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);
978 __isl_give isl_map *isl_map_remove_divs(
979 __isl_take isl_map *map);
981 To iterate over all the sets or maps in a union set or map, use
983 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
984 int (*fn)(__isl_take isl_set *set, void *user),
986 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
987 int (*fn)(__isl_take isl_map *map, void *user),
990 The number of sets or maps in a union set or map can be obtained
993 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
994 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
996 To extract the set or map from a union with a given dimension
999 __isl_give isl_set *isl_union_set_extract_set(
1000 __isl_keep isl_union_set *uset,
1001 __isl_take isl_dim *dim);
1002 __isl_give isl_map *isl_union_map_extract_map(
1003 __isl_keep isl_union_map *umap,
1004 __isl_take isl_dim *dim);
1006 To iterate over all the basic sets or maps in a set or map, use
1008 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1009 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1011 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1012 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1015 The callback function C<fn> should return 0 if successful and
1016 -1 if an error occurs. In the latter case, or if any other error
1017 occurs, the above functions will return -1.
1019 It should be noted that C<isl> does not guarantee that
1020 the basic sets or maps passed to C<fn> are disjoint.
1021 If this is required, then the user should call one of
1022 the following functions first.
1024 __isl_give isl_set *isl_set_make_disjoint(
1025 __isl_take isl_set *set);
1026 __isl_give isl_map *isl_map_make_disjoint(
1027 __isl_take isl_map *map);
1029 The number of basic sets in a set can be obtained
1032 int isl_set_n_basic_set(__isl_keep isl_set *set);
1034 To iterate over the constraints of a basic set or map, use
1036 #include <isl/constraint.h>
1038 int isl_basic_map_foreach_constraint(
1039 __isl_keep isl_basic_map *bmap,
1040 int (*fn)(__isl_take isl_constraint *c, void *user),
1042 void isl_constraint_free(struct isl_constraint *c);
1044 Again, the callback function C<fn> should return 0 if successful and
1045 -1 if an error occurs. In the latter case, or if any other error
1046 occurs, the above functions will return -1.
1047 The constraint C<c> represents either an equality or an inequality.
1048 Use the following function to find out whether a constraint
1049 represents an equality. If not, it represents an inequality.
1051 int isl_constraint_is_equality(
1052 __isl_keep isl_constraint *constraint);
1054 The coefficients of the constraints can be inspected using
1055 the following functions.
1057 void isl_constraint_get_constant(
1058 __isl_keep isl_constraint *constraint, isl_int *v);
1059 void isl_constraint_get_coefficient(
1060 __isl_keep isl_constraint *constraint,
1061 enum isl_dim_type type, int pos, isl_int *v);
1063 The explicit representations of the existentially quantified
1064 variables can be inspected using the following functions.
1065 Note that the user is only allowed to use these functions
1066 if the inspected set or map is the result of a call
1067 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1069 __isl_give isl_div *isl_constraint_div(
1070 __isl_keep isl_constraint *constraint, int pos);
1071 void isl_div_get_constant(__isl_keep isl_div *div,
1073 void isl_div_get_denominator(__isl_keep isl_div *div,
1075 void isl_div_get_coefficient(__isl_keep isl_div *div,
1076 enum isl_dim_type type, int pos, isl_int *v);
1078 To obtain the constraints of a basic set or map in matrix
1079 form, use the following functions.
1081 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1082 __isl_keep isl_basic_set *bset,
1083 enum isl_dim_type c1, enum isl_dim_type c2,
1084 enum isl_dim_type c3, enum isl_dim_type c4);
1085 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1086 __isl_keep isl_basic_set *bset,
1087 enum isl_dim_type c1, enum isl_dim_type c2,
1088 enum isl_dim_type c3, enum isl_dim_type c4);
1089 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1090 __isl_keep isl_basic_map *bmap,
1091 enum isl_dim_type c1,
1092 enum isl_dim_type c2, enum isl_dim_type c3,
1093 enum isl_dim_type c4, enum isl_dim_type c5);
1094 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1095 __isl_keep isl_basic_map *bmap,
1096 enum isl_dim_type c1,
1097 enum isl_dim_type c2, enum isl_dim_type c3,
1098 enum isl_dim_type c4, enum isl_dim_type c5);
1100 The C<isl_dim_type> arguments dictate the order in which
1101 different kinds of variables appear in the resulting matrix
1102 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1103 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1105 The names of the domain and range spaces of a set or relation can be
1106 read off using the following functions.
1108 const char *isl_basic_set_get_tuple_name(
1109 __isl_keep isl_basic_set *bset);
1110 const char *isl_set_get_tuple_name(
1111 __isl_keep isl_set *set);
1112 const char *isl_basic_map_get_tuple_name(
1113 __isl_keep isl_basic_map *bmap,
1114 enum isl_dim_type type);
1115 const char *isl_map_get_tuple_name(
1116 __isl_keep isl_map *map,
1117 enum isl_dim_type type);
1119 As with C<isl_dim_get_tuple_name>, the value returned points to
1120 an internal data structure.
1121 The names of individual dimensions can be read off using
1122 the following functions.
1124 const char *isl_constraint_get_dim_name(
1125 __isl_keep isl_constraint *constraint,
1126 enum isl_dim_type type, unsigned pos);
1127 const char *isl_basic_set_get_dim_name(
1128 __isl_keep isl_basic_set *bset,
1129 enum isl_dim_type type, unsigned pos);
1130 const char *isl_set_get_dim_name(
1131 __isl_keep isl_set *set,
1132 enum isl_dim_type type, unsigned pos);
1133 const char *isl_basic_map_get_dim_name(
1134 __isl_keep isl_basic_map *bmap,
1135 enum isl_dim_type type, unsigned pos);
1136 const char *isl_map_get_dim_name(
1137 __isl_keep isl_map *map,
1138 enum isl_dim_type type, unsigned pos);
1140 These functions are mostly useful to obtain the names
1145 =head3 Unary Properties
1151 The following functions test whether the given set or relation
1152 contains any integer points. The ``fast'' variants do not perform
1153 any computations, but simply check if the given set or relation
1154 is already known to be empty.
1156 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1157 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1158 int isl_set_is_empty(__isl_keep isl_set *set);
1159 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1160 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1161 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1162 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1163 int isl_map_is_empty(__isl_keep isl_map *map);
1164 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1166 =item * Universality
1168 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1169 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1170 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1172 =item * Single-valuedness
1174 int isl_map_is_single_valued(__isl_keep isl_map *map);
1178 int isl_map_is_bijective(__isl_keep isl_map *map);
1182 The following functions check whether the domain of the given
1183 (basic) set is a wrapped relation.
1185 int isl_basic_set_is_wrapping(
1186 __isl_keep isl_basic_set *bset);
1187 int isl_set_is_wrapping(__isl_keep isl_set *set);
1189 =item * Internal Product
1191 int isl_basic_map_can_zip(
1192 __isl_keep isl_basic_map *bmap);
1193 int isl_map_can_zip(__isl_keep isl_map *map);
1195 Check whether the product of domain and range of the given relation
1197 i.e., whether both domain and range are nested relations.
