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.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
40 The source of C<isl> can be obtained either as a tarball
41 or from the git repository. Both are available from
42 L<http://freshmeat.net/projects/isl/>.
43 The installation process depends on how you obtained
46 =head2 Installation from the git repository
50 =item 1 Clone or update the repository
52 The first time the source is obtained, you need to clone
55 git clone git://repo.or.cz/isl.git
57 To obtain updates, you need to pull in the latest changes
61 =item 2 Get submodule (optional)
63 C<isl> can optionally use the C<piplib> library and provides
64 this library as a submodule. If you want to use it, then
65 after you have cloned C<isl>, you need to grab the submodules
70 To obtain updates, you only need
74 Note that C<isl> currently does not use any C<piplib>
75 functionality by default.
77 =item 3 Generate C<configure>
83 After performing the above steps, continue
84 with the L<Common installation instructions>.
86 =head2 Common installation instructions
92 Building C<isl> requires C<GMP>, including its headers files.
93 Your distribution may not provide these header files by default
94 and you may need to install a package called C<gmp-devel> or something
95 similar. Alternatively, C<GMP> can be built from
96 source, available from L<http://gmplib.org/>.
100 C<isl> uses the standard C<autoconf> C<configure> script.
105 optionally followed by some configure options.
106 A complete list of options can be obtained by running
110 Below we discuss some of the more common options.
112 C<isl> can optionally use C<piplib>, but no
113 C<piplib> functionality is currently used by default.
114 The C<--with-piplib> option can
115 be used to specify which C<piplib>
116 library to use, either an installed version (C<system>),
117 an externally built version (C<build>)
118 or no version (C<no>). The option C<build> is mostly useful
119 in C<configure> scripts of larger projects that bundle both C<isl>
126 Installation prefix for C<isl>
128 =item C<--with-gmp-prefix>
130 Installation prefix for C<GMP> (architecture-independent files).
132 =item C<--with-gmp-exec-prefix>
134 Installation prefix for C<GMP> (architecture-dependent files).
136 =item C<--with-piplib>
138 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
140 =item C<--with-piplib-prefix>
142 Installation prefix for C<system> C<piplib> (architecture-independent files).
144 =item C<--with-piplib-exec-prefix>
146 Installation prefix for C<system> C<piplib> (architecture-dependent files).
148 =item C<--with-piplib-builddir>
150 Location where C<build> C<piplib> was built.
158 =item 4 Install (optional)
166 =head2 Initialization
168 All manipulations of integer sets and relations occur within
169 the context of an C<isl_ctx>.
170 A given C<isl_ctx> can only be used within a single thread.
171 All arguments of a function are required to have been allocated
172 within the same context.
173 There are currently no functions available for moving an object
174 from one C<isl_ctx> to another C<isl_ctx>. This means that
175 there is currently no way of safely moving an object from one
176 thread to another, unless the whole C<isl_ctx> is moved.
178 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
179 freed using C<isl_ctx_free>.
180 All objects allocated within an C<isl_ctx> should be freed
181 before the C<isl_ctx> itself is freed.
183 isl_ctx *isl_ctx_alloc();
184 void isl_ctx_free(isl_ctx *ctx);
188 All operations on integers, mainly the coefficients
189 of the constraints describing the sets and relations,
190 are performed in exact integer arithmetic using C<GMP>.
191 However, to allow future versions of C<isl> to optionally
192 support fixed integer arithmetic, all calls to C<GMP>
193 are wrapped inside C<isl> specific macros.
194 The basic type is C<isl_int> and the following operations
195 are available on this type.
196 The meanings of these operations are essentially the same
197 as their C<GMP> C<mpz_> counterparts.
198 As always with C<GMP> types, C<isl_int>s need to be
199 initialized with C<isl_int_init> before they can be used
200 and they need to be released with C<isl_int_clear>
205 =item isl_int_init(i)
207 =item isl_int_clear(i)
209 =item isl_int_set(r,i)
211 =item isl_int_set_si(r,i)
213 =item isl_int_abs(r,i)
215 =item isl_int_neg(r,i)
217 =item isl_int_swap(i,j)
219 =item isl_int_swap_or_set(i,j)
221 =item isl_int_add_ui(r,i,j)
223 =item isl_int_sub_ui(r,i,j)
225 =item isl_int_add(r,i,j)
227 =item isl_int_sub(r,i,j)
229 =item isl_int_mul(r,i,j)
231 =item isl_int_mul_ui(r,i,j)
233 =item isl_int_addmul(r,i,j)
235 =item isl_int_submul(r,i,j)
237 =item isl_int_gcd(r,i,j)
239 =item isl_int_lcm(r,i,j)
241 =item isl_int_divexact(r,i,j)
243 =item isl_int_cdiv_q(r,i,j)
245 =item isl_int_fdiv_q(r,i,j)
247 =item isl_int_fdiv_r(r,i,j)
249 =item isl_int_fdiv_q_ui(r,i,j)
251 =item isl_int_read(r,s)
253 =item isl_int_print(out,i,width)
257 =item isl_int_cmp(i,j)
259 =item isl_int_cmp_si(i,si)
261 =item isl_int_eq(i,j)
263 =item isl_int_ne(i,j)
265 =item isl_int_lt(i,j)
267 =item isl_int_le(i,j)
269 =item isl_int_gt(i,j)
271 =item isl_int_ge(i,j)
273 =item isl_int_abs_eq(i,j)
275 =item isl_int_abs_ne(i,j)
277 =item isl_int_abs_lt(i,j)
279 =item isl_int_abs_gt(i,j)
281 =item isl_int_abs_ge(i,j)
283 =item isl_int_is_zero(i)
285 =item isl_int_is_one(i)
287 =item isl_int_is_negone(i)
289 =item isl_int_is_pos(i)
291 =item isl_int_is_neg(i)
293 =item isl_int_is_nonpos(i)
295 =item isl_int_is_nonneg(i)
297 =item isl_int_is_divisible_by(i,j)
301 =head2 Sets and Relations
303 C<isl> uses four types of objects for representing sets and relations,
304 C<isl_basic_set>, C<isl_basic_map>, C<isl_set> and C<isl_map>.
305 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
306 can be described as a conjunction of affine constraints, while
307 C<isl_set> and C<isl_map> represent unions of
308 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
309 The difference between sets and relations (maps) is that sets have
310 one set of variables, while relations have two sets of variables,
311 input variables and output variables.
313 =head2 Memory Management
315 Since a high-level operation on sets and/or relations usually involves
316 several substeps and since the user is usually not interested in
317 the intermediate results, most functions that return a new object
318 will also release all the objects passed as arguments.
319 If the user still wants to use one or more of these arguments
320 after the function call, she should pass along a copy of the
321 object rather than the object itself.
322 The user is then responsible for make sure that the original
323 object gets used somewhere else or is explicitly freed.
325 The arguments and return values of all documents functions are
326 annotated to make clear which arguments are released and which
327 arguments are preserved. In particular, the following annotations
334 C<__isl_give> means that a new object is returned.
335 The user should make sure that the returned pointer is
336 used exactly once as a value for an C<__isl_take> argument.
337 In between, it can be used as a value for as many
338 C<__isl_keep> arguments as the user likes.
339 There is one exception, and that is the case where the
340 pointer returned is C<NULL>. Is this case, the user
341 is free to use it as an C<__isl_take> argument or not.
