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 objects that live in the
375 same space as some other object. This can be accomplished
376 by creating the new objects
377 (see L<Creating New Sets and Relations> or
378 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
379 specification of the original object.
382 __isl_give isl_dim *isl_basic_set_get_dim(
383 __isl_keep isl_basic_set *bset);
384 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
387 __isl_give isl_dim *isl_basic_map_get_dim(
388 __isl_keep isl_basic_map *bmap);
389 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
391 #include <isl_polynomial.h>
392 __isl_give isl_dim *isl_qpolynomial_get_dim(
393 __isl_keep isl_qpolynomial *qp);
394 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
395 __isl_keep isl_pw_qpolynomial *pwqp);
397 The names of the individual dimensions may be set or read off
398 using the following functions.
401 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
402 enum isl_dim_type type, unsigned pos,
403 __isl_keep const char *name);
404 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
405 enum isl_dim_type type, unsigned pos);
407 Note that C<isl_dim_get_name> returns a pointer to some internal
408 data structure, so the result can only be used while the
409 corresponding C<isl_dim> is alive.
410 Also note that every function that operates on two sets or relations
411 requires that both arguments have the same parameters. This also
412 means that if one of the arguments has named parameters, then the
413 other needs to have named parameters too and the names need to match.
415 =head2 Input and Output
417 C<isl> supports its own input/output format, which is similar
418 to the C<Omega> format, but also supports the C<PolyLib> format
423 The C<isl> format is similar to that of C<Omega>, but has a different
424 syntax for describing the parameters and allows for the definition
425 of an existentially quantified variable as the integer division
426 of an affine expression.
427 For example, the set of integers C<i> between C<0> and C<n>
428 such that C<i % 10 <= 6> can be described as
430 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
433 A set or relation can have several disjuncts, separated
434 by the keyword C<or>. Each disjunct is either a conjunction
435 of constraints or a projection (C<exists>) of a conjunction
436 of constraints. The constraints are separated by the keyword
439 =head3 C<PolyLib> format
441 If the represented set is a union, then the first line
442 contains a single number representing the number of disjuncts.
443 Otherwise, a line containing the number C<1> is optional.
445 Each disjunct is represented by a matrix of constraints.
446 The first line contains two numbers representing
447 the number of rows and columns,
448 where the number of rows is equal to the number of constraints
449 and the number of columns is equal to two plus the number of variables.
450 The following lines contain the actual rows of the constraint matrix.
451 In each row, the first column indicates whether the constraint
452 is an equality (C<0>) or inequality (C<1>). The final column
453 corresponds to the constant term.
455 If the set is parametric, then the coefficients of the parameters
456 appear in the last columns before the constant column.
457 The coefficients of any existentially quantified variables appear
458 between those of the set variables and those of the parameters.
463 __isl_give isl_basic_set *isl_basic_set_read_from_file(
464 isl_ctx *ctx, FILE *input, int nparam);
465 __isl_give isl_basic_set *isl_basic_set_read_from_str(
466 isl_ctx *ctx, const char *str, int nparam);
467 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
468 FILE *input, int nparam);
469 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
470 const char *str, int nparam);
473 __isl_give isl_basic_map *isl_basic_map_read_from_file(
474 isl_ctx *ctx, FILE *input, int nparam);
475 __isl_give isl_basic_map *isl_basic_map_read_from_str(
476 isl_ctx *ctx, const char *str, int nparam);
477 __isl_give isl_map *isl_map_read_from_file(
478 struct isl_ctx *ctx, FILE *input, int nparam);
479 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
480 const char *str, int nparam);
482 The input format is autodetected and may be either the C<PolyLib> format
483 or the C<isl> format.
484 C<nparam> specifies how many of the final columns in
485 the C<PolyLib> format correspond to parameters.
486 If input is given in the C<isl> format, then the number
487 of parameters needs to be equal to C<nparam>.
488 If C<nparam> is negative, then any number of parameters
489 is accepted in the C<isl> format and zero parameters
490 are assumed in the C<PolyLib> format.
494 Before anything can be printed, an C<isl_printer> needs to
497 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
499 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
500 void isl_printer_free(__isl_take isl_printer *printer);
501 __isl_give char *isl_printer_get_str(
502 __isl_keep isl_printer *printer);
504 The behavior of the printer can be modified in various ways
506 __isl_give isl_printer *isl_printer_set_output_format(
507 __isl_take isl_printer *p, int output_format);
508 __isl_give isl_printer *isl_printer_set_indent(
509 __isl_take isl_printer *p, int indent);
510 __isl_give isl_printer *isl_printer_set_prefix(
511 __isl_take isl_printer *p, const char *prefix);
512 __isl_give isl_printer *isl_printer_set_suffix(
513 __isl_take isl_printer *p, const char *suffix);
515 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
516 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
517 Each line in the output is indented by C<indent> spaces
518 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
519 In the C<PolyLib> format output,
520 the coefficients of the existentially quantified variables
521 appear between those of the set variables and those
524 To actually print something, use
527 __isl_give isl_printer *isl_printer_print_basic_set(
528 __isl_take isl_printer *printer,
529 __isl_keep isl_basic_set *bset);
530 __isl_give isl_printer *isl_printer_print_set(
531 __isl_take isl_printer *printer,
532 __isl_keep isl_set *set);
535 __isl_give isl_printer *isl_printer_print_basic_map(
536 __isl_take isl_printer *printer,
537 __isl_keep isl_basic_map *bmap);
538 __isl_give isl_printer *isl_printer_print_map(
539 __isl_take isl_printer *printer,
540 __isl_keep isl_map *map);
542 When called on a file printer, the following function flushes
543 the file. When called on a string printer, the buffer is cleared.