1201 =head3 Binary Properties
1207 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1208 __isl_keep isl_set *set2);
1209 int isl_set_is_equal(__isl_keep isl_set *set1,
1210 __isl_keep isl_set *set2);
1211 int isl_union_set_is_equal(
1212 __isl_keep isl_union_set *uset1,
1213 __isl_keep isl_union_set *uset2);
1214 int isl_basic_map_is_equal(
1215 __isl_keep isl_basic_map *bmap1,
1216 __isl_keep isl_basic_map *bmap2);
1217 int isl_map_is_equal(__isl_keep isl_map *map1,
1218 __isl_keep isl_map *map2);
1219 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1220 __isl_keep isl_map *map2);
1221 int isl_union_map_is_equal(
1222 __isl_keep isl_union_map *umap1,
1223 __isl_keep isl_union_map *umap2);
1225 =item * Disjointness
1227 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1228 __isl_keep isl_set *set2);
1232 int isl_set_is_subset(__isl_keep isl_set *set1,
1233 __isl_keep isl_set *set2);
1234 int isl_set_is_strict_subset(
1235 __isl_keep isl_set *set1,
1236 __isl_keep isl_set *set2);
1237 int isl_union_set_is_subset(
1238 __isl_keep isl_union_set *uset1,
1239 __isl_keep isl_union_set *uset2);
1240 int isl_union_set_is_strict_subset(
1241 __isl_keep isl_union_set *uset1,
1242 __isl_keep isl_union_set *uset2);
1243 int isl_basic_map_is_subset(
1244 __isl_keep isl_basic_map *bmap1,
1245 __isl_keep isl_basic_map *bmap2);
1246 int isl_basic_map_is_strict_subset(
1247 __isl_keep isl_basic_map *bmap1,
1248 __isl_keep isl_basic_map *bmap2);
1249 int isl_map_is_subset(
1250 __isl_keep isl_map *map1,
1251 __isl_keep isl_map *map2);
1252 int isl_map_is_strict_subset(
1253 __isl_keep isl_map *map1,
1254 __isl_keep isl_map *map2);
1255 int isl_union_map_is_subset(
1256 __isl_keep isl_union_map *umap1,
1257 __isl_keep isl_union_map *umap2);
1258 int isl_union_map_is_strict_subset(
1259 __isl_keep isl_union_map *umap1,
1260 __isl_keep isl_union_map *umap2);
1264 =head2 Unary Operations
1270 __isl_give isl_set *isl_set_complement(
1271 __isl_take isl_set *set);
1275 __isl_give isl_basic_map *isl_basic_map_reverse(
1276 __isl_take isl_basic_map *bmap);
1277 __isl_give isl_map *isl_map_reverse(
1278 __isl_take isl_map *map);
1279 __isl_give isl_union_map *isl_union_map_reverse(
1280 __isl_take isl_union_map *umap);
1284 __isl_give isl_basic_set *isl_basic_set_project_out(
1285 __isl_take isl_basic_set *bset,
1286 enum isl_dim_type type, unsigned first, unsigned n);
1287 __isl_give isl_basic_map *isl_basic_map_project_out(
1288 __isl_take isl_basic_map *bmap,
1289 enum isl_dim_type type, unsigned first, unsigned n);
1290 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1291 enum isl_dim_type type, unsigned first, unsigned n);
1292 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1293 enum isl_dim_type type, unsigned first, unsigned n);
1294 __isl_give isl_basic_set *isl_basic_map_domain(
1295 __isl_take isl_basic_map *bmap);
1296 __isl_give isl_basic_set *isl_basic_map_range(
1297 __isl_take isl_basic_map *bmap);
1298 __isl_give isl_set *isl_map_domain(
1299 __isl_take isl_map *bmap);
1300 __isl_give isl_set *isl_map_range(
1301 __isl_take isl_map *map);
1302 __isl_give isl_union_set *isl_union_map_domain(
1303 __isl_take isl_union_map *umap);
1304 __isl_give isl_union_set *isl_union_map_range(
1305 __isl_take isl_union_map *umap);
1307 __isl_give isl_basic_map *isl_basic_map_domain_map(
1308 __isl_take isl_basic_map *bmap);
1309 __isl_give isl_basic_map *isl_basic_map_range_map(
1310 __isl_take isl_basic_map *bmap);
1311 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1312 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1313 __isl_give isl_union_map *isl_union_map_domain_map(
1314 __isl_take isl_union_map *umap);
1315 __isl_give isl_union_map *isl_union_map_range_map(
1316 __isl_take isl_union_map *umap);
1318 The functions above construct a (basic, regular or union) relation
1319 that maps (a wrapped version of) the input relation to its domain or range.
1323 __isl_give isl_map *isl_set_identity(
1324 __isl_take isl_set *set);
1325 __isl_give isl_union_map *isl_union_set_identity(
1326 __isl_take isl_union_set *uset);
1328 Construct an identity relation on the given (union) set.
1332 __isl_give isl_basic_set *isl_basic_map_deltas(
1333 __isl_take isl_basic_map *bmap);
1334 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1335 __isl_give isl_union_set *isl_union_map_deltas(
1336 __isl_take isl_union_map *umap);
1338 These functions return a (basic) set containing the differences
1339 between image elements and corresponding domain elements in the input.
1341 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1342 __isl_take isl_basic_map *bmap);
1343 __isl_give isl_map *isl_map_deltas_map(
1344 __isl_take isl_map *map);
1345 __isl_give isl_union_map *isl_union_map_deltas_map(
1346 __isl_take isl_union_map *umap);
1348 The functions above construct a (basic, regular or union) relation
1349 that maps (a wrapped version of) the input relation to its delta set.
1353 Simplify the representation of a set or relation by trying
1354 to combine pairs of basic sets or relations into a single
1355 basic set or relation.
1357 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1358 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1359 __isl_give isl_union_set *isl_union_set_coalesce(
1360 __isl_take isl_union_set *uset);
1361 __isl_give isl_union_map *isl_union_map_coalesce(
1362 __isl_take isl_union_map *umap);
1364 =item * Detecting equalities
1366 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1367 __isl_take isl_basic_set *bset);
1368 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1369 __isl_take isl_basic_map *bmap);
1370 __isl_give isl_set *isl_set_detect_equalities(
1371 __isl_take isl_set *set);
1372 __isl_give isl_map *isl_map_detect_equalities(
1373 __isl_take isl_map *map);
1374 __isl_give isl_union_set *isl_union_set_detect_equalities(
1375 __isl_take isl_union_set *uset);
1376 __isl_give isl_union_map *isl_union_map_detect_equalities(
1377 __isl_take isl_union_map *umap);
1379 Simplify the representation of a set or relation by detecting implicit
1384 __isl_give isl_basic_set *isl_set_convex_hull(
1385 __isl_take isl_set *set);
1386 __isl_give isl_basic_map *isl_map_convex_hull(
1387 __isl_take isl_map *map);
1389 If the input set or relation has any existentially quantified
1390 variables, then the result of these operations is currently undefined.
1394 __isl_give isl_basic_set *isl_set_simple_hull(
1395 __isl_take isl_set *set);
1396 __isl_give isl_basic_map *isl_map_simple_hull(
1397 __isl_take isl_map *map);
1398 __isl_give isl_union_map *isl_union_map_simple_hull(
1399 __isl_take isl_union_map *umap);
1401 These functions compute a single basic set or relation
1402 that contains the whole input set or relation.
1403 In particular, the output is described by translates
1404 of the constraints describing the basic sets or relations in the input.
1408 (See \autoref{s:simple hull}.)
1414 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1415 __isl_take isl_basic_set *bset);
1416 __isl_give isl_basic_set *isl_set_affine_hull(
1417 __isl_take isl_set *set);
1418 __isl_give isl_union_set *isl_union_set_affine_hull(
1419 __isl_take isl_union_set *uset);
1420 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1421 __isl_take isl_basic_map *bmap);
1422 __isl_give isl_basic_map *isl_map_affine_hull(
1423 __isl_take isl_map *map);
1424 __isl_give isl_union_map *isl_union_map_affine_hull(
1425 __isl_take isl_union_map *umap);
1427 In case of union sets and relations, the affine hull is computed
1430 =item * Polyhedral hull
1432 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1433 __isl_take isl_set *set);
1434 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1435 __isl_take isl_map *map);
1436 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1437 __isl_take isl_union_set *uset);
1438 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1439 __isl_take isl_union_map *umap);
1441 These functions compute a single basic set or relation
1442 not involving any existentially quantified variables
1443 that contains the whole input set or relation.
1444 In case of union sets and relations, the polyhedral hull is computed
1449 The following functions compute either the set of (rational) coefficient
1450 values of valid constraints for the given set or the set of (rational)
1451 values satisfying the constraints with coefficients from the given set.
1452 Internally, these two sets of functions perform essentially the
1453 same operations, except that the set of coefficients is assumed to
1454 be a cone, while the set of values may be any polyhedron.
