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.
74 The source of C<isl> can be obtained either as a tarball
75 or from the git repository. Both are available from
76 L<http://freshmeat.net/projects/isl/>.
77 The installation process depends on how you obtained
80 =head2 Installation from the git repository
84 =item 1 Clone or update the repository
86 The first time the source is obtained, you need to clone
89 git clone git://repo.or.cz/isl.git
91 To obtain updates, you need to pull in the latest changes
95 =item 2 Generate C<configure>
101 After performing the above steps, continue
102 with the L<Common installation instructions>.
104 =head2 Common installation instructions
108 =item 1 Obtain C<GMP>
110 Building C<isl> requires C<GMP>, including its headers files.
111 Your distribution may not provide these header files by default
112 and you may need to install a package called C<gmp-devel> or something
113 similar. Alternatively, C<GMP> can be built from
114 source, available from L<http://gmplib.org/>.
118 C<isl> uses the standard C<autoconf> C<configure> script.
123 optionally followed by some configure options.
124 A complete list of options can be obtained by running
128 Below we discuss some of the more common options.
130 C<isl> can optionally use C<piplib>, but no
131 C<piplib> functionality is currently used by default.
132 The C<--with-piplib> option can
133 be used to specify which C<piplib>
134 library to use, either an installed version (C<system>),
135 an externally built version (C<build>)
136 or no version (C<no>). The option C<build> is mostly useful
137 in C<configure> scripts of larger projects that bundle both C<isl>
144 Installation prefix for C<isl>
146 =item C<--with-gmp-prefix>
148 Installation prefix for C<GMP> (architecture-independent files).
150 =item C<--with-gmp-exec-prefix>
152 Installation prefix for C<GMP> (architecture-dependent files).
154 =item C<--with-piplib>
156 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
158 =item C<--with-piplib-prefix>
160 Installation prefix for C<system> C<piplib> (architecture-independent files).
162 =item C<--with-piplib-exec-prefix>
164 Installation prefix for C<system> C<piplib> (architecture-dependent files).
166 =item C<--with-piplib-builddir>
168 Location where C<build> C<piplib> was built.
176 =item 4 Install (optional)
184 =head2 Initialization
186 All manipulations of integer sets and relations occur within
187 the context of an C<isl_ctx>.
188 A given C<isl_ctx> can only be used within a single thread.
189 All arguments of a function are required to have been allocated
190 within the same context.
191 There are currently no functions available for moving an object
192 from one C<isl_ctx> to another C<isl_ctx>. This means that
193 there is currently no way of safely moving an object from one
194 thread to another, unless the whole C<isl_ctx> is moved.
196 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
197 freed using C<isl_ctx_free>.
198 All objects allocated within an C<isl_ctx> should be freed
199 before the C<isl_ctx> itself is freed.
201 isl_ctx *isl_ctx_alloc();
202 void isl_ctx_free(isl_ctx *ctx);
206 All operations on integers, mainly the coefficients
207 of the constraints describing the sets and relations,
208 are performed in exact integer arithmetic using C<GMP>.
209 However, to allow future versions of C<isl> to optionally
210 support fixed integer arithmetic, all calls to C<GMP>
211 are wrapped inside C<isl> specific macros.
212 The basic type is C<isl_int> and the operations below
213 are available on this type.
214 The meanings of these operations are essentially the same
215 as their C<GMP> C<mpz_> counterparts.
216 As always with C<GMP> types, C<isl_int>s need to be
217 initialized with C<isl_int_init> before they can be used
218 and they need to be released with C<isl_int_clear>
220 The user should not assume that an C<isl_int> is represented
221 as a C<mpz_t>, but should instead explicitly convert between
222 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
223 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
227 =item isl_int_init(i)
229 =item isl_int_clear(i)
231 =item isl_int_set(r,i)
233 =item isl_int_set_si(r,i)
235 =item isl_int_set_gmp(r,g)
237 =item isl_int_get_gmp(i,g)
239 =item isl_int_abs(r,i)
241 =item isl_int_neg(r,i)
243 =item isl_int_swap(i,j)
245 =item isl_int_swap_or_set(i,j)
247 =item isl_int_add_ui(r,i,j)
249 =item isl_int_sub_ui(r,i,j)
251 =item isl_int_add(r,i,j)
253 =item isl_int_sub(r,i,j)
255 =item isl_int_mul(r,i,j)
257 =item isl_int_mul_ui(r,i,j)
259 =item isl_int_addmul(r,i,j)
261 =item isl_int_submul(r,i,j)
263 =item isl_int_gcd(r,i,j)
265 =item isl_int_lcm(r,i,j)
267 =item isl_int_divexact(r,i,j)
269 =item isl_int_cdiv_q(r,i,j)
271 =item isl_int_fdiv_q(r,i,j)
273 =item isl_int_fdiv_r(r,i,j)
275 =item isl_int_fdiv_q_ui(r,i,j)
277 =item isl_int_read(r,s)
279 =item isl_int_print(out,i,width)
283 =item isl_int_cmp(i,j)
285 =item isl_int_cmp_si(i,si)
287 =item isl_int_eq(i,j)
289 =item isl_int_ne(i,j)
291 =item isl_int_lt(i,j)
293 =item isl_int_le(i,j)
295 =item isl_int_gt(i,j)
297 =item isl_int_ge(i,j)
299 =item isl_int_abs_eq(i,j)
301 =item isl_int_abs_ne(i,j)
303 =item isl_int_abs_lt(i,j)
305 =item isl_int_abs_gt(i,j)
307 =item isl_int_abs_ge(i,j)
309 =item isl_int_is_zero(i)
311 =item isl_int_is_one(i)
313 =item isl_int_is_negone(i)
315 =item isl_int_is_pos(i)
317 =item isl_int_is_neg(i)
319 =item isl_int_is_nonpos(i)
321 =item isl_int_is_nonneg(i)
323 =item isl_int_is_divisible_by(i,j)
327 =head2 Sets and Relations
329 C<isl> uses six types of objects for representing sets and relations,
330 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
331 C<isl_union_set> and C<isl_union_map>.
332 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
333 can be described as a conjunction of affine constraints, while
334 C<isl_set> and C<isl_map> represent unions of
335 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
336 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
337 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
338 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
339 where dimensions with different space names
340 (see L<Dimension Specifications>) are considered different as well.
341 The difference between sets and relations (maps) is that sets have
342 one set of variables, while relations have two sets of variables,
343 input variables and output variables.
345 =head2 Memory Management
347 Since a high-level operation on sets and/or relations usually involves
348 several substeps and since the user is usually not interested in
349 the intermediate results, most functions that return a new object
350 will also release all the objects passed as arguments.
351 If the user still wants to use one or more of these arguments
352 after the function call, she should pass along a copy of the
353 object rather than the object itself.
354 The user is then responsible for make sure that the original
355 object gets used somewhere else or is explicitly freed.
357 The arguments and return values of all documents functions are
358 annotated to make clear which arguments are released and which
359 arguments are preserved. In particular, the following annotations
366 C<__isl_give> means that a new object is returned.
367 The user should make sure that the returned pointer is
368 used exactly once as a value for an C<__isl_take> argument.
369 In between, it can be used as a value for as many
370 C<__isl_keep> arguments as the user likes.
371 There is one exception, and that is the case where the
372 pointer returned is C<NULL>. Is this case, the user
373 is free to use it as an C<__isl_take> argument or not.
377 C<__isl_take> means that the object the argument points to
378 is taken over by the function and may no longer be used
379 by the user as an argument to any other function.
380 The pointer value must be one returned by a function
381 returning an C<__isl_give> pointer.
382 If the user passes in a C<NULL> value, then this will
383 be treated as an error in the sense that the function will
384 not perform its usual operation. However, it will still
385 make sure that all the the other C<__isl_take> arguments
390 C<__isl_keep> means that the function will only use the object
391 temporarily. After the function has finished, the user
392 can still use it as an argument to other functions.
393 A C<NULL> value will be treated in the same way as
394 a C<NULL> value for an C<__isl_take> argument.
398 =head2 Dimension Specifications
400 Whenever a new set or relation is created from scratch,
401 its dimension needs to be specified using an C<isl_dim>.
404 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
405 unsigned nparam, unsigned n_in, unsigned n_out);
406 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
407 unsigned nparam, unsigned dim);
408 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
409 void isl_dim_free(__isl_take isl_dim *dim);
410 unsigned isl_dim_size(__isl_keep isl_dim *dim,
411 enum isl_dim_type type);
413 The dimension specification used for creating a set
414 needs to be created using C<isl_dim_set_alloc>, while
415 that for creating a relation
416 needs to be created using C<isl_dim_alloc>.
417 C<isl_dim_size> can be used
418 to find out the number of dimensions of each type in
419 a dimension specification, where type may be
420 C<isl_dim_param>, C<isl_dim_in> (only for relations),
421 C<isl_dim_out> (only for relations), C<isl_dim_set>
422 (only for sets) or C<isl_dim_all>.
424 It is often useful to create objects that live in the
425 same space as some other object. This can be accomplished
426 by creating the new objects
427 (see L<Creating New Sets and Relations> or
428 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
429 specification of the original object.
432 __isl_give isl_dim *isl_basic_set_get_dim(
433 __isl_keep isl_basic_set *bset);
434 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
436 #include <isl/union_set.h>
437 __isl_give isl_dim *isl_union_set_get_dim(
438 __isl_keep isl_union_set *uset);
441 __isl_give isl_dim *isl_basic_map_get_dim(
442 __isl_keep isl_basic_map *bmap);
443 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
445 #include <isl/union_map.h>
446 __isl_give isl_dim *isl_union_map_get_dim(
447 __isl_keep isl_union_map *umap);
449 #include <isl/polynomial.h>
450 __isl_give isl_dim *isl_qpolynomial_get_dim(
451 __isl_keep isl_qpolynomial *qp);
452 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
453 __isl_keep isl_pw_qpolynomial *pwqp);
454 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
455 __isl_keep isl_union_pw_qpolynomial *upwqp);
456 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
457 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
459 The names of the individual dimensions may be set or read off
460 using the following functions.
463 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
464 enum isl_dim_type type, unsigned pos,
465 __isl_keep const char *name);
466 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
467 enum isl_dim_type type, unsigned pos);
469 Note that C<isl_dim_get_name> returns a pointer to some internal
470 data structure, so the result can only be used while the
471 corresponding C<isl_dim> is alive.
472 Also note that every function that operates on two sets or relations
473 requires that both arguments have the same parameters. This also
474 means that if one of the arguments has named parameters, then the
475 other needs to have named parameters too and the names need to match.
476 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
477 have different parameters (as long as they are named), in which case
478 the result will have as parameters the union of the parameters of
481 The names of entire spaces may be set or read off
482 using the following functions.
485 __isl_give isl_dim *isl_dim_set_tuple_name(
486 __isl_take isl_dim *dim,
487 enum isl_dim_type type, const char *s);
488 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
489 enum isl_dim_type type);
491 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
492 or C<isl_dim_set>. As with C<isl_dim_get_name>,
493 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
495 Binary operations require the corresponding spaces of their arguments
496 to have the same name.
