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>.
40 The source of C<isl> can be obtained either as a tarball
41 or from the git repository. Both are available from
42 L<http://freshmeat.net/projects/isl/>.
43 The installation process depends on how you obtained
46 =head2 Installation from the git repository
50 =item 1 Clone or update the repository
52 The first time the source is obtained, you need to clone
55 git clone git://repo.or.cz/isl.git
57 To obtain updates, you need to pull in the latest changes
61 =item 2 Get submodule (optional)
63 C<isl> can optionally use the C<piplib> library and provides
64 this library as a submodule. If you want to use it, then
65 after you have cloned C<isl>, you need to grab the submodules
70 To obtain updates, you only need
74 Note that C<isl> currently does not use any C<piplib>
75 functionality by default.
77 =item 3 Generate C<configure>
83 After performing the above steps, continue
84 with the L<Common installation instructions>.
86 =head2 Common installation instructions
92 Building C<isl> requires C<GMP>, including its headers files.
93 Your distribution may not provide these header files by default
94 and you may need to install a package called C<gmp-devel> or something
95 similar. Alternatively, C<GMP> can be built from
96 source, available from L<http://gmplib.org/>.
100 C<isl> uses the standard C<autoconf> C<configure> script.
105 optionally followed by some configure options.
106 A complete list of options can be obtained by running
110 Below we discuss some of the more common options.
112 C<isl> can optionally use C<piplib>, but no
113 C<piplib> functionality is currently used by default.
114 The C<--with-piplib> option can
115 be used to specify which C<piplib>
116 library to use, either an installed version (C<system>),
117 an externally built version (C<build>)
118 or no version (C<no>). The option C<build> is mostly useful
119 in C<configure> scripts of larger projects that bundle both C<isl>
126 Installation prefix for C<isl>
128 =item C<--with-gmp-prefix>
130 Installation prefix for C<GMP> (architecture-independent files).
132 =item C<--with-gmp-exec-prefix>
134 Installation prefix for C<GMP> (architecture-dependent files).
136 =item C<--with-piplib>
138 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
140 =item C<--with-piplib-prefix>
142 Installation prefix for C<system> C<piplib> (architecture-independent files).
144 =item C<--with-piplib-exec-prefix>
146 Installation prefix for C<system> C<piplib> (architecture-dependent files).
148 =item C<--with-piplib-builddir>
150 Location where C<build> C<piplib> was built.
158 =item 4 Install (optional)
166 =head2 Initialization
168 All manipulations of integer sets and relations occur within
169 the context of an C<isl_ctx>.
170 A given C<isl_ctx> can only be used within a single thread.
171 All arguments of a function are required to have been allocated
172 within the same context.
173 There are currently no functions available for moving an object
174 from one C<isl_ctx> to another C<isl_ctx>. This means that
175 there is currently no way of safely moving an object from one
176 thread to another, unless the whole C<isl_ctx> is moved.
178 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
179 freed using C<isl_ctx_free>.
180 All objects allocated within an C<isl_ctx> should be freed
181 before the C<isl_ctx> itself is freed.
183 isl_ctx *isl_ctx_alloc();
184 void isl_ctx_free(isl_ctx *ctx);
188 All operations on integers, mainly the coefficients
189 of the constraints describing the sets and relations,
190 are performed in exact integer arithmetic using C<GMP>.
191 However, to allow future versions of C<isl> to optionally
192 support fixed integer arithmetic, all calls to C<GMP>
193 are wrapped inside C<isl> specific macros.
194 The basic type is C<isl_int> and the following operations
195 are available on this type.
196 The meanings of these operations are essentially the same
197 as their C<GMP> C<mpz_> counterparts.
198 As always with C<GMP> types, C<isl_int>s need to be
199 initialized with C<isl_int_init> before they can be used
200 and they need to be released with C<isl_int_clear>
205 =item isl_int_init(i)
207 =item isl_int_clear(i)
209 =item isl_int_set(r,i)
211 =item isl_int_set_si(r,i)
213 =item isl_int_abs(r,i)
215 =item isl_int_neg(r,i)
217 =item isl_int_swap(i,j)
219 =item isl_int_swap_or_set(i,j)
221 =item isl_int_add_ui(r,i,j)
223 =item isl_int_sub_ui(r,i,j)
225 =item isl_int_add(r,i,j)
227 =item isl_int_sub(r,i,j)
229 =item isl_int_mul(r,i,j)
231 =item isl_int_mul_ui(r,i,j)
233 =item isl_int_addmul(r,i,j)
235 =item isl_int_submul(r,i,j)
237 =item isl_int_gcd(r,i,j)
239 =item isl_int_lcm(r,i,j)
241 =item isl_int_divexact(r,i,j)
243 =item isl_int_cdiv_q(r,i,j)
245 =item isl_int_fdiv_q(r,i,j)
247 =item isl_int_fdiv_r(r,i,j)
249 =item isl_int_fdiv_q_ui(r,i,j)
251 =item isl_int_read(r,s)
253 =item isl_int_print(out,i,width)
257 =item isl_int_cmp(i,j)
259 =item isl_int_cmp_si(i,si)
261 =item isl_int_eq(i,j)
263 =item isl_int_ne(i,j)
265 =item isl_int_lt(i,j)
267 =item isl_int_le(i,j)
269 =item isl_int_gt(i,j)
271 =item isl_int_ge(i,j)
273 =item isl_int_abs_eq(i,j)
275 =item isl_int_abs_ne(i,j)
277 =item isl_int_abs_lt(i,j)
279 =item isl_int_abs_gt(i,j)
281 =item isl_int_abs_ge(i,j)
283 =item isl_int_is_zero(i)
285 =item isl_int_is_one(i)
287 =item isl_int_is_negone(i)
289 =item isl_int_is_pos(i)
291 =item isl_int_is_neg(i)
293 =item isl_int_is_nonpos(i)
295 =item isl_int_is_nonneg(i)
297 =item isl_int_is_divisible_by(i,j)
301 =head2 Sets and Relations
303 C<isl> uses six types of objects for representing sets and relations,
304 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
305 C<isl_union_set> and C<isl_union_map>.
306 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
307 can be described as a conjunction of affine constraints, while
308 C<isl_set> and C<isl_map> represent unions of
309 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
310 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
311 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
312 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
313 where dimensions with different space names
314 (see L<Dimension Specifications>) are considered different as well.
315 The difference between sets and relations (maps) is that sets have
316 one set of variables, while relations have two sets of variables,
317 input variables and output variables.
319 =head2 Memory Management
321 Since a high-level operation on sets and/or relations usually involves
322 several substeps and since the user is usually not interested in
323 the intermediate results, most functions that return a new object
324 will also release all the objects passed as arguments.
325 If the user still wants to use one or more of these arguments
326 after the function call, she should pass along a copy of the
327 object rather than the object itself.
328 The user is then responsible for make sure that the original
329 object gets used somewhere else or is explicitly freed.
331 The arguments and return values of all documents functions are
332 annotated to make clear which arguments are released and which
333 arguments are preserved. In particular, the following annotations
340 C<__isl_give> means that a new object is returned.
341 The user should make sure that the returned pointer is
342 used exactly once as a value for an C<__isl_take> argument.
343 In between, it can be used as a value for as many
344 C<__isl_keep> arguments as the user likes.
345 There is one exception, and that is the case where the
346 pointer returned is C<NULL>. Is this case, the user
347 is free to use it as an C<__isl_take> argument or not.
351 C<__isl_take> means that the object the argument points to
352 is taken over by the function and may no longer be used
353 by the user as an argument to any other function.
354 The pointer value must be one returned by a function
355 returning an C<__isl_give> pointer.
356 If the user passes in a C<NULL> value, then this will
357 be treated as an error in the sense that the function will
358 not perform its usual operation. However, it will still
359 make sure that all the the other C<__isl_take> arguments
364 C<__isl_keep> means that the function will only use the object
365 temporarily. After the function has finished, the user
366 can still use it as an argument to other functions.
367 A C<NULL> value will be treated in the same way as
368 a C<NULL> value for an C<__isl_take> argument.
372 =head2 Dimension Specifications
374 Whenever a new set or relation is created from scratch,
375 its dimension needs to be specified using an C<isl_dim>.
378 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
379 unsigned nparam, unsigned n_in, unsigned n_out);
380 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
381 unsigned nparam, unsigned dim);
382 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
383 void isl_dim_free(__isl_take isl_dim *dim);
384 unsigned isl_dim_size(__isl_keep isl_dim *dim,
385 enum isl_dim_type type);
387 The dimension specification used for creating a set
388 needs to be created using C<isl_dim_set_alloc>, while
389 that for creating a relation
390 needs to be created using C<isl_dim_alloc>.