345 C<__isl_take> means that the object the argument points to
346 is taken over by the function and may no longer be used
347 by the user as an argument to any other function.
348 The pointer value must be one returned by a function
349 returning an C<__isl_give> pointer.
350 If the user passes in a C<NULL> value, then this will
351 be treated as an error in the sense that the function will
352 not perform its usual operation. However, it will still
353 make sure that all the the other C<__isl_take> arguments
358 C<__isl_keep> means that the function will only use the object
359 temporarily. After the function has finished, the user
360 can still use it as an argument to other functions.
361 A C<NULL> value will be treated in the same way as
362 a C<NULL> value for an C<__isl_take> argument.
366 =head2 Dimension Specifications
368 Whenever a new set or relation is created from scratch,
369 its dimension needs to be specified using an C<isl_dim>.
372 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
373 unsigned nparam, unsigned n_in, unsigned n_out);
374 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
375 unsigned nparam, unsigned dim);
376 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
377 void isl_dim_free(__isl_take isl_dim *dim);
378 unsigned isl_dim_size(__isl_keep isl_dim *dim,
379 enum isl_dim_type type);
381 The dimension specification used for creating a set
382 needs to be created using C<isl_dim_set_alloc>, while
383 that for creating a relation
384 needs to be created using C<isl_dim_alloc>.
385 C<isl_dim_size> can be used
386 to find out the number of dimensions of each type in
387 a dimension specification, where type may be
388 C<isl_dim_param>, C<isl_dim_in> (only for relations),
389 C<isl_dim_out> (only for relations), C<isl_dim_set>
390 (only for sets) or C<isl_dim_all>.
392 It is often useful to create objects that live in the
393 same space as some other object. This can be accomplished
394 by creating the new objects
395 (see L<Creating New Sets and Relations> or
396 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
397 specification of the original object.
400 __isl_give isl_dim *isl_basic_set_get_dim(
401 __isl_keep isl_basic_set *bset);
402 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
405 __isl_give isl_dim *isl_basic_map_get_dim(
406 __isl_keep isl_basic_map *bmap);
407 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
409 #include <isl_polynomial.h>
410 __isl_give isl_dim *isl_qpolynomial_get_dim(
411 __isl_keep isl_qpolynomial *qp);
412 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
413 __isl_keep isl_pw_qpolynomial *pwqp);
415 The names of the individual dimensions may be set or read off
416 using the following functions.
419 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
420 enum isl_dim_type type, unsigned pos,
421 __isl_keep const char *name);
422 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
423 enum isl_dim_type type, unsigned pos);
425 Note that C<isl_dim_get_name> returns a pointer to some internal
426 data structure, so the result can only be used while the
427 corresponding C<isl_dim> is alive.
428 Also note that every function that operates on two sets or relations
429 requires that both arguments have the same parameters. This also
430 means that if one of the arguments has named parameters, then the
431 other needs to have named parameters too and the names need to match.
433 =head2 Input and Output
435 C<isl> supports its own input/output format, which is similar
436 to the C<Omega> format, but also supports the C<PolyLib> format
441 The C<isl> format is similar to that of C<Omega>, but has a different
442 syntax for describing the parameters and allows for the definition
443 of an existentially quantified variable as the integer division
444 of an affine expression.
445 For example, the set of integers C<i> between C<0> and C<n>
446 such that C<i % 10 <= 6> can be described as
448 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
451 A set or relation can have several disjuncts, separated
452 by the keyword C<or>. Each disjunct is either a conjunction
453 of constraints or a projection (C<exists>) of a conjunction
454 of constraints. The constraints are separated by the keyword
457 =head3 C<PolyLib> format
459 If the represented set is a union, then the first line
460 contains a single number representing the number of disjuncts.
461 Otherwise, a line containing the number C<1> is optional.
463 Each disjunct is represented by a matrix of constraints.
464 The first line contains two numbers representing
465 the number of rows and columns,
466 where the number of rows is equal to the number of constraints
467 and the number of columns is equal to two plus the number of variables.
468 The following lines contain the actual rows of the constraint matrix.
469 In each row, the first column indicates whether the constraint
470 is an equality (C<0>) or inequality (C<1>). The final column
471 corresponds to the constant term.
473 If the set is parametric, then the coefficients of the parameters
474 appear in the last columns before the constant column.
475 The coefficients of any existentially quantified variables appear
476 between those of the set variables and those of the parameters.
481 __isl_give isl_basic_set *isl_basic_set_read_from_file(
482 isl_ctx *ctx, FILE *input, int nparam);
483 __isl_give isl_basic_set *isl_basic_set_read_from_str(
484 isl_ctx *ctx, const char *str, int nparam);
485 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
486 FILE *input, int nparam);
487 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
488 const char *str, int nparam);
491 __isl_give isl_basic_map *isl_basic_map_read_from_file(
492 isl_ctx *ctx, FILE *input, int nparam);
493 __isl_give isl_basic_map *isl_basic_map_read_from_str(
494 isl_ctx *ctx, const char *str, int nparam);
495 __isl_give isl_map *isl_map_read_from_file(
496 struct isl_ctx *ctx, FILE *input, int nparam);
497 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
498 const char *str, int nparam);
500 The input format is autodetected and may be either the C<PolyLib> format
501 or the C<isl> format.
502 C<nparam> specifies how many of the final columns in
503 the C<PolyLib> format correspond to parameters.
504 If input is given in the C<isl> format, then the number
505 of parameters needs to be equal to C<nparam>.
506 If C<nparam> is negative, then any number of parameters
507 is accepted in the C<isl> format and zero parameters
508 are assumed in the C<PolyLib> format.
512 Before anything can be printed, an C<isl_printer> needs to
515 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
517 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
518 void isl_printer_free(__isl_take isl_printer *printer);
519 __isl_give char *isl_printer_get_str(
520 __isl_keep isl_printer *printer);
522 The behavior of the printer can be modified in various ways
524 __isl_give isl_printer *isl_printer_set_output_format(
525 __isl_take isl_printer *p, int output_format);
526 __isl_give isl_printer *isl_printer_set_indent(
527 __isl_take isl_printer *p, int indent);
528 __isl_give isl_printer *isl_printer_set_prefix(
529 __isl_take isl_printer *p, const char *prefix);
530 __isl_give isl_printer *isl_printer_set_suffix(
531 __isl_take isl_printer *p, const char *suffix);
533 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>
534 or C<ISL_FORMAT_POLYLIB> and defaults to C<ISL_FORMAT_ISL>.
535 Each line in the output is indented by C<indent> spaces
536 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
537 In the C<PolyLib> format output,
538 the coefficients of the existentially quantified variables
539 appear between those of the set variables and those
542 To actually print something, use
545 __isl_give isl_printer *isl_printer_print_basic_set(
546 __isl_take isl_printer *printer,
547 __isl_keep isl_basic_set *bset);
548 __isl_give isl_printer *isl_printer_print_set(
549 __isl_take isl_printer *printer,
550 __isl_keep isl_set *set);
553 __isl_give isl_printer *isl_printer_print_basic_map(
554 __isl_take isl_printer *printer,
555 __isl_keep isl_basic_map *bmap);
556 __isl_give isl_printer *isl_printer_print_map(
557 __isl_take isl_printer *printer,
558 __isl_keep isl_map *map);
560 When called on a file printer, the following function flushes
561 the file. When called on a string printer, the buffer is cleared.