1455 The current implementation is based on the Farkas lemma and
1456 Fourier-Motzkin elimination, but this may change or be made optional
1457 in future. In particular, future implementations may use different
1458 dualization algorithms or skip the elimination step.
1460 __isl_give isl_basic_set *isl_basic_set_coefficients(
1461 __isl_take isl_basic_set *bset);
1462 __isl_give isl_basic_set *isl_set_coefficients(
1463 __isl_take isl_set *set);
1464 __isl_give isl_union_set *isl_union_set_coefficients(
1465 __isl_take isl_union_set *bset);
1466 __isl_give isl_basic_set *isl_basic_set_solutions(
1467 __isl_take isl_basic_set *bset);
1468 __isl_give isl_basic_set *isl_set_solutions(
1469 __isl_take isl_set *set);
1470 __isl_give isl_union_set *isl_union_set_solutions(
1471 __isl_take isl_union_set *bset);
1475 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1477 __isl_give isl_union_map *isl_union_map_power(
1478 __isl_take isl_union_map *umap, int *exact);
1480 Compute a parametric representation for all positive powers I<k> of C<map>.
1481 The result maps I<k> to a nested relation corresponding to the
1482 I<k>th power of C<map>.
1483 The result may be an overapproximation. If the result is known to be exact,
1484 then C<*exact> is set to C<1>.
1486 =item * Transitive closure
1488 __isl_give isl_map *isl_map_transitive_closure(
1489 __isl_take isl_map *map, int *exact);
1490 __isl_give isl_union_map *isl_union_map_transitive_closure(
1491 __isl_take isl_union_map *umap, int *exact);
1493 Compute the transitive closure of C<map>.
1494 The result may be an overapproximation. If the result is known to be exact,
1495 then C<*exact> is set to C<1>.
1497 =item * Reaching path lengths
1499 __isl_give isl_map *isl_map_reaching_path_lengths(
1500 __isl_take isl_map *map, int *exact);
1502 Compute a relation that maps each element in the range of C<map>
1503 to the lengths of all paths composed of edges in C<map> that
1504 end up in the given element.
1505 The result may be an overapproximation. If the result is known to be exact,
1506 then C<*exact> is set to C<1>.
1507 To compute the I<maximal> path length, the resulting relation
1508 should be postprocessed by C<isl_map_lexmax>.
1509 In particular, if the input relation is a dependence relation
1510 (mapping sources to sinks), then the maximal path length corresponds
1511 to the free schedule.
1512 Note, however, that C<isl_map_lexmax> expects the maximum to be
1513 finite, so if the path lengths are unbounded (possibly due to
1514 the overapproximation), then you will get an error message.
1518 __isl_give isl_basic_set *isl_basic_map_wrap(
1519 __isl_take isl_basic_map *bmap);
1520 __isl_give isl_set *isl_map_wrap(
1521 __isl_take isl_map *map);
1522 __isl_give isl_union_set *isl_union_map_wrap(
1523 __isl_take isl_union_map *umap);
1524 __isl_give isl_basic_map *isl_basic_set_unwrap(
1525 __isl_take isl_basic_set *bset);
1526 __isl_give isl_map *isl_set_unwrap(
1527 __isl_take isl_set *set);
1528 __isl_give isl_union_map *isl_union_set_unwrap(
1529 __isl_take isl_union_set *uset);
1533 Remove any internal structure of domain (and range) of the given
1534 set or relation. If there is any such internal structure in the input,
1535 then the name of the space is also removed.
1537 __isl_give isl_basic_set *isl_basic_set_flatten(
1538 __isl_take isl_basic_set *bset);
1539 __isl_give isl_set *isl_set_flatten(
1540 __isl_take isl_set *set);
1541 __isl_give isl_basic_map *isl_basic_map_flatten(
1542 __isl_take isl_basic_map *bmap);
1543 __isl_give isl_map *isl_map_flatten(
1544 __isl_take isl_map *map);
1546 __isl_give isl_map *isl_set_flatten_map(
1547 __isl_take isl_set *set);
1549 The function above constructs a relation
1550 that maps the input set to a flattened version of the set.
1554 Lift the input set to a space with extra dimensions corresponding
1555 to the existentially quantified variables in the input.
1556 In particular, the result lives in a wrapped map where the domain
1557 is the original space and the range corresponds to the original
1558 existentially quantified variables.
1560 __isl_give isl_basic_set *isl_basic_set_lift(
1561 __isl_take isl_basic_set *bset);
1562 __isl_give isl_set *isl_set_lift(
1563 __isl_take isl_set *set);
1564 __isl_give isl_union_set *isl_union_set_lift(
1565 __isl_take isl_union_set *uset);
1567 =item * Internal Product
1569 __isl_give isl_basic_map *isl_basic_map_zip(
1570 __isl_take isl_basic_map *bmap);
1571 __isl_give isl_map *isl_map_zip(
1572 __isl_take isl_map *map);
1573 __isl_give isl_union_map *isl_union_map_zip(
1574 __isl_take isl_union_map *umap);
1576 Given a relation with nested relations for domain and range,
1577 interchange the range of the domain with the domain of the range.
1579 =item * Dimension manipulation
1581 __isl_give isl_set *isl_set_add_dims(
1582 __isl_take isl_set *set,
1583 enum isl_dim_type type, unsigned n);
1584 __isl_give isl_map *isl_map_add_dims(
1585 __isl_take isl_map *map,
1586 enum isl_dim_type type, unsigned n);
1588 It is usually not advisable to directly change the (input or output)
1589 space of a set or a relation as this removes the name and the internal
1590 structure of the space. However, the above functions can be useful
1591 to add new parameters.
1595 =head2 Binary Operations
1597 The two arguments of a binary operation not only need to live
1598 in the same C<isl_ctx>, they currently also need to have
1599 the same (number of) parameters.
