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>
60 The source of C<isl> can be obtained either as a tarball
61 or from the git repository. Both are available from
62 L<http://freshmeat.net/projects/isl/>.
63 The installation process depends on how you obtained
66 =head2 Installation from the git repository
70 =item 1 Clone or update the repository
72 The first time the source is obtained, you need to clone
75 git clone git://repo.or.cz/isl.git
77 To obtain updates, you need to pull in the latest changes
81 =item 2 Generate C<configure>
87 After performing the above steps, continue
88 with the L<Common installation instructions>.
90 =head2 Common installation instructions
96 Building C<isl> requires C<GMP>, including its headers files.
97 Your distribution may not provide these header files by default
98 and you may need to install a package called C<gmp-devel> or something
99 similar. Alternatively, C<GMP> can be built from
100 source, available from L<http://gmplib.org/>.
104 C<isl> uses the standard C<autoconf> C<configure> script.
109 optionally followed by some configure options.
110 A complete list of options can be obtained by running
114 Below we discuss some of the more common options.
116 C<isl> can optionally use C<piplib>, but no
117 C<piplib> functionality is currently used by default.
118 The C<--with-piplib> option can
119 be used to specify which C<piplib>
120 library to use, either an installed version (C<system>),
121 an externally built version (C<build>)
122 or no version (C<no>). The option C<build> is mostly useful
123 in C<configure> scripts of larger projects that bundle both C<isl>
130 Installation prefix for C<isl>
132 =item C<--with-gmp-prefix>
134 Installation prefix for C<GMP> (architecture-independent files).
136 =item C<--with-gmp-exec-prefix>
138 Installation prefix for C<GMP> (architecture-dependent files).
140 =item C<--with-piplib>
142 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
144 =item C<--with-piplib-prefix>
146 Installation prefix for C<system> C<piplib> (architecture-independent files).
148 =item C<--with-piplib-exec-prefix>
150 Installation prefix for C<system> C<piplib> (architecture-dependent files).
152 =item C<--with-piplib-builddir>
154 Location where C<build> C<piplib> was built.
162 =item 4 Install (optional)
170 =head2 Initialization
172 All manipulations of integer sets and relations occur within
173 the context of an C<isl_ctx>.
174 A given C<isl_ctx> can only be used within a single thread.
175 All arguments of a function are required to have been allocated
176 within the same context.
177 There are currently no functions available for moving an object
178 from one C<isl_ctx> to another C<isl_ctx>. This means that
179 there is currently no way of safely moving an object from one
180 thread to another, unless the whole C<isl_ctx> is moved.
182 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
183 freed using C<isl_ctx_free>.
184 All objects allocated within an C<isl_ctx> should be freed
185 before the C<isl_ctx> itself is freed.
187 isl_ctx *isl_ctx_alloc();
188 void isl_ctx_free(isl_ctx *ctx);
192 All operations on integers, mainly the coefficients
193 of the constraints describing the sets and relations,
194 are performed in exact integer arithmetic using C<GMP>.
195 However, to allow future versions of C<isl> to optionally
196 support fixed integer arithmetic, all calls to C<GMP>
197 are wrapped inside C<isl> specific macros.
198 The basic type is C<isl_int> and the following operations
199 are available on this type.
200 The meanings of these operations are essentially the same
201 as their C<GMP> C<mpz_> counterparts.
202 As always with C<GMP> types, C<isl_int>s need to be
203 initialized with C<isl_int_init> before they can be used
204 and they need to be released with C<isl_int_clear>
209 =item isl_int_init(i)
211 =item isl_int_clear(i)
213 =item isl_int_set(r,i)
215 =item isl_int_set_si(r,i)
217 =item isl_int_set_gmp(r,g)
219 =item isl_int_get_gmp(i,g)
221 =item isl_int_abs(r,i)
223 =item isl_int_neg(r,i)
225 =item isl_int_swap(i,j)
227 =item isl_int_swap_or_set(i,j)
229 =item isl_int_add_ui(r,i,j)
231 =item isl_int_sub_ui(r,i,j)
233 =item isl_int_add(r,i,j)
235 =item isl_int_sub(r,i,j)
237 =item isl_int_mul(r,i,j)
239 =item isl_int_mul_ui(r,i,j)
241 =item isl_int_addmul(r,i,j)
243 =item isl_int_submul(r,i,j)
245 =item isl_int_gcd(r,i,j)
247 =item isl_int_lcm(r,i,j)
249 =item isl_int_divexact(r,i,j)
251 =item isl_int_cdiv_q(r,i,j)
253 =item isl_int_fdiv_q(r,i,j)
255 =item isl_int_fdiv_r(r,i,j)
257 =item isl_int_fdiv_q_ui(r,i,j)
259 =item isl_int_read(r,s)
261 =item isl_int_print(out,i,width)
265 =item isl_int_cmp(i,j)
267 =item isl_int_cmp_si(i,si)
269 =item isl_int_eq(i,j)
271 =item isl_int_ne(i,j)
273 =item isl_int_lt(i,j)
275 =item isl_int_le(i,j)
277 =item isl_int_gt(i,j)
279 =item isl_int_ge(i,j)
281 =item isl_int_abs_eq(i,j)
283 =item isl_int_abs_ne(i,j)
285 =item isl_int_abs_lt(i,j)
287 =item isl_int_abs_gt(i,j)
289 =item isl_int_abs_ge(i,j)
291 =item isl_int_is_zero(i)
293 =item isl_int_is_one(i)
295 =item isl_int_is_negone(i)
297 =item isl_int_is_pos(i)
299 =item isl_int_is_neg(i)
301 =item isl_int_is_nonpos(i)
303 =item isl_int_is_nonneg(i)
305 =item isl_int_is_divisible_by(i,j)
309 =head2 Sets and Relations
311 C<isl> uses six types of objects for representing sets and relations,
312 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
313 C<isl_union_set> and C<isl_union_map>.
314 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
315 can be described as a conjunction of affine constraints, while
316 C<isl_set> and C<isl_map> represent unions of
317 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
318 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
319 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
320 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
321 where dimensions with different space names
322 (see L<Dimension Specifications>) are considered different as well.
323 The difference between sets and relations (maps) is that sets have
324 one set of variables, while relations have two sets of variables,
325 input variables and output variables.
327 =head2 Memory Management
329 Since a high-level operation on sets and/or relations usually involves
330 several substeps and since the user is usually not interested in
331 the intermediate results, most functions that return a new object
332 will also release all the objects passed as arguments.
333 If the user still wants to use one or more of these arguments
334 after the function call, she should pass along a copy of the
335 object rather than the object itself.
336 The user is then responsible for make sure that the original
337 object gets used somewhere else or is explicitly freed.
339 The arguments and return values of all documents functions are
340 annotated to make clear which arguments are released and which
341 arguments are preserved. In particular, the following annotations
348 C<__isl_give> means that a new object is returned.
349 The user should make sure that the returned pointer is
350 used exactly once as a value for an C<__isl_take> argument.
351 In between, it can be used as a value for as many
352 C<__isl_keep> arguments as the user likes.
353 There is one exception, and that is the case where the
354 pointer returned is C<NULL>. Is this case, the user
355 is free to use it as an C<__isl_take> argument or not.
359 C<__isl_take> means that the object the argument points to
360 is taken over by the function and may no longer be used
361 by the user as an argument to any other function.
362 The pointer value must be one returned by a function
363 returning an C<__isl_give> pointer.
364 If the user passes in a C<NULL> value, then this will
365 be treated as an error in the sense that the function will
366 not perform its usual operation. However, it will still
367 make sure that all the the other C<__isl_take> arguments
372 C<__isl_keep> means that the function will only use the object
373 temporarily. After the function has finished, the user
374 can still use it as an argument to other functions.
375 A C<NULL> value will be treated in the same way as
376 a C<NULL> value for an C<__isl_take> argument.
380 =head2 Dimension Specifications
382 Whenever a new set or relation is created from scratch,
383 its dimension needs to be specified using an C<isl_dim>.
386 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
387 unsigned nparam, unsigned n_in, unsigned n_out);
388 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
389 unsigned nparam, unsigned dim);
390 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
391 void isl_dim_free(__isl_take isl_dim *dim);
392 unsigned isl_dim_size(__isl_keep isl_dim *dim,
393 enum isl_dim_type type);
395 The dimension specification used for creating a set
396 needs to be created using C<isl_dim_set_alloc>, while
397 that for creating a relation
398 needs to be created using C<isl_dim_alloc>.
399 C<isl_dim_size> can be used
400 to find out the number of dimensions of each type in
401 a dimension specification, where type may be
402 C<isl_dim_param>, C<isl_dim_in> (only for relations),
403 C<isl_dim_out> (only for relations), C<isl_dim_set>
404 (only for sets) or C<isl_dim_all>.
406 It is often useful to create objects that live in the
407 same space as some other object. This can be accomplished
408 by creating the new objects
409 (see L<Creating New Sets and Relations> or
410 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
411 specification of the original object.
414 __isl_give isl_dim *isl_basic_set_get_dim(
415 __isl_keep isl_basic_set *bset);
416 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
418 #include <isl/union_set.h>
419 __isl_give isl_dim *isl_union_set_get_dim(
420 __isl_keep isl_union_set *uset);
423 __isl_give isl_dim *isl_basic_map_get_dim(
424 __isl_keep isl_basic_map *bmap);
425 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
427 #include <isl/union_map.h>
428 __isl_give isl_dim *isl_union_map_get_dim(
429 __isl_keep isl_union_map *umap);
431 #include <isl/polynomial.h>
432 __isl_give isl_dim *isl_qpolynomial_get_dim(
433 __isl_keep isl_qpolynomial *qp);
434 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
435 __isl_keep isl_pw_qpolynomial *pwqp);
436 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
437 __isl_keep isl_union_pw_qpolynomial *upwqp);
438 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
439 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
441 The names of the individual dimensions may be set or read off
442 using the following functions.
445 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
446 enum isl_dim_type type, unsigned pos,
447 __isl_keep const char *name);
448 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
449 enum isl_dim_type type, unsigned pos);
451 Note that C<isl_dim_get_name> returns a pointer to some internal
452 data structure, so the result can only be used while the
453 corresponding C<isl_dim> is alive.
454 Also note that every function that operates on two sets or relations
455 requires that both arguments have the same parameters. This also
456 means that if one of the arguments has named parameters, then the
457 other needs to have named parameters too and the names need to match.
