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 The names of the individual dimensions may be set or read off
391 using the following functions.
394 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
395 enum isl_dim_type type, unsigned pos,
396 __isl_keep const char *name);
397 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
398 enum isl_dim_type type, unsigned pos);
400 Note that C<isl_dim_get_name> returns a pointer to some internal
401 data structure, so the result can only be used while the
402 corresponding C<isl_dim> is alive.
403 Also note that every function that operates on two sets or relations
404 requires that both arguments have the same parameters. This also
405 means that if one of the arguments has named parameters, then the
406 other needs to have named parameters too and the names need to match.
408 =head2 Input and Output
410 C<isl> supports its own input/output format, which is similar
411 to the C<Omega> format, but also supports the C<PolyLib> format
416 The C<isl> format is similar to that of C<Omega>, but has a different
417 syntax for describing the parameters and allows for the definition
418 of an existentially quantified variable as the integer division
419 of an affine expression.
420 For example, the set of integers C<i> between C<0> and C<n>
421 such that C<i % 10 <= 6> can be described as
423 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
426 A set or relation can have several disjuncts, separated
427 by the keyword C<or>. Each disjunct is either a conjunction
428 of constraints or a projection (C<exists>) of a conjunction
429 of constraints. The constraints are separated by the keyword
432 =head3 C<PolyLib> format
434 If the represented set is a union, then the first line
435 contains a single number representing the number of disjuncts.
436 Otherwise, a line containing the number C<1> is optional.
438 Each disjunct is represented by a matrix of constraints.
439 The first line contains two numbers representing
440 the number of rows and columns,
441 where the number of rows is equal to the number of constraints
442 and the number of columns is equal to two plus the number of variables.
443 The following lines contain the actual rows of the constraint matrix.
444 In each row, the first column indicates whether the constraint
445 is an equality (C<0>) or inequality (C<1>). The final column
446 corresponds to the constant term.
448 If the set is parametric, then the coefficients of the parameters
449 appear in the last columns before the constant column.
450 The coefficients of any existentially quantified variables appear
451 between those of the set variables and those of the parameters.
456 __isl_give isl_basic_set *isl_basic_set_read_from_file(
457 isl_ctx *ctx, FILE *input, int nparam);
458 __isl_give isl_basic_set *isl_basic_set_read_from_str(
459 isl_ctx *ctx, const char *str, int nparam);
460 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
461 FILE *input, int nparam);
462 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
463 const char *str, int nparam);
466 __isl_give isl_basic_map *isl_basic_map_read_from_file(
467 isl_ctx *ctx, FILE *input, int nparam);
468 __isl_give isl_basic_map *isl_basic_map_read_from_str(
469 isl_ctx *ctx, const char *str, int nparam);
470 __isl_give isl_map *isl_map_read_from_file(
471 struct isl_ctx *ctx, FILE *input, int nparam);
472 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
473 const char *str, int nparam);
475 The input format is autodetected and may be either the C<PolyLib> format
476 or the C<isl> format.
477 C<nparam> specifies how many of the final columns in
478 the C<PolyLib> format correspond to parameters.
479 If input is given in the C<isl> format, then the number
480 of parameters needs to be equal to C<nparam>.
481 If C<nparam> is negative, then any number of parameters
482 is accepted in the C<isl> format and zero parameters
483 are assumed in the C<PolyLib> format.
487 Before anything can be printed, an C<isl_printer> needs to
490 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
492 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
493 void isl_printer_free(__isl_take isl_printer *printer);
494 __isl_give char *isl_printer_get_str(
495 __isl_keep isl_printer *printer);
497 The behavior of the printer can be modified in various ways
499 __isl_give isl_printer *isl_printer_set_output_format(
500 __isl_take isl_printer *p, int output_format);
501 __isl_give isl_printer *isl_printer_set_indent(
502 __isl_take isl_printer *p, int indent);
503 __isl_give isl_printer *isl_printer_set_prefix(
504 __isl_take isl_printer *p, const char *prefix);
505 __isl_give isl_printer *isl_printer_set_suffix(
506 __isl_take isl_printer *p, const char *suffix);
508 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
509 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
510 Each line in the output is indented by C<indent> spaces
511 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
512 In the C<PolyLib> format output,
513 the coefficients of the existentially quantified variables
514 appear between those of the set variables and those
517 To actually print something, use
520 __isl_give isl_printer *isl_printer_print_basic_set(
521 __isl_take isl_printer *printer,
522 __isl_keep isl_basic_set *bset);
523 __isl_give isl_printer *isl_printer_print_set(
524 __isl_take isl_printer *printer,
525 __isl_keep isl_set *set);
528 __isl_give isl_printer *isl_printer_print_basic_map(
529 __isl_take isl_printer *printer,
530 __isl_keep isl_basic_map *bmap);
531 __isl_give isl_printer *isl_printer_print_map(
532 __isl_take isl_printer *printer,
533 __isl_keep isl_map *map);