563 __isl_give isl_printer *isl_printer_flush(
564 __isl_take isl_printer *p);
566 =head2 Creating New Sets and Relations
568 C<isl> has functions for creating some standard sets and relations.
572 =item * Empty sets and relations
574 __isl_give isl_basic_set *isl_basic_set_empty(
575 __isl_take isl_dim *dim);
576 __isl_give isl_basic_map *isl_basic_map_empty(
577 __isl_take isl_dim *dim);
578 __isl_give isl_set *isl_set_empty(
579 __isl_take isl_dim *dim);
580 __isl_give isl_map *isl_map_empty(
581 __isl_take isl_dim *dim);
583 =item * Universe sets and relations
585 __isl_give isl_basic_set *isl_basic_set_universe(
586 __isl_take isl_dim *dim);
587 __isl_give isl_basic_map *isl_basic_map_universe(
588 __isl_take isl_dim *dim);
589 __isl_give isl_set *isl_set_universe(
590 __isl_take isl_dim *dim);
591 __isl_give isl_map *isl_map_universe(
592 __isl_take isl_dim *dim);
594 =item * Identity relations
596 __isl_give isl_basic_map *isl_basic_map_identity(
597 __isl_take isl_dim *set_dim);
598 __isl_give isl_map *isl_map_identity(
599 __isl_take isl_dim *set_dim);
601 These functions take a dimension specification for a B<set>
602 and return an identity relation between two such sets.
604 =item * Lexicographic order
606 __isl_give isl_map *isl_map_lex_lt(
607 __isl_take isl_dim *set_dim);
608 __isl_give isl_map *isl_map_lex_le(
609 __isl_take isl_dim *set_dim);
610 __isl_give isl_map *isl_map_lex_gt(
611 __isl_take isl_dim *set_dim);
612 __isl_give isl_map *isl_map_lex_ge(
613 __isl_take isl_dim *set_dim);
614 __isl_give isl_map *isl_map_lex_lt_first(
615 __isl_take isl_dim *dim, unsigned n);
616 __isl_give isl_map *isl_map_lex_le_first(
617 __isl_take isl_dim *dim, unsigned n);
618 __isl_give isl_map *isl_map_lex_gt_first(
619 __isl_take isl_dim *dim, unsigned n);
620 __isl_give isl_map *isl_map_lex_ge_first(
621 __isl_take isl_dim *dim, unsigned n);
623 The first four functions take a dimension specification for a B<set>
624 and return relations that express that the elements in the domain
625 are lexicographically less
626 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
627 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
628 than the elements in the range.
629 The last four functions take a dimension specification for a map
630 and return relations that express that the first C<n> dimensions
631 in the domain are lexicographically less
632 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
633 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
634 than the first C<n> dimensions in the range.
638 A basic set or relation can be converted to a set or relation
639 using the following functions.
641 __isl_give isl_set *isl_set_from_basic_set(
642 __isl_take isl_basic_set *bset);
643 __isl_give isl_map *isl_map_from_basic_map(
644 __isl_take isl_basic_map *bmap);
646 Sets and relations can be copied and freed again using the following
649 __isl_give isl_basic_set *isl_basic_set_copy(
650 __isl_keep isl_basic_set *bset);
651 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
652 __isl_give isl_basic_map *isl_basic_map_copy(
653 __isl_keep isl_basic_map *bmap);
654 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
655 void isl_basic_set_free(__isl_take isl_basic_set *bset);
656 void isl_set_free(__isl_take isl_set *set);
657 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
658 void isl_map_free(__isl_take isl_map *map);
660 Other sets and relations can be constructed by starting
661 from a universe set or relation, adding equality and/or
662 inequality constraints and then projecting out the
663 existentially quantified variables, if any.
664 Constraints can be constructed, manipulated and
665 added to basic sets and relations using the following functions.
667 #include <isl_constraint.h>
668 __isl_give isl_constraint *isl_equality_alloc(
669 __isl_take isl_dim *dim);
670 __isl_give isl_constraint *isl_inequality_alloc(
671 __isl_take isl_dim *dim);
672 void isl_constraint_set_constant(
673 __isl_keep isl_constraint *constraint, isl_int v);
674 void isl_constraint_set_coefficient(
675 __isl_keep isl_constraint *constraint,
676 enum isl_dim_type type, int pos, isl_int v);
677 __isl_give isl_basic_map *isl_basic_map_add_constraint(
678 __isl_take isl_basic_map *bmap,
679 __isl_take isl_constraint *constraint);
680 __isl_give isl_basic_set *isl_basic_set_add_constraint(
681 __isl_take isl_basic_set *bset,
682 __isl_take isl_constraint *constraint);
684 For example, to create a set containing the even integers
685 between 10 and 42, you would use the following code.
689 struct isl_constraint *c;
690 struct isl_basic_set *bset;
693 dim = isl_dim_set_alloc(ctx, 0, 2);
694 bset = isl_basic_set_universe(isl_dim_copy(dim));
696 c = isl_equality_alloc(isl_dim_copy(dim));
697 isl_int_set_si(v, -1);
698 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
699 isl_int_set_si(v, 2);
700 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
701 bset = isl_basic_set_add_constraint(bset, c);
703 c = isl_inequality_alloc(isl_dim_copy(dim));
704 isl_int_set_si(v, -10);
705 isl_constraint_set_constant(c, v);
706 isl_int_set_si(v, 1);
707 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
708 bset = isl_basic_set_add_constraint(bset, c);
710 c = isl_inequality_alloc(dim);
711 isl_int_set_si(v, 42);
712 isl_constraint_set_constant(c, v);
713 isl_int_set_si(v, -1);
714 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
715 bset = isl_basic_set_add_constraint(bset, c);
717 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
723 struct isl_basic_set *bset;
724 bset = isl_basic_set_read_from_str(ctx,
725 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
727 =head2 Inspecting Sets and Relations
729 Usually, the user should not have to care about the actual constraints
730 of the sets and maps, but should instead apply the abstract operations
731 explained in the following sections.
732 Occasionally, however, it may be required to inspect the individual
733 coefficients of the constraints. This section explains how to do so.
734 In these cases, it may also be useful to have C<isl> compute
735 an explicit representation of the existentially quantified variables.
737 __isl_give isl_set *isl_set_compute_divs(
738 __isl_take isl_set *set);
739 __isl_give isl_map *isl_map_compute_divs(
740 __isl_take isl_map *map);
742 This explicit representation defines the existentially quantified
743 variables as integer divisions of the other variables, possibly
744 including earlier existentially quantified variables.
745 An explicitly represented existentially quantified variable therefore
746 has a unique value when the values of the other variables are known.
747 If, furthermore, the same existentials, i.e., existentials
748 with the same explicit representations, should appear in the
749 same order in each of the disjuncts of a set or map, then the user should call
750 either of the following functions.
752 __isl_give isl_set *isl_set_align_divs(
753 __isl_take isl_set *set);
754 __isl_give isl_map *isl_map_align_divs(
755 __isl_take isl_map *map);
757 To iterate over all the basic sets or maps in a set or map, use
759 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
760 int (*fn)(__isl_take isl_basic_set *bset, void *user),
762 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
763 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
766 The callback function C<fn> should return 0 if successful and
767 -1 if an error occurs. In the latter case, or if any other error
768 occurs, the above functions will return -1.
770 It should be noted that C<isl> does not guarantee that
771 the basic sets or maps passed to C<fn> are disjoint.
772 If this is required, then the user should call one of
773 the following functions first.
