3 C<isl> is a thread-safe C library for manipulating
4 sets and relations of integer points bounded by affine constraints.
5 The descriptions of the sets and relations may involve
6 both parameters and existentially quantified variables.
7 All computations are performed in exact integer arithmetic
9 The C<isl> library offers functionality that is similar
10 to that offered by the C<Omega> and C<Omega+> libraries,
11 but the underlying algorithms are in most cases completely different.
13 The library is by no means complete and some fairly basic
14 functionality is still missing.
15 Still, even in its current form, the library has been successfully
16 used as a backend polyhedral library for the polyhedral
17 scanner C<CLooG> and as part of an equivalence checker of
18 static affine programs.
19 For bug reports, feature requests and questions,
20 visit the the discussion group at
21 L<http://groups.google.com/group/isl-development>.
23 =head2 Backward Incompatible Changes
25 =head3 Changes since isl-0.02
29 =item * The old printing functions have been deprecated
30 and replaced by C<isl_printer> functions, see L<Input and Output>.
32 =item * Most functions related to dependence analysis have acquired
33 an extra C<must> argument. To obtain the old behavior, this argument
34 should be given the value 1. See L<Dependence Analysis>.
38 =head3 Changes since isl-0.03
42 =item * The function C<isl_pw_qpolynomial_fold_add> has been
43 renamed to C<isl_pw_qpolynomial_fold_fold>.
44 Similarly, C<isl_union_pw_qpolynomial_fold_add> has been
45 renamed to C<isl_union_pw_qpolynomial_fold_fold>.
49 =head3 Changes since isl-0.04
53 =item * All header files have been renamed from C<isl_header.h>
58 =head3 Changes since isl-0.05
62 =item * The functions C<isl_printer_print_basic_set> and
63 C<isl_printer_print_basic_map> no longer print a newline.
65 =item * The functions C<isl_flow_get_no_source>
66 and C<isl_union_map_compute_flow> now return
67 the accesses for which no source could be found instead of
68 the iterations where those accesses occur.
70 =item * The functions C<isl_basic_map_identity> and
71 C<isl_map_identity> now take the dimension specification
72 of a B<map> as input. An old call
73 C<isl_map_identity(dim)> can be rewritten to
74 C<isl_map_identity(isl_dim_map_from_set(dim))>.
76 =item * The function C<isl_map_power> no longer takes
77 a parameter position as input. Instead, the exponent
78 is now expressed as the domain of the resulting relation.
84 The source of C<isl> can be obtained either as a tarball
85 or from the git repository. Both are available from
86 L<http://freshmeat.net/projects/isl/>.
87 The installation process depends on how you obtained
90 =head2 Installation from the git repository
94 =item 1 Clone or update the repository
96 The first time the source is obtained, you need to clone
99 git clone git://repo.or.cz/isl.git
101 To obtain updates, you need to pull in the latest changes
105 =item 2 Generate C<configure>
111 After performing the above steps, continue
112 with the L<Common installation instructions>.
114 =head2 Common installation instructions
118 =item 1 Obtain C<GMP>
120 Building C<isl> requires C<GMP>, including its headers files.
121 Your distribution may not provide these header files by default
122 and you may need to install a package called C<gmp-devel> or something
123 similar. Alternatively, C<GMP> can be built from
124 source, available from L<http://gmplib.org/>.
128 C<isl> uses the standard C<autoconf> C<configure> script.
133 optionally followed by some configure options.
134 A complete list of options can be obtained by running
138 Below we discuss some of the more common options.
140 C<isl> can optionally use C<piplib>, but no
141 C<piplib> functionality is currently used by default.
142 The C<--with-piplib> option can
143 be used to specify which C<piplib>
144 library to use, either an installed version (C<system>),
145 an externally built version (C<build>)
146 or no version (C<no>). The option C<build> is mostly useful
147 in C<configure> scripts of larger projects that bundle both C<isl>
154 Installation prefix for C<isl>
156 =item C<--with-gmp-prefix>
158 Installation prefix for C<GMP> (architecture-independent files).
160 =item C<--with-gmp-exec-prefix>
162 Installation prefix for C<GMP> (architecture-dependent files).
164 =item C<--with-piplib>
166 Which copy of C<piplib> to use, either C<no> (default), C<system> or C<build>.
168 =item C<--with-piplib-prefix>
170 Installation prefix for C<system> C<piplib> (architecture-independent files).
172 =item C<--with-piplib-exec-prefix>
174 Installation prefix for C<system> C<piplib> (architecture-dependent files).
176 =item C<--with-piplib-builddir>
178 Location where C<build> C<piplib> was built.
186 =item 4 Install (optional)
194 =head2 Initialization
196 All manipulations of integer sets and relations occur within
197 the context of an C<isl_ctx>.
198 A given C<isl_ctx> can only be used within a single thread.
199 All arguments of a function are required to have been allocated
200 within the same context.
201 There are currently no functions available for moving an object
202 from one C<isl_ctx> to another C<isl_ctx>. This means that
203 there is currently no way of safely moving an object from one
204 thread to another, unless the whole C<isl_ctx> is moved.
206 An C<isl_ctx> can be allocated using C<isl_ctx_alloc> and
207 freed using C<isl_ctx_free>.
208 All objects allocated within an C<isl_ctx> should be freed
209 before the C<isl_ctx> itself is freed.
211 isl_ctx *isl_ctx_alloc();
212 void isl_ctx_free(isl_ctx *ctx);
216 All operations on integers, mainly the coefficients
217 of the constraints describing the sets and relations,
218 are performed in exact integer arithmetic using C<GMP>.
219 However, to allow future versions of C<isl> to optionally
220 support fixed integer arithmetic, all calls to C<GMP>
221 are wrapped inside C<isl> specific macros.
222 The basic type is C<isl_int> and the operations below
223 are available on this type.
224 The meanings of these operations are essentially the same
225 as their C<GMP> C<mpz_> counterparts.
226 As always with C<GMP> types, C<isl_int>s need to be
227 initialized with C<isl_int_init> before they can be used
228 and they need to be released with C<isl_int_clear>
230 The user should not assume that an C<isl_int> is represented
231 as a C<mpz_t>, but should instead explicitly convert between
232 C<mpz_t>s and C<isl_int>s using C<isl_int_set_gmp> and
233 C<isl_int_get_gmp> whenever a C<mpz_t> is required.
237 =item isl_int_init(i)
239 =item isl_int_clear(i)
241 =item isl_int_set(r,i)
243 =item isl_int_set_si(r,i)
245 =item isl_int_set_gmp(r,g)
247 =item isl_int_get_gmp(i,g)
249 =item isl_int_abs(r,i)
251 =item isl_int_neg(r,i)
253 =item isl_int_swap(i,j)
255 =item isl_int_swap_or_set(i,j)
257 =item isl_int_add_ui(r,i,j)
259 =item isl_int_sub_ui(r,i,j)
261 =item isl_int_add(r,i,j)
263 =item isl_int_sub(r,i,j)
265 =item isl_int_mul(r,i,j)
267 =item isl_int_mul_ui(r,i,j)
269 =item isl_int_addmul(r,i,j)
271 =item isl_int_submul(r,i,j)
273 =item isl_int_gcd(r,i,j)
275 =item isl_int_lcm(r,i,j)
277 =item isl_int_divexact(r,i,j)
279 =item isl_int_cdiv_q(r,i,j)
281 =item isl_int_fdiv_q(r,i,j)
283 =item isl_int_fdiv_r(r,i,j)
285 =item isl_int_fdiv_q_ui(r,i,j)
287 =item isl_int_read(r,s)
289 =item isl_int_print(out,i,width)
293 =item isl_int_cmp(i,j)
295 =item isl_int_cmp_si(i,si)
297 =item isl_int_eq(i,j)
299 =item isl_int_ne(i,j)
301 =item isl_int_lt(i,j)
303 =item isl_int_le(i,j)
305 =item isl_int_gt(i,j)
307 =item isl_int_ge(i,j)
309 =item isl_int_abs_eq(i,j)
311 =item isl_int_abs_ne(i,j)
313 =item isl_int_abs_lt(i,j)
315 =item isl_int_abs_gt(i,j)
317 =item isl_int_abs_ge(i,j)
319 =item isl_int_is_zero(i)
321 =item isl_int_is_one(i)
323 =item isl_int_is_negone(i)
325 =item isl_int_is_pos(i)
327 =item isl_int_is_neg(i)
329 =item isl_int_is_nonpos(i)
331 =item isl_int_is_nonneg(i)
333 =item isl_int_is_divisible_by(i,j)
337 =head2 Sets and Relations
339 C<isl> uses six types of objects for representing sets and relations,
340 C<isl_basic_set>, C<isl_basic_map>, C<isl_set>, C<isl_map>,
341 C<isl_union_set> and C<isl_union_map>.
342 C<isl_basic_set> and C<isl_basic_map> represent sets and relations that
343 can be described as a conjunction of affine constraints, while
344 C<isl_set> and C<isl_map> represent unions of
345 C<isl_basic_set>s and C<isl_basic_map>s, respectively.
346 However, all C<isl_basic_set>s or C<isl_basic_map>s in the union need
347 to have the same dimension. C<isl_union_set>s and C<isl_union_map>s
348 represent unions of C<isl_set>s or C<isl_map>s of I<different> dimensions,
349 where dimensions with different space names
350 (see L<Dimension Specifications>) are considered different as well.
351 The difference between sets and relations (maps) is that sets have
352 one set of variables, while relations have two sets of variables,
353 input variables and output variables.
355 =head2 Memory Management
357 Since a high-level operation on sets and/or relations usually involves
358 several substeps and since the user is usually not interested in
359 the intermediate results, most functions that return a new object
360 will also release all the objects passed as arguments.
361 If the user still wants to use one or more of these arguments
362 after the function call, she should pass along a copy of the
363 object rather than the object itself.
364 The user is then responsible for making sure that the original
365 object gets used somewhere else or is explicitly freed.
367 The arguments and return values of all documents functions are
368 annotated to make clear which arguments are released and which
369 arguments are preserved. In particular, the following annotations
376 C<__isl_give> means that a new object is returned.
377 The user should make sure that the returned pointer is
378 used exactly once as a value for an C<__isl_take> argument.
379 In between, it can be used as a value for as many
380 C<__isl_keep> arguments as the user likes.
381 There is one exception, and that is the case where the
382 pointer returned is C<NULL>. Is this case, the user
383 is free to use it as an C<__isl_take> argument or not.
387 C<__isl_take> means that the object the argument points to
388 is taken over by the function and may no longer be used
389 by the user as an argument to any other function.
390 The pointer value must be one returned by a function
391 returning an C<__isl_give> pointer.
392 If the user passes in a C<NULL> value, then this will
393 be treated as an error in the sense that the function will
394 not perform its usual operation. However, it will still
395 make sure that all the the other C<__isl_take> arguments
400 C<__isl_keep> means that the function will only use the object
401 temporarily. After the function has finished, the user
402 can still use it as an argument to other functions.
403 A C<NULL> value will be treated in the same way as
404 a C<NULL> value for an C<__isl_take> argument.
408 =head2 Dimension Specifications
410 Whenever a new set or relation is created from scratch,
411 its dimension needs to be specified using an C<isl_dim>.
414 __isl_give isl_dim *isl_dim_alloc(isl_ctx *ctx,
415 unsigned nparam, unsigned n_in, unsigned n_out);
416 __isl_give isl_dim *isl_dim_set_alloc(isl_ctx *ctx,
417 unsigned nparam, unsigned dim);
418 __isl_give isl_dim *isl_dim_copy(__isl_keep isl_dim *dim);
419 void isl_dim_free(__isl_take isl_dim *dim);
420 unsigned isl_dim_size(__isl_keep isl_dim *dim,
421 enum isl_dim_type type);
423 The dimension specification used for creating a set
424 needs to be created using C<isl_dim_set_alloc>, while
425 that for creating a relation
426 needs to be created using C<isl_dim_alloc>.
427 C<isl_dim_size> can be used
428 to find out the number of dimensions of each type in
429 a dimension specification, where type may be
430 C<isl_dim_param>, C<isl_dim_in> (only for relations),
431 C<isl_dim_out> (only for relations), C<isl_dim_set>
432 (only for sets) or C<isl_dim_all>.
434 It is often useful to create objects that live in the
435 same space as some other object. This can be accomplished
436 by creating the new objects
437 (see L<Creating New Sets and Relations> or
438 L<Creating New (Piecewise) Quasipolynomials>) based on the dimension
439 specification of the original object.
442 __isl_give isl_dim *isl_basic_set_get_dim(
443 __isl_keep isl_basic_set *bset);
444 __isl_give isl_dim *isl_set_get_dim(__isl_keep isl_set *set);
446 #include <isl/union_set.h>
447 __isl_give isl_dim *isl_union_set_get_dim(
448 __isl_keep isl_union_set *uset);
451 __isl_give isl_dim *isl_basic_map_get_dim(
452 __isl_keep isl_basic_map *bmap);
453 __isl_give isl_dim *isl_map_get_dim(__isl_keep isl_map *map);
455 #include <isl/union_map.h>
456 __isl_give isl_dim *isl_union_map_get_dim(
457 __isl_keep isl_union_map *umap);
459 #include <isl/constraint.h>
460 __isl_give isl_dim *isl_constraint_get_dim(
461 __isl_keep isl_constraint *constraint);
463 #include <isl/polynomial.h>
464 __isl_give isl_dim *isl_qpolynomial_get_dim(
465 __isl_keep isl_qpolynomial *qp);
466 __isl_give isl_dim *isl_pw_qpolynomial_get_dim(
467 __isl_keep isl_pw_qpolynomial *pwqp);
468 __isl_give isl_dim *isl_union_pw_qpolynomial_get_dim(
469 __isl_keep isl_union_pw_qpolynomial *upwqp);
470 __isl_give isl_dim *isl_union_pw_qpolynomial_fold_get_dim(
471 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
473 The names of the individual dimensions may be set or read off
474 using the following functions.
