3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
80 The source of C<isl> can be obtained either as a tarball
81 or from the git repository. Both are available from
82 L<http://freshmeat.net/projects/isl/>.
83 The installation process depends on how you obtained
86 =head2 Installation from the git repository
90 =item 1 Clone or update the repository
92 The first time the source is obtained, you need to clone
95 git clone git://repo.or.cz/isl.git
97 To obtain updates, you need to pull in the latest changes
101 =item 2 Generate C<configure>
107 After performing the above steps, continue
108 with the L<Common installation instructions>.
110 =head2 Common installation instructions
114 =item 1 Obtain C<GMP>
116 Building C<isl> requires C<GMP>, including its headers files.
117 Your distribution may not provide these header files by default
118 and you may need to install a package called C<gmp-devel> or something
119 similar. Alternatively, C<GMP> can be built from
120 source, available from L<http://gmplib.org/>.
124 C<isl> uses the standard C<autoconf> C<configure> script.
129 optionally followed by some configure options.
130 A complete list of options can be obtained by running
134 Below we discuss some of the more common options.
136 C<isl> can optionally use C<piplib>, but no
137 C<piplib> functionality is currently used by default.
138 The C<--with-piplib> option can
139 be used to specify which C<piplib>
140 library to use, either an installed version (C<system>),
141 an externally built version (C<build>)
142 or no version (C<no>). The option C<build> is mostly useful
143 in C<configure> scripts of larger projects that bundle both C<isl>
150 Installation prefix for C<isl>
152 =item C<--with-gmp-prefix>
154 Installation prefix for C<GMP> (architecture-independent files).
156 =item C<--with-gmp-exec-prefix>
158 Installation prefix for C<GMP> (architecture-dependent files).
160 =item C<--with-piplib>
162 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
164 =item C<--with-piplib-prefix>
166 Installation prefix for C<system> C<piplib> (architecture-independent files).
168 =item C<--with-piplib-exec-prefix>
170 Installation prefix for C<system> C<piplib> (architecture-dependent files).
172 =item C<--with-piplib-builddir>
174 Location where C<build> C<piplib> was built.
182 =item 4 Install (optional)
190 =head2 Initialization
192 All manipulations of integer sets and relations occur within
193 the context of an C<isl_ctx>.
194 A given C<isl_ctx> can only be used within a single thread.
195 All arguments of a function are required to have been allocated
196 within the same context.
197 There are currently no functions available for moving an object
198 from one C<isl_ctx> to another C<isl_ctx>. This means that
199 there is currently no way of safely moving an object from one
200 thread to another, unless the whole C<isl_ctx> is moved.
202 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
203 freed using C<isl_ctx_free>.
204 All objects allocated within an C<isl_ctx> should be freed
205 before the C<isl_ctx> itself is freed.
207 isl_ctx *isl_ctx_alloc();
208 void isl_ctx_free(isl_ctx *ctx);
212 All operations on integers, mainly the coefficients
213 of the constraints describing the sets and relations,
214 are performed in exact integer arithmetic using C<GMP>.
215 However, to allow future versions of C<isl> to optionally
216 support fixed integer arithmetic, all calls to C<GMP>
217 are wrapped inside C<isl> specific macros.
218 The basic type is C<isl_int> and the operations below
219 are available on this type.
220 The meanings of these operations are essentially the same
221 as their C<GMP> C<mpz_> counterparts.
222 As always with C<GMP> types, C<isl_int>s need to be
223 initialized with C<isl_int_init> before they can be used
224 and they need to be released with C<isl_int_clear>
226 The user should not assume that an C<isl_int> is represented
227 as a C<mpz_t>, but should instead explicitly convert between
228 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
229 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
233 =item isl_int_init(i)
235 =item isl_int_clear(i)
237 =item isl_int_set(r,i)
239 =item isl_int_set_si(r,i)
241 =item isl_int_set_gmp(r,g)
243 =item isl_int_get_gmp(i,g)
245 =item isl_int_abs(r,i)
247 =item isl_int_neg(r,i)
249 =item isl_int_swap(i,j)
251 =item isl_int_swap_or_set(i,j)
253 =item isl_int_add_ui(r,i,j)
255 =item isl_int_sub_ui(r,i,j)
257 =item isl_int_add(r,i,j)
259 =item isl_int_sub(r,i,j)
261 =item isl_int_mul(r,i,j)
263 =item isl_int_mul_ui(r,i,j)
265 =item isl_int_addmul(r,i,j)
267 =item isl_int_submul(r,i,j)
269 =item isl_int_gcd(r,i,j)
271 =item isl_int_lcm(r,i,j)
273 =item isl_int_divexact(r,i,j)
275 =item isl_int_cdiv_q(r,i,j)
277 =item isl_int_fdiv_q(r,i,j)
279 =item isl_int_fdiv_r(r,i,j)
281 =item isl_int_fdiv_q_ui(r,i,j)
283 =item isl_int_read(r,s)
285 =item isl_int_print(out,i,width)
289 =item isl_int_cmp(i,j)
291 =item isl_int_cmp_si(i,si)
293 =item isl_int_eq(i,j)
295 =item isl_int_ne(i,j)
297 =item isl_int_lt(i,j)
299 =item isl_int_le(i,j)
301 =item isl_int_gt(i,j)
303 =item isl_int_ge(i,j)
305 =item isl_int_abs_eq(i,j)
307 =item isl_int_abs_ne(i,j)
309 =item isl_int_abs_lt(i,j)
311 =item isl_int_abs_gt(i,j)
313 =item isl_int_abs_ge(i,j)
315 =item isl_int_is_zero(i)
317 =item isl_int_is_one(i)
319 =item isl_int_is_negone(i)
321 =item isl_int_is_pos(i)
323 =item isl_int_is_neg(i)
325 =item isl_int_is_nonpos(i)
327 =item isl_int_is_nonneg(i)
329 =item isl_int_is_divisible_by(i,j)
333 =head2 Sets and Relations
335 C<isl> uses six types of objects for representing sets and relations,
336 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
337 C<isl_union_set> and C<isl_union_map>.
338 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
339 can be described as a conjunction of affine constraints, while
340 C<isl_set> and C<isl_map> represent unions of
341 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
342 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
343 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
344 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
345 where dimensions with different space names
346 (see L<Dimension Specifications>) are considered different as well.
347 The difference between sets and relations (maps) is that sets have
348 one set of variables, while relations have two sets of variables,
349 input variables and output variables.
351 =head2 Memory Management
353 Since a high-level operation on sets and/or relations usually involves
354 several substeps and since the user is usually not interested in
355 the intermediate results, most functions that return a new object
356 will also release all the objects passed as arguments.
357 If the user still wants to use one or more of these arguments
358 after the function call, she should pass along a copy of the
359 object rather than the object itself.
360 The user is then responsible for making sure that the original
361 object gets used somewhere else or is explicitly freed.
363 The arguments and return values of all documents functions are
364 annotated to make clear which arguments are released and which
365 arguments are preserved. In particular, the following annotations
372 C<__isl_give> means that a new object is returned.
373 The user should make sure that the returned pointer is
374 used exactly once as a value for an C<__isl_take> argument.
375 In between, it can be used as a value for as many
376 C<__isl_keep> arguments as the user likes.
377 There is one exception, and that is the case where the
378 pointer returned is C<NULL>. Is this case, the user
379 is free to use it as an C<__isl_take> argument or not.
383 C<__isl_take> means that the object the argument points to
384 is taken over by the function and may no longer be used
385 by the user as an argument to any other function.
386 The pointer value must be one returned by a function
387 returning an C<__isl_give> pointer.
388 If the user passes in a C<NULL> value, then this will
389 be treated as an error in the sense that the function will
390 not perform its usual operation. However, it will still
391 make sure that all the the other C<__isl_take> arguments
396 C<__isl_keep> means that the function will only use the object
397 temporarily. After the function has finished, the user
398 can still use it as an argument to other functions.
399 A C<NULL> value will be treated in the same way as
400 a C<NULL> value for an C<__isl_take> argument.
404 =head2 Dimension Specifications
406 Whenever a new set or relation is created from scratch,
407 its dimension needs to be specified using an C<isl_dim>.
410 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
411 unsigned nparam, unsigned n_in, unsigned n_out);
412 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
413 unsigned nparam, unsigned dim);
414 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
415 void isl_dim_free(__isl_take isl_dim *dim);
416 unsigned isl_dim_size(__isl_keep isl_dim *dim,
417 enum isl_dim_type type);
419 The dimension specification used for creating a set
420 needs to be created using C<isl_dim_set_alloc>, while
421 that for creating a relation
422 needs to be created using C<isl_dim_alloc>.
423 C<isl_dim_size> can be used
424 to find out the number of dimensions of each type in
425 a dimension specification, where type may be
426 C<isl_dim_param>, C<isl_dim_in> (only for relations),
427 C<isl_dim_out> (only for relations), C<isl_dim_set>
428 (only for sets) or C<isl_dim_all>.
430 It is often useful to create objects that live in the
431 same space as some other object. This can be accomplished
432 by creating the new objects
433 (see L<Creating New Sets and Relations> or
434 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
435 specification of the original object.
438 __isl_give isl_dim *isl_basic_set_get_dim(
439 __isl_keep isl_basic_set *bset);
440 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
442 #include <isl/union_set.h>
443 __isl_give isl_dim *isl_union_set_get_dim(
444 __isl_keep isl_union_set *uset);
447 __isl_give isl_dim *isl_basic_map_get_dim(
448 __isl_keep isl_basic_map *bmap);
449 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
451 #include <isl/union_map.h>
452 __isl_give isl_dim *isl_union_map_get_dim(
453 __isl_keep isl_union_map *umap);
455 #include <isl/polynomial.h>
456 __isl_give isl_dim *isl_qpolynomial_get_dim(
457 __isl_keep isl_qpolynomial *qp);
458 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
459 __isl_keep isl_pw_qpolynomial *pwqp);
460 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
461 __isl_keep isl_union_pw_qpolynomial *upwqp);
462 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
463 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
465 The names of the individual dimensions may be set or read off
466 using the following functions.
469 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
470 enum isl_dim_type type, unsigned pos,
471 __isl_keep const char *name);
472 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
473 enum isl_dim_type type, unsigned pos);
475 Note that C<isl_dim_get_name> returns a pointer to some internal
476 data structure, so the result can only be used while the
477 corresponding C<isl_dim> is alive.
478 Also note that every function that operates on two sets or relations
479 requires that both arguments have the same parameters. This also
480 means that if one of the arguments has named parameters, then the
481 other needs to have named parameters too and the names need to match.
482 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
483 have different parameters (as long as they are named), in which case
484 the result will have as parameters the union of the parameters of
487 The names of entire spaces may be set or read off
488 using the following functions.
491 __isl_give isl_dim *isl_dim_set_tuple_name(
492 __isl_take isl_dim *dim,
493 enum isl_dim_type type, const char *s);
494 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
495 enum isl_dim_type type);
497 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
498 or C<isl_dim_set>. As with C<isl_dim_get_name>,
499 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
501 Binary operations require the corresponding spaces of their arguments
502 to have the same name.
504 Spaces can be nested. In particular, the domain of a set or
505 the domain or range of a relation can be a nested relation.