458 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
459 have different parameters (as long as they are named), in which case
460 the result will have as parameters the union of the parameters of
463 The names of entire spaces may be set or read off
464 using the following functions.
467 __isl_give isl_dim *isl_dim_set_tuple_name(
468 __isl_take isl_dim *dim,
469 enum isl_dim_type type, const char *s);
470 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
471 enum isl_dim_type type);
473 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
474 or C<isl_dim_set>. As with C<isl_dim_get_name>,
475 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
477 Binary operations require the corresponding spaces of their arguments
478 to have the same name.
480 Spaces can be nested. In particular, the domain of a set or
481 the domain or range of a relation can be a nested relation.
482 The following functions can be used to construct and deconstruct
483 such nested dimension specifications.
486 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
487 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
488 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
490 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
491 be the dimension specification of a set, while that of
492 C<isl_dim_wrap> should be the dimension specification of a relation.
493 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
494 of a relation, while that of C<isl_dim_wrap> is the dimension specification
497 Dimension specifications can be created from other dimension
498 specifications using the following functions.
500 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
501 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
502 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
503 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
504 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
505 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
506 __isl_take isl_dim *right);
507 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
508 enum isl_dim_type type, unsigned pos, unsigned n);
509 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
510 enum isl_dim_type type, unsigned n);
511 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
512 enum isl_dim_type type, unsigned first, unsigned n);
514 Note that if dimensions are added or removed from a space, then
515 the name and the internal structure are lost.
517 =head2 Input and Output
519 C<isl> supports its own input/output format, which is similar
520 to the C<Omega> format, but also supports the C<PolyLib> format
525 The C<isl> format is similar to that of C<Omega>, but has a different
526 syntax for describing the parameters and allows for the definition
527 of an existentially quantified variable as the integer division
528 of an affine expression.
529 For example, the set of integers C<i> between C<0> and C<n>
530 such that C<i % 10 <= 6> can be described as
532 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
535 A set or relation can have several disjuncts, separated
536 by the keyword C<or>. Each disjunct is either a conjunction
537 of constraints or a projection (C<exists>) of a conjunction
538 of constraints. The constraints are separated by the keyword
541 =head3 C<PolyLib> format
543 If the represented set is a union, then the first line
544 contains a single number representing the number of disjuncts.
545 Otherwise, a line containing the number C<1> is optional.
547 Each disjunct is represented by a matrix of constraints.
548 The first line contains two numbers representing
549 the number of rows and columns,
550 where the number of rows is equal to the number of constraints
551 and the number of columns is equal to two plus the number of variables.
552 The following lines contain the actual rows of the constraint matrix.
553 In each row, the first column indicates whether the constraint
554 is an equality (C<0>) or inequality (C<1>). The final column
555 corresponds to the constant term.
557 If the set is parametric, then the coefficients of the parameters
558 appear in the last columns before the constant column.
559 The coefficients of any existentially quantified variables appear
560 between those of the set variables and those of the parameters.
562 =head3 Extended C<PolyLib> format
564 The extended C<PolyLib> format is nearly identical to the
565 C<PolyLib> format. The only difference is that the line
566 containing the number of rows and columns of a constraint matrix
567 also contains four additional numbers:
568 the number of output dimensions, the number of input dimensions,
569 the number of local dimensions (i.e., the number of existentially
570 quantified variables) and the number of parameters.
571 For sets, the number of ``output'' dimensions is equal
572 to the number of set dimensions, while the number of ``input''
578 __isl_give isl_basic_set *isl_basic_set_read_from_file(
579 isl_ctx *ctx, FILE *input, int nparam);
580 __isl_give isl_basic_set *isl_basic_set_read_from_str(
581 isl_ctx *ctx, const char *str, int nparam);
582 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
583 FILE *input, int nparam);
584 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
585 const char *str, int nparam);
588 __isl_give isl_basic_map *isl_basic_map_read_from_file(
589 isl_ctx *ctx, FILE *input, int nparam);
590 __isl_give isl_basic_map *isl_basic_map_read_from_str(
591 isl_ctx *ctx, const char *str, int nparam);
592 __isl_give isl_map *isl_map_read_from_file(
593 struct isl_ctx *ctx, FILE *input, int nparam);
594 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
595 const char *str, int nparam);
597 #include <isl/union_set.h>
598 __isl_give isl_union_set *isl_union_set_read_from_str(
599 struct isl_ctx *ctx, const char *str);
601 #include <isl/union_map.h>
602 __isl_give isl_union_map *isl_union_map_read_from_str(
603 struct isl_ctx *ctx, const char *str);
605 The input format is autodetected and may be either the C<PolyLib> format
606 or the C<isl> format.
607 C<nparam> specifies how many of the final columns in
608 the C<PolyLib> format correspond to parameters.
609 If input is given in the C<isl> format, then the number
610 of parameters needs to be equal to C<nparam>.
611 If C<nparam> is negative, then any number of parameters
612 is accepted in the C<isl> format and zero parameters
613 are assumed in the C<PolyLib> format.
617 Before anything can be printed, an C<isl_printer> needs to
620 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
622 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
623 void isl_printer_free(__isl_take isl_printer *printer);
624 __isl_give char *isl_printer_get_str(
625 __isl_keep isl_printer *printer);
627 The behavior of the printer can be modified in various ways
629 __isl_give isl_printer *isl_printer_set_output_format(
630 __isl_take isl_printer *p, int output_format);
631 __isl_give isl_printer *isl_printer_set_indent(
632 __isl_take isl_printer *p, int indent);
633 __isl_give isl_printer *isl_printer_set_prefix(
634 __isl_take isl_printer *p, const char *prefix);
635 __isl_give isl_printer *isl_printer_set_suffix(
636 __isl_take isl_printer *p, const char *suffix);
638 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
639 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
640 and defaults to C<ISL_FORMAT_ISL>.
641 Each line in the output is indented by C<indent> spaces
642 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
643 In the C<PolyLib> format output,
644 the coefficients of the existentially quantified variables
645 appear between those of the set variables and those
648 To actually print something, use
651 __isl_give isl_printer *isl_printer_print_basic_set(
652 __isl_take isl_printer *printer,
653 __isl_keep isl_basic_set *bset);
654 __isl_give isl_printer *isl_printer_print_set(
655 __isl_take isl_printer *printer,
656 __isl_keep isl_set *set);
659 __isl_give isl_printer *isl_printer_print_basic_map(
660 __isl_take isl_printer *printer,
661 __isl_keep isl_basic_map *bmap);
662 __isl_give isl_printer *isl_printer_print_map(
663 __isl_take isl_printer *printer,
664 __isl_keep isl_map *map);
666 #include <isl/union_set.h>
667 __isl_give isl_printer *isl_printer_print_union_set(
668 __isl_take isl_printer *p,
669 __isl_keep isl_union_set *uset);
671 #include <isl/union_map.h>
672 __isl_give isl_printer *isl_printer_print_union_map(
673 __isl_take isl_printer *p,
674 __isl_keep isl_union_map *umap);
676 When called on a file printer, the following function flushes
677 the file. When called on a string printer, the buffer is cleared.
679 __isl_give isl_printer *isl_printer_flush(
680 __isl_take isl_printer *p);
682 =head2 Creating New Sets and Relations
684 C<isl> has functions for creating some standard sets and relations.
688 =item * Empty sets and relations
690 __isl_give isl_basic_set *isl_basic_set_empty(
691 __isl_take isl_dim *dim);
692 __isl_give isl_basic_map *isl_basic_map_empty(
693 __isl_take isl_dim *dim);
694 __isl_give isl_set *isl_set_empty(
695 __isl_take isl_dim *dim);
696 __isl_give isl_map *isl_map_empty(
697 __isl_take isl_dim *dim);
698 __isl_give isl_union_set *isl_union_set_empty(
699 __isl_take isl_dim *dim);
700 __isl_give isl_union_map *isl_union_map_empty(
701 __isl_take isl_dim *dim);
703 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
704 is only used to specify the parameters.
706 =item * Universe sets and relations
708 __isl_give isl_basic_set *isl_basic_set_universe(
709 __isl_take isl_dim *dim);
710 __isl_give isl_basic_map *isl_basic_map_universe(
711 __isl_take isl_dim *dim);
712 __isl_give isl_set *isl_set_universe(
713 __isl_take isl_dim *dim);
714 __isl_give isl_map *isl_map_universe(
715 __isl_take isl_dim *dim);
717 =item * Identity relations
719 __isl_give isl_basic_map *isl_basic_map_identity(
720 __isl_take isl_dim *set_dim);
721 __isl_give isl_map *isl_map_identity(
722 __isl_take isl_dim *set_dim);
724 These functions take a dimension specification for a B<set>
725 and return an identity relation between two such sets.
727 =item * Lexicographic order
729 __isl_give isl_map *isl_map_lex_lt(
730 __isl_take isl_dim *set_dim);
731 __isl_give isl_map *isl_map_lex_le(
732 __isl_take isl_dim *set_dim);
733 __isl_give isl_map *isl_map_lex_gt(
734 __isl_take isl_dim *set_dim);
735 __isl_give isl_map *isl_map_lex_ge(
736 __isl_take isl_dim *set_dim);
737 __isl_give isl_map *isl_map_lex_lt_first(
738 __isl_take isl_dim *dim, unsigned n);
739 __isl_give isl_map *isl_map_lex_le_first(
740 __isl_take isl_dim *dim, unsigned n);
741 __isl_give isl_map *isl_map_lex_gt_first(
742 __isl_take isl_dim *dim, unsigned n);
743 __isl_give isl_map *isl_map_lex_ge_first(
744 __isl_take isl_dim *dim, unsigned n);
746 The first four functions take a dimension specification for a B<set>
747 and return relations that express that the elements in the domain
748 are lexicographically less
749 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
750 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
751 than the elements in the range.
752 The last four functions take a dimension specification for a map
753 and return relations that express that the first C<n> dimensions
754 in the domain are lexicographically less
755 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
756 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
757 than the first C<n> dimensions in the range.
761 A basic set or relation can be converted to a set or relation
762 using the following functions.
764 __isl_give isl_set *isl_set_from_basic_set(
765 __isl_take isl_basic_set *bset);
766 __isl_give isl_map *isl_map_from_basic_map(
767 __isl_take isl_basic_map *bmap);
769 Sets and relations can be converted to union sets and relations
770 using the following functions.
