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 Generate C<configure>
67 After performing the above steps, continue
68 with the L<Common installation instructions>.
70 =head2 Common installation instructions
76 Building C<isl> requires C<GMP>, including its headers files.
77 Your distribution may not provide these header files by default
78 and you may need to install a package called C<gmp-devel> or something
79 similar. Alternatively, C<GMP> can be built from
80 source, available from L<http://gmplib.org/>.
84 C<isl> uses the standard C<autoconf> C<configure> script.
89 optionally followed by some configure options.
90 A complete list of options can be obtained by running
94 Below we discuss some of the more common options.
96 C<isl> can optionally use C<piplib>, but no
97 C<piplib> functionality is currently used by default.
98 The C<--with-piplib> option can
99 be used to specify which C<piplib>
100 library to use, either an installed version (C<system>),
101 an externally built version (C<build>)
102 or no version (C<no>). The option C<build> is mostly useful
103 in C<configure> scripts of larger projects that bundle both C<isl>
110 Installation prefix for C<isl>
112 =item C<--with-gmp-prefix>
114 Installation prefix for C<GMP> (architecture-independent files).
116 =item C<--with-gmp-exec-prefix>
118 Installation prefix for C<GMP> (architecture-dependent files).
120 =item C<--with-piplib>
122 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
124 =item C<--with-piplib-prefix>
126 Installation prefix for C<system> C<piplib> (architecture-independent files).
128 =item C<--with-piplib-exec-prefix>
130 Installation prefix for C<system> C<piplib> (architecture-dependent files).
132 =item C<--with-piplib-builddir>
134 Location where C<build> C<piplib> was built.
142 =item 4 Install (optional)
150 =head2 Initialization
152 All manipulations of integer sets and relations occur within
153 the context of an C<isl_ctx>.
154 A given C<isl_ctx> can only be used within a single thread.
155 All arguments of a function are required to have been allocated
156 within the same context.
157 There are currently no functions available for moving an object
158 from one C<isl_ctx> to another C<isl_ctx>. This means that
159 there is currently no way of safely moving an object from one
160 thread to another, unless the whole C<isl_ctx> is moved.
162 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
163 freed using C<isl_ctx_free>.
164 All objects allocated within an C<isl_ctx> should be freed
165 before the C<isl_ctx> itself is freed.
167 isl_ctx *isl_ctx_alloc();
168 void isl_ctx_free(isl_ctx *ctx);
172 All operations on integers, mainly the coefficients
173 of the constraints describing the sets and relations,
174 are performed in exact integer arithmetic using C<GMP>.
175 However, to allow future versions of C<isl> to optionally
176 support fixed integer arithmetic, all calls to C<GMP>
177 are wrapped inside C<isl> specific macros.
178 The basic type is C<isl_int> and the following operations
179 are available on this type.
180 The meanings of these operations are essentially the same
181 as their C<GMP> C<mpz_> counterparts.
182 As always with C<GMP> types, C<isl_int>s need to be
183 initialized with C<isl_int_init> before they can be used
184 and they need to be released with C<isl_int_clear>
189 =item isl_int_init(i)
191 =item isl_int_clear(i)
193 =item isl_int_set(r,i)
195 =item isl_int_set_si(r,i)
197 =item isl_int_abs(r,i)
199 =item isl_int_neg(r,i)
201 =item isl_int_swap(i,j)
203 =item isl_int_swap_or_set(i,j)
205 =item isl_int_add_ui(r,i,j)
207 =item isl_int_sub_ui(r,i,j)
209 =item isl_int_add(r,i,j)
211 =item isl_int_sub(r,i,j)
213 =item isl_int_mul(r,i,j)
215 =item isl_int_mul_ui(r,i,j)
217 =item isl_int_addmul(r,i,j)
219 =item isl_int_submul(r,i,j)
221 =item isl_int_gcd(r,i,j)
223 =item isl_int_lcm(r,i,j)
225 =item isl_int_divexact(r,i,j)
227 =item isl_int_cdiv_q(r,i,j)
229 =item isl_int_fdiv_q(r,i,j)
231 =item isl_int_fdiv_r(r,i,j)
233 =item isl_int_fdiv_q_ui(r,i,j)
235 =item isl_int_read(r,s)
237 =item isl_int_print(out,i,width)
241 =item isl_int_cmp(i,j)
243 =item isl_int_cmp_si(i,si)
245 =item isl_int_eq(i,j)
247 =item isl_int_ne(i,j)
249 =item isl_int_lt(i,j)
251 =item isl_int_le(i,j)
253 =item isl_int_gt(i,j)
255 =item isl_int_ge(i,j)
257 =item isl_int_abs_eq(i,j)
259 =item isl_int_abs_ne(i,j)
261 =item isl_int_abs_lt(i,j)
263 =item isl_int_abs_gt(i,j)
265 =item isl_int_abs_ge(i,j)
267 =item isl_int_is_zero(i)
269 =item isl_int_is_one(i)
271 =item isl_int_is_negone(i)
273 =item isl_int_is_pos(i)
275 =item isl_int_is_neg(i)
277 =item isl_int_is_nonpos(i)
279 =item isl_int_is_nonneg(i)
281 =item isl_int_is_divisible_by(i,j)
285 =head2 Sets and Relations
287 C<isl> uses six types of objects for representing sets and relations,
288 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
289 C<isl_union_set> and C<isl_union_map>.
290 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
291 can be described as a conjunction of affine constraints, while
292 C<isl_set> and C<isl_map> represent unions of
293 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
294 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
295 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
296 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
297 where dimensions with different space names
298 (see L<Dimension Specifications>) are considered different as well.
299 The difference between sets and relations (maps) is that sets have
300 one set of variables, while relations have two sets of variables,
301 input variables and output variables.
303 =head2 Memory Management
305 Since a high-level operation on sets and/or relations usually involves
306 several substeps and since the user is usually not interested in
307 the intermediate results, most functions that return a new object
308 will also release all the objects passed as arguments.
309 If the user still wants to use one or more of these arguments
310 after the function call, she should pass along a copy of the
311 object rather than the object itself.
312 The user is then responsible for make sure that the original
313 object gets used somewhere else or is explicitly freed.
315 The arguments and return values of all documents functions are
316 annotated to make clear which arguments are released and which
317 arguments are preserved. In particular, the following annotations
324 C<__isl_give> means that a new object is returned.
325 The user should make sure that the returned pointer is
326 used exactly once as a value for an C<__isl_take> argument.
327 In between, it can be used as a value for as many
328 C<__isl_keep> arguments as the user likes.
329 There is one exception, and that is the case where the
330 pointer returned is C<NULL>. Is this case, the user
331 is free to use it as an C<__isl_take> argument or not.
335 C<__isl_take> means that the object the argument points to
336 is taken over by the function and may no longer be used
337 by the user as an argument to any other function.
338 The pointer value must be one returned by a function
339 returning an C<__isl_give> pointer.
340 If the user passes in a C<NULL> value, then this will
341 be treated as an error in the sense that the function will
342 not perform its usual operation. However, it will still
343 make sure that all the the other C<__isl_take> arguments
348 C<__isl_keep> means that the function will only use the object
349 temporarily. After the function has finished, the user
350 can still use it as an argument to other functions.
351 A C<NULL> value will be treated in the same way as
352 a C<NULL> value for an C<__isl_take> argument.
356 =head2 Dimension Specifications
358 Whenever a new set or relation is created from scratch,
359 its dimension needs to be specified using an C<isl_dim>.
362 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
363 unsigned nparam, unsigned n_in, unsigned n_out);
364 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
365 unsigned nparam, unsigned dim);
366 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
367 void isl_dim_free(__isl_take isl_dim *dim);
368 unsigned isl_dim_size(__isl_keep isl_dim *dim,
369 enum isl_dim_type type);
371 The dimension specification used for creating a set
372 needs to be created using C<isl_dim_set_alloc>, while
373 that for creating a relation
374 needs to be created using C<isl_dim_alloc>.
375 C<isl_dim_size> can be used
376 to find out the number of dimensions of each type in
377 a dimension specification, where type may be
378 C<isl_dim_param>, C<isl_dim_in> (only for relations),
379 C<isl_dim_out> (only for relations), C<isl_dim_set>
380 (only for sets) or C<isl_dim_all>.
382 It is often useful to create objects that live in the
383 same space as some other object. This can be accomplished
384 by creating the new objects
385 (see L<Creating New Sets and Relations> or
386 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
387 specification of the original object.