477 __isl_give isl_dim *isl_dim_set_name(__isl_take isl_dim *dim,
478 enum isl_dim_type type, unsigned pos,
479 __isl_keep const char *name);
480 __isl_keep const char *isl_dim_get_name(__isl_keep isl_dim *dim,
481 enum isl_dim_type type, unsigned pos);
483 Note that C<isl_dim_get_name> returns a pointer to some internal
484 data structure, so the result can only be used while the
485 corresponding C<isl_dim> is alive.
486 Also note that every function that operates on two sets or relations
487 requires that both arguments have the same parameters. This also
488 means that if one of the arguments has named parameters, then the
489 other needs to have named parameters too and the names need to match.
490 Pairs of C<isl_union_set> and/or C<isl_union_map> arguments may
491 have different parameters (as long as they are named), in which case
492 the result will have as parameters the union of the parameters of
495 The names of entire spaces may be set or read off
496 using the following functions.
499 __isl_give isl_dim *isl_dim_set_tuple_name(
500 __isl_take isl_dim *dim,
501 enum isl_dim_type type, const char *s);
502 const char *isl_dim_get_tuple_name(__isl_keep isl_dim *dim,
503 enum isl_dim_type type);
505 The C<dim> argument needs to be one of C<isl_dim_in>, C<isl_dim_out>
506 or C<isl_dim_set>. As with C<isl_dim_get_name>,
507 the C<isl_dim_get_tuple_name> function returns a pointer to some internal
509 Binary operations require the corresponding spaces of their arguments
510 to have the same name.
512 Spaces can be nested. In particular, the domain of a set or
513 the domain or range of a relation can be a nested relation.
514 The following functions can be used to construct and deconstruct
515 such nested dimension specifications.
518 int isl_dim_is_wrapping(__isl_keep isl_dim *dim);
519 __isl_give isl_dim *isl_dim_wrap(__isl_take isl_dim *dim);
520 __isl_give isl_dim *isl_dim_unwrap(__isl_take isl_dim *dim);
522 The input to C<isl_dim_is_wrapping> and C<isl_dim_unwrap> should
523 be the dimension specification of a set, while that of
524 C<isl_dim_wrap> should be the dimension specification of a relation.
525 Conversely, the output of C<isl_dim_unwrap> is the dimension specification
526 of a relation, while that of C<isl_dim_wrap> is the dimension specification
529 Dimension specifications can be created from other dimension
530 specifications using the following functions.
532 __isl_give isl_dim *isl_dim_domain(__isl_take isl_dim *dim);
533 __isl_give isl_dim *isl_dim_from_domain(__isl_take isl_dim *dim);
534 __isl_give isl_dim *isl_dim_range(__isl_take isl_dim *dim);
535 __isl_give isl_dim *isl_dim_from_range(__isl_take isl_dim *dim);
536 __isl_give isl_dim *isl_dim_reverse(__isl_take isl_dim *dim);
537 __isl_give isl_dim *isl_dim_join(__isl_take isl_dim *left,
538 __isl_take isl_dim *right);
539 __isl_give isl_dim *isl_dim_insert(__isl_take isl_dim *dim,
540 enum isl_dim_type type, unsigned pos, unsigned n);
541 __isl_give isl_dim *isl_dim_add(__isl_take isl_dim *dim,
542 enum isl_dim_type type, unsigned n);
543 __isl_give isl_dim *isl_dim_drop(__isl_take isl_dim *dim,
544 enum isl_dim_type type, unsigned first, unsigned n);
545 __isl_give isl_dim *isl_dim_map_from_set(
546 __isl_take isl_dim *dim);
547 __isl_give isl_dim *isl_dim_zip(__isl_take isl_dim *dim);
549 Note that if dimensions are added or removed from a space, then
550 the name and the internal structure are lost.
552 =head2 Input and Output
554 C<isl> supports its own input/output format, which is similar
555 to the C<Omega> format, but also supports the C<PolyLib> format
560 The C<isl> format is similar to that of C<Omega>, but has a different
561 syntax for describing the parameters and allows for the definition
562 of an existentially quantified variable as the integer division
563 of an affine expression.
564 For example, the set of integers C<i> between C<0> and C<n>
565 such that C<i % 10 <= 6> can be described as
567 [n] -> { [i] : exists (a = [i/10] : 0 <= i and i <= n and
570 A set or relation can have several disjuncts, separated
571 by the keyword C<or>. Each disjunct is either a conjunction
572 of constraints or a projection (C<exists>) of a conjunction
573 of constraints. The constraints are separated by the keyword
576 =head3 C<PolyLib> format
578 If the represented set is a union, then the first line
579 contains a single number representing the number of disjuncts.
580 Otherwise, a line containing the number C<1> is optional.
582 Each disjunct is represented by a matrix of constraints.
583 The first line contains two numbers representing
584 the number of rows and columns,
585 where the number of rows is equal to the number of constraints
586 and the number of columns is equal to two plus the number of variables.
587 The following lines contain the actual rows of the constraint matrix.
588 In each row, the first column indicates whether the constraint
589 is an equality (C<0>) or inequality (C<1>). The final column
590 corresponds to the constant term.
592 If the set is parametric, then the coefficients of the parameters
593 appear in the last columns before the constant column.
594 The coefficients of any existentially quantified variables appear
595 between those of the set variables and those of the parameters.
597 =head3 Extended C<PolyLib> format
599 The extended C<PolyLib> format is nearly identical to the
600 C<PolyLib> format. The only difference is that the line
601 containing the number of rows and columns of a constraint matrix
602 also contains four additional numbers:
603 the number of output dimensions, the number of input dimensions,
604 the number of local dimensions (i.e., the number of existentially
605 quantified variables) and the number of parameters.
606 For sets, the number of ``output'' dimensions is equal
607 to the number of set dimensions, while the number of ``input''
613 __isl_give isl_basic_set *isl_basic_set_read_from_file(
614 isl_ctx *ctx, FILE *input, int nparam);
615 __isl_give isl_basic_set *isl_basic_set_read_from_str(
616 isl_ctx *ctx, const char *str, int nparam);
617 __isl_give isl_set *isl_set_read_from_file(isl_ctx *ctx,
618 FILE *input, int nparam);
619 __isl_give isl_set *isl_set_read_from_str(isl_ctx *ctx,
620 const char *str, int nparam);
623 __isl_give isl_basic_map *isl_basic_map_read_from_file(
624 isl_ctx *ctx, FILE *input, int nparam);
625 __isl_give isl_basic_map *isl_basic_map_read_from_str(
626 isl_ctx *ctx, const char *str, int nparam);
627 __isl_give isl_map *isl_map_read_from_file(
628 struct isl_ctx *ctx, FILE *input, int nparam);
629 __isl_give isl_map *isl_map_read_from_str(isl_ctx *ctx,
630 const char *str, int nparam);
632 #include <isl/union_set.h>
633 __isl_give isl_union_set *isl_union_set_read_from_file(
634 isl_ctx *ctx, FILE *input);
635 __isl_give isl_union_set *isl_union_set_read_from_str(
636 struct isl_ctx *ctx, const char *str);
638 #include <isl/union_map.h>
639 __isl_give isl_union_map *isl_union_map_read_from_file(
640 isl_ctx *ctx, FILE *input);
641 __isl_give isl_union_map *isl_union_map_read_from_str(
642 struct isl_ctx *ctx, const char *str);
644 The input format is autodetected and may be either the C<PolyLib> format
645 or the C<isl> format.
646 C<nparam> specifies how many of the final columns in
647 the C<PolyLib> format correspond to parameters.
648 If input is given in the C<isl> format, then the number
649 of parameters needs to be equal to C<nparam>.
650 If C<nparam> is negative, then any number of parameters
651 is accepted in the C<isl> format and zero parameters
652 are assumed in the C<PolyLib> format.
656 Before anything can be printed, an C<isl_printer> needs to
659 __isl_give isl_printer *isl_printer_to_file(isl_ctx *ctx,
661 __isl_give isl_printer *isl_printer_to_str(isl_ctx *ctx);
662 void isl_printer_free(__isl_take isl_printer *printer);
663 __isl_give char *isl_printer_get_str(
664 __isl_keep isl_printer *printer);
666 The behavior of the printer can be modified in various ways
668 __isl_give isl_printer *isl_printer_set_output_format(
669 __isl_take isl_printer *p, int output_format);
670 __isl_give isl_printer *isl_printer_set_indent(
671 __isl_take isl_printer *p, int indent);
672 __isl_give isl_printer *isl_printer_set_prefix(
673 __isl_take isl_printer *p, const char *prefix);
674 __isl_give isl_printer *isl_printer_set_suffix(
675 __isl_take isl_printer *p, const char *suffix);
677 The C<output_format> may be either C<ISL_FORMAT_ISL>, C<ISL_FORMAT_OMEGA>,
678 C<ISL_FORMAT_POLYLIB>, C<ISL_FORMAT_EXT_POLYLIB> or C<ISL_FORMAT_LATEX>
679 and defaults to C<ISL_FORMAT_ISL>.
680 Each line in the output is indented by C<indent> spaces
681 (default: 0), prefixed by C<prefix> and suffixed by C<suffix>.
682 In the C<PolyLib> format output,
683 the coefficients of the existentially quantified variables
684 appear between those of the set variables and those
687 To actually print something, use
690 __isl_give isl_printer *isl_printer_print_basic_set(
691 __isl_take isl_printer *printer,
692 __isl_keep isl_basic_set *bset);
693 __isl_give isl_printer *isl_printer_print_set(
694 __isl_take isl_printer *printer,
695 __isl_keep isl_set *set);
698 __isl_give isl_printer *isl_printer_print_basic_map(
699 __isl_take isl_printer *printer,
700 __isl_keep isl_basic_map *bmap);
701 __isl_give isl_printer *isl_printer_print_map(
702 __isl_take isl_printer *printer,
703 __isl_keep isl_map *map);
705 #include <isl/union_set.h>
706 __isl_give isl_printer *isl_printer_print_union_set(
707 __isl_take isl_printer *p,
708 __isl_keep isl_union_set *uset);
710 #include <isl/union_map.h>
711 __isl_give isl_printer *isl_printer_print_union_map(
712 __isl_take isl_printer *p,
713 __isl_keep isl_union_map *umap);
715 When called on a file printer, the following function flushes
716 the file. When called on a string printer, the buffer is cleared.
718 __isl_give isl_printer *isl_printer_flush(
719 __isl_take isl_printer *p);
721 =head2 Creating New Sets and Relations
723 C<isl> has functions for creating some standard sets and relations.
727 =item * Empty sets and relations
729 __isl_give isl_basic_set *isl_basic_set_empty(
730 __isl_take isl_dim *dim);
731 __isl_give isl_basic_map *isl_basic_map_empty(
732 __isl_take isl_dim *dim);
733 __isl_give isl_set *isl_set_empty(
734 __isl_take isl_dim *dim);
735 __isl_give isl_map *isl_map_empty(
736 __isl_take isl_dim *dim);
737 __isl_give isl_union_set *isl_union_set_empty(
738 __isl_take isl_dim *dim);
739 __isl_give isl_union_map *isl_union_map_empty(
740 __isl_take isl_dim *dim);
742 For C<isl_union_set>s and C<isl_union_map>s, the dimensions specification
743 is only used to specify the parameters.
745 =item * Universe sets and relations
747 __isl_give isl_basic_set *isl_basic_set_universe(
748 __isl_take isl_dim *dim);
749 __isl_give isl_basic_map *isl_basic_map_universe(
750 __isl_take isl_dim *dim);
751 __isl_give isl_set *isl_set_universe(
752 __isl_take isl_dim *dim);
753 __isl_give isl_map *isl_map_universe(
754 __isl_take isl_dim *dim);
755 __isl_give isl_union_set *isl_union_set_universe(
756 __isl_take isl_union_set *uset);
757 __isl_give isl_union_map *isl_union_map_universe(
758 __isl_take isl_union_map *umap);
760 The sets and relations constructed by the functions above
761 contain all integer values, while those constructed by the
762 functions below only contain non-negative values.
764 __isl_give isl_basic_set *isl_basic_set_nat_universe(
765 __isl_take isl_dim *dim);
766 __isl_give isl_basic_map *isl_basic_map_nat_universe(
767 __isl_take isl_dim *dim);
768 __isl_give isl_set *isl_set_nat_universe(
769 __isl_take isl_dim *dim);
770 __isl_give isl_map *isl_map_nat_universe(
771 __isl_take isl_dim *dim);
773 =item * Identity relations
775 __isl_give isl_basic_map *isl_basic_map_identity(
776 __isl_take isl_dim *dim);
777 __isl_give isl_map *isl_map_identity(
778 __isl_take isl_dim *dim);
780 The number of input and output dimensions in C<dim> needs
783 =item * Lexicographic order
785 __isl_give isl_map *isl_map_lex_lt(
786 __isl_take isl_dim *set_dim);
787 __isl_give isl_map *isl_map_lex_le(
788 __isl_take isl_dim *set_dim);
789 __isl_give isl_map *isl_map_lex_gt(
790 __isl_take isl_dim *set_dim);
791 __isl_give isl_map *isl_map_lex_ge(
792 __isl_take isl_dim *set_dim);
793 __isl_give isl_map *isl_map_lex_lt_first(
794 __isl_take isl_dim *dim, unsigned n);
795 __isl_give isl_map *isl_map_lex_le_first(
796 __isl_take isl_dim *dim, unsigned n);
797 __isl_give isl_map *isl_map_lex_gt_first(
798 __isl_take isl_dim *dim, unsigned n);
799 __isl_give isl_map *isl_map_lex_ge_first(
800 __isl_take isl_dim *dim, unsigned n);
802 The first four functions take a dimension specification for a B<set>
803 and return relations that express that the elements in the domain
804 are lexicographically less
805 (C<isl_map_lex_lt>), less or equal (C<isl_map_lex_le>),
806 greater (C<isl_map_lex_gt>) or greater or equal (C<isl_map_lex_ge>)
807 than the elements in the range.
