3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
84 The source of C<isl> can be obtained either as a tarball
85 or from the git repository. Both are available from
86 L<http://freshmeat.net/projects/isl/>.
87 The installation process depends on how you obtained
90 =head2 Installation from the git repository
94 =item 1 Clone or update the repository
96 The first time the source is obtained, you need to clone
99 git clone git://repo.or.cz/isl.git
101 To obtain updates, you need to pull in the latest changes
105 =item 2 Generate C<configure>
111 After performing the above steps, continue
112 with the L<Common installation instructions>.
114 =head2 Common installation instructions
118 =item 1 Obtain C<GMP>
120 Building C<isl> requires C<GMP>, including its headers files.
121 Your distribution may not provide these header files by default
122 and you may need to install a package called C<gmp-devel> or something
123 similar. Alternatively, C<GMP> can be built from
124 source, available from L<http://gmplib.org/>.
128 C<isl> uses the standard C<autoconf> C<configure> script.
133 optionally followed by some configure options.
134 A complete list of options can be obtained by running
138 Below we discuss some of the more common options.
140 C<isl> can optionally use C<piplib>, but no
141 C<piplib> functionality is currently used by default.
142 The C<--with-piplib> option can
143 be used to specify which C<piplib>
144 library to use, either an installed version (C<system>),
145 an externally built version (C<build>)
146 or no version (C<no>). The option C<build> is mostly useful
147 in C<configure> scripts of larger projects that bundle both C<isl>
154 Installation prefix for C<isl>
156 =item C<--with-gmp-prefix>
158 Installation prefix for C<GMP> (architecture-independent files).
160 =item C<--with-gmp-exec-prefix>
162 Installation prefix for C<GMP> (architecture-dependent files).
164 =item C<--with-piplib>
166 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
168 =item C<--with-piplib-prefix>
170 Installation prefix for C<system> C<piplib> (architecture-independent files).
172 =item C<--with-piplib-exec-prefix>
174 Installation prefix for C<system> C<piplib> (architecture-dependent files).
176 =item C<--with-piplib-builddir>
178 Location where C<build> C<piplib> was built.
186 =item 4 Install (optional)
194 =head2 Initialization
196 All manipulations of integer sets and relations occur within
197 the context of an C<isl_ctx>.
198 A given C<isl_ctx> can only be used within a single thread.
199 All arguments of a function are required to have been allocated
200 within the same context.
201 There are currently no functions available for moving an object
202 from one C<isl_ctx> to another C<isl_ctx>. This means that
203 there is currently no way of safely moving an object from one
204 thread to another, unless the whole C<isl_ctx> is moved.
206 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
207 freed using C<isl_ctx_free>.
208 All objects allocated within an C<isl_ctx> should be freed
209 before the C<isl_ctx> itself is freed.
211 isl_ctx *isl_ctx_alloc();
212 void isl_ctx_free(isl_ctx *ctx);
216 All operations on integers, mainly the coefficients
217 of the constraints describing the sets and relations,
218 are performed in exact integer arithmetic using C<GMP>.
219 However, to allow future versions of C<isl> to optionally
220 support fixed integer arithmetic, all calls to C<GMP>
221 are wrapped inside C<isl> specific macros.
222 The basic type is C<isl_int> and the operations below
223 are available on this type.
224 The meanings of these operations are essentially the same
225 as their C<GMP> C<mpz_> counterparts.
226 As always with C<GMP> types, C<isl_int>s need to be
227 initialized with C<isl_int_init> before they can be used
228 and they need to be released with C<isl_int_clear>
230 The user should not assume that an C<isl_int> is represented
231 as a C<mpz_t>, but should instead explicitly convert between
232 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
233 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
237 =item isl_int_init(i)
239 =item isl_int_clear(i)
241 =item isl_int_set(r,i)
243 =item isl_int_set_si(r,i)
245 =item isl_int_set_gmp(r,g)
247 =item isl_int_get_gmp(i,g)
249 =item isl_int_abs(r,i)
251 =item isl_int_neg(r,i)
253 =item isl_int_swap(i,j)
255 =item isl_int_swap_or_set(i,j)
257 =item isl_int_add_ui(r,i,j)
259 =item isl_int_sub_ui(r,i,j)
261 =item isl_int_add(r,i,j)
263 =item isl_int_sub(r,i,j)
265 =item isl_int_mul(r,i,j)
267 =item isl_int_mul_ui(r,i,j)
269 =item isl_int_addmul(r,i,j)
271 =item isl_int_submul(r,i,j)
273 =item isl_int_gcd(r,i,j)
275 =item isl_int_lcm(r,i,j)
277 =item isl_int_divexact(r,i,j)
279 =item isl_int_cdiv_q(r,i,j)
281 =item isl_int_fdiv_q(r,i,j)
283 =item isl_int_fdiv_r(r,i,j)
285 =item isl_int_fdiv_q_ui(r,i,j)
287 =item isl_int_read(r,s)
289 =item isl_int_print(out,i,width)
293 =item isl_int_cmp(i,j)
295 =item isl_int_cmp_si(i,si)
297 =item isl_int_eq(i,j)
299 =item isl_int_ne(i,j)
301 =item isl_int_lt(i,j)
303 =item isl_int_le(i,j)
305 =item isl_int_gt(i,j)
307 =item isl_int_ge(i,j)
309 =item isl_int_abs_eq(i,j)
311 =item isl_int_abs_ne(i,j)
313 =item isl_int_abs_lt(i,j)
315 =item isl_int_abs_gt(i,j)
317 =item isl_int_abs_ge(i,j)
319 =item isl_int_is_zero(i)
321 =item isl_int_is_one(i)
323 =item isl_int_is_negone(i)
325 =item isl_int_is_pos(i)
327 =item isl_int_is_neg(i)
329 =item isl_int_is_nonpos(i)
331 =item isl_int_is_nonneg(i)
333 =item isl_int_is_divisible_by(i,j)
337 =head2 Sets and Relations
339 C<isl> uses six types of objects for representing sets and relations,
340 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
341 C<isl_union_set> and C<isl_union_map>.
342 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
343 can be described as a conjunction of affine constraints, while
344 C<isl_set> and C<isl_map> represent unions of
345 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
346 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
347 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
348 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
349 where dimensions with different space names
350 (see L<Dimension Specifications>) are considered different as well.
351 The difference between sets and relations (maps) is that sets have
352 one set of variables, while relations have two sets of variables,
353 input variables and output variables.
355 =head2 Memory Management
357 Since a high-level operation on sets and/or relations usually involves
358 several substeps and since the user is usually not interested in
359 the intermediate results, most functions that return a new object
360 will also release all the objects passed as arguments.
361 If the user still wants to use one or more of these arguments
362 after the function call, she should pass along a copy of the
363 object rather than the object itself.
364 The user is then responsible for making sure that the original
365 object gets used somewhere else or is explicitly freed.
367 The arguments and return values of all documents functions are
368 annotated to make clear which arguments are released and which
369 arguments are preserved. In particular, the following annotations
376 C<__isl_give> means that a new object is returned.
377 The user should make sure that the returned pointer is
378 used exactly once as a value for an C<__isl_take> argument.
379 In between, it can be used as a value for as many
380 C<__isl_keep> arguments as the user likes.
381 There is one exception, and that is the case where the
382 pointer returned is C<NULL>. Is this case, the user
383 is free to use it as an C<__isl_take> argument or not.
387 C<__isl_take> means that the object the argument points to
388 is taken over by the function and may no longer be used
389 by the user as an argument to any other function.
390 The pointer value must be one returned by a function
391 returning an C<__isl_give> pointer.
392 If the user passes in a C<NULL> value, then this will
393 be treated as an error in the sense that the function will
394 not perform its usual operation. However, it will still
395 make sure that all the the other C<__isl_take> arguments
400 C<__isl_keep> means that the function will only use the object
401 temporarily. After the function has finished, the user
402 can still use it as an argument to other functions.
403 A C<NULL> value will be treated in the same way as
404 a C<NULL> value for an C<__isl_take> argument.
408 =head2 Dimension Specifications
410 Whenever a new set or relation is created from scratch,
411 its dimension needs to be specified using an C<isl_dim>.
414 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
415 unsigned nparam, unsigned n_in, unsigned n_out);
416 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
417 unsigned nparam, unsigned dim);
418 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
419 void isl_dim_free(__isl_take isl_dim *dim);
420 unsigned isl_dim_size(__isl_keep isl_dim *dim,
421 enum isl_dim_type type);
423 The dimension specification used for creating a set
424 needs to be created using C<isl_dim_set_alloc>, while
425 that for creating a relation
426 needs to be created using C<isl_dim_alloc>.
427 C<isl_dim_size> can be used
428 to find out the number of dimensions of each type in
429 a dimension specification, where type may be
430 C<isl_dim_param>, C<isl_dim_in> (only for relations),
431 C<isl_dim_out> (only for relations), C<isl_dim_set>
432 (only for sets) or C<isl_dim_all>.
434 It is often useful to create objects that live in the
435 same space as some other object. This can be accomplished
436 by creating the new objects
437 (see L<Creating New Sets and Relations> or
438 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
439 specification of the original object.
442 __isl_give isl_dim *isl_basic_set_get_dim(
443 __isl_keep isl_basic_set *bset);
444 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
446 #include <isl/union_set.h>
447 __isl_give isl_dim *isl_union_set_get_dim(
448 __isl_keep isl_union_set *uset);
451 __isl_give isl_dim *isl_basic_map_get_dim(
452 __isl_keep isl_basic_map *bmap);
453 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
455 #include <isl/union_map.h>
456 __isl_give isl_dim *isl_union_map_get_dim(
457 __isl_keep isl_union_map *umap);
459 #include <isl/polynomial.h>
460 __isl_give isl_dim *isl_qpolynomial_get_dim(
461 __isl_keep isl_qpolynomial *qp);
462 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
463 __isl_keep isl_pw_qpolynomial *pwqp);
464 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
465 __isl_keep isl_union_pw_qpolynomial *upwqp);
466 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
467 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
469 The names of the individual dimensions may be set or read off
470 using the following functions.
473 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
474 enum isl_dim_type type, unsigned pos,
475 __isl_keep const char *name);
476 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
477 enum isl_dim_type type, unsigned pos);
479 Note that C<isl_dim_get_name> returns a pointer to some internal
480 data structure, so the result can only be used while the
481 corresponding C<isl_dim> is alive.
482 Also note that every function that operates on two sets or relations
483 requires that both arguments have the same parameters. This also
484 means that if one of the arguments has named parameters, then the
485 other needs to have named parameters too and the names need to match.
486 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
487 have different parameters (as long as they are named), in which case
488 the result will have as parameters the union of the parameters of
491 The names of entire spaces may be set or read off
492 using the following functions.
495 __isl_give isl_dim *isl_dim_set_tuple_name(
496 __isl_take isl_dim *dim,
497 enum isl_dim_type type, const char *s);
498 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
499 enum isl_dim_type type);
501 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
502 or C<isl_dim_set>. As with C<isl_dim_get_name>,
503 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
505 Binary operations require the corresponding spaces of their arguments
506 to have the same name.
508 Spaces can be nested. In particular, the domain of a set or
509 the domain or range of a relation can be a nested relation.