535 =head2 Creating New Sets and Relations
537 C<isl> has functions for creating some standard sets and relations.
541 =item * Empty sets and relations
543 __isl_give isl_basic_set *isl_basic_set_empty(
544 __isl_take isl_dim *dim);
545 __isl_give isl_basic_map *isl_basic_map_empty(
546 __isl_take isl_dim *dim);
547 __isl_give isl_set *isl_set_empty(
548 __isl_take isl_dim *dim);
549 __isl_give isl_map *isl_map_empty(
550 __isl_take isl_dim *dim);
552 =item * Universe sets and relations
554 __isl_give isl_basic_set *isl_basic_set_universe(
555 __isl_take isl_dim *dim);
556 __isl_give isl_basic_map *isl_basic_map_universe(
557 __isl_take isl_dim *dim);
558 __isl_give isl_set *isl_set_universe(
559 __isl_take isl_dim *dim);
560 __isl_give isl_map *isl_map_universe(
561 __isl_take isl_dim *dim);
563 =item * Identity relations
565 __isl_give isl_basic_map *isl_basic_map_identity(
566 __isl_take isl_dim *set_dim);
567 __isl_give isl_map *isl_map_identity(
568 __isl_take isl_dim *set_dim);
570 These functions take a dimension specification for a B<set>
571 and return an identity relation between two such sets.
573 =item * Lexicographic order
575 __isl_give isl_map *isl_map_lex_lt(
576 __isl_take isl_dim *set_dim);
577 __isl_give isl_map *isl_map_lex_le(
578 __isl_take isl_dim *set_dim);
579 __isl_give isl_map *isl_map_lex_gt(
580 __isl_take isl_dim *set_dim);
581 __isl_give isl_map *isl_map_lex_ge(
582 __isl_take isl_dim *set_dim);
584 These functions take a dimension specification for a B<set>
585 and return relations that express that the elements in the domain
586 are lexicographically less
587 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
588 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
589 than the elements in the range.
593 A basic set or relation can be converted to a set or relation
594 using the following functions.
596 __isl_give isl_set *isl_set_from_basic_set(
597 __isl_take isl_basic_set *bset);
598 __isl_give isl_map *isl_map_from_basic_map(
599 __isl_take isl_basic_map *bmap);
601 Sets and relations can be copied and freed again using the following
604 __isl_give isl_basic_set *isl_basic_set_copy(
605 __isl_keep isl_basic_set *bset);
606 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
607 __isl_give isl_basic_map *isl_basic_map_copy(
608 __isl_keep isl_basic_map *bmap);
609 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
610 void isl_basic_set_free(__isl_take isl_basic_set *bset);
611 void isl_set_free(__isl_take isl_set *set);
612 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
613 void isl_map_free(__isl_take isl_map *map);
615 Other sets and relations can be constructed by starting
616 from a universe set or relation, adding equality and/or
617 inequality constraints and then projecting out the
618 existentially quantified variables, if any.
619 Constraints can be constructed, manipulated and
620 added to basic sets and relations using the following functions.
622 #include <isl_constraint.h>
623 __isl_give isl_constraint *isl_equality_alloc(
624 __isl_take isl_dim *dim);
625 __isl_give isl_constraint *isl_inequality_alloc(
626 __isl_take isl_dim *dim);
627 void isl_constraint_set_constant(
628 __isl_keep isl_constraint *constraint, isl_int v);
629 void isl_constraint_set_coefficient(
630 __isl_keep isl_constraint *constraint,
631 enum isl_dim_type type, int pos, isl_int v);
632 __isl_give isl_basic_map *isl_basic_map_add_constraint(
633 __isl_take isl_basic_map *bmap,
634 __isl_take isl_constraint *constraint);
635 __isl_give isl_basic_set *isl_basic_set_add_constraint(
636 __isl_take isl_basic_set *bset,
637 __isl_take isl_constraint *constraint);
639 For example, to create a set containing the even integers
640 between 10 and 42, you would use the following code.
644 struct isl_constraint *c;
645 struct isl_basic_set *bset;
648 dim = isl_dim_set_alloc(ctx, 0, 2);
649 bset = isl_basic_set_universe(isl_dim_copy(dim));
651 c = isl_equality_alloc(isl_dim_copy(dim));
652 isl_int_set_si(v, -1);
653 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
654 isl_int_set_si(v, 2);
655 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
656 bset = isl_basic_set_add_constraint(bset, c);
658 c = isl_inequality_alloc(isl_dim_copy(dim));
659 isl_int_set_si(v, -10);
660 isl_constraint_set_constant(c, v);
661 isl_int_set_si(v, 1);
662 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
663 bset = isl_basic_set_add_constraint(bset, c);
665 c = isl_inequality_alloc(dim);
666 isl_int_set_si(v, 42);
667 isl_constraint_set_constant(c, v);
668 isl_int_set_si(v, -1);
669 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
670 bset = isl_basic_set_add_constraint(bset, c);
672 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
678 struct isl_basic_set *bset;
679 bset = isl_basic_set_read_from_str(ctx,
680 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
682 =head2 Inspecting Sets and Relations
684 Usually, the user should not have to care about the actual constraints
685 of the sets and maps, but should instead apply the abstract operations
686 explained in the following sections.
