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>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
80 The source of C<isl> can be obtained either as a tarball
81 or from the git repository. Both are available from
82 L<http://freshmeat.net/projects/isl/>.
83 The installation process depends on how you obtained
86 =head2 Installation from the git repository
90 =item 1 Clone or update the repository
92 The first time the source is obtained, you need to clone
95 git clone git://repo.or.cz/isl.git
97 To obtain updates, you need to pull in the latest changes
101 =item 2 Generate C<configure>
107 After performing the above steps, continue
108 with the L<Common installation instructions>.
110 =head2 Common installation instructions
114 =item 1 Obtain C<GMP>
116 Building C<isl> requires C<GMP>, including its headers files.
117 Your distribution may not provide these header files by default
118 and you may need to install a package called C<gmp-devel> or something
119 similar. Alternatively, C<GMP> can be built from
120 source, available from L<http://gmplib.org/>.
124 C<isl> uses the standard C<autoconf> C<configure> script.
129 optionally followed by some configure options.
130 A complete list of options can be obtained by running
134 Below we discuss some of the more common options.
136 C<isl> can optionally use C<piplib>, but no
137 C<piplib> functionality is currently used by default.
138 The C<--with-piplib> option can
139 be used to specify which C<piplib>
140 library to use, either an installed version (C<system>),
141 an externally built version (C<build>)
142 or no version (C<no>). The option C<build> is mostly useful
143 in C<configure> scripts of larger projects that bundle both C<isl>
150 Installation prefix for C<isl>
152 =item C<--with-gmp-prefix>
154 Installation prefix for C<GMP> (architecture-independent files).
156 =item C<--with-gmp-exec-prefix>
158 Installation prefix for C<GMP> (architecture-dependent files).
160 =item C<--with-piplib>
162 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
164 =item C<--with-piplib-prefix>
166 Installation prefix for C<system> C<piplib> (architecture-independent files).
168 =item C<--with-piplib-exec-prefix>
170 Installation prefix for C<system> C<piplib> (architecture-dependent files).
172 =item C<--with-piplib-builddir>
174 Location where C<build> C<piplib> was built.
182 =item 4 Install (optional)
190 =head2 Initialization
192 All manipulations of integer sets and relations occur within
193 the context of an C<isl_ctx>.
194 A given C<isl_ctx> can only be used within a single thread.
195 All arguments of a function are required to have been allocated
196 within the same context.
197 There are currently no functions available for moving an object
198 from one C<isl_ctx> to another C<isl_ctx>. This means that
199 there is currently no way of safely moving an object from one
200 thread to another, unless the whole C<isl_ctx> is moved.
202 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
203 freed using C<isl_ctx_free>.
204 All objects allocated within an C<isl_ctx> should be freed
205 before the C<isl_ctx> itself is freed.
207 isl_ctx *isl_ctx_alloc();
208 void isl_ctx_free(isl_ctx *ctx);
212 All operations on integers, mainly the coefficients
213 of the constraints describing the sets and relations,
214 are performed in exact integer arithmetic using C<GMP>.
215 However, to allow future versions of C<isl> to optionally
216 support fixed integer arithmetic, all calls to C<GMP>
217 are wrapped inside C<isl> specific macros.
218 The basic type is C<isl_int> and the operations below
219 are available on this type.
220 The meanings of these operations are essentially the same
221 as their C<GMP> C<mpz_> counterparts.
222 As always with C<GMP> types, C<isl_int>s need to be
223 initialized with C<isl_int_init> before they can be used
224 and they need to be released with C<isl_int_clear>
226 The user should not assume that an C<isl_int> is represented
227 as a C<mpz_t>, but should instead explicitly convert between
228 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
229 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
233 =item isl_int_init(i)
235 =item isl_int_clear(i)
237 =item isl_int_set(r,i)
239 =item isl_int_set_si(r,i)
241 =item isl_int_set_gmp(r,g)
243 =item isl_int_get_gmp(i,g)
245 =item isl_int_abs(r,i)
247 =item isl_int_neg(r,i)
249 =item isl_int_swap(i,j)
251 =item isl_int_swap_or_set(i,j)
253 =item isl_int_add_ui(r,i,j)
255 =item isl_int_sub_ui(r,i,j)
257 =item isl_int_add(r,i,j)
259 =item isl_int_sub(r,i,j)
261 =item isl_int_mul(r,i,j)
263 =item isl_int_mul_ui(r,i,j)
265 =item isl_int_addmul(r,i,j)
267 =item isl_int_submul(r,i,j)
269 =item isl_int_gcd(r,i,j)
271 =item isl_int_lcm(r,i,j)
273 =item isl_int_divexact(r,i,j)
275 =item isl_int_cdiv_q(r,i,j)
277 =item isl_int_fdiv_q(r,i,j)
279 =item isl_int_fdiv_r(r,i,j)
281 =item isl_int_fdiv_q_ui(r,i,j)
283 =item isl_int_read(r,s)
285 =item isl_int_print(out,i,width)
289 =item isl_int_cmp(i,j)
291 =item isl_int_cmp_si(i,si)
293 =item isl_int_eq(i,j)
295 =item isl_int_ne(i,j)
297 =item isl_int_lt(i,j)
299 =item isl_int_le(i,j)
301 =item isl_int_gt(i,j)
303 =item isl_int_ge(i,j)
305 =item isl_int_abs_eq(i,j)
307 =item isl_int_abs_ne(i,j)
309 =item isl_int_abs_lt(i,j)
311 =item isl_int_abs_gt(i,j)
313 =item isl_int_abs_ge(i,j)
315 =item isl_int_is_zero(i)
317 =item isl_int_is_one(i)
319 =item isl_int_is_negone(i)
321 =item isl_int_is_pos(i)
323 =item isl_int_is_neg(i)
325 =item isl_int_is_nonpos(i)
327 =item isl_int_is_nonneg(i)
329 =item isl_int_is_divisible_by(i,j)
333 =head2 Sets and Relations
335 C<isl> uses six types of objects for representing sets and relations,
336 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
337 C<isl_union_set> and C<isl_union_map>.
338 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
339 can be described as a conjunction of affine constraints, while
340 C<isl_set> and C<isl_map> represent unions of
341 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
342 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
343 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
344 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
345 where dimensions with different space names
346 (see L<Dimension Specifications>) are considered different as well.
347 The difference between sets and relations (maps) is that sets have
348 one set of variables, while relations have two sets of variables,
349 input variables and output variables.
351 =head2 Memory Management
353 Since a high-level operation on sets and/or relations usually involves
354 several substeps and since the user is usually not interested in
355 the intermediate results, most functions that return a new object
356 will also release all the objects passed as arguments.
357 If the user still wants to use one or more of these arguments
358 after the function call, she should pass along a copy of the
359 object rather than the object itself.
360 The user is then responsible for making sure that the original
361 object gets used somewhere else or is explicitly freed.
363 The arguments and return values of all documents functions are
364 annotated to make clear which arguments are released and which
365 arguments are preserved. In particular, the following annotations
372 C<__isl_give> means that a new object is returned.
373 The user should make sure that the returned pointer is
374 used exactly once as a value for an C<__isl_take> argument.
375 In between, it can be used as a value for as many
376 C<__isl_keep> arguments as the user likes.
377 There is one exception, and that is the case where the
378 pointer returned is C<NULL>. Is this case, the user
379 is free to use it as an C<__isl_take> argument or not.
383 C<__isl_take> means that the object the argument points to
384 is taken over by the function and may no longer be used
385 by the user as an argument to any other function.
386 The pointer value must be one returned by a function
387 returning an C<__isl_give> pointer.
388 If the user passes in a C<NULL> value, then this will
389 be treated as an error in the sense that the function will
390 not perform its usual operation. However, it will still
391 make sure that all the the other C<__isl_take> arguments
396 C<__isl_keep> means that the function will only use the object
397 temporarily. After the function has finished, the user
398 can still use it as an argument to other functions.
399 A C<NULL> value will be treated in the same way as
400 a C<NULL> value for an C<__isl_take> argument.
404 =head2 Dimension Specifications
406 Whenever a new set or relation is created from scratch,
407 its dimension needs to be specified using an C<isl_dim>.
410 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
411 unsigned nparam, unsigned n_in, unsigned n_out);
412 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
413 unsigned nparam, unsigned dim);
414 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
415 void isl_dim_free(__isl_take isl_dim *dim);
416 unsigned isl_dim_size(__isl_keep isl_dim *dim,
417 enum isl_dim_type type);
419 The dimension specification used for creating a set
420 needs to be created using C<isl_dim_set_alloc>, while
421 that for creating a relation
422 needs to be created using C<isl_dim_alloc>.
423 C<isl_dim_size> can be used
424 to find out the number of dimensions of each type in
425 a dimension specification, where type may be
426 C<isl_dim_param>, C<isl_dim_in> (only for relations),
427 C<isl_dim_out> (only for relations), C<isl_dim_set>
428 (only for sets) or C<isl_dim_all>.
430 It is often useful to create objects that live in the
431 same space as some other object. This can be accomplished
432 by creating the new objects
433 (see L<Creating New Sets and Relations> or
434 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
435 specification of the original object.
438 __isl_give isl_dim *isl_basic_set_get_dim(
439 __isl_keep isl_basic_set *bset);
440 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
442 #include <isl/union_set.h>
443 __isl_give isl_dim *isl_union_set_get_dim(
444 __isl_keep isl_union_set *uset);
447 __isl_give isl_dim *isl_basic_map_get_dim(
448 __isl_keep isl_basic_map *bmap);
449 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
451 #include <isl/union_map.h>
452 __isl_give isl_dim *isl_union_map_get_dim(
453 __isl_keep isl_union_map *umap);
455 #include <isl/polynomial.h>
456 __isl_give isl_dim *isl_qpolynomial_get_dim(
457 __isl_keep isl_qpolynomial *qp);
458 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
459 __isl_keep isl_pw_qpolynomial *pwqp);
460 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
461 __isl_keep isl_union_pw_qpolynomial *upwqp);
462 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
463 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
465 The names of the individual dimensions may be set or read off
466 using the following functions.
469 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
470 enum isl_dim_type type, unsigned pos,
471 __isl_keep const char *name);
472 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
473 enum isl_dim_type type, unsigned pos);
475 Note that C<isl_dim_get_name> returns a pointer to some internal
476 data structure, so the result can only be used while the
477 corresponding C<isl_dim> is alive.
478 Also note that every function that operates on two sets or relations
479 requires that both arguments have the same parameters. This also
480 means that if one of the arguments has named parameters, then the
481 other needs to have named parameters too and the names need to match.
482 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
483 have different parameters (as long as they are named), in which case
484 the result will have as parameters the union of the parameters of
487 The names of entire spaces may be set or read off
488 using the following functions.
491 __isl_give isl_dim *isl_dim_set_tuple_name(
492 __isl_take isl_dim *dim,
493 enum isl_dim_type type, const char *s);
494 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
495 enum isl_dim_type type);
497 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
498 or C<isl_dim_set>. As with C<isl_dim_get_name>,
499 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
501 Binary operations require the corresponding spaces of their arguments
502 to have the same name.