390 __isl_give isl_dim *isl_basic_set_get_dim(
391 __isl_keep isl_basic_set *bset);
392 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
394 #include <isl_union_set.h>
395 __isl_give isl_dim *isl_union_set_get_dim(
396 __isl_keep isl_union_set *uset);
399 __isl_give isl_dim *isl_basic_map_get_dim(
400 __isl_keep isl_basic_map *bmap);
401 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
403 #include <isl_union_map.h>
404 __isl_give isl_dim *isl_union_map_get_dim(
405 __isl_keep isl_union_map *umap);
407 #include <isl_polynomial.h>
408 __isl_give isl_dim *isl_qpolynomial_get_dim(
409 __isl_keep isl_qpolynomial *qp);
410 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
411 __isl_keep isl_pw_qpolynomial *pwqp);
412 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
413 __isl_keep isl_union_pw_qpolynomial *upwqp);
414 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
415 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
417 The names of the individual dimensions may be set or read off
418 using the following functions.
421 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
422 enum isl_dim_type type, unsigned pos,
423 __isl_keep const char *name);
424 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
425 enum isl_dim_type type, unsigned pos);
427 Note that C<isl_dim_get_name> returns a pointer to some internal
428 data structure, so the result can only be used while the
429 corresponding C<isl_dim> is alive.
430 Also note that every function that operates on two sets or relations
431 requires that both arguments have the same parameters. This also
432 means that if one of the arguments has named parameters, then the
433 other needs to have named parameters too and the names need to match.
435 The names of entire spaces may be set or read off
436 using the following functions.
439 __isl_give isl_dim *isl_dim_set_tuple_name(
440 __isl_take isl_dim *dim,
441 enum isl_dim_type type, const char *s);
442 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
443 enum isl_dim_type type);
445 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
446 or C<isl_dim_set>. As with C<isl_dim_get_name>,
447 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
449 Binary operations require the corresponding spaces of their arguments
450 to have the same name.
452 =head2 Input and Output
454 C<isl> supports its own input/output format, which is similar
455 to the C<Omega> format, but also supports the C<PolyLib> format
460 The C<isl> format is similar to that of C<Omega>, but has a different
461 syntax for describing the parameters and allows for the definition
462 of an existentially quantified variable as the integer division
463 of an affine expression.
464 For example, the set of integers C<i> between C<0> and C<n>
465 such that C<i % 10 <= 6> can be described as
467 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
470 A set or relation can have several disjuncts, separated
471 by the keyword C<or>. Each disjunct is either a conjunction
472 of constraints or a projection (C<exists>) of a conjunction
473 of constraints. The constraints are separated by the keyword
476 =head3 C<PolyLib> format
478 If the represented set is a union, then the first line
479 contains a single number representing the number of disjuncts.
480 Otherwise, a line containing the number C<1> is optional.
482 Each disjunct is represented by a matrix of constraints.
483 The first line contains two numbers representing
484 the number of rows and columns,
485 where the number of rows is equal to the number of constraints
486 and the number of columns is equal to two plus the number of variables.
487 The following lines contain the actual rows of the constraint matrix.
488 In each row, the first column indicates whether the constraint
489 is an equality (C<0>) or inequality (C<1>). The final column
490 corresponds to the constant term.
492 If the set is parametric, then the coefficients of the parameters
493 appear in the last columns before the constant column.
494 The coefficients of any existentially quantified variables appear
495 between those of the set variables and those of the parameters.
500 __isl_give isl_basic_set *isl_basic_set_read_from_file(
501 isl_ctx *ctx, FILE *input, int nparam);
502 __isl_give isl_basic_set *isl_basic_set_read_from_str(
503 isl_ctx *ctx, const char *str, int nparam);
504 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
505 FILE *input, int nparam);
506 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
507 const char *str, int nparam);
510 __isl_give isl_basic_map *isl_basic_map_read_from_file(
511 isl_ctx *ctx, FILE *input, int nparam);
512 __isl_give isl_basic_map *isl_basic_map_read_from_str(
513 isl_ctx *ctx, const char *str, int nparam);
514 __isl_give isl_map *isl_map_read_from_file(
515 struct isl_ctx *ctx, FILE *input, int nparam);
516 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
517 const char *str, int nparam);
519 The input format is autodetected and may be either the C<PolyLib> format
520 or the C<isl> format.
521 C<nparam> specifies how many of the final columns in
522 the C<PolyLib> format correspond to parameters.
523 If input is given in the C<isl> format, then the number
524 of parameters needs to be equal to C<nparam>.
525 If C<nparam> is negative, then any number of parameters
526 is accepted in the C<isl> format and zero parameters
527 are assumed in the C<PolyLib> format.
531 Before anything can be printed, an C<isl_printer> needs to
534 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
536 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
537 void isl_printer_free(__isl_take isl_printer *printer);
538 __isl_give char *isl_printer_get_str(
539 __isl_keep isl_printer *printer);
541 The behavior of the printer can be modified in various ways
543 __isl_give isl_printer *isl_printer_set_output_format(
544 __isl_take isl_printer *p, int output_format);
545 __isl_give isl_printer *isl_printer_set_indent(
546 __isl_take isl_printer *p, int indent);
547 __isl_give isl_printer *isl_printer_set_prefix(
548 __isl_take isl_printer *p, const char *prefix);
549 __isl_give isl_printer *isl_printer_set_suffix(
550 __isl_take isl_printer *p, const char *suffix);
552 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
553 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
554 Each line in the output is indented by C<indent> spaces
555 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
556 In the C<PolyLib> format output,
557 the coefficients of the existentially quantified variables
558 appear between those of the set variables and those
561 To actually print something, use
564 __isl_give isl_printer *isl_printer_print_basic_set(
565 __isl_take isl_printer *printer,
566 __isl_keep isl_basic_set *bset);
567 __isl_give isl_printer *isl_printer_print_set(
568 __isl_take isl_printer *printer,
569 __isl_keep isl_set *set);
572 __isl_give isl_printer *isl_printer_print_basic_map(
573 __isl_take isl_printer *printer,
574 __isl_keep isl_basic_map *bmap);
575 __isl_give isl_printer *isl_printer_print_map(
576 __isl_take isl_printer *printer,
577 __isl_keep isl_map *map);
579 #include <isl_union_set.h>
580 __isl_give isl_printer *isl_printer_print_union_set(
581 __isl_take isl_printer *p,
582 __isl_keep isl_union_set *uset);
584 #include <isl_union_map.h>
585 __isl_give isl_printer *isl_printer_print_union_map(
586 __isl_take isl_printer *p,
587 __isl_keep isl_union_map *umap);
589 When called on a file printer, the following function flushes
590 the file. When called on a string printer, the buffer is cleared.
592 __isl_give isl_printer *isl_printer_flush(
593 __isl_take isl_printer *p);
595 =head2 Creating New Sets and Relations
597 C<isl> has functions for creating some standard sets and relations.
601 =item * Empty sets and relations
603 __isl_give isl_basic_set *isl_basic_set_empty(
604 __isl_take isl_dim *dim);
605 __isl_give isl_basic_map *isl_basic_map_empty(
606 __isl_take isl_dim *dim);
607 __isl_give isl_set *isl_set_empty(
608 __isl_take isl_dim *dim);
609 __isl_give isl_map *isl_map_empty(
610 __isl_take isl_dim *dim);
611 __isl_give isl_union_set *isl_union_set_empty(
612 __isl_take isl_dim *dim);
613 __isl_give isl_union_map *isl_union_map_empty(
614 __isl_take isl_dim *dim);
616 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
617 is only used to specify the parameters.
619 =item * Universe sets and relations
621 __isl_give isl_basic_set *isl_basic_set_universe(
622 __isl_take isl_dim *dim);
623 __isl_give isl_basic_map *isl_basic_map_universe(
624 __isl_take isl_dim *dim);
625 __isl_give isl_set *isl_set_universe(
626 __isl_take isl_dim *dim);
627 __isl_give isl_map *isl_map_universe(
628 __isl_take isl_dim *dim);
630 =item * Identity relations
632 __isl_give isl_basic_map *isl_basic_map_identity(
633 __isl_take isl_dim *set_dim);
634 __isl_give isl_map *isl_map_identity(
635 __isl_take isl_dim *set_dim);
637 These functions take a dimension specification for a B<set>
638 and return an identity relation between two such sets.
