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_set *
2339 isl_basic_set_drop_constraints_not_involving_dims(
2340 __isl_take isl_basic_set *bset,
2341 enum isl_dim_type type,
2342 unsigned first, unsigned n);
2343 __isl_give isl_set *
2344 isl_set_drop_constraints_involving_dims(
2345 __isl_take isl_set *set,
2346 enum isl_dim_type type,
2347 unsigned first, unsigned n);
2348 __isl_give isl_map *
2349 isl_map_drop_constraints_involving_dims(
2350 __isl_take isl_map *map,
2351 enum isl_dim_type type,
2352 unsigned first, unsigned n);
2354 These functions drop any constraints (not) involving the specified dimensions.
2355 Note that the result depends on the representation of the input.
2359 __isl_give isl_basic_set *isl_basic_set_sample(
2360 __isl_take isl_basic_set *bset);
2361 __isl_give isl_basic_set *isl_set_sample(
2362 __isl_take isl_set *set);
2363 __isl_give isl_basic_map *isl_basic_map_sample(
2364 __isl_take isl_basic_map *bmap);
2365 __isl_give isl_basic_map *isl_map_sample(
2366 __isl_take isl_map *map);
2368 If the input (basic) set or relation is non-empty, then return
2369 a singleton subset of the input. Otherwise, return an empty set.
2371 =item * Optimization
2373 #include <isl/ilp.h>
2374 enum isl_lp_result isl_basic_set_max(
2375 __isl_keep isl_basic_set *bset,
2376 __isl_keep isl_aff *obj, isl_int *opt)
2377 enum isl_lp_result isl_set_min(__isl_keep isl_set *set,
2378 __isl_keep isl_aff *obj, isl_int *opt);
2379 enum isl_lp_result isl_set_max(__isl_keep isl_set *set,
2380 __isl_keep isl_aff *obj, isl_int *opt);
2382 Compute the minimum or maximum of the integer affine expression C<obj>
2383 over the points in C<set>, returning the result in C<opt>.
2384 The return value may be one of C<isl_lp_error>,
2385 C<isl_lp_ok>, C<isl_lp_unbounded> or C<isl_lp_empty>.
2387 =item * Parametric optimization
2389 __isl_give isl_pw_aff *isl_set_dim_min(
2390 __isl_take isl_set *set, int pos);
2391 __isl_give isl_pw_aff *isl_set_dim_max(
2392 __isl_take isl_set *set, int pos);
2393 __isl_give isl_pw_aff *isl_map_dim_max(
2394 __isl_take isl_map *map, int pos);
2396 Compute the minimum or maximum of the given set or output dimension
2397 as a function of the parameters (and input dimensions), but independently
2398 of the other set or output dimensions.
2399 For lexicographic optimization, see L<"Lexicographic Optimization">.
2403 The following functions compute either the set of (rational) coefficient
2404 values of valid constraints for the given set or the set of (rational)
2405 values satisfying the constraints with coefficients from the given set.
2406 Internally, these two sets of functions perform essentially the
2407 same operations, except that the set of coefficients is assumed to
2408 be a cone, while the set of values may be any polyhedron.
2409 The current implementation is based on the Farkas lemma and
2410 Fourier-Motzkin elimination, but this may change or be made optional
2411 in future. In particular, future implementations may use different
2412 dualization algorithms or skip the elimination step.
2414 __isl_give isl_basic_set *isl_basic_set_coefficients(
2415 __isl_take isl_basic_set *bset);
2416 __isl_give isl_basic_set *isl_set_coefficients(
2417 __isl_take isl_set *set);
2418 __isl_give isl_union_set *isl_union_set_coefficients(
2419 __isl_take isl_union_set *bset);
2420 __isl_give isl_basic_set *isl_basic_set_solutions(
2421 __isl_take isl_basic_set *bset);
2422 __isl_give isl_basic_set *isl_set_solutions(
2423 __isl_take isl_set *set);
2424 __isl_give isl_union_set *isl_union_set_solutions(
2425 __isl_take isl_union_set *bset);
2429 __isl_give isl_map *isl_map_fixed_power(
2430 __isl_take isl_map *map, isl_int exp);
2431 __isl_give isl_union_map *isl_union_map_fixed_power(
2432 __isl_take isl_union_map *umap, isl_int exp);
2434 Compute the given power of C<map>, where C<exp> is assumed to be non-zero.
2435 If the exponent C<exp> is negative, then the -C<exp> th power of the inverse
2436 of C<map> is computed.
2438 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
2440 __isl_give isl_union_map *isl_union_map_power(
2441 __isl_take isl_union_map *umap, int *exact);
2443 Compute a parametric representation for all positive powers I<k> of C<map>.
2444 The result maps I<k> to a nested relation corresponding to the
2445 I<k>th power of C<map>.
2446 The result may be an overapproximation. If the result is known to be exact,
2447 then C<*exact> is set to C<1>.
2449 =item * Transitive closure
2451 __isl_give isl_map *isl_map_transitive_closure(
2452 __isl_take isl_map *map, int *exact);
2453 __isl_give isl_union_map *isl_union_map_transitive_closure(
2454 __isl_take isl_union_map *umap, int *exact);
2456 Compute the transitive closure of C<map>.
2457 The result may be an overapproximation. If the result is known to be exact,
2458 then C<*exact> is set to C<1>.
2460 =item * Reaching path lengths
2462 __isl_give isl_map *isl_map_reaching_path_lengths(
2463 __isl_take isl_map *map, int *exact);
2465 Compute a relation that maps each element in the range of C<map>
2466 to the lengths of all paths composed of edges in C<map> that
2467 end up in the given element.
2468 The result may be an overapproximation. If the result is known to be exact,
2469 then C<*exact> is set to C<1>.
2470 To compute the I<maximal> path length, the resulting relation
2471 should be postprocessed by C<isl_map_lexmax>.
2472 In particular, if the input relation is a dependence relation
2473 (mapping sources to sinks), then the maximal path length corresponds
2474 to the free schedule.
2475 Note, however, that C<isl_map_lexmax> expects the maximum to be
2476 finite, so if the path lengths are unbounded (possibly due to
2477 the overapproximation), then you will get an error message.
2481 __isl_give isl_basic_set *isl_basic_map_wrap(
2482 __isl_take isl_basic_map *bmap);
2483 __isl_give isl_set *isl_map_wrap(
2484 __isl_take isl_map *map);
2485 __isl_give isl_union_set *isl_union_map_wrap(
2486 __isl_take isl_union_map *umap);
2487 __isl_give isl_basic_map *isl_basic_set_unwrap(
2488 __isl_take isl_basic_set *bset);
2489 __isl_give isl_map *isl_set_unwrap(
2490 __isl_take isl_set *set);
2491 __isl_give isl_union_map *isl_union_set_unwrap(
2492 __isl_take isl_union_set *uset);
2496 Remove any internal structure of domain (and range) of the given
2497 set or relation. If there is any such internal structure in the input,
2498 then the name of the space is also removed.
2500 __isl_give isl_basic_set *isl_basic_set_flatten(
2501 __isl_take isl_basic_set *bset);
2502 __isl_give isl_set *isl_set_flatten(
2503 __isl_take isl_set *set);
2504 __isl_give isl_basic_map *isl_basic_map_flatten_domain(
2505 __isl_take isl_basic_map *bmap);
2506 __isl_give isl_basic_map *isl_basic_map_flatten_range(
2507 __isl_take isl_basic_map *bmap);
2508 __isl_give isl_map *isl_map_flatten_range(
2509 __isl_take isl_map *map);
2510 __isl_give isl_map *isl_map_flatten_domain(
2511 __isl_take isl_map *map);
2512 __isl_give isl_basic_map *isl_basic_map_flatten(
2513 __isl_take isl_basic_map *bmap);
2514 __isl_give isl_map *isl_map_flatten(
2515 __isl_take isl_map *map);
2517 __isl_give isl_map *isl_set_flatten_map(
2518 __isl_take isl_set *set);
2520 The function above constructs a relation
2521 that maps the input set to a flattened version of the set.
2525 Lift the input set to a space with extra dimensions corresponding
2526 to the existentially quantified variables in the input.
2527 In particular, the result lives in a wrapped map where the domain
2528 is the original space and the range corresponds to the original
2529 existentially quantified variables.
2531 __isl_give isl_basic_set *isl_basic_set_lift(
2532 __isl_take isl_basic_set *bset);
2533 __isl_give isl_set *isl_set_lift(
2534 __isl_take isl_set *set);
2535 __isl_give isl_union_set *isl_union_set_lift(
2536 __isl_take isl_union_set *uset);
2538 Given a local space that contains the existentially quantified
2539 variables of a set, a basic relation that, when applied to
2540 a basic set, has essentially the same effect as C<isl_basic_set_lift>,
2541 can be constructed using the following function.
2543 #include <isl/local_space.h>
2544 __isl_give isl_basic_map *isl_local_space_lifting(
2545 __isl_take isl_local_space *ls);
2547 =item * Internal Product
2549 __isl_give isl_basic_map *isl_basic_map_zip(
2550 __isl_take isl_basic_map *bmap);
2551 __isl_give isl_map *isl_map_zip(
2552 __isl_take isl_map *map);
2553 __isl_give isl_union_map *isl_union_map_zip(
2554 __isl_take isl_union_map *umap);
2556 Given a relation with nested relations for domain and range,
2557 interchange the range of the domain with the domain of the range.
2561 __isl_give isl_basic_map *isl_basic_map_curry(
2562 __isl_take isl_basic_map *bmap);
2563 __isl_give isl_basic_map *isl_basic_map_uncurry(
2564 __isl_take isl_basic_map *bmap);
2565 __isl_give isl_map *isl_map_curry(
2566 __isl_take isl_map *map);
2567 __isl_give isl_map *isl_map_uncurry(
2568 __isl_take isl_map *map);
2569 __isl_give isl_union_map *isl_union_map_curry(
2570 __isl_take isl_union_map *umap);
2571 __isl_give isl_union_map *isl_union_map_uncurry(
2572 __isl_take isl_union_map *umap);
2574 Given a relation with a nested relation for domain,
2575 the C<curry> functions
2576 move the range of the nested relation out of the domain
2577 and use it as the domain of a nested relation in the range,
2578 with the original range as range of this nested relation.
2579 The C<uncurry> functions perform the inverse operation.
2581 =item * Aligning parameters
2583 __isl_give isl_basic_set *isl_basic_set_align_params(
2584 __isl_take isl_basic_set *bset,
2585 __isl_take isl_space *model);
2586 __isl_give isl_set *isl_set_align_params(
2587 __isl_take isl_set *set,
2588 __isl_take isl_space *model);
2589 __isl_give isl_basic_map *isl_basic_map_align_params(
2590 __isl_take isl_basic_map *bmap,
2591 __isl_take isl_space *model);
2592 __isl_give isl_map *isl_map_align_params(
2593 __isl_take isl_map *map,
2594 __isl_take isl_space *model);
2596 Change the order of the parameters of the given set or relation
2597 such that the first parameters match those of C<model>.
2598 This may involve the introduction of extra parameters.
2599 All parameters need to be named.
2601 =item * Dimension manipulation
2603 __isl_give isl_basic_set *isl_basic_set_add_dims(
2604 __isl_take isl_basic_set *bset,
2605 enum isl_dim_type type, unsigned n);
2606 __isl_give isl_set *isl_set_add_dims(
2607 __isl_take isl_set *set,
2608 enum isl_dim_type type, unsigned n);
2609 __isl_give isl_map *isl_map_add_dims(
2610 __isl_take isl_map *map,
2611 enum isl_dim_type type, unsigned n);
2612 __isl_give isl_basic_set *isl_basic_set_insert_dims(
2613 __isl_take isl_basic_set *bset,
2614 enum isl_dim_type type, unsigned pos,
2616 __isl_give isl_basic_map *isl_basic_map_insert_dims(
2617 __isl_take isl_basic_map *bmap,
2618 enum isl_dim_type type, unsigned pos,
2620 __isl_give isl_set *isl_set_insert_dims(
2621 __isl_take isl_set *set,
2622 enum isl_dim_type type, unsigned pos, unsigned n);
2623 __isl_give isl_map *isl_map_insert_dims(
2624 __isl_take isl_map *map,
2625 enum isl_dim_type type, unsigned pos, unsigned n);
2626 __isl_give isl_basic_set *isl_basic_set_move_dims(
2627 __isl_take isl_basic_set *bset,
2628 enum isl_dim_type dst_type, unsigned dst_pos,
2629 enum isl_dim_type src_type, unsigned src_pos,
2631 __isl_give isl_basic_map *isl_basic_map_move_dims(
2632 __isl_take isl_basic_map *bmap,
2633 enum isl_dim_type dst_type, unsigned dst_pos,
2634 enum isl_dim_type src_type, unsigned src_pos,
2636 __isl_give isl_set *isl_set_move_dims(
2637 __isl_take isl_set *set,
2638 enum isl_dim_type dst_type, unsigned dst_pos,
2639 enum isl_dim_type src_type, unsigned src_pos,
2641 __isl_give isl_map *isl_map_move_dims(
2642 __isl_take isl_map *map,
2643 enum isl_dim_type dst_type, unsigned dst_pos,
2644 enum isl_dim_type src_type, unsigned src_pos,
2647 It is usually not advisable to directly change the (input or output)
2648 space of a set or a relation as this removes the name and the internal
2649 structure of the space. However, the above functions can be useful
2650 to add new parameters, assuming
2651 C<isl_set_align_params> and C<isl_map_align_params>
2656 =head2 Binary Operations
2658 The two arguments of a binary operation not only need to live
2659 in the same C<isl_ctx>, they currently also need to have
2660 the same (number of) parameters.
2662 =head3 Basic Operations
2666 =item * Intersection
2668 __isl_give isl_basic_set *isl_basic_set_intersect_params(
2669 __isl_take isl_basic_set *bset1,
2670 __isl_take isl_basic_set *bset2);
2671 __isl_give isl_basic_set *isl_basic_set_intersect(
2672 __isl_take isl_basic_set *bset1,
2673 __isl_take isl_basic_set *bset2);
2674 __isl_give isl_set *isl_set_intersect_params(
2675 __isl_take isl_set *set,
2676 __isl_take isl_set *params);
2677 __isl_give isl_set *isl_set_intersect(
2678 __isl_take isl_set *set1,
2679 __isl_take isl_set *set2);
2680 __isl_give isl_union_set *isl_union_set_intersect_params(
2681 __isl_take isl_union_set *uset,
2682 __isl_take isl_set *set);
2683 __isl_give isl_union_map *isl_union_map_intersect_params(
2684 __isl_take isl_union_map *umap,
2685 __isl_take isl_set *set);
2686 __isl_give isl_union_set *isl_union_set_intersect(
2687 __isl_take isl_union_set *uset1,
2688 __isl_take isl_union_set *uset2);
2689 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
2690 __isl_take isl_basic_map *bmap,
2691 __isl_take isl_basic_set *bset);
2692 __isl_give isl_basic_map *isl_basic_map_intersect_range(
2693 __isl_take isl_basic_map *bmap,
2694 __isl_take isl_basic_set *bset);
2695 __isl_give isl_basic_map *isl_basic_map_intersect(
2696 __isl_take isl_basic_map *bmap1,
2697 __isl_take isl_basic_map *bmap2);
2698 __isl_give isl_map *isl_map_intersect_params(
2699 __isl_take isl_map *map,
2700 __isl_take isl_set *params);
2701 __isl_give isl_map *isl_map_intersect_domain(
2702 __isl_take isl_map *map,
2703 __isl_take isl_set *set);
2704 __isl_give isl_map *isl_map_intersect_range(
2705 __isl_take isl_map *map,
2706 __isl_take isl_set *set);
2707 __isl_give isl_map *isl_map_intersect(
2708 __isl_take isl_map *map1,
2709 __isl_take isl_map *map2);
2710 __isl_give isl_union_map *isl_union_map_intersect_domain(
2711 __isl_take isl_union_map *umap,
2712 __isl_take isl_union_set *uset);
2713 __isl_give isl_union_map *isl_union_map_intersect_range(
2714 __isl_take isl_union_map *umap,
2715 __isl_take isl_union_set *uset);
2716 __isl_give isl_union_map *isl_union_map_intersect(
2717 __isl_take isl_union_map *umap1,
2718 __isl_take isl_union_map *umap2);
2720 The second argument to the C<_params> functions needs to be
2721 a parametric (basic) set. For the other functions, a parametric set
2722 for either argument is only allowed if the other argument is
2723 a parametric set as well.
2727 __isl_give isl_set *isl_basic_set_union(
2728 __isl_take isl_basic_set *bset1,
2729 __isl_take isl_basic_set *bset2);
2730 __isl_give isl_map *isl_basic_map_union(
2731 __isl_take isl_basic_map *bmap1,
2732 __isl_take isl_basic_map *bmap2);
2733 __isl_give isl_set *isl_set_union(
2734 __isl_take isl_set *set1,
2735 __isl_take isl_set *set2);
2736 __isl_give isl_map *isl_map_union(
2737 __isl_take isl_map *map1,
2738 __isl_take isl_map *map2);
2739 __isl_give isl_union_set *isl_union_set_union(
2740 __isl_take isl_union_set *uset1,
2741 __isl_take isl_union_set *uset2);
2742 __isl_give isl_union_map *isl_union_map_union(
2743 __isl_take isl_union_map *umap1,
2744 __isl_take isl_union_map *umap2);
2746 =item * Set difference
2748 __isl_give isl_set *isl_set_subtract(
2749 __isl_take isl_set *set1,
2750 __isl_take isl_set *set2);
2751 __isl_give isl_map *isl_map_subtract(
2752 __isl_take isl_map *map1,
2753 __isl_take isl_map *map2);
2754 __isl_give isl_map *isl_map_subtract_domain(
2755 __isl_take isl_map *map,
2756 __isl_take isl_set *dom);
2757 __isl_give isl_map *isl_map_subtract_range(
2758 __isl_take isl_map *map,
2759 __isl_take isl_set *dom);
2760 __isl_give isl_union_set *isl_union_set_subtract(
2761 __isl_take isl_union_set *uset1,
2762 __isl_take isl_union_set *uset2);
2763 __isl_give isl_union_map *isl_union_map_subtract(
2764 __isl_take isl_union_map *umap1,
2765 __isl_take isl_union_map *umap2);
2766 __isl_give isl_union_map *isl_union_map_subtract_domain(
2767 __isl_take isl_union_map *umap,
2768 __isl_take isl_union_set *dom);
2769 __isl_give isl_union_map *isl_union_map_subtract_range(
2770 __isl_take isl_union_map *umap,
2771 __isl_take isl_union_set *dom);
2775 __isl_give isl_basic_set *isl_basic_set_apply(
2776 __isl_take isl_basic_set *bset,
2777 __isl_take isl_basic_map *bmap);
2778 __isl_give isl_set *isl_set_apply(
2779 __isl_take isl_set *set,
2780 __isl_take isl_map *map);
2781 __isl_give isl_union_set *isl_union_set_apply(
2782 __isl_take isl_union_set *uset,
2783 __isl_take isl_union_map *umap);
2784 __isl_give isl_basic_map *isl_basic_map_apply_domain(
2785 __isl_take isl_basic_map *bmap1,
2786 __isl_take isl_basic_map *bmap2);
2787 __isl_give isl_basic_map *isl_basic_map_apply_range(
2788 __isl_take isl_basic_map *bmap1,
2789 __isl_take isl_basic_map *bmap2);
2790 __isl_give isl_map *isl_map_apply_domain(
2791 __isl_take isl_map *map1,
2792 __isl_take isl_map *map2);
2793 __isl_give isl_union_map *isl_union_map_apply_domain(
2794 __isl_take isl_union_map *umap1,
2795 __isl_take isl_union_map *umap2);
2796 __isl_give isl_map *isl_map_apply_range(
2797 __isl_take isl_map *map1,
2798 __isl_take isl_map *map2);
2799 __isl_give isl_union_map *isl_union_map_apply_range(
2800 __isl_take isl_union_map *umap1,
2801 __isl_take isl_union_map *umap2);
2805 __isl_give isl_basic_set *
2806 isl_basic_set_preimage_multi_aff(
2807 __isl_take isl_basic_set *bset,
2808 __isl_take isl_multi_aff *ma);
2809 __isl_give isl_set *isl_set_preimage_multi_aff(
2810 __isl_take isl_set *set,
2811 __isl_take isl_multi_aff *ma);
2812 __isl_give isl_set *isl_set_preimage_pw_multi_aff(
2813 __isl_take isl_set *set,
2814 __isl_take isl_pw_multi_aff *pma);
2816 These functions compute the preimage of the given set under
2817 the given function. In other words, the expression is plugged
2818 into the set description.
