep isl_basic_set *bset,
1659 enum isl_dim_type type);
1660 unsigned isl_basic_map_dim(__isl_keep isl_basic_map *bmap,
1661 enum isl_dim_type type);
1662 unsigned isl_set_dim(__isl_keep isl_set *set,
1663 enum isl_dim_type type);
1664 unsigned isl_map_dim(__isl_keep isl_map *map,
1665 enum isl_dim_type type);
1667 To check whether the description of a set or relation depends
1668 on one or more given dimensions, it is not necessary to iterate over all
1669 constraints. Instead the following functions can be used.
1671 int isl_basic_set_involves_dims(
1672 __isl_keep isl_basic_set *bset,
1673 enum isl_dim_type type, unsigned first, unsigned n);
1674 int isl_set_involves_dims(__isl_keep isl_set *set,
1675 enum isl_dim_type type, unsigned first, unsigned n);
1676 int isl_basic_map_involves_dims(
1677 __isl_keep isl_basic_map *bmap,
1678 enum isl_dim_type type, unsigned first, unsigned n);
1679 int isl_map_involves_dims(__isl_keep isl_map *map,
1680 enum isl_dim_type type, unsigned first, unsigned n);
1682 Similarly, the following functions can be used to check whether
1683 a given dimension is involved in any lower or upper bound.
1685 int isl_set_dim_has_any_lower_bound(__isl_keep isl_set *set,
1686 enum isl_dim_type type, unsigned pos);
1687 int isl_set_dim_has_any_upper_bound(__isl_keep isl_set *set,
1688 enum isl_dim_type type, unsigned pos);
1690 Note that these functions return true even if there is a bound on
1691 the dimension on only some of the basic sets of C<set>.
1692 To check if they have a bound for all of the basic sets in C<set>,
1693 use the following functions instead.
1695 int isl_set_dim_has_lower_bound(__isl_keep isl_set *set,
1696 enum isl_dim_type type, unsigned pos);
1697 int isl_set_dim_has_upper_bound(__isl_keep isl_set *set,
1698 enum isl_dim_type type, unsigned pos);
1700 The identifiers or names of the domain and range spaces of a set
1701 or relation can be read off or set using the following functions.
1703 __isl_give isl_set *isl_set_set_tuple_id(
1704 __isl_take isl_set *set, __isl_take isl_id *id);
1705 __isl_give isl_set *isl_set_reset_tuple_id(
1706 __isl_take isl_set *set);
1707 int isl_set_has_tuple_id(__isl_keep isl_set *set);
1708 __isl_give isl_id *isl_set_get_tuple_id(
1709 __isl_keep isl_set *set);
1710 __isl_give isl_map *isl_map_set_tuple_id(
1711 __isl_take isl_map *map, enum isl_dim_type type,
1712 __isl_take isl_id *id);
1713 __isl_give isl_map *isl_map_reset_tuple_id(
1714 __isl_take isl_map *map, enum isl_dim_type type);
1715 int isl_map_has_tuple_id(__isl_keep isl_map *map,
1716 enum isl_dim_type type);
1717 __isl_give isl_id *isl_map_get_tuple_id(
1718 __isl_keep isl_map *map, enum isl_dim_type type);
1720 const char *isl_basic_set_get_tuple_name(
1721 __isl_keep isl_basic_set *bset);
1722 __isl_give isl_basic_set *isl_basic_set_set_tuple_name(
1723 __isl_take isl_basic_set *set, const char *s);
1724 int isl_set_has_tuple_name(__isl_keep isl_set *set);
1725 const char *isl_set_get_tuple_name(
1726 __isl_keep isl_set *set);
1727 const char *isl_basic_map_get_tuple_name(
1728 __isl_keep isl_basic_map *bmap,
1729 enum isl_dim_type type);
1730 __isl_give isl_basic_map *isl_basic_map_set_tuple_name(
1731 __isl_take isl_basic_map *bmap,
1732 enum isl_dim_type type, const char *s);
1733 int isl_map_has_tuple_name(__isl_keep isl_map *map,
1734 enum isl_dim_type type);
1735 const char *isl_map_get_tuple_name(
1736 __isl_keep isl_map *map,
1737 enum isl_dim_type type);
1739 As with C<isl_space_get_tuple_name>, the value returned points to
1740 an internal data structure.
1741 The identifiers, positions or names of individual dimensions can be
1742 read off using the following functions.
1744 __isl_give isl_id *isl_basic_set_get_dim_id(
1745 __isl_keep isl_basic_set *bset,
1746 enum isl_dim_type type, unsigned pos);
1747 __isl_give isl_set *isl_set_set_dim_id(
1748 __isl_take isl_set *set, enum isl_dim_type type,
1749 unsigned pos, __isl_take isl_id *id);
1750 int isl_set_has_dim_id(__isl_keep isl_set *set,
1751 enum isl_dim_type type, unsigned pos);
1752 __isl_give isl_id *isl_set_get_dim_id(
1753 __isl_keep isl_set *set, enum isl_dim_type type,
1755 int isl_basic_map_has_dim_id(
1756 __isl_keep isl_basic_map *bmap,
1757 enum isl_dim_type type, unsigned pos);
1758 __isl_give isl_map *isl_map_set_dim_id(
1759 __isl_take isl_map *map, enum isl_dim_type type,
1760 unsigned pos, __isl_take isl_id *id);
1761 int isl_map_has_dim_id(__isl_keep isl_map *map,
1762 enum isl_dim_type type, unsigned pos);
1763 __isl_give isl_id *isl_map_get_dim_id(
1764 __isl_keep isl_map *map, enum isl_dim_type type,
1767 int isl_set_find_dim_by_id(__isl_keep isl_set *set,
1768 enum isl_dim_type type, __isl_keep isl_id *id);
1769 int isl_map_find_dim_by_id(__isl_keep isl_map *map,
1770 enum isl_dim_type type, __isl_keep isl_id *id);
1771 int isl_set_find_dim_by_name(__isl_keep isl_set *set,
1772 enum isl_dim_type type, const char *name);
1773 int isl_map_find_dim_by_name(__isl_keep isl_map *map,
1774 enum isl_dim_type type, const char *name);
1776 const char *isl_constraint_get_dim_name(
1777 __isl_keep isl_constraint *constraint,
1778 enum isl_dim_type type, unsigned pos);
1779 const char *isl_basic_set_get_dim_name(
1780 __isl_keep isl_basic_set *bset,
1781 enum isl_dim_type type, unsigned pos);
1782 int isl_set_has_dim_name(__isl_keep isl_set *set,
1783 enum isl_dim_type type, unsigned pos);
1784 const char *isl_set_get_dim_name(
1785 __isl_keep isl_set *set,
1786 enum isl_dim_type type, unsigned pos);
1787 const char *isl_basic_map_get_dim_name(
1788 __isl_keep isl_basic_map *bmap,
1789 enum isl_dim_type type, unsigned pos);
1790 int isl_map_has_dim_name(__isl_keep isl_map *map,
1791 enum isl_dim_type type, unsigned pos);
1792 const char *isl_map_get_dim_name(
1793 __isl_keep isl_map *map,
1794 enum isl_dim_type type, unsigned pos);
1796 These functions are mostly useful to obtain the identifiers, positions
1797 or names of the parameters. Identifiers of individual dimensions are
1798 essentially only useful for printing. They are ignored by all other
1799 operations and may not be preserved across those operations.
1803 =head3 Unary Properties
1809 The following functions test whether the given set or relation
1810 contains any integer points. The ``plain'' variants do not perform
1811 any computations, but simply check if the given set or relation
1812 is already known to be empty.
1814 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1815 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1816 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1817 int isl_set_is_empty(__isl_keep isl_set *set);
1818 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1819 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1820 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1821 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1822 int isl_map_is_empty(__isl_keep isl_map *map);
1823 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1825 =item * Universality
1827 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1828 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1829 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1831 =item * Single-valuedness
1833 int isl_basic_map_is_single_valued(
1834 __isl_keep isl_basic_map *bmap);
1835 int isl_map_plain_is_single_valued(
1836 __isl_keep isl_map *map);
1837 int isl_map_is_single_valued(__isl_keep isl_map *map);
1838 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1842 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1843 int isl_map_is_injective(__isl_keep isl_map *map);
1844 int isl_union_map_plain_is_injective(
1845 __isl_keep isl_union_map *umap);
1846 int isl_union_map_is_injective(
1847 __isl_keep isl_union_map *umap);
1851 int isl_map_is_bijective(__isl_keep isl_map *map);
1852 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1856 int isl_basic_map_plain_is_fixed(
1857 __isl_keep isl_basic_map *bmap,
1858 enum isl_dim_type type, unsigned pos,
1860 int isl_set_plain_is_fixed(__isl_keep isl_set *set,
1861 enum isl_dim_type type, unsigned pos,
1863 int isl_map_plain_is_fixed(__isl_keep isl_map *map,
1864 enum isl_dim_type type, unsigned pos,
1867 Check if the relation obviously lies on a hyperplane where the given dimension
1868 has a fixed value and if so, return that value in C<*val>.
1872 To check whether a set is a parameter domain, use this function:
1874 int isl_set_is_params(__isl_keep isl_set *set);
1875 int isl_union_set_is_params(
1876 __isl_keep isl_union_set *uset);
1880 The following functions check whether the domain of the given
1881 (basic) set is a wrapped relation.
1883 int isl_basic_set_is_wrapping(
1884 __isl_keep isl_basic_set *bset);
1885 int isl_set_is_wrapping(__isl_keep isl_set *set);
1887 =item * Internal Product
1889 int isl_basic_map_can_zip(
1890 __isl_keep isl_basic_map *bmap);
1891 int isl_map_can_zip(__isl_keep isl_map *map);
1893 Check whether the product of domain and range of the given relation
1895 i.e., whether both domain and range are nested relations.
1899 int isl_basic_map_can_curry(
1900 __isl_keep isl_basic_map *bmap);
1901 int isl_map_can_curry(__isl_keep isl_map *map);
1903 Check whether the domain of the (basic) relation is a wrapped relation.
1905 int isl_basic_map_can_uncurry(
1906 __isl_keep isl_basic_map *bmap);
1907 int isl_map_can_uncurry(__isl_keep isl_map *map);
1909 Check whether the range of the (basic) relation is a wrapped relation.
1913 =head3 Binary Properties
1919 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1920 __isl_keep isl_set *set2);
1921 int isl_set_is_equal(__isl_keep isl_set *set1,
1922 __isl_keep isl_set *set2);
1923 int isl_union_set_is_equal(
1924 __isl_keep isl_union_set *uset1,
1925 __isl_keep isl_union_set *uset2);
1926 int isl_basic_map_is_equal(
1927 __isl_keep isl_basic_map *bmap1,
1928 __isl_keep isl_basic_map *bmap2);
1929 int isl_map_is_equal(__isl_keep isl_map *map1,
1930 __isl_keep isl_map *map2);
1931 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1932 __isl_keep isl_map *map2);
1933 int isl_union_map_is_equal(
1934 __isl_keep isl_union_map *umap1,
1935 __isl_keep isl_union_map *umap2);
1937 =item * Disjointness
1939 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1940 __isl_keep isl_set *set2);
1941 int isl_set_is_disjoint(__isl_keep isl_set *set1,
1942 __isl_keep isl_set *set2);
1943 int isl_map_is_disjoint(__isl_keep isl_map *map1,
1944 __isl_keep isl_map *map2);
1948 int isl_basic_set_is_subset(
1949 __isl_keep isl_basic_set *bset1,
1950 __isl_keep isl_basic_set *bset2);
1951 int isl_set_is_subset(__isl_keep isl_set *set1,
1952 __isl_keep isl_set *set2);
1953 int isl_set_is_strict_subset(
1954 __isl_keep isl_set *set1,
1955 __isl_keep isl_set *set2);
1956 int isl_union_set_is_subset(
1957 __isl_keep isl_union_set *uset1,
1958 __isl_keep isl_union_set *uset2);
1959 int isl_union_set_is_strict_subset(
1960 __isl_keep isl_union_set *uset1,
1961 __isl_keep isl_union_set *uset2);
1962 int isl_basic_map_is_subset(
1963 __isl_keep isl_basic_map *bmap1,
1964 __isl_keep isl_basic_map *bmap2);
1965 int isl_basic_map_is_strict_subset(
1966 __isl_keep isl_basic_map *bmap1,
1967 __isl_keep isl_basic_map *bmap2);
1968 int isl_map_is_subset(
1969 __isl_keep isl_map *map1,
1970 __isl_keep isl_map *map2);
1971 int isl_map_is_strict_subset(
1972 __isl_keep isl_map *map1,
1973 __isl_keep isl_map *map2);
1974 int isl_union_map_is_subset(
1975 __isl_keep isl_union_map *umap1,
1976 __isl_keep isl_union_map *umap2);
1977 int isl_union_map_is_strict_subset(
1978 __isl_keep isl_union_map *umap1,
1979 __isl_keep isl_union_map *umap2);
1981 Check whether the first argument is a (strict) subset of the
1986 int isl_set_plain_cmp(__isl_keep isl_set *set1,
1987 __isl_keep isl_set *set2);
1989 This function is useful for sorting C<isl_set>s.
1990 The order depends on the internal representation of the inputs.
1991 The order is fixed over different calls to the function (assuming
1992 the internal representation of the inputs has not changed), but may
1993 change over different versions of C<isl>.
1997 =head2 Unary Operations
2003 __isl_give isl_set *isl_set_complement(
2004 __isl_take isl_set *set);
2005 __isl_give isl_map *isl_map_complement(
2006 __isl_take isl_map *map);
2010 __isl_give isl_basic_map *isl_basic_map_reverse(
2011 __isl_take isl_basic_map *bmap);
2012 __isl_give isl_map *isl_map_reverse(
2013 __isl_take isl_map *map);
2014 __isl_give isl_union_map *isl_union_map_reverse(
2015 __isl_take isl_union_map *umap);
2019 __isl_give isl_basic_set *isl_basic_set_project_out(
2020 __isl_take isl_basic_set *bset,
2021 enum isl_dim_type type, unsigned first, unsigned n);
2022 __isl_give isl_basic_map *isl_basic_map_project_out(
2023 __isl_take isl_basic_map *bmap,
2024 enum isl_dim_type type, unsigned first, unsigned n);
2025 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
2026 enum isl_dim_type type, unsigned first, unsigned n);
2027 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
2028 enum isl_dim_type type, unsigned first, unsigned n);
2029 __isl_give isl_basic_set *isl_basic_set_params(
2030 __isl_take isl_basic_set *bset);
2031 __isl_give isl_basic_set *isl_basic_map_domain(
2032 __isl_take isl_basic_map *bmap);
2033 __isl_give isl_basic_set *isl_basic_map_range(
2034 __isl_take isl_basic_map *bmap);
2035 __isl_give isl_set *isl_set_params(__isl_take isl_set *set);
2036 __isl_give isl_set *isl_map_params(__isl_take isl_map *map);
2037 __isl_give isl_set *isl_map_domain(
2038 __isl_take isl_map *bmap);
2039 __isl_give isl_set *isl_map_range(
2040 __isl_take isl_map *map);
2041 __isl_give isl_set *isl_union_set_params(
2042 __isl_take isl_union_set *uset);
2043 __isl_give isl_set *isl_union_map_params(
2044 __isl_take isl_union_map *umap);
2045 __isl_give isl_union_set *isl_union_map_domain(
2046 __isl_take isl_union_map *umap);
2047 __isl_give isl_union_set *isl_union_map_range(
2048 __isl_take isl_union_map *umap);
2050 __isl_give isl_basic_map *isl_basic_map_domain_map(
2051 __isl_take isl_basic_map *bmap);
2052 __isl_give isl_basic_map *isl_basic_map_range_map(
2053 __isl_take isl_basic_map *bmap);
2054 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
2055 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
2056 __isl_give isl_union_map *isl_union_map_domain_map(
2057 __isl_take isl_union_map *umap);
2058 __isl_give isl_union_map *isl_union_map_range_map(
2059 __isl_take isl_union_map *umap);
2061 The functions above construct a (basic, regular or union) relation
2062 that maps (a wrapped version of) the input relation to its domain or range.
2066 __isl_give isl_basic_set *isl_basic_set_eliminate(
2067 __isl_take isl_basic_set *bset,
2068 enum isl_dim_type type,
2069 unsigned first, unsigned n);
2070 __isl_give isl_set *isl_set_eliminate(
2071 __isl_take isl_set *set, enum isl_dim_type type,
2072 unsigned first, unsigned n);
2073 __isl_give isl_basic_map *isl_basic_map_eliminate(
2074 __isl_take isl_basic_map *bmap,
2075 enum isl_dim_type type,
2076 unsigned first, unsigned n);
2077 __isl_give isl_map *isl_map_eliminate(
2078 __isl_take isl_map *map, enum isl_dim_type type,
2079 unsigned first, unsigned n);
2081 Eliminate the coefficients for the given dimensions from the constraints,
2082 without removing the dimensions.
2086 __isl_give isl_basic_set *isl_basic_set_fix(
2087 __isl_take isl_basic_set *bset,
2088 enum isl_dim_type type, unsigned pos,
2090 __isl_give isl_basic_set *isl_basic_set_fix_si(
2091 __isl_take isl_basic_set *bset,
2092 enum isl_dim_type type, unsigned pos, int value);
2093 __isl_give isl_set *isl_set_fix(__isl_take isl_set *set,
2094 enum isl_dim_type type, unsigned pos,
2096 __isl_give isl_set *isl_set_fix_si(__isl_take isl_set *set,
2097 enum isl_dim_type type, unsigned pos, int value);
2098 __isl_give isl_basic_map *isl_basic_map_fix_si(
2099 __isl_take isl_basic_map *bmap,
2100 enum isl_dim_type type, unsigned pos, int value);
2101 __isl_give isl_map *isl_map_fix(__isl_take isl_map *map,
2102 enum isl_dim_type type, unsigned pos,
2104 __isl_give isl_map *isl_map_fix_si(__isl_take isl_map *map,
2105 enum isl_dim_type type, unsigned pos, int value);
2107 Intersect the set or relation with the hyperplane where the given
2108 dimension has the fixed given value.
2110 __isl_give isl_basic_map *isl_basic_map_lower_bound_si(
2111 __isl_take isl_basic_map *bmap,
2112 enum isl_dim_type type, unsigned pos, int value);
2113 __isl_give isl_basic_map *isl_basic_map_upper_bound_si(
2114 __isl_take isl_basic_map *bmap,
2115 enum isl_dim_type type, unsigned pos, int value);
2116 __isl_give isl_set *isl_set_lower_bound(
2117 __isl_take isl_set *set,
2118 enum isl_dim_type type, unsigned pos,
2120 __isl_give isl_set *isl_set_lower_bound_si(
2121 __isl_take isl_set *set,
2122 enum isl_dim_type type, unsigned pos, int value);
2123 __isl_give isl_map *isl_map_lower_bound_si(
2124 __isl_take isl_map *map,
2125 enum isl_dim_type type, unsigned pos, int value);
2126 __isl_give isl_set *isl_set_upper_bound(
2127 __isl_take isl_set *set,
2128 enum isl_dim_type type, unsigned pos,
2130 __isl_give isl_set *isl_set_upper_bound_si(
2131 __isl_take isl_set *set,
2132 enum isl_dim_type type, unsigned pos, int value);
2133 __isl_give isl_map *isl_map_upper_bound_si(
2134 __isl_take isl_map *map,
2135 enum isl_dim_type type, unsigned pos, int value);
2137 Intersect the set or relation with the half-space where the given
2138 dimension has a value bounded by the fixed given value.
2140 __isl_give isl_set *isl_set_equate(__isl_take isl_set *set,
2141 enum isl_dim_type type1, int pos1,
2142 enum isl_dim_type type2, int pos2);
2143 __isl_give isl_basic_map *isl_basic_map_equate(
2144 __isl_take isl_basic_map *bmap,
2145 enum isl_dim_type type1, int pos1,
2146 enum isl_dim_type type2, int pos2);
2147 __isl_give isl_map *isl_map_equate(__isl_take isl_map *map,
2148 enum isl_dim_type type1, int pos1,
2149 enum isl_dim_type type2, int pos2);
2151 Intersect the set or relation with the hyperplane where the given
2152 dimensions are equal to each other.
2154 __isl_give isl_map *isl_map_oppose(__isl_take isl_map *map,
2155 enum isl_dim_type type1, int pos1,
2156 enum isl_dim_type type2, int pos2);
2158 Intersect the relation with the hyperplane where the given
2159 dimensions have opposite values.
2161 __isl_give isl_basic_map *isl_basic_map_order_ge(
2162 __isl_take isl_basic_map *bmap,
2163 enum isl_dim_type type1, int pos1,
2164 enum isl_dim_type type2, int pos2);
2165 __isl_give isl_map *isl_map_order_lt(__isl_take isl_map *map,
2166 enum isl_dim_type type1, int pos1,
2167 enum isl_dim_type type2, int pos2);
2168 __isl_give isl_map *isl_map_order_gt(__isl_take isl_map *map,
2169 enum isl_dim_type type1, int pos1,
2170 enum isl_dim_type type2, int pos2);
2172 Intersect the relation with the half-space where the given
2173 dimensions satisfy the given ordering.