775 __isl_give isl_set *isl_set_make_disjoint(
776 __isl_take isl_set *set);
777 __isl_give isl_map *isl_map_make_disjoint(
778 __isl_take isl_map *map);
780 To iterate over the constraints of a basic set or map, use
782 #include <isl_constraint.h>
784 int isl_basic_map_foreach_constraint(
785 __isl_keep isl_basic_map *bmap,
786 int (*fn)(__isl_take isl_constraint *c, void *user),
788 void isl_constraint_free(struct isl_constraint *c);
790 Again, the callback function C<fn> should return 0 if successful and
791 -1 if an error occurs. In the latter case, or if any other error
792 occurs, the above functions will return -1.
793 The constraint C<c> represents either an equality or an inequality.
794 Use the following function to find out whether a constraint
795 represents an equality. If not, it represents an inequality.
797 int isl_constraint_is_equality(
798 __isl_keep isl_constraint *constraint);
800 The coefficients of the constraints can be inspected using
801 the following functions.
803 void isl_constraint_get_constant(
804 __isl_keep isl_constraint *constraint, isl_int *v);
805 void isl_constraint_get_coefficient(
806 __isl_keep isl_constraint *constraint,
807 enum isl_dim_type type, int pos, isl_int *v);
809 The explicit representations of the existentially quantified
810 variables can be inspected using the following functions.
811 Note that the user is only allowed to use these functions
812 if the inspected set or map is the result of a call
813 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
815 __isl_give isl_div *isl_constraint_div(
816 __isl_keep isl_constraint *constraint, int pos);
817 void isl_div_get_constant(__isl_keep isl_div *div,
819 void isl_div_get_denominator(__isl_keep isl_div *div,
821 void isl_div_get_coefficient(__isl_keep isl_div *div,
822 enum isl_dim_type type, int pos, isl_int *v);
826 =head3 Unary Properties
832 The following functions test whether the given set or relation
833 contains any integer points. The ``fast'' variants do not perform
834 any computations, but simply check if the given set or relation
835 is already known to be empty.
837 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
838 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
839 int isl_set_is_empty(__isl_keep isl_set *set);
840 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
841 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
842 int isl_map_fast_is_empty(__isl_keep isl_map *map);
843 int isl_map_is_empty(__isl_keep isl_map *map);
847 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
848 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
849 int isl_set_fast_is_universe(__isl_keep isl_set *set);
851 =item * Single-valuedness
853 int isl_map_is_single_valued(__isl_keep isl_map *map);
857 int isl_map_is_bijective(__isl_keep isl_map *map);
861 =head3 Binary Properties
867 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
868 __isl_keep isl_set *set2);
869 int isl_set_is_equal(__isl_keep isl_set *set1,
870 __isl_keep isl_set *set2);
871 int isl_map_is_equal(__isl_keep isl_map *map1,
872 __isl_keep isl_map *map2);
873 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
874 __isl_keep isl_map *map2);
875 int isl_basic_map_is_equal(
876 __isl_keep isl_basic_map *bmap1,
877 __isl_keep isl_basic_map *bmap2);
881 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
882 __isl_keep isl_set *set2);
886 int isl_set_is_subset(__isl_keep isl_set *set1,
887 __isl_keep isl_set *set2);
888 int isl_set_is_strict_subset(
889 __isl_keep isl_set *set1,
890 __isl_keep isl_set *set2);
891 int isl_basic_map_is_subset(
892 __isl_keep isl_basic_map *bmap1,
893 __isl_keep isl_basic_map *bmap2);
894 int isl_basic_map_is_strict_subset(
895 __isl_keep isl_basic_map *bmap1,
896 __isl_keep isl_basic_map *bmap2);
897 int isl_map_is_subset(
898 __isl_keep isl_map *map1,
899 __isl_keep isl_map *map2);
900 int isl_map_is_strict_subset(
901 __isl_keep isl_map *map1,
902 __isl_keep isl_map *map2);
906 =head2 Unary Operations
912 __isl_give isl_set *isl_set_complement(
913 __isl_take isl_set *set);
917 __isl_give isl_basic_map *isl_basic_map_reverse(
918 __isl_take isl_basic_map *bmap);
919 __isl_give isl_map *isl_map_reverse(
920 __isl_take isl_map *map);
924 __isl_give isl_basic_set *isl_basic_set_project_out(
925 __isl_take isl_basic_set *bset,
926 enum isl_dim_type type, unsigned first, unsigned n);
927 __isl_give isl_basic_map *isl_basic_map_project_out(
928 __isl_take isl_basic_map *bmap,
929 enum isl_dim_type type, unsigned first, unsigned n);
930 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
931 enum isl_dim_type type, unsigned first, unsigned n);
932 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
933 enum isl_dim_type type, unsigned first, unsigned n);
934 __isl_give isl_basic_set *isl_basic_map_domain(
935 __isl_take isl_basic_map *bmap);
936 __isl_give isl_basic_set *isl_basic_map_range(
937 __isl_take isl_basic_map *bmap);
938 __isl_give isl_set *isl_map_domain(
939 __isl_take isl_map *bmap);
940 __isl_give isl_set *isl_map_range(
941 __isl_take isl_map *map);
945 __isl_give isl_basic_set *isl_basic_map_deltas(
946 __isl_take isl_basic_map *bmap);
947 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
949 These functions return a (basic) set containing the differences
950 between image elements and corresponding domain elements in the input.
954 Simplify the representation of a set or relation by trying
955 to combine pairs of basic sets or relations into a single
956 basic set or relation.
958 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
959 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
963 __isl_give isl_basic_set *isl_set_convex_hull(
964 __isl_take isl_set *set);
965 __isl_give isl_basic_map *isl_map_convex_hull(
966 __isl_take isl_map *map);
968 If the input set or relation has any existentially quantified
969 variables, then the result of these operations is currently undefined.
973 __isl_give isl_basic_set *isl_set_simple_hull(
974 __isl_take isl_set *set);
975 __isl_give isl_basic_map *isl_map_simple_hull(
976 __isl_take isl_map *map);
978 These functions compute a single basic set or relation
979 that contains the whole input set or relation.
980 In particular, the output is described by translates
981 of the constraints describing the basic sets or relations in the input.
985 (See \autoref{s:simple hull}.)
991 __isl_give isl_basic_set *isl_basic_set_affine_hull(
992 __isl_take isl_basic_set *bset);
993 __isl_give isl_basic_set *isl_set_affine_hull(
994 __isl_take isl_set *set);
995 __isl_give isl_basic_map *isl_basic_map_affine_hull(
996 __isl_take isl_basic_map *bmap);
997 __isl_give isl_basic_map *isl_map_affine_hull(
998 __isl_take isl_map *map);
1002 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1003 unsigned param, int *exact);
1005 Compute a parametric representation for all positive powers I<k> of C<map>.
1006 The power I<k> is equated to the parameter at position C<param>.
1007 The result may be an overapproximation. If the result is exact,
1008 then C<*exact> is set to C<1>.
1009 The current implementation only produces exact results for particular
1010 cases of piecewise translations (i.e., piecewise uniform dependences).
1012 =item * Transitive closure
1014 __isl_give isl_map *isl_map_transitive_closure(
1015 __isl_take isl_map *map, int *exact);
1017 Compute the transitive closure of C<map>.
1018 The result may be an overapproximation. If the result is known to be exact,
1019 then C<*exact> is set to C<1>.