1601 =head3 Basic Operations
1605 =item * Intersection
1607 __isl_give isl_basic_set *isl_basic_set_intersect(
1608 __isl_take isl_basic_set *bset1,
1609 __isl_take isl_basic_set *bset2);
1610 __isl_give isl_set *isl_set_intersect(
1611 __isl_take isl_set *set1,
1612 __isl_take isl_set *set2);
1613 __isl_give isl_union_set *isl_union_set_intersect(
1614 __isl_take isl_union_set *uset1,
1615 __isl_take isl_union_set *uset2);
1616 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1617 __isl_take isl_basic_map *bmap,
1618 __isl_take isl_basic_set *bset);
1619 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1620 __isl_take isl_basic_map *bmap,
1621 __isl_take isl_basic_set *bset);
1622 __isl_give isl_basic_map *isl_basic_map_intersect(
1623 __isl_take isl_basic_map *bmap1,
1624 __isl_take isl_basic_map *bmap2);
1625 __isl_give isl_map *isl_map_intersect_domain(
1626 __isl_take isl_map *map,
1627 __isl_take isl_set *set);
1628 __isl_give isl_map *isl_map_intersect_range(
1629 __isl_take isl_map *map,
1630 __isl_take isl_set *set);
1631 __isl_give isl_map *isl_map_intersect(
1632 __isl_take isl_map *map1,
1633 __isl_take isl_map *map2);
1634 __isl_give isl_union_map *isl_union_map_intersect_domain(
1635 __isl_take isl_union_map *umap,
1636 __isl_take isl_union_set *uset);
1637 __isl_give isl_union_map *isl_union_map_intersect_range(
1638 __isl_take isl_union_map *umap,
1639 __isl_take isl_union_set *uset);
1640 __isl_give isl_union_map *isl_union_map_intersect(
1641 __isl_take isl_union_map *umap1,
1642 __isl_take isl_union_map *umap2);
1646 __isl_give isl_set *isl_basic_set_union(
1647 __isl_take isl_basic_set *bset1,
1648 __isl_take isl_basic_set *bset2);
1649 __isl_give isl_map *isl_basic_map_union(
1650 __isl_take isl_basic_map *bmap1,
1651 __isl_take isl_basic_map *bmap2);
1652 __isl_give isl_set *isl_set_union(
1653 __isl_take isl_set *set1,
1654 __isl_take isl_set *set2);
1655 __isl_give isl_map *isl_map_union(
1656 __isl_take isl_map *map1,
1657 __isl_take isl_map *map2);
1658 __isl_give isl_union_set *isl_union_set_union(
1659 __isl_take isl_union_set *uset1,
1660 __isl_take isl_union_set *uset2);
1661 __isl_give isl_union_map *isl_union_map_union(
1662 __isl_take isl_union_map *umap1,
1663 __isl_take isl_union_map *umap2);
1665 =item * Set difference
1667 __isl_give isl_set *isl_set_subtract(
1668 __isl_take isl_set *set1,
1669 __isl_take isl_set *set2);
1670 __isl_give isl_map *isl_map_subtract(
1671 __isl_take isl_map *map1,
1672 __isl_take isl_map *map2);
1673 __isl_give isl_union_set *isl_union_set_subtract(
1674 __isl_take isl_union_set *uset1,
1675 __isl_take isl_union_set *uset2);
1676 __isl_give isl_union_map *isl_union_map_subtract(
1677 __isl_take isl_union_map *umap1,
1678 __isl_take isl_union_map *umap2);
1682 __isl_give isl_basic_set *isl_basic_set_apply(
1683 __isl_take isl_basic_set *bset,
1684 __isl_take isl_basic_map *bmap);
1685 __isl_give isl_set *isl_set_apply(
1686 __isl_take isl_set *set,
1687 __isl_take isl_map *map);
1688 __isl_give isl_union_set *isl_union_set_apply(
1689 __isl_take isl_union_set *uset,
1690 __isl_take isl_union_map *umap);
1691 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1692 __isl_take isl_basic_map *bmap1,
1693 __isl_take isl_basic_map *bmap2);
1694 __isl_give isl_basic_map *isl_basic_map_apply_range(
1695 __isl_take isl_basic_map *bmap1,
1696 __isl_take isl_basic_map *bmap2);
1697 __isl_give isl_map *isl_map_apply_domain(
1698 __isl_take isl_map *map1,
1699 __isl_take isl_map *map2);
1700 __isl_give isl_union_map *isl_union_map_apply_domain(
1701 __isl_take isl_union_map *umap1,
1702 __isl_take isl_union_map *umap2);
1703 __isl_give isl_map *isl_map_apply_range(
1704 __isl_take isl_map *map1,
1705 __isl_take isl_map *map2);
1706 __isl_give isl_union_map *isl_union_map_apply_range(
1707 __isl_take isl_union_map *umap1,
1708 __isl_take isl_union_map *umap2);
1710 =item * Cartesian Product
1712 __isl_give isl_set *isl_set_product(
1713 __isl_take isl_set *set1,
1714 __isl_take isl_set *set2);
1715 __isl_give isl_union_set *isl_union_set_product(
1716 __isl_take isl_union_set *uset1,
1717 __isl_take isl_union_set *uset2);
1718 __isl_give isl_basic_map *isl_basic_map_range_product(
1719 __isl_take isl_basic_map *bmap1,
1720 __isl_take isl_basic_map *bmap2);
1721 __isl_give isl_map *isl_map_range_product(
1722 __isl_take isl_map *map1,
1723 __isl_take isl_map *map2);
1724 __isl_give isl_union_map *isl_union_map_range_product(
1725 __isl_take isl_union_map *umap1,
1726 __isl_take isl_union_map *umap2);
1727 __isl_give isl_map *isl_map_product(
1728 __isl_take isl_map *map1,
1729 __isl_take isl_map *map2);
1730 __isl_give isl_union_map *isl_union_map_product(
1731 __isl_take isl_union_map *umap1,
1732 __isl_take isl_union_map *umap2);
1734 The above functions compute the cross product of the given
1735 sets or relations. The domains and ranges of the results
1736 are wrapped maps between domains and ranges of the inputs.
1737 To obtain a ``flat'' product, use the following functions
1740 __isl_give isl_basic_set *isl_basic_set_flat_product(
1741 __isl_take isl_basic_set *bset1,
1742 __isl_take isl_basic_set *bset2);
1743 __isl_give isl_set *isl_set_flat_product(
1744 __isl_take isl_set *set1,
1745 __isl_take isl_set *set2);
1746 __isl_give isl_basic_map *isl_basic_map_flat_product(
1747 __isl_take isl_basic_map *bmap1,
1748 __isl_take isl_basic_map *bmap2);
1749 __isl_give isl_map *isl_map_flat_product(
1750 __isl_take isl_map *map1,
1751 __isl_take isl_map *map2);
1753 =item * Simplification
1755 __isl_give isl_basic_set *isl_basic_set_gist(
1756 __isl_take isl_basic_set *bset,
1757 __isl_take isl_basic_set *context);
1758 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1759 __isl_take isl_set *context);
1760 __isl_give isl_union_set *isl_union_set_gist(
1761 __isl_take isl_union_set *uset,
1762 __isl_take isl_union_set *context);
1763 __isl_give isl_basic_map *isl_basic_map_gist(
1764 __isl_take isl_basic_map *bmap,
1765 __isl_take isl_basic_map *context);
1766 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1767 __isl_take isl_map *context);
1768 __isl_give isl_union_map *isl_union_map_gist(
1769 __isl_take isl_union_map *umap,
1770 __isl_take isl_union_map *context);
1772 The gist operation returns a set or relation that has the
1773 same intersection with the context as the input set or relation.
1774 Any implicit equality in the intersection is made explicit in the result,
1775 while all inequalities that are redundant with respect to the intersection
1777 In case of union sets and relations, the gist operation is performed
1782 =head3 Lexicographic Optimization
1784 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1785 the following functions
1786 compute a set that contains the lexicographic minimum or maximum
1787 of the elements in C<set> (or C<bset>) for those values of the parameters
1788 that satisfy C<dom>.
1789 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1790 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1792 In other words, the union of the parameter values
1793 for which the result is non-empty and of C<*empty>
1796 __isl_give isl_set *isl_basic_set_partial_lexmin(
1797 __isl_take isl_basic_set *bset,
1798 __isl_take isl_basic_set *dom,
1799 __isl_give isl_set **empty);
1800 __isl_give isl_set *isl_basic_set_partial_lexmax(
1801 __isl_take isl_basic_set *bset,
1802 __isl_take isl_basic_set *dom,
1803 __isl_give isl_set **empty);
1804 __isl_give isl_set *isl_set_partial_lexmin(
1805 __isl_take isl_set *set, __isl_take isl_set *dom,
1806 __isl_give isl_set **empty);
1807 __isl_give isl_set *isl_set_partial_lexmax(
1808 __isl_take isl_set *set, __isl_take isl_set *dom,
1809 __isl_give isl_set **empty);
1811 Given a (basic) set C<set> (or C<bset>), the following functions simply
1812 return a set containing the lexicographic minimum or maximum
1813 of the elements in C<set> (or C<bset>).
1814 In case of union sets, the optimum is computed per space.
1816 __isl_give isl_set *isl_basic_set_lexmin(
1817 __isl_take isl_basic_set *bset);
1818 __isl_give isl_set *isl_basic_set_lexmax(
1819 __isl_take isl_basic_set *bset);
1820 __isl_give isl_set *isl_set_lexmin(
1821 __isl_take isl_set *set);
1822 __isl_give isl_set *isl_set_lexmax(
1823 __isl_take isl_set *set);
1824 __isl_give isl_union_set *isl_union_set_lexmin(
1825 __isl_take isl_union_set *uset);
1826 __isl_give isl_union_set *isl_union_set_lexmax(
1827 __isl_take isl_union_set *uset);
1829 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1830 the following functions
1831 compute a relation that maps each element of C<dom>
1832 to the single lexicographic minimum or maximum
1833 of the elements that are associated to that same
1834 element in C<map> (or C<bmap>).
1835 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1836 that contains the elements in C<dom> that do not map
1837 to any elements in C<map> (or C<bmap>).