2177 __isl_give isl_map *isl_set_identity(
2178 __isl_take isl_set *set);
2179 __isl_give isl_union_map *isl_union_set_identity(
2180 __isl_take isl_union_set *uset);
2182 Construct an identity relation on the given (union) set.
2186 __isl_give isl_basic_set *isl_basic_map_deltas(
2187 __isl_take isl_basic_map *bmap);
2188 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
2189 __isl_give isl_union_set *isl_union_map_deltas(
2190 __isl_take isl_union_map *umap);
2192 These functions return a (basic) set containing the differences
2193 between image elements and corresponding domain elements in the input.
2195 __isl_give isl_basic_map *isl_basic_map_deltas_map(
2196 __isl_take isl_basic_map *bmap);
2197 __isl_give isl_map *isl_map_deltas_map(
2198 __isl_take isl_map *map);
2199 __isl_give isl_union_map *isl_union_map_deltas_map(
2200 __isl_take isl_union_map *umap);
2202 The functions above construct a (basic, regular or union) relation
2203 that maps (a wrapped version of) the input relation to its delta set.
2207 Simplify the representation of a set or relation by trying
2208 to combine pairs of basic sets or relations into a single
2209 basic set or relation.
2211 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
2212 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
2213 __isl_give isl_union_set *isl_union_set_coalesce(
2214 __isl_take isl_union_set *uset);
2215 __isl_give isl_union_map *isl_union_map_coalesce(
2216 __isl_take isl_union_map *umap);
2218 One of the methods for combining pairs of basic sets or relations
2219 can result in coefficients that are much larger than those that appear
2220 in the constraints of the input. By default, the coefficients are
2221 not allowed to grow larger, but this can be changed by unsetting
2222 the following option.
2224 int isl_options_set_coalesce_bounded_wrapping(
2225 isl_ctx *ctx, int val);
2226 int isl_options_get_coalesce_bounded_wrapping(
2229 =item * Detecting equalities
2231 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
2232 __isl_take isl_basic_set *bset);
2233 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
2234 __isl_take isl_basic_map *bmap);
2235 __isl_give isl_set *isl_set_detect_equalities(
2236 __isl_take isl_set *set);
2237 __isl_give isl_map *isl_map_detect_equalities(
2238 __isl_take isl_map *map);
2239 __isl_give isl_union_set *isl_union_set_detect_equalities(
2240 __isl_take isl_union_set *uset);
2241 __isl_give isl_union_map *isl_union_map_detect_equalities(
2242 __isl_take isl_union_map *umap);
2244 Simplify the representation of a set or relation by detecting implicit
2247 =item * Removing redundant constraints
2249 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
2250 __isl_take isl_basic_set *bset);
2251 __isl_give isl_set *isl_set_remove_redundancies(
2252 __isl_take isl_set *set);
2253 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
2254 __isl_take isl_basic_map *bmap);
2255 __isl_give isl_map *isl_map_remove_redundancies(
2256 __isl_take isl_map *map);
2260 __isl_give isl_basic_set *isl_set_convex_hull(
2261 __isl_take isl_set *set);
2262 __isl_give isl_basic_map *isl_map_convex_hull(
2263 __isl_take isl_map *map);
2265 If the input set or relation has any existentially quantified
2266 variables, then the result of these operations is currently undefined.
2270 __isl_give isl_basic_set *
2271 isl_set_unshifted_simple_hull(
2272 __isl_take isl_set *set);
2273 __isl_give isl_basic_map *
2274 isl_map_unshifted_simple_hull(
2275 __isl_take isl_map *map);
2276 __isl_give isl_basic_set *isl_set_simple_hull(
2277 __isl_take isl_set *set);
2278 __isl_give isl_basic_map *isl_map_simple_hull(
2279 __isl_take isl_map *map);
2280 __isl_give isl_union_map *isl_union_map_simple_hull(
2281 __isl_take isl_union_map *umap);
2283 These functions compute a single basic set or relation
2284 that contains the whole input set or relation.
2285 In particular, the output is described by translates
2286 of the constraints describing the basic sets or relations in the input.
2287 In case of C<isl_set_unshifted_simple_hull>, only the original
2288 constraints are used, without any translation.
2292 (See \autoref{s:simple hull}.)
2298 __isl_give isl_basic_set *isl_basic_set_affine_hull(
2299 __isl_take isl_basic_set *bset);
2300 __isl_give isl_basic_set *isl_set_affine_hull(
2301 __isl_take isl_set *set);
2302 __isl_give isl_union_set *isl_union_set_affine_hull(
2303 __isl_take isl_union_set *uset);
2304 __isl_give isl_basic_map *isl_basic_map_affine_hull(
2305 __isl_take isl_basic_map *bmap);
2306 __isl_give isl_basic_map *isl_map_affine_hull(
2307 __isl_take isl_map *map);
2308 __isl_give isl_union_map *isl_union_map_affine_hull(
2309 __isl_take isl_union_map *umap);
2311 In case of union sets and relations, the affine hull is computed
2314 =item * Polyhedral hull
2316 __isl_give isl_basic_set *isl_set_polyhedral_hull(
2317 __isl_take isl_set *set);
2318 __isl_give isl_basic_map *isl_map_polyhedral_hull(
2319 __isl_take isl_map *map);
2320 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
2321 __isl_take isl_union_set *uset);
2322 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
2323 __isl_take isl_union_map *umap);
2325 These functions compute a single basic set or relation
2326 not involving any existentially quantified variables
2327 that contains the whole input set or relation.
2328 In case of union sets and relations, the polyhedral hull is computed
2331 =item * Other approximations
2333 __isl_give isl_basic_set *
2334 isl_basic_set_drop_constraints_involving_dims(
2335 __isl_take isl_basic_set *bset,
2336 enum isl_dim_type type,
2337 unsigned first, unsigned n);
2338 __isl_give isl_basic_map *
2339 isl_basic_map_drop_constraints_involving_dims(
2340 __isl_take isl_basic_map *bmap,
2341 enum isl_dim_type type,
2342 unsigned first, unsigned n);
2343 __isl_give isl_basic_set *
2344 isl_basic_set_drop_constraints_not_involving_dims(
2345 __isl_take isl_basic_set *bset,
2346 enum isl_dim_type type,
2347 unsigned first, unsigned n);
2348 __isl_give isl_set *
2349 isl_set_drop_constraints_involving_dims(
2350 __isl_take isl_set *set,
2351 enum isl_dim_type type,
2352 unsigned first, unsigned n);
2353 __isl_give isl_map *
2354 isl_map_drop_constraints_involving_dims(
2355 __isl_take isl_map *map,
2356 enum isl_dim_type type,
2357 unsigned first, unsigned n);
2359 These functions drop any constraints (not) involving the specified dimensions.
2360 Note that the result depends on the representation of the input.
2364 __isl_give isl_basic_set *isl_basic_set_sample(
2365 __isl_take isl_basic_set *bset);
2366 __isl_give isl_basic_set *isl_set_sample(
2367 __isl_take isl_set *set);
2368 __isl_give isl_basic_map *isl_basic_map_sample(
2369 __isl_take isl_basic_map *bmap);
2370 __isl_give isl_basic_map *isl_map_sample(
2371 __isl_take isl_map *map);
2373 If the input (basic) set or relation is non-empty, then return
2374 a singleton subset of the input. Otherwise, return an empty set.
2376 =item * Optimization
2378 #include <isl/ilp.h>
2379 enum isl_lp_result isl_basic_set_max(
2380 __isl_keep isl_basic_set *bset,
2381 __isl_keep isl_aff *obj, isl_int *opt)
2382 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2383 __isl_keep isl_aff *obj, isl_int *opt);
2384 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2385 __isl_keep isl_aff *obj, isl_int *opt);
2387 Compute the minimum or maximum of the integer affine expression C<obj>
2388 over the points in C<set>, returning the result in C<opt>.
2389 The return value may be one of C<isl_lp_error>,
2390 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2392 =item * Parametric optimization
2394 __isl_give isl_pw_aff *isl_set_dim_min(
2395 __isl_take isl_set *set, int pos);
2396 __isl_give isl_pw_aff *isl_set_dim_max(
2397 __isl_take isl_set *set, int pos);
2398 __isl_give isl_pw_aff *isl_map_dim_max(
2399 __isl_take isl_map *map, int pos);
2401 Compute the minimum or maximum of the given set or output dimension
2402 as a function of the parameters (and input dimensions), but independently
2403 of the other set or output dimensions.
2404 For lexicographic optimization, see L<"Lexicographic Optimization">.
2408 The following functions compute either the set of (rational) coefficient
2409 values of valid constraints for the given set or the set of (rational)
2410 values satisfying the constraints with coefficients from the given set.
2411 Internally, these two sets of functions perform essentially the
2412 same operations, except that the set of coefficients is assumed to
2413 be a cone, while the set of values may be any polyhedron.
2414 The current implementation is based on the Farkas lemma and
2415 Fourier-Motzkin elimination, but this may change or be made optional
2416 in future. In particular, future implementations may use different
2417 dualization algorithms or skip the elimination step.
2419 __isl_give isl_basic_set *isl_basic_set_coefficients(
2420 __isl_take isl_basic_set *bset);
2421 __isl_give isl_basic_set *isl_set_coefficients(
2422 __isl_take isl_set *set);
2423 __isl_give isl_union_set *isl_union_set_coefficients(
2424 __isl_take isl_union_set *bset);
2425 __isl_give isl_basic_set *isl_basic_set_solutions(
2426 __isl_take isl_basic_set *bset);
2427 __isl_give isl_basic_set *isl_set_solutions(
2428 __isl_take isl_set *set);
2429 __isl_give isl_union_set *isl_union_set_solutions(
2430 __isl_take isl_union_set *bset);
2434 __isl_give isl_map *isl_map_fixed_power(
2435 __isl_take isl_map *map, isl_int exp);
2436 __isl_give isl_union_map *isl_union_map_fixed_power(
2437 __isl_take isl_union_map *umap, isl_int exp);
2439 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2440 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2441 of C<map> is computed.
2443 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2445 __isl_give isl_union_map *isl_union_map_power(
2446 __isl_take isl_union_map *umap, int *exact);
2448 Compute a parametric representation for all positive powers I<k> of C<map>.
2449 The result maps I<k> to a nested relation corresponding to the
2450 I<k>th power of C<map>.
2451 The result may be an overapproximation. If the result is known to be exact,
2452 then C<*exact> is set to C<1>.
2454 =item * Transitive closure
2456 __isl_give isl_map *isl_map_transitive_closure(
2457 __isl_take isl_map *map, int *exact);
2458 __isl_give isl_union_map *isl_union_map_transitive_closure(
2459 __isl_take isl_union_map *umap, int *exact);
2461 Compute the transitive closure of C<map>.
2462 The result may be an overapproximation. If the result is known to be exact,
2463 then C<*exact> is set to C<1>.
2465 =item * Reaching path lengths
2467 __isl_give isl_map *isl_map_reaching_path_lengths(
2468 __isl_take isl_map *map, int *exact);
2470 Compute a relation that maps each element in the range of C<map>
2471 to the lengths of all paths composed of edges in C<map> that
2472 end up in the given element.
2473 The result may be an overapproximation. If the result is known to be exact,
2474 then C<*exact> is set to C<1>.
2475 To compute the I<maximal> path length, the resulting relation
2476 should be postprocessed by C<isl_map_lexmax>.
2477 In particular, if the input relation is a dependence relation
2478 (mapping sources to sinks), then the maximal path length corresponds
2479 to the free schedule.
2480 Note, however, that C<isl_map_lexmax> expects the maximum to be
2481 finite, so if the path lengths are unbounded (possibly due to
2482 the overapproximation), then you will get an error message.
2486 __isl_give isl_basic_set *isl_basic_map_wrap(
2487 __isl_take isl_basic_map *bmap);
2488 __isl_give isl_set *isl_map_wrap(
2489 __isl_take isl_map *map);
2490 __isl_give isl_union_set *isl_union_map_wrap(
2491 __isl_take isl_union_map *umap);
2492 __isl_give isl_basic_map *isl_basic_set_unwrap(
2493 __isl_take isl_basic_set *bset);
2494 __isl_give isl_map *isl_set_unwrap(
2495 __isl_take isl_set *set);
2496 __isl_give isl_union_map *isl_union_set_unwrap(
2497 __isl_take isl_union_set *uset);
2501 Remove any internal structure of domain (and range) of the given
2502 set or relation. If there is any such internal structure in the input,
2503 then the name of the space is also removed.
2505 __isl_give isl_basic_set *isl_basic_set_flatten(
2506 __isl_take isl_basic_set *bset);
2507 __isl_give isl_set *isl_set_flatten(
2508 __isl_take isl_set *set);
2509 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2510 __isl_take isl_basic_map *bmap);
2511 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2512 __isl_take isl_basic_map *bmap);
2513 __isl_give isl_map *isl_map_flatten_range(
2514 __isl_take isl_map *map);
2515 __isl_give isl_map *isl_map_flatten_domain(
2516 __isl_take isl_map *map);
2517 __isl_give isl_basic_map *isl_basic_map_flatten(
2518 __isl_take isl_basic_map *bmap);
2519 __isl_give isl_map *isl_map_flatten(
2520 __isl_take isl_map *map);
2522 __isl_give isl_map *isl_set_flatten_map(
2523 __isl_take isl_set *set);
2525 The function above constructs a relation
2526 that maps the input set to a flattened version of the set.
2530 Lift the input set to a space with extra dimensions corresponding
2531 to the existentially quantified variables in the input.
2532 In particular, the result lives in a wrapped map where the domain
2533 is the original space and the range corresponds to the original
2534 existentially quantified variables.
2536 __isl_give isl_basic_set *isl_basic_set_lift(
2537 __isl_take isl_basic_set *bset);
2538 __isl_give isl_set *isl_set_lift(
2539 __isl_take isl_set *set);
2540 __isl_give isl_union_set *isl_union_set_lift(
2541 __isl_take isl_union_set *uset);
2543 Given a local space that contains the existentially quantified
2544 variables of a set, a basic relation that, when applied to
2545 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2546 can be constructed using the following function.
2548 #include <isl/local_space.h>
2549 __isl_give isl_basic_map *isl_local_space_lifting(
2550 __isl_take isl_local_space *ls);
2552 =item * Internal Product
2554 __isl_give isl_basic_map *isl_basic_map_zip(
2555 __isl_take isl_basic_map *bmap);
2556 __isl_give isl_map *isl_map_zip(
2557 __isl_take isl_map *map);
2558 __isl_give isl_union_map *isl_union_map_zip(
2559 __isl_take isl_union_map *umap);
2561 Given a relation with nested relations for domain and range,
2562 interchange the range of the domain with the domain of the range.
2566 __isl_give isl_basic_map *isl_basic_map_curry(
2567 __isl_take isl_basic_map *bmap);
2568 __isl_give isl_basic_map *isl_basic_map_uncurry(
2569 __isl_take isl_basic_map *bmap);
2570 __isl_give isl_map *isl_map_curry(
2571 __isl_take isl_map *map);
2572 __isl_give isl_map *isl_map_uncurry(
2573 __isl_take isl_map *map);
2574 __isl_give isl_union_map *isl_union_map_curry(
2575 __isl_take isl_union_map *umap);
2576 __isl_give isl_union_map *isl_union_map_uncurry(
2577 __isl_take isl_union_map *umap);
2579 Given a relation with a nested relation for domain,
2580 the C<curry> functions
2581 move the range of the nested relation out of the domain
2582 and use it as the domain of a nested relation in the range,
2583 with the original range as range of this nested relation.
2584 The C<uncurry> functions perform the inverse operation.
2586 =item * Aligning parameters
2588 __isl_give isl_basic_set *isl_basic_set_align_params(
2589 __isl_take isl_basic_set *bset,
2590 __isl_take isl_space *model);
2591 __isl_give isl_set *isl_set_align_params(
2592 __isl_take isl_set *set,
2593 __isl_take isl_space *model);
2594 __isl_give isl_basic_map *isl_basic_map_align_params(
2595 __isl_take isl_basic_map *bmap,
2596 __isl_take isl_space *model);
2597 __isl_give isl_map *isl_map_align_params(
2598 __isl_take isl_map *map,
2599 __isl_take isl_space *model);
2601 Change the order of the parameters of the given set or relation
2602 such that the first parameters match those of C<model>.
2603 This may involve the introduction of extra parameters.
2604 All parameters need to be named.
2606 =item * Dimension manipulation
2608 __isl_give isl_basic_set *isl_basic_set_add_dims(
2609 __isl_take isl_basic_set *bset,
2610 enum isl_dim_type type, unsigned n);
2611 __isl_give isl_set *isl_set_add_dims(
2612 __isl_take isl_set *set,
2613 enum isl_dim_type type, unsigned n);
2614 __isl_give isl_map *isl_map_add_dims(
2615 __isl_take isl_map *map,
2616 enum isl_dim_type type, unsigned n);
2617 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2618 __isl_take isl_basic_set *bset,
2619 enum isl_dim_type type, unsigned pos,
2621 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2622 __isl_take isl_basic_map *bmap,
2623 enum isl_dim_type type, unsigned pos,
2625 __isl_give isl_set *isl_set_insert_dims(
2626 __isl_take isl_set *set,
2627 enum isl_dim_type type, unsigned pos, unsigned n);
2628 __isl_give isl_map *isl_map_insert_dims(
2629 __isl_take isl_map *map,
2630 enum isl_dim_type type, unsigned pos, unsigned n);
2631 __isl_give isl_basic_set *isl_basic_set_move_dims(
2632 __isl_take isl_basic_set *bset,
2633 enum isl_dim_type dst_type, unsigned dst_pos,
2634 enum isl_dim_type src_type, unsigned src_pos,
2636 __isl_give isl_basic_map *isl_basic_map_move_dims(
2637 __isl_take isl_basic_map *bmap,
2638 enum isl_dim_type dst_type, unsigned dst_pos,
2639 enum isl_dim_type src_type, unsigned src_pos,
2641 __isl_give isl_set *isl_set_move_dims(
2642 __isl_take isl_set *set,
2643 enum isl_dim_type dst_type, unsigned dst_pos,
2644 enum isl_dim_type src_type, unsigned src_pos,
2646 __isl_give isl_map *isl_map_move_dims(
2647 __isl_take isl_map *map,
2648 enum isl_dim_type dst_type, unsigned dst_pos,
2649 enum isl_dim_type src_type, unsigned src_pos,
2652 It is usually not advisable to directly change the (input or output)
2653 space of a set or a relation as this removes the name and the internal
2654 structure of the space. However, the above functions can be useful
2655 to add new parameters, assuming
2656 C<isl_set_align_params> and C<isl_map_align_params>
2661 =head2 Binary Operations
2663 The two arguments of a binary operation not only need to live
2664 in the same C<isl_ctx>, they currently also need to have
2665 the same (number of) parameters.
2667 =head3 Basic Operations
2671 =item * Intersection
2673 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2674 __isl_take isl_basic_set *bset1,
2675 __isl_take isl_basic_set *bset2);
2676 __isl_give isl_basic_set *isl_basic_set_intersect(
2677 __isl_take isl_basic_set *bset1,
2678 __isl_take isl_basic_set *bset2);
2679 __isl_give isl_set *isl_set_intersect_params(
2680 __isl_take isl_set *set,
2681 __isl_take isl_set *params);
2682 __isl_give isl_set *isl_set_intersect(
2683 __isl_take isl_set *set1,
2684 __isl_take isl_set *set2);
2685 __isl_give isl_union_set *isl_union_set_intersect_params(
2686 __isl_take isl_union_set *uset,
2687 __isl_take isl_set *set);
2688 __isl_give isl_union_map *isl_union_map_intersect_params(
2689 __isl_take isl_union_map *umap,
2690 __isl_take isl_set *set);
2691 __isl_give isl_union_set *isl_union_set_intersect(
2692 __isl_take isl_union_set *uset1,
2693 __isl_take isl_union_set *uset2);
2694 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2695 __isl_take isl_basic_map *bmap,
2696 __isl_take isl_basic_set *bset);
2697 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2698 __isl_take isl_basic_map *bmap,
2699 __isl_take isl_basic_set *bset);
2700 __isl_give isl_basic_map *isl_basic_map_intersect(
2701 __isl_take isl_basic_map *bmap1,
2702 __isl_take isl_basic_map *bmap2);
2703 __isl_give isl_map *isl_map_intersect_params(
2704 __isl_take isl_map *map,
2705 __isl_take isl_set *params);
2706 __isl_give isl_map *isl_map_intersect_domain(
2707 __isl_take isl_map *map,
2708 __isl_take isl_set *set);
2709 __isl_give isl_map *isl_map_intersect_range(
2710 __isl_take isl_map *map,
2711 __isl_take isl_set *set);
2712 __isl_give isl_map *isl_map_intersect(
2713 __isl_take isl_map *map1,
2714 __isl_take isl_map *map2);
2715 __isl_give isl_union_map *isl_union_map_intersect_domain(
2716 __isl_take isl_union_map *umap,
2717 __isl_take isl_union_set *uset);
2718 __isl_give isl_union_map *isl_union_map_intersect_range(
2719 __isl_take isl_union_map *umap,
2720 __isl_take isl_union_set *uset);
2721 __isl_give isl_union_map *isl_union_map_intersect(
2722 __isl_take isl_union_map *umap1,
2723 __isl_take isl_union_map *umap2);
2725 The second argument to the C<_params> functions needs to be
2726 a parametric (basic) set. For the other functions, a parametric set
2727 for either argument is only allowed if the other argument is
2728 a parametric set as well.