772 __isl_give isl_union_map *isl_union_map_from_map(
773 __isl_take isl_map *map);
774 __isl_give isl_union_set *isl_union_set_from_set(
775 __isl_take isl_set *set);
777 Sets and relations can be copied and freed again using the following
780 __isl_give isl_basic_set *isl_basic_set_copy(
781 __isl_keep isl_basic_set *bset);
782 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
783 __isl_give isl_union_set *isl_union_set_copy(
784 __isl_keep isl_union_set *uset);
785 __isl_give isl_basic_map *isl_basic_map_copy(
786 __isl_keep isl_basic_map *bmap);
787 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
788 __isl_give isl_union_map *isl_union_map_copy(
789 __isl_keep isl_union_map *umap);
790 void isl_basic_set_free(__isl_take isl_basic_set *bset);
791 void isl_set_free(__isl_take isl_set *set);
792 void isl_union_set_free(__isl_take isl_union_set *uset);
793 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
794 void isl_map_free(__isl_take isl_map *map);
795 void isl_union_map_free(__isl_take isl_union_map *umap);
797 Other sets and relations can be constructed by starting
798 from a universe set or relation, adding equality and/or
799 inequality constraints and then projecting out the
800 existentially quantified variables, if any.
801 Constraints can be constructed, manipulated and
802 added to basic sets and relations using the following functions.
804 #include <isl/constraint.h>
805 __isl_give isl_constraint *isl_equality_alloc(
806 __isl_take isl_dim *dim);
807 __isl_give isl_constraint *isl_inequality_alloc(
808 __isl_take isl_dim *dim);
809 void isl_constraint_set_constant(
810 __isl_keep isl_constraint *constraint, isl_int v);
811 void isl_constraint_set_coefficient(
812 __isl_keep isl_constraint *constraint,
813 enum isl_dim_type type, int pos, isl_int v);
814 __isl_give isl_basic_map *isl_basic_map_add_constraint(
815 __isl_take isl_basic_map *bmap,
816 __isl_take isl_constraint *constraint);
817 __isl_give isl_basic_set *isl_basic_set_add_constraint(
818 __isl_take isl_basic_set *bset,
819 __isl_take isl_constraint *constraint);
821 For example, to create a set containing the even integers
822 between 10 and 42, you would use the following code.
826 struct isl_constraint *c;
827 struct isl_basic_set *bset;
830 dim = isl_dim_set_alloc(ctx, 0, 2);
831 bset = isl_basic_set_universe(isl_dim_copy(dim));
833 c = isl_equality_alloc(isl_dim_copy(dim));
834 isl_int_set_si(v, -1);
835 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
836 isl_int_set_si(v, 2);
837 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
838 bset = isl_basic_set_add_constraint(bset, c);
840 c = isl_inequality_alloc(isl_dim_copy(dim));
841 isl_int_set_si(v, -10);
842 isl_constraint_set_constant(c, v);
843 isl_int_set_si(v, 1);
844 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
845 bset = isl_basic_set_add_constraint(bset, c);
847 c = isl_inequality_alloc(dim);
848 isl_int_set_si(v, 42);
849 isl_constraint_set_constant(c, v);
850 isl_int_set_si(v, -1);
851 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
852 bset = isl_basic_set_add_constraint(bset, c);
854 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
860 struct isl_basic_set *bset;
861 bset = isl_basic_set_read_from_str(ctx,
862 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
864 A basic set or relation can also be constructed from two matrices
865 describing the equalities and the inequalities.
867 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
868 __isl_take isl_dim *dim,
869 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
870 enum isl_dim_type c1,
871 enum isl_dim_type c2, enum isl_dim_type c3,
872 enum isl_dim_type c4);
873 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
874 __isl_take isl_dim *dim,
875 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
876 enum isl_dim_type c1,
877 enum isl_dim_type c2, enum isl_dim_type c3,
878 enum isl_dim_type c4, enum isl_dim_type c5);
880 The C<isl_dim_type> arguments indicate the order in which
881 different kinds of variables appear in the input matrices
882 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
883 C<isl_dim_set> and C<isl_dim_div> for sets and
884 of C<isl_dim_cst>, C<isl_dim_param>,
885 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
887 =head2 Inspecting Sets and Relations
889 Usually, the user should not have to care about the actual constraints
890 of the sets and maps, but should instead apply the abstract operations
891 explained in the following sections.
892 Occasionally, however, it may be required to inspect the individual
893 coefficients of the constraints. This section explains how to do so.
894 In these cases, it may also be useful to have C<isl> compute
895 an explicit representation of the existentially quantified variables.
897 __isl_give isl_set *isl_set_compute_divs(
898 __isl_take isl_set *set);
899 __isl_give isl_map *isl_map_compute_divs(
900 __isl_take isl_map *map);
901 __isl_give isl_union_set *isl_union_set_compute_divs(
902 __isl_take isl_union_set *uset);
903 __isl_give isl_union_map *isl_union_map_compute_divs(
904 __isl_take isl_union_map *umap);
906 This explicit representation defines the existentially quantified
907 variables as integer divisions of the other variables, possibly
908 including earlier existentially quantified variables.
909 An explicitly represented existentially quantified variable therefore
910 has a unique value when the values of the other variables are known.
911 If, furthermore, the same existentials, i.e., existentials
912 with the same explicit representations, should appear in the
913 same order in each of the disjuncts of a set or map, then the user should call
914 either of the following functions.
916 __isl_give isl_set *isl_set_align_divs(
917 __isl_take isl_set *set);
918 __isl_give isl_map *isl_map_align_divs(
919 __isl_take isl_map *map);
921 Alternatively, the existentially quantified variables can be removed
922 using the following functions, which compute an overapproximation.
924 __isl_give isl_basic_set *isl_basic_set_remove_divs(
925 __isl_take isl_basic_set *bset);
926 __isl_give isl_basic_map *isl_basic_map_remove_divs(
927 __isl_take isl_basic_map *bmap);
928 __isl_give isl_set *isl_set_remove_divs(
929 __isl_take isl_set *set);
931 To iterate over all the sets or maps in a union set or map, use
933 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
934 int (*fn)(__isl_take isl_set *set, void *user),
936 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
937 int (*fn)(__isl_take isl_map *map, void *user),
940 The number of sets or maps in a union set or map can be obtained
943 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
944 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
946 To extract the set or map from a union with a given dimension
949 __isl_give isl_set *isl_union_set_extract_set(
950 __isl_keep isl_union_set *uset,
951 __isl_take isl_dim *dim);
952 __isl_give isl_map *isl_union_map_extract_map(
953 __isl_keep isl_union_map *umap,
954 __isl_take isl_dim *dim);
956 To iterate over all the basic sets or maps in a set or map, use
958 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
959 int (*fn)(__isl_take isl_basic_set *bset, void *user),
961 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
962 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
965 The callback function C<fn> should return 0 if successful and
966 -1 if an error occurs. In the latter case, or if any other error
967 occurs, the above functions will return -1.
969 It should be noted that C<isl> does not guarantee that
970 the basic sets or maps passed to C<fn> are disjoint.
971 If this is required, then the user should call one of
972 the following functions first.
974 __isl_give isl_set *isl_set_make_disjoint(
975 __isl_take isl_set *set);
976 __isl_give isl_map *isl_map_make_disjoint(
977 __isl_take isl_map *map);
979 The number of basic sets in a set can be obtained
982 int isl_set_n_basic_set(__isl_keep isl_set *set);
984 To iterate over the constraints of a basic set or map, use
986 #include <isl/constraint.h>
988 int isl_basic_map_foreach_constraint(
989 __isl_keep isl_basic_map *bmap,
990 int (*fn)(__isl_take isl_constraint *c, void *user),
992 void isl_constraint_free(struct isl_constraint *c);
994 Again, the callback function C<fn> should return 0 if successful and
995 -1 if an error occurs. In the latter case, or if any other error
996 occurs, the above functions will return -1.
997 The constraint C<c> represents either an equality or an inequality.
998 Use the following function to find out whether a constraint
999 represents an equality. If not, it represents an inequality.
1001 int isl_constraint_is_equality(
1002 __isl_keep isl_constraint *constraint);
1004 The coefficients of the constraints can be inspected using
1005 the following functions.
1007 void isl_constraint_get_constant(
1008 __isl_keep isl_constraint *constraint, isl_int *v);
1009 void isl_constraint_get_coefficient(
1010 __isl_keep isl_constraint *constraint,
1011 enum isl_dim_type type, int pos, isl_int *v);
1013 The explicit representations of the existentially quantified
1014 variables can be inspected using the following functions.
1015 Note that the user is only allowed to use these functions
1016 if the inspected set or map is the result of a call
1017 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1019 __isl_give isl_div *isl_constraint_div(
1020 __isl_keep isl_constraint *constraint, int pos);
1021 void isl_div_get_constant(__isl_keep isl_div *div,
1023 void isl_div_get_denominator(__isl_keep isl_div *div,
1025 void isl_div_get_coefficient(__isl_keep isl_div *div,
1026 enum isl_dim_type type, int pos, isl_int *v);
1028 To obtain the constraints of a basic map in matrix
1029 form, use the following functions.
1031 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1032 __isl_keep isl_basic_map *bmap,
1033 enum isl_dim_type c1,
1034 enum isl_dim_type c2, enum isl_dim_type c3,
1035 enum isl_dim_type c4, enum isl_dim_type c5);
1036 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1037 __isl_keep isl_basic_map *bmap,
1038 enum isl_dim_type c1,
1039 enum isl_dim_type c2, enum isl_dim_type c3,
1040 enum isl_dim_type c4, enum isl_dim_type c5);
1042 The C<isl_dim_type> arguments dictate the order in which
1043 different kinds of variables appear in the resulting matrix
1044 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1045 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1047 The names of the domain and range spaces of a set or relation can be
1048 read off using the following functions.
1050 const char *isl_set_get_tuple_name(
1051 __isl_keep isl_set *set);
1052 const char *isl_basic_map_get_tuple_name(
1053 __isl_keep isl_basic_map *bmap,
1054 enum isl_dim_type type);
1055 const char *isl_map_get_tuple_name(
1056 __isl_keep isl_map *map,
1057 enum isl_dim_type type);
1059 As with C<isl_dim_get_tuple_name>, the value returned points to
1060 an internal data structure.
1061 The names of individual dimensions can be read off using
1062 the following functions.
