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 operations below
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>
206 The user should not assume that an C<isl_int> is represented
207 as a C<mpz_t>, but should instead explicitly convert between
208 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
209 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
213 =item isl_int_init(i)
215 =item isl_int_clear(i)
217 =item isl_int_set(r,i)
219 =item isl_int_set_si(r,i)
221 =item isl_int_set_gmp(r,g)
223 =item isl_int_get_gmp(i,g)
225 =item isl_int_abs(r,i)
227 =item isl_int_neg(r,i)
229 =item isl_int_swap(i,j)
231 =item isl_int_swap_or_set(i,j)
233 =item isl_int_add_ui(r,i,j)
235 =item isl_int_sub_ui(r,i,j)
237 =item isl_int_add(r,i,j)
239 =item isl_int_sub(r,i,j)
241 =item isl_int_mul(r,i,j)
243 =item isl_int_mul_ui(r,i,j)
245 =item isl_int_addmul(r,i,j)
247 =item isl_int_submul(r,i,j)
249 =item isl_int_gcd(r,i,j)
251 =item isl_int_lcm(r,i,j)
253 =item isl_int_divexact(r,i,j)
255 =item isl_int_cdiv_q(r,i,j)
257 =item isl_int_fdiv_q(r,i,j)
259 =item isl_int_fdiv_r(r,i,j)
261 =item isl_int_fdiv_q_ui(r,i,j)
263 =item isl_int_read(r,s)
265 =item isl_int_print(out,i,width)
269 =item isl_int_cmp(i,j)
271 =item isl_int_cmp_si(i,si)
273 =item isl_int_eq(i,j)
275 =item isl_int_ne(i,j)
277 =item isl_int_lt(i,j)
279 =item isl_int_le(i,j)
281 =item isl_int_gt(i,j)
283 =item isl_int_ge(i,j)
285 =item isl_int_abs_eq(i,j)
287 =item isl_int_abs_ne(i,j)
289 =item isl_int_abs_lt(i,j)
291 =item isl_int_abs_gt(i,j)
293 =item isl_int_abs_ge(i,j)
295 =item isl_int_is_zero(i)
297 =item isl_int_is_one(i)
299 =item isl_int_is_negone(i)
301 =item isl_int_is_pos(i)
303 =item isl_int_is_neg(i)
305 =item isl_int_is_nonpos(i)
307 =item isl_int_is_nonneg(i)
309 =item isl_int_is_divisible_by(i,j)
313 =head2 Sets and Relations
315 C<isl> uses six types of objects for representing sets and relations,
316 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
317 C<isl_union_set> and C<isl_union_map>.
318 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
319 can be described as a conjunction of affine constraints, while
320 C<isl_set> and C<isl_map> represent unions of
321 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
322 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
323 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
324 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
325 where dimensions with different space names
326 (see L<Dimension Specifications>) are considered different as well.
327 The difference between sets and relations (maps) is that sets have
328 one set of variables, while relations have two sets of variables,
329 input variables and output variables.
331 =head2 Memory Management
333 Since a high-level operation on sets and/or relations usually involves
334 several substeps and since the user is usually not interested in
335 the intermediate results, most functions that return a new object
336 will also release all the objects passed as arguments.
337 If the user still wants to use one or more of these arguments
338 after the function call, she should pass along a copy of the
339 object rather than the object itself.
340 The user is then responsible for make sure that the original
341 object gets used somewhere else or is explicitly freed.
343 The arguments and return values of all documents functions are
344 annotated to make clear which arguments are released and which
345 arguments are preserved. In particular, the following annotations
352 C<__isl_give> means that a new object is returned.
353 The user should make sure that the returned pointer is
354 used exactly once as a value for an C<__isl_take> argument.
355 In between, it can be used as a value for as many
356 C<__isl_keep> arguments as the user likes.
357 There is one exception, and that is the case where the
358 pointer returned is C<NULL>. Is this case, the user
359 is free to use it as an C<__isl_take> argument or not.
363 C<__isl_take> means that the object the argument points to
364 is taken over by the function and may no longer be used
365 by the user as an argument to any other function.
366 The pointer value must be one returned by a function
367 returning an C<__isl_give> pointer.
368 If the user passes in a C<NULL> value, then this will
369 be treated as an error in the sense that the function will
370 not perform its usual operation. However, it will still
371 make sure that all the the other C<__isl_take> arguments
376 C<__isl_keep> means that the function will only use the object
377 temporarily. After the function has finished, the user
378 can still use it as an argument to other functions.
379 A C<NULL> value will be treated in the same way as
380 a C<NULL> value for an C<__isl_take> argument.
384 =head2 Dimension Specifications
386 Whenever a new set or relation is created from scratch,
387 its dimension needs to be specified using an C<isl_dim>.
390 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
391 unsigned nparam, unsigned n_in, unsigned n_out);
392 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
393 unsigned nparam, unsigned dim);
394 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
395 void isl_dim_free(__isl_take isl_dim *dim);
396 unsigned isl_dim_size(__isl_keep isl_dim *dim,
397 enum isl_dim_type type);
399 The dimension specification used for creating a set
400 needs to be created using C<isl_dim_set_alloc>, while
401 that for creating a relation
402 needs to be created using C<isl_dim_alloc>.
403 C<isl_dim_size> can be used
404 to find out the number of dimensions of each type in
405 a dimension specification, where type may be
406 C<isl_dim_param>, C<isl_dim_in> (only for relations),
407 C<isl_dim_out> (only for relations), C<isl_dim_set>
408 (only for sets) or C<isl_dim_all>.
410 It is often useful to create objects that live in the
411 same space as some other object. This can be accomplished
412 by creating the new objects
413 (see L<Creating New Sets and Relations> or
414 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
415 specification of the original object.
418 __isl_give isl_dim *isl_basic_set_get_dim(
419 __isl_keep isl_basic_set *bset);
420 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
422 #include <isl/union_set.h>
423 __isl_give isl_dim *isl_union_set_get_dim(
424 __isl_keep isl_union_set *uset);
427 __isl_give isl_dim *isl_basic_map_get_dim(
428 __isl_keep isl_basic_map *bmap);
429 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
431 #include <isl/union_map.h>
432 __isl_give isl_dim *isl_union_map_get_dim(
433 __isl_keep isl_union_map *umap);
435 #include <isl/polynomial.h>
436 __isl_give isl_dim *isl_qpolynomial_get_dim(
437 __isl_keep isl_qpolynomial *qp);
438 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
439 __isl_keep isl_pw_qpolynomial *pwqp);
440 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
441 __isl_keep isl_union_pw_qpolynomial *upwqp);
442 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
443 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
445 The names of the individual dimensions may be set or read off
446 using the following functions.
449 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
450 enum isl_dim_type type, unsigned pos,
451 __isl_keep const char *name);
452 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
453 enum isl_dim_type type, unsigned pos);
455 Note that C<isl_dim_get_name> returns a pointer to some internal
456 data structure, so the result can only be used while the
457 corresponding C<isl_dim> is alive.
458 Also note that every function that operates on two sets or relations
459 requires that both arguments have the same parameters. This also
460 means that if one of the arguments has named parameters, then the
461 other needs to have named parameters too and the names need to match.
462 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
463 have different parameters (as long as they are named), in which case
464 the result will have as parameters the union of the parameters of
467 The names of entire spaces may be set or read off
468 using the following functions.
471 __isl_give isl_dim *isl_dim_set_tuple_name(
472 __isl_take isl_dim *dim,
473 enum isl_dim_type type, const char *s);
474 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
475 enum isl_dim_type type);
477 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
478 or C<isl_dim_set>. As with C<isl_dim_get_name>,
479 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
481 Binary operations require the corresponding spaces of their arguments
482 to have the same name.
484 Spaces can be nested. In particular, the domain of a set or
485 the domain or range of a relation can be a nested relation.
486 The following functions can be used to construct and deconstruct
487 such nested dimension specifications.
490 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
491 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
492 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
494 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
495 be the dimension specification of a set, while that of
496 C<isl_dim_wrap> should be the dimension specification of a relation.
497 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
498 of a relation, while that of C<isl_dim_wrap> is the dimension specification
501 Dimension specifications can be created from other dimension
502 specifications using the following functions.
504 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
505 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
506 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
507 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
508 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
509 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
510 __isl_take isl_dim *right);
511 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
512 enum isl_dim_type type, unsigned pos, unsigned n);
513 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
514 enum isl_dim_type type, unsigned n);
515 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
516 enum isl_dim_type type, unsigned first, unsigned n);
518 Note that if dimensions are added or removed from a space, then
519 the name and the internal structure are lost.
521 =head2 Input and Output
523 C<isl> supports its own input/output format, which is similar
524 to the C<Omega> format, but also supports the C<PolyLib> format
529 The C<isl> format is similar to that of C<Omega>, but has a different
530 syntax for describing the parameters and allows for the definition
531 of an existentially quantified variable as the integer division
532 of an affine expression.
533 For example, the set of integers C<i> between C<0> and C<n>
534 such that C<i % 10 <= 6> can be described as
536 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
539 A set or relation can have several disjuncts, separated
540 by the keyword C<or>. Each disjunct is either a conjunction
541 of constraints or a projection (C<exists>) of a conjunction
542 of constraints. The constraints are separated by the keyword
545 =head3 C<PolyLib> format
547 If the represented set is a union, then the first line
548 contains a single number representing the number of disjuncts.
549 Otherwise, a line containing the number C<1> is optional.
551 Each disjunct is represented by a matrix of constraints.
552 The first line contains two numbers representing
553 the number of rows and columns,
554 where the number of rows is equal to the number of constraints
555 and the number of columns is equal to two plus the number of variables.
556 The following lines contain the actual rows of the constraint matrix.
557 In each row, the first column indicates whether the constraint
558 is an equality (C<0>) or inequality (C<1>). The final column
559 corresponds to the constant term.
561 If the set is parametric, then the coefficients of the parameters
562 appear in the last columns before the constant column.
563 The coefficients of any existentially quantified variables appear
564 between those of the set variables and those of the parameters.