2819 Objects of types C<isl_multi_aff> and C<isl_pw_multi_aff> are described in
2820 L</"Piecewise Multiple Quasi Affine Expressions">.
2822 =item * Cartesian Product
2824 __isl_give isl_set *isl_set_product(
2825 __isl_take isl_set *set1,
2826 __isl_take isl_set *set2);
2827 __isl_give isl_union_set *isl_union_set_product(
2828 __isl_take isl_union_set *uset1,
2829 __isl_take isl_union_set *uset2);
2830 __isl_give isl_basic_map *isl_basic_map_domain_product(
2831 __isl_take isl_basic_map *bmap1,
2832 __isl_take isl_basic_map *bmap2);
2833 __isl_give isl_basic_map *isl_basic_map_range_product(
2834 __isl_take isl_basic_map *bmap1,
2835 __isl_take isl_basic_map *bmap2);
2836 __isl_give isl_basic_map *isl_basic_map_product(
2837 __isl_take isl_basic_map *bmap1,
2838 __isl_take isl_basic_map *bmap2);
2839 __isl_give isl_map *isl_map_domain_product(
2840 __isl_take isl_map *map1,
2841 __isl_take isl_map *map2);
2842 __isl_give isl_map *isl_map_range_product(
2843 __isl_take isl_map *map1,
2844 __isl_take isl_map *map2);
2845 __isl_give isl_union_map *isl_union_map_domain_product(
2846 __isl_take isl_union_map *umap1,
2847 __isl_take isl_union_map *umap2);
2848 __isl_give isl_union_map *isl_union_map_range_product(
2849 __isl_take isl_union_map *umap1,
2850 __isl_take isl_union_map *umap2);
2851 __isl_give isl_map *isl_map_product(
2852 __isl_take isl_map *map1,
2853 __isl_take isl_map *map2);
2854 __isl_give isl_union_map *isl_union_map_product(
2855 __isl_take isl_union_map *umap1,
2856 __isl_take isl_union_map *umap2);
2858 The above functions compute the cross product of the given
2859 sets or relations. The domains and ranges of the results
2860 are wrapped maps between domains and ranges of the inputs.
2861 To obtain a ``flat'' product, use the following functions
2864 __isl_give isl_basic_set *isl_basic_set_flat_product(
2865 __isl_take isl_basic_set *bset1,
2866 __isl_take isl_basic_set *bset2);
2867 __isl_give isl_set *isl_set_flat_product(
2868 __isl_take isl_set *set1,
2869 __isl_take isl_set *set2);
2870 __isl_give isl_basic_map *isl_basic_map_flat_range_product(
2871 __isl_take isl_basic_map *bmap1,
2872 __isl_take isl_basic_map *bmap2);
2873 __isl_give isl_map *isl_map_flat_domain_product(
2874 __isl_take isl_map *map1,
2875 __isl_take isl_map *map2);
2876 __isl_give isl_map *isl_map_flat_range_product(
2877 __isl_take isl_map *map1,
2878 __isl_take isl_map *map2);
2879 __isl_give isl_union_map *isl_union_map_flat_range_product(
2880 __isl_take isl_union_map *umap1,
2881 __isl_take isl_union_map *umap2);
2882 __isl_give isl_basic_map *isl_basic_map_flat_product(
2883 __isl_take isl_basic_map *bmap1,
2884 __isl_take isl_basic_map *bmap2);
2885 __isl_give isl_map *isl_map_flat_product(
2886 __isl_take isl_map *map1,
2887 __isl_take isl_map *map2);
2889 =item * Simplification
2891 __isl_give isl_basic_set *isl_basic_set_gist(
2892 __isl_take isl_basic_set *bset,
2893 __isl_take isl_basic_set *context);
2894 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
2895 __isl_take isl_set *context);
2896 __isl_give isl_set *isl_set_gist_params(
2897 __isl_take isl_set *set,
2898 __isl_take isl_set *context);
2899 __isl_give isl_union_set *isl_union_set_gist(
2900 __isl_take isl_union_set *uset,
2901 __isl_take isl_union_set *context);
2902 __isl_give isl_union_set *isl_union_set_gist_params(
2903 __isl_take isl_union_set *uset,
2904 __isl_take isl_set *set);
2905 __isl_give isl_basic_map *isl_basic_map_gist(
2906 __isl_take isl_basic_map *bmap,
2907 __isl_take isl_basic_map *context);
2908 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
2909 __isl_take isl_map *context);
2910 __isl_give isl_map *isl_map_gist_params(
2911 __isl_take isl_map *map,
2912 __isl_take isl_set *context);
2913 __isl_give isl_map *isl_map_gist_domain(
2914 __isl_take isl_map *map,
2915 __isl_take isl_set *context);
2916 __isl_give isl_map *isl_map_gist_range(
2917 __isl_take isl_map *map,
2918 __isl_take isl_set *context);
2919 __isl_give isl_union_map *isl_union_map_gist(
2920 __isl_take isl_union_map *umap,
2921 __isl_take isl_union_map *context);
2922 __isl_give isl_union_map *isl_union_map_gist_params(
2923 __isl_take isl_union_map *umap,
2924 __isl_take isl_set *set);
2925 __isl_give isl_union_map *isl_union_map_gist_domain(
2926 __isl_take isl_union_map *umap,
2927 __isl_take isl_union_set *uset);
2928 __isl_give isl_union_map *isl_union_map_gist_range(
2929 __isl_take isl_union_map *umap,
2930 __isl_take isl_union_set *uset);
2932 The gist operation returns a set or relation that has the
2933 same intersection with the context as the input set or relation.
2934 Any implicit equality in the intersection is made explicit in the result,
2935 while all inequalities that are redundant with respect to the intersection
2937 In case of union sets and relations, the gist operation is performed
2942 =head3 Lexicographic Optimization
2944 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
2945 the following functions
2946 compute a set that contains the lexicographic minimum or maximum
2947 of the elements in C<set> (or C<bset>) for those values of the parameters
2948 that satisfy C<dom>.
2949 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2950 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
2952 In other words, the union of the parameter values
2953 for which the result is non-empty and of C<*empty>
2956 __isl_give isl_set *isl_basic_set_partial_lexmin(
2957 __isl_take isl_basic_set *bset,
2958 __isl_take isl_basic_set *dom,
2959 __isl_give isl_set **empty);
2960 __isl_give isl_set *isl_basic_set_partial_lexmax(
2961 __isl_take isl_basic_set *bset,
2962 __isl_take isl_basic_set *dom,
2963 __isl_give isl_set **empty);
2964 __isl_give isl_set *isl_set_partial_lexmin(
2965 __isl_take isl_set *set, __isl_take isl_set *dom,
2966 __isl_give isl_set **empty);
2967 __isl_give isl_set *isl_set_partial_lexmax(
2968 __isl_take isl_set *set, __isl_take isl_set *dom,
2969 __isl_give isl_set **empty);
2971 Given a (basic) set C<set> (or C<bset>), the following functions simply
2972 return a set containing the lexicographic minimum or maximum
2973 of the elements in C<set> (or C<bset>).
2974 In case of union sets, the optimum is computed per space.
2976 __isl_give isl_set *isl_basic_set_lexmin(
2977 __isl_take isl_basic_set *bset);
2978 __isl_give isl_set *isl_basic_set_lexmax(
2979 __isl_take isl_basic_set *bset);
2980 __isl_give isl_set *isl_set_lexmin(
2981 __isl_take isl_set *set);
2982 __isl_give isl_set *isl_set_lexmax(
2983 __isl_take isl_set *set);
2984 __isl_give isl_union_set *isl_union_set_lexmin(
2985 __isl_take isl_union_set *uset);
2986 __isl_give isl_union_set *isl_union_set_lexmax(
2987 __isl_take isl_union_set *uset);
2989 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
2990 the following functions
2991 compute a relation that maps each element of C<dom>
2992 to the single lexicographic minimum or maximum
2993 of the elements that are associated to that same
2994 element in C<map> (or C<bmap>).
2995 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
2996 that contains the elements in C<dom> that do not map
2997 to any elements in C<map> (or C<bmap>).
2998 In other words, the union of the domain of the result and of C<*empty>
3001 __isl_give isl_map *isl_basic_map_partial_lexmax(
3002 __isl_take isl_basic_map *bmap,
3003 __isl_take isl_basic_set *dom,
3004 __isl_give isl_set **empty);
3005 __isl_give isl_map *isl_basic_map_partial_lexmin(
3006 __isl_take isl_basic_map *bmap,
3007 __isl_take isl_basic_set *dom,
3008 __isl_give isl_set **empty);
3009 __isl_give isl_map *isl_map_partial_lexmax(
3010 __isl_take isl_map *map, __isl_take isl_set *dom,
3011 __isl_give isl_set **empty);
3012 __isl_give isl_map *isl_map_partial_lexmin(
3013 __isl_take isl_map *map, __isl_take isl_set *dom,
3014 __isl_give isl_set **empty);
3016 Given a (basic) map C<map> (or C<bmap>), the following functions simply
3017 return a map mapping each element in the domain of
3018 C<map> (or C<bmap>) to the lexicographic minimum or maximum
3019 of all elements associated to that element.
3020 In case of union relations, the optimum is computed per space.
3022 __isl_give isl_map *isl_basic_map_lexmin(
3023 __isl_take isl_basic_map *bmap);
3024 __isl_give isl_map *isl_basic_map_lexmax(
3025 __isl_take isl_basic_map *bmap);
3026 __isl_give isl_map *isl_map_lexmin(
3027 __isl_take isl_map *map);
3028 __isl_give isl_map *isl_map_lexmax(
3029 __isl_take isl_map *map);
3030 __isl_give isl_union_map *isl_union_map_lexmin(
3031 __isl_take isl_union_map *umap);
3032 __isl_give isl_union_map *isl_union_map_lexmax(
3033 __isl_take isl_union_map *umap);
3035 The following functions return their result in the form of
3036 a piecewise multi-affine expression
3037 (See L<"Piecewise Multiple Quasi Affine Expressions">),
3038 but are otherwise equivalent to the corresponding functions
3039 returning a basic set or relation.
3041 __isl_give isl_pw_multi_aff *
3042 isl_basic_map_lexmin_pw_multi_aff(
3043 __isl_take isl_basic_map *bmap);
3044 __isl_give isl_pw_multi_aff *
3045 isl_basic_set_partial_lexmin_pw_multi_aff(
3046 __isl_take isl_basic_set *bset,
3047 __isl_take isl_basic_set *dom,
3048 __isl_give isl_set **empty);
3049 __isl_give isl_pw_multi_aff *
3050 isl_basic_set_partial_lexmax_pw_multi_aff(
3051 __isl_take isl_basic_set *bset,
3052 __isl_take isl_basic_set *dom,
3053 __isl_give isl_set **empty);
3054 __isl_give isl_pw_multi_aff *
3055 isl_basic_map_partial_lexmin_pw_multi_aff(
3056 __isl_take isl_basic_map *bmap,
3057 __isl_take isl_basic_set *dom,
3058 __isl_give isl_set **empty);
3059 __isl_give isl_pw_multi_aff *
3060 isl_basic_map_partial_lexmax_pw_multi_aff(
3061 __isl_take isl_basic_map *bmap,
3062 __isl_take isl_basic_set *dom,
3063 __isl_give isl_set **empty);
3064 __isl_give isl_pw_multi_aff *isl_map_lexmin_pw_multi_aff(
3065 __isl_take isl_map *map);
3066 __isl_give isl_pw_multi_aff *isl_map_lexmax_pw_multi_aff(
3067 __isl_take isl_map *map);
3071 Lists are defined over several element types, including
3072 C<isl_id>, C<isl_aff>, C<isl_pw_aff>, C<isl_constraint>,
3073 C<isl_basic_set>, C<isl_set>, C<isl_ast_expr> and C<isl_ast_node>.
3074 Here we take lists of C<isl_set>s as an example.
3075 Lists can be created, copied, modified and freed using the following functions.
3077 #include <isl/list.h>
3078 __isl_give isl_set_list *isl_set_list_from_set(
3079 __isl_take isl_set *el);
3080 __isl_give isl_set_list *isl_set_list_alloc(
3081 isl_ctx *ctx, int n);
3082 __isl_give isl_set_list *isl_set_list_copy(
3083 __isl_keep isl_set_list *list);
3084 __isl_give isl_set_list *isl_set_list_insert(
3085 __isl_take isl_set_list *list, unsigned pos,
3086 __isl_take isl_set *el);
3087 __isl_give isl_set_list *isl_set_list_add(
3088 __isl_take isl_set_list *list,
3089 __isl_take isl_set *el);
3090 __isl_give isl_set_list *isl_set_list_drop(
3091 __isl_take isl_set_list *list,
3092 unsigned first, unsigned n);
3093 __isl_give isl_set_list *isl_set_list_set_set(
3094 __isl_take isl_set_list *list, int index,
3095 __isl_take isl_set *set);
3096 __isl_give isl_set_list *isl_set_list_concat(
3097 __isl_take isl_set_list *list1,
3098 __isl_take isl_set_list *list2);
3099 void *isl_set_list_free(__isl_take isl_set_list *list);
3101 C<isl_set_list_alloc> creates an empty list with a capacity for
3102 C<n> elements. C<isl_set_list_from_set> creates a list with a single
3105 Lists can be inspected using the following functions.
3107 #include <isl/list.h>
3108 isl_ctx *isl_set_list_get_ctx(__isl_keep isl_set_list *list);
3109 int isl_set_list_n_set(__isl_keep isl_set_list *list);
3110 __isl_give isl_set *isl_set_list_get_set(
3111 __isl_keep isl_set_list *list, int index);
3112 int isl_set_list_foreach(__isl_keep isl_set_list *list,
3113 int (*fn)(__isl_take isl_set *el, void *user),
3116 Lists can be printed using
3118 #include <isl/list.h>
3119 __isl_give isl_printer *isl_printer_print_set_list(
3120 __isl_take isl_printer *p,
3121 __isl_keep isl_set_list *list);
3125 Vectors can be created, copied and freed using the following functions.
3127 #include <isl/vec.h>
3128 __isl_give isl_vec *isl_vec_alloc(isl_ctx *ctx,
3130 __isl_give isl_vec *isl_vec_copy(__isl_keep isl_vec *vec);
3131 void *isl_vec_free(__isl_take isl_vec *vec);
3133 Note that the elements of a newly created vector may have arbitrary values.
3134 The elements can be changed and inspected using the following functions.
3136 isl_ctx *isl_vec_get_ctx(__isl_keep isl_vec *vec);
3137 int isl_vec_size(__isl_keep isl_vec *vec);
3138 int isl_vec_get_element(__isl_keep isl_vec *vec,
3139 int pos, isl_int *v);
3140 __isl_give isl_vec *isl_vec_set_element(
3141 __isl_take isl_vec *vec, int pos, isl_int v);
3142 __isl_give isl_vec *isl_vec_set_element_si(
3143 __isl_take isl_vec *vec, int pos, int v);
3144 __isl_give isl_vec *isl_vec_set(__isl_take isl_vec *vec,
3146 __isl_give isl_vec *isl_vec_set_si(__isl_take isl_vec *vec,
3148 __isl_give isl_vec *isl_vec_fdiv_r(__isl_take isl_vec *vec,
3151 C<isl_vec_get_element> will return a negative value if anything went wrong.
3152 In that case, the value of C<*v> is undefined.
3154 The following function can be used to concatenate two vectors.
3156 __isl_give isl_vec *isl_vec_concat(__isl_take isl_vec *vec1,
3157 __isl_take isl_vec *vec2);
3161 Matrices can be created, copied and freed using the following functions.
3163 #include <isl/mat.h>
3164 __isl_give isl_mat *isl_mat_alloc(isl_ctx *ctx,
3165 unsigned n_row, unsigned n_col);
3166 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
3167 void isl_mat_free(__isl_take isl_mat *mat);
3169 Note that the elements of a newly created matrix may have arbitrary values.
3170 The elements can be changed and inspected using the following functions.
3172 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
3173 int isl_mat_rows(__isl_keep isl_mat *mat);
3174 int isl_mat_cols(__isl_keep isl_mat *mat);
3175 int isl_mat_get_element(__isl_keep isl_mat *mat,
3176 int row, int col, isl_int *v);
3177 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
3178 int row, int col, isl_int v);
3179 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
3180 int row, int col, int v);
3182 C<isl_mat_get_element> will return a negative value if anything went wrong.
3183 In that case, the value of C<*v> is undefined.
3185 The following function can be used to compute the (right) inverse
3186 of a matrix, i.e., a matrix such that the product of the original
3187 and the inverse (in that order) is a multiple of the identity matrix.
3188 The input matrix is assumed to be of full row-rank.
3190 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
3192 The following function can be used to compute the (right) kernel
3193 (or null space) of a matrix, i.e., a matrix such that the product of
3194 the original and the kernel (in that order) is the zero matrix.
3196 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
3198 =head2 Piecewise Quasi Affine Expressions
3200 The zero quasi affine expression or the quasi affine expression
3201 that is equal to a specified dimension on a given domain can be created using
3203 __isl_give isl_aff *isl_aff_zero_on_domain(
3204 __isl_take isl_local_space *ls);
3205 __isl_give isl_pw_aff *isl_pw_aff_zero_on_domain(
3206 __isl_take isl_local_space *ls);
3207 __isl_give isl_aff *isl_aff_var_on_domain(
3208 __isl_take isl_local_space *ls,
3209 enum isl_dim_type type, unsigned pos);
3210 __isl_give isl_pw_aff *isl_pw_aff_var_on_domain(
3211 __isl_take isl_local_space *ls,
3212 enum isl_dim_type type, unsigned pos);
3214 Note that the space in which the resulting objects live is a map space
3215 with the given space as domain and a one-dimensional range.
3217 An empty piecewise quasi affine expression (one with no cells)
3218 or a piecewise quasi affine expression with a single cell can
3219 be created using the following functions.
3221 #include <isl/aff.h>
3222 __isl_give isl_pw_aff *isl_pw_aff_empty(
3223 __isl_take isl_space *space);
3224 __isl_give isl_pw_aff *isl_pw_aff_alloc(
3225 __isl_take isl_set *set, __isl_take isl_aff *aff);
3226 __isl_give isl_pw_aff *isl_pw_aff_from_aff(
3227 __isl_take isl_aff *aff);
3229 A piecewise quasi affine expression that is equal to 1 on a set
3230 and 0 outside the set can be created using the following function.
3232 #include <isl/aff.h>
3233 __isl_give isl_pw_aff *isl_set_indicator_function(
3234 __isl_take isl_set *set);
3236 Quasi affine expressions can be copied and freed using
3238 #include <isl/aff.h>
3239 __isl_give isl_aff *isl_aff_copy(__isl_keep isl_aff *aff);
3240 void *isl_aff_free(__isl_take isl_aff *aff);
3242 __isl_give isl_pw_aff *isl_pw_aff_copy(
3243 __isl_keep isl_pw_aff *pwaff);
3244 void *isl_pw_aff_free(__isl_take isl_pw_aff *pwaff);
3246 A (rational) bound on a dimension can be extracted from an C<isl_constraint>
3247 using the following function. The constraint is required to have
3248 a non-zero coefficient for the specified dimension.
3250 #include <isl/constraint.h>
3251 __isl_give isl_aff *isl_constraint_get_bound(
3252 __isl_keep isl_constraint *constraint,
3253 enum isl_dim_type type, int pos);
3255 The entire affine expression of the constraint can also be extracted
3256 using the following function.