504 Spaces can be nested. In particular, the domain of a set or
505 the domain or range of a relation can be a nested relation.
506 The following functions can be used to construct and deconstruct
507 such nested dimension specifications.
510 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
511 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
512 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
514 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
515 be the dimension specification of a set, while that of
516 C<isl_dim_wrap> should be the dimension specification of a relation.
517 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
518 of a relation, while that of C<isl_dim_wrap> is the dimension specification
521 Dimension specifications can be created from other dimension
522 specifications using the following functions.
524 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
525 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
526 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
527 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
528 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
529 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
530 __isl_take isl_dim *right);
531 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
532 enum isl_dim_type type, unsigned pos, unsigned n);
533 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
534 enum isl_dim_type type, unsigned n);
535 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
536 enum isl_dim_type type, unsigned first, unsigned n);
537 __isl_give isl_dim *isl_dim_map_from_set(
538 __isl_take isl_dim *dim);
540 Note that if dimensions are added or removed from a space, then
541 the name and the internal structure are lost.
543 =head2 Input and Output
545 C<isl> supports its own input/output format, which is similar
546 to the C<Omega> format, but also supports the C<PolyLib> format
551 The C<isl> format is similar to that of C<Omega>, but has a different
552 syntax for describing the parameters and allows for the definition
553 of an existentially quantified variable as the integer division
554 of an affine expression.
555 For example, the set of integers C<i> between C<0> and C<n>
556 such that C<i % 10 <= 6> can be described as
558 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
561 A set or relation can have several disjuncts, separated
562 by the keyword C<or>. Each disjunct is either a conjunction
563 of constraints or a projection (C<exists>) of a conjunction
564 of constraints. The constraints are separated by the keyword
567 =head3 C<PolyLib> format
569 If the represented set is a union, then the first line
570 contains a single number representing the number of disjuncts.
571 Otherwise, a line containing the number C<1> is optional.
573 Each disjunct is represented by a matrix of constraints.
574 The first line contains two numbers representing
575 the number of rows and columns,
576 where the number of rows is equal to the number of constraints
577 and the number of columns is equal to two plus the number of variables.
578 The following lines contain the actual rows of the constraint matrix.
579 In each row, the first column indicates whether the constraint
580 is an equality (C<0>) or inequality (C<1>). The final column
581 corresponds to the constant term.
583 If the set is parametric, then the coefficients of the parameters
584 appear in the last columns before the constant column.
585 The coefficients of any existentially quantified variables appear
586 between those of the set variables and those of the parameters.
588 =head3 Extended C<PolyLib> format
590 The extended C<PolyLib> format is nearly identical to the
591 C<PolyLib> format. The only difference is that the line
592 containing the number of rows and columns of a constraint matrix
593 also contains four additional numbers:
594 the number of output dimensions, the number of input dimensions,
595 the number of local dimensions (i.e., the number of existentially
596 quantified variables) and the number of parameters.
597 For sets, the number of ``output'' dimensions is equal
598 to the number of set dimensions, while the number of ``input''
604 __isl_give isl_basic_set *isl_basic_set_read_from_file(
605 isl_ctx *ctx, FILE *input, int nparam);
606 __isl_give isl_basic_set *isl_basic_set_read_from_str(
607 isl_ctx *ctx, const char *str, int nparam);
608 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
609 FILE *input, int nparam);
610 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
611 const char *str, int nparam);
614 __isl_give isl_basic_map *isl_basic_map_read_from_file(
615 isl_ctx *ctx, FILE *input, int nparam);
616 __isl_give isl_basic_map *isl_basic_map_read_from_str(
617 isl_ctx *ctx, const char *str, int nparam);
618 __isl_give isl_map *isl_map_read_from_file(
619 struct isl_ctx *ctx, FILE *input, int nparam);
620 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
621 const char *str, int nparam);
623 #include <isl/union_set.h>
624 __isl_give isl_union_set *isl_union_set_read_from_file(
625 isl_ctx *ctx, FILE *input);
626 __isl_give isl_union_set *isl_union_set_read_from_str(
627 struct isl_ctx *ctx, const char *str);
629 #include <isl/union_map.h>
630 __isl_give isl_union_map *isl_union_map_read_from_file(
631 isl_ctx *ctx, FILE *input);
632 __isl_give isl_union_map *isl_union_map_read_from_str(
633 struct isl_ctx *ctx, const char *str);
635 The input format is autodetected and may be either the C<PolyLib> format
636 or the C<isl> format.
637 C<nparam> specifies how many of the final columns in
638 the C<PolyLib> format correspond to parameters.
639 If input is given in the C<isl> format, then the number
640 of parameters needs to be equal to C<nparam>.
641 If C<nparam> is negative, then any number of parameters
642 is accepted in the C<isl> format and zero parameters
643 are assumed in the C<PolyLib> format.
647 Before anything can be printed, an C<isl_printer> needs to
650 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
652 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
653 void isl_printer_free(__isl_take isl_printer *printer);
654 __isl_give char *isl_printer_get_str(
655 __isl_keep isl_printer *printer);
657 The behavior of the printer can be modified in various ways
659 __isl_give isl_printer *isl_printer_set_output_format(
660 __isl_take isl_printer *p, int output_format);
661 __isl_give isl_printer *isl_printer_set_indent(
662 __isl_take isl_printer *p, int indent);
663 __isl_give isl_printer *isl_printer_set_prefix(
664 __isl_take isl_printer *p, const char *prefix);
665 __isl_give isl_printer *isl_printer_set_suffix(
666 __isl_take isl_printer *p, const char *suffix);
668 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
669 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
670 and defaults to C<ISL_FORMAT_ISL>.
671 Each line in the output is indented by C<indent> spaces
672 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
673 In the C<PolyLib> format output,
674 the coefficients of the existentially quantified variables
675 appear between those of the set variables and those
678 To actually print something, use
681 __isl_give isl_printer *isl_printer_print_basic_set(
682 __isl_take isl_printer *printer,
683 __isl_keep isl_basic_set *bset);
684 __isl_give isl_printer *isl_printer_print_set(
685 __isl_take isl_printer *printer,
686 __isl_keep isl_set *set);
689 __isl_give isl_printer *isl_printer_print_basic_map(
690 __isl_take isl_printer *printer,
691 __isl_keep isl_basic_map *bmap);
692 __isl_give isl_printer *isl_printer_print_map(
693 __isl_take isl_printer *printer,
694 __isl_keep isl_map *map);
696 #include <isl/union_set.h>
697 __isl_give isl_printer *isl_printer_print_union_set(
698 __isl_take isl_printer *p,
699 __isl_keep isl_union_set *uset);
701 #include <isl/union_map.h>
702 __isl_give isl_printer *isl_printer_print_union_map(
703 __isl_take isl_printer *p,
704 __isl_keep isl_union_map *umap);
706 When called on a file printer, the following function flushes
707 the file. When called on a string printer, the buffer is cleared.
709 __isl_give isl_printer *isl_printer_flush(
710 __isl_take isl_printer *p);
712 =head2 Creating New Sets and Relations
714 C<isl> has functions for creating some standard sets and relations.
718 =item * Empty sets and relations
720 __isl_give isl_basic_set *isl_basic_set_empty(
721 __isl_take isl_dim *dim);
722 __isl_give isl_basic_map *isl_basic_map_empty(
723 __isl_take isl_dim *dim);
724 __isl_give isl_set *isl_set_empty(
725 __isl_take isl_dim *dim);
726 __isl_give isl_map *isl_map_empty(
727 __isl_take isl_dim *dim);
728 __isl_give isl_union_set *isl_union_set_empty(
729 __isl_take isl_dim *dim);
730 __isl_give isl_union_map *isl_union_map_empty(
731 __isl_take isl_dim *dim);
733 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
734 is only used to specify the parameters.
736 =item * Universe sets and relations
738 __isl_give isl_basic_set *isl_basic_set_universe(
739 __isl_take isl_dim *dim);
740 __isl_give isl_basic_map *isl_basic_map_universe(
741 __isl_take isl_dim *dim);
742 __isl_give isl_set *isl_set_universe(
743 __isl_take isl_dim *dim);
744 __isl_give isl_map *isl_map_universe(
745 __isl_take isl_dim *dim);
747 The sets and relations constructed by the functions above
748 contain all integer values, while those constructed by the
749 functions below only contain non-negative values.
751 __isl_give isl_basic_set *isl_basic_set_nat_universe(
752 __isl_take isl_dim *dim);
753 __isl_give isl_basic_map *isl_basic_map_nat_universe(
754 __isl_take isl_dim *dim);
755 __isl_give isl_set *isl_set_nat_universe(
756 __isl_take isl_dim *dim);
757 __isl_give isl_map *isl_map_nat_universe(
758 __isl_take isl_dim *dim);
760 =item * Identity relations
762 __isl_give isl_basic_map *isl_basic_map_identity(
763 __isl_take isl_dim *dim);
764 __isl_give isl_map *isl_map_identity(
765 __isl_take isl_dim *dim);
767 The number of input and output dimensions in C<dim> needs
770 =item * Lexicographic order
772 __isl_give isl_map *isl_map_lex_lt(
773 __isl_take isl_dim *set_dim);
774 __isl_give isl_map *isl_map_lex_le(
775 __isl_take isl_dim *set_dim);
776 __isl_give isl_map *isl_map_lex_gt(
777 __isl_take isl_dim *set_dim);
778 __isl_give isl_map *isl_map_lex_ge(
779 __isl_take isl_dim *set_dim);
780 __isl_give isl_map *isl_map_lex_lt_first(
781 __isl_take isl_dim *dim, unsigned n);
782 __isl_give isl_map *isl_map_lex_le_first(
783 __isl_take isl_dim *dim, unsigned n);
784 __isl_give isl_map *isl_map_lex_gt_first(
785 __isl_take isl_dim *dim, unsigned n);
786 __isl_give isl_map *isl_map_lex_ge_first(
787 __isl_take isl_dim *dim, unsigned n);
789 The first four functions take a dimension specification for a B<set>
790 and return relations that express that the elements in the domain
791 are lexicographically less
792 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
793 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
794 than the elements in the range.
795 The last four functions take a dimension specification for a map
796 and return relations that express that the first C<n> dimensions
797 in the domain are lexicographically less
798 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
799 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
800 than the first C<n> dimensions in the range.
804 A basic set or relation can be converted to a set or relation
805 using the following functions.
807 __isl_give isl_set *isl_set_from_basic_set(
808 __isl_take isl_basic_set *bset);
809 __isl_give isl_map *isl_map_from_basic_map(
810 __isl_take isl_basic_map *bmap);
812 Sets and relations can be converted to union sets and relations
813 using the following functions.