506 The following functions can be used to construct and deconstruct
507 such nested dimension specifications.
510 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
511 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
512 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
514 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
515 be the dimension specification of a set, while that of
516 C<isl_dim_wrap> should be the dimension specification of a relation.
517 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
518 of a relation, while that of C<isl_dim_wrap> is the dimension specification
521 Dimension specifications can be created from other dimension
522 specifications using the following functions.
524 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
525 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
526 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
527 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
528 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
529 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
530 __isl_take isl_dim *right);
531 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
532 enum isl_dim_type type, unsigned pos, unsigned n);
533 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
534 enum isl_dim_type type, unsigned n);
535 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
536 enum isl_dim_type type, unsigned first, unsigned n);
537 __isl_give isl_dim *isl_dim_map_from_set(
538 __isl_take isl_dim *dim);
539 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
541 Note that if dimensions are added or removed from a space, then
542 the name and the internal structure are lost.
544 =head2 Input and Output
546 C<isl> supports its own input/output format, which is similar
547 to the C<Omega> format, but also supports the C<PolyLib> format
552 The C<isl> format is similar to that of C<Omega>, but has a different
553 syntax for describing the parameters and allows for the definition
554 of an existentially quantified variable as the integer division
555 of an affine expression.
556 For example, the set of integers C<i> between C<0> and C<n>
557 such that C<i % 10 <= 6> can be described as
559 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
562 A set or relation can have several disjuncts, separated
563 by the keyword C<or>. Each disjunct is either a conjunction
564 of constraints or a projection (C<exists>) of a conjunction
565 of constraints. The constraints are separated by the keyword
568 =head3 C<PolyLib> format
570 If the represented set is a union, then the first line
571 contains a single number representing the number of disjuncts.
572 Otherwise, a line containing the number C<1> is optional.
574 Each disjunct is represented by a matrix of constraints.
575 The first line contains two numbers representing
576 the number of rows and columns,
577 where the number of rows is equal to the number of constraints
578 and the number of columns is equal to two plus the number of variables.
579 The following lines contain the actual rows of the constraint matrix.
580 In each row, the first column indicates whether the constraint
581 is an equality (C<0>) or inequality (C<1>). The final column
582 corresponds to the constant term.
584 If the set is parametric, then the coefficients of the parameters
585 appear in the last columns before the constant column.
586 The coefficients of any existentially quantified variables appear
587 between those of the set variables and those of the parameters.
589 =head3 Extended C<PolyLib> format
591 The extended C<PolyLib> format is nearly identical to the
592 C<PolyLib> format. The only difference is that the line
593 containing the number of rows and columns of a constraint matrix
594 also contains four additional numbers:
595 the number of output dimensions, the number of input dimensions,
596 the number of local dimensions (i.e., the number of existentially
597 quantified variables) and the number of parameters.
598 For sets, the number of ``output'' dimensions is equal
599 to the number of set dimensions, while the number of ``input''
605 __isl_give isl_basic_set *isl_basic_set_read_from_file(
606 isl_ctx *ctx, FILE *input, int nparam);
607 __isl_give isl_basic_set *isl_basic_set_read_from_str(
608 isl_ctx *ctx, const char *str, int nparam);
609 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
610 FILE *input, int nparam);
611 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
612 const char *str, int nparam);
615 __isl_give isl_basic_map *isl_basic_map_read_from_file(
616 isl_ctx *ctx, FILE *input, int nparam);
617 __isl_give isl_basic_map *isl_basic_map_read_from_str(
618 isl_ctx *ctx, const char *str, int nparam);
619 __isl_give isl_map *isl_map_read_from_file(
620 struct isl_ctx *ctx, FILE *input, int nparam);
621 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
622 const char *str, int nparam);
624 #include <isl/union_set.h>
625 __isl_give isl_union_set *isl_union_set_read_from_file(
626 isl_ctx *ctx, FILE *input);
627 __isl_give isl_union_set *isl_union_set_read_from_str(
628 struct isl_ctx *ctx, const char *str);
630 #include <isl/union_map.h>
631 __isl_give isl_union_map *isl_union_map_read_from_file(
632 isl_ctx *ctx, FILE *input);
633 __isl_give isl_union_map *isl_union_map_read_from_str(
634 struct isl_ctx *ctx, const char *str);
636 The input format is autodetected and may be either the C<PolyLib> format
637 or the C<isl> format.
638 C<nparam> specifies how many of the final columns in
639 the C<PolyLib> format correspond to parameters.
640 If input is given in the C<isl> format, then the number
641 of parameters needs to be equal to C<nparam>.
642 If C<nparam> is negative, then any number of parameters
643 is accepted in the C<isl> format and zero parameters
644 are assumed in the C<PolyLib> format.
648 Before anything can be printed, an C<isl_printer> needs to
651 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
653 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
654 void isl_printer_free(__isl_take isl_printer *printer);
655 __isl_give char *isl_printer_get_str(
656 __isl_keep isl_printer *printer);
658 The behavior of the printer can be modified in various ways
660 __isl_give isl_printer *isl_printer_set_output_format(
661 __isl_take isl_printer *p, int output_format);
662 __isl_give isl_printer *isl_printer_set_indent(
663 __isl_take isl_printer *p, int indent);
664 __isl_give isl_printer *isl_printer_set_prefix(
665 __isl_take isl_printer *p, const char *prefix);
666 __isl_give isl_printer *isl_printer_set_suffix(
667 __isl_take isl_printer *p, const char *suffix);
669 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
670 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
671 and defaults to C<ISL_FORMAT_ISL>.
672 Each line in the output is indented by C<indent> spaces
673 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
674 In the C<PolyLib> format output,
675 the coefficients of the existentially quantified variables
676 appear between those of the set variables and those
679 To actually print something, use
682 __isl_give isl_printer *isl_printer_print_basic_set(
683 __isl_take isl_printer *printer,
684 __isl_keep isl_basic_set *bset);
685 __isl_give isl_printer *isl_printer_print_set(
686 __isl_take isl_printer *printer,
687 __isl_keep isl_set *set);
690 __isl_give isl_printer *isl_printer_print_basic_map(
691 __isl_take isl_printer *printer,
692 __isl_keep isl_basic_map *bmap);
693 __isl_give isl_printer *isl_printer_print_map(
694 __isl_take isl_printer *printer,
695 __isl_keep isl_map *map);
697 #include <isl/union_set.h>
698 __isl_give isl_printer *isl_printer_print_union_set(
699 __isl_take isl_printer *p,
700 __isl_keep isl_union_set *uset);
702 #include <isl/union_map.h>
703 __isl_give isl_printer *isl_printer_print_union_map(
704 __isl_take isl_printer *p,
705 __isl_keep isl_union_map *umap);
707 When called on a file printer, the following function flushes
708 the file. When called on a string printer, the buffer is cleared.
710 __isl_give isl_printer *isl_printer_flush(
711 __isl_take isl_printer *p);
713 =head2 Creating New Sets and Relations
715 C<isl> has functions for creating some standard sets and relations.
719 =item * Empty sets and relations
721 __isl_give isl_basic_set *isl_basic_set_empty(
722 __isl_take isl_dim *dim);
723 __isl_give isl_basic_map *isl_basic_map_empty(
724 __isl_take isl_dim *dim);
725 __isl_give isl_set *isl_set_empty(
726 __isl_take isl_dim *dim);
727 __isl_give isl_map *isl_map_empty(
728 __isl_take isl_dim *dim);
729 __isl_give isl_union_set *isl_union_set_empty(
730 __isl_take isl_dim *dim);
731 __isl_give isl_union_map *isl_union_map_empty(
732 __isl_take isl_dim *dim);
734 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
735 is only used to specify the parameters.
737 =item * Universe sets and relations
739 __isl_give isl_basic_set *isl_basic_set_universe(
740 __isl_take isl_dim *dim);
741 __isl_give isl_basic_map *isl_basic_map_universe(
742 __isl_take isl_dim *dim);
743 __isl_give isl_set *isl_set_universe(
744 __isl_take isl_dim *dim);
745 __isl_give isl_map *isl_map_universe(
746 __isl_take isl_dim *dim);
748 The sets and relations constructed by the functions above
749 contain all integer values, while those constructed by the
750 functions below only contain non-negative values.
752 __isl_give isl_basic_set *isl_basic_set_nat_universe(
753 __isl_take isl_dim *dim);
754 __isl_give isl_basic_map *isl_basic_map_nat_universe(
755 __isl_take isl_dim *dim);
756 __isl_give isl_set *isl_set_nat_universe(
757 __isl_take isl_dim *dim);
758 __isl_give isl_map *isl_map_nat_universe(
759 __isl_take isl_dim *dim);
761 =item * Identity relations
763 __isl_give isl_basic_map *isl_basic_map_identity(
764 __isl_take isl_dim *dim);
765 __isl_give isl_map *isl_map_identity(
766 __isl_take isl_dim *dim);
768 The number of input and output dimensions in C<dim> needs
771 =item * Lexicographic order
773 __isl_give isl_map *isl_map_lex_lt(
774 __isl_take isl_dim *set_dim);
775 __isl_give isl_map *isl_map_lex_le(
776 __isl_take isl_dim *set_dim);
777 __isl_give isl_map *isl_map_lex_gt(
778 __isl_take isl_dim *set_dim);
779 __isl_give isl_map *isl_map_lex_ge(
780 __isl_take isl_dim *set_dim);
781 __isl_give isl_map *isl_map_lex_lt_first(
782 __isl_take isl_dim *dim, unsigned n);
783 __isl_give isl_map *isl_map_lex_le_first(
784 __isl_take isl_dim *dim, unsigned n);
785 __isl_give isl_map *isl_map_lex_gt_first(
786 __isl_take isl_dim *dim, unsigned n);
787 __isl_give isl_map *isl_map_lex_ge_first(
788 __isl_take isl_dim *dim, unsigned n);
790 The first four functions take a dimension specification for a B<set>
791 and return relations that express that the elements in the domain
792 are lexicographically less
793 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
794 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
795 than the elements in the range.
796 The last four functions take a dimension specification for a map
797 and return relations that express that the first C<n> dimensions
798 in the domain are lexicographically less
799 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
800 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
801 than the first C<n> dimensions in the range.
805 A basic set or relation can be converted to a set or relation
806 using the following functions.
808 __isl_give isl_set *isl_set_from_basic_set(
809 __isl_take isl_basic_set *bset);
810 __isl_give isl_map *isl_map_from_basic_map(
811 __isl_take isl_basic_map *bmap);
813 Sets and relations can be converted to union sets and relations
814 using the following functions.
816 __isl_give isl_union_map *isl_union_map_from_map(
817 __isl_take isl_map *map);
818 __isl_give isl_union_set *isl_union_set_from_set(
819 __isl_take isl_set *set);
821 Sets and relations can be copied and freed again using the following
824 __isl_give isl_basic_set *isl_basic_set_copy(
825 __isl_keep isl_basic_set *bset);
826 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
827 __isl_give isl_union_set *isl_union_set_copy(
828 __isl_keep isl_union_set *uset);
829 __isl_give isl_basic_map *isl_basic_map_copy(
830 __isl_keep isl_basic_map *bmap);
831 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
832 __isl_give isl_union_map *isl_union_map_copy(
833 __isl_keep isl_union_map *umap);
834 void isl_basic_set_free(__isl_take isl_basic_set *bset);
835 void isl_set_free(__isl_take isl_set *set);
836 void isl_union_set_free(__isl_take isl_union_set *uset);
837 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
838 void isl_map_free(__isl_take isl_map *map);
839 void isl_union_map_free(__isl_take isl_union_map *umap);
841 Other sets and relations can be constructed by starting
842 from a universe set or relation, adding equality and/or
843 inequality constraints and then projecting out the
844 existentially quantified variables, if any.