498 Spaces can be nested. In particular, the domain of a set or
499 the domain or range of a relation can be a nested relation.
500 The following functions can be used to construct and deconstruct
501 such nested dimension specifications.
504 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
505 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
506 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
508 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
509 be the dimension specification of a set, while that of
510 C<isl_dim_wrap> should be the dimension specification of a relation.
511 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
512 of a relation, while that of C<isl_dim_wrap> is the dimension specification
515 Dimension specifications can be created from other dimension
516 specifications using the following functions.
518 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
519 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
520 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
521 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
522 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
523 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
524 __isl_take isl_dim *right);
525 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
526 enum isl_dim_type type, unsigned pos, unsigned n);
527 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
528 enum isl_dim_type type, unsigned n);
529 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
530 enum isl_dim_type type, unsigned first, unsigned n);
532 Note that if dimensions are added or removed from a space, then
533 the name and the internal structure are lost.
535 =head2 Input and Output
537 C<isl> supports its own input/output format, which is similar
538 to the C<Omega> format, but also supports the C<PolyLib> format
543 The C<isl> format is similar to that of C<Omega>, but has a different
544 syntax for describing the parameters and allows for the definition
545 of an existentially quantified variable as the integer division
546 of an affine expression.
547 For example, the set of integers C<i> between C<0> and C<n>
548 such that C<i % 10 <= 6> can be described as
550 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
553 A set or relation can have several disjuncts, separated
554 by the keyword C<or>. Each disjunct is either a conjunction
555 of constraints or a projection (C<exists>) of a conjunction
556 of constraints. The constraints are separated by the keyword
559 =head3 C<PolyLib> format
561 If the represented set is a union, then the first line
562 contains a single number representing the number of disjuncts.
563 Otherwise, a line containing the number C<1> is optional.
565 Each disjunct is represented by a matrix of constraints.
566 The first line contains two numbers representing
567 the number of rows and columns,
568 where the number of rows is equal to the number of constraints
569 and the number of columns is equal to two plus the number of variables.
570 The following lines contain the actual rows of the constraint matrix.
571 In each row, the first column indicates whether the constraint
572 is an equality (C<0>) or inequality (C<1>). The final column
573 corresponds to the constant term.
575 If the set is parametric, then the coefficients of the parameters
576 appear in the last columns before the constant column.
577 The coefficients of any existentially quantified variables appear
578 between those of the set variables and those of the parameters.
580 =head3 Extended C<PolyLib> format
582 The extended C<PolyLib> format is nearly identical to the
583 C<PolyLib> format. The only difference is that the line
584 containing the number of rows and columns of a constraint matrix
585 also contains four additional numbers:
586 the number of output dimensions, the number of input dimensions,
587 the number of local dimensions (i.e., the number of existentially
588 quantified variables) and the number of parameters.
589 For sets, the number of ``output'' dimensions is equal
590 to the number of set dimensions, while the number of ``input''
596 __isl_give isl_basic_set *isl_basic_set_read_from_file(
597 isl_ctx *ctx, FILE *input, int nparam);
598 __isl_give isl_basic_set *isl_basic_set_read_from_str(
599 isl_ctx *ctx, const char *str, int nparam);
600 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
601 FILE *input, int nparam);
602 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
603 const char *str, int nparam);
606 __isl_give isl_basic_map *isl_basic_map_read_from_file(
607 isl_ctx *ctx, FILE *input, int nparam);
608 __isl_give isl_basic_map *isl_basic_map_read_from_str(
609 isl_ctx *ctx, const char *str, int nparam);
610 __isl_give isl_map *isl_map_read_from_file(
611 struct isl_ctx *ctx, FILE *input, int nparam);
612 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
613 const char *str, int nparam);
615 #include <isl/union_set.h>
616 __isl_give isl_union_set *isl_union_set_read_from_file(
617 isl_ctx *ctx, FILE *input);
618 __isl_give isl_union_set *isl_union_set_read_from_str(
619 struct isl_ctx *ctx, const char *str);
621 #include <isl/union_map.h>
622 __isl_give isl_union_map *isl_union_map_read_from_file(
623 isl_ctx *ctx, FILE *input);
624 __isl_give isl_union_map *isl_union_map_read_from_str(
625 struct isl_ctx *ctx, const char *str);
627 The input format is autodetected and may be either the C<PolyLib> format
628 or the C<isl> format.
629 C<nparam> specifies how many of the final columns in
630 the C<PolyLib> format correspond to parameters.
631 If input is given in the C<isl> format, then the number
632 of parameters needs to be equal to C<nparam>.
633 If C<nparam> is negative, then any number of parameters
634 is accepted in the C<isl> format and zero parameters
635 are assumed in the C<PolyLib> format.
639 Before anything can be printed, an C<isl_printer> needs to
642 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
644 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
645 void isl_printer_free(__isl_take isl_printer *printer);
646 __isl_give char *isl_printer_get_str(
647 __isl_keep isl_printer *printer);
649 The behavior of the printer can be modified in various ways
651 __isl_give isl_printer *isl_printer_set_output_format(
652 __isl_take isl_printer *p, int output_format);
653 __isl_give isl_printer *isl_printer_set_indent(
654 __isl_take isl_printer *p, int indent);
655 __isl_give isl_printer *isl_printer_set_prefix(
656 __isl_take isl_printer *p, const char *prefix);
657 __isl_give isl_printer *isl_printer_set_suffix(
658 __isl_take isl_printer *p, const char *suffix);
660 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
661 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
662 and defaults to C<ISL_FORMAT_ISL>.
663 Each line in the output is indented by C<indent> spaces
664 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
665 In the C<PolyLib> format output,
666 the coefficients of the existentially quantified variables
667 appear between those of the set variables and those
670 To actually print something, use
673 __isl_give isl_printer *isl_printer_print_basic_set(
674 __isl_take isl_printer *printer,
675 __isl_keep isl_basic_set *bset);
676 __isl_give isl_printer *isl_printer_print_set(
677 __isl_take isl_printer *printer,
678 __isl_keep isl_set *set);
681 __isl_give isl_printer *isl_printer_print_basic_map(
682 __isl_take isl_printer *printer,
683 __isl_keep isl_basic_map *bmap);
684 __isl_give isl_printer *isl_printer_print_map(
685 __isl_take isl_printer *printer,
686 __isl_keep isl_map *map);
688 #include <isl/union_set.h>
689 __isl_give isl_printer *isl_printer_print_union_set(
690 __isl_take isl_printer *p,
691 __isl_keep isl_union_set *uset);
693 #include <isl/union_map.h>
694 __isl_give isl_printer *isl_printer_print_union_map(
695 __isl_take isl_printer *p,
696 __isl_keep isl_union_map *umap);
698 When called on a file printer, the following function flushes
699 the file. When called on a string printer, the buffer is cleared.
701 __isl_give isl_printer *isl_printer_flush(
702 __isl_take isl_printer *p);
704 =head2 Creating New Sets and Relations
706 C<isl> has functions for creating some standard sets and relations.
710 =item * Empty sets and relations
712 __isl_give isl_basic_set *isl_basic_set_empty(
713 __isl_take isl_dim *dim);
714 __isl_give isl_basic_map *isl_basic_map_empty(
715 __isl_take isl_dim *dim);
716 __isl_give isl_set *isl_set_empty(
717 __isl_take isl_dim *dim);
718 __isl_give isl_map *isl_map_empty(
719 __isl_take isl_dim *dim);
720 __isl_give isl_union_set *isl_union_set_empty(
721 __isl_take isl_dim *dim);
722 __isl_give isl_union_map *isl_union_map_empty(
723 __isl_take isl_dim *dim);
725 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
726 is only used to specify the parameters.
728 =item * Universe sets and relations
730 __isl_give isl_basic_set *isl_basic_set_universe(
731 __isl_take isl_dim *dim);
732 __isl_give isl_basic_map *isl_basic_map_universe(
733 __isl_take isl_dim *dim);
734 __isl_give isl_set *isl_set_universe(
735 __isl_take isl_dim *dim);
736 __isl_give isl_map *isl_map_universe(
737 __isl_take isl_dim *dim);
739 The sets and relations constructed by the functions above
740 contain all integer values, while those constructed by the
741 functions below only contain non-negative values.
743 __isl_give isl_basic_set *isl_basic_set_nat_universe(
744 __isl_take isl_dim *dim);
745 __isl_give isl_basic_map *isl_basic_map_nat_universe(
746 __isl_take isl_dim *dim);
747 __isl_give isl_set *isl_set_nat_universe(
748 __isl_take isl_dim *dim);
749 __isl_give isl_map *isl_map_nat_universe(
750 __isl_take isl_dim *dim);
752 =item * Identity relations
754 __isl_give isl_basic_map *isl_basic_map_identity(
755 __isl_take isl_dim *set_dim);
756 __isl_give isl_map *isl_map_identity(
757 __isl_take isl_dim *set_dim);
759 These functions take a dimension specification for a B<set>
760 and return an identity relation between two such sets.
762 =item * Lexicographic order
764 __isl_give isl_map *isl_map_lex_lt(
765 __isl_take isl_dim *set_dim);
766 __isl_give isl_map *isl_map_lex_le(
767 __isl_take isl_dim *set_dim);
768 __isl_give isl_map *isl_map_lex_gt(
769 __isl_take isl_dim *set_dim);
770 __isl_give isl_map *isl_map_lex_ge(
771 __isl_take isl_dim *set_dim);
772 __isl_give isl_map *isl_map_lex_lt_first(
773 __isl_take isl_dim *dim, unsigned n);
774 __isl_give isl_map *isl_map_lex_le_first(
775 __isl_take isl_dim *dim, unsigned n);
776 __isl_give isl_map *isl_map_lex_gt_first(
777 __isl_take isl_dim *dim, unsigned n);
778 __isl_give isl_map *isl_map_lex_ge_first(
779 __isl_take isl_dim *dim, unsigned n);
781 The first four functions take a dimension specification for a B<set>
782 and return relations that express that the elements in the domain
783 are lexicographically less
784 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
785 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
786 than the elements in the range.
787 The last four functions take a dimension specification for a map
788 and return relations that express that the first C<n> dimensions
789 in the domain are lexicographically less
790 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
791 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
792 than the first C<n> dimensions in the range.
796 A basic set or relation can be converted to a set or relation
797 using the following functions.
799 __isl_give isl_set *isl_set_from_basic_set(
800 __isl_take isl_basic_set *bset);
801 __isl_give isl_map *isl_map_from_basic_map(
802 __isl_take isl_basic_map *bmap);
804 Sets and relations can be converted to union sets and relations
805 using the following functions.