1064 const char *isl_constraint_get_dim_name(
1065 __isl_keep isl_constraint *constraint,
1066 enum isl_dim_type type, unsigned pos);
1067 const char *isl_set_get_dim_name(
1068 __isl_keep isl_set *set,
1069 enum isl_dim_type type, unsigned pos);
1070 const char *isl_basic_map_get_dim_name(
1071 __isl_keep isl_basic_map *bmap,
1072 enum isl_dim_type type, unsigned pos);
1073 const char *isl_map_get_dim_name(
1074 __isl_keep isl_map *map,
1075 enum isl_dim_type type, unsigned pos);
1077 These functions are mostly useful to obtain the names
1082 =head3 Unary Properties
1088 The following functions test whether the given set or relation
1089 contains any integer points. The ``fast'' variants do not perform
1090 any computations, but simply check if the given set or relation
1091 is already known to be empty.
1093 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1094 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1095 int isl_set_is_empty(__isl_keep isl_set *set);
1096 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1097 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1098 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1099 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1100 int isl_map_is_empty(__isl_keep isl_map *map);
1101 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1103 =item * Universality
1105 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1106 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1107 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1109 =item * Single-valuedness
1111 int isl_map_is_single_valued(__isl_keep isl_map *map);
1115 int isl_map_is_bijective(__isl_keep isl_map *map);
1119 The followning functions check whether the domain of the given
1120 (basic) set is a wrapped relation.
1122 int isl_basic_set_is_wrapping(
1123 __isl_keep isl_basic_set *bset);
1124 int isl_set_is_wrapping(__isl_keep isl_set *set);
1128 =head3 Binary Properties
1134 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1135 __isl_keep isl_set *set2);
1136 int isl_set_is_equal(__isl_keep isl_set *set1,
1137 __isl_keep isl_set *set2);
1138 int isl_union_set_is_equal(
1139 __isl_keep isl_union_set *uset1,
1140 __isl_keep isl_union_set *uset2);
1141 int isl_basic_map_is_equal(
1142 __isl_keep isl_basic_map *bmap1,
1143 __isl_keep isl_basic_map *bmap2);
1144 int isl_map_is_equal(__isl_keep isl_map *map1,
1145 __isl_keep isl_map *map2);
1146 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1147 __isl_keep isl_map *map2);
1148 int isl_union_map_is_equal(
1149 __isl_keep isl_union_map *umap1,
1150 __isl_keep isl_union_map *umap2);
1152 =item * Disjointness
1154 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1155 __isl_keep isl_set *set2);
1159 int isl_set_is_subset(__isl_keep isl_set *set1,
1160 __isl_keep isl_set *set2);
1161 int isl_set_is_strict_subset(
1162 __isl_keep isl_set *set1,
1163 __isl_keep isl_set *set2);
1164 int isl_union_set_is_subset(
1165 __isl_keep isl_union_set *uset1,
1166 __isl_keep isl_union_set *uset2);
1167 int isl_union_set_is_strict_subset(
1168 __isl_keep isl_union_set *uset1,
1169 __isl_keep isl_union_set *uset2);
1170 int isl_basic_map_is_subset(
1171 __isl_keep isl_basic_map *bmap1,
1172 __isl_keep isl_basic_map *bmap2);
1173 int isl_basic_map_is_strict_subset(
1174 __isl_keep isl_basic_map *bmap1,
1175 __isl_keep isl_basic_map *bmap2);
1176 int isl_map_is_subset(
1177 __isl_keep isl_map *map1,
1178 __isl_keep isl_map *map2);
1179 int isl_map_is_strict_subset(
1180 __isl_keep isl_map *map1,
1181 __isl_keep isl_map *map2);
1182 int isl_union_map_is_subset(
1183 __isl_keep isl_union_map *umap1,
1184 __isl_keep isl_union_map *umap2);
1185 int isl_union_map_is_strict_subset(
1186 __isl_keep isl_union_map *umap1,
1187 __isl_keep isl_union_map *umap2);
1191 =head2 Unary Operations
1197 __isl_give isl_set *isl_set_complement(
1198 __isl_take isl_set *set);
1202 __isl_give isl_basic_map *isl_basic_map_reverse(
1203 __isl_take isl_basic_map *bmap);
1204 __isl_give isl_map *isl_map_reverse(
1205 __isl_take isl_map *map);
1206 __isl_give isl_union_map *isl_union_map_reverse(
1207 __isl_take isl_union_map *umap);
1211 __isl_give isl_basic_set *isl_basic_set_project_out(
1212 __isl_take isl_basic_set *bset,
1213 enum isl_dim_type type, unsigned first, unsigned n);
1214 __isl_give isl_basic_map *isl_basic_map_project_out(
1215 __isl_take isl_basic_map *bmap,
1216 enum isl_dim_type type, unsigned first, unsigned n);
1217 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1218 enum isl_dim_type type, unsigned first, unsigned n);
1219 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1220 enum isl_dim_type type, unsigned first, unsigned n);
1221 __isl_give isl_basic_set *isl_basic_map_domain(
1222 __isl_take isl_basic_map *bmap);
1223 __isl_give isl_basic_set *isl_basic_map_range(
1224 __isl_take isl_basic_map *bmap);
1225 __isl_give isl_set *isl_map_domain(
1226 __isl_take isl_map *bmap);
1227 __isl_give isl_set *isl_map_range(
1228 __isl_take isl_map *map);
1229 __isl_give isl_union_set *isl_union_map_domain(
1230 __isl_take isl_union_map *umap);
1231 __isl_give isl_union_set *isl_union_map_range(
1232 __isl_take isl_union_map *umap);
1234 __isl_give isl_basic_map *isl_basic_map_domain_map(
1235 __isl_take isl_basic_map *bmap);
1236 __isl_give isl_basic_map *isl_basic_map_range_map(
1237 __isl_take isl_basic_map *bmap);
1238 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1239 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1240 __isl_give isl_union_map *isl_union_map_domain_map(
1241 __isl_take isl_union_map *umap);
1242 __isl_give isl_union_map *isl_union_map_range_map(
1243 __isl_take isl_union_map *umap);
1245 The functions above construct a (basic, regular or union) relation
1246 that maps (a wrapped version of) the input relation to its domain or range.
1250 __isl_give isl_map *isl_set_identity(
1251 __isl_take isl_set *set);
1252 __isl_give isl_union_map *isl_union_set_identity(
1253 __isl_take isl_union_set *uset);
1255 Construct an identity relation on the given (union) set.
1259 __isl_give isl_basic_set *isl_basic_map_deltas(
1260 __isl_take isl_basic_map *bmap);
1261 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1262 __isl_give isl_union_set *isl_union_map_deltas(
1263 __isl_take isl_union_map *umap);
1265 These functions return a (basic) set containing the differences
1266 between image elements and corresponding domain elements in the input.
1270 Simplify the representation of a set or relation by trying
1271 to combine pairs of basic sets or relations into a single
1272 basic set or relation.
1274 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1275 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1276 __isl_give isl_union_set *isl_union_set_coalesce(
1277 __isl_take isl_union_set *uset);
1278 __isl_give isl_union_map *isl_union_map_coalesce(
1279 __isl_take isl_union_map *umap);
1283 __isl_give isl_basic_set *isl_set_convex_hull(
1284 __isl_take isl_set *set);
1285 __isl_give isl_basic_map *isl_map_convex_hull(
1286 __isl_take isl_map *map);
1288 If the input set or relation has any existentially quantified
1289 variables, then the result of these operations is currently undefined.
1293 __isl_give isl_basic_set *isl_set_simple_hull(
1294 __isl_take isl_set *set);
1295 __isl_give isl_basic_map *isl_map_simple_hull(
1296 __isl_take isl_map *map);
1298 These functions compute a single basic set or relation
1299 that contains the whole input set or relation.
1300 In particular, the output is described by translates
1301 of the constraints describing the basic sets or relations in the input.
1305 (See \autoref{s:simple hull}.)
1311 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1312 __isl_take isl_basic_set *bset);
1313 __isl_give isl_basic_set *isl_set_affine_hull(
1314 __isl_take isl_set *set);
1315 __isl_give isl_union_set *isl_union_set_affine_hull(
1316 __isl_take isl_union_set *uset);
1317 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1318 __isl_take isl_basic_map *bmap);
1319 __isl_give isl_basic_map *isl_map_affine_hull(
1320 __isl_take isl_map *map);
1321 __isl_give isl_union_map *isl_union_map_affine_hull(
1322 __isl_take isl_union_map *umap);
1324 In case of union sets and relations, the affine hull is computed
1327 =item * Polyhedral hull
1329 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1330 __isl_take isl_set *set);
1331 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1332 __isl_take isl_map *map);
1333 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1334 __isl_take isl_union_set *uset);
1335 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1336 __isl_take isl_union_map *umap);
1338 These functions compute a single basic set or relation
1339 not involving any existentially quantified variables
1340 that contains the whole input set or relation.
1341 In case of union sets and relations, the polyhedral hull is computed
1346 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1347 unsigned param, int *exact);
1349 Compute a parametric representation for all positive powers I<k> of C<map>.
1350 The power I<k> is equated to the parameter at position C<param>.
1351 The result may be an overapproximation. If the result is exact,
1352 then C<*exact> is set to C<1>.
1353 The current implementation only produces exact results for particular
1354 cases of piecewise translations (i.e., piecewise uniform dependences).
1356 =item * Transitive closure
1358 __isl_give isl_map *isl_map_transitive_closure(
1359 __isl_take isl_map *map, int *exact);
1360 __isl_give isl_union_map *isl_union_map_transitive_closure(
1361 __isl_take isl_union_map *umap, int *exact);
1363 Compute the transitive closure of C<map>.
1364 The result may be an overapproximation. If the result is known to be exact,
1365 then C<*exact> is set to C<1>.
1366 The current implementation only produces exact results for particular
1367 cases of piecewise translations (i.e., piecewise uniform dependences).
1369 =item * Reaching path lengths
1371 __isl_give isl_map *isl_map_reaching_path_lengths(
1372 __isl_take isl_map *map, int *exact);
1374 Compute a relation that maps each element in the range of C<map>
1375 to the lengths of all paths composed of edges in C<map> that
1376 end up in the given element.
1377 The result may be an overapproximation. If the result is known to be exact,
1378 then C<*exact> is set to C<1>.
1379 To compute the I<maximal> path length, the resulting relation
1380 should be postprocessed by C<isl_map_lexmax>.
1381 In particular, if the input relation is a dependence relation
1382 (mapping sources to sinks), then the maximal path length corresponds
1383 to the free schedule.
