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 When called on a file printer, the following function flushes
536 the file. When called on a string printer, the buffer is cleared.
538 __isl_give isl_printer *isl_printer_flush(
539 __isl_take isl_printer *p);
541 =head2 Creating New Sets and Relations
543 C<isl> has functions for creating some standard sets and relations.
547 =item * Empty sets and relations
549 __isl_give isl_basic_set *isl_basic_set_empty(
550 __isl_take isl_dim *dim);
551 __isl_give isl_basic_map *isl_basic_map_empty(
552 __isl_take isl_dim *dim);
553 __isl_give isl_set *isl_set_empty(
554 __isl_take isl_dim *dim);
555 __isl_give isl_map *isl_map_empty(
556 __isl_take isl_dim *dim);
558 =item * Universe sets and relations
560 __isl_give isl_basic_set *isl_basic_set_universe(
561 __isl_take isl_dim *dim);
562 __isl_give isl_basic_map *isl_basic_map_universe(
563 __isl_take isl_dim *dim);
564 __isl_give isl_set *isl_set_universe(
565 __isl_take isl_dim *dim);
566 __isl_give isl_map *isl_map_universe(
567 __isl_take isl_dim *dim);
569 =item * Identity relations
571 __isl_give isl_basic_map *isl_basic_map_identity(
572 __isl_take isl_dim *set_dim);
573 __isl_give isl_map *isl_map_identity(
574 __isl_take isl_dim *set_dim);
576 These functions take a dimension specification for a B<set>
577 and return an identity relation between two such sets.
579 =item * Lexicographic order
581 __isl_give isl_map *isl_map_lex_lt(
582 __isl_take isl_dim *set_dim);
583 __isl_give isl_map *isl_map_lex_le(
584 __isl_take isl_dim *set_dim);
585 __isl_give isl_map *isl_map_lex_gt(
586 __isl_take isl_dim *set_dim);
587 __isl_give isl_map *isl_map_lex_ge(
588 __isl_take isl_dim *set_dim);
589 __isl_give isl_map *isl_map_lex_lt_first(
590 __isl_take isl_dim *dim, unsigned n);
591 __isl_give isl_map *isl_map_lex_le_first(
592 __isl_take isl_dim *dim, unsigned n);
593 __isl_give isl_map *isl_map_lex_gt_first(
594 __isl_take isl_dim *dim, unsigned n);
595 __isl_give isl_map *isl_map_lex_ge_first(
596 __isl_take isl_dim *dim, unsigned n);
598 The first four functions take a dimension specification for a B<set>
599 and return relations that express that the elements in the domain
600 are lexicographically less
601 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
602 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
603 than the elements in the range.
604 The last four functions take a dimension specification for a map
605 and return relations that express that the first C<n> dimensions
606 in the domain are lexicographically less
607 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
608 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
609 than the first C<n> dimensions in the range.
613 A basic set or relation can be converted to a set or relation
614 using the following functions.
616 __isl_give isl_set *isl_set_from_basic_set(
617 __isl_take isl_basic_set *bset);
618 __isl_give isl_map *isl_map_from_basic_map(
619 __isl_take isl_basic_map *bmap);
621 Sets and relations can be copied and freed again using the following
624 __isl_give isl_basic_set *isl_basic_set_copy(
625 __isl_keep isl_basic_set *bset);
626 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
627 __isl_give isl_basic_map *isl_basic_map_copy(
628 __isl_keep isl_basic_map *bmap);
629 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
630 void isl_basic_set_free(__isl_take isl_basic_set *bset);
631 void isl_set_free(__isl_take isl_set *set);
632 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
633 void isl_map_free(__isl_take isl_map *map);
635 Other sets and relations can be constructed by starting
636 from a universe set or relation, adding equality and/or
637 inequality constraints and then projecting out the
638 existentially quantified variables, if any.
639 Constraints can be constructed, manipulated and
640 added to basic sets and relations using the following functions.
642 #include <isl_constraint.h>
643 __isl_give isl_constraint *isl_equality_alloc(
644 __isl_take isl_dim *dim);
645 __isl_give isl_constraint *isl_inequality_alloc(
646 __isl_take isl_dim *dim);
647 void isl_constraint_set_constant(
648 __isl_keep isl_constraint *constraint, isl_int v);
649 void isl_constraint_set_coefficient(
650 __isl_keep isl_constraint *constraint,
651 enum isl_dim_type type, int pos, isl_int v);
652 __isl_give isl_basic_map *isl_basic_map_add_constraint(
653 __isl_take isl_basic_map *bmap,
654 __isl_take isl_constraint *constraint);
655 __isl_give isl_basic_set *isl_basic_set_add_constraint(
656 __isl_take isl_basic_set *bset,
657 __isl_take isl_constraint *constraint);
659 For example, to create a set containing the even integers
660 between 10 and 42, you would use the following code.