566 =head3 Extended C<PolyLib> format
568 The extended C<PolyLib> format is nearly identical to the
569 C<PolyLib> format. The only difference is that the line
570 containing the number of rows and columns of a constraint matrix
571 also contains four additional numbers:
572 the number of output dimensions, the number of input dimensions,
573 the number of local dimensions (i.e., the number of existentially
574 quantified variables) and the number of parameters.
575 For sets, the number of ``output'' dimensions is equal
576 to the number of set dimensions, while the number of ``input''
582 __isl_give isl_basic_set *isl_basic_set_read_from_file(
583 isl_ctx *ctx, FILE *input, int nparam);
584 __isl_give isl_basic_set *isl_basic_set_read_from_str(
585 isl_ctx *ctx, const char *str, int nparam);
586 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
587 FILE *input, int nparam);
588 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
589 const char *str, int nparam);
592 __isl_give isl_basic_map *isl_basic_map_read_from_file(
593 isl_ctx *ctx, FILE *input, int nparam);
594 __isl_give isl_basic_map *isl_basic_map_read_from_str(
595 isl_ctx *ctx, const char *str, int nparam);
596 __isl_give isl_map *isl_map_read_from_file(
597 struct isl_ctx *ctx, FILE *input, int nparam);
598 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
599 const char *str, int nparam);
601 #include <isl/union_set.h>
602 __isl_give isl_union_set *isl_union_set_read_from_str(
603 struct isl_ctx *ctx, const char *str);
605 #include <isl/union_map.h>
606 __isl_give isl_union_map *isl_union_map_read_from_str(
607 struct isl_ctx *ctx, const char *str);
609 The input format is autodetected and may be either the C<PolyLib> format
610 or the C<isl> format.
611 C<nparam> specifies how many of the final columns in
612 the C<PolyLib> format correspond to parameters.
613 If input is given in the C<isl> format, then the number
614 of parameters needs to be equal to C<nparam>.
615 If C<nparam> is negative, then any number of parameters
616 is accepted in the C<isl> format and zero parameters
617 are assumed in the C<PolyLib> format.
621 Before anything can be printed, an C<isl_printer> needs to
624 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
626 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
627 void isl_printer_free(__isl_take isl_printer *printer);
628 __isl_give char *isl_printer_get_str(
629 __isl_keep isl_printer *printer);
631 The behavior of the printer can be modified in various ways
633 __isl_give isl_printer *isl_printer_set_output_format(
634 __isl_take isl_printer *p, int output_format);
635 __isl_give isl_printer *isl_printer_set_indent(
636 __isl_take isl_printer *p, int indent);
637 __isl_give isl_printer *isl_printer_set_prefix(
638 __isl_take isl_printer *p, const char *prefix);
639 __isl_give isl_printer *isl_printer_set_suffix(
640 __isl_take isl_printer *p, const char *suffix);
642 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
643 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
644 and defaults to C<ISL_FORMAT_ISL>.
645 Each line in the output is indented by C<indent> spaces
646 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
647 In the C<PolyLib> format output,
648 the coefficients of the existentially quantified variables
649 appear between those of the set variables and those
652 To actually print something, use
655 __isl_give isl_printer *isl_printer_print_basic_set(
656 __isl_take isl_printer *printer,
657 __isl_keep isl_basic_set *bset);
658 __isl_give isl_printer *isl_printer_print_set(
659 __isl_take isl_printer *printer,
660 __isl_keep isl_set *set);
663 __isl_give isl_printer *isl_printer_print_basic_map(
664 __isl_take isl_printer *printer,
665 __isl_keep isl_basic_map *bmap);
666 __isl_give isl_printer *isl_printer_print_map(
667 __isl_take isl_printer *printer,
668 __isl_keep isl_map *map);
670 #include <isl/union_set.h>
671 __isl_give isl_printer *isl_printer_print_union_set(
672 __isl_take isl_printer *p,
673 __isl_keep isl_union_set *uset);
675 #include <isl/union_map.h>
676 __isl_give isl_printer *isl_printer_print_union_map(
677 __isl_take isl_printer *p,
678 __isl_keep isl_union_map *umap);
680 When called on a file printer, the following function flushes
681 the file. When called on a string printer, the buffer is cleared.
683 __isl_give isl_printer *isl_printer_flush(
684 __isl_take isl_printer *p);
686 =head2 Creating New Sets and Relations
688 C<isl> has functions for creating some standard sets and relations.
692 =item * Empty sets and relations
694 __isl_give isl_basic_set *isl_basic_set_empty(
695 __isl_take isl_dim *dim);
696 __isl_give isl_basic_map *isl_basic_map_empty(
697 __isl_take isl_dim *dim);
698 __isl_give isl_set *isl_set_empty(
699 __isl_take isl_dim *dim);
700 __isl_give isl_map *isl_map_empty(
701 __isl_take isl_dim *dim);
702 __isl_give isl_union_set *isl_union_set_empty(
703 __isl_take isl_dim *dim);
704 __isl_give isl_union_map *isl_union_map_empty(
705 __isl_take isl_dim *dim);
707 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
708 is only used to specify the parameters.
710 =item * Universe sets and relations
712 __isl_give isl_basic_set *isl_basic_set_universe(
713 __isl_take isl_dim *dim);
714 __isl_give isl_basic_map *isl_basic_map_universe(
715 __isl_take isl_dim *dim);
716 __isl_give isl_set *isl_set_universe(
717 __isl_take isl_dim *dim);
718 __isl_give isl_map *isl_map_universe(
719 __isl_take isl_dim *dim);
721 =item * Identity relations
723 __isl_give isl_basic_map *isl_basic_map_identity(
724 __isl_take isl_dim *set_dim);
725 __isl_give isl_map *isl_map_identity(
726 __isl_take isl_dim *set_dim);
728 These functions take a dimension specification for a B<set>
729 and return an identity relation between two such sets.
731 =item * Lexicographic order
733 __isl_give isl_map *isl_map_lex_lt(
734 __isl_take isl_dim *set_dim);
735 __isl_give isl_map *isl_map_lex_le(
736 __isl_take isl_dim *set_dim);
737 __isl_give isl_map *isl_map_lex_gt(
738 __isl_take isl_dim *set_dim);
739 __isl_give isl_map *isl_map_lex_ge(
740 __isl_take isl_dim *set_dim);
741 __isl_give isl_map *isl_map_lex_lt_first(
742 __isl_take isl_dim *dim, unsigned n);
743 __isl_give isl_map *isl_map_lex_le_first(
744 __isl_take isl_dim *dim, unsigned n);
745 __isl_give isl_map *isl_map_lex_gt_first(
746 __isl_take isl_dim *dim, unsigned n);
747 __isl_give isl_map *isl_map_lex_ge_first(
748 __isl_take isl_dim *dim, unsigned n);
750 The first four functions take a dimension specification for a B<set>
751 and return relations that express that the elements in the domain
752 are lexicographically less
753 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
754 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
755 than the elements in the range.
756 The last four functions take a dimension specification for a map
757 and return relations that express that the first C<n> dimensions
758 in the domain are lexicographically less
759 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
760 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
761 than the first C<n> dimensions in the range.
765 A basic set or relation can be converted to a set or relation
766 using the following functions.
768 __isl_give isl_set *isl_set_from_basic_set(
769 __isl_take isl_basic_set *bset);
770 __isl_give isl_map *isl_map_from_basic_map(
771 __isl_take isl_basic_map *bmap);
773 Sets and relations can be converted to union sets and relations
774 using the following functions.
776 __isl_give isl_union_map *isl_union_map_from_map(
777 __isl_take isl_map *map);
778 __isl_give isl_union_set *isl_union_set_from_set(
779 __isl_take isl_set *set);
781 Sets and relations can be copied and freed again using the following
784 __isl_give isl_basic_set *isl_basic_set_copy(
785 __isl_keep isl_basic_set *bset);
786 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
787 __isl_give isl_union_set *isl_union_set_copy(
788 __isl_keep isl_union_set *uset);
789 __isl_give isl_basic_map *isl_basic_map_copy(
790 __isl_keep isl_basic_map *bmap);
791 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
792 __isl_give isl_union_map *isl_union_map_copy(
793 __isl_keep isl_union_map *umap);
794 void isl_basic_set_free(__isl_take isl_basic_set *bset);
795 void isl_set_free(__isl_take isl_set *set);
796 void isl_union_set_free(__isl_take isl_union_set *uset);
797 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
798 void isl_map_free(__isl_take isl_map *map);
799 void isl_union_map_free(__isl_take isl_union_map *umap);
801 Other sets and relations can be constructed by starting
802 from a universe set or relation, adding equality and/or
803 inequality constraints and then projecting out the
804 existentially quantified variables, if any.
805 Constraints can be constructed, manipulated and
806 added to basic sets and relations using the following functions.
808 #include <isl/constraint.h>
809 __isl_give isl_constraint *isl_equality_alloc(
810 __isl_take isl_dim *dim);
811 __isl_give isl_constraint *isl_inequality_alloc(
812 __isl_take isl_dim *dim);
813 void isl_constraint_set_constant(
814 __isl_keep isl_constraint *constraint, isl_int v);
815 void isl_constraint_set_coefficient(
816 __isl_keep isl_constraint *constraint,
817 enum isl_dim_type type, int pos, isl_int v);
818 __isl_give isl_basic_map *isl_basic_map_add_constraint(
819 __isl_take isl_basic_map *bmap,
820 __isl_take isl_constraint *constraint);
821 __isl_give isl_basic_set *isl_basic_set_add_constraint(
822 __isl_take isl_basic_set *bset,
823 __isl_take isl_constraint *constraint);
825 For example, to create a set containing the even integers
826 between 10 and 42, you would use the following code.