808 The last four functions take a dimension specification for a map
809 and return relations that express that the first C<n> dimensions
810 in the domain are lexicographically less
811 (C<isl_map_lex_lt_first>), less or equal (C<isl_map_lex_le_first>),
812 greater (C<isl_map_lex_gt_first>) or greater or equal (C<isl_map_lex_ge_first>)
813 than the first C<n> dimensions in the range.
817 A basic set or relation can be converted to a set or relation
818 using the following functions.
820 __isl_give isl_set *isl_set_from_basic_set(
821 __isl_take isl_basic_set *bset);
822 __isl_give isl_map *isl_map_from_basic_map(
823 __isl_take isl_basic_map *bmap);
825 Sets and relations can be converted to union sets and relations
826 using the following functions.
828 __isl_give isl_union_map *isl_union_map_from_map(
829 __isl_take isl_map *map);
830 __isl_give isl_union_set *isl_union_set_from_set(
831 __isl_take isl_set *set);
833 Sets and relations can be copied and freed again using the following
836 __isl_give isl_basic_set *isl_basic_set_copy(
837 __isl_keep isl_basic_set *bset);
838 __isl_give isl_set *isl_set_copy(__isl_keep isl_set *set);
839 __isl_give isl_union_set *isl_union_set_copy(
840 __isl_keep isl_union_set *uset);
841 __isl_give isl_basic_map *isl_basic_map_copy(
842 __isl_keep isl_basic_map *bmap);
843 __isl_give isl_map *isl_map_copy(__isl_keep isl_map *map);
844 __isl_give isl_union_map *isl_union_map_copy(
845 __isl_keep isl_union_map *umap);
846 void isl_basic_set_free(__isl_take isl_basic_set *bset);
847 void isl_set_free(__isl_take isl_set *set);
848 void isl_union_set_free(__isl_take isl_union_set *uset);
849 void isl_basic_map_free(__isl_take isl_basic_map *bmap);
850 void isl_map_free(__isl_take isl_map *map);
851 void isl_union_map_free(__isl_take isl_union_map *umap);
853 Other sets and relations can be constructed by starting
854 from a universe set or relation, adding equality and/or
855 inequality constraints and then projecting out the
856 existentially quantified variables, if any.
857 Constraints can be constructed, manipulated and
858 added to basic sets and relations using the following functions.
860 #include <isl/constraint.h>
861 __isl_give isl_constraint *isl_equality_alloc(
862 __isl_take isl_dim *dim);
863 __isl_give isl_constraint *isl_inequality_alloc(
864 __isl_take isl_dim *dim);
865 void isl_constraint_set_constant(
866 __isl_keep isl_constraint *constraint, isl_int v);
867 void isl_constraint_set_coefficient(
868 __isl_keep isl_constraint *constraint,
869 enum isl_dim_type type, int pos, isl_int v);
870 __isl_give isl_basic_map *isl_basic_map_add_constraint(
871 __isl_take isl_basic_map *bmap,
872 __isl_take isl_constraint *constraint);
873 __isl_give isl_basic_set *isl_basic_set_add_constraint(
874 __isl_take isl_basic_set *bset,
875 __isl_take isl_constraint *constraint);
877 For example, to create a set containing the even integers
878 between 10 and 42, you would use the following code.
882 struct isl_constraint *c;
883 struct isl_basic_set *bset;
886 dim = isl_dim_set_alloc(ctx, 0, 2);
887 bset = isl_basic_set_universe(isl_dim_copy(dim));
889 c = isl_equality_alloc(isl_dim_copy(dim));
890 isl_int_set_si(v, -1);
891 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
892 isl_int_set_si(v, 2);
893 isl_constraint_set_coefficient(c, isl_dim_set, 1, v);
894 bset = isl_basic_set_add_constraint(bset, c);
896 c = isl_inequality_alloc(isl_dim_copy(dim));
897 isl_int_set_si(v, -10);
898 isl_constraint_set_constant(c, v);
899 isl_int_set_si(v, 1);
900 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
901 bset = isl_basic_set_add_constraint(bset, c);
903 c = isl_inequality_alloc(dim);
904 isl_int_set_si(v, 42);
905 isl_constraint_set_constant(c, v);
906 isl_int_set_si(v, -1);
907 isl_constraint_set_coefficient(c, isl_dim_set, 0, v);
908 bset = isl_basic_set_add_constraint(bset, c);
910 bset = isl_basic_set_project_out(bset, isl_dim_set, 1, 1);
916 struct isl_basic_set *bset;
917 bset = isl_basic_set_read_from_str(ctx,
918 "{[i] : exists (a : i = 2a and i >= 10 and i <= 42)}", -1);
920 A basic set or relation can also be constructed from two matrices
921 describing the equalities and the inequalities.
923 __isl_give isl_basic_set *isl_basic_set_from_constraint_matrices(
924 __isl_take isl_dim *dim,
925 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
926 enum isl_dim_type c1,
927 enum isl_dim_type c2, enum isl_dim_type c3,
928 enum isl_dim_type c4);
929 __isl_give isl_basic_map *isl_basic_map_from_constraint_matrices(
930 __isl_take isl_dim *dim,
931 __isl_take isl_mat *eq, __isl_take isl_mat *ineq,
932 enum isl_dim_type c1,
933 enum isl_dim_type c2, enum isl_dim_type c3,
934 enum isl_dim_type c4, enum isl_dim_type c5);
936 The C<isl_dim_type> arguments indicate the order in which
937 different kinds of variables appear in the input matrices
938 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
939 C<isl_dim_set> and C<isl_dim_div> for sets and
940 of C<isl_dim_cst>, C<isl_dim_param>,
941 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div> for relations.
943 =head2 Inspecting Sets and Relations
945 Usually, the user should not have to care about the actual constraints
946 of the sets and maps, but should instead apply the abstract operations
947 explained in the following sections.
948 Occasionally, however, it may be required to inspect the individual
949 coefficients of the constraints. This section explains how to do so.
950 In these cases, it may also be useful to have C<isl> compute
951 an explicit representation of the existentially quantified variables.
953 __isl_give isl_set *isl_set_compute_divs(
954 __isl_take isl_set *set);
955 __isl_give isl_map *isl_map_compute_divs(
956 __isl_take isl_map *map);
957 __isl_give isl_union_set *isl_union_set_compute_divs(
958 __isl_take isl_union_set *uset);
959 __isl_give isl_union_map *isl_union_map_compute_divs(
960 __isl_take isl_union_map *umap);
962 This explicit representation defines the existentially quantified
963 variables as integer divisions of the other variables, possibly
964 including earlier existentially quantified variables.
965 An explicitly represented existentially quantified variable therefore
966 has a unique value when the values of the other variables are known.
967 If, furthermore, the same existentials, i.e., existentials
968 with the same explicit representations, should appear in the
969 same order in each of the disjuncts of a set or map, then the user should call
970 either of the following functions.
972 __isl_give isl_set *isl_set_align_divs(
973 __isl_take isl_set *set);
974 __isl_give isl_map *isl_map_align_divs(
975 __isl_take isl_map *map);
977 Alternatively, the existentially quantified variables can be removed
978 using the following functions, which compute an overapproximation.
980 __isl_give isl_basic_set *isl_basic_set_remove_divs(
981 __isl_take isl_basic_set *bset);
982 __isl_give isl_basic_map *isl_basic_map_remove_divs(
983 __isl_take isl_basic_map *bmap);
984 __isl_give isl_set *isl_set_remove_divs(
985 __isl_take isl_set *set);
986 __isl_give isl_map *isl_map_remove_divs(
987 __isl_take isl_map *map);
989 To iterate over all the sets or maps in a union set or map, use
991 int isl_union_set_foreach_set(__isl_keep isl_union_set *uset,
992 int (*fn)(__isl_take isl_set *set, void *user),
994 int isl_union_map_foreach_map(__isl_keep isl_union_map *umap,
995 int (*fn)(__isl_take isl_map *map, void *user),
998 The number of sets or maps in a union set or map can be obtained
1001 int isl_union_set_n_set(__isl_keep isl_union_set *uset);
1002 int isl_union_map_n_map(__isl_keep isl_union_map *umap);
1004 To extract the set or map from a union with a given dimension
1007 __isl_give isl_set *isl_union_set_extract_set(
1008 __isl_keep isl_union_set *uset,
1009 __isl_take isl_dim *dim);
1010 __isl_give isl_map *isl_union_map_extract_map(
1011 __isl_keep isl_union_map *umap,
1012 __isl_take isl_dim *dim);
1014 To iterate over all the basic sets or maps in a set or map, use
1016 int isl_set_foreach_basic_set(__isl_keep isl_set *set,
1017 int (*fn)(__isl_take isl_basic_set *bset, void *user),
1019 int isl_map_foreach_basic_map(__isl_keep isl_map *map,
1020 int (*fn)(__isl_take isl_basic_map *bmap, void *user),
1023 The callback function C<fn> should return 0 if successful and
1024 -1 if an error occurs. In the latter case, or if any other error
1025 occurs, the above functions will return -1.
1027 It should be noted that C<isl> does not guarantee that
1028 the basic sets or maps passed to C<fn> are disjoint.
1029 If this is required, then the user should call one of
1030 the following functions first.
1032 __isl_give isl_set *isl_set_make_disjoint(
1033 __isl_take isl_set *set);
1034 __isl_give isl_map *isl_map_make_disjoint(
1035 __isl_take isl_map *map);
1037 The number of basic sets in a set can be obtained
1040 int isl_set_n_basic_set(__isl_keep isl_set *set);
1042 To iterate over the constraints of a basic set or map, use
1044 #include <isl/constraint.h>
1046 int isl_basic_map_foreach_constraint(
1047 __isl_keep isl_basic_map *bmap,
1048 int (*fn)(__isl_take isl_constraint *c, void *user),
1050 void isl_constraint_free(struct isl_constraint *c);
1052 Again, the callback function C<fn> should return 0 if successful and
1053 -1 if an error occurs. In the latter case, or if any other error
1054 occurs, the above functions will return -1.
1055 The constraint C<c> represents either an equality or an inequality.
1056 Use the following function to find out whether a constraint
1057 represents an equality. If not, it represents an inequality.
1059 int isl_constraint_is_equality(
1060 __isl_keep isl_constraint *constraint);
1062 The coefficients of the constraints can be inspected using
1063 the following functions.
1065 void isl_constraint_get_constant(
1066 __isl_keep isl_constraint *constraint, isl_int *v);
1067 void isl_constraint_get_coefficient(
1068 __isl_keep isl_constraint *constraint,
1069 enum isl_dim_type type, int pos, isl_int *v);
1071 The explicit representations of the existentially quantified
1072 variables can be inspected using the following functions.
1073 Note that the user is only allowed to use these functions
1074 if the inspected set or map is the result of a call
1075 to C<isl_set_compute_divs> or C<isl_map_compute_divs>.
1077 __isl_give isl_div *isl_constraint_div(
1078 __isl_keep isl_constraint *constraint, int pos);
1079 void isl_div_get_constant(__isl_keep isl_div *div,
1081 void isl_div_get_denominator(__isl_keep isl_div *div,
1083 void isl_div_get_coefficient(__isl_keep isl_div *div,
1084 enum isl_dim_type type, int pos, isl_int *v);
1086 To obtain the constraints of a basic set or map in matrix
1087 form, use the following functions.
1089 __isl_give isl_mat *isl_basic_set_equalities_matrix(
1090 __isl_keep isl_basic_set *bset,
1091 enum isl_dim_type c1, enum isl_dim_type c2,
1092 enum isl_dim_type c3, enum isl_dim_type c4);
1093 __isl_give isl_mat *isl_basic_set_inequalities_matrix(
1094 __isl_keep isl_basic_set *bset,
1095 enum isl_dim_type c1, enum isl_dim_type c2,
1096 enum isl_dim_type c3, enum isl_dim_type c4);
1097 __isl_give isl_mat *isl_basic_map_equalities_matrix(
1098 __isl_keep isl_basic_map *bmap,
1099 enum isl_dim_type c1,
1100 enum isl_dim_type c2, enum isl_dim_type c3,
1101 enum isl_dim_type c4, enum isl_dim_type c5);
1102 __isl_give isl_mat *isl_basic_map_inequalities_matrix(
1103 __isl_keep isl_basic_map *bmap,
1104 enum isl_dim_type c1,
1105 enum isl_dim_type c2, enum isl_dim_type c3,
1106 enum isl_dim_type c4, enum isl_dim_type c5);
1108 The C<isl_dim_type> arguments dictate the order in which
1109 different kinds of variables appear in the resulting matrix
1110 and should be a permutation of C<isl_dim_cst>, C<isl_dim_param>,
1111 C<isl_dim_in>, C<isl_dim_out> and C<isl_dim_div>.
1113 The names of the domain and range spaces of a set or relation can be
1114 read off using the following functions.
1116 const char *isl_basic_set_get_tuple_name(
1117 __isl_keep isl_basic_set *bset);
1118 const char *isl_set_get_tuple_name(
1119 __isl_keep isl_set *set);
1120 const char *isl_basic_map_get_tuple_name(
1121 __isl_keep isl_basic_map *bmap,
1122 enum isl_dim_type type);
1123 const char *isl_map_get_tuple_name(
1124 __isl_keep isl_map *map,
1125 enum isl_dim_type type);
1127 As with C<isl_dim_get_tuple_name>, the value returned points to
1128 an internal data structure.
1129 The names of individual dimensions can be read off using
1130 the following functions.
1132 const char *isl_constraint_get_dim_name(
1133 __isl_keep isl_constraint *constraint,
1134 enum isl_dim_type type, unsigned pos);
1135 const char *isl_basic_set_get_dim_name(
1136 __isl_keep isl_basic_set *bset,
1137 enum isl_dim_type type, unsigned pos);
1138 const char *isl_set_get_dim_name(
1139 __isl_keep isl_set *set,
1140 enum isl_dim_type type, unsigned pos);
1141 const char *isl_basic_map_get_dim_name(
1142 __isl_keep isl_basic_map *bmap,
1143 enum isl_dim_type type, unsigned pos);
1144 const char *isl_map_get_dim_name(
1145 __isl_keep isl_map *map,
1146 enum isl_dim_type type, unsigned pos);
1148 These functions are mostly useful to obtain the names
1153 =head3 Unary Properties
1159 The following functions test whether the given set or relation
1160 contains any integer points. The ``plain'' variants do not perform
1161 any computations, but simply check if the given set or relation
1162 is already known to be empty.
