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.
82 =head3 Changes since isl-0.06
86 =item * The format of C<isl_printer_print_qpolynomial>'s
87 C<ISL_FORMAT_ISL> output has changed.
88 Use C<ISL_FORMAT_C> to obtain the old output.
94 The source of C<isl> can be obtained either as a tarball
95 or from the git repository. Both are available from
96 L<http://freshmeat.net/projects/isl/>.
97 The installation process depends on how you obtained
100 =head2 Installation from the git repository
104 =item 1 Clone or update the repository
106 The first time the source is obtained, you need to clone
109 git clone git://repo.or.cz/isl.git
111 To obtain updates, you need to pull in the latest changes
115 =item 2 Generate C<configure>
121 After performing the above steps, continue
122 with the L<Common installation instructions>.
124 =head2 Common installation instructions
128 =item 1 Obtain C<GMP>
130 Building C<isl> requires C<GMP>, including its headers files.
131 Your distribution may not provide these header files by default
132 and you may need to install a package called C<gmp-devel> or something
133 similar. Alternatively, C<GMP> can be built from
134 source, available from L<http://gmplib.org/>.
138 C<isl> uses the standard C<autoconf> C<configure> script.
143 optionally followed by some configure options.
144 A complete list of options can be obtained by running
148 Below we discuss some of the more common options.
150 C<isl> can optionally use C<piplib>, but no
151 C<piplib> functionality is currently used by default.
152 The C<--with-piplib> option can
153 be used to specify which C<piplib>
154 library to use, either an installed version (C<system>),
155 an externally built version (C<build>)
156 or no version (C<no>). The option C<build> is mostly useful
157 in C<configure> scripts of larger projects that bundle both C<isl>
164 Installation prefix for C<isl>
166 =item C<--with-gmp-prefix>
168 Installation prefix for C<GMP> (architecture-independent files).
170 =item C<--with-gmp-exec-prefix>
172 Installation prefix for C<GMP> (architecture-dependent files).
174 =item C<--with-piplib>
176 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
178 =item C<--with-piplib-prefix>
180 Installation prefix for C<system> C<piplib> (architecture-independent files).
182 =item C<--with-piplib-exec-prefix>
184 Installation prefix for C<system> C<piplib> (architecture-dependent files).
186 =item C<--with-piplib-builddir>
188 Location where C<build> C<piplib> was built.
196 =item 4 Install (optional)
204 =head2 Initialization
206 All manipulations of integer sets and relations occur within
207 the context of an C<isl_ctx>.
208 A given C<isl_ctx> can only be used within a single thread.
209 All arguments of a function are required to have been allocated
210 within the same context.
211 There are currently no functions available for moving an object
212 from one C<isl_ctx> to another C<isl_ctx>. This means that
213 there is currently no way of safely moving an object from one
214 thread to another, unless the whole C<isl_ctx> is moved.
216 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
217 freed using C<isl_ctx_free>.
218 All objects allocated within an C<isl_ctx> should be freed
219 before the C<isl_ctx> itself is freed.
221 isl_ctx *isl_ctx_alloc();
222 void isl_ctx_free(isl_ctx *ctx);
226 All operations on integers, mainly the coefficients
227 of the constraints describing the sets and relations,
228 are performed in exact integer arithmetic using C<GMP>.
229 However, to allow future versions of C<isl> to optionally
230 support fixed integer arithmetic, all calls to C<GMP>
231 are wrapped inside C<isl> specific macros.
232 The basic type is C<isl_int> and the operations below
233 are available on this type.
234 The meanings of these operations are essentially the same
235 as their C<GMP> C<mpz_> counterparts.
236 As always with C<GMP> types, C<isl_int>s need to be
237 initialized with C<isl_int_init> before they can be used
238 and they need to be released with C<isl_int_clear>
240 The user should not assume that an C<isl_int> is represented
241 as a C<mpz_t>, but should instead explicitly convert between
242 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
243 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
247 =item isl_int_init(i)
249 =item isl_int_clear(i)
251 =item isl_int_set(r,i)
253 =item isl_int_set_si(r,i)
255 =item isl_int_set_gmp(r,g)
257 =item isl_int_get_gmp(i,g)
259 =item isl_int_abs(r,i)
261 =item isl_int_neg(r,i)
263 =item isl_int_swap(i,j)
265 =item isl_int_swap_or_set(i,j)
267 =item isl_int_add_ui(r,i,j)
269 =item isl_int_sub_ui(r,i,j)
271 =item isl_int_add(r,i,j)
273 =item isl_int_sub(r,i,j)
275 =item isl_int_mul(r,i,j)
277 =item isl_int_mul_ui(r,i,j)
279 =item isl_int_addmul(r,i,j)
281 =item isl_int_submul(r,i,j)
283 =item isl_int_gcd(r,i,j)
285 =item isl_int_lcm(r,i,j)
287 =item isl_int_divexact(r,i,j)
289 =item isl_int_cdiv_q(r,i,j)
291 =item isl_int_fdiv_q(r,i,j)
293 =item isl_int_fdiv_r(r,i,j)
295 =item isl_int_fdiv_q_ui(r,i,j)
297 =item isl_int_read(r,s)
299 =item isl_int_print(out,i,width)
303 =item isl_int_cmp(i,j)
305 =item isl_int_cmp_si(i,si)
307 =item isl_int_eq(i,j)
309 =item isl_int_ne(i,j)
311 =item isl_int_lt(i,j)
313 =item isl_int_le(i,j)
315 =item isl_int_gt(i,j)
317 =item isl_int_ge(i,j)
319 =item isl_int_abs_eq(i,j)
321 =item isl_int_abs_ne(i,j)
323 =item isl_int_abs_lt(i,j)
325 =item isl_int_abs_gt(i,j)
327 =item isl_int_abs_ge(i,j)
329 =item isl_int_is_zero(i)
331 =item isl_int_is_one(i)
333 =item isl_int_is_negone(i)
335 =item isl_int_is_pos(i)
337 =item isl_int_is_neg(i)
339 =item isl_int_is_nonpos(i)
341 =item isl_int_is_nonneg(i)
343 =item isl_int_is_divisible_by(i,j)
347 =head2 Sets and Relations
349 C<isl> uses six types of objects for representing sets and relations,
350 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
351 C<isl_union_set> and C<isl_union_map>.
352 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
353 can be described as a conjunction of affine constraints, while
354 C<isl_set> and C<isl_map> represent unions of
355 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
356 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
357 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
358 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
359 where dimensions with different space names
360 (see L<Dimension Specifications>) are considered different as well.
361 The difference between sets and relations (maps) is that sets have
362 one set of variables, while relations have two sets of variables,
363 input variables and output variables.
365 =head2 Memory Management
367 Since a high-level operation on sets and/or relations usually involves
368 several substeps and since the user is usually not interested in
369 the intermediate results, most functions that return a new object
370 will also release all the objects passed as arguments.
371 If the user still wants to use one or more of these arguments
372 after the function call, she should pass along a copy of the
373 object rather than the object itself.
374 The user is then responsible for making sure that the original
375 object gets used somewhere else or is explicitly freed.
377 The arguments and return values of all documents functions are
378 annotated to make clear which arguments are released and which
379 arguments are preserved. In particular, the following annotations
386 C<__isl_give> means that a new object is returned.
387 The user should make sure that the returned pointer is
388 used exactly once as a value for an C<__isl_take> argument.
389 In between, it can be used as a value for as many
390 C<__isl_keep> arguments as the user likes.
391 There is one exception, and that is the case where the
392 pointer returned is C<NULL>. Is this case, the user
393 is free to use it as an C<__isl_take> argument or not.
397 C<__isl_take> means that the object the argument points to
398 is taken over by the function and may no longer be used
399 by the user as an argument to any other function.
400 The pointer value must be one returned by a function
401 returning an C<__isl_give> pointer.
402 If the user passes in a C<NULL> value, then this will
403 be treated as an error in the sense that the function will
404 not perform its usual operation. However, it will still
405 make sure that all the the other C<__isl_take> arguments
410 C<__isl_keep> means that the function will only use the object
411 temporarily. After the function has finished, the user
412 can still use it as an argument to other functions.
413 A C<NULL> value will be treated in the same way as
414 a C<NULL> value for an C<__isl_take> argument.
418 =head2 Dimension Specifications
420 Whenever a new set or relation is created from scratch,
421 its dimension needs to be specified using an C<isl_dim>.
424 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
425 unsigned nparam, unsigned n_in, unsigned n_out);
426 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
427 unsigned nparam, unsigned dim);
428 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
429 void isl_dim_free(__isl_take isl_dim *dim);
430 unsigned isl_dim_size(__isl_keep isl_dim *dim,
431 enum isl_dim_type type);
433 The dimension specification used for creating a set
434 needs to be created using C<isl_dim_set_alloc>, while
435 that for creating a relation
436 needs to be created using C<isl_dim_alloc>.
437 C<isl_dim_size> can be used
438 to find out the number of dimensions of each type in
439 a dimension specification, where type may be
440 C<isl_dim_param>, C<isl_dim_in> (only for relations),
441 C<isl_dim_out> (only for relations), C<isl_dim_set>
442 (only for sets) or C<isl_dim_all>.
444 It is often useful to create objects that live in the
445 same space as some other object. This can be accomplished
446 by creating the new objects
447 (see L<Creating New Sets and Relations> or
448 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
449 specification of the original object.
452 __isl_give isl_dim *isl_basic_set_get_dim(
453 __isl_keep isl_basic_set *bset);
454 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
456 #include <isl/union_set.h>
457 __isl_give isl_dim *isl_union_set_get_dim(
458 __isl_keep isl_union_set *uset);
461 __isl_give isl_dim *isl_basic_map_get_dim(
462 __isl_keep isl_basic_map *bmap);
463 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
465 #include <isl/union_map.h>
466 __isl_give isl_dim *isl_union_map_get_dim(
467 __isl_keep isl_union_map *umap);
469 #include <isl/constraint.h>
470 __isl_give isl_dim *isl_constraint_get_dim(
471 __isl_keep isl_constraint *constraint);
473 #include <isl/polynomial.h>
474 __isl_give isl_dim *isl_qpolynomial_get_dim(
475 __isl_keep isl_qpolynomial *qp);
476 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
477 __isl_keep isl_pw_qpolynomial *pwqp);
478 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
479 __isl_keep isl_union_pw_qpolynomial *upwqp);
480 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
481 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
483 The names of the individual dimensions may be set or read off
484 using the following functions.
487 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
488 enum isl_dim_type type, unsigned pos,
489 __isl_keep const char *name);
490 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
491 enum isl_dim_type type, unsigned pos);
493 Note that C<isl_dim_get_name> returns a pointer to some internal
494 data structure, so the result can only be used while the
495 corresponding C<isl_dim> is alive.
496 Also note that every function that operates on two sets or relations
497 requires that both arguments have the same parameters. This also
498 means that if one of the arguments has named parameters, then the
499 other needs to have named parameters too and the names need to match.
500 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
501 have different parameters (as long as they are named), in which case
502 the result will have as parameters the union of the parameters of
505 The names of entire spaces may be set or read off
506 using the following functions.
509 __isl_give isl_dim *isl_dim_set_tuple_name(
510 __isl_take isl_dim *dim,
511 enum isl_dim_type type, const char *s);
512 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
513 enum isl_dim_type type);
515 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
516 or C<isl_dim_set>. As with C<isl_dim_get_name>,
517 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
519 Binary operations require the corresponding spaces of their arguments
520 to have the same name.
522 Spaces can be nested. In particular, the domain of a set or
523 the domain or range of a relation can be a nested relation.
524 The following functions can be used to construct and deconstruct
525 such nested dimension specifications.
528 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
529 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
530 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
532 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
533 be the dimension specification of a set, while that of
534 C<isl_dim_wrap> should be the dimension specification of a relation.
535 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
536 of a relation, while that of C<isl_dim_wrap> is the dimension specification
539 Dimension specifications can be created from other dimension
540 specifications using the following functions.