391 C<isl_dim_size> can be used
392 to find out the number of dimensions of each type in
393 a dimension specification, where type may be
394 C<isl_dim_param>, C<isl_dim_in> (only for relations),
395 C<isl_dim_out> (only for relations), C<isl_dim_set>
396 (only for sets) or C<isl_dim_all>.
398 It is often useful to create objects that live in the
399 same space as some other object. This can be accomplished
400 by creating the new objects
401 (see L<Creating New Sets and Relations> or
402 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
403 specification of the original object.
406 __isl_give isl_dim *isl_basic_set_get_dim(
407 __isl_keep isl_basic_set *bset);
408 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
410 #include <isl_union_set.h>
411 __isl_give isl_dim *isl_union_set_get_dim(
412 __isl_keep isl_union_set *uset);
415 __isl_give isl_dim *isl_basic_map_get_dim(
416 __isl_keep isl_basic_map *bmap);
417 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
419 #include <isl_union_map.h>
420 __isl_give isl_dim *isl_union_map_get_dim(
421 __isl_keep isl_union_map *umap);
423 #include <isl_polynomial.h>
424 __isl_give isl_dim *isl_qpolynomial_get_dim(
425 __isl_keep isl_qpolynomial *qp);
426 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
427 __isl_keep isl_pw_qpolynomial *pwqp);
428 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
429 __isl_keep isl_union_pw_qpolynomial *upwqp);
430 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
431 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
433 The names of the individual dimensions may be set or read off
434 using the following functions.
437 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
438 enum isl_dim_type type, unsigned pos,
439 __isl_keep const char *name);
440 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
441 enum isl_dim_type type, unsigned pos);
443 Note that C<isl_dim_get_name> returns a pointer to some internal
444 data structure, so the result can only be used while the
445 corresponding C<isl_dim> is alive.
446 Also note that every function that operates on two sets or relations
447 requires that both arguments have the same parameters. This also
448 means that if one of the arguments has named parameters, then the
449 other needs to have named parameters too and the names need to match.
451 The names of entire spaces may be set or read off
452 using the following functions.
455 __isl_give isl_dim *isl_dim_set_tuple_name(
456 __isl_take isl_dim *dim,
457 enum isl_dim_type type, const char *s);
458 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
459 enum isl_dim_type type);
461 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
462 or C<isl_dim_set>. As with C<isl_dim_get_name>,
463 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
465 Binary operations require the corresponding spaces of their arguments
466 to have the same name.
468 =head2 Input and Output
470 C<isl> supports its own input/output format, which is similar
471 to the C<Omega> format, but also supports the C<PolyLib> format
476 The C<isl> format is similar to that of C<Omega>, but has a different
477 syntax for describing the parameters and allows for the definition
478 of an existentially quantified variable as the integer division
479 of an affine expression.
480 For example, the set of integers C<i> between C<0> and C<n>
481 such that C<i % 10 <= 6> can be described as
483 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
486 A set or relation can have several disjuncts, separated
487 by the keyword C<or>. Each disjunct is either a conjunction
488 of constraints or a projection (C<exists>) of a conjunction
489 of constraints. The constraints are separated by the keyword
492 =head3 C<PolyLib> format
494 If the represented set is a union, then the first line
495 contains a single number representing the number of disjuncts.
496 Otherwise, a line containing the number C<1> is optional.
498 Each disjunct is represented by a matrix of constraints.
499 The first line contains two numbers representing
500 the number of rows and columns,
501 where the number of rows is equal to the number of constraints
502 and the number of columns is equal to two plus the number of variables.
503 The following lines contain the actual rows of the constraint matrix.
504 In each row, the first column indicates whether the constraint
505 is an equality (C<0>) or inequality (C<1>). The final column
506 corresponds to the constant term.
508 If the set is parametric, then the coefficients of the parameters
509 appear in the last columns before the constant column.
510 The coefficients of any existentially quantified variables appear
511 between those of the set variables and those of the parameters.
516 __isl_give isl_basic_set *isl_basic_set_read_from_file(
517 isl_ctx *ctx, FILE *input, int nparam);
518 __isl_give isl_basic_set *isl_basic_set_read_from_str(
519 isl_ctx *ctx, const char *str, int nparam);
520 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
521 FILE *input, int nparam);
522 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
523 const char *str, int nparam);
526 __isl_give isl_basic_map *isl_basic_map_read_from_file(
527 isl_ctx *ctx, FILE *input, int nparam);
528 __isl_give isl_basic_map *isl_basic_map_read_from_str(
529 isl_ctx *ctx, const char *str, int nparam);
530 __isl_give isl_map *isl_map_read_from_file(
531 struct isl_ctx *ctx, FILE *input, int nparam);
532 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
533 const char *str, int nparam);
535 The input format is autodetected and may be either the C<PolyLib> format
536 or the C<isl> format.
537 C<nparam> specifies how many of the final columns in
538 the C<PolyLib> format correspond to parameters.
539 If input is given in the C<isl> format, then the number
540 of parameters needs to be equal to C<nparam>.
541 If C<nparam> is negative, then any number of parameters
542 is accepted in the C<isl> format and zero parameters
543 are assumed in the C<PolyLib> format.
547 Before anything can be printed, an C<isl_printer> needs to
550 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
552 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
553 void isl_printer_free(__isl_take isl_printer *printer);
554 __isl_give char *isl_printer_get_str(
555 __isl_keep isl_printer *printer);
557 The behavior of the printer can be modified in various ways
559 __isl_give isl_printer *isl_printer_set_output_format(
560 __isl_take isl_printer *p, int output_format);
561 __isl_give isl_printer *isl_printer_set_indent(
562 __isl_take isl_printer *p, int indent);
563 __isl_give isl_printer *isl_printer_set_prefix(
564 __isl_take isl_printer *p, const char *prefix);
565 __isl_give isl_printer *isl_printer_set_suffix(
566 __isl_take isl_printer *p, const char *suffix);
568 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
569 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
570 Each line in the output is indented by C<indent> spaces
571 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
572 In the C<PolyLib> format output,
573 the coefficients of the existentially quantified variables
574 appear between those of the set variables and those
577 To actually print something, use
580 __isl_give isl_printer *isl_printer_print_basic_set(
581 __isl_take isl_printer *printer,
582 __isl_keep isl_basic_set *bset);
583 __isl_give isl_printer *isl_printer_print_set(
584 __isl_take isl_printer *printer,
585 __isl_keep isl_set *set);
588 __isl_give isl_printer *isl_printer_print_basic_map(
589 __isl_take isl_printer *printer,
590 __isl_keep isl_basic_map *bmap);
591 __isl_give isl_printer *isl_printer_print_map(
592 __isl_take isl_printer *printer,
593 __isl_keep isl_map *map);
595 #include <isl_union_set.h>
596 __isl_give isl_printer *isl_printer_print_union_set(
597 __isl_take isl_printer *p,
598 __isl_keep isl_union_set *uset);
600 #include <isl_union_map.h>
601 __isl_give isl_printer *isl_printer_print_union_map(
602 __isl_take isl_printer *p,
603 __isl_keep isl_union_map *umap);
605 When called on a file printer, the following function flushes
606 the file. When called on a string printer, the buffer is cleared.
608 __isl_give isl_printer *isl_printer_flush(
609 __isl_take isl_printer *p);
611 =head2 Creating New Sets and Relations
613 C<isl> has functions for creating some standard sets and relations.
617 =item * Empty sets and relations
619 __isl_give isl_basic_set *isl_basic_set_empty(
620 __isl_take isl_dim *dim);
621 __isl_give isl_basic_map *isl_basic_map_empty(
622 __isl_take isl_dim *dim);
623 __isl_give isl_set *isl_set_empty(
624 __isl_take isl_dim *dim);
625 __isl_give isl_map *isl_map_empty(
626 __isl_take isl_dim *dim);
627 __isl_give isl_union_set *isl_union_set_empty(
628 __isl_take isl_dim *dim);
629 __isl_give isl_union_map *isl_union_map_empty(
630 __isl_take isl_dim *dim);
632 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
633 is only used to specify the parameters.
635 =item * Universe sets and relations
637 __isl_give isl_basic_set *isl_basic_set_universe(
638 __isl_take isl_dim *dim);
639 __isl_give isl_basic_map *isl_basic_map_universe(
640 __isl_take isl_dim *dim);
641 __isl_give isl_set *isl_set_universe(
642 __isl_take isl_dim *dim);
643 __isl_give isl_map *isl_map_universe(
644 __isl_take isl_dim *dim);
646 =item * Identity relations
648 __isl_give isl_basic_map *isl_basic_map_identity(
649 __isl_take isl_dim *set_dim);
650 __isl_give isl_map *isl_map_identity(
651 __isl_take isl_dim *set_dim);
653 These functions take a dimension specification for a B<set>
654 and return an identity relation between two such sets.