3258 #include <isl/constraint.h>
3259 __isl_give isl_aff *isl_constraint_get_aff(
3260 __isl_keep isl_constraint *constraint);
3262 Conversely, an equality constraint equating
3263 the affine expression to zero or an inequality constraint enforcing
3264 the affine expression to be non-negative, can be constructed using
3266 __isl_give isl_constraint *isl_equality_from_aff(
3267 __isl_take isl_aff *aff);
3268 __isl_give isl_constraint *isl_inequality_from_aff(
3269 __isl_take isl_aff *aff);
3271 The expression can be inspected using
3273 #include <isl/aff.h>
3274 isl_ctx *isl_aff_get_ctx(__isl_keep isl_aff *aff);
3275 int isl_aff_dim(__isl_keep isl_aff *aff,
3276 enum isl_dim_type type);
3277 __isl_give isl_local_space *isl_aff_get_domain_local_space(
3278 __isl_keep isl_aff *aff);
3279 __isl_give isl_local_space *isl_aff_get_local_space(
3280 __isl_keep isl_aff *aff);
3281 const char *isl_aff_get_dim_name(__isl_keep isl_aff *aff,
3282 enum isl_dim_type type, unsigned pos);
3283 const char *isl_pw_aff_get_dim_name(
3284 __isl_keep isl_pw_aff *pa,
3285 enum isl_dim_type type, unsigned pos);
3286 int isl_pw_aff_has_dim_id(__isl_keep isl_pw_aff *pa,
3287 enum isl_dim_type type, unsigned pos);
3288 __isl_give isl_id *isl_pw_aff_get_dim_id(
3289 __isl_keep isl_pw_aff *pa,
3290 enum isl_dim_type type, unsigned pos);
3291 __isl_give isl_id *isl_pw_aff_get_tuple_id(
3292 __isl_keep isl_pw_aff *pa,
3293 enum isl_dim_type type);
3294 int isl_aff_get_constant(__isl_keep isl_aff *aff,
3296 int isl_aff_get_coefficient(__isl_keep isl_aff *aff,
3297 enum isl_dim_type type, int pos, isl_int *v);
3298 int isl_aff_get_denominator(__isl_keep isl_aff *aff,
3300 __isl_give isl_aff *isl_aff_get_div(
3301 __isl_keep isl_aff *aff, int pos);
3303 int isl_pw_aff_n_piece(__isl_keep isl_pw_aff *pwaff);
3304 int isl_pw_aff_foreach_piece(__isl_keep isl_pw_aff *pwaff,
3305 int (*fn)(__isl_take isl_set *set,
3306 __isl_take isl_aff *aff,
3307 void *user), void *user);
3309 int isl_aff_is_cst(__isl_keep isl_aff *aff);
3310 int isl_pw_aff_is_cst(__isl_keep isl_pw_aff *pwaff);
3312 int isl_aff_involves_dims(__isl_keep isl_aff *aff,
3313 enum isl_dim_type type, unsigned first, unsigned n);
3314 int isl_pw_aff_involves_dims(__isl_keep isl_pw_aff *pwaff,
3315 enum isl_dim_type type, unsigned first, unsigned n);
3317 isl_ctx *isl_pw_aff_get_ctx(__isl_keep isl_pw_aff *pwaff);
3318 unsigned isl_pw_aff_dim(__isl_keep isl_pw_aff *pwaff,
3319 enum isl_dim_type type);
3320 int isl_pw_aff_is_empty(__isl_keep isl_pw_aff *pwaff);
3322 It can be modified using
3324 #include <isl/aff.h>
3325 __isl_give isl_pw_aff *isl_pw_aff_set_tuple_id(
3326 __isl_take isl_pw_aff *pwaff,
3327 enum isl_dim_type type, __isl_take isl_id *id);
3328 __isl_give isl_aff *isl_aff_set_dim_name(
3329 __isl_take isl_aff *aff, enum isl_dim_type type,
3330 unsigned pos, const char *s);
3331 __isl_give isl_aff *isl_aff_set_dim_id(
3332 __isl_take isl_aff *aff, enum isl_dim_type type,
3333 unsigned pos, __isl_take isl_id *id);
3334 __isl_give isl_pw_aff *isl_pw_aff_set_dim_id(
3335 __isl_take isl_pw_aff *pma,
3336 enum isl_dim_type type, unsigned pos,
3337 __isl_take isl_id *id);
3338 __isl_give isl_aff *isl_aff_set_constant(
3339 __isl_take isl_aff *aff, isl_int v);
3340 __isl_give isl_aff *isl_aff_set_constant_si(
3341 __isl_take isl_aff *aff, int v);
3342 __isl_give isl_aff *isl_aff_set_coefficient(
3343 __isl_take isl_aff *aff,
3344 enum isl_dim_type type, int pos, isl_int v);
3345 __isl_give isl_aff *isl_aff_set_coefficient_si(
3346 __isl_take isl_aff *aff,
3347 enum isl_dim_type type, int pos, int v);
3348 __isl_give isl_aff *isl_aff_set_denominator(
3349 __isl_take isl_aff *aff, isl_int v);
3351 __isl_give isl_aff *isl_aff_add_constant(
3352 __isl_take isl_aff *aff, isl_int v);
3353 __isl_give isl_aff *isl_aff_add_constant_si(
3354 __isl_take isl_aff *aff, int v);
3355 __isl_give isl_aff *isl_aff_add_constant_num(
3356 __isl_take isl_aff *aff, isl_int v);
3357 __isl_give isl_aff *isl_aff_add_constant_num_si(
3358 __isl_take isl_aff *aff, int v);
3359 __isl_give isl_aff *isl_aff_add_coefficient(
3360 __isl_take isl_aff *aff,
3361 enum isl_dim_type type, int pos, isl_int v);
3362 __isl_give isl_aff *isl_aff_add_coefficient_si(
3363 __isl_take isl_aff *aff,
3364 enum isl_dim_type type, int pos, int v);
3366 __isl_give isl_aff *isl_aff_insert_dims(
3367 __isl_take isl_aff *aff,
3368 enum isl_dim_type type, unsigned first, unsigned n);
3369 __isl_give isl_pw_aff *isl_pw_aff_insert_dims(
3370 __isl_take isl_pw_aff *pwaff,
3371 enum isl_dim_type type, unsigned first, unsigned n);
3372 __isl_give isl_aff *isl_aff_add_dims(
3373 __isl_take isl_aff *aff,
3374 enum isl_dim_type type, unsigned n);
3375 __isl_give isl_pw_aff *isl_pw_aff_add_dims(
3376 __isl_take isl_pw_aff *pwaff,
3377 enum isl_dim_type type, unsigned n);
3378 __isl_give isl_aff *isl_aff_drop_dims(
3379 __isl_take isl_aff *aff,
3380 enum isl_dim_type type, unsigned first, unsigned n);
3381 __isl_give isl_pw_aff *isl_pw_aff_drop_dims(
3382 __isl_take isl_pw_aff *pwaff,
3383 enum isl_dim_type type, unsigned first, unsigned n);
3385 Note that the C<set_constant> and C<set_coefficient> functions
3386 set the I<numerator> of the constant or coefficient, while
3387 C<add_constant> and C<add_coefficient> add an integer value to
3388 the possibly rational constant or coefficient.
3389 The C<add_constant_num> functions add an integer value to
3392 To check whether an affine expressions is obviously zero
3393 or obviously equal to some other affine expression, use
3395 #include <isl/aff.h>
3396 int isl_aff_plain_is_zero(__isl_keep isl_aff *aff);
3397 int isl_aff_plain_is_equal(__isl_keep isl_aff *aff1,
3398 __isl_keep isl_aff *aff2);
3399 int isl_pw_aff_plain_is_equal(
3400 __isl_keep isl_pw_aff *pwaff1,
3401 __isl_keep isl_pw_aff *pwaff2);
3405 #include <isl/aff.h>
3406 __isl_give isl_aff *isl_aff_add(__isl_take isl_aff *aff1,
3407 __isl_take isl_aff *aff2);
3408 __isl_give isl_pw_aff *isl_pw_aff_add(
3409 __isl_take isl_pw_aff *pwaff1,
3410 __isl_take isl_pw_aff *pwaff2);
3411 __isl_give isl_pw_aff *isl_pw_aff_min(
3412 __isl_take isl_pw_aff *pwaff1,
3413 __isl_take isl_pw_aff *pwaff2);
3414 __isl_give isl_pw_aff *isl_pw_aff_max(
3415 __isl_take isl_pw_aff *pwaff1,
3416 __isl_take isl_pw_aff *pwaff2);
3417 __isl_give isl_aff *isl_aff_sub(__isl_take isl_aff *aff1,
3418 __isl_take isl_aff *aff2);
3419 __isl_give isl_pw_aff *isl_pw_aff_sub(
3420 __isl_take isl_pw_aff *pwaff1,
3421 __isl_take isl_pw_aff *pwaff2);
3422 __isl_give isl_aff *isl_aff_neg(__isl_take isl_aff *aff);
3423 __isl_give isl_pw_aff *isl_pw_aff_neg(
3424 __isl_take isl_pw_aff *pwaff);
3425 __isl_give isl_aff *isl_aff_ceil(__isl_take isl_aff *aff);
3426 __isl_give isl_pw_aff *isl_pw_aff_ceil(
3427 __isl_take isl_pw_aff *pwaff);
3428 __isl_give isl_aff *isl_aff_floor(__isl_take isl_aff *aff);
3429 __isl_give isl_pw_aff *isl_pw_aff_floor(
3430 __isl_take isl_pw_aff *pwaff);
3431 __isl_give isl_aff *isl_aff_mod(__isl_take isl_aff *aff,
3433 __isl_give isl_pw_aff *isl_pw_aff_mod(
3434 __isl_take isl_pw_aff *pwaff, isl_int mod);
3435 __isl_give isl_aff *isl_aff_scale(__isl_take isl_aff *aff,
3437 __isl_give isl_pw_aff *isl_pw_aff_scale(
3438 __isl_take isl_pw_aff *pwaff, isl_int f);
3439 __isl_give isl_aff *isl_aff_scale_down(__isl_take isl_aff *aff,
3441 __isl_give isl_aff *isl_aff_scale_down_ui(
3442 __isl_take isl_aff *aff, unsigned f);
3443 __isl_give isl_pw_aff *isl_pw_aff_scale_down(
3444 __isl_take isl_pw_aff *pwaff, isl_int f);
3446 __isl_give isl_pw_aff *isl_pw_aff_list_min(
3447 __isl_take isl_pw_aff_list *list);
3448 __isl_give isl_pw_aff *isl_pw_aff_list_max(
3449 __isl_take isl_pw_aff_list *list);
3451 __isl_give isl_pw_aff *isl_pw_aff_coalesce(
3452 __isl_take isl_pw_aff *pwqp);
3454 __isl_give isl_aff *isl_aff_align_params(
3455 __isl_take isl_aff *aff,
3456 __isl_take isl_space *model);
3457 __isl_give isl_pw_aff *isl_pw_aff_align_params(
3458 __isl_take isl_pw_aff *pwaff,
3459 __isl_take isl_space *model);
3461 __isl_give isl_aff *isl_aff_project_domain_on_params(
3462 __isl_take isl_aff *aff);
3464 __isl_give isl_aff *isl_aff_gist_params(
3465 __isl_take isl_aff *aff,
3466 __isl_take isl_set *context);
3467 __isl_give isl_aff *isl_aff_gist(__isl_take isl_aff *aff,
3468 __isl_take isl_set *context);
3469 __isl_give isl_pw_aff *isl_pw_aff_gist_params(
3470 __isl_take isl_pw_aff *pwaff,
3471 __isl_take isl_set *context);
3472 __isl_give isl_pw_aff *isl_pw_aff_gist(
3473 __isl_take isl_pw_aff *pwaff,
3474 __isl_take isl_set *context);
3476 __isl_give isl_set *isl_pw_aff_domain(
3477 __isl_take isl_pw_aff *pwaff);
3478 __isl_give isl_pw_aff *isl_pw_aff_intersect_domain(
3479 __isl_take isl_pw_aff *pa,
3480 __isl_take isl_set *set);
3481 __isl_give isl_pw_aff *isl_pw_aff_intersect_params(
3482 __isl_take isl_pw_aff *pa,
3483 __isl_take isl_set *set);
3485 __isl_give isl_aff *isl_aff_mul(__isl_take isl_aff *aff1,
3486 __isl_take isl_aff *aff2);
3487 __isl_give isl_aff *isl_aff_div(__isl_take isl_aff *aff1,
3488 __isl_take isl_aff *aff2);
3489 __isl_give isl_pw_aff *isl_pw_aff_mul(
3490 __isl_take isl_pw_aff *pwaff1,
3491 __isl_take isl_pw_aff *pwaff2);
3492 __isl_give isl_pw_aff *isl_pw_aff_div(
3493 __isl_take isl_pw_aff *pa1,
3494 __isl_take isl_pw_aff *pa2);
3495 __isl_give isl_pw_aff *isl_pw_aff_tdiv_q(
3496 __isl_take isl_pw_aff *pa1,
3497 __isl_take isl_pw_aff *pa2);
3498 __isl_give isl_pw_aff *isl_pw_aff_tdiv_r(
3499 __isl_take isl_pw_aff *pa1,
3500 __isl_take isl_pw_aff *pa2);
3502 When multiplying two affine expressions, at least one of the two needs
3503 to be a constant. Similarly, when dividing an affine expression by another,
3504 the second expression needs to be a constant.
3505 C<isl_pw_aff_tdiv_q> computes the quotient of an integer division with
3506 rounding towards zero. C<isl_pw_aff_tdiv_r> computes the corresponding
3509 #include <isl/aff.h>
3510 __isl_give isl_aff *isl_aff_pullback_multi_aff(
3511 __isl_take isl_aff *aff,
3512 __isl_take isl_multi_aff *ma);
3513 __isl_give isl_pw_aff *isl_pw_aff_pullback_multi_aff(
3514 __isl_take isl_pw_aff *pa,
3515 __isl_take isl_multi_aff *ma);
3516 __isl_give isl_pw_aff *isl_pw_aff_pullback_pw_multi_aff(
3517 __isl_take isl_pw_aff *pa,
3518 __isl_take isl_pw_multi_aff *pma);
3520 These functions precompose the input expression by the given
3521 C<isl_multi_aff> or C<isl_pw_multi_aff>. In other words,
3522 the C<isl_multi_aff> or C<isl_pw_multi_aff> is plugged
3523 into the (piecewise) affine expression.
3524 Objects of type C<isl_multi_aff> are described in
3525 L</"Piecewise Multiple Quasi Affine Expressions">.
3527 #include <isl/aff.h>
3528 __isl_give isl_basic_set *isl_aff_zero_basic_set(
3529 __isl_take isl_aff *aff);
3530 __isl_give isl_basic_set *isl_aff_neg_basic_set(
3531 __isl_take isl_aff *aff);
3532 __isl_give isl_basic_set *isl_aff_le_basic_set(
3533 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3534 __isl_give isl_basic_set *isl_aff_ge_basic_set(
3535 __isl_take isl_aff *aff1, __isl_take isl_aff *aff2);
3536 __isl_give isl_set *isl_pw_aff_eq_set(
3537 __isl_take isl_pw_aff *pwaff1,
3538 __isl_take isl_pw_aff *pwaff2);
3539 __isl_give isl_set *isl_pw_aff_ne_set(
3540 __isl_take isl_pw_aff *pwaff1,
3541 __isl_take isl_pw_aff *pwaff2);
3542 __isl_give isl_set *isl_pw_aff_le_set(
3543 __isl_take isl_pw_aff *pwaff1,
3544 __isl_take isl_pw_aff *pwaff2);
3545 __isl_give isl_set *isl_pw_aff_lt_set(
3546 __isl_take isl_pw_aff *pwaff1,
3547 __isl_take isl_pw_aff *pwaff2);
3548 __isl_give isl_set *isl_pw_aff_ge_set(
3549 __isl_take isl_pw_aff *pwaff1,
3550 __isl_take isl_pw_aff *pwaff2);
3551 __isl_give isl_set *isl_pw_aff_gt_set(
3552 __isl_take isl_pw_aff *pwaff1,
3553 __isl_take isl_pw_aff *pwaff2);
3555 __isl_give isl_set *isl_pw_aff_list_eq_set(
3556 __isl_take isl_pw_aff_list *list1,
3557 __isl_take isl_pw_aff_list *list2);
3558 __isl_give isl_set *isl_pw_aff_list_ne_set(
3559 __isl_take isl_pw_aff_list *list1,
3560 __isl_take isl_pw_aff_list *list2);
3561 __isl_give isl_set *isl_pw_aff_list_le_set(
3562 __isl_take isl_pw_aff_list *list1,
3563 __isl_take isl_pw_aff_list *list2);
3564 __isl_give isl_set *isl_pw_aff_list_lt_set(
3565 __isl_take isl_pw_aff_list *list1,
3566 __isl_take isl_pw_aff_list *list2);
3567 __isl_give isl_set *isl_pw_aff_list_ge_set(
3568 __isl_take isl_pw_aff_list *list1,
3569 __isl_take isl_pw_aff_list *list2);
3570 __isl_give isl_set *isl_pw_aff_list_gt_set(
3571 __isl_take isl_pw_aff_list *list1,
3572 __isl_take isl_pw_aff_list *list2);
3574 The function C<isl_aff_neg_basic_set> returns a basic set
3575 containing those elements in the domain space
3576 of C<aff> where C<aff> is negative.
3577 The function C<isl_aff_ge_basic_set> returns a basic set
3578 containing those elements in the shared space
3579 of C<aff1> and C<aff2> where C<aff1> is greater than or equal to C<aff2>.
3580 The function C<isl_pw_aff_ge_set> returns a set
3581 containing those elements in the shared domain
3582 of C<pwaff1> and C<pwaff2> where C<pwaff1> is greater than or equal to C<pwaff2>.
3583 The functions operating on C<isl_pw_aff_list> apply the corresponding
3584 C<isl_pw_aff> function to each pair of elements in the two lists.
3586 #include <isl/aff.h>
3587 __isl_give isl_set *isl_pw_aff_nonneg_set(
3588 __isl_take isl_pw_aff *pwaff);
3589 __isl_give isl_set *isl_pw_aff_zero_set(
3590 __isl_take isl_pw_aff *pwaff);
3591 __isl_give isl_set *isl_pw_aff_non_zero_set(
3592 __isl_take isl_pw_aff *pwaff);
3594 The function C<isl_pw_aff_nonneg_set> returns a set
3595 containing those elements in the domain
3596 of C<pwaff> where C<pwaff> is non-negative.
3598 #include <isl/aff.h>
3599 __isl_give isl_pw_aff *isl_pw_aff_cond(
3600 __isl_take isl_pw_aff *cond,
3601 __isl_take isl_pw_aff *pwaff_true,
3602 __isl_take isl_pw_aff *pwaff_false);
3604 The function C<isl_pw_aff_cond> performs a conditional operator
3605 and returns an expression that is equal to C<pwaff_true>
3606 for elements where C<cond> is non-zero and equal to C<pwaff_false> for elements
3607 where C<cond> is zero.
3609 #include <isl/aff.h>
3610 __isl_give isl_pw_aff *isl_pw_aff_union_min(
3611 __isl_take isl_pw_aff *pwaff1,
3612 __isl_take isl_pw_aff *pwaff2);
3613 __isl_give isl_pw_aff *isl_pw_aff_union_max(
3614 __isl_take isl_pw_aff *pwaff1,
3615 __isl_take isl_pw_aff *pwaff2);
3616 __isl_give isl_pw_aff *isl_pw_aff_union_add(
3617 __isl_take isl_pw_aff *pwaff1,
3618 __isl_take isl_pw_aff *pwaff2);
3620 The function C<isl_pw_aff_union_max> computes a piecewise quasi-affine
3621 expression with a domain that is the union of those of C<pwaff1> and
3622 C<pwaff2> and such that on each cell, the quasi-affine expression is
3623 the maximum of those of C<pwaff1> and C<pwaff2>. If only one of
3624 C<pwaff1> or C<pwaff2> is defined on a given cell, then the
3625 associated expression is the defined one.