510 The following functions can be used to construct and deconstruct
511 such nested dimension specifications.
514 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
515 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
516 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
518 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
519 be the dimension specification of a set, while that of
520 C<isl_dim_wrap> should be the dimension specification of a relation.
521 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
522 of a relation, while that of C<isl_dim_wrap> is the dimension specification
525 Dimension specifications can be created from other dimension
526 specifications using the following functions.
528 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
529 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
530 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
531 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
532 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
533 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
534 __isl_take isl_dim *right);
535 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
536 enum isl_dim_type type, unsigned pos, unsigned n);
537 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
538 enum isl_dim_type type, unsigned n);
539 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
540 enum isl_dim_type type, unsigned first, unsigned n);
541 __isl_give isl_dim *isl_dim_map_from_set(
542 __isl_take isl_dim *dim);
543 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
545 Note that if dimensions are added or removed from a space, then
546 the name and the internal structure are lost.
548 =head2 Input and Output
550 C<isl> supports its own input/output format, which is similar
551 to the C<Omega> format, but also supports the C<PolyLib> format
556 The C<isl> format is similar to that of C<Omega>, but has a different
557 syntax for describing the parameters and allows for the definition
558 of an existentially quantified variable as the integer division
559 of an affine expression.
560 For example, the set of integers C<i> between C<0> and C<n>
561 such that C<i % 10 <= 6> can be described as
563 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
566 A set or relation can have several disjuncts, separated
567 by the keyword C<or>. Each disjunct is either a conjunction
568 of constraints or a projection (C<exists>) of a conjunction
569 of constraints. The constraints are separated by the keyword
572 =head3 C<PolyLib> format
574 If the represented set is a union, then the first line
575 contains a single number representing the number of disjuncts.
576 Otherwise, a line containing the number C<1> is optional.
578 Each disjunct is represented by a matrix of constraints.
579 The first line contains two numbers representing
580 the number of rows and columns,
581 where the number of rows is equal to the number of constraints
582 and the number of columns is equal to two plus the number of variables.
583 The following lines contain the actual rows of the constraint matrix.
584 In each row, the first column indicates whether the constraint
585 is an equality (C<0>) or inequality (C<1>). The final column
586 corresponds to the constant term.
588 If the set is parametric, then the coefficients of the parameters
589 appear in the last columns before the constant column.
590 The coefficients of any existentially quantified variables appear
591 between those of the set variables and those of the parameters.
593 =head3 Extended C<PolyLib> format
595 The extended C<PolyLib> format is nearly identical to the
596 C<PolyLib> format. The only difference is that the line
597 containing the number of rows and columns of a constraint matrix
598 also contains four additional numbers:
599 the number of output dimensions, the number of input dimensions,
600 the number of local dimensions (i.e., the number of existentially
601 quantified variables) and the number of parameters.
602 For sets, the number of ``output'' dimensions is equal
603 to the number of set dimensions, while the number of ``input''
609 __isl_give isl_basic_set *isl_basic_set_read_from_file(
610 isl_ctx *ctx, FILE *input, int nparam);
611 __isl_give isl_basic_set *isl_basic_set_read_from_str(
612 isl_ctx *ctx, const char *str, int nparam);
613 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
614 FILE *input, int nparam);
615 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
616 const char *str, int nparam);
619 __isl_give isl_basic_map *isl_basic_map_read_from_file(
620 isl_ctx *ctx, FILE *input, int nparam);
621 __isl_give isl_basic_map *isl_basic_map_read_from_str(
622 isl_ctx *ctx, const char *str, int nparam);
623 __isl_give isl_map *isl_map_read_from_file(
624 struct isl_ctx *ctx, FILE *input, int nparam);
625 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
626 const char *str, int nparam);
628 #include <isl/union_set.h>
629 __isl_give isl_union_set *isl_union_set_read_from_file(
630 isl_ctx *ctx, FILE *input);
631 __isl_give isl_union_set *isl_union_set_read_from_str(
632 struct isl_ctx *ctx, const char *str);
634 #include <isl/union_map.h>
635 __isl_give isl_union_map *isl_union_map_read_from_file(
636 isl_ctx *ctx, FILE *input);
637 __isl_give isl_union_map *isl_union_map_read_from_str(
638 struct isl_ctx *ctx, const char *str);
640 The input format is autodetected and may be either the C<PolyLib> format
641 or the C<isl> format.
642 C<nparam> specifies how many of the final columns in
643 the C<PolyLib> format correspond to parameters.
644 If input is given in the C<isl> format, then the number
645 of parameters needs to be equal to C<nparam>.
646 If C<nparam> is negative, then any number of parameters
647 is accepted in the C<isl> format and zero parameters
648 are assumed in the C<PolyLib> format.
652 Before anything can be printed, an C<isl_printer> needs to
655 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
657 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
658 void isl_printer_free(__isl_take isl_printer *printer);
659 __isl_give char *isl_printer_get_str(
660 __isl_keep isl_printer *printer);
662 The behavior of the printer can be modified in various ways
664 __isl_give isl_printer *isl_printer_set_output_format(
665 __isl_take isl_printer *p, int output_format);
666 __isl_give isl_printer *isl_printer_set_indent(
667 __isl_take isl_printer *p, int indent);
668 __isl_give isl_printer *isl_printer_set_prefix(
669 __isl_take isl_printer *p, const char *prefix);
670 __isl_give isl_printer *isl_printer_set_suffix(
671 __isl_take isl_printer *p, const char *suffix);
673 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
674 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
675 and defaults to C<ISL_FORMAT_ISL>.
676 Each line in the output is indented by C<indent> spaces
677 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
678 In the C<PolyLib> format output,
679 the coefficients of the existentially quantified variables
680 appear between those of the set variables and those
683 To actually print something, use
686 __isl_give isl_printer *isl_printer_print_basic_set(
687 __isl_take isl_printer *printer,
688 __isl_keep isl_basic_set *bset);
689 __isl_give isl_printer *isl_printer_print_set(
690 __isl_take isl_printer *printer,
691 __isl_keep isl_set *set);
694 __isl_give isl_printer *isl_printer_print_basic_map(
695 __isl_take isl_printer *printer,
696 __isl_keep isl_basic_map *bmap);
697 __isl_give isl_printer *isl_printer_print_map(
698 __isl_take isl_printer *printer,
699 __isl_keep isl_map *map);
701 #include <isl/union_set.h>
702 __isl_give isl_printer *isl_printer_print_union_set(
703 __isl_take isl_printer *p,
704 __isl_keep isl_union_set *uset);
706 #include <isl/union_map.h>
707 __isl_give isl_printer *isl_printer_print_union_map(
708 __isl_take isl_printer *p,
709 __isl_keep isl_union_map *umap);
711 When called on a file printer, the following function flushes
712 the file. When called on a string printer, the buffer is cleared.
714 __isl_give isl_printer *isl_printer_flush(
715 __isl_take isl_printer *p);
717 =head2 Creating New Sets and Relations
719 C<isl> has functions for creating some standard sets and relations.
723 =item * Empty sets and relations
725 __isl_give isl_basic_set *isl_basic_set_empty(
726 __isl_take isl_dim *dim);
727 __isl_give isl_basic_map *isl_basic_map_empty(
728 __isl_take isl_dim *dim);
729 __isl_give isl_set *isl_set_empty(
730 __isl_take isl_dim *dim);
731 __isl_give isl_map *isl_map_empty(
732 __isl_take isl_dim *dim);
733 __isl_give isl_union_set *isl_union_set_empty(
734 __isl_take isl_dim *dim);
735 __isl_give isl_union_map *isl_union_map_empty(
736 __isl_take isl_dim *dim);
738 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
739 is only used to specify the parameters.
741 =item * Universe sets and relations
743 __isl_give isl_basic_set *isl_basic_set_universe(
744 __isl_take isl_dim *dim);
745 __isl_give isl_basic_map *isl_basic_map_universe(
746 __isl_take isl_dim *dim);
747 __isl_give isl_set *isl_set_universe(
748 __isl_take isl_dim *dim);
749 __isl_give isl_map *isl_map_universe(
750 __isl_take isl_dim *dim);
752 The sets and relations constructed by the functions above
753 contain all integer values, while those constructed by the
754 functions below only contain non-negative values.
756 __isl_give isl_basic_set *isl_basic_set_nat_universe(
757 __isl_take isl_dim *dim);
758 __isl_give isl_basic_map *isl_basic_map_nat_universe(
759 __isl_take isl_dim *dim);
760 __isl_give isl_set *isl_set_nat_universe(
761 __isl_take isl_dim *dim);
762 __isl_give isl_map *isl_map_nat_universe(
763 __isl_take isl_dim *dim);
765 =item * Identity relations
767 __isl_give isl_basic_map *isl_basic_map_identity(
768 __isl_take isl_dim *dim);
769 __isl_give isl_map *isl_map_identity(
770 __isl_take isl_dim *dim);
772 The number of input and output dimensions in C<dim> needs
775 =item * Lexicographic order
777 __isl_give isl_map *isl_map_lex_lt(
778 __isl_take isl_dim *set_dim);
779 __isl_give isl_map *isl_map_lex_le(
780 __isl_take isl_dim *set_dim);
781 __isl_give isl_map *isl_map_lex_gt(
782 __isl_take isl_dim *set_dim);
783 __isl_give isl_map *isl_map_lex_ge(
784 __isl_take isl_dim *set_dim);
785 __isl_give isl_map *isl_map_lex_lt_first(
786 __isl_take isl_dim *dim, unsigned n);
787 __isl_give isl_map *isl_map_lex_le_first(
788 __isl_take isl_dim *dim, unsigned n);
789 __isl_give isl_map *isl_map_lex_gt_first(
790 __isl_take isl_dim *dim, unsigned n);
791 __isl_give isl_map *isl_map_lex_ge_first(
792 __isl_take isl_dim *dim, unsigned n);
794 The first four functions take a dimension specification for a B<set>
795 and return relations that express that the elements in the domain
796 are lexicographically less
797 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
798 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
799 than the elements in the range.
800 The last four functions take a dimension specification for a map
801 and return relations that express that the first C<n> dimensions
802 in the domain are lexicographically less
803 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
804 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
805 than the first C<n> dimensions in the range.
809 A basic set or relation can be converted to a set or relation
810 using the following functions.
812 __isl_give isl_set *isl_set_from_basic_set(
813 __isl_take isl_basic_set *bset);
814 __isl_give isl_map *isl_map_from_basic_map(
815 __isl_take isl_basic_map *bmap);
817 Sets and relations can be converted to union sets and relations
818 using the following functions.
820 __isl_give isl_union_map *isl_union_map_from_map(
821 __isl_take isl_map *map);
822 __isl_give isl_union_set *isl_union_set_from_set(
823 __isl_take isl_set *set);
825 Sets and relations can be copied and freed again using the following
828 __isl_give isl_basic_set *isl_basic_set_copy(
829 __isl_keep isl_basic_set *bset);
830 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
831 __isl_give isl_union_set *isl_union_set_copy(
832 __isl_keep isl_union_set *uset);
833 __isl_give isl_basic_map *isl_basic_map_copy(
834 __isl_keep isl_basic_map *bmap);
835 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
836 __isl_give isl_union_map *isl_union_map_copy(
837 __isl_keep isl_union_map *umap);
838 void isl_basic_set_free(__isl_take isl_basic_set *bset);
839 void isl_set_free(__isl_take isl_set *set);
840 void isl_union_set_free(__isl_take isl_union_set *uset);
841 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
842 void isl_map_free(__isl_take isl_map *map);
843 void isl_union_map_free(__isl_take isl_union_map *umap);
845 Other sets and relations can be constructed by starting
846 from a universe set or relation, adding equality and/or
847 inequality constraints and then projecting out the
848 existentially quantified variables, if any.