830 struct isl_constraint *c;
831 struct isl_basic_set *bset;
834 dim = isl_dim_set_alloc(ctx, 0, 2);
835 bset = isl_basic_set_universe(isl_dim_copy(dim));
837 c = isl_equality_alloc(isl_dim_copy(dim));
838 isl_int_set_si(v, -1);
839 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
840 isl_int_set_si(v, 2);
841 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
842 bset = isl_basic_set_add_constraint(bset, c);
844 c = isl_inequality_alloc(isl_dim_copy(dim));
845 isl_int_set_si(v, -10);
846 isl_constraint_set_constant(c, v);
847 isl_int_set_si(v, 1);
848 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
849 bset = isl_basic_set_add_constraint(bset, c);
851 c = isl_inequality_alloc(dim);
852 isl_int_set_si(v, 42);
853 isl_constraint_set_constant(c, v);
854 isl_int_set_si(v, -1);
855 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
856 bset = isl_basic_set_add_constraint(bset, c);
858 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
864 struct isl_basic_set *bset;
865 bset = isl_basic_set_read_from_str(ctx,
866 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
868 A basic set or relation can also be constructed from two matrices
869 describing the equalities and the inequalities.
871 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
872 __isl_take isl_dim *dim,
873 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
874 enum isl_dim_type c1,
875 enum isl_dim_type c2, enum isl_dim_type c3,
876 enum isl_dim_type c4);
877 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
878 __isl_take isl_dim *dim,
879 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
880 enum isl_dim_type c1,
881 enum isl_dim_type c2, enum isl_dim_type c3,
882 enum isl_dim_type c4, enum isl_dim_type c5);
884 The C<isl_dim_type> arguments indicate the order in which
885 different kinds of variables appear in the input matrices
886 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
887 C<isl_dim_set> and C<isl_dim_div> for sets and
888 of C<isl_dim_cst>, C<isl_dim_param>,
889 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
891 =head2 Inspecting Sets and Relations
893 Usually, the user should not have to care about the actual constraints
894 of the sets and maps, but should instead apply the abstract operations
895 explained in the following sections.
896 Occasionally, however, it may be required to inspect the individual
897 coefficients of the constraints. This section explains how to do so.
898 In these cases, it may also be useful to have C<isl> compute
899 an explicit representation of the existentially quantified variables.
901 __isl_give isl_set *isl_set_compute_divs(
902 __isl_take isl_set *set);
903 __isl_give isl_map *isl_map_compute_divs(
904 __isl_take isl_map *map);
905 __isl_give isl_union_set *isl_union_set_compute_divs(
906 __isl_take isl_union_set *uset);
907 __isl_give isl_union_map *isl_union_map_compute_divs(
908 __isl_take isl_union_map *umap);
910 This explicit representation defines the existentially quantified
911 variables as integer divisions of the other variables, possibly
912 including earlier existentially quantified variables.
913 An explicitly represented existentially quantified variable therefore
914 has a unique value when the values of the other variables are known.
915 If, furthermore, the same existentials, i.e., existentials
916 with the same explicit representations, should appear in the
917 same order in each of the disjuncts of a set or map, then the user should call
918 either of the following functions.
920 __isl_give isl_set *isl_set_align_divs(
921 __isl_take isl_set *set);
922 __isl_give isl_map *isl_map_align_divs(
923 __isl_take isl_map *map);
925 Alternatively, the existentially quantified variables can be removed
926 using the following functions, which compute an overapproximation.
928 __isl_give isl_basic_set *isl_basic_set_remove_divs(
929 __isl_take isl_basic_set *bset);
930 __isl_give isl_basic_map *isl_basic_map_remove_divs(
931 __isl_take isl_basic_map *bmap);
932 __isl_give isl_set *isl_set_remove_divs(
933 __isl_take isl_set *set);
935 To iterate over all the sets or maps in a union set or map, use
937 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
938 int (*fn)(__isl_take isl_set *set, void *user),
940 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
941 int (*fn)(__isl_take isl_map *map, void *user),
944 The number of sets or maps in a union set or map can be obtained
947 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
948 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
950 To extract the set or map from a union with a given dimension
953 __isl_give isl_set *isl_union_set_extract_set(
954 __isl_keep isl_union_set *uset,
955 __isl_take isl_dim *dim);
956 __isl_give isl_map *isl_union_map_extract_map(
957 __isl_keep isl_union_map *umap,
958 __isl_take isl_dim *dim);
960 To iterate over all the basic sets or maps in a set or map, use
962 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
963 int (*fn)(__isl_take isl_basic_set *bset, void *user),
965 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
966 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
969 The callback function C<fn> should return 0 if successful and
970 -1 if an error occurs. In the latter case, or if any other error
971 occurs, the above functions will return -1.
973 It should be noted that C<isl> does not guarantee that
974 the basic sets or maps passed to C<fn> are disjoint.
975 If this is required, then the user should call one of
976 the following functions first.
978 __isl_give isl_set *isl_set_make_disjoint(
979 __isl_take isl_set *set);
980 __isl_give isl_map *isl_map_make_disjoint(
981 __isl_take isl_map *map);
983 The number of basic sets in a set can be obtained
986 int isl_set_n_basic_set(__isl_keep isl_set *set);
988 To iterate over the constraints of a basic set or map, use
990 #include <isl/constraint.h>
992 int isl_basic_map_foreach_constraint(
993 __isl_keep isl_basic_map *bmap,
994 int (*fn)(__isl_take isl_constraint *c, void *user),
996 void isl_constraint_free(struct isl_constraint *c);
998 Again, the callback function C<fn> should return 0 if successful and
999 -1 if an error occurs. In the latter case, or if any other error
1000 occurs, the above functions will return -1.
1001 The constraint C<c> represents either an equality or an inequality.
1002 Use the following function to find out whether a constraint
1003 represents an equality. If not, it represents an inequality.
1005 int isl_constraint_is_equality(
1006 __isl_keep isl_constraint *constraint);
1008 The coefficients of the constraints can be inspected using
1009 the following functions.
1011 void isl_constraint_get_constant(
1012 __isl_keep isl_constraint *constraint, isl_int *v);
1013 void isl_constraint_get_coefficient(
1014 __isl_keep isl_constraint *constraint,
1015 enum isl_dim_type type, int pos, isl_int *v);
1017 The explicit representations of the existentially quantified
1018 variables can be inspected using the following functions.
1019 Note that the user is only allowed to use these functions
1020 if the inspected set or map is the result of a call
1021 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1023 __isl_give isl_div *isl_constraint_div(
1024 __isl_keep isl_constraint *constraint, int pos);
1025 void isl_div_get_constant(__isl_keep isl_div *div,
1027 void isl_div_get_denominator(__isl_keep isl_div *div,
1029 void isl_div_get_coefficient(__isl_keep isl_div *div,
1030 enum isl_dim_type type, int pos, isl_int *v);
1032 To obtain the constraints of a basic set or map in matrix
1033 form, use the following functions.
1035 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1036 __isl_keep isl_basic_set *bset,
1037 enum isl_dim_type c1, enum isl_dim_type c2,
1038 enum isl_dim_type c3, enum isl_dim_type c4);
1039 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1040 __isl_keep isl_basic_set *bset,
1041 enum isl_dim_type c1, enum isl_dim_type c2,
1042 enum isl_dim_type c3, enum isl_dim_type c4);
1043 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1044 __isl_keep isl_basic_map *bmap,
1045 enum isl_dim_type c1,
1046 enum isl_dim_type c2, enum isl_dim_type c3,
1047 enum isl_dim_type c4, enum isl_dim_type c5);
1048 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1049 __isl_keep isl_basic_map *bmap,
1050 enum isl_dim_type c1,
1051 enum isl_dim_type c2, enum isl_dim_type c3,
1052 enum isl_dim_type c4, enum isl_dim_type c5);
1054 The C<isl_dim_type> arguments dictate the order in which
1055 different kinds of variables appear in the resulting matrix
1056 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1057 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1059 The names of the domain and range spaces of a set or relation can be
1060 read off using the following functions.
1062 const char *isl_set_get_tuple_name(
1063 __isl_keep isl_set *set);
1064 const char *isl_basic_map_get_tuple_name(
1065 __isl_keep isl_basic_map *bmap,
1066 enum isl_dim_type type);
1067 const char *isl_map_get_tuple_name(
1068 __isl_keep isl_map *map,
1069 enum isl_dim_type type);
1071 As with C<isl_dim_get_tuple_name>, the value returned points to
1072 an internal data structure.
1073 The names of individual dimensions can be read off using
1074 the following functions.
1076 const char *isl_constraint_get_dim_name(
1077 __isl_keep isl_constraint *constraint,
1078 enum isl_dim_type type, unsigned pos);
1079 const char *isl_set_get_dim_name(
1080 __isl_keep isl_set *set,
1081 enum isl_dim_type type, unsigned pos);
1082 const char *isl_basic_map_get_dim_name(
1083 __isl_keep isl_basic_map *bmap,
1084 enum isl_dim_type type, unsigned pos);
1085 const char *isl_map_get_dim_name(
1086 __isl_keep isl_map *map,
1087 enum isl_dim_type type, unsigned pos);
1089 These functions are mostly useful to obtain the names
1094 =head3 Unary Properties
1100 The following functions test whether the given set or relation
1101 contains any integer points. The ``fast'' variants do not perform
1102 any computations, but simply check if the given set or relation
1103 is already known to be empty.
1105 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1106 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1107 int isl_set_is_empty(__isl_keep isl_set *set);
1108 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1109 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1110 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1111 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1112 int isl_map_is_empty(__isl_keep isl_map *map);
1113 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1115 =item * Universality
1117 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1118 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1119 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1121 =item * Single-valuedness
1123 int isl_map_is_single_valued(__isl_keep isl_map *map);
1127 int isl_map_is_bijective(__isl_keep isl_map *map);
1131 The followning functions check whether the domain of the given
1132 (basic) set is a wrapped relation.