687 Occasionally, however, it may be required to inspect the individual
688 coefficients of the constraints. This section explains how to do so.
689 In these cases, it may also be useful to have C<isl> compute
690 an explicit representation of the existentially quantified variables.
692 __isl_give isl_set *isl_set_compute_divs(
693 __isl_take isl_set *set);
694 __isl_give isl_map *isl_map_compute_divs(
695 __isl_take isl_map *map);
697 This explicit representation defines the existentially quantified
698 variables as integer divisions of the other variables, possibly
699 including earlier existentially quantified variables.
700 An explicitly represented existentially quantified variable therefore
701 has a unique value when the values of the other variables are known.
702 If, furthermore, the same existentials, i.e., existentials
703 with the same explicit representations, should appear in the
704 same order in each of the disjuncts of a set or map, then the user should call
705 either of the following functions.
707 __isl_give isl_set *isl_set_align_divs(
708 __isl_take isl_set *set);
709 __isl_give isl_map *isl_map_align_divs(
710 __isl_take isl_map *map);
712 To iterate over all the basic sets or maps in a set or map, use
714 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
715 int (*fn)(__isl_take isl_basic_set *bset, void *user),
717 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
718 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
721 The callback function C<fn> should return 0 if successful and
722 -1 if an error occurs. In the latter case, or if any other error
723 occurs, the above functions will return -1.
725 It should be noted that C<isl> does not guarantee that
726 the basic sets or maps passed to C<fn> are disjoint.
727 If this is required, then the user should call one of
728 the following functions first.
730 __isl_give isl_set *isl_set_make_disjoint(
731 __isl_take isl_set *set);
732 __isl_give isl_map *isl_map_make_disjoint(
733 __isl_take isl_map *map);
735 To iterate over the constraints of a basic set or map, use
737 #include <isl_constraint.h>
739 int isl_basic_map_foreach_constraint(
740 __isl_keep isl_basic_map *bmap,
741 int (*fn)(__isl_take isl_constraint *c, void *user),
743 void isl_constraint_free(struct isl_constraint *c);
745 Again, the callback function C<fn> should return 0 if successful and
746 -1 if an error occurs. In the latter case, or if any other error
747 occurs, the above functions will return -1.
749 The coefficients of the constraints can be inspected using
750 the following functions.
752 void isl_constraint_get_constant(
753 __isl_keep isl_constraint *constraint, isl_int *v);
754 void isl_constraint_get_coefficient(
755 __isl_keep isl_constraint *constraint,
756 enum isl_dim_type type, int pos, isl_int *v);
758 The explicit representations of the existentially quantified
759 variables can be inspected using the following functions.
760 Note that the user is only allowed to use these functions
761 if the inspected set or map is the result of a call
762 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
764 __isl_give isl_div *isl_constraint_div(
765 __isl_keep isl_constraint *constraint, int pos);
766 void isl_div_get_constant(__isl_keep isl_div *div,
768 void isl_div_get_denominator(__isl_keep isl_div *div,
770 void isl_div_get_coefficient(__isl_keep isl_div *div,
771 enum isl_dim_type type, int pos, isl_int *v);
775 =head3 Unary Properties
781 The following functions test whether the given set or relation
782 contains any integer points. The ``fast'' variants do not perform
783 any computations, but simply check if the given set or relation
784 is already known to be empty.
786 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
787 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
788 int isl_set_is_empty(__isl_keep isl_set *set);
789 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
790 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
791 int isl_map_fast_is_empty(__isl_keep isl_map *map);
792 int isl_map_is_empty(__isl_keep isl_map *map);
796 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
797 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
798 int isl_set_fast_is_universe(__isl_keep isl_set *set);
802 =head3 Binary Properties
808 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
809 __isl_keep isl_set *set2);
810 int isl_set_is_equal(__isl_keep isl_set *set1,
811 __isl_keep isl_set *set2);
812 int isl_map_is_equal(__isl_keep isl_map *map1,
813 __isl_keep isl_map *map2);
814 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
815 __isl_keep isl_map *map2);
816 int isl_basic_map_is_equal(
817 __isl_keep isl_basic_map *bmap1,
818 __isl_keep isl_basic_map *bmap2);
822 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
823 __isl_keep isl_set *set2);
827 int isl_set_is_subset(__isl_keep isl_set *set1,
828 __isl_keep isl_set *set2);
829 int isl_set_is_strict_subset(
830 __isl_keep isl_set *set1,
831 __isl_keep isl_set *set2);
832 int isl_basic_map_is_subset(
833 __isl_keep isl_basic_map *bmap1,
834 __isl_keep isl_basic_map *bmap2);
835 int isl_basic_map_is_strict_subset(
836 __isl_keep isl_basic_map *bmap1,
837 __isl_keep isl_basic_map *bmap2);
838 int isl_map_is_subset(
839 __isl_keep isl_map *map1,
840 __isl_keep isl_map *map2);
841 int isl_map_is_strict_subset(
842 __isl_keep isl_map *map1,
843 __isl_keep isl_map *map2);
847 =head2 Unary Operations
853 __isl_give isl_set *isl_set_complement(
854 __isl_take isl_set *set);
858 __isl_give isl_basic_set *isl_basic_set_project_out(
859 __isl_take isl_basic_set *bset,
860 enum isl_dim_type type, unsigned first, unsigned n);
861 __isl_give isl_basic_map *isl_basic_map_project_out(
862 __isl_take isl_basic_map *bmap,
863 enum isl_dim_type type, unsigned first, unsigned n);
864 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
865 enum isl_dim_type type, unsigned first, unsigned n);
866 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
867 enum isl_dim_type type, unsigned first, unsigned n);
868 __isl_give isl_basic_set *isl_basic_map_domain(
869 __isl_take isl_basic_map *bmap);
870 __isl_give isl_basic_set *isl_basic_map_range(
871 __isl_take isl_basic_map *bmap);
872 __isl_give isl_set *isl_map_domain(
873 __isl_take isl_map *bmap);
874 __isl_give isl_set *isl_map_range(
875 __isl_take isl_map *map);
879 Simplify the representation of a set or relation by trying
880 to combine pairs of basic sets or relations into a single
881 basic set or relation.