545 __isl_give isl_printer *isl_printer_flush(
546 __isl_take isl_printer *p);
548 =head2 Creating New Sets and Relations
550 C<isl> has functions for creating some standard sets and relations.
554 =item * Empty sets and relations
556 __isl_give isl_basic_set *isl_basic_set_empty(
557 __isl_take isl_dim *dim);
558 __isl_give isl_basic_map *isl_basic_map_empty(
559 __isl_take isl_dim *dim);
560 __isl_give isl_set *isl_set_empty(
561 __isl_take isl_dim *dim);
562 __isl_give isl_map *isl_map_empty(
563 __isl_take isl_dim *dim);
565 =item * Universe sets and relations
567 __isl_give isl_basic_set *isl_basic_set_universe(
568 __isl_take isl_dim *dim);
569 __isl_give isl_basic_map *isl_basic_map_universe(
570 __isl_take isl_dim *dim);
571 __isl_give isl_set *isl_set_universe(
572 __isl_take isl_dim *dim);
573 __isl_give isl_map *isl_map_universe(
574 __isl_take isl_dim *dim);
576 =item * Identity relations
578 __isl_give isl_basic_map *isl_basic_map_identity(
579 __isl_take isl_dim *set_dim);
580 __isl_give isl_map *isl_map_identity(
581 __isl_take isl_dim *set_dim);
583 These functions take a dimension specification for a B<set>
584 and return an identity relation between two such sets.
586 =item * Lexicographic order
588 __isl_give isl_map *isl_map_lex_lt(
589 __isl_take isl_dim *set_dim);
590 __isl_give isl_map *isl_map_lex_le(
591 __isl_take isl_dim *set_dim);
592 __isl_give isl_map *isl_map_lex_gt(
593 __isl_take isl_dim *set_dim);
594 __isl_give isl_map *isl_map_lex_ge(
595 __isl_take isl_dim *set_dim);
596 __isl_give isl_map *isl_map_lex_lt_first(
597 __isl_take isl_dim *dim, unsigned n);
598 __isl_give isl_map *isl_map_lex_le_first(
599 __isl_take isl_dim *dim, unsigned n);
600 __isl_give isl_map *isl_map_lex_gt_first(
601 __isl_take isl_dim *dim, unsigned n);
602 __isl_give isl_map *isl_map_lex_ge_first(
603 __isl_take isl_dim *dim, unsigned n);
605 The first four functions take a dimension specification for a B<set>
606 and return relations that express that the elements in the domain
607 are lexicographically less
608 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
609 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
610 than the elements in the range.
611 The last four functions take a dimension specification for a map
612 and return relations that express that the first C<n> dimensions
613 in the domain are lexicographically less
614 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
615 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
616 than the first C<n> dimensions in the range.
620 A basic set or relation can be converted to a set or relation
621 using the following functions.
623 __isl_give isl_set *isl_set_from_basic_set(
624 __isl_take isl_basic_set *bset);
625 __isl_give isl_map *isl_map_from_basic_map(
626 __isl_take isl_basic_map *bmap);
628 Sets and relations can be copied and freed again using the following
631 __isl_give isl_basic_set *isl_basic_set_copy(
632 __isl_keep isl_basic_set *bset);
633 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
634 __isl_give isl_basic_map *isl_basic_map_copy(
635 __isl_keep isl_basic_map *bmap);
636 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
637 void isl_basic_set_free(__isl_take isl_basic_set *bset);
638 void isl_set_free(__isl_take isl_set *set);
639 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
640 void isl_map_free(__isl_take isl_map *map);
642 Other sets and relations can be constructed by starting
643 from a universe set or relation, adding equality and/or
644 inequality constraints and then projecting out the
645 existentially quantified variables, if any.
646 Constraints can be constructed, manipulated and
647 added to basic sets and relations using the following functions.
649 #include <isl_constraint.h>
650 __isl_give isl_constraint *isl_equality_alloc(
651 __isl_take isl_dim *dim);
652 __isl_give isl_constraint *isl_inequality_alloc(
653 __isl_take isl_dim *dim);
654 void isl_constraint_set_constant(
655 __isl_keep isl_constraint *constraint, isl_int v);
656 void isl_constraint_set_coefficient(
657 __isl_keep isl_constraint *constraint,
658 enum isl_dim_type type, int pos, isl_int v);
659 __isl_give isl_basic_map *isl_basic_map_add_constraint(
660 __isl_take isl_basic_map *bmap,
661 __isl_take isl_constraint *constraint);
662 __isl_give isl_basic_set *isl_basic_set_add_constraint(
663 __isl_take isl_basic_set *bset,
664 __isl_take isl_constraint *constraint);
666 For example, to create a set containing the even integers
667 between 10 and 42, you would use the following code.
671 struct isl_constraint *c;
672 struct isl_basic_set *bset;
675 dim = isl_dim_set_alloc(ctx, 0, 2);
676 bset = isl_basic_set_universe(isl_dim_copy(dim));
678 c = isl_equality_alloc(isl_dim_copy(dim));
679 isl_int_set_si(v, -1);
680 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
681 isl_int_set_si(v, 2);
682 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
683 bset = isl_basic_set_add_constraint(bset, c);
685 c = isl_inequality_alloc(isl_dim_copy(dim));
686 isl_int_set_si(v, -10);
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 c = isl_inequality_alloc(dim);
693 isl_int_set_si(v, 42);
694 isl_constraint_set_constant(c, v);
695 isl_int_set_si(v, -1);
696 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
697 bset = isl_basic_set_add_constraint(bset, c);
699 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
705 struct isl_basic_set *bset;
706 bset = isl_basic_set_read_from_str(ctx,
707 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
709 =head2 Inspecting Sets and Relations
711 Usually, the user should not have to care about the actual constraints
712 of the sets and maps, but should instead apply the abstract operations
713 explained in the following sections.
714 Occasionally, however, it may be required to inspect the individual
715 coefficients of the constraints. This section explains how to do so.
716 In these cases, it may also be useful to have C<isl> compute
717 an explicit representation of the existentially quantified variables.
719 __isl_give isl_set *isl_set_compute_divs(
720 __isl_take isl_set *set);
721 __isl_give isl_map *isl_map_compute_divs(
722 __isl_take isl_map *map);
724 This explicit representation defines the existentially quantified
725 variables as integer divisions of the other variables, possibly
726 including earlier existentially quantified variables.
727 An explicitly represented existentially quantified variable therefore
728 has a unique value when the values of the other variables are known.
729 If, furthermore, the same existentials, i.e., existentials
730 with the same explicit representations, should appear in the
731 same order in each of the disjuncts of a set or map, then the user should call
732 either of the following functions.