1134 int isl_basic_set_is_wrapping(
1135 __isl_keep isl_basic_set *bset);
1136 int isl_set_is_wrapping(__isl_keep isl_set *set);
1140 =head3 Binary Properties
1146 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1147 __isl_keep isl_set *set2);
1148 int isl_set_is_equal(__isl_keep isl_set *set1,
1149 __isl_keep isl_set *set2);
1150 int isl_union_set_is_equal(
1151 __isl_keep isl_union_set *uset1,
1152 __isl_keep isl_union_set *uset2);
1153 int isl_basic_map_is_equal(
1154 __isl_keep isl_basic_map *bmap1,
1155 __isl_keep isl_basic_map *bmap2);
1156 int isl_map_is_equal(__isl_keep isl_map *map1,
1157 __isl_keep isl_map *map2);
1158 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1159 __isl_keep isl_map *map2);
1160 int isl_union_map_is_equal(
1161 __isl_keep isl_union_map *umap1,
1162 __isl_keep isl_union_map *umap2);
1164 =item * Disjointness
1166 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1167 __isl_keep isl_set *set2);
1171 int isl_set_is_subset(__isl_keep isl_set *set1,
1172 __isl_keep isl_set *set2);
1173 int isl_set_is_strict_subset(
1174 __isl_keep isl_set *set1,
1175 __isl_keep isl_set *set2);
1176 int isl_union_set_is_subset(
1177 __isl_keep isl_union_set *uset1,
1178 __isl_keep isl_union_set *uset2);
1179 int isl_union_set_is_strict_subset(
1180 __isl_keep isl_union_set *uset1,
1181 __isl_keep isl_union_set *uset2);
1182 int isl_basic_map_is_subset(
1183 __isl_keep isl_basic_map *bmap1,
1184 __isl_keep isl_basic_map *bmap2);
1185 int isl_basic_map_is_strict_subset(
1186 __isl_keep isl_basic_map *bmap1,
1187 __isl_keep isl_basic_map *bmap2);
1188 int isl_map_is_subset(
1189 __isl_keep isl_map *map1,
1190 __isl_keep isl_map *map2);
1191 int isl_map_is_strict_subset(
1192 __isl_keep isl_map *map1,
1193 __isl_keep isl_map *map2);
1194 int isl_union_map_is_subset(
1195 __isl_keep isl_union_map *umap1,
1196 __isl_keep isl_union_map *umap2);
1197 int isl_union_map_is_strict_subset(
1198 __isl_keep isl_union_map *umap1,
1199 __isl_keep isl_union_map *umap2);
1203 =head2 Unary Operations
1209 __isl_give isl_set *isl_set_complement(
1210 __isl_take isl_set *set);
1214 __isl_give isl_basic_map *isl_basic_map_reverse(
1215 __isl_take isl_basic_map *bmap);
1216 __isl_give isl_map *isl_map_reverse(
1217 __isl_take isl_map *map);
1218 __isl_give isl_union_map *isl_union_map_reverse(
1219 __isl_take isl_union_map *umap);
1223 __isl_give isl_basic_set *isl_basic_set_project_out(
1224 __isl_take isl_basic_set *bset,
1225 enum isl_dim_type type, unsigned first, unsigned n);
1226 __isl_give isl_basic_map *isl_basic_map_project_out(
1227 __isl_take isl_basic_map *bmap,
1228 enum isl_dim_type type, unsigned first, unsigned n);
1229 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1230 enum isl_dim_type type, unsigned first, unsigned n);
1231 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1232 enum isl_dim_type type, unsigned first, unsigned n);
1233 __isl_give isl_basic_set *isl_basic_map_domain(
1234 __isl_take isl_basic_map *bmap);
1235 __isl_give isl_basic_set *isl_basic_map_range(
1236 __isl_take isl_basic_map *bmap);
1237 __isl_give isl_set *isl_map_domain(
1238 __isl_take isl_map *bmap);
1239 __isl_give isl_set *isl_map_range(
1240 __isl_take isl_map *map);
1241 __isl_give isl_union_set *isl_union_map_domain(
1242 __isl_take isl_union_map *umap);
1243 __isl_give isl_union_set *isl_union_map_range(
1244 __isl_take isl_union_map *umap);
1246 __isl_give isl_basic_map *isl_basic_map_domain_map(
1247 __isl_take isl_basic_map *bmap);
1248 __isl_give isl_basic_map *isl_basic_map_range_map(
1249 __isl_take isl_basic_map *bmap);
1250 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1251 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1252 __isl_give isl_union_map *isl_union_map_domain_map(
1253 __isl_take isl_union_map *umap);
1254 __isl_give isl_union_map *isl_union_map_range_map(
1255 __isl_take isl_union_map *umap);
1257 The functions above construct a (basic, regular or union) relation
1258 that maps (a wrapped version of) the input relation to its domain or range.
1262 __isl_give isl_map *isl_set_identity(
1263 __isl_take isl_set *set);
1264 __isl_give isl_union_map *isl_union_set_identity(
1265 __isl_take isl_union_set *uset);
1267 Construct an identity relation on the given (union) set.
1271 __isl_give isl_basic_set *isl_basic_map_deltas(
1272 __isl_take isl_basic_map *bmap);
1273 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1274 __isl_give isl_union_set *isl_union_map_deltas(
1275 __isl_take isl_union_map *umap);
1277 These functions return a (basic) set containing the differences
1278 between image elements and corresponding domain elements in the input.
1282 Simplify the representation of a set or relation by trying
1283 to combine pairs of basic sets or relations into a single
1284 basic set or relation.
1286 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1287 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1288 __isl_give isl_union_set *isl_union_set_coalesce(
1289 __isl_take isl_union_set *uset);
1290 __isl_give isl_union_map *isl_union_map_coalesce(
1291 __isl_take isl_union_map *umap);
1295 __isl_give isl_basic_set *isl_set_convex_hull(
1296 __isl_take isl_set *set);
1297 __isl_give isl_basic_map *isl_map_convex_hull(
1298 __isl_take isl_map *map);
1300 If the input set or relation has any existentially quantified
1301 variables, then the result of these operations is currently undefined.
1305 __isl_give isl_basic_set *isl_set_simple_hull(
1306 __isl_take isl_set *set);
1307 __isl_give isl_basic_map *isl_map_simple_hull(
1308 __isl_take isl_map *map);
1310 These functions compute a single basic set or relation
1311 that contains the whole input set or relation.
1312 In particular, the output is described by translates
1313 of the constraints describing the basic sets or relations in the input.
1317 (See \autoref{s:simple hull}.)
1323 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1324 __isl_take isl_basic_set *bset);
1325 __isl_give isl_basic_set *isl_set_affine_hull(
1326 __isl_take isl_set *set);
1327 __isl_give isl_union_set *isl_union_set_affine_hull(
1328 __isl_take isl_union_set *uset);
1329 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1330 __isl_take isl_basic_map *bmap);
1331 __isl_give isl_basic_map *isl_map_affine_hull(
1332 __isl_take isl_map *map);
1333 __isl_give isl_union_map *isl_union_map_affine_hull(
1334 __isl_take isl_union_map *umap);
1336 In case of union sets and relations, the affine hull is computed
1339 =item * Polyhedral hull
1341 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1342 __isl_take isl_set *set);
1343 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1344 __isl_take isl_map *map);
1345 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1346 __isl_take isl_union_set *uset);
1347 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1348 __isl_take isl_union_map *umap);
1350 These functions compute a single basic set or relation
1351 not involving any existentially quantified variables
1352 that contains the whole input set or relation.
1353 In case of union sets and relations, the polyhedral hull is computed
1358 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1359 unsigned param, int *exact);
1361 Compute a parametric representation for all positive powers I<k> of C<map>.
1362 The power I<k> is equated to the parameter at position C<param>.
1363 The result may be an overapproximation. If the result is exact,
1364 then C<*exact> is set to C<1>.
1365 The current implementation only produces exact results for particular
1366 cases of piecewise translations (i.e., piecewise uniform dependences).
1368 =item * Transitive closure
1370 __isl_give isl_map *isl_map_transitive_closure(
1371 __isl_take isl_map *map, int *exact);
1372 __isl_give isl_union_map *isl_union_map_transitive_closure(
1373 __isl_take isl_union_map *umap, int *exact);
1375 Compute the transitive closure of C<map>.
1376 The result may be an overapproximation. If the result is known to be exact,
1377 then C<*exact> is set to C<1>.
1378 The current implementation only produces exact results for particular
1379 cases of piecewise translations (i.e., piecewise uniform dependences).
1381 =item * Reaching path lengths
1383 __isl_give isl_map *isl_map_reaching_path_lengths(
1384 __isl_take isl_map *map, int *exact);
1386 Compute a relation that maps each element in the range of C<map>
1387 to the lengths of all paths composed of edges in C<map> that
1388 end up in the given element.
1389 The result may be an overapproximation. If the result is known to be exact,
1390 then C<*exact> is set to C<1>.
1391 To compute the I<maximal> path length, the resulting relation
1392 should be postprocessed by C<isl_map_lexmax>.
1393 In particular, if the input relation is a dependence relation
1394 (mapping sources to sinks), then the maximal path length corresponds
1395 to the free schedule.
1396 Note, however, that C<isl_map_lexmax> expects the maximum to be
1397 finite, so if the path lengths are unbounded (possibly due to
1398 the overapproximation), then you will get an error message.
1402 __isl_give isl_basic_set *isl_basic_map_wrap(
1403 __isl_take isl_basic_map *bmap);
1404 __isl_give isl_set *isl_map_wrap(
1405 __isl_take isl_map *map);
1406 __isl_give isl_union_set *isl_union_map_wrap(
1407 __isl_take isl_union_map *umap);
1408 __isl_give isl_basic_map *isl_basic_set_unwrap(
1409 __isl_take isl_basic_set *bset);
1410 __isl_give isl_map *isl_set_unwrap(
1411 __isl_take isl_set *set);
1412 __isl_give isl_union_map *isl_union_set_unwrap(
1413 __isl_take isl_union_set *uset);
1417 Remove any internal structure of domain (and range) of the given
1418 set or relation. If there is any such internal structure in the input,
1419 then the name of the space is also removed.
1421 __isl_give isl_set *isl_set_flatten(
1422 __isl_take isl_set *set);
1423 __isl_give isl_map *isl_map_flatten(
1424 __isl_take isl_map *map);
1426 __isl_give isl_map *isl_set_flatten_map(
1427 __isl_take isl_set *set);
1429 The function above constructs a relation
1430 that maps the input set to a flattened version of the set.