1384 Note, however, that C<isl_map_lexmax> expects the maximum to be
1385 finite, so if the path lengths are unbounded (possibly due to
1386 the overapproximation), then you will get an error message.
1390 __isl_give isl_basic_set *isl_basic_map_wrap(
1391 __isl_take isl_basic_map *bmap);
1392 __isl_give isl_set *isl_map_wrap(
1393 __isl_take isl_map *map);
1394 __isl_give isl_union_set *isl_union_map_wrap(
1395 __isl_take isl_union_map *umap);
1396 __isl_give isl_basic_map *isl_basic_set_unwrap(
1397 __isl_take isl_basic_set *bset);
1398 __isl_give isl_map *isl_set_unwrap(
1399 __isl_take isl_set *set);
1400 __isl_give isl_union_map *isl_union_set_unwrap(
1401 __isl_take isl_union_set *uset);
1405 Remove any internal structure of domain (and range) of the given
1406 set or relation. If there is any such internal structure in the input,
1407 then the name of the space is also removed.
1409 __isl_give isl_set *isl_set_flatten(
1410 __isl_take isl_set *set);
1411 __isl_give isl_map *isl_map_flatten(
1412 __isl_take isl_map *map);
1414 __isl_give isl_map *isl_set_flatten_map(
1415 __isl_take isl_set *set);
1417 The function above constructs a relation
1418 that maps the input set to a flattened version of the set.
1420 =item * Dimension manipulation
1422 __isl_give isl_set *isl_set_add_dims(
1423 __isl_take isl_set *set,
1424 enum isl_dim_type type, unsigned n);
1425 __isl_give isl_map *isl_map_add_dims(
1426 __isl_take isl_map *map,
1427 enum isl_dim_type type, unsigned n);
1429 It is usually not advisable to directly change the (input or output)
1430 space of a set or a relation as this removes the name and the internal
1431 structure of the space. However, the above functions can be useful
1432 to add new parameters.
1436 =head2 Binary Operations
1438 The two arguments of a binary operation not only need to live
1439 in the same C<isl_ctx>, they currently also need to have
1440 the same (number of) parameters.
1442 =head3 Basic Operations
1446 =item * Intersection
1448 __isl_give isl_basic_set *isl_basic_set_intersect(
1449 __isl_take isl_basic_set *bset1,
1450 __isl_take isl_basic_set *bset2);
1451 __isl_give isl_set *isl_set_intersect(
1452 __isl_take isl_set *set1,
1453 __isl_take isl_set *set2);
1454 __isl_give isl_union_set *isl_union_set_intersect(
1455 __isl_take isl_union_set *uset1,
1456 __isl_take isl_union_set *uset2);
1457 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1458 __isl_take isl_basic_map *bmap,
1459 __isl_take isl_basic_set *bset);
1460 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1461 __isl_take isl_basic_map *bmap,
1462 __isl_take isl_basic_set *bset);
1463 __isl_give isl_basic_map *isl_basic_map_intersect(
1464 __isl_take isl_basic_map *bmap1,
1465 __isl_take isl_basic_map *bmap2);
1466 __isl_give isl_map *isl_map_intersect_domain(
1467 __isl_take isl_map *map,
1468 __isl_take isl_set *set);
1469 __isl_give isl_map *isl_map_intersect_range(
1470 __isl_take isl_map *map,
1471 __isl_take isl_set *set);
1472 __isl_give isl_map *isl_map_intersect(
1473 __isl_take isl_map *map1,
1474 __isl_take isl_map *map2);
1475 __isl_give isl_union_map *isl_union_map_intersect_domain(
1476 __isl_take isl_union_map *umap,
1477 __isl_take isl_union_set *uset);
1478 __isl_give isl_union_map *isl_union_map_intersect_range(
1479 __isl_take isl_union_map *umap,
1480 __isl_take isl_union_set *uset);
1481 __isl_give isl_union_map *isl_union_map_intersect(
1482 __isl_take isl_union_map *umap1,
1483 __isl_take isl_union_map *umap2);
1487 __isl_give isl_set *isl_basic_set_union(
1488 __isl_take isl_basic_set *bset1,
1489 __isl_take isl_basic_set *bset2);
1490 __isl_give isl_map *isl_basic_map_union(
1491 __isl_take isl_basic_map *bmap1,
1492 __isl_take isl_basic_map *bmap2);
1493 __isl_give isl_set *isl_set_union(
1494 __isl_take isl_set *set1,
1495 __isl_take isl_set *set2);
1496 __isl_give isl_map *isl_map_union(
1497 __isl_take isl_map *map1,
1498 __isl_take isl_map *map2);
1499 __isl_give isl_union_set *isl_union_set_union(
1500 __isl_take isl_union_set *uset1,
1501 __isl_take isl_union_set *uset2);
1502 __isl_give isl_union_map *isl_union_map_union(
1503 __isl_take isl_union_map *umap1,
1504 __isl_take isl_union_map *umap2);
1506 =item * Set difference
1508 __isl_give isl_set *isl_set_subtract(
1509 __isl_take isl_set *set1,
1510 __isl_take isl_set *set2);
1511 __isl_give isl_map *isl_map_subtract(
1512 __isl_take isl_map *map1,
1513 __isl_take isl_map *map2);
1514 __isl_give isl_union_set *isl_union_set_subtract(
1515 __isl_take isl_union_set *uset1,
1516 __isl_take isl_union_set *uset2);
1517 __isl_give isl_union_map *isl_union_map_subtract(
1518 __isl_take isl_union_map *umap1,
1519 __isl_take isl_union_map *umap2);
1523 __isl_give isl_basic_set *isl_basic_set_apply(
1524 __isl_take isl_basic_set *bset,
1525 __isl_take isl_basic_map *bmap);
1526 __isl_give isl_set *isl_set_apply(
1527 __isl_take isl_set *set,
1528 __isl_take isl_map *map);
1529 __isl_give isl_union_set *isl_union_set_apply(
1530 __isl_take isl_union_set *uset,
1531 __isl_take isl_union_map *umap);
1532 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1533 __isl_take isl_basic_map *bmap1,
1534 __isl_take isl_basic_map *bmap2);
1535 __isl_give isl_basic_map *isl_basic_map_apply_range(
1536 __isl_take isl_basic_map *bmap1,
1537 __isl_take isl_basic_map *bmap2);
1538 __isl_give isl_map *isl_map_apply_domain(
1539 __isl_take isl_map *map1,
1540 __isl_take isl_map *map2);
1541 __isl_give isl_union_map *isl_union_map_apply_domain(
1542 __isl_take isl_union_map *umap1,
1543 __isl_take isl_union_map *umap2);
1544 __isl_give isl_map *isl_map_apply_range(
1545 __isl_take isl_map *map1,
1546 __isl_take isl_map *map2);
1547 __isl_give isl_union_map *isl_union_map_apply_range(
1548 __isl_take isl_union_map *umap1,
1549 __isl_take isl_union_map *umap2);
1551 =item * Simplification
1553 __isl_give isl_basic_set *isl_basic_set_gist(
1554 __isl_take isl_basic_set *bset,
1555 __isl_take isl_basic_set *context);
1556 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1557 __isl_take isl_set *context);
1558 __isl_give isl_union_set *isl_union_set_gist(
1559 __isl_take isl_union_set *uset,
1560 __isl_take isl_union_set *context);
1561 __isl_give isl_basic_map *isl_basic_map_gist(
1562 __isl_take isl_basic_map *bmap,
1563 __isl_take isl_basic_map *context);
1564 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1565 __isl_take isl_map *context);
1566 __isl_give isl_union_map *isl_union_map_gist(
1567 __isl_take isl_union_map *umap,
1568 __isl_take isl_union_map *context);
1570 The gist operation returns a set or relation that has the
1571 same intersection with the context as the input set or relation.
1572 Any implicit equality in the intersection is made explicit in the result,
1573 while all inequalities that are redundant with respect to the intersection
1575 In case of union sets and relations, the gist operation is performed
1580 =head3 Lexicographic Optimization
1582 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1583 the following functions
1584 compute a set that contains the lexicographic minimum or maximum
1585 of the elements in C<set> (or C<bset>) for those values of the parameters
1586 that satisfy C<dom>.
1587 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1588 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1590 In other words, the union of the parameter values
1591 for which the result is non-empty and of C<*empty>
1594 __isl_give isl_set *isl_basic_set_partial_lexmin(
1595 __isl_take isl_basic_set *bset,
1596 __isl_take isl_basic_set *dom,
1597 __isl_give isl_set **empty);
1598 __isl_give isl_set *isl_basic_set_partial_lexmax(
1599 __isl_take isl_basic_set *bset,
1600 __isl_take isl_basic_set *dom,
1601 __isl_give isl_set **empty);
1602 __isl_give isl_set *isl_set_partial_lexmin(
1603 __isl_take isl_set *set, __isl_take isl_set *dom,
1604 __isl_give isl_set **empty);
1605 __isl_give isl_set *isl_set_partial_lexmax(
1606 __isl_take isl_set *set, __isl_take isl_set *dom,
1607 __isl_give isl_set **empty);
1609 Given a (basic) set C<set> (or C<bset>), the following functions simply
1610 return a set containing the lexicographic minimum or maximum
1611 of the elements in C<set> (or C<bset>).
1612 In case of union sets, the optimum is computed per space.
1614 __isl_give isl_set *isl_basic_set_lexmin(
1615 __isl_take isl_basic_set *bset);
1616 __isl_give isl_set *isl_basic_set_lexmax(
1617 __isl_take isl_basic_set *bset);
1618 __isl_give isl_set *isl_set_lexmin(
1619 __isl_take isl_set *set);
1620 __isl_give isl_set *isl_set_lexmax(
1621 __isl_take isl_set *set);
1622 __isl_give isl_union_set *isl_union_set_lexmin(
1623 __isl_take isl_union_set *uset);
1624 __isl_give isl_union_set *isl_union_set_lexmax(
1625 __isl_take isl_union_set *uset);
1627 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1628 the following functions
1629 compute a relation that maps each element of C<dom>
1630 to the single lexicographic minimum or maximum
1631 of the elements that are associated to that same
1632 element in C<map> (or C<bmap>).
1633 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1634 that contains the elements in C<dom> that do not map
1635 to any elements in C<map> (or C<bmap>).