2732 __isl_give isl_set *isl_basic_set_union(
2733 __isl_take isl_basic_set *bset1,
2734 __isl_take isl_basic_set *bset2);
2735 __isl_give isl_map *isl_basic_map_union(
2736 __isl_take isl_basic_map *bmap1,
2737 __isl_take isl_basic_map *bmap2);
2738 __isl_give isl_set *isl_set_union(
2739 __isl_take isl_set *set1,
2740 __isl_take isl_set *set2);
2741 __isl_give isl_map *isl_map_union(
2742 __isl_take isl_map *map1,
2743 __isl_take isl_map *map2);
2744 __isl_give isl_union_set *isl_union_set_union(
2745 __isl_take isl_union_set *uset1,
2746 __isl_take isl_union_set *uset2);
2747 __isl_give isl_union_map *isl_union_map_union(
2748 __isl_take isl_union_map *umap1,
2749 __isl_take isl_union_map *umap2);
2751 =item * Set difference
2753 __isl_give isl_set *isl_set_subtract(
2754 __isl_take isl_set *set1,
2755 __isl_take isl_set *set2);
2756 __isl_give isl_map *isl_map_subtract(
2757 __isl_take isl_map *map1,
2758 __isl_take isl_map *map2);
2759 __isl_give isl_map *isl_map_subtract_domain(
2760 __isl_take isl_map *map,
2761 __isl_take isl_set *dom);
2762 __isl_give isl_map *isl_map_subtract_range(
2763 __isl_take isl_map *map,
2764 __isl_take isl_set *dom);
2765 __isl_give isl_union_set *isl_union_set_subtract(
2766 __isl_take isl_union_set *uset1,
2767 __isl_take isl_union_set *uset2);
2768 __isl_give isl_union_map *isl_union_map_subtract(
2769 __isl_take isl_union_map *umap1,
2770 __isl_take isl_union_map *umap2);
2771 __isl_give isl_union_map *isl_union_map_subtract_domain(
2772 __isl_take isl_union_map *umap,
2773 __isl_take isl_union_set *dom);
2774 __isl_give isl_union_map *isl_union_map_subtract_range(
2775 __isl_take isl_union_map *umap,
2776 __isl_take isl_union_set *dom);
2780 __isl_give isl_basic_set *isl_basic_set_apply(
2781 __isl_take isl_basic_set *bset,
2782 __isl_take isl_basic_map *bmap);
2783 __isl_give isl_set *isl_set_apply(
2784 __isl_take isl_set *set,
2785 __isl_take isl_map *map);
2786 __isl_give isl_union_set *isl_union_set_apply(
2787 __isl_take isl_union_set *uset,
2788 __isl_take isl_union_map *umap);
2789 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2790 __isl_take isl_basic_map *bmap1,
2791 __isl_take isl_basic_map *bmap2);
2792 __isl_give isl_basic_map *isl_basic_map_apply_range(
2793 __isl_take isl_basic_map *bmap1,
2794 __isl_take isl_basic_map *bmap2);
2795 __isl_give isl_map *isl_map_apply_domain(
2796 __isl_take isl_map *map1,
2797 __isl_take isl_map *map2);
2798 __isl_give isl_union_map *isl_union_map_apply_domain(
2799 __isl_take isl_union_map *umap1,
2800 __isl_take isl_union_map *umap2);
2801 __isl_give isl_map *isl_map_apply_range(
2802 __isl_take isl_map *map1,
2803 __isl_take isl_map *map2);
2804 __isl_give isl_union_map *isl_union_map_apply_range(
2805 __isl_take isl_union_map *umap1,
2806 __isl_take isl_union_map *umap2);
2810 __isl_give isl_basic_set *
2811 isl_basic_set_preimage_multi_aff(
2812 __isl_take isl_basic_set *bset,
2813 __isl_take isl_multi_aff *ma);
2814 __isl_give isl_set *isl_set_preimage_multi_aff(
2815 __isl_take isl_set *set,
2816 __isl_take isl_multi_aff *ma);
2817 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2818 __isl_take isl_set *set,
2819 __isl_take isl_pw_multi_aff *pma);
2820 __isl_give isl_map *isl_map_preimage_domain_multi_aff(
2821 __isl_take isl_map *map,
2822 __isl_take isl_multi_aff *ma);
2823 __isl_give isl_union_map *
2824 isl_union_map_preimage_domain_multi_aff(
2825 __isl_take isl_union_map *umap,
2826 __isl_take isl_multi_aff *ma);
2828 These functions compute the preimage of the given set or map domain under
2829 the given function. In other words, the expression is plugged
2830 into the set description or into the domain of the map.
2831 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2832 L</"Piecewise Multiple Quasi Affine Expressions">.
2834 =item * Cartesian Product
2836 __isl_give isl_set *isl_set_product(
2837 __isl_take isl_set *set1,
2838 __isl_take isl_set *set2);
2839 __isl_give isl_union_set *isl_union_set_product(
2840 __isl_take isl_union_set *uset1,
2841 __isl_take isl_union_set *uset2);
2842 __isl_give isl_basic_map *isl_basic_map_domain_product(
2843 __isl_take isl_basic_map *bmap1,
2844 __isl_take isl_basic_map *bmap2);
2845 __isl_give isl_basic_map *isl_basic_map_range_product(
2846 __isl_take isl_basic_map *bmap1,
2847 __isl_take isl_basic_map *bmap2);
2848 __isl_give isl_basic_map *isl_basic_map_product(
2849 __isl_take isl_basic_map *bmap1,
2850 __isl_take isl_basic_map *bmap2);
2851 __isl_give isl_map *isl_map_domain_product(
2852 __isl_take isl_map *map1,
2853 __isl_take isl_map *map2);
2854 __isl_give isl_map *isl_map_range_product(
2855 __isl_take isl_map *map1,
2856 __isl_take isl_map *map2);
2857 __isl_give isl_union_map *isl_union_map_domain_product(
2858 __isl_take isl_union_map *umap1,
2859 __isl_take isl_union_map *umap2);
2860 __isl_give isl_union_map *isl_union_map_range_product(
2861 __isl_take isl_union_map *umap1,
2862 __isl_take isl_union_map *umap2);
2863 __isl_give isl_map *isl_map_product(
2864 __isl_take isl_map *map1,
2865 __isl_take isl_map *map2);
2866 __isl_give isl_union_map *isl_union_map_product(
2867 __isl_take isl_union_map *umap1,
2868 __isl_take isl_union_map *umap2);
2870 The above functions compute the cross product of the given
2871 sets or relations. The domains and ranges of the results
2872 are wrapped maps between domains and ranges of the inputs.
2873 To obtain a ``flat'' product, use the following functions
2876 __isl_give isl_basic_set *isl_basic_set_flat_product(
2877 __isl_take isl_basic_set *bset1,
2878 __isl_take isl_basic_set *bset2);
2879 __isl_give isl_set *isl_set_flat_product(
2880 __isl_take isl_set *set1,
2881 __isl_take isl_set *set2);
2882 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2883 __isl_take isl_basic_map *bmap1,
2884 __isl_take isl_basic_map *bmap2);
2885 __isl_give isl_map *isl_map_flat_domain_product(
2886 __isl_take isl_map *map1,
2887 __isl_take isl_map *map2);
2888 __isl_give isl_map *isl_map_flat_range_product(
2889 __isl_take isl_map *map1,
2890 __isl_take isl_map *map2);
2891 __isl_give isl_union_map *isl_union_map_flat_range_product(
2892 __isl_take isl_union_map *umap1,
2893 __isl_take isl_union_map *umap2);
2894 __isl_give isl_basic_map *isl_basic_map_flat_product(
2895 __isl_take isl_basic_map *bmap1,
2896 __isl_take isl_basic_map *bmap2);
2897 __isl_give isl_map *isl_map_flat_product(
2898 __isl_take isl_map *map1,
2899 __isl_take isl_map *map2);
2901 =item * Simplification
2903 __isl_give isl_basic_set *isl_basic_set_gist(
2904 __isl_take isl_basic_set *bset,
2905 __isl_take isl_basic_set *context);
2906 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2907 __isl_take isl_set *context);
2908 __isl_give isl_set *isl_set_gist_params(
2909 __isl_take isl_set *set,
2910 __isl_take isl_set *context);
2911 __isl_give isl_union_set *isl_union_set_gist(
2912 __isl_take isl_union_set *uset,
2913 __isl_take isl_union_set *context);
2914 __isl_give isl_union_set *isl_union_set_gist_params(
2915 __isl_take isl_union_set *uset,
2916 __isl_take isl_set *set);
2917 __isl_give isl_basic_map *isl_basic_map_gist(
2918 __isl_take isl_basic_map *bmap,
2919 __isl_take isl_basic_map *context);
2920 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2921 __isl_take isl_map *context);
2922 __isl_give isl_map *isl_map_gist_params(
2923 __isl_take isl_map *map,
2924 __isl_take isl_set *context);
2925 __isl_give isl_map *isl_map_gist_domain(
2926 __isl_take isl_map *map,
2927 __isl_take isl_set *context);
2928 __isl_give isl_map *isl_map_gist_range(
2929 __isl_take isl_map *map,
2930 __isl_take isl_set *context);
2931 __isl_give isl_union_map *isl_union_map_gist(
2932 __isl_take isl_union_map *umap,
2933 __isl_take isl_union_map *context);
2934 __isl_give isl_union_map *isl_union_map_gist_params(
2935 __isl_take isl_union_map *umap,
2936 __isl_take isl_set *set);
2937 __isl_give isl_union_map *isl_union_map_gist_domain(
2938 __isl_take isl_union_map *umap,
2939 __isl_take isl_union_set *uset);
2940 __isl_give isl_union_map *isl_union_map_gist_range(
2941 __isl_take isl_union_map *umap,
2942 __isl_take isl_union_set *uset);
2944 The gist operation returns a set or relation that has the
2945 same intersection with the context as the input set or relation.
2946 Any implicit equality in the intersection is made explicit in the result,
2947 while all inequalities that are redundant with respect to the intersection
2949 In case of union sets and relations, the gist operation is performed
2954 =head3 Lexicographic Optimization
2956 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2957 the following functions
2958 compute a set that contains the lexicographic minimum or maximum
2959 of the elements in C<set> (or C<bset>) for those values of the parameters
2960 that satisfy C<dom>.
2961 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2962 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2964 In other words, the union of the parameter values
2965 for which the result is non-empty and of C<*empty>
2968 __isl_give isl_set *isl_basic_set_partial_lexmin(
2969 __isl_take isl_basic_set *bset,
2970 __isl_take isl_basic_set *dom,
2971 __isl_give isl_set **empty);
2972 __isl_give isl_set *isl_basic_set_partial_lexmax(
2973 __isl_take isl_basic_set *bset,
2974 __isl_take isl_basic_set *dom,
2975 __isl_give isl_set **empty);
2976 __isl_give isl_set *isl_set_partial_lexmin(
2977 __isl_take isl_set *set, __isl_take isl_set *dom,
2978 __isl_give isl_set **empty);
2979 __isl_give isl_set *isl_set_partial_lexmax(
2980 __isl_take isl_set *set, __isl_take isl_set *dom,
2981 __isl_give isl_set **empty);
2983 Given a (basic) set C<set> (or C<bset>), the following functions simply
2984 return a set containing the lexicographic minimum or maximum
2985 of the elements in C<set> (or C<bset>).
2986 In case of union sets, the optimum is computed per space.
2988 __isl_give isl_set *isl_basic_set_lexmin(
2989 __isl_take isl_basic_set *bset);
2990 __isl_give isl_set *isl_basic_set_lexmax(
2991 __isl_take isl_basic_set *bset);
2992 __isl_give isl_set *isl_set_lexmin(
2993 __isl_take isl_set *set);
2994 __isl_give isl_set *isl_set_lexmax(
2995 __isl_take isl_set *set);
2996 __isl_give isl_union_set *isl_union_set_lexmin(
2997 __isl_take isl_union_set *uset);
2998 __isl_give isl_union_set *isl_union_set_lexmax(
2999 __isl_take isl_union_set *uset);
3001 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
3002 the following functions
3003 compute a relation that maps each element of C<dom>
3004 to the single lexicographic minimum or maximum
3005 of the elements that are associated to that same
3006 element in C<map> (or C<bmap>).
3007 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
3008 that contains the elements in C<dom> that do not map
3009 to any elements in C<map> (or C<bmap>).
3010 In other words, the union of the domain of the result and of C<*empty>
3013 __isl_give isl_map *isl_basic_map_partial_lexmax(
3014 __isl_take isl_basic_map *bmap,
3015 __isl_take isl_basic_set *dom,
3016 __isl_give isl_set **empty);
3017 __isl_give isl_map *isl_basic_map_partial_lexmin(
3018 __isl_take isl_basic_map *bmap,
3019 __isl_take isl_basic_set *dom,
3020 __isl_give isl_set **empty);
3021 __isl_give isl_map *isl_map_partial_lexmax(
3022 __isl_take isl_map *map, __isl_take isl_set *dom,
3023 __isl_give isl_set **empty);
3024 __isl_give isl_map *isl_map_partial_lexmin(
3025 __isl_take isl_map *map, __isl_take isl_set *dom,
3026 __isl_give isl_set **empty);
3028 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3029 return a map mapping each element in the domain of
3030 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3031 of all elements associated to that element.
3032 In case of union relations, the optimum is computed per space.
3034 __isl_give isl_map *isl_basic_map_lexmin(
3035 __isl_take isl_basic_map *bmap);
3036 __isl_give isl_map *isl_basic_map_lexmax(
3037 __isl_take isl_basic_map *bmap);
3038 __isl_give isl_map *isl_map_lexmin(
3039 __isl_take isl_map *map);
3040 __isl_give isl_map *isl_map_lexmax(
3041 __isl_take isl_map *map);
3042 __isl_give isl_union_map *isl_union_map_lexmin(
3043 __isl_take isl_union_map *umap);
3044 __isl_give isl_union_map *isl_union_map_lexmax(
3045 __isl_take isl_union_map *umap);
3047 The following functions return their result in the form of
3048 a piecewise multi-affine expression
3049 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3050 but are otherwise equivalent to the corresponding functions
3051 returning a basic set or relation.
3053 __isl_give isl_pw_multi_aff *
3054 isl_basic_map_lexmin_pw_multi_aff(
3055 __isl_take isl_basic_map *bmap);
3056 __isl_give isl_pw_multi_aff *
3057 isl_basic_set_partial_lexmin_pw_multi_aff(
3058 __isl_take isl_basic_set *bset,
3059 __isl_take isl_basic_set *dom,
3060 __isl_give isl_set **empty);
3061 __isl_give isl_pw_multi_aff *
3062 isl_basic_set_partial_lexmax_pw_multi_aff(
3063 __isl_take isl_basic_set *bset,
3064 __isl_take isl_basic_set *dom,
3065 __isl_give isl_set **empty);
3066 __isl_give isl_pw_multi_aff *
3067 isl_basic_map_partial_lexmin_pw_multi_aff(
3068 __isl_take isl_basic_map *bmap,
3069 __isl_take isl_basic_set *dom,
3070 __isl_give isl_set **empty);
3071 __isl_give isl_pw_multi_aff *
3072 isl_basic_map_partial_lexmax_pw_multi_aff(
3073 __isl_take isl_basic_map *bmap,
3074 __isl_take isl_basic_set *dom,
3075 __isl_give isl_set **empty);
3076 __isl_give isl_pw_multi_aff *isl_set_lexmin_pw_multi_aff(
3077 __isl_take isl_set *set);
3078 __isl_give isl_pw_multi_aff *isl_set_lexmax_pw_multi_aff(
3079 __isl_take isl_set *set);
3080 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3081 __isl_take isl_map *map);
3082 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3083 __isl_take isl_map *map);
3087 Lists are defined over several element types, including
3088 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3089 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3090 Here we take lists of C<isl_set>s as an example.
3091 Lists can be created, copied, modified and freed using the following functions.
3093 #include <isl/list.h>
3094 __isl_give isl_set_list *isl_set_list_from_set(
3095 __isl_take isl_set *el);
3096 __isl_give isl_set_list *isl_set_list_alloc(
3097 isl_ctx *ctx, int n);
3098 __isl_give isl_set_list *isl_set_list_copy(
3099 __isl_keep isl_set_list *list);
3100 __isl_give isl_set_list *isl_set_list_insert(
3101 __isl_take isl_set_list *list, unsigned pos,
3102 __isl_take isl_set *el);
3103 __isl_give isl_set_list *isl_set_list_add(
3104 __isl_take isl_set_list *list,
3105 __isl_take isl_set *el);
3106 __isl_give isl_set_list *isl_set_list_drop(
3107 __isl_take isl_set_list *list,
3108 unsigned first, unsigned n);
3109 __isl_give isl_set_list *isl_set_list_set_set(
3110 __isl_take isl_set_list *list, int index,
3111 __isl_take isl_set *set);
3112 __isl_give isl_set_list *isl_set_list_concat(
3113 __isl_take isl_set_list *list1,
3114 __isl_take isl_set_list *list2);
3115 __isl_give isl_set_list *isl_set_list_sort(
3116 __isl_take isl_set_list *list,
3117 int (*cmp)(__isl_keep isl_set *a,
3118 __isl_keep isl_set *b, void *user),
3120 void *isl_set_list_free(__isl_take isl_set_list *list);
3122 C<isl_set_list_alloc> creates an empty list with a capacity for
3123 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3126 Lists can be inspected using the following functions.
3128 #include <isl/list.h>
3129 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3130 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3131 __isl_give isl_set *isl_set_list_get_set(
3132 __isl_keep isl_set_list *list, int index);
3133 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3134 int (*fn)(__isl_take isl_set *el, void *user),
3136 int isl_set_list_foreach_scc(__isl_keep isl_set_list *list,
3137 int (*follows)(__isl_keep isl_set *a,
3138 __isl_keep isl_set *b, void *user),
3140 int (*fn)(__isl_take isl_set *el, void *user),
3143 The function C<isl_set_list_foreach_scc> calls C<fn> on each of the
3144 strongly connected components of the graph with as vertices the elements
3145 of C<list> and a directed edge from vertex C<b> to vertex C<a>
3146 iff C<follows(a, b)> returns C<1>. The callbacks C<follows> and C<fn>
3147 should return C<-1> on error.
3149 Lists can be printed using
3151 #include <isl/list.h>
3152 __isl_give isl_printer *isl_printer_print_set_list(
3153 __isl_take isl_printer *p,
3154 __isl_keep isl_set_list *list);
3158 Vectors can be created, copied and freed using the following functions.
3160 #include <isl/vec.h>
3161 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3163 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3164 void *isl_vec_free(__isl_take isl_vec *vec);
3166 Note that the elements of a newly created vector may have arbitrary values.
3167 The elements can be changed and inspected using the following functions.
3169 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3170 int isl_vec_size(__isl_keep isl_vec *vec);
3171 int isl_vec_get_element(__isl_keep isl_vec *vec,
3172 int pos, isl_int *v);
3173 __isl_give isl_vec *isl_vec_set_element(
3174 __isl_take isl_vec *vec, int pos, isl_int v);
3175 __isl_give isl_vec *isl_vec_set_element_si(
3176 __isl_take isl_vec *vec, int pos, int v);
3177 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3179 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3181 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3184 C<isl_vec_get_element> will return a negative value if anything went wrong.
3185 In that case, the value of C<*v> is undefined.
3187 The following function can be used to concatenate two vectors.
3189 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3190 __isl_take isl_vec *vec2);
3194 Matrices can be created, copied and freed using the following functions.
3196 #include <isl/mat.h>
3197 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3198 unsigned n_row, unsigned n_col);
3199 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3200 void *isl_mat_free(__isl_take isl_mat *mat);
3202 Note that the elements of a newly created matrix may have arbitrary values.
3203 The elements can be changed and inspected using the following functions.
3205 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3206 int isl_mat_rows(__isl_keep isl_mat *mat);
3207 int isl_mat_cols(__isl_keep isl_mat *mat);
3208 int isl_mat_get_element(__isl_keep isl_mat *mat,
3209 int row, int col, isl_int *v);
3210 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3211 int row, int col, isl_int v);
3212 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3213 int row, int col, int v);
3215 C<isl_mat_get_element> will return a negative value if anything went wrong.
3216 In that case, the value of C<*v> is undefined.
3218 The following function can be used to compute the (right) inverse
3219 of a matrix, i.e., a matrix such that the product of the original
3220 and the inverse (in that order) is a multiple of the identity matrix.
3221 The input matrix is assumed to be of full row-rank.
3223 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3225 The following function can be used to compute the (right) kernel
3226 (or null space) of a matrix, i.e., a matrix such that the product of
3227 the original and the kernel (in that order) is the zero matrix.
3229 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3231 =head2 Piecewise Quasi Affine Expressions
3233 The zero quasi affine expression or the quasi affine expression
3234 that is equal to a specified dimension on a given domain can be created using
3236 __isl_give isl_aff *isl_aff_zero_on_domain(
3237 __isl_take isl_local_space *ls);
3238 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3239 __isl_take isl_local_space *ls);
3240 __isl_give isl_aff *isl_aff_var_on_domain(
3241 __isl_take isl_local_space *ls,
3242 enum isl_dim_type type, unsigned pos);
3243 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3244 __isl_take isl_local_space *ls,
3245 enum isl_dim_type type, unsigned pos);
3247 Note that the space in which the resulting objects live is a map space
3248 with the given space as domain and a one-dimensional range.