734 __isl_give isl_set *isl_set_align_divs(
735 __isl_take isl_set *set);
736 __isl_give isl_map *isl_map_align_divs(
737 __isl_take isl_map *map);
739 To iterate over all the basic sets or maps in a set or map, use
741 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
742 int (*fn)(__isl_take isl_basic_set *bset, void *user),
744 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
745 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
748 The callback function C<fn> should return 0 if successful and
749 -1 if an error occurs. In the latter case, or if any other error
750 occurs, the above functions will return -1.
752 It should be noted that C<isl> does not guarantee that
753 the basic sets or maps passed to C<fn> are disjoint.
754 If this is required, then the user should call one of
755 the following functions first.
757 __isl_give isl_set *isl_set_make_disjoint(
758 __isl_take isl_set *set);
759 __isl_give isl_map *isl_map_make_disjoint(
760 __isl_take isl_map *map);
762 To iterate over the constraints of a basic set or map, use
764 #include <isl_constraint.h>
766 int isl_basic_map_foreach_constraint(
767 __isl_keep isl_basic_map *bmap,
768 int (*fn)(__isl_take isl_constraint *c, void *user),
770 void isl_constraint_free(struct isl_constraint *c);
772 Again, the callback function C<fn> should return 0 if successful and
773 -1 if an error occurs. In the latter case, or if any other error
774 occurs, the above functions will return -1.
775 The constraint C<c> represents either an equality or an inequality.
776 Use the following function to find out whether a constraint
777 represents an equality. If not, it represents an inequality.
779 int isl_constraint_is_equality(
780 __isl_keep isl_constraint *constraint);
782 The coefficients of the constraints can be inspected using
783 the following functions.
785 void isl_constraint_get_constant(
786 __isl_keep isl_constraint *constraint, isl_int *v);
787 void isl_constraint_get_coefficient(
788 __isl_keep isl_constraint *constraint,
789 enum isl_dim_type type, int pos, isl_int *v);
791 The explicit representations of the existentially quantified
792 variables can be inspected using the following functions.
793 Note that the user is only allowed to use these functions
794 if the inspected set or map is the result of a call
795 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
797 __isl_give isl_div *isl_constraint_div(
798 __isl_keep isl_constraint *constraint, int pos);
799 void isl_div_get_constant(__isl_keep isl_div *div,
801 void isl_div_get_denominator(__isl_keep isl_div *div,
803 void isl_div_get_coefficient(__isl_keep isl_div *div,
804 enum isl_dim_type type, int pos, isl_int *v);
808 =head3 Unary Properties
814 The following functions test whether the given set or relation
815 contains any integer points. The ``fast'' variants do not perform
816 any computations, but simply check if the given set or relation
817 is already known to be empty.
819 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
820 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
821 int isl_set_is_empty(__isl_keep isl_set *set);
822 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
823 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
824 int isl_map_fast_is_empty(__isl_keep isl_map *map);
825 int isl_map_is_empty(__isl_keep isl_map *map);
829 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
830 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
831 int isl_set_fast_is_universe(__isl_keep isl_set *set);
833 =item * Single-valuedness
835 int isl_map_is_single_valued(__isl_keep isl_map *map);
839 =head3 Binary Properties
845 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
846 __isl_keep isl_set *set2);
847 int isl_set_is_equal(__isl_keep isl_set *set1,
848 __isl_keep isl_set *set2);
849 int isl_map_is_equal(__isl_keep isl_map *map1,
850 __isl_keep isl_map *map2);
851 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
852 __isl_keep isl_map *map2);
853 int isl_basic_map_is_equal(
854 __isl_keep isl_basic_map *bmap1,
855 __isl_keep isl_basic_map *bmap2);
859 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
860 __isl_keep isl_set *set2);
864 int isl_set_is_subset(__isl_keep isl_set *set1,
865 __isl_keep isl_set *set2);
866 int isl_set_is_strict_subset(
867 __isl_keep isl_set *set1,
868 __isl_keep isl_set *set2);
869 int isl_basic_map_is_subset(
870 __isl_keep isl_basic_map *bmap1,
871 __isl_keep isl_basic_map *bmap2);
872 int isl_basic_map_is_strict_subset(
873 __isl_keep isl_basic_map *bmap1,
874 __isl_keep isl_basic_map *bmap2);
875 int isl_map_is_subset(
876 __isl_keep isl_map *map1,
877 __isl_keep isl_map *map2);
878 int isl_map_is_strict_subset(
879 __isl_keep isl_map *map1,
880 __isl_keep isl_map *map2);
884 =head2 Unary Operations
890 __isl_give isl_set *isl_set_complement(
891 __isl_take isl_set *set);
895 __isl_give isl_basic_map *isl_basic_map_reverse(
896 __isl_take isl_basic_map *bmap);
897 __isl_give isl_map *isl_map_reverse(
898 __isl_take isl_map *map);
902 __isl_give isl_basic_set *isl_basic_set_project_out(
903 __isl_take isl_basic_set *bset,
904 enum isl_dim_type type, unsigned first, unsigned n);
905 __isl_give isl_basic_map *isl_basic_map_project_out(
906 __isl_take isl_basic_map *bmap,
907 enum isl_dim_type type, unsigned first, unsigned n);
908 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
909 enum isl_dim_type type, unsigned first, unsigned n);
910 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
911 enum isl_dim_type type, unsigned first, unsigned n);
912 __isl_give isl_basic_set *isl_basic_map_domain(
913 __isl_take isl_basic_map *bmap);
914 __isl_give isl_basic_set *isl_basic_map_range(
915 __isl_take isl_basic_map *bmap);
916 __isl_give isl_set *isl_map_domain(
917 __isl_take isl_map *bmap);
918 __isl_give isl_set *isl_map_range(
919 __isl_take isl_map *map);
923 Simplify the representation of a set or relation by trying
924 to combine pairs of basic sets or relations into a single
925 basic set or relation.
927 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
928 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
932 __isl_give isl_basic_set *isl_set_convex_hull(
933 __isl_take isl_set *set);
934 __isl_give isl_basic_map *isl_map_convex_hull(
935 __isl_take isl_map *map);
937 If the input set or relation has any existentially quantified
938 variables, then the result of these operations is currently undefined.
