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);
1078 =head3 Lexicographic Optimization
1080 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1081 the following functions
1082 compute a set that contains the lexicographic minimum or maximum
1083 of the elements in C<set> (or C<bset>) for those values of the parameters
1084 that satisfy C<dom>.
1085 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1086 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1088 In other words, the union of the parameter values
1089 for which the result is non-empty and of C<*empty>
1092 __isl_give isl_set *isl_basic_set_partial_lexmin(
1093 __isl_take isl_basic_set *bset,
1094 __isl_take isl_basic_set *dom,
1095 __isl_give isl_set **empty);
1096 __isl_give isl_set *isl_basic_set_partial_lexmax(
1097 __isl_take isl_basic_set *bset,
1098 __isl_take isl_basic_set *dom,
1099 __isl_give isl_set **empty);
1100 __isl_give isl_set *isl_set_partial_lexmin(
1101 __isl_take isl_set *set, __isl_take isl_set *dom,
1102 __isl_give isl_set **empty);
1103 __isl_give isl_set *isl_set_partial_lexmax(
1104 __isl_take isl_set *set, __isl_take isl_set *dom,
1105 __isl_give isl_set **empty);
1107 Given a (basic) set C<set> (or C<bset>), the following functions simply
1108 return a set containing the lexicographic minimum or maximum
1109 of the elements in C<set> (or C<bset>).
1111 __isl_give isl_set *isl_basic_set_lexmin(
1112 __isl_take isl_basic_set *bset);
1113 __isl_give isl_set *isl_basic_set_lexmax(
1114 __isl_take isl_basic_set *bset);
1115 __isl_give isl_set *isl_set_lexmin(
1116 __isl_take isl_set *set);
1117 __isl_give isl_set *isl_set_lexmax(
1118 __isl_take isl_set *set);
1120 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1121 the following functions
1122 compute a relation that maps each element of C<dom>
1123 to the single lexicographic minimum or maximum
1124 of the elements that are associated to that same
1125 element in C<map> (or C<bmap>).
1126 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1127 that contains the elements in C<dom> that do not map
1128 to any elements in C<map> (or C<bmap>).
1129 In other words, the union of the domain of the result and of C<*empty>
1132 __isl_give isl_map *isl_basic_map_partial_lexmax(
1133 __isl_take isl_basic_map *bmap,
1134 __isl_take isl_basic_set *dom,
1135 __isl_give isl_set **empty);
1136 __isl_give isl_map *isl_basic_map_partial_lexmin(
1137 __isl_take isl_basic_map *bmap,
1138 __isl_take isl_basic_set *dom,
1139 __isl_give isl_set **empty);
1140 __isl_give isl_map *isl_map_partial_lexmax(
1141 __isl_take isl_map *map, __isl_take isl_set *dom,
1142 __isl_give isl_set **empty);
1143 __isl_give isl_map *isl_map_partial_lexmin(
1144 __isl_take isl_map *map, __isl_take isl_set *dom,
1145 __isl_give isl_set **empty);
1147 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1148 return a map mapping each element in the domain of
1149 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1150 of all elements associated to that element.
1152 __isl_give isl_map *isl_basic_map_lexmin(
1153 __isl_take isl_basic_map *bmap);
1154 __isl_give isl_map *isl_basic_map_lexmax(
1155 __isl_take isl_basic_map *bmap);
1156 __isl_give isl_map *isl_map_lexmin(
1157 __isl_take isl_map *map);
1158 __isl_give isl_map *isl_map_lexmax(
1159 __isl_take isl_map *map);
1163 Points are elements of a set. They can be used to construct
1164 simple sets (boxes) or they can be used to represent the
1165 individual elements of a set.