1838 In other words, the union of the domain of the result and of C<*empty>
1841 __isl_give isl_map *isl_basic_map_partial_lexmax(
1842 __isl_take isl_basic_map *bmap,
1843 __isl_take isl_basic_set *dom,
1844 __isl_give isl_set **empty);
1845 __isl_give isl_map *isl_basic_map_partial_lexmin(
1846 __isl_take isl_basic_map *bmap,
1847 __isl_take isl_basic_set *dom,
1848 __isl_give isl_set **empty);
1849 __isl_give isl_map *isl_map_partial_lexmax(
1850 __isl_take isl_map *map, __isl_take isl_set *dom,
1851 __isl_give isl_set **empty);
1852 __isl_give isl_map *isl_map_partial_lexmin(
1853 __isl_take isl_map *map, __isl_take isl_set *dom,
1854 __isl_give isl_set **empty);
1856 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1857 return a map mapping each element in the domain of
1858 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1859 of all elements associated to that element.
1860 In case of union relations, the optimum is computed per space.
1862 __isl_give isl_map *isl_basic_map_lexmin(
1863 __isl_take isl_basic_map *bmap);
1864 __isl_give isl_map *isl_basic_map_lexmax(
1865 __isl_take isl_basic_map *bmap);
1866 __isl_give isl_map *isl_map_lexmin(
1867 __isl_take isl_map *map);
1868 __isl_give isl_map *isl_map_lexmax(
1869 __isl_take isl_map *map);
1870 __isl_give isl_union_map *isl_union_map_lexmin(
1871 __isl_take isl_union_map *umap);
1872 __isl_give isl_union_map *isl_union_map_lexmax(
1873 __isl_take isl_union_map *umap);
1877 Matrices can be created, copied and freed using the following functions.
1879 #include <isl/mat.h>
1880 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1881 unsigned n_row, unsigned n_col);
1882 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1883 void isl_mat_free(__isl_take isl_mat *mat);
1885 Note that the elements of a newly created matrix may have arbitrary values.
1886 The elements can be changed and inspected using the following functions.
1888 int isl_mat_rows(__isl_keep isl_mat *mat);
1889 int isl_mat_cols(__isl_keep isl_mat *mat);
1890 int isl_mat_get_element(__isl_keep isl_mat *mat,
1891 int row, int col, isl_int *v);
1892 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1893 int row, int col, isl_int v);
1894 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
1895 int row, int col, int v);
1897 C<isl_mat_get_element> will return a negative value if anything went wrong.
1898 In that case, the value of C<*v> is undefined.
1900 The following function can be used to compute the (right) inverse
1901 of a matrix, i.e., a matrix such that the product of the original
1902 and the inverse (in that order) is a multiple of the identity matrix.
1903 The input matrix is assumed to be of full row-rank.
1905 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1907 The following function can be used to compute the (right) kernel
1908 (or null space) of a matrix, i.e., a matrix such that the product of
1909 the original and the kernel (in that order) is the zero matrix.
1911 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1915 Points are elements of a set. They can be used to construct
1916 simple sets (boxes) or they can be used to represent the
1917 individual elements of a set.
1918 The zero point (the origin) can be created using
1920 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1922 The coordinates of a point can be inspected, set and changed
1925 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1926 enum isl_dim_type type, int pos, isl_int *v);
1927 __isl_give isl_point *isl_point_set_coordinate(
1928 __isl_take isl_point *pnt,
1929 enum isl_dim_type type, int pos, isl_int v);
1931 __isl_give isl_point *isl_point_add_ui(
1932 __isl_take isl_point *pnt,
1933 enum isl_dim_type type, int pos, unsigned val);
1934 __isl_give isl_point *isl_point_sub_ui(
1935 __isl_take isl_point *pnt,
1936 enum isl_dim_type type, int pos, unsigned val);
1938 Points can be copied or freed using
1940 __isl_give isl_point *isl_point_copy(
1941 __isl_keep isl_point *pnt);
1942 void isl_point_free(__isl_take isl_point *pnt);
1944 A singleton set can be created from a point using
1946 __isl_give isl_basic_set *isl_basic_set_from_point(
1947 __isl_take isl_point *pnt);
1948 __isl_give isl_set *isl_set_from_point(
1949 __isl_take isl_point *pnt);
1951 and a box can be created from two opposite extremal points using
1953 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1954 __isl_take isl_point *pnt1,
1955 __isl_take isl_point *pnt2);
1956 __isl_give isl_set *isl_set_box_from_points(
1957 __isl_take isl_point *pnt1,
1958 __isl_take isl_point *pnt2);
1960 All elements of a B<bounded> (union) set can be enumerated using
1961 the following functions.
1963 int isl_set_foreach_point(__isl_keep isl_set *set,
1964 int (*fn)(__isl_take isl_point *pnt, void *user),
1966 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1967 int (*fn)(__isl_take isl_point *pnt, void *user),
1970 The function C<fn> is called for each integer point in
1971 C<set> with as second argument the last argument of
1972 the C<isl_set_foreach_point> call. The function C<fn>
1973 should return C<0> on success and C<-1> on failure.
1974 In the latter case, C<isl_set_foreach_point> will stop
1975 enumerating and return C<-1> as well.
1976 If the enumeration is performed successfully and to completion,
1977 then C<isl_set_foreach_point> returns C<0>.
1979 To obtain a single point of a (basic) set, use
1981 __isl_give isl_point *isl_basic_set_sample_point(
1982 __isl_take isl_basic_set *bset);
1983 __isl_give isl_point *isl_set_sample_point(
1984 __isl_take isl_set *set);
1986 If C<set> does not contain any (integer) points, then the
1987 resulting point will be ``void'', a property that can be
1990 int isl_point_is_void(__isl_keep isl_point *pnt);
1992 =head2 Piecewise Quasipolynomials
1994 A piecewise quasipolynomial is a particular kind of function that maps
1995 a parametric point to a rational value.
1996 More specifically, a quasipolynomial is a polynomial expression in greatest
1997 integer parts of affine expressions of parameters and variables.
1998 A piecewise quasipolynomial is a subdivision of a given parametric
1999 domain into disjoint cells with a quasipolynomial associated to
2000 each cell. The value of the piecewise quasipolynomial at a given
2001 point is the value of the quasipolynomial associated to the cell
2002 that contains the point. Outside of the union of cells,
2003 the value is assumed to be zero.
2004 For example, the piecewise quasipolynomial
2006 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2008 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2009 A given piecewise quasipolynomial has a fixed domain dimension.
2010 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2011 defined over different domains.
2012 Piecewise quasipolynomials are mainly used by the C<barvinok>
2013 library for representing the number of elements in a parametric set or map.
2014 For example, the piecewise quasipolynomial above represents
2015 the number of points in the map
2017 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2019 =head3 Printing (Piecewise) Quasipolynomials
2021 Quasipolynomials and piecewise quasipolynomials can be printed
2022 using the following functions.
2024 __isl_give isl_printer *isl_printer_print_qpolynomial(
2025 __isl_take isl_printer *p,
2026 __isl_keep isl_qpolynomial *qp);
2028 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2029 __isl_take isl_printer *p,
2030 __isl_keep isl_pw_qpolynomial *pwqp);
2032 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2033 __isl_take isl_printer *p,
2034 __isl_keep isl_union_pw_qpolynomial *upwqp);
2036 The output format of the printer
2037 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2038 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2040 In case of printing in C<ISL_FORMAT_C>, the user may want
2041 to set the names of all dimensions
2043 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2044 __isl_take isl_qpolynomial *qp,
2045 enum isl_dim_type type, unsigned pos,
2047 __isl_give isl_pw_qpolynomial *
2048 isl_pw_qpolynomial_set_dim_name(
2049 __isl_take isl_pw_qpolynomial *pwqp,
2050 enum isl_dim_type type, unsigned pos,
2053 =head3 Creating New (Piecewise) Quasipolynomials
2055 Some simple quasipolynomials can be created using the following functions.
2056 More complicated quasipolynomials can be created by applying
2057 operations such as addition and multiplication
2058 on the resulting quasipolynomials
2060 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2061 __isl_take isl_dim *dim);
2062 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2063 __isl_take isl_dim *dim);
2064 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2065 __isl_take isl_dim *dim);
2066 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2067 __isl_take isl_dim *dim);
2068 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2069 __isl_take isl_dim *dim);
2070 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2071 __isl_take isl_dim *dim,
2072 const isl_int n, const isl_int d);
2073 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2074 __isl_take isl_div *div);
2075 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2076 __isl_take isl_dim *dim,
2077 enum isl_dim_type type, unsigned pos);
2079 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2080 with a single cell can be created using the following functions.