807 __isl_give isl_union_map *isl_union_map_from_map(
808 __isl_take isl_map *map);
809 __isl_give isl_union_set *isl_union_set_from_set(
810 __isl_take isl_set *set);
812 Sets and relations can be copied and freed again using the following
815 __isl_give isl_basic_set *isl_basic_set_copy(
816 __isl_keep isl_basic_set *bset);
817 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
818 __isl_give isl_union_set *isl_union_set_copy(
819 __isl_keep isl_union_set *uset);
820 __isl_give isl_basic_map *isl_basic_map_copy(
821 __isl_keep isl_basic_map *bmap);
822 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
823 __isl_give isl_union_map *isl_union_map_copy(
824 __isl_keep isl_union_map *umap);
825 void isl_basic_set_free(__isl_take isl_basic_set *bset);
826 void isl_set_free(__isl_take isl_set *set);
827 void isl_union_set_free(__isl_take isl_union_set *uset);
828 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
829 void isl_map_free(__isl_take isl_map *map);
830 void isl_union_map_free(__isl_take isl_union_map *umap);
832 Other sets and relations can be constructed by starting
833 from a universe set or relation, adding equality and/or
834 inequality constraints and then projecting out the
835 existentially quantified variables, if any.
836 Constraints can be constructed, manipulated and
837 added to basic sets and relations using the following functions.
839 #include <isl/constraint.h>
840 __isl_give isl_constraint *isl_equality_alloc(
841 __isl_take isl_dim *dim);
842 __isl_give isl_constraint *isl_inequality_alloc(
843 __isl_take isl_dim *dim);
844 void isl_constraint_set_constant(
845 __isl_keep isl_constraint *constraint, isl_int v);
846 void isl_constraint_set_coefficient(
847 __isl_keep isl_constraint *constraint,
848 enum isl_dim_type type, int pos, isl_int v);
849 __isl_give isl_basic_map *isl_basic_map_add_constraint(
850 __isl_take isl_basic_map *bmap,
851 __isl_take isl_constraint *constraint);
852 __isl_give isl_basic_set *isl_basic_set_add_constraint(
853 __isl_take isl_basic_set *bset,
854 __isl_take isl_constraint *constraint);
856 For example, to create a set containing the even integers
857 between 10 and 42, you would use the following code.
861 struct isl_constraint *c;
862 struct isl_basic_set *bset;
865 dim = isl_dim_set_alloc(ctx, 0, 2);
866 bset = isl_basic_set_universe(isl_dim_copy(dim));
868 c = isl_equality_alloc(isl_dim_copy(dim));
869 isl_int_set_si(v, -1);
870 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
871 isl_int_set_si(v, 2);
872 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
873 bset = isl_basic_set_add_constraint(bset, c);
875 c = isl_inequality_alloc(isl_dim_copy(dim));
876 isl_int_set_si(v, -10);
877 isl_constraint_set_constant(c, v);
878 isl_int_set_si(v, 1);
879 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
880 bset = isl_basic_set_add_constraint(bset, c);
882 c = isl_inequality_alloc(dim);
883 isl_int_set_si(v, 42);
884 isl_constraint_set_constant(c, v);
885 isl_int_set_si(v, -1);
886 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
887 bset = isl_basic_set_add_constraint(bset, c);
889 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
895 struct isl_basic_set *bset;
896 bset = isl_basic_set_read_from_str(ctx,
897 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
899 A basic set or relation can also be constructed from two matrices
900 describing the equalities and the inequalities.
902 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
903 __isl_take isl_dim *dim,
904 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
905 enum isl_dim_type c1,
906 enum isl_dim_type c2, enum isl_dim_type c3,
907 enum isl_dim_type c4);
908 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
909 __isl_take isl_dim *dim,
910 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
911 enum isl_dim_type c1,
912 enum isl_dim_type c2, enum isl_dim_type c3,
913 enum isl_dim_type c4, enum isl_dim_type c5);
915 The C<isl_dim_type> arguments indicate the order in which
916 different kinds of variables appear in the input matrices
917 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
918 C<isl_dim_set> and C<isl_dim_div> for sets and
919 of C<isl_dim_cst>, C<isl_dim_param>,
920 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
922 =head2 Inspecting Sets and Relations
924 Usually, the user should not have to care about the actual constraints
925 of the sets and maps, but should instead apply the abstract operations
926 explained in the following sections.
927 Occasionally, however, it may be required to inspect the individual
928 coefficients of the constraints. This section explains how to do so.
929 In these cases, it may also be useful to have C<isl> compute
930 an explicit representation of the existentially quantified variables.
932 __isl_give isl_set *isl_set_compute_divs(
933 __isl_take isl_set *set);
934 __isl_give isl_map *isl_map_compute_divs(
935 __isl_take isl_map *map);
936 __isl_give isl_union_set *isl_union_set_compute_divs(
937 __isl_take isl_union_set *uset);
938 __isl_give isl_union_map *isl_union_map_compute_divs(
939 __isl_take isl_union_map *umap);
941 This explicit representation defines the existentially quantified
942 variables as integer divisions of the other variables, possibly
943 including earlier existentially quantified variables.
944 An explicitly represented existentially quantified variable therefore
945 has a unique value when the values of the other variables are known.
946 If, furthermore, the same existentials, i.e., existentials
947 with the same explicit representations, should appear in the
948 same order in each of the disjuncts of a set or map, then the user should call
949 either of the following functions.
951 __isl_give isl_set *isl_set_align_divs(
952 __isl_take isl_set *set);
953 __isl_give isl_map *isl_map_align_divs(
954 __isl_take isl_map *map);
956 Alternatively, the existentially quantified variables can be removed
957 using the following functions, which compute an overapproximation.
959 __isl_give isl_basic_set *isl_basic_set_remove_divs(
960 __isl_take isl_basic_set *bset);
961 __isl_give isl_basic_map *isl_basic_map_remove_divs(
962 __isl_take isl_basic_map *bmap);
963 __isl_give isl_set *isl_set_remove_divs(
964 __isl_take isl_set *set);
966 To iterate over all the sets or maps in a union set or map, use
968 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
969 int (*fn)(__isl_take isl_set *set, void *user),
971 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
972 int (*fn)(__isl_take isl_map *map, void *user),
975 The number of sets or maps in a union set or map can be obtained
978 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
979 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
981 To extract the set or map from a union with a given dimension
984 __isl_give isl_set *isl_union_set_extract_set(
985 __isl_keep isl_union_set *uset,
986 __isl_take isl_dim *dim);
987 __isl_give isl_map *isl_union_map_extract_map(
988 __isl_keep isl_union_map *umap,
989 __isl_take isl_dim *dim);
991 To iterate over all the basic sets or maps in a set or map, use
993 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
994 int (*fn)(__isl_take isl_basic_set *bset, void *user),
996 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
997 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1000 The callback function C<fn> should return 0 if successful and
1001 -1 if an error occurs. In the latter case, or if any other error
1002 occurs, the above functions will return -1.
1004 It should be noted that C<isl> does not guarantee that
1005 the basic sets or maps passed to C<fn> are disjoint.
1006 If this is required, then the user should call one of
1007 the following functions first.
1009 __isl_give isl_set *isl_set_make_disjoint(
1010 __isl_take isl_set *set);
1011 __isl_give isl_map *isl_map_make_disjoint(
1012 __isl_take isl_map *map);
1014 The number of basic sets in a set can be obtained
1017 int isl_set_n_basic_set(__isl_keep isl_set *set);
1019 To iterate over the constraints of a basic set or map, use
1021 #include <isl/constraint.h>
1023 int isl_basic_map_foreach_constraint(
1024 __isl_keep isl_basic_map *bmap,
1025 int (*fn)(__isl_take isl_constraint *c, void *user),
1027 void isl_constraint_free(struct isl_constraint *c);
1029 Again, the callback function C<fn> should return 0 if successful and
1030 -1 if an error occurs. In the latter case, or if any other error
1031 occurs, the above functions will return -1.
1032 The constraint C<c> represents either an equality or an inequality.
1033 Use the following function to find out whether a constraint
1034 represents an equality. If not, it represents an inequality.
1036 int isl_constraint_is_equality(
1037 __isl_keep isl_constraint *constraint);
1039 The coefficients of the constraints can be inspected using
1040 the following functions.
1042 void isl_constraint_get_constant(
1043 __isl_keep isl_constraint *constraint, isl_int *v);
1044 void isl_constraint_get_coefficient(
1045 __isl_keep isl_constraint *constraint,
1046 enum isl_dim_type type, int pos, isl_int *v);
1048 The explicit representations of the existentially quantified
1049 variables can be inspected using the following functions.
1050 Note that the user is only allowed to use these functions
1051 if the inspected set or map is the result of a call
1052 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1054 __isl_give isl_div *isl_constraint_div(
1055 __isl_keep isl_constraint *constraint, int pos);
1056 void isl_div_get_constant(__isl_keep isl_div *div,
1058 void isl_div_get_denominator(__isl_keep isl_div *div,
1060 void isl_div_get_coefficient(__isl_keep isl_div *div,
1061 enum isl_dim_type type, int pos, isl_int *v);
1063 To obtain the constraints of a basic set or map in matrix
1064 form, use the following functions.
1066 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1067 __isl_keep isl_basic_set *bset,
1068 enum isl_dim_type c1, enum isl_dim_type c2,
1069 enum isl_dim_type c3, enum isl_dim_type c4);
1070 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1071 __isl_keep isl_basic_set *bset,
1072 enum isl_dim_type c1, enum isl_dim_type c2,
1073 enum isl_dim_type c3, enum isl_dim_type c4);
1074 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1075 __isl_keep isl_basic_map *bmap,
1076 enum isl_dim_type c1,
1077 enum isl_dim_type c2, enum isl_dim_type c3,
1078 enum isl_dim_type c4, enum isl_dim_type c5);
1079 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1080 __isl_keep isl_basic_map *bmap,
1081 enum isl_dim_type c1,
1082 enum isl_dim_type c2, enum isl_dim_type c3,
1083 enum isl_dim_type c4, enum isl_dim_type c5);
1085 The C<isl_dim_type> arguments dictate the order in which
1086 different kinds of variables appear in the resulting matrix
1087 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1088 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1090 The names of the domain and range spaces of a set or relation can be
1091 read off using the following functions.
1093 const char *isl_basic_set_get_tuple_name(
1094 __isl_keep isl_basic_set *bset);
1095 const char *isl_set_get_tuple_name(
1096 __isl_keep isl_set *set);
1097 const char *isl_basic_map_get_tuple_name(
1098 __isl_keep isl_basic_map *bmap,
1099 enum isl_dim_type type);
1100 const char *isl_map_get_tuple_name(
1101 __isl_keep isl_map *map,
1102 enum isl_dim_type type);
1104 As with C<isl_dim_get_tuple_name>, the value returned points to
1105 an internal data structure.
1106 The names of individual dimensions can be read off using
1107 the following functions.
1109 const char *isl_constraint_get_dim_name(
1110 __isl_keep isl_constraint *constraint,
1111 enum isl_dim_type type, unsigned pos);
1112 const char *isl_set_get_dim_name(
1113 __isl_keep isl_set *set,
1114 enum isl_dim_type type, unsigned pos);
1115 const char *isl_basic_map_get_dim_name(
1116 __isl_keep isl_basic_map *bmap,
1117 enum isl_dim_type type, unsigned pos);
1118 const char *isl_map_get_dim_name(
1119 __isl_keep isl_map *map,
1120 enum isl_dim_type type, unsigned pos);
1122 These functions are mostly useful to obtain the names
1127 =head3 Unary Properties
1133 The following functions test whether the given set or relation
1134 contains any integer points. The ``fast'' variants do not perform
1135 any computations, but simply check if the given set or relation
1136 is already known to be empty.