664 struct isl_constraint *c;
665 struct isl_basic_set *bset;
668 dim = isl_dim_set_alloc(ctx, 0, 2);
669 bset = isl_basic_set_universe(isl_dim_copy(dim));
671 c = isl_equality_alloc(isl_dim_copy(dim));
672 isl_int_set_si(v, -1);
673 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
674 isl_int_set_si(v, 2);
675 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
676 bset = isl_basic_set_add_constraint(bset, c);
678 c = isl_inequality_alloc(isl_dim_copy(dim));
679 isl_int_set_si(v, -10);
680 isl_constraint_set_constant(c, v);
681 isl_int_set_si(v, 1);
682 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
683 bset = isl_basic_set_add_constraint(bset, c);
685 c = isl_inequality_alloc(dim);
686 isl_int_set_si(v, 42);
687 isl_constraint_set_constant(c, v);
688 isl_int_set_si(v, -1);
689 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
690 bset = isl_basic_set_add_constraint(bset, c);
692 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
698 struct isl_basic_set *bset;
699 bset = isl_basic_set_read_from_str(ctx,
700 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
702 =head2 Inspecting Sets and Relations
704 Usually, the user should not have to care about the actual constraints
705 of the sets and maps, but should instead apply the abstract operations
706 explained in the following sections.
707 Occasionally, however, it may be required to inspect the individual
708 coefficients of the constraints. This section explains how to do so.
709 In these cases, it may also be useful to have C<isl> compute
710 an explicit representation of the existentially quantified variables.
712 __isl_give isl_set *isl_set_compute_divs(
713 __isl_take isl_set *set);
714 __isl_give isl_map *isl_map_compute_divs(
715 __isl_take isl_map *map);
717 This explicit representation defines the existentially quantified
718 variables as integer divisions of the other variables, possibly
719 including earlier existentially quantified variables.
720 An explicitly represented existentially quantified variable therefore
721 has a unique value when the values of the other variables are known.
722 If, furthermore, the same existentials, i.e., existentials
723 with the same explicit representations, should appear in the
724 same order in each of the disjuncts of a set or map, then the user should call
725 either of the following functions.
727 __isl_give isl_set *isl_set_align_divs(
728 __isl_take isl_set *set);
729 __isl_give isl_map *isl_map_align_divs(
730 __isl_take isl_map *map);
732 To iterate over all the basic sets or maps in a set or map, use
734 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
735 int (*fn)(__isl_take isl_basic_set *bset, void *user),
737 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
738 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
741 The callback function C<fn> should return 0 if successful and
742 -1 if an error occurs. In the latter case, or if any other error
743 occurs, the above functions will return -1.
745 It should be noted that C<isl> does not guarantee that
746 the basic sets or maps passed to C<fn> are disjoint.
747 If this is required, then the user should call one of
748 the following functions first.
750 __isl_give isl_set *isl_set_make_disjoint(
751 __isl_take isl_set *set);
752 __isl_give isl_map *isl_map_make_disjoint(
753 __isl_take isl_map *map);
755 To iterate over the constraints of a basic set or map, use
757 #include <isl_constraint.h>
759 int isl_basic_map_foreach_constraint(
760 __isl_keep isl_basic_map *bmap,
761 int (*fn)(__isl_take isl_constraint *c, void *user),
763 void isl_constraint_free(struct isl_constraint *c);
765 Again, the callback function C<fn> should return 0 if successful and
766 -1 if an error occurs. In the latter case, or if any other error
767 occurs, the above functions will return -1.
769 The coefficients of the constraints can be inspected using
770 the following functions.
772 void isl_constraint_get_constant(
773 __isl_keep isl_constraint *constraint, isl_int *v);
774 void isl_constraint_get_coefficient(
775 __isl_keep isl_constraint *constraint,
776 enum isl_dim_type type, int pos, isl_int *v);
778 The explicit representations of the existentially quantified
779 variables can be inspected using the following functions.