640 =item * Lexicographic order
642 __isl_give isl_map *isl_map_lex_lt(
643 __isl_take isl_dim *set_dim);
644 __isl_give isl_map *isl_map_lex_le(
645 __isl_take isl_dim *set_dim);
646 __isl_give isl_map *isl_map_lex_gt(
647 __isl_take isl_dim *set_dim);
648 __isl_give isl_map *isl_map_lex_ge(
649 __isl_take isl_dim *set_dim);
650 __isl_give isl_map *isl_map_lex_lt_first(
651 __isl_take isl_dim *dim, unsigned n);
652 __isl_give isl_map *isl_map_lex_le_first(
653 __isl_take isl_dim *dim, unsigned n);
654 __isl_give isl_map *isl_map_lex_gt_first(
655 __isl_take isl_dim *dim, unsigned n);
656 __isl_give isl_map *isl_map_lex_ge_first(
657 __isl_take isl_dim *dim, unsigned n);
659 The first four functions take a dimension specification for a B<set>
660 and return relations that express that the elements in the domain
661 are lexicographically less
662 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
663 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
664 than the elements in the range.
665 The last four functions take a dimension specification for a map
666 and return relations that express that the first C<n> dimensions
667 in the domain are lexicographically less
668 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
669 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
670 than the first C<n> dimensions in the range.
674 A basic set or relation can be converted to a set or relation
675 using the following functions.
677 __isl_give isl_set *isl_set_from_basic_set(
678 __isl_take isl_basic_set *bset);
679 __isl_give isl_map *isl_map_from_basic_map(
680 __isl_take isl_basic_map *bmap);
682 Sets and relations can be converted to union sets and relations
683 using the following functions.
685 __isl_give isl_union_map *isl_union_map_from_map(
686 __isl_take isl_map *map);
687 __isl_give isl_union_set *isl_union_set_from_set(
688 __isl_take isl_set *set);
690 Sets and relations can be copied and freed again using the following
693 __isl_give isl_basic_set *isl_basic_set_copy(
694 __isl_keep isl_basic_set *bset);
695 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
696 __isl_give isl_union_set *isl_union_set_copy(
697 __isl_keep isl_union_set *uset);
698 __isl_give isl_basic_map *isl_basic_map_copy(
699 __isl_keep isl_basic_map *bmap);
700 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
701 __isl_give isl_union_map *isl_union_map_copy(
702 __isl_keep isl_union_map *umap);
703 void isl_basic_set_free(__isl_take isl_basic_set *bset);
704 void isl_set_free(__isl_take isl_set *set);
705 void isl_union_set_free(__isl_take isl_union_set *uset);
706 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
707 void isl_map_free(__isl_take isl_map *map);
708 void isl_union_map_free(__isl_take isl_union_map *umap);
710 Other sets and relations can be constructed by starting
711 from a universe set or relation, adding equality and/or
712 inequality constraints and then projecting out the
713 existentially quantified variables, if any.
714 Constraints can be constructed, manipulated and
715 added to basic sets and relations using the following functions.
717 #include <isl_constraint.h>
718 __isl_give isl_constraint *isl_equality_alloc(
719 __isl_take isl_dim *dim);
720 __isl_give isl_constraint *isl_inequality_alloc(
721 __isl_take isl_dim *dim);
722 void isl_constraint_set_constant(
723 __isl_keep isl_constraint *constraint, isl_int v);
724 void isl_constraint_set_coefficient(
725 __isl_keep isl_constraint *constraint,
726 enum isl_dim_type type, int pos, isl_int v);
727 __isl_give isl_basic_map *isl_basic_map_add_constraint(
728 __isl_take isl_basic_map *bmap,
729 __isl_take isl_constraint *constraint);
730 __isl_give isl_basic_set *isl_basic_set_add_constraint(
731 __isl_take isl_basic_set *bset,
732 __isl_take isl_constraint *constraint);
734 For example, to create a set containing the even integers
735 between 10 and 42, you would use the following code.
739 struct isl_constraint *c;
740 struct isl_basic_set *bset;
743 dim = isl_dim_set_alloc(ctx, 0, 2);
744 bset = isl_basic_set_universe(isl_dim_copy(dim));
746 c = isl_equality_alloc(isl_dim_copy(dim));
747 isl_int_set_si(v, -1);
748 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
749 isl_int_set_si(v, 2);
750 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
751 bset = isl_basic_set_add_constraint(bset, c);
753 c = isl_inequality_alloc(isl_dim_copy(dim));
754 isl_int_set_si(v, -10);
755 isl_constraint_set_constant(c, v);
756 isl_int_set_si(v, 1);
757 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
758 bset = isl_basic_set_add_constraint(bset, c);
760 c = isl_inequality_alloc(dim);
761 isl_int_set_si(v, 42);
762 isl_constraint_set_constant(c, v);
763 isl_int_set_si(v, -1);
764 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
765 bset = isl_basic_set_add_constraint(bset, c);
767 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
773 struct isl_basic_set *bset;
774 bset = isl_basic_set_read_from_str(ctx,
775 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
777 =head2 Inspecting Sets and Relations
779 Usually, the user should not have to care about the actual constraints
780 of the sets and maps, but should instead apply the abstract operations
781 explained in the following sections.
782 Occasionally, however, it may be required to inspect the individual
783 coefficients of the constraints. This section explains how to do so.
784 In these cases, it may also be useful to have C<isl> compute
785 an explicit representation of the existentially quantified variables.
787 __isl_give isl_set *isl_set_compute_divs(
788 __isl_take isl_set *set);
789 __isl_give isl_map *isl_map_compute_divs(
790 __isl_take isl_map *map);
791 __isl_give isl_union_set *isl_union_set_compute_divs(
792 __isl_take isl_union_set *uset);
793 __isl_give isl_union_map *isl_union_map_compute_divs(
794 __isl_take isl_union_map *umap);
796 This explicit representation defines the existentially quantified
797 variables as integer divisions of the other variables, possibly
798 including earlier existentially quantified variables.
799 An explicitly represented existentially quantified variable therefore
800 has a unique value when the values of the other variables are known.
801 If, furthermore, the same existentials, i.e., existentials
802 with the same explicit representations, should appear in the
803 same order in each of the disjuncts of a set or map, then the user should call
804 either of the following functions.
806 __isl_give isl_set *isl_set_align_divs(
807 __isl_take isl_set *set);
808 __isl_give isl_map *isl_map_align_divs(
809 __isl_take isl_map *map);
811 To iterate over all the sets or maps in a union set or map, use
813 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
814 int (*fn)(__isl_take isl_set *set, void *user),
816 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
817 int (*fn)(__isl_take isl_map *map, void *user),
820 To iterate over all the basic sets or maps in a set or map, use
822 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
823 int (*fn)(__isl_take isl_basic_set *bset, void *user),
825 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
826 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
829 The callback function C<fn> should return 0 if successful and
830 -1 if an error occurs. In the latter case, or if any other error
831 occurs, the above functions will return -1.
833 It should be noted that C<isl> does not guarantee that
834 the basic sets or maps passed to C<fn> are disjoint.
835 If this is required, then the user should call one of
836 the following functions first.
838 __isl_give isl_set *isl_set_make_disjoint(
839 __isl_take isl_set *set);
840 __isl_give isl_map *isl_map_make_disjoint(
841 __isl_take isl_map *map);
843 To iterate over the constraints of a basic set or map, use
845 #include <isl_constraint.h>
847 int isl_basic_map_foreach_constraint(
848 __isl_keep isl_basic_map *bmap,
849 int (*fn)(__isl_take isl_constraint *c, void *user),
851 void isl_constraint_free(struct isl_constraint *c);
853 Again, the callback function C<fn> should return 0 if successful and
854 -1 if an error occurs. In the latter case, or if any other error
855 occurs, the above functions will return -1.
856 The constraint C<c> represents either an equality or an inequality.
857 Use the following function to find out whether a constraint
858 represents an equality. If not, it represents an inequality.
860 int isl_constraint_is_equality(
861 __isl_keep isl_constraint *constraint);
863 The coefficients of the constraints can be inspected using
864 the following functions.
866 void isl_constraint_get_constant(
867 __isl_keep isl_constraint *constraint, isl_int *v);
868 void isl_constraint_get_coefficient(
869 __isl_keep isl_constraint *constraint,
870 enum isl_dim_type type, int pos, isl_int *v);
872 The explicit representations of the existentially quantified
873 variables can be inspected using the following functions.
874 Note that the user is only allowed to use these functions
875 if the inspected set or map is the result of a call
876 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
878 __isl_give isl_div *isl_constraint_div(
879 __isl_keep isl_constraint *constraint, int pos);
880 void isl_div_get_constant(__isl_keep isl_div *div,
882 void isl_div_get_denominator(__isl_keep isl_div *div,
884 void isl_div_get_coefficient(__isl_keep isl_div *div,
885 enum isl_dim_type type, int pos, isl_int *v);
889 =head3 Unary Properties
895 The following functions test whether the given set or relation
896 contains any integer points. The ``fast'' variants do not perform
897 any computations, but simply check if the given set or relation
898 is already known to be empty.
