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.
22 The source of C<isl> can be obtained either as a tarball
23 or from the git repository. Both are available from
24 L<http://freshmeat.net/projects/isl/>.
25 The installation process depends on how you obtained
28 =head2 Installation from the git repository
32 =item 1 Clone or update the repository
34 The first time the source is obtained, you need to clone
37 git clone git://repo.or.cz/isl.git
39 To obtain updates, you need to pull in the latest changes
43 =item 2 Get submodule (optional)
45 C<isl> can optionally use the C<piplib> library and provides
46 this library as a submodule. If you want to use it, then
47 after you have cloned C<isl>, you need to grab the submodules
52 To obtain updates, you only need
56 Note that C<isl> currently does not use any C<piplib>
57 functionality by default.
59 =item 3 Generate C<configure>
65 After performing the above steps, continue
66 with the L<Common installation instructions>.
68 =head2 Common installation instructions
74 Building C<isl> requires C<GMP>, including its headers files.
75 Your distribution may not provide these header files by default
76 and you may need to install a package called C<gmp-devel> or something
77 similar. Alternatively, C<GMP> can be built from
78 source, available from L<http://gmplib.org/>.
82 C<isl> uses the standard C<autoconf> C<configure> script.
87 optionally followed by some configure options.
88 A complete list of options can be obtained by running
92 Below we discuss some of the more common options.
94 C<isl> can optionally use C<piplib>, but no
95 C<piplib> functionality is currently used by default.
96 The C<--with-piplib> option can
97 be used to specify which C<piplib>
98 library to use, either an installed version (C<system>),
99 an externally built version (C<build>)
100 or no version (C<no>). The option C<build> is mostly useful
101 in C<configure> scripts of larger projects that bundle both C<isl>
108 Installation prefix for C<isl>
110 =item C<--with-gmp-prefix>
112 Installation prefix for C<GMP> (architecture-independent files).
114 =item C<--with-gmp-exec-prefix>
116 Installation prefix for C<GMP> (architecture-dependent files).
118 =item C<--with-piplib>
120 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
122 =item C<--with-piplib-prefix>
124 Installation prefix for C<system> C<piplib> (architecture-independent files).
126 =item C<--with-piplib-exec-prefix>
128 Installation prefix for C<system> C<piplib> (architecture-dependent files).
130 =item C<--with-piplib-builddir>
132 Location where C<build> C<piplib> was built.
140 =item 4 Install (optional)
148 =head2 Initialization
150 All manipulations of integer sets and relations occur within
151 the context of an C<isl_ctx>.
152 A given C<isl_ctx> can only be used within a single thread.
153 All arguments of a function are required to have been allocated
154 within the same context.
155 There are currently no functions available for moving an object
156 from one C<isl_ctx> to another C<isl_ctx>. This means that
157 there is currently no way of safely moving an object from one
158 thread to another, unless the whole C<isl_ctx> is moved.
160 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
161 freed using C<isl_ctx_free>.
162 All objects allocated within an C<isl_ctx> should be freed
163 before the C<isl_ctx> itself is freed.
165 isl_ctx *isl_ctx_alloc();
166 void isl_ctx_free(isl_ctx *ctx);
170 All operations on integers, mainly the coefficients
171 of the constraints describing the sets and relations,
172 are performed in exact integer arithmetic using C<GMP>.
173 However, to allow future versions of C<isl> to optionally
174 support fixed integer arithmetic, all calls to C<GMP>
175 are wrapped inside C<isl> specific macros.
176 The basic type is C<isl_int> and the following operations
177 are available on this type.
178 The meanings of these operations are essentially the same
179 as their C<GMP> C<mpz_> counterparts.
180 As always with C<GMP> types, C<isl_int>s need to be
181 initialized with C<isl_int_init> before they can be used
182 and they need to be released with C<isl_int_clear>
187 =item isl_int_init(i)
189 =item isl_int_clear(i)
191 =item isl_int_set(r,i)
193 =item isl_int_set_si(r,i)
195 =item isl_int_abs(r,i)
197 =item isl_int_neg(r,i)
199 =item isl_int_swap(i,j)
201 =item isl_int_swap_or_set(i,j)
203 =item isl_int_add_ui(r,i,j)
205 =item isl_int_sub_ui(r,i,j)
207 =item isl_int_add(r,i,j)
209 =item isl_int_sub(r,i,j)
211 =item isl_int_mul(r,i,j)
213 =item isl_int_mul_ui(r,i,j)
215 =item isl_int_addmul(r,i,j)
217 =item isl_int_submul(r,i,j)
219 =item isl_int_gcd(r,i,j)
221 =item isl_int_lcm(r,i,j)
223 =item isl_int_divexact(r,i,j)
225 =item isl_int_cdiv_q(r,i,j)
227 =item isl_int_fdiv_q(r,i,j)
229 =item isl_int_fdiv_r(r,i,j)
231 =item isl_int_fdiv_q_ui(r,i,j)
233 =item isl_int_read(r,s)
235 =item isl_int_print(out,i,width)
239 =item isl_int_cmp(i,j)
241 =item isl_int_cmp_si(i,si)
243 =item isl_int_eq(i,j)
245 =item isl_int_ne(i,j)
247 =item isl_int_lt(i,j)
249 =item isl_int_le(i,j)
251 =item isl_int_gt(i,j)
253 =item isl_int_ge(i,j)
255 =item isl_int_abs_eq(i,j)
257 =item isl_int_abs_ne(i,j)
259 =item isl_int_abs_lt(i,j)
261 =item isl_int_abs_gt(i,j)
263 =item isl_int_abs_ge(i,j)
265 =item isl_int_is_zero(i)
267 =item isl_int_is_one(i)
269 =item isl_int_is_negone(i)
271 =item isl_int_is_pos(i)
273 =item isl_int_is_neg(i)
275 =item isl_int_is_nonpos(i)
277 =item isl_int_is_nonneg(i)
279 =item isl_int_is_divisible_by(i,j)
283 =head2 Sets and Relations
285 C<isl> uses four types of objects for representing sets and relations,
286 C<isl_basic_set>, C<isl_basic_map>, C<isl_set> and C<isl_map>.
287 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
288 can be described as a conjunction of affine constraints, while
289 C<isl_set> and C<isl_map> represent unions of
290 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
291 The difference between sets and relations (maps) is that sets have
292 one set of variables, while relations have two sets of variables,
293 input variables and output variables.