780 Note that the user is only allowed to use these functions
781 if the inspected set or map is the result of a call
782 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
784 __isl_give isl_div *isl_constraint_div(
785 __isl_keep isl_constraint *constraint, int pos);
786 void isl_div_get_constant(__isl_keep isl_div *div,
788 void isl_div_get_denominator(__isl_keep isl_div *div,
790 void isl_div_get_coefficient(__isl_keep isl_div *div,
791 enum isl_dim_type type, int pos, isl_int *v);
795 =head3 Unary Properties
801 The following functions test whether the given set or relation
802 contains any integer points. The ``fast'' variants do not perform
803 any computations, but simply check if the given set or relation
804 is already known to be empty.
806 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
807 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
808 int isl_set_is_empty(__isl_keep isl_set *set);
809 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
810 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
811 int isl_map_fast_is_empty(__isl_keep isl_map *map);
812 int isl_map_is_empty(__isl_keep isl_map *map);
816 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
817 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
818 int isl_set_fast_is_universe(__isl_keep isl_set *set);
822 =head3 Binary Properties
828 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
829 __isl_keep isl_set *set2);
830 int isl_set_is_equal(__isl_keep isl_set *set1,
831 __isl_keep isl_set *set2);
832 int isl_map_is_equal(__isl_keep isl_map *map1,
833 __isl_keep isl_map *map2);
834 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
835 __isl_keep isl_map *map2);
836 int isl_basic_map_is_equal(
837 __isl_keep isl_basic_map *bmap1,
838 __isl_keep isl_basic_map *bmap2);
842 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
843 __isl_keep isl_set *set2);
847 int isl_set_is_subset(__isl_keep isl_set *set1,
848 __isl_keep isl_set *set2);
849 int isl_set_is_strict_subset(
850 __isl_keep isl_set *set1,
851 __isl_keep isl_set *set2);
852 int isl_basic_map_is_subset(
853 __isl_keep isl_basic_map *bmap1,
854 __isl_keep isl_basic_map *bmap2);
855 int isl_basic_map_is_strict_subset(
856 __isl_keep isl_basic_map *bmap1,
857 __isl_keep isl_basic_map *bmap2);
858 int isl_map_is_subset(
859 __isl_keep isl_map *map1,
860 __isl_keep isl_map *map2);
861 int isl_map_is_strict_subset(
862 __isl_keep isl_map *map1,
863 __isl_keep isl_map *map2);
867 =head2 Unary Operations
873 __isl_give isl_set *isl_set_complement(
874 __isl_take isl_set *set);
878 __isl_give isl_basic_map *isl_basic_map_reverse(
879 __isl_take isl_basic_map *bmap);
880 __isl_give isl_map *isl_map_reverse(
881 __isl_take isl_map *map);
885 __isl_give isl_basic_set *isl_basic_set_project_out(
886 __isl_take isl_basic_set *bset,
887 enum isl_dim_type type, unsigned first, unsigned n);
888 __isl_give isl_basic_map *isl_basic_map_project_out(
889 __isl_take isl_basic_map *bmap,
890 enum isl_dim_type type, unsigned first, unsigned n);
891 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
892 enum isl_dim_type type, unsigned first, unsigned n);
893 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
894 enum isl_dim_type type, unsigned first, unsigned n);
895 __isl_give isl_basic_set *isl_basic_map_domain(
896 __isl_take isl_basic_map *bmap);
897 __isl_give isl_basic_set *isl_basic_map_range(
898 __isl_take isl_basic_map *bmap);
899 __isl_give isl_set *isl_map_domain(
900 __isl_take isl_map *bmap);
901 __isl_give isl_set *isl_map_range(
902 __isl_take isl_map *map);
906 Simplify the representation of a set or relation by trying
907 to combine pairs of basic sets or relations into a single
908 basic set or relation.
910 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
911 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
915 __isl_give isl_basic_set *isl_set_convex_hull(
916 __isl_take isl_set *set);
917 __isl_give isl_basic_map *isl_map_convex_hull(
918 __isl_take isl_map *map);
920 If the input set or relation has any existentially quantified
921 variables, then the result of these operations is currently undefined.
925 __isl_give isl_basic_set *isl_set_simple_hull(
926 __isl_take isl_set *set);
927 __isl_give isl_basic_map *isl_map_simple_hull(
928 __isl_take isl_map *map);
930 These functions compute a single basic set or relation
931 that contains the whole input set or relation.
932 In particular, the output is described by translates
933 of the constraints describing the basic sets or relations in the input.
937 (See \autoref{s:simple hull}.)