1636 In other words, the union of the domain of the result and of C<*empty>
1639 __isl_give isl_map *isl_basic_map_partial_lexmax(
1640 __isl_take isl_basic_map *bmap,
1641 __isl_take isl_basic_set *dom,
1642 __isl_give isl_set **empty);
1643 __isl_give isl_map *isl_basic_map_partial_lexmin(
1644 __isl_take isl_basic_map *bmap,
1645 __isl_take isl_basic_set *dom,
1646 __isl_give isl_set **empty);
1647 __isl_give isl_map *isl_map_partial_lexmax(
1648 __isl_take isl_map *map, __isl_take isl_set *dom,
1649 __isl_give isl_set **empty);
1650 __isl_give isl_map *isl_map_partial_lexmin(
1651 __isl_take isl_map *map, __isl_take isl_set *dom,
1652 __isl_give isl_set **empty);
1654 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1655 return a map mapping each element in the domain of
1656 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1657 of all elements associated to that element.
1658 In case of union relations, the optimum is computed per space.
1660 __isl_give isl_map *isl_basic_map_lexmin(
1661 __isl_take isl_basic_map *bmap);
1662 __isl_give isl_map *isl_basic_map_lexmax(
1663 __isl_take isl_basic_map *bmap);
1664 __isl_give isl_map *isl_map_lexmin(
1665 __isl_take isl_map *map);
1666 __isl_give isl_map *isl_map_lexmax(
1667 __isl_take isl_map *map);
1668 __isl_give isl_union_map *isl_union_map_lexmin(
1669 __isl_take isl_union_map *umap);
1670 __isl_give isl_union_map *isl_union_map_lexmax(
1671 __isl_take isl_union_map *umap);
1675 Matrices can be created, copied and freed using the following functions.
1677 #include <isl/mat.h>
1678 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1679 unsigned n_row, unsigned n_col);
1680 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1681 void isl_mat_free(__isl_take isl_mat *mat);
1683 Note that the elements of a newly created matrix may have arbitrary values.
1684 The elements can be changed and inspected using the following functions.
1686 int isl_mat_rows(__isl_keep isl_mat *mat);
1687 int isl_mat_cols(__isl_keep isl_mat *mat);
1688 int isl_mat_get_element(__isl_keep isl_mat *mat,
1689 int row, int col, isl_int *v);
1690 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1691 int row, int col, isl_int v);
1693 C<isl_mat_get_element> will return a negative value if anything went wrong.
1694 In that case, the value of C<*v> is undefined.
1696 The following function can be used to compute the (right) inverse
1697 of a matrix, i.e., a matrix such that the product of the original
1698 and the inverse (in that order) is a multiple of the identity matrix.
1699 The input matrix is assumed to be of full row-rank.
1701 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1703 The following function can be used to compute the (right) kernel
1704 (or null space) of a matrix, i.e., a matrix such that the product of
1705 the original and the kernel (in that order) is the zero matrix.
1707 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1711 Points are elements of a set. They can be used to construct
1712 simple sets (boxes) or they can be used to represent the
1713 individual elements of a set.
1714 The zero point (the origin) can be created using
1716 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1718 The coordinates of a point can be inspected, set and changed
1721 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1722 enum isl_dim_type type, int pos, isl_int *v);
1723 __isl_give isl_point *isl_point_set_coordinate(
1724 __isl_take isl_point *pnt,
1725 enum isl_dim_type type, int pos, isl_int v);
1727 __isl_give isl_point *isl_point_add_ui(
1728 __isl_take isl_point *pnt,
1729 enum isl_dim_type type, int pos, unsigned val);
1730 __isl_give isl_point *isl_point_sub_ui(
1731 __isl_take isl_point *pnt,
1732 enum isl_dim_type type, int pos, unsigned val);
1734 Points can be copied or freed using
1736 __isl_give isl_point *isl_point_copy(
1737 __isl_keep isl_point *pnt);
1738 void isl_point_free(__isl_take isl_point *pnt);
1740 A singleton set can be created from a point using
1742 __isl_give isl_basic_set *isl_basic_set_from_point(
1743 __isl_take isl_point *pnt);
1744 __isl_give isl_set *isl_set_from_point(
1745 __isl_take isl_point *pnt);
1747 and a box can be created from two opposite extremal points using
1749 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1750 __isl_take isl_point *pnt1,
1751 __isl_take isl_point *pnt2);
1752 __isl_give isl_set *isl_set_box_from_points(
1753 __isl_take isl_point *pnt1,
1754 __isl_take isl_point *pnt2);
1756 All elements of a B<bounded> (union) set can be enumerated using
1757 the following functions.
1759 int isl_set_foreach_point(__isl_keep isl_set *set,
1760 int (*fn)(__isl_take isl_point *pnt, void *user),
1762 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1763 int (*fn)(__isl_take isl_point *pnt, void *user),
1766 The function C<fn> is called for each integer point in
1767 C<set> with as second argument the last argument of
1768 the C<isl_set_foreach_point> call. The function C<fn>
1769 should return C<0> on success and C<-1> on failure.
1770 In the latter case, C<isl_set_foreach_point> will stop
1771 enumerating and return C<-1> as well.
1772 If the enumeration is performed successfully and to completion,
1773 then C<isl_set_foreach_point> returns C<0>.
1775 To obtain a single point of a (basic) set, use
1777 __isl_give isl_point *isl_basic_set_sample_point(
1778 __isl_take isl_basic_set *bset);
1779 __isl_give isl_point *isl_set_sample_point(
1780 __isl_take isl_set *set);
1782 If C<set> does not contain any (integer) points, then the
1783 resulting point will be ``void'', a property that can be
1786 int isl_point_is_void(__isl_keep isl_point *pnt);
1788 =head2 Piecewise Quasipolynomials
1790 A piecewise quasipolynomial is a particular kind of function that maps
1791 a parametric point to a rational value.
1792 More specifically, a quasipolynomial is a polynomial expression in greatest
1793 integer parts of affine expressions of parameters and variables.
1794 A piecewise quasipolynomial is a subdivision of a given parametric
1795 domain into disjoint cells with a quasipolynomial associated to
1796 each cell. The value of the piecewise quasipolynomial at a given
1797 point is the value of the quasipolynomial associated to the cell
1798 that contains the point. Outside of the union of cells,
1799 the value is assumed to be zero.
1800 For example, the piecewise quasipolynomial
1802 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1804 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1805 A given piecewise quasipolynomial has a fixed domain dimension.
1806 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1807 defined over different domains.
1808 Piecewise quasipolynomials are mainly used by the C<barvinok>
1809 library for representing the number of elements in a parametric set or map.
1810 For example, the piecewise quasipolynomial above represents
1811 the number of points in the map
1813 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1815 =head3 Printing (Piecewise) Quasipolynomials
1817 Quasipolynomials and piecewise quasipolynomials can be printed
1818 using the following functions.
1820 __isl_give isl_printer *isl_printer_print_qpolynomial(
1821 __isl_take isl_printer *p,
1822 __isl_keep isl_qpolynomial *qp);
1824 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1825 __isl_take isl_printer *p,
1826 __isl_keep isl_pw_qpolynomial *pwqp);
1828 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1829 __isl_take isl_printer *p,
1830 __isl_keep isl_union_pw_qpolynomial *upwqp);
1832 The output format of the printer
1833 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1834 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1836 In case of printing in C<ISL_FORMAT_C>, the user may want
1837 to set the names of all dimensions
1839 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1840 __isl_take isl_qpolynomial *qp,
1841 enum isl_dim_type type, unsigned pos,
1843 __isl_give isl_pw_qpolynomial *
1844 isl_pw_qpolynomial_set_dim_name(
1845 __isl_take isl_pw_qpolynomial *pwqp,
1846 enum isl_dim_type type, unsigned pos,
1849 =head3 Creating New (Piecewise) Quasipolynomials
1851 Some simple quasipolynomials can be created using the following functions.
1852 More complicated quasipolynomials can be created by applying
1853 operations such as addition and multiplication
1854 on the resulting quasipolynomials
1856 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1857 __isl_take isl_dim *dim);
1858 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1859 __isl_take isl_dim *dim);
1860 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1861 __isl_take isl_dim *dim);
1862 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1863 __isl_take isl_dim *dim);
1864 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1865 __isl_take isl_dim *dim);
1866 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1867 __isl_take isl_dim *dim,
1868 const isl_int n, const isl_int d);
1869 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1870 __isl_take isl_div *div);
1871 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1872 __isl_take isl_dim *dim,
1873 enum isl_dim_type type, unsigned pos);
1875 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1876 with a single cell can be created using the following functions.
1877 Multiple of these single cell piecewise quasipolynomials can
1878 be combined to create more complicated piecewise quasipolynomials.
1880 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1881 __isl_take isl_dim *dim);
1882 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1883 __isl_take isl_set *set,
1884 __isl_take isl_qpolynomial *qp);
1886 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1887 __isl_take isl_dim *dim);
1888 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1889 __isl_take isl_pw_qpolynomial *pwqp);
1890 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1891 __isl_take isl_union_pw_qpolynomial *upwqp,
1892 __isl_take isl_pw_qpolynomial *pwqp);
1894 Quasipolynomials can be copied and freed again using the following
1897 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1898 __isl_keep isl_qpolynomial *qp);
1899 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1901 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1902 __isl_keep isl_pw_qpolynomial *pwqp);
1903 void isl_pw_qpolynomial_free(
1904 __isl_take isl_pw_qpolynomial *pwqp);
1906 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1907 __isl_keep isl_union_pw_qpolynomial *upwqp);
1908 void isl_union_pw_qpolynomial_free(
1909 __isl_take isl_union_pw_qpolynomial *upwqp);
1911 =head3 Inspecting (Piecewise) Quasipolynomials
1913 To iterate over all piecewise quasipolynomials in a union
1914 piecewise quasipolynomial, use the following function
1916 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1917 __isl_keep isl_union_pw_qpolynomial *upwqp,
1918 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1921 To extract the piecewise quasipolynomial from a union with a given dimension
1924 __isl_give isl_pw_qpolynomial *
1925 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
1926 __isl_keep isl_union_pw_qpolynomial *upwqp,
1927 __isl_take isl_dim *dim);
1929 To iterate over the cells in a piecewise quasipolynomial,
1930 use either of the following two functions
1932 int isl_pw_qpolynomial_foreach_piece(
1933 __isl_keep isl_pw_qpolynomial *pwqp,
1934 int (*fn)(__isl_take isl_set *set,
1935 __isl_take isl_qpolynomial *qp,
1936 void *user), void *user);
1937 int isl_pw_qpolynomial_foreach_lifted_piece(
1938 __isl_keep isl_pw_qpolynomial *pwqp,
1939 int (*fn)(__isl_take isl_set *set,
1940 __isl_take isl_qpolynomial *qp,
1941 void *user), void *user);
1943 As usual, the function C<fn> should return C<0> on success
1944 and C<-1> on failure. The difference between
1945 C<isl_pw_qpolynomial_foreach_piece> and
1946 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1947 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1948 compute unique representations for all existentially quantified
1949 variables and then turn these existentially quantified variables
1950 into extra set variables, adapting the associated quasipolynomial
1951 accordingly. This means that the C<set> passed to C<fn>
1952 will not have any existentially quantified variables, but that
1953 the dimensions of the sets may be different for different
1954 invocations of C<fn>.