1166 The zero point (the origin) can be created using
1168 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1170 The coordinates of a point can be inspected, set and changed
1173 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1174 enum isl_dim_type type, int pos, isl_int *v);
1175 __isl_give isl_point *isl_point_set_coordinate(
1176 __isl_take isl_point *pnt,
1177 enum isl_dim_type type, int pos, isl_int v);
1179 __isl_give isl_point *isl_point_add_ui(
1180 __isl_take isl_point *pnt,
1181 enum isl_dim_type type, int pos, unsigned val);
1182 __isl_give isl_point *isl_point_sub_ui(
1183 __isl_take isl_point *pnt,
1184 enum isl_dim_type type, int pos, unsigned val);
1186 Points can be copied or freed using
1188 __isl_give isl_point *isl_point_copy(
1189 __isl_keep isl_point *pnt);
1190 void isl_point_free(__isl_take isl_point *pnt);
1192 A singleton set can be created from a point using
1194 __isl_give isl_set *isl_set_from_point(
1195 __isl_take isl_point *pnt);
1197 and a box can be created from two opposite extremal points using
1199 __isl_give isl_set *isl_set_box_from_points(
1200 __isl_take isl_point *pnt1,
1201 __isl_take isl_point *pnt2);
1203 All elements of a B<bounded> set can be enumerated using
1204 the following function.
1206 int isl_set_foreach_point(__isl_keep isl_set *set,
1207 int (*fn)(__isl_take isl_point *pnt, void *user),
1210 The function C<fn> is called for each integer point in
1211 C<set> with as second argument the last argument of
1212 the C<isl_set_foreach_point> call. The function C<fn>
1213 should return C<0> on success and C<-1> on failure.
1214 In the latter case, C<isl_set_foreach_point> will stop
1215 enumerating and return C<-1> as well.
1216 If the enumeration is performed successfully and to completion,
1217 then C<isl_set_foreach_point> returns C<0>.
1219 To obtain a single point of a set, use
1221 __isl_give isl_point *isl_set_sample_point(
1222 __isl_take isl_set *set);
1224 If C<set> does not contain any (integer) points, then the
1225 resulting point will be ``void'', a property that can be
1228 int isl_point_is_void(__isl_keep isl_point *pnt);
1230 =head2 Piecewise Quasipolynomials
1232 A piecewise quasipolynomial is a particular kind of function that maps
1233 a parametric point to a rational value.
1234 More specifically, a quasipolynomial is a polynomial expression in greatest
1235 integer parts of affine expressions of parameters and variables.
1236 A piecewise quasipolynomial is a subdivision of a given parametric
1237 domain into disjoint cells with a quasipolynomial associated to
1238 each cell. The value of the piecewise quasipolynomial at a given
1239 point is the value of the quasipolynomial associated to the cell
1240 that contains the point. Outside of the union of cells,
1241 the value is assumed to be zero.
1242 For example, the piecewise quasipolynomial
1244 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1246 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1247 Piecewise quasipolynomials are mainly used by the C<barvinok>
1248 library for representing the number of elements in a parametric set or map.
1249 For example, the piecewise quasipolynomial above represents
1250 the number of point in the map
1252 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1254 =head3 Printing (Piecewise) Quasipolynomials
1256 Quasipolynomials and piecewise quasipolynomials can be printed
1257 using the following functions.
1259 __isl_give isl_printer *isl_printer_print_qpolynomial(
1260 __isl_take isl_printer *p,
1261 __isl_keep isl_qpolynomial *qp);
1263 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1264 __isl_take isl_printer *p,
1265 __isl_keep isl_pw_qpolynomial *pwqp);
1267 The output format of the printer
1268 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1270 =head3 Creating New (Piecewise) Quasipolynomials
1272 Some simple quasipolynomials can be created using the following functions.
1273 More complicated quasipolynomials can be created by applying
1274 operations such as addition and multiplication
1275 on the resulting quasipolynomials
1277 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1278 __isl_take isl_dim *dim);
1279 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1280 __isl_take isl_dim *dim);
1281 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1282 __isl_take isl_dim *dim);
1283 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1284 __isl_take isl_dim *dim);
1285 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1286 __isl_take isl_dim *dim,
1287 const isl_int n, const isl_int d);
1288 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1289 __isl_take isl_div *div);
1290 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1291 __isl_take isl_dim *dim,
1292 enum isl_dim_type type, unsigned pos);
1294 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1295 with a single cell can be created using the following functions.