656 =item * Lexicographic order
658 __isl_give isl_map *isl_map_lex_lt(
659 __isl_take isl_dim *set_dim);
660 __isl_give isl_map *isl_map_lex_le(
661 __isl_take isl_dim *set_dim);
662 __isl_give isl_map *isl_map_lex_gt(
663 __isl_take isl_dim *set_dim);
664 __isl_give isl_map *isl_map_lex_ge(
665 __isl_take isl_dim *set_dim);
666 __isl_give isl_map *isl_map_lex_lt_first(
667 __isl_take isl_dim *dim, unsigned n);
668 __isl_give isl_map *isl_map_lex_le_first(
669 __isl_take isl_dim *dim, unsigned n);
670 __isl_give isl_map *isl_map_lex_gt_first(
671 __isl_take isl_dim *dim, unsigned n);
672 __isl_give isl_map *isl_map_lex_ge_first(
673 __isl_take isl_dim *dim, unsigned n);
675 The first four functions take a dimension specification for a B<set>
676 and return relations that express that the elements in the domain
677 are lexicographically less
678 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
679 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
680 than the elements in the range.
681 The last four functions take a dimension specification for a map
682 and return relations that express that the first C<n> dimensions
683 in the domain are lexicographically less
684 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
685 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
686 than the first C<n> dimensions in the range.
690 A basic set or relation can be converted to a set or relation
691 using the following functions.
693 __isl_give isl_set *isl_set_from_basic_set(
694 __isl_take isl_basic_set *bset);
695 __isl_give isl_map *isl_map_from_basic_map(
696 __isl_take isl_basic_map *bmap);
698 Sets and relations can be converted to union sets and relations
699 using the following functions.
701 __isl_give isl_union_map *isl_union_map_from_map(
702 __isl_take isl_map *map);
703 __isl_give isl_union_set *isl_union_set_from_set(
704 __isl_take isl_set *set);
706 Sets and relations can be copied and freed again using the following
709 __isl_give isl_basic_set *isl_basic_set_copy(
710 __isl_keep isl_basic_set *bset);
711 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
712 __isl_give isl_union_set *isl_union_set_copy(
713 __isl_keep isl_union_set *uset);
714 __isl_give isl_basic_map *isl_basic_map_copy(
715 __isl_keep isl_basic_map *bmap);
716 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
717 __isl_give isl_union_map *isl_union_map_copy(
718 __isl_keep isl_union_map *umap);
719 void isl_basic_set_free(__isl_take isl_basic_set *bset);
720 void isl_set_free(__isl_take isl_set *set);
721 void isl_union_set_free(__isl_take isl_union_set *uset);
722 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
723 void isl_map_free(__isl_take isl_map *map);
724 void isl_union_map_free(__isl_take isl_union_map *umap);
726 Other sets and relations can be constructed by starting
727 from a universe set or relation, adding equality and/or
728 inequality constraints and then projecting out the
729 existentially quantified variables, if any.
730 Constraints can be constructed, manipulated and
731 added to basic sets and relations using the following functions.
733 #include <isl_constraint.h>
734 __isl_give isl_constraint *isl_equality_alloc(
735 __isl_take isl_dim *dim);
736 __isl_give isl_constraint *isl_inequality_alloc(
737 __isl_take isl_dim *dim);
738 void isl_constraint_set_constant(
739 __isl_keep isl_constraint *constraint, isl_int v);
740 void isl_constraint_set_coefficient(
741 __isl_keep isl_constraint *constraint,
742 enum isl_dim_type type, int pos, isl_int v);
743 __isl_give isl_basic_map *isl_basic_map_add_constraint(
744 __isl_take isl_basic_map *bmap,
745 __isl_take isl_constraint *constraint);
746 __isl_give isl_basic_set *isl_basic_set_add_constraint(
747 __isl_take isl_basic_set *bset,
748 __isl_take isl_constraint *constraint);
750 For example, to create a set containing the even integers
751 between 10 and 42, you would use the following code.
755 struct isl_constraint *c;
756 struct isl_basic_set *bset;
759 dim = isl_dim_set_alloc(ctx, 0, 2);
760 bset = isl_basic_set_universe(isl_dim_copy(dim));
762 c = isl_equality_alloc(isl_dim_copy(dim));
763 isl_int_set_si(v, -1);
764 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
765 isl_int_set_si(v, 2);
766 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
767 bset = isl_basic_set_add_constraint(bset, c);
769 c = isl_inequality_alloc(isl_dim_copy(dim));
770 isl_int_set_si(v, -10);
771 isl_constraint_set_constant(c, v);
772 isl_int_set_si(v, 1);
773 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
774 bset = isl_basic_set_add_constraint(bset, c);
776 c = isl_inequality_alloc(dim);
777 isl_int_set_si(v, 42);
778 isl_constraint_set_constant(c, v);
779 isl_int_set_si(v, -1);
780 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
781 bset = isl_basic_set_add_constraint(bset, c);
783 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
789 struct isl_basic_set *bset;
790 bset = isl_basic_set_read_from_str(ctx,
791 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
793 =head2 Inspecting Sets and Relations
795 Usually, the user should not have to care about the actual constraints
796 of the sets and maps, but should instead apply the abstract operations
797 explained in the following sections.
798 Occasionally, however, it may be required to inspect the individual
799 coefficients of the constraints. This section explains how to do so.
800 In these cases, it may also be useful to have C<isl> compute
801 an explicit representation of the existentially quantified variables.
803 __isl_give isl_set *isl_set_compute_divs(
804 __isl_take isl_set *set);
805 __isl_give isl_map *isl_map_compute_divs(
806 __isl_take isl_map *map);
807 __isl_give isl_union_set *isl_union_set_compute_divs(
808 __isl_take isl_union_set *uset);
809 __isl_give isl_union_map *isl_union_map_compute_divs(
810 __isl_take isl_union_map *umap);
812 This explicit representation defines the existentially quantified
813 variables as integer divisions of the other variables, possibly
814 including earlier existentially quantified variables.
815 An explicitly represented existentially quantified variable therefore
816 has a unique value when the values of the other variables are known.
817 If, furthermore, the same existentials, i.e., existentials
818 with the same explicit representations, should appear in the
819 same order in each of the disjuncts of a set or map, then the user should call
820 either of the following functions.
822 __isl_give isl_set *isl_set_align_divs(
823 __isl_take isl_set *set);
824 __isl_give isl_map *isl_map_align_divs(
825 __isl_take isl_map *map);
827 To iterate over all the sets or maps in a union set or map, use
829 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
830 int (*fn)(__isl_take isl_set *set, void *user),
832 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
833 int (*fn)(__isl_take isl_map *map, void *user),
836 To iterate over all the basic sets or maps in a set or map, use
838 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
839 int (*fn)(__isl_take isl_basic_set *bset, void *user),
841 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
842 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
845 The callback function C<fn> should return 0 if successful and
846 -1 if an error occurs. In the latter case, or if any other error
847 occurs, the above functions will return -1.
849 It should be noted that C<isl> does not guarantee that
850 the basic sets or maps passed to C<fn> are disjoint.
851 If this is required, then the user should call one of
852 the following functions first.
854 __isl_give isl_set *isl_set_make_disjoint(
855 __isl_take isl_set *set);
856 __isl_give isl_map *isl_map_make_disjoint(
857 __isl_take isl_map *map);
859 To iterate over the constraints of a basic set or map, use
861 #include <isl_constraint.h>
863 int isl_basic_map_foreach_constraint(
864 __isl_keep isl_basic_map *bmap,
865 int (*fn)(__isl_take isl_constraint *c, void *user),
867 void isl_constraint_free(struct isl_constraint *c);
869 Again, the callback function C<fn> should return 0 if successful and
870 -1 if an error occurs. In the latter case, or if any other error
871 occurs, the above functions will return -1.
872 The constraint C<c> represents either an equality or an inequality.
873 Use the following function to find out whether a constraint
874 represents an equality. If not, it represents an inequality.
876 int isl_constraint_is_equality(
877 __isl_keep isl_constraint *constraint);
879 The coefficients of the constraints can be inspected using
880 the following functions.
882 void isl_constraint_get_constant(
883 __isl_keep isl_constraint *constraint, isl_int *v);
884 void isl_constraint_get_coefficient(
885 __isl_keep isl_constraint *constraint,
886 enum isl_dim_type type, int pos, isl_int *v);
888 The explicit representations of the existentially quantified
889 variables can be inspected using the following functions.