542 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
543 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
544 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
545 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
546 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
548 __isl_take isl_dim *right);
549 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
550 enum isl_dim_type type, unsigned pos, unsigned n);
551 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
552 enum isl_dim_type type, unsigned n);
553 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
554 enum isl_dim_type type, unsigned first, unsigned n);
555 __isl_give isl_dim *isl_dim_map_from_set(
556 __isl_take isl_dim *dim);
557 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
559 Note that if dimensions are added or removed from a space, then
560 the name and the internal structure are lost.
562 =head2 Input and Output
564 C<isl> supports its own input/output format, which is similar
565 to the C<Omega> format, but also supports the C<PolyLib> format
570 The C<isl> format is similar to that of C<Omega>, but has a different
571 syntax for describing the parameters and allows for the definition
572 of an existentially quantified variable as the integer division
573 of an affine expression.
574 For example, the set of integers C<i> between C<0> and C<n>
575 such that C<i % 10 <= 6> can be described as
577 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
580 A set or relation can have several disjuncts, separated
581 by the keyword C<or>. Each disjunct is either a conjunction
582 of constraints or a projection (C<exists>) of a conjunction
583 of constraints. The constraints are separated by the keyword
586 =head3 C<PolyLib> format
588 If the represented set is a union, then the first line
589 contains a single number representing the number of disjuncts.
590 Otherwise, a line containing the number C<1> is optional.
592 Each disjunct is represented by a matrix of constraints.
593 The first line contains two numbers representing
594 the number of rows and columns,
595 where the number of rows is equal to the number of constraints
596 and the number of columns is equal to two plus the number of variables.
597 The following lines contain the actual rows of the constraint matrix.
598 In each row, the first column indicates whether the constraint
599 is an equality (C<0>) or inequality (C<1>). The final column
600 corresponds to the constant term.
602 If the set is parametric, then the coefficients of the parameters
603 appear in the last columns before the constant column.
604 The coefficients of any existentially quantified variables appear
605 between those of the set variables and those of the parameters.
607 =head3 Extended C<PolyLib> format
609 The extended C<PolyLib> format is nearly identical to the
610 C<PolyLib> format. The only difference is that the line
611 containing the number of rows and columns of a constraint matrix
612 also contains four additional numbers:
613 the number of output dimensions, the number of input dimensions,
614 the number of local dimensions (i.e., the number of existentially
615 quantified variables) and the number of parameters.
616 For sets, the number of ``output'' dimensions is equal
617 to the number of set dimensions, while the number of ``input''
623 __isl_give isl_basic_set *isl_basic_set_read_from_file(
624 isl_ctx *ctx, FILE *input, int nparam);
625 __isl_give isl_basic_set *isl_basic_set_read_from_str(
626 isl_ctx *ctx, const char *str, int nparam);
627 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
628 FILE *input, int nparam);
629 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
630 const char *str, int nparam);
633 __isl_give isl_basic_map *isl_basic_map_read_from_file(
634 isl_ctx *ctx, FILE *input, int nparam);
635 __isl_give isl_basic_map *isl_basic_map_read_from_str(
636 isl_ctx *ctx, const char *str, int nparam);
637 __isl_give isl_map *isl_map_read_from_file(
638 struct isl_ctx *ctx, FILE *input, int nparam);
639 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
640 const char *str, int nparam);
642 #include <isl/union_set.h>
643 __isl_give isl_union_set *isl_union_set_read_from_file(
644 isl_ctx *ctx, FILE *input);
645 __isl_give isl_union_set *isl_union_set_read_from_str(
646 struct isl_ctx *ctx, const char *str);
648 #include <isl/union_map.h>
649 __isl_give isl_union_map *isl_union_map_read_from_file(
650 isl_ctx *ctx, FILE *input);
651 __isl_give isl_union_map *isl_union_map_read_from_str(
652 struct isl_ctx *ctx, const char *str);
654 The input format is autodetected and may be either the C<PolyLib> format
655 or the C<isl> format.
656 C<nparam> specifies how many of the final columns in
657 the C<PolyLib> format correspond to parameters.
658 If input is given in the C<isl> format, then the number
659 of parameters needs to be equal to C<nparam>.
660 If C<nparam> is negative, then any number of parameters
661 is accepted in the C<isl> format and zero parameters
662 are assumed in the C<PolyLib> format.
666 Before anything can be printed, an C<isl_printer> needs to
669 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
671 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
672 void isl_printer_free(__isl_take isl_printer *printer);
673 __isl_give char *isl_printer_get_str(
674 __isl_keep isl_printer *printer);
676 The behavior of the printer can be modified in various ways
678 __isl_give isl_printer *isl_printer_set_output_format(
679 __isl_take isl_printer *p, int output_format);
680 __isl_give isl_printer *isl_printer_set_indent(
681 __isl_take isl_printer *p, int indent);
682 __isl_give isl_printer *isl_printer_set_prefix(
683 __isl_take isl_printer *p, const char *prefix);
684 __isl_give isl_printer *isl_printer_set_suffix(
685 __isl_take isl_printer *p, const char *suffix);
687 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
688 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
689 and defaults to C<ISL_FORMAT_ISL>.
690 Each line in the output is indented by C<indent> spaces
691 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
692 In the C<PolyLib> format output,
693 the coefficients of the existentially quantified variables
694 appear between those of the set variables and those
697 To actually print something, use
700 __isl_give isl_printer *isl_printer_print_basic_set(
701 __isl_take isl_printer *printer,
702 __isl_keep isl_basic_set *bset);
703 __isl_give isl_printer *isl_printer_print_set(
704 __isl_take isl_printer *printer,
705 __isl_keep isl_set *set);
708 __isl_give isl_printer *isl_printer_print_basic_map(
709 __isl_take isl_printer *printer,
710 __isl_keep isl_basic_map *bmap);
711 __isl_give isl_printer *isl_printer_print_map(
712 __isl_take isl_printer *printer,
713 __isl_keep isl_map *map);
715 #include <isl/union_set.h>
716 __isl_give isl_printer *isl_printer_print_union_set(
717 __isl_take isl_printer *p,
718 __isl_keep isl_union_set *uset);
720 #include <isl/union_map.h>
721 __isl_give isl_printer *isl_printer_print_union_map(
722 __isl_take isl_printer *p,
723 __isl_keep isl_union_map *umap);
725 When called on a file printer, the following function flushes
726 the file. When called on a string printer, the buffer is cleared.
728 __isl_give isl_printer *isl_printer_flush(
729 __isl_take isl_printer *p);
731 =head2 Creating New Sets and Relations
733 C<isl> has functions for creating some standard sets and relations.
737 =item * Empty sets and relations
739 __isl_give isl_basic_set *isl_basic_set_empty(
740 __isl_take isl_dim *dim);
741 __isl_give isl_basic_map *isl_basic_map_empty(
742 __isl_take isl_dim *dim);
743 __isl_give isl_set *isl_set_empty(
744 __isl_take isl_dim *dim);
745 __isl_give isl_map *isl_map_empty(
746 __isl_take isl_dim *dim);
747 __isl_give isl_union_set *isl_union_set_empty(
748 __isl_take isl_dim *dim);
749 __isl_give isl_union_map *isl_union_map_empty(
750 __isl_take isl_dim *dim);
752 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
753 is only used to specify the parameters.
755 =item * Universe sets and relations
757 __isl_give isl_basic_set *isl_basic_set_universe(
758 __isl_take isl_dim *dim);
759 __isl_give isl_basic_map *isl_basic_map_universe(
760 __isl_take isl_dim *dim);
761 __isl_give isl_set *isl_set_universe(
762 __isl_take isl_dim *dim);
763 __isl_give isl_map *isl_map_universe(
764 __isl_take isl_dim *dim);
765 __isl_give isl_union_set *isl_union_set_universe(
766 __isl_take isl_union_set *uset);
767 __isl_give isl_union_map *isl_union_map_universe(
768 __isl_take isl_union_map *umap);
770 The sets and relations constructed by the functions above
771 contain all integer values, while those constructed by the
772 functions below only contain non-negative values.
774 __isl_give isl_basic_set *isl_basic_set_nat_universe(
775 __isl_take isl_dim *dim);
776 __isl_give isl_basic_map *isl_basic_map_nat_universe(
777 __isl_take isl_dim *dim);
778 __isl_give isl_set *isl_set_nat_universe(
779 __isl_take isl_dim *dim);
780 __isl_give isl_map *isl_map_nat_universe(
781 __isl_take isl_dim *dim);
783 =item * Identity relations
785 __isl_give isl_basic_map *isl_basic_map_identity(
786 __isl_take isl_dim *dim);
787 __isl_give isl_map *isl_map_identity(
788 __isl_take isl_dim *dim);
790 The number of input and output dimensions in C<dim> needs
793 =item * Lexicographic order
795 __isl_give isl_map *isl_map_lex_lt(
796 __isl_take isl_dim *set_dim);
797 __isl_give isl_map *isl_map_lex_le(
798 __isl_take isl_dim *set_dim);
799 __isl_give isl_map *isl_map_lex_gt(
800 __isl_take isl_dim *set_dim);
801 __isl_give isl_map *isl_map_lex_ge(
802 __isl_take isl_dim *set_dim);
803 __isl_give isl_map *isl_map_lex_lt_first(
804 __isl_take isl_dim *dim, unsigned n);
805 __isl_give isl_map *isl_map_lex_le_first(
806 __isl_take isl_dim *dim, unsigned n);
807 __isl_give isl_map *isl_map_lex_gt_first(
808 __isl_take isl_dim *dim, unsigned n);
809 __isl_give isl_map *isl_map_lex_ge_first(
810 __isl_take isl_dim *dim, unsigned n);
812 The first four functions take a dimension specification for a B<set>
813 and return relations that express that the elements in the domain
814 are lexicographically less
815 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
816 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
817 than the elements in the range.
818 The last four functions take a dimension specification for a map
819 and return relations that express that the first C<n> dimensions
820 in the domain are lexicographically less
821 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
822 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
823 than the first C<n> dimensions in the range.
827 A basic set or relation can be converted to a set or relation
828 using the following functions.
830 __isl_give isl_set *isl_set_from_basic_set(
831 __isl_take isl_basic_set *bset);
832 __isl_give isl_map *isl_map_from_basic_map(
833 __isl_take isl_basic_map *bmap);
835 Sets and relations can be converted to union sets and relations
836 using the following functions.
838 __isl_give isl_union_map *isl_union_map_from_map(
839 __isl_take isl_map *map);
840 __isl_give isl_union_set *isl_union_set_from_set(
841 __isl_take isl_set *set);
843 Sets and relations can be copied and freed again using the following
846 __isl_give isl_basic_set *isl_basic_set_copy(
847 __isl_keep isl_basic_set *bset);
848 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
849 __isl_give isl_union_set *isl_union_set_copy(
850 __isl_keep isl_union_set *uset);
851 __isl_give isl_basic_map *isl_basic_map_copy(
852 __isl_keep isl_basic_map *bmap);
853 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
854 __isl_give isl_union_map *isl_union_map_copy(
855 __isl_keep isl_union_map *umap);
856 void isl_basic_set_free(__isl_take isl_basic_set *bset);
857 void isl_set_free(__isl_take isl_set *set);
858 void isl_union_set_free(__isl_take isl_union_set *uset);
859 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
860 void isl_map_free(__isl_take isl_map *map);
861 void isl_union_map_free(__isl_take isl_union_map *umap);
863 Other sets and relations can be constructed by starting
864 from a universe set or relation, adding equality and/or
865 inequality constraints and then projecting out the
866 existentially quantified variables, if any.
867 Constraints can be constructed, manipulated and
868 added to basic sets and relations using the following functions.