1296 Multiple of these single cell piecewise quasipolynomials can
1297 be combined to create more complicated piecewise quasipolynomials.
1299 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1300 __isl_take isl_dim *dim);
1301 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1302 __isl_take isl_set *set,
1303 __isl_take isl_qpolynomial *qp);
1305 Quasipolynomials can be copied and freed again using the following
1308 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1309 __isl_keep isl_qpolynomial *qp);
1310 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1312 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1313 __isl_keep isl_pw_qpolynomial *pwqp);
1314 void isl_pw_qpolynomial_free(
1315 __isl_take isl_pw_qpolynomial *pwqp);
1317 =head3 Inspecting (Piecewise) Quasipolynomials
1319 To iterate over the cells in a piecewise quasipolynomial,
1320 use either of the following two functions
1322 int isl_pw_qpolynomial_foreach_piece(
1323 __isl_keep isl_pw_qpolynomial *pwqp,
1324 int (*fn)(__isl_take isl_set *set,
1325 __isl_take isl_qpolynomial *qp,
1326 void *user), void *user);
1327 int isl_pw_qpolynomial_foreach_lifted_piece(
1328 __isl_keep isl_pw_qpolynomial *pwqp,
1329 int (*fn)(__isl_take isl_set *set,
1330 __isl_take isl_qpolynomial *qp,
1331 void *user), void *user);
1333 As usual, the function C<fn> should return C<0> on success
1334 and C<-1> on failure. The difference between
1335 C<isl_pw_qpolynomial_foreach_piece> and
1336 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1337 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1338 compute unique representations for all existentially quantified
1339 variables and then turn these existentially quantified variables
1340 into extra set variables, adapting the associated quasipolynomial
1341 accordingly. This means that the C<set> passed to C<fn>
1342 will not have any existentially quantified variables, but that
1343 the dimensions of the sets may be different for different
1344 invocations of C<fn>.
1346 To iterate over all terms in a quasipolynomial,
1349 int isl_qpolynomial_foreach_term(
1350 __isl_keep isl_qpolynomial *qp,
1351 int (*fn)(__isl_take isl_term *term,
1352 void *user), void *user);
1354 The terms themselves can be inspected and freed using
1357 unsigned isl_term_dim(__isl_keep isl_term *term,
1358 enum isl_dim_type type);
1359 void isl_term_get_num(__isl_keep isl_term *term,
1361 void isl_term_get_den(__isl_keep isl_term *term,
1363 int isl_term_get_exp(__isl_keep isl_term *term,
1364 enum isl_dim_type type, unsigned pos);
1365 __isl_give isl_div *isl_term_get_div(
1366 __isl_keep isl_term *term, unsigned pos);
1367 void isl_term_free(__isl_take isl_term *term);
1369 Each term is a product of parameters, set variables and
1370 integer divisions. The function C<isl_term_get_exp>
1371 returns the exponent of a given dimensions in the given term.
1372 The C<isl_int>s in the arguments of C<isl_term_get_num>
1373 and C<isl_term_get_den> need to have been initialized
1374 using C<isl_int_init> before calling these functions.
1376 =head3 Properties of (Piecewise) Quasipolynomials
1378 To check whether a quasipolynomial is actually a constant,
1379 use the following function.
1381 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1382 isl_int *n, isl_int *d);
1384 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1385 then the numerator and denominator of the constant
1386 are returned in C<*n> and C<*d>, respectively.