890 Note that the user is only allowed to use these functions
891 if the inspected set or map is the result of a call
892 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
894 __isl_give isl_div *isl_constraint_div(
895 __isl_keep isl_constraint *constraint, int pos);
896 void isl_div_get_constant(__isl_keep isl_div *div,
898 void isl_div_get_denominator(__isl_keep isl_div *div,
900 void isl_div_get_coefficient(__isl_keep isl_div *div,
901 enum isl_dim_type type, int pos, isl_int *v);
905 =head3 Unary Properties
911 The following functions test whether the given set or relation
912 contains any integer points. The ``fast'' variants do not perform
913 any computations, but simply check if the given set or relation
914 is already known to be empty.
916 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
917 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
918 int isl_set_is_empty(__isl_keep isl_set *set);
919 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
920 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
921 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
922 int isl_map_fast_is_empty(__isl_keep isl_map *map);
923 int isl_map_is_empty(__isl_keep isl_map *map);
924 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
928 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
929 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
930 int isl_set_fast_is_universe(__isl_keep isl_set *set);
932 =item * Single-valuedness
934 int isl_map_is_single_valued(__isl_keep isl_map *map);
938 int isl_map_is_bijective(__isl_keep isl_map *map);
942 =head3 Binary Properties
948 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
949 __isl_keep isl_set *set2);
950 int isl_set_is_equal(__isl_keep isl_set *set1,
951 __isl_keep isl_set *set2);
952 int isl_basic_map_is_equal(
953 __isl_keep isl_basic_map *bmap1,
954 __isl_keep isl_basic_map *bmap2);
955 int isl_map_is_equal(__isl_keep isl_map *map1,
956 __isl_keep isl_map *map2);
957 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
958 __isl_keep isl_map *map2);
959 int isl_union_map_is_equal(
960 __isl_keep isl_union_map *umap1,
961 __isl_keep isl_union_map *umap2);
965 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
966 __isl_keep isl_set *set2);
970 int isl_set_is_subset(__isl_keep isl_set *set1,
971 __isl_keep isl_set *set2);
972 int isl_set_is_strict_subset(
973 __isl_keep isl_set *set1,
974 __isl_keep isl_set *set2);
975 int isl_basic_map_is_subset(
976 __isl_keep isl_basic_map *bmap1,
977 __isl_keep isl_basic_map *bmap2);
978 int isl_basic_map_is_strict_subset(
979 __isl_keep isl_basic_map *bmap1,
980 __isl_keep isl_basic_map *bmap2);
981 int isl_map_is_subset(
982 __isl_keep isl_map *map1,
983 __isl_keep isl_map *map2);
984 int isl_map_is_strict_subset(
985 __isl_keep isl_map *map1,
986 __isl_keep isl_map *map2);
987 int isl_union_map_is_subset(
988 __isl_keep isl_union_map *umap1,
989 __isl_keep isl_union_map *umap2);
990 int isl_union_map_is_strict_subset(
991 __isl_keep isl_union_map *umap1,
992 __isl_keep isl_union_map *umap2);
996 =head2 Unary Operations
1002 __isl_give isl_set *isl_set_complement(
1003 __isl_take isl_set *set);
1007 __isl_give isl_basic_map *isl_basic_map_reverse(
1008 __isl_take isl_basic_map *bmap);
1009 __isl_give isl_map *isl_map_reverse(
1010 __isl_take isl_map *map);
1011 __isl_give isl_union_map *isl_union_map_reverse(
1012 __isl_take isl_union_map *umap);
1016 __isl_give isl_basic_set *isl_basic_set_project_out(
1017 __isl_take isl_basic_set *bset,
1018 enum isl_dim_type type, unsigned first, unsigned n);
1019 __isl_give isl_basic_map *isl_basic_map_project_out(
1020 __isl_take isl_basic_map *bmap,
1021 enum isl_dim_type type, unsigned first, unsigned n);
1022 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1023 enum isl_dim_type type, unsigned first, unsigned n);
1024 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1025 enum isl_dim_type type, unsigned first, unsigned n);
1026 __isl_give isl_basic_set *isl_basic_map_domain(
1027 __isl_take isl_basic_map *bmap);
1028 __isl_give isl_basic_set *isl_basic_map_range(
1029 __isl_take isl_basic_map *bmap);
1030 __isl_give isl_set *isl_map_domain(
1031 __isl_take isl_map *bmap);
1032 __isl_give isl_set *isl_map_range(
1033 __isl_take isl_map *map);
1034 __isl_give isl_union_set *isl_union_map_domain(
1035 __isl_take isl_union_map *umap);
1036 __isl_give isl_union_set *isl_union_map_range(
1037 __isl_take isl_union_map *umap);
1041 __isl_give isl_basic_set *isl_basic_map_deltas(
1042 __isl_take isl_basic_map *bmap);
1043 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1044 __isl_give isl_union_set *isl_union_map_deltas(
1045 __isl_take isl_union_map *umap);
1047 These functions return a (basic) set containing the differences
1048 between image elements and corresponding domain elements in the input.
1052 Simplify the representation of a set or relation by trying
1053 to combine pairs of basic sets or relations into a single
1054 basic set or relation.
1056 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1057 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1058 __isl_give isl_union_set *isl_union_set_coalesce(
1059 __isl_take isl_union_set *uset);
1060 __isl_give isl_union_map *isl_union_map_coalesce(
1061 __isl_take isl_union_map *umap);
1065 __isl_give isl_basic_set *isl_set_convex_hull(
1066 __isl_take isl_set *set);
1067 __isl_give isl_basic_map *isl_map_convex_hull(
1068 __isl_take isl_map *map);
1070 If the input set or relation has any existentially quantified
1071 variables, then the result of these operations is currently undefined.
1075 __isl_give isl_basic_set *isl_set_simple_hull(
1076 __isl_take isl_set *set);
1077 __isl_give isl_basic_map *isl_map_simple_hull(
1078 __isl_take isl_map *map);
1080 These functions compute a single basic set or relation
1081 that contains the whole input set or relation.
1082 In particular, the output is described by translates
1083 of the constraints describing the basic sets or relations in the input.
1087 (See \autoref{s:simple hull}.)
1093 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1094 __isl_take isl_basic_set *bset);
1095 __isl_give isl_basic_set *isl_set_affine_hull(
1096 __isl_take isl_set *set);
1097 __isl_give isl_union_set *isl_union_set_affine_hull(
1098 __isl_take isl_union_set *uset);
1099 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1100 __isl_take isl_basic_map *bmap);
1101 __isl_give isl_basic_map *isl_map_affine_hull(
1102 __isl_take isl_map *map);
1103 __isl_give isl_union_map *isl_union_map_affine_hull(
1104 __isl_take isl_union_map *umap);
1106 In case of union sets and relations, the affine hull is computed
1111 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1112 unsigned param, int *exact);
1114 Compute a parametric representation for all positive powers I<k> of C<map>.
1115 The power I<k> is equated to the parameter at position C<param>.
1116 The result may be an overapproximation. If the result is exact,
1117 then C<*exact> is set to C<1>.
1118 The current implementation only produces exact results for particular
1119 cases of piecewise translations (i.e., piecewise uniform dependences).
1121 =item * Transitive closure
1123 __isl_give isl_map *isl_map_transitive_closure(
1124 __isl_take isl_map *map, int *exact);
1125 __isl_give isl_union_map *isl_union_map_transitive_closure(
1126 __isl_take isl_union_map *umap, int *exact);
1128 Compute the transitive closure of C<map>.
1129 The result may be an overapproximation. If the result is known to be exact,
1130 then C<*exact> is set to C<1>.
1131 The current implementation only produces exact results for particular
1132 cases of piecewise translations (i.e., piecewise uniform dependences).
1134 =item * Reaching path lengths
1136 __isl_give isl_map *isl_map_reaching_path_lengths(
1137 __isl_take isl_map *map, int *exact);
1139 Compute a relation that maps each element in the range of C<map>
1140 to the lengths of all paths composed of edges in C<map> that
1141 end up in the given element.
1142 The result may be an overapproximation. If the result is known to be exact,
1143 then C<*exact> is set to C<1>.
1144 To compute the I<maximal> path length, the resulting relation
1145 should be postprocessed by C<isl_map_lexmax>.
1146 In particular, if the input relation is a dependence relation
1147 (mapping sources to sinks), then the maximal path length corresponds
1148 to the free schedule.
1149 Note, however, that C<isl_map_lexmax> expects the maximum to be
1150 finite, so if the path lengths are unbounded (possibly due to
1151 the overapproximation), then you will get an error message.