2081 Multiple of these single cell piecewise quasipolynomials can
2082 be combined to create more complicated piecewise quasipolynomials.
2084 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2085 __isl_take isl_dim *dim);
2086 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2087 __isl_take isl_set *set,
2088 __isl_take isl_qpolynomial *qp);
2090 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2091 __isl_take isl_dim *dim);
2092 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2093 __isl_take isl_pw_qpolynomial *pwqp);
2094 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2095 __isl_take isl_union_pw_qpolynomial *upwqp,
2096 __isl_take isl_pw_qpolynomial *pwqp);
2098 Quasipolynomials can be copied and freed again using the following
2101 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2102 __isl_keep isl_qpolynomial *qp);
2103 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2105 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2106 __isl_keep isl_pw_qpolynomial *pwqp);
2107 void isl_pw_qpolynomial_free(
2108 __isl_take isl_pw_qpolynomial *pwqp);
2110 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2111 __isl_keep isl_union_pw_qpolynomial *upwqp);
2112 void isl_union_pw_qpolynomial_free(
2113 __isl_take isl_union_pw_qpolynomial *upwqp);
2115 =head3 Inspecting (Piecewise) Quasipolynomials
2117 To iterate over all piecewise quasipolynomials in a union
2118 piecewise quasipolynomial, use the following function
2120 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2121 __isl_keep isl_union_pw_qpolynomial *upwqp,
2122 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2125 To extract the piecewise quasipolynomial from a union with a given dimension
2128 __isl_give isl_pw_qpolynomial *
2129 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2130 __isl_keep isl_union_pw_qpolynomial *upwqp,
2131 __isl_take isl_dim *dim);
2133 To iterate over the cells in a piecewise quasipolynomial,
2134 use either of the following two functions
2136 int isl_pw_qpolynomial_foreach_piece(
2137 __isl_keep isl_pw_qpolynomial *pwqp,
2138 int (*fn)(__isl_take isl_set *set,
2139 __isl_take isl_qpolynomial *qp,
2140 void *user), void *user);
2141 int isl_pw_qpolynomial_foreach_lifted_piece(
2142 __isl_keep isl_pw_qpolynomial *pwqp,
2143 int (*fn)(__isl_take isl_set *set,
2144 __isl_take isl_qpolynomial *qp,
2145 void *user), void *user);
2147 As usual, the function C<fn> should return C<0> on success
2148 and C<-1> on failure. The difference between
2149 C<isl_pw_qpolynomial_foreach_piece> and
2150 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2151 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2152 compute unique representations for all existentially quantified
2153 variables and then turn these existentially quantified variables
2154 into extra set variables, adapting the associated quasipolynomial
2155 accordingly. This means that the C<set> passed to C<fn>
2156 will not have any existentially quantified variables, but that
2157 the dimensions of the sets may be different for different
2158 invocations of C<fn>.
2160 To iterate over all terms in a quasipolynomial,
2163 int isl_qpolynomial_foreach_term(
2164 __isl_keep isl_qpolynomial *qp,
2165 int (*fn)(__isl_take isl_term *term,
2166 void *user), void *user);
2168 The terms themselves can be inspected and freed using
2171 unsigned isl_term_dim(__isl_keep isl_term *term,
2172 enum isl_dim_type type);
2173 void isl_term_get_num(__isl_keep isl_term *term,
2175 void isl_term_get_den(__isl_keep isl_term *term,
2177 int isl_term_get_exp(__isl_keep isl_term *term,
2178 enum isl_dim_type type, unsigned pos);
2179 __isl_give isl_div *isl_term_get_div(
2180 __isl_keep isl_term *term, unsigned pos);
2181 void isl_term_free(__isl_take isl_term *term);
2183 Each term is a product of parameters, set variables and
2184 integer divisions. The function C<isl_term_get_exp>
2185 returns the exponent of a given dimensions in the given term.
2186 The C<isl_int>s in the arguments of C<isl_term_get_num>
2187 and C<isl_term_get_den> need to have been initialized
2188 using C<isl_int_init> before calling these functions.
2190 =head3 Properties of (Piecewise) Quasipolynomials
2192 To check whether a quasipolynomial is actually a constant,
2193 use the following function.
2195 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2196 isl_int *n, isl_int *d);
2198 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2199 then the numerator and denominator of the constant
2200 are returned in C<*n> and C<*d>, respectively.
2202 =head3 Operations on (Piecewise) Quasipolynomials
2204 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2205 __isl_take isl_qpolynomial *qp);
2206 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2207 __isl_take isl_qpolynomial *qp1,
2208 __isl_take isl_qpolynomial *qp2);
2209 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2210 __isl_take isl_qpolynomial *qp1,
2211 __isl_take isl_qpolynomial *qp2);
2212 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2213 __isl_take isl_qpolynomial *qp1,
2214 __isl_take isl_qpolynomial *qp2);
2215 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2216 __isl_take isl_qpolynomial *qp, unsigned exponent);
2218 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2219 __isl_take isl_pw_qpolynomial *pwqp1,
2220 __isl_take isl_pw_qpolynomial *pwqp2);
2221 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2222 __isl_take isl_pw_qpolynomial *pwqp1,
2223 __isl_take isl_pw_qpolynomial *pwqp2);
2224 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2225 __isl_take isl_pw_qpolynomial *pwqp1,
2226 __isl_take isl_pw_qpolynomial *pwqp2);
2227 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2228 __isl_take isl_pw_qpolynomial *pwqp);
2229 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2230 __isl_take isl_pw_qpolynomial *pwqp1,
2231 __isl_take isl_pw_qpolynomial *pwqp2);
2233 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2234 __isl_take isl_union_pw_qpolynomial *upwqp1,
2235 __isl_take isl_union_pw_qpolynomial *upwqp2);
2236 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2237 __isl_take isl_union_pw_qpolynomial *upwqp1,
2238 __isl_take isl_union_pw_qpolynomial *upwqp2);
2239 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2240 __isl_take isl_union_pw_qpolynomial *upwqp1,
2241 __isl_take isl_union_pw_qpolynomial *upwqp2);
2243 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2244 __isl_take isl_pw_qpolynomial *pwqp,
2245 __isl_take isl_point *pnt);
2247 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2248 __isl_take isl_union_pw_qpolynomial *upwqp,
2249 __isl_take isl_point *pnt);
2251 __isl_give isl_set *isl_pw_qpolynomial_domain(
2252 __isl_take isl_pw_qpolynomial *pwqp);
2253 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2254 __isl_take isl_pw_qpolynomial *pwpq,
2255 __isl_take isl_set *set);
2257 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2258 __isl_take isl_union_pw_qpolynomial *upwqp);
2259 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2260 __isl_take isl_union_pw_qpolynomial *upwpq,
2261 __isl_take isl_union_set *uset);
2263 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2264 __isl_take isl_union_pw_qpolynomial *upwqp);
2266 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2267 __isl_take isl_pw_qpolynomial *pwqp,
2268 __isl_take isl_set *context);
2270 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2271 __isl_take isl_union_pw_qpolynomial *upwqp,
2272 __isl_take isl_union_set *context);
2274 The gist operation applies the gist operation to each of
2275 the cells in the domain of the input piecewise quasipolynomial.
2276 The context is also exploited
2277 to simplify the quasipolynomials associated to each cell.
2279 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2280 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2281 __isl_give isl_union_pw_qpolynomial *
2282 isl_union_pw_qpolynomial_to_polynomial(
2283 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2285 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2286 the polynomial will be an overapproximation. If C<sign> is negative,
2287 it will be an underapproximation. If C<sign> is zero, the approximation
2288 will lie somewhere in between.