900 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
901 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
902 int isl_set_is_empty(__isl_keep isl_set *set);
903 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
904 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
905 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
906 int isl_map_fast_is_empty(__isl_keep isl_map *map);
907 int isl_map_is_empty(__isl_keep isl_map *map);
908 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
912 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
913 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
914 int isl_set_fast_is_universe(__isl_keep isl_set *set);
916 =item * Single-valuedness
918 int isl_map_is_single_valued(__isl_keep isl_map *map);
922 int isl_map_is_bijective(__isl_keep isl_map *map);
926 =head3 Binary Properties
932 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
933 __isl_keep isl_set *set2);
934 int isl_set_is_equal(__isl_keep isl_set *set1,
935 __isl_keep isl_set *set2);
936 int isl_basic_map_is_equal(
937 __isl_keep isl_basic_map *bmap1,
938 __isl_keep isl_basic_map *bmap2);
939 int isl_map_is_equal(__isl_keep isl_map *map1,
940 __isl_keep isl_map *map2);
941 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
942 __isl_keep isl_map *map2);
943 int isl_union_map_is_equal(
944 __isl_keep isl_union_map *umap1,
945 __isl_keep isl_union_map *umap2);
949 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
950 __isl_keep isl_set *set2);
954 int isl_set_is_subset(__isl_keep isl_set *set1,
955 __isl_keep isl_set *set2);
956 int isl_set_is_strict_subset(
957 __isl_keep isl_set *set1,
958 __isl_keep isl_set *set2);
959 int isl_basic_map_is_subset(
960 __isl_keep isl_basic_map *bmap1,
961 __isl_keep isl_basic_map *bmap2);
962 int isl_basic_map_is_strict_subset(
963 __isl_keep isl_basic_map *bmap1,
964 __isl_keep isl_basic_map *bmap2);
965 int isl_map_is_subset(
966 __isl_keep isl_map *map1,
967 __isl_keep isl_map *map2);
968 int isl_map_is_strict_subset(
969 __isl_keep isl_map *map1,
970 __isl_keep isl_map *map2);
971 int isl_union_map_is_subset(
972 __isl_keep isl_union_map *umap1,
973 __isl_keep isl_union_map *umap2);
974 int isl_union_map_is_strict_subset(
975 __isl_keep isl_union_map *umap1,
976 __isl_keep isl_union_map *umap2);
980 =head2 Unary Operations
986 __isl_give isl_set *isl_set_complement(
987 __isl_take isl_set *set);
991 __isl_give isl_basic_map *isl_basic_map_reverse(
992 __isl_take isl_basic_map *bmap);
993 __isl_give isl_map *isl_map_reverse(
994 __isl_take isl_map *map);
995 __isl_give isl_union_map *isl_union_map_reverse(
996 __isl_take isl_union_map *umap);
1000 __isl_give isl_basic_set *isl_basic_set_project_out(
1001 __isl_take isl_basic_set *bset,
1002 enum isl_dim_type type, unsigned first, unsigned n);
1003 __isl_give isl_basic_map *isl_basic_map_project_out(
1004 __isl_take isl_basic_map *bmap,
1005 enum isl_dim_type type, unsigned first, unsigned n);
1006 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1007 enum isl_dim_type type, unsigned first, unsigned n);
1008 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1009 enum isl_dim_type type, unsigned first, unsigned n);
1010 __isl_give isl_basic_set *isl_basic_map_domain(
1011 __isl_take isl_basic_map *bmap);
1012 __isl_give isl_basic_set *isl_basic_map_range(
1013 __isl_take isl_basic_map *bmap);
1014 __isl_give isl_set *isl_map_domain(
1015 __isl_take isl_map *bmap);
1016 __isl_give isl_set *isl_map_range(
1017 __isl_take isl_map *map);
1018 __isl_give isl_union_set *isl_union_map_domain(
1019 __isl_take isl_union_map *umap);
1020 __isl_give isl_union_set *isl_union_map_range(
1021 __isl_take isl_union_map *umap);
1025 __isl_give isl_basic_set *isl_basic_map_deltas(
1026 __isl_take isl_basic_map *bmap);
1027 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1028 __isl_give isl_union_set *isl_union_map_deltas(
1029 __isl_take isl_union_map *umap);
1031 These functions return a (basic) set containing the differences
1032 between image elements and corresponding domain elements in the input.
1036 Simplify the representation of a set or relation by trying
1037 to combine pairs of basic sets or relations into a single
1038 basic set or relation.
1040 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1041 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1042 __isl_give isl_union_set *isl_union_set_coalesce(
1043 __isl_take isl_union_set *uset);
1044 __isl_give isl_union_map *isl_union_map_coalesce(
1045 __isl_take isl_union_map *umap);
1049 __isl_give isl_basic_set *isl_set_convex_hull(
1050 __isl_take isl_set *set);
1051 __isl_give isl_basic_map *isl_map_convex_hull(
1052 __isl_take isl_map *map);
1054 If the input set or relation has any existentially quantified
1055 variables, then the result of these operations is currently undefined.
1059 __isl_give isl_basic_set *isl_set_simple_hull(
1060 __isl_take isl_set *set);
1061 __isl_give isl_basic_map *isl_map_simple_hull(
1062 __isl_take isl_map *map);
1064 These functions compute a single basic set or relation
1065 that contains the whole input set or relation.
1066 In particular, the output is described by translates
1067 of the constraints describing the basic sets or relations in the input.
1071 (See \autoref{s:simple hull}.)
1077 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1078 __isl_take isl_basic_set *bset);
1079 __isl_give isl_basic_set *isl_set_affine_hull(
1080 __isl_take isl_set *set);
1081 __isl_give isl_union_set *isl_union_set_affine_hull(
1082 __isl_take isl_union_set *uset);
1083 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1084 __isl_take isl_basic_map *bmap);
1085 __isl_give isl_basic_map *isl_map_affine_hull(
1086 __isl_take isl_map *map);
1087 __isl_give isl_union_map *isl_union_map_affine_hull(
1088 __isl_take isl_union_map *umap);
1090 In case of union sets and relations, the affine hull is computed
1095 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1096 unsigned param, int *exact);
1098 Compute a parametric representation for all positive powers I<k> of C<map>.
1099 The power I<k> is equated to the parameter at position C<param>.
1100 The result may be an overapproximation. If the result is exact,
1101 then C<*exact> is set to C<1>.
1102 The current implementation only produces exact results for particular
1103 cases of piecewise translations (i.e., piecewise uniform dependences).
1105 =item * Transitive closure
1107 __isl_give isl_map *isl_map_transitive_closure(
1108 __isl_take isl_map *map, int *exact);
1109 __isl_give isl_union_map *isl_union_map_transitive_closure(
1110 __isl_take isl_union_map *umap, int *exact);
1112 Compute the transitive closure of C<map>.
1113 The result may be an overapproximation. If the result is known to be exact,
1114 then C<*exact> is set to C<1>.
1115 The current implementation only produces exact results for particular
1116 cases of piecewise translations (i.e., piecewise uniform dependences).
1118 =item * Reaching path lengths
1120 __isl_give isl_map *isl_map_reaching_path_lengths(
1121 __isl_take isl_map *map, int *exact);
1123 Compute a relation that maps each element in the range of C<map>
1124 to the lengths of all paths composed of edges in C<map> that
1125 end up in the given element.
1126 The result may be an overapproximation. If the result is known to be exact,
1127 then C<*exact> is set to C<1>.
1128 To compute the I<maximal> path length, the resulting relation
1129 should be postprocessed by C<isl_map_lexmax>.
1130 In particular, if the input relation is a dependence relation
1131 (mapping sources to sinks), then the maximal path length corresponds
1132 to the free schedule.
1133 Note, however, that C<isl_map_lexmax> expects the maximum to be
1134 finite, so if the path lengths are unbounded (possibly due to
1135 the overapproximation), then you will get an error message.
1139 =head2 Binary Operations
1141 The two arguments of a binary operation not only need to live
1142 in the same C<isl_ctx>, they currently also need to have
1143 the same (number of) parameters.