1155 =head2 Binary Operations
1157 The two arguments of a binary operation not only need to live
1158 in the same C<isl_ctx>, they currently also need to have
1159 the same (number of) parameters.
1161 =head3 Basic Operations
1165 =item * Intersection
1167 __isl_give isl_basic_set *isl_basic_set_intersect(
1168 __isl_take isl_basic_set *bset1,
1169 __isl_take isl_basic_set *bset2);
1170 __isl_give isl_set *isl_set_intersect(
1171 __isl_take isl_set *set1,
1172 __isl_take isl_set *set2);
1173 __isl_give isl_union_set *isl_union_set_intersect(
1174 __isl_take isl_union_set *uset1,
1175 __isl_take isl_union_set *uset2);
1176 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1177 __isl_take isl_basic_map *bmap,
1178 __isl_take isl_basic_set *bset);
1179 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1180 __isl_take isl_basic_map *bmap,
1181 __isl_take isl_basic_set *bset);
1182 __isl_give isl_basic_map *isl_basic_map_intersect(
1183 __isl_take isl_basic_map *bmap1,
1184 __isl_take isl_basic_map *bmap2);
1185 __isl_give isl_map *isl_map_intersect_domain(
1186 __isl_take isl_map *map,
1187 __isl_take isl_set *set);
1188 __isl_give isl_map *isl_map_intersect_range(
1189 __isl_take isl_map *map,
1190 __isl_take isl_set *set);
1191 __isl_give isl_map *isl_map_intersect(
1192 __isl_take isl_map *map1,
1193 __isl_take isl_map *map2);
1194 __isl_give isl_union_map *isl_union_map_intersect_domain(
1195 __isl_take isl_union_map *umap,
1196 __isl_take isl_union_set *uset);
1197 __isl_give isl_union_map *isl_union_map_intersect(
1198 __isl_take isl_union_map *umap1,
1199 __isl_take isl_union_map *umap2);
1203 __isl_give isl_set *isl_basic_set_union(
1204 __isl_take isl_basic_set *bset1,
1205 __isl_take isl_basic_set *bset2);
1206 __isl_give isl_map *isl_basic_map_union(
1207 __isl_take isl_basic_map *bmap1,
1208 __isl_take isl_basic_map *bmap2);
1209 __isl_give isl_set *isl_set_union(
1210 __isl_take isl_set *set1,
1211 __isl_take isl_set *set2);
1212 __isl_give isl_map *isl_map_union(
1213 __isl_take isl_map *map1,
1214 __isl_take isl_map *map2);
1215 __isl_give isl_union_set *isl_union_set_union(
1216 __isl_take isl_union_set *uset1,
1217 __isl_take isl_union_set *uset2);
1218 __isl_give isl_union_map *isl_union_map_union(
1219 __isl_take isl_union_map *umap1,
1220 __isl_take isl_union_map *umap2);
1222 =item * Set difference
1224 __isl_give isl_set *isl_set_subtract(
1225 __isl_take isl_set *set1,
1226 __isl_take isl_set *set2);
1227 __isl_give isl_map *isl_map_subtract(
1228 __isl_take isl_map *map1,
1229 __isl_take isl_map *map2);
1230 __isl_give isl_union_set *isl_union_set_subtract(
1231 __isl_take isl_union_set *uset1,
1232 __isl_take isl_union_set *uset2);
1233 __isl_give isl_union_map *isl_union_map_subtract(
1234 __isl_take isl_union_map *umap1,
1235 __isl_take isl_union_map *umap2);
1239 __isl_give isl_basic_set *isl_basic_set_apply(
1240 __isl_take isl_basic_set *bset,
1241 __isl_take isl_basic_map *bmap);
1242 __isl_give isl_set *isl_set_apply(
1243 __isl_take isl_set *set,
1244 __isl_take isl_map *map);
1245 __isl_give isl_union_set *isl_union_set_apply(
1246 __isl_take isl_union_set *uset,
1247 __isl_take isl_union_map *umap);
1248 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1249 __isl_take isl_basic_map *bmap1,
1250 __isl_take isl_basic_map *bmap2);
1251 __isl_give isl_basic_map *isl_basic_map_apply_range(
1252 __isl_take isl_basic_map *bmap1,
1253 __isl_take isl_basic_map *bmap2);
1254 __isl_give isl_map *isl_map_apply_domain(
1255 __isl_take isl_map *map1,
1256 __isl_take isl_map *map2);
1257 __isl_give isl_map *isl_map_apply_range(
1258 __isl_take isl_map *map1,
1259 __isl_take isl_map *map2);
1260 __isl_give isl_union_map *isl_union_map_apply_range(
1261 __isl_take isl_union_map *umap1,
1262 __isl_take isl_union_map *umap2);
1264 =item * Simplification
1266 __isl_give isl_basic_set *isl_basic_set_gist(
1267 __isl_take isl_basic_set *bset,
1268 __isl_take isl_basic_set *context);
1269 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1270 __isl_take isl_set *context);
1271 __isl_give isl_union_set *isl_union_set_gist(
1272 __isl_take isl_union_set *uset,
1273 __isl_take isl_union_set *context);
1274 __isl_give isl_basic_map *isl_basic_map_gist(
1275 __isl_take isl_basic_map *bmap,
1276 __isl_take isl_basic_map *context);
1277 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1278 __isl_take isl_map *context);
1279 __isl_give isl_union_map *isl_union_map_gist(
1280 __isl_take isl_union_map *umap,
1281 __isl_take isl_union_map *context);
1283 The gist operation returns a set or relation that has the
1284 same intersection with the context as the input set or relation.
1285 Any implicit equality in the intersection is made explicit in the result,
1286 while all inequalities that are redundant with respect to the intersection
1288 In case of union sets and relations, the gist operation is performed
1293 =head3 Lexicographic Optimization
1295 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1296 the following functions
1297 compute a set that contains the lexicographic minimum or maximum
1298 of the elements in C<set> (or C<bset>) for those values of the parameters
1299 that satisfy C<dom>.
1300 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1301 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1303 In other words, the union of the parameter values
1304 for which the result is non-empty and of C<*empty>
1307 __isl_give isl_set *isl_basic_set_partial_lexmin(
1308 __isl_take isl_basic_set *bset,
1309 __isl_take isl_basic_set *dom,
1310 __isl_give isl_set **empty);
1311 __isl_give isl_set *isl_basic_set_partial_lexmax(
1312 __isl_take isl_basic_set *bset,
1313 __isl_take isl_basic_set *dom,
1314 __isl_give isl_set **empty);
1315 __isl_give isl_set *isl_set_partial_lexmin(
1316 __isl_take isl_set *set, __isl_take isl_set *dom,
1317 __isl_give isl_set **empty);
1318 __isl_give isl_set *isl_set_partial_lexmax(
1319 __isl_take isl_set *set, __isl_take isl_set *dom,
1320 __isl_give isl_set **empty);
1322 Given a (basic) set C<set> (or C<bset>), the following functions simply
1323 return a set containing the lexicographic minimum or maximum
1324 of the elements in C<set> (or C<bset>).
1325 In case of union sets, the optimum is computed per dimension.
1327 __isl_give isl_set *isl_basic_set_lexmin(
1328 __isl_take isl_basic_set *bset);
1329 __isl_give isl_set *isl_basic_set_lexmax(
1330 __isl_take isl_basic_set *bset);
1331 __isl_give isl_set *isl_set_lexmin(
1332 __isl_take isl_set *set);
1333 __isl_give isl_set *isl_set_lexmax(
1334 __isl_take isl_set *set);
1335 __isl_give isl_union_set *isl_union_set_lexmin(
1336 __isl_take isl_union_set *uset);
1337 __isl_give isl_union_set *isl_union_set_lexmax(
1338 __isl_take isl_union_set *uset);
1340 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1341 the following functions
1342 compute a relation that maps each element of C<dom>
1343 to the single lexicographic minimum or maximum
1344 of the elements that are associated to that same
1345 element in C<map> (or C<bmap>).
1346 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1347 that contains the elements in C<dom> that do not map
1348 to any elements in C<map> (or C<bmap>).
1349 In other words, the union of the domain of the result and of C<*empty>
1352 __isl_give isl_map *isl_basic_map_partial_lexmax(
1353 __isl_take isl_basic_map *bmap,
1354 __isl_take isl_basic_set *dom,
1355 __isl_give isl_set **empty);
1356 __isl_give isl_map *isl_basic_map_partial_lexmin(
1357 __isl_take isl_basic_map *bmap,
1358 __isl_take isl_basic_set *dom,
1359 __isl_give isl_set **empty);
1360 __isl_give isl_map *isl_map_partial_lexmax(
1361 __isl_take isl_map *map, __isl_take isl_set *dom,
1362 __isl_give isl_set **empty);
1363 __isl_give isl_map *isl_map_partial_lexmin(
1364 __isl_take isl_map *map, __isl_take isl_set *dom,
1365 __isl_give isl_set **empty);
1367 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1368 return a map mapping each element in the domain of
1369 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1370 of all elements associated to that element.