3250 An empty piecewise quasi affine expression (one with no cells)
3251 or a piecewise quasi affine expression with a single cell can
3252 be created using the following functions.
3254 #include <isl/aff.h>
3255 __isl_give isl_pw_aff *isl_pw_aff_empty(
3256 __isl_take isl_space *space);
3257 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3258 __isl_take isl_set *set, __isl_take isl_aff *aff);
3259 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3260 __isl_take isl_aff *aff);
3262 A piecewise quasi affine expression that is equal to 1 on a set
3263 and 0 outside the set can be created using the following function.
3265 #include <isl/aff.h>
3266 __isl_give isl_pw_aff *isl_set_indicator_function(
3267 __isl_take isl_set *set);
3269 Quasi affine expressions can be copied and freed using
3271 #include <isl/aff.h>
3272 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3273 void *isl_aff_free(__isl_take isl_aff *aff);
3275 __isl_give isl_pw_aff *isl_pw_aff_copy(
3276 __isl_keep isl_pw_aff *pwaff);
3277 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3279 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3280 using the following function. The constraint is required to have
3281 a non-zero coefficient for the specified dimension.
3283 #include <isl/constraint.h>
3284 __isl_give isl_aff *isl_constraint_get_bound(
3285 __isl_keep isl_constraint *constraint,
3286 enum isl_dim_type type, int pos);
3288 The entire affine expression of the constraint can also be extracted
3289 using the following function.
3291 #include <isl/constraint.h>
3292 __isl_give isl_aff *isl_constraint_get_aff(
3293 __isl_keep isl_constraint *constraint);
3295 Conversely, an equality constraint equating
3296 the affine expression to zero or an inequality constraint enforcing
3297 the affine expression to be non-negative, can be constructed using
3299 __isl_give isl_constraint *isl_equality_from_aff(
3300 __isl_take isl_aff *aff);
3301 __isl_give isl_constraint *isl_inequality_from_aff(
3302 __isl_take isl_aff *aff);
3304 The expression can be inspected using
3306 #include <isl/aff.h>
3307 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3308 int isl_aff_dim(__isl_keep isl_aff *aff,
3309 enum isl_dim_type type);
3310 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3311 __isl_keep isl_aff *aff);
3312 __isl_give isl_local_space *isl_aff_get_local_space(
3313 __isl_keep isl_aff *aff);
3314 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3315 enum isl_dim_type type, unsigned pos);
3316 const char *isl_pw_aff_get_dim_name(
3317 __isl_keep isl_pw_aff *pa,
3318 enum isl_dim_type type, unsigned pos);
3319 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3320 enum isl_dim_type type, unsigned pos);
3321 __isl_give isl_id *isl_pw_aff_get_dim_id(
3322 __isl_keep isl_pw_aff *pa,
3323 enum isl_dim_type type, unsigned pos);
3324 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3325 __isl_keep isl_pw_aff *pa,
3326 enum isl_dim_type type);
3327 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3329 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3330 enum isl_dim_type type, int pos, isl_int *v);
3331 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3333 __isl_give isl_aff *isl_aff_get_div(
3334 __isl_keep isl_aff *aff, int pos);
3336 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3337 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3338 int (*fn)(__isl_take isl_set *set,
3339 __isl_take isl_aff *aff,
3340 void *user), void *user);
3342 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3343 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3345 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3346 enum isl_dim_type type, unsigned first, unsigned n);
3347 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3348 enum isl_dim_type type, unsigned first, unsigned n);
3350 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3351 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3352 enum isl_dim_type type);
3353 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3355 It can be modified using
3357 #include <isl/aff.h>
3358 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3359 __isl_take isl_pw_aff *pwaff,
3360 enum isl_dim_type type, __isl_take isl_id *id);
3361 __isl_give isl_aff *isl_aff_set_dim_name(
3362 __isl_take isl_aff *aff, enum isl_dim_type type,
3363 unsigned pos, const char *s);
3364 __isl_give isl_aff *isl_aff_set_dim_id(
3365 __isl_take isl_aff *aff, enum isl_dim_type type,
3366 unsigned pos, __isl_take isl_id *id);
3367 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3368 __isl_take isl_pw_aff *pma,
3369 enum isl_dim_type type, unsigned pos,
3370 __isl_take isl_id *id);
3371 __isl_give isl_aff *isl_aff_set_constant(
3372 __isl_take isl_aff *aff, isl_int v);
3373 __isl_give isl_aff *isl_aff_set_constant_si(
3374 __isl_take isl_aff *aff, int v);
3375 __isl_give isl_aff *isl_aff_set_coefficient(
3376 __isl_take isl_aff *aff,
3377 enum isl_dim_type type, int pos, isl_int v);
3378 __isl_give isl_aff *isl_aff_set_coefficient_si(
3379 __isl_take isl_aff *aff,
3380 enum isl_dim_type type, int pos, int v);
3381 __isl_give isl_aff *isl_aff_set_denominator(
3382 __isl_take isl_aff *aff, isl_int v);
3384 __isl_give isl_aff *isl_aff_add_constant(
3385 __isl_take isl_aff *aff, isl_int v);
3386 __isl_give isl_aff *isl_aff_add_constant_si(
3387 __isl_take isl_aff *aff, int v);
3388 __isl_give isl_aff *isl_aff_add_constant_num(
3389 __isl_take isl_aff *aff, isl_int v);
3390 __isl_give isl_aff *isl_aff_add_constant_num_si(
3391 __isl_take isl_aff *aff, int v);
3392 __isl_give isl_aff *isl_aff_add_coefficient(
3393 __isl_take isl_aff *aff,
3394 enum isl_dim_type type, int pos, isl_int v);
3395 __isl_give isl_aff *isl_aff_add_coefficient_si(
3396 __isl_take isl_aff *aff,
3397 enum isl_dim_type type, int pos, int v);
3399 __isl_give isl_aff *isl_aff_insert_dims(
3400 __isl_take isl_aff *aff,
3401 enum isl_dim_type type, unsigned first, unsigned n);
3402 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3403 __isl_take isl_pw_aff *pwaff,
3404 enum isl_dim_type type, unsigned first, unsigned n);
3405 __isl_give isl_aff *isl_aff_add_dims(
3406 __isl_take isl_aff *aff,
3407 enum isl_dim_type type, unsigned n);
3408 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3409 __isl_take isl_pw_aff *pwaff,
3410 enum isl_dim_type type, unsigned n);
3411 __isl_give isl_aff *isl_aff_drop_dims(
3412 __isl_take isl_aff *aff,
3413 enum isl_dim_type type, unsigned first, unsigned n);
3414 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3415 __isl_take isl_pw_aff *pwaff,
3416 enum isl_dim_type type, unsigned first, unsigned n);
3418 Note that the C<set_constant> and C<set_coefficient> functions
3419 set the I<numerator> of the constant or coefficient, while
3420 C<add_constant> and C<add_coefficient> add an integer value to
3421 the possibly rational constant or coefficient.
3422 The C<add_constant_num> functions add an integer value to
3425 To check whether an affine expressions is obviously zero
3426 or obviously equal to some other affine expression, use
3428 #include <isl/aff.h>
3429 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3430 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3431 __isl_keep isl_aff *aff2);
3432 int isl_pw_aff_plain_is_equal(
3433 __isl_keep isl_pw_aff *pwaff1,
3434 __isl_keep isl_pw_aff *pwaff2);
3438 #include <isl/aff.h>
3439 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3440 __isl_take isl_aff *aff2);
3441 __isl_give isl_pw_aff *isl_pw_aff_add(
3442 __isl_take isl_pw_aff *pwaff1,
3443 __isl_take isl_pw_aff *pwaff2);
3444 __isl_give isl_pw_aff *isl_pw_aff_min(
3445 __isl_take isl_pw_aff *pwaff1,
3446 __isl_take isl_pw_aff *pwaff2);
3447 __isl_give isl_pw_aff *isl_pw_aff_max(
3448 __isl_take isl_pw_aff *pwaff1,
3449 __isl_take isl_pw_aff *pwaff2);
3450 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3451 __isl_take isl_aff *aff2);
3452 __isl_give isl_pw_aff *isl_pw_aff_sub(
3453 __isl_take isl_pw_aff *pwaff1,
3454 __isl_take isl_pw_aff *pwaff2);
3455 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3456 __isl_give isl_pw_aff *isl_pw_aff_neg(
3457 __isl_take isl_pw_aff *pwaff);
3458 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3459 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3460 __isl_take isl_pw_aff *pwaff);
3461 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3462 __isl_give isl_pw_aff *isl_pw_aff_floor(
3463 __isl_take isl_pw_aff *pwaff);
3464 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3466 __isl_give isl_pw_aff *isl_pw_aff_mod(
3467 __isl_take isl_pw_aff *pwaff, isl_int mod);
3468 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3470 __isl_give isl_pw_aff *isl_pw_aff_scale(
3471 __isl_take isl_pw_aff *pwaff, isl_int f);
3472 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3474 __isl_give isl_aff *isl_aff_scale_down_ui(
3475 __isl_take isl_aff *aff, unsigned f);
3476 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3477 __isl_take isl_pw_aff *pwaff, isl_int f);
3479 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3480 __isl_take isl_pw_aff_list *list);
3481 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3482 __isl_take isl_pw_aff_list *list);
3484 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3485 __isl_take isl_pw_aff *pwqp);
3487 __isl_give isl_aff *isl_aff_align_params(
3488 __isl_take isl_aff *aff,
3489 __isl_take isl_space *model);
3490 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3491 __isl_take isl_pw_aff *pwaff,
3492 __isl_take isl_space *model);
3494 __isl_give isl_aff *isl_aff_project_domain_on_params(
3495 __isl_take isl_aff *aff);
3497 __isl_give isl_aff *isl_aff_gist_params(
3498 __isl_take isl_aff *aff,
3499 __isl_take isl_set *context);
3500 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3501 __isl_take isl_set *context);
3502 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3503 __isl_take isl_pw_aff *pwaff,
3504 __isl_take isl_set *context);
3505 __isl_give isl_pw_aff *isl_pw_aff_gist(
3506 __isl_take isl_pw_aff *pwaff,
3507 __isl_take isl_set *context);
3509 __isl_give isl_set *isl_pw_aff_domain(
3510 __isl_take isl_pw_aff *pwaff);
3511 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3512 __isl_take isl_pw_aff *pa,
3513 __isl_take isl_set *set);
3514 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3515 __isl_take isl_pw_aff *pa,
3516 __isl_take isl_set *set);
3518 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3519 __isl_take isl_aff *aff2);
3520 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3521 __isl_take isl_aff *aff2);
3522 __isl_give isl_pw_aff *isl_pw_aff_mul(
3523 __isl_take isl_pw_aff *pwaff1,
3524 __isl_take isl_pw_aff *pwaff2);
3525 __isl_give isl_pw_aff *isl_pw_aff_div(
3526 __isl_take isl_pw_aff *pa1,
3527 __isl_take isl_pw_aff *pa2);
3528 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3529 __isl_take isl_pw_aff *pa1,
3530 __isl_take isl_pw_aff *pa2);
3531 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3532 __isl_take isl_pw_aff *pa1,
3533 __isl_take isl_pw_aff *pa2);
3535 When multiplying two affine expressions, at least one of the two needs
3536 to be a constant. Similarly, when dividing an affine expression by another,
3537 the second expression needs to be a constant.
3538 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3539 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3542 #include <isl/aff.h>
3543 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3544 __isl_take isl_aff *aff,
3545 __isl_take isl_multi_aff *ma);
3546 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3547 __isl_take isl_pw_aff *pa,
3548 __isl_take isl_multi_aff *ma);
3549 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3550 __isl_take isl_pw_aff *pa,
3551 __isl_take isl_pw_multi_aff *pma);
3553 These functions precompose the input expression by the given
3554 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3555 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3556 into the (piecewise) affine expression.
3557 Objects of type C<isl_multi_aff> are described in
3558 L</"Piecewise Multiple Quasi Affine Expressions">.
3560 #include <isl/aff.h>
3561 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3562 __isl_take isl_aff *aff);
3563 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3564 __isl_take isl_aff *aff);
3565 __isl_give isl_basic_set *isl_aff_le_basic_set(
3566 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3567 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3568 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3569 __isl_give isl_set *isl_pw_aff_eq_set(
3570 __isl_take isl_pw_aff *pwaff1,
3571 __isl_take isl_pw_aff *pwaff2);
3572 __isl_give isl_set *isl_pw_aff_ne_set(
3573 __isl_take isl_pw_aff *pwaff1,
3574 __isl_take isl_pw_aff *pwaff2);
3575 __isl_give isl_set *isl_pw_aff_le_set(
3576 __isl_take isl_pw_aff *pwaff1,
3577 __isl_take isl_pw_aff *pwaff2);
3578 __isl_give isl_set *isl_pw_aff_lt_set(
3579 __isl_take isl_pw_aff *pwaff1,
3580 __isl_take isl_pw_aff *pwaff2);
3581 __isl_give isl_set *isl_pw_aff_ge_set(
3582 __isl_take isl_pw_aff *pwaff1,
3583 __isl_take isl_pw_aff *pwaff2);
3584 __isl_give isl_set *isl_pw_aff_gt_set(
3585 __isl_take isl_pw_aff *pwaff1,
3586 __isl_take isl_pw_aff *pwaff2);
3588 __isl_give isl_set *isl_pw_aff_list_eq_set(
3589 __isl_take isl_pw_aff_list *list1,
3590 __isl_take isl_pw_aff_list *list2);
3591 __isl_give isl_set *isl_pw_aff_list_ne_set(
3592 __isl_take isl_pw_aff_list *list1,
3593 __isl_take isl_pw_aff_list *list2);
3594 __isl_give isl_set *isl_pw_aff_list_le_set(
3595 __isl_take isl_pw_aff_list *list1,
3596 __isl_take isl_pw_aff_list *list2);
3597 __isl_give isl_set *isl_pw_aff_list_lt_set(
3598 __isl_take isl_pw_aff_list *list1,
3599 __isl_take isl_pw_aff_list *list2);
3600 __isl_give isl_set *isl_pw_aff_list_ge_set(
3601 __isl_take isl_pw_aff_list *list1,
3602 __isl_take isl_pw_aff_list *list2);
3603 __isl_give isl_set *isl_pw_aff_list_gt_set(
3604 __isl_take isl_pw_aff_list *list1,
3605 __isl_take isl_pw_aff_list *list2);
3607 The function C<isl_aff_neg_basic_set> returns a basic set
3608 containing those elements in the domain space
3609 of C<aff> where C<aff> is negative.
3610 The function C<isl_aff_ge_basic_set> returns a basic set
3611 containing those elements in the shared space
3612 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3613 The function C<isl_pw_aff_ge_set> returns a set
3614 containing those elements in the shared domain
3615 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3616 The functions operating on C<isl_pw_aff_list> apply the corresponding
3617 C<isl_pw_aff> function to each pair of elements in the two lists.
3619 #include <isl/aff.h>
3620 __isl_give isl_set *isl_pw_aff_nonneg_set(
3621 __isl_take isl_pw_aff *pwaff);
3622 __isl_give isl_set *isl_pw_aff_zero_set(
3623 __isl_take isl_pw_aff *pwaff);
3624 __isl_give isl_set *isl_pw_aff_non_zero_set(
3625 __isl_take isl_pw_aff *pwaff);
3627 The function C<isl_pw_aff_nonneg_set> returns a set
3628 containing those elements in the domain
3629 of C<pwaff> where C<pwaff> is non-negative.
3631 #include <isl/aff.h>
3632 __isl_give isl_pw_aff *isl_pw_aff_cond(
3633 __isl_take isl_pw_aff *cond,
3634 __isl_take isl_pw_aff *pwaff_true,
3635 __isl_take isl_pw_aff *pwaff_false);
3637 The function C<isl_pw_aff_cond> performs a conditional operator
3638 and returns an expression that is equal to C<pwaff_true>
3639 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3640 where C<cond> is zero.
3642 #include <isl/aff.h>
3643 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3644 __isl_take isl_pw_aff *pwaff1,
3645 __isl_take isl_pw_aff *pwaff2);
3646 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3647 __isl_take isl_pw_aff *pwaff1,
3648 __isl_take isl_pw_aff *pwaff2);
3649 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3650 __isl_take isl_pw_aff *pwaff1,
3651 __isl_take isl_pw_aff *pwaff2);
3653 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3654 expression with a domain that is the union of those of C<pwaff1> and
3655 C<pwaff2> and such that on each cell, the quasi-affine expression is
3656 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3657 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3658 associated expression is the defined one.
3660 An expression can be read from input using
3662 #include <isl/aff.h>
3663 __isl_give isl_aff *isl_aff_read_from_str(
3664 isl_ctx *ctx, const char *str);
3665 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3666 isl_ctx *ctx, const char *str);
3668 An expression can be printed using
3670 #include <isl/aff.h>
3671 __isl_give isl_printer *isl_printer_print_aff(
3672 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3674 __isl_give isl_printer *isl_printer_print_pw_aff(
3675 __isl_take isl_printer *p,
3676 __isl_keep isl_pw_aff *pwaff);
3678 =head2 Piecewise Multiple Quasi Affine Expressions
3680 An C<isl_multi_aff> object represents a sequence of
3681 zero or more affine expressions, all defined on the same domain space.
3682 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3683 zero or more piecewise affine expressions.
3685 An C<isl_multi_aff> can be constructed from a single
3686 C<isl_aff> or an C<isl_aff_list> using the
3687 following functions. Similarly for C<isl_multi_pw_aff>.
3689 #include <isl/aff.h>
3690 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3691 __isl_take isl_aff *aff);
3692 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3693 __isl_take isl_pw_aff *pa);
3694 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3695 __isl_take isl_space *space,
3696 __isl_take isl_aff_list *list);
3698 An empty piecewise multiple quasi affine expression (one with no cells),
3699 the zero piecewise multiple quasi affine expression (with value zero
3700 for each output dimension),
3701 a piecewise multiple quasi affine expression with a single cell (with
3702 either a universe or a specified domain) or
3703 a zero-dimensional piecewise multiple quasi affine expression
3705 can be created using the following functions.
3707 #include <isl/aff.h>
3708 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3709 __isl_take isl_space *space);
3710 __isl_give isl_multi_aff *isl_multi_aff_zero(
3711 __isl_take isl_space *space);
3712 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3713 __isl_take isl_space *space);
3714 __isl_give isl_multi_aff *isl_multi_aff_identity(
3715 __isl_take isl_space *space);
3716 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3717 __isl_take isl_space *space);
3718 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3719 __isl_take isl_space *space);
3720 __isl_give isl_pw_multi_aff *
3721 isl_pw_multi_aff_from_multi_aff(
3722 __isl_take isl_multi_aff *ma);
3723 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3724 __isl_take isl_set *set,
3725 __isl_take isl_multi_aff *maff);
3726 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3727 __isl_take isl_set *set);
3729 __isl_give isl_union_pw_multi_aff *
3730 isl_union_pw_multi_aff_empty(
3731 __isl_take isl_space *space);
3732 __isl_give isl_union_pw_multi_aff *
3733 isl_union_pw_multi_aff_add_pw_multi_aff(
3734 __isl_take isl_union_pw_multi_aff *upma,
3735 __isl_take isl_pw_multi_aff *pma);
3736 __isl_give isl_union_pw_multi_aff *
3737 isl_union_pw_multi_aff_from_domain(
3738 __isl_take isl_union_set *uset);
3740 A piecewise multiple quasi affine expression can also be initialized
3741 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3742 and the C<isl_map> is single-valued.