815 __isl_give isl_union_map *isl_union_map_from_map(
816 __isl_take isl_map *map);
817 __isl_give isl_union_set *isl_union_set_from_set(
818 __isl_take isl_set *set);
820 Sets and relations can be copied and freed again using the following
823 __isl_give isl_basic_set *isl_basic_set_copy(
824 __isl_keep isl_basic_set *bset);
825 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
826 __isl_give isl_union_set *isl_union_set_copy(
827 __isl_keep isl_union_set *uset);
828 __isl_give isl_basic_map *isl_basic_map_copy(
829 __isl_keep isl_basic_map *bmap);
830 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
831 __isl_give isl_union_map *isl_union_map_copy(
832 __isl_keep isl_union_map *umap);
833 void isl_basic_set_free(__isl_take isl_basic_set *bset);
834 void isl_set_free(__isl_take isl_set *set);
835 void isl_union_set_free(__isl_take isl_union_set *uset);
836 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
837 void isl_map_free(__isl_take isl_map *map);
838 void isl_union_map_free(__isl_take isl_union_map *umap);
840 Other sets and relations can be constructed by starting
841 from a universe set or relation, adding equality and/or
842 inequality constraints and then projecting out the
843 existentially quantified variables, if any.
844 Constraints can be constructed, manipulated and
845 added to basic sets and relations using the following functions.
847 #include <isl/constraint.h>
848 __isl_give isl_constraint *isl_equality_alloc(
849 __isl_take isl_dim *dim);
850 __isl_give isl_constraint *isl_inequality_alloc(
851 __isl_take isl_dim *dim);
852 void isl_constraint_set_constant(
853 __isl_keep isl_constraint *constraint, isl_int v);
854 void isl_constraint_set_coefficient(
855 __isl_keep isl_constraint *constraint,
856 enum isl_dim_type type, int pos, isl_int v);
857 __isl_give isl_basic_map *isl_basic_map_add_constraint(
858 __isl_take isl_basic_map *bmap,
859 __isl_take isl_constraint *constraint);
860 __isl_give isl_basic_set *isl_basic_set_add_constraint(
861 __isl_take isl_basic_set *bset,
862 __isl_take isl_constraint *constraint);
864 For example, to create a set containing the even integers
865 between 10 and 42, you would use the following code.
869 struct isl_constraint *c;
870 struct isl_basic_set *bset;
873 dim = isl_dim_set_alloc(ctx, 0, 2);
874 bset = isl_basic_set_universe(isl_dim_copy(dim));
876 c = isl_equality_alloc(isl_dim_copy(dim));
877 isl_int_set_si(v, -1);
878 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
879 isl_int_set_si(v, 2);
880 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
881 bset = isl_basic_set_add_constraint(bset, c);
883 c = isl_inequality_alloc(isl_dim_copy(dim));
884 isl_int_set_si(v, -10);
885 isl_constraint_set_constant(c, v);
886 isl_int_set_si(v, 1);
887 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
888 bset = isl_basic_set_add_constraint(bset, c);
890 c = isl_inequality_alloc(dim);
891 isl_int_set_si(v, 42);
892 isl_constraint_set_constant(c, v);
893 isl_int_set_si(v, -1);
894 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
895 bset = isl_basic_set_add_constraint(bset, c);
897 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
903 struct isl_basic_set *bset;
904 bset = isl_basic_set_read_from_str(ctx,
905 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
907 A basic set or relation can also be constructed from two matrices
908 describing the equalities and the inequalities.
910 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
911 __isl_take isl_dim *dim,
912 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
913 enum isl_dim_type c1,
914 enum isl_dim_type c2, enum isl_dim_type c3,
915 enum isl_dim_type c4);
916 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
917 __isl_take isl_dim *dim,
918 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
919 enum isl_dim_type c1,
920 enum isl_dim_type c2, enum isl_dim_type c3,
921 enum isl_dim_type c4, enum isl_dim_type c5);
923 The C<isl_dim_type> arguments indicate the order in which
924 different kinds of variables appear in the input matrices
925 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
926 C<isl_dim_set> and C<isl_dim_div> for sets and
927 of C<isl_dim_cst>, C<isl_dim_param>,
928 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
930 =head2 Inspecting Sets and Relations
932 Usually, the user should not have to care about the actual constraints
933 of the sets and maps, but should instead apply the abstract operations
934 explained in the following sections.
935 Occasionally, however, it may be required to inspect the individual
936 coefficients of the constraints. This section explains how to do so.
937 In these cases, it may also be useful to have C<isl> compute
938 an explicit representation of the existentially quantified variables.
940 __isl_give isl_set *isl_set_compute_divs(
941 __isl_take isl_set *set);
942 __isl_give isl_map *isl_map_compute_divs(
943 __isl_take isl_map *map);
944 __isl_give isl_union_set *isl_union_set_compute_divs(
945 __isl_take isl_union_set *uset);
946 __isl_give isl_union_map *isl_union_map_compute_divs(
947 __isl_take isl_union_map *umap);
949 This explicit representation defines the existentially quantified
950 variables as integer divisions of the other variables, possibly
951 including earlier existentially quantified variables.
952 An explicitly represented existentially quantified variable therefore
953 has a unique value when the values of the other variables are known.
954 If, furthermore, the same existentials, i.e., existentials
955 with the same explicit representations, should appear in the
956 same order in each of the disjuncts of a set or map, then the user should call
957 either of the following functions.
959 __isl_give isl_set *isl_set_align_divs(
960 __isl_take isl_set *set);
961 __isl_give isl_map *isl_map_align_divs(
962 __isl_take isl_map *map);
964 Alternatively, the existentially quantified variables can be removed
965 using the following functions, which compute an overapproximation.
967 __isl_give isl_basic_set *isl_basic_set_remove_divs(
968 __isl_take isl_basic_set *bset);
969 __isl_give isl_basic_map *isl_basic_map_remove_divs(
970 __isl_take isl_basic_map *bmap);
971 __isl_give isl_set *isl_set_remove_divs(
972 __isl_take isl_set *set);
974 To iterate over all the sets or maps in a union set or map, use
976 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
977 int (*fn)(__isl_take isl_set *set, void *user),
979 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
980 int (*fn)(__isl_take isl_map *map, void *user),
983 The number of sets or maps in a union set or map can be obtained
986 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
987 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
989 To extract the set or map from a union with a given dimension
992 __isl_give isl_set *isl_union_set_extract_set(
993 __isl_keep isl_union_set *uset,
994 __isl_take isl_dim *dim);
995 __isl_give isl_map *isl_union_map_extract_map(
996 __isl_keep isl_union_map *umap,
997 __isl_take isl_dim *dim);
999 To iterate over all the basic sets or maps in a set or map, use
1001 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1002 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1004 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1005 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1008 The callback function C<fn> should return 0 if successful and
1009 -1 if an error occurs. In the latter case, or if any other error
1010 occurs, the above functions will return -1.
1012 It should be noted that C<isl> does not guarantee that
1013 the basic sets or maps passed to C<fn> are disjoint.
1014 If this is required, then the user should call one of
1015 the following functions first.
1017 __isl_give isl_set *isl_set_make_disjoint(
1018 __isl_take isl_set *set);
1019 __isl_give isl_map *isl_map_make_disjoint(
1020 __isl_take isl_map *map);
1022 The number of basic sets in a set can be obtained
1025 int isl_set_n_basic_set(__isl_keep isl_set *set);
1027 To iterate over the constraints of a basic set or map, use
1029 #include <isl/constraint.h>
1031 int isl_basic_map_foreach_constraint(
1032 __isl_keep isl_basic_map *bmap,
1033 int (*fn)(__isl_take isl_constraint *c, void *user),
1035 void isl_constraint_free(struct isl_constraint *c);
1037 Again, the callback function C<fn> should return 0 if successful and
1038 -1 if an error occurs. In the latter case, or if any other error
1039 occurs, the above functions will return -1.
1040 The constraint C<c> represents either an equality or an inequality.
1041 Use the following function to find out whether a constraint
1042 represents an equality. If not, it represents an inequality.
1044 int isl_constraint_is_equality(
1045 __isl_keep isl_constraint *constraint);
1047 The coefficients of the constraints can be inspected using
1048 the following functions.
1050 void isl_constraint_get_constant(
1051 __isl_keep isl_constraint *constraint, isl_int *v);
1052 void isl_constraint_get_coefficient(
1053 __isl_keep isl_constraint *constraint,
1054 enum isl_dim_type type, int pos, isl_int *v);
1056 The explicit representations of the existentially quantified
1057 variables can be inspected using the following functions.
1058 Note that the user is only allowed to use these functions
1059 if the inspected set or map is the result of a call
1060 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1062 __isl_give isl_div *isl_constraint_div(
1063 __isl_keep isl_constraint *constraint, int pos);
1064 void isl_div_get_constant(__isl_keep isl_div *div,
1066 void isl_div_get_denominator(__isl_keep isl_div *div,
1068 void isl_div_get_coefficient(__isl_keep isl_div *div,
1069 enum isl_dim_type type, int pos, isl_int *v);
1071 To obtain the constraints of a basic set or map in matrix
1072 form, use the following functions.
1074 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1075 __isl_keep isl_basic_set *bset,
1076 enum isl_dim_type c1, enum isl_dim_type c2,
1077 enum isl_dim_type c3, enum isl_dim_type c4);
1078 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1079 __isl_keep isl_basic_set *bset,
1080 enum isl_dim_type c1, enum isl_dim_type c2,
1081 enum isl_dim_type c3, enum isl_dim_type c4);
1082 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1083 __isl_keep isl_basic_map *bmap,
1084 enum isl_dim_type c1,
1085 enum isl_dim_type c2, enum isl_dim_type c3,
1086 enum isl_dim_type c4, enum isl_dim_type c5);
1087 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1088 __isl_keep isl_basic_map *bmap,
1089 enum isl_dim_type c1,
1090 enum isl_dim_type c2, enum isl_dim_type c3,
1091 enum isl_dim_type c4, enum isl_dim_type c5);
1093 The C<isl_dim_type> arguments dictate the order in which
1094 different kinds of variables appear in the resulting matrix
1095 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1096 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1098 The names of the domain and range spaces of a set or relation can be
1099 read off using the following functions.
1101 const char *isl_basic_set_get_tuple_name(
1102 __isl_keep isl_basic_set *bset);
1103 const char *isl_set_get_tuple_name(
1104 __isl_keep isl_set *set);
1105 const char *isl_basic_map_get_tuple_name(
1106 __isl_keep isl_basic_map *bmap,
1107 enum isl_dim_type type);
1108 const char *isl_map_get_tuple_name(
1109 __isl_keep isl_map *map,
1110 enum isl_dim_type type);
1112 As with C<isl_dim_get_tuple_name>, the value returned points to
1113 an internal data structure.
1114 The names of individual dimensions can be read off using
1115 the following functions.
1117 const char *isl_constraint_get_dim_name(
1118 __isl_keep isl_constraint *constraint,
1119 enum isl_dim_type type, unsigned pos);
1120 const char *isl_basic_set_get_dim_name(
1121 __isl_keep isl_basic_set *bset,
1122 enum isl_dim_type type, unsigned pos);
1123 const char *isl_set_get_dim_name(
1124 __isl_keep isl_set *set,
1125 enum isl_dim_type type, unsigned pos);
1126 const char *isl_basic_map_get_dim_name(
1127 __isl_keep isl_basic_map *bmap,
1128 enum isl_dim_type type, unsigned pos);
1129 const char *isl_map_get_dim_name(
1130 __isl_keep isl_map *map,
1131 enum isl_dim_type type, unsigned pos);
1133 These functions are mostly useful to obtain the names
1138 =head3 Unary Properties
1144 The following functions test whether the given set or relation
1145 contains any integer points. The ``fast'' variants do not perform
1146 any computations, but simply check if the given set or relation
1147 is already known to be empty.