295 =head2 Memory Management
297 Since a high-level operation on sets and/or relations usually involves
298 several substeps and since the user is usually not interested in
299 the intermediate results, most functions that return a new object
300 will also release all the objects passed as arguments.
301 If the user still wants to use one or more of these arguments
302 after the function call, she should pass along a copy of the
303 object rather than the object itself.
304 The user is then responsible for make sure that the original
305 object gets used somewhere else or is explicitly freed.
307 The arguments and return values of all documents functions are
308 annotated to make clear which arguments are released and which
309 arguments are preserved. In particular, the following annotations
316 C<__isl_give> means that a new object is returned.
317 The user should make sure that the returned pointer is
318 used exactly once as a value for an C<__isl_take> argument.
319 In between, it can be used as a value for as many
320 C<__isl_keep> arguments as the user likes.
321 There is one exception, and that is the case where the
322 pointer returned is C<NULL>. Is this case, the user
323 is free to use it as an C<__isl_take> argument or not.
327 C<__isl_take> means that the object the argument points to
328 is taken over by the function and may no longer be used
329 by the user as an argument to any other function.
330 The pointer value must be one returned by a function
331 returning an C<__isl_give> pointer.
332 If the user passes in a C<NULL> value, then this will
333 be treated as an error in the sense that the function will
334 not perform its usual operation. However, it will still
335 make sure that all the the other C<__isl_take> arguments
340 C<__isl_keep> means that the function will only use the object
341 temporarily. After the function has finished, the user
342 can still use it as an argument to other functions.
343 A C<NULL> value will be treated in the same way as
344 a C<NULL> value for an C<__isl_take> argument.
348 =head2 Dimension Specifications
350 Whenever a new set or relation is created from scratch,
351 its dimension needs to be specified using an C<isl_dim>.
354 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
355 unsigned nparam, unsigned n_in, unsigned n_out);
356 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
357 unsigned nparam, unsigned dim);
358 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
359 void isl_dim_free(__isl_take isl_dim *dim);
360 unsigned isl_dim_size(__isl_keep isl_dim *dim,
361 enum isl_dim_type type);
363 The dimension specification used for creating a set
364 needs to be created using C<isl_dim_set_alloc>, while
365 that for creating a relation
366 needs to be created using C<isl_dim_alloc>.
367 C<isl_dim_size> can be used
368 to find out the number of dimensions of each type in
369 a dimension specification, where type may be
370 C<isl_dim_param>, C<isl_dim_in> (only for relations),
371 C<isl_dim_out> (only for relations), C<isl_dim_set>
372 (only for sets) or C<isl_dim_all>.
374 It is often useful to create sets or maps that live in the
375 same space as some other set or map. This can be accomplished
376 by creating the new sets or maps
377 (see L<Creating New Sets and Relations>) based on the dimension
378 specification of the original set or map.
381 __isl_give isl_dim *isl_basic_set_get_dim(
382 __isl_keep isl_basic_set *bset);
383 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
386 __isl_give isl_dim *isl_basic_map_get_dim(
387 __isl_keep isl_basic_map *bmap);
388 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
390 =head2 Input and Output
392 C<isl> supports its own input/output format, which is similar
393 to the C<Omega> format, but also supports the C<PolyLib> format
398 The C<isl> format is similar to that of C<Omega>, but has a different
399 syntax for describing the parameters and allows for the definition
400 of an existentially quantified variable as the integer division
401 of an affine expression.
402 For example, the set of integers C<i> between C<0> and C<n>
403 such that C<i % 10 <= 6> can be described as
405 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
408 A set or relation can have several disjuncts, separated
409 by the keyword C<or>. Each disjunct is either a conjunction
410 of constraints or a projection (C<exists>) of a conjunction
411 of constraints. The constraints are separated by the keyword
414 =head3 C<PolyLib> format
416 If the represented set is a union, then the first line
417 contains a single number representing the number of disjuncts.
418 Otherwise, a line containing the number C<1> is optional.
420 Each disjunct is represented by a matrix of constraints.
421 The first line contains two numbers representing
422 the number of rows and columns,
423 where the number of rows is equal to the number of constraints
424 and the number of columns is equal to two plus the number of variables.
425 The following lines contain the actual rows of the constraint matrix.
426 In each row, the first column indicates whether the constraint
427 is an equality (C<0>) or inequality (C<1>). The final column
428 corresponds to the constant term.
430 If the set is parametric, then the coefficients of the parameters
431 appear in the last columns before the constant column.
432 The coefficients of any existentially quantified variables appear
433 between those of the set variables and those of the parameters.
438 __isl_give isl_basic_set *isl_basic_set_read_from_file(
439 isl_ctx *ctx, FILE *input, int nparam);
440 __isl_give isl_basic_set *isl_basic_set_read_from_str(
441 isl_ctx *ctx, const char *str, int nparam);
442 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
443 FILE *input, int nparam);
444 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
445 const char *str, int nparam);
448 __isl_give isl_basic_map *isl_basic_map_read_from_file(
449 isl_ctx *ctx, FILE *input, int nparam);
450 __isl_give isl_basic_map *isl_basic_map_read_from_str(
451 isl_ctx *ctx, const char *str, int nparam);
452 __isl_give isl_map *isl_map_read_from_file(
453 struct isl_ctx *ctx, FILE *input, int nparam);
454 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
455 const char *str, int nparam);
457 The input format is autodetected and may be either the C<PolyLib> format
458 or the C<isl> format.
459 C<nparam> specifies how many of the final columns in
460 the C<PolyLib> format correspond to parameters.
461 If input is given in the C<isl> format, then the number
462 of parameters needs to be equal to C<nparam>.