942 __isl_give isl_basic_set *isl_set_simple_hull(
943 __isl_take isl_set *set);
944 __isl_give isl_basic_map *isl_map_simple_hull(
945 __isl_take isl_map *map);
947 These functions compute a single basic set or relation
948 that contains the whole input set or relation.
949 In particular, the output is described by translates
950 of the constraints describing the basic sets or relations in the input.
954 (See \autoref{s:simple hull}.)
960 __isl_give isl_basic_set *isl_basic_set_affine_hull(
961 __isl_take isl_basic_set *bset);
962 __isl_give isl_basic_set *isl_set_affine_hull(
963 __isl_take isl_set *set);
964 __isl_give isl_basic_map *isl_basic_map_affine_hull(
965 __isl_take isl_basic_map *bmap);
966 __isl_give isl_basic_map *isl_map_affine_hull(
967 __isl_take isl_map *map);
971 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
972 unsigned param, int *exact);
974 Compute a parametric representation for all positive powers I<k> of C<map>.
975 The power I<k> is equated to the parameter at position C<param>.
976 The result may be an overapproximation. If the result is exact,
977 then C<*exact> is set to C<1>.
978 The current implementation only produces exact results for particular
979 cases of piecewise translations (i.e., piecewise uniform dependences).
981 =item * Transitive closure
983 __isl_give isl_map *isl_map_transitive_closure(
984 __isl_take isl_map *map, int *exact);
986 Compute the transitive closure of C<map>.
987 The result may be an overapproximation. If the result is known to be exact,
988 then C<*exact> is set to C<1>.
989 The current implementation only produces exact results for particular
990 cases of piecewise translations (i.e., piecewise uniform dependences).
994 =head2 Binary Operations
996 The two arguments of a binary operation not only need to live
997 in the same C<isl_ctx>, they currently also need to have
998 the same (number of) parameters.
1000 =head3 Basic Operations
1004 =item * Intersection
1006 __isl_give isl_basic_set *isl_basic_set_intersect(
1007 __isl_take isl_basic_set *bset1,
1008 __isl_take isl_basic_set *bset2);
1009 __isl_give isl_set *isl_set_intersect(
1010 __isl_take isl_set *set1,
1011 __isl_take isl_set *set2);
1012 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1013 __isl_take isl_basic_map *bmap,
1014 __isl_take isl_basic_set *bset);
1015 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1016 __isl_take isl_basic_map *bmap,
1017 __isl_take isl_basic_set *bset);
1018 __isl_give isl_basic_map *isl_basic_map_intersect(
1019 __isl_take isl_basic_map *bmap1,
1020 __isl_take isl_basic_map *bmap2);
1021 __isl_give isl_map *isl_map_intersect_domain(
1022 __isl_take isl_map *map,
1023 __isl_take isl_set *set);
1024 __isl_give isl_map *isl_map_intersect_range(
1025 __isl_take isl_map *map,
1026 __isl_take isl_set *set);
1027 __isl_give isl_map *isl_map_intersect(
1028 __isl_take isl_map *map1,
1029 __isl_take isl_map *map2);
1033 __isl_give isl_set *isl_basic_set_union(
1034 __isl_take isl_basic_set *bset1,
1035 __isl_take isl_basic_set *bset2);
1036 __isl_give isl_map *isl_basic_map_union(
1037 __isl_take isl_basic_map *bmap1,
1038 __isl_take isl_basic_map *bmap2);
1039 __isl_give isl_set *isl_set_union(
1040 __isl_take isl_set *set1,
1041 __isl_take isl_set *set2);
1042 __isl_give isl_map *isl_map_union(
1043 __isl_take isl_map *map1,
1044 __isl_take isl_map *map2);
1046 =item * Set difference
1048 __isl_give isl_set *isl_set_subtract(
1049 __isl_take isl_set *set1,
1050 __isl_take isl_set *set2);
1051 __isl_give isl_map *isl_map_subtract(
1052 __isl_take isl_map *map1,
1053 __isl_take isl_map *map2);
1057 __isl_give isl_basic_set *isl_basic_set_apply(
1058 __isl_take isl_basic_set *bset,
1059 __isl_take isl_basic_map *bmap);
1060 __isl_give isl_set *isl_set_apply(
1061 __isl_take isl_set *set,
1062 __isl_take isl_map *map);
1063 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1064 __isl_take isl_basic_map *bmap1,
1065 __isl_take isl_basic_map *bmap2);
1066 __isl_give isl_basic_map *isl_basic_map_apply_range(
1067 __isl_take isl_basic_map *bmap1,
1068 __isl_take isl_basic_map *bmap2);
1069 __isl_give isl_map *isl_map_apply_domain(
1070 __isl_take isl_map *map1,
1071 __isl_take isl_map *map2);
1072 __isl_give isl_map *isl_map_apply_range(
1073 __isl_take isl_map *map1,
1074 __isl_take isl_map *map2);
1076 =item * Simplification
1078 __isl_give isl_basic_set *isl_basic_set_gist(
1079 __isl_take isl_basic_set *bset,
1080 __isl_take isl_basic_set *context);
1081 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1082 __isl_take isl_set *context);
1083 __isl_give isl_basic_map *isl_basic_map_gist(
1084 __isl_take isl_basic_map *bmap,
1085 __isl_take isl_basic_map *context);
1086 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1087 __isl_take isl_map *context);
1089 The gist operation returns a set or relation that has the
1090 same intersection with the context as the input set or relation.
1091 Any implicit equality in the intersection is made explicit in the result,
1092 while all inequalities that are redundant with respect to the intersection
1097 =head3 Lexicographic Optimization
1099 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1100 the following functions
1101 compute a set that contains the lexicographic minimum or maximum
1102 of the elements in C<set> (or C<bset>) for those values of the parameters
1103 that satisfy C<dom>.