845 Constraints can be constructed, manipulated and
846 added to basic sets and relations using the following functions.
848 #include <isl/constraint.h>
849 __isl_give isl_constraint *isl_equality_alloc(
850 __isl_take isl_dim *dim);
851 __isl_give isl_constraint *isl_inequality_alloc(
852 __isl_take isl_dim *dim);
853 void isl_constraint_set_constant(
854 __isl_keep isl_constraint *constraint, isl_int v);
855 void isl_constraint_set_coefficient(
856 __isl_keep isl_constraint *constraint,
857 enum isl_dim_type type, int pos, isl_int v);
858 __isl_give isl_basic_map *isl_basic_map_add_constraint(
859 __isl_take isl_basic_map *bmap,
860 __isl_take isl_constraint *constraint);
861 __isl_give isl_basic_set *isl_basic_set_add_constraint(
862 __isl_take isl_basic_set *bset,
863 __isl_take isl_constraint *constraint);
865 For example, to create a set containing the even integers
866 between 10 and 42, you would use the following code.
870 struct isl_constraint *c;
871 struct isl_basic_set *bset;
874 dim = isl_dim_set_alloc(ctx, 0, 2);
875 bset = isl_basic_set_universe(isl_dim_copy(dim));
877 c = isl_equality_alloc(isl_dim_copy(dim));
878 isl_int_set_si(v, -1);
879 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
880 isl_int_set_si(v, 2);
881 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
882 bset = isl_basic_set_add_constraint(bset, c);
884 c = isl_inequality_alloc(isl_dim_copy(dim));
885 isl_int_set_si(v, -10);
886 isl_constraint_set_constant(c, v);
887 isl_int_set_si(v, 1);
888 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
889 bset = isl_basic_set_add_constraint(bset, c);
891 c = isl_inequality_alloc(dim);
892 isl_int_set_si(v, 42);
893 isl_constraint_set_constant(c, v);
894 isl_int_set_si(v, -1);
895 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
896 bset = isl_basic_set_add_constraint(bset, c);
898 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
904 struct isl_basic_set *bset;
905 bset = isl_basic_set_read_from_str(ctx,
906 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
908 A basic set or relation can also be constructed from two matrices
909 describing the equalities and the inequalities.
911 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
912 __isl_take isl_dim *dim,
913 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
914 enum isl_dim_type c1,
915 enum isl_dim_type c2, enum isl_dim_type c3,
916 enum isl_dim_type c4);
917 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
918 __isl_take isl_dim *dim,
919 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
920 enum isl_dim_type c1,
921 enum isl_dim_type c2, enum isl_dim_type c3,
922 enum isl_dim_type c4, enum isl_dim_type c5);
924 The C<isl_dim_type> arguments indicate the order in which
925 different kinds of variables appear in the input matrices
926 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
927 C<isl_dim_set> and C<isl_dim_div> for sets and
928 of C<isl_dim_cst>, C<isl_dim_param>,
929 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
931 =head2 Inspecting Sets and Relations
933 Usually, the user should not have to care about the actual constraints
934 of the sets and maps, but should instead apply the abstract operations
935 explained in the following sections.
936 Occasionally, however, it may be required to inspect the individual
937 coefficients of the constraints. This section explains how to do so.
938 In these cases, it may also be useful to have C<isl> compute
939 an explicit representation of the existentially quantified variables.
941 __isl_give isl_set *isl_set_compute_divs(
942 __isl_take isl_set *set);
943 __isl_give isl_map *isl_map_compute_divs(
944 __isl_take isl_map *map);
945 __isl_give isl_union_set *isl_union_set_compute_divs(
946 __isl_take isl_union_set *uset);
947 __isl_give isl_union_map *isl_union_map_compute_divs(
948 __isl_take isl_union_map *umap);
950 This explicit representation defines the existentially quantified
951 variables as integer divisions of the other variables, possibly
952 including earlier existentially quantified variables.
953 An explicitly represented existentially quantified variable therefore
954 has a unique value when the values of the other variables are known.
955 If, furthermore, the same existentials, i.e., existentials
956 with the same explicit representations, should appear in the
957 same order in each of the disjuncts of a set or map, then the user should call
958 either of the following functions.
960 __isl_give isl_set *isl_set_align_divs(
961 __isl_take isl_set *set);
962 __isl_give isl_map *isl_map_align_divs(
963 __isl_take isl_map *map);
965 Alternatively, the existentially quantified variables can be removed
966 using the following functions, which compute an overapproximation.
968 __isl_give isl_basic_set *isl_basic_set_remove_divs(
969 __isl_take isl_basic_set *bset);
970 __isl_give isl_basic_map *isl_basic_map_remove_divs(
971 __isl_take isl_basic_map *bmap);
972 __isl_give isl_set *isl_set_remove_divs(
973 __isl_take isl_set *set);
975 To iterate over all the sets or maps in a union set or map, use
977 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
978 int (*fn)(__isl_take isl_set *set, void *user),
980 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
981 int (*fn)(__isl_take isl_map *map, void *user),
984 The number of sets or maps in a union set or map can be obtained
987 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
988 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
990 To extract the set or map from a union with a given dimension
993 __isl_give isl_set *isl_union_set_extract_set(
994 __isl_keep isl_union_set *uset,
995 __isl_take isl_dim *dim);
996 __isl_give isl_map *isl_union_map_extract_map(
997 __isl_keep isl_union_map *umap,
998 __isl_take isl_dim *dim);
1000 To iterate over all the basic sets or maps in a set or map, use
1002 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1003 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1005 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1006 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1009 The callback function C<fn> should return 0 if successful and
1010 -1 if an error occurs. In the latter case, or if any other error
1011 occurs, the above functions will return -1.
1013 It should be noted that C<isl> does not guarantee that
1014 the basic sets or maps passed to C<fn> are disjoint.
1015 If this is required, then the user should call one of
1016 the following functions first.
1018 __isl_give isl_set *isl_set_make_disjoint(
1019 __isl_take isl_set *set);
1020 __isl_give isl_map *isl_map_make_disjoint(
1021 __isl_take isl_map *map);
1023 The number of basic sets in a set can be obtained
1026 int isl_set_n_basic_set(__isl_keep isl_set *set);
1028 To iterate over the constraints of a basic set or map, use
1030 #include <isl/constraint.h>
1032 int isl_basic_map_foreach_constraint(
1033 __isl_keep isl_basic_map *bmap,
1034 int (*fn)(__isl_take isl_constraint *c, void *user),
1036 void isl_constraint_free(struct isl_constraint *c);
1038 Again, the callback function C<fn> should return 0 if successful and
1039 -1 if an error occurs. In the latter case, or if any other error
1040 occurs, the above functions will return -1.
1041 The constraint C<c> represents either an equality or an inequality.
1042 Use the following function to find out whether a constraint
1043 represents an equality. If not, it represents an inequality.
1045 int isl_constraint_is_equality(
1046 __isl_keep isl_constraint *constraint);
1048 The coefficients of the constraints can be inspected using
1049 the following functions.
1051 void isl_constraint_get_constant(
1052 __isl_keep isl_constraint *constraint, isl_int *v);
1053 void isl_constraint_get_coefficient(
1054 __isl_keep isl_constraint *constraint,
1055 enum isl_dim_type type, int pos, isl_int *v);
1057 The explicit representations of the existentially quantified
1058 variables can be inspected using the following functions.
1059 Note that the user is only allowed to use these functions
1060 if the inspected set or map is the result of a call
1061 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1063 __isl_give isl_div *isl_constraint_div(
1064 __isl_keep isl_constraint *constraint, int pos);
1065 void isl_div_get_constant(__isl_keep isl_div *div,
1067 void isl_div_get_denominator(__isl_keep isl_div *div,
1069 void isl_div_get_coefficient(__isl_keep isl_div *div,
1070 enum isl_dim_type type, int pos, isl_int *v);
1072 To obtain the constraints of a basic set or map in matrix
1073 form, use the following functions.
1075 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1076 __isl_keep isl_basic_set *bset,
1077 enum isl_dim_type c1, enum isl_dim_type c2,
1078 enum isl_dim_type c3, enum isl_dim_type c4);
1079 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1080 __isl_keep isl_basic_set *bset,
1081 enum isl_dim_type c1, enum isl_dim_type c2,
1082 enum isl_dim_type c3, enum isl_dim_type c4);
1083 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1084 __isl_keep isl_basic_map *bmap,
1085 enum isl_dim_type c1,
1086 enum isl_dim_type c2, enum isl_dim_type c3,
1087 enum isl_dim_type c4, enum isl_dim_type c5);
1088 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1089 __isl_keep isl_basic_map *bmap,
1090 enum isl_dim_type c1,
1091 enum isl_dim_type c2, enum isl_dim_type c3,
1092 enum isl_dim_type c4, enum isl_dim_type c5);
1094 The C<isl_dim_type> arguments dictate the order in which
1095 different kinds of variables appear in the resulting matrix
1096 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1097 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1099 The names of the domain and range spaces of a set or relation can be
1100 read off using the following functions.
1102 const char *isl_basic_set_get_tuple_name(
1103 __isl_keep isl_basic_set *bset);
1104 const char *isl_set_get_tuple_name(
1105 __isl_keep isl_set *set);
1106 const char *isl_basic_map_get_tuple_name(
1107 __isl_keep isl_basic_map *bmap,
1108 enum isl_dim_type type);
1109 const char *isl_map_get_tuple_name(
1110 __isl_keep isl_map *map,
1111 enum isl_dim_type type);
1113 As with C<isl_dim_get_tuple_name>, the value returned points to
1114 an internal data structure.
1115 The names of individual dimensions can be read off using
1116 the following functions.
1118 const char *isl_constraint_get_dim_name(
1119 __isl_keep isl_constraint *constraint,
1120 enum isl_dim_type type, unsigned pos);
1121 const char *isl_basic_set_get_dim_name(
1122 __isl_keep isl_basic_set *bset,
1123 enum isl_dim_type type, unsigned pos);
1124 const char *isl_set_get_dim_name(
1125 __isl_keep isl_set *set,
1126 enum isl_dim_type type, unsigned pos);
1127 const char *isl_basic_map_get_dim_name(
1128 __isl_keep isl_basic_map *bmap,
1129 enum isl_dim_type type, unsigned pos);
1130 const char *isl_map_get_dim_name(
1131 __isl_keep isl_map *map,
1132 enum isl_dim_type type, unsigned pos);
1134 These functions are mostly useful to obtain the names
1139 =head3 Unary Properties
1145 The following functions test whether the given set or relation
1146 contains any integer points. The ``fast'' variants do not perform
1147 any computations, but simply check if the given set or relation
1148 is already known to be empty.