463 If C<nparam> is negative, then any number of parameters
464 is accepted in the C<isl> format and zero parameters
465 are assumed in the C<PolyLib> format.
469 Before anything can be printed, an C<isl_printer> needs to
472 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
474 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
475 void isl_printer_free(__isl_take isl_printer *printer);
476 __isl_give char *isl_printer_get_str(
477 __isl_keep isl_printer *printer);
479 The behavior of the printer can be modified in various ways
481 __isl_give isl_printer *isl_printer_set_output_format(
482 __isl_take isl_printer *p, int output_format);
483 __isl_give isl_printer *isl_printer_set_indent(
484 __isl_take isl_printer *p, int indent);
485 __isl_give isl_printer *isl_printer_set_prefix(
486 __isl_take isl_printer *p, const char *prefix);
487 __isl_give isl_printer *isl_printer_set_suffix(
488 __isl_take isl_printer *p, const char *suffix);
490 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
491 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
492 Each line in the output is indented by C<indent> spaces
493 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
494 In the C<PolyLib> format output,
495 the coefficients of the existentially quantified variables
496 appear between those of the set variables and those
499 To actually print something, use
502 __isl_give isl_printer *isl_printer_print_basic_set(
503 __isl_take isl_printer *printer,
504 __isl_keep isl_basic_set *bset);
505 __isl_give isl_printer *isl_printer_print_set(
506 __isl_take isl_printer *printer,
507 __isl_keep isl_set *set);
510 __isl_give isl_printer *isl_printer_print_basic_map(
511 __isl_take isl_printer *printer,
512 __isl_keep isl_basic_map *bmap);
513 __isl_give isl_printer *isl_printer_print_map(
514 __isl_take isl_printer *printer,
515 __isl_keep isl_map *map);
517 =head2 Creating New Sets and Relations
519 C<isl> has functions for creating some standard sets and relations.
523 =item * Empty sets and relations
525 __isl_give isl_basic_set *isl_basic_set_empty(
526 __isl_take isl_dim *dim);
527 __isl_give isl_basic_map *isl_basic_map_empty(
528 __isl_take isl_dim *dim);
529 __isl_give isl_set *isl_set_empty(
530 __isl_take isl_dim *dim);
531 __isl_give isl_map *isl_map_empty(
532 __isl_take isl_dim *dim);
534 =item * Universe sets and relations
536 __isl_give isl_basic_set *isl_basic_set_universe(
537 __isl_take isl_dim *dim);
538 __isl_give isl_basic_map *isl_basic_map_universe(
539 __isl_take isl_dim *dim);
540 __isl_give isl_set *isl_set_universe(
541 __isl_take isl_dim *dim);
542 __isl_give isl_map *isl_map_universe(
543 __isl_take isl_dim *dim);
545 =item * Identity relations
547 __isl_give isl_basic_map *isl_basic_map_identity(
548 __isl_take isl_dim *set_dim);
549 __isl_give isl_map *isl_map_identity(
550 __isl_take isl_dim *set_dim);
552 These functions take a dimension specification for a B<set>
553 and return an identity relation between two such sets.
555 =item * Lexicographic order
557 __isl_give isl_map *isl_map_lex_lt(
558 __isl_take isl_dim *set_dim);
559 __isl_give isl_map *isl_map_lex_le(
560 __isl_take isl_dim *set_dim);
561 __isl_give isl_map *isl_map_lex_gt(
562 __isl_take isl_dim *set_dim);
563 __isl_give isl_map *isl_map_lex_ge(
564 __isl_take isl_dim *set_dim);
566 These functions take a dimension specification for a B<set>
567 and return relations that express that the elements in the domain
568 are lexicographically less
569 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
570 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
571 than the elements in the range.
575 A basic set or relation can be converted to a set or relation
576 using the following functions.
578 __isl_give isl_set *isl_set_from_basic_set(
579 __isl_take isl_basic_set *bset);
580 __isl_give isl_map *isl_map_from_basic_map(
581 __isl_take isl_basic_map *bmap);
583 Sets and relations can be copied and freed again using the following
586 __isl_give isl_basic_set *isl_basic_set_copy(
587 __isl_keep isl_basic_set *bset);
588 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
589 __isl_give isl_basic_map *isl_basic_map_copy(
590 __isl_keep isl_basic_map *bmap);
591 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
592 void isl_basic_set_free(__isl_take isl_basic_set *bset);
593 void isl_set_free(__isl_take isl_set *set);
594 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
595 void isl_map_free(__isl_take isl_map *map);
597 Other sets and relations can be constructed by starting
598 from a universe set or relation, adding equality and/or
599 inequality constraints and then projecting out the
600 existentially quantified variables, if any.
601 Constraints can be constructed, manipulated and
602 added to basic sets and relations using the following functions.
604 #include <isl_constraint.h>
605 __isl_give isl_constraint *isl_equality_alloc(
606 __isl_take isl_dim *dim);
607 __isl_give isl_constraint *isl_inequality_alloc(
608 __isl_take isl_dim *dim);
609 void isl_constraint_set_constant(
610 __isl_keep isl_constraint *constraint, isl_int v);
611 void isl_constraint_set_coefficient(
612 __isl_keep isl_constraint *constraint,
613 enum isl_dim_type type, int pos, isl_int v);
614 __isl_give isl_basic_map *isl_basic_map_add_constraint(
615 __isl_take isl_basic_map *bmap,
616 __isl_take isl_constraint *constraint);
617 __isl_give isl_basic_set *isl_basic_set_add_constraint(
618 __isl_take isl_basic_set *bset,
619 __isl_take isl_constraint *constraint);
621 For example, to create a set containing the even integers
622 between 10 and 42, you would use the following code.