1164 int isl_basic_set_plain_is_empty(__isl_keep isl_basic_set *bset);
1165 int isl_basic_set_is_empty(__isl_keep isl_basic_set *bset);
1166 int isl_set_plain_is_empty(__isl_keep isl_set *set);
1167 int isl_set_is_empty(__isl_keep isl_set *set);
1168 int isl_union_set_is_empty(__isl_keep isl_union_set *uset);
1169 int isl_basic_map_plain_is_empty(__isl_keep isl_basic_map *bmap);
1170 int isl_basic_map_is_empty(__isl_keep isl_basic_map *bmap);
1171 int isl_map_plain_is_empty(__isl_keep isl_map *map);
1172 int isl_map_is_empty(__isl_keep isl_map *map);
1173 int isl_union_map_is_empty(__isl_keep isl_union_map *umap);
1175 =item * Universality
1177 int isl_basic_set_is_universe(__isl_keep isl_basic_set *bset);
1178 int isl_basic_map_is_universe(__isl_keep isl_basic_map *bmap);
1179 int isl_set_plain_is_universe(__isl_keep isl_set *set);
1181 =item * Single-valuedness
1183 int isl_map_is_single_valued(__isl_keep isl_map *map);
1184 int isl_union_map_is_single_valued(__isl_keep isl_union_map *umap);
1188 int isl_map_is_injective(__isl_keep isl_map *map);
1189 int isl_union_map_is_injective(__isl_keep isl_union_map *umap);
1193 int isl_map_is_bijective(__isl_keep isl_map *map);
1194 int isl_union_map_is_bijective(__isl_keep isl_union_map *umap);
1198 The following functions check whether the domain of the given
1199 (basic) set is a wrapped relation.
1201 int isl_basic_set_is_wrapping(
1202 __isl_keep isl_basic_set *bset);
1203 int isl_set_is_wrapping(__isl_keep isl_set *set);
1205 =item * Internal Product
1207 int isl_basic_map_can_zip(
1208 __isl_keep isl_basic_map *bmap);
1209 int isl_map_can_zip(__isl_keep isl_map *map);
1211 Check whether the product of domain and range of the given relation
1213 i.e., whether both domain and range are nested relations.
1217 =head3 Binary Properties
1223 int isl_set_plain_is_equal(__isl_keep isl_set *set1,
1224 __isl_keep isl_set *set2);
1225 int isl_set_is_equal(__isl_keep isl_set *set1,
1226 __isl_keep isl_set *set2);
1227 int isl_union_set_is_equal(
1228 __isl_keep isl_union_set *uset1,
1229 __isl_keep isl_union_set *uset2);
1230 int isl_basic_map_is_equal(
1231 __isl_keep isl_basic_map *bmap1,
1232 __isl_keep isl_basic_map *bmap2);
1233 int isl_map_is_equal(__isl_keep isl_map *map1,
1234 __isl_keep isl_map *map2);
1235 int isl_map_plain_is_equal(__isl_keep isl_map *map1,
1236 __isl_keep isl_map *map2);
1237 int isl_union_map_is_equal(
1238 __isl_keep isl_union_map *umap1,
1239 __isl_keep isl_union_map *umap2);
1241 =item * Disjointness
1243 int isl_set_plain_is_disjoint(__isl_keep isl_set *set1,
1244 __isl_keep isl_set *set2);
1248 int isl_set_is_subset(__isl_keep isl_set *set1,
1249 __isl_keep isl_set *set2);
1250 int isl_set_is_strict_subset(
1251 __isl_keep isl_set *set1,
1252 __isl_keep isl_set *set2);
1253 int isl_union_set_is_subset(
1254 __isl_keep isl_union_set *uset1,
1255 __isl_keep isl_union_set *uset2);
1256 int isl_union_set_is_strict_subset(
1257 __isl_keep isl_union_set *uset1,
1258 __isl_keep isl_union_set *uset2);
1259 int isl_basic_map_is_subset(
1260 __isl_keep isl_basic_map *bmap1,
1261 __isl_keep isl_basic_map *bmap2);
1262 int isl_basic_map_is_strict_subset(
1263 __isl_keep isl_basic_map *bmap1,
1264 __isl_keep isl_basic_map *bmap2);
1265 int isl_map_is_subset(
1266 __isl_keep isl_map *map1,
1267 __isl_keep isl_map *map2);
1268 int isl_map_is_strict_subset(
1269 __isl_keep isl_map *map1,
1270 __isl_keep isl_map *map2);
1271 int isl_union_map_is_subset(
1272 __isl_keep isl_union_map *umap1,
1273 __isl_keep isl_union_map *umap2);
1274 int isl_union_map_is_strict_subset(
1275 __isl_keep isl_union_map *umap1,
1276 __isl_keep isl_union_map *umap2);
1280 =head2 Unary Operations
1286 __isl_give isl_set *isl_set_complement(
1287 __isl_take isl_set *set);
1291 __isl_give isl_basic_map *isl_basic_map_reverse(
1292 __isl_take isl_basic_map *bmap);
1293 __isl_give isl_map *isl_map_reverse(
1294 __isl_take isl_map *map);
1295 __isl_give isl_union_map *isl_union_map_reverse(
1296 __isl_take isl_union_map *umap);
1300 __isl_give isl_basic_set *isl_basic_set_project_out(
1301 __isl_take isl_basic_set *bset,
1302 enum isl_dim_type type, unsigned first, unsigned n);
1303 __isl_give isl_basic_map *isl_basic_map_project_out(
1304 __isl_take isl_basic_map *bmap,
1305 enum isl_dim_type type, unsigned first, unsigned n);
1306 __isl_give isl_set *isl_set_project_out(__isl_take isl_set *set,
1307 enum isl_dim_type type, unsigned first, unsigned n);
1308 __isl_give isl_map *isl_map_project_out(__isl_take isl_map *map,
1309 enum isl_dim_type type, unsigned first, unsigned n);
1310 __isl_give isl_basic_set *isl_basic_map_domain(
1311 __isl_take isl_basic_map *bmap);
1312 __isl_give isl_basic_set *isl_basic_map_range(
1313 __isl_take isl_basic_map *bmap);
1314 __isl_give isl_set *isl_map_domain(
1315 __isl_take isl_map *bmap);
1316 __isl_give isl_set *isl_map_range(
1317 __isl_take isl_map *map);
1318 __isl_give isl_union_set *isl_union_map_domain(
1319 __isl_take isl_union_map *umap);
1320 __isl_give isl_union_set *isl_union_map_range(
1321 __isl_take isl_union_map *umap);
1323 __isl_give isl_basic_map *isl_basic_map_domain_map(
1324 __isl_take isl_basic_map *bmap);
1325 __isl_give isl_basic_map *isl_basic_map_range_map(
1326 __isl_take isl_basic_map *bmap);
1327 __isl_give isl_map *isl_map_domain_map(__isl_take isl_map *map);
1328 __isl_give isl_map *isl_map_range_map(__isl_take isl_map *map);
1329 __isl_give isl_union_map *isl_union_map_domain_map(
1330 __isl_take isl_union_map *umap);
1331 __isl_give isl_union_map *isl_union_map_range_map(
1332 __isl_take isl_union_map *umap);
1334 The functions above construct a (basic, regular or union) relation
1335 that maps (a wrapped version of) the input relation to its domain or range.
1339 __isl_give isl_map *isl_set_identity(
1340 __isl_take isl_set *set);
1341 __isl_give isl_union_map *isl_union_set_identity(
1342 __isl_take isl_union_set *uset);
1344 Construct an identity relation on the given (union) set.
1348 __isl_give isl_basic_set *isl_basic_map_deltas(
1349 __isl_take isl_basic_map *bmap);
1350 __isl_give isl_set *isl_map_deltas(__isl_take isl_map *map);
1351 __isl_give isl_union_set *isl_union_map_deltas(
1352 __isl_take isl_union_map *umap);
1354 These functions return a (basic) set containing the differences
1355 between image elements and corresponding domain elements in the input.
1357 __isl_give isl_basic_map *isl_basic_map_deltas_map(
1358 __isl_take isl_basic_map *bmap);
1359 __isl_give isl_map *isl_map_deltas_map(
1360 __isl_take isl_map *map);
1361 __isl_give isl_union_map *isl_union_map_deltas_map(
1362 __isl_take isl_union_map *umap);
1364 The functions above construct a (basic, regular or union) relation
1365 that maps (a wrapped version of) the input relation to its delta set.
1369 Simplify the representation of a set or relation by trying
1370 to combine pairs of basic sets or relations into a single
1371 basic set or relation.
1373 __isl_give isl_set *isl_set_coalesce(__isl_take isl_set *set);
1374 __isl_give isl_map *isl_map_coalesce(__isl_take isl_map *map);
1375 __isl_give isl_union_set *isl_union_set_coalesce(
1376 __isl_take isl_union_set *uset);
1377 __isl_give isl_union_map *isl_union_map_coalesce(
1378 __isl_take isl_union_map *umap);
1380 =item * Detecting equalities
1382 __isl_give isl_basic_set *isl_basic_set_detect_equalities(
1383 __isl_take isl_basic_set *bset);
1384 __isl_give isl_basic_map *isl_basic_map_detect_equalities(
1385 __isl_take isl_basic_map *bmap);
1386 __isl_give isl_set *isl_set_detect_equalities(
1387 __isl_take isl_set *set);
1388 __isl_give isl_map *isl_map_detect_equalities(
1389 __isl_take isl_map *map);
1390 __isl_give isl_union_set *isl_union_set_detect_equalities(
1391 __isl_take isl_union_set *uset);
1392 __isl_give isl_union_map *isl_union_map_detect_equalities(
1393 __isl_take isl_union_map *umap);
1395 Simplify the representation of a set or relation by detecting implicit
1400 __isl_give isl_basic_set *isl_set_convex_hull(
1401 __isl_take isl_set *set);
1402 __isl_give isl_basic_map *isl_map_convex_hull(
1403 __isl_take isl_map *map);
1405 If the input set or relation has any existentially quantified
1406 variables, then the result of these operations is currently undefined.
1410 __isl_give isl_basic_set *isl_set_simple_hull(
1411 __isl_take isl_set *set);
1412 __isl_give isl_basic_map *isl_map_simple_hull(
1413 __isl_take isl_map *map);
1414 __isl_give isl_union_map *isl_union_map_simple_hull(
1415 __isl_take isl_union_map *umap);
1417 These functions compute a single basic set or relation
1418 that contains the whole input set or relation.
1419 In particular, the output is described by translates
1420 of the constraints describing the basic sets or relations in the input.
1424 (See \autoref{s:simple hull}.)
1430 __isl_give isl_basic_set *isl_basic_set_affine_hull(
1431 __isl_take isl_basic_set *bset);
1432 __isl_give isl_basic_set *isl_set_affine_hull(
1433 __isl_take isl_set *set);
1434 __isl_give isl_union_set *isl_union_set_affine_hull(
1435 __isl_take isl_union_set *uset);
1436 __isl_give isl_basic_map *isl_basic_map_affine_hull(
1437 __isl_take isl_basic_map *bmap);
1438 __isl_give isl_basic_map *isl_map_affine_hull(
1439 __isl_take isl_map *map);
1440 __isl_give isl_union_map *isl_union_map_affine_hull(
1441 __isl_take isl_union_map *umap);
1443 In case of union sets and relations, the affine hull is computed
1446 =item * Polyhedral hull
1448 __isl_give isl_basic_set *isl_set_polyhedral_hull(
1449 __isl_take isl_set *set);
1450 __isl_give isl_basic_map *isl_map_polyhedral_hull(
1451 __isl_take isl_map *map);
1452 __isl_give isl_union_set *isl_union_set_polyhedral_hull(
1453 __isl_take isl_union_set *uset);
1454 __isl_give isl_union_map *isl_union_map_polyhedral_hull(
1455 __isl_take isl_union_map *umap);
1457 These functions compute a single basic set or relation
1458 not involving any existentially quantified variables
1459 that contains the whole input set or relation.
1460 In case of union sets and relations, the polyhedral hull is computed
1465 The following functions compute either the set of (rational) coefficient
1466 values of valid constraints for the given set or the set of (rational)
1467 values satisfying the constraints with coefficients from the given set.
1468 Internally, these two sets of functions perform essentially the
1469 same operations, except that the set of coefficients is assumed to
1470 be a cone, while the set of values may be any polyhedron.
1471 The current implementation is based on the Farkas lemma and
1472 Fourier-Motzkin elimination, but this may change or be made optional
1473 in future. In particular, future implementations may use different
1474 dualization algorithms or skip the elimination step.
1476 __isl_give isl_basic_set *isl_basic_set_coefficients(
1477 __isl_take isl_basic_set *bset);
1478 __isl_give isl_basic_set *isl_set_coefficients(
1479 __isl_take isl_set *set);
1480 __isl_give isl_union_set *isl_union_set_coefficients(
1481 __isl_take isl_union_set *bset);
1482 __isl_give isl_basic_set *isl_basic_set_solutions(
1483 __isl_take isl_basic_set *bset);
1484 __isl_give isl_basic_set *isl_set_solutions(
1485 __isl_take isl_set *set);
1486 __isl_give isl_union_set *isl_union_set_solutions(
1487 __isl_take isl_union_set *bset);
1491 __isl_give isl_map *isl_map_power(__isl_take isl_map *map,
1493 __isl_give isl_union_map *isl_union_map_power(
1494 __isl_take isl_union_map *umap, int *exact);
1496 Compute a parametric representation for all positive powers I<k> of C<map>.
1497 The result maps I<k> to a nested relation corresponding to the
1498 I<k>th power of C<map>.
1499 The result may be an overapproximation. If the result is known to be exact,
1500 then C<*exact> is set to C<1>.