2290 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2292 A piecewise quasipolynomial reduction is a piecewise
2293 reduction (or fold) of quasipolynomials.
2294 In particular, the reduction can be maximum or a minimum.
2295 The objects are mainly used to represent the result of
2296 an upper or lower bound on a quasipolynomial over its domain,
2297 i.e., as the result of the following function.
2299 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2300 __isl_take isl_pw_qpolynomial *pwqp,
2301 enum isl_fold type, int *tight);
2303 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2304 __isl_take isl_union_pw_qpolynomial *upwqp,
2305 enum isl_fold type, int *tight);
2307 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2308 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2309 is the returned bound is known be tight, i.e., for each value
2310 of the parameters there is at least
2311 one element in the domain that reaches the bound.
2312 If the domain of C<pwqp> is not wrapping, then the bound is computed
2313 over all elements in that domain and the result has a purely parametric
2314 domain. If the domain of C<pwqp> is wrapping, then the bound is
2315 computed over the range of the wrapped relation. The domain of the
2316 wrapped relation becomes the domain of the result.
2318 A (piecewise) quasipolynomial reduction can be copied or freed using the
2319 following functions.
2321 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2322 __isl_keep isl_qpolynomial_fold *fold);
2323 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2324 __isl_keep isl_pw_qpolynomial_fold *pwf);
2325 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2326 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2327 void isl_qpolynomial_fold_free(
2328 __isl_take isl_qpolynomial_fold *fold);
2329 void isl_pw_qpolynomial_fold_free(
2330 __isl_take isl_pw_qpolynomial_fold *pwf);
2331 void isl_union_pw_qpolynomial_fold_free(
2332 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2334 =head3 Printing Piecewise Quasipolynomial Reductions
2336 Piecewise quasipolynomial reductions can be printed
2337 using the following function.
2339 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2340 __isl_take isl_printer *p,
2341 __isl_keep isl_pw_qpolynomial_fold *pwf);
2342 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2343 __isl_take isl_printer *p,
2344 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2346 For C<isl_printer_print_pw_qpolynomial_fold>,
2347 output format of the printer
2348 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2349 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2350 output format of the printer
2351 needs to be set to C<ISL_FORMAT_ISL>.
2352 In case of printing in C<ISL_FORMAT_C>, the user may want
2353 to set the names of all dimensions
2355 __isl_give isl_pw_qpolynomial_fold *
2356 isl_pw_qpolynomial_fold_set_dim_name(
2357 __isl_take isl_pw_qpolynomial_fold *pwf,
2358 enum isl_dim_type type, unsigned pos,
2361 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2363 To iterate over all piecewise quasipolynomial reductions in a union
2364 piecewise quasipolynomial reduction, use the following function
2366 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2367 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2368 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2369 void *user), void *user);
2371 To iterate over the cells in a piecewise quasipolynomial reduction,
2372 use either of the following two functions
2374 int isl_pw_qpolynomial_fold_foreach_piece(
2375 __isl_keep isl_pw_qpolynomial_fold *pwf,
2376 int (*fn)(__isl_take isl_set *set,
2377 __isl_take isl_qpolynomial_fold *fold,
2378 void *user), void *user);
2379 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2380 __isl_keep isl_pw_qpolynomial_fold *pwf,
2381 int (*fn)(__isl_take isl_set *set,
2382 __isl_take isl_qpolynomial_fold *fold,
2383 void *user), void *user);
2385 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2386 of the difference between these two functions.
2388 To iterate over all quasipolynomials in a reduction, use
2390 int isl_qpolynomial_fold_foreach_qpolynomial(
2391 __isl_keep isl_qpolynomial_fold *fold,
2392 int (*fn)(__isl_take isl_qpolynomial *qp,
2393 void *user), void *user);
2395 =head3 Operations on Piecewise Quasipolynomial Reductions
2397 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2398 __isl_take isl_pw_qpolynomial_fold *pwf1,
2399 __isl_take isl_pw_qpolynomial_fold *pwf2);
2401 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2402 __isl_take isl_pw_qpolynomial_fold *pwf1,
2403 __isl_take isl_pw_qpolynomial_fold *pwf2);
2405 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2406 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2407 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2409 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2410 __isl_take isl_pw_qpolynomial_fold *pwf,
2411 __isl_take isl_point *pnt);
2413 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2414 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2415 __isl_take isl_point *pnt);
2417 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2418 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2419 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2420 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2421 __isl_take isl_union_set *uset);
2423 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2424 __isl_take isl_pw_qpolynomial_fold *pwf);
2426 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2427 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2429 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2430 __isl_take isl_pw_qpolynomial_fold *pwf,
2431 __isl_take isl_set *context);
2433 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2434 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2435 __isl_take isl_union_set *context);
2437 The gist operation applies the gist operation to each of
2438 the cells in the domain of the input piecewise quasipolynomial reduction.
2439 In future, the operation will also exploit the context
2440 to simplify the quasipolynomial reductions associated to each cell.
2442 __isl_give isl_pw_qpolynomial_fold *
2443 isl_set_apply_pw_qpolynomial_fold(
2444 __isl_take isl_set *set,
2445 __isl_take isl_pw_qpolynomial_fold *pwf,
2447 __isl_give isl_pw_qpolynomial_fold *
2448 isl_map_apply_pw_qpolynomial_fold(
2449 __isl_take isl_map *map,
2450 __isl_take isl_pw_qpolynomial_fold *pwf,
2452 __isl_give isl_union_pw_qpolynomial_fold *
2453 isl_union_set_apply_union_pw_qpolynomial_fold(
2454 __isl_take isl_union_set *uset,
2455 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2457 __isl_give isl_union_pw_qpolynomial_fold *
2458 isl_union_map_apply_union_pw_qpolynomial_fold(
2459 __isl_take isl_union_map *umap,
2460 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2463 The functions taking a map
2464 compose the given map with the given piecewise quasipolynomial reduction.
2465 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2466 over all elements in the intersection of the range of the map
2467 and the domain of the piecewise quasipolynomial reduction
2468 as a function of an element in the domain of the map.
2469 The functions taking a set compute a bound over all elements in the
2470 intersection of the set and the domain of the
2471 piecewise quasipolynomial reduction.
2473 =head2 Dependence Analysis
2475 C<isl> contains specialized functionality for performing
2476 array dataflow analysis. That is, given a I<sink> access relation
2477 and a collection of possible I<source> access relations,
2478 C<isl> can compute relations that describe
2479 for each iteration of the sink access, which iteration
2480 of which of the source access relations was the last
2481 to access the same data element before the given iteration
2483 To compute standard flow dependences, the sink should be
2484 a read, while the sources should be writes.
2485 If any of the source accesses are marked as being I<may>
2486 accesses, then there will be a dependence to the last
2487 I<must> access B<and> to any I<may> access that follows
2488 this last I<must> access.
2489 In particular, if I<all> sources are I<may> accesses,
2490 then memory based dependence analysis is performed.
2491 If, on the other hand, all sources are I<must> accesses,
2492 then value based dependence analysis is performed.
2494 #include <isl/flow.h>
2496 typedef int (*isl_access_level_before)(void *first, void *second);
2498 __isl_give isl_access_info *isl_access_info_alloc(
2499 __isl_take isl_map *sink,
2500 void *sink_user, isl_access_level_before fn,
2502 __isl_give isl_access_info *isl_access_info_add_source(
2503 __isl_take isl_access_info *acc,
2504 __isl_take isl_map *source, int must,
2506 void isl_access_info_free(__isl_take isl_access_info *acc);
2508 __isl_give isl_flow *isl_access_info_compute_flow(
2509 __isl_take isl_access_info *acc);
2511 int isl_flow_foreach(__isl_keep isl_flow *deps,
2512 int (*fn)(__isl_take isl_map *dep, int must,
2513 void *dep_user, void *user),
2515 __isl_give isl_map *isl_flow_get_no_source(
2516 __isl_keep isl_flow *deps, int must);
2517 void isl_flow_free(__isl_take isl_flow *deps);
2519 The function C<isl_access_info_compute_flow> performs the actual
2520 dependence analysis. The other functions are used to construct
2521 the input for this function or to read off the output.