626 struct isl_constraint *c;
627 struct isl_basic_set *bset;
630 dim = isl_dim_set_alloc(ctx, 0, 2);
631 bset = isl_basic_set_universe(isl_dim_copy(dim));
633 c = isl_equality_alloc(isl_dim_copy(dim));
634 isl_int_set_si(v, -1);
635 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
636 isl_int_set_si(v, 2);
637 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
638 bset = isl_basic_set_add_constraint(bset, c);
640 c = isl_inequality_alloc(isl_dim_copy(dim));
641 isl_int_set_si(v, -10);
642 isl_constraint_set_constant(c, v);
643 isl_int_set_si(v, 1);
644 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
645 bset = isl_basic_set_add_constraint(bset, c);
647 c = isl_inequality_alloc(dim);
648 isl_int_set_si(v, 42);
649 isl_constraint_set_constant(c, v);
650 isl_int_set_si(v, -1);
651 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
652 bset = isl_basic_set_add_constraint(bset, c);
654 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
660 struct isl_basic_set *bset;
661 bset = isl_basic_set_read_from_str(ctx,
662 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
664 =head2 Inspecting Sets and Relations
666 Usually, the user should not have to care about the actual constraints
667 of the sets and maps, but should instead apply the abstract operations
668 explained in the following sections.
669 Occasionally, however, it may be required to inspect the individual
670 coefficients of the constraints. This section explains how to do so.
671 In these cases, it may also be useful to have C<isl> compute
672 an explicit representation of the existentially quantified variables.
674 __isl_give isl_set *isl_set_compute_divs(
675 __isl_take isl_set *set);
676 __isl_give isl_map *isl_map_compute_divs(
677 __isl_take isl_map *map);
679 This explicit representation defines the existentially quantified
680 variables as integer divisions of the other variables, possibly
681 including earlier existentially quantified variables.
682 An explicitly represented existentially quantified variable therefore
683 has a unique value when the values of the other variables are known.
684 If, furthermore, the same existentials, i.e., existentials
685 with the same explicit representations, should appear in the
686 same order in each of the disjuncts of a set or map, then the user should call
687 either of the following functions.
689 __isl_give isl_set *isl_set_align_divs(
690 __isl_take isl_set *set);
691 __isl_give isl_map *isl_map_align_divs(
692 __isl_take isl_map *map);
694 To iterate over all the basic sets or maps in a set or map, use
696 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
697 int (*fn)(__isl_take isl_basic_set *bset, void *user),
699 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
700 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
703 The callback function C<fn> should return 0 if successful and
704 -1 if an error occurs. In the latter case, or if any other error
705 occurs, the above functions will return -1.
707 It should be noted that C<isl> does not guarantee that
708 the basic sets or maps passed to C<fn> are disjoint.
709 If this is required, then the user should call one of
710 the following functions first.
712 __isl_give isl_set *isl_set_make_disjoint(
713 __isl_take isl_set *set);
714 __isl_give isl_map *isl_map_make_disjoint(
715 __isl_take isl_map *map);
717 To iterate over the constraints of a basic set or map, use
719 #include <isl_constraint.h>
721 int isl_basic_map_foreach_constraint(
722 __isl_keep isl_basic_map *bmap,
723 int (*fn)(__isl_take isl_constraint *c, void *user),
725 void isl_constraint_free(struct isl_constraint *c);
727 Again, the callback function C<fn> should return 0 if successful and
728 -1 if an error occurs. In the latter case, or if any other error
729 occurs, the above functions will return -1.
731 The coefficients of the constraints can be inspected using
732 the following functions.
734 void isl_constraint_get_constant(
735 __isl_keep isl_constraint *constraint, isl_int *v);
736 void isl_constraint_get_coefficient(
737 __isl_keep isl_constraint *constraint,
738 enum isl_dim_type type, int pos, isl_int *v);
740 The explicit representations of the existentially quantified
741 variables can be inspected using the following functions.
742 Note that the user is only allowed to use these functions
743 if the inspected set or map is the result of a call
744 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
746 __isl_give isl_div *isl_constraint_div(
747 __isl_keep isl_constraint *constraint, int pos);
748 void isl_div_get_constant(__isl_keep isl_div *div,
750 void isl_div_get_denominator(__isl_keep isl_div *div,
752 void isl_div_get_coefficient(__isl_keep isl_div *div,
753 enum isl_dim_type type, int pos, isl_int *v);
757 =head3 Unary Properties
763 The following functions test whether the given set or relation
764 contains any integer points. The ``fast'' variants do not perform
765 any computations, but simply check if the given set or relation
766 is already known to be empty.
768 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
769 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
770 int isl_set_is_empty(__isl_keep isl_set *set);
771 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
772 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
773 int isl_map_fast_is_empty(__isl_keep isl_map *map);
774 int isl_map_is_empty(__isl_keep isl_map *map);
778 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
779 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
780 int isl_set_fast_is_universe(__isl_keep isl_set *set);
784 =head3 Binary Properties
790 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
791 __isl_keep isl_set *set2);
792 int isl_set_is_equal(__isl_keep isl_set *set1,
793 __isl_keep isl_set *set2);
794 int isl_map_is_equal(__isl_keep isl_map *map1,
795 __isl_keep isl_map *map2);
796 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
797 __isl_keep isl_map *map2);
798 int isl_basic_map_is_equal(
799 __isl_keep isl_basic_map *bmap1,
800 __isl_keep isl_basic_map *bmap2);
804 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
805 __isl_keep isl_set *set2);
809 int isl_set_is_subset(__isl_keep isl_set *set1,
810 __isl_keep isl_set *set2);
811 int isl_set_is_strict_subset(
812 __isl_keep isl_set *set1,
813 __isl_keep isl_set *set2);
814 int isl_basic_map_is_subset(
815 __isl_keep isl_basic_map *bmap1,
816 __isl_keep isl_basic_map *bmap2);
817 int isl_basic_map_is_strict_subset(
818 __isl_keep isl_basic_map *bmap1,
819 __isl_keep isl_basic_map *bmap2);
820 int isl_map_is_subset(
821 __isl_keep isl_map *map1,
822 __isl_keep isl_map *map2);
823 int isl_map_is_strict_subset(
824 __isl_keep isl_map *map1,
825 __isl_keep isl_map *map2);
829 =head2 Unary Operations
835 __isl_give isl_set *isl_set_complement(
836 __isl_take isl_set *set);
840 __isl_give isl_basic_set *isl_basic_set_project_out(
841 __isl_take isl_basic_set *bset,
842 enum isl_dim_type type, unsigned first, unsigned n);
843 __isl_give isl_basic_map *isl_basic_map_project_out(
844 __isl_take isl_basic_map *bmap,
845 enum isl_dim_type type, unsigned first, unsigned n);
846 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
847 enum isl_dim_type type, unsigned first, unsigned n);
848 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
849 enum isl_dim_type type, unsigned first, unsigned n);
850 __isl_give isl_basic_set *isl_basic_map_domain(
851 __isl_take isl_basic_map *bmap);
852 __isl_give isl_basic_set *isl_basic_map_range(
853 __isl_take isl_basic_map *bmap);
854 __isl_give isl_set *isl_map_domain(
855 __isl_take isl_map *bmap);
856 __isl_give isl_set *isl_map_range(
857 __isl_take isl_map *map);
861 Simplify the representation of a set or relation by trying
862 to combine pairs of basic sets or relations into a single
863 basic set or relation.