870 #include <isl/constraint.h>
871 __isl_give isl_constraint *isl_equality_alloc(
872 __isl_take isl_dim *dim);
873 __isl_give isl_constraint *isl_inequality_alloc(
874 __isl_take isl_dim *dim);
875 void isl_constraint_set_constant(
876 __isl_keep isl_constraint *constraint, isl_int v);
877 void isl_constraint_set_coefficient(
878 __isl_keep isl_constraint *constraint,
879 enum isl_dim_type type, int pos, isl_int v);
880 __isl_give isl_basic_map *isl_basic_map_add_constraint(
881 __isl_take isl_basic_map *bmap,
882 __isl_take isl_constraint *constraint);
883 __isl_give isl_basic_set *isl_basic_set_add_constraint(
884 __isl_take isl_basic_set *bset,
885 __isl_take isl_constraint *constraint);
887 For example, to create a set containing the even integers
888 between 10 and 42, you would use the following code.
892 struct isl_constraint *c;
893 struct isl_basic_set *bset;
896 dim = isl_dim_set_alloc(ctx, 0, 2);
897 bset = isl_basic_set_universe(isl_dim_copy(dim));
899 c = isl_equality_alloc(isl_dim_copy(dim));
900 isl_int_set_si(v, -1);
901 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
902 isl_int_set_si(v, 2);
903 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
904 bset = isl_basic_set_add_constraint(bset, c);
906 c = isl_inequality_alloc(isl_dim_copy(dim));
907 isl_int_set_si(v, -10);
908 isl_constraint_set_constant(c, v);
909 isl_int_set_si(v, 1);
910 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
911 bset = isl_basic_set_add_constraint(bset, c);
913 c = isl_inequality_alloc(dim);
914 isl_int_set_si(v, 42);
915 isl_constraint_set_constant(c, v);
916 isl_int_set_si(v, -1);
917 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
918 bset = isl_basic_set_add_constraint(bset, c);
920 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
926 struct isl_basic_set *bset;
927 bset = isl_basic_set_read_from_str(ctx,
928 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
930 A basic set or relation can also be constructed from two matrices
931 describing the equalities and the inequalities.
933 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
934 __isl_take isl_dim *dim,
935 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
936 enum isl_dim_type c1,
937 enum isl_dim_type c2, enum isl_dim_type c3,
938 enum isl_dim_type c4);
939 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
940 __isl_take isl_dim *dim,
941 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
942 enum isl_dim_type c1,
943 enum isl_dim_type c2, enum isl_dim_type c3,
944 enum isl_dim_type c4, enum isl_dim_type c5);
946 The C<isl_dim_type> arguments indicate the order in which
947 different kinds of variables appear in the input matrices
948 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
949 C<isl_dim_set> and C<isl_dim_div> for sets and
950 of C<isl_dim_cst>, C<isl_dim_param>,
951 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
953 =head2 Inspecting Sets and Relations
955 Usually, the user should not have to care about the actual constraints
956 of the sets and maps, but should instead apply the abstract operations
957 explained in the following sections.
958 Occasionally, however, it may be required to inspect the individual
959 coefficients of the constraints. This section explains how to do so.
960 In these cases, it may also be useful to have C<isl> compute
961 an explicit representation of the existentially quantified variables.
963 __isl_give isl_set *isl_set_compute_divs(
964 __isl_take isl_set *set);
965 __isl_give isl_map *isl_map_compute_divs(
966 __isl_take isl_map *map);
967 __isl_give isl_union_set *isl_union_set_compute_divs(
968 __isl_take isl_union_set *uset);
969 __isl_give isl_union_map *isl_union_map_compute_divs(
970 __isl_take isl_union_map *umap);
972 This explicit representation defines the existentially quantified
973 variables as integer divisions of the other variables, possibly
974 including earlier existentially quantified variables.
975 An explicitly represented existentially quantified variable therefore
976 has a unique value when the values of the other variables are known.
977 If, furthermore, the same existentials, i.e., existentials
978 with the same explicit representations, should appear in the
979 same order in each of the disjuncts of a set or map, then the user should call
980 either of the following functions.
982 __isl_give isl_set *isl_set_align_divs(
983 __isl_take isl_set *set);
984 __isl_give isl_map *isl_map_align_divs(
985 __isl_take isl_map *map);
987 Alternatively, the existentially quantified variables can be removed
988 using the following functions, which compute an overapproximation.
990 __isl_give isl_basic_set *isl_basic_set_remove_divs(
991 __isl_take isl_basic_set *bset);
992 __isl_give isl_basic_map *isl_basic_map_remove_divs(
993 __isl_take isl_basic_map *bmap);
994 __isl_give isl_set *isl_set_remove_divs(
995 __isl_take isl_set *set);
996 __isl_give isl_map *isl_map_remove_divs(
997 __isl_take isl_map *map);
999 To iterate over all the sets or maps in a union set or map, use
1001 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
1002 int (*fn)(__isl_take isl_set *set, void *user),
1004 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
1005 int (*fn)(__isl_take isl_map *map, void *user),
1008 The number of sets or maps in a union set or map can be obtained
1011 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1012 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1014 To extract the set or map from a union with a given dimension
1017 __isl_give isl_set *isl_union_set_extract_set(
1018 __isl_keep isl_union_set *uset,
1019 __isl_take isl_dim *dim);
1020 __isl_give isl_map *isl_union_map_extract_map(
1021 __isl_keep isl_union_map *umap,
1022 __isl_take isl_dim *dim);
1024 To iterate over all the basic sets or maps in a set or map, use
1026 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1027 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1029 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1030 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1033 The callback function C<fn> should return 0 if successful and
1034 -1 if an error occurs. In the latter case, or if any other error
1035 occurs, the above functions will return -1.
1037 It should be noted that C<isl> does not guarantee that
1038 the basic sets or maps passed to C<fn> are disjoint.
1039 If this is required, then the user should call one of
1040 the following functions first.
1042 __isl_give isl_set *isl_set_make_disjoint(
1043 __isl_take isl_set *set);
1044 __isl_give isl_map *isl_map_make_disjoint(
1045 __isl_take isl_map *map);
1047 The number of basic sets in a set can be obtained
1050 int isl_set_n_basic_set(__isl_keep isl_set *set);
1052 To iterate over the constraints of a basic set or map, use
1054 #include <isl/constraint.h>
1056 int isl_basic_map_foreach_constraint(
1057 __isl_keep isl_basic_map *bmap,
1058 int (*fn)(__isl_take isl_constraint *c, void *user),
1060 void isl_constraint_free(struct isl_constraint *c);
1062 Again, the callback function C<fn> should return 0 if successful and
1063 -1 if an error occurs. In the latter case, or if any other error
1064 occurs, the above functions will return -1.
1065 The constraint C<c> represents either an equality or an inequality.
1066 Use the following function to find out whether a constraint
1067 represents an equality. If not, it represents an inequality.
1069 int isl_constraint_is_equality(
1070 __isl_keep isl_constraint *constraint);
1072 The coefficients of the constraints can be inspected using
1073 the following functions.
1075 void isl_constraint_get_constant(
1076 __isl_keep isl_constraint *constraint, isl_int *v);
1077 void isl_constraint_get_coefficient(
1078 __isl_keep isl_constraint *constraint,
1079 enum isl_dim_type type, int pos, isl_int *v);
1080 int isl_constraint_involves_dims(
1081 __isl_keep isl_constraint *constraint,
1082 enum isl_dim_type type, unsigned first, unsigned n);
1084 The explicit representations of the existentially quantified
1085 variables can be inspected using the following functions.
1086 Note that the user is only allowed to use these functions
1087 if the inspected set or map is the result of a call
1088 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1090 __isl_give isl_div *isl_constraint_div(
1091 __isl_keep isl_constraint *constraint, int pos);
1092 isl_ctx *isl_div_get_ctx(__isl_keep isl_div *div);
1093 void isl_div_get_constant(__isl_keep isl_div *div,
1095 void isl_div_get_denominator(__isl_keep isl_div *div,
1097 void isl_div_get_coefficient(__isl_keep isl_div *div,
1098 enum isl_dim_type type, int pos, isl_int *v);
1100 To obtain the constraints of a basic set or map in matrix
1101 form, use the following functions.
1103 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1104 __isl_keep isl_basic_set *bset,
1105 enum isl_dim_type c1, enum isl_dim_type c2,
1106 enum isl_dim_type c3, enum isl_dim_type c4);
1107 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1108 __isl_keep isl_basic_set *bset,
1109 enum isl_dim_type c1, enum isl_dim_type c2,
1110 enum isl_dim_type c3, enum isl_dim_type c4);
1111 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1112 __isl_keep isl_basic_map *bmap,
1113 enum isl_dim_type c1,
1114 enum isl_dim_type c2, enum isl_dim_type c3,
1115 enum isl_dim_type c4, enum isl_dim_type c5);
1116 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1117 __isl_keep isl_basic_map *bmap,
1118 enum isl_dim_type c1,
1119 enum isl_dim_type c2, enum isl_dim_type c3,
1120 enum isl_dim_type c4, enum isl_dim_type c5);
1122 The C<isl_dim_type> arguments dictate the order in which
1123 different kinds of variables appear in the resulting matrix
1124 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1125 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1127 The names of the domain and range spaces of a set or relation can be
1128 read off using the following functions.
1130 const char *isl_basic_set_get_tuple_name(
1131 __isl_keep isl_basic_set *bset);
1132 const char *isl_set_get_tuple_name(
1133 __isl_keep isl_set *set);
1134 const char *isl_basic_map_get_tuple_name(
1135 __isl_keep isl_basic_map *bmap,
1136 enum isl_dim_type type);
1137 const char *isl_map_get_tuple_name(
1138 __isl_keep isl_map *map,
1139 enum isl_dim_type type);
1141 As with C<isl_dim_get_tuple_name>, the value returned points to
1142 an internal data structure.
1143 The names of individual dimensions can be read off using
1144 the following functions.
1146 const char *isl_constraint_get_dim_name(
1147 __isl_keep isl_constraint *constraint,
1148 enum isl_dim_type type, unsigned pos);
1149 const char *isl_basic_set_get_dim_name(
1150 __isl_keep isl_basic_set *bset,
1151 enum isl_dim_type type, unsigned pos);
1152 const char *isl_set_get_dim_name(
1153 __isl_keep isl_set *set,
1154 enum isl_dim_type type, unsigned pos);
1155 const char *isl_basic_map_get_dim_name(
1156 __isl_keep isl_basic_map *bmap,
1157 enum isl_dim_type type, unsigned pos);
1158 const char *isl_map_get_dim_name(
1159 __isl_keep isl_map *map,
1160 enum isl_dim_type type, unsigned pos);
1162 These functions are mostly useful to obtain the names
1167 =head3 Unary Properties
1173 The following functions test whether the given set or relation
1174 contains any integer points. The ``plain'' variants do not perform
1175 any computations, but simply check if the given set or relation
1176 is already known to be empty.
1178 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1179 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1180 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1181 int isl_set_is_empty(__isl_keep isl_set *set);
1182 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1183 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1184 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1185 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1186 int isl_map_is_empty(__isl_keep isl_map *map);
1187 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1189 =item * Universality
1191 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1192 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1193 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1195 =item * Single-valuedness
1197 int isl_map_is_single_valued(__isl_keep isl_map *map);
1198 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1202 int isl_map_plain_is_injective(__isl_keep isl_map *map);
1203 int isl_map_is_injective(__isl_keep isl_map *map);
1204 int isl_union_map_plain_is_injective(
1205 __isl_keep isl_union_map *umap);
1206 int isl_union_map_is_injective(
1207 __isl_keep isl_union_map *umap);
1211 int isl_map_is_bijective(__isl_keep isl_map *map);
1212 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1216 The following functions check whether the domain of the given
1217 (basic) set is a wrapped relation.