943 __isl_give isl_basic_set *isl_basic_set_affine_hull(
944 __isl_take isl_basic_set *bset);
945 __isl_give isl_basic_set *isl_set_affine_hull(
946 __isl_take isl_set *set);
947 __isl_give isl_basic_map *isl_basic_map_affine_hull(
948 __isl_take isl_basic_map *bmap);
949 __isl_give isl_basic_map *isl_map_affine_hull(
950 __isl_take isl_map *map);
954 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
955 unsigned param, int *exact);
957 Compute a parametric representation for all positive powers I<k> of C<map>.
958 The power I<k> is equated to the parameter at position C<param>.
959 The result may be an overapproximation. If the result is exact,
960 then C<*exact> is set to C<1>.
961 The current implementation only produces exact results for particular
962 cases of piecewise translations (i.e., piecewise uniform dependences).
964 =item * Transitive closure
966 __isl_give isl_map *isl_map_transitive_closure(
967 __isl_take isl_map *map, int *exact);
969 Compute the transitive closure of C<map>.
970 The result may be an overapproximation. If the result is known to be exact,
971 then C<*exact> is set to C<1>.
972 The current implementation only produces exact results for particular
973 cases of piecewise translations (i.e., piecewise uniform dependences).
977 =head2 Binary Operations
979 The two arguments of a binary operation not only need to live
980 in the same C<isl_ctx>, they currently also need to have
981 the same (number of) parameters.
983 =head3 Basic Operations
989 __isl_give isl_basic_set *isl_basic_set_intersect(
990 __isl_take isl_basic_set *bset1,
991 __isl_take isl_basic_set *bset2);
992 __isl_give isl_set *isl_set_intersect(
993 __isl_take isl_set *set1,
994 __isl_take isl_set *set2);
995 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
996 __isl_take isl_basic_map *bmap,
997 __isl_take isl_basic_set *bset);
998 __isl_give isl_basic_map *isl_basic_map_intersect_range(
999 __isl_take isl_basic_map *bmap,
1000 __isl_take isl_basic_set *bset);
1001 __isl_give isl_basic_map *isl_basic_map_intersect(
1002 __isl_take isl_basic_map *bmap1,
1003 __isl_take isl_basic_map *bmap2);
1004 __isl_give isl_map *isl_map_intersect_domain(
1005 __isl_take isl_map *map,
1006 __isl_take isl_set *set);
1007 __isl_give isl_map *isl_map_intersect_range(
1008 __isl_take isl_map *map,
1009 __isl_take isl_set *set);
1010 __isl_give isl_map *isl_map_intersect(
1011 __isl_take isl_map *map1,
1012 __isl_take isl_map *map2);
1016 __isl_give isl_set *isl_basic_set_union(
1017 __isl_take isl_basic_set *bset1,
1018 __isl_take isl_basic_set *bset2);
1019 __isl_give isl_map *isl_basic_map_union(
1020 __isl_take isl_basic_map *bmap1,
1021 __isl_take isl_basic_map *bmap2);
1022 __isl_give isl_set *isl_set_union(
1023 __isl_take isl_set *set1,
1024 __isl_take isl_set *set2);
1025 __isl_give isl_map *isl_map_union(
1026 __isl_take isl_map *map1,
1027 __isl_take isl_map *map2);
1029 =item * Set difference
1031 __isl_give isl_set *isl_set_subtract(
1032 __isl_take isl_set *set1,
1033 __isl_take isl_set *set2);
1034 __isl_give isl_map *isl_map_subtract(
1035 __isl_take isl_map *map1,
1036 __isl_take isl_map *map2);
1040 __isl_give isl_basic_set *isl_basic_set_apply(
1041 __isl_take isl_basic_set *bset,
1042 __isl_take isl_basic_map *bmap);
1043 __isl_give isl_set *isl_set_apply(
1044 __isl_take isl_set *set,
1045 __isl_take isl_map *map);
1046 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1047 __isl_take isl_basic_map *bmap1,
1048 __isl_take isl_basic_map *bmap2);
1049 __isl_give isl_basic_map *isl_basic_map_apply_range(
1050 __isl_take isl_basic_map *bmap1,
1051 __isl_take isl_basic_map *bmap2);
1052 __isl_give isl_map *isl_map_apply_domain(
1053 __isl_take isl_map *map1,
1054 __isl_take isl_map *map2);
1055 __isl_give isl_map *isl_map_apply_range(
1056 __isl_take isl_map *map1,
1057 __isl_take isl_map *map2);
1061 =head3 Lexicographic Optimization
1063 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1064 the following functions
1065 compute a set that contains the lexicographic minimum or maximum
1066 of the elements in C<set> (or C<bset>) for those values of the parameters
1067 that satisfy C<dom>.