849 Constraints can be constructed, manipulated and
850 added to basic sets and relations using the following functions.
852 #include <isl/constraint.h>
853 __isl_give isl_constraint *isl_equality_alloc(
854 __isl_take isl_dim *dim);
855 __isl_give isl_constraint *isl_inequality_alloc(
856 __isl_take isl_dim *dim);
857 void isl_constraint_set_constant(
858 __isl_keep isl_constraint *constraint, isl_int v);
859 void isl_constraint_set_coefficient(
860 __isl_keep isl_constraint *constraint,
861 enum isl_dim_type type, int pos, isl_int v);
862 __isl_give isl_basic_map *isl_basic_map_add_constraint(
863 __isl_take isl_basic_map *bmap,
864 __isl_take isl_constraint *constraint);
865 __isl_give isl_basic_set *isl_basic_set_add_constraint(
866 __isl_take isl_basic_set *bset,
867 __isl_take isl_constraint *constraint);
869 For example, to create a set containing the even integers
870 between 10 and 42, you would use the following code.
874 struct isl_constraint *c;
875 struct isl_basic_set *bset;
878 dim = isl_dim_set_alloc(ctx, 0, 2);
879 bset = isl_basic_set_universe(isl_dim_copy(dim));
881 c = isl_equality_alloc(isl_dim_copy(dim));
882 isl_int_set_si(v, -1);
883 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
884 isl_int_set_si(v, 2);
885 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
886 bset = isl_basic_set_add_constraint(bset, c);
888 c = isl_inequality_alloc(isl_dim_copy(dim));
889 isl_int_set_si(v, -10);
890 isl_constraint_set_constant(c, v);
891 isl_int_set_si(v, 1);
892 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
893 bset = isl_basic_set_add_constraint(bset, c);
895 c = isl_inequality_alloc(dim);
896 isl_int_set_si(v, 42);
897 isl_constraint_set_constant(c, v);
898 isl_int_set_si(v, -1);
899 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
900 bset = isl_basic_set_add_constraint(bset, c);
902 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
908 struct isl_basic_set *bset;
909 bset = isl_basic_set_read_from_str(ctx,
910 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
912 A basic set or relation can also be constructed from two matrices
913 describing the equalities and the inequalities.
915 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
916 __isl_take isl_dim *dim,
917 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
918 enum isl_dim_type c1,
919 enum isl_dim_type c2, enum isl_dim_type c3,
920 enum isl_dim_type c4);
921 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
922 __isl_take isl_dim *dim,
923 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
924 enum isl_dim_type c1,
925 enum isl_dim_type c2, enum isl_dim_type c3,
926 enum isl_dim_type c4, enum isl_dim_type c5);
928 The C<isl_dim_type> arguments indicate the order in which
929 different kinds of variables appear in the input matrices
930 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
931 C<isl_dim_set> and C<isl_dim_div> for sets and
932 of C<isl_dim_cst>, C<isl_dim_param>,
933 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
935 =head2 Inspecting Sets and Relations
937 Usually, the user should not have to care about the actual constraints
938 of the sets and maps, but should instead apply the abstract operations
939 explained in the following sections.
940 Occasionally, however, it may be required to inspect the individual
941 coefficients of the constraints. This section explains how to do so.
942 In these cases, it may also be useful to have C<isl> compute
943 an explicit representation of the existentially quantified variables.
945 __isl_give isl_set *isl_set_compute_divs(
946 __isl_take isl_set *set);
947 __isl_give isl_map *isl_map_compute_divs(
948 __isl_take isl_map *map);
949 __isl_give isl_union_set *isl_union_set_compute_divs(
950 __isl_take isl_union_set *uset);
951 __isl_give isl_union_map *isl_union_map_compute_divs(
952 __isl_take isl_union_map *umap);
954 This explicit representation defines the existentially quantified
955 variables as integer divisions of the other variables, possibly
956 including earlier existentially quantified variables.
957 An explicitly represented existentially quantified variable therefore
958 has a unique value when the values of the other variables are known.
959 If, furthermore, the same existentials, i.e., existentials
960 with the same explicit representations, should appear in the
961 same order in each of the disjuncts of a set or map, then the user should call
962 either of the following functions.
964 __isl_give isl_set *isl_set_align_divs(
965 __isl_take isl_set *set);
966 __isl_give isl_map *isl_map_align_divs(
967 __isl_take isl_map *map);
969 Alternatively, the existentially quantified variables can be removed
970 using the following functions, which compute an overapproximation.
972 __isl_give isl_basic_set *isl_basic_set_remove_divs(
973 __isl_take isl_basic_set *bset);
974 __isl_give isl_basic_map *isl_basic_map_remove_divs(
975 __isl_take isl_basic_map *bmap);
976 __isl_give isl_set *isl_set_remove_divs(
977 __isl_take isl_set *set);
979 To iterate over all the sets or maps in a union set or map, use
981 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
982 int (*fn)(__isl_take isl_set *set, void *user),
984 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
985 int (*fn)(__isl_take isl_map *map, void *user),
988 The number of sets or maps in a union set or map can be obtained
991 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
992 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
994 To extract the set or map from a union with a given dimension
997 __isl_give isl_set *isl_union_set_extract_set(
998 __isl_keep isl_union_set *uset,
999 __isl_take isl_dim *dim);
1000 __isl_give isl_map *isl_union_map_extract_map(
1001 __isl_keep isl_union_map *umap,
1002 __isl_take isl_dim *dim);
1004 To iterate over all the basic sets or maps in a set or map, use
1006 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1007 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1009 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1010 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1013 The callback function C<fn> should return 0 if successful and
1014 -1 if an error occurs. In the latter case, or if any other error
1015 occurs, the above functions will return -1.
1017 It should be noted that C<isl> does not guarantee that
1018 the basic sets or maps passed to C<fn> are disjoint.
1019 If this is required, then the user should call one of
1020 the following functions first.
1022 __isl_give isl_set *isl_set_make_disjoint(
1023 __isl_take isl_set *set);
1024 __isl_give isl_map *isl_map_make_disjoint(
1025 __isl_take isl_map *map);
1027 The number of basic sets in a set can be obtained
1030 int isl_set_n_basic_set(__isl_keep isl_set *set);
1032 To iterate over the constraints of a basic set or map, use
1034 #include <isl/constraint.h>
1036 int isl_basic_map_foreach_constraint(
1037 __isl_keep isl_basic_map *bmap,
1038 int (*fn)(__isl_take isl_constraint *c, void *user),
1040 void isl_constraint_free(struct isl_constraint *c);
1042 Again, the callback function C<fn> should return 0 if successful and
1043 -1 if an error occurs. In the latter case, or if any other error
1044 occurs, the above functions will return -1.
1045 The constraint C<c> represents either an equality or an inequality.
1046 Use the following function to find out whether a constraint
1047 represents an equality. If not, it represents an inequality.
1049 int isl_constraint_is_equality(
1050 __isl_keep isl_constraint *constraint);
1052 The coefficients of the constraints can be inspected using
1053 the following functions.
1055 void isl_constraint_get_constant(
1056 __isl_keep isl_constraint *constraint, isl_int *v);
1057 void isl_constraint_get_coefficient(
1058 __isl_keep isl_constraint *constraint,
1059 enum isl_dim_type type, int pos, isl_int *v);
1061 The explicit representations of the existentially quantified
1062 variables can be inspected using the following functions.
1063 Note that the user is only allowed to use these functions
1064 if the inspected set or map is the result of a call
1065 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1067 __isl_give isl_div *isl_constraint_div(
1068 __isl_keep isl_constraint *constraint, int pos);
1069 void isl_div_get_constant(__isl_keep isl_div *div,
1071 void isl_div_get_denominator(__isl_keep isl_div *div,
1073 void isl_div_get_coefficient(__isl_keep isl_div *div,
1074 enum isl_dim_type type, int pos, isl_int *v);
1076 To obtain the constraints of a basic set or map in matrix
1077 form, use the following functions.
1079 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1080 __isl_keep isl_basic_set *bset,
1081 enum isl_dim_type c1, enum isl_dim_type c2,
1082 enum isl_dim_type c3, enum isl_dim_type c4);
1083 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1084 __isl_keep isl_basic_set *bset,
1085 enum isl_dim_type c1, enum isl_dim_type c2,
1086 enum isl_dim_type c3, enum isl_dim_type c4);
1087 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1088 __isl_keep isl_basic_map *bmap,
1089 enum isl_dim_type c1,
1090 enum isl_dim_type c2, enum isl_dim_type c3,
1091 enum isl_dim_type c4, enum isl_dim_type c5);
1092 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1093 __isl_keep isl_basic_map *bmap,
1094 enum isl_dim_type c1,
1095 enum isl_dim_type c2, enum isl_dim_type c3,
1096 enum isl_dim_type c4, enum isl_dim_type c5);
1098 The C<isl_dim_type> arguments dictate the order in which
1099 different kinds of variables appear in the resulting matrix
1100 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1101 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1103 The names of the domain and range spaces of a set or relation can be
1104 read off using the following functions.
1106 const char *isl_basic_set_get_tuple_name(
1107 __isl_keep isl_basic_set *bset);
1108 const char *isl_set_get_tuple_name(
1109 __isl_keep isl_set *set);
1110 const char *isl_basic_map_get_tuple_name(
1111 __isl_keep isl_basic_map *bmap,
1112 enum isl_dim_type type);
1113 const char *isl_map_get_tuple_name(
1114 __isl_keep isl_map *map,
1115 enum isl_dim_type type);
1117 As with C<isl_dim_get_tuple_name>, the value returned points to
1118 an internal data structure.
1119 The names of individual dimensions can be read off using
1120 the following functions.
1122 const char *isl_constraint_get_dim_name(
1123 __isl_keep isl_constraint *constraint,
1124 enum isl_dim_type type, unsigned pos);
1125 const char *isl_basic_set_get_dim_name(
1126 __isl_keep isl_basic_set *bset,
1127 enum isl_dim_type type, unsigned pos);
1128 const char *isl_set_get_dim_name(
1129 __isl_keep isl_set *set,
1130 enum isl_dim_type type, unsigned pos);
1131 const char *isl_basic_map_get_dim_name(
1132 __isl_keep isl_basic_map *bmap,
1133 enum isl_dim_type type, unsigned pos);
1134 const char *isl_map_get_dim_name(
1135 __isl_keep isl_map *map,
1136 enum isl_dim_type type, unsigned pos);
1138 These functions are mostly useful to obtain the names
1143 =head3 Unary Properties
1149 The following functions test whether the given set or relation
1150 contains any integer points. The ``fast'' variants do not perform
1151 any computations, but simply check if the given set or relation
1152 is already known to be empty.