1150 int isl_basic_set_fast_is_empty(__isl_keep isl_basic_set *bset);
1151 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1152 int isl_set_is_empty(__isl_keep isl_set *set);
1153 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1154 int isl_basic_map_fast_is_empty(__isl_keep isl_basic_map *bmap);
1155 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1156 int isl_map_fast_is_empty(__isl_keep isl_map *map);
1157 int isl_map_is_empty(__isl_keep isl_map *map);
1158 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1160 =item * Universality
1162 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1163 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1164 int isl_set_fast_is_universe(__isl_keep isl_set *set);
1166 =item * Single-valuedness
1168 int isl_map_is_single_valued(__isl_keep isl_map *map);
1172 int isl_map_is_bijective(__isl_keep isl_map *map);
1176 The followning functions check whether the domain of the given
1177 (basic) set is a wrapped relation.
1179 int isl_basic_set_is_wrapping(
1180 __isl_keep isl_basic_set *bset);
1181 int isl_set_is_wrapping(__isl_keep isl_set *set);
1183 =item * Internal Product
1185 int isl_basic_map_can_zip(
1186 __isl_keep isl_basic_map *bmap);
1187 int isl_map_can_zip(__isl_keep isl_map *map);
1189 Check whether the product of domain and range of the given relation
1191 i.e., whether both domain and range are nested relations.
1195 =head3 Binary Properties
1201 int isl_set_fast_is_equal(__isl_keep isl_set *set1,
1202 __isl_keep isl_set *set2);
1203 int isl_set_is_equal(__isl_keep isl_set *set1,
1204 __isl_keep isl_set *set2);
1205 int isl_union_set_is_equal(
1206 __isl_keep isl_union_set *uset1,
1207 __isl_keep isl_union_set *uset2);
1208 int isl_basic_map_is_equal(
1209 __isl_keep isl_basic_map *bmap1,
1210 __isl_keep isl_basic_map *bmap2);
1211 int isl_map_is_equal(__isl_keep isl_map *map1,
1212 __isl_keep isl_map *map2);
1213 int isl_map_fast_is_equal(__isl_keep isl_map *map1,
1214 __isl_keep isl_map *map2);
1215 int isl_union_map_is_equal(
1216 __isl_keep isl_union_map *umap1,
1217 __isl_keep isl_union_map *umap2);
1219 =item * Disjointness
1221 int isl_set_fast_is_disjoint(__isl_keep isl_set *set1,
1222 __isl_keep isl_set *set2);
1226 int isl_set_is_subset(__isl_keep isl_set *set1,
1227 __isl_keep isl_set *set2);
1228 int isl_set_is_strict_subset(
1229 __isl_keep isl_set *set1,
1230 __isl_keep isl_set *set2);
1231 int isl_union_set_is_subset(
1232 __isl_keep isl_union_set *uset1,
1233 __isl_keep isl_union_set *uset2);
1234 int isl_union_set_is_strict_subset(
1235 __isl_keep isl_union_set *uset1,
1236 __isl_keep isl_union_set *uset2);
1237 int isl_basic_map_is_subset(
1238 __isl_keep isl_basic_map *bmap1,
1239 __isl_keep isl_basic_map *bmap2);
1240 int isl_basic_map_is_strict_subset(
1241 __isl_keep isl_basic_map *bmap1,
1242 __isl_keep isl_basic_map *bmap2);
1243 int isl_map_is_subset(
1244 __isl_keep isl_map *map1,
1245 __isl_keep isl_map *map2);
1246 int isl_map_is_strict_subset(
1247 __isl_keep isl_map *map1,
1248 __isl_keep isl_map *map2);
1249 int isl_union_map_is_subset(
1250 __isl_keep isl_union_map *umap1,
1251 __isl_keep isl_union_map *umap2);
1252 int isl_union_map_is_strict_subset(
1253 __isl_keep isl_union_map *umap1,
1254 __isl_keep isl_union_map *umap2);
1258 =head2 Unary Operations
1264 __isl_give isl_set *isl_set_complement(
1265 __isl_take isl_set *set);
1269 __isl_give isl_basic_map *isl_basic_map_reverse(
1270 __isl_take isl_basic_map *bmap);
1271 __isl_give isl_map *isl_map_reverse(
1272 __isl_take isl_map *map);
1273 __isl_give isl_union_map *isl_union_map_reverse(
1274 __isl_take isl_union_map *umap);
1278 __isl_give isl_basic_set *isl_basic_set_project_out(
1279 __isl_take isl_basic_set *bset,
1280 enum isl_dim_type type, unsigned first, unsigned n);
1281 __isl_give isl_basic_map *isl_basic_map_project_out(
1282 __isl_take isl_basic_map *bmap,
1283 enum isl_dim_type type, unsigned first, unsigned n);
1284 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1285 enum isl_dim_type type, unsigned first, unsigned n);
1286 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1287 enum isl_dim_type type, unsigned first, unsigned n);
1288 __isl_give isl_basic_set *isl_basic_map_domain(
1289 __isl_take isl_basic_map *bmap);
1290 __isl_give isl_basic_set *isl_basic_map_range(
1291 __isl_take isl_basic_map *bmap);
1292 __isl_give isl_set *isl_map_domain(
1293 __isl_take isl_map *bmap);
1294 __isl_give isl_set *isl_map_range(
1295 __isl_take isl_map *map);
1296 __isl_give isl_union_set *isl_union_map_domain(
1297 __isl_take isl_union_map *umap);
1298 __isl_give isl_union_set *isl_union_map_range(
1299 __isl_take isl_union_map *umap);
1301 __isl_give isl_basic_map *isl_basic_map_domain_map(
1302 __isl_take isl_basic_map *bmap);
1303 __isl_give isl_basic_map *isl_basic_map_range_map(
1304 __isl_take isl_basic_map *bmap);
1305 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1306 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1307 __isl_give isl_union_map *isl_union_map_domain_map(
1308 __isl_take isl_union_map *umap);
1309 __isl_give isl_union_map *isl_union_map_range_map(
1310 __isl_take isl_union_map *umap);
1312 The functions above construct a (basic, regular or union) relation
1313 that maps (a wrapped version of) the input relation to its domain or range.
1317 __isl_give isl_map *isl_set_identity(
1318 __isl_take isl_set *set);
1319 __isl_give isl_union_map *isl_union_set_identity(
1320 __isl_take isl_union_set *uset);
1322 Construct an identity relation on the given (union) set.
1326 __isl_give isl_basic_set *isl_basic_map_deltas(
1327 __isl_take isl_basic_map *bmap);
1328 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1329 __isl_give isl_union_set *isl_union_map_deltas(
1330 __isl_take isl_union_map *umap);
1332 These functions return a (basic) set containing the differences
1333 between image elements and corresponding domain elements in the input.
1335 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1336 __isl_take isl_basic_map *bmap);
1337 __isl_give isl_map *isl_map_deltas_map(
1338 __isl_take isl_map *map);
1339 __isl_give isl_union_map *isl_union_map_deltas_map(
1340 __isl_take isl_union_map *umap);
1342 The functions above construct a (basic, regular or union) relation
1343 that maps (a wrapped version of) the input relation to its delta set.
1347 Simplify the representation of a set or relation by trying
1348 to combine pairs of basic sets or relations into a single
1349 basic set or relation.
1351 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1352 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1353 __isl_give isl_union_set *isl_union_set_coalesce(
1354 __isl_take isl_union_set *uset);
1355 __isl_give isl_union_map *isl_union_map_coalesce(
1356 __isl_take isl_union_map *umap);
1358 =item * Detecting equalities
1360 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1361 __isl_take isl_basic_set *bset);
1362 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1363 __isl_take isl_basic_map *bmap);
1364 __isl_give isl_set *isl_set_detect_equalities(
1365 __isl_take isl_set *set);
1366 __isl_give isl_map *isl_map_detect_equalities(
1367 __isl_take isl_map *map);
1368 __isl_give isl_union_set *isl_union_set_detect_equalities(
1369 __isl_take isl_union_set *uset);
1370 __isl_give isl_union_map *isl_union_map_detect_equalities(
1371 __isl_take isl_union_map *umap);
1373 Simplify the representation of a set or relation by detecting implicit
1378 __isl_give isl_basic_set *isl_set_convex_hull(
1379 __isl_take isl_set *set);
1380 __isl_give isl_basic_map *isl_map_convex_hull(
1381 __isl_take isl_map *map);
1383 If the input set or relation has any existentially quantified
1384 variables, then the result of these operations is currently undefined.
1388 __isl_give isl_basic_set *isl_set_simple_hull(
1389 __isl_take isl_set *set);
1390 __isl_give isl_basic_map *isl_map_simple_hull(
1391 __isl_take isl_map *map);
1392 __isl_give isl_union_map *isl_union_map_simple_hull(
1393 __isl_take isl_union_map *umap);
1395 These functions compute a single basic set or relation
1396 that contains the whole input set or relation.
1397 In particular, the output is described by translates
1398 of the constraints describing the basic sets or relations in the input.
1402 (See \autoref{s:simple hull}.)
1408 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1409 __isl_take isl_basic_set *bset);
1410 __isl_give isl_basic_set *isl_set_affine_hull(
1411 __isl_take isl_set *set);
1412 __isl_give isl_union_set *isl_union_set_affine_hull(
1413 __isl_take isl_union_set *uset);
1414 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1415 __isl_take isl_basic_map *bmap);
1416 __isl_give isl_basic_map *isl_map_affine_hull(
1417 __isl_take isl_map *map);
1418 __isl_give isl_union_map *isl_union_map_affine_hull(
1419 __isl_take isl_union_map *umap);
1421 In case of union sets and relations, the affine hull is computed
1424 =item * Polyhedral hull
1426 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1427 __isl_take isl_set *set);
1428 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1429 __isl_take isl_map *map);
1430 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1431 __isl_take isl_union_set *uset);
1432 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1433 __isl_take isl_union_map *umap);
1435 These functions compute a single basic set or relation
1436 not involving any existentially quantified variables
1437 that contains the whole input set or relation.
1438 In case of union sets and relations, the polyhedral hull is computed
1443 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1444 unsigned param, int *exact);
1446 Compute a parametric representation for all positive powers I<k> of C<map>.
1447 The power I<k> is equated to the parameter at position C<param>.
1448 The result may be an overapproximation. If the result is known to be exact,
1449 then C<*exact> is set to C<1>.
1451 =item * Transitive closure
1453 __isl_give isl_map *isl_map_transitive_closure(
1454 __isl_take isl_map *map, int *exact);
1455 __isl_give isl_union_map *isl_union_map_transitive_closure(
1456 __isl_take isl_union_map *umap, int *exact);
1458 Compute the transitive closure of C<map>.
1459 The result may be an overapproximation. If the result is known to be exact,
1460 then C<*exact> is set to C<1>.
1462 =item * Reaching path lengths
1464 __isl_give isl_map *isl_map_reaching_path_lengths(
1465 __isl_take isl_map *map, int *exact);
1467 Compute a relation that maps each element in the range of C<map>
1468 to the lengths of all paths composed of edges in C<map> that
1469 end up in the given element.
1470 The result may be an overapproximation. If the result is known to be exact,
1471 then C<*exact> is set to C<1>.
1472 To compute the I<maximal> path length, the resulting relation
1473 should be postprocessed by C<isl_map_lexmax>.