1149 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1150 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1151 int isl_set_is_empty(__isl_keep isl_set *set);
1152 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1153 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1154 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1155 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1156 int isl_map_is_empty(__isl_keep isl_map *map);
1157 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1159 =item * Universality
1161 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1162 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1163 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1165 =item * Single-valuedness
1167 int isl_map_is_single_valued(__isl_keep isl_map *map);
1171 int isl_map_is_bijective(__isl_keep isl_map *map);
1175 The followning functions check whether the domain of the given
1176 (basic) set is a wrapped relation.
1178 int isl_basic_set_is_wrapping(
1179 __isl_keep isl_basic_set *bset);
1180 int isl_set_is_wrapping(__isl_keep isl_set *set);
1184 =head3 Binary Properties
1190 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1191 __isl_keep isl_set *set2);
1192 int isl_set_is_equal(__isl_keep isl_set *set1,
1193 __isl_keep isl_set *set2);
1194 int isl_union_set_is_equal(
1195 __isl_keep isl_union_set *uset1,
1196 __isl_keep isl_union_set *uset2);
1197 int isl_basic_map_is_equal(
1198 __isl_keep isl_basic_map *bmap1,
1199 __isl_keep isl_basic_map *bmap2);
1200 int isl_map_is_equal(__isl_keep isl_map *map1,
1201 __isl_keep isl_map *map2);
1202 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1203 __isl_keep isl_map *map2);
1204 int isl_union_map_is_equal(
1205 __isl_keep isl_union_map *umap1,
1206 __isl_keep isl_union_map *umap2);
1208 =item * Disjointness
1210 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1211 __isl_keep isl_set *set2);
1215 int isl_set_is_subset(__isl_keep isl_set *set1,
1216 __isl_keep isl_set *set2);
1217 int isl_set_is_strict_subset(
1218 __isl_keep isl_set *set1,
1219 __isl_keep isl_set *set2);
1220 int isl_union_set_is_subset(
1221 __isl_keep isl_union_set *uset1,
1222 __isl_keep isl_union_set *uset2);
1223 int isl_union_set_is_strict_subset(
1224 __isl_keep isl_union_set *uset1,
1225 __isl_keep isl_union_set *uset2);
1226 int isl_basic_map_is_subset(
1227 __isl_keep isl_basic_map *bmap1,
1228 __isl_keep isl_basic_map *bmap2);
1229 int isl_basic_map_is_strict_subset(
1230 __isl_keep isl_basic_map *bmap1,
1231 __isl_keep isl_basic_map *bmap2);
1232 int isl_map_is_subset(
1233 __isl_keep isl_map *map1,
1234 __isl_keep isl_map *map2);
1235 int isl_map_is_strict_subset(
1236 __isl_keep isl_map *map1,
1237 __isl_keep isl_map *map2);
1238 int isl_union_map_is_subset(
1239 __isl_keep isl_union_map *umap1,
1240 __isl_keep isl_union_map *umap2);
1241 int isl_union_map_is_strict_subset(
1242 __isl_keep isl_union_map *umap1,
1243 __isl_keep isl_union_map *umap2);
1247 =head2 Unary Operations
1253 __isl_give isl_set *isl_set_complement(
1254 __isl_take isl_set *set);
1258 __isl_give isl_basic_map *isl_basic_map_reverse(
1259 __isl_take isl_basic_map *bmap);
1260 __isl_give isl_map *isl_map_reverse(
1261 __isl_take isl_map *map);
1262 __isl_give isl_union_map *isl_union_map_reverse(
1263 __isl_take isl_union_map *umap);
1267 __isl_give isl_basic_set *isl_basic_set_project_out(
1268 __isl_take isl_basic_set *bset,
1269 enum isl_dim_type type, unsigned first, unsigned n);
1270 __isl_give isl_basic_map *isl_basic_map_project_out(
1271 __isl_take isl_basic_map *bmap,
1272 enum isl_dim_type type, unsigned first, unsigned n);
1273 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1274 enum isl_dim_type type, unsigned first, unsigned n);
1275 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1276 enum isl_dim_type type, unsigned first, unsigned n);
1277 __isl_give isl_basic_set *isl_basic_map_domain(
1278 __isl_take isl_basic_map *bmap);
1279 __isl_give isl_basic_set *isl_basic_map_range(
1280 __isl_take isl_basic_map *bmap);
1281 __isl_give isl_set *isl_map_domain(
1282 __isl_take isl_map *bmap);
1283 __isl_give isl_set *isl_map_range(
1284 __isl_take isl_map *map);
1285 __isl_give isl_union_set *isl_union_map_domain(
1286 __isl_take isl_union_map *umap);
1287 __isl_give isl_union_set *isl_union_map_range(
1288 __isl_take isl_union_map *umap);
1290 __isl_give isl_basic_map *isl_basic_map_domain_map(
1291 __isl_take isl_basic_map *bmap);
1292 __isl_give isl_basic_map *isl_basic_map_range_map(
1293 __isl_take isl_basic_map *bmap);
1294 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1295 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1296 __isl_give isl_union_map *isl_union_map_domain_map(
1297 __isl_take isl_union_map *umap);
1298 __isl_give isl_union_map *isl_union_map_range_map(
1299 __isl_take isl_union_map *umap);
1301 The functions above construct a (basic, regular or union) relation
1302 that maps (a wrapped version of) the input relation to its domain or range.
1306 __isl_give isl_map *isl_set_identity(
1307 __isl_take isl_set *set);
1308 __isl_give isl_union_map *isl_union_set_identity(
1309 __isl_take isl_union_set *uset);
1311 Construct an identity relation on the given (union) set.
1315 __isl_give isl_basic_set *isl_basic_map_deltas(
1316 __isl_take isl_basic_map *bmap);
1317 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1318 __isl_give isl_union_set *isl_union_map_deltas(
1319 __isl_take isl_union_map *umap);
1321 These functions return a (basic) set containing the differences
1322 between image elements and corresponding domain elements in the input.
1324 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1325 __isl_take isl_basic_map *bmap);
1326 __isl_give isl_map *isl_map_deltas_map(
1327 __isl_take isl_map *map);
1328 __isl_give isl_union_map *isl_union_map_deltas_map(
1329 __isl_take isl_union_map *umap);
1331 The functions above construct a (basic, regular or union) relation
1332 that maps (a wrapped version of) the input relation to its delta set.
1336 Simplify the representation of a set or relation by trying
1337 to combine pairs of basic sets or relations into a single
1338 basic set or relation.
1340 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1341 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1342 __isl_give isl_union_set *isl_union_set_coalesce(
1343 __isl_take isl_union_set *uset);
1344 __isl_give isl_union_map *isl_union_map_coalesce(
1345 __isl_take isl_union_map *umap);
1347 =item * Detecting equalities
1349 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1350 __isl_take isl_basic_set *bset);
1351 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1352 __isl_take isl_basic_map *bmap);
1353 __isl_give isl_set *isl_set_detect_equalities(
1354 __isl_take isl_set *set);
1355 __isl_give isl_map *isl_map_detect_equalities(
1356 __isl_take isl_map *map);
1357 __isl_give isl_union_set *isl_union_set_detect_equalities(
1358 __isl_take isl_union_set *uset);
1359 __isl_give isl_union_map *isl_union_map_detect_equalities(
1360 __isl_take isl_union_map *umap);
1362 Simplify the representation of a set or relation by detecting implicit
1367 __isl_give isl_basic_set *isl_set_convex_hull(
1368 __isl_take isl_set *set);
1369 __isl_give isl_basic_map *isl_map_convex_hull(
1370 __isl_take isl_map *map);
1372 If the input set or relation has any existentially quantified
1373 variables, then the result of these operations is currently undefined.
1377 __isl_give isl_basic_set *isl_set_simple_hull(
1378 __isl_take isl_set *set);
1379 __isl_give isl_basic_map *isl_map_simple_hull(
1380 __isl_take isl_map *map);
1381 __isl_give isl_union_map *isl_union_map_simple_hull(
1382 __isl_take isl_union_map *umap);
1384 These functions compute a single basic set or relation
1385 that contains the whole input set or relation.
1386 In particular, the output is described by translates
1387 of the constraints describing the basic sets or relations in the input.
1391 (See \autoref{s:simple hull}.)
1397 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1398 __isl_take isl_basic_set *bset);
1399 __isl_give isl_basic_set *isl_set_affine_hull(
1400 __isl_take isl_set *set);
1401 __isl_give isl_union_set *isl_union_set_affine_hull(
1402 __isl_take isl_union_set *uset);
1403 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1404 __isl_take isl_basic_map *bmap);
1405 __isl_give isl_basic_map *isl_map_affine_hull(
1406 __isl_take isl_map *map);
1407 __isl_give isl_union_map *isl_union_map_affine_hull(
1408 __isl_take isl_union_map *umap);
1410 In case of union sets and relations, the affine hull is computed
1413 =item * Polyhedral hull
1415 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1416 __isl_take isl_set *set);
1417 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1418 __isl_take isl_map *map);
1419 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1420 __isl_take isl_union_set *uset);
1421 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1422 __isl_take isl_union_map *umap);
1424 These functions compute a single basic set or relation
1425 not involving any existentially quantified variables
1426 that contains the whole input set or relation.
1427 In case of union sets and relations, the polyhedral hull is computed
1432 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1433 unsigned param, int *exact);
1435 Compute a parametric representation for all positive powers I<k> of C<map>.
1436 The power I<k> is equated to the parameter at position C<param>.
1437 The result may be an overapproximation. If the result is known to be exact,
1438 then C<*exact> is set to C<1>.
1440 =item * Transitive closure
1442 __isl_give isl_map *isl_map_transitive_closure(
1443 __isl_take isl_map *map, int *exact);
1444 __isl_give isl_union_map *isl_union_map_transitive_closure(
1445 __isl_take isl_union_map *umap, int *exact);
1447 Compute the transitive closure of C<map>.
1448 The result may be an overapproximation. If the result is known to be exact,
1449 then C<*exact> is set to C<1>.
1451 =item * Reaching path lengths
1453 __isl_give isl_map *isl_map_reaching_path_lengths(
1454 __isl_take isl_map *map, int *exact);
1456 Compute a relation that maps each element in the range of C<map>
1457 to the lengths of all paths composed of edges in C<map> that
1458 end up in the given element.
1459 The result may be an overapproximation. If the result is known to be exact,
1460 then C<*exact> is set to C<1>.
1461 To compute the I<maximal> path length, the resulting relation
1462 should be postprocessed by C<isl_map_lexmax>.
1463 In particular, if the input relation is a dependence relation
1464 (mapping sources to sinks), then the maximal path length corresponds
1465 to the free schedule.