1154 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1155 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1156 int isl_set_is_empty(__isl_keep isl_set *set);
1157 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1158 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1159 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1160 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1161 int isl_map_is_empty(__isl_keep isl_map *map);
1162 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1164 =item * Universality
1166 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1167 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1168 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1170 =item * Single-valuedness
1172 int isl_map_is_single_valued(__isl_keep isl_map *map);
1176 int isl_map_is_bijective(__isl_keep isl_map *map);
1180 The followning functions check whether the domain of the given
1181 (basic) set is a wrapped relation.
1183 int isl_basic_set_is_wrapping(
1184 __isl_keep isl_basic_set *bset);
1185 int isl_set_is_wrapping(__isl_keep isl_set *set);
1187 =item * Internal Product
1189 int isl_basic_map_can_zip(
1190 __isl_keep isl_basic_map *bmap);
1191 int isl_map_can_zip(__isl_keep isl_map *map);
1193 Check whether the product of domain and range of the given relation
1195 i.e., whether both domain and range are nested relations.
1199 =head3 Binary Properties
1205 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1206 __isl_keep isl_set *set2);
1207 int isl_set_is_equal(__isl_keep isl_set *set1,
1208 __isl_keep isl_set *set2);
1209 int isl_union_set_is_equal(
1210 __isl_keep isl_union_set *uset1,
1211 __isl_keep isl_union_set *uset2);
1212 int isl_basic_map_is_equal(
1213 __isl_keep isl_basic_map *bmap1,
1214 __isl_keep isl_basic_map *bmap2);
1215 int isl_map_is_equal(__isl_keep isl_map *map1,
1216 __isl_keep isl_map *map2);
1217 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1218 __isl_keep isl_map *map2);
1219 int isl_union_map_is_equal(
1220 __isl_keep isl_union_map *umap1,
1221 __isl_keep isl_union_map *umap2);
1223 =item * Disjointness
1225 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1226 __isl_keep isl_set *set2);
1230 int isl_set_is_subset(__isl_keep isl_set *set1,
1231 __isl_keep isl_set *set2);
1232 int isl_set_is_strict_subset(
1233 __isl_keep isl_set *set1,
1234 __isl_keep isl_set *set2);
1235 int isl_union_set_is_subset(
1236 __isl_keep isl_union_set *uset1,
1237 __isl_keep isl_union_set *uset2);
1238 int isl_union_set_is_strict_subset(
1239 __isl_keep isl_union_set *uset1,
1240 __isl_keep isl_union_set *uset2);
1241 int isl_basic_map_is_subset(
1242 __isl_keep isl_basic_map *bmap1,
1243 __isl_keep isl_basic_map *bmap2);
1244 int isl_basic_map_is_strict_subset(
1245 __isl_keep isl_basic_map *bmap1,
1246 __isl_keep isl_basic_map *bmap2);
1247 int isl_map_is_subset(
1248 __isl_keep isl_map *map1,
1249 __isl_keep isl_map *map2);
1250 int isl_map_is_strict_subset(
1251 __isl_keep isl_map *map1,
1252 __isl_keep isl_map *map2);
1253 int isl_union_map_is_subset(
1254 __isl_keep isl_union_map *umap1,
1255 __isl_keep isl_union_map *umap2);
1256 int isl_union_map_is_strict_subset(
1257 __isl_keep isl_union_map *umap1,
1258 __isl_keep isl_union_map *umap2);
1262 =head2 Unary Operations
1268 __isl_give isl_set *isl_set_complement(
1269 __isl_take isl_set *set);
1273 __isl_give isl_basic_map *isl_basic_map_reverse(
1274 __isl_take isl_basic_map *bmap);
1275 __isl_give isl_map *isl_map_reverse(
1276 __isl_take isl_map *map);
1277 __isl_give isl_union_map *isl_union_map_reverse(
1278 __isl_take isl_union_map *umap);
1282 __isl_give isl_basic_set *isl_basic_set_project_out(
1283 __isl_take isl_basic_set *bset,
1284 enum isl_dim_type type, unsigned first, unsigned n);
1285 __isl_give isl_basic_map *isl_basic_map_project_out(
1286 __isl_take isl_basic_map *bmap,
1287 enum isl_dim_type type, unsigned first, unsigned n);
1288 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1289 enum isl_dim_type type, unsigned first, unsigned n);
1290 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1291 enum isl_dim_type type, unsigned first, unsigned n);
1292 __isl_give isl_basic_set *isl_basic_map_domain(
1293 __isl_take isl_basic_map *bmap);
1294 __isl_give isl_basic_set *isl_basic_map_range(
1295 __isl_take isl_basic_map *bmap);
1296 __isl_give isl_set *isl_map_domain(
1297 __isl_take isl_map *bmap);
1298 __isl_give isl_set *isl_map_range(
1299 __isl_take isl_map *map);
1300 __isl_give isl_union_set *isl_union_map_domain(
1301 __isl_take isl_union_map *umap);
1302 __isl_give isl_union_set *isl_union_map_range(
1303 __isl_take isl_union_map *umap);
1305 __isl_give isl_basic_map *isl_basic_map_domain_map(
1306 __isl_take isl_basic_map *bmap);
1307 __isl_give isl_basic_map *isl_basic_map_range_map(
1308 __isl_take isl_basic_map *bmap);
1309 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1310 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1311 __isl_give isl_union_map *isl_union_map_domain_map(
1312 __isl_take isl_union_map *umap);
1313 __isl_give isl_union_map *isl_union_map_range_map(
1314 __isl_take isl_union_map *umap);
1316 The functions above construct a (basic, regular or union) relation
1317 that maps (a wrapped version of) the input relation to its domain or range.
1321 __isl_give isl_map *isl_set_identity(
1322 __isl_take isl_set *set);
1323 __isl_give isl_union_map *isl_union_set_identity(
1324 __isl_take isl_union_set *uset);
1326 Construct an identity relation on the given (union) set.
1330 __isl_give isl_basic_set *isl_basic_map_deltas(
1331 __isl_take isl_basic_map *bmap);
1332 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1333 __isl_give isl_union_set *isl_union_map_deltas(
1334 __isl_take isl_union_map *umap);
1336 These functions return a (basic) set containing the differences
1337 between image elements and corresponding domain elements in the input.
1339 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1340 __isl_take isl_basic_map *bmap);
1341 __isl_give isl_map *isl_map_deltas_map(
1342 __isl_take isl_map *map);
1343 __isl_give isl_union_map *isl_union_map_deltas_map(
1344 __isl_take isl_union_map *umap);
1346 The functions above construct a (basic, regular or union) relation
1347 that maps (a wrapped version of) the input relation to its delta set.
1351 Simplify the representation of a set or relation by trying
1352 to combine pairs of basic sets or relations into a single
1353 basic set or relation.
1355 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1356 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1357 __isl_give isl_union_set *isl_union_set_coalesce(
1358 __isl_take isl_union_set *uset);
1359 __isl_give isl_union_map *isl_union_map_coalesce(
1360 __isl_take isl_union_map *umap);
1362 =item * Detecting equalities
1364 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1365 __isl_take isl_basic_set *bset);
1366 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1367 __isl_take isl_basic_map *bmap);
1368 __isl_give isl_set *isl_set_detect_equalities(
1369 __isl_take isl_set *set);
1370 __isl_give isl_map *isl_map_detect_equalities(
1371 __isl_take isl_map *map);
1372 __isl_give isl_union_set *isl_union_set_detect_equalities(
1373 __isl_take isl_union_set *uset);
1374 __isl_give isl_union_map *isl_union_map_detect_equalities(
1375 __isl_take isl_union_map *umap);
1377 Simplify the representation of a set or relation by detecting implicit
1382 __isl_give isl_basic_set *isl_set_convex_hull(
1383 __isl_take isl_set *set);
1384 __isl_give isl_basic_map *isl_map_convex_hull(
1385 __isl_take isl_map *map);
1387 If the input set or relation has any existentially quantified
1388 variables, then the result of these operations is currently undefined.
1392 __isl_give isl_basic_set *isl_set_simple_hull(
1393 __isl_take isl_set *set);
1394 __isl_give isl_basic_map *isl_map_simple_hull(
1395 __isl_take isl_map *map);
1396 __isl_give isl_union_map *isl_union_map_simple_hull(
1397 __isl_take isl_union_map *umap);
1399 These functions compute a single basic set or relation
1400 that contains the whole input set or relation.
1401 In particular, the output is described by translates
1402 of the constraints describing the basic sets or relations in the input.
1406 (See \autoref{s:simple hull}.)
1412 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1413 __isl_take isl_basic_set *bset);
1414 __isl_give isl_basic_set *isl_set_affine_hull(
1415 __isl_take isl_set *set);
1416 __isl_give isl_union_set *isl_union_set_affine_hull(
1417 __isl_take isl_union_set *uset);
1418 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1419 __isl_take isl_basic_map *bmap);
1420 __isl_give isl_basic_map *isl_map_affine_hull(
1421 __isl_take isl_map *map);
1422 __isl_give isl_union_map *isl_union_map_affine_hull(
1423 __isl_take isl_union_map *umap);
1425 In case of union sets and relations, the affine hull is computed
1428 =item * Polyhedral hull
1430 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1431 __isl_take isl_set *set);
1432 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1433 __isl_take isl_map *map);
1434 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1435 __isl_take isl_union_set *uset);
1436 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1437 __isl_take isl_union_map *umap);
1439 These functions compute a single basic set or relation
1440 not involving any existentially quantified variables
1441 that contains the whole input set or relation.
1442 In case of union sets and relations, the polyhedral hull is computed
1447 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1449 __isl_give isl_union_map *isl_union_map_power(
1450 __isl_take isl_union_map *umap, int *exact);
1452 Compute a parametric representation for all positive powers I<k> of C<map>.
1453 The result maps I<k> to a nested relation corresponding to the
1454 I<k>th power of C<map>.
1455 The result may be an overapproximation. If the result is known to be exact,
1456 then C<*exact> is set to C<1>.
1458 =item * Transitive closure
1460 __isl_give isl_map *isl_map_transitive_closure(
1461 __isl_take isl_map *map, int *exact);
1462 __isl_give isl_union_map *isl_union_map_transitive_closure(
1463 __isl_take isl_union_map *umap, int *exact);
1465 Compute the transitive closure of C<map>.
1466 The result may be an overapproximation. If the result is known to be exact,
1467 then C<*exact> is set to C<1>.
1469 =item * Reaching path lengths
1471 __isl_give isl_map *isl_map_reaching_path_lengths(
1472 __isl_take isl_map *map, int *exact);
1474 Compute a relation that maps each element in the range of C<map>
1475 to the lengths of all paths composed of edges in C<map> that
1476 end up in the given element.
1477 The result may be an overapproximation. If the result is known to be exact,
1478 then C<*exact> is set to C<1>.
1479 To compute the I<maximal> path length, the resulting relation
1480 should be postprocessed by C<isl_map_lexmax>.
1481 In particular, if the input relation is a dependence relation
1482 (mapping sources to sinks), then the maximal path length corresponds
1483 to the free schedule.