1502 =item * Transitive closure
1504 __isl_give isl_map *isl_map_transitive_closure(
1505 __isl_take isl_map *map, int *exact);
1506 __isl_give isl_union_map *isl_union_map_transitive_closure(
1507 __isl_take isl_union_map *umap, int *exact);
1509 Compute the transitive closure of C<map>.
1510 The result may be an overapproximation. If the result is known to be exact,
1511 then C<*exact> is set to C<1>.
1513 =item * Reaching path lengths
1515 __isl_give isl_map *isl_map_reaching_path_lengths(
1516 __isl_take isl_map *map, int *exact);
1518 Compute a relation that maps each element in the range of C<map>
1519 to the lengths of all paths composed of edges in C<map> that
1520 end up in the given element.
1521 The result may be an overapproximation. If the result is known to be exact,
1522 then C<*exact> is set to C<1>.
1523 To compute the I<maximal> path length, the resulting relation
1524 should be postprocessed by C<isl_map_lexmax>.
1525 In particular, if the input relation is a dependence relation
1526 (mapping sources to sinks), then the maximal path length corresponds
1527 to the free schedule.
1528 Note, however, that C<isl_map_lexmax> expects the maximum to be
1529 finite, so if the path lengths are unbounded (possibly due to
1530 the overapproximation), then you will get an error message.
1534 __isl_give isl_basic_set *isl_basic_map_wrap(
1535 __isl_take isl_basic_map *bmap);
1536 __isl_give isl_set *isl_map_wrap(
1537 __isl_take isl_map *map);
1538 __isl_give isl_union_set *isl_union_map_wrap(
1539 __isl_take isl_union_map *umap);
1540 __isl_give isl_basic_map *isl_basic_set_unwrap(
1541 __isl_take isl_basic_set *bset);
1542 __isl_give isl_map *isl_set_unwrap(
1543 __isl_take isl_set *set);
1544 __isl_give isl_union_map *isl_union_set_unwrap(
1545 __isl_take isl_union_set *uset);
1549 Remove any internal structure of domain (and range) of the given
1550 set or relation. If there is any such internal structure in the input,
1551 then the name of the space is also removed.
1553 __isl_give isl_basic_set *isl_basic_set_flatten(
1554 __isl_take isl_basic_set *bset);
1555 __isl_give isl_set *isl_set_flatten(
1556 __isl_take isl_set *set);
1557 __isl_give isl_basic_map *isl_basic_map_flatten(
1558 __isl_take isl_basic_map *bmap);
1559 __isl_give isl_map *isl_map_flatten(
1560 __isl_take isl_map *map);
1562 __isl_give isl_map *isl_set_flatten_map(
1563 __isl_take isl_set *set);
1565 The function above constructs a relation
1566 that maps the input set to a flattened version of the set.
1570 Lift the input set to a space with extra dimensions corresponding
1571 to the existentially quantified variables in the input.
1572 In particular, the result lives in a wrapped map where the domain
1573 is the original space and the range corresponds to the original
1574 existentially quantified variables.
1576 __isl_give isl_basic_set *isl_basic_set_lift(
1577 __isl_take isl_basic_set *bset);
1578 __isl_give isl_set *isl_set_lift(
1579 __isl_take isl_set *set);
1580 __isl_give isl_union_set *isl_union_set_lift(
1581 __isl_take isl_union_set *uset);
1583 =item * Internal Product
1585 __isl_give isl_basic_map *isl_basic_map_zip(
1586 __isl_take isl_basic_map *bmap);
1587 __isl_give isl_map *isl_map_zip(
1588 __isl_take isl_map *map);
1589 __isl_give isl_union_map *isl_union_map_zip(
1590 __isl_take isl_union_map *umap);
1592 Given a relation with nested relations for domain and range,
1593 interchange the range of the domain with the domain of the range.
1595 =item * Dimension manipulation
1597 __isl_give isl_set *isl_set_add_dims(
1598 __isl_take isl_set *set,
1599 enum isl_dim_type type, unsigned n);
1600 __isl_give isl_map *isl_map_add_dims(
1601 __isl_take isl_map *map,
1602 enum isl_dim_type type, unsigned n);
1604 It is usually not advisable to directly change the (input or output)
1605 space of a set or a relation as this removes the name and the internal
1606 structure of the space. However, the above functions can be useful
1607 to add new parameters.
1611 =head2 Binary Operations
1613 The two arguments of a binary operation not only need to live
1614 in the same C<isl_ctx>, they currently also need to have
1615 the same (number of) parameters.
1617 =head3 Basic Operations
1621 =item * Intersection
1623 __isl_give isl_basic_set *isl_basic_set_intersect(
1624 __isl_take isl_basic_set *bset1,
1625 __isl_take isl_basic_set *bset2);
1626 __isl_give isl_set *isl_set_intersect(
1627 __isl_take isl_set *set1,
1628 __isl_take isl_set *set2);
1629 __isl_give isl_union_set *isl_union_set_intersect(
1630 __isl_take isl_union_set *uset1,
1631 __isl_take isl_union_set *uset2);
1632 __isl_give isl_basic_map *isl_basic_map_intersect_domain(
1633 __isl_take isl_basic_map *bmap,
1634 __isl_take isl_basic_set *bset);
1635 __isl_give isl_basic_map *isl_basic_map_intersect_range(
1636 __isl_take isl_basic_map *bmap,
1637 __isl_take isl_basic_set *bset);
1638 __isl_give isl_basic_map *isl_basic_map_intersect(
1639 __isl_take isl_basic_map *bmap1,
1640 __isl_take isl_basic_map *bmap2);
1641 __isl_give isl_map *isl_map_intersect_domain(
1642 __isl_take isl_map *map,
1643 __isl_take isl_set *set);
1644 __isl_give isl_map *isl_map_intersect_range(
1645 __isl_take isl_map *map,
1646 __isl_take isl_set *set);
1647 __isl_give isl_map *isl_map_intersect(
1648 __isl_take isl_map *map1,
1649 __isl_take isl_map *map2);
1650 __isl_give isl_union_map *isl_union_map_intersect_domain(
1651 __isl_take isl_union_map *umap,
1652 __isl_take isl_union_set *uset);
1653 __isl_give isl_union_map *isl_union_map_intersect_range(
1654 __isl_take isl_union_map *umap,
1655 __isl_take isl_union_set *uset);
1656 __isl_give isl_union_map *isl_union_map_intersect(
1657 __isl_take isl_union_map *umap1,
1658 __isl_take isl_union_map *umap2);
1662 __isl_give isl_set *isl_basic_set_union(
1663 __isl_take isl_basic_set *bset1,
1664 __isl_take isl_basic_set *bset2);
1665 __isl_give isl_map *isl_basic_map_union(
1666 __isl_take isl_basic_map *bmap1,
1667 __isl_take isl_basic_map *bmap2);
1668 __isl_give isl_set *isl_set_union(
1669 __isl_take isl_set *set1,
1670 __isl_take isl_set *set2);
1671 __isl_give isl_map *isl_map_union(
1672 __isl_take isl_map *map1,
1673 __isl_take isl_map *map2);
1674 __isl_give isl_union_set *isl_union_set_union(
1675 __isl_take isl_union_set *uset1,
1676 __isl_take isl_union_set *uset2);
1677 __isl_give isl_union_map *isl_union_map_union(
1678 __isl_take isl_union_map *umap1,
1679 __isl_take isl_union_map *umap2);
1681 =item * Set difference
1683 __isl_give isl_set *isl_set_subtract(
1684 __isl_take isl_set *set1,
1685 __isl_take isl_set *set2);
1686 __isl_give isl_map *isl_map_subtract(
1687 __isl_take isl_map *map1,
1688 __isl_take isl_map *map2);
1689 __isl_give isl_union_set *isl_union_set_subtract(
1690 __isl_take isl_union_set *uset1,
1691 __isl_take isl_union_set *uset2);
1692 __isl_give isl_union_map *isl_union_map_subtract(
1693 __isl_take isl_union_map *umap1,
1694 __isl_take isl_union_map *umap2);
1698 __isl_give isl_basic_set *isl_basic_set_apply(
1699 __isl_take isl_basic_set *bset,
1700 __isl_take isl_basic_map *bmap);
1701 __isl_give isl_set *isl_set_apply(
1702 __isl_take isl_set *set,
1703 __isl_take isl_map *map);
1704 __isl_give isl_union_set *isl_union_set_apply(
1705 __isl_take isl_union_set *uset,
1706 __isl_take isl_union_map *umap);
1707 __isl_give isl_basic_map *isl_basic_map_apply_domain(
1708 __isl_take isl_basic_map *bmap1,
1709 __isl_take isl_basic_map *bmap2);
1710 __isl_give isl_basic_map *isl_basic_map_apply_range(
1711 __isl_take isl_basic_map *bmap1,
1712 __isl_take isl_basic_map *bmap2);
1713 __isl_give isl_map *isl_map_apply_domain(
1714 __isl_take isl_map *map1,
1715 __isl_take isl_map *map2);
1716 __isl_give isl_union_map *isl_union_map_apply_domain(
1717 __isl_take isl_union_map *umap1,
1718 __isl_take isl_union_map *umap2);
1719 __isl_give isl_map *isl_map_apply_range(
1720 __isl_take isl_map *map1,
1721 __isl_take isl_map *map2);
1722 __isl_give isl_union_map *isl_union_map_apply_range(
1723 __isl_take isl_union_map *umap1,
1724 __isl_take isl_union_map *umap2);
1726 =item * Cartesian Product
1728 __isl_give isl_set *isl_set_product(
1729 __isl_take isl_set *set1,
1730 __isl_take isl_set *set2);
1731 __isl_give isl_union_set *isl_union_set_product(
1732 __isl_take isl_union_set *uset1,
1733 __isl_take isl_union_set *uset2);
1734 __isl_give isl_basic_map *isl_basic_map_range_product(
1735 __isl_take isl_basic_map *bmap1,
1736 __isl_take isl_basic_map *bmap2);
1737 __isl_give isl_map *isl_map_range_product(
1738 __isl_take isl_map *map1,
1739 __isl_take isl_map *map2);
1740 __isl_give isl_union_map *isl_union_map_range_product(
1741 __isl_take isl_union_map *umap1,
1742 __isl_take isl_union_map *umap2);
1743 __isl_give isl_map *isl_map_product(
1744 __isl_take isl_map *map1,
1745 __isl_take isl_map *map2);
1746 __isl_give isl_union_map *isl_union_map_product(
1747 __isl_take isl_union_map *umap1,
1748 __isl_take isl_union_map *umap2);
1750 The above functions compute the cross product of the given
1751 sets or relations. The domains and ranges of the results
1752 are wrapped maps between domains and ranges of the inputs.
1753 To obtain a ``flat'' product, use the following functions
1756 __isl_give isl_basic_set *isl_basic_set_flat_product(
1757 __isl_take isl_basic_set *bset1,
1758 __isl_take isl_basic_set *bset2);
1759 __isl_give isl_set *isl_set_flat_product(
1760 __isl_take isl_set *set1,
1761 __isl_take isl_set *set2);
1762 __isl_give isl_basic_map *isl_basic_map_flat_product(
1763 __isl_take isl_basic_map *bmap1,
1764 __isl_take isl_basic_map *bmap2);
1765 __isl_give isl_map *isl_map_flat_product(
1766 __isl_take isl_map *map1,
1767 __isl_take isl_map *map2);
1769 =item * Simplification
1771 __isl_give isl_basic_set *isl_basic_set_gist(
1772 __isl_take isl_basic_set *bset,
1773 __isl_take isl_basic_set *context);
1774 __isl_give isl_set *isl_set_gist(__isl_take isl_set *set,
1775 __isl_take isl_set *context);
1776 __isl_give isl_union_set *isl_union_set_gist(
1777 __isl_take isl_union_set *uset,
1778 __isl_take isl_union_set *context);
1779 __isl_give isl_basic_map *isl_basic_map_gist(
1780 __isl_take isl_basic_map *bmap,
1781 __isl_take isl_basic_map *context);
1782 __isl_give isl_map *isl_map_gist(__isl_take isl_map *map,
1783 __isl_take isl_map *context);
1784 __isl_give isl_union_map *isl_union_map_gist(
1785 __isl_take isl_union_map *umap,
1786 __isl_take isl_union_map *context);
1788 The gist operation returns a set or relation that has the
1789 same intersection with the context as the input set or relation.
1790 Any implicit equality in the intersection is made explicit in the result,
1791 while all inequalities that are redundant with respect to the intersection
1793 In case of union sets and relations, the gist operation is performed
1798 =head3 Lexicographic Optimization
1800 Given a (basic) set C<set> (or C<bset>) and a zero-dimensional domain C<dom>,
1801 the following functions
1802 compute a set that contains the lexicographic minimum or maximum
1803 of the elements in C<set> (or C<bset>) for those values of the parameters
1804 that satisfy C<dom>.
1805 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1806 that contains the parameter values in C<dom> for which C<set> (or C<bset>)
1808 In other words, the union of the parameter values
1809 for which the result is non-empty and of C<*empty>
1812 __isl_give isl_set *isl_basic_set_partial_lexmin(
1813 __isl_take isl_basic_set *bset,
1814 __isl_take isl_basic_set *dom,
1815 __isl_give isl_set **empty);
1816 __isl_give isl_set *isl_basic_set_partial_lexmax(
1817 __isl_take isl_basic_set *bset,
1818 __isl_take isl_basic_set *dom,
1819 __isl_give isl_set **empty);
1820 __isl_give isl_set *isl_set_partial_lexmin(
1821 __isl_take isl_set *set, __isl_take isl_set *dom,
1822 __isl_give isl_set **empty);
1823 __isl_give isl_set *isl_set_partial_lexmax(
1824 __isl_take isl_set *set, __isl_take isl_set *dom,
1825 __isl_give isl_set **empty);
1827 Given a (basic) set C<set> (or C<bset>), the following functions simply
1828 return a set containing the lexicographic minimum or maximum
1829 of the elements in C<set> (or C<bset>).