3743 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
3744 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
3746 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3747 __isl_take isl_set *set);
3748 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3749 __isl_take isl_map *map);
3751 __isl_give isl_union_pw_multi_aff *
3752 isl_union_pw_multi_aff_from_union_set(
3753 __isl_take isl_union_set *uset);
3754 __isl_give isl_union_pw_multi_aff *
3755 isl_union_pw_multi_aff_from_union_map(
3756 __isl_take isl_union_map *umap);
3758 Multiple quasi affine expressions can be copied and freed using
3760 #include <isl/aff.h>
3761 __isl_give isl_multi_aff *isl_multi_aff_copy(
3762 __isl_keep isl_multi_aff *maff);
3763 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3765 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3766 __isl_keep isl_pw_multi_aff *pma);
3767 void *isl_pw_multi_aff_free(
3768 __isl_take isl_pw_multi_aff *pma);
3770 __isl_give isl_union_pw_multi_aff *
3771 isl_union_pw_multi_aff_copy(
3772 __isl_keep isl_union_pw_multi_aff *upma);
3773 void *isl_union_pw_multi_aff_free(
3774 __isl_take isl_union_pw_multi_aff *upma);
3776 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3777 __isl_keep isl_multi_pw_aff *mpa);
3778 void *isl_multi_pw_aff_free(
3779 __isl_take isl_multi_pw_aff *mpa);
3781 The expression can be inspected using
3783 #include <isl/aff.h>
3784 isl_ctx *isl_multi_aff_get_ctx(
3785 __isl_keep isl_multi_aff *maff);
3786 isl_ctx *isl_pw_multi_aff_get_ctx(
3787 __isl_keep isl_pw_multi_aff *pma);
3788 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3789 __isl_keep isl_union_pw_multi_aff *upma);
3790 isl_ctx *isl_multi_pw_aff_get_ctx(
3791 __isl_keep isl_multi_pw_aff *mpa);
3792 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3793 enum isl_dim_type type);
3794 unsigned isl_pw_multi_aff_dim(
3795 __isl_keep isl_pw_multi_aff *pma,
3796 enum isl_dim_type type);
3797 unsigned isl_multi_pw_aff_dim(
3798 __isl_keep isl_multi_pw_aff *mpa,
3799 enum isl_dim_type type);
3800 __isl_give isl_aff *isl_multi_aff_get_aff(
3801 __isl_keep isl_multi_aff *multi, int pos);
3802 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3803 __isl_keep isl_pw_multi_aff *pma, int pos);
3804 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3805 __isl_keep isl_multi_pw_aff *mpa, int pos);
3806 const char *isl_pw_multi_aff_get_dim_name(
3807 __isl_keep isl_pw_multi_aff *pma,
3808 enum isl_dim_type type, unsigned pos);
3809 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3810 __isl_keep isl_pw_multi_aff *pma,
3811 enum isl_dim_type type, unsigned pos);
3812 const char *isl_multi_aff_get_tuple_name(
3813 __isl_keep isl_multi_aff *multi,
3814 enum isl_dim_type type);
3815 int isl_pw_multi_aff_has_tuple_name(
3816 __isl_keep isl_pw_multi_aff *pma,
3817 enum isl_dim_type type);
3818 const char *isl_pw_multi_aff_get_tuple_name(
3819 __isl_keep isl_pw_multi_aff *pma,
3820 enum isl_dim_type type);
3821 int isl_pw_multi_aff_has_tuple_id(
3822 __isl_keep isl_pw_multi_aff *pma,
3823 enum isl_dim_type type);
3824 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3825 __isl_keep isl_pw_multi_aff *pma,
3826 enum isl_dim_type type);
3828 int isl_pw_multi_aff_foreach_piece(
3829 __isl_keep isl_pw_multi_aff *pma,
3830 int (*fn)(__isl_take isl_set *set,
3831 __isl_take isl_multi_aff *maff,
3832 void *user), void *user);
3834 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3835 __isl_keep isl_union_pw_multi_aff *upma,
3836 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3837 void *user), void *user);
3839 It can be modified using
3841 #include <isl/aff.h>
3842 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3843 __isl_take isl_multi_aff *multi, int pos,
3844 __isl_take isl_aff *aff);
3845 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3846 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3847 __isl_take isl_pw_aff *pa);
3848 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3849 __isl_take isl_multi_aff *maff,
3850 enum isl_dim_type type, unsigned pos, const char *s);
3851 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
3852 __isl_take isl_multi_aff *maff,
3853 enum isl_dim_type type, const char *s);
3854 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3855 __isl_take isl_multi_aff *maff,
3856 enum isl_dim_type type, __isl_take isl_id *id);
3857 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3858 __isl_take isl_pw_multi_aff *pma,
3859 enum isl_dim_type type, __isl_take isl_id *id);
3861 __isl_give isl_multi_pw_aff *
3862 isl_multi_pw_aff_set_dim_name(
3863 __isl_take isl_multi_pw_aff *mpa,
3864 enum isl_dim_type type, unsigned pos, const char *s);
3865 __isl_give isl_multi_pw_aff *
3866 isl_multi_pw_aff_set_tuple_name(
3867 __isl_take isl_multi_pw_aff *mpa,
3868 enum isl_dim_type type, const char *s);
3870 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
3871 __isl_take isl_multi_aff *ma,
3872 enum isl_dim_type type, unsigned first, unsigned n);
3873 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
3874 __isl_take isl_multi_aff *ma,
3875 enum isl_dim_type type, unsigned n);
3876 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3877 __isl_take isl_multi_aff *maff,
3878 enum isl_dim_type type, unsigned first, unsigned n);
3879 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3880 __isl_take isl_pw_multi_aff *pma,
3881 enum isl_dim_type type, unsigned first, unsigned n);
3883 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
3884 __isl_take isl_multi_pw_aff *mpa,
3885 enum isl_dim_type type, unsigned first, unsigned n);
3886 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
3887 __isl_take isl_multi_pw_aff *mpa,
3888 enum isl_dim_type type, unsigned n);
3890 To check whether two multiple affine expressions are
3891 obviously equal to each other, use
3893 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3894 __isl_keep isl_multi_aff *maff2);
3895 int isl_pw_multi_aff_plain_is_equal(
3896 __isl_keep isl_pw_multi_aff *pma1,
3897 __isl_keep isl_pw_multi_aff *pma2);
3901 #include <isl/aff.h>
3902 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3903 __isl_take isl_pw_multi_aff *pma1,
3904 __isl_take isl_pw_multi_aff *pma2);
3905 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3906 __isl_take isl_pw_multi_aff *pma1,
3907 __isl_take isl_pw_multi_aff *pma2);
3908 __isl_give isl_multi_aff *isl_multi_aff_add(
3909 __isl_take isl_multi_aff *maff1,
3910 __isl_take isl_multi_aff *maff2);
3911 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3912 __isl_take isl_pw_multi_aff *pma1,
3913 __isl_take isl_pw_multi_aff *pma2);
3914 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3915 __isl_take isl_union_pw_multi_aff *upma1,
3916 __isl_take isl_union_pw_multi_aff *upma2);
3917 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3918 __isl_take isl_pw_multi_aff *pma1,
3919 __isl_take isl_pw_multi_aff *pma2);
3920 __isl_give isl_multi_aff *isl_multi_aff_sub(
3921 __isl_take isl_multi_aff *ma1,
3922 __isl_take isl_multi_aff *ma2);
3923 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_sub(
3924 __isl_take isl_pw_multi_aff *pma1,
3925 __isl_take isl_pw_multi_aff *pma2);
3926 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_sub(
3927 __isl_take isl_union_pw_multi_aff *upma1,
3928 __isl_take isl_union_pw_multi_aff *upma2);
3930 C<isl_multi_aff_sub> subtracts the second argument from the first.
3932 __isl_give isl_multi_aff *isl_multi_aff_scale(
3933 __isl_take isl_multi_aff *maff,
3935 __isl_give isl_multi_aff *isl_multi_aff_scale_vec(
3936 __isl_take isl_multi_aff *ma,
3937 __isl_take isl_vec *v);
3938 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_scale_vec(
3939 __isl_take isl_pw_multi_aff *pma,
3940 __isl_take isl_vec *v);
3941 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_scale_vec(
3942 __isl_take isl_union_pw_multi_aff *upma,
3943 __isl_take isl_vec *v);
3945 C<isl_multi_aff_scale_vec> scales the first elements of C<ma>
3946 by the corresponding elements of C<v>.
3948 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3949 __isl_take isl_pw_multi_aff *pma,
3950 __isl_take isl_set *set);
3951 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3952 __isl_take isl_pw_multi_aff *pma,
3953 __isl_take isl_set *set);
3954 __isl_give isl_union_pw_multi_aff *
3955 isl_union_pw_multi_aff_intersect_domain(
3956 __isl_take isl_union_pw_multi_aff *upma,
3957 __isl_take isl_union_set *uset);
3958 __isl_give isl_multi_aff *isl_multi_aff_lift(
3959 __isl_take isl_multi_aff *maff,
3960 __isl_give isl_local_space **ls);
3961 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3962 __isl_take isl_pw_multi_aff *pma);
3963 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3964 __isl_take isl_multi_aff *multi,
3965 __isl_take isl_space *model);
3966 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3967 __isl_take isl_pw_multi_aff *pma,
3968 __isl_take isl_space *model);
3969 __isl_give isl_pw_multi_aff *
3970 isl_pw_multi_aff_project_domain_on_params(
3971 __isl_take isl_pw_multi_aff *pma);
3972 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3973 __isl_take isl_multi_aff *maff,
3974 __isl_take isl_set *context);
3975 __isl_give isl_multi_aff *isl_multi_aff_gist(
3976 __isl_take isl_multi_aff *maff,
3977 __isl_take isl_set *context);
3978 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3979 __isl_take isl_pw_multi_aff *pma,
3980 __isl_take isl_set *set);
3981 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3982 __isl_take isl_pw_multi_aff *pma,
3983 __isl_take isl_set *set);
3984 __isl_give isl_set *isl_pw_multi_aff_domain(
3985 __isl_take isl_pw_multi_aff *pma);
3986 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3987 __isl_take isl_union_pw_multi_aff *upma);
3988 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
3989 __isl_take isl_multi_aff *ma1, unsigned pos,
3990 __isl_take isl_multi_aff *ma2);
3991 __isl_give isl_multi_aff *isl_multi_aff_splice(
3992 __isl_take isl_multi_aff *ma1,
3993 unsigned in_pos, unsigned out_pos,
3994 __isl_take isl_multi_aff *ma2);
3995 __isl_give isl_multi_aff *isl_multi_aff_range_product(
3996 __isl_take isl_multi_aff *ma1,
3997 __isl_take isl_multi_aff *ma2);
3998 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3999 __isl_take isl_multi_aff *ma1,
4000 __isl_take isl_multi_aff *ma2);
4001 __isl_give isl_multi_aff *isl_multi_aff_product(
4002 __isl_take isl_multi_aff *ma1,
4003 __isl_take isl_multi_aff *ma2);
4004 __isl_give isl_pw_multi_aff *
4005 isl_pw_multi_aff_range_product(
4006 __isl_take isl_pw_multi_aff *pma1,
4007 __isl_take isl_pw_multi_aff *pma2);
4008 __isl_give isl_pw_multi_aff *
4009 isl_pw_multi_aff_flat_range_product(
4010 __isl_take isl_pw_multi_aff *pma1,
4011 __isl_take isl_pw_multi_aff *pma2);
4012 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
4013 __isl_take isl_pw_multi_aff *pma1,
4014 __isl_take isl_pw_multi_aff *pma2);
4015 __isl_give isl_union_pw_multi_aff *
4016 isl_union_pw_multi_aff_flat_range_product(
4017 __isl_take isl_union_pw_multi_aff *upma1,
4018 __isl_take isl_union_pw_multi_aff *upma2);
4019 __isl_give isl_multi_pw_aff *
4020 isl_multi_pw_aff_range_splice(
4021 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
4022 __isl_take isl_multi_pw_aff *mpa2);
4023 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
4024 __isl_take isl_multi_pw_aff *mpa1,
4025 unsigned in_pos, unsigned out_pos,
4026 __isl_take isl_multi_pw_aff *mpa2);
4027 __isl_give isl_multi_pw_aff *
4028 isl_multi_pw_aff_range_product(
4029 __isl_take isl_multi_pw_aff *mpa1,
4030 __isl_take isl_multi_pw_aff *mpa2);
4031 __isl_give isl_multi_pw_aff *
4032 isl_multi_pw_aff_flat_range_product(
4033 __isl_take isl_multi_pw_aff *mpa1,
4034 __isl_take isl_multi_pw_aff *mpa2);
4036 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
4037 then it is assigned the local space that lies at the basis of
4038 the lifting applied.
4040 #include <isl/aff.h>
4041 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
4042 __isl_take isl_multi_aff *ma1,
4043 __isl_take isl_multi_aff *ma2);
4044 __isl_give isl_pw_multi_aff *
4045 isl_pw_multi_aff_pullback_multi_aff(
4046 __isl_take isl_pw_multi_aff *pma,
4047 __isl_take isl_multi_aff *ma);
4048 __isl_give isl_pw_multi_aff *
4049 isl_pw_multi_aff_pullback_pw_multi_aff(
4050 __isl_take isl_pw_multi_aff *pma1,
4051 __isl_take isl_pw_multi_aff *pma2);
4053 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
4054 In other words, C<ma2> is plugged
4057 __isl_give isl_set *isl_multi_aff_lex_le_set(
4058 __isl_take isl_multi_aff *ma1,
4059 __isl_take isl_multi_aff *ma2);
4060 __isl_give isl_set *isl_multi_aff_lex_ge_set(
4061 __isl_take isl_multi_aff *ma1,
4062 __isl_take isl_multi_aff *ma2);
4064 The function C<isl_multi_aff_lex_le_set> returns a set
4065 containing those elements in the shared domain space
4066 where C<ma1> is lexicographically smaller than or
4069 An expression can be read from input using
4071 #include <isl/aff.h>
4072 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4073 isl_ctx *ctx, const char *str);
4074 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4075 isl_ctx *ctx, const char *str);
4076 __isl_give isl_union_pw_multi_aff *
4077 isl_union_pw_multi_aff_read_from_str(
4078 isl_ctx *ctx, const char *str);
4080 An expression can be printed using
4082 #include <isl/aff.h>
4083 __isl_give isl_printer *isl_printer_print_multi_aff(
4084 __isl_take isl_printer *p,
4085 __isl_keep isl_multi_aff *maff);
4086 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4087 __isl_take isl_printer *p,
4088 __isl_keep isl_pw_multi_aff *pma);
4089 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4090 __isl_take isl_printer *p,
4091 __isl_keep isl_union_pw_multi_aff *upma);
4092 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4093 __isl_take isl_printer *p,
4094 __isl_keep isl_multi_pw_aff *mpa);
4098 Points are elements of a set. They can be used to construct
4099 simple sets (boxes) or they can be used to represent the
4100 individual elements of a set.
4101 The zero point (the origin) can be created using
4103 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4105 The coordinates of a point can be inspected, set and changed
4108 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4109 enum isl_dim_type type, int pos, isl_int *v);
4110 __isl_give isl_point *isl_point_set_coordinate(
4111 __isl_take isl_point *pnt,
4112 enum isl_dim_type type, int pos, isl_int v);
4114 __isl_give isl_point *isl_point_add_ui(
4115 __isl_take isl_point *pnt,
4116 enum isl_dim_type type, int pos, unsigned val);
4117 __isl_give isl_point *isl_point_sub_ui(
4118 __isl_take isl_point *pnt,
4119 enum isl_dim_type type, int pos, unsigned val);
4121 Other properties can be obtained using
4123 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4125 Points can be copied or freed using
4127 __isl_give isl_point *isl_point_copy(
4128 __isl_keep isl_point *pnt);
4129 void isl_point_free(__isl_take isl_point *pnt);
4131 A singleton set can be created from a point using
4133 __isl_give isl_basic_set *isl_basic_set_from_point(
4134 __isl_take isl_point *pnt);
4135 __isl_give isl_set *isl_set_from_point(
4136 __isl_take isl_point *pnt);
4138 and a box can be created from two opposite extremal points using
4140 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4141 __isl_take isl_point *pnt1,
4142 __isl_take isl_point *pnt2);
4143 __isl_give isl_set *isl_set_box_from_points(
4144 __isl_take isl_point *pnt1,
4145 __isl_take isl_point *pnt2);
4147 All elements of a B<bounded> (union) set can be enumerated using
4148 the following functions.
4150 int isl_set_foreach_point(__isl_keep isl_set *set,
4151 int (*fn)(__isl_take isl_point *pnt, void *user),
4153 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4154 int (*fn)(__isl_take isl_point *pnt, void *user),
4157 The function C<fn> is called for each integer point in
4158 C<set> with as second argument the last argument of
4159 the C<isl_set_foreach_point> call. The function C<fn>
4160 should return C<0> on success and C<-1> on failure.
4161 In the latter case, C<isl_set_foreach_point> will stop
4162 enumerating and return C<-1> as well.
4163 If the enumeration is performed successfully and to completion,
4164 then C<isl_set_foreach_point> returns C<0>.
4166 To obtain a single point of a (basic) set, use
4168 __isl_give isl_point *isl_basic_set_sample_point(
4169 __isl_take isl_basic_set *bset);
4170 __isl_give isl_point *isl_set_sample_point(
4171 __isl_take isl_set *set);
4173 If C<set> does not contain any (integer) points, then the
4174 resulting point will be ``void'', a property that can be
4177 int isl_point_is_void(__isl_keep isl_point *pnt);
4179 =head2 Piecewise Quasipolynomials
4181 A piecewise quasipolynomial is a particular kind of function that maps
4182 a parametric point to a rational value.
4183 More specifically, a quasipolynomial is a polynomial expression in greatest
4184 integer parts of affine expressions of parameters and variables.
4185 A piecewise quasipolynomial is a subdivision of a given parametric
4186 domain into disjoint cells with a quasipolynomial associated to
4187 each cell. The value of the piecewise quasipolynomial at a given
4188 point is the value of the quasipolynomial associated to the cell
4189 that contains the point. Outside of the union of cells,
4190 the value is assumed to be zero.
4191 For example, the piecewise quasipolynomial
4193 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4195 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4196 A given piecewise quasipolynomial has a fixed domain dimension.
4197 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4198 defined over different domains.
4199 Piecewise quasipolynomials are mainly used by the C<barvinok>
4200 library for representing the number of elements in a parametric set or map.
4201 For example, the piecewise quasipolynomial above represents
4202 the number of points in the map
4204 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4206 =head3 Input and Output
4208 Piecewise quasipolynomials can be read from input using
4210 __isl_give isl_union_pw_qpolynomial *
4211 isl_union_pw_qpolynomial_read_from_str(
4212 isl_ctx *ctx, const char *str);
4214 Quasipolynomials and piecewise quasipolynomials can be printed
4215 using the following functions.
4217 __isl_give isl_printer *isl_printer_print_qpolynomial(
4218 __isl_take isl_printer *p,
4219 __isl_keep isl_qpolynomial *qp);
4221 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4222 __isl_take isl_printer *p,
4223 __isl_keep isl_pw_qpolynomial *pwqp);
4225 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4226 __isl_take isl_printer *p,
4227 __isl_keep isl_union_pw_qpolynomial *upwqp);
4229 The output format of the printer
4230 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4231 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4233 In case of printing in C<ISL_FORMAT_C>, the user may want
4234 to set the names of all dimensions
4236 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4237 __isl_take isl_qpolynomial *qp,
4238 enum isl_dim_type type, unsigned pos,
4240 __isl_give isl_pw_qpolynomial *
4241 isl_pw_qpolynomial_set_dim_name(
4242 __isl_take isl_pw_qpolynomial *pwqp,
4243 enum isl_dim_type type, unsigned pos,
4246 =head3 Creating New (Piecewise) Quasipolynomials
4248 Some simple quasipolynomials can be created using the following functions.
4249 More complicated quasipolynomials can be created by applying
4250 operations such as addition and multiplication
4251 on the resulting quasipolynomials
4253 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4254 __isl_take isl_space *domain);
4255 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4256 __isl_take isl_space *domain);
4257 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4258 __isl_take isl_space *domain);
4259 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4260 __isl_take isl_space *domain);
4261 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4262 __isl_take isl_space *domain);
4263 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4264 __isl_take isl_space *domain,
4265 const isl_int n, const isl_int d);
4266 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4267 __isl_take isl_space *domain,
4268 enum isl_dim_type type, unsigned pos);
4269 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4270 __isl_take isl_aff *aff);
4272 Note that the space in which a quasipolynomial lives is a map space
4273 with a one-dimensional range. The C<domain> argument in some of
4274 the functions above corresponds to the domain of this map space.
4276 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4277 with a single cell can be created using the following functions.
4278 Multiple of these single cell piecewise quasipolynomials can
4279 be combined to create more complicated piecewise quasipolynomials.
4281 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4282 __isl_take isl_space *space);
4283 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4284 __isl_take isl_set *set,
4285 __isl_take isl_qpolynomial *qp);
4286 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4287 __isl_take isl_qpolynomial *qp);
4288 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4289 __isl_take isl_pw_aff *pwaff);
4291 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4292 __isl_take isl_space *space);
4293 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4294 __isl_take isl_pw_qpolynomial *pwqp);
4295 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4296 __isl_take isl_union_pw_qpolynomial *upwqp,
4297 __isl_take isl_pw_qpolynomial *pwqp);
4299 Quasipolynomials can be copied and freed again using the following
4302 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4303 __isl_keep isl_qpolynomial *qp);
4304 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4306 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4307 __isl_keep isl_pw_qpolynomial *pwqp);
4308 void *isl_pw_qpolynomial_free(
4309 __isl_take isl_pw_qpolynomial *pwqp);
4311 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4312 __isl_keep isl_union_pw_qpolynomial *upwqp);
4313 void *isl_union_pw_qpolynomial_free(
4314 __isl_take isl_union_pw_qpolynomial *upwqp);
4316 =head3 Inspecting (Piecewise) Quasipolynomials
4318 To iterate over all piecewise quasipolynomials in a union
4319 piecewise quasipolynomial, use the following function
4321 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4322 __isl_keep isl_union_pw_qpolynomial *upwqp,
4323 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4326 To extract the piecewise quasipolynomial in a given space from a union, use
4328 __isl_give isl_pw_qpolynomial *
4329 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4330 __isl_keep isl_union_pw_qpolynomial *upwqp,
4331 __isl_take isl_space *space);
4333 To iterate over the cells in a piecewise quasipolynomial,
4334 use either of the following two functions
4336 int isl_pw_qpolynomial_foreach_piece(
4337 __isl_keep isl_pw_qpolynomial *pwqp,
4338 int (*fn)(__isl_take isl_set *set,
4339 __isl_take isl_qpolynomial *qp,
4340 void *user), void *user);
4341 int isl_pw_qpolynomial_foreach_lifted_piece(
4342 __isl_keep isl_pw_qpolynomial *pwqp,
4343 int (*fn)(__isl_take isl_set *set,
4344 __isl_take isl_qpolynomial *qp,
4345 void *user), void *user);
4347 As usual, the function C<fn> should return C<0> on success
4348 and C<-1> on failure. The difference between
4349 C<isl_pw_qpolynomial_foreach_piece> and
4350 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4351 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4352 compute unique representations for all existentially quantified
4353 variables and then turn these existentially quantified variables
4354 into extra set variables, adapting the associated quasipolynomial
4355 accordingly. This means that the C<set> passed to C<fn>
4356 will not have any existentially quantified variables, but that
4357 the dimensions of the sets may be different for different
4358 invocations of C<fn>.