1466 Note, however, that C<isl_map_lexmax> expects the maximum to be
1467 finite, so if the path lengths are unbounded (possibly due to
1468 the overapproximation), then you will get an error message.
1472 __isl_give isl_basic_set *isl_basic_map_wrap(
1473 __isl_take isl_basic_map *bmap);
1474 __isl_give isl_set *isl_map_wrap(
1475 __isl_take isl_map *map);
1476 __isl_give isl_union_set *isl_union_map_wrap(
1477 __isl_take isl_union_map *umap);
1478 __isl_give isl_basic_map *isl_basic_set_unwrap(
1479 __isl_take isl_basic_set *bset);
1480 __isl_give isl_map *isl_set_unwrap(
1481 __isl_take isl_set *set);
1482 __isl_give isl_union_map *isl_union_set_unwrap(
1483 __isl_take isl_union_set *uset);
1487 Remove any internal structure of domain (and range) of the given
1488 set or relation. If there is any such internal structure in the input,
1489 then the name of the space is also removed.
1491 __isl_give isl_basic_set *isl_basic_set_flatten(
1492 __isl_take isl_basic_set *bset);
1493 __isl_give isl_set *isl_set_flatten(
1494 __isl_take isl_set *set);
1495 __isl_give isl_basic_map *isl_basic_map_flatten(
1496 __isl_take isl_basic_map *bmap);
1497 __isl_give isl_map *isl_map_flatten(
1498 __isl_take isl_map *map);
1500 __isl_give isl_map *isl_set_flatten_map(
1501 __isl_take isl_set *set);
1503 The function above constructs a relation
1504 that maps the input set to a flattened version of the set.
1506 =item * Dimension manipulation
1508 __isl_give isl_set *isl_set_add_dims(
1509 __isl_take isl_set *set,
1510 enum isl_dim_type type, unsigned n);
1511 __isl_give isl_map *isl_map_add_dims(
1512 __isl_take isl_map *map,
1513 enum isl_dim_type type, unsigned n);
1515 It is usually not advisable to directly change the (input or output)
1516 space of a set or a relation as this removes the name and the internal
1517 structure of the space. However, the above functions can be useful
1518 to add new parameters.
1522 =head2 Binary Operations
1524 The two arguments of a binary operation not only need to live
1525 in the same C<isl_ctx>, they currently also need to have
1526 the same (number of) parameters.
1528 =head3 Basic Operations
1532 =item * Intersection
1534 __isl_give isl_basic_set *isl_basic_set_intersect(
1535 __isl_take isl_basic_set *bset1,
1536 __isl_take isl_basic_set *bset2);
1537 __isl_give isl_set *isl_set_intersect(
1538 __isl_take isl_set *set1,
1539 __isl_take isl_set *set2);
1540 __isl_give isl_union_set *isl_union_set_intersect(
1541 __isl_take isl_union_set *uset1,
1542 __isl_take isl_union_set *uset2);
1543 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1544 __isl_take isl_basic_map *bmap,
1545 __isl_take isl_basic_set *bset);
1546 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1547 __isl_take isl_basic_map *bmap,
1548 __isl_take isl_basic_set *bset);
1549 __isl_give isl_basic_map *isl_basic_map_intersect(
1550 __isl_take isl_basic_map *bmap1,
1551 __isl_take isl_basic_map *bmap2);
1552 __isl_give isl_map *isl_map_intersect_domain(
1553 __isl_take isl_map *map,
1554 __isl_take isl_set *set);
1555 __isl_give isl_map *isl_map_intersect_range(
1556 __isl_take isl_map *map,
1557 __isl_take isl_set *set);
1558 __isl_give isl_map *isl_map_intersect(
1559 __isl_take isl_map *map1,
1560 __isl_take isl_map *map2);
1561 __isl_give isl_union_map *isl_union_map_intersect_domain(
1562 __isl_take isl_union_map *umap,
1563 __isl_take isl_union_set *uset);
1564 __isl_give isl_union_map *isl_union_map_intersect_range(
1565 __isl_take isl_union_map *umap,
1566 __isl_take isl_union_set *uset);
1567 __isl_give isl_union_map *isl_union_map_intersect(
1568 __isl_take isl_union_map *umap1,
1569 __isl_take isl_union_map *umap2);
1573 __isl_give isl_set *isl_basic_set_union(
1574 __isl_take isl_basic_set *bset1,
1575 __isl_take isl_basic_set *bset2);
1576 __isl_give isl_map *isl_basic_map_union(
1577 __isl_take isl_basic_map *bmap1,
1578 __isl_take isl_basic_map *bmap2);
1579 __isl_give isl_set *isl_set_union(
1580 __isl_take isl_set *set1,
1581 __isl_take isl_set *set2);
1582 __isl_give isl_map *isl_map_union(
1583 __isl_take isl_map *map1,
1584 __isl_take isl_map *map2);
1585 __isl_give isl_union_set *isl_union_set_union(
1586 __isl_take isl_union_set *uset1,
1587 __isl_take isl_union_set *uset2);
1588 __isl_give isl_union_map *isl_union_map_union(
1589 __isl_take isl_union_map *umap1,
1590 __isl_take isl_union_map *umap2);
1592 =item * Set difference
1594 __isl_give isl_set *isl_set_subtract(
1595 __isl_take isl_set *set1,
1596 __isl_take isl_set *set2);
1597 __isl_give isl_map *isl_map_subtract(
1598 __isl_take isl_map *map1,
1599 __isl_take isl_map *map2);
1600 __isl_give isl_union_set *isl_union_set_subtract(
1601 __isl_take isl_union_set *uset1,
1602 __isl_take isl_union_set *uset2);
1603 __isl_give isl_union_map *isl_union_map_subtract(
1604 __isl_take isl_union_map *umap1,
1605 __isl_take isl_union_map *umap2);
1609 __isl_give isl_basic_set *isl_basic_set_apply(
1610 __isl_take isl_basic_set *bset,
1611 __isl_take isl_basic_map *bmap);
1612 __isl_give isl_set *isl_set_apply(
1613 __isl_take isl_set *set,
1614 __isl_take isl_map *map);
1615 __isl_give isl_union_set *isl_union_set_apply(
1616 __isl_take isl_union_set *uset,
1617 __isl_take isl_union_map *umap);
1618 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1619 __isl_take isl_basic_map *bmap1,
1620 __isl_take isl_basic_map *bmap2);
1621 __isl_give isl_basic_map *isl_basic_map_apply_range(
1622 __isl_take isl_basic_map *bmap1,
1623 __isl_take isl_basic_map *bmap2);
1624 __isl_give isl_map *isl_map_apply_domain(
1625 __isl_take isl_map *map1,
1626 __isl_take isl_map *map2);
1627 __isl_give isl_union_map *isl_union_map_apply_domain(
1628 __isl_take isl_union_map *umap1,
1629 __isl_take isl_union_map *umap2);
1630 __isl_give isl_map *isl_map_apply_range(
1631 __isl_take isl_map *map1,
1632 __isl_take isl_map *map2);
1633 __isl_give isl_union_map *isl_union_map_apply_range(
1634 __isl_take isl_union_map *umap1,
1635 __isl_take isl_union_map *umap2);
1637 =item * Cartesian Product
1639 __isl_give isl_set *isl_set_product(
1640 __isl_take isl_set *set1,
1641 __isl_take isl_set *set2);
1642 __isl_give isl_union_set *isl_union_set_product(
1643 __isl_take isl_union_set *uset1,
1644 __isl_take isl_union_set *uset2);
1645 __isl_give isl_basic_map *isl_basic_map_range_product(
1646 __isl_take isl_basic_map *bmap1,
1647 __isl_take isl_basic_map *bmap2);
1648 __isl_give isl_map *isl_map_range_product(
1649 __isl_take isl_map *map1,
1650 __isl_take isl_map *map2);
1651 __isl_give isl_union_map *isl_union_map_range_product(
1652 __isl_take isl_union_map *umap1,
1653 __isl_take isl_union_map *umap2);
1654 __isl_give isl_map *isl_map_product(
1655 __isl_take isl_map *map1,
1656 __isl_take isl_map *map2);
1657 __isl_give isl_union_map *isl_union_map_product(
1658 __isl_take isl_union_map *umap1,
1659 __isl_take isl_union_map *umap2);
1661 The above functions compute the cross product of the given
1662 sets or relations. The domains and ranges of the results
1663 are wrapped maps between domains and ranges of the inputs.
1664 To obtain a ``flat'' product, use the following functions
1667 __isl_give isl_basic_set *isl_basic_set_flat_product(
1668 __isl_take isl_basic_set *bset1,
1669 __isl_take isl_basic_set *bset2);
1670 __isl_give isl_set *isl_set_flat_product(
1671 __isl_take isl_set *set1,
1672 __isl_take isl_set *set2);
1673 __isl_give isl_basic_map *isl_basic_map_flat_product(
1674 __isl_take isl_basic_map *bmap1,
1675 __isl_take isl_basic_map *bmap2);
1676 __isl_give isl_map *isl_map_flat_product(
1677 __isl_take isl_map *map1,
1678 __isl_take isl_map *map2);
1680 =item * Simplification
1682 __isl_give isl_basic_set *isl_basic_set_gist(
1683 __isl_take isl_basic_set *bset,
1684 __isl_take isl_basic_set *context);
1685 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1686 __isl_take isl_set *context);
1687 __isl_give isl_union_set *isl_union_set_gist(
1688 __isl_take isl_union_set *uset,
1689 __isl_take isl_union_set *context);
1690 __isl_give isl_basic_map *isl_basic_map_gist(
1691 __isl_take isl_basic_map *bmap,
1692 __isl_take isl_basic_map *context);
1693 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1694 __isl_take isl_map *context);
1695 __isl_give isl_union_map *isl_union_map_gist(
1696 __isl_take isl_union_map *umap,
1697 __isl_take isl_union_map *context);
1699 The gist operation returns a set or relation that has the
1700 same intersection with the context as the input set or relation.
1701 Any implicit equality in the intersection is made explicit in the result,
1702 while all inequalities that are redundant with respect to the intersection
1704 In case of union sets and relations, the gist operation is performed
1709 =head3 Lexicographic Optimization
1711 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1712 the following functions
1713 compute a set that contains the lexicographic minimum or maximum
1714 of the elements in C<set> (or C<bset>) for those values of the parameters
1715 that satisfy C<dom>.
1716 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1717 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1719 In other words, the union of the parameter values
1720 for which the result is non-empty and of C<*empty>
1723 __isl_give isl_set *isl_basic_set_partial_lexmin(
1724 __isl_take isl_basic_set *bset,
1725 __isl_take isl_basic_set *dom,
1726 __isl_give isl_set **empty);
1727 __isl_give isl_set *isl_basic_set_partial_lexmax(
1728 __isl_take isl_basic_set *bset,
1729 __isl_take isl_basic_set *dom,
1730 __isl_give isl_set **empty);
1731 __isl_give isl_set *isl_set_partial_lexmin(
1732 __isl_take isl_set *set, __isl_take isl_set *dom,
1733 __isl_give isl_set **empty);
1734 __isl_give isl_set *isl_set_partial_lexmax(
1735 __isl_take isl_set *set, __isl_take isl_set *dom,
1736 __isl_give isl_set **empty);
1738 Given a (basic) set C<set> (or C<bset>), the following functions simply
1739 return a set containing the lexicographic minimum or maximum
1740 of the elements in C<set> (or C<bset>).