1432 =item * Dimension manipulation
1434 __isl_give isl_set *isl_set_add_dims(
1435 __isl_take isl_set *set,
1436 enum isl_dim_type type, unsigned n);
1437 __isl_give isl_map *isl_map_add_dims(
1438 __isl_take isl_map *map,
1439 enum isl_dim_type type, unsigned n);
1441 It is usually not advisable to directly change the (input or output)
1442 space of a set or a relation as this removes the name and the internal
1443 structure of the space. However, the above functions can be useful
1444 to add new parameters.
1448 =head2 Binary Operations
1450 The two arguments of a binary operation not only need to live
1451 in the same C<isl_ctx>, they currently also need to have
1452 the same (number of) parameters.
1454 =head3 Basic Operations
1458 =item * Intersection
1460 __isl_give isl_basic_set *isl_basic_set_intersect(
1461 __isl_take isl_basic_set *bset1,
1462 __isl_take isl_basic_set *bset2);
1463 __isl_give isl_set *isl_set_intersect(
1464 __isl_take isl_set *set1,
1465 __isl_take isl_set *set2);
1466 __isl_give isl_union_set *isl_union_set_intersect(
1467 __isl_take isl_union_set *uset1,
1468 __isl_take isl_union_set *uset2);
1469 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1470 __isl_take isl_basic_map *bmap,
1471 __isl_take isl_basic_set *bset);
1472 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1473 __isl_take isl_basic_map *bmap,
1474 __isl_take isl_basic_set *bset);
1475 __isl_give isl_basic_map *isl_basic_map_intersect(
1476 __isl_take isl_basic_map *bmap1,
1477 __isl_take isl_basic_map *bmap2);
1478 __isl_give isl_map *isl_map_intersect_domain(
1479 __isl_take isl_map *map,
1480 __isl_take isl_set *set);
1481 __isl_give isl_map *isl_map_intersect_range(
1482 __isl_take isl_map *map,
1483 __isl_take isl_set *set);
1484 __isl_give isl_map *isl_map_intersect(
1485 __isl_take isl_map *map1,
1486 __isl_take isl_map *map2);
1487 __isl_give isl_union_map *isl_union_map_intersect_domain(
1488 __isl_take isl_union_map *umap,
1489 __isl_take isl_union_set *uset);
1490 __isl_give isl_union_map *isl_union_map_intersect_range(
1491 __isl_take isl_union_map *umap,
1492 __isl_take isl_union_set *uset);
1493 __isl_give isl_union_map *isl_union_map_intersect(
1494 __isl_take isl_union_map *umap1,
1495 __isl_take isl_union_map *umap2);
1499 __isl_give isl_set *isl_basic_set_union(
1500 __isl_take isl_basic_set *bset1,
1501 __isl_take isl_basic_set *bset2);
1502 __isl_give isl_map *isl_basic_map_union(
1503 __isl_take isl_basic_map *bmap1,
1504 __isl_take isl_basic_map *bmap2);
1505 __isl_give isl_set *isl_set_union(
1506 __isl_take isl_set *set1,
1507 __isl_take isl_set *set2);
1508 __isl_give isl_map *isl_map_union(
1509 __isl_take isl_map *map1,
1510 __isl_take isl_map *map2);
1511 __isl_give isl_union_set *isl_union_set_union(
1512 __isl_take isl_union_set *uset1,
1513 __isl_take isl_union_set *uset2);
1514 __isl_give isl_union_map *isl_union_map_union(
1515 __isl_take isl_union_map *umap1,
1516 __isl_take isl_union_map *umap2);
1518 =item * Set difference
1520 __isl_give isl_set *isl_set_subtract(
1521 __isl_take isl_set *set1,
1522 __isl_take isl_set *set2);
1523 __isl_give isl_map *isl_map_subtract(
1524 __isl_take isl_map *map1,
1525 __isl_take isl_map *map2);
1526 __isl_give isl_union_set *isl_union_set_subtract(
1527 __isl_take isl_union_set *uset1,
1528 __isl_take isl_union_set *uset2);
1529 __isl_give isl_union_map *isl_union_map_subtract(
1530 __isl_take isl_union_map *umap1,
1531 __isl_take isl_union_map *umap2);
1535 __isl_give isl_basic_set *isl_basic_set_apply(
1536 __isl_take isl_basic_set *bset,
1537 __isl_take isl_basic_map *bmap);
1538 __isl_give isl_set *isl_set_apply(
1539 __isl_take isl_set *set,
1540 __isl_take isl_map *map);
1541 __isl_give isl_union_set *isl_union_set_apply(
1542 __isl_take isl_union_set *uset,
1543 __isl_take isl_union_map *umap);
1544 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1545 __isl_take isl_basic_map *bmap1,
1546 __isl_take isl_basic_map *bmap2);
1547 __isl_give isl_basic_map *isl_basic_map_apply_range(
1548 __isl_take isl_basic_map *bmap1,
1549 __isl_take isl_basic_map *bmap2);
1550 __isl_give isl_map *isl_map_apply_domain(
1551 __isl_take isl_map *map1,
1552 __isl_take isl_map *map2);
1553 __isl_give isl_union_map *isl_union_map_apply_domain(
1554 __isl_take isl_union_map *umap1,
1555 __isl_take isl_union_map *umap2);
1556 __isl_give isl_map *isl_map_apply_range(
1557 __isl_take isl_map *map1,
1558 __isl_take isl_map *map2);
1559 __isl_give isl_union_map *isl_union_map_apply_range(
1560 __isl_take isl_union_map *umap1,
1561 __isl_take isl_union_map *umap2);
1563 =item * Simplification
1565 __isl_give isl_basic_set *isl_basic_set_gist(
1566 __isl_take isl_basic_set *bset,
1567 __isl_take isl_basic_set *context);
1568 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1569 __isl_take isl_set *context);
1570 __isl_give isl_union_set *isl_union_set_gist(
1571 __isl_take isl_union_set *uset,
1572 __isl_take isl_union_set *context);
1573 __isl_give isl_basic_map *isl_basic_map_gist(
1574 __isl_take isl_basic_map *bmap,
1575 __isl_take isl_basic_map *context);
1576 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1577 __isl_take isl_map *context);
1578 __isl_give isl_union_map *isl_union_map_gist(
1579 __isl_take isl_union_map *umap,
1580 __isl_take isl_union_map *context);
1582 The gist operation returns a set or relation that has the
1583 same intersection with the context as the input set or relation.
1584 Any implicit equality in the intersection is made explicit in the result,
1585 while all inequalities that are redundant with respect to the intersection
1587 In case of union sets and relations, the gist operation is performed
1592 =head3 Lexicographic Optimization
1594 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1595 the following functions
1596 compute a set that contains the lexicographic minimum or maximum
1597 of the elements in C<set> (or C<bset>) for those values of the parameters
1598 that satisfy C<dom>.
1599 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1600 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1602 In other words, the union of the parameter values
1603 for which the result is non-empty and of C<*empty>
1606 __isl_give isl_set *isl_basic_set_partial_lexmin(
1607 __isl_take isl_basic_set *bset,
1608 __isl_take isl_basic_set *dom,
1609 __isl_give isl_set **empty);
1610 __isl_give isl_set *isl_basic_set_partial_lexmax(
1611 __isl_take isl_basic_set *bset,
1612 __isl_take isl_basic_set *dom,
1613 __isl_give isl_set **empty);
1614 __isl_give isl_set *isl_set_partial_lexmin(
1615 __isl_take isl_set *set, __isl_take isl_set *dom,
1616 __isl_give isl_set **empty);
1617 __isl_give isl_set *isl_set_partial_lexmax(
1618 __isl_take isl_set *set, __isl_take isl_set *dom,
1619 __isl_give isl_set **empty);
1621 Given a (basic) set C<set> (or C<bset>), the following functions simply
1622 return a set containing the lexicographic minimum or maximum
1623 of the elements in C<set> (or C<bset>).
1624 In case of union sets, the optimum is computed per space.
1626 __isl_give isl_set *isl_basic_set_lexmin(
1627 __isl_take isl_basic_set *bset);
1628 __isl_give isl_set *isl_basic_set_lexmax(
1629 __isl_take isl_basic_set *bset);
1630 __isl_give isl_set *isl_set_lexmin(
1631 __isl_take isl_set *set);
1632 __isl_give isl_set *isl_set_lexmax(
1633 __isl_take isl_set *set);
1634 __isl_give isl_union_set *isl_union_set_lexmin(
1635 __isl_take isl_union_set *uset);
1636 __isl_give isl_union_set *isl_union_set_lexmax(
1637 __isl_take isl_union_set *uset);
1639 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1640 the following functions
1641 compute a relation that maps each element of C<dom>
1642 to the single lexicographic minimum or maximum
1643 of the elements that are associated to that same
1644 element in C<map> (or C<bmap>).
1645 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1646 that contains the elements in C<dom> that do not map
1647 to any elements in C<map> (or C<bmap>).
1648 In other words, the union of the domain of the result and of C<*empty>
1651 __isl_give isl_map *isl_basic_map_partial_lexmax(
1652 __isl_take isl_basic_map *bmap,
1653 __isl_take isl_basic_set *dom,
1654 __isl_give isl_set **empty);
1655 __isl_give isl_map *isl_basic_map_partial_lexmin(
1656 __isl_take isl_basic_map *bmap,
1657 __isl_take isl_basic_set *dom,
1658 __isl_give isl_set **empty);
1659 __isl_give isl_map *isl_map_partial_lexmax(
1660 __isl_take isl_map *map, __isl_take isl_set *dom,
1661 __isl_give isl_set **empty);
1662 __isl_give isl_map *isl_map_partial_lexmin(
1663 __isl_take isl_map *map, __isl_take isl_set *dom,
1664 __isl_give isl_set **empty);
1666 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1667 return a map mapping each element in the domain of
1668 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1669 of all elements associated to that element.