1388 =head3 Operations on (Piecewise) Quasipolynomials
1390 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1391 __isl_take isl_qpolynomial *qp);
1392 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1393 __isl_take isl_qpolynomial *qp1,
1394 __isl_take isl_qpolynomial *qp2);
1395 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1396 __isl_take isl_qpolynomial *qp1,
1397 __isl_take isl_qpolynomial *qp2);
1398 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1399 __isl_take isl_qpolynomial *qp1,
1400 __isl_take isl_qpolynomial *qp2);
1402 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1403 __isl_take isl_pw_qpolynomial *pwqp1,
1404 __isl_take isl_pw_qpolynomial *pwqp2);
1405 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1406 __isl_take isl_pw_qpolynomial *pwqp1,
1407 __isl_take isl_pw_qpolynomial *pwqp2);
1408 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1409 __isl_take isl_pw_qpolynomial *pwqp1,
1410 __isl_take isl_pw_qpolynomial *pwqp2);
1411 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1412 __isl_take isl_pw_qpolynomial *pwqp);
1413 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1414 __isl_take isl_pw_qpolynomial *pwqp1,
1415 __isl_take isl_pw_qpolynomial *pwqp2);
1417 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1418 __isl_take isl_pw_qpolynomial *pwqp,
1419 __isl_take isl_point *pnt);
1421 __isl_give isl_set *isl_pw_qpolynomial_domain(
1422 __isl_take isl_pw_qpolynomial *pwqp);
1423 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1424 __isl_take isl_pw_qpolynomial *pwpq,
1425 __isl_take isl_set *set);
1427 =head2 Dependence Analysis
1429 C<isl> contains specialized functionality for performing
1430 array dataflow analysis. That is, given a I<sink> access relation
1431 and a collection of possible I<source> access relations,
1432 C<isl> can compute relations that describe
1433 for each iteration of the sink access, which iteration
1434 of which of the source access relations was the last
1435 to access the same data element before the given iteration
1437 To compute standard flow dependences, the sink should be
1438 a read, while the sources should be writes.
1439 If any of the source accesses are marked as being I<may>
1440 accesses, then there will be a dependence to the last
1441 I<must> access B<and> to any I<may> access that follows
1442 this last I<must> access.
1443 In particular, if I<all> sources are I<may> accesses,
1444 then memory based dependence analysis is performed.
1445 If, on the other hand, all sources are I<must> accesses,
1446 then value based dependence analysis is performed.
1448 #include <isl_flow.h>
1450 __isl_give isl_access_info *isl_access_info_alloc(
1451 __isl_take isl_map *sink,
1452 void *sink_user, isl_access_level_before fn,
1454 __isl_give isl_access_info *isl_access_info_add_source(
1455 __isl_take isl_access_info *acc,
1456 __isl_take isl_map *source, int must,
1459 __isl_give isl_flow *isl_access_info_compute_flow(
1460 __isl_take isl_access_info *acc);
1462 int isl_flow_foreach(__isl_keep isl_flow *deps,
1463 int (*fn)(__isl_take isl_map *dep, int must,
1464 void *dep_user, void *user),
1466 __isl_give isl_set *isl_flow_get_no_source(
1467 __isl_keep isl_flow *deps, int must);
1468 void isl_flow_free(__isl_take isl_flow *deps);
1470 The function C<isl_access_info_compute_flow> performs the actual
1471 dependence analysis. The other functions are used to construct
1472 the input for this function or to read off the output.
1474 The input is collected in an C<isl_access_info>, which can
1475 be created through a call to C<isl_access_info_alloc>.
1476 The arguments to this functions are the sink access relation
1477 C<sink>, a token C<sink_user> used to identify the sink
1478 access to the user, a callback function for specifying the
1479 relative order of source and sink accesses, and the number
1480 of source access relations that will be added.
1481 The callback function has type C<int (*)(void *first, void *second)>.
1482 The function is called with two user supplied tokens identifying
1483 either a source or the sink and it should return the shared nesting
1484 level and the relative order of the two accesses.
1485 In particular, let I<n> be the number of loops shared by
1486 the two accesses. If C<first> precedes C<second> textually,
1487 then the function should return I<2 * n + 1>; otherwise,
1488 it should return I<2 * n>.