1474 In particular, if the input relation is a dependence relation
1475 (mapping sources to sinks), then the maximal path length corresponds
1476 to the free schedule.
1477 Note, however, that C<isl_map_lexmax> expects the maximum to be
1478 finite, so if the path lengths are unbounded (possibly due to
1479 the overapproximation), then you will get an error message.
1483 __isl_give isl_basic_set *isl_basic_map_wrap(
1484 __isl_take isl_basic_map *bmap);
1485 __isl_give isl_set *isl_map_wrap(
1486 __isl_take isl_map *map);
1487 __isl_give isl_union_set *isl_union_map_wrap(
1488 __isl_take isl_union_map *umap);
1489 __isl_give isl_basic_map *isl_basic_set_unwrap(
1490 __isl_take isl_basic_set *bset);
1491 __isl_give isl_map *isl_set_unwrap(
1492 __isl_take isl_set *set);
1493 __isl_give isl_union_map *isl_union_set_unwrap(
1494 __isl_take isl_union_set *uset);
1498 Remove any internal structure of domain (and range) of the given
1499 set or relation. If there is any such internal structure in the input,
1500 then the name of the space is also removed.
1502 __isl_give isl_basic_set *isl_basic_set_flatten(
1503 __isl_take isl_basic_set *bset);
1504 __isl_give isl_set *isl_set_flatten(
1505 __isl_take isl_set *set);
1506 __isl_give isl_basic_map *isl_basic_map_flatten(
1507 __isl_take isl_basic_map *bmap);
1508 __isl_give isl_map *isl_map_flatten(
1509 __isl_take isl_map *map);
1511 __isl_give isl_map *isl_set_flatten_map(
1512 __isl_take isl_set *set);
1514 The function above constructs a relation
1515 that maps the input set to a flattened version of the set.
1517 =item * Internal Product
1519 __isl_give isl_basic_map *isl_basic_map_zip(
1520 __isl_take isl_basic_map *bmap);
1521 __isl_give isl_map *isl_map_zip(
1522 __isl_take isl_map *map);
1523 __isl_give isl_union_map *isl_union_map_zip(
1524 __isl_take isl_union_map *umap);
1526 Given a relation with nested relations for domain and range,
1527 interchange the range of the domain with the domain of the range.
1529 =item * Dimension manipulation
1531 __isl_give isl_set *isl_set_add_dims(
1532 __isl_take isl_set *set,
1533 enum isl_dim_type type, unsigned n);
1534 __isl_give isl_map *isl_map_add_dims(
1535 __isl_take isl_map *map,
1536 enum isl_dim_type type, unsigned n);
1538 It is usually not advisable to directly change the (input or output)
1539 space of a set or a relation as this removes the name and the internal
1540 structure of the space. However, the above functions can be useful
1541 to add new parameters.
1545 =head2 Binary Operations
1547 The two arguments of a binary operation not only need to live
1548 in the same C<isl_ctx>, they currently also need to have
1549 the same (number of) parameters.
1551 =head3 Basic Operations
1555 =item * Intersection
1557 __isl_give isl_basic_set *isl_basic_set_intersect(
1558 __isl_take isl_basic_set *bset1,
1559 __isl_take isl_basic_set *bset2);
1560 __isl_give isl_set *isl_set_intersect(
1561 __isl_take isl_set *set1,
1562 __isl_take isl_set *set2);
1563 __isl_give isl_union_set *isl_union_set_intersect(
1564 __isl_take isl_union_set *uset1,
1565 __isl_take isl_union_set *uset2);
1566 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1567 __isl_take isl_basic_map *bmap,
1568 __isl_take isl_basic_set *bset);
1569 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1570 __isl_take isl_basic_map *bmap,
1571 __isl_take isl_basic_set *bset);
1572 __isl_give isl_basic_map *isl_basic_map_intersect(
1573 __isl_take isl_basic_map *bmap1,
1574 __isl_take isl_basic_map *bmap2);
1575 __isl_give isl_map *isl_map_intersect_domain(
1576 __isl_take isl_map *map,
1577 __isl_take isl_set *set);
1578 __isl_give isl_map *isl_map_intersect_range(
1579 __isl_take isl_map *map,
1580 __isl_take isl_set *set);
1581 __isl_give isl_map *isl_map_intersect(
1582 __isl_take isl_map *map1,
1583 __isl_take isl_map *map2);
1584 __isl_give isl_union_map *isl_union_map_intersect_domain(
1585 __isl_take isl_union_map *umap,
1586 __isl_take isl_union_set *uset);
1587 __isl_give isl_union_map *isl_union_map_intersect_range(
1588 __isl_take isl_union_map *umap,
1589 __isl_take isl_union_set *uset);
1590 __isl_give isl_union_map *isl_union_map_intersect(
1591 __isl_take isl_union_map *umap1,
1592 __isl_take isl_union_map *umap2);
1596 __isl_give isl_set *isl_basic_set_union(
1597 __isl_take isl_basic_set *bset1,
1598 __isl_take isl_basic_set *bset2);
1599 __isl_give isl_map *isl_basic_map_union(
1600 __isl_take isl_basic_map *bmap1,
1601 __isl_take isl_basic_map *bmap2);
1602 __isl_give isl_set *isl_set_union(
1603 __isl_take isl_set *set1,
1604 __isl_take isl_set *set2);
1605 __isl_give isl_map *isl_map_union(
1606 __isl_take isl_map *map1,
1607 __isl_take isl_map *map2);
1608 __isl_give isl_union_set *isl_union_set_union(
1609 __isl_take isl_union_set *uset1,
1610 __isl_take isl_union_set *uset2);
1611 __isl_give isl_union_map *isl_union_map_union(
1612 __isl_take isl_union_map *umap1,
1613 __isl_take isl_union_map *umap2);
1615 =item * Set difference
1617 __isl_give isl_set *isl_set_subtract(
1618 __isl_take isl_set *set1,
1619 __isl_take isl_set *set2);
1620 __isl_give isl_map *isl_map_subtract(
1621 __isl_take isl_map *map1,
1622 __isl_take isl_map *map2);
1623 __isl_give isl_union_set *isl_union_set_subtract(
1624 __isl_take isl_union_set *uset1,
1625 __isl_take isl_union_set *uset2);
1626 __isl_give isl_union_map *isl_union_map_subtract(
1627 __isl_take isl_union_map *umap1,
1628 __isl_take isl_union_map *umap2);
1632 __isl_give isl_basic_set *isl_basic_set_apply(
1633 __isl_take isl_basic_set *bset,
1634 __isl_take isl_basic_map *bmap);
1635 __isl_give isl_set *isl_set_apply(
1636 __isl_take isl_set *set,
1637 __isl_take isl_map *map);
1638 __isl_give isl_union_set *isl_union_set_apply(
1639 __isl_take isl_union_set *uset,
1640 __isl_take isl_union_map *umap);
1641 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1642 __isl_take isl_basic_map *bmap1,
1643 __isl_take isl_basic_map *bmap2);
1644 __isl_give isl_basic_map *isl_basic_map_apply_range(
1645 __isl_take isl_basic_map *bmap1,
1646 __isl_take isl_basic_map *bmap2);
1647 __isl_give isl_map *isl_map_apply_domain(
1648 __isl_take isl_map *map1,
1649 __isl_take isl_map *map2);
1650 __isl_give isl_union_map *isl_union_map_apply_domain(
1651 __isl_take isl_union_map *umap1,
1652 __isl_take isl_union_map *umap2);
1653 __isl_give isl_map *isl_map_apply_range(
1654 __isl_take isl_map *map1,
1655 __isl_take isl_map *map2);
1656 __isl_give isl_union_map *isl_union_map_apply_range(
1657 __isl_take isl_union_map *umap1,
1658 __isl_take isl_union_map *umap2);
1660 =item * Cartesian Product
1662 __isl_give isl_set *isl_set_product(
1663 __isl_take isl_set *set1,
1664 __isl_take isl_set *set2);
1665 __isl_give isl_union_set *isl_union_set_product(
1666 __isl_take isl_union_set *uset1,
1667 __isl_take isl_union_set *uset2);
1668 __isl_give isl_basic_map *isl_basic_map_range_product(
1669 __isl_take isl_basic_map *bmap1,
1670 __isl_take isl_basic_map *bmap2);
1671 __isl_give isl_map *isl_map_range_product(
1672 __isl_take isl_map *map1,
1673 __isl_take isl_map *map2);
1674 __isl_give isl_union_map *isl_union_map_range_product(
1675 __isl_take isl_union_map *umap1,
1676 __isl_take isl_union_map *umap2);
1677 __isl_give isl_map *isl_map_product(
1678 __isl_take isl_map *map1,
1679 __isl_take isl_map *map2);
1680 __isl_give isl_union_map *isl_union_map_product(
1681 __isl_take isl_union_map *umap1,
1682 __isl_take isl_union_map *umap2);
1684 The above functions compute the cross product of the given
1685 sets or relations. The domains and ranges of the results
1686 are wrapped maps between domains and ranges of the inputs.
1687 To obtain a ``flat'' product, use the following functions
1690 __isl_give isl_basic_set *isl_basic_set_flat_product(
1691 __isl_take isl_basic_set *bset1,
1692 __isl_take isl_basic_set *bset2);
1693 __isl_give isl_set *isl_set_flat_product(
1694 __isl_take isl_set *set1,
1695 __isl_take isl_set *set2);
1696 __isl_give isl_basic_map *isl_basic_map_flat_product(
1697 __isl_take isl_basic_map *bmap1,
1698 __isl_take isl_basic_map *bmap2);
1699 __isl_give isl_map *isl_map_flat_product(
1700 __isl_take isl_map *map1,
1701 __isl_take isl_map *map2);
1703 =item * Simplification
1705 __isl_give isl_basic_set *isl_basic_set_gist(
1706 __isl_take isl_basic_set *bset,
1707 __isl_take isl_basic_set *context);
1708 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1709 __isl_take isl_set *context);
1710 __isl_give isl_union_set *isl_union_set_gist(
1711 __isl_take isl_union_set *uset,
1712 __isl_take isl_union_set *context);
1713 __isl_give isl_basic_map *isl_basic_map_gist(
1714 __isl_take isl_basic_map *bmap,
1715 __isl_take isl_basic_map *context);
1716 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1717 __isl_take isl_map *context);
1718 __isl_give isl_union_map *isl_union_map_gist(
1719 __isl_take isl_union_map *umap,
1720 __isl_take isl_union_map *context);
1722 The gist operation returns a set or relation that has the
1723 same intersection with the context as the input set or relation.
1724 Any implicit equality in the intersection is made explicit in the result,
1725 while all inequalities that are redundant with respect to the intersection
1727 In case of union sets and relations, the gist operation is performed
1732 =head3 Lexicographic Optimization
1734 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1735 the following functions
1736 compute a set that contains the lexicographic minimum or maximum
1737 of the elements in C<set> (or C<bset>) for those values of the parameters
1738 that satisfy C<dom>.