1484 Note, however, that C<isl_map_lexmax> expects the maximum to be
1485 finite, so if the path lengths are unbounded (possibly due to
1486 the overapproximation), then you will get an error message.
1490 __isl_give isl_basic_set *isl_basic_map_wrap(
1491 __isl_take isl_basic_map *bmap);
1492 __isl_give isl_set *isl_map_wrap(
1493 __isl_take isl_map *map);
1494 __isl_give isl_union_set *isl_union_map_wrap(
1495 __isl_take isl_union_map *umap);
1496 __isl_give isl_basic_map *isl_basic_set_unwrap(
1497 __isl_take isl_basic_set *bset);
1498 __isl_give isl_map *isl_set_unwrap(
1499 __isl_take isl_set *set);
1500 __isl_give isl_union_map *isl_union_set_unwrap(
1501 __isl_take isl_union_set *uset);
1505 Remove any internal structure of domain (and range) of the given
1506 set or relation. If there is any such internal structure in the input,
1507 then the name of the space is also removed.
1509 __isl_give isl_basic_set *isl_basic_set_flatten(
1510 __isl_take isl_basic_set *bset);
1511 __isl_give isl_set *isl_set_flatten(
1512 __isl_take isl_set *set);
1513 __isl_give isl_basic_map *isl_basic_map_flatten(
1514 __isl_take isl_basic_map *bmap);
1515 __isl_give isl_map *isl_map_flatten(
1516 __isl_take isl_map *map);
1518 __isl_give isl_map *isl_set_flatten_map(
1519 __isl_take isl_set *set);
1521 The function above constructs a relation
1522 that maps the input set to a flattened version of the set.
1524 =item * Internal Product
1526 __isl_give isl_basic_map *isl_basic_map_zip(
1527 __isl_take isl_basic_map *bmap);
1528 __isl_give isl_map *isl_map_zip(
1529 __isl_take isl_map *map);
1530 __isl_give isl_union_map *isl_union_map_zip(
1531 __isl_take isl_union_map *umap);
1533 Given a relation with nested relations for domain and range,
1534 interchange the range of the domain with the domain of the range.
1536 =item * Dimension manipulation
1538 __isl_give isl_set *isl_set_add_dims(
1539 __isl_take isl_set *set,
1540 enum isl_dim_type type, unsigned n);
1541 __isl_give isl_map *isl_map_add_dims(
1542 __isl_take isl_map *map,
1543 enum isl_dim_type type, unsigned n);
1545 It is usually not advisable to directly change the (input or output)
1546 space of a set or a relation as this removes the name and the internal
1547 structure of the space. However, the above functions can be useful
1548 to add new parameters.
1552 =head2 Binary Operations
1554 The two arguments of a binary operation not only need to live
1555 in the same C<isl_ctx>, they currently also need to have
1556 the same (number of) parameters.
1558 =head3 Basic Operations
1562 =item * Intersection
1564 __isl_give isl_basic_set *isl_basic_set_intersect(
1565 __isl_take isl_basic_set *bset1,
1566 __isl_take isl_basic_set *bset2);
1567 __isl_give isl_set *isl_set_intersect(
1568 __isl_take isl_set *set1,
1569 __isl_take isl_set *set2);
1570 __isl_give isl_union_set *isl_union_set_intersect(
1571 __isl_take isl_union_set *uset1,
1572 __isl_take isl_union_set *uset2);
1573 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1574 __isl_take isl_basic_map *bmap,
1575 __isl_take isl_basic_set *bset);
1576 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1577 __isl_take isl_basic_map *bmap,
1578 __isl_take isl_basic_set *bset);
1579 __isl_give isl_basic_map *isl_basic_map_intersect(
1580 __isl_take isl_basic_map *bmap1,
1581 __isl_take isl_basic_map *bmap2);
1582 __isl_give isl_map *isl_map_intersect_domain(
1583 __isl_take isl_map *map,
1584 __isl_take isl_set *set);
1585 __isl_give isl_map *isl_map_intersect_range(
1586 __isl_take isl_map *map,
1587 __isl_take isl_set *set);
1588 __isl_give isl_map *isl_map_intersect(
1589 __isl_take isl_map *map1,
1590 __isl_take isl_map *map2);
1591 __isl_give isl_union_map *isl_union_map_intersect_domain(
1592 __isl_take isl_union_map *umap,
1593 __isl_take isl_union_set *uset);
1594 __isl_give isl_union_map *isl_union_map_intersect_range(
1595 __isl_take isl_union_map *umap,
1596 __isl_take isl_union_set *uset);
1597 __isl_give isl_union_map *isl_union_map_intersect(
1598 __isl_take isl_union_map *umap1,
1599 __isl_take isl_union_map *umap2);
1603 __isl_give isl_set *isl_basic_set_union(
1604 __isl_take isl_basic_set *bset1,
1605 __isl_take isl_basic_set *bset2);
1606 __isl_give isl_map *isl_basic_map_union(
1607 __isl_take isl_basic_map *bmap1,
1608 __isl_take isl_basic_map *bmap2);
1609 __isl_give isl_set *isl_set_union(
1610 __isl_take isl_set *set1,
1611 __isl_take isl_set *set2);
1612 __isl_give isl_map *isl_map_union(
1613 __isl_take isl_map *map1,
1614 __isl_take isl_map *map2);
1615 __isl_give isl_union_set *isl_union_set_union(
1616 __isl_take isl_union_set *uset1,
1617 __isl_take isl_union_set *uset2);
1618 __isl_give isl_union_map *isl_union_map_union(
1619 __isl_take isl_union_map *umap1,
1620 __isl_take isl_union_map *umap2);
1622 =item * Set difference
1624 __isl_give isl_set *isl_set_subtract(
1625 __isl_take isl_set *set1,
1626 __isl_take isl_set *set2);
1627 __isl_give isl_map *isl_map_subtract(
1628 __isl_take isl_map *map1,
1629 __isl_take isl_map *map2);
1630 __isl_give isl_union_set *isl_union_set_subtract(
1631 __isl_take isl_union_set *uset1,
1632 __isl_take isl_union_set *uset2);
1633 __isl_give isl_union_map *isl_union_map_subtract(
1634 __isl_take isl_union_map *umap1,
1635 __isl_take isl_union_map *umap2);
1639 __isl_give isl_basic_set *isl_basic_set_apply(
1640 __isl_take isl_basic_set *bset,
1641 __isl_take isl_basic_map *bmap);
1642 __isl_give isl_set *isl_set_apply(
1643 __isl_take isl_set *set,
1644 __isl_take isl_map *map);
1645 __isl_give isl_union_set *isl_union_set_apply(
1646 __isl_take isl_union_set *uset,
1647 __isl_take isl_union_map *umap);
1648 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1649 __isl_take isl_basic_map *bmap1,
1650 __isl_take isl_basic_map *bmap2);
1651 __isl_give isl_basic_map *isl_basic_map_apply_range(
1652 __isl_take isl_basic_map *bmap1,
1653 __isl_take isl_basic_map *bmap2);
1654 __isl_give isl_map *isl_map_apply_domain(
1655 __isl_take isl_map *map1,
1656 __isl_take isl_map *map2);
1657 __isl_give isl_union_map *isl_union_map_apply_domain(
1658 __isl_take isl_union_map *umap1,
1659 __isl_take isl_union_map *umap2);
1660 __isl_give isl_map *isl_map_apply_range(
1661 __isl_take isl_map *map1,
1662 __isl_take isl_map *map2);
1663 __isl_give isl_union_map *isl_union_map_apply_range(
1664 __isl_take isl_union_map *umap1,
1665 __isl_take isl_union_map *umap2);
1667 =item * Cartesian Product
1669 __isl_give isl_set *isl_set_product(
1670 __isl_take isl_set *set1,
1671 __isl_take isl_set *set2);
1672 __isl_give isl_union_set *isl_union_set_product(
1673 __isl_take isl_union_set *uset1,
1674 __isl_take isl_union_set *uset2);
1675 __isl_give isl_basic_map *isl_basic_map_range_product(
1676 __isl_take isl_basic_map *bmap1,
1677 __isl_take isl_basic_map *bmap2);
1678 __isl_give isl_map *isl_map_range_product(
1679 __isl_take isl_map *map1,
1680 __isl_take isl_map *map2);
1681 __isl_give isl_union_map *isl_union_map_range_product(
1682 __isl_take isl_union_map *umap1,
1683 __isl_take isl_union_map *umap2);
1684 __isl_give isl_map *isl_map_product(
1685 __isl_take isl_map *map1,
1686 __isl_take isl_map *map2);
1687 __isl_give isl_union_map *isl_union_map_product(
1688 __isl_take isl_union_map *umap1,
1689 __isl_take isl_union_map *umap2);
1691 The above functions compute the cross product of the given
1692 sets or relations. The domains and ranges of the results
1693 are wrapped maps between domains and ranges of the inputs.
1694 To obtain a ``flat'' product, use the following functions
1697 __isl_give isl_basic_set *isl_basic_set_flat_product(
1698 __isl_take isl_basic_set *bset1,
1699 __isl_take isl_basic_set *bset2);
1700 __isl_give isl_set *isl_set_flat_product(
1701 __isl_take isl_set *set1,
1702 __isl_take isl_set *set2);
1703 __isl_give isl_basic_map *isl_basic_map_flat_product(
1704 __isl_take isl_basic_map *bmap1,
1705 __isl_take isl_basic_map *bmap2);
1706 __isl_give isl_map *isl_map_flat_product(
1707 __isl_take isl_map *map1,
1708 __isl_take isl_map *map2);
1710 =item * Simplification
1712 __isl_give isl_basic_set *isl_basic_set_gist(
1713 __isl_take isl_basic_set *bset,
1714 __isl_take isl_basic_set *context);
1715 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1716 __isl_take isl_set *context);
1717 __isl_give isl_union_set *isl_union_set_gist(
1718 __isl_take isl_union_set *uset,
1719 __isl_take isl_union_set *context);
1720 __isl_give isl_basic_map *isl_basic_map_gist(
1721 __isl_take isl_basic_map *bmap,
1722 __isl_take isl_basic_map *context);
1723 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1724 __isl_take isl_map *context);
1725 __isl_give isl_union_map *isl_union_map_gist(
1726 __isl_take isl_union_map *umap,
1727 __isl_take isl_union_map *context);
1729 The gist operation returns a set or relation that has the
1730 same intersection with the context as the input set or relation.
1731 Any implicit equality in the intersection is made explicit in the result,
1732 while all inequalities that are redundant with respect to the intersection
1734 In case of union sets and relations, the gist operation is performed
1739 =head3 Lexicographic Optimization
1741 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1742 the following functions
1743 compute a set that contains the lexicographic minimum or maximum
1744 of the elements in C<set> (or C<bset>) for those values of the parameters
1745 that satisfy C<dom>.