3627 An expression can be read from input using
3629 #include <isl/aff.h>
3630 __isl_give isl_aff *isl_aff_read_from_str(
3631 isl_ctx *ctx, const char *str);
3632 __isl_give isl_pw_aff *isl_pw_aff_read_from_str(
3633 isl_ctx *ctx, const char *str);
3635 An expression can be printed using
3637 #include <isl/aff.h>
3638 __isl_give isl_printer *isl_printer_print_aff(
3639 __isl_take isl_printer *p, __isl_keep isl_aff *aff);
3641 __isl_give isl_printer *isl_printer_print_pw_aff(
3642 __isl_take isl_printer *p,
3643 __isl_keep isl_pw_aff *pwaff);
3645 =head2 Piecewise Multiple Quasi Affine Expressions
3647 An C<isl_multi_aff> object represents a sequence of
3648 zero or more affine expressions, all defined on the same domain space.
3649 Similarly, an C<isl_multi_pw_aff> object represents a sequence of
3650 zero or more piecewise affine expressions.
3652 An C<isl_multi_aff> can be constructed from a single
3653 C<isl_aff> or an C<isl_aff_list> using the
3654 following functions. Similarly for C<isl_multi_pw_aff>.
3656 #include <isl/aff.h>
3657 __isl_give isl_multi_aff *isl_multi_aff_from_aff(
3658 __isl_take isl_aff *aff);
3659 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_from_pw_aff(
3660 __isl_take isl_pw_aff *pa);
3661 __isl_give isl_multi_aff *isl_multi_aff_from_aff_list(
3662 __isl_take isl_space *space,
3663 __isl_take isl_aff_list *list);
3665 An empty piecewise multiple quasi affine expression (one with no cells),
3666 the zero piecewise multiple quasi affine expression (with value zero
3667 for each output dimension),
3668 a piecewise multiple quasi affine expression with a single cell (with
3669 either a universe or a specified domain) or
3670 a zero-dimensional piecewise multiple quasi affine expression
3672 can be created using the following functions.
3674 #include <isl/aff.h>
3675 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_empty(
3676 __isl_take isl_space *space);
3677 __isl_give isl_multi_aff *isl_multi_aff_zero(
3678 __isl_take isl_space *space);
3679 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_zero(
3680 __isl_take isl_space *space);
3681 __isl_give isl_multi_aff *isl_multi_aff_identity(
3682 __isl_take isl_space *space);
3683 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_identity(
3684 __isl_take isl_space *space);
3685 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_identity(
3686 __isl_take isl_space *space);
3687 __isl_give isl_pw_multi_aff *
3688 isl_pw_multi_aff_from_multi_aff(
3689 __isl_take isl_multi_aff *ma);
3690 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_alloc(
3691 __isl_take isl_set *set,
3692 __isl_take isl_multi_aff *maff);
3693 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_domain(
3694 __isl_take isl_set *set);
3696 __isl_give isl_union_pw_multi_aff *
3697 isl_union_pw_multi_aff_empty(
3698 __isl_take isl_space *space);
3699 __isl_give isl_union_pw_multi_aff *
3700 isl_union_pw_multi_aff_add_pw_multi_aff(
3701 __isl_take isl_union_pw_multi_aff *upma,
3702 __isl_take isl_pw_multi_aff *pma);
3703 __isl_give isl_union_pw_multi_aff *
3704 isl_union_pw_multi_aff_from_domain(
3705 __isl_take isl_union_set *uset);
3707 A piecewise multiple quasi affine expression can also be initialized
3708 from an C<isl_set> or C<isl_map>, provided the C<isl_set> is a singleton
3709 and the C<isl_map> is single-valued.
3710 In case of a conversion from an C<isl_union_set> or an C<isl_union_map>
3711 to an C<isl_union_pw_multi_aff>, these properties need to hold in each space.
3713 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_set(
3714 __isl_take isl_set *set);
3715 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_from_map(
3716 __isl_take isl_map *map);
3718 __isl_give isl_union_pw_multi_aff *
3719 isl_union_pw_multi_aff_from_union_set(
3720 __isl_take isl_union_set *uset);
3721 __isl_give isl_union_pw_multi_aff *
3722 isl_union_pw_multi_aff_from_union_map(
3723 __isl_take isl_union_map *umap);
3725 Multiple quasi affine expressions can be copied and freed using
3727 #include <isl/aff.h>
3728 __isl_give isl_multi_aff *isl_multi_aff_copy(
3729 __isl_keep isl_multi_aff *maff);
3730 void *isl_multi_aff_free(__isl_take isl_multi_aff *maff);
3732 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_copy(
3733 __isl_keep isl_pw_multi_aff *pma);
3734 void *isl_pw_multi_aff_free(
3735 __isl_take isl_pw_multi_aff *pma);
3737 __isl_give isl_union_pw_multi_aff *
3738 isl_union_pw_multi_aff_copy(
3739 __isl_keep isl_union_pw_multi_aff *upma);
3740 void *isl_union_pw_multi_aff_free(
3741 __isl_take isl_union_pw_multi_aff *upma);
3743 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_copy(
3744 __isl_keep isl_multi_pw_aff *mpa);
3745 void *isl_multi_pw_aff_free(
3746 __isl_take isl_multi_pw_aff *mpa);
3748 The expression can be inspected using
3750 #include <isl/aff.h>
3751 isl_ctx *isl_multi_aff_get_ctx(
3752 __isl_keep isl_multi_aff *maff);
3753 isl_ctx *isl_pw_multi_aff_get_ctx(
3754 __isl_keep isl_pw_multi_aff *pma);
3755 isl_ctx *isl_union_pw_multi_aff_get_ctx(
3756 __isl_keep isl_union_pw_multi_aff *upma);
3757 isl_ctx *isl_multi_pw_aff_get_ctx(
3758 __isl_keep isl_multi_pw_aff *mpa);
3759 unsigned isl_multi_aff_dim(__isl_keep isl_multi_aff *maff,
3760 enum isl_dim_type type);
3761 unsigned isl_pw_multi_aff_dim(
3762 __isl_keep isl_pw_multi_aff *pma,
3763 enum isl_dim_type type);
3764 unsigned isl_multi_pw_aff_dim(
3765 __isl_keep isl_multi_pw_aff *mpa,
3766 enum isl_dim_type type);
3767 __isl_give isl_aff *isl_multi_aff_get_aff(
3768 __isl_keep isl_multi_aff *multi, int pos);
3769 __isl_give isl_pw_aff *isl_pw_multi_aff_get_pw_aff(
3770 __isl_keep isl_pw_multi_aff *pma, int pos);
3771 __isl_give isl_pw_aff *isl_multi_pw_aff_get_pw_aff(
3772 __isl_keep isl_multi_pw_aff *mpa, int pos);
3773 const char *isl_pw_multi_aff_get_dim_name(
3774 __isl_keep isl_pw_multi_aff *pma,
3775 enum isl_dim_type type, unsigned pos);
3776 __isl_give isl_id *isl_pw_multi_aff_get_dim_id(
3777 __isl_keep isl_pw_multi_aff *pma,
3778 enum isl_dim_type type, unsigned pos);
3779 const char *isl_multi_aff_get_tuple_name(
3780 __isl_keep isl_multi_aff *multi,
3781 enum isl_dim_type type);
3782 int isl_pw_multi_aff_has_tuple_name(
3783 __isl_keep isl_pw_multi_aff *pma,
3784 enum isl_dim_type type);
3785 const char *isl_pw_multi_aff_get_tuple_name(
3786 __isl_keep isl_pw_multi_aff *pma,
3787 enum isl_dim_type type);
3788 int isl_pw_multi_aff_has_tuple_id(
3789 __isl_keep isl_pw_multi_aff *pma,
3790 enum isl_dim_type type);
3791 __isl_give isl_id *isl_pw_multi_aff_get_tuple_id(
3792 __isl_keep isl_pw_multi_aff *pma,
3793 enum isl_dim_type type);
3795 int isl_pw_multi_aff_foreach_piece(
3796 __isl_keep isl_pw_multi_aff *pma,
3797 int (*fn)(__isl_take isl_set *set,
3798 __isl_take isl_multi_aff *maff,
3799 void *user), void *user);
3801 int isl_union_pw_multi_aff_foreach_pw_multi_aff(
3802 __isl_keep isl_union_pw_multi_aff *upma,
3803 int (*fn)(__isl_take isl_pw_multi_aff *pma,
3804 void *user), void *user);
3806 It can be modified using
3808 #include <isl/aff.h>
3809 __isl_give isl_multi_aff *isl_multi_aff_set_aff(
3810 __isl_take isl_multi_aff *multi, int pos,
3811 __isl_take isl_aff *aff);
3812 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_pw_aff(
3813 __isl_take isl_pw_multi_aff *pma, unsigned pos,
3814 __isl_take isl_pw_aff *pa);
3815 __isl_give isl_multi_aff *isl_multi_aff_set_dim_name(
3816 __isl_take isl_multi_aff *maff,
3817 enum isl_dim_type type, unsigned pos, const char *s);
3818 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_name(
3819 __isl_take isl_multi_aff *maff,
3820 enum isl_dim_type type, const char *s);
3821 __isl_give isl_multi_aff *isl_multi_aff_set_tuple_id(
3822 __isl_take isl_multi_aff *maff,
3823 enum isl_dim_type type, __isl_take isl_id *id);
3824 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_set_tuple_id(
3825 __isl_take isl_pw_multi_aff *pma,
3826 enum isl_dim_type type, __isl_take isl_id *id);
3828 __isl_give isl_multi_pw_aff *
3829 isl_multi_pw_aff_set_dim_name(
3830 __isl_take isl_multi_pw_aff *mpa,
3831 enum isl_dim_type type, unsigned pos, const char *s);
3832 __isl_give isl_multi_pw_aff *
3833 isl_multi_pw_aff_set_tuple_name(
3834 __isl_take isl_multi_pw_aff *mpa,
3835 enum isl_dim_type type, const char *s);
3837 __isl_give isl_multi_aff *isl_multi_aff_insert_dims(
3838 __isl_take isl_multi_aff *ma,
3839 enum isl_dim_type type, unsigned first, unsigned n);
3840 __isl_give isl_multi_aff *isl_multi_aff_add_dims(
3841 __isl_take isl_multi_aff *ma,
3842 enum isl_dim_type type, unsigned n);
3843 __isl_give isl_multi_aff *isl_multi_aff_drop_dims(
3844 __isl_take isl_multi_aff *maff,
3845 enum isl_dim_type type, unsigned first, unsigned n);
3846 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_drop_dims(
3847 __isl_take isl_pw_multi_aff *pma,
3848 enum isl_dim_type type, unsigned first, unsigned n);
3850 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_insert_dims(
3851 __isl_take isl_multi_pw_aff *mpa,
3852 enum isl_dim_type type, unsigned first, unsigned n);
3853 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_add_dims(
3854 __isl_take isl_multi_pw_aff *mpa,
3855 enum isl_dim_type type, unsigned n);
3857 To check whether two multiple affine expressions are
3858 obviously equal to each other, use
3860 int isl_multi_aff_plain_is_equal(__isl_keep isl_multi_aff *maff1,
3861 __isl_keep isl_multi_aff *maff2);
3862 int isl_pw_multi_aff_plain_is_equal(
3863 __isl_keep isl_pw_multi_aff *pma1,
3864 __isl_keep isl_pw_multi_aff *pma2);
3868 #include <isl/aff.h>
3869 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmin(
3870 __isl_take isl_pw_multi_aff *pma1,
3871 __isl_take isl_pw_multi_aff *pma2);
3872 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_lexmax(
3873 __isl_take isl_pw_multi_aff *pma1,
3874 __isl_take isl_pw_multi_aff *pma2);
3875 __isl_give isl_multi_aff *isl_multi_aff_add(
3876 __isl_take isl_multi_aff *maff1,
3877 __isl_take isl_multi_aff *maff2);
3878 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_add(
3879 __isl_take isl_pw_multi_aff *pma1,
3880 __isl_take isl_pw_multi_aff *pma2);
3881 __isl_give isl_union_pw_multi_aff *isl_union_pw_multi_aff_add(
3882 __isl_take isl_union_pw_multi_aff *upma1,
3883 __isl_take isl_union_pw_multi_aff *upma2);
3884 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_union_add(
3885 __isl_take isl_pw_multi_aff *pma1,
3886 __isl_take isl_pw_multi_aff *pma2);
3887 __isl_give isl_multi_aff *isl_multi_aff_scale(
3888 __isl_take isl_multi_aff *maff,
3890 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_params(
3891 __isl_take isl_pw_multi_aff *pma,
3892 __isl_take isl_set *set);
3893 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_intersect_domain(
3894 __isl_take isl_pw_multi_aff *pma,
3895 __isl_take isl_set *set);
3896 __isl_give isl_multi_aff *isl_multi_aff_lift(
3897 __isl_take isl_multi_aff *maff,
3898 __isl_give isl_local_space **ls);
3899 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_coalesce(
3900 __isl_take isl_pw_multi_aff *pma);
3901 __isl_give isl_multi_aff *isl_multi_aff_align_params(
3902 __isl_take isl_multi_aff *multi,
3903 __isl_take isl_space *model);
3904 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_align_params(
3905 __isl_take isl_pw_multi_aff *pma,
3906 __isl_take isl_space *model);
3907 __isl_give isl_pw_multi_aff *
3908 isl_pw_multi_aff_project_domain_on_params(
3909 __isl_take isl_pw_multi_aff *pma);
3910 __isl_give isl_multi_aff *isl_multi_aff_gist_params(
3911 __isl_take isl_multi_aff *maff,
3912 __isl_take isl_set *context);
3913 __isl_give isl_multi_aff *isl_multi_aff_gist(
3914 __isl_take isl_multi_aff *maff,
3915 __isl_take isl_set *context);
3916 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist_params(
3917 __isl_take isl_pw_multi_aff *pma,
3918 __isl_take isl_set *set);
3919 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_gist(
3920 __isl_take isl_pw_multi_aff *pma,
3921 __isl_take isl_set *set);
3922 __isl_give isl_set *isl_pw_multi_aff_domain(
3923 __isl_take isl_pw_multi_aff *pma);
3924 __isl_give isl_union_set *isl_union_pw_multi_aff_domain(
3925 __isl_take isl_union_pw_multi_aff *upma);
3926 __isl_give isl_multi_aff *isl_multi_aff_range_splice(
3927 __isl_take isl_multi_aff *ma1, unsigned pos,
3928 __isl_take isl_multi_aff *ma2);
3929 __isl_give isl_multi_aff *isl_multi_aff_splice(
3930 __isl_take isl_multi_aff *ma1,
3931 unsigned in_pos, unsigned out_pos,
3932 __isl_take isl_multi_aff *ma2);
3933 __isl_give isl_multi_aff *isl_multi_aff_range_product(
3934 __isl_take isl_multi_aff *ma1,
3935 __isl_take isl_multi_aff *ma2);
3936 __isl_give isl_multi_aff *isl_multi_aff_flat_range_product(
3937 __isl_take isl_multi_aff *ma1,
3938 __isl_take isl_multi_aff *ma2);
3939 __isl_give isl_multi_aff *isl_multi_aff_product(
3940 __isl_take isl_multi_aff *ma1,
3941 __isl_take isl_multi_aff *ma2);
3942 __isl_give isl_pw_multi_aff *
3943 isl_pw_multi_aff_range_product(
3944 __isl_take isl_pw_multi_aff *pma1,
3945 __isl_take isl_pw_multi_aff *pma2);
3946 __isl_give isl_pw_multi_aff *
3947 isl_pw_multi_aff_flat_range_product(
3948 __isl_take isl_pw_multi_aff *pma1,
3949 __isl_take isl_pw_multi_aff *pma2);
3950 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_product(
3951 __isl_take isl_pw_multi_aff *pma1,
3952 __isl_take isl_pw_multi_aff *pma2);
3953 __isl_give isl_union_pw_multi_aff *
3954 isl_union_pw_multi_aff_flat_range_product(
3955 __isl_take isl_union_pw_multi_aff *upma1,
3956 __isl_take isl_union_pw_multi_aff *upma2);
3957 __isl_give isl_multi_pw_aff *
3958 isl_multi_pw_aff_range_splice(
3959 __isl_take isl_multi_pw_aff *mpa1, unsigned pos,
3960 __isl_take isl_multi_pw_aff *mpa2);
3961 __isl_give isl_multi_pw_aff *isl_multi_pw_aff_splice(
3962 __isl_take isl_multi_pw_aff *mpa1,
3963 unsigned in_pos, unsigned out_pos,
3964 __isl_take isl_multi_pw_aff *mpa2);
3965 __isl_give isl_multi_pw_aff *
3966 isl_multi_pw_aff_range_product(
3967 __isl_take isl_multi_pw_aff *mpa1,
3968 __isl_take isl_multi_pw_aff *mpa2);
3969 __isl_give isl_multi_pw_aff *
3970 isl_multi_pw_aff_flat_range_product(
3971 __isl_take isl_multi_pw_aff *mpa1,
3972 __isl_take isl_multi_pw_aff *mpa2);
3974 If the C<ls> argument of C<isl_multi_aff_lift> is not C<NULL>,
3975 then it is assigned the local space that lies at the basis of
3976 the lifting applied.
3978 #include <isl/aff.h>
3979 __isl_give isl_multi_aff *isl_multi_aff_pullback_multi_aff(
3980 __isl_take isl_multi_aff *ma1,
3981 __isl_take isl_multi_aff *ma2);
3982 __isl_give isl_pw_multi_aff *
3983 isl_pw_multi_aff_pullback_multi_aff(
3984 __isl_take isl_pw_multi_aff *pma,
3985 __isl_take isl_multi_aff *ma);
3986 __isl_give isl_pw_multi_aff *
3987 isl_pw_multi_aff_pullback_pw_multi_aff(
3988 __isl_take isl_pw_multi_aff *pma1,
3989 __isl_take isl_pw_multi_aff *pma2);
3991 The function C<isl_multi_aff_pullback_multi_aff> precomposes C<ma1> by C<ma2>.
3992 In other words, C<ma2> is plugged
3995 __isl_give isl_set *isl_multi_aff_lex_le_set(
3996 __isl_take isl_multi_aff *ma1,
3997 __isl_take isl_multi_aff *ma2);
3998 __isl_give isl_set *isl_multi_aff_lex_ge_set(
3999 __isl_take isl_multi_aff *ma1,
4000 __isl_take isl_multi_aff *ma2);
4002 The function C<isl_multi_aff_lex_le_set> returns a set
4003 containing those elements in the shared domain space
4004 where C<ma1> is lexicographically smaller than or
4007 An expression can be read from input using
4009 #include <isl/aff.h>
4010 __isl_give isl_multi_aff *isl_multi_aff_read_from_str(
4011 isl_ctx *ctx, const char *str);
4012 __isl_give isl_pw_multi_aff *isl_pw_multi_aff_read_from_str(
4013 isl_ctx *ctx, const char *str);
4014 __isl_give isl_union_pw_multi_aff *
4015 isl_union_pw_multi_aff_read_from_str(
4016 isl_ctx *ctx, const char *str);
4018 An expression can be printed using
4020 #include <isl/aff.h>
4021 __isl_give isl_printer *isl_printer_print_multi_aff(
4022 __isl_take isl_printer *p,
4023 __isl_keep isl_multi_aff *maff);
4024 __isl_give isl_printer *isl_printer_print_pw_multi_aff(
4025 __isl_take isl_printer *p,
4026 __isl_keep isl_pw_multi_aff *pma);
4027 __isl_give isl_printer *isl_printer_print_union_pw_multi_aff(
4028 __isl_take isl_printer *p,
4029 __isl_keep isl_union_pw_multi_aff *upma);
4030 __isl_give isl_printer *isl_printer_print_multi_pw_aff(
4031 __isl_take isl_printer *p,
4032 __isl_keep isl_multi_pw_aff *mpa);
4036 Points are elements of a set. They can be used to construct
4037 simple sets (boxes) or they can be used to represent the
4038 individual elements of a set.