1020 The current implementation only produces exact results for particular
1021 cases of piecewise translations (i.e., piecewise uniform dependences).
1025 =head2 Binary Operations
1027 The two arguments of a binary operation not only need to live
1028 in the same C<isl_ctx>, they currently also need to have
1029 the same (number of) parameters.
1031 =head3 Basic Operations
1035 =item * Intersection
1037 __isl_give isl_basic_set *isl_basic_set_intersect(
1038 __isl_take isl_basic_set *bset1,
1039 __isl_take isl_basic_set *bset2);
1040 __isl_give isl_set *isl_set_intersect(
1041 __isl_take isl_set *set1,
1042 __isl_take isl_set *set2);
1043 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1044 __isl_take isl_basic_map *bmap,
1045 __isl_take isl_basic_set *bset);
1046 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1047 __isl_take isl_basic_map *bmap,
1048 __isl_take isl_basic_set *bset);
1049 __isl_give isl_basic_map *isl_basic_map_intersect(
1050 __isl_take isl_basic_map *bmap1,
1051 __isl_take isl_basic_map *bmap2);
1052 __isl_give isl_map *isl_map_intersect_domain(
1053 __isl_take isl_map *map,
1054 __isl_take isl_set *set);
1055 __isl_give isl_map *isl_map_intersect_range(
1056 __isl_take isl_map *map,
1057 __isl_take isl_set *set);
1058 __isl_give isl_map *isl_map_intersect(
1059 __isl_take isl_map *map1,
1060 __isl_take isl_map *map2);
1064 __isl_give isl_set *isl_basic_set_union(
1065 __isl_take isl_basic_set *bset1,
1066 __isl_take isl_basic_set *bset2);
1067 __isl_give isl_map *isl_basic_map_union(
1068 __isl_take isl_basic_map *bmap1,
1069 __isl_take isl_basic_map *bmap2);
1070 __isl_give isl_set *isl_set_union(
1071 __isl_take isl_set *set1,
1072 __isl_take isl_set *set2);
1073 __isl_give isl_map *isl_map_union(
1074 __isl_take isl_map *map1,
1075 __isl_take isl_map *map2);
1077 =item * Set difference
1079 __isl_give isl_set *isl_set_subtract(
1080 __isl_take isl_set *set1,
1081 __isl_take isl_set *set2);
1082 __isl_give isl_map *isl_map_subtract(
1083 __isl_take isl_map *map1,
1084 __isl_take isl_map *map2);
1088 __isl_give isl_basic_set *isl_basic_set_apply(
1089 __isl_take isl_basic_set *bset,
1090 __isl_take isl_basic_map *bmap);
1091 __isl_give isl_set *isl_set_apply(
1092 __isl_take isl_set *set,
1093 __isl_take isl_map *map);
1094 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1095 __isl_take isl_basic_map *bmap1,
1096 __isl_take isl_basic_map *bmap2);
1097 __isl_give isl_basic_map *isl_basic_map_apply_range(
1098 __isl_take isl_basic_map *bmap1,
1099 __isl_take isl_basic_map *bmap2);
1100 __isl_give isl_map *isl_map_apply_domain(
1101 __isl_take isl_map *map1,
1102 __isl_take isl_map *map2);
1103 __isl_give isl_map *isl_map_apply_range(
1104 __isl_take isl_map *map1,
1105 __isl_take isl_map *map2);
1107 =item * Simplification
1109 __isl_give isl_basic_set *isl_basic_set_gist(
1110 __isl_take isl_basic_set *bset,
1111 __isl_take isl_basic_set *context);
1112 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1113 __isl_take isl_set *context);
1114 __isl_give isl_basic_map *isl_basic_map_gist(
1115 __isl_take isl_basic_map *bmap,
1116 __isl_take isl_basic_map *context);
1117 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1118 __isl_take isl_map *context);
1120 The gist operation returns a set or relation that has the
1121 same intersection with the context as the input set or relation.
1122 Any implicit equality in the intersection is made explicit in the result,
1123 while all inequalities that are redundant with respect to the intersection
1128 =head3 Lexicographic Optimization
1130 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1131 the following functions
1132 compute a set that contains the lexicographic minimum or maximum
1133 of the elements in C<set> (or C<bset>) for those values of the parameters
1134 that satisfy C<dom>.
1135 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1136 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1138 In other words, the union of the parameter values
1139 for which the result is non-empty and of C<*empty>
1142 __isl_give isl_set *isl_basic_set_partial_lexmin(
1143 __isl_take isl_basic_set *bset,
1144 __isl_take isl_basic_set *dom,
1145 __isl_give isl_set **empty);
1146 __isl_give isl_set *isl_basic_set_partial_lexmax(
1147 __isl_take isl_basic_set *bset,
1148 __isl_take isl_basic_set *dom,
1149 __isl_give isl_set **empty);
1150 __isl_give isl_set *isl_set_partial_lexmin(
1151 __isl_take isl_set *set, __isl_take isl_set *dom,
1152 __isl_give isl_set **empty);
1153 __isl_give isl_set *isl_set_partial_lexmax(
1154 __isl_take isl_set *set, __isl_take isl_set *dom,
1155 __isl_give isl_set **empty);
1157 Given a (basic) set C<set> (or C<bset>), the following functions simply
1158 return a set containing the lexicographic minimum or maximum
1159 of the elements in C<set> (or C<bset>).
1161 __isl_give isl_set *isl_basic_set_lexmin(
1162 __isl_take isl_basic_set *bset);
1163 __isl_give isl_set *isl_basic_set_lexmax(
1164 __isl_take isl_basic_set *bset);
1165 __isl_give isl_set *isl_set_lexmin(
1166 __isl_take isl_set *set);
1167 __isl_give isl_set *isl_set_lexmax(
1168 __isl_take isl_set *set);
1170 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1171 the following functions
1172 compute a relation that maps each element of C<dom>
1173 to the single lexicographic minimum or maximum
1174 of the elements that are associated to that same
1175 element in C<map> (or C<bmap>).
1176 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1177 that contains the elements in C<dom> that do not map
1178 to any elements in C<map> (or C<bmap>).
1179 In other words, the union of the domain of the result and of C<*empty>
1182 __isl_give isl_map *isl_basic_map_partial_lexmax(
1183 __isl_take isl_basic_map *bmap,
1184 __isl_take isl_basic_set *dom,
1185 __isl_give isl_set **empty);
1186 __isl_give isl_map *isl_basic_map_partial_lexmin(
1187 __isl_take isl_basic_map *bmap,
1188 __isl_take isl_basic_set *dom,
1189 __isl_give isl_set **empty);
1190 __isl_give isl_map *isl_map_partial_lexmax(
1191 __isl_take isl_map *map, __isl_take isl_set *dom,
1192 __isl_give isl_set **empty);
1193 __isl_give isl_map *isl_map_partial_lexmin(
1194 __isl_take isl_map *map, __isl_take isl_set *dom,
1195 __isl_give isl_set **empty);
1197 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1198 return a map mapping each element in the domain of
1199 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1200 of all elements associated to that element.
1202 __isl_give isl_map *isl_basic_map_lexmin(
1203 __isl_take isl_basic_map *bmap);
1204 __isl_give isl_map *isl_basic_map_lexmax(
1205 __isl_take isl_basic_map *bmap);
1206 __isl_give isl_map *isl_map_lexmin(
1207 __isl_take isl_map *map);
1208 __isl_give isl_map *isl_map_lexmax(
1209 __isl_take isl_map *map);
1213 Points are elements of a set. They can be used to construct
1214 simple sets (boxes) or they can be used to represent the
1215 individual elements of a set.