1371 In case of union relations, the optimum is computed per dimension.
1373 __isl_give isl_map *isl_basic_map_lexmin(
1374 __isl_take isl_basic_map *bmap);
1375 __isl_give isl_map *isl_basic_map_lexmax(
1376 __isl_take isl_basic_map *bmap);
1377 __isl_give isl_map *isl_map_lexmin(
1378 __isl_take isl_map *map);
1379 __isl_give isl_map *isl_map_lexmax(
1380 __isl_take isl_map *map);
1381 __isl_give isl_union_map *isl_union_map_lexmin(
1382 __isl_take isl_union_map *umap);
1383 __isl_give isl_union_map *isl_union_map_lexmax(
1384 __isl_take isl_union_map *umap);
1388 Points are elements of a set. They can be used to construct
1389 simple sets (boxes) or they can be used to represent the
1390 individual elements of a set.
1391 The zero point (the origin) can be created using
1393 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1395 The coordinates of a point can be inspected, set and changed
1398 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1399 enum isl_dim_type type, int pos, isl_int *v);
1400 __isl_give isl_point *isl_point_set_coordinate(
1401 __isl_take isl_point *pnt,
1402 enum isl_dim_type type, int pos, isl_int v);
1404 __isl_give isl_point *isl_point_add_ui(
1405 __isl_take isl_point *pnt,
1406 enum isl_dim_type type, int pos, unsigned val);
1407 __isl_give isl_point *isl_point_sub_ui(
1408 __isl_take isl_point *pnt,
1409 enum isl_dim_type type, int pos, unsigned val);
1411 Points can be copied or freed using
1413 __isl_give isl_point *isl_point_copy(
1414 __isl_keep isl_point *pnt);
1415 void isl_point_free(__isl_take isl_point *pnt);
1417 A singleton set can be created from a point using
1419 __isl_give isl_set *isl_set_from_point(
1420 __isl_take isl_point *pnt);
1422 and a box can be created from two opposite extremal points using
1424 __isl_give isl_set *isl_set_box_from_points(
1425 __isl_take isl_point *pnt1,
1426 __isl_take isl_point *pnt2);
1428 All elements of a B<bounded> (union) set can be enumerated using
1429 the following functions.
1431 int isl_set_foreach_point(__isl_keep isl_set *set,
1432 int (*fn)(__isl_take isl_point *pnt, void *user),
1434 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1435 int (*fn)(__isl_take isl_point *pnt, void *user),
1438 The function C<fn> is called for each integer point in
1439 C<set> with as second argument the last argument of
1440 the C<isl_set_foreach_point> call. The function C<fn>
1441 should return C<0> on success and C<-1> on failure.
1442 In the latter case, C<isl_set_foreach_point> will stop
1443 enumerating and return C<-1> as well.
1444 If the enumeration is performed successfully and to completion,
1445 then C<isl_set_foreach_point> returns C<0>.
1447 To obtain a single point of a set, use
1449 __isl_give isl_point *isl_set_sample_point(
1450 __isl_take isl_set *set);
1452 If C<set> does not contain any (integer) points, then the
1453 resulting point will be ``void'', a property that can be
1456 int isl_point_is_void(__isl_keep isl_point *pnt);
1458 =head2 Piecewise Quasipolynomials
1460 A piecewise quasipolynomial is a particular kind of function that maps
1461 a parametric point to a rational value.
1462 More specifically, a quasipolynomial is a polynomial expression in greatest
1463 integer parts of affine expressions of parameters and variables.
1464 A piecewise quasipolynomial is a subdivision of a given parametric
1465 domain into disjoint cells with a quasipolynomial associated to
1466 each cell. The value of the piecewise quasipolynomial at a given
1467 point is the value of the quasipolynomial associated to the cell
1468 that contains the point. Outside of the union of cells,
1469 the value is assumed to be zero.
1470 For example, the piecewise quasipolynomial
1472 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1474 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1475 A given piecewise quasipolynomial has a fixed domain dimension.
1476 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1477 defined over different domains.
1478 Piecewise quasipolynomials are mainly used by the C<barvinok>
1479 library for representing the number of elements in a parametric set or map.
1480 For example, the piecewise quasipolynomial above represents
1481 the number of points in the map
1483 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1485 =head3 Printing (Piecewise) Quasipolynomials
1487 Quasipolynomials and piecewise quasipolynomials can be printed
1488 using the following functions.
1490 __isl_give isl_printer *isl_printer_print_qpolynomial(
1491 __isl_take isl_printer *p,
1492 __isl_keep isl_qpolynomial *qp);
1494 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1495 __isl_take isl_printer *p,
1496 __isl_keep isl_pw_qpolynomial *pwqp);
1498 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1499 __isl_take isl_printer *p,
1500 __isl_keep isl_union_pw_qpolynomial *upwqp);
1502 The output format of the printer
1503 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1504 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1507 =head3 Creating New (Piecewise) Quasipolynomials
1509 Some simple quasipolynomials can be created using the following functions.
1510 More complicated quasipolynomials can be created by applying
1511 operations such as addition and multiplication
1512 on the resulting quasipolynomials
1514 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1515 __isl_take isl_dim *dim);
1516 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1517 __isl_take isl_dim *dim);
1518 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1519 __isl_take isl_dim *dim);
1520 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1521 __isl_take isl_dim *dim);
1522 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1523 __isl_take isl_dim *dim,
1524 const isl_int n, const isl_int d);
1525 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1526 __isl_take isl_div *div);
1527 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1528 __isl_take isl_dim *dim,
1529 enum isl_dim_type type, unsigned pos);
1531 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1532 with a single cell can be created using the following functions.
1533 Multiple of these single cell piecewise quasipolynomials can
1534 be combined to create more complicated piecewise quasipolynomials.
1536 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1537 __isl_take isl_dim *dim);
1538 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1539 __isl_take isl_set *set,
1540 __isl_take isl_qpolynomial *qp);
1542 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1543 __isl_take isl_dim *dim);
1544 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1545 __isl_take isl_pw_qpolynomial *pwqp);
1546 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1547 __isl_take isl_union_pw_qpolynomial *upwqp,
1548 __isl_take isl_pw_qpolynomial *pwqp);
1550 Quasipolynomials can be copied and freed again using the following
1553 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1554 __isl_keep isl_qpolynomial *qp);
1555 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1557 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1558 __isl_keep isl_pw_qpolynomial *pwqp);
1559 void isl_pw_qpolynomial_free(
1560 __isl_take isl_pw_qpolynomial *pwqp);
1562 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1563 __isl_keep isl_union_pw_qpolynomial *upwqp);
1564 void isl_union_pw_qpolynomial_free(
1565 __isl_take isl_union_pw_qpolynomial *upwqp);
1567 =head3 Inspecting (Piecewise) Quasipolynomials
1569 To iterate over all piecewise quasipolynomials in a union
1570 piecewise quasipolynomial, use the following function
1572 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1573 __isl_keep isl_union_pw_qpolynomial *upwqp,
1574 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1577 To iterate over the cells in a piecewise quasipolynomial,
1578 use either of the following two functions
1580 int isl_pw_qpolynomial_foreach_piece(
1581 __isl_keep isl_pw_qpolynomial *pwqp,
1582 int (*fn)(__isl_take isl_set *set,
1583 __isl_take isl_qpolynomial *qp,
1584 void *user), void *user);
1585 int isl_pw_qpolynomial_foreach_lifted_piece(
1586 __isl_keep isl_pw_qpolynomial *pwqp,
1587 int (*fn)(__isl_take isl_set *set,
1588 __isl_take isl_qpolynomial *qp,
1589 void *user), void *user);
1591 As usual, the function C<fn> should return C<0> on success
1592 and C<-1> on failure. The difference between
1593 C<isl_pw_qpolynomial_foreach_piece> and
1594 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1595 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1596 compute unique representations for all existentially quantified
1597 variables and then turn these existentially quantified variables
1598 into extra set variables, adapting the associated quasipolynomial
1599 accordingly. This means that the C<set> passed to C<fn>
1600 will not have any existentially quantified variables, but that
1601 the dimensions of the sets may be different for different
1602 invocations of C<fn>.