1670 In case of union relations, the optimum is computed per space.
1672 __isl_give isl_map *isl_basic_map_lexmin(
1673 __isl_take isl_basic_map *bmap);
1674 __isl_give isl_map *isl_basic_map_lexmax(
1675 __isl_take isl_basic_map *bmap);
1676 __isl_give isl_map *isl_map_lexmin(
1677 __isl_take isl_map *map);
1678 __isl_give isl_map *isl_map_lexmax(
1679 __isl_take isl_map *map);
1680 __isl_give isl_union_map *isl_union_map_lexmin(
1681 __isl_take isl_union_map *umap);
1682 __isl_give isl_union_map *isl_union_map_lexmax(
1683 __isl_take isl_union_map *umap);
1687 Matrices can be created, copied and freed using the following functions.
1689 #include <isl/mat.h>
1690 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1691 unsigned n_row, unsigned n_col);
1692 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1693 void isl_mat_free(__isl_take isl_mat *mat);
1695 Note that the elements of a newly created matrix may have arbitrary values.
1696 The elements can be changed and inspected using the following functions.
1698 int isl_mat_rows(__isl_keep isl_mat *mat);
1699 int isl_mat_cols(__isl_keep isl_mat *mat);
1700 int isl_mat_get_element(__isl_keep isl_mat *mat,
1701 int row, int col, isl_int *v);
1702 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1703 int row, int col, isl_int v);
1705 C<isl_mat_get_element> will return a negative value if anything went wrong.
1706 In that case, the value of C<*v> is undefined.
1708 The following function can be used to compute the (right) inverse
1709 of a matrix, i.e., a matrix such that the product of the original
1710 and the inverse (in that order) is a multiple of the identity matrix.
1711 The input matrix is assumed to be of full row-rank.
1713 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1715 The following function can be used to compute the (right) kernel
1716 (or null space) of a matrix, i.e., a matrix such that the product of
1717 the original and the kernel (in that order) is the zero matrix.
1719 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1723 Points are elements of a set. They can be used to construct
1724 simple sets (boxes) or they can be used to represent the
1725 individual elements of a set.
1726 The zero point (the origin) can be created using
1728 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1730 The coordinates of a point can be inspected, set and changed
1733 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1734 enum isl_dim_type type, int pos, isl_int *v);
1735 __isl_give isl_point *isl_point_set_coordinate(
1736 __isl_take isl_point *pnt,
1737 enum isl_dim_type type, int pos, isl_int v);
1739 __isl_give isl_point *isl_point_add_ui(
1740 __isl_take isl_point *pnt,
1741 enum isl_dim_type type, int pos, unsigned val);
1742 __isl_give isl_point *isl_point_sub_ui(
1743 __isl_take isl_point *pnt,
1744 enum isl_dim_type type, int pos, unsigned val);
1746 Points can be copied or freed using
1748 __isl_give isl_point *isl_point_copy(
1749 __isl_keep isl_point *pnt);
1750 void isl_point_free(__isl_take isl_point *pnt);
1752 A singleton set can be created from a point using
1754 __isl_give isl_basic_set *isl_basic_set_from_point(
1755 __isl_take isl_point *pnt);
1756 __isl_give isl_set *isl_set_from_point(
1757 __isl_take isl_point *pnt);
1759 and a box can be created from two opposite extremal points using
1761 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1762 __isl_take isl_point *pnt1,
1763 __isl_take isl_point *pnt2);
1764 __isl_give isl_set *isl_set_box_from_points(
1765 __isl_take isl_point *pnt1,
1766 __isl_take isl_point *pnt2);
1768 All elements of a B<bounded> (union) set can be enumerated using
1769 the following functions.
1771 int isl_set_foreach_point(__isl_keep isl_set *set,
1772 int (*fn)(__isl_take isl_point *pnt, void *user),
1774 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1775 int (*fn)(__isl_take isl_point *pnt, void *user),
1778 The function C<fn> is called for each integer point in
1779 C<set> with as second argument the last argument of
1780 the C<isl_set_foreach_point> call. The function C<fn>
1781 should return C<0> on success and C<-1> on failure.
1782 In the latter case, C<isl_set_foreach_point> will stop
1783 enumerating and return C<-1> as well.
1784 If the enumeration is performed successfully and to completion,
1785 then C<isl_set_foreach_point> returns C<0>.
1787 To obtain a single point of a (basic) set, use
1789 __isl_give isl_point *isl_basic_set_sample_point(
1790 __isl_take isl_basic_set *bset);
1791 __isl_give isl_point *isl_set_sample_point(
1792 __isl_take isl_set *set);
1794 If C<set> does not contain any (integer) points, then the
1795 resulting point will be ``void'', a property that can be
1798 int isl_point_is_void(__isl_keep isl_point *pnt);
1800 =head2 Piecewise Quasipolynomials
1802 A piecewise quasipolynomial is a particular kind of function that maps
1803 a parametric point to a rational value.
1804 More specifically, a quasipolynomial is a polynomial expression in greatest
1805 integer parts of affine expressions of parameters and variables.
1806 A piecewise quasipolynomial is a subdivision of a given parametric
1807 domain into disjoint cells with a quasipolynomial associated to
1808 each cell. The value of the piecewise quasipolynomial at a given
1809 point is the value of the quasipolynomial associated to the cell
1810 that contains the point. Outside of the union of cells,
1811 the value is assumed to be zero.
1812 For example, the piecewise quasipolynomial
1814 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1816 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1817 A given piecewise quasipolynomial has a fixed domain dimension.
1818 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1819 defined over different domains.
1820 Piecewise quasipolynomials are mainly used by the C<barvinok>
1821 library for representing the number of elements in a parametric set or map.
1822 For example, the piecewise quasipolynomial above represents
1823 the number of points in the map
1825 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1827 =head3 Printing (Piecewise) Quasipolynomials
1829 Quasipolynomials and piecewise quasipolynomials can be printed
1830 using the following functions.
1832 __isl_give isl_printer *isl_printer_print_qpolynomial(
1833 __isl_take isl_printer *p,
1834 __isl_keep isl_qpolynomial *qp);
1836 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1837 __isl_take isl_printer *p,
1838 __isl_keep isl_pw_qpolynomial *pwqp);
1840 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1841 __isl_take isl_printer *p,
1842 __isl_keep isl_union_pw_qpolynomial *upwqp);
1844 The output format of the printer
1845 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1846 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1848 In case of printing in C<ISL_FORMAT_C>, the user may want
1849 to set the names of all dimensions
1851 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1852 __isl_take isl_qpolynomial *qp,
1853 enum isl_dim_type type, unsigned pos,
1855 __isl_give isl_pw_qpolynomial *
1856 isl_pw_qpolynomial_set_dim_name(
1857 __isl_take isl_pw_qpolynomial *pwqp,
1858 enum isl_dim_type type, unsigned pos,
1861 =head3 Creating New (Piecewise) Quasipolynomials
1863 Some simple quasipolynomials can be created using the following functions.
1864 More complicated quasipolynomials can be created by applying
1865 operations such as addition and multiplication
1866 on the resulting quasipolynomials
1868 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1869 __isl_take isl_dim *dim);
1870 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1871 __isl_take isl_dim *dim);
1872 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1873 __isl_take isl_dim *dim);
1874 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1875 __isl_take isl_dim *dim);
1876 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1877 __isl_take isl_dim *dim);
1878 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1879 __isl_take isl_dim *dim,
1880 const isl_int n, const isl_int d);
1881 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1882 __isl_take isl_div *div);
1883 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1884 __isl_take isl_dim *dim,
1885 enum isl_dim_type type, unsigned pos);
1887 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1888 with a single cell can be created using the following functions.
1889 Multiple of these single cell piecewise quasipolynomials can
1890 be combined to create more complicated piecewise quasipolynomials.
1892 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1893 __isl_take isl_dim *dim);
1894 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1895 __isl_take isl_set *set,
1896 __isl_take isl_qpolynomial *qp);
1898 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1899 __isl_take isl_dim *dim);
1900 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1901 __isl_take isl_pw_qpolynomial *pwqp);
1902 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1903 __isl_take isl_union_pw_qpolynomial *upwqp,
1904 __isl_take isl_pw_qpolynomial *pwqp);
1906 Quasipolynomials can be copied and freed again using the following
1909 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1910 __isl_keep isl_qpolynomial *qp);
1911 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1913 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1914 __isl_keep isl_pw_qpolynomial *pwqp);
1915 void isl_pw_qpolynomial_free(
1916 __isl_take isl_pw_qpolynomial *pwqp);
1918 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1919 __isl_keep isl_union_pw_qpolynomial *upwqp);
1920 void isl_union_pw_qpolynomial_free(
1921 __isl_take isl_union_pw_qpolynomial *upwqp);
1923 =head3 Inspecting (Piecewise) Quasipolynomials
1925 To iterate over all piecewise quasipolynomials in a union
1926 piecewise quasipolynomial, use the following function
1928 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1929 __isl_keep isl_union_pw_qpolynomial *upwqp,
1930 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1933 To extract the piecewise quasipolynomial from a union with a given dimension
1936 __isl_give isl_pw_qpolynomial *
1937 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
1938 __isl_keep isl_union_pw_qpolynomial *upwqp,
1939 __isl_take isl_dim *dim);
1941 To iterate over the cells in a piecewise quasipolynomial,
1942 use either of the following two functions
1944 int isl_pw_qpolynomial_foreach_piece(
1945 __isl_keep isl_pw_qpolynomial *pwqp,
1946 int (*fn)(__isl_take isl_set *set,
1947 __isl_take isl_qpolynomial *qp,
1948 void *user), void *user);
1949 int isl_pw_qpolynomial_foreach_lifted_piece(
1950 __isl_keep isl_pw_qpolynomial *pwqp,
1951 int (*fn)(__isl_take isl_set *set,
1952 __isl_take isl_qpolynomial *qp,
1953 void *user), void *user);
1955 As usual, the function C<fn> should return C<0> on success
1956 and C<-1> on failure. The difference between
1957 C<isl_pw_qpolynomial_foreach_piece> and
1958 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1959 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1960 compute unique representations for all existentially quantified
1961 variables and then turn these existentially quantified variables
1962 into extra set variables, adapting the associated quasipolynomial
1963 accordingly. This means that the C<set> passed to C<fn>
1964 will not have any existentially quantified variables, but that
1965 the dimensions of the sets may be different for different
1966 invocations of C<fn>.