1219 int isl_basic_set_is_wrapping(
1220 __isl_keep isl_basic_set *bset);
1221 int isl_set_is_wrapping(__isl_keep isl_set *set);
1223 =item * Internal Product
1225 int isl_basic_map_can_zip(
1226 __isl_keep isl_basic_map *bmap);
1227 int isl_map_can_zip(__isl_keep isl_map *map);
1229 Check whether the product of domain and range of the given relation
1231 i.e., whether both domain and range are nested relations.
1235 =head3 Binary Properties
1241 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1242 __isl_keep isl_set *set2);
1243 int isl_set_is_equal(__isl_keep isl_set *set1,
1244 __isl_keep isl_set *set2);
1245 int isl_union_set_is_equal(
1246 __isl_keep isl_union_set *uset1,
1247 __isl_keep isl_union_set *uset2);
1248 int isl_basic_map_is_equal(
1249 __isl_keep isl_basic_map *bmap1,
1250 __isl_keep isl_basic_map *bmap2);
1251 int isl_map_is_equal(__isl_keep isl_map *map1,
1252 __isl_keep isl_map *map2);
1253 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1254 __isl_keep isl_map *map2);
1255 int isl_union_map_is_equal(
1256 __isl_keep isl_union_map *umap1,
1257 __isl_keep isl_union_map *umap2);
1259 =item * Disjointness
1261 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1262 __isl_keep isl_set *set2);
1266 int isl_set_is_subset(__isl_keep isl_set *set1,
1267 __isl_keep isl_set *set2);
1268 int isl_set_is_strict_subset(
1269 __isl_keep isl_set *set1,
1270 __isl_keep isl_set *set2);
1271 int isl_union_set_is_subset(
1272 __isl_keep isl_union_set *uset1,
1273 __isl_keep isl_union_set *uset2);
1274 int isl_union_set_is_strict_subset(
1275 __isl_keep isl_union_set *uset1,
1276 __isl_keep isl_union_set *uset2);
1277 int isl_basic_map_is_subset(
1278 __isl_keep isl_basic_map *bmap1,
1279 __isl_keep isl_basic_map *bmap2);
1280 int isl_basic_map_is_strict_subset(
1281 __isl_keep isl_basic_map *bmap1,
1282 __isl_keep isl_basic_map *bmap2);
1283 int isl_map_is_subset(
1284 __isl_keep isl_map *map1,
1285 __isl_keep isl_map *map2);
1286 int isl_map_is_strict_subset(
1287 __isl_keep isl_map *map1,
1288 __isl_keep isl_map *map2);
1289 int isl_union_map_is_subset(
1290 __isl_keep isl_union_map *umap1,
1291 __isl_keep isl_union_map *umap2);
1292 int isl_union_map_is_strict_subset(
1293 __isl_keep isl_union_map *umap1,
1294 __isl_keep isl_union_map *umap2);
1298 =head2 Unary Operations
1304 __isl_give isl_set *isl_set_complement(
1305 __isl_take isl_set *set);
1309 __isl_give isl_basic_map *isl_basic_map_reverse(
1310 __isl_take isl_basic_map *bmap);
1311 __isl_give isl_map *isl_map_reverse(
1312 __isl_take isl_map *map);
1313 __isl_give isl_union_map *isl_union_map_reverse(
1314 __isl_take isl_union_map *umap);
1318 __isl_give isl_basic_set *isl_basic_set_project_out(
1319 __isl_take isl_basic_set *bset,
1320 enum isl_dim_type type, unsigned first, unsigned n);
1321 __isl_give isl_basic_map *isl_basic_map_project_out(
1322 __isl_take isl_basic_map *bmap,
1323 enum isl_dim_type type, unsigned first, unsigned n);
1324 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1325 enum isl_dim_type type, unsigned first, unsigned n);
1326 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1327 enum isl_dim_type type, unsigned first, unsigned n);
1328 __isl_give isl_basic_set *isl_basic_map_domain(
1329 __isl_take isl_basic_map *bmap);
1330 __isl_give isl_basic_set *isl_basic_map_range(
1331 __isl_take isl_basic_map *bmap);
1332 __isl_give isl_set *isl_map_domain(
1333 __isl_take isl_map *bmap);
1334 __isl_give isl_set *isl_map_range(
1335 __isl_take isl_map *map);
1336 __isl_give isl_union_set *isl_union_map_domain(
1337 __isl_take isl_union_map *umap);
1338 __isl_give isl_union_set *isl_union_map_range(
1339 __isl_take isl_union_map *umap);
1341 __isl_give isl_basic_map *isl_basic_map_domain_map(
1342 __isl_take isl_basic_map *bmap);
1343 __isl_give isl_basic_map *isl_basic_map_range_map(
1344 __isl_take isl_basic_map *bmap);
1345 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1346 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1347 __isl_give isl_union_map *isl_union_map_domain_map(
1348 __isl_take isl_union_map *umap);
1349 __isl_give isl_union_map *isl_union_map_range_map(
1350 __isl_take isl_union_map *umap);
1352 The functions above construct a (basic, regular or union) relation
1353 that maps (a wrapped version of) the input relation to its domain or range.
1357 __isl_give isl_set *isl_set_eliminate(
1358 __isl_take isl_set *set, enum isl_dim_type type,
1359 unsigned first, unsigned n);
1361 Eliminate the coefficients for the given dimensions from the constraints,
1362 without removing the dimensions.
1366 __isl_give isl_map *isl_set_identity(
1367 __isl_take isl_set *set);
1368 __isl_give isl_union_map *isl_union_set_identity(
1369 __isl_take isl_union_set *uset);
1371 Construct an identity relation on the given (union) set.
1375 __isl_give isl_basic_set *isl_basic_map_deltas(
1376 __isl_take isl_basic_map *bmap);
1377 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1378 __isl_give isl_union_set *isl_union_map_deltas(
1379 __isl_take isl_union_map *umap);
1381 These functions return a (basic) set containing the differences
1382 between image elements and corresponding domain elements in the input.
1384 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1385 __isl_take isl_basic_map *bmap);
1386 __isl_give isl_map *isl_map_deltas_map(
1387 __isl_take isl_map *map);
1388 __isl_give isl_union_map *isl_union_map_deltas_map(
1389 __isl_take isl_union_map *umap);
1391 The functions above construct a (basic, regular or union) relation
1392 that maps (a wrapped version of) the input relation to its delta set.
1396 Simplify the representation of a set or relation by trying
1397 to combine pairs of basic sets or relations into a single
1398 basic set or relation.
1400 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1401 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1402 __isl_give isl_union_set *isl_union_set_coalesce(
1403 __isl_take isl_union_set *uset);
1404 __isl_give isl_union_map *isl_union_map_coalesce(
1405 __isl_take isl_union_map *umap);
1407 =item * Detecting equalities
1409 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1410 __isl_take isl_basic_set *bset);
1411 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1412 __isl_take isl_basic_map *bmap);
1413 __isl_give isl_set *isl_set_detect_equalities(
1414 __isl_take isl_set *set);
1415 __isl_give isl_map *isl_map_detect_equalities(
1416 __isl_take isl_map *map);
1417 __isl_give isl_union_set *isl_union_set_detect_equalities(
1418 __isl_take isl_union_set *uset);
1419 __isl_give isl_union_map *isl_union_map_detect_equalities(
1420 __isl_take isl_union_map *umap);
1422 Simplify the representation of a set or relation by detecting implicit
1425 =item * Removing redundant constraints
1427 __isl_give isl_basic_set *isl_basic_set_remove_redundancies(
1428 __isl_take isl_basic_set *bset);
1429 __isl_give isl_basic_map *isl_basic_map_remove_redundancies(
1430 __isl_take isl_basic_map *bmap);
1434 __isl_give isl_basic_set *isl_set_convex_hull(
1435 __isl_take isl_set *set);
1436 __isl_give isl_basic_map *isl_map_convex_hull(
1437 __isl_take isl_map *map);
1439 If the input set or relation has any existentially quantified
1440 variables, then the result of these operations is currently undefined.
1444 __isl_give isl_basic_set *isl_set_simple_hull(
1445 __isl_take isl_set *set);
1446 __isl_give isl_basic_map *isl_map_simple_hull(
1447 __isl_take isl_map *map);
1448 __isl_give isl_union_map *isl_union_map_simple_hull(
1449 __isl_take isl_union_map *umap);
1451 These functions compute a single basic set or relation
1452 that contains the whole input set or relation.
1453 In particular, the output is described by translates
1454 of the constraints describing the basic sets or relations in the input.
1458 (See \autoref{s:simple hull}.)
1464 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1465 __isl_take isl_basic_set *bset);
1466 __isl_give isl_basic_set *isl_set_affine_hull(
1467 __isl_take isl_set *set);
1468 __isl_give isl_union_set *isl_union_set_affine_hull(
1469 __isl_take isl_union_set *uset);
1470 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1471 __isl_take isl_basic_map *bmap);
1472 __isl_give isl_basic_map *isl_map_affine_hull(
1473 __isl_take isl_map *map);
1474 __isl_give isl_union_map *isl_union_map_affine_hull(
1475 __isl_take isl_union_map *umap);
1477 In case of union sets and relations, the affine hull is computed
1480 =item * Polyhedral hull
1482 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1483 __isl_take isl_set *set);
1484 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1485 __isl_take isl_map *map);
1486 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1487 __isl_take isl_union_set *uset);
1488 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1489 __isl_take isl_union_map *umap);
1491 These functions compute a single basic set or relation
1492 not involving any existentially quantified variables
1493 that contains the whole input set or relation.
1494 In case of union sets and relations, the polyhedral hull is computed
1499 The following functions compute either the set of (rational) coefficient
1500 values of valid constraints for the given set or the set of (rational)
1501 values satisfying the constraints with coefficients from the given set.
1502 Internally, these two sets of functions perform essentially the
1503 same operations, except that the set of coefficients is assumed to
1504 be a cone, while the set of values may be any polyhedron.
1505 The current implementation is based on the Farkas lemma and
1506 Fourier-Motzkin elimination, but this may change or be made optional
1507 in future. In particular, future implementations may use different
1508 dualization algorithms or skip the elimination step.
1510 __isl_give isl_basic_set *isl_basic_set_coefficients(
1511 __isl_take isl_basic_set *bset);
1512 __isl_give isl_basic_set *isl_set_coefficients(
1513 __isl_take isl_set *set);
1514 __isl_give isl_union_set *isl_union_set_coefficients(
1515 __isl_take isl_union_set *bset);
1516 __isl_give isl_basic_set *isl_basic_set_solutions(
1517 __isl_take isl_basic_set *bset);
1518 __isl_give isl_basic_set *isl_set_solutions(
1519 __isl_take isl_set *set);
1520 __isl_give isl_union_set *isl_union_set_solutions(
1521 __isl_take isl_union_set *bset);
1525 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1527 __isl_give isl_union_map *isl_union_map_power(
1528 __isl_take isl_union_map *umap, int *exact);
1530 Compute a parametric representation for all positive powers I<k> of C<map>.
1531 The result maps I<k> to a nested relation corresponding to the
1532 I<k>th power of C<map>.
1533 The result may be an overapproximation. If the result is known to be exact,
1534 then C<*exact> is set to C<1>.
1536 =item * Transitive closure
1538 __isl_give isl_map *isl_map_transitive_closure(
1539 __isl_take isl_map *map, int *exact);
1540 __isl_give isl_union_map *isl_union_map_transitive_closure(
1541 __isl_take isl_union_map *umap, int *exact);
1543 Compute the transitive closure of C<map>.
1544 The result may be an overapproximation. If the result is known to be exact,
1545 then C<*exact> is set to C<1>.
1547 =item * Reaching path lengths
1549 __isl_give isl_map *isl_map_reaching_path_lengths(
1550 __isl_take isl_map *map, int *exact);
1552 Compute a relation that maps each element in the range of C<map>
1553 to the lengths of all paths composed of edges in C<map> that
1554 end up in the given element.
1555 The result may be an overapproximation. If the result is known to be exact,
1556 then C<*exact> is set to C<1>.
1557 To compute the I<maximal> path length, the resulting relation
1558 should be postprocessed by C<isl_map_lexmax>.