1746 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1747 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1749 In other words, the union of the parameter values
1750 for which the result is non-empty and of C<*empty>
1753 __isl_give isl_set *isl_basic_set_partial_lexmin(
1754 __isl_take isl_basic_set *bset,
1755 __isl_take isl_basic_set *dom,
1756 __isl_give isl_set **empty);
1757 __isl_give isl_set *isl_basic_set_partial_lexmax(
1758 __isl_take isl_basic_set *bset,
1759 __isl_take isl_basic_set *dom,
1760 __isl_give isl_set **empty);
1761 __isl_give isl_set *isl_set_partial_lexmin(
1762 __isl_take isl_set *set, __isl_take isl_set *dom,
1763 __isl_give isl_set **empty);
1764 __isl_give isl_set *isl_set_partial_lexmax(
1765 __isl_take isl_set *set, __isl_take isl_set *dom,
1766 __isl_give isl_set **empty);
1768 Given a (basic) set C<set> (or C<bset>), the following functions simply
1769 return a set containing the lexicographic minimum or maximum
1770 of the elements in C<set> (or C<bset>).
1771 In case of union sets, the optimum is computed per space.
1773 __isl_give isl_set *isl_basic_set_lexmin(
1774 __isl_take isl_basic_set *bset);
1775 __isl_give isl_set *isl_basic_set_lexmax(
1776 __isl_take isl_basic_set *bset);
1777 __isl_give isl_set *isl_set_lexmin(
1778 __isl_take isl_set *set);
1779 __isl_give isl_set *isl_set_lexmax(
1780 __isl_take isl_set *set);
1781 __isl_give isl_union_set *isl_union_set_lexmin(
1782 __isl_take isl_union_set *uset);
1783 __isl_give isl_union_set *isl_union_set_lexmax(
1784 __isl_take isl_union_set *uset);
1786 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1787 the following functions
1788 compute a relation that maps each element of C<dom>
1789 to the single lexicographic minimum or maximum
1790 of the elements that are associated to that same
1791 element in C<map> (or C<bmap>).
1792 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1793 that contains the elements in C<dom> that do not map
1794 to any elements in C<map> (or C<bmap>).
1795 In other words, the union of the domain of the result and of C<*empty>
1798 __isl_give isl_map *isl_basic_map_partial_lexmax(
1799 __isl_take isl_basic_map *bmap,
1800 __isl_take isl_basic_set *dom,
1801 __isl_give isl_set **empty);
1802 __isl_give isl_map *isl_basic_map_partial_lexmin(
1803 __isl_take isl_basic_map *bmap,
1804 __isl_take isl_basic_set *dom,
1805 __isl_give isl_set **empty);
1806 __isl_give isl_map *isl_map_partial_lexmax(
1807 __isl_take isl_map *map, __isl_take isl_set *dom,
1808 __isl_give isl_set **empty);
1809 __isl_give isl_map *isl_map_partial_lexmin(
1810 __isl_take isl_map *map, __isl_take isl_set *dom,
1811 __isl_give isl_set **empty);
1813 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1814 return a map mapping each element in the domain of
1815 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1816 of all elements associated to that element.
1817 In case of union relations, the optimum is computed per space.
1819 __isl_give isl_map *isl_basic_map_lexmin(
1820 __isl_take isl_basic_map *bmap);
1821 __isl_give isl_map *isl_basic_map_lexmax(
1822 __isl_take isl_basic_map *bmap);
1823 __isl_give isl_map *isl_map_lexmin(
1824 __isl_take isl_map *map);
1825 __isl_give isl_map *isl_map_lexmax(
1826 __isl_take isl_map *map);
1827 __isl_give isl_union_map *isl_union_map_lexmin(
1828 __isl_take isl_union_map *umap);
1829 __isl_give isl_union_map *isl_union_map_lexmax(
1830 __isl_take isl_union_map *umap);
1834 Matrices can be created, copied and freed using the following functions.
1836 #include <isl/mat.h>
1837 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1838 unsigned n_row, unsigned n_col);
1839 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1840 void isl_mat_free(__isl_take isl_mat *mat);
1842 Note that the elements of a newly created matrix may have arbitrary values.
1843 The elements can be changed and inspected using the following functions.
1845 int isl_mat_rows(__isl_keep isl_mat *mat);
1846 int isl_mat_cols(__isl_keep isl_mat *mat);
1847 int isl_mat_get_element(__isl_keep isl_mat *mat,
1848 int row, int col, isl_int *v);
1849 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1850 int row, int col, isl_int v);
1852 C<isl_mat_get_element> will return a negative value if anything went wrong.
1853 In that case, the value of C<*v> is undefined.
1855 The following function can be used to compute the (right) inverse
1856 of a matrix, i.e., a matrix such that the product of the original
1857 and the inverse (in that order) is a multiple of the identity matrix.
1858 The input matrix is assumed to be of full row-rank.
1860 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1862 The following function can be used to compute the (right) kernel
1863 (or null space) of a matrix, i.e., a matrix such that the product of
1864 the original and the kernel (in that order) is the zero matrix.
1866 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1870 Points are elements of a set. They can be used to construct
1871 simple sets (boxes) or they can be used to represent the
1872 individual elements of a set.
1873 The zero point (the origin) can be created using
1875 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1877 The coordinates of a point can be inspected, set and changed
1880 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1881 enum isl_dim_type type, int pos, isl_int *v);
1882 __isl_give isl_point *isl_point_set_coordinate(
1883 __isl_take isl_point *pnt,
1884 enum isl_dim_type type, int pos, isl_int v);
1886 __isl_give isl_point *isl_point_add_ui(
1887 __isl_take isl_point *pnt,
1888 enum isl_dim_type type, int pos, unsigned val);
1889 __isl_give isl_point *isl_point_sub_ui(
1890 __isl_take isl_point *pnt,
1891 enum isl_dim_type type, int pos, unsigned val);
1893 Points can be copied or freed using
1895 __isl_give isl_point *isl_point_copy(
1896 __isl_keep isl_point *pnt);
1897 void isl_point_free(__isl_take isl_point *pnt);
1899 A singleton set can be created from a point using
1901 __isl_give isl_basic_set *isl_basic_set_from_point(
1902 __isl_take isl_point *pnt);
1903 __isl_give isl_set *isl_set_from_point(
1904 __isl_take isl_point *pnt);
1906 and a box can be created from two opposite extremal points using
1908 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1909 __isl_take isl_point *pnt1,
1910 __isl_take isl_point *pnt2);
1911 __isl_give isl_set *isl_set_box_from_points(
1912 __isl_take isl_point *pnt1,
1913 __isl_take isl_point *pnt2);
1915 All elements of a B<bounded> (union) set can be enumerated using
1916 the following functions.
1918 int isl_set_foreach_point(__isl_keep isl_set *set,
1919 int (*fn)(__isl_take isl_point *pnt, void *user),
1921 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1922 int (*fn)(__isl_take isl_point *pnt, void *user),
1925 The function C<fn> is called for each integer point in
1926 C<set> with as second argument the last argument of
1927 the C<isl_set_foreach_point> call. The function C<fn>
1928 should return C<0> on success and C<-1> on failure.
1929 In the latter case, C<isl_set_foreach_point> will stop
1930 enumerating and return C<-1> as well.
1931 If the enumeration is performed successfully and to completion,
1932 then C<isl_set_foreach_point> returns C<0>.
1934 To obtain a single point of a (basic) set, use
1936 __isl_give isl_point *isl_basic_set_sample_point(
1937 __isl_take isl_basic_set *bset);
1938 __isl_give isl_point *isl_set_sample_point(
1939 __isl_take isl_set *set);
1941 If C<set> does not contain any (integer) points, then the
1942 resulting point will be ``void'', a property that can be
1945 int isl_point_is_void(__isl_keep isl_point *pnt);
1947 =head2 Piecewise Quasipolynomials
1949 A piecewise quasipolynomial is a particular kind of function that maps
1950 a parametric point to a rational value.
1951 More specifically, a quasipolynomial is a polynomial expression in greatest
1952 integer parts of affine expressions of parameters and variables.
1953 A piecewise quasipolynomial is a subdivision of a given parametric
1954 domain into disjoint cells with a quasipolynomial associated to
1955 each cell. The value of the piecewise quasipolynomial at a given
1956 point is the value of the quasipolynomial associated to the cell
1957 that contains the point. Outside of the union of cells,
1958 the value is assumed to be zero.
1959 For example, the piecewise quasipolynomial
1961 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1963 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1964 A given piecewise quasipolynomial has a fixed domain dimension.
1965 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1966 defined over different domains.
1967 Piecewise quasipolynomials are mainly used by the C<barvinok>
1968 library for representing the number of elements in a parametric set or map.
1969 For example, the piecewise quasipolynomial above represents
1970 the number of points in the map
1972 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1974 =head3 Printing (Piecewise) Quasipolynomials
1976 Quasipolynomials and piecewise quasipolynomials can be printed
1977 using the following functions.
1979 __isl_give isl_printer *isl_printer_print_qpolynomial(
1980 __isl_take isl_printer *p,
1981 __isl_keep isl_qpolynomial *qp);
1983 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1984 __isl_take isl_printer *p,
1985 __isl_keep isl_pw_qpolynomial *pwqp);
1987 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1988 __isl_take isl_printer *p,
1989 __isl_keep isl_union_pw_qpolynomial *upwqp);
1991 The output format of the printer
1992 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1993 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1995 In case of printing in C<ISL_FORMAT_C>, the user may want
1996 to set the names of all dimensions
1998 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1999 __isl_take isl_qpolynomial *qp,
2000 enum isl_dim_type type, unsigned pos,
2002 __isl_give isl_pw_qpolynomial *
2003 isl_pw_qpolynomial_set_dim_name(
2004 __isl_take isl_pw_qpolynomial *pwqp,
2005 enum isl_dim_type type, unsigned pos,
2008 =head3 Creating New (Piecewise) Quasipolynomials
2010 Some simple quasipolynomials can be created using the following functions.
2011 More complicated quasipolynomials can be created by applying
2012 operations such as addition and multiplication
2013 on the resulting quasipolynomials
2015 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2016 __isl_take isl_dim *dim);
2017 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2018 __isl_take isl_dim *dim);
2019 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2020 __isl_take isl_dim *dim);
2021 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2022 __isl_take isl_dim *dim);
2023 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2024 __isl_take isl_dim *dim);
2025 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2026 __isl_take isl_dim *dim,
2027 const isl_int n, const isl_int d);
2028 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2029 __isl_take isl_div *div);
2030 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2031 __isl_take isl_dim *dim,
2032 enum isl_dim_type type, unsigned pos);
2034 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2035 with a single cell can be created using the following functions.
2036 Multiple of these single cell piecewise quasipolynomials can
2037 be combined to create more complicated piecewise quasipolynomials.