1104 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1105 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1107 In other words, the union of the parameter values
1108 for which the result is non-empty and of C<*empty>
1111 __isl_give isl_set *isl_basic_set_partial_lexmin(
1112 __isl_take isl_basic_set *bset,
1113 __isl_take isl_basic_set *dom,
1114 __isl_give isl_set **empty);
1115 __isl_give isl_set *isl_basic_set_partial_lexmax(
1116 __isl_take isl_basic_set *bset,
1117 __isl_take isl_basic_set *dom,
1118 __isl_give isl_set **empty);
1119 __isl_give isl_set *isl_set_partial_lexmin(
1120 __isl_take isl_set *set, __isl_take isl_set *dom,
1121 __isl_give isl_set **empty);
1122 __isl_give isl_set *isl_set_partial_lexmax(
1123 __isl_take isl_set *set, __isl_take isl_set *dom,
1124 __isl_give isl_set **empty);
1126 Given a (basic) set C<set> (or C<bset>), the following functions simply
1127 return a set containing the lexicographic minimum or maximum
1128 of the elements in C<set> (or C<bset>).
1130 __isl_give isl_set *isl_basic_set_lexmin(
1131 __isl_take isl_basic_set *bset);
1132 __isl_give isl_set *isl_basic_set_lexmax(
1133 __isl_take isl_basic_set *bset);
1134 __isl_give isl_set *isl_set_lexmin(
1135 __isl_take isl_set *set);
1136 __isl_give isl_set *isl_set_lexmax(
1137 __isl_take isl_set *set);
1139 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1140 the following functions
1141 compute a relation that maps each element of C<dom>
1142 to the single lexicographic minimum or maximum
1143 of the elements that are associated to that same
1144 element in C<map> (or C<bmap>).
1145 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1146 that contains the elements in C<dom> that do not map
1147 to any elements in C<map> (or C<bmap>).
1148 In other words, the union of the domain of the result and of C<*empty>
1151 __isl_give isl_map *isl_basic_map_partial_lexmax(
1152 __isl_take isl_basic_map *bmap,
1153 __isl_take isl_basic_set *dom,
1154 __isl_give isl_set **empty);
1155 __isl_give isl_map *isl_basic_map_partial_lexmin(
1156 __isl_take isl_basic_map *bmap,
1157 __isl_take isl_basic_set *dom,
1158 __isl_give isl_set **empty);
1159 __isl_give isl_map *isl_map_partial_lexmax(
1160 __isl_take isl_map *map, __isl_take isl_set *dom,
1161 __isl_give isl_set **empty);
1162 __isl_give isl_map *isl_map_partial_lexmin(
1163 __isl_take isl_map *map, __isl_take isl_set *dom,
1164 __isl_give isl_set **empty);
1166 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1167 return a map mapping each element in the domain of
1168 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1169 of all elements associated to that element.
1171 __isl_give isl_map *isl_basic_map_lexmin(
1172 __isl_take isl_basic_map *bmap);
1173 __isl_give isl_map *isl_basic_map_lexmax(
1174 __isl_take isl_basic_map *bmap);
1175 __isl_give isl_map *isl_map_lexmin(
1176 __isl_take isl_map *map);
1177 __isl_give isl_map *isl_map_lexmax(
1178 __isl_take isl_map *map);
1182 Points are elements of a set. They can be used to construct
1183 simple sets (boxes) or they can be used to represent the
1184 individual elements of a set.
1185 The zero point (the origin) can be created using
1187 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1189 The coordinates of a point can be inspected, set and changed
1192 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1193 enum isl_dim_type type, int pos, isl_int *v);
1194 __isl_give isl_point *isl_point_set_coordinate(
1195 __isl_take isl_point *pnt,
1196 enum isl_dim_type type, int pos, isl_int v);
1198 __isl_give isl_point *isl_point_add_ui(
1199 __isl_take isl_point *pnt,
1200 enum isl_dim_type type, int pos, unsigned val);
1201 __isl_give isl_point *isl_point_sub_ui(
1202 __isl_take isl_point *pnt,
1203 enum isl_dim_type type, int pos, unsigned val);
1205 Points can be copied or freed using
1207 __isl_give isl_point *isl_point_copy(
1208 __isl_keep isl_point *pnt);
1209 void isl_point_free(__isl_take isl_point *pnt);
1211 A singleton set can be created from a point using
1213 __isl_give isl_set *isl_set_from_point(
1214 __isl_take isl_point *pnt);
1216 and a box can be created from two opposite extremal points using
1218 __isl_give isl_set *isl_set_box_from_points(
1219 __isl_take isl_point *pnt1,
1220 __isl_take isl_point *pnt2);
1222 All elements of a B<bounded> set can be enumerated using
1223 the following function.
1225 int isl_set_foreach_point(__isl_keep isl_set *set,
1226 int (*fn)(__isl_take isl_point *pnt, void *user),
1229 The function C<fn> is called for each integer point in
1230 C<set> with as second argument the last argument of
1231 the C<isl_set_foreach_point> call. The function C<fn>
1232 should return C<0> on success and C<-1> on failure.
1233 In the latter case, C<isl_set_foreach_point> will stop
1234 enumerating and return C<-1> as well.
1235 If the enumeration is performed successfully and to completion,
1236 then C<isl_set_foreach_point> returns C<0>.
1238 To obtain a single point of a set, use
1240 __isl_give isl_point *isl_set_sample_point(
1241 __isl_take isl_set *set);
1243 If C<set> does not contain any (integer) points, then the
1244 resulting point will be ``void'', a property that can be
1247 int isl_point_is_void(__isl_keep isl_point *pnt);
1249 =head2 Piecewise Quasipolynomials
1251 A piecewise quasipolynomial is a particular kind of function that maps
1252 a parametric point to a rational value.
1253 More specifically, a quasipolynomial is a polynomial expression in greatest
1254 integer parts of affine expressions of parameters and variables.
1255 A piecewise quasipolynomial is a subdivision of a given parametric
1256 domain into disjoint cells with a quasipolynomial associated to
1257 each cell. The value of the piecewise quasipolynomial at a given
1258 point is the value of the quasipolynomial associated to the cell
1259 that contains the point. Outside of the union of cells,
1260 the value is assumed to be zero.
1261 For example, the piecewise quasipolynomial
1263 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1265 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1266 Piecewise quasipolynomials are mainly used by the C<barvinok>
1267 library for representing the number of elements in a parametric set or map.
1268 For example, the piecewise quasipolynomial above represents
1269 the number of points in the map
1271 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1273 =head3 Printing (Piecewise) Quasipolynomials
1275 Quasipolynomials and piecewise quasipolynomials can be printed
1276 using the following functions.