1216 The zero point (the origin) can be created using
1218 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1220 The coordinates of a point can be inspected, set and changed
1223 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1224 enum isl_dim_type type, int pos, isl_int *v);
1225 __isl_give isl_point *isl_point_set_coordinate(
1226 __isl_take isl_point *pnt,
1227 enum isl_dim_type type, int pos, isl_int v);
1229 __isl_give isl_point *isl_point_add_ui(
1230 __isl_take isl_point *pnt,
1231 enum isl_dim_type type, int pos, unsigned val);
1232 __isl_give isl_point *isl_point_sub_ui(
1233 __isl_take isl_point *pnt,
1234 enum isl_dim_type type, int pos, unsigned val);
1236 Points can be copied or freed using
1238 __isl_give isl_point *isl_point_copy(
1239 __isl_keep isl_point *pnt);
1240 void isl_point_free(__isl_take isl_point *pnt);
1242 A singleton set can be created from a point using
1244 __isl_give isl_set *isl_set_from_point(
1245 __isl_take isl_point *pnt);
1247 and a box can be created from two opposite extremal points using
1249 __isl_give isl_set *isl_set_box_from_points(
1250 __isl_take isl_point *pnt1,
1251 __isl_take isl_point *pnt2);
1253 All elements of a B<bounded> set can be enumerated using
1254 the following function.
1256 int isl_set_foreach_point(__isl_keep isl_set *set,
1257 int (*fn)(__isl_take isl_point *pnt, void *user),
1260 The function C<fn> is called for each integer point in
1261 C<set> with as second argument the last argument of
1262 the C<isl_set_foreach_point> call. The function C<fn>
1263 should return C<0> on success and C<-1> on failure.
1264 In the latter case, C<isl_set_foreach_point> will stop
1265 enumerating and return C<-1> as well.
1266 If the enumeration is performed successfully and to completion,
1267 then C<isl_set_foreach_point> returns C<0>.
1269 To obtain a single point of a set, use
1271 __isl_give isl_point *isl_set_sample_point(
1272 __isl_take isl_set *set);
1274 If C<set> does not contain any (integer) points, then the
1275 resulting point will be ``void'', a property that can be
1278 int isl_point_is_void(__isl_keep isl_point *pnt);
1280 =head2 Piecewise Quasipolynomials
1282 A piecewise quasipolynomial is a particular kind of function that maps
1283 a parametric point to a rational value.
1284 More specifically, a quasipolynomial is a polynomial expression in greatest
1285 integer parts of affine expressions of parameters and variables.
1286 A piecewise quasipolynomial is a subdivision of a given parametric
1287 domain into disjoint cells with a quasipolynomial associated to
1288 each cell. The value of the piecewise quasipolynomial at a given
1289 point is the value of the quasipolynomial associated to the cell
1290 that contains the point. Outside of the union of cells,
1291 the value is assumed to be zero.
1292 For example, the piecewise quasipolynomial
1294 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1296 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1297 Piecewise quasipolynomials are mainly used by the C<barvinok>
1298 library for representing the number of elements in a parametric set or map.
1299 For example, the piecewise quasipolynomial above represents
1300 the number of points in the map
1302 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1304 =head3 Printing (Piecewise) Quasipolynomials
1306 Quasipolynomials and piecewise quasipolynomials can be printed
1307 using the following functions.
1309 __isl_give isl_printer *isl_printer_print_qpolynomial(
1310 __isl_take isl_printer *p,
1311 __isl_keep isl_qpolynomial *qp);
1313 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1314 __isl_take isl_printer *p,
1315 __isl_keep isl_pw_qpolynomial *pwqp);
1317 The output format of the printer
1318 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1320 =head3 Creating New (Piecewise) Quasipolynomials
1322 Some simple quasipolynomials can be created using the following functions.
1323 More complicated quasipolynomials can be created by applying
1324 operations such as addition and multiplication
1325 on the resulting quasipolynomials
1327 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1328 __isl_take isl_dim *dim);
1329 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1330 __isl_take isl_dim *dim);
1331 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1332 __isl_take isl_dim *dim);
1333 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1334 __isl_take isl_dim *dim);
1335 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1336 __isl_take isl_dim *dim,
1337 const isl_int n, const isl_int d);
1338 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1339 __isl_take isl_div *div);
1340 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1341 __isl_take isl_dim *dim,
1342 enum isl_dim_type type, unsigned pos);
1344 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1345 with a single cell can be created using the following functions.
1346 Multiple of these single cell piecewise quasipolynomials can
1347 be combined to create more complicated piecewise quasipolynomials.
1349 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1350 __isl_take isl_dim *dim);
1351 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1352 __isl_take isl_set *set,
1353 __isl_take isl_qpolynomial *qp);
1355 Quasipolynomials can be copied and freed again using the following
1358 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
1359 __isl_keep isl_qpolynomial *qp);
1360 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
1362 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
1363 __isl_keep isl_pw_qpolynomial *pwqp);
1364 void isl_pw_qpolynomial_free(
1365 __isl_take isl_pw_qpolynomial *pwqp);
1367 =head3 Inspecting (Piecewise) Quasipolynomials
1369 To iterate over the cells in a piecewise quasipolynomial,
1370 use either of the following two functions
1372 int isl_pw_qpolynomial_foreach_piece(
1373 __isl_keep isl_pw_qpolynomial *pwqp,
1374 int (*fn)(__isl_take isl_set *set,
1375 __isl_take isl_qpolynomial *qp,
1376 void *user), void *user);
1377 int isl_pw_qpolynomial_foreach_lifted_piece(
1378 __isl_keep isl_pw_qpolynomial *pwqp,
1379 int (*fn)(__isl_take isl_set *set,
1380 __isl_take isl_qpolynomial *qp,
1381 void *user), void *user);
1383 As usual, the function C<fn> should return C<0> on success
1384 and C<-1> on failure. The difference between
1385 C<isl_pw_qpolynomial_foreach_piece> and
1386 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
1387 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
1388 compute unique representations for all existentially quantified
1389 variables and then turn these existentially quantified variables
1390 into extra set variables, adapting the associated quasipolynomial
1391 accordingly. This means that the C<set> passed to C<fn>
1392 will not have any existentially quantified variables, but that
1393 the dimensions of the sets may be different for different
1394 invocations of C<fn>.
1396 To iterate over all terms in a quasipolynomial,
1399 int isl_qpolynomial_foreach_term(
1400 __isl_keep isl_qpolynomial *qp,
1401 int (*fn)(__isl_take isl_term *term,
1402 void *user), void *user);
1404 The terms themselves can be inspected and freed using
1407 unsigned isl_term_dim(__isl_keep isl_term *term,
1408 enum isl_dim_type type);
1409 void isl_term_get_num(__isl_keep isl_term *term,
1411 void isl_term_get_den(__isl_keep isl_term *term,
1413 int isl_term_get_exp(__isl_keep isl_term *term,
1414 enum isl_dim_type type, unsigned pos);
1415 __isl_give isl_div *isl_term_get_div(
1416 __isl_keep isl_term *term, unsigned pos);
1417 void isl_term_free(__isl_take isl_term *term);
1419 Each term is a product of parameters, set variables and
1420 integer divisions. The function C<isl_term_get_exp>
1421 returns the exponent of a given dimensions in the given term.