1559 In particular, if the input relation is a dependence relation
1560 (mapping sources to sinks), then the maximal path length corresponds
1561 to the free schedule.
1562 Note, however, that C<isl_map_lexmax> expects the maximum to be
1563 finite, so if the path lengths are unbounded (possibly due to
1564 the overapproximation), then you will get an error message.
1568 __isl_give isl_basic_set *isl_basic_map_wrap(
1569 __isl_take isl_basic_map *bmap);
1570 __isl_give isl_set *isl_map_wrap(
1571 __isl_take isl_map *map);
1572 __isl_give isl_union_set *isl_union_map_wrap(
1573 __isl_take isl_union_map *umap);
1574 __isl_give isl_basic_map *isl_basic_set_unwrap(
1575 __isl_take isl_basic_set *bset);
1576 __isl_give isl_map *isl_set_unwrap(
1577 __isl_take isl_set *set);
1578 __isl_give isl_union_map *isl_union_set_unwrap(
1579 __isl_take isl_union_set *uset);
1583 Remove any internal structure of domain (and range) of the given
1584 set or relation. If there is any such internal structure in the input,
1585 then the name of the space is also removed.
1587 __isl_give isl_basic_set *isl_basic_set_flatten(
1588 __isl_take isl_basic_set *bset);
1589 __isl_give isl_set *isl_set_flatten(
1590 __isl_take isl_set *set);
1591 __isl_give isl_basic_map *isl_basic_map_flatten(
1592 __isl_take isl_basic_map *bmap);
1593 __isl_give isl_map *isl_map_flatten(
1594 __isl_take isl_map *map);
1596 __isl_give isl_map *isl_set_flatten_map(
1597 __isl_take isl_set *set);
1599 The function above constructs a relation
1600 that maps the input set to a flattened version of the set.
1604 Lift the input set to a space with extra dimensions corresponding
1605 to the existentially quantified variables in the input.
1606 In particular, the result lives in a wrapped map where the domain
1607 is the original space and the range corresponds to the original
1608 existentially quantified variables.
1610 __isl_give isl_basic_set *isl_basic_set_lift(
1611 __isl_take isl_basic_set *bset);
1612 __isl_give isl_set *isl_set_lift(
1613 __isl_take isl_set *set);
1614 __isl_give isl_union_set *isl_union_set_lift(
1615 __isl_take isl_union_set *uset);
1617 =item * Internal Product
1619 __isl_give isl_basic_map *isl_basic_map_zip(
1620 __isl_take isl_basic_map *bmap);
1621 __isl_give isl_map *isl_map_zip(
1622 __isl_take isl_map *map);
1623 __isl_give isl_union_map *isl_union_map_zip(
1624 __isl_take isl_union_map *umap);
1626 Given a relation with nested relations for domain and range,
1627 interchange the range of the domain with the domain of the range.
1629 =item * Aligning parameters
1631 __isl_give isl_set *isl_set_align_params(
1632 __isl_take isl_set *set,
1633 __isl_take isl_dim *model);
1634 __isl_give isl_map *isl_map_align_params(
1635 __isl_take isl_map *map,
1636 __isl_take isl_dim *model);
1638 Change the order of the parameters of the given set or relation
1639 such that the first parameters match those of C<model>.
1640 This may involve the introduction of extra parameters.
1641 All parameters need to be named.
1643 =item * Dimension manipulation
1645 __isl_give isl_set *isl_set_add_dims(
1646 __isl_take isl_set *set,
1647 enum isl_dim_type type, unsigned n);
1648 __isl_give isl_map *isl_map_add_dims(
1649 __isl_take isl_map *map,
1650 enum isl_dim_type type, unsigned n);
1652 It is usually not advisable to directly change the (input or output)
1653 space of a set or a relation as this removes the name and the internal
1654 structure of the space. However, the above functions can be useful
1655 to add new parameters, assuming
1656 C<isl_set_align_params> and C<isl_map_align_params>
1661 =head2 Binary Operations
1663 The two arguments of a binary operation not only need to live
1664 in the same C<isl_ctx>, they currently also need to have
1665 the same (number of) parameters.
1667 =head3 Basic Operations
1671 =item * Intersection
1673 __isl_give isl_basic_set *isl_basic_set_intersect(
1674 __isl_take isl_basic_set *bset1,
1675 __isl_take isl_basic_set *bset2);
1676 __isl_give isl_set *isl_set_intersect(
1677 __isl_take isl_set *set1,
1678 __isl_take isl_set *set2);
1679 __isl_give isl_union_set *isl_union_set_intersect(
1680 __isl_take isl_union_set *uset1,
1681 __isl_take isl_union_set *uset2);
1682 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1683 __isl_take isl_basic_map *bmap,
1684 __isl_take isl_basic_set *bset);
1685 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1686 __isl_take isl_basic_map *bmap,
1687 __isl_take isl_basic_set *bset);
1688 __isl_give isl_basic_map *isl_basic_map_intersect(
1689 __isl_take isl_basic_map *bmap1,
1690 __isl_take isl_basic_map *bmap2);
1691 __isl_give isl_map *isl_map_intersect_domain(
1692 __isl_take isl_map *map,
1693 __isl_take isl_set *set);
1694 __isl_give isl_map *isl_map_intersect_range(
1695 __isl_take isl_map *map,
1696 __isl_take isl_set *set);
1697 __isl_give isl_map *isl_map_intersect(
1698 __isl_take isl_map *map1,
1699 __isl_take isl_map *map2);
1700 __isl_give isl_union_map *isl_union_map_intersect_domain(
1701 __isl_take isl_union_map *umap,
1702 __isl_take isl_union_set *uset);
1703 __isl_give isl_union_map *isl_union_map_intersect_range(
1704 __isl_take isl_union_map *umap,
1705 __isl_take isl_union_set *uset);
1706 __isl_give isl_union_map *isl_union_map_intersect(
1707 __isl_take isl_union_map *umap1,
1708 __isl_take isl_union_map *umap2);
1712 __isl_give isl_set *isl_basic_set_union(
1713 __isl_take isl_basic_set *bset1,
1714 __isl_take isl_basic_set *bset2);
1715 __isl_give isl_map *isl_basic_map_union(
1716 __isl_take isl_basic_map *bmap1,
1717 __isl_take isl_basic_map *bmap2);
1718 __isl_give isl_set *isl_set_union(
1719 __isl_take isl_set *set1,
1720 __isl_take isl_set *set2);
1721 __isl_give isl_map *isl_map_union(
1722 __isl_take isl_map *map1,
1723 __isl_take isl_map *map2);
1724 __isl_give isl_union_set *isl_union_set_union(
1725 __isl_take isl_union_set *uset1,
1726 __isl_take isl_union_set *uset2);
1727 __isl_give isl_union_map *isl_union_map_union(
1728 __isl_take isl_union_map *umap1,
1729 __isl_take isl_union_map *umap2);
1731 =item * Set difference
1733 __isl_give isl_set *isl_set_subtract(
1734 __isl_take isl_set *set1,
1735 __isl_take isl_set *set2);
1736 __isl_give isl_map *isl_map_subtract(
1737 __isl_take isl_map *map1,
1738 __isl_take isl_map *map2);
1739 __isl_give isl_union_set *isl_union_set_subtract(
1740 __isl_take isl_union_set *uset1,
1741 __isl_take isl_union_set *uset2);
1742 __isl_give isl_union_map *isl_union_map_subtract(
1743 __isl_take isl_union_map *umap1,
1744 __isl_take isl_union_map *umap2);
1748 __isl_give isl_basic_set *isl_basic_set_apply(
1749 __isl_take isl_basic_set *bset,
1750 __isl_take isl_basic_map *bmap);
1751 __isl_give isl_set *isl_set_apply(
1752 __isl_take isl_set *set,
1753 __isl_take isl_map *map);
1754 __isl_give isl_union_set *isl_union_set_apply(
1755 __isl_take isl_union_set *uset,
1756 __isl_take isl_union_map *umap);
1757 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1758 __isl_take isl_basic_map *bmap1,
1759 __isl_take isl_basic_map *bmap2);
1760 __isl_give isl_basic_map *isl_basic_map_apply_range(
1761 __isl_take isl_basic_map *bmap1,
1762 __isl_take isl_basic_map *bmap2);
1763 __isl_give isl_map *isl_map_apply_domain(
1764 __isl_take isl_map *map1,
1765 __isl_take isl_map *map2);
1766 __isl_give isl_union_map *isl_union_map_apply_domain(
1767 __isl_take isl_union_map *umap1,
1768 __isl_take isl_union_map *umap2);
1769 __isl_give isl_map *isl_map_apply_range(
1770 __isl_take isl_map *map1,
1771 __isl_take isl_map *map2);
1772 __isl_give isl_union_map *isl_union_map_apply_range(
1773 __isl_take isl_union_map *umap1,
1774 __isl_take isl_union_map *umap2);
1776 =item * Cartesian Product
1778 __isl_give isl_set *isl_set_product(
1779 __isl_take isl_set *set1,
1780 __isl_take isl_set *set2);
1781 __isl_give isl_union_set *isl_union_set_product(
1782 __isl_take isl_union_set *uset1,
1783 __isl_take isl_union_set *uset2);
1784 __isl_give isl_basic_map *isl_basic_map_range_product(
1785 __isl_take isl_basic_map *bmap1,
1786 __isl_take isl_basic_map *bmap2);
1787 __isl_give isl_map *isl_map_range_product(
1788 __isl_take isl_map *map1,
1789 __isl_take isl_map *map2);
1790 __isl_give isl_union_map *isl_union_map_range_product(
1791 __isl_take isl_union_map *umap1,
1792 __isl_take isl_union_map *umap2);
1793 __isl_give isl_map *isl_map_product(
1794 __isl_take isl_map *map1,
1795 __isl_take isl_map *map2);
1796 __isl_give isl_union_map *isl_union_map_product(
1797 __isl_take isl_union_map *umap1,
1798 __isl_take isl_union_map *umap2);
1800 The above functions compute the cross product of the given
1801 sets or relations. The domains and ranges of the results
1802 are wrapped maps between domains and ranges of the inputs.
1803 To obtain a ``flat'' product, use the following functions
1806 __isl_give isl_basic_set *isl_basic_set_flat_product(
1807 __isl_take isl_basic_set *bset1,
1808 __isl_take isl_basic_set *bset2);
1809 __isl_give isl_set *isl_set_flat_product(
1810 __isl_take isl_set *set1,
1811 __isl_take isl_set *set2);
1812 __isl_give isl_basic_map *isl_basic_map_flat_product(
1813 __isl_take isl_basic_map *bmap1,
1814 __isl_take isl_basic_map *bmap2);
1815 __isl_give isl_map *isl_map_flat_product(
1816 __isl_take isl_map *map1,
1817 __isl_take isl_map *map2);
1819 =item * Simplification
1821 __isl_give isl_basic_set *isl_basic_set_gist(
1822 __isl_take isl_basic_set *bset,
1823 __isl_take isl_basic_set *context);
1824 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1825 __isl_take isl_set *context);
1826 __isl_give isl_union_set *isl_union_set_gist(
1827 __isl_take isl_union_set *uset,
1828 __isl_take isl_union_set *context);
1829 __isl_give isl_basic_map *isl_basic_map_gist(
1830 __isl_take isl_basic_map *bmap,
1831 __isl_take isl_basic_map *context);
1832 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1833 __isl_take isl_map *context);
1834 __isl_give isl_union_map *isl_union_map_gist(
1835 __isl_take isl_union_map *umap,
1836 __isl_take isl_union_map *context);
1838 The gist operation returns a set or relation that has the
1839 same intersection with the context as the input set or relation.