1068 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1069 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1071 In other words, the union of the parameter values
1072 for which the result is non-empty and of C<*empty>
1075 __isl_give isl_set *isl_basic_set_partial_lexmin(
1076 __isl_take isl_basic_set *bset,
1077 __isl_take isl_basic_set *dom,
1078 __isl_give isl_set **empty);
1079 __isl_give isl_set *isl_basic_set_partial_lexmax(
1080 __isl_take isl_basic_set *bset,
1081 __isl_take isl_basic_set *dom,
1082 __isl_give isl_set **empty);
1083 __isl_give isl_set *isl_set_partial_lexmin(
1084 __isl_take isl_set *set, __isl_take isl_set *dom,
1085 __isl_give isl_set **empty);
1086 __isl_give isl_set *isl_set_partial_lexmax(
1087 __isl_take isl_set *set, __isl_take isl_set *dom,
1088 __isl_give isl_set **empty);
1090 Given a (basic) set C<set> (or C<bset>), the following functions simply
1091 return a set containing the lexicographic minimum or maximum
1092 of the elements in C<set> (or C<bset>).
1094 __isl_give isl_set *isl_basic_set_lexmin(
1095 __isl_take isl_basic_set *bset);
1096 __isl_give isl_set *isl_basic_set_lexmax(
1097 __isl_take isl_basic_set *bset);
1098 __isl_give isl_set *isl_set_lexmin(
1099 __isl_take isl_set *set);
1100 __isl_give isl_set *isl_set_lexmax(
1101 __isl_take isl_set *set);
1103 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1104 the following functions
1105 compute a relation that maps each element of C<dom>
1106 to the single lexicographic minimum or maximum
1107 of the elements that are associated to that same
1108 element in C<map> (or C<bmap>).
1109 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1110 that contains the elements in C<dom> that do not map
1111 to any elements in C<map> (or C<bmap>).
1112 In other words, the union of the domain of the result and of C<*empty>
1115 __isl_give isl_map *isl_basic_map_partial_lexmax(
1116 __isl_take isl_basic_map *bmap,
1117 __isl_take isl_basic_set *dom,
1118 __isl_give isl_set **empty);
1119 __isl_give isl_map *isl_basic_map_partial_lexmin(
1120 __isl_take isl_basic_map *bmap,
1121 __isl_take isl_basic_set *dom,
1122 __isl_give isl_set **empty);
1123 __isl_give isl_map *isl_map_partial_lexmax(
1124 __isl_take isl_map *map, __isl_take isl_set *dom,
1125 __isl_give isl_set **empty);
1126 __isl_give isl_map *isl_map_partial_lexmin(
1127 __isl_take isl_map *map, __isl_take isl_set *dom,
1128 __isl_give isl_set **empty);
1130 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1131 return a map mapping each element in the domain of
1132 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1133 of all elements associated to that element.
1135 __isl_give isl_map *isl_basic_map_lexmin(
1136 __isl_take isl_basic_map *bmap);
1137 __isl_give isl_map *isl_basic_map_lexmax(
1138 __isl_take isl_basic_map *bmap);
1139 __isl_give isl_map *isl_map_lexmin(
1140 __isl_take isl_map *map);
1141 __isl_give isl_map *isl_map_lexmax(
1142 __isl_take isl_map *map);
1146 Points are elements of a set. They can be used to construct
1147 simple sets (boxes) or they can be used to represent the
1148 individual elements of a set.
1149 The zero point (the origin) can be created using
1151 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1153 The coordinates of a point can be inspected, set and changed
1156 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1157 enum isl_dim_type type, int pos, isl_int *v);
1158 __isl_give isl_point *isl_point_set_coordinate(
1159 __isl_take isl_point *pnt,
1160 enum isl_dim_type type, int pos, isl_int v);
1162 __isl_give isl_point *isl_point_add_ui(
1163 __isl_take isl_point *pnt,
1164 enum isl_dim_type type, int pos, unsigned val);
1165 __isl_give isl_point *isl_point_sub_ui(
1166 __isl_take isl_point *pnt,
1167 enum isl_dim_type type, int pos, unsigned val);
1169 Points can be copied or freed using
1171 __isl_give isl_point *isl_point_copy(
1172 __isl_keep isl_point *pnt);
1173 void isl_point_free(__isl_take isl_point *pnt);
1175 A singleton set can be created from a point using
1177 __isl_give isl_set *isl_set_from_point(
1178 __isl_take isl_point *pnt);
1180 and a box can be created from two opposite extremal points using
1182 __isl_give isl_set *isl_set_box_from_points(
1183 __isl_take isl_point *pnt1,
1184 __isl_take isl_point *pnt2);
1186 All elements of a B<bounded> set can be enumerated using
1187 the following function.