1138 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1139 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1140 int isl_set_is_empty(__isl_keep isl_set *set);
1141 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1142 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1143 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1144 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1145 int isl_map_is_empty(__isl_keep isl_map *map);
1146 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1148 =item * Universality
1150 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1151 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1152 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1154 =item * Single-valuedness
1156 int isl_map_is_single_valued(__isl_keep isl_map *map);
1160 int isl_map_is_bijective(__isl_keep isl_map *map);
1164 The followning functions check whether the domain of the given
1165 (basic) set is a wrapped relation.
1167 int isl_basic_set_is_wrapping(
1168 __isl_keep isl_basic_set *bset);
1169 int isl_set_is_wrapping(__isl_keep isl_set *set);
1173 =head3 Binary Properties
1179 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1180 __isl_keep isl_set *set2);
1181 int isl_set_is_equal(__isl_keep isl_set *set1,
1182 __isl_keep isl_set *set2);
1183 int isl_union_set_is_equal(
1184 __isl_keep isl_union_set *uset1,
1185 __isl_keep isl_union_set *uset2);
1186 int isl_basic_map_is_equal(
1187 __isl_keep isl_basic_map *bmap1,
1188 __isl_keep isl_basic_map *bmap2);
1189 int isl_map_is_equal(__isl_keep isl_map *map1,
1190 __isl_keep isl_map *map2);
1191 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1192 __isl_keep isl_map *map2);
1193 int isl_union_map_is_equal(
1194 __isl_keep isl_union_map *umap1,
1195 __isl_keep isl_union_map *umap2);
1197 =item * Disjointness
1199 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1200 __isl_keep isl_set *set2);
1204 int isl_set_is_subset(__isl_keep isl_set *set1,
1205 __isl_keep isl_set *set2);
1206 int isl_set_is_strict_subset(
1207 __isl_keep isl_set *set1,
1208 __isl_keep isl_set *set2);
1209 int isl_union_set_is_subset(
1210 __isl_keep isl_union_set *uset1,
1211 __isl_keep isl_union_set *uset2);
1212 int isl_union_set_is_strict_subset(
1213 __isl_keep isl_union_set *uset1,
1214 __isl_keep isl_union_set *uset2);
1215 int isl_basic_map_is_subset(
1216 __isl_keep isl_basic_map *bmap1,
1217 __isl_keep isl_basic_map *bmap2);
1218 int isl_basic_map_is_strict_subset(
1219 __isl_keep isl_basic_map *bmap1,
1220 __isl_keep isl_basic_map *bmap2);
1221 int isl_map_is_subset(
1222 __isl_keep isl_map *map1,
1223 __isl_keep isl_map *map2);
1224 int isl_map_is_strict_subset(
1225 __isl_keep isl_map *map1,
1226 __isl_keep isl_map *map2);
1227 int isl_union_map_is_subset(
1228 __isl_keep isl_union_map *umap1,
1229 __isl_keep isl_union_map *umap2);
1230 int isl_union_map_is_strict_subset(
1231 __isl_keep isl_union_map *umap1,
1232 __isl_keep isl_union_map *umap2);
1236 =head2 Unary Operations
1242 __isl_give isl_set *isl_set_complement(
1243 __isl_take isl_set *set);
1247 __isl_give isl_basic_map *isl_basic_map_reverse(
1248 __isl_take isl_basic_map *bmap);
1249 __isl_give isl_map *isl_map_reverse(
1250 __isl_take isl_map *map);
1251 __isl_give isl_union_map *isl_union_map_reverse(
1252 __isl_take isl_union_map *umap);
1256 __isl_give isl_basic_set *isl_basic_set_project_out(
1257 __isl_take isl_basic_set *bset,
1258 enum isl_dim_type type, unsigned first, unsigned n);
1259 __isl_give isl_basic_map *isl_basic_map_project_out(
1260 __isl_take isl_basic_map *bmap,
1261 enum isl_dim_type type, unsigned first, unsigned n);
1262 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1263 enum isl_dim_type type, unsigned first, unsigned n);
1264 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1265 enum isl_dim_type type, unsigned first, unsigned n);
1266 __isl_give isl_basic_set *isl_basic_map_domain(
1267 __isl_take isl_basic_map *bmap);
1268 __isl_give isl_basic_set *isl_basic_map_range(
1269 __isl_take isl_basic_map *bmap);
1270 __isl_give isl_set *isl_map_domain(
1271 __isl_take isl_map *bmap);
1272 __isl_give isl_set *isl_map_range(
1273 __isl_take isl_map *map);
1274 __isl_give isl_union_set *isl_union_map_domain(
1275 __isl_take isl_union_map *umap);
1276 __isl_give isl_union_set *isl_union_map_range(
1277 __isl_take isl_union_map *umap);
1279 __isl_give isl_basic_map *isl_basic_map_domain_map(
1280 __isl_take isl_basic_map *bmap);
1281 __isl_give isl_basic_map *isl_basic_map_range_map(
1282 __isl_take isl_basic_map *bmap);
1283 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1284 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1285 __isl_give isl_union_map *isl_union_map_domain_map(
1286 __isl_take isl_union_map *umap);
1287 __isl_give isl_union_map *isl_union_map_range_map(
1288 __isl_take isl_union_map *umap);
1290 The functions above construct a (basic, regular or union) relation
1291 that maps (a wrapped version of) the input relation to its domain or range.
1295 __isl_give isl_map *isl_set_identity(
1296 __isl_take isl_set *set);
1297 __isl_give isl_union_map *isl_union_set_identity(
1298 __isl_take isl_union_set *uset);
1300 Construct an identity relation on the given (union) set.
1304 __isl_give isl_basic_set *isl_basic_map_deltas(
1305 __isl_take isl_basic_map *bmap);
1306 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1307 __isl_give isl_union_set *isl_union_map_deltas(
1308 __isl_take isl_union_map *umap);
1310 These functions return a (basic) set containing the differences
1311 between image elements and corresponding domain elements in the input.
1315 Simplify the representation of a set or relation by trying
1316 to combine pairs of basic sets or relations into a single
1317 basic set or relation.
1319 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1320 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1321 __isl_give isl_union_set *isl_union_set_coalesce(
1322 __isl_take isl_union_set *uset);
1323 __isl_give isl_union_map *isl_union_map_coalesce(
1324 __isl_take isl_union_map *umap);
1326 =item * Detecting equalities
1328 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1329 __isl_take isl_basic_set *bset);
1330 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1331 __isl_take isl_basic_map *bmap);
1332 __isl_give isl_set *isl_set_detect_equalities(
1333 __isl_take isl_set *set);
1334 __isl_give isl_map *isl_map_detect_equalities(
1335 __isl_take isl_map *map);
1336 __isl_give isl_union_set *isl_union_set_detect_equalities(
1337 __isl_take isl_union_set *uset);
1338 __isl_give isl_union_map *isl_union_map_detect_equalities(
1339 __isl_take isl_union_map *umap);
1341 Simplify the representation of a set or relation by detecting implicit
1346 __isl_give isl_basic_set *isl_set_convex_hull(
1347 __isl_take isl_set *set);
1348 __isl_give isl_basic_map *isl_map_convex_hull(
1349 __isl_take isl_map *map);
1351 If the input set or relation has any existentially quantified
1352 variables, then the result of these operations is currently undefined.
1356 __isl_give isl_basic_set *isl_set_simple_hull(
1357 __isl_take isl_set *set);
1358 __isl_give isl_basic_map *isl_map_simple_hull(
1359 __isl_take isl_map *map);
1360 __isl_give isl_union_map *isl_union_map_simple_hull(
1361 __isl_take isl_union_map *umap);
1363 These functions compute a single basic set or relation
1364 that contains the whole input set or relation.
1365 In particular, the output is described by translates
1366 of the constraints describing the basic sets or relations in the input.
1370 (See \autoref{s:simple hull}.)
1376 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1377 __isl_take isl_basic_set *bset);
1378 __isl_give isl_basic_set *isl_set_affine_hull(
1379 __isl_take isl_set *set);
1380 __isl_give isl_union_set *isl_union_set_affine_hull(
1381 __isl_take isl_union_set *uset);
1382 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1383 __isl_take isl_basic_map *bmap);
1384 __isl_give isl_basic_map *isl_map_affine_hull(
1385 __isl_take isl_map *map);
1386 __isl_give isl_union_map *isl_union_map_affine_hull(
1387 __isl_take isl_union_map *umap);
1389 In case of union sets and relations, the affine hull is computed
1392 =item * Polyhedral hull
1394 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1395 __isl_take isl_set *set);
1396 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1397 __isl_take isl_map *map);
1398 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1399 __isl_take isl_union_set *uset);
1400 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1401 __isl_take isl_union_map *umap);
1403 These functions compute a single basic set or relation
1404 not involving any existentially quantified variables
1405 that contains the whole input set or relation.
1406 In case of union sets and relations, the polyhedral hull is computed
1411 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1412 unsigned param, int *exact);
1414 Compute a parametric representation for all positive powers I<k> of C<map>.
1415 The power I<k> is equated to the parameter at position C<param>.
1416 The result may be an overapproximation. If the result is exact,
1417 then C<*exact> is set to C<1>.
1418 The current implementation only produces exact results for particular
1419 cases of piecewise translations (i.e., piecewise uniform dependences).
1421 =item * Transitive closure
1423 __isl_give isl_map *isl_map_transitive_closure(
1424 __isl_take isl_map *map, int *exact);
1425 __isl_give isl_union_map *isl_union_map_transitive_closure(
1426 __isl_take isl_union_map *umap, int *exact);
1428 Compute the transitive closure of C<map>.
1429 The result may be an overapproximation. If the result is known to be exact,
1430 then C<*exact> is set to C<1>.
1431 The current implementation only produces exact results for particular
1432 cases of piecewise translations (i.e., piecewise uniform dependences).
1434 =item * Reaching path lengths
1436 __isl_give isl_map *isl_map_reaching_path_lengths(
1437 __isl_take isl_map *map, int *exact);
1439 Compute a relation that maps each element in the range of C<map>
1440 to the lengths of all paths composed of edges in C<map> that
1441 end up in the given element.
1442 The result may be an overapproximation. If the result is known to be exact,
1443 then C<*exact> is set to C<1>.
1444 To compute the I<maximal> path length, the resulting relation
1445 should be postprocessed by C<isl_map_lexmax>.
1446 In particular, if the input relation is a dependence relation
1447 (mapping sources to sinks), then the maximal path length corresponds
1448 to the free schedule.
1449 Note, however, that C<isl_map_lexmax> expects the maximum to be
1450 finite, so if the path lengths are unbounded (possibly due to
1451 the overapproximation), then you will get an error message.