4360 To iterate over all terms in a quasipolynomial,
4363 int isl_qpolynomial_foreach_term(
4364 __isl_keep isl_qpolynomial *qp,
4365 int (*fn)(__isl_take isl_term *term,
4366 void *user), void *user);
4368 The terms themselves can be inspected and freed using
4371 unsigned isl_term_dim(__isl_keep isl_term *term,
4372 enum isl_dim_type type);
4373 void isl_term_get_num(__isl_keep isl_term *term,
4375 void isl_term_get_den(__isl_keep isl_term *term,
4377 int isl_term_get_exp(__isl_keep isl_term *term,
4378 enum isl_dim_type type, unsigned pos);
4379 __isl_give isl_aff *isl_term_get_div(
4380 __isl_keep isl_term *term, unsigned pos);
4381 void isl_term_free(__isl_take isl_term *term);
4383 Each term is a product of parameters, set variables and
4384 integer divisions. The function C<isl_term_get_exp>
4385 returns the exponent of a given dimensions in the given term.
4386 The C<isl_int>s in the arguments of C<isl_term_get_num>
4387 and C<isl_term_get_den> need to have been initialized
4388 using C<isl_int_init> before calling these functions.
4390 =head3 Properties of (Piecewise) Quasipolynomials
4392 To check whether a quasipolynomial is actually a constant,
4393 use the following function.
4395 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4396 isl_int *n, isl_int *d);
4398 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4399 then the numerator and denominator of the constant
4400 are returned in C<*n> and C<*d>, respectively.
4402 To check whether two union piecewise quasipolynomials are
4403 obviously equal, use
4405 int isl_union_pw_qpolynomial_plain_is_equal(
4406 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4407 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4409 =head3 Operations on (Piecewise) Quasipolynomials
4411 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4412 __isl_take isl_qpolynomial *qp, isl_int v);
4413 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4414 __isl_take isl_qpolynomial *qp);
4415 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4416 __isl_take isl_qpolynomial *qp1,
4417 __isl_take isl_qpolynomial *qp2);
4418 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4419 __isl_take isl_qpolynomial *qp1,
4420 __isl_take isl_qpolynomial *qp2);
4421 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4422 __isl_take isl_qpolynomial *qp1,
4423 __isl_take isl_qpolynomial *qp2);
4424 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4425 __isl_take isl_qpolynomial *qp, unsigned exponent);
4427 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4428 __isl_take isl_pw_qpolynomial *pwqp1,
4429 __isl_take isl_pw_qpolynomial *pwqp2);
4430 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4431 __isl_take isl_pw_qpolynomial *pwqp1,
4432 __isl_take isl_pw_qpolynomial *pwqp2);
4433 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4434 __isl_take isl_pw_qpolynomial *pwqp1,
4435 __isl_take isl_pw_qpolynomial *pwqp2);
4436 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4437 __isl_take isl_pw_qpolynomial *pwqp);
4438 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4439 __isl_take isl_pw_qpolynomial *pwqp1,
4440 __isl_take isl_pw_qpolynomial *pwqp2);
4441 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4442 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4444 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4445 __isl_take isl_union_pw_qpolynomial *upwqp1,
4446 __isl_take isl_union_pw_qpolynomial *upwqp2);
4447 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4448 __isl_take isl_union_pw_qpolynomial *upwqp1,
4449 __isl_take isl_union_pw_qpolynomial *upwqp2);
4450 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4451 __isl_take isl_union_pw_qpolynomial *upwqp1,
4452 __isl_take isl_union_pw_qpolynomial *upwqp2);
4454 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4455 __isl_take isl_pw_qpolynomial *pwqp,
4456 __isl_take isl_point *pnt);
4458 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4459 __isl_take isl_union_pw_qpolynomial *upwqp,
4460 __isl_take isl_point *pnt);
4462 __isl_give isl_set *isl_pw_qpolynomial_domain(
4463 __isl_take isl_pw_qpolynomial *pwqp);
4464 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4465 __isl_take isl_pw_qpolynomial *pwpq,
4466 __isl_take isl_set *set);
4467 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4468 __isl_take isl_pw_qpolynomial *pwpq,
4469 __isl_take isl_set *set);
4471 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4472 __isl_take isl_union_pw_qpolynomial *upwqp);
4473 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4474 __isl_take isl_union_pw_qpolynomial *upwpq,
4475 __isl_take isl_union_set *uset);
4476 __isl_give isl_union_pw_qpolynomial *
4477 isl_union_pw_qpolynomial_intersect_params(
4478 __isl_take isl_union_pw_qpolynomial *upwpq,
4479 __isl_take isl_set *set);
4481 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4482 __isl_take isl_qpolynomial *qp,
4483 __isl_take isl_space *model);
4485 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4486 __isl_take isl_qpolynomial *qp);
4487 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4488 __isl_take isl_pw_qpolynomial *pwqp);
4490 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4491 __isl_take isl_union_pw_qpolynomial *upwqp);
4493 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4494 __isl_take isl_qpolynomial *qp,
4495 __isl_take isl_set *context);
4496 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4497 __isl_take isl_qpolynomial *qp,
4498 __isl_take isl_set *context);
4500 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4501 __isl_take isl_pw_qpolynomial *pwqp,
4502 __isl_take isl_set *context);
4503 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4504 __isl_take isl_pw_qpolynomial *pwqp,
4505 __isl_take isl_set *context);
4507 __isl_give isl_union_pw_qpolynomial *
4508 isl_union_pw_qpolynomial_gist_params(
4509 __isl_take isl_union_pw_qpolynomial *upwqp,
4510 __isl_take isl_set *context);
4511 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4512 __isl_take isl_union_pw_qpolynomial *upwqp,
4513 __isl_take isl_union_set *context);
4515 The gist operation applies the gist operation to each of
4516 the cells in the domain of the input piecewise quasipolynomial.
4517 The context is also exploited
4518 to simplify the quasipolynomials associated to each cell.
4520 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4521 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4522 __isl_give isl_union_pw_qpolynomial *
4523 isl_union_pw_qpolynomial_to_polynomial(
4524 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4526 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4527 the polynomial will be an overapproximation. If C<sign> is negative,
4528 it will be an underapproximation. If C<sign> is zero, the approximation
4529 will lie somewhere in between.
4531 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4533 A piecewise quasipolynomial reduction is a piecewise
4534 reduction (or fold) of quasipolynomials.
4535 In particular, the reduction can be maximum or a minimum.
4536 The objects are mainly used to represent the result of
4537 an upper or lower bound on a quasipolynomial over its domain,
4538 i.e., as the result of the following function.
4540 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4541 __isl_take isl_pw_qpolynomial *pwqp,
4542 enum isl_fold type, int *tight);
4544 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4545 __isl_take isl_union_pw_qpolynomial *upwqp,
4546 enum isl_fold type, int *tight);
4548 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4549 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4550 is the returned bound is known be tight, i.e., for each value
4551 of the parameters there is at least
4552 one element in the domain that reaches the bound.
4553 If the domain of C<pwqp> is not wrapping, then the bound is computed
4554 over all elements in that domain and the result has a purely parametric
4555 domain. If the domain of C<pwqp> is wrapping, then the bound is
4556 computed over the range of the wrapped relation. The domain of the
4557 wrapped relation becomes the domain of the result.
4559 A (piecewise) quasipolynomial reduction can be copied or freed using the
4560 following functions.
4562 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4563 __isl_keep isl_qpolynomial_fold *fold);
4564 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4565 __isl_keep isl_pw_qpolynomial_fold *pwf);
4566 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4567 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4568 void isl_qpolynomial_fold_free(
4569 __isl_take isl_qpolynomial_fold *fold);
4570 void *isl_pw_qpolynomial_fold_free(
4571 __isl_take isl_pw_qpolynomial_fold *pwf);
4572 void *isl_union_pw_qpolynomial_fold_free(
4573 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4575 =head3 Printing Piecewise Quasipolynomial Reductions
4577 Piecewise quasipolynomial reductions can be printed
4578 using the following function.
4580 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4581 __isl_take isl_printer *p,
4582 __isl_keep isl_pw_qpolynomial_fold *pwf);
4583 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4584 __isl_take isl_printer *p,
4585 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4587 For C<isl_printer_print_pw_qpolynomial_fold>,
4588 output format of the printer
4589 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4590 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4591 output format of the printer
4592 needs to be set to C<ISL_FORMAT_ISL>.
4593 In case of printing in C<ISL_FORMAT_C>, the user may want
4594 to set the names of all dimensions
4596 __isl_give isl_pw_qpolynomial_fold *
4597 isl_pw_qpolynomial_fold_set_dim_name(
4598 __isl_take isl_pw_qpolynomial_fold *pwf,
4599 enum isl_dim_type type, unsigned pos,
4602 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4604 To iterate over all piecewise quasipolynomial reductions in a union
4605 piecewise quasipolynomial reduction, use the following function
4607 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4608 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4609 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4610 void *user), void *user);
4612 To iterate over the cells in a piecewise quasipolynomial reduction,
4613 use either of the following two functions
4615 int isl_pw_qpolynomial_fold_foreach_piece(
4616 __isl_keep isl_pw_qpolynomial_fold *pwf,
4617 int (*fn)(__isl_take isl_set *set,
4618 __isl_take isl_qpolynomial_fold *fold,
4619 void *user), void *user);
4620 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4621 __isl_keep isl_pw_qpolynomial_fold *pwf,
4622 int (*fn)(__isl_take isl_set *set,
4623 __isl_take isl_qpolynomial_fold *fold,
4624 void *user), void *user);
4626 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4627 of the difference between these two functions.
4629 To iterate over all quasipolynomials in a reduction, use
4631 int isl_qpolynomial_fold_foreach_qpolynomial(
4632 __isl_keep isl_qpolynomial_fold *fold,
4633 int (*fn)(__isl_take isl_qpolynomial *qp,
4634 void *user), void *user);
4636 =head3 Properties of Piecewise Quasipolynomial Reductions
4638 To check whether two union piecewise quasipolynomial reductions are
4639 obviously equal, use
4641 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4642 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4643 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4645 =head3 Operations on Piecewise Quasipolynomial Reductions
4647 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4648 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4650 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4651 __isl_take isl_pw_qpolynomial_fold *pwf1,
4652 __isl_take isl_pw_qpolynomial_fold *pwf2);
4654 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4655 __isl_take isl_pw_qpolynomial_fold *pwf1,
4656 __isl_take isl_pw_qpolynomial_fold *pwf2);
4658 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4659 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4660 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4662 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4663 __isl_take isl_pw_qpolynomial_fold *pwf,
4664 __isl_take isl_point *pnt);
4666 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4667 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4668 __isl_take isl_point *pnt);
4670 __isl_give isl_pw_qpolynomial_fold *
4671 isl_pw_qpolynomial_fold_intersect_params(
4672 __isl_take isl_pw_qpolynomial_fold *pwf,
4673 __isl_take isl_set *set);
4675 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4676 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4677 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4678 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4679 __isl_take isl_union_set *uset);
4680 __isl_give isl_union_pw_qpolynomial_fold *
4681 isl_union_pw_qpolynomial_fold_intersect_params(
4682 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4683 __isl_take isl_set *set);
4685 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4686 __isl_take isl_pw_qpolynomial_fold *pwf);
4688 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4689 __isl_take isl_pw_qpolynomial_fold *pwf);
4691 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4692 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4694 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4695 __isl_take isl_qpolynomial_fold *fold,
4696 __isl_take isl_set *context);
4697 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4698 __isl_take isl_qpolynomial_fold *fold,
4699 __isl_take isl_set *context);
4701 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4702 __isl_take isl_pw_qpolynomial_fold *pwf,
4703 __isl_take isl_set *context);
4704 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4705 __isl_take isl_pw_qpolynomial_fold *pwf,
4706 __isl_take isl_set *context);
4708 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4709 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4710 __isl_take isl_union_set *context);
4711 __isl_give isl_union_pw_qpolynomial_fold *
4712 isl_union_pw_qpolynomial_fold_gist_params(
4713 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4714 __isl_take isl_set *context);
4716 The gist operation applies the gist operation to each of
4717 the cells in the domain of the input piecewise quasipolynomial reduction.
4718 In future, the operation will also exploit the context
4719 to simplify the quasipolynomial reductions associated to each cell.
4721 __isl_give isl_pw_qpolynomial_fold *
4722 isl_set_apply_pw_qpolynomial_fold(
4723 __isl_take isl_set *set,
4724 __isl_take isl_pw_qpolynomial_fold *pwf,
4726 __isl_give isl_pw_qpolynomial_fold *
4727 isl_map_apply_pw_qpolynomial_fold(
4728 __isl_take isl_map *map,
4729 __isl_take isl_pw_qpolynomial_fold *pwf,
4731 __isl_give isl_union_pw_qpolynomial_fold *
4732 isl_union_set_apply_union_pw_qpolynomial_fold(
4733 __isl_take isl_union_set *uset,
4734 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4736 __isl_give isl_union_pw_qpolynomial_fold *
4737 isl_union_map_apply_union_pw_qpolynomial_fold(
4738 __isl_take isl_union_map *umap,
4739 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4742 The functions taking a map
4743 compose the given map with the given piecewise quasipolynomial reduction.
4744 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4745 over all elements in the intersection of the range of the map
4746 and the domain of the piecewise quasipolynomial reduction
4747 as a function of an element in the domain of the map.
4748 The functions taking a set compute a bound over all elements in the
4749 intersection of the set and the domain of the
4750 piecewise quasipolynomial reduction.
4752 =head2 Parametric Vertex Enumeration
4754 The parametric vertex enumeration described in this section
4755 is mainly intended to be used internally and by the C<barvinok>
4758 #include <isl/vertices.h>
4759 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4760 __isl_keep isl_basic_set *bset);
4762 The function C<isl_basic_set_compute_vertices> performs the
4763 actual computation of the parametric vertices and the chamber
4764 decomposition and store the result in an C<isl_vertices> object.
4765 This information can be queried by either iterating over all
4766 the vertices or iterating over all the chambers or cells
4767 and then iterating over all vertices that are active on the chamber.
4769 int isl_vertices_foreach_vertex(
4770 __isl_keep isl_vertices *vertices,
4771 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4774 int isl_vertices_foreach_cell(
4775 __isl_keep isl_vertices *vertices,
4776 int (*fn)(__isl_take isl_cell *cell, void *user),
4778 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4779 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4782 Other operations that can be performed on an C<isl_vertices> object are
4785 isl_ctx *isl_vertices_get_ctx(
4786 __isl_keep isl_vertices *vertices);
4787 int isl_vertices_get_n_vertices(
4788 __isl_keep isl_vertices *vertices);
4789 void isl_vertices_free(__isl_take isl_vertices *vertices);
4791 Vertices can be inspected and destroyed using the following functions.
4793 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4794 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4795 __isl_give isl_basic_set *isl_vertex_get_domain(
4796 __isl_keep isl_vertex *vertex);
4797 __isl_give isl_basic_set *isl_vertex_get_expr(
4798 __isl_keep isl_vertex *vertex);
4799 void isl_vertex_free(__isl_take isl_vertex *vertex);
4801 C<isl_vertex_get_expr> returns a singleton parametric set describing
4802 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4804 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4805 B<rational> basic sets, so they should mainly be used for inspection
4806 and should not be mixed with integer sets.
4808 Chambers can be inspected and destroyed using the following functions.
4810 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4811 __isl_give isl_basic_set *isl_cell_get_domain(
4812 __isl_keep isl_cell *cell);
4813 void isl_cell_free(__isl_take isl_cell *cell);
4815 =head1 Polyhedral Compilation Library
4817 This section collects functionality in C<isl> that has been specifically
4818 designed for use during polyhedral compilation.
4820 =head2 Dependence Analysis
4822 C<isl> contains specialized functionality for performing
4823 array dataflow analysis. That is, given a I<sink> access relation
4824 and a collection of possible I<source> access relations,
4825 C<isl> can compute relations that describe
4826 for each iteration of the sink access, which iteration
4827 of which of the source access relations was the last
4828 to access the same data element before the given iteration
4830 The resulting dependence relations map source iterations
4831 to the corresponding sink iterations.
4832 To compute standard flow dependences, the sink should be
4833 a read, while the sources should be writes.
4834 If any of the source accesses are marked as being I<may>
4835 accesses, then there will be a dependence from the last
4836 I<must> access B<and> from any I<may> access that follows
4837 this last I<must> access.
4838 In particular, if I<all> sources are I<may> accesses,
4839 then memory based dependence analysis is performed.
4840 If, on the other hand, all sources are I<must> accesses,
4841 then value based dependence analysis is performed.
4843 #include <isl/flow.h>
4845 typedef int (*isl_access_level_before)(void *first, void *second);
4847 __isl_give isl_access_info *isl_access_info_alloc(
4848 __isl_take isl_map *sink,
4849 void *sink_user, isl_access_level_before fn,
4851 __isl_give isl_access_info *isl_access_info_add_source(
4852 __isl_take isl_access_info *acc,
4853 __isl_take isl_map *source, int must,
4855 void *isl_access_info_free(__isl_take isl_access_info *acc);
4857 __isl_give isl_flow *isl_access_info_compute_flow(
4858 __isl_take isl_access_info *acc);
4860 int isl_flow_foreach(__isl_keep isl_flow *deps,
4861 int (*fn)(__isl_take isl_map *dep, int must,
4862 void *dep_user, void *user),
4864 __isl_give isl_map *isl_flow_get_no_source(
4865 __isl_keep isl_flow *deps, int must);
4866 void isl_flow_free(__isl_take isl_flow *deps);
4868 The function C<isl_access_info_compute_flow> performs the actual
4869 dependence analysis. The other functions are used to construct
4870 the input for this function or to read off the output.
4872 The input is collected in an C<isl_access_info>, which can
4873 be created through a call to C<isl_access_info_alloc>.
4874 The arguments to this functions are the sink access relation
4875 C<sink>, a token C<sink_user> used to identify the sink
4876 access to the user, a callback function for specifying the
4877 relative order of source and sink accesses, and the number
4878 of source access relations that will be added.
4879 The callback function has type C<int (*)(void *first, void *second)>.
4880 The function is called with two user supplied tokens identifying
4881 either a source or the sink and it should return the shared nesting
4882 level and the relative order of the two accesses.
4883 In particular, let I<n> be the number of loops shared by
4884 the two accesses. If C<first> precedes C<second> textually,
4885 then the function should return I<2 * n + 1>; otherwise,
4886 it should return I<2 * n>.
4887 The sources can be added to the C<isl_access_info> by performing
4888 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4889 C<must> indicates whether the source is a I<must> access
4890 or a I<may> access. Note that a multi-valued access relation
4891 should only be marked I<must> if every iteration in the domain
4892 of the relation accesses I<all> elements in its image.
4893 The C<source_user> token is again used to identify
4894 the source access. The range of the source access relation
4895 C<source> should have the same dimension as the range
4896 of the sink access relation.
4897 The C<isl_access_info_free> function should usually not be
4898 called explicitly, because it is called implicitly by
4899 C<isl_access_info_compute_flow>.
4901 The result of the dependence analysis is collected in an
4902 C<isl_flow>. There may be elements of
4903 the sink access for which no preceding source access could be
4904 found or for which all preceding sources are I<may> accesses.
4905 The relations containing these elements can be obtained through
4906 calls to C<isl_flow_get_no_source>, the first with C<must> set
4907 and the second with C<must> unset.
4908 In the case of standard flow dependence analysis,
4909 with the sink a read and the sources I<must> writes,
4910 the first relation corresponds to the reads from uninitialized
4911 array elements and the second relation is empty.
4912 The actual flow dependences can be extracted using
4913 C<isl_flow_foreach>. This function will call the user-specified
4914 callback function C<fn> for each B<non-empty> dependence between
4915 a source and the sink. The callback function is called
4916 with four arguments, the actual flow dependence relation
4917 mapping source iterations to sink iterations, a boolean that
4918 indicates whether it is a I<must> or I<may> dependence, a token
4919 identifying the source and an additional C<void *> with value
4920 equal to the third argument of the C<isl_flow_foreach> call.
4921 A dependence is marked I<must> if it originates from a I<must>
4922 source and if it is not followed by any I<may> sources.
4924 After finishing with an C<isl_flow>, the user should call
4925 C<isl_flow_free> to free all associated memory.
4927 A higher-level interface to dependence analysis is provided
4928 by the following function.
4930 #include <isl/flow.h>
4932 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4933 __isl_take isl_union_map *must_source,
4934 __isl_take isl_union_map *may_source,
4935 __isl_take isl_union_map *schedule,
4936 __isl_give isl_union_map **must_dep,
4937 __isl_give isl_union_map **may_dep,
4938 __isl_give isl_union_map **must_no_source,
4939 __isl_give isl_union_map **may_no_source);
4941 The arrays are identified by the tuple names of the ranges
4942 of the accesses. The iteration domains by the tuple names
4943 of the domains of the accesses and of the schedule.
4944 The relative order of the iteration domains is given by the
4945 schedule. The relations returned through C<must_no_source>
4946 and C<may_no_source> are subsets of C<sink>.
4947 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4948 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4949 any of the other arguments is treated as an error.