1189 int isl_set_foreach_point(__isl_keep isl_set *set,
1190 int (*fn)(__isl_take isl_point *pnt, void *user),
1193 The function C<fn> is called for each integer point in
1194 C<set> with as second argument the last argument of
1195 the C<isl_set_foreach_point> call. The function C<fn>
1196 should return C<0> on success and C<-1> on failure.
1197 In the latter case, C<isl_set_foreach_point> will stop
1198 enumerating and return C<-1> as well.
1199 If the enumeration is performed successfully and to completion,
1200 then C<isl_set_foreach_point> returns C<0>.
1202 To obtain a single point of a set, use
1204 __isl_give isl_point *isl_set_sample_point(
1205 __isl_take isl_set *set);
1207 If C<set> does not contain any (integer) points, then the
1208 resulting point will be ``void'', a property that can be
1211 int isl_point_is_void(__isl_keep isl_point *pnt);
1213 =head2 Piecewise Quasipolynomials
1215 A piecewise quasipolynomial is a particular kind of function that maps
1216 a parametric point to a rational value.
1217 More specifically, a quasipolynomial is a polynomial expression in greatest
1218 integer parts of affine expressions of parameters and variables.
1219 A piecewise quasipolynomial is a subdivision of a given parametric
1220 domain into disjoint cells with a quasipolynomial associated to
1221 each cell. The value of the piecewise quasipolynomial at a given
1222 point is the value of the quasipolynomial associated to the cell
1223 that contains the point. Outside of the union of cells,
1224 the value is assumed to be zero.
1225 For example, the piecewise quasipolynomial
1227 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1229 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1230 Piecewise quasipolynomials are mainly used by the C<barvinok>
1231 library for representing the number of elements in a parametric set or map.
1232 For example, the piecewise quasipolynomial above represents
1233 the number of point in the map
1235 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1237 =head3 Printing (Piecewise) Quasipolynomials
1239 Quasipolynomials and piecewise quasipolynomials can be printed
1240 using the following functions.
1242 __isl_give isl_printer *isl_printer_print_qpolynomial(
1243 __isl_take isl_printer *p,
1244 __isl_keep isl_qpolynomial *qp);
1246 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1247 __isl_take isl_printer *p,
1248 __isl_keep isl_pw_qpolynomial *pwqp);
1250 The output format of the printer
1251 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1253 =head3 Creating New (Piecewise) Quasipolynomials
1255 Some simple quasipolynomials can be created using the following functions.
1256 More complicated quasipolynomials can be created by applying
1257 operations such as addition and multiplication
1258 on the resulting quasipolynomials
1260 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1261 __isl_take isl_dim *dim);
1262 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1263 __isl_take isl_dim *dim);
1264 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1265 __isl_take isl_dim *dim);
1266 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1267 __isl_take isl_dim *dim,
1268 const isl_int n, const isl_int d);
1269 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1270 __isl_take isl_div *div);
1271 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1272 __isl_take isl_dim *dim,
1273 enum isl_dim_type type, unsigned pos);
1275 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1276 with a single cell can be created using the following functions.
1277 Multiple of these single cell piecewise quasipolynomials can
1278 be combined to create more complicated piecewise quasipolynomials.
1280 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1281 __isl_take isl_dim *dim);
1282 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1283 __isl_take isl_set *set,
1284 __isl_take isl_qpolynomial *qp);
1286 Quasipolynomials can be copied and freed again using the following
1289 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1290 __isl_keep isl_qpolynomial *qp);
1291 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1293 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1294 __isl_keep isl_pw_qpolynomial *pwqp);
1295 void isl_pw_qpolynomial_free(
1296 __isl_take isl_pw_qpolynomial *pwqp);
1298 =head3 Inspecting (Piecewise) Quasipolynomials
1300 To iterate over the cells in a piecewise quasipolynomial,
1301 use either of the following two functions
1303 int isl_pw_qpolynomial_foreach_piece(
1304 __isl_keep isl_pw_qpolynomial *pwqp,
1305 int (*fn)(__isl_take isl_set *set,
1306 __isl_take isl_qpolynomial *qp,
1307 void *user), void *user);
1308 int isl_pw_qpolynomial_foreach_lifted_piece(
1309 __isl_keep isl_pw_qpolynomial *pwqp,
1310 int (*fn)(__isl_take isl_set *set,
1311 __isl_take isl_qpolynomial *qp,
1312 void *user), void *user);
1314 As usual, the function C<fn> should return C<0> on success
1315 and C<-1> on failure. The difference between
1316 C<isl_pw_qpolynomial_foreach_piece> and
1317 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1318 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1319 compute unique representations for all existentially quantified
1320 variables and then turn these existentially quantified variables
1321 into extra set variables, adapting the associated quasipolynomial
1322 accordingly. This means that the C<set> passed to C<fn>
1323 will not have any existentially quantified variables, but that
1324 the dimensions of the sets may be different for different
1325 invocations of C<fn>.