1145 =head3 Basic Operations
1149 =item * Intersection
1151 __isl_give isl_basic_set *isl_basic_set_intersect(
1152 __isl_take isl_basic_set *bset1,
1153 __isl_take isl_basic_set *bset2);
1154 __isl_give isl_set *isl_set_intersect(
1155 __isl_take isl_set *set1,
1156 __isl_take isl_set *set2);
1157 __isl_give isl_union_set *isl_union_set_intersect(
1158 __isl_take isl_union_set *uset1,
1159 __isl_take isl_union_set *uset2);
1160 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1161 __isl_take isl_basic_map *bmap,
1162 __isl_take isl_basic_set *bset);
1163 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1164 __isl_take isl_basic_map *bmap,
1165 __isl_take isl_basic_set *bset);
1166 __isl_give isl_basic_map *isl_basic_map_intersect(
1167 __isl_take isl_basic_map *bmap1,
1168 __isl_take isl_basic_map *bmap2);
1169 __isl_give isl_map *isl_map_intersect_domain(
1170 __isl_take isl_map *map,
1171 __isl_take isl_set *set);
1172 __isl_give isl_map *isl_map_intersect_range(
1173 __isl_take isl_map *map,
1174 __isl_take isl_set *set);
1175 __isl_give isl_map *isl_map_intersect(
1176 __isl_take isl_map *map1,
1177 __isl_take isl_map *map2);
1178 __isl_give isl_union_map *isl_union_map_intersect_domain(
1179 __isl_take isl_union_map *umap,
1180 __isl_take isl_union_set *uset);
1181 __isl_give isl_union_map *isl_union_map_intersect(
1182 __isl_take isl_union_map *umap1,
1183 __isl_take isl_union_map *umap2);
1187 __isl_give isl_set *isl_basic_set_union(
1188 __isl_take isl_basic_set *bset1,
1189 __isl_take isl_basic_set *bset2);
1190 __isl_give isl_map *isl_basic_map_union(
1191 __isl_take isl_basic_map *bmap1,
1192 __isl_take isl_basic_map *bmap2);
1193 __isl_give isl_set *isl_set_union(
1194 __isl_take isl_set *set1,
1195 __isl_take isl_set *set2);
1196 __isl_give isl_map *isl_map_union(
1197 __isl_take isl_map *map1,
1198 __isl_take isl_map *map2);
1199 __isl_give isl_union_set *isl_union_set_union(
1200 __isl_take isl_union_set *uset1,
1201 __isl_take isl_union_set *uset2);
1202 __isl_give isl_union_map *isl_union_map_union(
1203 __isl_take isl_union_map *umap1,
1204 __isl_take isl_union_map *umap2);
1206 =item * Set difference
1208 __isl_give isl_set *isl_set_subtract(
1209 __isl_take isl_set *set1,
1210 __isl_take isl_set *set2);
1211 __isl_give isl_map *isl_map_subtract(
1212 __isl_take isl_map *map1,
1213 __isl_take isl_map *map2);
1214 __isl_give isl_union_set *isl_union_set_subtract(
1215 __isl_take isl_union_set *uset1,
1216 __isl_take isl_union_set *uset2);
1217 __isl_give isl_union_map *isl_union_map_subtract(
1218 __isl_take isl_union_map *umap1,
1219 __isl_take isl_union_map *umap2);
1223 __isl_give isl_basic_set *isl_basic_set_apply(
1224 __isl_take isl_basic_set *bset,
1225 __isl_take isl_basic_map *bmap);
1226 __isl_give isl_set *isl_set_apply(
1227 __isl_take isl_set *set,
1228 __isl_take isl_map *map);
1229 __isl_give isl_union_set *isl_union_set_apply(
1230 __isl_take isl_union_set *uset,
1231 __isl_take isl_union_map *umap);
1232 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1233 __isl_take isl_basic_map *bmap1,
1234 __isl_take isl_basic_map *bmap2);
1235 __isl_give isl_basic_map *isl_basic_map_apply_range(
1236 __isl_take isl_basic_map *bmap1,
1237 __isl_take isl_basic_map *bmap2);
1238 __isl_give isl_map *isl_map_apply_domain(
1239 __isl_take isl_map *map1,
1240 __isl_take isl_map *map2);
1241 __isl_give isl_map *isl_map_apply_range(
1242 __isl_take isl_map *map1,
1243 __isl_take isl_map *map2);
1244 __isl_give isl_union_map *isl_union_map_apply_range(
1245 __isl_take isl_union_map *umap1,
1246 __isl_take isl_union_map *umap2);
1248 =item * Simplification
1250 __isl_give isl_basic_set *isl_basic_set_gist(
1251 __isl_take isl_basic_set *bset,
1252 __isl_take isl_basic_set *context);
1253 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1254 __isl_take isl_set *context);
1255 __isl_give isl_union_set *isl_union_set_gist(
1256 __isl_take isl_union_set *uset,
1257 __isl_take isl_union_set *context);
1258 __isl_give isl_basic_map *isl_basic_map_gist(
1259 __isl_take isl_basic_map *bmap,
1260 __isl_take isl_basic_map *context);
1261 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1262 __isl_take isl_map *context);
1263 __isl_give isl_union_map *isl_union_map_gist(
1264 __isl_take isl_union_map *umap,
1265 __isl_take isl_union_map *context);
1267 The gist operation returns a set or relation that has the
1268 same intersection with the context as the input set or relation.
1269 Any implicit equality in the intersection is made explicit in the result,
1270 while all inequalities that are redundant with respect to the intersection
1272 In case of union sets and relations, the gist operation is performed
1277 =head3 Lexicographic Optimization
1279 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1280 the following functions
1281 compute a set that contains the lexicographic minimum or maximum
1282 of the elements in C<set> (or C<bset>) for those values of the parameters
1283 that satisfy C<dom>.
1284 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1285 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1287 In other words, the union of the parameter values
1288 for which the result is non-empty and of C<*empty>
1291 __isl_give isl_set *isl_basic_set_partial_lexmin(
1292 __isl_take isl_basic_set *bset,
1293 __isl_take isl_basic_set *dom,
1294 __isl_give isl_set **empty);
1295 __isl_give isl_set *isl_basic_set_partial_lexmax(
1296 __isl_take isl_basic_set *bset,
1297 __isl_take isl_basic_set *dom,
1298 __isl_give isl_set **empty);
1299 __isl_give isl_set *isl_set_partial_lexmin(
1300 __isl_take isl_set *set, __isl_take isl_set *dom,
1301 __isl_give isl_set **empty);
1302 __isl_give isl_set *isl_set_partial_lexmax(
1303 __isl_take isl_set *set, __isl_take isl_set *dom,
1304 __isl_give isl_set **empty);
1306 Given a (basic) set C<set> (or C<bset>), the following functions simply
1307 return a set containing the lexicographic minimum or maximum
1308 of the elements in C<set> (or C<bset>).
1309 In case of union sets, the optimum is computed per dimension.
1311 __isl_give isl_set *isl_basic_set_lexmin(
1312 __isl_take isl_basic_set *bset);
1313 __isl_give isl_set *isl_basic_set_lexmax(
1314 __isl_take isl_basic_set *bset);
1315 __isl_give isl_set *isl_set_lexmin(
1316 __isl_take isl_set *set);
1317 __isl_give isl_set *isl_set_lexmax(
1318 __isl_take isl_set *set);
1319 __isl_give isl_union_set *isl_union_set_lexmin(
1320 __isl_take isl_union_set *uset);
1321 __isl_give isl_union_set *isl_union_set_lexmax(
1322 __isl_take isl_union_set *uset);
1324 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1325 the following functions
1326 compute a relation that maps each element of C<dom>
1327 to the single lexicographic minimum or maximum
1328 of the elements that are associated to that same
1329 element in C<map> (or C<bmap>).
1330 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1331 that contains the elements in C<dom> that do not map
1332 to any elements in C<map> (or C<bmap>).
1333 In other words, the union of the domain of the result and of C<*empty>
1336 __isl_give isl_map *isl_basic_map_partial_lexmax(
1337 __isl_take isl_basic_map *bmap,
1338 __isl_take isl_basic_set *dom,
1339 __isl_give isl_set **empty);
1340 __isl_give isl_map *isl_basic_map_partial_lexmin(
1341 __isl_take isl_basic_map *bmap,
1342 __isl_take isl_basic_set *dom,
1343 __isl_give isl_set **empty);
1344 __isl_give isl_map *isl_map_partial_lexmax(
1345 __isl_take isl_map *map, __isl_take isl_set *dom,
1346 __isl_give isl_set **empty);
1347 __isl_give isl_map *isl_map_partial_lexmin(
1348 __isl_take isl_map *map, __isl_take isl_set *dom,
1349 __isl_give isl_set **empty);
1351 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1352 return a map mapping each element in the domain of
1353 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1354 of all elements associated to that element.