1278 __isl_give isl_printer *isl_printer_print_qpolynomial(
1279 __isl_take isl_printer *p,
1280 __isl_keep isl_qpolynomial *qp);
1282 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1283 __isl_take isl_printer *p,
1284 __isl_keep isl_pw_qpolynomial *pwqp);
1286 The output format of the printer
1287 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1289 =head3 Creating New (Piecewise) Quasipolynomials
1291 Some simple quasipolynomials can be created using the following functions.
1292 More complicated quasipolynomials can be created by applying
1293 operations such as addition and multiplication
1294 on the resulting quasipolynomials
1296 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1297 __isl_take isl_dim *dim);
1298 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1299 __isl_take isl_dim *dim);
1300 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1301 __isl_take isl_dim *dim);
1302 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1303 __isl_take isl_dim *dim);
1304 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1305 __isl_take isl_dim *dim,
1306 const isl_int n, const isl_int d);
1307 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1308 __isl_take isl_div *div);
1309 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1310 __isl_take isl_dim *dim,
1311 enum isl_dim_type type, unsigned pos);
1313 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1314 with a single cell can be created using the following functions.
1315 Multiple of these single cell piecewise quasipolynomials can
1316 be combined to create more complicated piecewise quasipolynomials.
1318 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1319 __isl_take isl_dim *dim);
1320 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1321 __isl_take isl_set *set,
1322 __isl_take isl_qpolynomial *qp);
1324 Quasipolynomials can be copied and freed again using the following
1327 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1328 __isl_keep isl_qpolynomial *qp);
1329 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1331 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1332 __isl_keep isl_pw_qpolynomial *pwqp);
1333 void isl_pw_qpolynomial_free(
1334 __isl_take isl_pw_qpolynomial *pwqp);
1336 =head3 Inspecting (Piecewise) Quasipolynomials
1338 To iterate over the cells in a piecewise quasipolynomial,
1339 use either of the following two functions
1341 int isl_pw_qpolynomial_foreach_piece(
1342 __isl_keep isl_pw_qpolynomial *pwqp,
1343 int (*fn)(__isl_take isl_set *set,
1344 __isl_take isl_qpolynomial *qp,
1345 void *user), void *user);
1346 int isl_pw_qpolynomial_foreach_lifted_piece(
1347 __isl_keep isl_pw_qpolynomial *pwqp,
1348 int (*fn)(__isl_take isl_set *set,
1349 __isl_take isl_qpolynomial *qp,
1350 void *user), void *user);
1352 As usual, the function C<fn> should return C<0> on success
1353 and C<-1> on failure. The difference between
1354 C<isl_pw_qpolynomial_foreach_piece> and
1355 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1356 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1357 compute unique representations for all existentially quantified
1358 variables and then turn these existentially quantified variables
1359 into extra set variables, adapting the associated quasipolynomial
1360 accordingly. This means that the C<set> passed to C<fn>
1361 will not have any existentially quantified variables, but that
1362 the dimensions of the sets may be different for different
1363 invocations of C<fn>.
1365 To iterate over all terms in a quasipolynomial,
1368 int isl_qpolynomial_foreach_term(
1369 __isl_keep isl_qpolynomial *qp,
1370 int (*fn)(__isl_take isl_term *term,
1371 void *user), void *user);
1373 The terms themselves can be inspected and freed using
1376 unsigned isl_term_dim(__isl_keep isl_term *term,
1377 enum isl_dim_type type);
1378 void isl_term_get_num(__isl_keep isl_term *term,
1380 void isl_term_get_den(__isl_keep isl_term *term,
1382 int isl_term_get_exp(__isl_keep isl_term *term,
1383 enum isl_dim_type type, unsigned pos);
1384 __isl_give isl_div *isl_term_get_div(
1385 __isl_keep isl_term *term, unsigned pos);
1386 void isl_term_free(__isl_take isl_term *term);
1388 Each term is a product of parameters, set variables and
1389 integer divisions. The function C<isl_term_get_exp>
1390 returns the exponent of a given dimensions in the given term.
1391 The C<isl_int>s in the arguments of C<isl_term_get_num>
1392 and C<isl_term_get_den> need to have been initialized
1393 using C<isl_int_init> before calling these functions.
1395 =head3 Properties of (Piecewise) Quasipolynomials
1397 To check whether a quasipolynomial is actually a constant,
1398 use the following function.
1400 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1401 isl_int *n, isl_int *d);
1403 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1404 then the numerator and denominator of the constant
1405 are returned in C<*n> and C<*d>, respectively.
1407 =head3 Operations on (Piecewise) Quasipolynomials
1409 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1410 __isl_take isl_qpolynomial *qp);
1411 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1412 __isl_take isl_qpolynomial *qp1,
1413 __isl_take isl_qpolynomial *qp2);
1414 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1415 __isl_take isl_qpolynomial *qp1,
1416 __isl_take isl_qpolynomial *qp2);
1417 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1418 __isl_take isl_qpolynomial *qp1,
1419 __isl_take isl_qpolynomial *qp2);
1421 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1422 __isl_take isl_pw_qpolynomial *pwqp1,
1423 __isl_take isl_pw_qpolynomial *pwqp2);
1424 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1425 __isl_take isl_pw_qpolynomial *pwqp1,
1426 __isl_take isl_pw_qpolynomial *pwqp2);
1427 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1428 __isl_take isl_pw_qpolynomial *pwqp1,
1429 __isl_take isl_pw_qpolynomial *pwqp2);
1430 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1431 __isl_take isl_pw_qpolynomial *pwqp);
1432 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1433 __isl_take isl_pw_qpolynomial *pwqp1,
1434 __isl_take isl_pw_qpolynomial *pwqp2);
1436 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1437 __isl_take isl_pw_qpolynomial *pwqp,
1438 __isl_take isl_point *pnt);
1440 __isl_give isl_set *isl_pw_qpolynomial_domain(
1441 __isl_take isl_pw_qpolynomial *pwqp);
1442 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1443 __isl_take isl_pw_qpolynomial *pwpq,
1444 __isl_take isl_set *set);
1446 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1447 __isl_take isl_pw_qpolynomial *pwqp,
1448 __isl_take isl_set *context);
1450 The gist operation applies the gist operation to each of
1451 the cells in the domain of the input piecewise quasipolynomial.