1830 In case of union sets, the optimum is computed per space.
1832 __isl_give isl_set *isl_basic_set_lexmin(
1833 __isl_take isl_basic_set *bset);
1834 __isl_give isl_set *isl_basic_set_lexmax(
1835 __isl_take isl_basic_set *bset);
1836 __isl_give isl_set *isl_set_lexmin(
1837 __isl_take isl_set *set);
1838 __isl_give isl_set *isl_set_lexmax(
1839 __isl_take isl_set *set);
1840 __isl_give isl_union_set *isl_union_set_lexmin(
1841 __isl_take isl_union_set *uset);
1842 __isl_give isl_union_set *isl_union_set_lexmax(
1843 __isl_take isl_union_set *uset);
1845 Given a (basic) relation C<map> (or C<bmap>) and a domain C<dom>,
1846 the following functions
1847 compute a relation that maps each element of C<dom>
1848 to the single lexicographic minimum or maximum
1849 of the elements that are associated to that same
1850 element in C<map> (or C<bmap>).
1851 If C<empty> is not C<NULL>, then C<*empty> is assigned a set
1852 that contains the elements in C<dom> that do not map
1853 to any elements in C<map> (or C<bmap>).
1854 In other words, the union of the domain of the result and of C<*empty>
1857 __isl_give isl_map *isl_basic_map_partial_lexmax(
1858 __isl_take isl_basic_map *bmap,
1859 __isl_take isl_basic_set *dom,
1860 __isl_give isl_set **empty);
1861 __isl_give isl_map *isl_basic_map_partial_lexmin(
1862 __isl_take isl_basic_map *bmap,
1863 __isl_take isl_basic_set *dom,
1864 __isl_give isl_set **empty);
1865 __isl_give isl_map *isl_map_partial_lexmax(
1866 __isl_take isl_map *map, __isl_take isl_set *dom,
1867 __isl_give isl_set **empty);
1868 __isl_give isl_map *isl_map_partial_lexmin(
1869 __isl_take isl_map *map, __isl_take isl_set *dom,
1870 __isl_give isl_set **empty);
1872 Given a (basic) map C<map> (or C<bmap>), the following functions simply
1873 return a map mapping each element in the domain of
1874 C<map> (or C<bmap>) to the lexicographic minimum or maximum
1875 of all elements associated to that element.
1876 In case of union relations, the optimum is computed per space.
1878 __isl_give isl_map *isl_basic_map_lexmin(
1879 __isl_take isl_basic_map *bmap);
1880 __isl_give isl_map *isl_basic_map_lexmax(
1881 __isl_take isl_basic_map *bmap);
1882 __isl_give isl_map *isl_map_lexmin(
1883 __isl_take isl_map *map);
1884 __isl_give isl_map *isl_map_lexmax(
1885 __isl_take isl_map *map);
1886 __isl_give isl_union_map *isl_union_map_lexmin(
1887 __isl_take isl_union_map *umap);
1888 __isl_give isl_union_map *isl_union_map_lexmax(
1889 __isl_take isl_union_map *umap);
1893 Matrices can be created, copied and freed using the following functions.
1895 #include <isl/mat.h>
1896 __isl_give isl_mat *isl_mat_alloc(struct isl_ctx *ctx,
1897 unsigned n_row, unsigned n_col);
1898 __isl_give isl_mat *isl_mat_copy(__isl_keep isl_mat *mat);
1899 void isl_mat_free(__isl_take isl_mat *mat);
1901 Note that the elements of a newly created matrix may have arbitrary values.
1902 The elements can be changed and inspected using the following functions.
1904 int isl_mat_rows(__isl_keep isl_mat *mat);
1905 int isl_mat_cols(__isl_keep isl_mat *mat);
1906 int isl_mat_get_element(__isl_keep isl_mat *mat,
1907 int row, int col, isl_int *v);
1908 __isl_give isl_mat *isl_mat_set_element(__isl_take isl_mat *mat,
1909 int row, int col, isl_int v);
1910 __isl_give isl_mat *isl_mat_set_element_si(__isl_take isl_mat *mat,
1911 int row, int col, int v);
1913 C<isl_mat_get_element> will return a negative value if anything went wrong.
1914 In that case, the value of C<*v> is undefined.
1916 The following function can be used to compute the (right) inverse
1917 of a matrix, i.e., a matrix such that the product of the original
1918 and the inverse (in that order) is a multiple of the identity matrix.
1919 The input matrix is assumed to be of full row-rank.
1921 __isl_give isl_mat *isl_mat_right_inverse(__isl_take isl_mat *mat);
1923 The following function can be used to compute the (right) kernel
1924 (or null space) of a matrix, i.e., a matrix such that the product of
1925 the original and the kernel (in that order) is the zero matrix.
1927 __isl_give isl_mat *isl_mat_right_kernel(__isl_take isl_mat *mat);
1931 Points are elements of a set. They can be used to construct
1932 simple sets (boxes) or they can be used to represent the
1933 individual elements of a set.
1934 The zero point (the origin) can be created using
1936 __isl_give isl_point *isl_point_zero(__isl_take isl_dim *dim);
1938 The coordinates of a point can be inspected, set and changed
1941 void isl_point_get_coordinate(__isl_keep isl_point *pnt,
1942 enum isl_dim_type type, int pos, isl_int *v);
1943 __isl_give isl_point *isl_point_set_coordinate(
1944 __isl_take isl_point *pnt,
1945 enum isl_dim_type type, int pos, isl_int v);
1947 __isl_give isl_point *isl_point_add_ui(
1948 __isl_take isl_point *pnt,
1949 enum isl_dim_type type, int pos, unsigned val);
1950 __isl_give isl_point *isl_point_sub_ui(
1951 __isl_take isl_point *pnt,
1952 enum isl_dim_type type, int pos, unsigned val);
1954 Points can be copied or freed using
1956 __isl_give isl_point *isl_point_copy(
1957 __isl_keep isl_point *pnt);
1958 void isl_point_free(__isl_take isl_point *pnt);
1960 A singleton set can be created from a point using
1962 __isl_give isl_basic_set *isl_basic_set_from_point(
1963 __isl_take isl_point *pnt);
1964 __isl_give isl_set *isl_set_from_point(
1965 __isl_take isl_point *pnt);
1967 and a box can be created from two opposite extremal points using
1969 __isl_give isl_basic_set *isl_basic_set_box_from_points(
1970 __isl_take isl_point *pnt1,
1971 __isl_take isl_point *pnt2);
1972 __isl_give isl_set *isl_set_box_from_points(
1973 __isl_take isl_point *pnt1,
1974 __isl_take isl_point *pnt2);
1976 All elements of a B<bounded> (union) set can be enumerated using
1977 the following functions.
1979 int isl_set_foreach_point(__isl_keep isl_set *set,
1980 int (*fn)(__isl_take isl_point *pnt, void *user),
1982 int isl_union_set_foreach_point(__isl_keep isl_union_set *uset,
1983 int (*fn)(__isl_take isl_point *pnt, void *user),
1986 The function C<fn> is called for each integer point in
1987 C<set> with as second argument the last argument of
1988 the C<isl_set_foreach_point> call. The function C<fn>
1989 should return C<0> on success and C<-1> on failure.
1990 In the latter case, C<isl_set_foreach_point> will stop
1991 enumerating and return C<-1> as well.
1992 If the enumeration is performed successfully and to completion,
1993 then C<isl_set_foreach_point> returns C<0>.
1995 To obtain a single point of a (basic) set, use
1997 __isl_give isl_point *isl_basic_set_sample_point(
1998 __isl_take isl_basic_set *bset);
1999 __isl_give isl_point *isl_set_sample_point(
2000 __isl_take isl_set *set);
2002 If C<set> does not contain any (integer) points, then the
2003 resulting point will be ``void'', a property that can be
2006 int isl_point_is_void(__isl_keep isl_point *pnt);
2008 =head2 Piecewise Quasipolynomials
2010 A piecewise quasipolynomial is a particular kind of function that maps
2011 a parametric point to a rational value.
2012 More specifically, a quasipolynomial is a polynomial expression in greatest
2013 integer parts of affine expressions of parameters and variables.
2014 A piecewise quasipolynomial is a subdivision of a given parametric
2015 domain into disjoint cells with a quasipolynomial associated to
2016 each cell. The value of the piecewise quasipolynomial at a given
2017 point is the value of the quasipolynomial associated to the cell
2018 that contains the point. Outside of the union of cells,
2019 the value is assumed to be zero.
2020 For example, the piecewise quasipolynomial
2022 [n] -> { [x] -> ((1 + n) - x) : x <= n and x >= 0 }
2024 maps C<x> to C<1 + n - x> for values of C<x> between C<0> and C<n>.
2025 A given piecewise quasipolynomial has a fixed domain dimension.
2026 Union piecewise quasipolynomials are used to contain piecewise quasipolynomials
2027 defined over different domains.
2028 Piecewise quasipolynomials are mainly used by the C<barvinok>
2029 library for representing the number of elements in a parametric set or map.
2030 For example, the piecewise quasipolynomial above represents
2031 the number of points in the map
2033 [n] -> { [x] -> [y] : x,y >= 0 and 0 <= x + y <= n }
2035 =head3 Printing (Piecewise) Quasipolynomials
2037 Quasipolynomials and piecewise quasipolynomials can be printed
2038 using the following functions.
2040 __isl_give isl_printer *isl_printer_print_qpolynomial(
2041 __isl_take isl_printer *p,
2042 __isl_keep isl_qpolynomial *qp);
2044 __isl_give isl_printer *isl_printer_print_pw_qpolynomial(
2045 __isl_take isl_printer *p,
2046 __isl_keep isl_pw_qpolynomial *pwqp);
2048 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial(
2049 __isl_take isl_printer *p,
2050 __isl_keep isl_union_pw_qpolynomial *upwqp);
2052 The output format of the printer
2053 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2054 For C<isl_printer_print_union_pw_qpolynomial>, only C<ISL_FORMAT_ISL>
2056 In case of printing in C<ISL_FORMAT_C>, the user may want
2057 to set the names of all dimensions
2059 __isl_give isl_qpolynomial *isl_qpolynomial_set_dim_name(
2060 __isl_take isl_qpolynomial *qp,
2061 enum isl_dim_type type, unsigned pos,
2063 __isl_give isl_pw_qpolynomial *
2064 isl_pw_qpolynomial_set_dim_name(
2065 __isl_take isl_pw_qpolynomial *pwqp,
2066 enum isl_dim_type type, unsigned pos,
2069 =head3 Creating New (Piecewise) Quasipolynomials
2071 Some simple quasipolynomials can be created using the following functions.
2072 More complicated quasipolynomials can be created by applying
2073 operations such as addition and multiplication
2074 on the resulting quasipolynomials
2076 __isl_give isl_qpolynomial *isl_qpolynomial_zero(
2077 __isl_take isl_dim *dim);
2078 __isl_give isl_qpolynomial *isl_qpolynomial_one(
2079 __isl_take isl_dim *dim);
2080 __isl_give isl_qpolynomial *isl_qpolynomial_infty(
2081 __isl_take isl_dim *dim);
2082 __isl_give isl_qpolynomial *isl_qpolynomial_neginfty(
2083 __isl_take isl_dim *dim);
2084 __isl_give isl_qpolynomial *isl_qpolynomial_nan(
2085 __isl_take isl_dim *dim);
2086 __isl_give isl_qpolynomial *isl_qpolynomial_rat_cst(
2087 __isl_take isl_dim *dim,
2088 const isl_int n, const isl_int d);
2089 __isl_give isl_qpolynomial *isl_qpolynomial_div(
2090 __isl_take isl_div *div);
2091 __isl_give isl_qpolynomial *isl_qpolynomial_var(
2092 __isl_take isl_dim *dim,
2093 enum isl_dim_type type, unsigned pos);
2095 The zero piecewise quasipolynomial or a piecewise quasipolynomial
2096 with a single cell can be created using the following functions.
2097 Multiple of these single cell piecewise quasipolynomials can
2098 be combined to create more complicated piecewise quasipolynomials.
2100 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_zero(
2101 __isl_take isl_dim *dim);
2102 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_alloc(
2103 __isl_take isl_set *set,
2104 __isl_take isl_qpolynomial *qp);
2106 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_zero(
2107 __isl_take isl_dim *dim);
2108 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_from_pw_qpolynomial(
2109 __isl_take isl_pw_qpolynomial *pwqp);
2110 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add_pw_qpolynomial(
2111 __isl_take isl_union_pw_qpolynomial *upwqp,
2112 __isl_take isl_pw_qpolynomial *pwqp);
2114 Quasipolynomials can be copied and freed again using the following
2117 __isl_give isl_qpolynomial *isl_qpolynomial_copy(
2118 __isl_keep isl_qpolynomial *qp);
2119 void isl_qpolynomial_free(__isl_take isl_qpolynomial *qp);
2121 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_copy(
2122 __isl_keep isl_pw_qpolynomial *pwqp);
2123 void isl_pw_qpolynomial_free(
2124 __isl_take isl_pw_qpolynomial *pwqp);
2126 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_copy(
2127 __isl_keep isl_union_pw_qpolynomial *upwqp);
2128 void isl_union_pw_qpolynomial_free(
2129 __isl_take isl_union_pw_qpolynomial *upwqp);
2131 =head3 Inspecting (Piecewise) Quasipolynomials
2133 To iterate over all piecewise quasipolynomials in a union
2134 piecewise quasipolynomial, use the following function
2136 int isl_union_pw_qpolynomial_foreach_pw_qpolynomial(
2137 __isl_keep isl_union_pw_qpolynomial *upwqp,
2138 int (*fn)(__isl_take isl_pw_qpolynomial *pwqp, void *user),
2141 To extract the piecewise quasipolynomial from a union with a given dimension
2144 __isl_give isl_pw_qpolynomial *
2145 isl_union_pw_qpolynomial_extract_pw_qpolynomial(
2146 __isl_keep isl_union_pw_qpolynomial *upwqp,
2147 __isl_take isl_dim *dim);
2149 To iterate over the cells in a piecewise quasipolynomial,
2150 use either of the following two functions
2152 int isl_pw_qpolynomial_foreach_piece(
2153 __isl_keep isl_pw_qpolynomial *pwqp,
2154 int (*fn)(__isl_take isl_set *set,
2155 __isl_take isl_qpolynomial *qp,
2156 void *user), void *user);
2157 int isl_pw_qpolynomial_foreach_lifted_piece(
2158 __isl_keep isl_pw_qpolynomial *pwqp,
2159 int (*fn)(__isl_take isl_set *set,
2160 __isl_take isl_qpolynomial *qp,
2161 void *user), void *user);
2163 As usual, the function C<fn> should return C<0> on success
2164 and C<-1> on failure. The difference between
2165 C<isl_pw_qpolynomial_foreach_piece> and
2166 C<isl_pw_qpolynomial_foreach_lifted_piece> is that
2167 C<isl_pw_qpolynomial_foreach_lifted_piece> will first
2168 compute unique representations for all existentially quantified
2169 variables and then turn these existentially quantified variables
2170 into extra set variables, adapting the associated quasipolynomial
2171 accordingly. This means that the C<set> passed to C<fn>
2172 will not have any existentially quantified variables, but that
2173 the dimensions of the sets may be different for different
2174 invocations of C<fn>.