1741 In case of union sets, the optimum is computed per space.
1743 __isl_give isl_set *isl_basic_set_lexmin(
1744 __isl_take isl_basic_set *bset);
1745 __isl_give isl_set *isl_basic_set_lexmax(
1746 __isl_take isl_basic_set *bset);
1747 __isl_give isl_set *isl_set_lexmin(
1748 __isl_take isl_set *set);
1749 __isl_give isl_set *isl_set_lexmax(
1750 __isl_take isl_set *set);
1751 __isl_give isl_union_set *isl_union_set_lexmin(
1752 __isl_take isl_union_set *uset);
1753 __isl_give isl_union_set *isl_union_set_lexmax(
1754 __isl_take isl_union_set *uset);
1756 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1757 the following functions
1758 compute a relation that maps each element of C<dom>
1759 to the single lexicographic minimum or maximum
1760 of the elements that are associated to that same
1761 element in C<map> (or C<bmap>).
1762 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1763 that contains the elements in C<dom> that do not map
1764 to any elements in C<map> (or C<bmap>).
1765 In other words, the union of the domain of the result and of C<*empty>
1768 __isl_give isl_map *isl_basic_map_partial_lexmax(
1769 __isl_take isl_basic_map *bmap,
1770 __isl_take isl_basic_set *dom,
1771 __isl_give isl_set **empty);
1772 __isl_give isl_map *isl_basic_map_partial_lexmin(
1773 __isl_take isl_basic_map *bmap,
1774 __isl_take isl_basic_set *dom,
1775 __isl_give isl_set **empty);
1776 __isl_give isl_map *isl_map_partial_lexmax(
1777 __isl_take isl_map *map, __isl_take isl_set *dom,
1778 __isl_give isl_set **empty);
1779 __isl_give isl_map *isl_map_partial_lexmin(
1780 __isl_take isl_map *map, __isl_take isl_set *dom,
1781 __isl_give isl_set **empty);
1783 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1784 return a map mapping each element in the domain of
1785 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1786 of all elements associated to that element.
1787 In case of union relations, the optimum is computed per space.
1789 __isl_give isl_map *isl_basic_map_lexmin(
1790 __isl_take isl_basic_map *bmap);
1791 __isl_give isl_map *isl_basic_map_lexmax(
1792 __isl_take isl_basic_map *bmap);
1793 __isl_give isl_map *isl_map_lexmin(
1794 __isl_take isl_map *map);
1795 __isl_give isl_map *isl_map_lexmax(
1796 __isl_take isl_map *map);
1797 __isl_give isl_union_map *isl_union_map_lexmin(
1798 __isl_take isl_union_map *umap);
1799 __isl_give isl_union_map *isl_union_map_lexmax(
1800 __isl_take isl_union_map *umap);
1804 Matrices can be created, copied and freed using the following functions.
1806 #include <isl/mat.h>
1807 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1808 unsigned n_row, unsigned n_col);
1809 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1810 void isl_mat_free(__isl_take isl_mat *mat);
1812 Note that the elements of a newly created matrix may have arbitrary values.
1813 The elements can be changed and inspected using the following functions.
1815 int isl_mat_rows(__isl_keep isl_mat *mat);
1816 int isl_mat_cols(__isl_keep isl_mat *mat);
1817 int isl_mat_get_element(__isl_keep isl_mat *mat,
1818 int row, int col, isl_int *v);
1819 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1820 int row, int col, isl_int v);
1822 C<isl_mat_get_element> will return a negative value if anything went wrong.
1823 In that case, the value of C<*v> is undefined.
1825 The following function can be used to compute the (right) inverse
1826 of a matrix, i.e., a matrix such that the product of the original
1827 and the inverse (in that order) is a multiple of the identity matrix.
1828 The input matrix is assumed to be of full row-rank.
1830 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1832 The following function can be used to compute the (right) kernel
1833 (or null space) of a matrix, i.e., a matrix such that the product of
1834 the original and the kernel (in that order) is the zero matrix.
1836 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1840 Points are elements of a set. They can be used to construct
1841 simple sets (boxes) or they can be used to represent the
1842 individual elements of a set.
1843 The zero point (the origin) can be created using
1845 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1847 The coordinates of a point can be inspected, set and changed
1850 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1851 enum isl_dim_type type, int pos, isl_int *v);
1852 __isl_give isl_point *isl_point_set_coordinate(
1853 __isl_take isl_point *pnt,
1854 enum isl_dim_type type, int pos, isl_int v);
1856 __isl_give isl_point *isl_point_add_ui(
1857 __isl_take isl_point *pnt,
1858 enum isl_dim_type type, int pos, unsigned val);
1859 __isl_give isl_point *isl_point_sub_ui(
1860 __isl_take isl_point *pnt,
1861 enum isl_dim_type type, int pos, unsigned val);
1863 Points can be copied or freed using
1865 __isl_give isl_point *isl_point_copy(
1866 __isl_keep isl_point *pnt);
1867 void isl_point_free(__isl_take isl_point *pnt);
1869 A singleton set can be created from a point using
1871 __isl_give isl_basic_set *isl_basic_set_from_point(
1872 __isl_take isl_point *pnt);
1873 __isl_give isl_set *isl_set_from_point(
1874 __isl_take isl_point *pnt);
1876 and a box can be created from two opposite extremal points using
1878 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1879 __isl_take isl_point *pnt1,
1880 __isl_take isl_point *pnt2);
1881 __isl_give isl_set *isl_set_box_from_points(
1882 __isl_take isl_point *pnt1,
1883 __isl_take isl_point *pnt2);
1885 All elements of a B<bounded> (union) set can be enumerated using
1886 the following functions.
1888 int isl_set_foreach_point(__isl_keep isl_set *set,
1889 int (*fn)(__isl_take isl_point *pnt, void *user),
1891 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1892 int (*fn)(__isl_take isl_point *pnt, void *user),
1895 The function C<fn> is called for each integer point in
1896 C<set> with as second argument the last argument of
1897 the C<isl_set_foreach_point> call. The function C<fn>
1898 should return C<0> on success and C<-1> on failure.
1899 In the latter case, C<isl_set_foreach_point> will stop
1900 enumerating and return C<-1> as well.
1901 If the enumeration is performed successfully and to completion,
1902 then C<isl_set_foreach_point> returns C<0>.
1904 To obtain a single point of a (basic) set, use
1906 __isl_give isl_point *isl_basic_set_sample_point(
1907 __isl_take isl_basic_set *bset);
1908 __isl_give isl_point *isl_set_sample_point(
1909 __isl_take isl_set *set);
1911 If C<set> does not contain any (integer) points, then the
1912 resulting point will be ``void'', a property that can be
1915 int isl_point_is_void(__isl_keep isl_point *pnt);
1917 =head2 Piecewise Quasipolynomials
1919 A piecewise quasipolynomial is a particular kind of function that maps
1920 a parametric point to a rational value.
1921 More specifically, a quasipolynomial is a polynomial expression in greatest
1922 integer parts of affine expressions of parameters and variables.
1923 A piecewise quasipolynomial is a subdivision of a given parametric
1924 domain into disjoint cells with a quasipolynomial associated to
1925 each cell. The value of the piecewise quasipolynomial at a given
1926 point is the value of the quasipolynomial associated to the cell
1927 that contains the point. Outside of the union of cells,
1928 the value is assumed to be zero.
1929 For example, the piecewise quasipolynomial
1931 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1933 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1934 A given piecewise quasipolynomial has a fixed domain dimension.
1935 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1936 defined over different domains.
1937 Piecewise quasipolynomials are mainly used by the C<barvinok>
1938 library for representing the number of elements in a parametric set or map.
1939 For example, the piecewise quasipolynomial above represents
1940 the number of points in the map
1942 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1944 =head3 Printing (Piecewise) Quasipolynomials
1946 Quasipolynomials and piecewise quasipolynomials can be printed
1947 using the following functions.
1949 __isl_give isl_printer *isl_printer_print_qpolynomial(
1950 __isl_take isl_printer *p,
1951 __isl_keep isl_qpolynomial *qp);
1953 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1954 __isl_take isl_printer *p,
1955 __isl_keep isl_pw_qpolynomial *pwqp);
1957 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1958 __isl_take isl_printer *p,
1959 __isl_keep isl_union_pw_qpolynomial *upwqp);
1961 The output format of the printer
1962 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1963 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1965 In case of printing in C<ISL_FORMAT_C>, the user may want
1966 to set the names of all dimensions
1968 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1969 __isl_take isl_qpolynomial *qp,
1970 enum isl_dim_type type, unsigned pos,
1972 __isl_give isl_pw_qpolynomial *
1973 isl_pw_qpolynomial_set_dim_name(
1974 __isl_take isl_pw_qpolynomial *pwqp,
1975 enum isl_dim_type type, unsigned pos,
1978 =head3 Creating New (Piecewise) Quasipolynomials
1980 Some simple quasipolynomials can be created using the following functions.
1981 More complicated quasipolynomials can be created by applying
1982 operations such as addition and multiplication
1983 on the resulting quasipolynomials
1985 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1986 __isl_take isl_dim *dim);
1987 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1988 __isl_take isl_dim *dim);
1989 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1990 __isl_take isl_dim *dim);
1991 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1992 __isl_take isl_dim *dim);
1993 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1994 __isl_take isl_dim *dim);
1995 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1996 __isl_take isl_dim *dim,
1997 const isl_int n, const isl_int d);
1998 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1999 __isl_take isl_div *div);
2000 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2001 __isl_take isl_dim *dim,
2002 enum isl_dim_type type, unsigned pos);
2004 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2005 with a single cell can be created using the following functions.
2006 Multiple of these single cell piecewise quasipolynomials can
2007 be combined to create more complicated piecewise quasipolynomials.