1452 In future, the operation will also exploit the context
1453 to simplify the quasipolynomials associated to each cell.
1455 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1457 A piecewise quasipolynomial reduction is a piecewise
1458 reduction (or fold) of quasipolynomials.
1459 In particular, the reduction can be maximum or a minimum.
1460 The objects are mainly used to represent the result of
1461 an upper or lower bound on a quasipolynomial over its domain,
1462 i.e., as the result of the following function.
1464 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1465 __isl_take isl_pw_qpolynomial *pwqp,
1466 enum isl_fold type, int *tight);
1468 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1469 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1470 is the returned bound is known be tight, i.e., for each value
1471 of the parameters there is at least
1472 one element in the domain that reaches the bound.
1474 A (piecewise) quasipolynomial reduction can be copied or freed using the
1475 following functions.
1477 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1478 __isl_keep isl_qpolynomial_fold *fold);
1479 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1480 __isl_keep isl_pw_qpolynomial_fold *pwf);
1481 void isl_qpolynomial_fold_free(
1482 __isl_take isl_qpolynomial_fold *fold);
1483 void isl_pw_qpolynomial_fold_free(
1484 __isl_take isl_pw_qpolynomial_fold *pwf);
1486 =head3 Printing Piecewise Quasipolynomial Reductions
1488 Piecewise quasipolynomial reductions can be printed
1489 using the following function.
1491 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1492 __isl_take isl_printer *p,
1493 __isl_keep isl_pw_qpolynomial_fold *pwf);
1495 The output format of the printer
1496 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1498 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1500 To iterate over the cells in a piecewise quasipolynomial reduction,
1501 use either of the following two functions
1503 int isl_pw_qpolynomial_fold_foreach_piece(
1504 __isl_keep isl_pw_qpolynomial_fold *pwf,
1505 int (*fn)(__isl_take isl_set *set,
1506 __isl_take isl_qpolynomial_fold *fold,
1507 void *user), void *user);
1508 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1509 __isl_keep isl_pw_qpolynomial_fold *pwf,
1510 int (*fn)(__isl_take isl_set *set,
1511 __isl_take isl_qpolynomial_fold *fold,
1512 void *user), void *user);
1514 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
1515 of the difference between these two functions.
1517 To iterate over all quasipolynomials in a reduction, use
1519 int isl_qpolynomial_fold_foreach_qpolynomial(
1520 __isl_keep isl_qpolynomial_fold *fold,
1521 int (*fn)(__isl_take isl_qpolynomial *qp,
1522 void *user), void *user);
1524 =head3 Operations on Piecewise Quasipolynomial Reductions
1526 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
1527 __isl_take isl_pw_qpolynomial_fold *pwf1,
1528 __isl_take isl_pw_qpolynomial_fold *pwf2);
1530 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
1531 __isl_take isl_pw_qpolynomial_fold *pwf,
1532 __isl_take isl_point *pnt);
1534 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
1535 __isl_take isl_pw_qpolynomial_fold *pwf);
1537 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
1538 __isl_take isl_pw_qpolynomial_fold *pwf,
1539 __isl_take isl_set *context);
1541 The gist operation applies the gist operation to each of
1542 the cells in the domain of the input piecewise quasipolynomial reduction.
1543 In future, the operation will also exploit the context
1544 to simplify the quasipolynomial reductions associated to each cell.
1546 =head2 Dependence Analysis
1548 C<isl> contains specialized functionality for performing
1549 array dataflow analysis. That is, given a I<sink> access relation
1550 and a collection of possible I<source> access relations,
1551 C<isl> can compute relations that describe
1552 for each iteration of the sink access, which iteration
1553 of which of the source access relations was the last
1554 to access the same data element before the given iteration
1556 To compute standard flow dependences, the sink should be
1557 a read, while the sources should be writes.
1558 If any of the source accesses are marked as being I<may>
1559 accesses, then there will be a dependence to the last
1560 I<must> access B<and> to any I<may> access that follows
1561 this last I<must> access.
1562 In particular, if I<all> sources are I<may> accesses,
1563 then memory based dependence analysis is performed.
1564 If, on the other hand, all sources are I<must> accesses,
1565 then value based dependence analysis is performed.
1567 #include <isl_flow.h>
1569 __isl_give isl_access_info *isl_access_info_alloc(
1570 __isl_take isl_map *sink,
1571 void *sink_user, isl_access_level_before fn,
1573 __isl_give isl_access_info *isl_access_info_add_source(
1574 __isl_take isl_access_info *acc,
1575 __isl_take isl_map *source, int must,
1578 __isl_give isl_flow *isl_access_info_compute_flow(
1579 __isl_take isl_access_info *acc);
1581 int isl_flow_foreach(__isl_keep isl_flow *deps,
1582 int (*fn)(__isl_take isl_map *dep, int must,
1583 void *dep_user, void *user),
1585 __isl_give isl_set *isl_flow_get_no_source(
1586 __isl_keep isl_flow *deps, int must);
1587 void isl_flow_free(__isl_take isl_flow *deps);
1589 The function C<isl_access_info_compute_flow> performs the actual
1590 dependence analysis. The other functions are used to construct
1591 the input for this function or to read off the output.
1593 The input is collected in an C<isl_access_info>, which can
1594 be created through a call to C<isl_access_info_alloc>.
1595 The arguments to this functions are the sink access relation
1596 C<sink>, a token C<sink_user> used to identify the sink
1597 access to the user, a callback function for specifying the
1598 relative order of source and sink accesses, and the number
1599 of source access relations that will be added.
1600 The callback function has type C<int (*)(void *first, void *second)>.
1601 The function is called with two user supplied tokens identifying
1602 either a source or the sink and it should return the shared nesting
1603 level and the relative order of the two accesses.
1604 In particular, let I<n> be the number of loops shared by
1605 the two accesses. If C<first> precedes C<second> textually,
1606 then the function should return I<2 * n + 1>; otherwise,
1607 it should return I<2 * n>.
1608 The sources can be added to the C<isl_access_info> by performing
1609 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1610 C<must> indicates whether the source is a I<must> access
1611 or a I<may> access. Note that a multi-valued access relation
1612 should only be marked I<must> if every iteration in the domain
1613 of the relation accesses I<all> elements in its image.