4039 The zero point (the origin) can be created using
4041 __isl_give isl_point *isl_point_zero(__isl_take isl_space *space);
4043 The coordinates of a point can be inspected, set and changed
4046 int isl_point_get_coordinate(__isl_keep isl_point *pnt,
4047 enum isl_dim_type type, int pos, isl_int *v);
4048 __isl_give isl_point *isl_point_set_coordinate(
4049 __isl_take isl_point *pnt,
4050 enum isl_dim_type type, int pos, isl_int v);
4052 __isl_give isl_point *isl_point_add_ui(
4053 __isl_take isl_point *pnt,
4054 enum isl_dim_type type, int pos, unsigned val);
4055 __isl_give isl_point *isl_point_sub_ui(
4056 __isl_take isl_point *pnt,
4057 enum isl_dim_type type, int pos, unsigned val);
4059 Other properties can be obtained using
4061 isl_ctx *isl_point_get_ctx(__isl_keep isl_point *pnt);
4063 Points can be copied or freed using
4065 __isl_give isl_point *isl_point_copy(
4066 __isl_keep isl_point *pnt);
4067 void isl_point_free(__isl_take isl_point *pnt);
4069 A singleton set can be created from a point using
4071 __isl_give isl_basic_set *isl_basic_set_from_point(
4072 __isl_take isl_point *pnt);
4073 __isl_give isl_set *isl_set_from_point(
4074 __isl_take isl_point *pnt);
4076 and a box can be created from two opposite extremal points using
4078 __isl_give isl_basic_set *isl_basic_set_box_from_points(
4079 __isl_take isl_point *pnt1,
4080 __isl_take isl_point *pnt2);
4081 __isl_give isl_set *isl_set_box_from_points(
4082 __isl_take isl_point *pnt1,
4083 __isl_take isl_point *pnt2);
4085 All elements of a B<bounded> (union) set can be enumerated using
4086 the following functions.
4088 int isl_set_foreach_point(__isl_keep isl_set *set,
4089 int (*fn)(__isl_take isl_point *pnt, void *user),
4091 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
4092 int (*fn)(__isl_take isl_point *pnt, void *user),
4095 The function C<fn> is called for each integer point in
4096 C<set> with as second argument the last argument of
4097 the C<isl_set_foreach_point> call. The function C<fn>
4098 should return C<0> on success and C<-1> on failure.
4099 In the latter case, C<isl_set_foreach_point> will stop
4100 enumerating and return C<-1> as well.
4101 If the enumeration is performed successfully and to completion,
4102 then C<isl_set_foreach_point> returns C<0>.
4104 To obtain a single point of a (basic) set, use
4106 __isl_give isl_point *isl_basic_set_sample_point(
4107 __isl_take isl_basic_set *bset);
4108 __isl_give isl_point *isl_set_sample_point(
4109 __isl_take isl_set *set);
4111 If C<set> does not contain any (integer) points, then the
4112 resulting point will be ``void'', a property that can be
4115 int isl_point_is_void(__isl_keep isl_point *pnt);
4117 =head2 Piecewise Quasipolynomials
4119 A piecewise quasipolynomial is a particular kind of function that maps
4120 a parametric point to a rational value.
4121 More specifically, a quasipolynomial is a polynomial expression in greatest
4122 integer parts of affine expressions of parameters and variables.
4123 A piecewise quasipolynomial is a subdivision of a given parametric
4124 domain into disjoint cells with a quasipolynomial associated to
4125 each cell. The value of the piecewise quasipolynomial at a given
4126 point is the value of the quasipolynomial associated to the cell
4127 that contains the point. Outside of the union of cells,
4128 the value is assumed to be zero.
4129 For example, the piecewise quasipolynomial
4131 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
4133 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
4134 A given piecewise quasipolynomial has a fixed domain dimension.
4135 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
4136 defined over different domains.
4137 Piecewise quasipolynomials are mainly used by the C<barvinok>
4138 library for representing the number of elements in a parametric set or map.
4139 For example, the piecewise quasipolynomial above represents
4140 the number of points in the map
4142 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
4144 =head3 Input and Output
4146 Piecewise quasipolynomials can be read from input using
4148 __isl_give isl_union_pw_qpolynomial *
4149 isl_union_pw_qpolynomial_read_from_str(
4150 isl_ctx *ctx, const char *str);
4152 Quasipolynomials and piecewise quasipolynomials can be printed
4153 using the following functions.
4155 __isl_give isl_printer *isl_printer_print_qpolynomial(
4156 __isl_take isl_printer *p,
4157 __isl_keep isl_qpolynomial *qp);
4159 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
4160 __isl_take isl_printer *p,
4161 __isl_keep isl_pw_qpolynomial *pwqp);
4163 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
4164 __isl_take isl_printer *p,
4165 __isl_keep isl_union_pw_qpolynomial *upwqp);
4167 The output format of the printer
4168 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4169 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
4171 In case of printing in C<ISL_FORMAT_C>, the user may want
4172 to set the names of all dimensions
4174 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
4175 __isl_take isl_qpolynomial *qp,
4176 enum isl_dim_type type, unsigned pos,
4178 __isl_give isl_pw_qpolynomial *
4179 isl_pw_qpolynomial_set_dim_name(
4180 __isl_take isl_pw_qpolynomial *pwqp,
4181 enum isl_dim_type type, unsigned pos,
4184 =head3 Creating New (Piecewise) Quasipolynomials
4186 Some simple quasipolynomials can be created using the following functions.
4187 More complicated quasipolynomials can be created by applying
4188 operations such as addition and multiplication
4189 on the resulting quasipolynomials
4191 __isl_give isl_qpolynomial *isl_qpolynomial_zero_on_domain(
4192 __isl_take isl_space *domain);
4193 __isl_give isl_qpolynomial *isl_qpolynomial_one_on_domain(
4194 __isl_take isl_space *domain);
4195 __isl_give isl_qpolynomial *isl_qpolynomial_infty_on_domain(
4196 __isl_take isl_space *domain);
4197 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty_on_domain(
4198 __isl_take isl_space *domain);
4199 __isl_give isl_qpolynomial *isl_qpolynomial_nan_on_domain(
4200 __isl_take isl_space *domain);
4201 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst_on_domain(
4202 __isl_take isl_space *domain,
4203 const isl_int n, const isl_int d);
4204 __isl_give isl_qpolynomial *isl_qpolynomial_var_on_domain(
4205 __isl_take isl_space *domain,
4206 enum isl_dim_type type, unsigned pos);
4207 __isl_give isl_qpolynomial *isl_qpolynomial_from_aff(
4208 __isl_take isl_aff *aff);
4210 Note that the space in which a quasipolynomial lives is a map space
4211 with a one-dimensional range. The C<domain> argument in some of
4212 the functions above corresponds to the domain of this map space.
4214 The zero piecewise quasipolynomial or a piecewise quasipolynomial
4215 with a single cell can be created using the following functions.
4216 Multiple of these single cell piecewise quasipolynomials can
4217 be combined to create more complicated piecewise quasipolynomials.
4219 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
4220 __isl_take isl_space *space);
4221 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
4222 __isl_take isl_set *set,
4223 __isl_take isl_qpolynomial *qp);
4224 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_qpolynomial(
4225 __isl_take isl_qpolynomial *qp);
4226 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_from_pw_aff(
4227 __isl_take isl_pw_aff *pwaff);
4229 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
4230 __isl_take isl_space *space);
4231 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
4232 __isl_take isl_pw_qpolynomial *pwqp);
4233 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
4234 __isl_take isl_union_pw_qpolynomial *upwqp,
4235 __isl_take isl_pw_qpolynomial *pwqp);
4237 Quasipolynomials can be copied and freed again using the following
4240 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
4241 __isl_keep isl_qpolynomial *qp);
4242 void *isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
4244 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
4245 __isl_keep isl_pw_qpolynomial *pwqp);
4246 void *isl_pw_qpolynomial_free(
4247 __isl_take isl_pw_qpolynomial *pwqp);
4249 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
4250 __isl_keep isl_union_pw_qpolynomial *upwqp);
4251 void *isl_union_pw_qpolynomial_free(
4252 __isl_take isl_union_pw_qpolynomial *upwqp);
4254 =head3 Inspecting (Piecewise) Quasipolynomials
4256 To iterate over all piecewise quasipolynomials in a union
4257 piecewise quasipolynomial, use the following function
4259 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
4260 __isl_keep isl_union_pw_qpolynomial *upwqp,
4261 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
4264 To extract the piecewise quasipolynomial in a given space from a union, use
4266 __isl_give isl_pw_qpolynomial *
4267 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
4268 __isl_keep isl_union_pw_qpolynomial *upwqp,
4269 __isl_take isl_space *space);
4271 To iterate over the cells in a piecewise quasipolynomial,
4272 use either of the following two functions
4274 int isl_pw_qpolynomial_foreach_piece(
4275 __isl_keep isl_pw_qpolynomial *pwqp,
4276 int (*fn)(__isl_take isl_set *set,
4277 __isl_take isl_qpolynomial *qp,
4278 void *user), void *user);
4279 int isl_pw_qpolynomial_foreach_lifted_piece(
4280 __isl_keep isl_pw_qpolynomial *pwqp,
4281 int (*fn)(__isl_take isl_set *set,
4282 __isl_take isl_qpolynomial *qp,
4283 void *user), void *user);
4285 As usual, the function C<fn> should return C<0> on success
4286 and C<-1> on failure. The difference between
4287 C<isl_pw_qpolynomial_foreach_piece> and
4288 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
4289 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
4290 compute unique representations for all existentially quantified
4291 variables and then turn these existentially quantified variables
4292 into extra set variables, adapting the associated quasipolynomial
4293 accordingly. This means that the C<set> passed to C<fn>
4294 will not have any existentially quantified variables, but that
4295 the dimensions of the sets may be different for different
4296 invocations of C<fn>.
4298 To iterate over all terms in a quasipolynomial,
4301 int isl_qpolynomial_foreach_term(
4302 __isl_keep isl_qpolynomial *qp,
4303 int (*fn)(__isl_take isl_term *term,
4304 void *user), void *user);
4306 The terms themselves can be inspected and freed using
4309 unsigned isl_term_dim(__isl_keep isl_term *term,
4310 enum isl_dim_type type);
4311 void isl_term_get_num(__isl_keep isl_term *term,
4313 void isl_term_get_den(__isl_keep isl_term *term,
4315 int isl_term_get_exp(__isl_keep isl_term *term,
4316 enum isl_dim_type type, unsigned pos);
4317 __isl_give isl_aff *isl_term_get_div(
4318 __isl_keep isl_term *term, unsigned pos);
4319 void isl_term_free(__isl_take isl_term *term);
4321 Each term is a product of parameters, set variables and
4322 integer divisions. The function C<isl_term_get_exp>
4323 returns the exponent of a given dimensions in the given term.
4324 The C<isl_int>s in the arguments of C<isl_term_get_num>
4325 and C<isl_term_get_den> need to have been initialized
4326 using C<isl_int_init> before calling these functions.
4328 =head3 Properties of (Piecewise) Quasipolynomials
4330 To check whether a quasipolynomial is actually a constant,
4331 use the following function.
4333 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
4334 isl_int *n, isl_int *d);
4336 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
4337 then the numerator and denominator of the constant
4338 are returned in C<*n> and C<*d>, respectively.
4340 To check whether two union piecewise quasipolynomials are
4341 obviously equal, use
4343 int isl_union_pw_qpolynomial_plain_is_equal(
4344 __isl_keep isl_union_pw_qpolynomial *upwqp1,
4345 __isl_keep isl_union_pw_qpolynomial *upwqp2);
4347 =head3 Operations on (Piecewise) Quasipolynomials
4349 __isl_give isl_qpolynomial *isl_qpolynomial_scale(
4350 __isl_take isl_qpolynomial *qp, isl_int v);
4351 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
4352 __isl_take isl_qpolynomial *qp);
4353 __isl_give isl_qpolynomial *isl_qpolynomial_add(
4354 __isl_take isl_qpolynomial *qp1,
4355 __isl_take isl_qpolynomial *qp2);
4356 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
4357 __isl_take isl_qpolynomial *qp1,
4358 __isl_take isl_qpolynomial *qp2);
4359 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
4360 __isl_take isl_qpolynomial *qp1,
4361 __isl_take isl_qpolynomial *qp2);
4362 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
4363 __isl_take isl_qpolynomial *qp, unsigned exponent);
4365 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
4366 __isl_take isl_pw_qpolynomial *pwqp1,
4367 __isl_take isl_pw_qpolynomial *pwqp2);
4368 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
4369 __isl_take isl_pw_qpolynomial *pwqp1,
4370 __isl_take isl_pw_qpolynomial *pwqp2);
4371 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
4372 __isl_take isl_pw_qpolynomial *pwqp1,
4373 __isl_take isl_pw_qpolynomial *pwqp2);
4374 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
4375 __isl_take isl_pw_qpolynomial *pwqp);
4376 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
4377 __isl_take isl_pw_qpolynomial *pwqp1,
4378 __isl_take isl_pw_qpolynomial *pwqp2);
4379 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_pow(
4380 __isl_take isl_pw_qpolynomial *pwqp, unsigned exponent);
4382 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
4383 __isl_take isl_union_pw_qpolynomial *upwqp1,
4384 __isl_take isl_union_pw_qpolynomial *upwqp2);
4385 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
4386 __isl_take isl_union_pw_qpolynomial *upwqp1,
4387 __isl_take isl_union_pw_qpolynomial *upwqp2);
4388 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
4389 __isl_take isl_union_pw_qpolynomial *upwqp1,
4390 __isl_take isl_union_pw_qpolynomial *upwqp2);
4392 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
4393 __isl_take isl_pw_qpolynomial *pwqp,
4394 __isl_take isl_point *pnt);
4396 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
4397 __isl_take isl_union_pw_qpolynomial *upwqp,
4398 __isl_take isl_point *pnt);
4400 __isl_give isl_set *isl_pw_qpolynomial_domain(
4401 __isl_take isl_pw_qpolynomial *pwqp);
4402 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
4403 __isl_take isl_pw_qpolynomial *pwpq,
4404 __isl_take isl_set *set);
4405 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_params(
4406 __isl_take isl_pw_qpolynomial *pwpq,
4407 __isl_take isl_set *set);
4409 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
4410 __isl_take isl_union_pw_qpolynomial *upwqp);
4411 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
4412 __isl_take isl_union_pw_qpolynomial *upwpq,
4413 __isl_take isl_union_set *uset);
4414 __isl_give isl_union_pw_qpolynomial *
4415 isl_union_pw_qpolynomial_intersect_params(
4416 __isl_take isl_union_pw_qpolynomial *upwpq,
4417 __isl_take isl_set *set);
4419 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
4420 __isl_take isl_qpolynomial *qp,
4421 __isl_take isl_space *model);
4423 __isl_give isl_qpolynomial *isl_qpolynomial_project_domain_on_params(
4424 __isl_take isl_qpolynomial *qp);
4425 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_project_domain_on_params(
4426 __isl_take isl_pw_qpolynomial *pwqp);
4428 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
4429 __isl_take isl_union_pw_qpolynomial *upwqp);
4431 __isl_give isl_qpolynomial *isl_qpolynomial_gist_params(
4432 __isl_take isl_qpolynomial *qp,
4433 __isl_take isl_set *context);
4434 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
4435 __isl_take isl_qpolynomial *qp,
4436 __isl_take isl_set *context);
4438 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist_params(
4439 __isl_take isl_pw_qpolynomial *pwqp,
4440 __isl_take isl_set *context);
4441 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
4442 __isl_take isl_pw_qpolynomial *pwqp,
4443 __isl_take isl_set *context);
4445 __isl_give isl_union_pw_qpolynomial *
4446 isl_union_pw_qpolynomial_gist_params(
4447 __isl_take isl_union_pw_qpolynomial *upwqp,
4448 __isl_take isl_set *context);
4449 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
4450 __isl_take isl_union_pw_qpolynomial *upwqp,
4451 __isl_take isl_union_set *context);
4453 The gist operation applies the gist operation to each of
4454 the cells in the domain of the input piecewise quasipolynomial.
4455 The context is also exploited
4456 to simplify the quasipolynomials associated to each cell.
4458 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
4459 __isl_take isl_pw_qpolynomial *pwqp, int sign);
4460 __isl_give isl_union_pw_qpolynomial *
4461 isl_union_pw_qpolynomial_to_polynomial(
4462 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
4464 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
4465 the polynomial will be an overapproximation. If C<sign> is negative,
4466 it will be an underapproximation. If C<sign> is zero, the approximation
4467 will lie somewhere in between.
4469 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
4471 A piecewise quasipolynomial reduction is a piecewise
4472 reduction (or fold) of quasipolynomials.
4473 In particular, the reduction can be maximum or a minimum.
4474 The objects are mainly used to represent the result of
4475 an upper or lower bound on a quasipolynomial over its domain,
4476 i.e., as the result of the following function.
4478 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
4479 __isl_take isl_pw_qpolynomial *pwqp,
4480 enum isl_fold type, int *tight);
4482 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
4483 __isl_take isl_union_pw_qpolynomial *upwqp,
4484 enum isl_fold type, int *tight);
4486 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
4487 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
4488 is the returned bound is known be tight, i.e., for each value
4489 of the parameters there is at least
4490 one element in the domain that reaches the bound.
4491 If the domain of C<pwqp> is not wrapping, then the bound is computed
4492 over all elements in that domain and the result has a purely parametric
4493 domain. If the domain of C<pwqp> is wrapping, then the bound is
4494 computed over the range of the wrapped relation. The domain of the
4495 wrapped relation becomes the domain of the result.
4497 A (piecewise) quasipolynomial reduction can be copied or freed using the
4498 following functions.
4500 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
4501 __isl_keep isl_qpolynomial_fold *fold);
4502 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
4503 __isl_keep isl_pw_qpolynomial_fold *pwf);
4504 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
4505 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4506 void isl_qpolynomial_fold_free(
4507 __isl_take isl_qpolynomial_fold *fold);
4508 void *isl_pw_qpolynomial_fold_free(
4509 __isl_take isl_pw_qpolynomial_fold *pwf);
4510 void *isl_union_pw_qpolynomial_fold_free(
4511 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4513 =head3 Printing Piecewise Quasipolynomial Reductions
4515 Piecewise quasipolynomial reductions can be printed
4516 using the following function.
4518 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
4519 __isl_take isl_printer *p,
4520 __isl_keep isl_pw_qpolynomial_fold *pwf);
4521 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
4522 __isl_take isl_printer *p,
4523 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
4525 For C<isl_printer_print_pw_qpolynomial_fold>,
4526 output format of the printer
4527 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
4528 For C<isl_printer_print_union_pw_qpolynomial_fold>,
4529 output format of the printer
4530 needs to be set to C<ISL_FORMAT_ISL>.
4531 In case of printing in C<ISL_FORMAT_C>, the user may want
4532 to set the names of all dimensions
4534 __isl_give isl_pw_qpolynomial_fold *
4535 isl_pw_qpolynomial_fold_set_dim_name(
4536 __isl_take isl_pw_qpolynomial_fold *pwf,
4537 enum isl_dim_type type, unsigned pos,
4540 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
4542 To iterate over all piecewise quasipolynomial reductions in a union
4543 piecewise quasipolynomial reduction, use the following function
4545 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
4546 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
4547 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
4548 void *user), void *user);
4550 To iterate over the cells in a piecewise quasipolynomial reduction,
4551 use either of the following two functions
4553 int isl_pw_qpolynomial_fold_foreach_piece(
4554 __isl_keep isl_pw_qpolynomial_fold *pwf,
4555 int (*fn)(__isl_take isl_set *set,
4556 __isl_take isl_qpolynomial_fold *fold,
4557 void *user), void *user);
4558 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
4559 __isl_keep isl_pw_qpolynomial_fold *pwf,
4560 int (*fn)(__isl_take isl_set *set,
4561 __isl_take isl_qpolynomial_fold *fold,
4562 void *user), void *user);
4564 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
4565 of the difference between these two functions.