1422 The C<isl_int>s in the arguments of C<isl_term_get_num>
1423 and C<isl_term_get_den> need to have been initialized
1424 using C<isl_int_init> before calling these functions.
1426 =head3 Properties of (Piecewise) Quasipolynomials
1428 To check whether a quasipolynomial is actually a constant,
1429 use the following function.
1431 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
1432 isl_int *n, isl_int *d);
1434 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
1435 then the numerator and denominator of the constant
1436 are returned in C<*n> and C<*d>, respectively.
1438 =head3 Operations on (Piecewise) Quasipolynomials
1440 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
1441 __isl_take isl_qpolynomial *qp);
1442 __isl_give isl_qpolynomial *isl_qpolynomial_add(
1443 __isl_take isl_qpolynomial *qp1,
1444 __isl_take isl_qpolynomial *qp2);
1445 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
1446 __isl_take isl_qpolynomial *qp1,
1447 __isl_take isl_qpolynomial *qp2);
1448 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
1449 __isl_take isl_qpolynomial *qp1,
1450 __isl_take isl_qpolynomial *qp2);
1452 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
1453 __isl_take isl_pw_qpolynomial *pwqp1,
1454 __isl_take isl_pw_qpolynomial *pwqp2);
1455 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
1456 __isl_take isl_pw_qpolynomial *pwqp1,
1457 __isl_take isl_pw_qpolynomial *pwqp2);
1458 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
1459 __isl_take isl_pw_qpolynomial *pwqp1,
1460 __isl_take isl_pw_qpolynomial *pwqp2);
1461 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
1462 __isl_take isl_pw_qpolynomial *pwqp);
1463 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
1464 __isl_take isl_pw_qpolynomial *pwqp1,
1465 __isl_take isl_pw_qpolynomial *pwqp2);
1467 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
1468 __isl_take isl_pw_qpolynomial *pwqp,
1469 __isl_take isl_point *pnt);
1471 __isl_give isl_set *isl_pw_qpolynomial_domain(
1472 __isl_take isl_pw_qpolynomial *pwqp);
1473 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
1474 __isl_take isl_pw_qpolynomial *pwpq,
1475 __isl_take isl_set *set);
1477 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
1478 __isl_take isl_pw_qpolynomial *pwqp,
1479 __isl_take isl_set *context);
1481 The gist operation applies the gist operation to each of
1482 the cells in the domain of the input piecewise quasipolynomial.
1483 In future, the operation will also exploit the context
1484 to simplify the quasipolynomials associated to each cell.
1486 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
1488 A piecewise quasipolynomial reduction is a piecewise
1489 reduction (or fold) of quasipolynomials.
1490 In particular, the reduction can be maximum or a minimum.
1491 The objects are mainly used to represent the result of
1492 an upper or lower bound on a quasipolynomial over its domain,
1493 i.e., as the result of the following function.
1495 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
1496 __isl_take isl_pw_qpolynomial *pwqp,
1497 enum isl_fold type, int *tight);
1499 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
1500 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
1501 is the returned bound is known be tight, i.e., for each value
1502 of the parameters there is at least
1503 one element in the domain that reaches the bound.
1505 A (piecewise) quasipolynomial reduction can be copied or freed using the
1506 following functions.
1508 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
1509 __isl_keep isl_qpolynomial_fold *fold);
1510 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
1511 __isl_keep isl_pw_qpolynomial_fold *pwf);
1512 void isl_qpolynomial_fold_free(
1513 __isl_take isl_qpolynomial_fold *fold);
1514 void isl_pw_qpolynomial_fold_free(
1515 __isl_take isl_pw_qpolynomial_fold *pwf);
1517 =head3 Printing Piecewise Quasipolynomial Reductions
1519 Piecewise quasipolynomial reductions can be printed
1520 using the following function.
1522 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
1523 __isl_take isl_printer *p,
1524 __isl_keep isl_pw_qpolynomial_fold *pwf);
1526 The output format of the printer
1527 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1529 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
1531 To iterate over the cells in a piecewise quasipolynomial reduction,
1532 use either of the following two functions
1534 int isl_pw_qpolynomial_fold_foreach_piece(
1535 __isl_keep isl_pw_qpolynomial_fold *pwf,
1536 int (*fn)(__isl_take isl_set *set,
1537 __isl_take isl_qpolynomial_fold *fold,
1538 void *user), void *user);
1539 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
1540 __isl_keep isl_pw_qpolynomial_fold *pwf,
1541 int (*fn)(__isl_take isl_set *set,
1542 __isl_take isl_qpolynomial_fold *fold,
1543 void *user), void *user);
1545 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
1546 of the difference between these two functions.
1548 To iterate over all quasipolynomials in a reduction, use
1550 int isl_qpolynomial_fold_foreach_qpolynomial(
1551 __isl_keep isl_qpolynomial_fold *fold,
1552 int (*fn)(__isl_take isl_qpolynomial *qp,
1553 void *user), void *user);
1555 =head3 Operations on Piecewise Quasipolynomial Reductions
1557 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
1558 __isl_take isl_pw_qpolynomial_fold *pwf1,
1559 __isl_take isl_pw_qpolynomial_fold *pwf2);
1561 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
1562 __isl_take isl_pw_qpolynomial_fold *pwf,
1563 __isl_take isl_point *pnt);
1565 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
1566 __isl_take isl_pw_qpolynomial_fold *pwf);
1568 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
1569 __isl_take isl_pw_qpolynomial_fold *pwf,
1570 __isl_take isl_set *context);
1572 The gist operation applies the gist operation to each of
1573 the cells in the domain of the input piecewise quasipolynomial reduction.
1574 In future, the operation will also exploit the context
1575 to simplify the quasipolynomial reductions associated to each cell.
1577 =head2 Dependence Analysis
1579 C<isl> contains specialized functionality for performing
1580 array dataflow analysis. That is, given a I<sink> access relation
1581 and a collection of possible I<source> access relations,
1582 C<isl> can compute relations that describe
1583 for each iteration of the sink access, which iteration
1584 of which of the source access relations was the last
1585 to access the same data element before the given iteration
1587 To compute standard flow dependences, the sink should be
1588 a read, while the sources should be writes.
1589 If any of the source accesses are marked as being I<may>
1590 accesses, then there will be a dependence to the last
1591 I<must> access B<and> to any I<may> access that follows
1592 this last I<must> access.
1593 In particular, if I<all> sources are I<may> accesses,
1594 then memory based dependence analysis is performed.
1595 If, on the other hand, all sources are I<must> accesses,
1596 then value based dependence analysis is performed.
1598 #include <isl_flow.h>
1600 __isl_give isl_access_info *isl_access_info_alloc(
1601 __isl_take isl_map *sink,
1602 void *sink_user, isl_access_level_before fn,
1604 __isl_give isl_access_info *isl_access_info_add_source(
1605 __isl_take isl_access_info *acc,
1606 __isl_take isl_map *source, int must,
1609 __isl_give isl_flow *isl_access_info_compute_flow(
1610 __isl_take isl_access_info *acc);
1612 int isl_flow_foreach(__isl_keep isl_flow *deps,
1613 int (*fn)(__isl_take isl_map *dep, int must,
1614 void *dep_user, void *user),
1616 __isl_give isl_set *isl_flow_get_no_source(
1617 __isl_keep isl_flow *deps, int must);
1618 void isl_flow_free(__isl_take isl_flow *deps);
1620 The function C<isl_access_info_compute_flow> performs the actual
1621 dependence analysis. The other functions are used to construct
1622 the input for this function or to read off the output.