2009 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2010 __isl_take isl_dim *dim);
2011 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2012 __isl_take isl_set *set,
2013 __isl_take isl_qpolynomial *qp);
2015 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2016 __isl_take isl_dim *dim);
2017 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2018 __isl_take isl_pw_qpolynomial *pwqp);
2019 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2020 __isl_take isl_union_pw_qpolynomial *upwqp,
2021 __isl_take isl_pw_qpolynomial *pwqp);
2023 Quasipolynomials can be copied and freed again using the following
2026 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2027 __isl_keep isl_qpolynomial *qp);
2028 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2030 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2031 __isl_keep isl_pw_qpolynomial *pwqp);
2032 void isl_pw_qpolynomial_free(
2033 __isl_take isl_pw_qpolynomial *pwqp);
2035 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2036 __isl_keep isl_union_pw_qpolynomial *upwqp);
2037 void isl_union_pw_qpolynomial_free(
2038 __isl_take isl_union_pw_qpolynomial *upwqp);
2040 =head3 Inspecting (Piecewise) Quasipolynomials
2042 To iterate over all piecewise quasipolynomials in a union
2043 piecewise quasipolynomial, use the following function
2045 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2046 __isl_keep isl_union_pw_qpolynomial *upwqp,
2047 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2050 To extract the piecewise quasipolynomial from a union with a given dimension
2053 __isl_give isl_pw_qpolynomial *
2054 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2055 __isl_keep isl_union_pw_qpolynomial *upwqp,
2056 __isl_take isl_dim *dim);
2058 To iterate over the cells in a piecewise quasipolynomial,
2059 use either of the following two functions
2061 int isl_pw_qpolynomial_foreach_piece(
2062 __isl_keep isl_pw_qpolynomial *pwqp,
2063 int (*fn)(__isl_take isl_set *set,
2064 __isl_take isl_qpolynomial *qp,
2065 void *user), void *user);
2066 int isl_pw_qpolynomial_foreach_lifted_piece(
2067 __isl_keep isl_pw_qpolynomial *pwqp,
2068 int (*fn)(__isl_take isl_set *set,
2069 __isl_take isl_qpolynomial *qp,
2070 void *user), void *user);
2072 As usual, the function C<fn> should return C<0> on success
2073 and C<-1> on failure. The difference between
2074 C<isl_pw_qpolynomial_foreach_piece> and
2075 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2076 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2077 compute unique representations for all existentially quantified
2078 variables and then turn these existentially quantified variables
2079 into extra set variables, adapting the associated quasipolynomial
2080 accordingly. This means that the C<set> passed to C<fn>
2081 will not have any existentially quantified variables, but that
2082 the dimensions of the sets may be different for different
2083 invocations of C<fn>.
2085 To iterate over all terms in a quasipolynomial,
2088 int isl_qpolynomial_foreach_term(
2089 __isl_keep isl_qpolynomial *qp,
2090 int (*fn)(__isl_take isl_term *term,
2091 void *user), void *user);
2093 The terms themselves can be inspected and freed using
2096 unsigned isl_term_dim(__isl_keep isl_term *term,
2097 enum isl_dim_type type);
2098 void isl_term_get_num(__isl_keep isl_term *term,
2100 void isl_term_get_den(__isl_keep isl_term *term,
2102 int isl_term_get_exp(__isl_keep isl_term *term,
2103 enum isl_dim_type type, unsigned pos);
2104 __isl_give isl_div *isl_term_get_div(
2105 __isl_keep isl_term *term, unsigned pos);
2106 void isl_term_free(__isl_take isl_term *term);
2108 Each term is a product of parameters, set variables and
2109 integer divisions. The function C<isl_term_get_exp>
2110 returns the exponent of a given dimensions in the given term.
2111 The C<isl_int>s in the arguments of C<isl_term_get_num>
2112 and C<isl_term_get_den> need to have been initialized
2113 using C<isl_int_init> before calling these functions.
2115 =head3 Properties of (Piecewise) Quasipolynomials
2117 To check whether a quasipolynomial is actually a constant,
2118 use the following function.
2120 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2121 isl_int *n, isl_int *d);
2123 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2124 then the numerator and denominator of the constant
2125 are returned in C<*n> and C<*d>, respectively.
2127 =head3 Operations on (Piecewise) Quasipolynomials
2129 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2130 __isl_take isl_qpolynomial *qp);
2131 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2132 __isl_take isl_qpolynomial *qp1,
2133 __isl_take isl_qpolynomial *qp2);
2134 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2135 __isl_take isl_qpolynomial *qp1,
2136 __isl_take isl_qpolynomial *qp2);
2137 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2138 __isl_take isl_qpolynomial *qp1,
2139 __isl_take isl_qpolynomial *qp2);
2140 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2141 __isl_take isl_qpolynomial *qp, unsigned exponent);
2143 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2144 __isl_take isl_pw_qpolynomial *pwqp1,
2145 __isl_take isl_pw_qpolynomial *pwqp2);
2146 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2147 __isl_take isl_pw_qpolynomial *pwqp1,
2148 __isl_take isl_pw_qpolynomial *pwqp2);
2149 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2150 __isl_take isl_pw_qpolynomial *pwqp1,
2151 __isl_take isl_pw_qpolynomial *pwqp2);
2152 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2153 __isl_take isl_pw_qpolynomial *pwqp);
2154 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2155 __isl_take isl_pw_qpolynomial *pwqp1,
2156 __isl_take isl_pw_qpolynomial *pwqp2);
2158 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2159 __isl_take isl_union_pw_qpolynomial *upwqp1,
2160 __isl_take isl_union_pw_qpolynomial *upwqp2);
2161 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2162 __isl_take isl_union_pw_qpolynomial *upwqp1,
2163 __isl_take isl_union_pw_qpolynomial *upwqp2);
2164 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2165 __isl_take isl_union_pw_qpolynomial *upwqp1,
2166 __isl_take isl_union_pw_qpolynomial *upwqp2);
2168 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2169 __isl_take isl_pw_qpolynomial *pwqp,
2170 __isl_take isl_point *pnt);
2172 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2173 __isl_take isl_union_pw_qpolynomial *upwqp,
2174 __isl_take isl_point *pnt);
2176 __isl_give isl_set *isl_pw_qpolynomial_domain(
2177 __isl_take isl_pw_qpolynomial *pwqp);
2178 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2179 __isl_take isl_pw_qpolynomial *pwpq,
2180 __isl_take isl_set *set);
2182 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2183 __isl_take isl_union_pw_qpolynomial *upwqp);
2184 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2185 __isl_take isl_union_pw_qpolynomial *upwpq,
2186 __isl_take isl_union_set *uset);
2188 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2189 __isl_take isl_union_pw_qpolynomial *upwqp);
2191 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2192 __isl_take isl_pw_qpolynomial *pwqp,
2193 __isl_take isl_set *context);
2195 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2196 __isl_take isl_union_pw_qpolynomial *upwqp,
2197 __isl_take isl_union_set *context);
2199 The gist operation applies the gist operation to each of
2200 the cells in the domain of the input piecewise quasipolynomial.
2201 The context is also exploited
2202 to simplify the quasipolynomials associated to each cell.
2204 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2205 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2206 __isl_give isl_union_pw_qpolynomial *
2207 isl_union_pw_qpolynomial_to_polynomial(
2208 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2210 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2211 the polynomial will be an overapproximation. If C<sign> is negative,
2212 it will be an underapproximation. If C<sign> is zero, the approximation
2213 will lie somewhere in between.
2215 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2217 A piecewise quasipolynomial reduction is a piecewise
2218 reduction (or fold) of quasipolynomials.
2219 In particular, the reduction can be maximum or a minimum.
2220 The objects are mainly used to represent the result of
2221 an upper or lower bound on a quasipolynomial over its domain,
2222 i.e., as the result of the following function.
2224 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2225 __isl_take isl_pw_qpolynomial *pwqp,
2226 enum isl_fold type, int *tight);
2228 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2229 __isl_take isl_union_pw_qpolynomial *upwqp,
2230 enum isl_fold type, int *tight);
2232 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2233 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2234 is the returned bound is known be tight, i.e., for each value
2235 of the parameters there is at least
2236 one element in the domain that reaches the bound.
2237 If the domain of C<pwqp> is not wrapping, then the bound is computed
2238 over all elements in that domain and the result has a purely parametric
2239 domain. If the domain of C<pwqp> is wrapping, then the bound is
2240 computed over the range of the wrapped relation. The domain of the
2241 wrapped relation becomes the domain of the result.
2243 A (piecewise) quasipolynomial reduction can be copied or freed using the
2244 following functions.
2246 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2247 __isl_keep isl_qpolynomial_fold *fold);
2248 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2249 __isl_keep isl_pw_qpolynomial_fold *pwf);
2250 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2251 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2252 void isl_qpolynomial_fold_free(
2253 __isl_take isl_qpolynomial_fold *fold);
2254 void isl_pw_qpolynomial_fold_free(
2255 __isl_take isl_pw_qpolynomial_fold *pwf);
2256 void isl_union_pw_qpolynomial_fold_free(
2257 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2259 =head3 Printing Piecewise Quasipolynomial Reductions
2261 Piecewise quasipolynomial reductions can be printed
2262 using the following function.
2264 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2265 __isl_take isl_printer *p,
2266 __isl_keep isl_pw_qpolynomial_fold *pwf);
2267 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2268 __isl_take isl_printer *p,
2269 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2271 For C<isl_printer_print_pw_qpolynomial_fold>,
2272 output format of the printer
2273 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2274 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2275 output format of the printer
2276 needs to be set to C<ISL_FORMAT_ISL>.
2277 In case of printing in C<ISL_FORMAT_C>, the user may want
2278 to set the names of all dimensions
2280 __isl_give isl_pw_qpolynomial_fold *
2281 isl_pw_qpolynomial_fold_set_dim_name(
2282 __isl_take isl_pw_qpolynomial_fold *pwf,
2283 enum isl_dim_type type, unsigned pos,
2286 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2288 To iterate over all piecewise quasipolynomial reductions in a union
2289 piecewise quasipolynomial reduction, use the following function
2291 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2292 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2293 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2294 void *user), void *user);
2296 To iterate over the cells in a piecewise quasipolynomial reduction,
2297 use either of the following two functions
2299 int isl_pw_qpolynomial_fold_foreach_piece(
2300 __isl_keep isl_pw_qpolynomial_fold *pwf,
2301 int (*fn)(__isl_take isl_set *set,
2302 __isl_take isl_qpolynomial_fold *fold,
2303 void *user), void *user);
2304 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2305 __isl_keep isl_pw_qpolynomial_fold *pwf,
2306 int (*fn)(__isl_take isl_set *set,
2307 __isl_take isl_qpolynomial_fold *fold,
2308 void *user), void *user);
2310 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2311 of the difference between these two functions.
2313 To iterate over all quasipolynomials in a reduction, use
2315 int isl_qpolynomial_fold_foreach_qpolynomial(
2316 __isl_keep isl_qpolynomial_fold *fold,
2317 int (*fn)(__isl_take isl_qpolynomial *qp,
2318 void *user), void *user);
2320 =head3 Operations on Piecewise Quasipolynomial Reductions
2322 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2323 __isl_take isl_pw_qpolynomial_fold *pwf1,
2324 __isl_take isl_pw_qpolynomial_fold *pwf2);
2326 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2327 __isl_take isl_pw_qpolynomial_fold *pwf1,
2328 __isl_take isl_pw_qpolynomial_fold *pwf2);
2330 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2331 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2332 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2334 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2335 __isl_take isl_pw_qpolynomial_fold *pwf,
2336 __isl_take isl_point *pnt);
2338 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2339 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2340 __isl_take isl_point *pnt);
2342 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2343 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2344 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2345 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2346 __isl_take isl_union_set *uset);
2348 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2349 __isl_take isl_pw_qpolynomial_fold *pwf);
2351 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2352 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2354 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2355 __isl_take isl_pw_qpolynomial_fold *pwf,
2356 __isl_take isl_set *context);
2358 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2359 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2360 __isl_take isl_union_set *context);
2362 The gist operation applies the gist operation to each of
2363 the cells in the domain of the input piecewise quasipolynomial reduction.