1489 The sources can be added to the C<isl_access_info> by performing
1490 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1491 C<must> indicates whether the source is a I<must> access
1492 or a I<may> access. Note that a multi-valued access relation
1493 should only be marked I<must> if every iteration in the domain
1494 of the relation accesses I<all> elements in its image.
1495 The C<source_user> token is again used to identify
1496 the source access. The range of the source access relation
1497 C<source> should have the same dimension as the range
1498 of the sink access relation.
1500 The result of the dependence analysis is collected in an
1501 C<isl_flow>. There may be elements in the domain of
1502 the sink access for which no preceding source access could be
1503 found or for which all preceding sources are I<may> accesses.
1504 The sets of these elements can be obtained through
1505 calls to C<isl_flow_get_no_source>, the first with C<must> set
1506 and the second with C<must> unset.
1507 In the case of standard flow dependence analysis,
1508 with the sink a read and the sources I<must> writes,
1509 the first set corresponds to the reads from uninitialized
1510 array elements and the second set is empty.
1511 The actual flow dependences can be extracted using
1512 C<isl_flow_foreach>. This function will call the user-specified
1513 callback function C<fn> for each B<non-empty> dependence between
1514 a source and the sink. The callback function is called
1515 with four arguments, the actual flow dependence relation
1516 mapping source iterations to sink iterations, a boolean that
1517 indicates whether it is a I<must> or I<may> dependence, a token
1518 identifying the source and an additional C<void *> with value
1519 equal to the third argument of the C<isl_flow_foreach> call.
1520 A dependence is marked I<must> if it originates from a I<must>
1521 source and if it is not followed by any I<may> sources.
1523 After finishing with an C<isl_flow>, the user should call
1524 C<isl_flow_free> to free all associated memory.
1528 Although C<isl> is mainly meant to be used as a library,
1529 it also contains some basic applications that use some
1530 of the functionality of C<isl>.
1531 The input may be specified in either the L<isl format>
1532 or the L<PolyLib format>.
1534 =head2 C<isl_polyhedron_sample>
1536 C<isl_polyhedron_sample> takes a polyhedron as input and prints
1537 an integer element of the polyhedron, if there is any.
1538 The first column in the output is the denominator and is always
1539 equal to 1. If the polyhedron contains no integer points,
1540 then a vector of length zero is printed.
1544 C<isl_pip> takes the same input as the C<example> program
1545 from the C<piplib> distribution, i.e., a set of constraints
1546 on the parameters, a line contains only -1 and finally a set
1547 of constraints on a parametric polyhedron.
1548 The coefficients of the parameters appear in the last columns
1549 (but before the final constant column).
1550 The output is the lexicographic minimum of the parametric polyhedron.
1551 As C<isl> currently does not have its own output format, the output
1552 is just a dump of the internal state.
1554 =head2 C<isl_polyhedron_minimize>
1556 C<isl_polyhedron_minimize> computes the minimum of some linear
1557 or affine objective function over the integer points in a polyhedron.
1558 If an affine objective function
1559 is given, then the constant should appear in the last column.
1561 =head2 C<isl_polytope_scan>
1563 Given a polytope, C<isl_polytope_scan> prints
1564 all integer points in the polytope.
1566 =head1 C<isl-polylib>
1568 The C<isl-polylib> library provides the following functions for converting
1569 between C<isl> objects and C<PolyLib> objects.
1570 The library is distributed separately for licensing reasons.
1572 #include <isl_set_polylib.h>
1573 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
1574 Polyhedron *P, __isl_take isl_dim *dim);
1575 Polyhedron *isl_basic_set_to_polylib(
1576 __isl_keep isl_basic_set *bset);
1577 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
1578 __isl_take isl_dim *dim);
1579 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
1581 #include <isl_map_polylib.h>
1582 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
1583 Polyhedron *P, __isl_take isl_dim *dim);
1584 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
1585 __isl_take isl_dim *dim);
1586 Polyhedron *isl_basic_map_to_polylib(
1587 __isl_keep isl_basic_map *bmap);
1588 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);