1956 To iterate over all terms in a quasipolynomial,
1959 int isl_qpolynomial_foreach_term(
1960 __isl_keep isl_qpolynomial *qp,
1961 int (*fn)(__isl_take isl_term *term,
1962 void *user), void *user);
1964 The terms themselves can be inspected and freed using
1967 unsigned isl_term_dim(__isl_keep isl_term *term,
1968 enum isl_dim_type type);
1969 void isl_term_get_num(__isl_keep isl_term *term,
1971 void isl_term_get_den(__isl_keep isl_term *term,
1973 int isl_term_get_exp(__isl_keep isl_term *term,
1974 enum isl_dim_type type, unsigned pos);
1975 __isl_give isl_div *isl_term_get_div(
1976 __isl_keep isl_term *term, unsigned pos);
1977 void isl_term_free(__isl_take isl_term *term);
1979 Each term is a product of parameters, set variables and
1980 integer divisions. The function C<isl_term_get_exp>
1981 returns the exponent of a given dimensions in the given term.
1982 The C<isl_int>s in the arguments of C<isl_term_get_num>
1983 and C<isl_term_get_den> need to have been initialized
1984 using C<isl_int_init> before calling these functions.
1986 =head3 Properties of (Piecewise) Quasipolynomials
1988 To check whether a quasipolynomial is actually a constant,
1989 use the following function.
1991 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1992 isl_int *n, isl_int *d);
1994 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1995 then the numerator and denominator of the constant
1996 are returned in C<*n> and C<*d>, respectively.
1998 =head3 Operations on (Piecewise) Quasipolynomials
2000 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2001 __isl_take isl_qpolynomial *qp);
2002 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2003 __isl_take isl_qpolynomial *qp1,
2004 __isl_take isl_qpolynomial *qp2);
2005 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2006 __isl_take isl_qpolynomial *qp1,
2007 __isl_take isl_qpolynomial *qp2);
2008 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2009 __isl_take isl_qpolynomial *qp1,
2010 __isl_take isl_qpolynomial *qp2);
2012 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2013 __isl_take isl_pw_qpolynomial *pwqp1,
2014 __isl_take isl_pw_qpolynomial *pwqp2);
2015 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2016 __isl_take isl_pw_qpolynomial *pwqp1,
2017 __isl_take isl_pw_qpolynomial *pwqp2);
2018 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2019 __isl_take isl_pw_qpolynomial *pwqp1,
2020 __isl_take isl_pw_qpolynomial *pwqp2);
2021 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2022 __isl_take isl_pw_qpolynomial *pwqp);
2023 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2024 __isl_take isl_pw_qpolynomial *pwqp1,
2025 __isl_take isl_pw_qpolynomial *pwqp2);
2027 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2028 __isl_take isl_union_pw_qpolynomial *upwqp1,
2029 __isl_take isl_union_pw_qpolynomial *upwqp2);
2030 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2031 __isl_take isl_union_pw_qpolynomial *upwqp1,
2032 __isl_take isl_union_pw_qpolynomial *upwqp2);
2033 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2034 __isl_take isl_union_pw_qpolynomial *upwqp1,
2035 __isl_take isl_union_pw_qpolynomial *upwqp2);
2037 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2038 __isl_take isl_pw_qpolynomial *pwqp,
2039 __isl_take isl_point *pnt);
2041 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2042 __isl_take isl_union_pw_qpolynomial *upwqp,
2043 __isl_take isl_point *pnt);
2045 __isl_give isl_set *isl_pw_qpolynomial_domain(
2046 __isl_take isl_pw_qpolynomial *pwqp);
2047 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2048 __isl_take isl_pw_qpolynomial *pwpq,
2049 __isl_take isl_set *set);
2051 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2052 __isl_take isl_union_pw_qpolynomial *upwqp);
2053 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2054 __isl_take isl_union_pw_qpolynomial *upwpq,
2055 __isl_take isl_union_set *uset);
2057 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2058 __isl_take isl_union_pw_qpolynomial *upwqp);
2060 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2061 __isl_take isl_pw_qpolynomial *pwqp,
2062 __isl_take isl_set *context);
2064 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2065 __isl_take isl_union_pw_qpolynomial *upwqp,
2066 __isl_take isl_union_set *context);
2068 The gist operation applies the gist operation to each of
2069 the cells in the domain of the input piecewise quasipolynomial.
2070 The context is also exploited
2071 to simplify the quasipolynomials associated to each cell.
2073 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2074 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2075 __isl_give isl_union_pw_qpolynomial *
2076 isl_union_pw_qpolynomial_to_polynomial(
2077 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2079 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2080 the polynomial will be an overapproximation. If C<sign> is negative,
2081 it will be an underapproximation. If C<sign> is zero, the approximation
2082 will lie somewhere in between.
2084 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2086 A piecewise quasipolynomial reduction is a piecewise
2087 reduction (or fold) of quasipolynomials.
2088 In particular, the reduction can be maximum or a minimum.
2089 The objects are mainly used to represent the result of
2090 an upper or lower bound on a quasipolynomial over its domain,
2091 i.e., as the result of the following function.
2093 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2094 __isl_take isl_pw_qpolynomial *pwqp,
2095 enum isl_fold type, int *tight);
2097 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2098 __isl_take isl_union_pw_qpolynomial *upwqp,
2099 enum isl_fold type, int *tight);
2101 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2102 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2103 is the returned bound is known be tight, i.e., for each value
2104 of the parameters there is at least
2105 one element in the domain that reaches the bound.
2106 If the domain of C<pwqp> is not wrapping, then the bound is computed
2107 over all elements in that domain and the result has a purely parametric
2108 domain. If the domain of C<pwqp> is wrapping, then the bound is
2109 computed over the range of the wrapped relation. The domain of the
2110 wrapped relation becomes the domain of the result.
2112 A (piecewise) quasipolynomial reduction can be copied or freed using the
2113 following functions.
2115 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2116 __isl_keep isl_qpolynomial_fold *fold);
2117 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2118 __isl_keep isl_pw_qpolynomial_fold *pwf);
2119 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2120 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2121 void isl_qpolynomial_fold_free(
2122 __isl_take isl_qpolynomial_fold *fold);
2123 void isl_pw_qpolynomial_fold_free(
2124 __isl_take isl_pw_qpolynomial_fold *pwf);
2125 void isl_union_pw_qpolynomial_fold_free(
2126 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2128 =head3 Printing Piecewise Quasipolynomial Reductions
2130 Piecewise quasipolynomial reductions can be printed
2131 using the following function.
2133 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2134 __isl_take isl_printer *p,
2135 __isl_keep isl_pw_qpolynomial_fold *pwf);
2136 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2137 __isl_take isl_printer *p,
2138 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2140 For C<isl_printer_print_pw_qpolynomial_fold>,
2141 output format of the printer
2142 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2143 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2144 output format of the printer
2145 needs to be set to C<ISL_FORMAT_ISL>.
2146 In case of printing in C<ISL_FORMAT_C>, the user may want
2147 to set the names of all dimensions
2149 __isl_give isl_pw_qpolynomial_fold *
2150 isl_pw_qpolynomial_fold_set_dim_name(
2151 __isl_take isl_pw_qpolynomial_fold *pwf,
2152 enum isl_dim_type type, unsigned pos,
2155 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2157 To iterate over all piecewise quasipolynomial reductions in a union
2158 piecewise quasipolynomial reduction, use the following function
2160 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2161 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2162 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2163 void *user), void *user);
2165 To iterate over the cells in a piecewise quasipolynomial reduction,
2166 use either of the following two functions
2168 int isl_pw_qpolynomial_fold_foreach_piece(
2169 __isl_keep isl_pw_qpolynomial_fold *pwf,
2170 int (*fn)(__isl_take isl_set *set,
2171 __isl_take isl_qpolynomial_fold *fold,
2172 void *user), void *user);
2173 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2174 __isl_keep isl_pw_qpolynomial_fold *pwf,
2175 int (*fn)(__isl_take isl_set *set,
2176 __isl_take isl_qpolynomial_fold *fold,
2177 void *user), void *user);
2179 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2180 of the difference between these two functions.
2182 To iterate over all quasipolynomials in a reduction, use
2184 int isl_qpolynomial_fold_foreach_qpolynomial(
2185 __isl_keep isl_qpolynomial_fold *fold,
2186 int (*fn)(__isl_take isl_qpolynomial *qp,
2187 void *user), void *user);
2189 =head3 Operations on Piecewise Quasipolynomial Reductions
2191 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2192 __isl_take isl_pw_qpolynomial_fold *pwf1,
2193 __isl_take isl_pw_qpolynomial_fold *pwf2);
2195 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2196 __isl_take isl_pw_qpolynomial_fold *pwf1,
2197 __isl_take isl_pw_qpolynomial_fold *pwf2);
2199 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2200 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2201 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2203 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2204 __isl_take isl_pw_qpolynomial_fold *pwf,
2205 __isl_take isl_point *pnt);
2207 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2208 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2209 __isl_take isl_point *pnt);
2211 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2212 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2213 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2214 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2215 __isl_take isl_union_set *uset);
2217 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2218 __isl_take isl_pw_qpolynomial_fold *pwf);
2220 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2221 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2223 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2224 __isl_take isl_pw_qpolynomial_fold *pwf,
2225 __isl_take isl_set *context);
2227 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2228 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2229 __isl_take isl_union_set *context);
2231 The gist operation applies the gist operation to each of
2232 the cells in the domain of the input piecewise quasipolynomial reduction.
2233 In future, the operation will also exploit the context
2234 to simplify the quasipolynomial reductions associated to each cell.