1455 __isl_give isl_basic_set *isl_basic_map_wrap(
1456 __isl_take isl_basic_map *bmap);
1457 __isl_give isl_set *isl_map_wrap(
1458 __isl_take isl_map *map);
1459 __isl_give isl_union_set *isl_union_map_wrap(
1460 __isl_take isl_union_map *umap);
1461 __isl_give isl_basic_map *isl_basic_set_unwrap(
1462 __isl_take isl_basic_set *bset);
1463 __isl_give isl_map *isl_set_unwrap(
1464 __isl_take isl_set *set);
1465 __isl_give isl_union_map *isl_union_set_unwrap(
1466 __isl_take isl_union_set *uset);
1470 Remove any internal structure of domain (and range) of the given
1471 set or relation. If there is any such internal structure in the input,
1472 then the name of the space is also removed.
1474 __isl_give isl_basic_set *isl_basic_set_flatten(
1475 __isl_take isl_basic_set *bset);
1476 __isl_give isl_set *isl_set_flatten(
1477 __isl_take isl_set *set);
1478 __isl_give isl_basic_map *isl_basic_map_flatten(
1479 __isl_take isl_basic_map *bmap);
1480 __isl_give isl_map *isl_map_flatten(
1481 __isl_take isl_map *map);
1483 __isl_give isl_map *isl_set_flatten_map(
1484 __isl_take isl_set *set);
1486 The function above constructs a relation
1487 that maps the input set to a flattened version of the set.
1489 =item * Dimension manipulation
1491 __isl_give isl_set *isl_set_add_dims(
1492 __isl_take isl_set *set,
1493 enum isl_dim_type type, unsigned n);
1494 __isl_give isl_map *isl_map_add_dims(
1495 __isl_take isl_map *map,
1496 enum isl_dim_type type, unsigned n);
1498 It is usually not advisable to directly change the (input or output)
1499 space of a set or a relation as this removes the name and the internal
1500 structure of the space. However, the above functions can be useful
1501 to add new parameters.
1505 =head2 Binary Operations
1507 The two arguments of a binary operation not only need to live
1508 in the same C<isl_ctx>, they currently also need to have
1509 the same (number of) parameters.
1511 =head3 Basic Operations
1515 =item * Intersection
1517 __isl_give isl_basic_set *isl_basic_set_intersect(
1518 __isl_take isl_basic_set *bset1,
1519 __isl_take isl_basic_set *bset2);
1520 __isl_give isl_set *isl_set_intersect(
1521 __isl_take isl_set *set1,
1522 __isl_take isl_set *set2);
1523 __isl_give isl_union_set *isl_union_set_intersect(
1524 __isl_take isl_union_set *uset1,
1525 __isl_take isl_union_set *uset2);
1526 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1527 __isl_take isl_basic_map *bmap,
1528 __isl_take isl_basic_set *bset);
1529 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1530 __isl_take isl_basic_map *bmap,
1531 __isl_take isl_basic_set *bset);
1532 __isl_give isl_basic_map *isl_basic_map_intersect(
1533 __isl_take isl_basic_map *bmap1,
1534 __isl_take isl_basic_map *bmap2);
1535 __isl_give isl_map *isl_map_intersect_domain(
1536 __isl_take isl_map *map,
1537 __isl_take isl_set *set);
1538 __isl_give isl_map *isl_map_intersect_range(
1539 __isl_take isl_map *map,
1540 __isl_take isl_set *set);
1541 __isl_give isl_map *isl_map_intersect(
1542 __isl_take isl_map *map1,
1543 __isl_take isl_map *map2);
1544 __isl_give isl_union_map *isl_union_map_intersect_domain(
1545 __isl_take isl_union_map *umap,
1546 __isl_take isl_union_set *uset);
1547 __isl_give isl_union_map *isl_union_map_intersect_range(
1548 __isl_take isl_union_map *umap,
1549 __isl_take isl_union_set *uset);
1550 __isl_give isl_union_map *isl_union_map_intersect(
1551 __isl_take isl_union_map *umap1,
1552 __isl_take isl_union_map *umap2);
1556 __isl_give isl_set *isl_basic_set_union(
1557 __isl_take isl_basic_set *bset1,
1558 __isl_take isl_basic_set *bset2);
1559 __isl_give isl_map *isl_basic_map_union(
1560 __isl_take isl_basic_map *bmap1,
1561 __isl_take isl_basic_map *bmap2);
1562 __isl_give isl_set *isl_set_union(
1563 __isl_take isl_set *set1,
1564 __isl_take isl_set *set2);
1565 __isl_give isl_map *isl_map_union(
1566 __isl_take isl_map *map1,
1567 __isl_take isl_map *map2);
1568 __isl_give isl_union_set *isl_union_set_union(
1569 __isl_take isl_union_set *uset1,
1570 __isl_take isl_union_set *uset2);
1571 __isl_give isl_union_map *isl_union_map_union(
1572 __isl_take isl_union_map *umap1,
1573 __isl_take isl_union_map *umap2);
1575 =item * Set difference
1577 __isl_give isl_set *isl_set_subtract(
1578 __isl_take isl_set *set1,
1579 __isl_take isl_set *set2);
1580 __isl_give isl_map *isl_map_subtract(
1581 __isl_take isl_map *map1,
1582 __isl_take isl_map *map2);
1583 __isl_give isl_union_set *isl_union_set_subtract(
1584 __isl_take isl_union_set *uset1,
1585 __isl_take isl_union_set *uset2);
1586 __isl_give isl_union_map *isl_union_map_subtract(
1587 __isl_take isl_union_map *umap1,
1588 __isl_take isl_union_map *umap2);
1592 __isl_give isl_basic_set *isl_basic_set_apply(
1593 __isl_take isl_basic_set *bset,
1594 __isl_take isl_basic_map *bmap);
1595 __isl_give isl_set *isl_set_apply(
1596 __isl_take isl_set *set,
1597 __isl_take isl_map *map);
1598 __isl_give isl_union_set *isl_union_set_apply(
1599 __isl_take isl_union_set *uset,
1600 __isl_take isl_union_map *umap);
1601 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1602 __isl_take isl_basic_map *bmap1,
1603 __isl_take isl_basic_map *bmap2);
1604 __isl_give isl_basic_map *isl_basic_map_apply_range(
1605 __isl_take isl_basic_map *bmap1,
1606 __isl_take isl_basic_map *bmap2);
1607 __isl_give isl_map *isl_map_apply_domain(
1608 __isl_take isl_map *map1,
1609 __isl_take isl_map *map2);
1610 __isl_give isl_union_map *isl_union_map_apply_domain(
1611 __isl_take isl_union_map *umap1,
1612 __isl_take isl_union_map *umap2);
1613 __isl_give isl_map *isl_map_apply_range(
1614 __isl_take isl_map *map1,
1615 __isl_take isl_map *map2);
1616 __isl_give isl_union_map *isl_union_map_apply_range(
1617 __isl_take isl_union_map *umap1,
1618 __isl_take isl_union_map *umap2);
1620 =item * Cartesian Product
1622 __isl_give isl_set *isl_set_product(
1623 __isl_take isl_set *set1,
1624 __isl_take isl_set *set2);
1625 __isl_give isl_union_set *isl_union_set_product(
1626 __isl_take isl_union_set *uset1,
1627 __isl_take isl_union_set *uset2);
1628 __isl_give isl_basic_map *isl_basic_map_range_product(
1629 __isl_take isl_basic_map *bmap1,
1630 __isl_take isl_basic_map *bmap2);
1631 __isl_give isl_map *isl_map_range_product(
1632 __isl_take isl_map *map1,
1633 __isl_take isl_map *map2);
1634 __isl_give isl_union_map *isl_union_map_range_product(
1635 __isl_take isl_union_map *umap1,
1636 __isl_take isl_union_map *umap2);
1637 __isl_give isl_map *isl_map_product(
1638 __isl_take isl_map *map1,
1639 __isl_take isl_map *map2);
1640 __isl_give isl_union_map *isl_union_map_product(
1641 __isl_take isl_union_map *umap1,
1642 __isl_take isl_union_map *umap2);
1644 The above functions compute the cross product of the given
1645 sets or relations. The domains and ranges of the results
1646 are wrapped maps between domains and ranges of the inputs.
1647 To obtain a ``flat'' product, use the following functions
1650 __isl_give isl_basic_set *isl_basic_set_flat_product(
1651 __isl_take isl_basic_set *bset1,
1652 __isl_take isl_basic_set *bset2);
1653 __isl_give isl_set *isl_set_flat_product(
1654 __isl_take isl_set *set1,
1655 __isl_take isl_set *set2);
1656 __isl_give isl_basic_map *isl_basic_map_flat_product(
1657 __isl_take isl_basic_map *bmap1,
1658 __isl_take isl_basic_map *bmap2);
1659 __isl_give isl_map *isl_map_flat_product(
1660 __isl_take isl_map *map1,
1661 __isl_take isl_map *map2);
1663 =item * Simplification
1665 __isl_give isl_basic_set *isl_basic_set_gist(
1666 __isl_take isl_basic_set *bset,
1667 __isl_take isl_basic_set *context);
1668 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1669 __isl_take isl_set *context);
1670 __isl_give isl_union_set *isl_union_set_gist(
1671 __isl_take isl_union_set *uset,
1672 __isl_take isl_union_set *context);
1673 __isl_give isl_basic_map *isl_basic_map_gist(
1674 __isl_take isl_basic_map *bmap,
1675 __isl_take isl_basic_map *context);
1676 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1677 __isl_take isl_map *context);
1678 __isl_give isl_union_map *isl_union_map_gist(
1679 __isl_take isl_union_map *umap,
1680 __isl_take isl_union_map *context);
1682 The gist operation returns a set or relation that has the
1683 same intersection with the context as the input set or relation.
1684 Any implicit equality in the intersection is made explicit in the result,
1685 while all inequalities that are redundant with respect to the intersection
1687 In case of union sets and relations, the gist operation is performed
1692 =head3 Lexicographic Optimization
1694 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1695 the following functions
1696 compute a set that contains the lexicographic minimum or maximum
1697 of the elements in C<set> (or C<bset>) for those values of the parameters
1698 that satisfy C<dom>.
1699 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1700 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1702 In other words, the union of the parameter values
1703 for which the result is non-empty and of C<*empty>
1706 __isl_give isl_set *isl_basic_set_partial_lexmin(
1707 __isl_take isl_basic_set *bset,
1708 __isl_take isl_basic_set *dom,
1709 __isl_give isl_set **empty);
1710 __isl_give isl_set *isl_basic_set_partial_lexmax(
1711 __isl_take isl_basic_set *bset,
1712 __isl_take isl_basic_set *dom,
1713 __isl_give isl_set **empty);
1714 __isl_give isl_set *isl_set_partial_lexmin(
1715 __isl_take isl_set *set, __isl_take isl_set *dom,
1716 __isl_give isl_set **empty);
1717 __isl_give isl_set *isl_set_partial_lexmax(
1718 __isl_take isl_set *set, __isl_take isl_set *dom,
1719 __isl_give isl_set **empty);
1721 Given a (basic) set C<set> (or C<bset>), the following functions simply
1722 return a set containing the lexicographic minimum or maximum
1723 of the elements in C<set> (or C<bset>).