1327 To iterate over all terms in a quasipolynomial,
1330 int isl_qpolynomial_foreach_term(
1331 __isl_keep isl_qpolynomial *qp,
1332 int (*fn)(__isl_take isl_term *term,
1333 void *user), void *user);
1335 The terms themselves can be inspected and freed using
1338 unsigned isl_term_dim(__isl_keep isl_term *term,
1339 enum isl_dim_type type);
1340 void isl_term_get_num(__isl_keep isl_term *term,
1342 void isl_term_get_den(__isl_keep isl_term *term,
1344 int isl_term_get_exp(__isl_keep isl_term *term,
1345 enum isl_dim_type type, unsigned pos);
1346 __isl_give isl_div *isl_term_get_div(
1347 __isl_keep isl_term *term, unsigned pos);
1348 void isl_term_free(__isl_take isl_term *term);
1350 Each term is a product of parameters, set variables and
1351 integer divisions. The function C<isl_term_get_exp>
1352 returns the exponent of a given dimensions in the given term.
1353 The C<isl_int>s in the arguments of C<isl_term_get_num>
1354 and C<isl_term_get_den> need to have been initialized
1355 using C<isl_int_init> before calling these functions.
1357 =head3 Properties of (Piecewise) Quasipolynomials
1359 To check whether a quasipolynomial is actually a constant,
1360 use the following function.
1362 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1363 isl_int *n, isl_int *d);
1365 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1366 then the numerator and denominator of the constant
1367 are returned in C<*n> and C<*d>, respectively.
1369 =head3 Operations on (Piecewise) Quasipolynomials
1371 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1372 __isl_take isl_qpolynomial *qp);
1373 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1374 __isl_take isl_qpolynomial *qp1,
1375 __isl_take isl_qpolynomial *qp2);
1376 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1377 __isl_take isl_qpolynomial *qp1,
1378 __isl_take isl_qpolynomial *qp2);
1380 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1381 __isl_take isl_pw_qpolynomial *pwqp1,
1382 __isl_take isl_pw_qpolynomial *pwqp2);
1383 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1384 __isl_take isl_pw_qpolynomial *pwqp1,
1385 __isl_take isl_pw_qpolynomial *pwqp2);
1386 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1387 __isl_take isl_pw_qpolynomial *pwqp1,
1388 __isl_take isl_pw_qpolynomial *pwqp2);
1389 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1390 __isl_take isl_pw_qpolynomial *pwqp);
1391 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1392 __isl_take isl_pw_qpolynomial *pwqp1,
1393 __isl_take isl_pw_qpolynomial *pwqp2);
1395 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1396 __isl_take isl_pw_qpolynomial *pwqp,
1397 __isl_take isl_point *pnt);
1399 __isl_give isl_set *isl_pw_qpolynomial_domain(
1400 __isl_take isl_pw_qpolynomial *pwqp);
1401 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1402 __isl_take isl_pw_qpolynomial *pwpq,
1403 __isl_take isl_set *set);
1405 =head2 Dependence Analysis
1407 C<isl> contains specialized functionality for performing
1408 array dataflow analysis. That is, given a I<sink> access relation
1409 and a collection of possible I<source> access relations,
1410 C<isl> can compute relations that describe
1411 for each iteration of the sink access, which iteration
1412 of which of the source access relations was the last
1413 to access the same data element before the given iteration
1415 To compute standard flow dependences, the sink should be
1416 a read, while the sources should be writes.
1418 #include <isl_flow.h>
1420 __isl_give isl_access_info *isl_access_info_alloc(
1421 __isl_take isl_map *sink,
1422 void *sink_user, isl_access_level_before fn,
1424 __isl_give isl_access_info *isl_access_info_add_source(
1425 __isl_take isl_access_info *acc,
1426 __isl_take isl_map *source, void *source_user);
1428 __isl_give isl_flow *isl_access_info_compute_flow(
1429 __isl_take isl_access_info *acc);
1431 int isl_flow_foreach(__isl_keep isl_flow *deps,
1432 int (*fn)(__isl_take isl_map *dep, void *dep_user,
1435 __isl_give isl_set *isl_flow_get_no_source(
1436 __isl_keep isl_flow *deps);
1437 void isl_flow_free(__isl_take isl_flow *deps);
1439 The function C<isl_access_info_compute_flow> performs the actual
1440 dependence analysis. The other functions are used to construct
1441 the input for this function or to read off the output.