4567 To iterate over all quasipolynomials in a reduction, use
4569 int isl_qpolynomial_fold_foreach_qpolynomial(
4570 __isl_keep isl_qpolynomial_fold *fold,
4571 int (*fn)(__isl_take isl_qpolynomial *qp,
4572 void *user), void *user);
4574 =head3 Properties of Piecewise Quasipolynomial Reductions
4576 To check whether two union piecewise quasipolynomial reductions are
4577 obviously equal, use
4579 int isl_union_pw_qpolynomial_fold_plain_is_equal(
4580 __isl_keep isl_union_pw_qpolynomial_fold *upwf1,
4581 __isl_keep isl_union_pw_qpolynomial_fold *upwf2);
4583 =head3 Operations on Piecewise Quasipolynomial Reductions
4585 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_scale(
4586 __isl_take isl_qpolynomial_fold *fold, isl_int v);
4588 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
4589 __isl_take isl_pw_qpolynomial_fold *pwf1,
4590 __isl_take isl_pw_qpolynomial_fold *pwf2);
4592 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
4593 __isl_take isl_pw_qpolynomial_fold *pwf1,
4594 __isl_take isl_pw_qpolynomial_fold *pwf2);
4596 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
4597 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
4598 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
4600 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
4601 __isl_take isl_pw_qpolynomial_fold *pwf,
4602 __isl_take isl_point *pnt);
4604 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
4605 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4606 __isl_take isl_point *pnt);
4608 __isl_give isl_pw_qpolynomial_fold *
4609 isl_pw_qpolynomial_fold_intersect_params(
4610 __isl_take isl_pw_qpolynomial_fold *pwf,
4611 __isl_take isl_set *set);
4613 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
4614 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4615 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
4616 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4617 __isl_take isl_union_set *uset);
4618 __isl_give isl_union_pw_qpolynomial_fold *
4619 isl_union_pw_qpolynomial_fold_intersect_params(
4620 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4621 __isl_take isl_set *set);
4623 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_project_domain_on_params(
4624 __isl_take isl_pw_qpolynomial_fold *pwf);
4626 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
4627 __isl_take isl_pw_qpolynomial_fold *pwf);
4629 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
4630 __isl_take isl_union_pw_qpolynomial_fold *upwf);
4632 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist_params(
4633 __isl_take isl_qpolynomial_fold *fold,
4634 __isl_take isl_set *context);
4635 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_gist(
4636 __isl_take isl_qpolynomial_fold *fold,
4637 __isl_take isl_set *context);
4639 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
4640 __isl_take isl_pw_qpolynomial_fold *pwf,
4641 __isl_take isl_set *context);
4642 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist_params(
4643 __isl_take isl_pw_qpolynomial_fold *pwf,
4644 __isl_take isl_set *context);
4646 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
4647 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4648 __isl_take isl_union_set *context);
4649 __isl_give isl_union_pw_qpolynomial_fold *
4650 isl_union_pw_qpolynomial_fold_gist_params(
4651 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4652 __isl_take isl_set *context);
4654 The gist operation applies the gist operation to each of
4655 the cells in the domain of the input piecewise quasipolynomial reduction.
4656 In future, the operation will also exploit the context
4657 to simplify the quasipolynomial reductions associated to each cell.
4659 __isl_give isl_pw_qpolynomial_fold *
4660 isl_set_apply_pw_qpolynomial_fold(
4661 __isl_take isl_set *set,
4662 __isl_take isl_pw_qpolynomial_fold *pwf,
4664 __isl_give isl_pw_qpolynomial_fold *
4665 isl_map_apply_pw_qpolynomial_fold(
4666 __isl_take isl_map *map,
4667 __isl_take isl_pw_qpolynomial_fold *pwf,
4669 __isl_give isl_union_pw_qpolynomial_fold *
4670 isl_union_set_apply_union_pw_qpolynomial_fold(
4671 __isl_take isl_union_set *uset,
4672 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4674 __isl_give isl_union_pw_qpolynomial_fold *
4675 isl_union_map_apply_union_pw_qpolynomial_fold(
4676 __isl_take isl_union_map *umap,
4677 __isl_take isl_union_pw_qpolynomial_fold *upwf,
4680 The functions taking a map
4681 compose the given map with the given piecewise quasipolynomial reduction.
4682 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
4683 over all elements in the intersection of the range of the map
4684 and the domain of the piecewise quasipolynomial reduction
4685 as a function of an element in the domain of the map.
4686 The functions taking a set compute a bound over all elements in the
4687 intersection of the set and the domain of the
4688 piecewise quasipolynomial reduction.
4690 =head2 Parametric Vertex Enumeration
4692 The parametric vertex enumeration described in this section
4693 is mainly intended to be used internally and by the C<barvinok>
4696 #include <isl/vertices.h>
4697 __isl_give isl_vertices *isl_basic_set_compute_vertices(
4698 __isl_keep isl_basic_set *bset);
4700 The function C<isl_basic_set_compute_vertices> performs the
4701 actual computation of the parametric vertices and the chamber
4702 decomposition and store the result in an C<isl_vertices> object.
4703 This information can be queried by either iterating over all
4704 the vertices or iterating over all the chambers or cells
4705 and then iterating over all vertices that are active on the chamber.
4707 int isl_vertices_foreach_vertex(
4708 __isl_keep isl_vertices *vertices,
4709 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4712 int isl_vertices_foreach_cell(
4713 __isl_keep isl_vertices *vertices,
4714 int (*fn)(__isl_take isl_cell *cell, void *user),
4716 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
4717 int (*fn)(__isl_take isl_vertex *vertex, void *user),
4720 Other operations that can be performed on an C<isl_vertices> object are
4723 isl_ctx *isl_vertices_get_ctx(
4724 __isl_keep isl_vertices *vertices);
4725 int isl_vertices_get_n_vertices(
4726 __isl_keep isl_vertices *vertices);
4727 void isl_vertices_free(__isl_take isl_vertices *vertices);
4729 Vertices can be inspected and destroyed using the following functions.
4731 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
4732 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
4733 __isl_give isl_basic_set *isl_vertex_get_domain(
4734 __isl_keep isl_vertex *vertex);
4735 __isl_give isl_basic_set *isl_vertex_get_expr(
4736 __isl_keep isl_vertex *vertex);
4737 void isl_vertex_free(__isl_take isl_vertex *vertex);
4739 C<isl_vertex_get_expr> returns a singleton parametric set describing
4740 the vertex, while C<isl_vertex_get_domain> returns the activity domain
4742 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
4743 B<rational> basic sets, so they should mainly be used for inspection
4744 and should not be mixed with integer sets.
4746 Chambers can be inspected and destroyed using the following functions.
4748 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
4749 __isl_give isl_basic_set *isl_cell_get_domain(
4750 __isl_keep isl_cell *cell);
4751 void isl_cell_free(__isl_take isl_cell *cell);
4753 =head1 Polyhedral Compilation Library
4755 This section collects functionality in C<isl> that has been specifically
4756 designed for use during polyhedral compilation.
4758 =head2 Dependence Analysis
4760 C<isl> contains specialized functionality for performing
4761 array dataflow analysis. That is, given a I<sink> access relation
4762 and a collection of possible I<source> access relations,
4763 C<isl> can compute relations that describe
4764 for each iteration of the sink access, which iteration
4765 of which of the source access relations was the last
4766 to access the same data element before the given iteration
4768 The resulting dependence relations map source iterations
4769 to the corresponding sink iterations.
4770 To compute standard flow dependences, the sink should be
4771 a read, while the sources should be writes.
4772 If any of the source accesses are marked as being I<may>
4773 accesses, then there will be a dependence from the last
4774 I<must> access B<and> from any I<may> access that follows
4775 this last I<must> access.
4776 In particular, if I<all> sources are I<may> accesses,
4777 then memory based dependence analysis is performed.
4778 If, on the other hand, all sources are I<must> accesses,
4779 then value based dependence analysis is performed.
4781 #include <isl/flow.h>
4783 typedef int (*isl_access_level_before)(void *first, void *second);
4785 __isl_give isl_access_info *isl_access_info_alloc(
4786 __isl_take isl_map *sink,
4787 void *sink_user, isl_access_level_before fn,
4789 __isl_give isl_access_info *isl_access_info_add_source(
4790 __isl_take isl_access_info *acc,
4791 __isl_take isl_map *source, int must,
4793 void *isl_access_info_free(__isl_take isl_access_info *acc);
4795 __isl_give isl_flow *isl_access_info_compute_flow(
4796 __isl_take isl_access_info *acc);
4798 int isl_flow_foreach(__isl_keep isl_flow *deps,
4799 int (*fn)(__isl_take isl_map *dep, int must,
4800 void *dep_user, void *user),
4802 __isl_give isl_map *isl_flow_get_no_source(
4803 __isl_keep isl_flow *deps, int must);
4804 void isl_flow_free(__isl_take isl_flow *deps);
4806 The function C<isl_access_info_compute_flow> performs the actual
4807 dependence analysis. The other functions are used to construct
4808 the input for this function or to read off the output.
4810 The input is collected in an C<isl_access_info>, which can
4811 be created through a call to C<isl_access_info_alloc>.
4812 The arguments to this functions are the sink access relation
4813 C<sink>, a token C<sink_user> used to identify the sink
4814 access to the user, a callback function for specifying the
4815 relative order of source and sink accesses, and the number
4816 of source access relations that will be added.
4817 The callback function has type C<int (*)(void *first, void *second)>.
4818 The function is called with two user supplied tokens identifying
4819 either a source or the sink and it should return the shared nesting
4820 level and the relative order of the two accesses.
4821 In particular, let I<n> be the number of loops shared by
4822 the two accesses. If C<first> precedes C<second> textually,
4823 then the function should return I<2 * n + 1>; otherwise,
4824 it should return I<2 * n>.
4825 The sources can be added to the C<isl_access_info> by performing
4826 (at most) C<max_source> calls to C<isl_access_info_add_source>.
4827 C<must> indicates whether the source is a I<must> access
4828 or a I<may> access. Note that a multi-valued access relation
4829 should only be marked I<must> if every iteration in the domain
4830 of the relation accesses I<all> elements in its image.
4831 The C<source_user> token is again used to identify
4832 the source access. The range of the source access relation
4833 C<source> should have the same dimension as the range
4834 of the sink access relation.
4835 The C<isl_access_info_free> function should usually not be
4836 called explicitly, because it is called implicitly by
4837 C<isl_access_info_compute_flow>.
4839 The result of the dependence analysis is collected in an
4840 C<isl_flow>. There may be elements of
4841 the sink access for which no preceding source access could be
4842 found or for which all preceding sources are I<may> accesses.
4843 The relations containing these elements can be obtained through
4844 calls to C<isl_flow_get_no_source>, the first with C<must> set
4845 and the second with C<must> unset.
4846 In the case of standard flow dependence analysis,
4847 with the sink a read and the sources I<must> writes,
4848 the first relation corresponds to the reads from uninitialized
4849 array elements and the second relation is empty.
4850 The actual flow dependences can be extracted using
4851 C<isl_flow_foreach>. This function will call the user-specified
4852 callback function C<fn> for each B<non-empty> dependence between
4853 a source and the sink. The callback function is called
4854 with four arguments, the actual flow dependence relation
4855 mapping source iterations to sink iterations, a boolean that
4856 indicates whether it is a I<must> or I<may> dependence, a token
4857 identifying the source and an additional C<void *> with value
4858 equal to the third argument of the C<isl_flow_foreach> call.
4859 A dependence is marked I<must> if it originates from a I<must>
4860 source and if it is not followed by any I<may> sources.
4862 After finishing with an C<isl_flow>, the user should call
4863 C<isl_flow_free> to free all associated memory.
4865 A higher-level interface to dependence analysis is provided
4866 by the following function.
4868 #include <isl/flow.h>
4870 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
4871 __isl_take isl_union_map *must_source,
4872 __isl_take isl_union_map *may_source,
4873 __isl_take isl_union_map *schedule,
4874 __isl_give isl_union_map **must_dep,
4875 __isl_give isl_union_map **may_dep,
4876 __isl_give isl_union_map **must_no_source,
4877 __isl_give isl_union_map **may_no_source);
4879 The arrays are identified by the tuple names of the ranges
4880 of the accesses. The iteration domains by the tuple names
4881 of the domains of the accesses and of the schedule.
4882 The relative order of the iteration domains is given by the
4883 schedule. The relations returned through C<must_no_source>
4884 and C<may_no_source> are subsets of C<sink>.
4885 Any of C<must_dep>, C<may_dep>, C<must_no_source>
4886 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
4887 any of the other arguments is treated as an error.
4889 =head3 Interaction with Dependence Analysis
4891 During the dependence analysis, we frequently need to perform
4892 the following operation. Given a relation between sink iterations
4893 and potential source iterations from a particular source domain,
4894 what is the last potential source iteration corresponding to each
4895 sink iteration. It can sometimes be convenient to adjust
4896 the set of potential source iterations before or after each such operation.
4897 The prototypical example is fuzzy array dataflow analysis,
4898 where we need to analyze if, based on data-dependent constraints,
4899 the sink iteration can ever be executed without one or more of
4900 the corresponding potential source iterations being executed.
4901 If so, we can introduce extra parameters and select an unknown
4902 but fixed source iteration from the potential source iterations.
4903 To be able to perform such manipulations, C<isl> provides the following
4906 #include <isl/flow.h>
4908 typedef __isl_give isl_restriction *(*isl_access_restrict)(
4909 __isl_keep isl_map *source_map,
4910 __isl_keep isl_set *sink, void *source_user,
4912 __isl_give isl_access_info *isl_access_info_set_restrict(
4913 __isl_take isl_access_info *acc,
4914 isl_access_restrict fn, void *user);
4916 The function C<isl_access_info_set_restrict> should be called
4917 before calling C<isl_access_info_compute_flow> and registers a callback function
4918 that will be called any time C<isl> is about to compute the last
4919 potential source. The first argument is the (reverse) proto-dependence,
4920 mapping sink iterations to potential source iterations.
4921 The second argument represents the sink iterations for which
4922 we want to compute the last source iteration.
4923 The third argument is the token corresponding to the source
4924 and the final argument is the token passed to C<isl_access_info_set_restrict>.
4925 The callback is expected to return a restriction on either the input or
4926 the output of the operation computing the last potential source.
4927 If the input needs to be restricted then restrictions are needed
4928 for both the source and the sink iterations. The sink iterations
4929 and the potential source iterations will be intersected with these sets.
4930 If the output needs to be restricted then only a restriction on the source
4931 iterations is required.
4932 If any error occurs, the callback should return C<NULL>.
4933 An C<isl_restriction> object can be created, freed and inspected
4934 using the following functions.
4936 #include <isl/flow.h>
4938 __isl_give isl_restriction *isl_restriction_input(
4939 __isl_take isl_set *source_restr,
4940 __isl_take isl_set *sink_restr);
4941 __isl_give isl_restriction *isl_restriction_output(
4942 __isl_take isl_set *source_restr);
4943 __isl_give isl_restriction *isl_restriction_none(
4944 __isl_take isl_map *source_map);
4945 __isl_give isl_restriction *isl_restriction_empty(
4946 __isl_take isl_map *source_map);
4947 void *isl_restriction_free(
4948 __isl_take isl_restriction *restr);
4949 isl_ctx *isl_restriction_get_ctx(
4950 __isl_keep isl_restriction *restr);
4952 C<isl_restriction_none> and C<isl_restriction_empty> are special
4953 cases of C<isl_restriction_input>. C<isl_restriction_none>
4954 is essentially equivalent to
4956 isl_restriction_input(isl_set_universe(
4957 isl_space_range(isl_map_get_space(source_map))),
4959 isl_space_domain(isl_map_get_space(source_map))));
4961 whereas C<isl_restriction_empty> is essentially equivalent to
4963 isl_restriction_input(isl_set_empty(
4964 isl_space_range(isl_map_get_space(source_map))),
4966 isl_space_domain(isl_map_get_space(source_map))));
4970 B<The functionality described in this section is fairly new
4971 and may be subject to change.>
4973 The following function can be used to compute a schedule
4974 for a union of domains.
4975 By default, the algorithm used to construct the schedule is similar
4976 to that of C<Pluto>.
4977 Alternatively, Feautrier's multi-dimensional scheduling algorithm can
4979 The generated schedule respects all C<validity> dependences.
4980 That is, all dependence distances over these dependences in the
4981 scheduled space are lexicographically positive.
4982 The default algorithm tries to minimize the dependence distances over
4983 C<proximity> dependences.
4984 Moreover, it tries to obtain sequences (bands) of schedule dimensions
4985 for groups of domains where the dependence distances have only
4986 non-negative values.
4987 When using Feautrier's algorithm, the C<proximity> dependence
4988 distances are only minimized during the extension to a
4989 full-dimensional schedule.
4991 #include <isl/schedule.h>
4992 __isl_give isl_schedule *isl_union_set_compute_schedule(
4993 __isl_take isl_union_set *domain,
4994 __isl_take isl_union_map *validity,
4995 __isl_take isl_union_map *proximity);
4996 void *isl_schedule_free(__isl_take isl_schedule *sched);
4998 A mapping from the domains to the scheduled space can be obtained
4999 from an C<isl_schedule> using the following function.
5001 __isl_give isl_union_map *isl_schedule_get_map(
5002 __isl_keep isl_schedule *sched);
5004 A representation of the schedule can be printed using
5006 __isl_give isl_printer *isl_printer_print_schedule(
5007 __isl_take isl_printer *p,
5008 __isl_keep isl_schedule *schedule);
5010 A representation of the schedule as a forest of bands can be obtained
5011 using the following function.
5013 __isl_give isl_band_list *isl_schedule_get_band_forest(
5014 __isl_keep isl_schedule *schedule);
5016 The individual bands can be visited in depth-first post-order
5017 using the following function.
5019 #include <isl/schedule.h>
5020 int isl_schedule_foreach_band(
5021 __isl_keep isl_schedule *sched,
5022 int (*fn)(__isl_keep isl_band *band, void *user),
5025 The list can be manipulated as explained in L<"Lists">.
5026 The bands inside the list can be copied and freed using the following
5029 #include <isl/band.h>
5030 __isl_give isl_band *isl_band_copy(
5031 __isl_keep isl_band *band);
5032 void *isl_band_free(__isl_take isl_band *band);
5034 Each band contains zero or more scheduling dimensions.
5035 These are referred to as the members of the band.
5036 The section of the schedule that corresponds to the band is
5037 referred to as the partial schedule of the band.
5038 For those nodes that participate in a band, the outer scheduling
5039 dimensions form the prefix schedule, while the inner scheduling
5040 dimensions form the suffix schedule.
5041 That is, if we take a cut of the band forest, then the union of
5042 the concatenations of the prefix, partial and suffix schedules of
5043 each band in the cut is equal to the entire schedule (modulo
5044 some possible padding at the end with zero scheduling dimensions).
5045 The properties of a band can be inspected using the following functions.
5047 #include <isl/band.h>
5048 isl_ctx *isl_band_get_ctx(__isl_keep isl_band *band);
5050 int isl_band_has_children(__isl_keep isl_band *band);
5051 __isl_give isl_band_list *isl_band_get_children(
5052 __isl_keep isl_band *band);
5054 __isl_give isl_union_map *isl_band_get_prefix_schedule(
5055 __isl_keep isl_band *band);
5056 __isl_give isl_union_map *isl_band_get_partial_schedule(
5057 __isl_keep isl_band *band);
5058 __isl_give isl_union_map *isl_band_get_suffix_schedule(
5059 __isl_keep isl_band *band);
5061 int isl_band_n_member(__isl_keep isl_band *band);
5062 int isl_band_member_is_zero_distance(
5063 __isl_keep isl_band *band, int pos);
5065 int isl_band_list_foreach_band(
5066 __isl_keep isl_band_list *list,
5067 int (*fn)(__isl_keep isl_band *band, void *user),
5070 Note that a scheduling dimension is considered to be ``zero
5071 distance'' if it does not carry any proximity dependences
5073 That is, if the dependence distances of the proximity
5074 dependences are all zero in that direction (for fixed
5075 iterations of outer bands).