865 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
866 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
870 __isl_give isl_basic_set *isl_set_convex_hull(
871 __isl_take isl_set *set);
872 __isl_give isl_basic_map *isl_map_convex_hull(
873 __isl_take isl_map *map);
875 If the input set or relation has any existentially quantified
876 variables, then the result of these operations is currently undefined.
880 __isl_give isl_basic_set *isl_basic_set_affine_hull(
881 __isl_take isl_basic_set *bset);
882 __isl_give isl_basic_set *isl_set_affine_hull(
883 __isl_take isl_set *set);
884 __isl_give isl_basic_map *isl_basic_map_affine_hull(
885 __isl_take isl_basic_map *bmap);
886 __isl_give isl_basic_map *isl_map_affine_hull(
887 __isl_take isl_map *map);
891 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
892 unsigned param, int *exact);
894 Compute a parametric representation for all positive powers I<k> of C<map>.
895 The power I<k> is equated to the parameter at position C<param>.
896 The result may be an overapproximation. If the result is exact,
897 then C<*exact> is set to C<1>.
898 The current implementation only produces exact results for particular
899 cases of piecewise translations (i.e., piecewise uniform dependences).
901 =item * Transitive closure
903 __isl_give isl_map *isl_map_transitive_closure(
904 __isl_take isl_map *map, int *exact);
906 Compute the transitive closure of C<map>.
907 The result may be an overapproximation. If the result is known to be exact,
908 then C<*exact> is set to C<1>.
909 The current implementation only produces exact results for particular
910 cases of piecewise translations (i.e., piecewise uniform dependences).
914 =head2 Binary Operations
916 The two arguments of a binary operation not only need to live
917 in the same C<isl_ctx>, they currently also need to have
918 the same (number of) parameters.
920 =head3 Basic Operations
926 __isl_give isl_basic_set *isl_basic_set_intersect(
927 __isl_take isl_basic_set *bset1,
928 __isl_take isl_basic_set *bset2);
929 __isl_give isl_set *isl_set_intersect(
930 __isl_take isl_set *set1,
931 __isl_take isl_set *set2);
932 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
933 __isl_take isl_basic_map *bmap,
934 __isl_take isl_basic_set *bset);
935 __isl_give isl_basic_map *isl_basic_map_intersect_range(
936 __isl_take isl_basic_map *bmap,
937 __isl_take isl_basic_set *bset);
938 __isl_give isl_basic_map *isl_basic_map_intersect(
939 __isl_take isl_basic_map *bmap1,
940 __isl_take isl_basic_map *bmap2);
941 __isl_give isl_map *isl_map_intersect_domain(
942 __isl_take isl_map *map,
943 __isl_take isl_set *set);
944 __isl_give isl_map *isl_map_intersect_range(
945 __isl_take isl_map *map,
946 __isl_take isl_set *set);
947 __isl_give isl_map *isl_map_intersect(
948 __isl_take isl_map *map1,
949 __isl_take isl_map *map2);
953 __isl_give isl_set *isl_basic_set_union(
954 __isl_take isl_basic_set *bset1,
955 __isl_take isl_basic_set *bset2);
956 __isl_give isl_map *isl_basic_map_union(
957 __isl_take isl_basic_map *bmap1,
958 __isl_take isl_basic_map *bmap2);
959 __isl_give isl_set *isl_set_union(
960 __isl_take isl_set *set1,
961 __isl_take isl_set *set2);
962 __isl_give isl_map *isl_map_union(
963 __isl_take isl_map *map1,
964 __isl_take isl_map *map2);
966 =item * Set difference
968 __isl_give isl_set *isl_set_subtract(
969 __isl_take isl_set *set1,
970 __isl_take isl_set *set2);
971 __isl_give isl_map *isl_map_subtract(
972 __isl_take isl_map *map1,
973 __isl_take isl_map *map2);
977 __isl_give isl_basic_set *isl_basic_set_apply(
978 __isl_take isl_basic_set *bset,
979 __isl_take isl_basic_map *bmap);
980 __isl_give isl_set *isl_set_apply(
981 __isl_take isl_set *set,
982 __isl_take isl_map *map);
983 __isl_give isl_basic_map *isl_basic_map_apply_domain(
984 __isl_take isl_basic_map *bmap1,
985 __isl_take isl_basic_map *bmap2);
986 __isl_give isl_basic_map *isl_basic_map_apply_range(
987 __isl_take isl_basic_map *bmap1,
988 __isl_take isl_basic_map *bmap2);
989 __isl_give isl_map *isl_map_apply_domain(
990 __isl_take isl_map *map1,
991 __isl_take isl_map *map2);
992 __isl_give isl_map *isl_map_apply_range(
993 __isl_take isl_map *map1,
994 __isl_take isl_map *map2);
998 =head3 Lexicographic Optimization
1000 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1001 the following functions
1002 compute a set that contains the lexicographic minimum or maximum
1003 of the elements in C<set> (or C<bset>) for those values of the parameters
1004 that satisfy C<dom>.