1724 In case of union sets, the optimum is computed per space.
1726 __isl_give isl_set *isl_basic_set_lexmin(
1727 __isl_take isl_basic_set *bset);
1728 __isl_give isl_set *isl_basic_set_lexmax(
1729 __isl_take isl_basic_set *bset);
1730 __isl_give isl_set *isl_set_lexmin(
1731 __isl_take isl_set *set);
1732 __isl_give isl_set *isl_set_lexmax(
1733 __isl_take isl_set *set);
1734 __isl_give isl_union_set *isl_union_set_lexmin(
1735 __isl_take isl_union_set *uset);
1736 __isl_give isl_union_set *isl_union_set_lexmax(
1737 __isl_take isl_union_set *uset);
1739 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1740 the following functions
1741 compute a relation that maps each element of C<dom>
1742 to the single lexicographic minimum or maximum
1743 of the elements that are associated to that same
1744 element in C<map> (or C<bmap>).
1745 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1746 that contains the elements in C<dom> that do not map
1747 to any elements in C<map> (or C<bmap>).
1748 In other words, the union of the domain of the result and of C<*empty>
1751 __isl_give isl_map *isl_basic_map_partial_lexmax(
1752 __isl_take isl_basic_map *bmap,
1753 __isl_take isl_basic_set *dom,
1754 __isl_give isl_set **empty);
1755 __isl_give isl_map *isl_basic_map_partial_lexmin(
1756 __isl_take isl_basic_map *bmap,
1757 __isl_take isl_basic_set *dom,
1758 __isl_give isl_set **empty);
1759 __isl_give isl_map *isl_map_partial_lexmax(
1760 __isl_take isl_map *map, __isl_take isl_set *dom,
1761 __isl_give isl_set **empty);
1762 __isl_give isl_map *isl_map_partial_lexmin(
1763 __isl_take isl_map *map, __isl_take isl_set *dom,
1764 __isl_give isl_set **empty);
1766 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1767 return a map mapping each element in the domain of
1768 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1769 of all elements associated to that element.
1770 In case of union relations, the optimum is computed per space.
1772 __isl_give isl_map *isl_basic_map_lexmin(
1773 __isl_take isl_basic_map *bmap);
1774 __isl_give isl_map *isl_basic_map_lexmax(
1775 __isl_take isl_basic_map *bmap);
1776 __isl_give isl_map *isl_map_lexmin(
1777 __isl_take isl_map *map);
1778 __isl_give isl_map *isl_map_lexmax(
1779 __isl_take isl_map *map);
1780 __isl_give isl_union_map *isl_union_map_lexmin(
1781 __isl_take isl_union_map *umap);
1782 __isl_give isl_union_map *isl_union_map_lexmax(
1783 __isl_take isl_union_map *umap);
1787 Matrices can be created, copied and freed using the following functions.
1789 #include <isl/mat.h>
1790 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1791 unsigned n_row, unsigned n_col);
1792 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1793 void isl_mat_free(__isl_take isl_mat *mat);
1795 Note that the elements of a newly created matrix may have arbitrary values.
1796 The elements can be changed and inspected using the following functions.
1798 int isl_mat_rows(__isl_keep isl_mat *mat);
1799 int isl_mat_cols(__isl_keep isl_mat *mat);
1800 int isl_mat_get_element(__isl_keep isl_mat *mat,
1801 int row, int col, isl_int *v);
1802 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1803 int row, int col, isl_int v);
1805 C<isl_mat_get_element> will return a negative value if anything went wrong.
1806 In that case, the value of C<*v> is undefined.
1808 The following function can be used to compute the (right) inverse
1809 of a matrix, i.e., a matrix such that the product of the original
1810 and the inverse (in that order) is a multiple of the identity matrix.
1811 The input matrix is assumed to be of full row-rank.
1813 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1815 The following function can be used to compute the (right) kernel
1816 (or null space) of a matrix, i.e., a matrix such that the product of
1817 the original and the kernel (in that order) is the zero matrix.
1819 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1823 Points are elements of a set. They can be used to construct
1824 simple sets (boxes) or they can be used to represent the
1825 individual elements of a set.
1826 The zero point (the origin) can be created using
1828 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1830 The coordinates of a point can be inspected, set and changed
1833 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1834 enum isl_dim_type type, int pos, isl_int *v);
1835 __isl_give isl_point *isl_point_set_coordinate(
1836 __isl_take isl_point *pnt,
1837 enum isl_dim_type type, int pos, isl_int v);
1839 __isl_give isl_point *isl_point_add_ui(
1840 __isl_take isl_point *pnt,
1841 enum isl_dim_type type, int pos, unsigned val);
1842 __isl_give isl_point *isl_point_sub_ui(
1843 __isl_take isl_point *pnt,
1844 enum isl_dim_type type, int pos, unsigned val);
1846 Points can be copied or freed using
1848 __isl_give isl_point *isl_point_copy(
1849 __isl_keep isl_point *pnt);
1850 void isl_point_free(__isl_take isl_point *pnt);
1852 A singleton set can be created from a point using
1854 __isl_give isl_basic_set *isl_basic_set_from_point(
1855 __isl_take isl_point *pnt);
1856 __isl_give isl_set *isl_set_from_point(
1857 __isl_take isl_point *pnt);
1859 and a box can be created from two opposite extremal points using
1861 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1862 __isl_take isl_point *pnt1,
1863 __isl_take isl_point *pnt2);
1864 __isl_give isl_set *isl_set_box_from_points(
1865 __isl_take isl_point *pnt1,
1866 __isl_take isl_point *pnt2);
1868 All elements of a B<bounded> (union) set can be enumerated using
1869 the following functions.
1871 int isl_set_foreach_point(__isl_keep isl_set *set,
1872 int (*fn)(__isl_take isl_point *pnt, void *user),
1874 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1875 int (*fn)(__isl_take isl_point *pnt, void *user),
1878 The function C<fn> is called for each integer point in
1879 C<set> with as second argument the last argument of
1880 the C<isl_set_foreach_point> call. The function C<fn>
1881 should return C<0> on success and C<-1> on failure.
1882 In the latter case, C<isl_set_foreach_point> will stop
1883 enumerating and return C<-1> as well.
1884 If the enumeration is performed successfully and to completion,
1885 then C<isl_set_foreach_point> returns C<0>.
1887 To obtain a single point of a (basic) set, use
1889 __isl_give isl_point *isl_basic_set_sample_point(
1890 __isl_take isl_basic_set *bset);
1891 __isl_give isl_point *isl_set_sample_point(
1892 __isl_take isl_set *set);
1894 If C<set> does not contain any (integer) points, then the
1895 resulting point will be ``void'', a property that can be
1898 int isl_point_is_void(__isl_keep isl_point *pnt);
1900 =head2 Piecewise Quasipolynomials
1902 A piecewise quasipolynomial is a particular kind of function that maps
1903 a parametric point to a rational value.
1904 More specifically, a quasipolynomial is a polynomial expression in greatest
1905 integer parts of affine expressions of parameters and variables.
1906 A piecewise quasipolynomial is a subdivision of a given parametric
1907 domain into disjoint cells with a quasipolynomial associated to
1908 each cell. The value of the piecewise quasipolynomial at a given
1909 point is the value of the quasipolynomial associated to the cell
1910 that contains the point. Outside of the union of cells,
1911 the value is assumed to be zero.
1912 For example, the piecewise quasipolynomial
1914 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1916 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1917 A given piecewise quasipolynomial has a fixed domain dimension.
1918 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1919 defined over different domains.
1920 Piecewise quasipolynomials are mainly used by the C<barvinok>
1921 library for representing the number of elements in a parametric set or map.
1922 For example, the piecewise quasipolynomial above represents
1923 the number of points in the map
1925 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1927 =head3 Printing (Piecewise) Quasipolynomials
1929 Quasipolynomials and piecewise quasipolynomials can be printed
1930 using the following functions.
1932 __isl_give isl_printer *isl_printer_print_qpolynomial(
1933 __isl_take isl_printer *p,
1934 __isl_keep isl_qpolynomial *qp);
1936 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1937 __isl_take isl_printer *p,
1938 __isl_keep isl_pw_qpolynomial *pwqp);
1940 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1941 __isl_take isl_printer *p,
1942 __isl_keep isl_union_pw_qpolynomial *upwqp);
1944 The output format of the printer
1945 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1946 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1948 In case of printing in C<ISL_FORMAT_C>, the user may want
1949 to set the names of all dimensions
1951 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1952 __isl_take isl_qpolynomial *qp,
1953 enum isl_dim_type type, unsigned pos,
1955 __isl_give isl_pw_qpolynomial *
1956 isl_pw_qpolynomial_set_dim_name(
1957 __isl_take isl_pw_qpolynomial *pwqp,
1958 enum isl_dim_type type, unsigned pos,
1961 =head3 Creating New (Piecewise) Quasipolynomials
1963 Some simple quasipolynomials can be created using the following functions.
1964 More complicated quasipolynomials can be created by applying
1965 operations such as addition and multiplication
1966 on the resulting quasipolynomials
1968 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
1969 __isl_take isl_dim *dim);
1970 __isl_give isl_qpolynomial *isl_qpolynomial_one(
1971 __isl_take isl_dim *dim);
1972 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
1973 __isl_take isl_dim *dim);
1974 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
1975 __isl_take isl_dim *dim);
1976 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
1977 __isl_take isl_dim *dim);
1978 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
1979 __isl_take isl_dim *dim,
1980 const isl_int n, const isl_int d);
1981 __isl_give isl_qpolynomial *isl_qpolynomial_div(
1982 __isl_take isl_div *div);
1983 __isl_give isl_qpolynomial *isl_qpolynomial_var(
1984 __isl_take isl_dim *dim,
1985 enum isl_dim_type type, unsigned pos);
1987 The zero piecewise quasipolynomial or a piecewise quasipolynomial
1988 with a single cell can be created using the following functions.
1989 Multiple of these single cell piecewise quasipolynomials can
1990 be combined to create more complicated piecewise quasipolynomials.