4951 =head3 Interaction with Dependence Analysis
4953 During the dependence analysis, we frequently need to perform
4954 the following operation. Given a relation between sink iterations
4955 and potential source iterations from a particular source domain,
4956 what is the last potential source iteration corresponding to each
4957 sink iteration. It can sometimes be convenient to adjust
4958 the set of potential source iterations before or after each such operation.
4959 The prototypical example is fuzzy array dataflow analysis,
4960 where we need to analyze if, based on data-dependent constraints,
4961 the sink iteration can ever be executed without one or more of
4962 the corresponding potential source iterations being executed.
4963 If so, we can introduce extra parameters and select an unknown
4964 but fixed source iteration from the potential source iterations.
4965 To be able to perform such manipulations, C<isl> provides the following
4968 #include <isl/flow.h>
4970 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4971 __isl_keep isl_map *source_map,
4972 __isl_keep isl_set *sink, void *source_user,
4974 __isl_give isl_access_info *isl_access_info_set_restrict(
4975 __isl_take isl_access_info *acc,
4976 isl_access_restrict fn, void *user);
4978 The function C<isl_access_info_set_restrict> should be called
4979 before calling C<isl_access_info_compute_flow> and registers a callback function
4980 that will be called any time C<isl> is about to compute the last
4981 potential source. The first argument is the (reverse) proto-dependence,
4982 mapping sink iterations to potential source iterations.
4983 The second argument represents the sink iterations for which
4984 we want to compute the last source iteration.
4985 The third argument is the token corresponding to the source
4986 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4987 The callback is expected to return a restriction on either the input or
4988 the output of the operation computing the last potential source.
4989 If the input needs to be restricted then restrictions are needed
4990 for both the source and the sink iterations. The sink iterations
4991 and the potential source iterations will be intersected with these sets.
4992 If the output needs to be restricted then only a restriction on the source
4993 iterations is required.
4994 If any error occurs, the callback should return C<NULL>.
4995 An C<isl_restriction> object can be created, freed and inspected
4996 using the following functions.
4998 #include <isl/flow.h>
5000 __isl_give isl_restriction *isl_restriction_input(
5001 __isl_take isl_set *source_restr,
5002 __isl_take isl_set *sink_restr);
5003 __isl_give isl_restriction *isl_restriction_output(
5004 __isl_take isl_set *source_restr);
5005 __isl_give isl_restriction *isl_restriction_none(
5006 __isl_take isl_map *source_map);
5007 __isl_give isl_restriction *isl_restriction_empty(
5008 __isl_take isl_map *source_map);
5009 void *isl_restriction_free(
5010 __isl_take isl_restriction *restr);
5011 isl_ctx *isl_restriction_get_ctx(
5012 __isl_keep isl_restriction *restr);
5014 C<isl_restriction_none> and C<isl_restriction_empty> are special
5015 cases of C<isl_restriction_input>. C<isl_restriction_none>
5016 is essentially equivalent to
5018 isl_restriction_input(isl_set_universe(
5019 isl_space_range(isl_map_get_space(source_map))),
5021 isl_space_domain(isl_map_get_space(source_map))));
5023 whereas C<isl_restriction_empty> is essentially equivalent to
5025 isl_restriction_input(isl_set_empty(
5026 isl_space_range(isl_map_get_space(source_map))),
5028 isl_space_domain(isl_map_get_space(source_map))));
5032 B<The functionality described in this section is fairly new
5033 and may be subject to change.>
5035 The following function can be used to compute a schedule
5036 for a union of domains.
5037 By default, the algorithm used to construct the schedule is similar
5038 to that of C<Pluto>.
5039 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
5041 The generated schedule respects all C<validity> dependences.
5042 That is, all dependence distances over these dependences in the
5043 scheduled space are lexicographically positive.
5044 The default algorithm tries to minimize the dependence distances over
5045 C<proximity> dependences.
5046 Moreover, it tries to obtain sequences (bands) of schedule dimensions
5047 for groups of domains where the dependence distances have only
5048 non-negative values.
5049 When using Feautrier's algorithm, the C<proximity> dependence
5050 distances are only minimized during the extension to a
5051 full-dimensional schedule.
5053 #include <isl/schedule.h>
5054 __isl_give isl_schedule *isl_union_set_compute_schedule(
5055 __isl_take isl_union_set *domain,
5056 __isl_take isl_union_map *validity,
5057 __isl_take isl_union_map *proximity);
5058 void *isl_schedule_free(__isl_take isl_schedule *sched);
5060 A mapping from the domains to the scheduled space can be obtained
5061 from an C<isl_schedule> using the following function.
5063 __isl_give isl_union_map *isl_schedule_get_map(
5064 __isl_keep isl_schedule *sched);
5066 A representation of the schedule can be printed using
5068 __isl_give isl_printer *isl_printer_print_schedule(
5069 __isl_take isl_printer *p,
5070 __isl_keep isl_schedule *schedule);
5072 A representation of the schedule as a forest of bands can be obtained
5073 using the following function.
5075 __isl_give isl_band_list *isl_schedule_get_band_forest(
5076 __isl_keep isl_schedule *schedule);
5078 The individual bands can be visited in depth-first post-order
5079 using the following function.
5081 #include <isl/schedule.h>
5082 int isl_schedule_foreach_band(
5083 __isl_keep isl_schedule *sched,
5084 int (*fn)(__isl_keep isl_band *band, void *user),
5087 The list can be manipulated as explained in L<"Lists">.
5088 The bands inside the list can be copied and freed using the following
5091 #include <isl/band.h>
5092 __isl_give isl_band *isl_band_copy(
5093 __isl_keep isl_band *band);
5094 void *isl_band_free(__isl_take isl_band *band);
5096 Each band contains zero or more scheduling dimensions.
5097 These are referred to as the members of the band.
5098 The section of the schedule that corresponds to the band is
5099 referred to as the partial schedule of the band.
5100 For those nodes that participate in a band, the outer scheduling
5101 dimensions form the prefix schedule, while the inner scheduling
5102 dimensions form the suffix schedule.
5103 That is, if we take a cut of the band forest, then the union of
5104 the concatenations of the prefix, partial and suffix schedules of
5105 each band in the cut is equal to the entire schedule (modulo
5106 some possible padding at the end with zero scheduling dimensions).
5107 The properties of a band can be inspected using the following functions.
5109 #include <isl/band.h>
5110 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5112 int isl_band_has_children(__isl_keep isl_band *band);
5113 __isl_give isl_band_list *isl_band_get_children(
5114 __isl_keep isl_band *band);
5116 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5117 __isl_keep isl_band *band);
5118 __isl_give isl_union_map *isl_band_get_partial_schedule(
5119 __isl_keep isl_band *band);
5120 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5121 __isl_keep isl_band *band);
5123 int isl_band_n_member(__isl_keep isl_band *band);
5124 int isl_band_member_is_zero_distance(
5125 __isl_keep isl_band *band, int pos);
5127 int isl_band_list_foreach_band(
5128 __isl_keep isl_band_list *list,
5129 int (*fn)(__isl_keep isl_band *band, void *user),
5132 Note that a scheduling dimension is considered to be ``zero
5133 distance'' if it does not carry any proximity dependences
5135 That is, if the dependence distances of the proximity
5136 dependences are all zero in that direction (for fixed
5137 iterations of outer bands).
5138 Like C<isl_schedule_foreach_band>,
5139 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5140 in depth-first post-order.
5142 A band can be tiled using the following function.
5144 #include <isl/band.h>
5145 int isl_band_tile(__isl_keep isl_band *band,
5146 __isl_take isl_vec *sizes);
5148 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5150 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5151 int isl_options_set_tile_shift_point_loops(isl_ctx *ctx,
5153 int isl_options_get_tile_shift_point_loops(isl_ctx *ctx);
5155 The C<isl_band_tile> function tiles the band using the given tile sizes
5156 inside its schedule.
5157 A new child band is created to represent the point loops and it is
5158 inserted between the modified band and its children.
5159 The C<tile_scale_tile_loops> option specifies whether the tile
5160 loops iterators should be scaled by the tile sizes.
5161 If the C<tile_shift_point_loops> option is set, then the point loops
5162 are shifted to start at zero.
5164 A band can be split into two nested bands using the following function.
5166 int isl_band_split(__isl_keep isl_band *band, int pos);
5168 The resulting outer band contains the first C<pos> dimensions of C<band>
5169 while the inner band contains the remaining dimensions.
5171 A representation of the band can be printed using
5173 #include <isl/band.h>
5174 __isl_give isl_printer *isl_printer_print_band(
5175 __isl_take isl_printer *p,
5176 __isl_keep isl_band *band);
5180 #include <isl/schedule.h>
5181 int isl_options_set_schedule_max_coefficient(
5182 isl_ctx *ctx, int val);
5183 int isl_options_get_schedule_max_coefficient(
5185 int isl_options_set_schedule_max_constant_term(
5186 isl_ctx *ctx, int val);
5187 int isl_options_get_schedule_max_constant_term(
5189 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5190 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5191 int isl_options_set_schedule_maximize_band_depth(
5192 isl_ctx *ctx, int val);
5193 int isl_options_get_schedule_maximize_band_depth(
5195 int isl_options_set_schedule_outer_zero_distance(
5196 isl_ctx *ctx, int val);
5197 int isl_options_get_schedule_outer_zero_distance(
5199 int isl_options_set_schedule_split_scaled(
5200 isl_ctx *ctx, int val);
5201 int isl_options_get_schedule_split_scaled(
5203 int isl_options_set_schedule_algorithm(
5204 isl_ctx *ctx, int val);
5205 int isl_options_get_schedule_algorithm(
5207 int isl_options_set_schedule_separate_components(
5208 isl_ctx *ctx, int val);
5209 int isl_options_get_schedule_separate_components(
5214 =item * schedule_max_coefficient
5216 This option enforces that the coefficients for variable and parameter
5217 dimensions in the calculated schedule are not larger than the specified value.
5218 This option can significantly increase the speed of the scheduling calculation
5219 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5220 this option does not introduce bounds on the variable or parameter
5223 =item * schedule_max_constant_term
5225 This option enforces that the constant coefficients in the calculated schedule
5226 are not larger than the maximal constant term. This option can significantly
5227 increase the speed of the scheduling calculation and may also prevent fusing of
5228 unrelated dimensions. A value of -1 means that this option does not introduce
5229 bounds on the constant coefficients.
5231 =item * schedule_fuse
5233 This option controls the level of fusion.
5234 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5235 resulting schedule will be distributed as much as possible.
5236 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5237 try to fuse loops in the resulting schedule.
5239 =item * schedule_maximize_band_depth
5241 If this option is set, we do not split bands at the point
5242 where we detect splitting is necessary. Instead, we
5243 backtrack and split bands as early as possible. This
5244 reduces the number of splits and maximizes the width of
5245 the bands. Wider bands give more possibilities for tiling.
5246 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5247 then bands will be split as early as possible, even if there is no need.
5248 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5250 =item * schedule_outer_zero_distance
5252 If this option is set, then we try to construct schedules
5253 where the outermost scheduling dimension in each band
5254 results in a zero dependence distance over the proximity
5257 =item * schedule_split_scaled
5259 If this option is set, then we try to construct schedules in which the
5260 constant term is split off from the linear part if the linear parts of
5261 the scheduling rows for all nodes in the graphs have a common non-trivial
5263 The constant term is then placed in a separate band and the linear
5266 =item * schedule_algorithm
5268 Selects the scheduling algorithm to be used.
5269 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5270 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5272 =item * schedule_separate_components
5274 If at any point the dependence graph contains any (weakly connected) components,
5275 then these components are scheduled separately.
5276 If this option is not set, then some iterations of the domains
5277 in these components may be scheduled together.
5278 If this option is set, then the components are given consecutive
5283 =head2 AST Generation
5285 This section describes the C<isl> functionality for generating
5286 ASTs that visit all the elements
5287 in a domain in an order specified by a schedule.
5288 In particular, given a C<isl_union_map>, an AST is generated
5289 that visits all the elements in the domain of the C<isl_union_map>
5290 according to the lexicographic order of the corresponding image
5291 element(s). If the range of the C<isl_union_map> consists of
5292 elements in more than one space, then each of these spaces is handled
5293 separately in an arbitrary order.
5294 It should be noted that the image elements only specify the I<order>
5295 in which the corresponding domain elements should be visited.
5296 No direct relation between the image elements and the loop iterators
5297 in the generated AST should be assumed.
5299 Each AST is generated within a build. The initial build
5300 simply specifies the constraints on the parameters (if any)
5301 and can be created, inspected, copied and freed using the following functions.
5303 #include <isl/ast_build.h>
5304 __isl_give isl_ast_build *isl_ast_build_from_context(
5305 __isl_take isl_set *set);
5306 isl_ctx *isl_ast_build_get_ctx(
5307 __isl_keep isl_ast_build *build);
5308 __isl_give isl_ast_build *isl_ast_build_copy(
5309 __isl_keep isl_ast_build *build);
5310 void *isl_ast_build_free(
5311 __isl_take isl_ast_build *build);
5313 The C<set> argument is usually a parameter set with zero or more parameters.
5314 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5315 and L</"Fine-grained Control over AST Generation">.
5316 Finally, the AST itself can be constructed using the following
5319 #include <isl/ast_build.h>
5320 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5321 __isl_keep isl_ast_build *build,
5322 __isl_take isl_union_map *schedule);
5324 =head3 Inspecting the AST
5326 The basic properties of an AST node can be obtained as follows.
5328 #include <isl/ast.h>
5329 isl_ctx *isl_ast_node_get_ctx(
5330 __isl_keep isl_ast_node *node);
5331 enum isl_ast_node_type isl_ast_node_get_type(
5332 __isl_keep isl_ast_node *node);
5334 The type of an AST node is one of
5335 C<isl_ast_node_for>,
5337 C<isl_ast_node_block> or
5338 C<isl_ast_node_user>.
5339 An C<isl_ast_node_for> represents a for node.
5340 An C<isl_ast_node_if> represents an if node.
5341 An C<isl_ast_node_block> represents a compound node.
5342 An C<isl_ast_node_user> represents an expression statement.
5343 An expression statement typically corresponds to a domain element, i.e.,
5344 one of the elements that is visited by the AST.
5346 Each type of node has its own additional properties.
5348 #include <isl/ast.h>
5349 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5350 __isl_keep isl_ast_node *node);
5351 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5352 __isl_keep isl_ast_node *node);
5353 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5354 __isl_keep isl_ast_node *node);
5355 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5356 __isl_keep isl_ast_node *node);
5357 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5358 __isl_keep isl_ast_node *node);
5359 int isl_ast_node_for_is_degenerate(
5360 __isl_keep isl_ast_node *node);
5362 An C<isl_ast_for> is considered degenerate if it is known to execute
5365 #include <isl/ast.h>
5366 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5367 __isl_keep isl_ast_node *node);
5368 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5369 __isl_keep isl_ast_node *node);
5370 int isl_ast_node_if_has_else(
5371 __isl_keep isl_ast_node *node);
5372 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5373 __isl_keep isl_ast_node *node);
5375 __isl_give isl_ast_node_list *
5376 isl_ast_node_block_get_children(
5377 __isl_keep isl_ast_node *node);
5379 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5380 __isl_keep isl_ast_node *node);
5382 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5383 the following functions.
5385 #include <isl/ast.h>
5386 isl_ctx *isl_ast_expr_get_ctx(
5387 __isl_keep isl_ast_expr *expr);
5388 enum isl_ast_expr_type isl_ast_expr_get_type(
5389 __isl_keep isl_ast_expr *expr);
5391 The type of an AST expression is one of
5393 C<isl_ast_expr_id> or
5394 C<isl_ast_expr_int>.
5395 An C<isl_ast_expr_op> represents the result of an operation.
5396 An C<isl_ast_expr_id> represents an identifier.
5397 An C<isl_ast_expr_int> represents an integer value.
5399 Each type of expression has its own additional properties.
5401 #include <isl/ast.h>
5402 enum isl_ast_op_type isl_ast_expr_get_op_type(
5403 __isl_keep isl_ast_expr *expr);
5404 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5405 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5406 __isl_keep isl_ast_expr *expr, int pos);
5407 int isl_ast_node_foreach_ast_op_type(
5408 __isl_keep isl_ast_node *node,
5409 int (*fn)(enum isl_ast_op_type type, void *user),
5412 C<isl_ast_expr_get_op_type> returns the type of the operation
5413 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5414 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5416 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5417 C<isl_ast_op_type> that appears in C<node>.
5418 The operation type is one of the following.
5422 =item C<isl_ast_op_and>
5424 Logical I<and> of two arguments.
5425 Both arguments can be evaluated.
5427 =item C<isl_ast_op_and_then>
5429 Logical I<and> of two arguments.
5430 The second argument can only be evaluated if the first evaluates to true.
5432 =item C<isl_ast_op_or>
5434 Logical I<or> of two arguments.
5435 Both arguments can be evaluated.
5437 =item C<isl_ast_op_or_else>
5439 Logical I<or> of two arguments.
5440 The second argument can only be evaluated if the first evaluates to false.
5442 =item C<isl_ast_op_max>
5444 Maximum of two or more arguments.
5446 =item C<isl_ast_op_min>
5448 Minimum of two or more arguments.
5450 =item C<isl_ast_op_minus>
5454 =item C<isl_ast_op_add>
5456 Sum of two arguments.
5458 =item C<isl_ast_op_sub>
5460 Difference of two arguments.
5462 =item C<isl_ast_op_mul>
5464 Product of two arguments.
5466 =item C<isl_ast_op_div>
5468 Exact division. That is, the result is known to be an integer.
5470 =item C<isl_ast_op_fdiv_q>
5472 Result of integer division, rounded towards negative
5475 =item C<isl_ast_op_pdiv_q>
5477 Result of integer division, where dividend is known to be non-negative.
5479 =item C<isl_ast_op_pdiv_r>
5481 Remainder of integer division, where dividend is known to be non-negative.
5483 =item C<isl_ast_op_cond>
5485 Conditional operator defined on three arguments.
5486 If the first argument evaluates to true, then the result
5487 is equal to the second argument. Otherwise, the result
5488 is equal to the third argument.
5489 The second and third argument may only be evaluated if
5490 the first argument evaluates to true and false, respectively.
5491 Corresponds to C<a ? b : c> in C.
5493 =item C<isl_ast_op_select>
5495 Conditional operator defined on three arguments.
5496 If the first argument evaluates to true, then the result
5497 is equal to the second argument. Otherwise, the result
5498 is equal to the third argument.
5499 The second and third argument may be evaluated independently
5500 of the value of the first argument.
5501 Corresponds to C<a * b + (1 - a) * c> in C.
5503 =item C<isl_ast_op_eq>
5507 =item C<isl_ast_op_le>
5509 Less than or equal relation.
5511 =item C<isl_ast_op_lt>
5515 =item C<isl_ast_op_ge>
5517 Greater than or equal relation.
5519 =item C<isl_ast_op_gt>
5521 Greater than relation.
5523 =item C<isl_ast_op_call>
5526 The number of arguments of the C<isl_ast_expr> is one more than
5527 the number of arguments in the function call, the first argument
5528 representing the function being called.
5532 #include <isl/ast.h>
5533 __isl_give isl_id *isl_ast_expr_get_id(
5534 __isl_keep isl_ast_expr *expr);
5536 Return the identifier represented by the AST expression.
5538 #include <isl/ast.h>
5539 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5542 Return the integer represented by the AST expression.
5543 Note that the integer is returned through the C<v> argument.
5544 The return value of the function itself indicates whether the
5545 operation was performed successfully.
5547 =head3 Manipulating and printing the AST
5549 AST nodes can be copied and freed using the following functions.
5551 #include <isl/ast.h>
5552 __isl_give isl_ast_node *isl_ast_node_copy(
5553 __isl_keep isl_ast_node *node);
5554 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5556 AST expressions can be copied and freed using the following functions.
5558 #include <isl/ast.h>
5559 __isl_give isl_ast_expr *isl_ast_expr_copy(
5560 __isl_keep isl_ast_expr *expr);
5561 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5563 New AST expressions can be created either directly or within
5564 the context of an C<isl_ast_build>.
5566 #include <isl/ast.h>
5567 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5568 __isl_take isl_id *id);
5569 __isl_give isl_ast_expr *isl_ast_expr_neg(
5570 __isl_take isl_ast_expr *expr);
5571 __isl_give isl_ast_expr *isl_ast_expr_add(
5572 __isl_take isl_ast_expr *expr1,
5573 __isl_take isl_ast_expr *expr2);
5574 __isl_give isl_ast_expr *isl_ast_expr_sub(
5575 __isl_take isl_ast_expr *expr1,
5576 __isl_take isl_ast_expr *expr2);
5577 __isl_give isl_ast_expr *isl_ast_expr_mul(
5578 __isl_take isl_ast_expr *expr1,
5579 __isl_take isl_ast_expr *expr2);
5580 __isl_give isl_ast_expr *isl_ast_expr_div(
5581 __isl_take isl_ast_expr *expr1,
5582 __isl_take isl_ast_expr *expr2);
5583 __isl_give isl_ast_expr *isl_ast_expr_and(
5584 __isl_take isl_ast_expr *expr1,
5585 __isl_take isl_ast_expr *expr2)
5586 __isl_give isl_ast_expr *isl_ast_expr_or(
5587 __isl_take isl_ast_expr *expr1,
5588 __isl_take isl_ast_expr *expr2)
5590 #include <isl/ast_build.h>
5591 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5592 __isl_keep isl_ast_build *build,
5593 __isl_take isl_pw_aff *pa);
5594 __isl_give isl_ast_expr *
5595 isl_ast_build_call_from_pw_multi_aff(
5596 __isl_keep isl_ast_build *build,
5597 __isl_take isl_pw_multi_aff *pma);
5599 The domains of C<pa> and C<pma> should correspond
5600 to the schedule space of C<build>.