2176 To iterate over all terms in a quasipolynomial,
2179 int isl_qpolynomial_foreach_term(
2180 __isl_keep isl_qpolynomial *qp,
2181 int (*fn)(__isl_take isl_term *term,
2182 void *user), void *user);
2184 The terms themselves can be inspected and freed using
2187 unsigned isl_term_dim(__isl_keep isl_term *term,
2188 enum isl_dim_type type);
2189 void isl_term_get_num(__isl_keep isl_term *term,
2191 void isl_term_get_den(__isl_keep isl_term *term,
2193 int isl_term_get_exp(__isl_keep isl_term *term,
2194 enum isl_dim_type type, unsigned pos);
2195 __isl_give isl_div *isl_term_get_div(
2196 __isl_keep isl_term *term, unsigned pos);
2197 void isl_term_free(__isl_take isl_term *term);
2199 Each term is a product of parameters, set variables and
2200 integer divisions. The function C<isl_term_get_exp>
2201 returns the exponent of a given dimensions in the given term.
2202 The C<isl_int>s in the arguments of C<isl_term_get_num>
2203 and C<isl_term_get_den> need to have been initialized
2204 using C<isl_int_init> before calling these functions.
2206 =head3 Properties of (Piecewise) Quasipolynomials
2208 To check whether a quasipolynomial is actually a constant,
2209 use the following function.
2211 int isl_qpolynomial_is_cst(__isl_keep isl_qpolynomial *qp,
2212 isl_int *n, isl_int *d);
2214 If C<qp> is a constant and if C<n> and C<d> are not C<NULL>
2215 then the numerator and denominator of the constant
2216 are returned in C<*n> and C<*d>, respectively.
2218 =head3 Operations on (Piecewise) Quasipolynomials
2220 __isl_give isl_qpolynomial *isl_qpolynomial_neg(
2221 __isl_take isl_qpolynomial *qp);
2222 __isl_give isl_qpolynomial *isl_qpolynomial_add(
2223 __isl_take isl_qpolynomial *qp1,
2224 __isl_take isl_qpolynomial *qp2);
2225 __isl_give isl_qpolynomial *isl_qpolynomial_sub(
2226 __isl_take isl_qpolynomial *qp1,
2227 __isl_take isl_qpolynomial *qp2);
2228 __isl_give isl_qpolynomial *isl_qpolynomial_mul(
2229 __isl_take isl_qpolynomial *qp1,
2230 __isl_take isl_qpolynomial *qp2);
2231 __isl_give isl_qpolynomial *isl_qpolynomial_pow(
2232 __isl_take isl_qpolynomial *qp, unsigned exponent);
2234 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add(
2235 __isl_take isl_pw_qpolynomial *pwqp1,
2236 __isl_take isl_pw_qpolynomial *pwqp2);
2237 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_sub(
2238 __isl_take isl_pw_qpolynomial *pwqp1,
2239 __isl_take isl_pw_qpolynomial *pwqp2);
2240 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_add_disjoint(
2241 __isl_take isl_pw_qpolynomial *pwqp1,
2242 __isl_take isl_pw_qpolynomial *pwqp2);
2243 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_neg(
2244 __isl_take isl_pw_qpolynomial *pwqp);
2245 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_mul(
2246 __isl_take isl_pw_qpolynomial *pwqp1,
2247 __isl_take isl_pw_qpolynomial *pwqp2);
2249 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_add(
2250 __isl_take isl_union_pw_qpolynomial *upwqp1,
2251 __isl_take isl_union_pw_qpolynomial *upwqp2);
2252 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_sub(
2253 __isl_take isl_union_pw_qpolynomial *upwqp1,
2254 __isl_take isl_union_pw_qpolynomial *upwqp2);
2255 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_mul(
2256 __isl_take isl_union_pw_qpolynomial *upwqp1,
2257 __isl_take isl_union_pw_qpolynomial *upwqp2);
2259 __isl_give isl_qpolynomial *isl_pw_qpolynomial_eval(
2260 __isl_take isl_pw_qpolynomial *pwqp,
2261 __isl_take isl_point *pnt);
2263 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_eval(
2264 __isl_take isl_union_pw_qpolynomial *upwqp,
2265 __isl_take isl_point *pnt);
2267 __isl_give isl_set *isl_pw_qpolynomial_domain(
2268 __isl_take isl_pw_qpolynomial *pwqp);
2269 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_intersect_domain(
2270 __isl_take isl_pw_qpolynomial *pwpq,
2271 __isl_take isl_set *set);
2273 __isl_give isl_union_set *isl_union_pw_qpolynomial_domain(
2274 __isl_take isl_union_pw_qpolynomial *upwqp);
2275 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_intersect_domain(
2276 __isl_take isl_union_pw_qpolynomial *upwpq,
2277 __isl_take isl_union_set *uset);
2279 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_coalesce(
2280 __isl_take isl_union_pw_qpolynomial *upwqp);
2282 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_gist(
2283 __isl_take isl_pw_qpolynomial *pwqp,
2284 __isl_take isl_set *context);
2286 __isl_give isl_union_pw_qpolynomial *isl_union_pw_qpolynomial_gist(
2287 __isl_take isl_union_pw_qpolynomial *upwqp,
2288 __isl_take isl_union_set *context);
2290 The gist operation applies the gist operation to each of
2291 the cells in the domain of the input piecewise quasipolynomial.
2292 The context is also exploited
2293 to simplify the quasipolynomials associated to each cell.
2295 __isl_give isl_pw_qpolynomial *isl_pw_qpolynomial_to_polynomial(
2296 __isl_take isl_pw_qpolynomial *pwqp, int sign);
2297 __isl_give isl_union_pw_qpolynomial *
2298 isl_union_pw_qpolynomial_to_polynomial(
2299 __isl_take isl_union_pw_qpolynomial *upwqp, int sign);
2301 Approximate each quasipolynomial by a polynomial. If C<sign> is positive,
2302 the polynomial will be an overapproximation. If C<sign> is negative,
2303 it will be an underapproximation. If C<sign> is zero, the approximation
2304 will lie somewhere in between.
2306 =head2 Bounds on Piecewise Quasipolynomials and Piecewise Quasipolynomial Reductions
2308 A piecewise quasipolynomial reduction is a piecewise
2309 reduction (or fold) of quasipolynomials.
2310 In particular, the reduction can be maximum or a minimum.
2311 The objects are mainly used to represent the result of
2312 an upper or lower bound on a quasipolynomial over its domain,
2313 i.e., as the result of the following function.
2315 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_bound(
2316 __isl_take isl_pw_qpolynomial *pwqp,
2317 enum isl_fold type, int *tight);
2319 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_bound(
2320 __isl_take isl_union_pw_qpolynomial *upwqp,
2321 enum isl_fold type, int *tight);
2323 The C<type> argument may be either C<isl_fold_min> or C<isl_fold_max>.
2324 If C<tight> is not C<NULL>, then C<*tight> is set to C<1>
2325 is the returned bound is known be tight, i.e., for each value
2326 of the parameters there is at least
2327 one element in the domain that reaches the bound.
2328 If the domain of C<pwqp> is not wrapping, then the bound is computed
2329 over all elements in that domain and the result has a purely parametric
2330 domain. If the domain of C<pwqp> is wrapping, then the bound is
2331 computed over the range of the wrapped relation. The domain of the
2332 wrapped relation becomes the domain of the result.
2334 A (piecewise) quasipolynomial reduction can be copied or freed using the
2335 following functions.
2337 __isl_give isl_qpolynomial_fold *isl_qpolynomial_fold_copy(
2338 __isl_keep isl_qpolynomial_fold *fold);
2339 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_copy(
2340 __isl_keep isl_pw_qpolynomial_fold *pwf);
2341 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_copy(
2342 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2343 void isl_qpolynomial_fold_free(
2344 __isl_take isl_qpolynomial_fold *fold);
2345 void isl_pw_qpolynomial_fold_free(
2346 __isl_take isl_pw_qpolynomial_fold *pwf);
2347 void isl_union_pw_qpolynomial_fold_free(
2348 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2350 =head3 Printing Piecewise Quasipolynomial Reductions
2352 Piecewise quasipolynomial reductions can be printed
2353 using the following function.
2355 __isl_give isl_printer *isl_printer_print_pw_qpolynomial_fold(
2356 __isl_take isl_printer *p,
2357 __isl_keep isl_pw_qpolynomial_fold *pwf);
2358 __isl_give isl_printer *isl_printer_print_union_pw_qpolynomial_fold(
2359 __isl_take isl_printer *p,
2360 __isl_keep isl_union_pw_qpolynomial_fold *upwf);
2362 For C<isl_printer_print_pw_qpolynomial_fold>,
2363 output format of the printer
2364 needs to be set to either C<ISL_FORMAT_ISL> or C<ISL_FORMAT_C>.
2365 For C<isl_printer_print_union_pw_qpolynomial_fold>,
2366 output format of the printer
2367 needs to be set to C<ISL_FORMAT_ISL>.
2368 In case of printing in C<ISL_FORMAT_C>, the user may want
2369 to set the names of all dimensions
2371 __isl_give isl_pw_qpolynomial_fold *
2372 isl_pw_qpolynomial_fold_set_dim_name(
2373 __isl_take isl_pw_qpolynomial_fold *pwf,
2374 enum isl_dim_type type, unsigned pos,
2377 =head3 Inspecting (Piecewise) Quasipolynomial Reductions
2379 To iterate over all piecewise quasipolynomial reductions in a union
2380 piecewise quasipolynomial reduction, use the following function
2382 int isl_union_pw_qpolynomial_fold_foreach_pw_qpolynomial_fold(
2383 __isl_keep isl_union_pw_qpolynomial_fold *upwf,
2384 int (*fn)(__isl_take isl_pw_qpolynomial_fold *pwf,
2385 void *user), void *user);
2387 To iterate over the cells in a piecewise quasipolynomial reduction,
2388 use either of the following two functions
2390 int isl_pw_qpolynomial_fold_foreach_piece(
2391 __isl_keep isl_pw_qpolynomial_fold *pwf,
2392 int (*fn)(__isl_take isl_set *set,
2393 __isl_take isl_qpolynomial_fold *fold,
2394 void *user), void *user);
2395 int isl_pw_qpolynomial_fold_foreach_lifted_piece(
2396 __isl_keep isl_pw_qpolynomial_fold *pwf,
2397 int (*fn)(__isl_take isl_set *set,
2398 __isl_take isl_qpolynomial_fold *fold,
2399 void *user), void *user);
2401 See L<Inspecting (Piecewise) Quasipolynomials> for an explanation
2402 of the difference between these two functions.
2404 To iterate over all quasipolynomials in a reduction, use
2406 int isl_qpolynomial_fold_foreach_qpolynomial(
2407 __isl_keep isl_qpolynomial_fold *fold,
2408 int (*fn)(__isl_take isl_qpolynomial *qp,
2409 void *user), void *user);
2411 =head3 Operations on Piecewise Quasipolynomial Reductions
2413 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_add(
2414 __isl_take isl_pw_qpolynomial_fold *pwf1,
2415 __isl_take isl_pw_qpolynomial_fold *pwf2);
2417 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_fold(
2418 __isl_take isl_pw_qpolynomial_fold *pwf1,
2419 __isl_take isl_pw_qpolynomial_fold *pwf2);
2421 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_fold(
2422 __isl_take isl_union_pw_qpolynomial_fold *upwf1,
2423 __isl_take isl_union_pw_qpolynomial_fold *upwf2);
2425 __isl_give isl_qpolynomial *isl_pw_qpolynomial_fold_eval(
2426 __isl_take isl_pw_qpolynomial_fold *pwf,
2427 __isl_take isl_point *pnt);
2429 __isl_give isl_qpolynomial *isl_union_pw_qpolynomial_fold_eval(
2430 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2431 __isl_take isl_point *pnt);
2433 __isl_give isl_union_set *isl_union_pw_qpolynomial_fold_domain(
2434 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2435 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_intersect_domain(
2436 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2437 __isl_take isl_union_set *uset);
2439 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_coalesce(
2440 __isl_take isl_pw_qpolynomial_fold *pwf);
2442 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_coalesce(
2443 __isl_take isl_union_pw_qpolynomial_fold *upwf);
2445 __isl_give isl_pw_qpolynomial_fold *isl_pw_qpolynomial_fold_gist(
2446 __isl_take isl_pw_qpolynomial_fold *pwf,
2447 __isl_take isl_set *context);
2449 __isl_give isl_union_pw_qpolynomial_fold *isl_union_pw_qpolynomial_fold_gist(
2450 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2451 __isl_take isl_union_set *context);
2453 The gist operation applies the gist operation to each of
2454 the cells in the domain of the input piecewise quasipolynomial reduction.
2455 In future, the operation will also exploit the context
2456 to simplify the quasipolynomial reductions associated to each cell.