1992 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
1993 __isl_take isl_dim *dim);
1994 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
1995 __isl_take isl_set *set,
1996 __isl_take isl_qpolynomial *qp);
1998 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
1999 __isl_take isl_dim *dim);
2000 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2001 __isl_take isl_pw_qpolynomial *pwqp);
2002 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2003 __isl_take isl_union_pw_qpolynomial *upwqp,
2004 __isl_take isl_pw_qpolynomial *pwqp);
2006 Quasipolynomials can be copied and freed again using the following
2009 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2010 __isl_keep isl_qpolynomial *qp);
2011 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2013 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2014 __isl_keep isl_pw_qpolynomial *pwqp);
2015 void isl_pw_qpolynomial_free(
2016 __isl_take isl_pw_qpolynomial *pwqp);
2018 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2019 __isl_keep isl_union_pw_qpolynomial *upwqp);
2020 void isl_union_pw_qpolynomial_free(
2021 __isl_take isl_union_pw_qpolynomial *upwqp);
2023 =head3 Inspecting (Piecewise) Quasipolynomials
2025 To iterate over all piecewise quasipolynomials in a union
2026 piecewise quasipolynomial, use the following function
2028 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2029 __isl_keep isl_union_pw_qpolynomial *upwqp,
2030 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2033 To extract the piecewise quasipolynomial from a union with a given dimension
2036 __isl_give isl_pw_qpolynomial *
2037 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2038 __isl_keep isl_union_pw_qpolynomial *upwqp,
2039 __isl_take isl_dim *dim);
2041 To iterate over the cells in a piecewise quasipolynomial,
2042 use either of the following two functions
2044 int isl_pw_qpolynomial_foreach_piece(
2045 __isl_keep isl_pw_qpolynomial *pwqp,
2046 int (*fn)(__isl_take isl_set *set,
2047 __isl_take isl_qpolynomial *qp,
2048 void *user), void *user);
2049 int isl_pw_qpolynomial_foreach_lifted_piece(
2050 __isl_keep isl_pw_qpolynomial *pwqp,
2051 int (*fn)(__isl_take isl_set *set,
2052 __isl_take isl_qpolynomial *qp,
2053 void *user), void *user);
2055 As usual, the function C<fn> should return C<0> on success
2056 and C<-1> on failure. The difference between
2057 C<isl_pw_qpolynomial_foreach_piece> and
2058 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2059 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2060 compute unique representations for all existentially quantified
2061 variables and then turn these existentially quantified variables
2062 into extra set variables, adapting the associated quasipolynomial
2063 accordingly. This means that the C<set> passed to C<fn>
2064 will not have any existentially quantified variables, but that
2065 the dimensions of the sets may be different for different
2066 invocations of C<fn>.
2068 To iterate over all terms in a quasipolynomial,
2071 int isl_qpolynomial_foreach_term(
2072 __isl_keep isl_qpolynomial *qp,
2073 int (*fn)(__isl_take isl_term *term,
2074 void *user), void *user);
2076 The terms themselves can be inspected and freed using
2079 unsigned isl_term_dim(__isl_keep isl_term *term,
2080 enum isl_dim_type type);
2081 void isl_term_get_num(__isl_keep isl_term *term,
2083 void isl_term_get_den(__isl_keep isl_term *term,
2085 int isl_term_get_exp(__isl_keep isl_term *term,
2086 enum isl_dim_type type, unsigned pos);
2087 __isl_give isl_div *isl_term_get_div(
2088 __isl_keep isl_term *term, unsigned pos);
2089 void isl_term_free(__isl_take isl_term *term);
2091 Each term is a product of parameters, set variables and
2092 integer divisions. The function C<isl_term_get_exp>
2093 returns the exponent of a given dimensions in the given term.
2094 The C<isl_int>s in the arguments of C<isl_term_get_num>
2095 and C<isl_term_get_den> need to have been initialized
2096 using C<isl_int_init> before calling these functions.
2098 =head3 Properties of (Piecewise) Quasipolynomials
2100 To check whether a quasipolynomial is actually a constant,
2101 use the following function.
2103 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2104 isl_int *n, isl_int *d);
2106 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2107 then the numerator and denominator of the constant
2108 are returned in C<*n> and C<*d>, respectively.
2110 =head3 Operations on (Piecewise) Quasipolynomials
2112 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2113 __isl_take isl_qpolynomial *qp);
2114 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2115 __isl_take isl_qpolynomial *qp1,
2116 __isl_take isl_qpolynomial *qp2);
2117 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2118 __isl_take isl_qpolynomial *qp1,
2119 __isl_take isl_qpolynomial *qp2);
2120 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2121 __isl_take isl_qpolynomial *qp1,
2122 __isl_take isl_qpolynomial *qp2);
2123 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2124 __isl_take isl_qpolynomial *qp, unsigned exponent);
2126 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2127 __isl_take isl_pw_qpolynomial *pwqp1,
2128 __isl_take isl_pw_qpolynomial *pwqp2);
2129 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2130 __isl_take isl_pw_qpolynomial *pwqp1,
2131 __isl_take isl_pw_qpolynomial *pwqp2);
2132 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2133 __isl_take isl_pw_qpolynomial *pwqp1,
2134 __isl_take isl_pw_qpolynomial *pwqp2);
2135 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2136 __isl_take isl_pw_qpolynomial *pwqp);
2137 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2138 __isl_take isl_pw_qpolynomial *pwqp1,
2139 __isl_take isl_pw_qpolynomial *pwqp2);
2141 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2142 __isl_take isl_union_pw_qpolynomial *upwqp1,
2143 __isl_take isl_union_pw_qpolynomial *upwqp2);
2144 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2145 __isl_take isl_union_pw_qpolynomial *upwqp1,
2146 __isl_take isl_union_pw_qpolynomial *upwqp2);
2147 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2148 __isl_take isl_union_pw_qpolynomial *upwqp1,
2149 __isl_take isl_union_pw_qpolynomial *upwqp2);
2151 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2152 __isl_take isl_pw_qpolynomial *pwqp,
2153 __isl_take isl_point *pnt);
2155 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2156 __isl_take isl_union_pw_qpolynomial *upwqp,
2157 __isl_take isl_point *pnt);
2159 __isl_give isl_set *isl_pw_qpolynomial_domain(
2160 __isl_take isl_pw_qpolynomial *pwqp);
2161 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2162 __isl_take isl_pw_qpolynomial *pwpq,
2163 __isl_take isl_set *set);
2165 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2166 __isl_take isl_union_pw_qpolynomial *upwqp);
2167 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2168 __isl_take isl_union_pw_qpolynomial *upwpq,
2169 __isl_take isl_union_set *uset);
2171 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2172 __isl_take isl_union_pw_qpolynomial *upwqp);
2174 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2175 __isl_take isl_pw_qpolynomial *pwqp,
2176 __isl_take isl_set *context);
2178 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2179 __isl_take isl_union_pw_qpolynomial *upwqp,
2180 __isl_take isl_union_set *context);
2182 The gist operation applies the gist operation to each of
2183 the cells in the domain of the input piecewise quasipolynomial.
2184 The context is also exploited
2185 to simplify the quasipolynomials associated to each cell.
2187 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2188 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2189 __isl_give isl_union_pw_qpolynomial *
2190 isl_union_pw_qpolynomial_to_polynomial(
2191 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2193 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2194 the polynomial will be an overapproximation. If C<sign> is negative,
2195 it will be an underapproximation. If C<sign> is zero, the approximation
2196 will lie somewhere in between.
2198 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2200 A piecewise quasipolynomial reduction is a piecewise
2201 reduction (or fold) of quasipolynomials.
2202 In particular, the reduction can be maximum or a minimum.
2203 The objects are mainly used to represent the result of
2204 an upper or lower bound on a quasipolynomial over its domain,
2205 i.e., as the result of the following function.
2207 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2208 __isl_take isl_pw_qpolynomial *pwqp,
2209 enum isl_fold type, int *tight);
2211 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2212 __isl_take isl_union_pw_qpolynomial *upwqp,
2213 enum isl_fold type, int *tight);
2215 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2216 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2217 is the returned bound is known be tight, i.e., for each value
2218 of the parameters there is at least
2219 one element in the domain that reaches the bound.
2220 If the domain of C<pwqp> is not wrapping, then the bound is computed
2221 over all elements in that domain and the result has a purely parametric
2222 domain. If the domain of C<pwqp> is wrapping, then the bound is
2223 computed over the range of the wrapped relation. The domain of the
2224 wrapped relation becomes the domain of the result.
2226 A (piecewise) quasipolynomial reduction can be copied or freed using the
2227 following functions.
2229 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2230 __isl_keep isl_qpolynomial_fold *fold);
2231 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2232 __isl_keep isl_pw_qpolynomial_fold *pwf);
2233 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2234 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2235 void isl_qpolynomial_fold_free(
2236 __isl_take isl_qpolynomial_fold *fold);
2237 void isl_pw_qpolynomial_fold_free(
2238 __isl_take isl_pw_qpolynomial_fold *pwf);
2239 void isl_union_pw_qpolynomial_fold_free(
2240 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2242 =head3 Printing Piecewise Quasipolynomial Reductions
2244 Piecewise quasipolynomial reductions can be printed
2245 using the following function.
2247 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2248 __isl_take isl_printer *p,
2249 __isl_keep isl_pw_qpolynomial_fold *pwf);
2250 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2251 __isl_take isl_printer *p,
2252 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2254 For C<isl_printer_print_pw_qpolynomial_fold>,
2255 output format of the printer
2256 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2257 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2258 output format of the printer
2259 needs to be set to C<ISL_FORMAT_ISL>.
2260 In case of printing in C<ISL_FORMAT_C>, the user may want
2261 to set the names of all dimensions
2263 __isl_give isl_pw_qpolynomial_fold *
2264 isl_pw_qpolynomial_fold_set_dim_name(
2265 __isl_take isl_pw_qpolynomial_fold *pwf,
2266 enum isl_dim_type type, unsigned pos,
2269 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2271 To iterate over all piecewise quasipolynomial reductions in a union
2272 piecewise quasipolynomial reduction, use the following function
2274 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2275 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2276 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2277 void *user), void *user);
2279 To iterate over the cells in a piecewise quasipolynomial reduction,
2280 use either of the following two functions
2282 int isl_pw_qpolynomial_fold_foreach_piece(
2283 __isl_keep isl_pw_qpolynomial_fold *pwf,
2284 int (*fn)(__isl_take isl_set *set,
2285 __isl_take isl_qpolynomial_fold *fold,
2286 void *user), void *user);
2287 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2288 __isl_keep isl_pw_qpolynomial_fold *pwf,
2289 int (*fn)(__isl_take isl_set *set,
2290 __isl_take isl_qpolynomial_fold *fold,
2291 void *user), void *user);
2293 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2294 of the difference between these two functions.
2296 To iterate over all quasipolynomials in a reduction, use
2298 int isl_qpolynomial_fold_foreach_qpolynomial(
2299 __isl_keep isl_qpolynomial_fold *fold,
2300 int (*fn)(__isl_take isl_qpolynomial *qp,
2301 void *user), void *user);
2303 =head3 Operations on Piecewise Quasipolynomial Reductions
2305 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2306 __isl_take isl_pw_qpolynomial_fold *pwf1,
2307 __isl_take isl_pw_qpolynomial_fold *pwf2);
2309 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2310 __isl_take isl_pw_qpolynomial_fold *pwf1,
2311 __isl_take isl_pw_qpolynomial_fold *pwf2);
2313 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2314 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2315 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2317 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2318 __isl_take isl_pw_qpolynomial_fold *pwf,
2319 __isl_take isl_point *pnt);
2321 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2322 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2323 __isl_take isl_point *pnt);
2325 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2326 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2327 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2328 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2329 __isl_take isl_union_set *uset);
2331 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2332 __isl_take isl_pw_qpolynomial_fold *pwf);
2334 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2335 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2337 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2338 __isl_take isl_pw_qpolynomial_fold *pwf,
2339 __isl_take isl_set *context);
2341 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2342 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2343 __isl_take isl_union_set *context);
2345 The gist operation applies the gist operation to each of
2346 the cells in the domain of the input piecewise quasipolynomial reduction.