5076 Like C<isl_schedule_foreach_band>,
5077 the function C<isl_band_list_foreach_band> calls C<fn> on the bands
5078 in depth-first post-order.
5080 A band can be tiled using the following function.
5082 #include <isl/band.h>
5083 int isl_band_tile(__isl_keep isl_band *band,
5084 __isl_take isl_vec *sizes);
5086 int isl_options_set_tile_scale_tile_loops(isl_ctx *ctx,
5088 int isl_options_get_tile_scale_tile_loops(isl_ctx *ctx);
5090 The C<isl_band_tile> function tiles the band using the given tile sizes
5091 inside its schedule.
5092 A new child band is created to represent the point loops and it is
5093 inserted between the modified band and its children.
5094 The C<tile_scale_tile_loops> option specifies whether the tile
5095 loops iterators should be scaled by the tile sizes.
5097 A representation of the band can be printed using
5099 #include <isl/band.h>
5100 __isl_give isl_printer *isl_printer_print_band(
5101 __isl_take isl_printer *p,
5102 __isl_keep isl_band *band);
5106 #include <isl/schedule.h>
5107 int isl_options_set_schedule_max_coefficient(
5108 isl_ctx *ctx, int val);
5109 int isl_options_get_schedule_max_coefficient(
5111 int isl_options_set_schedule_max_constant_term(
5112 isl_ctx *ctx, int val);
5113 int isl_options_get_schedule_max_constant_term(
5115 int isl_options_set_schedule_fuse(isl_ctx *ctx, int val);
5116 int isl_options_get_schedule_fuse(isl_ctx *ctx);
5117 int isl_options_set_schedule_maximize_band_depth(
5118 isl_ctx *ctx, int val);
5119 int isl_options_get_schedule_maximize_band_depth(
5121 int isl_options_set_schedule_outer_zero_distance(
5122 isl_ctx *ctx, int val);
5123 int isl_options_get_schedule_outer_zero_distance(
5125 int isl_options_set_schedule_split_scaled(
5126 isl_ctx *ctx, int val);
5127 int isl_options_get_schedule_split_scaled(
5129 int isl_options_set_schedule_algorithm(
5130 isl_ctx *ctx, int val);
5131 int isl_options_get_schedule_algorithm(
5133 int isl_options_set_schedule_separate_components(
5134 isl_ctx *ctx, int val);
5135 int isl_options_get_schedule_separate_components(
5140 =item * schedule_max_coefficient
5142 This option enforces that the coefficients for variable and parameter
5143 dimensions in the calculated schedule are not larger than the specified value.
5144 This option can significantly increase the speed of the scheduling calculation
5145 and may also prevent fusing of unrelated dimensions. A value of -1 means that
5146 this option does not introduce bounds on the variable or parameter
5149 =item * schedule_max_constant_term
5151 This option enforces that the constant coefficients in the calculated schedule
5152 are not larger than the maximal constant term. This option can significantly
5153 increase the speed of the scheduling calculation and may also prevent fusing of
5154 unrelated dimensions. A value of -1 means that this option does not introduce
5155 bounds on the constant coefficients.
5157 =item * schedule_fuse
5159 This option controls the level of fusion.
5160 If this option is set to C<ISL_SCHEDULE_FUSE_MIN>, then loops in the
5161 resulting schedule will be distributed as much as possible.
5162 If this option is set to C<ISL_SCHEDULE_FUSE_MAX>, then C<isl> will
5163 try to fuse loops in the resulting schedule.
5165 =item * schedule_maximize_band_depth
5167 If this option is set, we do not split bands at the point
5168 where we detect splitting is necessary. Instead, we
5169 backtrack and split bands as early as possible. This
5170 reduces the number of splits and maximizes the width of
5171 the bands. Wider bands give more possibilities for tiling.
5172 Note that if the C<schedule_fuse> option is set to C<ISL_SCHEDULE_FUSE_MIN>,
5173 then bands will be split as early as possible, even if there is no need.
5174 The C<schedule_maximize_band_depth> option therefore has no effect in this case.
5176 =item * schedule_outer_zero_distance
5178 If this option is set, then we try to construct schedules
5179 where the outermost scheduling dimension in each band
5180 results in a zero dependence distance over the proximity
5183 =item * schedule_split_scaled
5185 If this option is set, then we try to construct schedules in which the
5186 constant term is split off from the linear part if the linear parts of
5187 the scheduling rows for all nodes in the graphs have a common non-trivial
5189 The constant term is then placed in a separate band and the linear
5192 =item * schedule_algorithm
5194 Selects the scheduling algorithm to be used.
5195 Available scheduling algorithms are C<ISL_SCHEDULE_ALGORITHM_ISL>
5196 and C<ISL_SCHEDULE_ALGORITHM_FEAUTRIER>.
5198 =item * schedule_separate_components
5200 If at any point the dependence graph contains any (weakly connected) components,
5201 then these components are scheduled separately.
5202 If this option is not set, then some iterations of the domains
5203 in these components may be scheduled together.
5204 If this option is set, then the components are given consecutive
5209 =head2 AST Generation
5211 This section describes the C<isl> functionality for generating
5212 ASTs that visit all the elements
5213 in a domain in an order specified by a schedule.
5214 In particular, given a C<isl_union_map>, an AST is generated
5215 that visits all the elements in the domain of the C<isl_union_map>
5216 according to the lexicographic order of the corresponding image
5217 element(s). If the range of the C<isl_union_map> consists of
5218 elements in more than one space, then each of these spaces is handled
5219 separately in an arbitrary order.
5220 It should be noted that the image elements only specify the I<order>
5221 in which the corresponding domain elements should be visited.
5222 No direct relation between the image elements and the loop iterators
5223 in the generated AST should be assumed.
5225 Each AST is generated within a build. The initial build
5226 simply specifies the constraints on the parameters (if any)
5227 and can be created, inspected, copied and freed using the following functions.
5229 #include <isl/ast_build.h>
5230 __isl_give isl_ast_build *isl_ast_build_from_context(
5231 __isl_take isl_set *set);
5232 isl_ctx *isl_ast_build_get_ctx(
5233 __isl_keep isl_ast_build *build);
5234 __isl_give isl_ast_build *isl_ast_build_copy(
5235 __isl_keep isl_ast_build *build);
5236 void *isl_ast_build_free(
5237 __isl_take isl_ast_build *build);
5239 The C<set> argument is usually a parameter set with zero or more parameters.
5240 More C<isl_ast_build> functions are described in L</"Nested AST Generation">
5241 and L</"Fine-grained Control over AST Generation">.
5242 Finally, the AST itself can be constructed using the following
5245 #include <isl/ast_build.h>
5246 __isl_give isl_ast_node *isl_ast_build_ast_from_schedule(
5247 __isl_keep isl_ast_build *build,
5248 __isl_take isl_union_map *schedule);
5250 =head3 Inspecting the AST
5252 The basic properties of an AST node can be obtained as follows.
5254 #include <isl/ast.h>
5255 isl_ctx *isl_ast_node_get_ctx(
5256 __isl_keep isl_ast_node *node);
5257 enum isl_ast_node_type isl_ast_node_get_type(
5258 __isl_keep isl_ast_node *node);
5260 The type of an AST node is one of
5261 C<isl_ast_node_for>,
5263 C<isl_ast_node_block> or
5264 C<isl_ast_node_user>.
5265 An C<isl_ast_node_for> represents a for node.
5266 An C<isl_ast_node_if> represents an if node.
5267 An C<isl_ast_node_block> represents a compound node.
5268 An C<isl_ast_node_user> represents an expression statement.
5269 An expression statement typically corresponds to a domain element, i.e.,
5270 one of the elements that is visited by the AST.
5272 Each type of node has its own additional properties.
5274 #include <isl/ast.h>
5275 __isl_give isl_ast_expr *isl_ast_node_for_get_iterator(
5276 __isl_keep isl_ast_node *node);
5277 __isl_give isl_ast_expr *isl_ast_node_for_get_init(
5278 __isl_keep isl_ast_node *node);
5279 __isl_give isl_ast_expr *isl_ast_node_for_get_cond(
5280 __isl_keep isl_ast_node *node);
5281 __isl_give isl_ast_expr *isl_ast_node_for_get_inc(
5282 __isl_keep isl_ast_node *node);
5283 __isl_give isl_ast_node *isl_ast_node_for_get_body(
5284 __isl_keep isl_ast_node *node);
5285 int isl_ast_node_for_is_degenerate(
5286 __isl_keep isl_ast_node *node);
5288 An C<isl_ast_for> is considered degenerate if it is known to execute
5291 #include <isl/ast.h>
5292 __isl_give isl_ast_expr *isl_ast_node_if_get_cond(
5293 __isl_keep isl_ast_node *node);
5294 __isl_give isl_ast_node *isl_ast_node_if_get_then(
5295 __isl_keep isl_ast_node *node);
5296 int isl_ast_node_if_has_else(
5297 __isl_keep isl_ast_node *node);
5298 __isl_give isl_ast_node *isl_ast_node_if_get_else(
5299 __isl_keep isl_ast_node *node);
5301 __isl_give isl_ast_node_list *
5302 isl_ast_node_block_get_children(
5303 __isl_keep isl_ast_node *node);
5305 __isl_give isl_ast_expr *isl_ast_node_user_get_expr(
5306 __isl_keep isl_ast_node *node);
5308 Each of the returned C<isl_ast_expr>s can in turn be inspected using
5309 the following functions.
5311 #include <isl/ast.h>
5312 isl_ctx *isl_ast_expr_get_ctx(
5313 __isl_keep isl_ast_expr *expr);
5314 enum isl_ast_expr_type isl_ast_expr_get_type(
5315 __isl_keep isl_ast_expr *expr);
5317 The type of an AST expression is one of
5319 C<isl_ast_expr_id> or
5320 C<isl_ast_expr_int>.
5321 An C<isl_ast_expr_op> represents the result of an operation.
5322 An C<isl_ast_expr_id> represents an identifier.
5323 An C<isl_ast_expr_int> represents an integer value.
5325 Each type of expression has its own additional properties.
5327 #include <isl/ast.h>
5328 enum isl_ast_op_type isl_ast_expr_get_op_type(
5329 __isl_keep isl_ast_expr *expr);
5330 int isl_ast_expr_get_op_n_arg(__isl_keep isl_ast_expr *expr);
5331 __isl_give isl_ast_expr *isl_ast_expr_get_op_arg(
5332 __isl_keep isl_ast_expr *expr, int pos);
5333 int isl_ast_node_foreach_ast_op_type(
5334 __isl_keep isl_ast_node *node,
5335 int (*fn)(enum isl_ast_op_type type, void *user),
5338 C<isl_ast_expr_get_op_type> returns the type of the operation
5339 performed. C<isl_ast_expr_get_op_n_arg> returns the number of
5340 arguments. C<isl_ast_expr_get_op_arg> returns the specified
5342 C<isl_ast_node_foreach_ast_op_type> calls C<fn> for each distinct
5343 C<isl_ast_op_type> that appears in C<node>.
5344 The operation type is one of the following.
5348 =item C<isl_ast_op_and>
5350 Logical I<and> of two arguments.
5351 Both arguments can be evaluated.
5353 =item C<isl_ast_op_and_then>
5355 Logical I<and> of two arguments.
5356 The second argument can only be evaluated if the first evaluates to true.
5358 =item C<isl_ast_op_or>
5360 Logical I<or> of two arguments.
5361 Both arguments can be evaluated.
5363 =item C<isl_ast_op_or_else>
5365 Logical I<or> of two arguments.
5366 The second argument can only be evaluated if the first evaluates to false.
5368 =item C<isl_ast_op_max>
5370 Maximum of two or more arguments.
5372 =item C<isl_ast_op_min>
5374 Minimum of two or more arguments.
5376 =item C<isl_ast_op_minus>
5380 =item C<isl_ast_op_add>
5382 Sum of two arguments.
5384 =item C<isl_ast_op_sub>
5386 Difference of two arguments.
5388 =item C<isl_ast_op_mul>
5390 Product of two arguments.
5392 =item C<isl_ast_op_div>
5394 Exact division. That is, the result is known to be an integer.
5396 =item C<isl_ast_op_fdiv_q>
5398 Result of integer division, rounded towards negative
5401 =item C<isl_ast_op_pdiv_q>
5403 Result of integer division, where dividend is known to be non-negative.
5405 =item C<isl_ast_op_pdiv_r>
5407 Remainder of integer division, where dividend is known to be non-negative.
5409 =item C<isl_ast_op_cond>
5411 Conditional operator defined on three arguments.
5412 If the first argument evaluates to true, then the result
5413 is equal to the second argument. Otherwise, the result
5414 is equal to the third argument.
5415 The second and third argument may only be evaluated if
5416 the first argument evaluates to true and false, respectively.
5417 Corresponds to C<a ? b : c> in C.
5419 =item C<isl_ast_op_select>
5421 Conditional operator defined on three arguments.
5422 If the first argument evaluates to true, then the result
5423 is equal to the second argument. Otherwise, the result
5424 is equal to the third argument.
5425 The second and third argument may be evaluated independently
5426 of the value of the first argument.
5427 Corresponds to C<a * b + (1 - a) * c> in C.
5429 =item C<isl_ast_op_eq>
5433 =item C<isl_ast_op_le>
5435 Less than or equal relation.
5437 =item C<isl_ast_op_lt>
5441 =item C<isl_ast_op_ge>
5443 Greater than or equal relation.
5445 =item C<isl_ast_op_gt>
5447 Greater than relation.
5449 =item C<isl_ast_op_call>
5452 The number of arguments of the C<isl_ast_expr> is one more than
5453 the number of arguments in the function call, the first argument
5454 representing the function being called.
5458 #include <isl/ast.h>
5459 __isl_give isl_id *isl_ast_expr_get_id(
5460 __isl_keep isl_ast_expr *expr);
5462 Return the identifier represented by the AST expression.
5464 #include <isl/ast.h>
5465 int isl_ast_expr_get_int(__isl_keep isl_ast_expr *expr,
5468 Return the integer represented by the AST expression.
5469 Note that the integer is returned through the C<v> argument.
5470 The return value of the function itself indicates whether the
5471 operation was performed successfully.
5473 =head3 Manipulating and printing the AST
5475 AST nodes can be copied and freed using the following functions.
5477 #include <isl/ast.h>
5478 __isl_give isl_ast_node *isl_ast_node_copy(
5479 __isl_keep isl_ast_node *node);
5480 void *isl_ast_node_free(__isl_take isl_ast_node *node);
5482 AST expressions can be copied and freed using the following functions.
5484 #include <isl/ast.h>
5485 __isl_give isl_ast_expr *isl_ast_expr_copy(
5486 __isl_keep isl_ast_expr *expr);
5487 void *isl_ast_expr_free(__isl_take isl_ast_expr *expr);
5489 New AST expressions can be created either directly or within
5490 the context of an C<isl_ast_build>.
5492 #include <isl/ast.h>
5493 __isl_give isl_ast_expr *isl_ast_expr_from_id(
5494 __isl_take isl_id *id);
5495 __isl_give isl_ast_expr *isl_ast_expr_neg(
5496 __isl_take isl_ast_expr *expr);
5497 __isl_give isl_ast_expr *isl_ast_expr_add(
5498 __isl_take isl_ast_expr *expr1,
5499 __isl_take isl_ast_expr *expr2);
5500 __isl_give isl_ast_expr *isl_ast_expr_sub(
5501 __isl_take isl_ast_expr *expr1,
5502 __isl_take isl_ast_expr *expr2);
5503 __isl_give isl_ast_expr *isl_ast_expr_mul(
5504 __isl_take isl_ast_expr *expr1,
5505 __isl_take isl_ast_expr *expr2);
5506 __isl_give isl_ast_expr *isl_ast_expr_div(
5507 __isl_take isl_ast_expr *expr1,
5508 __isl_take isl_ast_expr *expr2);
5509 __isl_give isl_ast_expr *isl_ast_expr_and(
5510 __isl_take isl_ast_expr *expr1,
5511 __isl_take isl_ast_expr *expr2)
5512 __isl_give isl_ast_expr *isl_ast_expr_or(
5513 __isl_take isl_ast_expr *expr1,
5514 __isl_take isl_ast_expr *expr2)
5516 #include <isl/ast_build.h>
5517 __isl_give isl_ast_expr *isl_ast_build_expr_from_pw_aff(
5518 __isl_keep isl_ast_build *build,
5519 __isl_take isl_pw_aff *pa);
5520 __isl_give isl_ast_expr *
5521 isl_ast_build_call_from_pw_multi_aff(
5522 __isl_keep isl_ast_build *build,
5523 __isl_take isl_pw_multi_aff *pma);
5525 The domains of C<pa> and C<pma> should correspond
5526 to the schedule space of C<build>.
5527 The tuple id of C<pma> is used as the function being called.
5529 User specified data can be attached to an C<isl_ast_node> and obtained
5530 from the same C<isl_ast_node> using the following functions.
5532 #include <isl/ast.h>
5533 __isl_give isl_ast_node *isl_ast_node_set_annotation(
5534 __isl_take isl_ast_node *node,
5535 __isl_take isl_id *annotation);
5536 __isl_give isl_id *isl_ast_node_get_annotation(
5537 __isl_keep isl_ast_node *node);
5539 Basic printing can be performed using the following functions.
5541 #include <isl/ast.h>
5542 __isl_give isl_printer *isl_printer_print_ast_expr(
5543 __isl_take isl_printer *p,
5544 __isl_keep isl_ast_expr *expr);
5545 __isl_give isl_printer *isl_printer_print_ast_node(
5546 __isl_take isl_printer *p,
5547 __isl_keep isl_ast_node *node);
5549 More advanced printing can be performed using the following functions.
5551 #include <isl/ast.h>
5552 __isl_give isl_printer *isl_ast_op_type_print_macro(
5553 enum isl_ast_op_type type,
5554 __isl_take isl_printer *p);
5555 __isl_give isl_printer *isl_ast_node_print_macros(
5556 __isl_keep isl_ast_node *node,
5557 __isl_take isl_printer *p);
5558 __isl_give isl_printer *isl_ast_node_print(
5559 __isl_keep isl_ast_node *node,
5560 __isl_take isl_printer *p,
5561 __isl_take isl_ast_print_options *options);
5562 __isl_give isl_printer *isl_ast_node_for_print(
5563 __isl_keep isl_ast_node *node,
5564 __isl_take isl_printer *p,
5565 __isl_take isl_ast_print_options *options);
5566 __isl_give isl_printer *isl_ast_node_if_print(
5567 __isl_keep isl_ast_node *node,
5568 __isl_take isl_printer *p,
5569 __isl_take isl_ast_print_options *options);
5571 While printing an C<isl_ast_node> in C<ISL_FORMAT_C>,
5572 C<isl> may print out an AST that makes use of macros such
5573 as C<floord>, C<min> and C<max>.
5574 C<isl_ast_op_type_print_macro> prints out the macro
5575 corresponding to a specific C<isl_ast_op_type>.
5576 C<isl_ast_node_print_macros> scans the C<isl_ast_node>
5577 for expressions where these macros would be used and prints
5578 out the required macro definitions.
5579 Essentially, C<isl_ast_node_print_macros> calls
5580 C<isl_ast_node_foreach_ast_op_type> with C<isl_ast_op_type_print_macro>
5581 as function argument.
5582 C<isl_ast_node_print>, C<isl_ast_node_for_print> and
5583 C<isl_ast_node_if_print> print an C<isl_ast_node>
5584 in C<ISL_FORMAT_C>, but allow for some extra control
5585 through an C<isl_ast_print_options> object.