1355 In case of union relations, the optimum is computed per dimension.
1357 __isl_give isl_map *isl_basic_map_lexmin(
1358 __isl_take isl_basic_map *bmap);
1359 __isl_give isl_map *isl_basic_map_lexmax(
1360 __isl_take isl_basic_map *bmap);
1361 __isl_give isl_map *isl_map_lexmin(
1362 __isl_take isl_map *map);
1363 __isl_give isl_map *isl_map_lexmax(
1364 __isl_take isl_map *map);
1365 __isl_give isl_union_map *isl_union_map_lexmin(
1366 __isl_take isl_union_map *umap);
1367 __isl_give isl_union_map *isl_union_map_lexmax(
1368 __isl_take isl_union_map *umap);
1372 Points are elements of a set. They can be used to construct
1373 simple sets (boxes) or they can be used to represent the
1374 individual elements of a set.
1375 The zero point (the origin) can be created using
1377 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1379 The coordinates of a point can be inspected, set and changed
1382 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1383 enum isl_dim_type type, int pos, isl_int *v);
1384 __isl_give isl_point *isl_point_set_coordinate(
1385 __isl_take isl_point *pnt,
1386 enum isl_dim_type type, int pos, isl_int v);
1388 __isl_give isl_point *isl_point_add_ui(
1389 __isl_take isl_point *pnt,
1390 enum isl_dim_type type, int pos, unsigned val);
1391 __isl_give isl_point *isl_point_sub_ui(
1392 __isl_take isl_point *pnt,
1393 enum isl_dim_type type, int pos, unsigned val);
1395 Points can be copied or freed using
1397 __isl_give isl_point *isl_point_copy(
1398 __isl_keep isl_point *pnt);
1399 void isl_point_free(__isl_take isl_point *pnt);
1401 A singleton set can be created from a point using
1403 __isl_give isl_set *isl_set_from_point(
1404 __isl_take isl_point *pnt);
1406 and a box can be created from two opposite extremal points using
1408 __isl_give isl_set *isl_set_box_from_points(
1409 __isl_take isl_point *pnt1,
1410 __isl_take isl_point *pnt2);
1412 All elements of a B<bounded> (union) set can be enumerated using
1413 the following functions.
1415 int isl_set_foreach_point(__isl_keep isl_set *set,
1416 int (*fn)(__isl_take isl_point *pnt, void *user),
1418 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1419 int (*fn)(__isl_take isl_point *pnt, void *user),
1422 The function C<fn> is called for each integer point in
1423 C<set> with as second argument the last argument of
1424 the C<isl_set_foreach_point> call. The function C<fn>
1425 should return C<0> on success and C<-1> on failure.
1426 In the latter case, C<isl_set_foreach_point> will stop
1427 enumerating and return C<-1> as well.
1428 If the enumeration is performed successfully and to completion,
1429 then C<isl_set_foreach_point> returns C<0>.
1431 To obtain a single point of a set, use
1433 __isl_give isl_point *isl_set_sample_point(
1434 __isl_take isl_set *set);
1436 If C<set> does not contain any (integer) points, then the
1437 resulting point will be ``void'', a property that can be
1440 int isl_point_is_void(__isl_keep isl_point *pnt);
1442 =head2 Piecewise Quasipolynomials
1444 A piecewise quasipolynomial is a particular kind of function that maps
1445 a parametric point to a rational value.
1446 More specifically, a quasipolynomial is a polynomial expression in greatest
1447 integer parts of affine expressions of parameters and variables.
1448 A piecewise quasipolynomial is a subdivision of a given parametric
1449 domain into disjoint cells with a quasipolynomial associated to
1450 each cell. The value of the piecewise quasipolynomial at a given
1451 point is the value of the quasipolynomial associated to the cell
1452 that contains the point. Outside of the union of cells,
1453 the value is assumed to be zero.
1454 For example, the piecewise quasipolynomial
1456 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1458 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1459 A given piecewise quasipolynomial has a fixed domain dimension.
1460 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1461 defined over different domains.
1462 Piecewise quasipolynomials are mainly used by the C<barvinok>
1463 library for representing the number of elements in a parametric set or map.
1464 For example, the piecewise quasipolynomial above represents
1465 the number of points in the map
1467 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1469 =head3 Printing (Piecewise) Quasipolynomials
1471 Quasipolynomials and piecewise quasipolynomials can be printed
1472 using the following functions.
1474 __isl_give isl_printer *isl_printer_print_qpolynomial(
1475 __isl_take isl_printer *p,
1476 __isl_keep isl_qpolynomial *qp);
1478 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1479 __isl_take isl_printer *p,
1480 __isl_keep isl_pw_qpolynomial *pwqp);
1482 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1483 __isl_take isl_printer *p,
1484 __isl_keep isl_union_pw_qpolynomial *upwqp);
1486 The output format of the printer
1487 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1488 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1491 =head3 Creating New (Piecewise) Quasipolynomials
1493 Some simple quasipolynomials can be created using the following functions.
1494 More complicated quasipolynomials can be created by applying
1495 operations such as addition and multiplication
1496 on the resulting quasipolynomials
1498 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1499 __isl_take isl_dim *dim);
1500 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1501 __isl_take isl_dim *dim);
1502 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1503 __isl_take isl_dim *dim);
1504 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1505 __isl_take isl_dim *dim);
1506 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1507 __isl_take isl_dim *dim,
1508 const isl_int n, const isl_int d);
1509 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1510 __isl_take isl_div *div);
1511 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1512 __isl_take isl_dim *dim,
1513 enum isl_dim_type type, unsigned pos);
1515 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1516 with a single cell can be created using the following functions.
1517 Multiple of these single cell piecewise quasipolynomials can
1518 be combined to create more complicated piecewise quasipolynomials.
1520 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1521 __isl_take isl_dim *dim);
1522 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1523 __isl_take isl_set *set,
1524 __isl_take isl_qpolynomial *qp);
1526 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1527 __isl_take isl_dim *dim);
1528 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
1529 __isl_take isl_pw_qpolynomial *pwqp);
1530 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
1531 __isl_take isl_union_pw_qpolynomial *upwqp,
1532 __isl_take isl_pw_qpolynomial *pwqp);
1534 Quasipolynomials can be copied and freed again using the following
1537 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1538 __isl_keep isl_qpolynomial *qp);
1539 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1541 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1542 __isl_keep isl_pw_qpolynomial *pwqp);
1543 void isl_pw_qpolynomial_free(
1544 __isl_take isl_pw_qpolynomial *pwqp);
1546 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
1547 __isl_keep isl_union_pw_qpolynomial *upwqp);
1548 void isl_union_pw_qpolynomial_free(
1549 __isl_take isl_union_pw_qpolynomial *upwqp);
1551 =head3 Inspecting (Piecewise) Quasipolynomials
1553 To iterate over all piecewise quasipolynomials in a union
1554 piecewise quasipolynomial, use the following function
1556 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
1557 __isl_keep isl_union_pw_qpolynomial *upwqp,
1558 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
1561 To iterate over the cells in a piecewise quasipolynomial,
1562 use either of the following two functions
1564 int isl_pw_qpolynomial_foreach_piece(
1565 __isl_keep isl_pw_qpolynomial *pwqp,
1566 int (*fn)(__isl_take isl_set *set,
1567 __isl_take isl_qpolynomial *qp,
1568 void *user), void *user);
1569 int isl_pw_qpolynomial_foreach_lifted_piece(
1570 __isl_keep isl_pw_qpolynomial *pwqp,
1571 int (*fn)(__isl_take isl_set *set,
1572 __isl_take isl_qpolynomial *qp,
1573 void *user), void *user);
1575 As usual, the function C<fn> should return C<0> on success
1576 and C<-1> on failure. The difference between
1577 C<isl_pw_qpolynomial_foreach_piece> and
1578 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1579 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1580 compute unique representations for all existentially quantified
1581 variables and then turn these existentially quantified variables
1582 into extra set variables, adapting the associated quasipolynomial
1583 accordingly. This means that the C<set> passed to C<fn>
1584 will not have any existentially quantified variables, but that
1585 the dimensions of the sets may be different for different
1586 invocations of C<fn>.