1968 To iterate over all terms in a quasipolynomial,
1971 int isl_qpolynomial_foreach_term(
1972 __isl_keep isl_qpolynomial *qp,
1973 int (*fn)(__isl_take isl_term *term,
1974 void *user), void *user);
1976 The terms themselves can be inspected and freed using
1979 unsigned isl_term_dim(__isl_keep isl_term *term,
1980 enum isl_dim_type type);
1981 void isl_term_get_num(__isl_keep isl_term *term,
1983 void isl_term_get_den(__isl_keep isl_term *term,
1985 int isl_term_get_exp(__isl_keep isl_term *term,
1986 enum isl_dim_type type, unsigned pos);
1987 __isl_give isl_div *isl_term_get_div(
1988 __isl_keep isl_term *term, unsigned pos);
1989 void isl_term_free(__isl_take isl_term *term);
1991 Each term is a product of parameters, set variables and
1992 integer divisions. The function C<isl_term_get_exp>
1993 returns the exponent of a given dimensions in the given term.
1994 The C<isl_int>s in the arguments of C<isl_term_get_num>
1995 and C<isl_term_get_den> need to have been initialized
1996 using C<isl_int_init> before calling these functions.
1998 =head3 Properties of (Piecewise) Quasipolynomials
2000 To check whether a quasipolynomial is actually a constant,
2001 use the following function.
2003 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2004 isl_int *n, isl_int *d);
2006 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2007 then the numerator and denominator of the constant
2008 are returned in C<*n> and C<*d>, respectively.
2010 =head3 Operations on (Piecewise) Quasipolynomials
2012 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2013 __isl_take isl_qpolynomial *qp);
2014 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2015 __isl_take isl_qpolynomial *qp1,
2016 __isl_take isl_qpolynomial *qp2);
2017 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2018 __isl_take isl_qpolynomial *qp1,
2019 __isl_take isl_qpolynomial *qp2);
2020 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2021 __isl_take isl_qpolynomial *qp1,
2022 __isl_take isl_qpolynomial *qp2);
2023 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2024 __isl_take isl_qpolynomial *qp, unsigned exponent);
2026 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2027 __isl_take isl_pw_qpolynomial *pwqp1,
2028 __isl_take isl_pw_qpolynomial *pwqp2);
2029 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2030 __isl_take isl_pw_qpolynomial *pwqp1,
2031 __isl_take isl_pw_qpolynomial *pwqp2);
2032 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2033 __isl_take isl_pw_qpolynomial *pwqp1,
2034 __isl_take isl_pw_qpolynomial *pwqp2);
2035 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2036 __isl_take isl_pw_qpolynomial *pwqp);
2037 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2038 __isl_take isl_pw_qpolynomial *pwqp1,
2039 __isl_take isl_pw_qpolynomial *pwqp2);
2041 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2042 __isl_take isl_union_pw_qpolynomial *upwqp1,
2043 __isl_take isl_union_pw_qpolynomial *upwqp2);
2044 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2045 __isl_take isl_union_pw_qpolynomial *upwqp1,
2046 __isl_take isl_union_pw_qpolynomial *upwqp2);
2047 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2048 __isl_take isl_union_pw_qpolynomial *upwqp1,
2049 __isl_take isl_union_pw_qpolynomial *upwqp2);
2051 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2052 __isl_take isl_pw_qpolynomial *pwqp,
2053 __isl_take isl_point *pnt);
2055 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2056 __isl_take isl_union_pw_qpolynomial *upwqp,
2057 __isl_take isl_point *pnt);
2059 __isl_give isl_set *isl_pw_qpolynomial_domain(
2060 __isl_take isl_pw_qpolynomial *pwqp);
2061 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2062 __isl_take isl_pw_qpolynomial *pwpq,
2063 __isl_take isl_set *set);
2065 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2066 __isl_take isl_union_pw_qpolynomial *upwqp);
2067 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2068 __isl_take isl_union_pw_qpolynomial *upwpq,
2069 __isl_take isl_union_set *uset);
2071 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2072 __isl_take isl_union_pw_qpolynomial *upwqp);
2074 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2075 __isl_take isl_pw_qpolynomial *pwqp,
2076 __isl_take isl_set *context);
2078 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2079 __isl_take isl_union_pw_qpolynomial *upwqp,
2080 __isl_take isl_union_set *context);
2082 The gist operation applies the gist operation to each of
2083 the cells in the domain of the input piecewise quasipolynomial.
2084 The context is also exploited
2085 to simplify the quasipolynomials associated to each cell.
2087 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2088 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2089 __isl_give isl_union_pw_qpolynomial *
2090 isl_union_pw_qpolynomial_to_polynomial(
2091 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2093 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2094 the polynomial will be an overapproximation. If C<sign> is negative,
2095 it will be an underapproximation. If C<sign> is zero, the approximation
2096 will lie somewhere in between.
2098 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2100 A piecewise quasipolynomial reduction is a piecewise
2101 reduction (or fold) of quasipolynomials.
2102 In particular, the reduction can be maximum or a minimum.
2103 The objects are mainly used to represent the result of
2104 an upper or lower bound on a quasipolynomial over its domain,
2105 i.e., as the result of the following function.
2107 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2108 __isl_take isl_pw_qpolynomial *pwqp,
2109 enum isl_fold type, int *tight);
2111 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2112 __isl_take isl_union_pw_qpolynomial *upwqp,
2113 enum isl_fold type, int *tight);
2115 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2116 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2117 is the returned bound is known be tight, i.e., for each value
2118 of the parameters there is at least
2119 one element in the domain that reaches the bound.
2120 If the domain of C<pwqp> is not wrapping, then the bound is computed
2121 over all elements in that domain and the result has a purely parametric
2122 domain. If the domain of C<pwqp> is wrapping, then the bound is
2123 computed over the range of the wrapped relation. The domain of the
2124 wrapped relation becomes the domain of the result.
2126 A (piecewise) quasipolynomial reduction can be copied or freed using the
2127 following functions.
2129 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2130 __isl_keep isl_qpolynomial_fold *fold);
2131 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2132 __isl_keep isl_pw_qpolynomial_fold *pwf);
2133 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2134 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2135 void isl_qpolynomial_fold_free(
2136 __isl_take isl_qpolynomial_fold *fold);
2137 void isl_pw_qpolynomial_fold_free(
2138 __isl_take isl_pw_qpolynomial_fold *pwf);
2139 void isl_union_pw_qpolynomial_fold_free(
2140 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2142 =head3 Printing Piecewise Quasipolynomial Reductions
2144 Piecewise quasipolynomial reductions can be printed
2145 using the following function.
2147 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2148 __isl_take isl_printer *p,
2149 __isl_keep isl_pw_qpolynomial_fold *pwf);
2150 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2151 __isl_take isl_printer *p,
2152 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2154 For C<isl_printer_print_pw_qpolynomial_fold>,
2155 output format of the printer
2156 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2157 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2158 output format of the printer
2159 needs to be set to C<ISL_FORMAT_ISL>.
2160 In case of printing in C<ISL_FORMAT_C>, the user may want
2161 to set the names of all dimensions
2163 __isl_give isl_pw_qpolynomial_fold *
2164 isl_pw_qpolynomial_fold_set_dim_name(
2165 __isl_take isl_pw_qpolynomial_fold *pwf,
2166 enum isl_dim_type type, unsigned pos,
2169 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2171 To iterate over all piecewise quasipolynomial reductions in a union
2172 piecewise quasipolynomial reduction, use the following function
2174 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2175 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2176 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2177 void *user), void *user);
2179 To iterate over the cells in a piecewise quasipolynomial reduction,
2180 use either of the following two functions
2182 int isl_pw_qpolynomial_fold_foreach_piece(
2183 __isl_keep isl_pw_qpolynomial_fold *pwf,
2184 int (*fn)(__isl_take isl_set *set,
2185 __isl_take isl_qpolynomial_fold *fold,
2186 void *user), void *user);
2187 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2188 __isl_keep isl_pw_qpolynomial_fold *pwf,
2189 int (*fn)(__isl_take isl_set *set,
2190 __isl_take isl_qpolynomial_fold *fold,
2191 void *user), void *user);
2193 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2194 of the difference between these two functions.
2196 To iterate over all quasipolynomials in a reduction, use
2198 int isl_qpolynomial_fold_foreach_qpolynomial(
2199 __isl_keep isl_qpolynomial_fold *fold,
2200 int (*fn)(__isl_take isl_qpolynomial *qp,
2201 void *user), void *user);
2203 =head3 Operations on Piecewise Quasipolynomial Reductions
2205 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2206 __isl_take isl_pw_qpolynomial_fold *pwf1,
2207 __isl_take isl_pw_qpolynomial_fold *pwf2);
2209 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2210 __isl_take isl_pw_qpolynomial_fold *pwf1,
2211 __isl_take isl_pw_qpolynomial_fold *pwf2);
2213 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2214 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2215 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2217 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2218 __isl_take isl_pw_qpolynomial_fold *pwf,
2219 __isl_take isl_point *pnt);
2221 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2222 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2223 __isl_take isl_point *pnt);
2225 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2226 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2227 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2228 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2229 __isl_take isl_union_set *uset);
2231 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2232 __isl_take isl_pw_qpolynomial_fold *pwf);
2234 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2235 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2237 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2238 __isl_take isl_pw_qpolynomial_fold *pwf,
2239 __isl_take isl_set *context);
2241 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2242 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2243 __isl_take isl_union_set *context);
2245 The gist operation applies the gist operation to each of
2246 the cells in the domain of the input piecewise quasipolynomial reduction.
2247 In future, the operation will also exploit the context
2248 to simplify the quasipolynomial reductions associated to each cell.
2250 __isl_give isl_pw_qpolynomial_fold *
2251 isl_map_apply_pw_qpolynomial_fold(
2252 __isl_take isl_map *map,
2253 __isl_take isl_pw_qpolynomial_fold *pwf,
2255 __isl_give isl_union_pw_qpolynomial_fold *
2256 isl_union_map_apply_union_pw_qpolynomial_fold(
2257 __isl_take isl_union_map *umap,
2258 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2262 compose the given map with the given piecewise quasipolynomial reduction.