1840 Any implicit equality in the intersection is made explicit in the result,
1841 while all inequalities that are redundant with respect to the intersection
1843 In case of union sets and relations, the gist operation is performed
1848 =head3 Lexicographic Optimization
1850 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1851 the following functions
1852 compute a set that contains the lexicographic minimum or maximum
1853 of the elements in C<set> (or C<bset>) for those values of the parameters
1854 that satisfy C<dom>.
1855 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1856 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1858 In other words, the union of the parameter values
1859 for which the result is non-empty and of C<*empty>
1862 __isl_give isl_set *isl_basic_set_partial_lexmin(
1863 __isl_take isl_basic_set *bset,
1864 __isl_take isl_basic_set *dom,
1865 __isl_give isl_set **empty);
1866 __isl_give isl_set *isl_basic_set_partial_lexmax(
1867 __isl_take isl_basic_set *bset,
1868 __isl_take isl_basic_set *dom,
1869 __isl_give isl_set **empty);
1870 __isl_give isl_set *isl_set_partial_lexmin(
1871 __isl_take isl_set *set, __isl_take isl_set *dom,
1872 __isl_give isl_set **empty);
1873 __isl_give isl_set *isl_set_partial_lexmax(
1874 __isl_take isl_set *set, __isl_take isl_set *dom,
1875 __isl_give isl_set **empty);
1877 Given a (basic) set C<set> (or C<bset>), the following functions simply
1878 return a set containing the lexicographic minimum or maximum
1879 of the elements in C<set> (or C<bset>).
1880 In case of union sets, the optimum is computed per space.
1882 __isl_give isl_set *isl_basic_set_lexmin(
1883 __isl_take isl_basic_set *bset);
1884 __isl_give isl_set *isl_basic_set_lexmax(
1885 __isl_take isl_basic_set *bset);
1886 __isl_give isl_set *isl_set_lexmin(
1887 __isl_take isl_set *set);
1888 __isl_give isl_set *isl_set_lexmax(
1889 __isl_take isl_set *set);
1890 __isl_give isl_union_set *isl_union_set_lexmin(
1891 __isl_take isl_union_set *uset);
1892 __isl_give isl_union_set *isl_union_set_lexmax(
1893 __isl_take isl_union_set *uset);
1895 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1896 the following functions
1897 compute a relation that maps each element of C<dom>
1898 to the single lexicographic minimum or maximum
1899 of the elements that are associated to that same
1900 element in C<map> (or C<bmap>).
1901 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1902 that contains the elements in C<dom> that do not map
1903 to any elements in C<map> (or C<bmap>).
1904 In other words, the union of the domain of the result and of C<*empty>
1907 __isl_give isl_map *isl_basic_map_partial_lexmax(
1908 __isl_take isl_basic_map *bmap,
1909 __isl_take isl_basic_set *dom,
1910 __isl_give isl_set **empty);
1911 __isl_give isl_map *isl_basic_map_partial_lexmin(
1912 __isl_take isl_basic_map *bmap,
1913 __isl_take isl_basic_set *dom,
1914 __isl_give isl_set **empty);
1915 __isl_give isl_map *isl_map_partial_lexmax(
1916 __isl_take isl_map *map, __isl_take isl_set *dom,
1917 __isl_give isl_set **empty);
1918 __isl_give isl_map *isl_map_partial_lexmin(
1919 __isl_take isl_map *map, __isl_take isl_set *dom,
1920 __isl_give isl_set **empty);
1922 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1923 return a map mapping each element in the domain of
1924 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1925 of all elements associated to that element.
1926 In case of union relations, the optimum is computed per space.
1928 __isl_give isl_map *isl_basic_map_lexmin(
1929 __isl_take isl_basic_map *bmap);
1930 __isl_give isl_map *isl_basic_map_lexmax(
1931 __isl_take isl_basic_map *bmap);
1932 __isl_give isl_map *isl_map_lexmin(
1933 __isl_take isl_map *map);
1934 __isl_give isl_map *isl_map_lexmax(
1935 __isl_take isl_map *map);
1936 __isl_give isl_union_map *isl_union_map_lexmin(
1937 __isl_take isl_union_map *umap);
1938 __isl_give isl_union_map *isl_union_map_lexmax(
1939 __isl_take isl_union_map *umap);
1943 Matrices can be created, copied and freed using the following functions.
1945 #include <isl/mat.h>
1946 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1947 unsigned n_row, unsigned n_col);
1948 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1949 void isl_mat_free(__isl_take isl_mat *mat);
1951 Note that the elements of a newly created matrix may have arbitrary values.
1952 The elements can be changed and inspected using the following functions.
1954 isl_ctx *isl_mat_get_ctx(__isl_keep isl_mat *mat);
1955 int isl_mat_rows(__isl_keep isl_mat *mat);
1956 int isl_mat_cols(__isl_keep isl_mat *mat);
1957 int isl_mat_get_element(__isl_keep isl_mat *mat,
1958 int row, int col, isl_int *v);
1959 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1960 int row, int col, isl_int v);
1961 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
1962 int row, int col, int v);
1964 C<isl_mat_get_element> will return a negative value if anything went wrong.
1965 In that case, the value of C<*v> is undefined.
1967 The following function can be used to compute the (right) inverse
1968 of a matrix, i.e., a matrix such that the product of the original
1969 and the inverse (in that order) is a multiple of the identity matrix.
1970 The input matrix is assumed to be of full row-rank.
1972 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1974 The following function can be used to compute the (right) kernel
1975 (or null space) of a matrix, i.e., a matrix such that the product of
1976 the original and the kernel (in that order) is the zero matrix.
1978 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1982 Points are elements of a set. They can be used to construct
1983 simple sets (boxes) or they can be used to represent the
1984 individual elements of a set.
1985 The zero point (the origin) can be created using
1987 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1989 The coordinates of a point can be inspected, set and changed
1992 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1993 enum isl_dim_type type, int pos, isl_int *v);
1994 __isl_give isl_point *isl_point_set_coordinate(
1995 __isl_take isl_point *pnt,
1996 enum isl_dim_type type, int pos, isl_int v);
1998 __isl_give isl_point *isl_point_add_ui(
1999 __isl_take isl_point *pnt,
2000 enum isl_dim_type type, int pos, unsigned val);
2001 __isl_give isl_point *isl_point_sub_ui(
2002 __isl_take isl_point *pnt,
2003 enum isl_dim_type type, int pos, unsigned val);
2005 Points can be copied or freed using
2007 __isl_give isl_point *isl_point_copy(
2008 __isl_keep isl_point *pnt);
2009 void isl_point_free(__isl_take isl_point *pnt);
2011 A singleton set can be created from a point using
2013 __isl_give isl_basic_set *isl_basic_set_from_point(
2014 __isl_take isl_point *pnt);
2015 __isl_give isl_set *isl_set_from_point(
2016 __isl_take isl_point *pnt);
2018 and a box can be created from two opposite extremal points using
2020 __isl_give isl_basic_set *isl_basic_set_box_from_points(
2021 __isl_take isl_point *pnt1,
2022 __isl_take isl_point *pnt2);
2023 __isl_give isl_set *isl_set_box_from_points(
2024 __isl_take isl_point *pnt1,
2025 __isl_take isl_point *pnt2);
2027 All elements of a B<bounded> (union) set can be enumerated using
2028 the following functions.
2030 int isl_set_foreach_point(__isl_keep isl_set *set,
2031 int (*fn)(__isl_take isl_point *pnt, void *user),
2033 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
2034 int (*fn)(__isl_take isl_point *pnt, void *user),
2037 The function C<fn> is called for each integer point in
2038 C<set> with as second argument the last argument of
2039 the C<isl_set_foreach_point> call. The function C<fn>
2040 should return C<0> on success and C<-1> on failure.
2041 In the latter case, C<isl_set_foreach_point> will stop
2042 enumerating and return C<-1> as well.
2043 If the enumeration is performed successfully and to completion,
2044 then C<isl_set_foreach_point> returns C<0>.
2046 To obtain a single point of a (basic) set, use
2048 __isl_give isl_point *isl_basic_set_sample_point(
2049 __isl_take isl_basic_set *bset);
2050 __isl_give isl_point *isl_set_sample_point(
2051 __isl_take isl_set *set);
2053 If C<set> does not contain any (integer) points, then the
2054 resulting point will be ``void'', a property that can be
2057 int isl_point_is_void(__isl_keep isl_point *pnt);
2059 =head2 Piecewise Quasipolynomials
2061 A piecewise quasipolynomial is a particular kind of function that maps
2062 a parametric point to a rational value.
2063 More specifically, a quasipolynomial is a polynomial expression in greatest
2064 integer parts of affine expressions of parameters and variables.
2065 A piecewise quasipolynomial is a subdivision of a given parametric
2066 domain into disjoint cells with a quasipolynomial associated to
2067 each cell. The value of the piecewise quasipolynomial at a given
2068 point is the value of the quasipolynomial associated to the cell
2069 that contains the point. Outside of the union of cells,
2070 the value is assumed to be zero.
2071 For example, the piecewise quasipolynomial
2073 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2075 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2076 A given piecewise quasipolynomial has a fixed domain dimension.
2077 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2078 defined over different domains.
2079 Piecewise quasipolynomials are mainly used by the C<barvinok>
2080 library for representing the number of elements in a parametric set or map.
2081 For example, the piecewise quasipolynomial above represents
2082 the number of points in the map
2084 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2086 =head3 Printing (Piecewise) Quasipolynomials
2088 Quasipolynomials and piecewise quasipolynomials can be printed
2089 using the following functions.
2091 __isl_give isl_printer *isl_printer_print_qpolynomial(
2092 __isl_take isl_printer *p,
2093 __isl_keep isl_qpolynomial *qp);
2095 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2096 __isl_take isl_printer *p,
2097 __isl_keep isl_pw_qpolynomial *pwqp);
2099 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2100 __isl_take isl_printer *p,
2101 __isl_keep isl_union_pw_qpolynomial *upwqp);
2103 The output format of the printer
2104 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2105 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2107 In case of printing in C<ISL_FORMAT_C>, the user may want
2108 to set the names of all dimensions
2110 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2111 __isl_take isl_qpolynomial *qp,
2112 enum isl_dim_type type, unsigned pos,
2114 __isl_give isl_pw_qpolynomial *
2115 isl_pw_qpolynomial_set_dim_name(
2116 __isl_take isl_pw_qpolynomial *pwqp,
2117 enum isl_dim_type type, unsigned pos,
2120 =head3 Creating New (Piecewise) Quasipolynomials
2122 Some simple quasipolynomials can be created using the following functions.
2123 More complicated quasipolynomials can be created by applying
2124 operations such as addition and multiplication
2125 on the resulting quasipolynomials
2127 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2128 __isl_take isl_dim *dim);
2129 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2130 __isl_take isl_dim *dim);
2131 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2132 __isl_take isl_dim *dim);
2133 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2134 __isl_take isl_dim *dim);
2135 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2136 __isl_take isl_dim *dim);
2137 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2138 __isl_take isl_dim *dim,
2139 const isl_int n, const isl_int d);
2140 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2141 __isl_take isl_div *div);
2142 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2143 __isl_take isl_dim *dim,
2144 enum isl_dim_type type, unsigned pos);
2146 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2147 with a single cell can be created using the following functions.
2148 Multiple of these single cell piecewise quasipolynomials can
2149 be combined to create more complicated piecewise quasipolynomials.