1588 To iterate over all terms in a quasipolynomial,
1591 int isl_qpolynomial_foreach_term(
1592 __isl_keep isl_qpolynomial *qp,
1593 int (*fn)(__isl_take isl_term *term,
1594 void *user), void *user);
1596 The terms themselves can be inspected and freed using
1599 unsigned isl_term_dim(__isl_keep isl_term *term,
1600 enum isl_dim_type type);
1601 void isl_term_get_num(__isl_keep isl_term *term,
1603 void isl_term_get_den(__isl_keep isl_term *term,
1605 int isl_term_get_exp(__isl_keep isl_term *term,
1606 enum isl_dim_type type, unsigned pos);
1607 __isl_give isl_div *isl_term_get_div(
1608 __isl_keep isl_term *term, unsigned pos);
1609 void isl_term_free(__isl_take isl_term *term);
1611 Each term is a product of parameters, set variables and
1612 integer divisions. The function C<isl_term_get_exp>
1613 returns the exponent of a given dimensions in the given term.
1614 The C<isl_int>s in the arguments of C<isl_term_get_num>
1615 and C<isl_term_get_den> need to have been initialized
1616 using C<isl_int_init> before calling these functions.
1618 =head3 Properties of (Piecewise) Quasipolynomials
1620 To check whether a quasipolynomial is actually a constant,
1621 use the following function.
1623 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1624 isl_int *n, isl_int *d);
1626 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1627 then the numerator and denominator of the constant
1628 are returned in C<*n> and C<*d>, respectively.
1630 =head3 Operations on (Piecewise) Quasipolynomials
1632 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1633 __isl_take isl_qpolynomial *qp);
1634 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1635 __isl_take isl_qpolynomial *qp1,
1636 __isl_take isl_qpolynomial *qp2);
1637 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1638 __isl_take isl_qpolynomial *qp1,
1639 __isl_take isl_qpolynomial *qp2);
1640 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1641 __isl_take isl_qpolynomial *qp1,
1642 __isl_take isl_qpolynomial *qp2);
1644 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1645 __isl_take isl_pw_qpolynomial *pwqp1,
1646 __isl_take isl_pw_qpolynomial *pwqp2);
1647 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1648 __isl_take isl_pw_qpolynomial *pwqp1,
1649 __isl_take isl_pw_qpolynomial *pwqp2);
1650 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1651 __isl_take isl_pw_qpolynomial *pwqp1,
1652 __isl_take isl_pw_qpolynomial *pwqp2);
1653 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1654 __isl_take isl_pw_qpolynomial *pwqp);
1655 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1656 __isl_take isl_pw_qpolynomial *pwqp1,
1657 __isl_take isl_pw_qpolynomial *pwqp2);
1659 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
1660 __isl_take isl_union_pw_qpolynomial *upwqp1,
1661 __isl_take isl_union_pw_qpolynomial *upwqp2);
1662 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
1663 __isl_take isl_union_pw_qpolynomial *upwqp1,
1664 __isl_take isl_union_pw_qpolynomial *upwqp2);
1665 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
1666 __isl_take isl_union_pw_qpolynomial *upwqp1,
1667 __isl_take isl_union_pw_qpolynomial *upwqp2);
1669 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1670 __isl_take isl_pw_qpolynomial *pwqp,
1671 __isl_take isl_point *pnt);
1673 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
1674 __isl_take isl_union_pw_qpolynomial *upwqp,
1675 __isl_take isl_point *pnt);
1677 __isl_give isl_set *isl_pw_qpolynomial_domain(
1678 __isl_take isl_pw_qpolynomial *pwqp);
1679 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1680 __isl_take isl_pw_qpolynomial *pwpq,
1681 __isl_take isl_set *set);
1683 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
1684 __isl_take isl_union_pw_qpolynomial *upwqp);
1685 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
1686 __isl_take isl_union_pw_qpolynomial *upwpq,
1687 __isl_take isl_union_set *uset);
1689 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
1690 __isl_take isl_union_pw_qpolynomial *upwqp);
1692 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1693 __isl_take isl_pw_qpolynomial *pwqp,
1694 __isl_take isl_set *context);
1696 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
1697 __isl_take isl_union_pw_qpolynomial *upwqp,
1698 __isl_take isl_union_set *context);
1700 The gist operation applies the gist operation to each of
1701 the cells in the domain of the input piecewise quasipolynomial.
1702 In future, the operation will also exploit the context
1703 to simplify the quasipolynomials associated to each cell.
1705 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1707 A piecewise quasipolynomial reduction is a piecewise
1708 reduction (or fold) of quasipolynomials.
1709 In particular, the reduction can be maximum or a minimum.
1710 The objects are mainly used to represent the result of
1711 an upper or lower bound on a quasipolynomial over its domain,
1712 i.e., as the result of the following function.
1714 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1715 __isl_take isl_pw_qpolynomial *pwqp,
1716 enum isl_fold type, int *tight);
1718 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
1719 __isl_take isl_union_pw_qpolynomial *upwqp,
1720 enum isl_fold type, int *tight);
1722 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1723 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1724 is the returned bound is known be tight, i.e., for each value
1725 of the parameters there is at least
1726 one element in the domain that reaches the bound.
1728 A (piecewise) quasipolynomial reduction can be copied or freed using the
1729 following functions.
1731 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1732 __isl_keep isl_qpolynomial_fold *fold);
1733 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1734 __isl_keep isl_pw_qpolynomial_fold *pwf);
1735 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
1736 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1737 void isl_qpolynomial_fold_free(
1738 __isl_take isl_qpolynomial_fold *fold);
1739 void isl_pw_qpolynomial_fold_free(
1740 __isl_take isl_pw_qpolynomial_fold *pwf);
1741 void isl_union_pw_qpolynomial_fold_free(
1742 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1744 =head3 Printing Piecewise Quasipolynomial Reductions
1746 Piecewise quasipolynomial reductions can be printed
1747 using the following function.
1749 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1750 __isl_take isl_printer *p,
1751 __isl_keep isl_pw_qpolynomial_fold *pwf);
1752 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
1753 __isl_take isl_printer *p,
1754 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
1756 For C<isl_printer_print_pw_qpolynomial_fold>,
1757 output format of the printer
1758 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1759 For C<isl_printer_print_union_pw_qpolynomial_fold>,
1760 output format of the printer
1761 needs to be set to either C<ISL_FORMAT_ISL>.
1763 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1765 To iterate over all piecewise quasipolynomial reductions in a union
1766 piecewise quasipolynomial reduction, use the following function
1768 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
1769 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
1770 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
1771 void *user), void *user);
1773 To iterate over the cells in a piecewise quasipolynomial reduction,
1774 use either of the following two functions
1776 int isl_pw_qpolynomial_fold_foreach_piece(
1777 __isl_keep isl_pw_qpolynomial_fold *pwf,
1778 int (*fn)(__isl_take isl_set *set,
1779 __isl_take isl_qpolynomial_fold *fold,
1780 void *user), void *user);
1781 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1782 __isl_keep isl_pw_qpolynomial_fold *pwf,
1783 int (*fn)(__isl_take isl_set *set,
1784 __isl_take isl_qpolynomial_fold *fold,
1785 void *user), void *user);
1787 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
1788 of the difference between these two functions.
1790 To iterate over all quasipolynomials in a reduction, use
1792 int isl_qpolynomial_fold_foreach_qpolynomial(
1793 __isl_keep isl_qpolynomial_fold *fold,
1794 int (*fn)(__isl_take isl_qpolynomial *qp,
1795 void *user), void *user);
1797 =head3 Operations on Piecewise Quasipolynomial Reductions
1799 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
1800 __isl_take isl_pw_qpolynomial_fold *pwf1,
1801 __isl_take isl_pw_qpolynomial_fold *pwf2);
1803 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_add(
1804 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
1805 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
1807 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
1808 __isl_take isl_pw_qpolynomial_fold *pwf,
1809 __isl_take isl_point *pnt);
1811 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
1812 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1813 __isl_take isl_point *pnt);
1815 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
1816 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1817 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
1818 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1819 __isl_take isl_union_set *uset);
1821 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
1822 __isl_take isl_pw_qpolynomial_fold *pwf);
1824 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
1825 __isl_take isl_union_pw_qpolynomial_fold *upwf);
1827 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
1828 __isl_take isl_pw_qpolynomial_fold *pwf,
1829 __isl_take isl_set *context);
1831 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
1832 __isl_take isl_union_pw_qpolynomial_fold *upwf,
1833 __isl_take isl_union_set *context);
1835 The gist operation applies the gist operation to each of
1836 the cells in the domain of the input piecewise quasipolynomial reduction.
1837 In future, the operation will also exploit the context
1838 to simplify the quasipolynomial reductions associated to each cell.
1840 =head2 Dependence Analysis
1842 C<isl> contains specialized functionality for performing
1843 array dataflow analysis. That is, given a I<sink> access relation
1844 and a collection of possible I<source> access relations,
1845 C<isl> can compute relations that describe
1846 for each iteration of the sink access, which iteration
1847 of which of the source access relations was the last
1848 to access the same data element before the given iteration
1850 To compute standard flow dependences, the sink should be
1851 a read, while the sources should be writes.