2523 The input is collected in an C<isl_access_info>, which can
2524 be created through a call to C<isl_access_info_alloc>.
2525 The arguments to this functions are the sink access relation
2526 C<sink>, a token C<sink_user> used to identify the sink
2527 access to the user, a callback function for specifying the
2528 relative order of source and sink accesses, and the number
2529 of source access relations that will be added.
2530 The callback function has type C<int (*)(void *first, void *second)>.
2531 The function is called with two user supplied tokens identifying
2532 either a source or the sink and it should return the shared nesting
2533 level and the relative order of the two accesses.
2534 In particular, let I<n> be the number of loops shared by
2535 the two accesses. If C<first> precedes C<second> textually,
2536 then the function should return I<2 * n + 1>; otherwise,
2537 it should return I<2 * n>.
2538 The sources can be added to the C<isl_access_info> by performing
2539 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2540 C<must> indicates whether the source is a I<must> access
2541 or a I<may> access. Note that a multi-valued access relation
2542 should only be marked I<must> if every iteration in the domain
2543 of the relation accesses I<all> elements in its image.
2544 The C<source_user> token is again used to identify
2545 the source access. The range of the source access relation
2546 C<source> should have the same dimension as the range
2547 of the sink access relation.
2548 The C<isl_access_info_free> function should usually not be
2549 called explicitly, because it is called implicitly by
2550 C<isl_access_info_compute_flow>.
2552 The result of the dependence analysis is collected in an
2553 C<isl_flow>. There may be elements of
2554 the sink access for which no preceding source access could be
2555 found or for which all preceding sources are I<may> accesses.
2556 The relations containing these elements can be obtained through
2557 calls to C<isl_flow_get_no_source>, the first with C<must> set
2558 and the second with C<must> unset.
2559 In the case of standard flow dependence analysis,
2560 with the sink a read and the sources I<must> writes,
2561 the first relation corresponds to the reads from uninitialized
2562 array elements and the second relation is empty.
2563 The actual flow dependences can be extracted using
2564 C<isl_flow_foreach>. This function will call the user-specified
2565 callback function C<fn> for each B<non-empty> dependence between
2566 a source and the sink. The callback function is called
2567 with four arguments, the actual flow dependence relation
2568 mapping source iterations to sink iterations, a boolean that
2569 indicates whether it is a I<must> or I<may> dependence, a token
2570 identifying the source and an additional C<void *> with value
2571 equal to the third argument of the C<isl_flow_foreach> call.
2572 A dependence is marked I<must> if it originates from a I<must>
2573 source and if it is not followed by any I<may> sources.
2575 After finishing with an C<isl_flow>, the user should call
2576 C<isl_flow_free> to free all associated memory.
2578 A higher-level interface to dependence analysis is provided
2579 by the following function.
2581 #include <isl/flow.h>
2583 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2584 __isl_take isl_union_map *must_source,
2585 __isl_take isl_union_map *may_source,
2586 __isl_take isl_union_map *schedule,
2587 __isl_give isl_union_map **must_dep,
2588 __isl_give isl_union_map **may_dep,
2589 __isl_give isl_union_map **must_no_source,
2590 __isl_give isl_union_map **may_no_source);
2592 The arrays are identified by the tuple names of the ranges
2593 of the accesses. The iteration domains by the tuple names
2594 of the domains of the accesses and of the schedule.
2595 The relative order of the iteration domains is given by the
2596 schedule. The relations returned through C<must_no_source>
2597 and C<may_no_source> are subsets of C<sink>.
2598 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2599 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2600 any of the other arguments is treated as an error.
2602 =head2 Parametric Vertex Enumeration
2604 The parametric vertex enumeration described in this section
2605 is mainly intended to be used internally and by the C<barvinok>
2608 #include <isl/vertices.h>
2609 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2610 __isl_keep isl_basic_set *bset);
2612 The function C<isl_basic_set_compute_vertices> performs the
2613 actual computation of the parametric vertices and the chamber
2614 decomposition and store the result in an C<isl_vertices> object.
2615 This information can be queried by either iterating over all
2616 the vertices or iterating over all the chambers or cells
2617 and then iterating over all vertices that are active on the chamber.
2619 int isl_vertices_foreach_vertex(
2620 __isl_keep isl_vertices *vertices,
2621 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2624 int isl_vertices_foreach_cell(
2625 __isl_keep isl_vertices *vertices,
2626 int (*fn)(__isl_take isl_cell *cell, void *user),
2628 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2629 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2632 Other operations that can be performed on an C<isl_vertices> object are
2635 isl_ctx *isl_vertices_get_ctx(
2636 __isl_keep isl_vertices *vertices);
2637 int isl_vertices_get_n_vertices(
2638 __isl_keep isl_vertices *vertices);
2639 void isl_vertices_free(__isl_take isl_vertices *vertices);
2641 Vertices can be inspected and destroyed using the following functions.
2643 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2644 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2645 __isl_give isl_basic_set *isl_vertex_get_domain(
2646 __isl_keep isl_vertex *vertex);
2647 __isl_give isl_basic_set *isl_vertex_get_expr(
2648 __isl_keep isl_vertex *vertex);
2649 void isl_vertex_free(__isl_take isl_vertex *vertex);
2651 C<isl_vertex_get_expr> returns a singleton parametric set describing
2652 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2654 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2655 B<rational> basic sets, so they should mainly be used for inspection
2656 and should not be mixed with integer sets.
2658 Chambers can be inspected and destroyed using the following functions.
2660 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2661 __isl_give isl_basic_set *isl_cell_get_domain(
2662 __isl_keep isl_cell *cell);
2663 void isl_cell_free(__isl_take isl_cell *cell);
2667 Although C<isl> is mainly meant to be used as a library,
2668 it also contains some basic applications that use some
2669 of the functionality of C<isl>.
2670 The input may be specified in either the L<isl format>
2671 or the L<PolyLib format>.
2673 =head2 C<isl_polyhedron_sample>
2675 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2676 an integer element of the polyhedron, if there is any.
2677 The first column in the output is the denominator and is always
2678 equal to 1. If the polyhedron contains no integer points,
2679 then a vector of length zero is printed.
2683 C<isl_pip> takes the same input as the C<example> program
2684 from the C<piplib> distribution, i.e., a set of constraints
2685 on the parameters, a line containing only -1 and finally a set
2686 of constraints on a parametric polyhedron.
2687 The coefficients of the parameters appear in the last columns
2688 (but before the final constant column).
2689 The output is the lexicographic minimum of the parametric polyhedron.
2690 As C<isl> currently does not have its own output format, the output
2691 is just a dump of the internal state.
2693 =head2 C<isl_polyhedron_minimize>
2695 C<isl_polyhedron_minimize> computes the minimum of some linear
2696 or affine objective function over the integer points in a polyhedron.
2697 If an affine objective function
2698 is given, then the constant should appear in the last column.
2700 =head2 C<isl_polytope_scan>
2702 Given a polytope, C<isl_polytope_scan> prints
2703 all integer points in the polytope.
2705 =head1 C<isl-polylib>
2707 The C<isl-polylib> library provides the following functions for converting
2708 between C<isl> objects and C<PolyLib> objects.
2709 The library is distributed separately for licensing reasons.
2711 #include <isl_set_polylib.h>
2712 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2713 Polyhedron *P, __isl_take isl_dim *dim);
2714 Polyhedron *isl_basic_set_to_polylib(
2715 __isl_keep isl_basic_set *bset);
2716 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2717 __isl_take isl_dim *dim);
2718 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2720 #include <isl_map_polylib.h>
2721 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2722 Polyhedron *P, __isl_take isl_dim *dim);
2723 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2724 __isl_take isl_dim *dim);
2725 Polyhedron *isl_basic_map_to_polylib(
2726 __isl_keep isl_basic_map *bmap);
2727 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);