2263 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2264 over all elements in the intersection of the range of the map
2265 and the domain of the piecewise quasipolynomial reduction
2266 as a function of an element in the domain of the map.
2268 =head2 Dependence Analysis
2270 C<isl> contains specialized functionality for performing
2271 array dataflow analysis. That is, given a I<sink> access relation
2272 and a collection of possible I<source> access relations,
2273 C<isl> can compute relations that describe
2274 for each iteration of the sink access, which iteration
2275 of which of the source access relations was the last
2276 to access the same data element before the given iteration
2278 To compute standard flow dependences, the sink should be
2279 a read, while the sources should be writes.
2280 If any of the source accesses are marked as being I<may>
2281 accesses, then there will be a dependence to the last
2282 I<must> access B<and> to any I<may> access that follows
2283 this last I<must> access.
2284 In particular, if I<all> sources are I<may> accesses,
2285 then memory based dependence analysis is performed.
2286 If, on the other hand, all sources are I<must> accesses,
2287 then value based dependence analysis is performed.
2289 #include <isl/flow.h>
2291 typedef int (*isl_access_level_before)(void *first, void *second);
2293 __isl_give isl_access_info *isl_access_info_alloc(
2294 __isl_take isl_map *sink,
2295 void *sink_user, isl_access_level_before fn,
2297 __isl_give isl_access_info *isl_access_info_add_source(
2298 __isl_take isl_access_info *acc,
2299 __isl_take isl_map *source, int must,
2301 void isl_access_info_free(__isl_take isl_access_info *acc);
2303 __isl_give isl_flow *isl_access_info_compute_flow(
2304 __isl_take isl_access_info *acc);
2306 int isl_flow_foreach(__isl_keep isl_flow *deps,
2307 int (*fn)(__isl_take isl_map *dep, int must,
2308 void *dep_user, void *user),
2310 __isl_give isl_set *isl_flow_get_no_source(
2311 __isl_keep isl_flow *deps, int must);
2312 void isl_flow_free(__isl_take isl_flow *deps);
2314 The function C<isl_access_info_compute_flow> performs the actual
2315 dependence analysis. The other functions are used to construct
2316 the input for this function or to read off the output.
2318 The input is collected in an C<isl_access_info>, which can
2319 be created through a call to C<isl_access_info_alloc>.
2320 The arguments to this functions are the sink access relation
2321 C<sink>, a token C<sink_user> used to identify the sink
2322 access to the user, a callback function for specifying the
2323 relative order of source and sink accesses, and the number
2324 of source access relations that will be added.
2325 The callback function has type C<int (*)(void *first, void *second)>.
2326 The function is called with two user supplied tokens identifying
2327 either a source or the sink and it should return the shared nesting
2328 level and the relative order of the two accesses.
2329 In particular, let I<n> be the number of loops shared by
2330 the two accesses. If C<first> precedes C<second> textually,
2331 then the function should return I<2 * n + 1>; otherwise,
2332 it should return I<2 * n>.
2333 The sources can be added to the C<isl_access_info> by performing
2334 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2335 C<must> indicates whether the source is a I<must> access
2336 or a I<may> access. Note that a multi-valued access relation
2337 should only be marked I<must> if every iteration in the domain
2338 of the relation accesses I<all> elements in its image.
2339 The C<source_user> token is again used to identify
2340 the source access. The range of the source access relation
2341 C<source> should have the same dimension as the range
2342 of the sink access relation.
2343 The C<isl_access_info_free> function should usually not be
2344 called explicitly, because it is called implicitly by
2345 C<isl_access_info_compute_flow>.
2347 The result of the dependence analysis is collected in an
2348 C<isl_flow>. There may be elements in the domain of
2349 the sink access for which no preceding source access could be
2350 found or for which all preceding sources are I<may> accesses.
2351 The sets of these elements can be obtained through
2352 calls to C<isl_flow_get_no_source>, the first with C<must> set
2353 and the second with C<must> unset.
2354 In the case of standard flow dependence analysis,
2355 with the sink a read and the sources I<must> writes,
2356 the first set corresponds to the reads from uninitialized
2357 array elements and the second set is empty.
2358 The actual flow dependences can be extracted using
2359 C<isl_flow_foreach>. This function will call the user-specified
2360 callback function C<fn> for each B<non-empty> dependence between
2361 a source and the sink. The callback function is called
2362 with four arguments, the actual flow dependence relation
2363 mapping source iterations to sink iterations, a boolean that
2364 indicates whether it is a I<must> or I<may> dependence, a token
2365 identifying the source and an additional C<void *> with value
2366 equal to the third argument of the C<isl_flow_foreach> call.
2367 A dependence is marked I<must> if it originates from a I<must>
2368 source and if it is not followed by any I<may> sources.
2370 After finishing with an C<isl_flow>, the user should call
2371 C<isl_flow_free> to free all associated memory.
2373 A higher-level interface to dependence analysis is provided
2374 by the following function.
2376 #include <isl/flow.h>
2378 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2379 __isl_take isl_union_map *must_source,
2380 __isl_take isl_union_map *may_source,
2381 __isl_take isl_union_map *schedule,
2382 __isl_give isl_union_map **must_dep,
2383 __isl_give isl_union_map **may_dep,
2384 __isl_give isl_union_set **must_no_source,
2385 __isl_give isl_union_set **may_no_source);
2387 The arrays are identified by the tuple names of the ranges
2388 of the accesses. The iteration domains by the tuple names
2389 of the domains of the accesses and of the schedule.
2390 The relative order of the iteration domains is given by the
2391 schedule. Any of C<must_dep>, C<may_dep>, C<must_no_source>
2392 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2393 any of the other arguments is treated as an error.
2395 =head2 Parametric Vertex Enumeration
2397 The parametric vertex enumeration described in this section
2398 is mainly intended to be used internally and by the C<barvinok>
2401 #include <isl/vertices.h>
2402 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2403 __isl_keep isl_basic_set *bset);
2405 The function C<isl_basic_set_compute_vertices> performs the
2406 actual computation of the parametric vertices and the chamber
2407 decomposition and store the result in an C<isl_vertices> object.
2408 This information can be queried by either iterating over all
2409 the vertices or iterating over all the chambers or cells
2410 and then iterating over all vertices that are active on the chamber.
2412 int isl_vertices_foreach_vertex(
2413 __isl_keep isl_vertices *vertices,
2414 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2417 int isl_vertices_foreach_cell(
2418 __isl_keep isl_vertices *vertices,
2419 int (*fn)(__isl_take isl_cell *cell, void *user),
2421 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2422 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2425 Other operations that can be performed on an C<isl_vertices> object are
2428 isl_ctx *isl_vertices_get_ctx(
2429 __isl_keep isl_vertices *vertices);
2430 int isl_vertices_get_n_vertices(
2431 __isl_keep isl_vertices *vertices);
2432 void isl_vertices_free(__isl_take isl_vertices *vertices);
2434 Vertices can be inspected and destroyed using the following functions.
2436 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2437 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2438 __isl_give isl_basic_set *isl_vertex_get_domain(
2439 __isl_keep isl_vertex *vertex);
2440 __isl_give isl_basic_set *isl_vertex_get_expr(
2441 __isl_keep isl_vertex *vertex);
2442 void isl_vertex_free(__isl_take isl_vertex *vertex);
2444 C<isl_vertex_get_expr> returns a singleton parametric set describing
2445 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2447 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2448 B<rational> basic sets, so they should mainly be used for inspection
2449 and should not be mixed with integer sets.
2451 Chambers can be inspected and destroyed using the following functions.
2453 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2454 __isl_give isl_basic_set *isl_cell_get_domain(
2455 __isl_keep isl_cell *cell);
2456 void isl_cell_free(__isl_take isl_cell *cell);
2460 Although C<isl> is mainly meant to be used as a library,
2461 it also contains some basic applications that use some
2462 of the functionality of C<isl>.
2463 The input may be specified in either the L<isl format>
2464 or the L<PolyLib format>.
2466 =head2 C<isl_polyhedron_sample>
2468 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2469 an integer element of the polyhedron, if there is any.
2470 The first column in the output is the denominator and is always
2471 equal to 1. If the polyhedron contains no integer points,
2472 then a vector of length zero is printed.
2476 C<isl_pip> takes the same input as the C<example> program
2477 from the C<piplib> distribution, i.e., a set of constraints
2478 on the parameters, a line containing only -1 and finally a set
2479 of constraints on a parametric polyhedron.
2480 The coefficients of the parameters appear in the last columns
2481 (but before the final constant column).
2482 The output is the lexicographic minimum of the parametric polyhedron.
2483 As C<isl> currently does not have its own output format, the output
2484 is just a dump of the internal state.
2486 =head2 C<isl_polyhedron_minimize>
2488 C<isl_polyhedron_minimize> computes the minimum of some linear
2489 or affine objective function over the integer points in a polyhedron.
2490 If an affine objective function
2491 is given, then the constant should appear in the last column.
2493 =head2 C<isl_polytope_scan>
2495 Given a polytope, C<isl_polytope_scan> prints
2496 all integer points in the polytope.
2498 =head1 C<isl-polylib>
2500 The C<isl-polylib> library provides the following functions for converting
2501 between C<isl> objects and C<PolyLib> objects.
2502 The library is distributed separately for licensing reasons.
2504 #include <isl_set_polylib.h>
2505 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2506 Polyhedron *P, __isl_take isl_dim *dim);
2507 Polyhedron *isl_basic_set_to_polylib(
2508 __isl_keep isl_basic_set *bset);
2509 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2510 __isl_take isl_dim *dim);
2511 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2513 #include <isl_map_polylib.h>
2514 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2515 Polyhedron *P, __isl_take isl_dim *dim);
2516 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2517 __isl_take isl_dim *dim);
2518 Polyhedron *isl_basic_map_to_polylib(
2519 __isl_keep isl_basic_map *bmap);
2520 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);