2039 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2040 __isl_take isl_dim *dim);
2041 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2042 __isl_take isl_set *set,
2043 __isl_take isl_qpolynomial *qp);
2045 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2046 __isl_take isl_dim *dim);
2047 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2048 __isl_take isl_pw_qpolynomial *pwqp);
2049 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2050 __isl_take isl_union_pw_qpolynomial *upwqp,
2051 __isl_take isl_pw_qpolynomial *pwqp);
2053 Quasipolynomials can be copied and freed again using the following
2056 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2057 __isl_keep isl_qpolynomial *qp);
2058 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2060 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2061 __isl_keep isl_pw_qpolynomial *pwqp);
2062 void isl_pw_qpolynomial_free(
2063 __isl_take isl_pw_qpolynomial *pwqp);
2065 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2066 __isl_keep isl_union_pw_qpolynomial *upwqp);
2067 void isl_union_pw_qpolynomial_free(
2068 __isl_take isl_union_pw_qpolynomial *upwqp);
2070 =head3 Inspecting (Piecewise) Quasipolynomials
2072 To iterate over all piecewise quasipolynomials in a union
2073 piecewise quasipolynomial, use the following function
2075 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2076 __isl_keep isl_union_pw_qpolynomial *upwqp,
2077 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2080 To extract the piecewise quasipolynomial from a union with a given dimension
2083 __isl_give isl_pw_qpolynomial *
2084 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2085 __isl_keep isl_union_pw_qpolynomial *upwqp,
2086 __isl_take isl_dim *dim);
2088 To iterate over the cells in a piecewise quasipolynomial,
2089 use either of the following two functions
2091 int isl_pw_qpolynomial_foreach_piece(
2092 __isl_keep isl_pw_qpolynomial *pwqp,
2093 int (*fn)(__isl_take isl_set *set,
2094 __isl_take isl_qpolynomial *qp,
2095 void *user), void *user);
2096 int isl_pw_qpolynomial_foreach_lifted_piece(
2097 __isl_keep isl_pw_qpolynomial *pwqp,
2098 int (*fn)(__isl_take isl_set *set,
2099 __isl_take isl_qpolynomial *qp,
2100 void *user), void *user);
2102 As usual, the function C<fn> should return C<0> on success
2103 and C<-1> on failure. The difference between
2104 C<isl_pw_qpolynomial_foreach_piece> and
2105 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2106 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2107 compute unique representations for all existentially quantified
2108 variables and then turn these existentially quantified variables
2109 into extra set variables, adapting the associated quasipolynomial
2110 accordingly. This means that the C<set> passed to C<fn>
2111 will not have any existentially quantified variables, but that
2112 the dimensions of the sets may be different for different
2113 invocations of C<fn>.
2115 To iterate over all terms in a quasipolynomial,
2118 int isl_qpolynomial_foreach_term(
2119 __isl_keep isl_qpolynomial *qp,
2120 int (*fn)(__isl_take isl_term *term,
2121 void *user), void *user);
2123 The terms themselves can be inspected and freed using
2126 unsigned isl_term_dim(__isl_keep isl_term *term,
2127 enum isl_dim_type type);
2128 void isl_term_get_num(__isl_keep isl_term *term,
2130 void isl_term_get_den(__isl_keep isl_term *term,
2132 int isl_term_get_exp(__isl_keep isl_term *term,
2133 enum isl_dim_type type, unsigned pos);
2134 __isl_give isl_div *isl_term_get_div(
2135 __isl_keep isl_term *term, unsigned pos);
2136 void isl_term_free(__isl_take isl_term *term);
2138 Each term is a product of parameters, set variables and
2139 integer divisions. The function C<isl_term_get_exp>
2140 returns the exponent of a given dimensions in the given term.
2141 The C<isl_int>s in the arguments of C<isl_term_get_num>
2142 and C<isl_term_get_den> need to have been initialized
2143 using C<isl_int_init> before calling these functions.
2145 =head3 Properties of (Piecewise) Quasipolynomials
2147 To check whether a quasipolynomial is actually a constant,
2148 use the following function.
2150 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2151 isl_int *n, isl_int *d);
2153 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2154 then the numerator and denominator of the constant
2155 are returned in C<*n> and C<*d>, respectively.
2157 =head3 Operations on (Piecewise) Quasipolynomials
2159 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2160 __isl_take isl_qpolynomial *qp);
2161 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2162 __isl_take isl_qpolynomial *qp1,
2163 __isl_take isl_qpolynomial *qp2);
2164 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2165 __isl_take isl_qpolynomial *qp1,
2166 __isl_take isl_qpolynomial *qp2);
2167 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2168 __isl_take isl_qpolynomial *qp1,
2169 __isl_take isl_qpolynomial *qp2);
2170 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2171 __isl_take isl_qpolynomial *qp, unsigned exponent);
2173 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2174 __isl_take isl_pw_qpolynomial *pwqp1,
2175 __isl_take isl_pw_qpolynomial *pwqp2);
2176 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2177 __isl_take isl_pw_qpolynomial *pwqp1,
2178 __isl_take isl_pw_qpolynomial *pwqp2);
2179 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2180 __isl_take isl_pw_qpolynomial *pwqp1,
2181 __isl_take isl_pw_qpolynomial *pwqp2);
2182 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2183 __isl_take isl_pw_qpolynomial *pwqp);
2184 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2185 __isl_take isl_pw_qpolynomial *pwqp1,
2186 __isl_take isl_pw_qpolynomial *pwqp2);
2188 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2189 __isl_take isl_union_pw_qpolynomial *upwqp1,
2190 __isl_take isl_union_pw_qpolynomial *upwqp2);
2191 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2192 __isl_take isl_union_pw_qpolynomial *upwqp1,
2193 __isl_take isl_union_pw_qpolynomial *upwqp2);
2194 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2195 __isl_take isl_union_pw_qpolynomial *upwqp1,
2196 __isl_take isl_union_pw_qpolynomial *upwqp2);
2198 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2199 __isl_take isl_pw_qpolynomial *pwqp,
2200 __isl_take isl_point *pnt);
2202 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2203 __isl_take isl_union_pw_qpolynomial *upwqp,
2204 __isl_take isl_point *pnt);
2206 __isl_give isl_set *isl_pw_qpolynomial_domain(
2207 __isl_take isl_pw_qpolynomial *pwqp);
2208 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2209 __isl_take isl_pw_qpolynomial *pwpq,
2210 __isl_take isl_set *set);
2212 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2213 __isl_take isl_union_pw_qpolynomial *upwqp);
2214 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2215 __isl_take isl_union_pw_qpolynomial *upwpq,
2216 __isl_take isl_union_set *uset);
2218 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2219 __isl_take isl_union_pw_qpolynomial *upwqp);
2221 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2222 __isl_take isl_pw_qpolynomial *pwqp,
2223 __isl_take isl_set *context);
2225 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2226 __isl_take isl_union_pw_qpolynomial *upwqp,
2227 __isl_take isl_union_set *context);
2229 The gist operation applies the gist operation to each of
2230 the cells in the domain of the input piecewise quasipolynomial.
2231 The context is also exploited
2232 to simplify the quasipolynomials associated to each cell.
2234 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2235 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2236 __isl_give isl_union_pw_qpolynomial *
2237 isl_union_pw_qpolynomial_to_polynomial(
2238 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2240 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2241 the polynomial will be an overapproximation. If C<sign> is negative,
2242 it will be an underapproximation. If C<sign> is zero, the approximation
2243 will lie somewhere in between.
2245 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2247 A piecewise quasipolynomial reduction is a piecewise
2248 reduction (or fold) of quasipolynomials.
2249 In particular, the reduction can be maximum or a minimum.
2250 The objects are mainly used to represent the result of
2251 an upper or lower bound on a quasipolynomial over its domain,
2252 i.e., as the result of the following function.
2254 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2255 __isl_take isl_pw_qpolynomial *pwqp,
2256 enum isl_fold type, int *tight);
2258 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2259 __isl_take isl_union_pw_qpolynomial *upwqp,
2260 enum isl_fold type, int *tight);
2262 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2263 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2264 is the returned bound is known be tight, i.e., for each value
2265 of the parameters there is at least
2266 one element in the domain that reaches the bound.
2267 If the domain of C<pwqp> is not wrapping, then the bound is computed
2268 over all elements in that domain and the result has a purely parametric
2269 domain. If the domain of C<pwqp> is wrapping, then the bound is
2270 computed over the range of the wrapped relation. The domain of the
2271 wrapped relation becomes the domain of the result.
2273 A (piecewise) quasipolynomial reduction can be copied or freed using the
2274 following functions.
2276 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2277 __isl_keep isl_qpolynomial_fold *fold);
2278 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2279 __isl_keep isl_pw_qpolynomial_fold *pwf);
2280 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2281 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2282 void isl_qpolynomial_fold_free(
2283 __isl_take isl_qpolynomial_fold *fold);
2284 void isl_pw_qpolynomial_fold_free(
2285 __isl_take isl_pw_qpolynomial_fold *pwf);
2286 void isl_union_pw_qpolynomial_fold_free(
2287 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2289 =head3 Printing Piecewise Quasipolynomial Reductions
2291 Piecewise quasipolynomial reductions can be printed
2292 using the following function.
2294 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2295 __isl_take isl_printer *p,
2296 __isl_keep isl_pw_qpolynomial_fold *pwf);
2297 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2298 __isl_take isl_printer *p,
2299 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2301 For C<isl_printer_print_pw_qpolynomial_fold>,
2302 output format of the printer
2303 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2304 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2305 output format of the printer
2306 needs to be set to C<ISL_FORMAT_ISL>.
2307 In case of printing in C<ISL_FORMAT_C>, the user may want
2308 to set the names of all dimensions
2310 __isl_give isl_pw_qpolynomial_fold *
2311 isl_pw_qpolynomial_fold_set_dim_name(
2312 __isl_take isl_pw_qpolynomial_fold *pwf,
2313 enum isl_dim_type type, unsigned pos,
2316 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2318 To iterate over all piecewise quasipolynomial reductions in a union
2319 piecewise quasipolynomial reduction, use the following function
2321 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2322 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2323 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2324 void *user), void *user);
2326 To iterate over the cells in a piecewise quasipolynomial reduction,
2327 use either of the following two functions
2329 int isl_pw_qpolynomial_fold_foreach_piece(
2330 __isl_keep isl_pw_qpolynomial_fold *pwf,
2331 int (*fn)(__isl_take isl_set *set,
2332 __isl_take isl_qpolynomial_fold *fold,
2333 void *user), void *user);
2334 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2335 __isl_keep isl_pw_qpolynomial_fold *pwf,
2336 int (*fn)(__isl_take isl_set *set,
2337 __isl_take isl_qpolynomial_fold *fold,
2338 void *user), void *user);
2340 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2341 of the difference between these two functions.
2343 To iterate over all quasipolynomials in a reduction, use
2345 int isl_qpolynomial_fold_foreach_qpolynomial(
2346 __isl_keep isl_qpolynomial_fold *fold,
2347 int (*fn)(__isl_take isl_qpolynomial *qp,
2348 void *user), void *user);
2350 =head3 Operations on Piecewise Quasipolynomial Reductions
2352 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2353 __isl_take isl_pw_qpolynomial_fold *pwf1,
2354 __isl_take isl_pw_qpolynomial_fold *pwf2);
2356 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2357 __isl_take isl_pw_qpolynomial_fold *pwf1,
2358 __isl_take isl_pw_qpolynomial_fold *pwf2);
2360 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2361 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2362 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2364 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2365 __isl_take isl_pw_qpolynomial_fold *pwf,
2366 __isl_take isl_point *pnt);
2368 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2369 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2370 __isl_take isl_point *pnt);
2372 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2373 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2374 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2375 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2376 __isl_take isl_union_set *uset);
2378 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2379 __isl_take isl_pw_qpolynomial_fold *pwf);
2381 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2382 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2384 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2385 __isl_take isl_pw_qpolynomial_fold *pwf,
2386 __isl_take isl_set *context);
2388 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2389 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2390 __isl_take isl_union_set *context);
2392 The gist operation applies the gist operation to each of
2393 the cells in the domain of the input piecewise quasipolynomial reduction.