883 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
884 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
888 __isl_give isl_basic_set *isl_set_convex_hull(
889 __isl_take isl_set *set);
890 __isl_give isl_basic_map *isl_map_convex_hull(
891 __isl_take isl_map *map);
893 If the input set or relation has any existentially quantified
894 variables, then the result of these operations is currently undefined.
898 __isl_give isl_basic_set *isl_set_simple_hull(
899 __isl_take isl_set *set);
900 __isl_give isl_basic_map *isl_map_simple_hull(
901 __isl_take isl_map *map);
903 These functions compute a single basic set or relation
904 that contains the whole input set or relation.
905 In particular, the output is described by translates
906 of the constraints describing the basic sets or relations in the input.
910 (See \autoref{s:simple hull}.)
916 __isl_give isl_basic_set *isl_basic_set_affine_hull(
917 __isl_take isl_basic_set *bset);
918 __isl_give isl_basic_set *isl_set_affine_hull(
919 __isl_take isl_set *set);
920 __isl_give isl_basic_map *isl_basic_map_affine_hull(
921 __isl_take isl_basic_map *bmap);
922 __isl_give isl_basic_map *isl_map_affine_hull(
923 __isl_take isl_map *map);
927 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
928 unsigned param, int *exact);
930 Compute a parametric representation for all positive powers I<k> of C<map>.
931 The power I<k> is equated to the parameter at position C<param>.
932 The result may be an overapproximation. If the result is exact,
933 then C<*exact> is set to C<1>.
934 The current implementation only produces exact results for particular
935 cases of piecewise translations (i.e., piecewise uniform dependences).
937 =item * Transitive closure
939 __isl_give isl_map *isl_map_transitive_closure(
940 __isl_take isl_map *map, int *exact);
942 Compute the transitive closure of C<map>.
943 The result may be an overapproximation. If the result is known to be exact,
944 then C<*exact> is set to C<1>.
945 The current implementation only produces exact results for particular
946 cases of piecewise translations (i.e., piecewise uniform dependences).
950 =head2 Binary Operations
952 The two arguments of a binary operation not only need to live
953 in the same C<isl_ctx>, they currently also need to have
954 the same (number of) parameters.