1604 To iterate over all terms in a quasipolynomial,
1607 int isl_qpolynomial_foreach_term(
1608 __isl_keep isl_qpolynomial *qp,
1609 int (*fn)(__isl_take isl_term *term,
1610 void *user), void *user);
1612 The terms themselves can be inspected and freed using
1615 unsigned isl_term_dim(__isl_keep isl_term *term,
1616 enum isl_dim_type type);
1617 void isl_term_get_num(__isl_keep isl_term *term,
1619 void isl_term_get_den(__isl_keep isl_term *term,
1621 int isl_term_get_exp(__isl_keep isl_term *term,
1622 enum isl_dim_type type, unsigned pos);
1623 __isl_give isl_div *isl_term_get_div(
1624 __isl_keep isl_term *term, unsigned pos);
1625 void isl_term_free(__isl_take isl_term *term);
1627 Each term is a product of parameters, set variables and
1628 integer divisions. The function C<isl_term_get_exp>
1629 returns the exponent of a given dimensions in the given term.
1630 The C<isl_int>s in the arguments of C<isl_term_get_num>
1631 and C<isl_term_get_den> need to have been initialized
1632 using C<isl_int_init> before calling these functions.
1634 =head3 Properties of (Piecewise) Quasipolynomials
1636 To check whether a quasipolynomial is actually a constant,
1637 use the following function.
1639 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1640 isl_int *n, isl_int *d);
1642 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1643 then the numerator and denominator of the constant
1644 are returned in C<*n> and C<*d>, respectively.
1646 =head3 Operations on (Piecewise) Quasipolynomials
1648 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1649 __isl_take isl_qpolynomial *qp);
1650 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1651 __isl_take isl_qpolynomial *qp1,
1652 __isl_take isl_qpolynomial *qp2);
1653 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1654 __isl_take isl_qpolynomial *qp1,
1655 __isl_take isl_qpolynomial *qp2);
1656 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1657 __isl_take isl_qpolynomial *qp1,
1658 __isl_take isl_qpolynomial *qp2);
1660 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1661 __isl_take isl_pw_qpolynomial *pwqp1,
1662 __isl_take isl_pw_qpolynomial *pwqp2);
1663 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1664 __isl_take isl_pw_qpolynomial *pwqp1,
1665 __isl_take isl_pw_qpolynomial *pwqp2);
1666 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1667 __isl_take isl_pw_qpolynomial *pwqp1,
1668 __isl_take isl_pw_qpolynomial *pwqp2);
1669 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1670 __isl_take isl_pw_qpolynomial *pwqp);
1671 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1672 __isl_take isl_pw_qpolynomial *pwqp1,
1673 __isl_take isl_pw_qpolynomial *pwqp2);
1675 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1676 __isl_take isl_union_pw_qpolynomial *upwqp1,
1677 __isl_take isl_union_pw_qpolynomial *upwqp2);
1678 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1679 __isl_take isl_union_pw_qpolynomial *upwqp1,
1680 __isl_take isl_union_pw_qpolynomial *upwqp2);
1681 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1682 __isl_take isl_union_pw_qpolynomial *upwqp1,
1683 __isl_take isl_union_pw_qpolynomial *upwqp2);
1685 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1686 __isl_take isl_pw_qpolynomial *pwqp,
1687 __isl_take isl_point *pnt);
1689 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1690 __isl_take isl_union_pw_qpolynomial *upwqp,
1691 __isl_take isl_point *pnt);
1693 __isl_give isl_set *isl_pw_qpolynomial_domain(
1694 __isl_take isl_pw_qpolynomial *pwqp);
1695 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1696 __isl_take isl_pw_qpolynomial *pwpq,
1697 __isl_take isl_set *set);
1699 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1700 __isl_take isl_union_pw_qpolynomial *upwqp);
1701 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1702 __isl_take isl_union_pw_qpolynomial *upwpq,
1703 __isl_take isl_union_set *uset);
1705 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1706 __isl_take isl_union_pw_qpolynomial *upwqp);
1708 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1709 __isl_take isl_pw_qpolynomial *pwqp,
1710 __isl_take isl_set *context);
1712 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1713 __isl_take isl_union_pw_qpolynomial *upwqp,
1714 __isl_take isl_union_set *context);
1716 The gist operation applies the gist operation to each of
1717 the cells in the domain of the input piecewise quasipolynomial.
1718 In future, the operation will also exploit the context
1719 to simplify the quasipolynomials associated to each cell.
1721 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1723 A piecewise quasipolynomial reduction is a piecewise
1724 reduction (or fold) of quasipolynomials.
1725 In particular, the reduction can be maximum or a minimum.
1726 The objects are mainly used to represent the result of
1727 an upper or lower bound on a quasipolynomial over its domain,
1728 i.e., as the result of the following function.
1730 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1731 __isl_take isl_pw_qpolynomial *pwqp,
1732 enum isl_fold type, int *tight);
1734 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
1735 __isl_take isl_union_pw_qpolynomial *upwqp,
1736 enum isl_fold type, int *tight);
1738 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1739 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1740 is the returned bound is known be tight, i.e., for each value
1741 of the parameters there is at least
1742 one element in the domain that reaches the bound.
1744 A (piecewise) quasipolynomial reduction can be copied or freed using the
1745 following functions.
1747 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1748 __isl_keep isl_qpolynomial_fold *fold);
1749 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1750 __isl_keep isl_pw_qpolynomial_fold *pwf);
1751 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
1752 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1753 void isl_qpolynomial_fold_free(
1754 __isl_take isl_qpolynomial_fold *fold);
1755 void isl_pw_qpolynomial_fold_free(
1756 __isl_take isl_pw_qpolynomial_fold *pwf);
1757 void isl_union_pw_qpolynomial_fold_free(
1758 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1760 =head3 Printing Piecewise Quasipolynomial Reductions
1762 Piecewise quasipolynomial reductions can be printed
1763 using the following function.
1765 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1766 __isl_take isl_printer *p,
1767 __isl_keep isl_pw_qpolynomial_fold *pwf);
1768 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
1769 __isl_take isl_printer *p,
1770 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1772 For C<isl_printer_print_pw_qpolynomial_fold>,
1773 output format of the printer
1774 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1775 For C<isl_printer_print_union_pw_qpolynomial_fold>,
1776 output format of the printer
1777 needs to be set to either C<ISL_FORMAT_ISL>.
1779 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1781 To iterate over all piecewise quasipolynomial reductions in a union
1782 piecewise quasipolynomial reduction, use the following function
1784 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1785 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1786 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
1787 void *user), void *user);
1789 To iterate over the cells in a piecewise quasipolynomial reduction,
1790 use either of the following two functions
1792 int isl_pw_qpolynomial_fold_foreach_piece(
1793 __isl_keep isl_pw_qpolynomial_fold *pwf,
1794 int (*fn)(__isl_take isl_set *set,
1795 __isl_take isl_qpolynomial_fold *fold,
1796 void *user), void *user);
1797 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1798 __isl_keep isl_pw_qpolynomial_fold *pwf,
1799 int (*fn)(__isl_take isl_set *set,
1800 __isl_take isl_qpolynomial_fold *fold,
1801 void *user), void *user);
1803 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
1804 of the difference between these two functions.
1806 To iterate over all quasipolynomials in a reduction, use
1808 int isl_qpolynomial_fold_foreach_qpolynomial(
1809 __isl_keep isl_qpolynomial_fold *fold,
1810 int (*fn)(__isl_take isl_qpolynomial *qp,
1811 void *user), void *user);
1813 =head3 Operations on Piecewise Quasipolynomial Reductions
1815 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
1816 __isl_take isl_pw_qpolynomial_fold *pwf1,
1817 __isl_take isl_pw_qpolynomial_fold *pwf2);
1819 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add(
1820 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
1821 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
1823 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
1824 __isl_take isl_pw_qpolynomial_fold *pwf,
1825 __isl_take isl_point *pnt);
1827 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
1828 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1829 __isl_take isl_point *pnt);
1831 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
1832 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1833 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
1834 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1835 __isl_take isl_union_set *uset);
1837 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
1838 __isl_take isl_pw_qpolynomial_fold *pwf);
1840 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
1841 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1843 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
1844 __isl_take isl_pw_qpolynomial_fold *pwf,
1845 __isl_take isl_set *context);
1847 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
1848 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1849 __isl_take isl_union_set *context);
1851 The gist operation applies the gist operation to each of
1852 the cells in the domain of the input piecewise quasipolynomial reduction.
1853 In future, the operation will also exploit the context
1854 to simplify the quasipolynomial reductions associated to each cell.