2458 __isl_give isl_pw_qpolynomial_fold *
2459 isl_set_apply_pw_qpolynomial_fold(
2460 __isl_take isl_set *set,
2461 __isl_take isl_pw_qpolynomial_fold *pwf,
2463 __isl_give isl_pw_qpolynomial_fold *
2464 isl_map_apply_pw_qpolynomial_fold(
2465 __isl_take isl_map *map,
2466 __isl_take isl_pw_qpolynomial_fold *pwf,
2468 __isl_give isl_union_pw_qpolynomial_fold *
2469 isl_union_set_apply_union_pw_qpolynomial_fold(
2470 __isl_take isl_union_set *uset,
2471 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2473 __isl_give isl_union_pw_qpolynomial_fold *
2474 isl_union_map_apply_union_pw_qpolynomial_fold(
2475 __isl_take isl_union_map *umap,
2476 __isl_take isl_union_pw_qpolynomial_fold *upwf,
2479 The functions taking a map
2480 compose the given map with the given piecewise quasipolynomial reduction.
2481 That is, compute a bound (of the same type as C<pwf> or C<upwf> itself)
2482 over all elements in the intersection of the range of the map
2483 and the domain of the piecewise quasipolynomial reduction
2484 as a function of an element in the domain of the map.
2485 The functions taking a set compute a bound over all elements in the
2486 intersection of the set and the domain of the
2487 piecewise quasipolynomial reduction.
2489 =head2 Dependence Analysis
2491 C<isl> contains specialized functionality for performing
2492 array dataflow analysis. That is, given a I<sink> access relation
2493 and a collection of possible I<source> access relations,
2494 C<isl> can compute relations that describe
2495 for each iteration of the sink access, which iteration
2496 of which of the source access relations was the last
2497 to access the same data element before the given iteration
2499 To compute standard flow dependences, the sink should be
2500 a read, while the sources should be writes.
2501 If any of the source accesses are marked as being I<may>
2502 accesses, then there will be a dependence to the last
2503 I<must> access B<and> to any I<may> access that follows
2504 this last I<must> access.
2505 In particular, if I<all> sources are I<may> accesses,
2506 then memory based dependence analysis is performed.
2507 If, on the other hand, all sources are I<must> accesses,
2508 then value based dependence analysis is performed.
2510 #include <isl/flow.h>
2512 typedef int (*isl_access_level_before)(void *first, void *second);
2514 __isl_give isl_access_info *isl_access_info_alloc(
2515 __isl_take isl_map *sink,
2516 void *sink_user, isl_access_level_before fn,
2518 __isl_give isl_access_info *isl_access_info_add_source(
2519 __isl_take isl_access_info *acc,
2520 __isl_take isl_map *source, int must,
2522 void isl_access_info_free(__isl_take isl_access_info *acc);
2524 __isl_give isl_flow *isl_access_info_compute_flow(
2525 __isl_take isl_access_info *acc);
2527 int isl_flow_foreach(__isl_keep isl_flow *deps,
2528 int (*fn)(__isl_take isl_map *dep, int must,
2529 void *dep_user, void *user),
2531 __isl_give isl_map *isl_flow_get_no_source(
2532 __isl_keep isl_flow *deps, int must);
2533 void isl_flow_free(__isl_take isl_flow *deps);
2535 The function C<isl_access_info_compute_flow> performs the actual
2536 dependence analysis. The other functions are used to construct
2537 the input for this function or to read off the output.
2539 The input is collected in an C<isl_access_info>, which can
2540 be created through a call to C<isl_access_info_alloc>.
2541 The arguments to this functions are the sink access relation
2542 C<sink>, a token C<sink_user> used to identify the sink
2543 access to the user, a callback function for specifying the
2544 relative order of source and sink accesses, and the number
2545 of source access relations that will be added.
2546 The callback function has type C<int (*)(void *first, void *second)>.
2547 The function is called with two user supplied tokens identifying
2548 either a source or the sink and it should return the shared nesting
2549 level and the relative order of the two accesses.
2550 In particular, let I<n> be the number of loops shared by
2551 the two accesses. If C<first> precedes C<second> textually,
2552 then the function should return I<2 * n + 1>; otherwise,
2553 it should return I<2 * n>.
2554 The sources can be added to the C<isl_access_info> by performing
2555 (at most) C<max_source> calls to C<isl_access_info_add_source>.
2556 C<must> indicates whether the source is a I<must> access
2557 or a I<may> access. Note that a multi-valued access relation
2558 should only be marked I<must> if every iteration in the domain
2559 of the relation accesses I<all> elements in its image.
2560 The C<source_user> token is again used to identify
2561 the source access. The range of the source access relation
2562 C<source> should have the same dimension as the range
2563 of the sink access relation.
2564 The C<isl_access_info_free> function should usually not be
2565 called explicitly, because it is called implicitly by
2566 C<isl_access_info_compute_flow>.
2568 The result of the dependence analysis is collected in an
2569 C<isl_flow>. There may be elements of
2570 the sink access for which no preceding source access could be
2571 found or for which all preceding sources are I<may> accesses.
2572 The relations containing these elements can be obtained through
2573 calls to C<isl_flow_get_no_source>, the first with C<must> set
2574 and the second with C<must> unset.
2575 In the case of standard flow dependence analysis,
2576 with the sink a read and the sources I<must> writes,
2577 the first relation corresponds to the reads from uninitialized
2578 array elements and the second relation is empty.
2579 The actual flow dependences can be extracted using
2580 C<isl_flow_foreach>. This function will call the user-specified
2581 callback function C<fn> for each B<non-empty> dependence between
2582 a source and the sink. The callback function is called
2583 with four arguments, the actual flow dependence relation
2584 mapping source iterations to sink iterations, a boolean that
2585 indicates whether it is a I<must> or I<may> dependence, a token
2586 identifying the source and an additional C<void *> with value
2587 equal to the third argument of the C<isl_flow_foreach> call.
2588 A dependence is marked I<must> if it originates from a I<must>
2589 source and if it is not followed by any I<may> sources.
2591 After finishing with an C<isl_flow>, the user should call
2592 C<isl_flow_free> to free all associated memory.
2594 A higher-level interface to dependence analysis is provided
2595 by the following function.
2597 #include <isl/flow.h>
2599 int isl_union_map_compute_flow(__isl_take isl_union_map *sink,
2600 __isl_take isl_union_map *must_source,
2601 __isl_take isl_union_map *may_source,
2602 __isl_take isl_union_map *schedule,
2603 __isl_give isl_union_map **must_dep,
2604 __isl_give isl_union_map **may_dep,
2605 __isl_give isl_union_map **must_no_source,
2606 __isl_give isl_union_map **may_no_source);
2608 The arrays are identified by the tuple names of the ranges
2609 of the accesses. The iteration domains by the tuple names
2610 of the domains of the accesses and of the schedule.
2611 The relative order of the iteration domains is given by the
2612 schedule. The relations returned through C<must_no_source>
2613 and C<may_no_source> are subsets of C<sink>.
2614 Any of C<must_dep>, C<may_dep>, C<must_no_source>
2615 or C<may_no_source> may be C<NULL>, but a C<NULL> value for
2616 any of the other arguments is treated as an error.
2620 B<The functionality described in this section is fairly new
2621 and may be subject to change.>
2623 The following function can be used to compute a schedule
2624 for a union of domains. The generated schedule respects
2625 all C<validity> dependences. That is, all dependence distances
2626 over these dependences in the scheduled space are lexicographically
2627 positive. The generated schedule schedule also tries to minimize
2628 the dependence distances over C<proximity> dependences.
2629 Moreover, it tries to obtain sequences (bands) of schedule dimensions
2630 for groups of domains where the dependence distances have only
2631 non-negative values.
2632 The algorithm used to construct the schedule is similar to that
2635 #include <isl/schedule.h>
2636 __isl_give isl_schedule *isl_union_set_compute_schedule(
2637 __isl_take isl_union_set *domain,
2638 __isl_take isl_union_map *validity,
2639 __isl_take isl_union_map *proximity);
2640 void *isl_schedule_free(__isl_take isl_schedule *sched);
2642 A mapping from the domains to the scheduled space can be obtained
2643 from an C<isl_schedule> using the following function.
2645 __isl_give isl_union_map *isl_schedule_get_map(
2646 __isl_keep isl_schedule *sched);
2648 This mapping can also be obtained in pieces using the following functions.
2650 int isl_schedule_n_band(__isl_keep isl_schedule *sched);
2651 __isl_give isl_union_map *isl_schedule_get_band(
2652 __isl_keep isl_schedule *sched, unsigned band);
2654 C<isl_schedule_n_band> returns the maximal number of bands.
2655 C<isl_schedule_get_band> returns a union of mappings from a domain to
2656 the band of consecutive schedule dimensions with the given sequence
2657 number for that domain. Bands with the same sequence number but for
2658 different domains may be completely unrelated.
2659 Within a band, the corresponding coordinates of the distance vectors
2660 are all non-negative, assuming that the coordinates for all previous
2663 =head2 Parametric Vertex Enumeration
2665 The parametric vertex enumeration described in this section
2666 is mainly intended to be used internally and by the C<barvinok>
2669 #include <isl/vertices.h>
2670 __isl_give isl_vertices *isl_basic_set_compute_vertices(
2671 __isl_keep isl_basic_set *bset);
2673 The function C<isl_basic_set_compute_vertices> performs the
2674 actual computation of the parametric vertices and the chamber
2675 decomposition and store the result in an C<isl_vertices> object.
2676 This information can be queried by either iterating over all
2677 the vertices or iterating over all the chambers or cells
2678 and then iterating over all vertices that are active on the chamber.
2680 int isl_vertices_foreach_vertex(
2681 __isl_keep isl_vertices *vertices,
2682 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2685 int isl_vertices_foreach_cell(
2686 __isl_keep isl_vertices *vertices,
2687 int (*fn)(__isl_take isl_cell *cell, void *user),
2689 int isl_cell_foreach_vertex(__isl_keep isl_cell *cell,
2690 int (*fn)(__isl_take isl_vertex *vertex, void *user),
2693 Other operations that can be performed on an C<isl_vertices> object are
2696 isl_ctx *isl_vertices_get_ctx(
2697 __isl_keep isl_vertices *vertices);
2698 int isl_vertices_get_n_vertices(
2699 __isl_keep isl_vertices *vertices);
2700 void isl_vertices_free(__isl_take isl_vertices *vertices);
2702 Vertices can be inspected and destroyed using the following functions.
2704 isl_ctx *isl_vertex_get_ctx(__isl_keep isl_vertex *vertex);
2705 int isl_vertex_get_id(__isl_keep isl_vertex *vertex);
2706 __isl_give isl_basic_set *isl_vertex_get_domain(
2707 __isl_keep isl_vertex *vertex);
2708 __isl_give isl_basic_set *isl_vertex_get_expr(
2709 __isl_keep isl_vertex *vertex);
2710 void isl_vertex_free(__isl_take isl_vertex *vertex);
2712 C<isl_vertex_get_expr> returns a singleton parametric set describing
2713 the vertex, while C<isl_vertex_get_domain> returns the activity domain
2715 Note that C<isl_vertex_get_domain> and C<isl_vertex_get_expr> return
2716 B<rational> basic sets, so they should mainly be used for inspection
2717 and should not be mixed with integer sets.
2719 Chambers can be inspected and destroyed using the following functions.
2721 isl_ctx *isl_cell_get_ctx(__isl_keep isl_cell *cell);
2722 __isl_give isl_basic_set *isl_cell_get_domain(
2723 __isl_keep isl_cell *cell);
2724 void isl_cell_free(__isl_take isl_cell *cell);
2728 Although C<isl> is mainly meant to be used as a library,
2729 it also contains some basic applications that use some
2730 of the functionality of C<isl>.
2731 The input may be specified in either the L<isl format>
2732 or the L<PolyLib format>.
2734 =head2 C<isl_polyhedron_sample>
2736 C<isl_polyhedron_sample> takes a polyhedron as input and prints
2737 an integer element of the polyhedron, if there is any.
2738 The first column in the output is the denominator and is always
2739 equal to 1. If the polyhedron contains no integer points,
2740 then a vector of length zero is printed.
2744 C<isl_pip> takes the same input as the C<example> program
2745 from the C<piplib> distribution, i.e., a set of constraints
2746 on the parameters, a line containing only -1 and finally a set
2747 of constraints on a parametric polyhedron.
2748 The coefficients of the parameters appear in the last columns
2749 (but before the final constant column).
2750 The output is the lexicographic minimum of the parametric polyhedron.
2751 As C<isl> currently does not have its own output format, the output
2752 is just a dump of the internal state.
2754 =head2 C<isl_polyhedron_minimize>
2756 C<isl_polyhedron_minimize> computes the minimum of some linear
2757 or affine objective function over the integer points in a polyhedron.
2758 If an affine objective function
2759 is given, then the constant should appear in the last column.
2761 =head2 C<isl_polytope_scan>
2763 Given a polytope, C<isl_polytope_scan> prints
2764 all integer points in the polytope.
2766 =head1 C<isl-polylib>
2768 The C<isl-polylib> library provides the following functions for converting
2769 between C<isl> objects and C<PolyLib> objects.
2770 The library is distributed separately for licensing reasons.
2772 #include <isl_set_polylib.h>
2773 __isl_give isl_basic_set *isl_basic_set_new_from_polylib(
2774 Polyhedron *P, __isl_take isl_dim *dim);
2775 Polyhedron *isl_basic_set_to_polylib(
2776 __isl_keep isl_basic_set *bset);
2777 __isl_give isl_set *isl_set_new_from_polylib(Polyhedron *D,
2778 __isl_take isl_dim *dim);
2779 Polyhedron *isl_set_to_polylib(__isl_keep isl_set *set);
2781 #include <isl_map_polylib.h>
2782 __isl_give isl_basic_map *isl_basic_map_new_from_polylib(
2783 Polyhedron *P, __isl_take isl_dim *dim);
2784 __isl_give isl_map *isl_map_new_from_polylib(Polyhedron *D,
2785 __isl_take isl_dim *dim);
2786 Polyhedron *isl_basic_map_to_polylib(
2787 __isl_keep isl_basic_map *bmap);
2788 Polyhedron *isl_map_to_polylib(__isl_keep isl_map *map);