1005 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1006 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1008 In other words, the union of the parameter values
1009 for which the result is non-empty and of C<*empty>
1012 __isl_give isl_set *isl_basic_set_partial_lexmin(
1013 __isl_take isl_basic_set *bset,
1014 __isl_take isl_basic_set *dom,
1015 __isl_give isl_set **empty);
1016 __isl_give isl_set *isl_basic_set_partial_lexmax(
1017 __isl_take isl_basic_set *bset,
1018 __isl_take isl_basic_set *dom,
1019 __isl_give isl_set **empty);
1020 __isl_give isl_set *isl_set_partial_lexmin(
1021 __isl_take isl_set *set, __isl_take isl_set *dom,
1022 __isl_give isl_set **empty);
1023 __isl_give isl_set *isl_set_partial_lexmax(
1024 __isl_take isl_set *set, __isl_take isl_set *dom,
1025 __isl_give isl_set **empty);
1027 Given a (basic) set C<set> (or C<bset>), the following functions simply
1028 return a set containing the lexicographic minimum or maximum
1029 of the elements in C<set> (or C<bset>).
1031 __isl_give isl_set *isl_basic_set_lexmin(
1032 __isl_take isl_basic_set *bset);
1033 __isl_give isl_set *isl_basic_set_lexmax(
1034 __isl_take isl_basic_set *bset);
1035 __isl_give isl_set *isl_set_lexmin(
1036 __isl_take isl_set *set);
1037 __isl_give isl_set *isl_set_lexmax(
1038 __isl_take isl_set *set);
1040 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1041 the following functions
1042 compute a relation that maps each element of C<dom>
1043 to the single lexicographic minimum or maximum
1044 of the elements that are associated to that same
1045 element in C<map> (or C<bmap>).
1046 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1047 that contains the elements in C<dom> that do not map
1048 to any elements in C<map> (or C<bmap>).
1049 In other words, the union of the domain of the result and of C<*empty>
1052 __isl_give isl_map *isl_basic_map_partial_lexmax(
1053 __isl_take isl_basic_map *bmap,
1054 __isl_take isl_basic_set *dom,
1055 __isl_give isl_set **empty);
1056 __isl_give isl_map *isl_basic_map_partial_lexmin(
1057 __isl_take isl_basic_map *bmap,
1058 __isl_take isl_basic_set *dom,
1059 __isl_give isl_set **empty);
1060 __isl_give isl_map *isl_map_partial_lexmax(
1061 __isl_take isl_map *map, __isl_take isl_set *dom,
1062 __isl_give isl_set **empty);
1063 __isl_give isl_map *isl_map_partial_lexmin(
1064 __isl_take isl_map *map, __isl_take isl_set *dom,
1065 __isl_give isl_set **empty);
1067 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1068 return a map mapping each element in the domain of
1069 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1070 of all elements associated to that element.
1072 __isl_give isl_map *isl_basic_map_lexmin(
1073 __isl_take isl_basic_map *bmap);
1074 __isl_give isl_map *isl_basic_map_lexmax(
1075 __isl_take isl_basic_map *bmap);
1076 __isl_give isl_map *isl_map_lexmin(
1077 __isl_take isl_map *map);
1078 __isl_give isl_map *isl_map_lexmax(
1079 __isl_take isl_map *map);
1083 Points are elements of a set. They can be used to construct
1084 simple sets (boxes) or they can be used to represent the
1085 individual elements of a set.
1086 The zero point (the origin) can be created using
1088 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1090 The coordinates of a point can be inspected, set and changed
1093 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1094 enum isl_dim_type type, int pos, isl_int *v);
1095 __isl_give isl_point *isl_point_set_coordinate(
1096 __isl_take isl_point *pnt,
1097 enum isl_dim_type type, int pos, isl_int v);
1099 __isl_give isl_point *isl_point_add_ui(
1100 __isl_take isl_point *pnt,
1101 enum isl_dim_type type, int pos, unsigned val);
1102 __isl_give isl_point *isl_point_sub_ui(
1103 __isl_take isl_point *pnt,
1104 enum isl_dim_type type, int pos, unsigned val);
1106 Points can be copied or freed using
1108 __isl_give isl_point *isl_point_copy(
1109 __isl_keep isl_point *pnt);
1110 void isl_point_free(__isl_take isl_point *pnt);
1112 A singleton set can be created from a point using
1114 __isl_give isl_set *isl_set_from_point(
1115 __isl_take isl_point *pnt);
1117 and a box can be created from two opposite extremal points using
1119 __isl_give isl_set *isl_set_box_from_points(
1120 __isl_take isl_point *pnt1,
1121 __isl_take isl_point *pnt2);
1123 All elements of a B<bounded> set can be enumerated using
1124 the following function.
1126 int isl_set_foreach_point(__isl_keep isl_set *set,
1127 int (*fn)(__isl_take isl_point *pnt, void *user),
1130 The function C<fn> is called for each integer point in
1131 C<set> with as second argument the last argument of
1132 the C<isl_set_foreach_point> call. The function C<fn>
1133 should return C<0> on success and C<-1> on failure.
1134 In the latter case, C<isl_set_foreach_point> will stop
1135 enumerating and return C<-1> as well.
1136 If the enumeration is performed successfully and to completion,
1137 then C<isl_set_foreach_point> returns C<0>.
1139 To obtain a single point of a set, use
1141 __isl_give isl_point *isl_set_sample_point(
1142 __isl_take isl_set *set);
1144 If C<set> does not contain any (integer) points, then the
1145 resulting point will be ``void'', a property that can be
1148 int isl_point_is_void(__isl_keep isl_point *pnt);
1150 =head2 Piecewise Quasipolynomials
1152 A piecewise quasipolynomial is a particular kind of function that maps
1153 a parametric point to a rational value.
1154 More specifically, a quasipolynomial is a polynomial expression in greatest
1155 integer parts of affine expressions of parameters and variables.
1156 A piecewise quasipolynomial is a subdivision of a given parametric
1157 domain into disjoint cells with a quasipolynomial associated to
1158 each cell. The value of the piecewise quasipolynomial at a given
1159 point is the value of the quasipolynomial associated to the cell
1160 that contains the point. Outside of the union of cells,
1161 the value is assumed to be zero.