1614 The C<source_user> token is again used to identify
1615 the source access. The range of the source access relation
1616 C<source> should have the same dimension as the range
1617 of the sink access relation.
1619 The result of the dependence analysis is collected in an
1620 C<isl_flow>. There may be elements in the domain of
1621 the sink access for which no preceding source access could be
1622 found or for which all preceding sources are I<may> accesses.
1623 The sets of these elements can be obtained through
1624 calls to C<isl_flow_get_no_source>, the first with C<must> set
1625 and the second with C<must> unset.
1626 In the case of standard flow dependence analysis,
1627 with the sink a read and the sources I<must> writes,
1628 the first set corresponds to the reads from uninitialized
1629 array elements and the second set is empty.
1630 The actual flow dependences can be extracted using
1631 C<isl_flow_foreach>. This function will call the user-specified
1632 callback function C<fn> for each B<non-empty> dependence between
1633 a source and the sink. The callback function is called
1634 with four arguments, the actual flow dependence relation
1635 mapping source iterations to sink iterations, a boolean that
1636 indicates whether it is a I<must> or I<may> dependence, a token
1637 identifying the source and an additional C<void *> with value
1638 equal to the third argument of the C<isl_flow_foreach> call.
1639 A dependence is marked I<must> if it originates from a I<must>
1640 source and if it is not followed by any I<may> sources.
1642 After finishing with an C<isl_flow>, the user should call
1643 C<isl_flow_free> to free all associated memory.
1645 =head2 Parametric Vertex Enumeration
1647 The parametric vertex enumeration described in this section
1648 is mainly intended to be used internally and by the C<barvinok>
1651 #include <isl_vertices.h>
1652 __isl_give isl_vertices *isl_basic_set_compute_vertices(
1653 __isl_keep isl_basic_set *bset);
1655 The function C<isl_basic_set_compute_vertices> performs the
1656 actual computation of the parametric vertices and the chamber
1657 decomposition and store the result in an C<isl_vertices> object.
1658 This information can be queried by either iterating over all
1659 the vertices or iterating over all the chambers or cells
1660 and then iterating over all vertices that are active on the chamber.
1662 int isl_vertices_foreach_vertex(
1663 __isl_keep isl_vertices *vertices,
1664 int (*fn)(__isl_take isl_vertex *vertex, void *user),
1667 int isl_vertices_foreach_cell(
1668 __isl_keep isl_vertices *vertices,
1669 int (*fn)(__isl_take isl_cell *cell, void *user),
1671 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
1672 int (*fn)(__isl_take isl_vertex *vertex, void *user),
1675 Other operations that can be performed on an C<isl_vertices> object are
1678 isl_ctx *isl_vertices_get_ctx(
1679 __isl_keep isl_vertices *vertices);
1680 int isl_vertices_get_n_vertices(
1681 __isl_keep isl_vertices *vertices);
1682 void isl_vertices_free(__isl_take isl_vertices *vertices);
1684 Vertices can be inspected and destroyed using the following functions.
1686 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
1687 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
1688 __isl_give isl_basic_set *isl_vertex_get_domain(
1689 __isl_keep isl_vertex *vertex);
1690 __isl_give isl_basic_set *isl_vertex_get_expr(
1691 __isl_keep isl_vertex *vertex);
1692 void isl_vertex_free(__isl_take isl_vertex *vertex);
1694 C<isl_vertex_get_expr> returns a singleton parametric set describing
1695 the vertex, while C<isl_vertex_get_domain> returns the activity domain
1697 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
1698 B<rational> basic sets, so they should mainly be used for inspection
1699 and should not be mixed with integer sets.
1701 Chambers can be inspected and destroyed using the following functions.
1703 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
1704 __isl_give isl_basic_set *isl_cell_get_domain(
1705 __isl_keep isl_cell *cell);
1706 void isl_cell_free(__isl_take isl_cell *cell);
1710 Although C<isl> is mainly meant to be used as a library,
1711 it also contains some basic applications that use some
1712 of the functionality of C<isl>.
1713 The input may be specified in either the L<isl format>
1714 or the L<PolyLib format>.
1716 =head2 C<isl_polyhedron_sample>
1718 C<isl_polyhedron_sample> takes a polyhedron as input and prints
1719 an integer element of the polyhedron, if there is any.
1720 The first column in the output is the denominator and is always
1721 equal to 1. If the polyhedron contains no integer points,
1722 then a vector of length zero is printed.
1726 C<isl_pip> takes the same input as the C<example> program
1727 from the C<piplib> distribution, i.e., a set of constraints
1728 on the parameters, a line contains only -1 and finally a set
1729 of constraints on a parametric polyhedron.
1730 The coefficients of the parameters appear in the last columns
1731 (but before the final constant column).
1732 The output is the lexicographic minimum of the parametric polyhedron.
1733 As C<isl> currently does not have its own output format, the output
1734 is just a dump of the internal state.
1736 =head2 C<isl_polyhedron_minimize>
1738 C<isl_polyhedron_minimize> computes the minimum of some linear
1739 or affine objective function over the integer points in a polyhedron.
1740 If an affine objective function
1741 is given, then the constant should appear in the last column.
1743 =head2 C<isl_polytope_scan>
1745 Given a polytope, C<isl_polytope_scan> prints
1746 all integer points in the polytope.
1748 =head1 C<isl-polylib>
1750 The C<isl-polylib> library provides the following functions for converting
1751 between C<isl> objects and C<PolyLib> objects.
1752 The library is distributed separately for licensing reasons.
1754 #include <isl_set_polylib.h>
1755 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
1756 Polyhedron *P, __isl_take isl_dim *dim);
1757 Polyhedron *isl_basic_set_to_polylib(
1758 __isl_keep isl_basic_set *bset);
1759 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
1760 __isl_take isl_dim *dim);
1761 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
1763 #include <isl_map_polylib.h>
1764 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
1765 Polyhedron *P, __isl_take isl_dim *dim);
1766 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
1767 __isl_take isl_dim *dim);
1768 Polyhedron *isl_basic_map_to_polylib(
1769 __isl_keep isl_basic_map *bmap);
1770 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);