1624 The input is collected in an C<isl_access_info>, which can
1625 be created through a call to C<isl_access_info_alloc>.
1626 The arguments to this functions are the sink access relation
1627 C<sink>, a token C<sink_user> used to identify the sink
1628 access to the user, a callback function for specifying the
1629 relative order of source and sink accesses, and the number
1630 of source access relations that will be added.
1631 The callback function has type C<int (*)(void *first, void *second)>.
1632 The function is called with two user supplied tokens identifying
1633 either a source or the sink and it should return the shared nesting
1634 level and the relative order of the two accesses.
1635 In particular, let I<n> be the number of loops shared by
1636 the two accesses. If C<first> precedes C<second> textually,
1637 then the function should return I<2 * n + 1>; otherwise,
1638 it should return I<2 * n>.
1639 The sources can be added to the C<isl_access_info> by performing
1640 (at most) C<max_source> calls to C<isl_access_info_add_source>.
1641 C<must> indicates whether the source is a I<must> access
1642 or a I<may> access. Note that a multi-valued access relation
1643 should only be marked I<must> if every iteration in the domain
1644 of the relation accesses I<all> elements in its image.
1645 The C<source_user> token is again used to identify
1646 the source access. The range of the source access relation
1647 C<source> should have the same dimension as the range
1648 of the sink access relation.
1650 The result of the dependence analysis is collected in an
1651 C<isl_flow>. There may be elements in the domain of
1652 the sink access for which no preceding source access could be
1653 found or for which all preceding sources are I<may> accesses.
1654 The sets of these elements can be obtained through
1655 calls to C<isl_flow_get_no_source>, the first with C<must> set
1656 and the second with C<must> unset.
1657 In the case of standard flow dependence analysis,
1658 with the sink a read and the sources I<must> writes,
1659 the first set corresponds to the reads from uninitialized
1660 array elements and the second set is empty.
1661 The actual flow dependences can be extracted using
1662 C<isl_flow_foreach>. This function will call the user-specified
1663 callback function C<fn> for each B<non-empty> dependence between
1664 a source and the sink. The callback function is called
1665 with four arguments, the actual flow dependence relation
1666 mapping source iterations to sink iterations, a boolean that
1667 indicates whether it is a I<must> or I<may> dependence, a token
1668 identifying the source and an additional C<void *> with value
1669 equal to the third argument of the C<isl_flow_foreach> call.
1670 A dependence is marked I<must> if it originates from a I<must>
1671 source and if it is not followed by any I<may> sources.
1673 After finishing with an C<isl_flow>, the user should call
1674 C<isl_flow_free> to free all associated memory.
1676 =head2 Parametric Vertex Enumeration
1678 The parametric vertex enumeration described in this section
1679 is mainly intended to be used internally and by the C<barvinok>
1682 #include <isl_vertices.h>
1683 __isl_give isl_vertices *isl_basic_set_compute_vertices(
1684 __isl_keep isl_basic_set *bset);
1686 The function C<isl_basic_set_compute_vertices> performs the
1687 actual computation of the parametric vertices and the chamber
1688 decomposition and store the result in an C<isl_vertices> object.
1689 This information can be queried by either iterating over all
1690 the vertices or iterating over all the chambers or cells
1691 and then iterating over all vertices that are active on the chamber.
1693 int isl_vertices_foreach_vertex(
1694 __isl_keep isl_vertices *vertices,
1695 int (*fn)(__isl_take isl_vertex *vertex, void *user),
1698 int isl_vertices_foreach_cell(
1699 __isl_keep isl_vertices *vertices,
1700 int (*fn)(__isl_take isl_cell *cell, void *user),
1702 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
1703 int (*fn)(__isl_take isl_vertex *vertex, void *user),
1706 Other operations that can be performed on an C<isl_vertices> object are
1709 isl_ctx *isl_vertices_get_ctx(
1710 __isl_keep isl_vertices *vertices);
1711 int isl_vertices_get_n_vertices(
1712 __isl_keep isl_vertices *vertices);
1713 void isl_vertices_free(__isl_take isl_vertices *vertices);
1715 Vertices can be inspected and destroyed using the following functions.
1717 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
1718 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
1719 __isl_give isl_basic_set *isl_vertex_get_domain(
1720 __isl_keep isl_vertex *vertex);
1721 __isl_give isl_basic_set *isl_vertex_get_expr(
1722 __isl_keep isl_vertex *vertex);
1723 void isl_vertex_free(__isl_take isl_vertex *vertex);
1725 C<isl_vertex_get_expr> returns a singleton parametric set describing
1726 the vertex, while C<isl_vertex_get_domain> returns the activity domain
1728 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
1729 B<rational> basic sets, so they should mainly be used for inspection
1730 and should not be mixed with integer sets.
1732 Chambers can be inspected and destroyed using the following functions.
1734 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
1735 __isl_give isl_basic_set *isl_cell_get_domain(
1736 __isl_keep isl_cell *cell);
1737 void isl_cell_free(__isl_take isl_cell *cell);
1741 Although C<isl> is mainly meant to be used as a library,
1742 it also contains some basic applications that use some
1743 of the functionality of C<isl>.
1744 The input may be specified in either the L<isl format>
1745 or the L<PolyLib format>.
1747 =head2 C<isl_polyhedron_sample>
1749 C<isl_polyhedron_sample> takes a polyhedron as input and prints
1750 an integer element of the polyhedron, if there is any.
1751 The first column in the output is the denominator and is always
1752 equal to 1. If the polyhedron contains no integer points,
1753 then a vector of length zero is printed.
1757 C<isl_pip> takes the same input as the C<example> program
1758 from the C<piplib> distribution, i.e., a set of constraints
1759 on the parameters, a line contains only -1 and finally a set
1760 of constraints on a parametric polyhedron.
1761 The coefficients of the parameters appear in the last columns
1762 (but before the final constant column).
1763 The output is the lexicographic minimum of the parametric polyhedron.
1764 As C<isl> currently does not have its own output format, the output
1765 is just a dump of the internal state.
1767 =head2 C<isl_polyhedron_minimize>
1769 C<isl_polyhedron_minimize> computes the minimum of some linear
1770 or affine objective function over the integer points in a polyhedron.
1771 If an affine objective function
1772 is given, then the constant should appear in the last column.
1774 =head2 C<isl_polytope_scan>
1776 Given a polytope, C<isl_polytope_scan> prints
1777 all integer points in the polytope.
1779 =head1 C<isl-polylib>
1781 The C<isl-polylib> library provides the following functions for converting
1782 between C<isl> objects and C<PolyLib> objects.
1783 The library is distributed separately for licensing reasons.
1785 #include <isl_set_polylib.h>
1786 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
1787 Polyhedron *P, __isl_take isl_dim *dim);
1788 Polyhedron *isl_basic_set_to_polylib(
1789 __isl_keep isl_basic_set *bset);
1790 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
1791 __isl_take isl_dim *dim);
1792 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
1794 #include <isl_map_polylib.h>
1795 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
1796 Polyhedron *P, __isl_take isl_dim *dim);
1797 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
1798 __isl_take isl_dim *dim);
1799 Polyhedron *isl_basic_map_to_polylib(
1800 __isl_keep isl_basic_map *bmap);
1801 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);