1443 The input is collected in an C<isl_access_info>, which can
1444 be created through a call to C<isl_access_info_alloc>.
1445 The arguments to this functions are the sink access relation
1446 C<sink>, a token C<sink_user> used to identify the sink
1447 access to the user, a callback function for specifying the
1448 relative order of source and sink accesses, and the number
1449 of source access relations that will be added.
1450 The callback function has type C<int (*)(void *first, void *second)>.
1451 The function is called with two user supplied tokens identifying
1452 either a source or the sink and it should return the shared nesting
1453 level and the relative order of the two accesses.
1454 In particular, let I<n> be the number of loops shared by
1455 the two accesses. If C<first> precedes C<second> textually,
1456 then the function should return I<2 * n + 1>; otherwise,
1457 it should return I<2 * n>.
1458 The sources can be added to the C<isl_access_info> by performing
1459 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1460 The C<source_user> token is again used to identify
1461 the source access. The range of the source access relation
1462 C<source> should have the same dimension as the range
1463 of the sink access relation.
1465 The result of the dependence analysis is collected in an
1466 C<isl_flow>. There may be elements in the domain of
1467 the sink access for which no preceding source access could be
1468 find. The set of these elements can be obtained through
1469 a call to C<isl_flow_get_no_source>.
1470 In the case of standard flow dependence analysis,
1471 this set corresponds to the reads from uninitialized
1473 The actual flow dependences can be extracted using
1474 C<isl_flow_foreach>. This function will call the user-specified
1475 callback function C<fn> for each B<non-empty> dependence between
1476 a source and the sink. The callback function is called
1477 with three arguments, the actual flow dependence relation
1478 mapping source iterations to sink iterations, a token
1479 identifying the source and an additional C<void *> with value
1480 equal to the third argument of the C<isl_flow_foreach> call.
1482 After finishing with an C<isl_flow>, the user should call
1483 C<isl_flow_free> to free all associated memory.
1487 Although C<isl> is mainly meant to be used as a library,
1488 it also contains some basic applications that use some
1489 of the functionality of C<isl>.
1490 The input may be specified in either the L<isl format>
1491 or the L<PolyLib format>.
1493 =head2 C<isl_polyhedron_sample>
1495 C<isl_polyhedron_sample> takes a polyhedron as input and prints
1496 an integer element of the polyhedron, if there is any.
1497 The first column in the output is the denominator and is always
1498 equal to 1. If the polyhedron contains no integer points,
1499 then a vector of length zero is printed.
1503 C<isl_pip> takes the same input as the C<example> program
1504 from the C<piplib> distribution, i.e., a set of constraints
1505 on the parameters, a line contains only -1 and finally a set
1506 of constraints on a parametric polyhedron.
1507 The coefficients of the parameters appear in the last columns
1508 (but before the final constant column).
1509 The output is the lexicographic minimum of the parametric polyhedron.
1510 As C<isl> currently does not have its own output format, the output
1511 is just a dump of the internal state.
1513 =head2 C<isl_polyhedron_minimize>
1515 C<isl_polyhedron_minimize> computes the minimum of some linear
1516 or affine objective function over the integer points in a polyhedron.
1517 If an affine objective function
1518 is given, then the constant should appear in the last column.
1520 =head2 C<isl_polytope_scan>
1522 Given a polytope, C<isl_polytope_scan> prints
1523 all integer points in the polytope.
1525 =head1 C<isl-polylib>
1527 The C<isl-polylib> library provides the following functions for converting
1528 between C<isl> objects and C<PolyLib> objects.
1529 The library is distributed separately for licensing reasons.
1531 #include <isl_set_polylib.h>
1532 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
1533 Polyhedron *P, __isl_take isl_dim *dim);
1534 Polyhedron *isl_basic_set_to_polylib(
1535 __isl_keep isl_basic_set *bset);
1536 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
1537 __isl_take isl_dim *dim);
1538 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
1540 #include <isl_map_polylib.h>
1541 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
1542 Polyhedron *P, __isl_take isl_dim *dim);
1543 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
1544 __isl_take isl_dim *dim);
1545 Polyhedron *isl_basic_map_to_polylib(
1546 __isl_keep isl_basic_map *bmap);
1547 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);