1856 =head2 Dependence Analysis
1858 C<isl> contains specialized functionality for performing
1859 array dataflow analysis. That is, given a I<sink> access relation
1860 and a collection of possible I<source> access relations,
1861 C<isl> can compute relations that describe
1862 for each iteration of the sink access, which iteration
1863 of which of the source access relations was the last
1864 to access the same data element before the given iteration
1866 To compute standard flow dependences, the sink should be
1867 a read, while the sources should be writes.
1868 If any of the source accesses are marked as being I<may>
1869 accesses, then there will be a dependence to the last
1870 I<must> access B<and> to any I<may> access that follows
1871 this last I<must> access.
1872 In particular, if I<all> sources are I<may> accesses,
1873 then memory based dependence analysis is performed.
1874 If, on the other hand, all sources are I<must> accesses,
1875 then value based dependence analysis is performed.
1877 #include <isl_flow.h>
1879 __isl_give isl_access_info *isl_access_info_alloc(
1880 __isl_take isl_map *sink,
1881 void *sink_user, isl_access_level_before fn,
1883 __isl_give isl_access_info *isl_access_info_add_source(
1884 __isl_take isl_access_info *acc,
1885 __isl_take isl_map *source, int must,
1888 __isl_give isl_flow *isl_access_info_compute_flow(
1889 __isl_take isl_access_info *acc);
1891 int isl_flow_foreach(__isl_keep isl_flow *deps,
1892 int (*fn)(__isl_take isl_map *dep, int must,
1893 void *dep_user, void *user),
1895 __isl_give isl_set *isl_flow_get_no_source(
1896 __isl_keep isl_flow *deps, int must);
1897 void isl_flow_free(__isl_take isl_flow *deps);
1899 The function C<isl_access_info_compute_flow> performs the actual
1900 dependence analysis. The other functions are used to construct
1901 the input for this function or to read off the output.
1903 The input is collected in an C<isl_access_info>, which can
1904 be created through a call to C<isl_access_info_alloc>.
1905 The arguments to this functions are the sink access relation
1906 C<sink>, a token C<sink_user> used to identify the sink
1907 access to the user, a callback function for specifying the
1908 relative order of source and sink accesses, and the number
1909 of source access relations that will be added.
1910 The callback function has type C<int (*)(void *first, void *second)>.
1911 The function is called with two user supplied tokens identifying
1912 either a source or the sink and it should return the shared nesting
1913 level and the relative order of the two accesses.
1914 In particular, let I<n> be the number of loops shared by
1915 the two accesses. If C<first> precedes C<second> textually,
1916 then the function should return I<2 * n + 1>; otherwise,
1917 it should return I<2 * n>.
1918 The sources can be added to the C<isl_access_info> by performing
1919 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1920 C<must> indicates whether the source is a I<must> access
1921 or a I<may> access. Note that a multi-valued access relation
1922 should only be marked I<must> if every iteration in the domain
1923 of the relation accesses I<all> elements in its image.
1924 The C<source_user> token is again used to identify
1925 the source access. The range of the source access relation
1926 C<source> should have the same dimension as the range
1927 of the sink access relation.
1929 The result of the dependence analysis is collected in an
1930 C<isl_flow>. There may be elements in the domain of
1931 the sink access for which no preceding source access could be
1932 found or for which all preceding sources are I<may> accesses.
1933 The sets of these elements can be obtained through
1934 calls to C<isl_flow_get_no_source>, the first with C<must> set
1935 and the second with C<must> unset.
1936 In the case of standard flow dependence analysis,
1937 with the sink a read and the sources I<must> writes,
1938 the first set corresponds to the reads from uninitialized
1939 array elements and the second set is empty.
1940 The actual flow dependences can be extracted using
1941 C<isl_flow_foreach>. This function will call the user-specified
1942 callback function C<fn> for each B<non-empty> dependence between
1943 a source and the sink. The callback function is called
1944 with four arguments, the actual flow dependence relation
1945 mapping source iterations to sink iterations, a boolean that
1946 indicates whether it is a I<must> or I<may> dependence, a token
1947 identifying the source and an additional C<void *> with value
1948 equal to the third argument of the C<isl_flow_foreach> call.
1949 A dependence is marked I<must> if it originates from a I<must>
1950 source and if it is not followed by any I<may> sources.
1952 After finishing with an C<isl_flow>, the user should call
1953 C<isl_flow_free> to free all associated memory.
1955 =head2 Parametric Vertex Enumeration
1957 The parametric vertex enumeration described in this section
1958 is mainly intended to be used internally and by the C<barvinok>
1961 #include <isl_vertices.h>
1962 __isl_give isl_vertices *isl_basic_set_compute_vertices(
1963 __isl_keep isl_basic_set *bset);
1965 The function C<isl_basic_set_compute_vertices> performs the
1966 actual computation of the parametric vertices and the chamber
1967 decomposition and store the result in an C<isl_vertices> object.
1968 This information can be queried by either iterating over all
1969 the vertices or iterating over all the chambers or cells
1970 and then iterating over all vertices that are active on the chamber.
1972 int isl_vertices_foreach_vertex(
1973 __isl_keep isl_vertices *vertices,
1974 int (*fn)(__isl_take isl_vertex *vertex, void *user),
1977 int isl_vertices_foreach_cell(
1978 __isl_keep isl_vertices *vertices,
1979 int (*fn)(__isl_take isl_cell *cell, void *user),
1981 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
1982 int (*fn)(__isl_take isl_vertex *vertex, void *user),
1985 Other operations that can be performed on an C<isl_vertices> object are
1988 isl_ctx *isl_vertices_get_ctx(
1989 __isl_keep isl_vertices *vertices);
1990 int isl_vertices_get_n_vertices(
1991 __isl_keep isl_vertices *vertices);
1992 void isl_vertices_free(__isl_take isl_vertices *vertices);
1994 Vertices can be inspected and destroyed using the following functions.
1996 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
1997 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
1998 __isl_give isl_basic_set *isl_vertex_get_domain(
1999 __isl_keep isl_vertex *vertex);
2000 __isl_give isl_basic_set *isl_vertex_get_expr(
2001 __isl_keep isl_vertex *vertex);
2002 void isl_vertex_free(__isl_take isl_vertex *vertex);
2004 C<isl_vertex_get_expr> returns a singleton parametric set describing
2005 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2007 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2008 B<rational> basic sets, so they should mainly be used for inspection
2009 and should not be mixed with integer sets.
2011 Chambers can be inspected and destroyed using the following functions.
2013 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2014 __isl_give isl_basic_set *isl_cell_get_domain(
2015 __isl_keep isl_cell *cell);
2016 void isl_cell_free(__isl_take isl_cell *cell);
2020 Although C<isl> is mainly meant to be used as a library,
2021 it also contains some basic applications that use some
2022 of the functionality of C<isl>.
2023 The input may be specified in either the L<isl format>
2024 or the L<PolyLib format>.
2026 =head2 C<isl_polyhedron_sample>
2028 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2029 an integer element of the polyhedron, if there is any.
2030 The first column in the output is the denominator and is always
2031 equal to 1. If the polyhedron contains no integer points,
2032 then a vector of length zero is printed.
2036 C<isl_pip> takes the same input as the C<example> program
2037 from the C<piplib> distribution, i.e., a set of constraints
2038 on the parameters, a line contains only -1 and finally a set
2039 of constraints on a parametric polyhedron.
2040 The coefficients of the parameters appear in the last columns
2041 (but before the final constant column).
2042 The output is the lexicographic minimum of the parametric polyhedron.
2043 As C<isl> currently does not have its own output format, the output
2044 is just a dump of the internal state.
2046 =head2 C<isl_polyhedron_minimize>
2048 C<isl_polyhedron_minimize> computes the minimum of some linear
2049 or affine objective function over the integer points in a polyhedron.
2050 If an affine objective function
2051 is given, then the constant should appear in the last column.
2053 =head2 C<isl_polytope_scan>
2055 Given a polytope, C<isl_polytope_scan> prints
2056 all integer points in the polytope.
2058 =head1 C<isl-polylib>
2060 The C<isl-polylib> library provides the following functions for converting
2061 between C<isl> objects and C<PolyLib> objects.
2062 The library is distributed separately for licensing reasons.
2064 #include <isl_set_polylib.h>
2065 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2066 Polyhedron *P, __isl_take isl_dim *dim);
2067 Polyhedron *isl_basic_set_to_polylib(
2068 __isl_keep isl_basic_set *bset);
2069 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2070 __isl_take isl_dim *dim);
2071 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2073 #include <isl_map_polylib.h>
2074 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2075 Polyhedron *P, __isl_take isl_dim *dim);
2076 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2077 __isl_take isl_dim *dim);
2078 Polyhedron *isl_basic_map_to_polylib(
2079 __isl_keep isl_basic_map *bmap);
2080 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);