1162 For example, the piecewise quasipolynomial
1164 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1166 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1167 Piecewise quasipolynomials are mainly used by the C<barvinok>
1168 library for representing the number of elements in a parametric set or map.
1169 For example, the piecewise quasipolynomial above represents
1170 the number of point in the map
1172 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1174 =head3 Printing (Piecewise) Quasipolynomials
1176 Quasipolynomials and piecewise quasipolynomials can be printed
1177 using the following functions.
1179 __isl_give isl_printer *isl_printer_print_qpolynomial(
1180 __isl_take isl_printer *p,
1181 __isl_keep isl_qpolynomial *qp);
1183 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1184 __isl_take isl_printer *p,
1185 __isl_keep isl_pw_qpolynomial *pwqp);
1187 The output format of the printer
1188 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1190 =head3 Creating New (Piecewise) Quasipolynomials
1192 Some simple quasipolynomials can be created using the following functions.
1193 More complicated quasipolynomials can be created by applying
1194 operations such as addition and multiplication
1195 on the resulting quasipolynomials
1197 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1198 __isl_take isl_dim *dim);
1199 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1200 __isl_take isl_dim *dim);
1201 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1202 __isl_take isl_dim *dim);
1203 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1204 __isl_take isl_dim *dim,
1205 const isl_int n, const isl_int d);
1206 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1207 __isl_take isl_div *div);
1208 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1209 __isl_take isl_dim *dim,
1210 enum isl_dim_type type, unsigned pos);
1212 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1213 with a single cell can be created using the following functions.
1214 Multiple of these single cell piecewise quasipolynomials can
1215 be combined to create more complicated piecewise quasipolynomials.
1217 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1218 __isl_take isl_dim *dim);
1219 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1220 __isl_take isl_set *set,
1221 __isl_take isl_qpolynomial *qp);
1223 Quasipolynomials can be copied and freed again using the following
1226 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1227 __isl_keep isl_qpolynomial *qp);
1228 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1230 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1231 __isl_keep isl_pw_qpolynomial *pwqp);
1232 void isl_pw_qpolynomial_free(
1233 __isl_take isl_pw_qpolynomial *pwqp);
1235 =head3 Inspecting (Piecewise) Quasipolynomials
1237 To iterate over the cells in a piecewise quasipolynomial,
1238 use either of the following two functions
1240 int isl_pw_qpolynomial_foreach_piece(
1241 __isl_keep isl_pw_qpolynomial *pwqp,
1242 int (*fn)(__isl_take isl_set *set,
1243 __isl_take isl_qpolynomial *qp,
1244 void *user), void *user);
1245 int isl_pw_qpolynomial_foreach_lifted_piece(
1246 __isl_keep isl_pw_qpolynomial *pwqp,
1247 int (*fn)(__isl_take isl_set *set,
1248 __isl_take isl_qpolynomial *qp,
1249 void *user), void *user);
1251 As usual, the function C<fn> should return C<0> on success
1252 and C<-1> on failure. The difference between
1253 C<isl_pw_qpolynomial_foreach_piece> and
1254 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1255 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1256 compute unique representations for all existentially quantified
1257 variables and then turn these existentially quantified variables
1258 into extra set variables, adapting the associated quasipolynomial
1259 accordingly. This means that the C<set> passed to C<fn>
1260 will not have any existentially quantified variables, but that
1261 the dimensions of the sets may be different for different
1262 invocations of C<fn>.
1264 To iterate over all terms in a quasipolynomial,
1267 int isl_qpolynomial_foreach_term(
1268 __isl_keep isl_qpolynomial *qp,
1269 int (*fn)(__isl_take isl_term *term,
1270 void *user), void *user);
1272 The terms themselves can be inspected and freed using
1275 unsigned isl_term_dim(__isl_keep isl_term *term,
1276 enum isl_dim_type type);
1277 void isl_term_get_num(__isl_keep isl_term *term,
1279 void isl_term_get_den(__isl_keep isl_term *term,
1281 int isl_term_get_exp(__isl_keep isl_term *term,
1282 enum isl_dim_type type, unsigned pos);
1283 __isl_give isl_div *isl_term_get_div(
1284 __isl_keep isl_term *term, unsigned pos);
1285 void isl_term_free(__isl_take isl_term *term);
1287 Each term is a product of parameters, set variables and
1288 integer divisions. The function C<isl_term_get_exp>
1289 returns the exponent of a given dimensions in the given term.
1290 The C<isl_int>s in the arguments of C<isl_term_get_num>
1291 and C<isl_term_get_den> need to have been initialized
1292 using C<isl_int_init> before calling these functions.
1294 =head3 Properties of (Piecewise) Quasipolynomials
1296 To check whether a quasipolynomial is actually a constant,
1297 use the following function.
1299 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1300 isl_int *n, isl_int *d);
1302 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1303 then the numerator and denominator of the constant
1304 are returned in C<*n> and C<*d>, respectively.
1306 =head3 Operations on (Piecewise) Quasipolynomials
1308 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1309 __isl_take isl_qpolynomial *qp);
1310 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1311 __isl_take isl_qpolynomial *qp1,
1312 __isl_take isl_qpolynomial *qp2);
1313 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1314 __isl_take isl_qpolynomial *qp1,
1315 __isl_take isl_qpolynomial *qp2);
1317 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1318 __isl_take isl_pw_qpolynomial *pwqp1,
1319 __isl_take isl_pw_qpolynomial *pwqp2);
1320 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1321 __isl_take isl_pw_qpolynomial *pwqp1,
1322 __isl_take isl_pw_qpolynomial *pwqp2);
1323 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1324 __isl_take isl_pw_qpolynomial *pwqp1,
1325 __isl_take isl_pw_qpolynomial *pwqp2);
1326 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1327 __isl_take isl_pw_qpolynomial *pwqp);
1328 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1329 __isl_take isl_pw_qpolynomial *pwqp1,
1330 __isl_take isl_pw_qpolynomial *pwqp2);
1332 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1333 __isl_take isl_pw_qpolynomial *pwqp,
1334 __isl_take isl_point *pnt);
1336 __isl_give isl_set *isl_pw_qpolynomial_domain(
1337 __isl_take isl_pw_qpolynomial *pwqp);
1338 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1339 __isl_take isl_pw_qpolynomial *pwpq,
1340 __isl_take isl_set *set);
1342 =head2 Dependence Analysis
1344 C<isl> contains specialized functionality for performing
1345 array dataflow analysis. That is, given a I<sink> access relation
1346 and a collection of possible I<source> access relations,
1347 C<isl> can compute relations that describe
1348 for each iteration of the sink access, which iteration
1349 of which of the source access relations was the last
1350 to access the same data element before the given iteration
1352 To compute standard flow dependences, the sink should be
1353 a read, while the sources should be writes.