5586 This object can be created using the following functions.
5588 #include <isl/ast.h>
5589 __isl_give isl_ast_print_options *
5590 isl_ast_print_options_alloc(isl_ctx *ctx);
5591 __isl_give isl_ast_print_options *
5592 isl_ast_print_options_copy(
5593 __isl_keep isl_ast_print_options *options);
5594 void *isl_ast_print_options_free(
5595 __isl_take isl_ast_print_options *options);
5597 __isl_give isl_ast_print_options *
5598 isl_ast_print_options_set_print_user(
5599 __isl_take isl_ast_print_options *options,
5600 __isl_give isl_printer *(*print_user)(
5601 __isl_take isl_printer *p,
5602 __isl_take isl_ast_print_options *options,
5603 __isl_keep isl_ast_node *node, void *user),
5605 __isl_give isl_ast_print_options *
5606 isl_ast_print_options_set_print_for(
5607 __isl_take isl_ast_print_options *options,
5608 __isl_give isl_printer *(*print_for)(
5609 __isl_take isl_printer *p,
5610 __isl_take isl_ast_print_options *options,
5611 __isl_keep isl_ast_node *node, void *user),
5614 The callback set by C<isl_ast_print_options_set_print_user>
5615 is called whenever a node of type C<isl_ast_node_user> needs to
5617 The callback set by C<isl_ast_print_options_set_print_for>
5618 is called whenever a node of type C<isl_ast_node_for> needs to
5620 Note that C<isl_ast_node_for_print> will I<not> call the
5621 callback set by C<isl_ast_print_options_set_print_for> on the node
5622 on which C<isl_ast_node_for_print> is called, but only on nested
5623 nodes of type C<isl_ast_node_for>. It is therefore safe to
5624 call C<isl_ast_node_for_print> from within the callback set by
5625 C<isl_ast_print_options_set_print_for>.
5627 The following option determines the type to be used for iterators
5628 while printing the AST.
5630 int isl_options_set_ast_iterator_type(
5631 isl_ctx *ctx, const char *val);
5632 const char *isl_options_get_ast_iterator_type(
5637 #include <isl/ast_build.h>
5638 int isl_options_set_ast_build_atomic_upper_bound(
5639 isl_ctx *ctx, int val);
5640 int isl_options_get_ast_build_atomic_upper_bound(
5642 int isl_options_set_ast_build_prefer_pdiv(isl_ctx *ctx,
5644 int isl_options_get_ast_build_prefer_pdiv(isl_ctx *ctx);
5645 int isl_options_set_ast_build_exploit_nested_bounds(
5646 isl_ctx *ctx, int val);
5647 int isl_options_get_ast_build_exploit_nested_bounds(
5649 int isl_options_set_ast_build_group_coscheduled(
5650 isl_ctx *ctx, int val);
5651 int isl_options_get_ast_build_group_coscheduled(
5653 int isl_options_set_ast_build_scale_strides(
5654 isl_ctx *ctx, int val);
5655 int isl_options_get_ast_build_scale_strides(
5657 int isl_options_set_ast_build_allow_else(isl_ctx *ctx,
5659 int isl_options_get_ast_build_allow_else(isl_ctx *ctx);
5660 int isl_options_set_ast_build_allow_or(isl_ctx *ctx,
5662 int isl_options_get_ast_build_allow_or(isl_ctx *ctx);
5666 =item * ast_build_atomic_upper_bound
5668 Generate loop upper bounds that consist of the current loop iterator,
5669 an operator and an expression not involving the iterator.
5670 If this option is not set, then the current loop iterator may appear
5671 several times in the upper bound.
5672 For example, when this option is turned off, AST generation
5675 [n] -> { A[i] -> [i] : 0 <= i <= 100, n }
5679 for (int c0 = 0; c0 <= 100 && n >= c0; c0 += 1)
5682 When the option is turned on, the following AST is generated
5684 for (int c0 = 0; c0 <= min(100, n); c0 += 1)
5687 =item * ast_build_prefer_pdiv
5689 If this option is turned off, then the AST generation will
5690 produce ASTs that may only contain C<isl_ast_op_fdiv_q>
5691 operators, but no C<isl_ast_op_pdiv_q> or
5692 C<isl_ast_op_pdiv_r> operators.
5693 If this options is turned on, then C<isl> will try to convert
5694 some of the C<isl_ast_op_fdiv_q> operators to (expressions containing)
5695 C<isl_ast_op_pdiv_q> or C<isl_ast_op_pdiv_r> operators.
5697 =item * ast_build_exploit_nested_bounds
5699 Simplify conditions based on bounds of nested for loops.
5700 In particular, remove conditions that are implied by the fact
5701 that one or more nested loops have at least one iteration,
5702 meaning that the upper bound is at least as large as the lower bound.
5703 For example, when this option is turned off, AST generation
5706 [N,M] -> { A[i,j] -> [i,j] : 0 <= i <= N and
5712 for (int c0 = 0; c0 <= N; c0 += 1)
5713 for (int c1 = 0; c1 <= M; c1 += 1)
5716 When the option is turned on, the following AST is generated
5718 for (int c0 = 0; c0 <= N; c0 += 1)
5719 for (int c1 = 0; c1 <= M; c1 += 1)
5722 =item * ast_build_group_coscheduled
5724 If two domain elements are assigned the same schedule point, then
5725 they may be executed in any order and they may even appear in different
5726 loops. If this options is set, then the AST generator will make
5727 sure that coscheduled domain elements do not appear in separate parts
5728 of the AST. This is useful in case of nested AST generation
5729 if the outer AST generation is given only part of a schedule
5730 and the inner AST generation should handle the domains that are
5731 coscheduled by this initial part of the schedule together.
5732 For example if an AST is generated for a schedule
5734 { A[i] -> [0]; B[i] -> [0] }
5736 then the C<isl_ast_build_set_create_leaf> callback described
5737 below may get called twice, once for each domain.
5738 Setting this option ensures that the callback is only called once
5739 on both domains together.
5741 =item * ast_build_separation_bounds
5743 This option specifies which bounds to use during separation.
5744 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_IMPLICIT>
5745 then all (possibly implicit) bounds on the current dimension will
5746 be used during separation.
5747 If this option is set to C<ISL_AST_BUILD_SEPARATION_BOUNDS_EXPLICIT>
5748 then only those bounds that are explicitly available will
5749 be used during separation.
5751 =item * ast_build_scale_strides
5753 This option specifies whether the AST generator is allowed
5754 to scale down iterators of strided loops.
5756 =item * ast_build_allow_else
5758 This option specifies whether the AST generator is allowed
5759 to construct if statements with else branches.
5761 =item * ast_build_allow_or
5763 This option specifies whether the AST generator is allowed
5764 to construct if conditions with disjunctions.
5768 =head3 Fine-grained Control over AST Generation
5770 Besides specifying the constraints on the parameters,
5771 an C<isl_ast_build> object can be used to control
5772 various aspects of the AST generation process.
5773 The most prominent way of control is through ``options'',
5774 which can be set using the following function.
5776 #include <isl/ast_build.h>
5777 __isl_give isl_ast_build *
5778 isl_ast_build_set_options(
5779 __isl_take isl_ast_build *control,
5780 __isl_take isl_union_map *options);
5782 The options are encoded in an <isl_union_map>.
5783 The domain of this union relation refers to the schedule domain,
5784 i.e., the range of the schedule passed to C<isl_ast_build_ast_from_schedule>.
5785 In the case of nested AST generation (see L</"Nested AST Generation">),
5786 the domain of C<options> should refer to the extra piece of the schedule.
5787 That is, it should be equal to the range of the wrapped relation in the
5788 range of the schedule.
5789 The range of the options can consist of elements in one or more spaces,
5790 the names of which determine the effect of the option.
5791 The values of the range typically also refer to the schedule dimension
5792 to which the option applies. In case of nested AST generation
5793 (see L</"Nested AST Generation">), these values refer to the position
5794 of the schedule dimension within the innermost AST generation.
5795 The constraints on the domain elements of
5796 the option should only refer to this dimension and earlier dimensions.
5797 We consider the following spaces.
5801 =item C<separation_class>
5803 This space is a wrapped relation between two one dimensional spaces.
5804 The input space represents the schedule dimension to which the option
5805 applies and the output space represents the separation class.
5806 While constructing a loop corresponding to the specified schedule
5807 dimension(s), the AST generator will try to generate separate loops
5808 for domain elements that are assigned different classes.
5809 If only some of the elements are assigned a class, then those elements
5810 that are not assigned any class will be treated as belonging to a class
5811 that is separate from the explicitly assigned classes.
5812 The typical use case for this option is to separate full tiles from
5814 The other options, described below, are applied after the separation
5817 As an example, consider the separation into full and partial tiles
5818 of a tiling of a triangular domain.
5819 Take, for example, the domain
5821 { A[i,j] : 0 <= i,j and i + j <= 100 }
5823 and a tiling into tiles of 10 by 10. The input to the AST generator
5824 is then the schedule
5826 { A[i,j] -> [([i/10]),[j/10],i,j] : 0 <= i,j and
5829 Without any options, the following AST is generated
5831 for (int c0 = 0; c0 <= 10; c0 += 1)
5832 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
5833 for (int c2 = 10 * c0;
5834 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
5836 for (int c3 = 10 * c1;
5837 c3 <= min(10 * c1 + 9, -c2 + 100);
5841 Separation into full and partial tiles can be obtained by assigning
5842 a class, say C<0>, to the full tiles. The full tiles are represented by those
5843 values of the first and second schedule dimensions for which there are
5844 values of the third and fourth dimensions to cover an entire tile.
5845 That is, we need to specify the following option
5847 { [a,b,c,d] -> separation_class[[0]->[0]] :
5848 exists b': 0 <= 10a,10b' and
5849 10a+9+10b'+9 <= 100;
5850 [a,b,c,d] -> separation_class[[1]->[0]] :
5851 0 <= 10a,10b and 10a+9+10b+9 <= 100 }
5855 { [a, b, c, d] -> separation_class[[1] -> [0]] :
5856 a >= 0 and b >= 0 and b <= 8 - a;
5857 [a, b, c, d] -> separation_class[[0] -> [0]] :
5860 With this option, the generated AST is as follows
5863 for (int c0 = 0; c0 <= 8; c0 += 1) {
5864 for (int c1 = 0; c1 <= -c0 + 8; c1 += 1)
5865 for (int c2 = 10 * c0;
5866 c2 <= 10 * c0 + 9; c2 += 1)
5867 for (int c3 = 10 * c1;
5868 c3 <= 10 * c1 + 9; c3 += 1)
5870 for (int c1 = -c0 + 9; c1 <= -c0 + 10; c1 += 1)
5871 for (int c2 = 10 * c0;
5872 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
5874 for (int c3 = 10 * c1;
5875 c3 <= min(-c2 + 100, 10 * c1 + 9);
5879 for (int c0 = 9; c0 <= 10; c0 += 1)
5880 for (int c1 = 0; c1 <= -c0 + 10; c1 += 1)
5881 for (int c2 = 10 * c0;
5882 c2 <= min(-10 * c1 + 100, 10 * c0 + 9);
5884 for (int c3 = 10 * c1;
5885 c3 <= min(10 * c1 + 9, -c2 + 100);
5892 This is a single-dimensional space representing the schedule dimension(s)
5893 to which ``separation'' should be applied. Separation tries to split
5894 a loop into several pieces if this can avoid the generation of guards
5896 See also the C<atomic> option.
5900 This is a single-dimensional space representing the schedule dimension(s)
5901 for which the domains should be considered ``atomic''. That is, the
5902 AST generator will make sure that any given domain space will only appear
5903 in a single loop at the specified level.
5905 Consider the following schedule
5907 { a[i] -> [i] : 0 <= i < 10;
5908 b[i] -> [i+1] : 0 <= i < 10 }
5910 If the following option is specified
5912 { [i] -> separate[x] }
5914 then the following AST will be generated
5918 for (int c0 = 1; c0 <= 9; c0 += 1) {
5925 If, on the other hand, the following option is specified
5927 { [i] -> atomic[x] }
5929 then the following AST will be generated
5931 for (int c0 = 0; c0 <= 10; c0 += 1) {
5938 If neither C<atomic> nor C<separate> is specified, then the AST generator
5939 may produce either of these two results or some intermediate form.
5943 This is a single-dimensional space representing the schedule dimension(s)
5944 that should be I<completely> unrolled.
5945 To obtain a partial unrolling, the user should apply an additional
5946 strip-mining to the schedule and fully unroll the inner loop.
5950 Additional control is available through the following functions.
5952 #include <isl/ast_build.h>
5953 __isl_give isl_ast_build *
5954 isl_ast_build_set_iterators(
5955 __isl_take isl_ast_build *control,
5956 __isl_take isl_id_list *iterators);
5958 The function C<isl_ast_build_set_iterators> allows the user to
5959 specify a list of iterator C<isl_id>s to be used as iterators.
5960 If the input schedule is injective, then
5961 the number of elements in this list should be as large as the dimension
5962 of the schedule space, but no direct correspondence should be assumed
5963 between dimensions and elements.
5964 If the input schedule is not injective, then an additional number
5965 of C<isl_id>s equal to the largest dimension of the input domains
5967 If the number of provided C<isl_id>s is insufficient, then additional
5968 names are automatically generated.
5970 #include <isl/ast_build.h>
5971 __isl_give isl_ast_build *
5972 isl_ast_build_set_create_leaf(
5973 __isl_take isl_ast_build *control,
5974 __isl_give isl_ast_node *(*fn)(
5975 __isl_take isl_ast_build *build,
5976 void *user), void *user);
5979 C<isl_ast_build_set_create_leaf> function allows for the
5980 specification of a callback that should be called whenever the AST
5981 generator arrives at an element of the schedule domain.
5982 The callback should return an AST node that should be inserted
5983 at the corresponding position of the AST. The default action (when
5984 the callback is not set) is to continue generating parts of the AST to scan
5985 all the domain elements associated to the schedule domain element
5986 and to insert user nodes, ``calling'' the domain element, for each of them.
5987 The C<build> argument contains the current state of the C<isl_ast_build>.
5988 To ease nested AST generation (see L</"Nested AST Generation">),
5989 all control information that is
5990 specific to the current AST generation such as the options and
5991 the callbacks has been removed from this C<isl_ast_build>.
5992 The callback would typically return the result of a nested
5994 user defined node created using the following function.
5996 #include <isl/ast.h>
5997 __isl_give isl_ast_node *isl_ast_node_alloc_user(
5998 __isl_take isl_ast_expr *expr);
6000 #include <isl/ast_build.h>
6001 __isl_give isl_ast_build *
6002 isl_ast_build_set_at_each_domain(
6003 __isl_take isl_ast_build *build,
6004 __isl_give isl_ast_node *(*fn)(
6005 __isl_take isl_ast_node *node,
6006 __isl_keep isl_ast_build *build,
6007 void *user), void *user);
6008 __isl_give isl_ast_build *
6009 isl_ast_build_set_before_each_for(
6010 __isl_take isl_ast_build *build,
6011 __isl_give isl_id *(*fn)(
6012 __isl_keep isl_ast_build *build,
6013 void *user), void *user);
6014 __isl_give isl_ast_build *
6015 isl_ast_build_set_after_each_for(
6016 __isl_take isl_ast_build *build,
6017 __isl_give isl_ast_node *(*fn)(
6018 __isl_take isl_ast_node *node,
6019 __isl_keep isl_ast_build *build,
6020 void *user), void *user);
6022 The callback set by C<isl_ast_build_set_at_each_domain> will
6023 be called for each domain AST node.
6024 The callbacks set by C<isl_ast_build_set_before_each_for>
6025 and C<isl_ast_build_set_after_each_for> will be called
6026 for each for AST node. The first will be called in depth-first
6027 pre-order, while the second will be called in depth-first post-order.
6028 Since C<isl_ast_build_set_before_each_for> is called before the for
6029 node is actually constructed, it is only passed an C<isl_ast_build>.
6030 The returned C<isl_id> will be added as an annotation (using
6031 C<isl_ast_node_set_annotation>) to the constructed for node.
6032 In particular, if the user has also specified an C<after_each_for>
6033 callback, then the annotation can be retrieved from the node passed to
6034 that callback using C<isl_ast_node_get_annotation>.
6035 All callbacks should C<NULL> on failure.
6036 The given C<isl_ast_build> can be used to create new
6037 C<isl_ast_expr> objects using C<isl_ast_build_expr_from_pw_aff>
6038 or C<isl_ast_build_call_from_pw_multi_aff>.
6040 =head3 Nested AST Generation
6042 C<isl> allows the user to create an AST within the context
6043 of another AST. These nested ASTs are created using the
6044 same C<isl_ast_build_ast_from_schedule> function that is used to create the
6045 outer AST. The C<build> argument should be an C<isl_ast_build>
6046 passed to a callback set by
6047 C<isl_ast_build_set_create_leaf>.
6048 The space of the range of the C<schedule> argument should refer
6049 to this build. In particular, the space should be a wrapped
6050 relation and the domain of this wrapped relation should be the
6051 same as that of the range of the schedule returned by
6052 C<isl_ast_build_get_schedule> below.
6053 In practice, the new schedule is typically
6054 created by calling C<isl_union_map_range_product> on the old schedule
6055 and some extra piece of the schedule.
6056 The space of the schedule domain is also available from
6057 the C<isl_ast_build>.
6059 #include <isl/ast_build.h>
6060 __isl_give isl_union_map *isl_ast_build_get_schedule(
6061 __isl_keep isl_ast_build *build);
6062 __isl_give isl_space *isl_ast_build_get_schedule_space(
6063 __isl_keep isl_ast_build *build);
6064 __isl_give isl_ast_build *isl_ast_build_restrict(
6065 __isl_take isl_ast_build *build,
6066 __isl_take isl_set *set);
6068 The C<isl_ast_build_get_schedule> function returns a (partial)
6069 schedule for the domains elements for which part of the AST still needs to
6070 be generated in the current build.
6071 In particular, the domain elements are mapped to those iterations of the loops
6072 enclosing the current point of the AST generation inside which
6073 the domain elements are executed.
6074 No direct correspondence between
6075 the input schedule and this schedule should be assumed.
6076 The space obtained from C<isl_ast_build_get_schedule_space> can be used
6077 to create a set for C<isl_ast_build_restrict> to intersect
6078 with the current build. In particular, the set passed to
6079 C<isl_ast_build_restrict> can have additional parameters.
6080 The ids of the set dimensions in the space returned by
6081 C<isl_ast_build_get_schedule_space> correspond to the
6082 iterators of the already generated loops.
6083 The user should not rely on the ids of the output dimensions
6084 of the relations in the union relation returned by
6085 C<isl_ast_build_get_schedule> having any particular value.
6089 Although C<isl> is mainly meant to be used as a library,
6090 it also contains some basic applications that use some
6091 of the functionality of C<isl>.
6092 The input may be specified in either the L<isl format>
6093 or the L<PolyLib format>.
6095 =head2 C<isl_polyhedron_sample>
6097 C<isl_polyhedron_sample> takes a polyhedron as input and prints
6098 an integer element of the polyhedron, if there is any.
6099 The first column in the output is the denominator and is always
6100 equal to 1. If the polyhedron contains no integer points,
6101 then a vector of length zero is printed.
6105 C<isl_pip> takes the same input as the C<example> program
6106 from the C<piplib> distribution, i.e., a set of constraints
6107 on the parameters, a line containing only -1 and finally a set
6108 of constraints on a parametric polyhedron.
6109 The coefficients of the parameters appear in the last columns
6110 (but before the final constant column).
6111 The output is the lexicographic minimum of the parametric polyhedron.
6112 As C<isl> currently does not have its own output format, the output
6113 is just a dump of the internal state.
6115 =head2 C<isl_polyhedron_minimize>
6117 C<isl_polyhedron_minimize> computes the minimum of some linear
6118 or affine objective function over the integer points in a polyhedron.
6119 If an affine objective function
6120 is given, then the constant should appear in the last column.
6122 =head2 C<isl_polytope_scan>
6124 Given a polytope, C<isl_polytope_scan> prints
6125 all integer points in the polytope.
6127 =head2 C<isl_codegen>
6129 Given a schedule, a context set and an options relation,
6130 C<isl_codegen> prints out an AST that scans the domain elements
6131 of the schedule in the order of their image(s) taking into account
6132 the constraints in the context set.