1852 If any of the source accesses are marked as being I<may>
1853 accesses, then there will be a dependence to the last
1854 I<must> access B<and> to any I<may> access that follows
1855 this last I<must> access.
1856 In particular, if I<all> sources are I<may> accesses,
1857 then memory based dependence analysis is performed.
1858 If, on the other hand, all sources are I<must> accesses,
1859 then value based dependence analysis is performed.
1861 #include <isl_flow.h>
1863 __isl_give isl_access_info *isl_access_info_alloc(
1864 __isl_take isl_map *sink,
1865 void *sink_user, isl_access_level_before fn,
1867 __isl_give isl_access_info *isl_access_info_add_source(
1868 __isl_take isl_access_info *acc,
1869 __isl_take isl_map *source, int must,
1872 __isl_give isl_flow *isl_access_info_compute_flow(
1873 __isl_take isl_access_info *acc);
1875 int isl_flow_foreach(__isl_keep isl_flow *deps,
1876 int (*fn)(__isl_take isl_map *dep, int must,
1877 void *dep_user, void *user),
1879 __isl_give isl_set *isl_flow_get_no_source(
1880 __isl_keep isl_flow *deps, int must);
1881 void isl_flow_free(__isl_take isl_flow *deps);
1883 The function C<isl_access_info_compute_flow> performs the actual
1884 dependence analysis. The other functions are used to construct
1885 the input for this function or to read off the output.
1887 The input is collected in an C<isl_access_info>, which can
1888 be created through a call to C<isl_access_info_alloc>.
1889 The arguments to this functions are the sink access relation
1890 C<sink>, a token C<sink_user> used to identify the sink
1891 access to the user, a callback function for specifying the
1892 relative order of source and sink accesses, and the number
1893 of source access relations that will be added.
1894 The callback function has type C<int (*)(void *first, void *second)>.
1895 The function is called with two user supplied tokens identifying
1896 either a source or the sink and it should return the shared nesting
1897 level and the relative order of the two accesses.
1898 In particular, let I<n> be the number of loops shared by
1899 the two accesses. If C<first> precedes C<second> textually,
1900 then the function should return I<2 * n + 1>; otherwise,
1901 it should return I<2 * n>.
1902 The sources can be added to the C<isl_access_info> by performing
1903 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1904 C<must> indicates whether the source is a I<must> access
1905 or a I<may> access. Note that a multi-valued access relation
1906 should only be marked I<must> if every iteration in the domain
1907 of the relation accesses I<all> elements in its image.
1908 The C<source_user> token is again used to identify
1909 the source access. The range of the source access relation
1910 C<source> should have the same dimension as the range
1911 of the sink access relation.
1913 The result of the dependence analysis is collected in an
1914 C<isl_flow>. There may be elements in the domain of
1915 the sink access for which no preceding source access could be
1916 found or for which all preceding sources are I<may> accesses.
1917 The sets of these elements can be obtained through
1918 calls to C<isl_flow_get_no_source>, the first with C<must> set
1919 and the second with C<must> unset.
1920 In the case of standard flow dependence analysis,
1921 with the sink a read and the sources I<must> writes,
1922 the first set corresponds to the reads from uninitialized
1923 array elements and the second set is empty.
1924 The actual flow dependences can be extracted using
1925 C<isl_flow_foreach>. This function will call the user-specified
1926 callback function C<fn> for each B<non-empty> dependence between
1927 a source and the sink. The callback function is called
1928 with four arguments, the actual flow dependence relation
1929 mapping source iterations to sink iterations, a boolean that
1930 indicates whether it is a I<must> or I<may> dependence, a token
1931 identifying the source and an additional C<void *> with value
1932 equal to the third argument of the C<isl_flow_foreach> call.
1933 A dependence is marked I<must> if it originates from a I<must>
1934 source and if it is not followed by any I<may> sources.
1936 After finishing with an C<isl_flow>, the user should call
1937 C<isl_flow_free> to free all associated memory.
1939 =head2 Parametric Vertex Enumeration
1941 The parametric vertex enumeration described in this section
1942 is mainly intended to be used internally and by the C<barvinok>
1945 #include <isl_vertices.h>
1946 __isl_give isl_vertices *isl_basic_set_compute_vertices(
1947 __isl_keep isl_basic_set *bset);
1949 The function C<isl_basic_set_compute_vertices> performs the
1950 actual computation of the parametric vertices and the chamber
1951 decomposition and store the result in an C<isl_vertices> object.
1952 This information can be queried by either iterating over all
1953 the vertices or iterating over all the chambers or cells
1954 and then iterating over all vertices that are active on the chamber.
1956 int isl_vertices_foreach_vertex(
1957 __isl_keep isl_vertices *vertices,
1958 int (*fn)(__isl_take isl_vertex *vertex, void *user),
1961 int isl_vertices_foreach_cell(
1962 __isl_keep isl_vertices *vertices,
1963 int (*fn)(__isl_take isl_cell *cell, void *user),
1965 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
1966 int (*fn)(__isl_take isl_vertex *vertex, void *user),
1969 Other operations that can be performed on an C<isl_vertices> object are
1972 isl_ctx *isl_vertices_get_ctx(
1973 __isl_keep isl_vertices *vertices);
1974 int isl_vertices_get_n_vertices(
1975 __isl_keep isl_vertices *vertices);
1976 void isl_vertices_free(__isl_take isl_vertices *vertices);
1978 Vertices can be inspected and destroyed using the following functions.
1980 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
1981 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
1982 __isl_give isl_basic_set *isl_vertex_get_domain(
1983 __isl_keep isl_vertex *vertex);
1984 __isl_give isl_basic_set *isl_vertex_get_expr(
1985 __isl_keep isl_vertex *vertex);
1986 void isl_vertex_free(__isl_take isl_vertex *vertex);
1988 C<isl_vertex_get_expr> returns a singleton parametric set describing
1989 the vertex, while C<isl_vertex_get_domain> returns the activity domain
1991 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
1992 B<rational> basic sets, so they should mainly be used for inspection
1993 and should not be mixed with integer sets.
1995 Chambers can be inspected and destroyed using the following functions.
1997 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
1998 __isl_give isl_basic_set *isl_cell_get_domain(
1999 __isl_keep isl_cell *cell);
2000 void isl_cell_free(__isl_take isl_cell *cell);
2004 Although C<isl> is mainly meant to be used as a library,
2005 it also contains some basic applications that use some
2006 of the functionality of C<isl>.
2007 The input may be specified in either the L<isl format>
2008 or the L<PolyLib format>.
2010 =head2 C<isl_polyhedron_sample>
2012 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2013 an integer element of the polyhedron, if there is any.
2014 The first column in the output is the denominator and is always
2015 equal to 1. If the polyhedron contains no integer points,
2016 then a vector of length zero is printed.
2020 C<isl_pip> takes the same input as the C<example> program
2021 from the C<piplib> distribution, i.e., a set of constraints
2022 on the parameters, a line contains only -1 and finally a set
2023 of constraints on a parametric polyhedron.
2024 The coefficients of the parameters appear in the last columns
2025 (but before the final constant column).
2026 The output is the lexicographic minimum of the parametric polyhedron.
2027 As C<isl> currently does not have its own output format, the output
2028 is just a dump of the internal state.
2030 =head2 C<isl_polyhedron_minimize>
2032 C<isl_polyhedron_minimize> computes the minimum of some linear
2033 or affine objective function over the integer points in a polyhedron.
2034 If an affine objective function
2035 is given, then the constant should appear in the last column.
2037 =head2 C<isl_polytope_scan>
2039 Given a polytope, C<isl_polytope_scan> prints
2040 all integer points in the polytope.
2042 =head1 C<isl-polylib>
2044 The C<isl-polylib> library provides the following functions for converting
2045 between C<isl> objects and C<PolyLib> objects.
2046 The library is distributed separately for licensing reasons.
2048 #include <isl_set_polylib.h>
2049 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2050 Polyhedron *P, __isl_take isl_dim *dim);
2051 Polyhedron *isl_basic_set_to_polylib(
2052 __isl_keep isl_basic_set *bset);
2053 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2054 __isl_take isl_dim *dim);
2055 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2057 #include <isl_map_polylib.h>
2058 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2059 Polyhedron *P, __isl_take isl_dim *dim);
2060 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2061 __isl_take isl_dim *dim);
2062 Polyhedron *isl_basic_map_to_polylib(
2063 __isl_keep isl_basic_map *bmap);
2064 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);