2394 In future, the operation will also exploit the context
2395 to simplify the quasipolynomial reductions associated to each cell.
2397 __isl_give isl_pw_qpolynomial_fold *
2398 isl_set_apply_pw_qpolynomial_fold(
2399 __isl_take isl_set *set,
2400 __isl_take isl_pw_qpolynomial_fold *pwf,
2402 __isl_give isl_pw_qpolynomial_fold *
2403 isl_map_apply_pw_qpolynomial_fold(
2404 __isl_take isl_map *map,
2405 __isl_take isl_pw_qpolynomial_fold *pwf,
2407 __isl_give isl_union_pw_qpolynomial_fold *
2408 isl_union_set_apply_union_pw_qpolynomial_fold(
2409 __isl_take isl_union_set *uset,
2410 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2412 __isl_give isl_union_pw_qpolynomial_fold *
2413 isl_union_map_apply_union_pw_qpolynomial_fold(
2414 __isl_take isl_union_map *umap,
2415 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2418 The functions taking a map
2419 compose the given map with the given piecewise quasipolynomial reduction.
2420 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2421 over all elements in the intersection of the range of the map
2422 and the domain of the piecewise quasipolynomial reduction
2423 as a function of an element in the domain of the map.
2424 The functions taking a set compute a bound over all elements in the
2425 intersection of the set and the domain of the
2426 piecewise quasipolynomial reduction.
2428 =head2 Dependence Analysis
2430 C<isl> contains specialized functionality for performing
2431 array dataflow analysis. That is, given a I<sink> access relation
2432 and a collection of possible I<source> access relations,
2433 C<isl> can compute relations that describe
2434 for each iteration of the sink access, which iteration
2435 of which of the source access relations was the last
2436 to access the same data element before the given iteration
2438 To compute standard flow dependences, the sink should be
2439 a read, while the sources should be writes.
2440 If any of the source accesses are marked as being I<may>
2441 accesses, then there will be a dependence to the last
2442 I<must> access B<and> to any I<may> access that follows
2443 this last I<must> access.
2444 In particular, if I<all> sources are I<may> accesses,
2445 then memory based dependence analysis is performed.
2446 If, on the other hand, all sources are I<must> accesses,
2447 then value based dependence analysis is performed.
2449 #include <isl/flow.h>
2451 typedef int (*isl_access_level_before)(void *first, void *second);
2453 __isl_give isl_access_info *isl_access_info_alloc(
2454 __isl_take isl_map *sink,
2455 void *sink_user, isl_access_level_before fn,
2457 __isl_give isl_access_info *isl_access_info_add_source(
2458 __isl_take isl_access_info *acc,
2459 __isl_take isl_map *source, int must,
2461 void isl_access_info_free(__isl_take isl_access_info *acc);
2463 __isl_give isl_flow *isl_access_info_compute_flow(
2464 __isl_take isl_access_info *acc);
2466 int isl_flow_foreach(__isl_keep isl_flow *deps,
2467 int (*fn)(__isl_take isl_map *dep, int must,
2468 void *dep_user, void *user),
2470 __isl_give isl_map *isl_flow_get_no_source(
2471 __isl_keep isl_flow *deps, int must);
2472 void isl_flow_free(__isl_take isl_flow *deps);
2474 The function C<isl_access_info_compute_flow> performs the actual
2475 dependence analysis. The other functions are used to construct
2476 the input for this function or to read off the output.
2478 The input is collected in an C<isl_access_info>, which can
2479 be created through a call to C<isl_access_info_alloc>.
2480 The arguments to this functions are the sink access relation
2481 C<sink>, a token C<sink_user> used to identify the sink
2482 access to the user, a callback function for specifying the
2483 relative order of source and sink accesses, and the number
2484 of source access relations that will be added.
2485 The callback function has type C<int (*)(void *first, void *second)>.
2486 The function is called with two user supplied tokens identifying
2487 either a source or the sink and it should return the shared nesting
2488 level and the relative order of the two accesses.
2489 In particular, let I<n> be the number of loops shared by
2490 the two accesses. If C<first> precedes C<second> textually,
2491 then the function should return I<2 * n + 1>; otherwise,
2492 it should return I<2 * n>.
2493 The sources can be added to the C<isl_access_info> by performing
2494 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2495 C<must> indicates whether the source is a I<must> access
2496 or a I<may> access. Note that a multi-valued access relation
2497 should only be marked I<must> if every iteration in the domain
2498 of the relation accesses I<all> elements in its image.
2499 The C<source_user> token is again used to identify
2500 the source access. The range of the source access relation
2501 C<source> should have the same dimension as the range
2502 of the sink access relation.
2503 The C<isl_access_info_free> function should usually not be
2504 called explicitly, because it is called implicitly by
2505 C<isl_access_info_compute_flow>.
2507 The result of the dependence analysis is collected in an
2508 C<isl_flow>. There may be elements of
2509 the sink access for which no preceding source access could be
2510 found or for which all preceding sources are I<may> accesses.
2511 The relations containing these elements can be obtained through
2512 calls to C<isl_flow_get_no_source>, the first with C<must> set
2513 and the second with C<must> unset.
2514 In the case of standard flow dependence analysis,
2515 with the sink a read and the sources I<must> writes,
2516 the first relation corresponds to the reads from uninitialized
2517 array elements and the second relation is empty.
2518 The actual flow dependences can be extracted using
2519 C<isl_flow_foreach>. This function will call the user-specified
2520 callback function C<fn> for each B<non-empty> dependence between
2521 a source and the sink. The callback function is called
2522 with four arguments, the actual flow dependence relation
2523 mapping source iterations to sink iterations, a boolean that
2524 indicates whether it is a I<must> or I<may> dependence, a token
2525 identifying the source and an additional C<void *> with value
2526 equal to the third argument of the C<isl_flow_foreach> call.
2527 A dependence is marked I<must> if it originates from a I<must>
2528 source and if it is not followed by any I<may> sources.
2530 After finishing with an C<isl_flow>, the user should call
2531 C<isl_flow_free> to free all associated memory.
2533 A higher-level interface to dependence analysis is provided
2534 by the following function.
2536 #include <isl/flow.h>
2538 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2539 __isl_take isl_union_map *must_source,
2540 __isl_take isl_union_map *may_source,
2541 __isl_take isl_union_map *schedule,
2542 __isl_give isl_union_map **must_dep,
2543 __isl_give isl_union_map **may_dep,
2544 __isl_give isl_union_map **must_no_source,
2545 __isl_give isl_union_map **may_no_source);
2547 The arrays are identified by the tuple names of the ranges
2548 of the accesses. The iteration domains by the tuple names
2549 of the domains of the accesses and of the schedule.
2550 The relative order of the iteration domains is given by the
2551 schedule. The relations returned through C<must_no_source>
2552 and C<may_no_source> are subsets of C<sink>.
2553 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2554 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2555 any of the other arguments is treated as an error.
2557 =head2 Parametric Vertex Enumeration
2559 The parametric vertex enumeration described in this section
2560 is mainly intended to be used internally and by the C<barvinok>
2563 #include <isl/vertices.h>
2564 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2565 __isl_keep isl_basic_set *bset);
2567 The function C<isl_basic_set_compute_vertices> performs the
2568 actual computation of the parametric vertices and the chamber
2569 decomposition and store the result in an C<isl_vertices> object.
2570 This information can be queried by either iterating over all
2571 the vertices or iterating over all the chambers or cells
2572 and then iterating over all vertices that are active on the chamber.
2574 int isl_vertices_foreach_vertex(
2575 __isl_keep isl_vertices *vertices,
2576 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2579 int isl_vertices_foreach_cell(
2580 __isl_keep isl_vertices *vertices,
2581 int (*fn)(__isl_take isl_cell *cell, void *user),
2583 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2584 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2587 Other operations that can be performed on an C<isl_vertices> object are
2590 isl_ctx *isl_vertices_get_ctx(
2591 __isl_keep isl_vertices *vertices);
2592 int isl_vertices_get_n_vertices(
2593 __isl_keep isl_vertices *vertices);
2594 void isl_vertices_free(__isl_take isl_vertices *vertices);
2596 Vertices can be inspected and destroyed using the following functions.
2598 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2599 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2600 __isl_give isl_basic_set *isl_vertex_get_domain(
2601 __isl_keep isl_vertex *vertex);
2602 __isl_give isl_basic_set *isl_vertex_get_expr(
2603 __isl_keep isl_vertex *vertex);
2604 void isl_vertex_free(__isl_take isl_vertex *vertex);
2606 C<isl_vertex_get_expr> returns a singleton parametric set describing
2607 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2609 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2610 B<rational> basic sets, so they should mainly be used for inspection
2611 and should not be mixed with integer sets.
2613 Chambers can be inspected and destroyed using the following functions.
2615 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2616 __isl_give isl_basic_set *isl_cell_get_domain(
2617 __isl_keep isl_cell *cell);
2618 void isl_cell_free(__isl_take isl_cell *cell);
2622 Although C<isl> is mainly meant to be used as a library,
2623 it also contains some basic applications that use some
2624 of the functionality of C<isl>.
2625 The input may be specified in either the L<isl format>
2626 or the L<PolyLib format>.
2628 =head2 C<isl_polyhedron_sample>
2630 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2631 an integer element of the polyhedron, if there is any.
2632 The first column in the output is the denominator and is always
2633 equal to 1. If the polyhedron contains no integer points,
2634 then a vector of length zero is printed.
2638 C<isl_pip> takes the same input as the C<example> program
2639 from the C<piplib> distribution, i.e., a set of constraints
2640 on the parameters, a line containing only -1 and finally a set
2641 of constraints on a parametric polyhedron.
2642 The coefficients of the parameters appear in the last columns
2643 (but before the final constant column).
2644 The output is the lexicographic minimum of the parametric polyhedron.
2645 As C<isl> currently does not have its own output format, the output
2646 is just a dump of the internal state.
2648 =head2 C<isl_polyhedron_minimize>
2650 C<isl_polyhedron_minimize> computes the minimum of some linear
2651 or affine objective function over the integer points in a polyhedron.
2652 If an affine objective function
2653 is given, then the constant should appear in the last column.
2655 =head2 C<isl_polytope_scan>
2657 Given a polytope, C<isl_polytope_scan> prints
2658 all integer points in the polytope.
2660 =head1 C<isl-polylib>
2662 The C<isl-polylib> library provides the following functions for converting
2663 between C<isl> objects and C<PolyLib> objects.
2664 The library is distributed separately for licensing reasons.
2666 #include <isl_set_polylib.h>
2667 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2668 Polyhedron *P, __isl_take isl_dim *dim);
2669 Polyhedron *isl_basic_set_to_polylib(
2670 __isl_keep isl_basic_set *bset);
2671 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2672 __isl_take isl_dim *dim);
2673 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2675 #include <isl_map_polylib.h>
2676 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2677 Polyhedron *P, __isl_take isl_dim *dim);
2678 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2679 __isl_take isl_dim *dim);
2680 Polyhedron *isl_basic_map_to_polylib(
2681 __isl_keep isl_basic_map *bmap);
2682 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);