2364 In future, the operation will also exploit the context
2365 to simplify the quasipolynomial reductions associated to each cell.
2367 __isl_give isl_pw_qpolynomial_fold *
2368 isl_set_apply_pw_qpolynomial_fold(
2369 __isl_take isl_set *set,
2370 __isl_take isl_pw_qpolynomial_fold *pwf,
2372 __isl_give isl_pw_qpolynomial_fold *
2373 isl_map_apply_pw_qpolynomial_fold(
2374 __isl_take isl_map *map,
2375 __isl_take isl_pw_qpolynomial_fold *pwf,
2377 __isl_give isl_union_pw_qpolynomial_fold *
2378 isl_union_set_apply_union_pw_qpolynomial_fold(
2379 __isl_take isl_union_set *uset,
2380 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2382 __isl_give isl_union_pw_qpolynomial_fold *
2383 isl_union_map_apply_union_pw_qpolynomial_fold(
2384 __isl_take isl_union_map *umap,
2385 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2388 The functions taking a map
2389 compose the given map with the given piecewise quasipolynomial reduction.
2390 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2391 over all elements in the intersection of the range of the map
2392 and the domain of the piecewise quasipolynomial reduction
2393 as a function of an element in the domain of the map.
2394 The functions taking a set compute a bound over all elements in the
2395 intersection of the set and the domain of the
2396 piecewise quasipolynomial reduction.
2398 =head2 Dependence Analysis
2400 C<isl> contains specialized functionality for performing
2401 array dataflow analysis. That is, given a I<sink> access relation
2402 and a collection of possible I<source> access relations,
2403 C<isl> can compute relations that describe
2404 for each iteration of the sink access, which iteration
2405 of which of the source access relations was the last
2406 to access the same data element before the given iteration
2408 To compute standard flow dependences, the sink should be
2409 a read, while the sources should be writes.
2410 If any of the source accesses are marked as being I<may>
2411 accesses, then there will be a dependence to the last
2412 I<must> access B<and> to any I<may> access that follows
2413 this last I<must> access.
2414 In particular, if I<all> sources are I<may> accesses,
2415 then memory based dependence analysis is performed.
2416 If, on the other hand, all sources are I<must> accesses,
2417 then value based dependence analysis is performed.
2419 #include <isl/flow.h>
2421 typedef int (*isl_access_level_before)(void *first, void *second);
2423 __isl_give isl_access_info *isl_access_info_alloc(
2424 __isl_take isl_map *sink,
2425 void *sink_user, isl_access_level_before fn,
2427 __isl_give isl_access_info *isl_access_info_add_source(
2428 __isl_take isl_access_info *acc,
2429 __isl_take isl_map *source, int must,
2431 void isl_access_info_free(__isl_take isl_access_info *acc);
2433 __isl_give isl_flow *isl_access_info_compute_flow(
2434 __isl_take isl_access_info *acc);
2436 int isl_flow_foreach(__isl_keep isl_flow *deps,
2437 int (*fn)(__isl_take isl_map *dep, int must,
2438 void *dep_user, void *user),
2440 __isl_give isl_map *isl_flow_get_no_source(
2441 __isl_keep isl_flow *deps, int must);
2442 void isl_flow_free(__isl_take isl_flow *deps);
2444 The function C<isl_access_info_compute_flow> performs the actual
2445 dependence analysis. The other functions are used to construct
2446 the input for this function or to read off the output.
2448 The input is collected in an C<isl_access_info>, which can
2449 be created through a call to C<isl_access_info_alloc>.
2450 The arguments to this functions are the sink access relation
2451 C<sink>, a token C<sink_user> used to identify the sink
2452 access to the user, a callback function for specifying the
2453 relative order of source and sink accesses, and the number
2454 of source access relations that will be added.
2455 The callback function has type C<int (*)(void *first, void *second)>.
2456 The function is called with two user supplied tokens identifying
2457 either a source or the sink and it should return the shared nesting
2458 level and the relative order of the two accesses.
2459 In particular, let I<n> be the number of loops shared by
2460 the two accesses. If C<first> precedes C<second> textually,
2461 then the function should return I<2 * n + 1>; otherwise,
2462 it should return I<2 * n>.
2463 The sources can be added to the C<isl_access_info> by performing
2464 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2465 C<must> indicates whether the source is a I<must> access
2466 or a I<may> access. Note that a multi-valued access relation
2467 should only be marked I<must> if every iteration in the domain
2468 of the relation accesses I<all> elements in its image.
2469 The C<source_user> token is again used to identify
2470 the source access. The range of the source access relation
2471 C<source> should have the same dimension as the range
2472 of the sink access relation.
2473 The C<isl_access_info_free> function should usually not be
2474 called explicitly, because it is called implicitly by
2475 C<isl_access_info_compute_flow>.
2477 The result of the dependence analysis is collected in an
2478 C<isl_flow>. There may be elements of
2479 the sink access for which no preceding source access could be
2480 found or for which all preceding sources are I<may> accesses.
2481 The relations containing these elements can be obtained through
2482 calls to C<isl_flow_get_no_source>, the first with C<must> set
2483 and the second with C<must> unset.
2484 In the case of standard flow dependence analysis,
2485 with the sink a read and the sources I<must> writes,
2486 the first relation corresponds to the reads from uninitialized
2487 array elements and the second relation is empty.
2488 The actual flow dependences can be extracted using
2489 C<isl_flow_foreach>. This function will call the user-specified
2490 callback function C<fn> for each B<non-empty> dependence between
2491 a source and the sink. The callback function is called
2492 with four arguments, the actual flow dependence relation
2493 mapping source iterations to sink iterations, a boolean that
2494 indicates whether it is a I<must> or I<may> dependence, a token
2495 identifying the source and an additional C<void *> with value
2496 equal to the third argument of the C<isl_flow_foreach> call.
2497 A dependence is marked I<must> if it originates from a I<must>
2498 source and if it is not followed by any I<may> sources.
2500 After finishing with an C<isl_flow>, the user should call
2501 C<isl_flow_free> to free all associated memory.
2503 A higher-level interface to dependence analysis is provided
2504 by the following function.
2506 #include <isl/flow.h>
2508 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2509 __isl_take isl_union_map *must_source,
2510 __isl_take isl_union_map *may_source,
2511 __isl_take isl_union_map *schedule,
2512 __isl_give isl_union_map **must_dep,
2513 __isl_give isl_union_map **may_dep,
2514 __isl_give isl_union_map **must_no_source,
2515 __isl_give isl_union_map **may_no_source);
2517 The arrays are identified by the tuple names of the ranges
2518 of the accesses. The iteration domains by the tuple names
2519 of the domains of the accesses and of the schedule.
2520 The relative order of the iteration domains is given by the
2521 schedule. The relations returned through C<must_no_source>
2522 and C<may_no_source> are subsets of C<sink>.
2523 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2524 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2525 any of the other arguments is treated as an error.
2527 =head2 Parametric Vertex Enumeration
2529 The parametric vertex enumeration described in this section
2530 is mainly intended to be used internally and by the C<barvinok>
2533 #include <isl/vertices.h>
2534 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2535 __isl_keep isl_basic_set *bset);
2537 The function C<isl_basic_set_compute_vertices> performs the
2538 actual computation of the parametric vertices and the chamber
2539 decomposition and store the result in an C<isl_vertices> object.
2540 This information can be queried by either iterating over all
2541 the vertices or iterating over all the chambers or cells
2542 and then iterating over all vertices that are active on the chamber.
2544 int isl_vertices_foreach_vertex(
2545 __isl_keep isl_vertices *vertices,
2546 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2549 int isl_vertices_foreach_cell(
2550 __isl_keep isl_vertices *vertices,
2551 int (*fn)(__isl_take isl_cell *cell, void *user),
2553 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2554 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2557 Other operations that can be performed on an C<isl_vertices> object are
2560 isl_ctx *isl_vertices_get_ctx(
2561 __isl_keep isl_vertices *vertices);
2562 int isl_vertices_get_n_vertices(
2563 __isl_keep isl_vertices *vertices);
2564 void isl_vertices_free(__isl_take isl_vertices *vertices);
2566 Vertices can be inspected and destroyed using the following functions.
2568 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2569 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2570 __isl_give isl_basic_set *isl_vertex_get_domain(
2571 __isl_keep isl_vertex *vertex);
2572 __isl_give isl_basic_set *isl_vertex_get_expr(
2573 __isl_keep isl_vertex *vertex);
2574 void isl_vertex_free(__isl_take isl_vertex *vertex);
2576 C<isl_vertex_get_expr> returns a singleton parametric set describing
2577 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2579 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2580 B<rational> basic sets, so they should mainly be used for inspection
2581 and should not be mixed with integer sets.
2583 Chambers can be inspected and destroyed using the following functions.
2585 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2586 __isl_give isl_basic_set *isl_cell_get_domain(
2587 __isl_keep isl_cell *cell);
2588 void isl_cell_free(__isl_take isl_cell *cell);
2592 Although C<isl> is mainly meant to be used as a library,
2593 it also contains some basic applications that use some
2594 of the functionality of C<isl>.
2595 The input may be specified in either the L<isl format>
2596 or the L<PolyLib format>.
2598 =head2 C<isl_polyhedron_sample>
2600 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2601 an integer element of the polyhedron, if there is any.
2602 The first column in the output is the denominator and is always
2603 equal to 1. If the polyhedron contains no integer points,
2604 then a vector of length zero is printed.
2608 C<isl_pip> takes the same input as the C<example> program
2609 from the C<piplib> distribution, i.e., a set of constraints
2610 on the parameters, a line containing only -1 and finally a set
2611 of constraints on a parametric polyhedron.
2612 The coefficients of the parameters appear in the last columns
2613 (but before the final constant column).
2614 The output is the lexicographic minimum of the parametric polyhedron.
2615 As C<isl> currently does not have its own output format, the output
2616 is just a dump of the internal state.
2618 =head2 C<isl_polyhedron_minimize>
2620 C<isl_polyhedron_minimize> computes the minimum of some linear
2621 or affine objective function over the integer points in a polyhedron.
2622 If an affine objective function
2623 is given, then the constant should appear in the last column.
2625 =head2 C<isl_polytope_scan>
2627 Given a polytope, C<isl_polytope_scan> prints
2628 all integer points in the polytope.
2630 =head1 C<isl-polylib>
2632 The C<isl-polylib> library provides the following functions for converting
2633 between C<isl> objects and C<PolyLib> objects.
2634 The library is distributed separately for licensing reasons.
2636 #include <isl_set_polylib.h>
2637 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2638 Polyhedron *P, __isl_take isl_dim *dim);
2639 Polyhedron *isl_basic_set_to_polylib(
2640 __isl_keep isl_basic_set *bset);
2641 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2642 __isl_take isl_dim *dim);
2643 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2645 #include <isl_map_polylib.h>
2646 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2647 Polyhedron *P, __isl_take isl_dim *dim);
2648 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2649 __isl_take isl_dim *dim);
2650 Polyhedron *isl_basic_map_to_polylib(
2651 __isl_keep isl_basic_map *bmap);
2652 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);