2347 In future, the operation will also exploit the context
2348 to simplify the quasipolynomial reductions associated to each cell.
2350 __isl_give isl_pw_qpolynomial_fold *
2351 isl_set_apply_pw_qpolynomial_fold(
2352 __isl_take isl_set *set,
2353 __isl_take isl_pw_qpolynomial_fold *pwf,
2355 __isl_give isl_pw_qpolynomial_fold *
2356 isl_map_apply_pw_qpolynomial_fold(
2357 __isl_take isl_map *map,
2358 __isl_take isl_pw_qpolynomial_fold *pwf,
2360 __isl_give isl_union_pw_qpolynomial_fold *
2361 isl_union_set_apply_union_pw_qpolynomial_fold(
2362 __isl_take isl_union_set *uset,
2363 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2365 __isl_give isl_union_pw_qpolynomial_fold *
2366 isl_union_map_apply_union_pw_qpolynomial_fold(
2367 __isl_take isl_union_map *umap,
2368 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2371 The functions taking a map
2372 compose the given map with the given piecewise quasipolynomial reduction.
2373 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2374 over all elements in the intersection of the range of the map
2375 and the domain of the piecewise quasipolynomial reduction
2376 as a function of an element in the domain of the map.
2377 The functions taking a set compute a bound over all elements in the
2378 intersection of the set and the domain of the
2379 piecewise quasipolynomial reduction.
2381 =head2 Dependence Analysis
2383 C<isl> contains specialized functionality for performing
2384 array dataflow analysis. That is, given a I<sink> access relation
2385 and a collection of possible I<source> access relations,
2386 C<isl> can compute relations that describe
2387 for each iteration of the sink access, which iteration
2388 of which of the source access relations was the last
2389 to access the same data element before the given iteration
2391 To compute standard flow dependences, the sink should be
2392 a read, while the sources should be writes.
2393 If any of the source accesses are marked as being I<may>
2394 accesses, then there will be a dependence to the last
2395 I<must> access B<and> to any I<may> access that follows
2396 this last I<must> access.
2397 In particular, if I<all> sources are I<may> accesses,
2398 then memory based dependence analysis is performed.
2399 If, on the other hand, all sources are I<must> accesses,
2400 then value based dependence analysis is performed.
2402 #include <isl/flow.h>
2404 typedef int (*isl_access_level_before)(void *first, void *second);
2406 __isl_give isl_access_info *isl_access_info_alloc(
2407 __isl_take isl_map *sink,
2408 void *sink_user, isl_access_level_before fn,
2410 __isl_give isl_access_info *isl_access_info_add_source(
2411 __isl_take isl_access_info *acc,
2412 __isl_take isl_map *source, int must,
2414 void isl_access_info_free(__isl_take isl_access_info *acc);
2416 __isl_give isl_flow *isl_access_info_compute_flow(
2417 __isl_take isl_access_info *acc);
2419 int isl_flow_foreach(__isl_keep isl_flow *deps,
2420 int (*fn)(__isl_take isl_map *dep, int must,
2421 void *dep_user, void *user),
2423 __isl_give isl_map *isl_flow_get_no_source(
2424 __isl_keep isl_flow *deps, int must);
2425 void isl_flow_free(__isl_take isl_flow *deps);
2427 The function C<isl_access_info_compute_flow> performs the actual
2428 dependence analysis. The other functions are used to construct
2429 the input for this function or to read off the output.
2431 The input is collected in an C<isl_access_info>, which can
2432 be created through a call to C<isl_access_info_alloc>.
2433 The arguments to this functions are the sink access relation
2434 C<sink>, a token C<sink_user> used to identify the sink
2435 access to the user, a callback function for specifying the
2436 relative order of source and sink accesses, and the number
2437 of source access relations that will be added.
2438 The callback function has type C<int (*)(void *first, void *second)>.
2439 The function is called with two user supplied tokens identifying
2440 either a source or the sink and it should return the shared nesting
2441 level and the relative order of the two accesses.
2442 In particular, let I<n> be the number of loops shared by
2443 the two accesses. If C<first> precedes C<second> textually,
2444 then the function should return I<2 * n + 1>; otherwise,
2445 it should return I<2 * n>.
2446 The sources can be added to the C<isl_access_info> by performing
2447 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2448 C<must> indicates whether the source is a I<must> access
2449 or a I<may> access. Note that a multi-valued access relation
2450 should only be marked I<must> if every iteration in the domain
2451 of the relation accesses I<all> elements in its image.
2452 The C<source_user> token is again used to identify
2453 the source access. The range of the source access relation
2454 C<source> should have the same dimension as the range
2455 of the sink access relation.
2456 The C<isl_access_info_free> function should usually not be
2457 called explicitly, because it is called implicitly by
2458 C<isl_access_info_compute_flow>.
2460 The result of the dependence analysis is collected in an
2461 C<isl_flow>. There may be elements of
2462 the sink access for which no preceding source access could be
2463 found or for which all preceding sources are I<may> accesses.
2464 The relations containing these elements can be obtained through
2465 calls to C<isl_flow_get_no_source>, the first with C<must> set
2466 and the second with C<must> unset.
2467 In the case of standard flow dependence analysis,
2468 with the sink a read and the sources I<must> writes,
2469 the first relation corresponds to the reads from uninitialized
2470 array elements and the second relation is empty.
2471 The actual flow dependences can be extracted using
2472 C<isl_flow_foreach>. This function will call the user-specified
2473 callback function C<fn> for each B<non-empty> dependence between
2474 a source and the sink. The callback function is called
2475 with four arguments, the actual flow dependence relation
2476 mapping source iterations to sink iterations, a boolean that
2477 indicates whether it is a I<must> or I<may> dependence, a token
2478 identifying the source and an additional C<void *> with value
2479 equal to the third argument of the C<isl_flow_foreach> call.
2480 A dependence is marked I<must> if it originates from a I<must>
2481 source and if it is not followed by any I<may> sources.
2483 After finishing with an C<isl_flow>, the user should call
2484 C<isl_flow_free> to free all associated memory.
2486 A higher-level interface to dependence analysis is provided
2487 by the following function.
2489 #include <isl/flow.h>
2491 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2492 __isl_take isl_union_map *must_source,
2493 __isl_take isl_union_map *may_source,
2494 __isl_take isl_union_map *schedule,
2495 __isl_give isl_union_map **must_dep,
2496 __isl_give isl_union_map **may_dep,
2497 __isl_give isl_union_map **must_no_source,
2498 __isl_give isl_union_map **may_no_source);
2500 The arrays are identified by the tuple names of the ranges
2501 of the accesses. The iteration domains by the tuple names
2502 of the domains of the accesses and of the schedule.
2503 The relative order of the iteration domains is given by the
2504 schedule. The relations returned through C<must_no_source>
2505 and C<may_no_source> are subsets of C<sink>.
2506 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2507 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2508 any of the other arguments is treated as an error.
2510 =head2 Parametric Vertex Enumeration
2512 The parametric vertex enumeration described in this section
2513 is mainly intended to be used internally and by the C<barvinok>
2516 #include <isl/vertices.h>
2517 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2518 __isl_keep isl_basic_set *bset);
2520 The function C<isl_basic_set_compute_vertices> performs the
2521 actual computation of the parametric vertices and the chamber
2522 decomposition and store the result in an C<isl_vertices> object.
2523 This information can be queried by either iterating over all
2524 the vertices or iterating over all the chambers or cells
2525 and then iterating over all vertices that are active on the chamber.
2527 int isl_vertices_foreach_vertex(
2528 __isl_keep isl_vertices *vertices,
2529 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2532 int isl_vertices_foreach_cell(
2533 __isl_keep isl_vertices *vertices,
2534 int (*fn)(__isl_take isl_cell *cell, void *user),
2536 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2537 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2540 Other operations that can be performed on an C<isl_vertices> object are
2543 isl_ctx *isl_vertices_get_ctx(
2544 __isl_keep isl_vertices *vertices);
2545 int isl_vertices_get_n_vertices(
2546 __isl_keep isl_vertices *vertices);
2547 void isl_vertices_free(__isl_take isl_vertices *vertices);
2549 Vertices can be inspected and destroyed using the following functions.
2551 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2552 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2553 __isl_give isl_basic_set *isl_vertex_get_domain(
2554 __isl_keep isl_vertex *vertex);
2555 __isl_give isl_basic_set *isl_vertex_get_expr(
2556 __isl_keep isl_vertex *vertex);
2557 void isl_vertex_free(__isl_take isl_vertex *vertex);
2559 C<isl_vertex_get_expr> returns a singleton parametric set describing
2560 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2562 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2563 B<rational> basic sets, so they should mainly be used for inspection
2564 and should not be mixed with integer sets.
2566 Chambers can be inspected and destroyed using the following functions.
2568 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2569 __isl_give isl_basic_set *isl_cell_get_domain(
2570 __isl_keep isl_cell *cell);
2571 void isl_cell_free(__isl_take isl_cell *cell);
2575 Although C<isl> is mainly meant to be used as a library,
2576 it also contains some basic applications that use some
2577 of the functionality of C<isl>.
2578 The input may be specified in either the L<isl format>
2579 or the L<PolyLib format>.
2581 =head2 C<isl_polyhedron_sample>
2583 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2584 an integer element of the polyhedron, if there is any.
2585 The first column in the output is the denominator and is always
2586 equal to 1. If the polyhedron contains no integer points,
2587 then a vector of length zero is printed.
2591 C<isl_pip> takes the same input as the C<example> program
2592 from the C<piplib> distribution, i.e., a set of constraints
2593 on the parameters, a line containing only -1 and finally a set
2594 of constraints on a parametric polyhedron.
2595 The coefficients of the parameters appear in the last columns
2596 (but before the final constant column).
2597 The output is the lexicographic minimum of the parametric polyhedron.
2598 As C<isl> currently does not have its own output format, the output
2599 is just a dump of the internal state.
2601 =head2 C<isl_polyhedron_minimize>
2603 C<isl_polyhedron_minimize> computes the minimum of some linear
2604 or affine objective function over the integer points in a polyhedron.
2605 If an affine objective function
2606 is given, then the constant should appear in the last column.
2608 =head2 C<isl_polytope_scan>
2610 Given a polytope, C<isl_polytope_scan> prints
2611 all integer points in the polytope.
2613 =head1 C<isl-polylib>
2615 The C<isl-polylib> library provides the following functions for converting
2616 between C<isl> objects and C<PolyLib> objects.
2617 The library is distributed separately for licensing reasons.
2619 #include <isl_set_polylib.h>
2620 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2621 Polyhedron *P, __isl_take isl_dim *dim);
2622 Polyhedron *isl_basic_set_to_polylib(
2623 __isl_keep isl_basic_set *bset);
2624 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2625 __isl_take isl_dim *dim);
2626 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2628 #include <isl_map_polylib.h>
2629 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2630 Polyhedron *P, __isl_take isl_dim *dim);
2631 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2632 __isl_take isl_dim *dim);
2633 Polyhedron *isl_basic_map_to_polylib(
2634 __isl_keep isl_basic_map *bmap);
2635 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);