956 =head3 Basic Operations
962 __isl_give isl_basic_set *isl_basic_set_intersect(
963 __isl_take isl_basic_set *bset1,
964 __isl_take isl_basic_set *bset2);
965 __isl_give isl_set *isl_set_intersect(
966 __isl_take isl_set *set1,
967 __isl_take isl_set *set2);
968 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
969 __isl_take isl_basic_map *bmap,
970 __isl_take isl_basic_set *bset);
971 __isl_give isl_basic_map *isl_basic_map_intersect_range(
972 __isl_take isl_basic_map *bmap,
973 __isl_take isl_basic_set *bset);
974 __isl_give isl_basic_map *isl_basic_map_intersect(
975 __isl_take isl_basic_map *bmap1,
976 __isl_take isl_basic_map *bmap2);
977 __isl_give isl_map *isl_map_intersect_domain(
978 __isl_take isl_map *map,
979 __isl_take isl_set *set);
980 __isl_give isl_map *isl_map_intersect_range(
981 __isl_take isl_map *map,
982 __isl_take isl_set *set);
983 __isl_give isl_map *isl_map_intersect(
984 __isl_take isl_map *map1,
985 __isl_take isl_map *map2);
989 __isl_give isl_set *isl_basic_set_union(
990 __isl_take isl_basic_set *bset1,
991 __isl_take isl_basic_set *bset2);
992 __isl_give isl_map *isl_basic_map_union(
993 __isl_take isl_basic_map *bmap1,
994 __isl_take isl_basic_map *bmap2);
995 __isl_give isl_set *isl_set_union(
996 __isl_take isl_set *set1,
997 __isl_take isl_set *set2);
998 __isl_give isl_map *isl_map_union(
999 __isl_take isl_map *map1,
1000 __isl_take isl_map *map2);
1002 =item * Set difference
1004 __isl_give isl_set *isl_set_subtract(
1005 __isl_take isl_set *set1,
1006 __isl_take isl_set *set2);
1007 __isl_give isl_map *isl_map_subtract(
1008 __isl_take isl_map *map1,
1009 __isl_take isl_map *map2);
1013 __isl_give isl_basic_set *isl_basic_set_apply(
1014 __isl_take isl_basic_set *bset,
1015 __isl_take isl_basic_map *bmap);
1016 __isl_give isl_set *isl_set_apply(
1017 __isl_take isl_set *set,
1018 __isl_take isl_map *map);
1019 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1020 __isl_take isl_basic_map *bmap1,
1021 __isl_take isl_basic_map *bmap2);
1022 __isl_give isl_basic_map *isl_basic_map_apply_range(
1023 __isl_take isl_basic_map *bmap1,
1024 __isl_take isl_basic_map *bmap2);
1025 __isl_give isl_map *isl_map_apply_domain(
1026 __isl_take isl_map *map1,
1027 __isl_take isl_map *map2);
1028 __isl_give isl_map *isl_map_apply_range(
1029 __isl_take isl_map *map1,
1030 __isl_take isl_map *map2);
1034 =head3 Lexicographic Optimization
1036 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1037 the following functions
1038 compute a set that contains the lexicographic minimum or maximum
1039 of the elements in C<set> (or C<bset>) for those values of the parameters
1040 that satisfy C<dom>.
1041 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1042 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1044 In other words, the union of the parameter values
1045 for which the result is non-empty and of C<*empty>
1048 __isl_give isl_set *isl_basic_set_partial_lexmin(
1049 __isl_take isl_basic_set *bset,
1050 __isl_take isl_basic_set *dom,
1051 __isl_give isl_set **empty);
1052 __isl_give isl_set *isl_basic_set_partial_lexmax(
1053 __isl_take isl_basic_set *bset,
1054 __isl_take isl_basic_set *dom,
1055 __isl_give isl_set **empty);
1056 __isl_give isl_set *isl_set_partial_lexmin(
1057 __isl_take isl_set *set, __isl_take isl_set *dom,
1058 __isl_give isl_set **empty);
1059 __isl_give isl_set *isl_set_partial_lexmax(
1060 __isl_take isl_set *set, __isl_take isl_set *dom,
1061 __isl_give isl_set **empty);
1063 Given a (basic) set C<set> (or C<bset>), the following functions simply
1064 return a set containing the lexicographic minimum or maximum
1065 of the elements in C<set> (or C<bset>).
1067 __isl_give isl_set *isl_basic_set_lexmin(
1068 __isl_take isl_basic_set *bset);
1069 __isl_give isl_set *isl_basic_set_lexmax(
1070 __isl_take isl_basic_set *bset);
1071 __isl_give isl_set *isl_set_lexmin(
1072 __isl_take isl_set *set);
1073 __isl_give isl_set *isl_set_lexmax(
1074 __isl_take isl_set *set);
1076 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1077 the following functions
1078 compute a relation that maps each element of C<dom>
1079 to the single lexicographic minimum or maximum
1080 of the elements that are associated to that same
1081 element in C<map> (or C<bmap>).
1082 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1083 that contains the elements in C<dom> that do not map
1084 to any elements in C<map> (or C<bmap>).
1085 In other words, the union of the domain of the result and of C<*empty>
1088 __isl_give isl_map *isl_basic_map_partial_lexmax(
1089 __isl_take isl_basic_map *bmap,
1090 __isl_take isl_basic_set *dom,
1091 __isl_give isl_set **empty);
1092 __isl_give isl_map *isl_basic_map_partial_lexmin(
1093 __isl_take isl_basic_map *bmap,
1094 __isl_take isl_basic_set *dom,
1095 __isl_give isl_set **empty);
1096 __isl_give isl_map *isl_map_partial_lexmax(
1097 __isl_take isl_map *map, __isl_take isl_set *dom,
1098 __isl_give isl_set **empty);
1099 __isl_give isl_map *isl_map_partial_lexmin(
1100 __isl_take isl_map *map, __isl_take isl_set *dom,
1101 __isl_give isl_set **empty);
1103 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1104 return a map mapping each element in the domain of
1105 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1106 of all elements associated to that element.
1108 __isl_give isl_map *isl_basic_map_lexmin(
1109 __isl_take isl_basic_map *bmap);
1110 __isl_give isl_map *isl_basic_map_lexmax(
1111 __isl_take isl_basic_map *bmap);
1112 __isl_give isl_map *isl_map_lexmin(
1113 __isl_take isl_map *map);
1114 __isl_give isl_map *isl_map_lexmax(
1115 __isl_take isl_map *map);
1119 Points are elements of a set. They can be used to construct
1120 simple sets (boxes) or they can be used to represent the
1121 individual elements of a set.