2236 __isl_give isl_pw_qpolynomial_fold *
2237 isl_map_apply_pw_qpolynomial_fold(
2238 __isl_take isl_map *map,
2239 __isl_take isl_pw_qpolynomial_fold *pwf,
2241 __isl_give isl_union_pw_qpolynomial_fold *
2242 isl_union_map_apply_union_pw_qpolynomial_fold(
2243 __isl_take isl_union_map *umap,
2244 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2248 compose the given map with the given piecewise quasipolynomial reduction.
2249 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2250 over all elements in the intersection of the range of the map
2251 and the domain of the piecewise quasipolynomial reduction
2252 as a function of an element in the domain of the map.
2254 =head2 Dependence Analysis
2256 C<isl> contains specialized functionality for performing
2257 array dataflow analysis. That is, given a I<sink> access relation
2258 and a collection of possible I<source> access relations,
2259 C<isl> can compute relations that describe
2260 for each iteration of the sink access, which iteration
2261 of which of the source access relations was the last
2262 to access the same data element before the given iteration
2264 To compute standard flow dependences, the sink should be
2265 a read, while the sources should be writes.
2266 If any of the source accesses are marked as being I<may>
2267 accesses, then there will be a dependence to the last
2268 I<must> access B<and> to any I<may> access that follows
2269 this last I<must> access.
2270 In particular, if I<all> sources are I<may> accesses,
2271 then memory based dependence analysis is performed.
2272 If, on the other hand, all sources are I<must> accesses,
2273 then value based dependence analysis is performed.
2275 #include <isl/flow.h>
2277 typedef int (*isl_access_level_before)(void *first, void *second);
2279 __isl_give isl_access_info *isl_access_info_alloc(
2280 __isl_take isl_map *sink,
2281 void *sink_user, isl_access_level_before fn,
2283 __isl_give isl_access_info *isl_access_info_add_source(
2284 __isl_take isl_access_info *acc,
2285 __isl_take isl_map *source, int must,
2287 void isl_access_info_free(__isl_take isl_access_info *acc);
2289 __isl_give isl_flow *isl_access_info_compute_flow(
2290 __isl_take isl_access_info *acc);
2292 int isl_flow_foreach(__isl_keep isl_flow *deps,
2293 int (*fn)(__isl_take isl_map *dep, int must,
2294 void *dep_user, void *user),
2296 __isl_give isl_set *isl_flow_get_no_source(
2297 __isl_keep isl_flow *deps, int must);
2298 void isl_flow_free(__isl_take isl_flow *deps);
2300 The function C<isl_access_info_compute_flow> performs the actual
2301 dependence analysis. The other functions are used to construct
2302 the input for this function or to read off the output.
2304 The input is collected in an C<isl_access_info>, which can
2305 be created through a call to C<isl_access_info_alloc>.
2306 The arguments to this functions are the sink access relation
2307 C<sink>, a token C<sink_user> used to identify the sink
2308 access to the user, a callback function for specifying the
2309 relative order of source and sink accesses, and the number
2310 of source access relations that will be added.
2311 The callback function has type C<int (*)(void *first, void *second)>.
2312 The function is called with two user supplied tokens identifying
2313 either a source or the sink and it should return the shared nesting
2314 level and the relative order of the two accesses.
2315 In particular, let I<n> be the number of loops shared by
2316 the two accesses. If C<first> precedes C<second> textually,
2317 then the function should return I<2 * n + 1>; otherwise,
2318 it should return I<2 * n>.
2319 The sources can be added to the C<isl_access_info> by performing
2320 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2321 C<must> indicates whether the source is a I<must> access
2322 or a I<may> access. Note that a multi-valued access relation
2323 should only be marked I<must> if every iteration in the domain
2324 of the relation accesses I<all> elements in its image.
2325 The C<source_user> token is again used to identify
2326 the source access. The range of the source access relation
2327 C<source> should have the same dimension as the range
2328 of the sink access relation.
2329 The C<isl_access_info_free> function should usually not be
2330 called explicitly, because it is called implicitly by
2331 C<isl_access_info_compute_flow>.
2333 The result of the dependence analysis is collected in an
2334 C<isl_flow>. There may be elements in the domain of
2335 the sink access for which no preceding source access could be
2336 found or for which all preceding sources are I<may> accesses.
2337 The sets of these elements can be obtained through
2338 calls to C<isl_flow_get_no_source>, the first with C<must> set
2339 and the second with C<must> unset.
2340 In the case of standard flow dependence analysis,
2341 with the sink a read and the sources I<must> writes,
2342 the first set corresponds to the reads from uninitialized
2343 array elements and the second set is empty.
2344 The actual flow dependences can be extracted using
2345 C<isl_flow_foreach>. This function will call the user-specified
2346 callback function C<fn> for each B<non-empty> dependence between
2347 a source and the sink. The callback function is called
2348 with four arguments, the actual flow dependence relation
2349 mapping source iterations to sink iterations, a boolean that
2350 indicates whether it is a I<must> or I<may> dependence, a token
2351 identifying the source and an additional C<void *> with value
2352 equal to the third argument of the C<isl_flow_foreach> call.
2353 A dependence is marked I<must> if it originates from a I<must>
2354 source and if it is not followed by any I<may> sources.
2356 After finishing with an C<isl_flow>, the user should call
2357 C<isl_flow_free> to free all associated memory.
2359 A higher-level interface to dependence analysis is provided
2360 by the following function.
2362 #include <isl/flow.h>
2364 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2365 __isl_take isl_union_map *must_source,
2366 __isl_take isl_union_map *may_source,
2367 __isl_take isl_union_map *schedule,
2368 __isl_give isl_union_map **must_dep,
2369 __isl_give isl_union_map **may_dep,
2370 __isl_give isl_union_set **must_no_source,
2371 __isl_give isl_union_set **may_no_source);
2373 The arrays are identified by the tuple names of the ranges
2374 of the accesses. The iteration domains by the tuple names
2375 of the domains of the accesses and of the schedule.
2376 The relative order of the iteration domains is given by the
2377 schedule. Any of C<must_dep>, C<may_dep>, C<must_no_source>
2378 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2379 any of the other arguments is treated as an error.
2381 =head2 Parametric Vertex Enumeration
2383 The parametric vertex enumeration described in this section
2384 is mainly intended to be used internally and by the C<barvinok>
2387 #include <isl/vertices.h>
2388 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2389 __isl_keep isl_basic_set *bset);
2391 The function C<isl_basic_set_compute_vertices> performs the
2392 actual computation of the parametric vertices and the chamber
2393 decomposition and store the result in an C<isl_vertices> object.
2394 This information can be queried by either iterating over all
2395 the vertices or iterating over all the chambers or cells
2396 and then iterating over all vertices that are active on the chamber.
2398 int isl_vertices_foreach_vertex(
2399 __isl_keep isl_vertices *vertices,
2400 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2403 int isl_vertices_foreach_cell(
2404 __isl_keep isl_vertices *vertices,
2405 int (*fn)(__isl_take isl_cell *cell, void *user),
2407 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2408 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2411 Other operations that can be performed on an C<isl_vertices> object are
2414 isl_ctx *isl_vertices_get_ctx(
2415 __isl_keep isl_vertices *vertices);
2416 int isl_vertices_get_n_vertices(
2417 __isl_keep isl_vertices *vertices);
2418 void isl_vertices_free(__isl_take isl_vertices *vertices);
2420 Vertices can be inspected and destroyed using the following functions.
2422 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2423 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2424 __isl_give isl_basic_set *isl_vertex_get_domain(
2425 __isl_keep isl_vertex *vertex);
2426 __isl_give isl_basic_set *isl_vertex_get_expr(
2427 __isl_keep isl_vertex *vertex);
2428 void isl_vertex_free(__isl_take isl_vertex *vertex);
2430 C<isl_vertex_get_expr> returns a singleton parametric set describing
2431 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2433 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2434 B<rational> basic sets, so they should mainly be used for inspection
2435 and should not be mixed with integer sets.
2437 Chambers can be inspected and destroyed using the following functions.
2439 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2440 __isl_give isl_basic_set *isl_cell_get_domain(
2441 __isl_keep isl_cell *cell);
2442 void isl_cell_free(__isl_take isl_cell *cell);
2446 Although C<isl> is mainly meant to be used as a library,
2447 it also contains some basic applications that use some
2448 of the functionality of C<isl>.
2449 The input may be specified in either the L<isl format>
2450 or the L<PolyLib format>.
2452 =head2 C<isl_polyhedron_sample>
2454 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2455 an integer element of the polyhedron, if there is any.
2456 The first column in the output is the denominator and is always
2457 equal to 1. If the polyhedron contains no integer points,
2458 then a vector of length zero is printed.
2462 C<isl_pip> takes the same input as the C<example> program
2463 from the C<piplib> distribution, i.e., a set of constraints
2464 on the parameters, a line containing only -1 and finally a set
2465 of constraints on a parametric polyhedron.
2466 The coefficients of the parameters appear in the last columns
2467 (but before the final constant column).
2468 The output is the lexicographic minimum of the parametric polyhedron.
2469 As C<isl> currently does not have its own output format, the output
2470 is just a dump of the internal state.
2472 =head2 C<isl_polyhedron_minimize>
2474 C<isl_polyhedron_minimize> computes the minimum of some linear
2475 or affine objective function over the integer points in a polyhedron.
2476 If an affine objective function
2477 is given, then the constant should appear in the last column.
2479 =head2 C<isl_polytope_scan>
2481 Given a polytope, C<isl_polytope_scan> prints
2482 all integer points in the polytope.
2484 =head1 C<isl-polylib>
2486 The C<isl-polylib> library provides the following functions for converting
2487 between C<isl> objects and C<PolyLib> objects.
2488 The library is distributed separately for licensing reasons.
2490 #include <isl_set_polylib.h>
2491 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2492 Polyhedron *P, __isl_take isl_dim *dim);
2493 Polyhedron *isl_basic_set_to_polylib(
2494 __isl_keep isl_basic_set *bset);
2495 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2496 __isl_take isl_dim *dim);
2497 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2499 #include <isl_map_polylib.h>
2500 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2501 Polyhedron *P, __isl_take isl_dim *dim);
2502 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2503 __isl_take isl_dim *dim);
2504 Polyhedron *isl_basic_map_to_polylib(
2505 __isl_keep isl_basic_map *bmap);
2506 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);