1739 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1740 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1742 In other words, the union of the parameter values
1743 for which the result is non-empty and of C<*empty>
1746 __isl_give isl_set *isl_basic_set_partial_lexmin(
1747 __isl_take isl_basic_set *bset,
1748 __isl_take isl_basic_set *dom,
1749 __isl_give isl_set **empty);
1750 __isl_give isl_set *isl_basic_set_partial_lexmax(
1751 __isl_take isl_basic_set *bset,
1752 __isl_take isl_basic_set *dom,
1753 __isl_give isl_set **empty);
1754 __isl_give isl_set *isl_set_partial_lexmin(
1755 __isl_take isl_set *set, __isl_take isl_set *dom,
1756 __isl_give isl_set **empty);
1757 __isl_give isl_set *isl_set_partial_lexmax(
1758 __isl_take isl_set *set, __isl_take isl_set *dom,
1759 __isl_give isl_set **empty);
1761 Given a (basic) set C<set> (or C<bset>), the following functions simply
1762 return a set containing the lexicographic minimum or maximum
1763 of the elements in C<set> (or C<bset>).
1764 In case of union sets, the optimum is computed per space.
1766 __isl_give isl_set *isl_basic_set_lexmin(
1767 __isl_take isl_basic_set *bset);
1768 __isl_give isl_set *isl_basic_set_lexmax(
1769 __isl_take isl_basic_set *bset);
1770 __isl_give isl_set *isl_set_lexmin(
1771 __isl_take isl_set *set);
1772 __isl_give isl_set *isl_set_lexmax(
1773 __isl_take isl_set *set);
1774 __isl_give isl_union_set *isl_union_set_lexmin(
1775 __isl_take isl_union_set *uset);
1776 __isl_give isl_union_set *isl_union_set_lexmax(
1777 __isl_take isl_union_set *uset);
1779 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1780 the following functions
1781 compute a relation that maps each element of C<dom>
1782 to the single lexicographic minimum or maximum
1783 of the elements that are associated to that same
1784 element in C<map> (or C<bmap>).
1785 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1786 that contains the elements in C<dom> that do not map
1787 to any elements in C<map> (or C<bmap>).
1788 In other words, the union of the domain of the result and of C<*empty>
1791 __isl_give isl_map *isl_basic_map_partial_lexmax(
1792 __isl_take isl_basic_map *bmap,
1793 __isl_take isl_basic_set *dom,
1794 __isl_give isl_set **empty);
1795 __isl_give isl_map *isl_basic_map_partial_lexmin(
1796 __isl_take isl_basic_map *bmap,
1797 __isl_take isl_basic_set *dom,
1798 __isl_give isl_set **empty);
1799 __isl_give isl_map *isl_map_partial_lexmax(
1800 __isl_take isl_map *map, __isl_take isl_set *dom,
1801 __isl_give isl_set **empty);
1802 __isl_give isl_map *isl_map_partial_lexmin(
1803 __isl_take isl_map *map, __isl_take isl_set *dom,
1804 __isl_give isl_set **empty);
1806 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1807 return a map mapping each element in the domain of
1808 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1809 of all elements associated to that element.
1810 In case of union relations, the optimum is computed per space.
1812 __isl_give isl_map *isl_basic_map_lexmin(
1813 __isl_take isl_basic_map *bmap);
1814 __isl_give isl_map *isl_basic_map_lexmax(
1815 __isl_take isl_basic_map *bmap);
1816 __isl_give isl_map *isl_map_lexmin(
1817 __isl_take isl_map *map);
1818 __isl_give isl_map *isl_map_lexmax(
1819 __isl_take isl_map *map);
1820 __isl_give isl_union_map *isl_union_map_lexmin(
1821 __isl_take isl_union_map *umap);
1822 __isl_give isl_union_map *isl_union_map_lexmax(
1823 __isl_take isl_union_map *umap);
1827 Matrices can be created, copied and freed using the following functions.
1829 #include <isl/mat.h>
1830 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1831 unsigned n_row, unsigned n_col);
1832 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1833 void isl_mat_free(__isl_take isl_mat *mat);
1835 Note that the elements of a newly created matrix may have arbitrary values.
1836 The elements can be changed and inspected using the following functions.
1838 int isl_mat_rows(__isl_keep isl_mat *mat);
1839 int isl_mat_cols(__isl_keep isl_mat *mat);
1840 int isl_mat_get_element(__isl_keep isl_mat *mat,
1841 int row, int col, isl_int *v);
1842 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1843 int row, int col, isl_int v);
1845 C<isl_mat_get_element> will return a negative value if anything went wrong.
1846 In that case, the value of C<*v> is undefined.
1848 The following function can be used to compute the (right) inverse
1849 of a matrix, i.e., a matrix such that the product of the original
1850 and the inverse (in that order) is a multiple of the identity matrix.
1851 The input matrix is assumed to be of full row-rank.
1853 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1855 The following function can be used to compute the (right) kernel
1856 (or null space) of a matrix, i.e., a matrix such that the product of
1857 the original and the kernel (in that order) is the zero matrix.
1859 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1863 Points are elements of a set. They can be used to construct
1864 simple sets (boxes) or they can be used to represent the
1865 individual elements of a set.
1866 The zero point (the origin) can be created using
1868 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1870 The coordinates of a point can be inspected, set and changed
1873 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1874 enum isl_dim_type type, int pos, isl_int *v);
1875 __isl_give isl_point *isl_point_set_coordinate(
1876 __isl_take isl_point *pnt,
1877 enum isl_dim_type type, int pos, isl_int v);
1879 __isl_give isl_point *isl_point_add_ui(
1880 __isl_take isl_point *pnt,
1881 enum isl_dim_type type, int pos, unsigned val);
1882 __isl_give isl_point *isl_point_sub_ui(
1883 __isl_take isl_point *pnt,
1884 enum isl_dim_type type, int pos, unsigned val);
1886 Points can be copied or freed using
1888 __isl_give isl_point *isl_point_copy(
1889 __isl_keep isl_point *pnt);
1890 void isl_point_free(__isl_take isl_point *pnt);
1892 A singleton set can be created from a point using
1894 __isl_give isl_basic_set *isl_basic_set_from_point(
1895 __isl_take isl_point *pnt);
1896 __isl_give isl_set *isl_set_from_point(
1897 __isl_take isl_point *pnt);
1899 and a box can be created from two opposite extremal points using
1901 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1902 __isl_take isl_point *pnt1,
1903 __isl_take isl_point *pnt2);
1904 __isl_give isl_set *isl_set_box_from_points(
1905 __isl_take isl_point *pnt1,
1906 __isl_take isl_point *pnt2);
1908 All elements of a B<bounded> (union) set can be enumerated using
1909 the following functions.
1911 int isl_set_foreach_point(__isl_keep isl_set *set,
1912 int (*fn)(__isl_take isl_point *pnt, void *user),
1914 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1915 int (*fn)(__isl_take isl_point *pnt, void *user),
1918 The function C<fn> is called for each integer point in
1919 C<set> with as second argument the last argument of
1920 the C<isl_set_foreach_point> call. The function C<fn>
1921 should return C<0> on success and C<-1> on failure.
1922 In the latter case, C<isl_set_foreach_point> will stop
1923 enumerating and return C<-1> as well.
1924 If the enumeration is performed successfully and to completion,
1925 then C<isl_set_foreach_point> returns C<0>.
1927 To obtain a single point of a (basic) set, use
1929 __isl_give isl_point *isl_basic_set_sample_point(
1930 __isl_take isl_basic_set *bset);
1931 __isl_give isl_point *isl_set_sample_point(
1932 __isl_take isl_set *set);
1934 If C<set> does not contain any (integer) points, then the
1935 resulting point will be ``void'', a property that can be
1938 int isl_point_is_void(__isl_keep isl_point *pnt);
1940 =head2 Piecewise Quasipolynomials
1942 A piecewise quasipolynomial is a particular kind of function that maps
1943 a parametric point to a rational value.
1944 More specifically, a quasipolynomial is a polynomial expression in greatest
1945 integer parts of affine expressions of parameters and variables.
1946 A piecewise quasipolynomial is a subdivision of a given parametric
1947 domain into disjoint cells with a quasipolynomial associated to
1948 each cell. The value of the piecewise quasipolynomial at a given
1949 point is the value of the quasipolynomial associated to the cell
1950 that contains the point. Outside of the union of cells,
1951 the value is assumed to be zero.
1952 For example, the piecewise quasipolynomial
1954 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
1956 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
1957 A given piecewise quasipolynomial has a fixed domain dimension.
1958 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
1959 defined over different domains.
1960 Piecewise quasipolynomials are mainly used by the C<barvinok>
1961 library for representing the number of elements in a parametric set or map.
1962 For example, the piecewise quasipolynomial above represents
1963 the number of points in the map
1965 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
1967 =head3 Printing (Piecewise) Quasipolynomials
1969 Quasipolynomials and piecewise quasipolynomials can be printed
1970 using the following functions.
1972 __isl_give isl_printer *isl_printer_print_qpolynomial(
1973 __isl_take isl_printer *p,
1974 __isl_keep isl_qpolynomial *qp);
1976 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
1977 __isl_take isl_printer *p,
1978 __isl_keep isl_pw_qpolynomial *pwqp);
1980 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
1981 __isl_take isl_printer *p,
1982 __isl_keep isl_union_pw_qpolynomial *upwqp);
1984 The output format of the printer
1985 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
1986 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
1988 In case of printing in C<ISL_FORMAT_C>, the user may want
1989 to set the names of all dimensions
1991 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
1992 __isl_take isl_qpolynomial *qp,
1993 enum isl_dim_type type, unsigned pos,
1995 __isl_give isl_pw_qpolynomial *
1996 isl_pw_qpolynomial_set_dim_name(
1997 __isl_take isl_pw_qpolynomial *pwqp,
1998 enum isl_dim_type type, unsigned pos,
2001 =head3 Creating New (Piecewise) Quasipolynomials
2003 Some simple quasipolynomials can be created using the following functions.
2004 More complicated quasipolynomials can be created by applying
2005 operations such as addition and multiplication
2006 on the resulting quasipolynomials
2008 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2009 __isl_take isl_dim *dim);
2010 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2011 __isl_take isl_dim *dim);
2012 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2013 __isl_take isl_dim *dim);
2014 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2015 __isl_take isl_dim *dim);
2016 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2017 __isl_take isl_dim *dim);
2018 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2019 __isl_take isl_dim *dim,
2020 const isl_int n, const isl_int d);
2021 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2022 __isl_take isl_div *div);
2023 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2024 __isl_take isl_dim *dim,
2025 enum isl_dim_type type, unsigned pos);
2027 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2028 with a single cell can be created using the following functions.
2029 Multiple of these single cell piecewise quasipolynomials can
2030 be combined to create more complicated piecewise quasipolynomials.