1122 The zero point (the origin) can be created using
1124 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1126 The coordinates of a point can be inspected, set and changed
1129 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1130 enum isl_dim_type type, int pos, isl_int *v);
1131 __isl_give isl_point *isl_point_set_coordinate(
1132 __isl_take isl_point *pnt,
1133 enum isl_dim_type type, int pos, isl_int v);
1135 __isl_give isl_point *isl_point_add_ui(
1136 __isl_take isl_point *pnt,
1137 enum isl_dim_type type, int pos, unsigned val);
1138 __isl_give isl_point *isl_point_sub_ui(
1139 __isl_take isl_point *pnt,
1140 enum isl_dim_type type, int pos, unsigned val);
1142 Points can be copied or freed using
1144 __isl_give isl_point *isl_point_copy(
1145 __isl_keep isl_point *pnt);
1146 void isl_point_free(__isl_take isl_point *pnt);
1148 A singleton set can be created from a point using
1150 __isl_give isl_set *isl_set_from_point(
1151 __isl_take isl_point *pnt);
1153 and a box can be created from two opposite extremal points using
1155 __isl_give isl_set *isl_set_box_from_points(
1156 __isl_take isl_point *pnt1,
1157 __isl_take isl_point *pnt2);
1159 All elements of a B<bounded> set can be enumerated using
1160 the following function.
1162 int isl_set_foreach_point(__isl_keep isl_set *set,
1163 int (*fn)(__isl_take isl_point *pnt, void *user),
1166 The function C<fn> is called for each integer point in
1167 C<set> with as second argument the last argument of
1168 the C<isl_set_foreach_point> call. The function C<fn>
1169 should return C<0> on success and C<-1> on failure.
1170 In the latter case, C<isl_set_foreach_point> will stop
1171 enumerating and return C<-1> as well.
1172 If the enumeration is performed successfully and to completion,
1173 then C<isl_set_foreach_point> returns C<0>.
1175 To obtain a single point of a set, use
1177 __isl_give isl_point *isl_set_sample_point(
1178 __isl_take isl_set *set);
1180 If C<set> does not contain any (integer) points, then the
1181 resulting point will be ``void'', a property that can be
1184 int isl_point_is_void(__isl_keep isl_point *pnt);
1186 =head2 Piecewise Quasipolynomials
1188 A piecewise quasipolynomial is a particular kind of function that maps
1189 a parametric point to a rational value.
1190 More specifically, a quasipolynomial is a polynomial expression in greatest
1191 integer parts of affine expressions of parameters and variables.
1192 A piecewise quasipolynomial is a subdivision of a given parametric
1193 domain into disjoint cells with a quasipolynomial associated to
1194 each cell. The value of the piecewise quasipolynomial at a given
1195 point is the value of the quasipolynomial associated to the cell
1196 that contains the point. Outside of the union of cells,
1197 the value is assumed to be zero.
1198 For example, the piecewise quasipolynomial
1200 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1202 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1203 Piecewise quasipolynomials are mainly used by the C<barvinok>
1204 library for representing the number of elements in a parametric set or map.
1205 For example, the piecewise quasipolynomial above represents
1206 the number of point in the map
1208 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1210 =head3 Printing (Piecewise) Quasipolynomials
1212 Quasipolynomials and piecewise quasipolynomials can be printed
1213 using the following functions.
1215 __isl_give isl_printer *isl_printer_print_qpolynomial(
1216 __isl_take isl_printer *p,
1217 __isl_keep isl_qpolynomial *qp);
1219 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1220 __isl_take isl_printer *p,
1221 __isl_keep isl_pw_qpolynomial *pwqp);
1223 The output format of the printer
1224 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1226 =head3 Creating New (Piecewise) Quasipolynomials
1228 Some simple quasipolynomials can be created using the following functions.
1229 More complicated quasipolynomials can be created by applying
1230 operations such as addition and multiplication
1231 on the resulting quasipolynomials
1233 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1234 __isl_take isl_dim *dim);
1235 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1236 __isl_take isl_dim *dim);
1237 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1238 __isl_take isl_dim *dim);
1239 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1240 __isl_take isl_dim *dim,
1241 const isl_int n, const isl_int d);
1242 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1243 __isl_take isl_div *div);
1244 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1245 __isl_take isl_dim *dim,
1246 enum isl_dim_type type, unsigned pos);
1248 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1249 with a single cell can be created using the following functions.
1250 Multiple of these single cell piecewise quasipolynomials can
1251 be combined to create more complicated piecewise quasipolynomials.