1355 #include <isl_flow.h>
1357 __isl_give isl_access_info *isl_access_info_alloc(
1358 __isl_take isl_map *sink,
1359 void *sink_user, isl_access_level_before fn,
1361 __isl_give isl_access_info *isl_access_info_add_source(
1362 __isl_take isl_access_info *acc,
1363 __isl_take isl_map *source, void *source_user);
1365 __isl_give isl_flow *isl_access_info_compute_flow(
1366 __isl_take isl_access_info *acc);
1368 int isl_flow_foreach(__isl_keep isl_flow *deps,
1369 int (*fn)(__isl_take isl_map *dep, void *dep_user,
1372 __isl_give isl_set *isl_flow_get_no_source(
1373 __isl_keep isl_flow *deps);
1374 void isl_flow_free(__isl_take isl_flow *deps);
1376 The function C<isl_access_info_compute_flow> performs the actual
1377 dependence analysis. The other functions are used to construct
1378 the input for this function or to read off the output.
1380 The input is collected in an C<isl_access_info>, which can
1381 be created through a call to C<isl_access_info_alloc>.
1382 The arguments to this functions are the sink access relation
1383 C<sink>, a token C<sink_user> used to identify the sink
1384 access to the user, a callback function for specifying the
1385 relative order of source and sink accesses, and the number
1386 of source access relations that will be added.
1387 The callback function has type C<int (*)(void *first, void *second)>.
1388 The function is called with two user supplied tokens identifying
1389 either a source or the sink and it should return the shared nesting
1390 level and the relative order of the two accesses.
1391 In particular, let I<n> be the number of loops shared by
1392 the two accesses. If C<first> precedes C<second> textually,
1393 then the function should return I<2 * n + 1>; otherwise,
1394 it should return I<2 * n>.
1395 The sources can be added to the C<isl_access_info> by performing
1396 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1397 The C<source_user> token is again used to identify
1398 the source access. The range of the source access relation
1399 C<source> should have the same dimension as the range
1400 of the sink access relation.
1402 The result of the dependence analysis is collected in an
1403 C<isl_flow>. There may be elements in the domain of
1404 the sink access for which no preceding source access could be
1405 find. The set of these elements can be obtained through
1406 a call to C<isl_flow_get_no_source>.
1407 In the case of standard flow dependence analysis,
1408 this set corresponds to the reads from uninitialized
1410 The actual flow dependences can be extracted using
1411 C<isl_flow_foreach>. This function will call the user-specified
1412 callback function C<fn> for each B<non-empty> dependence between
1413 a source and the sink. The callback function is called
1414 with three arguments, the actual flow dependence relation
1415 mapping source iterations to sink iterations, a token
1416 identifying the source and an additional C<void *> with value
1417 equal to the third argument of the C<isl_flow_foreach> call.
1419 After finishing with an C<isl_flow>, the user should call
1420 C<isl_flow_free> to free all associated memory.
1424 Although C<isl> is mainly meant to be used as a library,
1425 it also contains some basic applications that use some
1426 of the functionality of C<isl>.
1427 The input may be specified in either the L<isl format>
1428 or the L<PolyLib format>.
1430 =head2 C<isl_polyhedron_sample>
1432 C<isl_polyhedron_sample> takes a polyhedron as input and prints
1433 an integer element of the polyhedron, if there is any.
1434 The first column in the output is the denominator and is always
1435 equal to 1. If the polyhedron contains no integer points,
1436 then a vector of length zero is printed.
1440 C<isl_pip> takes the same input as the C<example> program
1441 from the C<piplib> distribution, i.e., a set of constraints
1442 on the parameters, a line contains only -1 and finally a set
1443 of constraints on a parametric polyhedron.
1444 The coefficients of the parameters appear in the last columns
1445 (but before the final constant column).
1446 The output is the lexicographic minimum of the parametric polyhedron.
1447 As C<isl> currently does not have its own output format, the output
1448 is just a dump of the internal state.
1450 =head2 C<isl_polyhedron_minimize>
1452 C<isl_polyhedron_minimize> computes the minimum of some linear
1453 or affine objective function over the integer points in a polyhedron.
1454 If an affine objective function
1455 is given, then the constant should appear in the last column.
1457 =head2 C<isl_polytope_scan>
1459 Given a polytope, C<isl_polytope_scan> prints
1460 all integer points in the polytope.
1462 =head1 C<isl-polylib>
1464 The C<isl-polylib> library provides the following functions for converting
1465 between C<isl> objects and C<PolyLib> objects.
1466 The library is distributed separately for licensing reasons.
1468 #include <isl_set_polylib.h>
1469 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
1470 Polyhedron *P, __isl_take isl_dim *dim);
1471 Polyhedron *isl_basic_set_to_polylib(
1472 __isl_keep isl_basic_set *bset);
1473 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
1474 __isl_take isl_dim *dim);
1475 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
1477 #include <isl_map_polylib.h>
1478 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
1479 Polyhedron *P, __isl_take isl_dim *dim);
1480 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
1481 __isl_take isl_dim *dim);
1482 Polyhedron *isl_basic_map_to_polylib(
1483 __isl_keep isl_basic_map *bmap);
1484 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);