2151 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2152 __isl_take isl_dim *dim);
2153 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2154 __isl_take isl_set *set,
2155 __isl_take isl_qpolynomial *qp);
2157 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2158 __isl_take isl_dim *dim);
2159 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2160 __isl_take isl_pw_qpolynomial *pwqp);
2161 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2162 __isl_take isl_union_pw_qpolynomial *upwqp,
2163 __isl_take isl_pw_qpolynomial *pwqp);
2165 Quasipolynomials can be copied and freed again using the following
2168 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2169 __isl_keep isl_qpolynomial *qp);
2170 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2172 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2173 __isl_keep isl_pw_qpolynomial *pwqp);
2174 void isl_pw_qpolynomial_free(
2175 __isl_take isl_pw_qpolynomial *pwqp);
2177 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2178 __isl_keep isl_union_pw_qpolynomial *upwqp);
2179 void isl_union_pw_qpolynomial_free(
2180 __isl_take isl_union_pw_qpolynomial *upwqp);
2182 =head3 Inspecting (Piecewise) Quasipolynomials
2184 To iterate over all piecewise quasipolynomials in a union
2185 piecewise quasipolynomial, use the following function
2187 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2188 __isl_keep isl_union_pw_qpolynomial *upwqp,
2189 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2192 To extract the piecewise quasipolynomial from a union with a given dimension
2195 __isl_give isl_pw_qpolynomial *
2196 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2197 __isl_keep isl_union_pw_qpolynomial *upwqp,
2198 __isl_take isl_dim *dim);
2200 To iterate over the cells in a piecewise quasipolynomial,
2201 use either of the following two functions
2203 int isl_pw_qpolynomial_foreach_piece(
2204 __isl_keep isl_pw_qpolynomial *pwqp,
2205 int (*fn)(__isl_take isl_set *set,
2206 __isl_take isl_qpolynomial *qp,
2207 void *user), void *user);
2208 int isl_pw_qpolynomial_foreach_lifted_piece(
2209 __isl_keep isl_pw_qpolynomial *pwqp,
2210 int (*fn)(__isl_take isl_set *set,
2211 __isl_take isl_qpolynomial *qp,
2212 void *user), void *user);
2214 As usual, the function C<fn> should return C<0> on success
2215 and C<-1> on failure. The difference between
2216 C<isl_pw_qpolynomial_foreach_piece> and
2217 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2218 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2219 compute unique representations for all existentially quantified
2220 variables and then turn these existentially quantified variables
2221 into extra set variables, adapting the associated quasipolynomial
2222 accordingly. This means that the C<set> passed to C<fn>
2223 will not have any existentially quantified variables, but that
2224 the dimensions of the sets may be different for different
2225 invocations of C<fn>.
2227 To iterate over all terms in a quasipolynomial,
2230 int isl_qpolynomial_foreach_term(
2231 __isl_keep isl_qpolynomial *qp,
2232 int (*fn)(__isl_take isl_term *term,
2233 void *user), void *user);
2235 The terms themselves can be inspected and freed using
2238 unsigned isl_term_dim(__isl_keep isl_term *term,
2239 enum isl_dim_type type);
2240 void isl_term_get_num(__isl_keep isl_term *term,
2242 void isl_term_get_den(__isl_keep isl_term *term,
2244 int isl_term_get_exp(__isl_keep isl_term *term,
2245 enum isl_dim_type type, unsigned pos);
2246 __isl_give isl_div *isl_term_get_div(
2247 __isl_keep isl_term *term, unsigned pos);
2248 void isl_term_free(__isl_take isl_term *term);
2250 Each term is a product of parameters, set variables and
2251 integer divisions. The function C<isl_term_get_exp>
2252 returns the exponent of a given dimensions in the given term.
2253 The C<isl_int>s in the arguments of C<isl_term_get_num>
2254 and C<isl_term_get_den> need to have been initialized
2255 using C<isl_int_init> before calling these functions.
2257 =head3 Properties of (Piecewise) Quasipolynomials
2259 To check whether a quasipolynomial is actually a constant,
2260 use the following function.
2262 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2263 isl_int *n, isl_int *d);
2265 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2266 then the numerator and denominator of the constant
2267 are returned in C<*n> and C<*d>, respectively.
2269 =head3 Operations on (Piecewise) Quasipolynomials
2271 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2272 __isl_take isl_qpolynomial *qp);
2273 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2274 __isl_take isl_qpolynomial *qp1,
2275 __isl_take isl_qpolynomial *qp2);
2276 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2277 __isl_take isl_qpolynomial *qp1,
2278 __isl_take isl_qpolynomial *qp2);
2279 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2280 __isl_take isl_qpolynomial *qp1,
2281 __isl_take isl_qpolynomial *qp2);
2282 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2283 __isl_take isl_qpolynomial *qp, unsigned exponent);
2285 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2286 __isl_take isl_pw_qpolynomial *pwqp1,
2287 __isl_take isl_pw_qpolynomial *pwqp2);
2288 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2289 __isl_take isl_pw_qpolynomial *pwqp1,
2290 __isl_take isl_pw_qpolynomial *pwqp2);
2291 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2292 __isl_take isl_pw_qpolynomial *pwqp1,
2293 __isl_take isl_pw_qpolynomial *pwqp2);
2294 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2295 __isl_take isl_pw_qpolynomial *pwqp);
2296 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2297 __isl_take isl_pw_qpolynomial *pwqp1,
2298 __isl_take isl_pw_qpolynomial *pwqp2);
2300 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2301 __isl_take isl_union_pw_qpolynomial *upwqp1,
2302 __isl_take isl_union_pw_qpolynomial *upwqp2);
2303 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2304 __isl_take isl_union_pw_qpolynomial *upwqp1,
2305 __isl_take isl_union_pw_qpolynomial *upwqp2);
2306 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2307 __isl_take isl_union_pw_qpolynomial *upwqp1,
2308 __isl_take isl_union_pw_qpolynomial *upwqp2);
2310 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2311 __isl_take isl_pw_qpolynomial *pwqp,
2312 __isl_take isl_point *pnt);
2314 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2315 __isl_take isl_union_pw_qpolynomial *upwqp,
2316 __isl_take isl_point *pnt);
2318 __isl_give isl_set *isl_pw_qpolynomial_domain(
2319 __isl_take isl_pw_qpolynomial *pwqp);
2320 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2321 __isl_take isl_pw_qpolynomial *pwpq,
2322 __isl_take isl_set *set);
2324 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2325 __isl_take isl_union_pw_qpolynomial *upwqp);
2326 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2327 __isl_take isl_union_pw_qpolynomial *upwpq,
2328 __isl_take isl_union_set *uset);
2330 __isl_give isl_qpolynomial *isl_qpolynomial_align_params(
2331 __isl_take isl_qpolynomial *qp,
2332 __isl_take isl_dim *model);
2334 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2335 __isl_take isl_union_pw_qpolynomial *upwqp);
2337 __isl_give isl_qpolynomial *isl_qpolynomial_gist(
2338 __isl_take isl_qpolynomial *qp,
2339 __isl_take isl_set *context);
2341 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2342 __isl_take isl_pw_qpolynomial *pwqp,
2343 __isl_take isl_set *context);
2345 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2346 __isl_take isl_union_pw_qpolynomial *upwqp,
2347 __isl_take isl_union_set *context);
2349 The gist operation applies the gist operation to each of
2350 the cells in the domain of the input piecewise quasipolynomial.
2351 The context is also exploited
2352 to simplify the quasipolynomials associated to each cell.
2354 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2355 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2356 __isl_give isl_union_pw_qpolynomial *
2357 isl_union_pw_qpolynomial_to_polynomial(
2358 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2360 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2361 the polynomial will be an overapproximation. If C<sign> is negative,
2362 it will be an underapproximation. If C<sign> is zero, the approximation
2363 will lie somewhere in between.
2365 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2367 A piecewise quasipolynomial reduction is a piecewise
2368 reduction (or fold) of quasipolynomials.
2369 In particular, the reduction can be maximum or a minimum.
2370 The objects are mainly used to represent the result of
2371 an upper or lower bound on a quasipolynomial over its domain,
2372 i.e., as the result of the following function.
2374 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2375 __isl_take isl_pw_qpolynomial *pwqp,
2376 enum isl_fold type, int *tight);
2378 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2379 __isl_take isl_union_pw_qpolynomial *upwqp,
2380 enum isl_fold type, int *tight);
2382 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2383 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2384 is the returned bound is known be tight, i.e., for each value
2385 of the parameters there is at least
2386 one element in the domain that reaches the bound.
2387 If the domain of C<pwqp> is not wrapping, then the bound is computed
2388 over all elements in that domain and the result has a purely parametric
2389 domain. If the domain of C<pwqp> is wrapping, then the bound is
2390 computed over the range of the wrapped relation. The domain of the
2391 wrapped relation becomes the domain of the result.
2393 A (piecewise) quasipolynomial reduction can be copied or freed using the
2394 following functions.
2396 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2397 __isl_keep isl_qpolynomial_fold *fold);
2398 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2399 __isl_keep isl_pw_qpolynomial_fold *pwf);
2400 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2401 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2402 void isl_qpolynomial_fold_free(
2403 __isl_take isl_qpolynomial_fold *fold);
2404 void isl_pw_qpolynomial_fold_free(
2405 __isl_take isl_pw_qpolynomial_fold *pwf);
2406 void isl_union_pw_qpolynomial_fold_free(
2407 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2409 =head3 Printing Piecewise Quasipolynomial Reductions
2411 Piecewise quasipolynomial reductions can be printed
2412 using the following function.
2414 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2415 __isl_take isl_printer *p,
2416 __isl_keep isl_pw_qpolynomial_fold *pwf);
2417 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2418 __isl_take isl_printer *p,
2419 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2421 For C<isl_printer_print_pw_qpolynomial_fold>,
2422 output format of the printer
2423 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2424 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2425 output format of the printer
2426 needs to be set to C<ISL_FORMAT_ISL>.
2427 In case of printing in C<ISL_FORMAT_C>, the user may want
2428 to set the names of all dimensions
2430 __isl_give isl_pw_qpolynomial_fold *
2431 isl_pw_qpolynomial_fold_set_dim_name(
2432 __isl_take isl_pw_qpolynomial_fold *pwf,
2433 enum isl_dim_type type, unsigned pos,
2436 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2438 To iterate over all piecewise quasipolynomial reductions in a union
2439 piecewise quasipolynomial reduction, use the following function
2441 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2442 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2443 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2444 void *user), void *user);
2446 To iterate over the cells in a piecewise quasipolynomial reduction,
2447 use either of the following two functions
2449 int isl_pw_qpolynomial_fold_foreach_piece(
2450 __isl_keep isl_pw_qpolynomial_fold *pwf,
2451 int (*fn)(__isl_take isl_set *set,
2452 __isl_take isl_qpolynomial_fold *fold,
2453 void *user), void *user);
2454 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2455 __isl_keep isl_pw_qpolynomial_fold *pwf,
2456 int (*fn)(__isl_take isl_set *set,
2457 __isl_take isl_qpolynomial_fold *fold,
2458 void *user), void *user);
2460 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2461 of the difference between these two functions.
2463 To iterate over all quasipolynomials in a reduction, use
2465 int isl_qpolynomial_fold_foreach_qpolynomial(
2466 __isl_keep isl_qpolynomial_fold *fold,
2467 int (*fn)(__isl_take isl_qpolynomial *qp,
2468 void *user), void *user);
2470 =head3 Operations on Piecewise Quasipolynomial Reductions
2472 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2473 __isl_take isl_pw_qpolynomial_fold *pwf1,
2474 __isl_take isl_pw_qpolynomial_fold *pwf2);
2476 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2477 __isl_take isl_pw_qpolynomial_fold *pwf1,
2478 __isl_take isl_pw_qpolynomial_fold *pwf2);
2480 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2481 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2482 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2484 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2485 __isl_take isl_pw_qpolynomial_fold *pwf,
2486 __isl_take isl_point *pnt);
2488 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2489 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2490 __isl_take isl_point *pnt);
2492 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2493 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2494 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2495 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2496 __isl_take isl_union_set *uset);
2498 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2499 __isl_take isl_pw_qpolynomial_fold *pwf);
2501 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2502 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2504 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2505 __isl_take isl_pw_qpolynomial_fold *pwf,
2506 __isl_take isl_set *context);
2508 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2509 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2510 __isl_take isl_union_set *context);
2512 The gist operation applies the gist operation to each of
2513 the cells in the domain of the input piecewise quasipolynomial reduction.