1253 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1254 __isl_take isl_dim *dim);
1255 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1256 __isl_take isl_set *set,
1257 __isl_take isl_qpolynomial *qp);
1259 Quasipolynomials can be copied and freed again using the following
1262 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1263 __isl_keep isl_qpolynomial *qp);
1264 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1266 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1267 __isl_keep isl_pw_qpolynomial *pwqp);
1268 void isl_pw_qpolynomial_free(
1269 __isl_take isl_pw_qpolynomial *pwqp);
1271 =head3 Inspecting (Piecewise) Quasipolynomials
1273 To iterate over the cells in a piecewise quasipolynomial,
1274 use either of the following two functions
1276 int isl_pw_qpolynomial_foreach_piece(
1277 __isl_keep isl_pw_qpolynomial *pwqp,
1278 int (*fn)(__isl_take isl_set *set,
1279 __isl_take isl_qpolynomial *qp,
1280 void *user), void *user);
1281 int isl_pw_qpolynomial_foreach_lifted_piece(
1282 __isl_keep isl_pw_qpolynomial *pwqp,
1283 int (*fn)(__isl_take isl_set *set,
1284 __isl_take isl_qpolynomial *qp,
1285 void *user), void *user);
1287 As usual, the function C<fn> should return C<0> on success
1288 and C<-1> on failure. The difference between
1289 C<isl_pw_qpolynomial_foreach_piece> and
1290 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1291 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1292 compute unique representations for all existentially quantified
1293 variables and then turn these existentially quantified variables
1294 into extra set variables, adapting the associated quasipolynomial
1295 accordingly. This means that the C<set> passed to C<fn>
1296 will not have any existentially quantified variables, but that
1297 the dimensions of the sets may be different for different
1298 invocations of C<fn>.
1300 To iterate over all terms in a quasipolynomial,
1303 int isl_qpolynomial_foreach_term(
1304 __isl_keep isl_qpolynomial *qp,
1305 int (*fn)(__isl_take isl_term *term,
1306 void *user), void *user);
1308 The terms themselves can be inspected and freed using
1311 unsigned isl_term_dim(__isl_keep isl_term *term,
1312 enum isl_dim_type type);
1313 void isl_term_get_num(__isl_keep isl_term *term,
1315 void isl_term_get_den(__isl_keep isl_term *term,
1317 int isl_term_get_exp(__isl_keep isl_term *term,
1318 enum isl_dim_type type, unsigned pos);
1319 __isl_give isl_div *isl_term_get_div(
1320 __isl_keep isl_term *term, unsigned pos);
1321 void isl_term_free(__isl_take isl_term *term);
1323 Each term is a product of parameters, set variables and
1324 integer divisions. The function C<isl_term_get_exp>
1325 returns the exponent of a given dimensions in the given term.
1326 The C<isl_int>s in the arguments of C<isl_term_get_num>
1327 and C<isl_term_get_den> need to have been initialized
1328 using C<isl_int_init> before calling these functions.
1330 =head3 Properties of (Piecewise) Quasipolynomials
1332 To check whether a quasipolynomial is actually a constant,
1333 use the following function.
1335 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1336 isl_int *n, isl_int *d);
1338 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1339 then the numerator and denominator of the constant
1340 are returned in C<*n> and C<*d>, respectively.
1342 =head3 Operations on (Piecewise) Quasipolynomials
1344 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1345 __isl_take isl_qpolynomial *qp);
1346 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1347 __isl_take isl_qpolynomial *qp1,
1348 __isl_take isl_qpolynomial *qp2);
1349 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1350 __isl_take isl_qpolynomial *qp1,
1351 __isl_take isl_qpolynomial *qp2);
1353 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1354 __isl_take isl_pw_qpolynomial *pwqp1,
1355 __isl_take isl_pw_qpolynomial *pwqp2);
1356 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1357 __isl_take isl_pw_qpolynomial *pwqp1,
1358 __isl_take isl_pw_qpolynomial *pwqp2);
1359 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1360 __isl_take isl_pw_qpolynomial *pwqp1,
1361 __isl_take isl_pw_qpolynomial *pwqp2);
1362 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1363 __isl_take isl_pw_qpolynomial *pwqp);
1364 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1365 __isl_take isl_pw_qpolynomial *pwqp1,
1366 __isl_take isl_pw_qpolynomial *pwqp2);
1368 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1369 __isl_take isl_pw_qpolynomial *pwqp,
1370 __isl_take isl_point *pnt);
1372 __isl_give isl_set *isl_pw_qpolynomial_domain(
1373 __isl_take isl_pw_qpolynomial *pwqp);
1374 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1375 __isl_take isl_pw_qpolynomial *pwpq,
1376 __isl_take isl_set *set);
1378 =head2 Dependence Analysis
1380 C<isl> contains specialized functionality for performing
1381 array dataflow analysis. That is, given a I<sink> access relation
1382 and a collection of possible I<source> access relations,
1383 C<isl> can compute relations that describe
1384 for each iteration of the sink access, which iteration
1385 of which of the source access relations was the last
1386 to access the same data element before the given iteration
1388 To compute standard flow dependences, the sink should be
1389 a read, while the sources should be writes.