2032 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2033 __isl_take isl_dim *dim);
2034 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2035 __isl_take isl_set *set,
2036 __isl_take isl_qpolynomial *qp);
2038 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2039 __isl_take isl_dim *dim);
2040 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2041 __isl_take isl_pw_qpolynomial *pwqp);
2042 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2043 __isl_take isl_union_pw_qpolynomial *upwqp,
2044 __isl_take isl_pw_qpolynomial *pwqp);
2046 Quasipolynomials can be copied and freed again using the following
2049 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2050 __isl_keep isl_qpolynomial *qp);
2051 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2053 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2054 __isl_keep isl_pw_qpolynomial *pwqp);
2055 void isl_pw_qpolynomial_free(
2056 __isl_take isl_pw_qpolynomial *pwqp);
2058 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2059 __isl_keep isl_union_pw_qpolynomial *upwqp);
2060 void isl_union_pw_qpolynomial_free(
2061 __isl_take isl_union_pw_qpolynomial *upwqp);
2063 =head3 Inspecting (Piecewise) Quasipolynomials
2065 To iterate over all piecewise quasipolynomials in a union
2066 piecewise quasipolynomial, use the following function
2068 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2069 __isl_keep isl_union_pw_qpolynomial *upwqp,
2070 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2073 To extract the piecewise quasipolynomial from a union with a given dimension
2076 __isl_give isl_pw_qpolynomial *
2077 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2078 __isl_keep isl_union_pw_qpolynomial *upwqp,
2079 __isl_take isl_dim *dim);
2081 To iterate over the cells in a piecewise quasipolynomial,
2082 use either of the following two functions
2084 int isl_pw_qpolynomial_foreach_piece(
2085 __isl_keep isl_pw_qpolynomial *pwqp,
2086 int (*fn)(__isl_take isl_set *set,
2087 __isl_take isl_qpolynomial *qp,
2088 void *user), void *user);
2089 int isl_pw_qpolynomial_foreach_lifted_piece(
2090 __isl_keep isl_pw_qpolynomial *pwqp,
2091 int (*fn)(__isl_take isl_set *set,
2092 __isl_take isl_qpolynomial *qp,
2093 void *user), void *user);
2095 As usual, the function C<fn> should return C<0> on success
2096 and C<-1> on failure. The difference between
2097 C<isl_pw_qpolynomial_foreach_piece> and
2098 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2099 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2100 compute unique representations for all existentially quantified
2101 variables and then turn these existentially quantified variables
2102 into extra set variables, adapting the associated quasipolynomial
2103 accordingly. This means that the C<set> passed to C<fn>
2104 will not have any existentially quantified variables, but that
2105 the dimensions of the sets may be different for different
2106 invocations of C<fn>.
2108 To iterate over all terms in a quasipolynomial,
2111 int isl_qpolynomial_foreach_term(
2112 __isl_keep isl_qpolynomial *qp,
2113 int (*fn)(__isl_take isl_term *term,
2114 void *user), void *user);
2116 The terms themselves can be inspected and freed using
2119 unsigned isl_term_dim(__isl_keep isl_term *term,
2120 enum isl_dim_type type);
2121 void isl_term_get_num(__isl_keep isl_term *term,
2123 void isl_term_get_den(__isl_keep isl_term *term,
2125 int isl_term_get_exp(__isl_keep isl_term *term,
2126 enum isl_dim_type type, unsigned pos);
2127 __isl_give isl_div *isl_term_get_div(
2128 __isl_keep isl_term *term, unsigned pos);
2129 void isl_term_free(__isl_take isl_term *term);
2131 Each term is a product of parameters, set variables and
2132 integer divisions. The function C<isl_term_get_exp>
2133 returns the exponent of a given dimensions in the given term.
2134 The C<isl_int>s in the arguments of C<isl_term_get_num>
2135 and C<isl_term_get_den> need to have been initialized
2136 using C<isl_int_init> before calling these functions.
2138 =head3 Properties of (Piecewise) Quasipolynomials
2140 To check whether a quasipolynomial is actually a constant,
2141 use the following function.
2143 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2144 isl_int *n, isl_int *d);
2146 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2147 then the numerator and denominator of the constant
2148 are returned in C<*n> and C<*d>, respectively.
2150 =head3 Operations on (Piecewise) Quasipolynomials
2152 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2153 __isl_take isl_qpolynomial *qp);
2154 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2155 __isl_take isl_qpolynomial *qp1,
2156 __isl_take isl_qpolynomial *qp2);
2157 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2158 __isl_take isl_qpolynomial *qp1,
2159 __isl_take isl_qpolynomial *qp2);
2160 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2161 __isl_take isl_qpolynomial *qp1,
2162 __isl_take isl_qpolynomial *qp2);
2163 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2164 __isl_take isl_qpolynomial *qp, unsigned exponent);
2166 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2167 __isl_take isl_pw_qpolynomial *pwqp1,
2168 __isl_take isl_pw_qpolynomial *pwqp2);
2169 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2170 __isl_take isl_pw_qpolynomial *pwqp1,
2171 __isl_take isl_pw_qpolynomial *pwqp2);
2172 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2173 __isl_take isl_pw_qpolynomial *pwqp1,
2174 __isl_take isl_pw_qpolynomial *pwqp2);
2175 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2176 __isl_take isl_pw_qpolynomial *pwqp);
2177 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2178 __isl_take isl_pw_qpolynomial *pwqp1,
2179 __isl_take isl_pw_qpolynomial *pwqp2);
2181 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2182 __isl_take isl_union_pw_qpolynomial *upwqp1,
2183 __isl_take isl_union_pw_qpolynomial *upwqp2);
2184 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2185 __isl_take isl_union_pw_qpolynomial *upwqp1,
2186 __isl_take isl_union_pw_qpolynomial *upwqp2);
2187 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2188 __isl_take isl_union_pw_qpolynomial *upwqp1,
2189 __isl_take isl_union_pw_qpolynomial *upwqp2);
2191 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2192 __isl_take isl_pw_qpolynomial *pwqp,
2193 __isl_take isl_point *pnt);
2195 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2196 __isl_take isl_union_pw_qpolynomial *upwqp,
2197 __isl_take isl_point *pnt);
2199 __isl_give isl_set *isl_pw_qpolynomial_domain(
2200 __isl_take isl_pw_qpolynomial *pwqp);
2201 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2202 __isl_take isl_pw_qpolynomial *pwpq,
2203 __isl_take isl_set *set);
2205 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2206 __isl_take isl_union_pw_qpolynomial *upwqp);
2207 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2208 __isl_take isl_union_pw_qpolynomial *upwpq,
2209 __isl_take isl_union_set *uset);
2211 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2212 __isl_take isl_union_pw_qpolynomial *upwqp);
2214 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2215 __isl_take isl_pw_qpolynomial *pwqp,
2216 __isl_take isl_set *context);
2218 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2219 __isl_take isl_union_pw_qpolynomial *upwqp,
2220 __isl_take isl_union_set *context);
2222 The gist operation applies the gist operation to each of
2223 the cells in the domain of the input piecewise quasipolynomial.
2224 The context is also exploited
2225 to simplify the quasipolynomials associated to each cell.
2227 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2228 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2229 __isl_give isl_union_pw_qpolynomial *
2230 isl_union_pw_qpolynomial_to_polynomial(
2231 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2233 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2234 the polynomial will be an overapproximation. If C<sign> is negative,
2235 it will be an underapproximation. If C<sign> is zero, the approximation
2236 will lie somewhere in between.
2238 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2240 A piecewise quasipolynomial reduction is a piecewise
2241 reduction (or fold) of quasipolynomials.
2242 In particular, the reduction can be maximum or a minimum.
2243 The objects are mainly used to represent the result of
2244 an upper or lower bound on a quasipolynomial over its domain,
2245 i.e., as the result of the following function.
2247 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2248 __isl_take isl_pw_qpolynomial *pwqp,
2249 enum isl_fold type, int *tight);
2251 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2252 __isl_take isl_union_pw_qpolynomial *upwqp,
2253 enum isl_fold type, int *tight);
2255 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2256 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2257 is the returned bound is known be tight, i.e., for each value
2258 of the parameters there is at least
2259 one element in the domain that reaches the bound.
2260 If the domain of C<pwqp> is not wrapping, then the bound is computed
2261 over all elements in that domain and the result has a purely parametric
2262 domain. If the domain of C<pwqp> is wrapping, then the bound is
2263 computed over the range of the wrapped relation. The domain of the
2264 wrapped relation becomes the domain of the result.
2266 A (piecewise) quasipolynomial reduction can be copied or freed using the
2267 following functions.
2269 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2270 __isl_keep isl_qpolynomial_fold *fold);
2271 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2272 __isl_keep isl_pw_qpolynomial_fold *pwf);
2273 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2274 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2275 void isl_qpolynomial_fold_free(
2276 __isl_take isl_qpolynomial_fold *fold);
2277 void isl_pw_qpolynomial_fold_free(
2278 __isl_take isl_pw_qpolynomial_fold *pwf);
2279 void isl_union_pw_qpolynomial_fold_free(
2280 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2282 =head3 Printing Piecewise Quasipolynomial Reductions
2284 Piecewise quasipolynomial reductions can be printed
2285 using the following function.
2287 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2288 __isl_take isl_printer *p,
2289 __isl_keep isl_pw_qpolynomial_fold *pwf);
2290 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2291 __isl_take isl_printer *p,
2292 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2294 For C<isl_printer_print_pw_qpolynomial_fold>,
2295 output format of the printer
2296 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2297 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2298 output format of the printer
2299 needs to be set to C<ISL_FORMAT_ISL>.
2300 In case of printing in C<ISL_FORMAT_C>, the user may want
2301 to set the names of all dimensions
2303 __isl_give isl_pw_qpolynomial_fold *
2304 isl_pw_qpolynomial_fold_set_dim_name(
2305 __isl_take isl_pw_qpolynomial_fold *pwf,
2306 enum isl_dim_type type, unsigned pos,
2309 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2311 To iterate over all piecewise quasipolynomial reductions in a union
2312 piecewise quasipolynomial reduction, use the following function
2314 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2315 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2316 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2317 void *user), void *user);
2319 To iterate over the cells in a piecewise quasipolynomial reduction,
2320 use either of the following two functions
2322 int isl_pw_qpolynomial_fold_foreach_piece(
2323 __isl_keep isl_pw_qpolynomial_fold *pwf,
2324 int (*fn)(__isl_take isl_set *set,
2325 __isl_take isl_qpolynomial_fold *fold,
2326 void *user), void *user);
2327 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2328 __isl_keep isl_pw_qpolynomial_fold *pwf,
2329 int (*fn)(__isl_take isl_set *set,
2330 __isl_take isl_qpolynomial_fold *fold,
2331 void *user), void *user);
2333 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2334 of the difference between these two functions.
2336 To iterate over all quasipolynomials in a reduction, use
2338 int isl_qpolynomial_fold_foreach_qpolynomial(
2339 __isl_keep isl_qpolynomial_fold *fold,
2340 int (*fn)(__isl_take isl_qpolynomial *qp,
2341 void *user), void *user);
2343 =head3 Operations on Piecewise Quasipolynomial Reductions
2345 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2346 __isl_take isl_pw_qpolynomial_fold *pwf1,
2347 __isl_take isl_pw_qpolynomial_fold *pwf2);
2349 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2350 __isl_take isl_pw_qpolynomial_fold *pwf1,
2351 __isl_take isl_pw_qpolynomial_fold *pwf2);
2353 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2354 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2355 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2357 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2358 __isl_take isl_pw_qpolynomial_fold *pwf,
2359 __isl_take isl_point *pnt);
2361 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2362 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2363 __isl_take isl_point *pnt);
2365 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2366 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2367 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2368 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2369 __isl_take isl_union_set *uset);
2371 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2372 __isl_take isl_pw_qpolynomial_fold *pwf);
2374 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2375 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2377 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2378 __isl_take isl_pw_qpolynomial_fold *pwf,
2379 __isl_take isl_set *context);
2381 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2382 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2383 __isl_take isl_union_set *context);
2385 The gist operation applies the gist operation to each of
2386 the cells in the domain of the input piecewise quasipolynomial reduction.