2514 In future, the operation will also exploit the context
2515 to simplify the quasipolynomial reductions associated to each cell.
2517 __isl_give isl_pw_qpolynomial_fold *
2518 isl_set_apply_pw_qpolynomial_fold(
2519 __isl_take isl_set *set,
2520 __isl_take isl_pw_qpolynomial_fold *pwf,
2522 __isl_give isl_pw_qpolynomial_fold *
2523 isl_map_apply_pw_qpolynomial_fold(
2524 __isl_take isl_map *map,
2525 __isl_take isl_pw_qpolynomial_fold *pwf,
2527 __isl_give isl_union_pw_qpolynomial_fold *
2528 isl_union_set_apply_union_pw_qpolynomial_fold(
2529 __isl_take isl_union_set *uset,
2530 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2532 __isl_give isl_union_pw_qpolynomial_fold *
2533 isl_union_map_apply_union_pw_qpolynomial_fold(
2534 __isl_take isl_union_map *umap,
2535 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2538 The functions taking a map
2539 compose the given map with the given piecewise quasipolynomial reduction.
2540 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2541 over all elements in the intersection of the range of the map
2542 and the domain of the piecewise quasipolynomial reduction
2543 as a function of an element in the domain of the map.
2544 The functions taking a set compute a bound over all elements in the
2545 intersection of the set and the domain of the
2546 piecewise quasipolynomial reduction.
2548 =head2 Dependence Analysis
2550 C<isl> contains specialized functionality for performing
2551 array dataflow analysis. That is, given a I<sink> access relation
2552 and a collection of possible I<source> access relations,
2553 C<isl> can compute relations that describe
2554 for each iteration of the sink access, which iteration
2555 of which of the source access relations was the last
2556 to access the same data element before the given iteration
2558 To compute standard flow dependences, the sink should be
2559 a read, while the sources should be writes.
2560 If any of the source accesses are marked as being I<may>
2561 accesses, then there will be a dependence to the last
2562 I<must> access B<and> to any I<may> access that follows
2563 this last I<must> access.
2564 In particular, if I<all> sources are I<may> accesses,
2565 then memory based dependence analysis is performed.
2566 If, on the other hand, all sources are I<must> accesses,
2567 then value based dependence analysis is performed.
2569 #include <isl/flow.h>
2571 typedef int (*isl_access_level_before)(void *first, void *second);
2573 __isl_give isl_access_info *isl_access_info_alloc(
2574 __isl_take isl_map *sink,
2575 void *sink_user, isl_access_level_before fn,
2577 __isl_give isl_access_info *isl_access_info_add_source(
2578 __isl_take isl_access_info *acc,
2579 __isl_take isl_map *source, int must,
2581 void isl_access_info_free(__isl_take isl_access_info *acc);
2583 __isl_give isl_flow *isl_access_info_compute_flow(
2584 __isl_take isl_access_info *acc);
2586 int isl_flow_foreach(__isl_keep isl_flow *deps,
2587 int (*fn)(__isl_take isl_map *dep, int must,
2588 void *dep_user, void *user),
2590 __isl_give isl_map *isl_flow_get_no_source(
2591 __isl_keep isl_flow *deps, int must);
2592 void isl_flow_free(__isl_take isl_flow *deps);
2594 The function C<isl_access_info_compute_flow> performs the actual
2595 dependence analysis. The other functions are used to construct
2596 the input for this function or to read off the output.
2598 The input is collected in an C<isl_access_info>, which can
2599 be created through a call to C<isl_access_info_alloc>.
2600 The arguments to this functions are the sink access relation
2601 C<sink>, a token C<sink_user> used to identify the sink
2602 access to the user, a callback function for specifying the
2603 relative order of source and sink accesses, and the number
2604 of source access relations that will be added.
2605 The callback function has type C<int (*)(void *first, void *second)>.
2606 The function is called with two user supplied tokens identifying
2607 either a source or the sink and it should return the shared nesting
2608 level and the relative order of the two accesses.
2609 In particular, let I<n> be the number of loops shared by
2610 the two accesses. If C<first> precedes C<second> textually,
2611 then the function should return I<2 * n + 1>; otherwise,
2612 it should return I<2 * n>.
2613 The sources can be added to the C<isl_access_info> by performing
2614 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2615 C<must> indicates whether the source is a I<must> access
2616 or a I<may> access. Note that a multi-valued access relation
2617 should only be marked I<must> if every iteration in the domain
2618 of the relation accesses I<all> elements in its image.
2619 The C<source_user> token is again used to identify
2620 the source access. The range of the source access relation
2621 C<source> should have the same dimension as the range
2622 of the sink access relation.
2623 The C<isl_access_info_free> function should usually not be
2624 called explicitly, because it is called implicitly by
2625 C<isl_access_info_compute_flow>.
2627 The result of the dependence analysis is collected in an
2628 C<isl_flow>. There may be elements of
2629 the sink access for which no preceding source access could be
2630 found or for which all preceding sources are I<may> accesses.
2631 The relations containing these elements can be obtained through
2632 calls to C<isl_flow_get_no_source>, the first with C<must> set
2633 and the second with C<must> unset.
2634 In the case of standard flow dependence analysis,
2635 with the sink a read and the sources I<must> writes,
2636 the first relation corresponds to the reads from uninitialized
2637 array elements and the second relation is empty.
2638 The actual flow dependences can be extracted using
2639 C<isl_flow_foreach>. This function will call the user-specified
2640 callback function C<fn> for each B<non-empty> dependence between
2641 a source and the sink. The callback function is called
2642 with four arguments, the actual flow dependence relation
2643 mapping source iterations to sink iterations, a boolean that
2644 indicates whether it is a I<must> or I<may> dependence, a token
2645 identifying the source and an additional C<void *> with value
2646 equal to the third argument of the C<isl_flow_foreach> call.
2647 A dependence is marked I<must> if it originates from a I<must>
2648 source and if it is not followed by any I<may> sources.
2650 After finishing with an C<isl_flow>, the user should call
2651 C<isl_flow_free> to free all associated memory.
2653 A higher-level interface to dependence analysis is provided
2654 by the following function.
2656 #include <isl/flow.h>
2658 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2659 __isl_take isl_union_map *must_source,
2660 __isl_take isl_union_map *may_source,
2661 __isl_take isl_union_map *schedule,
2662 __isl_give isl_union_map **must_dep,
2663 __isl_give isl_union_map **may_dep,
2664 __isl_give isl_union_map **must_no_source,
2665 __isl_give isl_union_map **may_no_source);
2667 The arrays are identified by the tuple names of the ranges
2668 of the accesses. The iteration domains by the tuple names
2669 of the domains of the accesses and of the schedule.
2670 The relative order of the iteration domains is given by the
2671 schedule. The relations returned through C<must_no_source>
2672 and C<may_no_source> are subsets of C<sink>.
2673 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2674 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2675 any of the other arguments is treated as an error.
2679 B<The functionality described in this section is fairly new
2680 and may be subject to change.>
2682 The following function can be used to compute a schedule
2683 for a union of domains. The generated schedule respects
2684 all C<validity> dependences. That is, all dependence distances
2685 over these dependences in the scheduled space are lexicographically
2686 positive. The generated schedule schedule also tries to minimize
2687 the dependence distances over C<proximity> dependences.
2688 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2689 for groups of domains where the dependence distances have only
2690 non-negative values.
2691 The algorithm used to construct the schedule is similar to that
2694 #include <isl/schedule.h>
2695 __isl_give isl_schedule *isl_union_set_compute_schedule(
2696 __isl_take isl_union_set *domain,
2697 __isl_take isl_union_map *validity,
2698 __isl_take isl_union_map *proximity);
2699 void *isl_schedule_free(__isl_take isl_schedule *sched);
2701 A mapping from the domains to the scheduled space can be obtained
2702 from an C<isl_schedule> using the following function.
2704 __isl_give isl_union_map *isl_schedule_get_map(
2705 __isl_keep isl_schedule *sched);
2707 This mapping can also be obtained in pieces using the following functions.
2709 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
2710 __isl_give isl_union_map *isl_schedule_get_band(
2711 __isl_keep isl_schedule *sched, unsigned band);
2713 C<isl_schedule_n_band> returns the maximal number of bands.
2714 C<isl_schedule_get_band> returns a union of mappings from a domain to
2715 the band of consecutive schedule dimensions with the given sequence
2716 number for that domain. Bands with the same sequence number but for
2717 different domains may be completely unrelated.
2718 Within a band, the corresponding coordinates of the distance vectors
2719 are all non-negative, assuming that the coordinates for all previous
2722 =head2 Parametric Vertex Enumeration
2724 The parametric vertex enumeration described in this section
2725 is mainly intended to be used internally and by the C<barvinok>
2728 #include <isl/vertices.h>
2729 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2730 __isl_keep isl_basic_set *bset);
2732 The function C<isl_basic_set_compute_vertices> performs the
2733 actual computation of the parametric vertices and the chamber
2734 decomposition and store the result in an C<isl_vertices> object.
2735 This information can be queried by either iterating over all
2736 the vertices or iterating over all the chambers or cells
2737 and then iterating over all vertices that are active on the chamber.
2739 int isl_vertices_foreach_vertex(
2740 __isl_keep isl_vertices *vertices,
2741 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2744 int isl_vertices_foreach_cell(
2745 __isl_keep isl_vertices *vertices,
2746 int (*fn)(__isl_take isl_cell *cell, void *user),
2748 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2749 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2752 Other operations that can be performed on an C<isl_vertices> object are
2755 isl_ctx *isl_vertices_get_ctx(
2756 __isl_keep isl_vertices *vertices);
2757 int isl_vertices_get_n_vertices(
2758 __isl_keep isl_vertices *vertices);
2759 void isl_vertices_free(__isl_take isl_vertices *vertices);
2761 Vertices can be inspected and destroyed using the following functions.
2763 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2764 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2765 __isl_give isl_basic_set *isl_vertex_get_domain(
2766 __isl_keep isl_vertex *vertex);
2767 __isl_give isl_basic_set *isl_vertex_get_expr(
2768 __isl_keep isl_vertex *vertex);
2769 void isl_vertex_free(__isl_take isl_vertex *vertex);
2771 C<isl_vertex_get_expr> returns a singleton parametric set describing
2772 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2774 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2775 B<rational> basic sets, so they should mainly be used for inspection
2776 and should not be mixed with integer sets.
2778 Chambers can be inspected and destroyed using the following functions.
2780 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2781 __isl_give isl_basic_set *isl_cell_get_domain(
2782 __isl_keep isl_cell *cell);
2783 void isl_cell_free(__isl_take isl_cell *cell);
2787 Although C<isl> is mainly meant to be used as a library,
2788 it also contains some basic applications that use some
2789 of the functionality of C<isl>.
2790 The input may be specified in either the L<isl format>
2791 or the L<PolyLib format>.
2793 =head2 C<isl_polyhedron_sample>
2795 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2796 an integer element of the polyhedron, if there is any.
2797 The first column in the output is the denominator and is always
2798 equal to 1. If the polyhedron contains no integer points,
2799 then a vector of length zero is printed.
2803 C<isl_pip> takes the same input as the C<example> program
2804 from the C<piplib> distribution, i.e., a set of constraints
2805 on the parameters, a line containing only -1 and finally a set
2806 of constraints on a parametric polyhedron.
2807 The coefficients of the parameters appear in the last columns
2808 (but before the final constant column).
2809 The output is the lexicographic minimum of the parametric polyhedron.
2810 As C<isl> currently does not have its own output format, the output
2811 is just a dump of the internal state.
2813 =head2 C<isl_polyhedron_minimize>
2815 C<isl_polyhedron_minimize> computes the minimum of some linear
2816 or affine objective function over the integer points in a polyhedron.
2817 If an affine objective function
2818 is given, then the constant should appear in the last column.
2820 =head2 C<isl_polytope_scan>
2822 Given a polytope, C<isl_polytope_scan> prints
2823 all integer points in the polytope.