1391 #include <isl_flow.h>
1393 __isl_give isl_access_info *isl_access_info_alloc(
1394 __isl_take isl_map *sink,
1395 void *sink_user, isl_access_level_before fn,
1397 __isl_give isl_access_info *isl_access_info_add_source(
1398 __isl_take isl_access_info *acc,
1399 __isl_take isl_map *source, void *source_user);
1401 __isl_give isl_flow *isl_access_info_compute_flow(
1402 __isl_take isl_access_info *acc);
1404 int isl_flow_foreach(__isl_keep isl_flow *deps,
1405 int (*fn)(__isl_take isl_map *dep, void *dep_user,
1408 __isl_give isl_set *isl_flow_get_no_source(
1409 __isl_keep isl_flow *deps);
1410 void isl_flow_free(__isl_take isl_flow *deps);
1412 The function C<isl_access_info_compute_flow> performs the actual
1413 dependence analysis. The other functions are used to construct
1414 the input for this function or to read off the output.
1416 The input is collected in an C<isl_access_info>, which can
1417 be created through a call to C<isl_access_info_alloc>.
1418 The arguments to this functions are the sink access relation
1419 C<sink>, a token C<sink_user> used to identify the sink
1420 access to the user, a callback function for specifying the
1421 relative order of source and sink accesses, and the number
1422 of source access relations that will be added.
1423 The callback function has type C<int (*)(void *first, void *second)>.
1424 The function is called with two user supplied tokens identifying
1425 either a source or the sink and it should return the shared nesting
1426 level and the relative order of the two accesses.
1427 In particular, let I<n> be the number of loops shared by
1428 the two accesses. If C<first> precedes C<second> textually,
1429 then the function should return I<2 * n + 1>; otherwise,
1430 it should return I<2 * n>.
1431 The sources can be added to the C<isl_access_info> by performing
1432 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1433 The C<source_user> token is again used to identify
1434 the source access. The range of the source access relation
1435 C<source> should have the same dimension as the range
1436 of the sink access relation.
1438 The result of the dependence analysis is collected in an
1439 C<isl_flow>. There may be elements in the domain of
1440 the sink access for which no preceding source access could be
1441 find. The set of these elements can be obtained through
1442 a call to C<isl_flow_get_no_source>.
1443 In the case of standard flow dependence analysis,
1444 this set corresponds to the reads from uninitialized
1446 The actual flow dependences can be extracted using
1447 C<isl_flow_foreach>. This function will call the user-specified
1448 callback function C<fn> for each B<non-empty> dependence between
1449 a source and the sink. The callback function is called
1450 with three arguments, the actual flow dependence relation
1451 mapping source iterations to sink iterations, a token
1452 identifying the source and an additional C<void *> with value
1453 equal to the third argument of the C<isl_flow_foreach> call.
1455 After finishing with an C<isl_flow>, the user should call
1456 C<isl_flow_free> to free all associated memory.
1460 Although C<isl> is mainly meant to be used as a library,
1461 it also contains some basic applications that use some
1462 of the functionality of C<isl>.
1463 The input may be specified in either the L<isl format>
1464 or the L<PolyLib format>.
1466 =head2 C<isl_polyhedron_sample>
1468 C<isl_polyhedron_sample> takes a polyhedron as input and prints
1469 an integer element of the polyhedron, if there is any.
1470 The first column in the output is the denominator and is always
1471 equal to 1. If the polyhedron contains no integer points,
1472 then a vector of length zero is printed.
1476 C<isl_pip> takes the same input as the C<example> program
1477 from the C<piplib> distribution, i.e., a set of constraints
1478 on the parameters, a line contains only -1 and finally a set
1479 of constraints on a parametric polyhedron.
1480 The coefficients of the parameters appear in the last columns
1481 (but before the final constant column).
1482 The output is the lexicographic minimum of the parametric polyhedron.
1483 As C<isl> currently does not have its own output format, the output
1484 is just a dump of the internal state.
1486 =head2 C<isl_polyhedron_minimize>
1488 C<isl_polyhedron_minimize> computes the minimum of some linear
1489 or affine objective function over the integer points in a polyhedron.
1490 If an affine objective function
1491 is given, then the constant should appear in the last column.
1493 =head2 C<isl_polytope_scan>
1495 Given a polytope, C<isl_polytope_scan> prints
1496 all integer points in the polytope.
1498 =head1 C<isl-polylib>
1500 The C<isl-polylib> library provides the following functions for converting
1501 between C<isl> objects and C<PolyLib> objects.
1502 The library is distributed separately for licensing reasons.
1504 #include <isl_set_polylib.h>
1505 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
1506 Polyhedron *P, __isl_take isl_dim *dim);
1507 Polyhedron *isl_basic_set_to_polylib(
1508 __isl_keep isl_basic_set *bset);
1509 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
1510 __isl_take isl_dim *dim);
1511 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
1513 #include <isl_map_polylib.h>
1514 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
1515 Polyhedron *P, __isl_take isl_dim *dim);
1516 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
1517 __isl_take isl_dim *dim);
1518 Polyhedron *isl_basic_map_to_polylib(
1519 __isl_keep isl_basic_map *bmap);
1520 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);