2387 In future, the operation will also exploit the context
2388 to simplify the quasipolynomial reductions associated to each cell.
2390 __isl_give isl_pw_qpolynomial_fold *
2391 isl_set_apply_pw_qpolynomial_fold(
2392 __isl_take isl_set *set,
2393 __isl_take isl_pw_qpolynomial_fold *pwf,
2395 __isl_give isl_pw_qpolynomial_fold *
2396 isl_map_apply_pw_qpolynomial_fold(
2397 __isl_take isl_map *map,
2398 __isl_take isl_pw_qpolynomial_fold *pwf,
2400 __isl_give isl_union_pw_qpolynomial_fold *
2401 isl_union_set_apply_union_pw_qpolynomial_fold(
2402 __isl_take isl_union_set *uset,
2403 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2405 __isl_give isl_union_pw_qpolynomial_fold *
2406 isl_union_map_apply_union_pw_qpolynomial_fold(
2407 __isl_take isl_union_map *umap,
2408 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2411 The functions taking a map
2412 compose the given map with the given piecewise quasipolynomial reduction.
2413 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2414 over all elements in the intersection of the range of the map
2415 and the domain of the piecewise quasipolynomial reduction
2416 as a function of an element in the domain of the map.
2417 The functions taking a set compute a bound over all elements in the
2418 intersection of the set and the domain of the
2419 piecewise quasipolynomial reduction.
2421 =head2 Dependence Analysis
2423 C<isl> contains specialized functionality for performing
2424 array dataflow analysis. That is, given a I<sink> access relation
2425 and a collection of possible I<source> access relations,
2426 C<isl> can compute relations that describe
2427 for each iteration of the sink access, which iteration
2428 of which of the source access relations was the last
2429 to access the same data element before the given iteration
2431 To compute standard flow dependences, the sink should be
2432 a read, while the sources should be writes.
2433 If any of the source accesses are marked as being I<may>
2434 accesses, then there will be a dependence to the last
2435 I<must> access B<and> to any I<may> access that follows
2436 this last I<must> access.
2437 In particular, if I<all> sources are I<may> accesses,
2438 then memory based dependence analysis is performed.
2439 If, on the other hand, all sources are I<must> accesses,
2440 then value based dependence analysis is performed.
2442 #include <isl/flow.h>
2444 typedef int (*isl_access_level_before)(void *first, void *second);
2446 __isl_give isl_access_info *isl_access_info_alloc(
2447 __isl_take isl_map *sink,
2448 void *sink_user, isl_access_level_before fn,
2450 __isl_give isl_access_info *isl_access_info_add_source(
2451 __isl_take isl_access_info *acc,
2452 __isl_take isl_map *source, int must,
2454 void isl_access_info_free(__isl_take isl_access_info *acc);
2456 __isl_give isl_flow *isl_access_info_compute_flow(
2457 __isl_take isl_access_info *acc);
2459 int isl_flow_foreach(__isl_keep isl_flow *deps,
2460 int (*fn)(__isl_take isl_map *dep, int must,
2461 void *dep_user, void *user),
2463 __isl_give isl_map *isl_flow_get_no_source(
2464 __isl_keep isl_flow *deps, int must);
2465 void isl_flow_free(__isl_take isl_flow *deps);
2467 The function C<isl_access_info_compute_flow> performs the actual
2468 dependence analysis. The other functions are used to construct
2469 the input for this function or to read off the output.
2471 The input is collected in an C<isl_access_info>, which can
2472 be created through a call to C<isl_access_info_alloc>.
2473 The arguments to this functions are the sink access relation
2474 C<sink>, a token C<sink_user> used to identify the sink
2475 access to the user, a callback function for specifying the
2476 relative order of source and sink accesses, and the number
2477 of source access relations that will be added.
2478 The callback function has type C<int (*)(void *first, void *second)>.
2479 The function is called with two user supplied tokens identifying
2480 either a source or the sink and it should return the shared nesting
2481 level and the relative order of the two accesses.
2482 In particular, let I<n> be the number of loops shared by
2483 the two accesses. If C<first> precedes C<second> textually,
2484 then the function should return I<2 * n + 1>; otherwise,
2485 it should return I<2 * n>.
2486 The sources can be added to the C<isl_access_info> by performing
2487 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2488 C<must> indicates whether the source is a I<must> access
2489 or a I<may> access. Note that a multi-valued access relation
2490 should only be marked I<must> if every iteration in the domain
2491 of the relation accesses I<all> elements in its image.
2492 The C<source_user> token is again used to identify
2493 the source access. The range of the source access relation
2494 C<source> should have the same dimension as the range
2495 of the sink access relation.
2496 The C<isl_access_info_free> function should usually not be
2497 called explicitly, because it is called implicitly by
2498 C<isl_access_info_compute_flow>.
2500 The result of the dependence analysis is collected in an
2501 C<isl_flow>. There may be elements of
2502 the sink access for which no preceding source access could be
2503 found or for which all preceding sources are I<may> accesses.
2504 The relations containing these elements can be obtained through
2505 calls to C<isl_flow_get_no_source>, the first with C<must> set
2506 and the second with C<must> unset.
2507 In the case of standard flow dependence analysis,
2508 with the sink a read and the sources I<must> writes,
2509 the first relation corresponds to the reads from uninitialized
2510 array elements and the second relation is empty.
2511 The actual flow dependences can be extracted using
2512 C<isl_flow_foreach>. This function will call the user-specified
2513 callback function C<fn> for each B<non-empty> dependence between
2514 a source and the sink. The callback function is called
2515 with four arguments, the actual flow dependence relation
2516 mapping source iterations to sink iterations, a boolean that
2517 indicates whether it is a I<must> or I<may> dependence, a token
2518 identifying the source and an additional C<void *> with value
2519 equal to the third argument of the C<isl_flow_foreach> call.
2520 A dependence is marked I<must> if it originates from a I<must>
2521 source and if it is not followed by any I<may> sources.
2523 After finishing with an C<isl_flow>, the user should call
2524 C<isl_flow_free> to free all associated memory.
2526 A higher-level interface to dependence analysis is provided
2527 by the following function.
2529 #include <isl/flow.h>
2531 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2532 __isl_take isl_union_map *must_source,
2533 __isl_take isl_union_map *may_source,
2534 __isl_take isl_union_map *schedule,
2535 __isl_give isl_union_map **must_dep,
2536 __isl_give isl_union_map **may_dep,
2537 __isl_give isl_union_map **must_no_source,
2538 __isl_give isl_union_map **may_no_source);
2540 The arrays are identified by the tuple names of the ranges
2541 of the accesses. The iteration domains by the tuple names
2542 of the domains of the accesses and of the schedule.
2543 The relative order of the iteration domains is given by the
2544 schedule. The relations returned through C<must_no_source>
2545 and C<may_no_source> are subsets of C<sink>.
2546 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2547 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2548 any of the other arguments is treated as an error.
2550 =head2 Parametric Vertex Enumeration
2552 The parametric vertex enumeration described in this section
2553 is mainly intended to be used internally and by the C<barvinok>
2556 #include <isl/vertices.h>
2557 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2558 __isl_keep isl_basic_set *bset);
2560 The function C<isl_basic_set_compute_vertices> performs the
2561 actual computation of the parametric vertices and the chamber
2562 decomposition and store the result in an C<isl_vertices> object.
2563 This information can be queried by either iterating over all
2564 the vertices or iterating over all the chambers or cells
2565 and then iterating over all vertices that are active on the chamber.
2567 int isl_vertices_foreach_vertex(
2568 __isl_keep isl_vertices *vertices,
2569 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2572 int isl_vertices_foreach_cell(
2573 __isl_keep isl_vertices *vertices,
2574 int (*fn)(__isl_take isl_cell *cell, void *user),
2576 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2577 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2580 Other operations that can be performed on an C<isl_vertices> object are
2583 isl_ctx *isl_vertices_get_ctx(
2584 __isl_keep isl_vertices *vertices);
2585 int isl_vertices_get_n_vertices(
2586 __isl_keep isl_vertices *vertices);
2587 void isl_vertices_free(__isl_take isl_vertices *vertices);
2589 Vertices can be inspected and destroyed using the following functions.
2591 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2592 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2593 __isl_give isl_basic_set *isl_vertex_get_domain(
2594 __isl_keep isl_vertex *vertex);
2595 __isl_give isl_basic_set *isl_vertex_get_expr(
2596 __isl_keep isl_vertex *vertex);
2597 void isl_vertex_free(__isl_take isl_vertex *vertex);
2599 C<isl_vertex_get_expr> returns a singleton parametric set describing
2600 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2602 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2603 B<rational> basic sets, so they should mainly be used for inspection
2604 and should not be mixed with integer sets.
2606 Chambers can be inspected and destroyed using the following functions.
2608 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2609 __isl_give isl_basic_set *isl_cell_get_domain(
2610 __isl_keep isl_cell *cell);
2611 void isl_cell_free(__isl_take isl_cell *cell);
2615 Although C<isl> is mainly meant to be used as a library,
2616 it also contains some basic applications that use some
2617 of the functionality of C<isl>.
2618 The input may be specified in either the L<isl format>
2619 or the L<PolyLib format>.
2621 =head2 C<isl_polyhedron_sample>
2623 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2624 an integer element of the polyhedron, if there is any.
2625 The first column in the output is the denominator and is always
2626 equal to 1. If the polyhedron contains no integer points,
2627 then a vector of length zero is printed.
2631 C<isl_pip> takes the same input as the C<example> program
2632 from the C<piplib> distribution, i.e., a set of constraints
2633 on the parameters, a line containing only -1 and finally a set
2634 of constraints on a parametric polyhedron.
2635 The coefficients of the parameters appear in the last columns
2636 (but before the final constant column).
2637 The output is the lexicographic minimum of the parametric polyhedron.
2638 As C<isl> currently does not have its own output format, the output
2639 is just a dump of the internal state.
2641 =head2 C<isl_polyhedron_minimize>
2643 C<isl_polyhedron_minimize> computes the minimum of some linear
2644 or affine objective function over the integer points in a polyhedron.
2645 If an affine objective function
2646 is given, then the constant should appear in the last column.
2648 =head2 C<isl_polytope_scan>
2650 Given a polytope, C<isl_polytope_scan> prints
2651 all integer points in the polytope.
2653 =head1 C<isl-polylib>
2655 The C<isl-polylib> library provides the following functions for converting
2656 between C<isl> objects and C<PolyLib> objects.
2657 The library is distributed separately for licensing reasons.
2659 #include <isl_set_polylib.h>
2660 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2661 Polyhedron *P, __isl_take isl_dim *dim);
2662 Polyhedron *isl_basic_set_to_polylib(
2663 __isl_keep isl_basic_set *bset);
2664 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2665 __isl_take isl_dim *dim);
2666 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2668 #include <isl_map_polylib.h>
2669 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2670 Polyhedron *P, __isl_take isl_dim *dim);
2671 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2672 __isl_take isl_dim *dim);
2673 Polyhedron *isl_basic_map_to_polylib(
2674 __isl_keep isl_basic_map *bmap);
2675 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);