5601 The tuple id of C<pma> is used as the function being called.
5603 User specified data can be attached to an C<isl_ast_node> and obtained
5604 from the same C<isl_ast_node> using the following functions.
5606 #include <isl/ast.h>
5607 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5608 __isl_take isl_ast_node *node,
5609 __isl_take isl_id *annotation);
5610 __isl_give isl_id *isl_ast_node_get_annotation(
5611 __isl_keep isl_ast_node *node);
5613 Basic printing can be performed using the following functions.
5615 #include <isl/ast.h>
5616 __isl_give isl_printer *isl_printer_print_ast_expr(
5617 __isl_take isl_printer *p,
5618 __isl_keep isl_ast_expr *expr);
5619 __isl_give isl_printer *isl_printer_print_ast_node(
5620 __isl_take isl_printer *p,
5621 __isl_keep isl_ast_node *node);
5623 More advanced printing can be performed using the following functions.
5625 #include <isl/ast.h>
5626 __isl_give isl_printer *isl_ast_op_type_print_macro(
5627 enum isl_ast_op_type type,
5628 __isl_take isl_printer *p);
5629 __isl_give isl_printer *isl_ast_node_print_macros(
5630 __isl_keep isl_ast_node *node,
5631 __isl_take isl_printer *p);
5632 __isl_give isl_printer *isl_ast_node_print(
5633 __isl_keep isl_ast_node *node,
5634 __isl_take isl_printer *p,
5635 __isl_take isl_ast_print_options *options);
5636 __isl_give isl_printer *isl_ast_node_for_print(
5637 __isl_keep isl_ast_node *node,
5638 __isl_take isl_printer *p,
5639 __isl_take isl_ast_print_options *options);
5640 __isl_give isl_printer *isl_ast_node_if_print(
5641 __isl_keep isl_ast_node *node,
5642 __isl_take isl_printer *p,
5643 __isl_take isl_ast_print_options *options);
5645 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5646 C<isl> may print out an AST that makes use of macros such
5647 as C<floord>, C<min> and C<max>.
5648 C<isl_ast_op_type_print_macro> prints out the macro
5649 corresponding to a specific C<isl_ast_op_type>.
5650 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5651 for expressions where these macros would be used and prints
5652 out the required macro definitions.
5653 Essentially, C<isl_ast_node_print_macros> calls
5654 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5655 as function argument.
5656 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5657 C<isl_ast_node_if_print> print an C<isl_ast_node>
5658 in C<ISL_FORMAT_C>, but allow for some extra control
5659 through an C<isl_ast_print_options> object.
5660 This object can be created using the following functions.
5662 #include <isl/ast.h>
5663 __isl_give isl_ast_print_options *
5664 isl_ast_print_options_alloc(isl_ctx *ctx);
5665 __isl_give isl_ast_print_options *
5666 isl_ast_print_options_copy(
5667 __isl_keep isl_ast_print_options *options);
5668 void *isl_ast_print_options_free(
5669 __isl_take isl_ast_print_options *options);
5671 __isl_give isl_ast_print_options *
5672 isl_ast_print_options_set_print_user(
5673 __isl_take isl_ast_print_options *options,
5674 __isl_give isl_printer *(*print_user)(
5675 __isl_take isl_printer *p,
5676 __isl_take isl_ast_print_options *options,
5677 __isl_keep isl_ast_node *node, void *user),
5679 __isl_give isl_ast_print_options *
5680 isl_ast_print_options_set_print_for(
5681 __isl_take isl_ast_print_options *options,
5682 __isl_give isl_printer *(*print_for)(
5683 __isl_take isl_printer *p,
5684 __isl_take isl_ast_print_options *options,
5685 __isl_keep isl_ast_node *node, void *user),
5688 The callback set by C<isl_ast_print_options_set_print_user>
5689 is called whenever a node of type C<isl_ast_node_user> needs to
5691 The callback set by C<isl_ast_print_options_set_print_for>
5692 is called whenever a node of type C<isl_ast_node_for> needs to
5694 Note that C<isl_ast_node_for_print> will I<not> call the
5695 callback set by C<isl_ast_print_options_set_print_for> on the node
5696 on which C<isl_ast_node_for_print> is called, but only on nested
5697 nodes of type C<isl_ast_node_for>. It is therefore safe to
5698 call C<isl_ast_node_for_print> from within the callback set by
5699 C<isl_ast_print_options_set_print_for>.
5701 The following option determines the type to be used for iterators
5702 while printing the AST.
5704 int isl_options_set_ast_iterator_type(
5705 isl_ctx *ctx, const char *val);
5706 const char *isl_options_get_ast_iterator_type(
5711 #include <isl/ast_build.h>
5712 int isl_options_set_ast_build_atomic_upper_bound(
5713 isl_ctx *ctx, int val);
5714 int isl_options_get_ast_build_atomic_upper_bound(
5716 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
5718 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
5719 int isl_options_set_ast_build_exploit_nested_bounds(
5720 isl_ctx *ctx, int val);
5721 int isl_options_get_ast_build_exploit_nested_bounds(
5723 int isl_options_set_ast_build_group_coscheduled(
5724 isl_ctx *ctx, int val);
5725 int isl_options_get_ast_build_group_coscheduled(
5727 int isl_options_set_ast_build_scale_strides(
5728 isl_ctx *ctx, int val);
5729 int isl_options_get_ast_build_scale_strides(
5731 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
5733 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
5734 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
5736 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
5740 =item * ast_build_atomic_upper_bound
5742 Generate loop upper bounds that consist of the current loop iterator,
5743 an operator and an expression not involving the iterator.
5744 If this option is not set, then the current loop iterator may appear
5745 several times in the upper bound.
5746 For example, when this option is turned off, AST generation
5749 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
5753 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
5756 When the option is turned on, the following AST is generated
5758 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
5761 =item * ast_build_prefer_pdiv
5763 If this option is turned off, then the AST generation will
5764 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
5765 operators, but no C<isl_ast_op_pdiv_q> or
5766 C<isl_ast_op_pdiv_r> operators.
5767 If this options is turned on, then C<isl> will try to convert
5768 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
5769 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
5771 =item * ast_build_exploit_nested_bounds
5773 Simplify conditions based on bounds of nested for loops.
5774 In particular, remove conditions that are implied by the fact
5775 that one or more nested loops have at least one iteration,
5776 meaning that the upper bound is at least as large as the lower bound.
5777 For example, when this option is turned off, AST generation
5780 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
5786 for (int c0 = 0; c0 <= N; c0 += 1)
5787 for (int c1 = 0; c1 <= M; c1 += 1)
5790 When the option is turned on, the following AST is generated
5792 for (int c0 = 0; c0 <= N; c0 += 1)
5793 for (int c1 = 0; c1 <= M; c1 += 1)
5796 =item * ast_build_group_coscheduled
5798 If two domain elements are assigned the same schedule point, then
5799 they may be executed in any order and they may even appear in different
5800 loops. If this options is set, then the AST generator will make
5801 sure that coscheduled domain elements do not appear in separate parts
5802 of the AST. This is useful in case of nested AST generation
5803 if the outer AST generation is given only part of a schedule
5804 and the inner AST generation should handle the domains that are
5805 coscheduled by this initial part of the schedule together.
5806 For example if an AST is generated for a schedule
5808 { A[i] -> [0]; B[i] -> [0] }
5810 then the C<isl_ast_build_set_create_leaf> callback described
5811 below may get called twice, once for each domain.
5812 Setting this option ensures that the callback is only called once
5813 on both domains together.
5815 =item * ast_build_separation_bounds
5817 This option specifies which bounds to use during separation.
5818 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
5819 then all (possibly implicit) bounds on the current dimension will
5820 be used during separation.
5821 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
5822 then only those bounds that are explicitly available will
5823 be used during separation.
5825 =item * ast_build_scale_strides
5827 This option specifies whether the AST generator is allowed
5828 to scale down iterators of strided loops.
5830 =item * ast_build_allow_else
5832 This option specifies whether the AST generator is allowed
5833 to construct if statements with else branches.
5835 =item * ast_build_allow_or
5837 This option specifies whether the AST generator is allowed
5838 to construct if conditions with disjunctions.
5842 =head3 Fine-grained Control over AST Generation
5844 Besides specifying the constraints on the parameters,
5845 an C<isl_ast_build> object can be used to control
5846 various aspects of the AST generation process.
5847 The most prominent way of control is through ``options'',
5848 which can be set using the following function.
5850 #include <isl/ast_build.h>
5851 __isl_give isl_ast_build *
5852 isl_ast_build_set_options(
5853 __isl_take isl_ast_build *control,
5854 __isl_take isl_union_map *options);
5856 The options are encoded in an <isl_union_map>.
5857 The domain of this union relation refers to the schedule domain,
5858 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
5859 In the case of nested AST generation (see L</"Nested AST Generation">),
5860 the domain of C<options> should refer to the extra piece of the schedule.
5861 That is, it should be equal to the range of the wrapped relation in the
5862 range of the schedule.
5863 The range of the options can consist of elements in one or more spaces,
5864 the names of which determine the effect of the option.
5865 The values of the range typically also refer to the schedule dimension
5866 to which the option applies. In case of nested AST generation
5867 (see L</"Nested AST Generation">), these values refer to the position
5868 of the schedule dimension within the innermost AST generation.
5869 The constraints on the domain elements of
5870 the option should only refer to this dimension and earlier dimensions.
5871 We consider the following spaces.
5875 =item C<separation_class>
5877 This space is a wrapped relation between two one dimensional spaces.
5878 The input space represents the schedule dimension to which the option
5879 applies and the output space represents the separation class.
5880 While constructing a loop corresponding to the specified schedule
5881 dimension(s), the AST generator will try to generate separate loops
5882 for domain elements that are assigned different classes.
5883 If only some of the elements are assigned a class, then those elements
5884 that are not assigned any class will be treated as belonging to a class
5885 that is separate from the explicitly assigned classes.
5886 The typical use case for this option is to separate full tiles from
5888 The other options, described below, are applied after the separation
5891 As an example, consider the separation into full and partial tiles
5892 of a tiling of a triangular domain.
5893 Take, for example, the domain
5895 { A[i,j] : 0 <= i,j and i + j <= 100 }
5897 and a tiling into tiles of 10 by 10. The input to the AST generator
5898 is then the schedule
5900 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
5903 Without any options, the following AST is generated
5905 for (int c0 = 0; c0 <= 10; c0 += 1)
5906 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
5907 for (int c2 = 10 * c0;
5908 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
5910 for (int c3 = 10 * c1;
5911 c3 <= min(10 * c1 + 9, -c2 + 100);
5915 Separation into full and partial tiles can be obtained by assigning
5916 a class, say C<0>, to the full tiles. The full tiles are represented by those
5917 values of the first and second schedule dimensions for which there are
5918 values of the third and fourth dimensions to cover an entire tile.
5919 That is, we need to specify the following option
5921 { [a,b,c,d] -> separation_class[[0]->[0]] :
5922 exists b': 0 <= 10a,10b' and
5923 10a+9+10b'+9 <= 100;
5924 [a,b,c,d] -> separation_class[[1]->[0]] :
5925 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
5929 { [a, b, c, d] -> separation_class[[1] -> [0]] :
5930 a >= 0 and b >= 0 and b <= 8 - a;
5931 [a, b, c, d] -> separation_class[[0] -> [0]] :
5934 With this option, the generated AST is as follows
5937 for (int c0 = 0; c0 <= 8; c0 += 1) {
5938 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
5939 for (int c2 = 10 * c0;
5940 c2 <= 10 * c0 + 9; c2 += 1)
5941 for (int c3 = 10 * c1;
5942 c3 <= 10 * c1 + 9; c3 += 1)
5944 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
5945 for (int c2 = 10 * c0;
5946 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
5948 for (int c3 = 10 * c1;
5949 c3 <= min(-c2 + 100, 10 * c1 + 9);
5953 for (int c0 = 9; c0 <= 10; c0 += 1)
5954 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
5955 for (int c2 = 10 * c0;
5956 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
5958 for (int c3 = 10 * c1;
5959 c3 <= min(10 * c1 + 9, -c2 + 100);
5966 This is a single-dimensional space representing the schedule dimension(s)
5967 to which ``separation'' should be applied. Separation tries to split
5968 a loop into several pieces if this can avoid the generation of guards
5970 See also the C<atomic> option.
5974 This is a single-dimensional space representing the schedule dimension(s)
5975 for which the domains should be considered ``atomic''. That is, the
5976 AST generator will make sure that any given domain space will only appear
5977 in a single loop at the specified level.
5979 Consider the following schedule
5981 { a[i] -> [i] : 0 <= i < 10;
5982 b[i] -> [i+1] : 0 <= i < 10 }
5984 If the following option is specified
5986 { [i] -> separate[x] }
5988 then the following AST will be generated
5992 for (int c0 = 1; c0 <= 9; c0 += 1) {
5999 If, on the other hand, the following option is specified
6001 { [i] -> atomic[x] }
6003 then the following AST will be generated
6005 for (int c0 = 0; c0 <= 10; c0 += 1) {
6012 If neither C<atomic> nor C<separate> is specified, then the AST generator
6013 may produce either of these two results or some intermediate form.
6017 This is a single-dimensional space representing the schedule dimension(s)
6018 that should be I<completely> unrolled.
6019 To obtain a partial unrolling, the user should apply an additional
6020 strip-mining to the schedule and fully unroll the inner loop.
6024 Additional control is available through the following functions.
6026 #include <isl/ast_build.h>
6027 __isl_give isl_ast_build *
6028 isl_ast_build_set_iterators(
6029 __isl_take isl_ast_build *control,
6030 __isl_take isl_id_list *iterators);
6032 The function C<isl_ast_build_set_iterators> allows the user to
6033 specify a list of iterator C<isl_id>s to be used as iterators.
6034 If the input schedule is injective, then
6035 the number of elements in this list should be as large as the dimension
6036 of the schedule space, but no direct correspondence should be assumed
6037 between dimensions and elements.
6038 If the input schedule is not injective, then an additional number
6039 of C<isl_id>s equal to the largest dimension of the input domains
6041 If the number of provided C<isl_id>s is insufficient, then additional
6042 names are automatically generated.
6044 #include <isl/ast_build.h>
6045 __isl_give isl_ast_build *
6046 isl_ast_build_set_create_leaf(
6047 __isl_take isl_ast_build *control,
6048 __isl_give isl_ast_node *(*fn)(
6049 __isl_take isl_ast_build *build,
6050 void *user), void *user);
6053 C<isl_ast_build_set_create_leaf> function allows for the
6054 specification of a callback that should be called whenever the AST
6055 generator arrives at an element of the schedule domain.
6056 The callback should return an AST node that should be inserted
6057 at the corresponding position of the AST. The default action (when
6058 the callback is not set) is to continue generating parts of the AST to scan
6059 all the domain elements associated to the schedule domain element
6060 and to insert user nodes, ``calling'' the domain element, for each of them.
6061 The C<build> argument contains the current state of the C<isl_ast_build>.
6062 To ease nested AST generation (see L</"Nested AST Generation">),
6063 all control information that is
6064 specific to the current AST generation such as the options and
6065 the callbacks has been removed from this C<isl_ast_build>.
6066 The callback would typically return the result of a nested
6068 user defined node created using the following function.
6070 #include <isl/ast.h>
6071 __isl_give isl_ast_node *isl_ast_node_alloc_user(
6072 __isl_take isl_ast_expr *expr);
6074 #include <isl/ast_build.h>
6075 __isl_give isl_ast_build *
6076 isl_ast_build_set_at_each_domain(
6077 __isl_take isl_ast_build *build,
6078 __isl_give isl_ast_node *(*fn)(
6079 __isl_take isl_ast_node *node,
6080 __isl_keep isl_ast_build *build,
6081 void *user), void *user);
6082 __isl_give isl_ast_build *
6083 isl_ast_build_set_before_each_for(
6084 __isl_take isl_ast_build *build,
6085 __isl_give isl_id *(*fn)(
6086 __isl_keep isl_ast_build *build,
6087 void *user), void *user);
6088 __isl_give isl_ast_build *
6089 isl_ast_build_set_after_each_for(
6090 __isl_take isl_ast_build *build,
6091 __isl_give isl_ast_node *(*fn)(
6092 __isl_take isl_ast_node *node,
6093 __isl_keep isl_ast_build *build,
6094 void *user), void *user);
6096 The callback set by C<isl_ast_build_set_at_each_domain> will
6097 be called for each domain AST node.
6098 The callbacks set by C<isl_ast_build_set_before_each_for>
6099 and C<isl_ast_build_set_after_each_for> will be called
6100 for each for AST node. The first will be called in depth-first
6101 pre-order, while the second will be called in depth-first post-order.
6102 Since C<isl_ast_build_set_before_each_for> is called before the for
6103 node is actually constructed, it is only passed an C<isl_ast_build>.
6104 The returned C<isl_id> will be added as an annotation (using
6105 C<isl_ast_node_set_annotation>) to the constructed for node.
6106 In particular, if the user has also specified an C<after_each_for>
6107 callback, then the annotation can be retrieved from the node passed to
6108 that callback using C<isl_ast_node_get_annotation>.
6109 All callbacks should C<NULL> on failure.
6110 The given C<isl_ast_build> can be used to create new
6111 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6112 or C<isl_ast_build_call_from_pw_multi_aff>.
6114 =head3 Nested AST Generation
6116 C<isl> allows the user to create an AST within the context
6117 of another AST. These nested ASTs are created using the
6118 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6119 outer AST. The C<build> argument should be an C<isl_ast_build>
6120 passed to a callback set by
6121 C<isl_ast_build_set_create_leaf>.
6122 The space of the range of the C<schedule> argument should refer
6123 to this build. In particular, the space should be a wrapped
6124 relation and the domain of this wrapped relation should be the
6125 same as that of the range of the schedule returned by
6126 C<isl_ast_build_get_schedule> below.
6127 In practice, the new schedule is typically
6128 created by calling C<isl_union_map_range_product> on the old schedule
6129 and some extra piece of the schedule.
6130 The space of the schedule domain is also available from
6131 the C<isl_ast_build>.
6133 #include <isl/ast_build.h>
6134 __isl_give isl_union_map *isl_ast_build_get_schedule(
6135 __isl_keep isl_ast_build *build);
6136 __isl_give isl_space *isl_ast_build_get_schedule_space(
6137 __isl_keep isl_ast_build *build);
6138 __isl_give isl_ast_build *isl_ast_build_restrict(
6139 __isl_take isl_ast_build *build,
6140 __isl_take isl_set *set);
6142 The C<isl_ast_build_get_schedule> function returns a (partial)
6143 schedule for the domains elements for which part of the AST still needs to
6144 be generated in the current build.
6145 In particular, the domain elements are mapped to those iterations of the loops
6146 enclosing the current point of the AST generation inside which
6147 the domain elements are executed.
6148 No direct correspondence between
6149 the input schedule and this schedule should be assumed.
6150 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6151 to create a set for C<isl_ast_build_restrict> to intersect
6152 with the current build. In particular, the set passed to
6153 C<isl_ast_build_restrict> can have additional parameters.
6154 The ids of the set dimensions in the space returned by
6155 C<isl_ast_build_get_schedule_space> correspond to the
6156 iterators of the already generated loops.
6157 The user should not rely on the ids of the output dimensions
6158 of the relations in the union relation returned by
6159 C<isl_ast_build_get_schedule> having any particular value.
6163 Although C<isl> is mainly meant to be used as a library,
6164 it also contains some basic applications that use some
6165 of the functionality of C<isl>.
6166 The input may be specified in either the L<isl format>
6167 or the L<PolyLib format>.
6169 =head2 C<isl_polyhedron_sample>
6171 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6172 an integer element of the polyhedron, if there is any.
6173 The first column in the output is the denominator and is always
6174 equal to 1. If the polyhedron contains no integer points,
6175 then a vector of length zero is printed.
6179 C<isl_pip> takes the same input as the C<example> program
6180 from the C<piplib> distribution, i.e., a set of constraints
6181 on the parameters, a line containing only -1 and finally a set
6182 of constraints on a parametric polyhedron.
6183 The coefficients of the parameters appear in the last columns
6184 (but before the final constant column).
6185 The output is the lexicographic minimum of the parametric polyhedron.
6186 As C<isl> currently does not have its own output format, the output
6187 is just a dump of the internal state.
6189 =head2 C<isl_polyhedron_minimize>
6191 C<isl_polyhedron_minimize> computes the minimum of some linear
6192 or affine objective function over the integer points in a polyhedron.
6193 If an affine objective function
6194 is given, then the constant should appear in the last column.
6196 =head2 C<isl_polytope_scan>
6198 Given a polytope, C<isl_polytope_scan> prints
6199 all integer points in the polytope.
6201 =head2 C<isl_codegen>
6203 Given a schedule, a context set and an options relation,
6204 C<isl_codegen> prints out an AST that scans the domain elements
6205 of the schedule in the order of their image(s) taking into account
6206 the constraints in the context set.